Design and Development of Aerospace Vehicles and Propulsion Systems: Proceedings of SAROD 2018 [1 ed.] 981159600X, 9789811596001

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Lecture Notes in Mechanical Engineering

S. Kishore Kumar Indira Narayanaswamy V. Ramesh   Editors

Design and Development of Aerospace Vehicles and Propulsion Systems Proceedings of SAROD 2018

Lecture Notes in Mechanical Engineering Series Editors Francisco Cavas-Martínez, Departamento de Estructuras, Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesco Gherardini, Dipartimento di Ingegneria, Università di Modena e Reggio Emilia, Modena, Italy Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Vitalii Ivanov, Department of Manufacturing Engineering Machine and Tools, Sumy State University, Sumy, Ukraine Young W. Kwon, Department of Manufacturing Engineering and Aerospace Engineering, Graduate School of Engineering and Applied Science, Monterey, CA, USA Justyna Trojanowska, Poznan University of Technology, Poznan, Poland

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S. Kishore Kumar Indira Narayanaswamy V. Ramesh •

•

Editors

Design and Development of Aerospace Vehicles and Propulsion Systems Proceedings of SAROD 2018

123

Editors S. Kishore Kumar Gas Turbine Research Establishment Bengaluru, Karnataka, India

Indira Narayanaswamy M. S. Ramaiah University of Applied Sciences Bengaluru, Karnataka, India

V. Ramesh National Aerospace Laboratories Bengaluru, Karnataka, India

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-981-15-9600-1 ISBN 978-981-15-9601-8 (eBook) https://doi.org/10.1007/978-981-15-9601-8 © Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Contents

Mach Number Effect on Aeroacoustic Characteristics of Compressible Jet Due to Chevron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. R. Nikam and S. D. Sharma

1

Parametric Study of Turbulent Flow Past a Compression– Decompression Ramp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhea George and Raj Kiran Grandhi

15

Validation of Numerical Analysis Results for Pusher Configured Turboprop Engine Air Intake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. A. Vinay and S. Bhaskar Chakravarthy

25

Aero-elastic Analysis of High Aspect Ratio UAV Wing—Based on Two-Way Fluid Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . Vidit Sharma and S. Keshava Kumar

37

Numerical Study of Effect of Adjacent Blades Oscillation in a Compressor Cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shubham, M. C. Keerthi, and Abhijit Kushari

59

Effect of Incoming Wakes on Losses of a Low-Pressure Turbine of a Gas Turbine Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vishal Tandon, Gopalan Jagadeesh, and S. V. Ramana Murty

75

Effect of Axial Location on the Performance of a Control Jet in a Supersonic Cross Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Raj Kiran Grandhi and Arnab Roy

89

Effect of Chord Variation on Subsonic Aerodynamics of Grid Fins . . . . 105 Manish Tripathi, Mahesh M. Sucheendran, and Ajay Misra Numerical Investigation on the Effect of Propeller Slipstream on the Performance of Wing at Low Reynolds Numbers . . . . . . . . . . . . 129 K. Shruti and M. Sivapragasam

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Contents

Theoretical Design and Performance Evaluation of a Two-Ramp and a Three-Ramp Rectangular Mixed Compression Intake in the Mach Range of 2–4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Subrat Partha Sarathi Pattnaik and N. K. S. Rajan Sensitivity of Altitude Variation on Aerodynamics of a Typical Launch Vehicle During Hot Separation . . . . . . . . . . . . . . . . . . . . . . . . . 167 Jiju R. Justus, Sanjoy Kumar Saha, and Pankaj Priyadarshi Normal Shock Dynamics in Internal Supersonic Flows . . . . . . . . . . . . . 177 S. Vaisakh and T. M. Muruganandam Hinge Moment Characterization of All Movable Control Surface . . . . . 185 Manoj Kumar, G. Kadam Sunil, V. Shanmugam, and G. Balu 3D Computational Studies of Flapping Wing in Frontal Gusty Shear Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 M. De Manabendra, J. S. Mathur, and S. Vengadesan Investigation of Wind Tunnel Blockage Effect on Liftoff Aerodynamics of a Launch Vehicle Through Open-Source CFD Solver SU2 . . . . . . . . 211 Aaditya N. Chaphalkar, Amit Sachdeva, Vinod Kumar, and Pankaj Priyadarshi Observation of Low-Frequency Shock Oscillation Over a Forward-Facing Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Jayaprakash N. Murugan and Raghuraman N. Govardhan RANS Computations of Hypersonic Interference Heating on Flat Surface with Protuberances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 M. Mahendhran and C. Balaji Multi-fidelity Aerodynamic Optimization of an Airfoil at a Transitional Low Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . 239 R. Priyanka, M. Sivapragasam, and H. K. Narahari Aerodynamic Optimization of Transonic Wing for Light Jet Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 K. Sathyandra Rao, M. Sivapragasam, H. K. Narahari, and Aneash V. Bharadwaj Non-adiabatic Wall Effects on Transonic Shock/Boundary Layer Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Sahil Bhola and Tapan K. Sengupta An Adjoint Approach for Accurate Shape Sensitivities in 3D Compressible Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Srikanth Sathyanarayana, Anil Nemili, Ashish Bhole, and Praveen Chandrashekar

Contents

vii

Robust Flutter Prediction of an Airfoil Including Uncertainties . . . . . . . 305 A. Arun Kumar and Amit Kumar Onkar Effect of Vortex Generator on Flow in a Serpentine Air Intake Duct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 B. B. Shivakumar, H. K. Narahari, and Padmanabhan Jayasimha Supersonic Flow Behavior in Cartridge Starter . . . . . . . . . . . . . . . . . . . 331 Ritesh Gaur, Suparna Pal, Vimala Narayanan, D. Kishore Prasad, and N. Balamurali Krishnan High-Speed Shadowgraph Visualization Studies of the Effectiveness of Ventilating a V-Gutter Flame Holder to Mitigate Screech Combustion Instability in an Aero-Gas Turbine Afterburner . . . . . . . . 343 C. Rajashekar, Shambhoo, H. S. Raghukumar, R. M. Udaya Kumar, K. Ashirvadam, and J. J. Isaac Passive Reduction of Aerodynamic Rolling Moment for a Launch Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 Pankaj Priyadarshi, Amit Sachdeva, and Leya Joseph Design and Development of Miniature Mass Flow Control Unit for Air-Intake Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 D. B. Singh, P. Vinay Raya, Buddhadeb Nath, N. Srinivasan, Anju Sharma, and B. Sampath Rao The Effect of Variable Inlet Guide Vanes on the Performance of Military Engine Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Baljeet Kaur, Reza Abbas, and Ajay Pratap Transition Prediction for Flow Over a MAV Wing Using the Correlation Based Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 M. B. Subrahmanya and B. N. Rajani Rotor Flow Analysis in the Presence of Fuselage Using Unsteady Panel Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 K. R. Srilatha, Premalatha, and Vidyadhar Y. Mudkavi Numerical Analysis of High Reynolds Number Effects on the Performance of GAW-1 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . 425 D. S. Kulkarni and B. N. Rajani Investigation of the Effect of Booster Attachment Scheme on the Rolling Moment Characteristics of an Asymmetric Vehicle Using CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 P. K. Sinha, Munish Kumar Ralh, Naveed Ali, R. Krishnamohan Rao, and G. Balu

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Contents

Multi-objective Optimization Approach for Low RCS Aerodynamic Design of Aerospace Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 P. S. Shibu, Sandeep, Balamati Choudhury, and R. U. Nair Analysis of Propeller by Panel Method for Transport Aircraft . . . . . . . 457 Premalatha, K. R. Srilatha, and Vidyadhar Y. Mudkavi Effect of Reynolds Number on Typical Civil Transport Aircraft . . . . . . 471 Vishal S. Shirbhate, K. Siva Kumar, and K. Madhu Babu Prediction of MultiStore Separation from a Fighter Aircraft Using In-House Code—WISe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 S. Karthik, Jishnu Suresh, P. Karthikeya, S. Rajkumar, Mano Prakash, Sashi Kiran, and D. Narayan Shockwave Oscillations Over the Conical Heat Shield Region of a Typical Launch Vehicle at Mach 0.95 . . . . . . . . . . . . . . . . . . . . . . . 491 K. N. Murugan, T. Arunkumar, M. Prasath, and V. R. Ganesan Diverterless Supersonic Intake for a Generic Stealth Fighter Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 Sameer Karania, Manu Mohan, and Satya Prakash Analysis of Missile Plume Impact Characteristics on Engine Intake and Neighboring Stores for a Fighter Aircraft . . . . . . . . . . . . . . . . . . . . 511 Jishnu Suresh, S. Karthik, P. Karthikeya, S. Rajkumar, Mano Prakash, Sashi Kiran, D. Maharana, and D. Narayan Control of Tailless Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 T. S. Ganesh, M. C. Keerthi, Sabari Girish, S. Sreeja Kumar, and B. Mrunalini

About the Editors

Dr. S. Kishore Kumar is a DRDO fellow in the Gas and Turbine Research Establishment (GTRE), Associate Editor of Journal of Aerospace Sciences & Technologies of AeSI and Technical Adviser to National Design & Research Forum. He has previously served as Associate Director and Programme Director (GATET), GTRE. His areas of specialization include design & CFD analysis of Gas Turbine Engines, Optimization, mathematical modelling and dynamical systems. He has published 7 edited volumes and more than 100 research papers & technical reports. Dr. Indira Narayanaswamy is a Research Professor at Ramaiah University of Applied Sciences, Bangalore, India. She has previously served as a scientist and Technology Director at Aeronautical Development Agency, Bangalore. Dr. Narayanaswamy’s areas of specialization include CFD applications for Aerodynamic Shape Optimization and Multidisciplinary Design Optimization (MDO), MDO for MAV design and Numerical Investigations on Supersonic Retro Propulsion (SRP). She has authored more than 150 research papers and technical reports. She is one of the Editors of the Proceedings of the 2nd National Conference on MDAO, published by Springer Nature Singapore Pte Ltd, 2020. Dr. V. Ramesh is the head of the CTFD Division in NAL, an AcSIR Professor and the Secretary of the CFD Division of the Aeronautics Society of India. His research interests are primarily in aerospace science and technology, and includes Computational Fluid Dynamics (CFD), mesh free methods, and computational aero-elasticity. He has authored more than 150 research publications and reports.

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Mach Number Effect on Aeroacoustic Characteristics of Compressible Jet Due to Chevron S. R. Nikam and S. D. Sharma

Abstract The present experimental investigation reports the effect of chevron on flow characteristics and associated acoustic characteristics at different jet exit Mach numbers in high subsonic compressible jet. Flow characteristics are investigated with mean pressure measurement using miniature pitot tube in the flow, and acoustic characteristics are investigated using fluctuating pressure measurement with array of four microphones in the far field of jet. Chevron is used as a flow control device on the lip of the nozzle. Chevron converts axisymmetric jet development into corrugated shear layer, closer to the nozzle exit. This effect diminishes as jet grows downstream away from the nozzle exit. Corrugation of jet shear layer closer to the nozzle exit increases with increase in Mach number. Compressibility effect with change in Mach number is seen from potential core length and jet growth rate for base nozzle; however, chevron is found to reduce the compressibility effect with change in jet exit Mach number due to enhancement in mixing. Chevron reduces far-field overall sound pressure level at shallow polar angle (30°) by about to 2 dB at all the Mach number; however, increase in noise level at higher frequency observed at higher polar angle is mainly due to high-frequency noise sources produced from chevron petals. Noise level at higher polar angles and higher frequencies increases with increase in Mach number. Keywords Chevron · Potential core · Streamwise vortex

1 Introduction Considering increased frequency of aircraft operation, noise pollution due to aircraft became a major concern for the community around the airports. The regulations introduced by the International Civil Aviation Organization are becoming more stringent S. R. Nikam (B) Mechanical Engineering Department, K. J. Somaiya College of Engineering, Mumbai, India e-mail: [email protected] S. D. Sharma Aerospace Engineering Department, IIT Bombay, Mumbai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_1

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S. R. Nikam and S. D. Sharma

over a period considering the higher frequency of operation of aircraft. To meet the increasingly tough international regulation on aircraft noise, the aircraft manufacturers and researchers are devising the techniques to reduce the noise level. Major challenges in implementing these techniques are thrust and weight penalty along with increase in cost due to these devices and hence led to a demand for quieter and more efficient jet engine designs. Jet exhaust noise is one of the major sources of aircraft noise especially during takeoff. Jet exhaust noise is caused by the turbulent mixing of high-speed exhaust gases with the atmospheric air which occurs due to velocity gradients in the shear layer of jet. Various researchers tried different techniques like tabs [1, 2], microjet [3, 4], vortex generators [5], notches [6, 7] and chevrons [8–11] to reduce jet engine exhaust noise. However, chevron is found to be effective considering minimum thrust [12] and weight penalty. Chevron is saw-tooth serrations cut in the lip of the nozzle which produces the contra-rotating pair of streamwise vortices [8]. These streamwise vortices disrupt the azimuthal ring of vortices and enhance the mixing. Various researchers [10, 13, 14] investigated the effect of chevron and its geometric parameters on aero-acoustic characteristics of the jet. However, effect of Mach number in the presence of chevron on the aeroacoustics characteristics of jet flow in compressible subsonic range is not discussed much in the literature. The present experimental investigation reports the effect of Mach number (0.5–0.9) on the flow field and acoustic characteristics in the far field with chevron.

2 Experimental Setup and Test Nozzle Experiments were conducted in a high-pressure single flow freely expanding cold jet facility. Jet flow facility consists of a screw compressor to supply compressed air, pressure regulating valve and plenum chamber with the provision for attaching a test nozzle. Pressure in the plenum chamber was maintained by operating pressure regulating valve to get required nozzle exit Mach number. The jet exits into initially still ambient air. To minimize sound reflection from wall boundaries, roof and floor, a semi-anechoic enclosure was constructed using 65-mm-thick polyurethane (PU) foam sheets surrounding to test facility. Convergent nozzle with 30-mm nozzle exit diameter (D), 130 mm length and 1 mm lip thickness was used in the present investigation as base nozzle. The nozzle had included angle of 11° and its tapered wall provided the outer included angle of 16°. This base nozzle was modified into a chevron nozzle by capping a ring of chevrons with eight petals made out of 0.5-mmthick stainless steel sheet. Thus, chevron nozzle was constructed by fitting chevron ring over base nozzle. Figure 1 shows details of the chevron nozzle. Figure 1a shows a representative cut section schematic of chevron nozzle with parametric details such as petal crest angle (β) which is 45°, petal length (L) and penetration (R-Y ). Figure 1b shows a photograph of the base nozzle and chevron ring assembly.

Mach Number Effect on Aeroacoustic Characteristics of Compressible … Fig. 1 Chevron nozzle a sectional details and b photograph of chevron nozzle

3 L=14.8

8°

5.5°

R=15

Y=13.16 β

Chevron ring (a)

(b)

3 Experimental Methods Aerodynamic measurements are taken using a miniature pitot probe (0.7 mm diameter stainless steel hypodermic tube) inside the jet, and acoustics measurements are taken using array of four free-field microphones in the far field of jet. To position the measuring probe at a desired point, a computer-controlled Dantec Dynamics traverse is used which has a traverse range of 610 mm along each of the three orthogonal axes with a resolution of 0.01 mm. The plenum chamber pressure is determined using isentropic relation for required nozzle exit Mach number and maintained by operating pressure regulating valve. Pressures were registered by using Pressure Systems make transducers, PSI model 9116 with 16 channels. Mean pressure was measured using pitot tube along the jet centerline for M = 0.5, 0.6, 0.7, 0.8 and across the jet in transverse plane at three streamwise locations (x/D = 0.5, 2 and 5) in steps of 0.067D for M = 0.5 and 0.8. Chevron nozzle exit plane was considered aligned with the trough of the notch in chevron ring. The acoustic pressure fluctuations were measured in the far field for jet exit Mach number 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 at polar angles, θ, from 30° to 90° in steps of 10° at a fixed far-field

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distance of 45D in the horizontal plane. Four B&K, 6.53 mm (1/4 ) diameter 4939 free-field condenser microphones were used along with B&K 2970 pre-amplifiers for acoustic measurements. The microphones were powered by four-channel NEXUS model 2690-0S4 signal conditional amplifiers. Each microphone had flat frequency response from 4 Hz to 100 kHz and an open-circuit sensitivity of 4.5 mV/Pa. Before commencing the measurements, the microphones were calibrated using a B&K 4226 multifunction acoustic calibrator. Data acquisition was carried out using National Instrument PCI-4462 card-based DAQ and LabVIEW software. Hundred blocks of narrow band data are acquired at the rate of 200 kHz with 8192 samples which gives frequency band width of 24.41 Hz. Accuracy of acoustic measurement is within ±0.3 dB. The acquired data is post-processed to obtain sound pressure level, overall sound pressure level (OASPL) using MATLAB.

4 Results 4.1 Aerodynamics Results Centerline Velocity Distribution Figure 2 shows the jet centerline velocity distribution (u) at M = 0.5, 0.6, 0.7 and 0.8. Velocity is normalized with the jet exit velocity (U exit ), and the distance is normalized by the base nozzle exit diameter (D). At Mach 0.8, the potential core length for the base circular nozzle is about 5D, which agrees with many of the earlier measurements [8, 13, 15–17] by various techniques in Mach number range from 0.78 to 0.9. Potential core length obtained from the present measurement is Fig. 2 Axial velocity along centerline of jet

Mach Number Effect on Aeroacoustic Characteristics of Compressible … Table 1 Comparison of potential core length with empirically obtained values

5

Lau et al. [16]

Witze [18]

Present study

M = 0.8

4.9D

5.19D

5D

M = 0.5

4.48D

4.82D

4.5D

compared with the values obtained empirically as given by Lau et al. [16] and Witze [18]. Comparison of potential core length given in Table 1 indicates that the present measurements match very closely with the previous empirically established data. Effect of Mach number is clearly seen. Reduction in potential core is observed as Mach number is reduced from 0.8 to 0.5. Potential core length for the base nozzle at Mach 0.5 is obtained as 4.5 diameters downstream as compared to 5 diameters at M = 0.8. Velocity decay rate also increases with reduction in Mach number. Centerline velocity reduces from 75% at M = 0.8 to 69% at M = 0.5 for the measuring station located at x/D = 10. This difference in the potential core length and the centerline decay rate with Mach number is due to compressibility effect which increases with increase in the Mach number. Reduction in the potential core length and increase in the centerline velocity decay are noticed at all the Mach number for chevron nozzle as compared to base nozzle. Potential core length for chevron nozzle is about 3D at all the Mach number. For Mach 0.8, the centerline velocity decay from about 75% for base nozzle to 61% for chevron nozzle at the measuring station located at x/D = 10 is observed. Similar findings are reported by Bridges and Brown [13] for the chevron nozzle with six petals. It is interesting to note that for Mach 0.5, at measuring station x/D = 10, chevron nozzle reduces centerline velocity to 59% as compared to 69% for the base nozzle. This reduction in centerline velocity for chevron nozzle at M = 0.5 (59%) is almost same as that obtained at M = 0.8 with chevron (61%). Thus, decay rate is almost same for the chevron nozzle at both the Mach numbers indicating that enhanced mixing due to chevron reduces the effect of compressibility. Jet Flow Development Iso-velocity contours normalized by the jet exit velocity in the transverse (y–z) plane at x/D = 0.5 and 5 are shown in Figs. 3 and 4 for base and chevron nozzle, respectively, at M = 0.5 and 0.8. Jet develops axis symmetrically for base nozzle; however, chevron nozzle makes the flow corrugated in the shape of lobe. For the base nozzle as shown in Fig. 3 at x/D = 0.5, size of the jet is same at both the Mach numbers due to insignificant entrainment in the close proximity to the nozzle exit. However, at x/D = 5, size of the jet is different. Due to compressibility effect, at Mach 0.8, jet size is less as compared to Mach 0.5. For chevron nozzle (Fig. 4) at x/D = 0.5, Mach number has a strong effect on the jet cross section. Increase in Mach number enhances the bulging of the corrugated shear layer, thereby increasing the perimeter of the jet edge. Jet cross section becomes circular at x/D = 5 for chevron nozzle. Compared to the base nozzle, jets from chevron nozzle show larger cross-sectional area. It is believed that streamwise vortices produced from chevron petals make the jet corrugated which in turn increases the mixing. Increase in the size of lobe due to increase in Mach number indicates that strength of streamwise vortices increases due to increase in

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M = 0.8

M = 0.5

Fig. 3 Iso-velocity contours for base nozzle

Mach number. This variation in strength of vortices is due to change in the velocity gradient in the radial and azimuthal direction. For chevron nozzle, cross section of the jet at x/D = 5 is marginally less at lower Mach number. This observation is exactly reverse of base nozzle. Thus, higher strength of streamwise vortices produced at higher Mach number makes the mixing aggressive which gives slightly bigger cross section of the jet at higher Mach number. Mass Entrainment The mass flow rate is estimated using the isentropic relations for the density and the velocity distribution obtained from pressure measurement in grid at three longitudinal position (x/D = 0.5, 2 and 5) for the base and chevron nozzle as shown in Fig. 5. Nearly variation of mass flow rate for the base nozzle is seen. The entrainment ⎧ linear  ⎫ ⎨ d m˙ /m˙ ⎬ exit   rate for base nozzle at M = 0.8 and 0.5 is 0.15 and 0.20, respectively. ⎩ d x/D ⎭

Mach Number Effect on Aeroacoustic Characteristics of Compressible …

M = 0.8

7

M = 0.5

Fig. 4 Iso-velocity contours for chevron nozzle

These entrainment values compare well with the 0.13 reported by Arakeri et al. [19] at M = 0.9. Higher mass flow rate at lower Mach number is seen for base nozzle which is due to compressibility effect. Chevron does not show linear variation in mass flow rate. Mass flow rate shows rapid entrainment rate till x/D = 2 thereafter entrainment decreases. Thus, most of the entrainment due to chevron takes place within x/D = 2. Chevron shows maximum increase in mass flow rate by about 15%, at x/D = 5 and M = 0.8, whereas, for M = 0.5, chevron increases mass flow rate by about 5%. Increase in entrainment due to chevron is higher at higher Mach number due to chevron. Thus, the increase in the centerline velocity decay at higher Mach number found earlier for chevron nozzle in Fig. 2 is associated with increase in the mass entrainment.

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Fig. 5 Mass flow rate along the jet axis

4.2 Acoustics Results Far-field acoustic pressure fluctuations are recorded at polar angles 30° to 90° in a step of 10° for jet exit Mach number 0.4–0.9 at fixed radial distance of 45D using microphones. SPL and OASPL are obtained from these pressure fluctuations. Figure 6 shows sound pressure level against non-dimensional frequency Strouhal number (St) at polar angle 30° in 1/3—octave band. Peak SPL is obtained at Strouhal frequency of about 0.2. This peak frequency remains almost same at all the Mach number except marginal shift toward higher value at lower Mach number. Similar observations are reported by Bogey et al. [20]. Thus, noise at this location is mainly contributed by low-frequency noise sources. As expected, peak level decreases by about 30 dB as Mach number is reduced. Chevron is found to be equally effective at all the Mach number for reducing the noise by about 3 dB at peak frequency, whereas highfrequency noise remains almost unaffected with increase in Mach number due to chevron. Figure 7 shows SPL at polar angle 90°. Compared to SPL at 30°, spectra at 90° is broadband in nature with reduced levels. Chevron continues to reduce the level at low frequency at all the Mach number, but noise level increases due to chevron at high frequency. This increase in level is highest at higher Mach number. Change over frequency shifts toward higher value at low Mach number. Thus, chevron gives benefit of noise reduction at wide frequency band at low Mach number. OASPL obtained for three different ranges of frequency is shown in Fig. 8. OASPL for entire range of frequency (200–100,000 Hz) shows that OASPL increases as polar angle reduces. Rate of increase of OASPL reduces as Mach number reduces along with shift in peak OASPL from 30° at higher Mach numbers to about 50° at lower Mach number. Chevron reduces OASPL by about 2 dB at lower polar angle (30°) for all the Mach number, whereas OASPL increases at higher angles for Mach number

Mach Number Effect on Aeroacoustic Characteristics of Compressible …

9

Fig. 6 Far-field 30° noise spectra registered different Mach numbers for base nozzle (red color— continuous line) and chevron nozzle (blue color—dotted line)

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S. R. Nikam and S. D. Sharma

Fig. 7 Far-field 90° noise spectra registered different Mach numbers for base nozzle (red color— continuous line) and chevron nozzle (blue color—dotted line)

Mach Number Effect on Aeroacoustic Characteristics of Compressible … Fig. 8 Far-field OASPL directivity at different frequency bandwidth and Mach number for base nozzle (circle) and chevron nozzle (diamond)

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S. R. Nikam and S. D. Sharma

0.9, 0.8 and 0.7. Such increase in noise level at higher polar angle is not seen at lower Mach number. OASPL in lower frequency range (200–10,000 Hz) shows that chevron reduces the noise at all the Mach number and polar positions almost by equal amount, whereas, in high frequency range (10,000–100,000 Hz), chevron increases the noise at all the polar angles except 30°. Noise level due to chevron increases with increase in polar angle. This increase in level is more pronounced at higher Mach number. Thus, chevron reduces the strength of low-frequency noise sources which results in reduction in low-frequency noise in the far field at low polar angle. On the contrary, chevron increases the strength of high-frequency sources which increases the noise level at high frequency at higher polar angle in the far field. Strength of highfrequency noise sources increases with increase in velocity due to which increase in high-frequency noise is more at high Mach number.

5 Conclusion Important conclusions drawn from the present experimental investigation are • Formation of streamwise vortices from chevron petals makes the jet corrugated close to the nozzle exit which in turn enhances the mixing and reduces the potential core. Enhanced mixing in azimuthal and radial direction turns the corrugated jet in to axisymmetric, within five nozzle diameters with increased mixing as compared to base nozzle. • Chevron reduces the compressibility effect mainly due to aggressive mixing at higher Mach number. • Enhanced jet mixing due to chevron reduces the low-frequency noise at shallow angle to the jet axis in the far field along with increased high-frequency noise at higher angles. • For chevron, change in the Mach number does not affect much in reducing the noise level in far field at low frequency, whereas increased strength of streamwise vortices with increase in Mach number increases the far-field noise level at higher polar angle. These observations are seen with one particular chevron geometry; however, effect of chevron at different Mach numbers may vary as geometric parameters of chevron change.

References 1. Simonich JC, Narayanan S, Barber TJ, Nishimura M (2001) Aeroacoustic characterization, noise reduction, and dimensional scaling effects of high subsonic jets. AIAA J 39(11):2062– 2069 2. Samimy M, Zaman KBMQ, Reeder MF (1993) Effect of tabs on the flow and noise field of an axisymmetric jet. AIAA J 31(4):609–619

Mach Number Effect on Aeroacoustic Characteristics of Compressible …

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3. Arakeri VH, Krothapalli A, Siddavaram V, Alkislar MB, Lourenco LM (2003a) On the use of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet. J Fluid Mech 490:75–98 4. Castelain T, Sunyach M, Juvé D, Béra J-C (2008) Jet-noise reduction by impinging microjets: an acoustic investigation testing microjet parameters. AIAA J 46(5):1081–1087 5. Panickar P, Sharma S, Sarpotdar S, Raman G, Butler W (2011) New vortex generator design for nozzle internal modification. Int J Aerosp Innov 3(4):249–260 6. Verma SB, Rathakrishnan E (1999) An experimental study on the noise characteristics of notched circular-slot jets. J Sound Vib 226(2):383–396 7. Ahuja KK, Manes JP, Massey KC, Calloway AB (1990) An evaluation of various concepts of reducing supersonic jet noise. In: 13th aeroacoustics conference, AIAA Paper-90-3982 8. Alkislar MB, Krothapalli A, Butler GW (2007) The effect of streamwise vortices on the aeroacoustics of a Mach 0.9 jet. J Fluid Mech 578:139–169 9. Callender B, Gutmark E, Martens S (2008) Near-field investigation of chevron nozzle mechanisms. AIAA J 46(1):36–45 10. Callender B, Gutmark EJ, Martens S (2005) Far-field acoustic investigation into chevron nozzle mechanisms and trends. AIAA J 43(1):87–95 11. Wernet M, Brown C, Bridges J (2003) Control of jet noise through mixing enhancement. NASA/TM-2003-212335 12. Saiyed NH, Mikkelsen KL, Bridges JE (2003) Acoustics and thrust of quiet separate-flow high-bypass-ratio nozzles. AIAA J 41(3):372–378 13. Bridges J, Brown C (2004) Parametric testing of chevrons on single flow hot jets. In: AIAAPaper-2004-2824 14. Tide PS, Srinivasan K (2010) Effect of chevron count and penetration on the acoustic characteristics of chevron nozzles. Appl Acoust 71(3):201–220 15. Yu SCM, Lim KS, Chao W, Goh XP (2008) Mixing enhancement in subsonic jet flow using the air-tab technique. AIAA J 46(11):2966–2969 16. Lau JC, Morris PJ, Fisher MJ (1979) Measurements in subsonic and supersonic free jets using a laser velocimeter. J Fluid Mech 93(1):1–27 17. Kolpin MA (1964) The flow in the mixing region of a jet. J Fluid Mech 18(4):529–548 18. Witze PO (1974) Centerline velocity decay of compressible free jets. AIAA J 12(4):417–418 19. Arakeri VH, Krothapalli A, Siddavaram V, Alkislar MB, Lourenco LM (2003b) On the use of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet. J Fluid Mech 490:75–98 20. Bogey C, Barré S, Fleury V, Bailly C, Juvé D (2007) Experimental study of the spectral properties of near-field and far-field jet noise. Int J Aeroacous 6(2):73–92

Parametric Study of Turbulent Flow Past a Compression–Decompression Ramp Rhea George and Raj Kiran Grandhi

Abstract Shock wave-boundary layer interactions take place in many vehicle configurations of practical importance such as wing–body junctures, deflected control surfaces, high-speed inlets and forward-facing steps. The associated flowfield becomes complex when the interaction causes flow to separate. A parametric study is carried out for supersonic flow past a compression–decompression ramp (CDR), to determine the ramp inclination angle that minimizes the adverse effect of separated flow. The inclination angle below which weak interaction occurs is obtained from the numerical simulations. Keywords Compression–decompression ramp · Flow separation · Shock wave-boundary layer interaction

1 Introduction Shock wave-boundary layer interaction can cause flow to separate, thereby leading to increase in drag, loss in efficiency of control surface, increased turbulence level and heat transfer rates. The associated flowfield becomes complex when the interaction causes flow to separate. Shock-induced separation can cause unsteady loads that may lead to structural damage. Shock wave-boundary layer interactions may be utilized to improve fuel–air mixing in scramjet combustors. Hence, the study of this phenomenon assumes great importance in supersonic flows. A commercial computational fluid dynamics (CFD) solver ANSYS Fluent [1] is used to simulate this interaction. The flow solver is validated and then used to perform a parametric study of flow over a compression–decompression ramp (CDR). The literature on compression corner flows is relatively vast, but experimental results for compression–decompression ramp flows that can be used for CFD solver validation R. George (B) · R. K. Grandhi Advanced Systems Laboratory, Defence Research and Development Organisation, Hyderabad 500058, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_2

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R. George and R. K. Grandhi

are much scarcer. One of the few available papers [2] lists out the experimental results for a CDR of 25◦ inclination at a Mach number of 2.88. The flow solver has been validated for this configuration [3]. The present study attempts to conduct a parametric study over a typical CDR, the ramp inclination angle being the parameter that is varied, for constant ramp height. The governing equations are the compressible Navier-Stokes equations.

2 Flowfield in the Vicinity of CDR When the angle of inclination is sufficiently small, the compression waves coalesce into a single shock and the pressure downstream is similar to the inviscid case. For a sufficiently higher inclination angle, the boundary layer separates upstream of the compression corner and reattaches downstream [4]. The deflection of the boundary layer by the separated flow causes a rise in surface pressure, and the compression waves coalesce into a separation shock. A pressure ‘plateau’ occurs over the reversed flow region. A second compression wave system forms near the reattachment point and coalesces into the reattachment shock wave. The two shock waves intersect to form a λ-shock. The flow then expands about the decompression corner. The stages of shock–boundary layer turbulent interaction in the vicinity of compression–decompression ramps [4] have been classified as (i) unseparated flow, (ii) intermittent separation, (iii) developing small-scale separation, (iv) large-scale separation and (v) maximum-scale separation. As the inclination angle increases, the flow structure changes from unseparated flow to the subsequent stages of separation and finally maximum-scale separation. The maximum-scale separation corresponds to detached shock for inviscid flow.

3 Solver Validation Flow simulations are carried out for a freestream Mach number of 2.88 as per the experimental conditions [2]. These wind tunnel conditions are shown in Table 1. The CDR has an inclination of 25◦ as shown in Fig. 1. The origin is taken at the compression corner. The nondimensionalized static pressure over the walls, computed using various turbulence models, is plotted in Fig. 2. The pressure plot shows the rise in pressure

Table 1 Experimental conditions Mach number Temperature (K) 2.88

110.57

Pressure (kPa)

Velocity (m/s)

11.964

607

Parametric Study of Turbulent Flow Past a Compression–Decompression Ramp

17

Fig. 1 Compression–decompression ramp (all dimensions in mm) 5.0

std-kε realizable-kε sst-kω sa Experiment

4.5 4.0 p/p∞ →

3.5 3.0 2.5 2.0 1.5 1.0 0.5 -8

-6

-4

-2

0

2 4 x (cm) →

6

8

10

12

Fig. 2 Static pressure on walls

well ahead of the compression corner and expansion over the decompression corner. This plot also shows that the pressure in the separation region is well predicted by most of the models. The SST k-ω model predicts a larger reversed flow region, with a pressure peak below the experimental value, which is in line with the findings of [5, 6]. The remaining three turbulence models predict the pressure in the separated flow regime much more accurately. The one-equation Spalart–Allmaras (SA) turbulence method performs just as well as the two-equation models. The velocity vectors displaying the separation and reattachment regions near the compression corner are presented in Fig. 3. The sonic line and the zero velocity line, as shown in the velocity contours of Fig. 4, agree well with the measurements [4].

4 Grid Independence Grid independence studies are carried out to ensure that the grid size, used for the simulations, is adequate to capture the flow features. Three levels of grid sizes ranging from coarse (504 × 160 cells) to medium (620 × 200 cells) and fine (740 × 240 cells) are utilized. The first cell height normal to the walls is unchanged for all the grids, to maintain the wall y + less than 1 in all the cases. The results obtained from

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R. George and R. K. Grandhi

607 562 516 470 425 379 333 287 242 196 150 Reattachment

105 59 13 -32

Separation

-78 -124

Fig. 3 Velocity vectors in the vicinity of compression corner

Fig. 4 Velocity magnitude contours in the vicinity of compression–decompression corner

Parametric Study of Turbulent Flow Past a Compression–Decompression Ramp 4.5

19

coarse medium fine

4.0

p/p∞ →

3.5 3.0 2.5 2.0 1.5 1.0 -2

-1

0

1

2

3

x/h →

Fig. 5 Pressure variation with grids Table 2 Flowfield conditions Mach number Altitude (km) 2

12

Temperature (K)

Pressure (kPa)

225

21

these grids are compared to check for grid independence. It is observed from the plots of pressure in Fig. 5 that the results from the medium and fine grids are almost coincident. Hence, the medium grid is used for all the simulations.

5 Simulation Parameters Two-dimensional, viscous simulations are performed for CDR configuration with varying inclination angles in ANSYS Fluent, to determine the inclination angle that minimizes or avoids flow separation. Flow simulations are carried out at the conditions given in Table 2. The pressure inlet boundary is assigned over the inlet to the domain. The domain in the normal direction is taken to be sufficiently large in order to avoid shock reflection from the boundaries. The grid generated for this domain consists of 0.12 million cells. The height of the first row of cells is about 1 × 10−6 m, to ensure a wall y+ less than 0.4. Spalart–Allmaras (SA) turbulence method is used to model turbulence. The ramp inclination angles considered are 8, 10, 12, 14, 15, 16, 20 and 25◦ .

6 Simulation Results Nondimensionalized static pressure variation over the walls, computed for various inclination angles, is plotted in Fig. 6. It shows the rise in pressure, well ahead of the compression corner and expansion over the decompression corner. It is observed from

20

R. George and R. K. Grandhi 2.8

ο

8ο 10 12ο ο 14 ο 15ο 16ο 20ο 25

2.6 2.4

p/p∞ →

2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 -5

0

5

10

15

x/h →

Fig. 6 Pressure variation with angle of inclination of compression corner

Skin friction coefficient →

0.0025 0.0020 0.0015 0.0010 8ο 10ο ο 12 14ο ο 15 16ο 20ο 25ο

0.0005 0.0000

-0.0005

-0.0010

-0.0015 -3

-2

-1

0

1

2

x/h →

Fig. 7 Skin friction coefficient on the walls of compression–decompression corner

this plot that as the inclination angle increases, the peak pressure rises, due to increase in shock strength. The pressure profiles for smaller angles of inclination (8, 10 and 12◦ ) closely follow the inviscid pressure profile. This interaction is referred to as Weak Interaction [7]. As this angle increases, the pressure profile varies considerably from the inviscid profiles (Strong Interaction). The upstream influence of the compression corner increases with inclination angle. The variation of the skin friction coefficient with angle of inclination of the CDR in the vicinity of compression corner is presented in Fig. 7. The nature of the skin friction variation near the compression corner matches well with literature [4]. The separation and reattachment locations correspond to the points where the skin friction coefficient falls below zero and rises above zero, respectively. The extent of separated flow is evident from the region where the skin friction coefficient is negative. Separated flow region is minimal for the smaller inclination angles (8, 10 and 12◦ ). But the flow separation is significant for higher inclination angles. For an increase in inclination angle from 12 to 14◦ , the separated flow region

Parametric Study of Turbulent Flow Past a Compression–Decompression Ramp

21

2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00

Fig. 8 Mach number contours for ramp inclination angle of 12◦

widens considerably. At inclination angles of 20 and 25◦ , a change in the nature of the skin friction curve near the compression corner may be attributed to secondary flow separation.

6.1 Flow Features Mach number contours for ramp inclination angles of 12 and 25◦ are presented in Figs. 8 and 9, respectively. The difference in the flowfield structure is evident in these contours. The large separated flow region ahead of the 25◦ ramp is seen clearly in Fig. 9. The velocity vectors in the vicinity of the CDR of ramp inclination angle of 12◦ are shown in Fig. 10. It is observed from this figure that reversed flow is limited to the compression corner only. For ramp inclination angle of 25◦ , the velocity vectors are presented in Fig. 11. This figure clearly shows the attached flow well ahead of the CDR, separated flow just ahead of and aft of the compression corner and flow reattachment on the ramp.

6.2 Separated Flow Extents The separation length (L) is defined as the distance from the separation point to the compression corner. The variation of the separation length, normalized by the ramp height (h), with the ramp inclination angle is plotted in Fig. 12. The change in slope

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R. George and R. K. Grandhi 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00

Fig. 9 Mach number contours for ramp inclination angle of 25◦ 602 523 445 367 289 210 132 54 -25

Fig. 10 Velocity vectors in the vicinity of ramp with an inclination angle of 12◦

Parametric Study of Turbulent Flow Past a Compression–Decompression Ramp

23

602 510 418 327 235 143 52 -40 -131

Fig. 11 Velocity vectors in the vicinity of ramp with an inclination angle of 25◦ 2.0

separation length

1.8 1.6

L/h →

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 5

10

15

20

25

Inclination angle (degrees) →

Fig. 12 Separation length variation with angle of inclination of ramp

of the plot is observed at an angle of 16◦ . This value agrees with the value given in literature [4]. Separation initially appears at a small angle (onset of separation) and slowly increases with inclination angle. The angle at which the slope changes defines the onset of large-scale separation. As per literature [4], the inclination angle corresponding to onset of separation ranges from 6.5 to 12◦ , while large-scale separation onset occurs at inclination angles in the range of 15–19◦ .

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7 Summary The CFD software, ANSYS Fluent is successfully validated for compression– decompression ramp-induced separated flows. The pressure profiles match well with literature. It is also observed from the validation studies that the one-equation SA turbulence model predictions are as good as the two-equation models. It can be inferred from the present results that the changes in pressure and skin friction coefficient are adequately captured by the Fluent simulations for supersonic flow past compression–decompression ramps (CDR) of varying ramp inclination angles. Ramp inclination angles less than 12◦ minimize the adverse effects of separated flow for the conditions considered here. In general, flow separation can be avoided by reducing the ramp inclination angle.

References 1. Fluent User Manual. Fluent Inc. (2006) 2. Settles GS, Dodson LJ (1991) Hypersonic shock/boundary layer interaction database. Technical report, NASA CR 177577 3. George R, Grandhi RK, Gupta RK (2013) Validation of Fluent for turbulent separated flow past a compression-decompression ramp. In: ANSYS 2013 Convergence Conference 4. Babinsky H, Harvey JK (2011) Shock wave–boundary-layer interactions. Cambridge 5. Oliver AB, Lillard RP, Blaisdell GA, Lyrintzis AS (2006) Validation of high-speed turbulent boundary layer and shock-boundary layer interaction computations with the OVERFLOW Code. AIAA 2006-0894 6. Oliver AB, Lillard RP, Blaisdell GA, Lyrintzis AS (2007) Assessment of turbulent shockboundary layer interaction computations using the OVERFLOW Code. AIAA 2007-0104 7. Delery J, Marvin JG (1986) Shock-wave boundary layer interactions. Technical report, AGARDograph 280

Validation of Numerical Analysis Results for Pusher Configured Turboprop Engine Air Intake C. A. Vinay and S. Bhaskar Chakravarthy

Abstract In the course of an aircraft development program of LTA, a number of engine-related ground and flight tests have to be carried out to determine the losses particular to the engine installation. These installation losses must be determined in order to create the final aircraft power setting charts. During the course of configuration development, design analysis is a must to ensure that the proposed design will perform the intended operation within the estimated losses, this confidence should be assessed either in a bench tests or in CFD analysis. The numerical study of engine air intake performance is carried out using RANS-based k − ω SST using ANSYS FLUENT software. The study is carried out for minimum climb condition, as it is critical operation of any aircraft mission. The CFD results were compared with the flight test data for validation. The instrumentation that is necessary to measure installation losses and engine performance has been installed. Computational results agree well with the experimental results and were found satisfactory. The CFD results of air intake show that the total pressure is extensively recovered at the engine intake plenum (compressor inlet screen) region, and the inlet pressure loss and ram air recovery were within the acceptable limit as recommended by engine OEM. Keywords Nacelle air intake · Ram recovery · Total pressure loss · Oil cooler

1 Introduction The recent interest in design and development of light transport aircraft (LTA) has led to higher operating Mach number and higher altitudes, which certainly demands better engine air intake performance [1]. The air intake system of LTA is designed to provide the maximum possible total pressure at the compressor inlet screen over C. A. Vinay (B) · S. B. Chakravarthy CSIR-National Aerospace Laboratories, Bengaluru 560037, India e-mail: [email protected] S. B. Chakravarthy e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_3

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C. A. Vinay and S. B. Chakravarthy

a wide range of normal flight operations. The engine air intake is required to capture and efficiently compress requisite quantity of air for engine operation. The air inlet system delivers air to the plenum chambers, which indeed covers the inlet screen. The air intake should be effective in providing adequate mass flow of air as demanded by combustor. The overall vehicle performance depends greatly on the flow quality of the incoming air. Small loss in the air intake efficiency will have a greater adverse effect on the engine power output. Efficient ram air pressure recovery at the engine inlet is required to obtain maximum power levels and low specific fuel consumption. Therefore, the detailed analysis and study of flow behavior through the air intake ducts are important aspects in the design evaluation and estimation of the engine air intakes. Turboprop engines are widely used in commuter category airplanes. Aircraft design bureaus routinely conduct the flight tests to confirm the performance of the engine intakes to ensure the rated power extraction from the engines. Air intake designs are important because engine efficiency, specific fuel consumption, flat rating limits and efficient matching of engine with airframe, etc. much depend on the efficient intake system design. In this paper, the computational study on flow through and around the air intake along the nacelle is carried out for the given climb condition. The computational results were validated with the flight test data of LTA.

2 Geometry and Analysis 2.1 Geometry Details The geometric modeling was done using CATIA V5 software. The geometry consists of internal and external parts. The external parts include the nacelle and lip intake as shown in Fig. 1. Internal parts consist air intake duct, stopper and compressor screen (referred as plenum) as shown in Fig. 2. Geometric consideration when dealing with such a complex problem is to be realistic as possible keeping analysis time and cost into consideration. Therefore, the geometry is modeled as simple, by neglecting the minor and inconsequential structural details. In addition, the propeller and spinner assembly was not considered, and the propeller hub (downstream) portion is replaced by a smooth contour near the aft end of the nacelle. A parametric approach was adopted for the creation of flow in the domain. The completed geometry was exported as IGES format to the ANSYS ICEM-CFD software for meshing.

2.2 Mesh Details The commercially available ANSYS ICEM-CFD software was used to generate unstructured mesh. The inlet and outlet boundaries are located at 10 L and 15 L

Validation of Numerical Analysis Results for Pusher …

27

Fig. 1 External view of air intake and nacelle

Fig. 2 Symmetric cross-sectional view of nacelle

upstream and downstream. For the domain, the enclosure was set at 20D, where L is the length and D is the diameter of the nacelle. Coarse mesh was generated around the geometry and a finer mesh along the wall. To capture flow behavior in the air intake duct, finer mesh was generated along the air intake duct and at upstream of nacelle intake [2, 3]. Grid independence study (GIS) was carried out with three different grids: G1 with 14 million, G2 with 8.3 million and G3 with 4 million elements. G2 mesh with 8.3 million elements gave satisfactory results for minimum mesh count, and the same was selected for further computations. Figure 3 shows the global domain, and Fig. 4 shows the surface mesh on the model.

28

C. A. Vinay and S. B. Chakravarthy

Fig. 3 Global size of the domain

Fig. 4 Surface mesh on the nacelle

2.3 Numerical Details In the present computations, the flow field is considered to be turbulent. While the turbulent fluctuations are not solved, their efforts on the mean flow are modeled by solving the Reynolds-averaged Navier–Stokes equations using commercial finitevolume method-based code ANSYS-FLYENT software. Due to the presence of separation and reattachment regions in the flow field, it was decided to use k − ω shear stress transport (SST) model for the computations [2]. Spatial discretization of governing equations was done using second-order upwind scheme. The pressure

Validation of Numerical Analysis Results for Pusher …

29

Fig. 5 Global boundary conditions

velocity coupling was achieved using SIMPLE scheme. All the computations were performed using double-precision arithmetic.

2.4 Boundary Conditions Velocity inlet and pressure outlet boundary conditions are imposed at domain inlet and outlet, respectively. Domain far-field is set to pressure outlet and nacelle, and interior parts are set to wall boundary condition as shown in Fig. 5. At the nacelle cover and compressor screen, interior and pressure outlet with targeted mass flow rate is applied as shown in Fig. 6. The turbulent viscosity ratio of 5% is maintained throughout the computation.

3 CFD Results and Validation 3.1 Computational Results The operating conditions for given minimum climb case are shown in Table 1, and the results (static pressure and velocity contours) obtained from the computational study are presented in Table 2.

30

C. A. Vinay and S. B. Chakravarthy

Fig. 6 Internal boundary conditions

Table 1 Operating condition Altitude (ft)

OAT °C, (K)

P0 Free stream total inlet pressure (Pa)

P1 Engine Mass flow inlet screen rate, kg/s total (lb/s) pressure (Pa)

Angle of attack (°)

Speed m/s (M)

4500

6.1 (279.25)

88,578

85,908.6

6.60

71.46 (0.21)

4.036 (8.90)

Table 2 CFD results Altitude (ft)

4500

Compressor screen

Inlet (Throat)

Dynamic pressure (Pa)

Static pressure (Pa)

Total pressure (Pa)

Dynamic pressure (Pa)

Static pressure (Pa)

Total pressure (Pa)

565

1578

2160

2783

10.5

2794

Figure 7 depicts the contours of static pressure over the nacelle at minimum climb condition. The pressure gradually increases from the throat to plenum region. The maximum pressure is observed at the compressor inlet case. Due to high pressure at the air intake, the stagnation region is observed. The lower pressure region (suction pressure) is observed on the upstream of intake duct, and further downstream of the intake duct adverse pressure (diffuser) gradient is observed. Low pressure region is noticed on both the lower and upper portion of the nacelle due to its aerodynamic profile. However, the pressure drop at the throat is adequately recovered near the plenum to the significant extent.

Validation of Numerical Analysis Results for Pusher …

31

Fig. 7 Contours of static pressure at minimum climb condition

Figure 8 depicts the contours of total pressure of the nacelle and air intake duct at climb condition. It is observed that the total pressure is adequately recovered from the intake lip to engine intake, which indeed meets the engine requirements which in turn will improve the performance of engine. Figure 9 depicts the velocity vectors for minimum climb condition. High velocity is observed on the upper portion of the nacelle and gradually increases along the nacelle geometry. Due to the aerodynamic profile of the nacelle, higher velocity is observed along the half way of nacelle. Figures 10 and 11 depict the contours of Mach number and the flow path along the nacelle and air intake duct. As the Mach number indicates the real flight conditions, it also represents the altitude and temperature. From Fig. 10, it is observed the Mach contours are continuously changing along the flow field and approaches near the nacelle surface.

Fig. 8 Contours of total pressure at minimum climb condition

32

Fig. 9 Velocity vectors at minimum climb condition

Fig. 10 Mach number contours on the nacelle

Fig. 11 Flow path along the nacelle and air intake duct

C. A. Vinay and S. B. Chakravarthy

Validation of Numerical Analysis Results for Pusher …

33

3.2 Instrumentation and Flight Test The instrumentation that is necessary to measure installation losses and engine performance has been installed at the engine intake lip and at compressor inlet case. At the inlet plane (throat), the static and total pressure is measured. The inlet plane consists of 5 total pressure probes and 4 static pressure probes by means of tapping as shown in Fig. 12. The inlet pressure measurements are used to determine the inlet lip flow behavior. Engine plenum pressure is measured from the top and bottom dead center locations of the compressor inlet screens. Measured Parameters During Flight Test The measured data from the flight test during minimum climb condition is shown in Table 3. The operating altitude and calibrated aircraft speed during minimum climb condition were observed to be 4160 ft and 142 knots. Data Reduction The obtained pressure values from the actual flight test are converted to the quantitative results by using empirical relations as shown in Eqs. 1 and 2, respectively. Intake pressure loss

P0 − P1 P = P P0

(1)

Air Intake Lip

Vane Actuator Door

Static Pressure Probes

Total Pressure Probes

Fig. 12 Instrumentation of probes at air intake

Table 3 Flight test results Air intake parameters

LH

RH

Air inlet static pressure (psi)

12.83

12.85

0.36

0.40

Plenum chamber (compressor screen) differential pressure (psi)

Air inlet differential pressure (psi)

12.78

12.86

Air inlet total pressure (psi)

13.19

13.25

34

C. A. Vinay and S. B. Chakravarthy

P1 − Pamb P0 − Pamb

(2)

Mass flow rate = ρ × A × V

(3)

Ram recovery =

where P0 = Free stream total inlet pressure, psi P1 = Engine inlet screen total pressure, psi Pamb = Free stream static pressure, psi A = Air intake throat area, m V = Velocity, m/s ρ = Density, kg/m3 . Inlet Pressure Loss = Ram Recovery =

0.17 ×100 = 1.4% 12.6

12.7 − 13.3 × 100 = 97% 13.19 − 13.3

Mass flow rate (lb/s) = 1 .11 × 0.058 × 65.3 = 4.20 kg/s = 9.2 lb/s Thus, from the result, it is found that it is clear that for left-hand side engine, the intake pressure loss is 1.4% and ram recovery is 97% at 4160 ft.

3.3 Validation The computational results are validated with flight test data of LTA. The comparison between the flight test results and computational results is shown in Table 4. From the flight test result, the ram recovery at the intake is 97%, and from computational study, it was found to be 93.7%. It is clear that the experimental results of the intake pressure loss is slightly higher when compared with the CFD prediction whereas experiment data of ram recovery and mass flow agree reasonably well with computational results. Hence, from this baseline study, the numerical model used for Table 4 Validation of CFD and flight test data Air intake parameters

CFD study

Ram recovery (%)

93.7

Intake pressure loss (%) Mass flow (lb/s)

Flight test data (LH and RH engine) 97

97

0.93

1.4

1.3

10.29

9.2

9.5

Validation of Numerical Analysis Results for Pusher …

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this study was found satisfactory. Thus, CFD results are in good agreement with the flight test results and found 5% under prediction which is satisfactory.

4 Conclusion In this paper, the numerical simulation for evaluating the light transport aircraft engine air intake performance at minimum climb condition has been efficiently carried out. From the CFD results, it is observed that the total pressure loss at the air intake (throat) has been adequately recovered at the engine inlet plenum. The performance parameters are compared between CFD study and the measured flight test results. The numerical results agree well with the flight test data. Hence, the system pressure loss and ram recovery are within the acceptable limits as recommended by the engine OEM. Acknowledgements The authors would like to thank all partners and associated partners for their contribution to the program and for their permission to publish this paper.

References 1. Chakraborty D (2015) Numerical simulation of a hypersonic air intake. Def Sci J 65(3):189–195. https://doi.org/10.14429/dsj.65.8254 2. Tu J, Yeoh GH, Liu C (2008) Computational fluid dynamics, a practical approach, 1st edn. Elsevier, USA 3. Oliveira GL, Santos LC, Martins AL, Becker GB, Reis MVF, Spogis N, Silva RFAF (2008) A tool for parametric geometry and grid generation for aircraft configurations. ICAS

Aero-elastic Analysis of High Aspect Ratio UAV Wing—Based on Two-Way Fluid Structure Interaction Vidit Sharma

and S. Keshava Kumar

Abstract Aero-elasticity of a wing is the study of airflow around an elastic wing and their interaction. A two-way Fluid Structure Interaction (FSI) method has been advantageous in the study of aero-elastic behavior of lifting surfaces. Preliminary design of an UAV requires detailed understanding of aerodynamic and structural operational boundaries; to arrive at an optimal wing. High aspect ratio wings are being employed in Medium Altitude Long Endurance (MALE) and High-Altitude Long Endurance (HALE) UAVs. High aspect ratio wings are usually designed using composite materials because of their specific stiffness and strength customization ability. To this end, for designing a high aspect ratio wing, which is aero-elastically compliant and performs well at all flight conditions—understanding the aero-elastic behavior is necessary. Preliminary designs as well as detailed design incorporate reduced ordered models, however to evaluate the efficiency of reduced ordered models—a full scale 3D numerical model analysis or wind tunnel tests are required. Here aim is to perform and establish a baseline study of two-way coupled static aero-elastic analysis based on the existing experimental results of a composite flat plate wing and a large/high-aspect ratio wing, which in turn will work as a benchmark for flutter analysis and reduced ordered models to be developed. ANSYS package has been used to demonstrate the methodology to predict the onset of divergence, a static aeroelasticity phenomenon. The numerical simulation results from ANSYS are validated with existing experimental results available in the literature. Numerical simulation is carried out for a composite wing, and then the methodology is extended to high aspect ratio wing. The results obtained using bidirectional-coupled simulation studies are found to be in agreement with the results available in the literature. Keywords Composite materials · FSI · CFD · FEM · Divergence

V. Sharma · S. Keshava Kumar (B) Department of Aerospace Engineering, Defence Institute of Advanced Technology, Pune, Maharashtra 411025, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_4

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1 Introduction High Altitude Long Endurance (HALE) and Medium Altitude Long Endurance (MALE) UAVs are employed for remote sensing and aerial survey of inaccessible regions [1]. The design of a HALE or MALE UAV demands high aspect ratio wing, because of their aerodynamic advantages [1]. The high aspect ratio structural design of a wing requires incorporating composite materials, for their specific strength and specific stiffness capabilities. High strength/stiffness to weight ratio of composite materials makes them highly eligible for overall weight reduction of unmanned aerial vehicles, leading towards high payload capability. However, designing a tailored composite wing design is a complex process, as there are too many parameters to consider. Hence to design an aero-elastic compatible wing reduced ordered models are required [2], through which quick design iterations can be performed. But there are many reduced order models and to choose the appropriate model baseline result are required [2]. Albeit there are many reduced ordered models, very few are feasible for high aspect ratio wings [2]. Hence, to shortlist the appropriate model or to develop a new reduced ordered model, which can incorporate non-linearities inherent to high aspect ratio wings—we require benchmark results. To this end a 3D numerical simulation will serve the purpose [3]. Hence, a 3D two-way FSI simulation for a known wing model, for which experimental results are available, is performed first. By this the optimal simulation method of two-way FSI process shall be established, and then adopt the similar process for analyzing high aspect ratio wing. To achieve this aim, we proceed in a step-wise fashion. First, aero-elastic (divergence) analysis of flat laminated composite plate is performed, for which analytical as well as wind tunnel results are available [4–6], through this process and methodologies will be validated. Then this work will be extended to incorporate non-linearities in the wing structure. Among the various methods two-way Fluid Structure Interaction (FSI) provides a high-fidelity analysis tool to capture the structural and aerodynamic non-linearities.

2 Aero-elasticity Aero-elasticity study deals with two major areas, static aero-elasticity and dynamic aero-elasticity. Static aero-elasticity analysis has been performed in this paper, brief introduction of static aero-elasticity wing divergence is explained below. Static aero-elasticity includes the wing divergence phenomena due to the elastic nature of the wing and its interaction with fluid flow. Divergence occurs when lift produced at the center of pressure (or assumed to be aerodynamic center) produces a moment about the elastic axis of the wing which twists the wing to pitch up and cause the wing to fail structurally for torsional rigid wing, or induce stall due to large rotation of the cross-section, for torsional soft wing. For a two-dimensional airfoil attached to torsional spring (of stiffness constant kt placed at elastic axis/shear center)

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at rigid/root angle of attack, αr , subjected to a freestream air velocity, U∞ , the angle of attack, α, can be obtained as [7]: α=

αr , 1 − q/qD

α = αr + θ

(1)

where, q is the freestream dynamic pressure, qD is divergence dynamic pressure, and θ is the wing twist. Modifying the Eq. (1) leads us to an equation of straight line, expressed as:   qD 1 1 1 (2) = − θ αr q qD From Eq. (2), theoretical value of divergence dynamic pressure and divergence speed can be obtained for failure condition; where wing twist tends to infinity or 1/θ tends to zero. To obtain divergence pressure of a wing a minimum two data points are required, the data points can be obtained either from the experimental study or two-way fluid-structure interaction (CFD-FEM) [7]. The graphical representation for the calculation of divergence dynamic pressure is given in Fig. 1, the value of divergence dynamic pressure can be extrapolated from the fitted straight line, based on the wings static twist data; i.e. wing tip twist, θ , at corresponding freestream dynamic pressure, q, intersecting with 1/q-axis. Similar method was adopted by Blair and Weisshaar [8] in their experimental aero-elastic divergence analysis of a swept composite wing, they expressed it as Modified Southwell plot. Southwell plot method is employed in the present study to obtain tip divergence of the wing.

Fig. 1 Graphical representation of divergence dynamic pressure, qD , based on Eq. (2)

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3 Fluid-Structure Interaction Solvers for fluid flow and structural analysis are available in various software packages, and in general they are solved separately for aerodynamic and structural problems. Both processes require discretization of geometry into small control volumes/elements. Whereas, for aerodynamic study mesh around the body needs to be more refined as compared to that of a solid structure mesh in FEM. There are two general methods to perform FSI analysis, monolithic approach and partitioned approach [9].

3.1 Monolithic Approach The two participants in FSI analysis, CFD and FEM, are formulated as a single solver. Where the governing equations of both the participants are solved numerically as a one combined discretized set of algebraic equations. Data transfer between the structure and the fluid domain is synchronized and provides a stable solution due to conservation of properties at the interface of two domains. Monolithic approach is more feasible when we have weak coupling between two participants, i.e. influence of either of the participants on each other is negligible during simulation. Figure 2 shows the schematic of the monolithic approach, where Rf and Rs are the fluid and structural system equations respectively. The approach can be of steady or transient state. Although, this approach has been proven as a more robust method than that of the partitioned approach but it is more computationally expensive and cannot be formulated easily as that of a software modulated partitioned approach [9].

3.2 Partitioned Approach As opposed to the monolithic approach where conservation of interface proper-ties between the fluid and structural participants is synchronized, in partitioned approach conservation of properties is asynchronized because of the lag between the individually solved participants (fluid and structural). In the coupling step integration leading to the loss of interface properties conservation. In order to solve this problem, interface data mapping algorithms are incorporated.

Fig. 2 Representation of monolithic approach

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Fig. 3 Representation of partitioned approach

As represented in the Fig. 3, data mapping between the two participants takes place at each coupling step and each coupling step performs internal iterations to achieve sufficient convergence of the interface properties along with the convergence of each participant solver. This approached has been adopted (using ANSYS 17.2) in this paper, due to its less computational expense attributes and software modularity. The data exchange between the two participants of FSI analysis, is known as coupling and there are two methods to implement this approach [9].

3.2.1

One Way Coupling

To study the effect of fluid flow on a solid structure, one-way coupling is more than enough. Where the data mapping takes place in only one direction (fluid to solid). A representation of such process is displayed in Fig. 4. Usually it is known as weak coupling, i.e., for aero-elasticity analysis interpolation of pressure from CFD to FEM (using data mapping algorithms) will only provide the structural deformation/stress/strain results based on the CFD output. Steady as well as transient simulations can be performed with one-way coupling [10], providing close enough predictions at a very low computational time, and only if the effects of solid structure deformation on the fluid flow is negligible. It is usually employed, when fluid loads will not induce significant deformations in the structure. As for small deformations in the structures, will not induce substantial change in fluid domain results.

Fig. 4 Representation of one-way coupling

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Once the CFD solver performs calculation and obtains a converged solution, the surface pressure from CFD domain gets interpolated onto the mesh of the FEM solver and resulting forces gets transferred. Now, FEM solver performs the calculations until it reaches convergence. Whereas, in the case of large deformations of structures like high aspect ratio wings, the significant deformation in structure leads to substantial changes in fluid domain, and hence two-way coupling is required.

3.2.2

Two Way Coupling

Two-way coupling as called, is important for cases where the effect of solid structure deformation on the fluid flow is significantly large. This process is described in form of a flow chart in Fig. 5. For steady state case, for example static aero-elasticity (divergence study). In first coupling step, steady state CFD solution of a rigid wing is obtained and the surface pressure gets interpolated to the FEM solver using one of the mapping algorithms. Now, static structural solution is obtained by FEM solver which in return interpolates the nodal displacement to CFD solver. CFD solver deforms the fluid mesh based on the incoming displacement, this will repeat for certain amount of internal coupling iterations until the data transfer convergence is reached. Once the data transfer is converged, simulation will start next coupling step. For current study of static aeroelasticity, sufficient number of coupling steps are required so that the wing is in equilibrium state and further coupling steps does not change the displacement and forces of the wing, assuming the flow and solid structure to be under steady state conditions. For transient state case, dynamic aero-elasticity (flutter study), both solver or participants performs transient flow analysis (CFD) and dynamic structural analysis (FEM) while exchanging the interface properties at the interfaces and ensuring data

Fig. 5 Representation of two-way coupling

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transfer convergence at every coupling time step up to desired number of time steps. As the data exchange is initiated by both the participants, meaning in both ways, bidirectional coupling is considered to be a strong coupling.

3.3 Data Mapping Critical part of the FSI analysis is the coupling between the participants of the analysis, where pressure fluctuations in the CFD domain surrounding the FEM domain, has to be imposed as loads on the structure/FEM mesh. Also, the deformation of the structure in turn will change the flow domain, hence based on the deformations, the fluid domain has to be remeshed. Which is basically the data transfer between CFD and FEM solvers, where interface properties are required to be shared between the two separate meshes of different domains and nature. This is performed in two major processes and sub-processes, first process includes the mapping algorithms to matching the source and target mesh. Afterwards, source mesh sends the data to target mesh based on weight integration. There are two such algorithms, General Grid Interface (GGI) and Smart Bucket algorithm for conservative and non-conservative quantities respectively [9].

3.3.1

General Grid Interface (GGI)

Three-dimensional ‘n’ integration points (IP) are created using the method of dividing the elements faces of both source and target sides, which later are converted into twodimensional quadrilaterals, they are extrapolated into rows and columns of pixels. These pixels are then intersected to create overlapping surface areas known as control surfaces. Amount of intersections among the pixels determines the mapping weight contributions for each control surface, which are collected to obtain the value of mapping weights at each node. These weights are conservative in nature, see Fig. 6 and used for transferring the quantities like forces, mass and momentum in ANSYS Workbench [9]. GGI is used to transfer loads from the fluid domain to structure domain.

Fig. 6 General Grid Interface (GGI) mapping algorithm

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3.3.2

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Smart Bucket Algorithm

In this process the target and source mesh are divided into a grid of buckets (group of elements) to compute the mapping weights. For source mesh nodes associated with the buckets of target mesh, the mapping weights are calculated. There can be two possible cases which can exist, empty and non-empty bucket. For non-empty bucket, where it contains elements inside, one or more elements in the bucket of target side gets matched to the node of the source side and is executed using an iso-parametric mapping. For an empty bucket, the closest non-empty bucket is tagged and isoparametric mapping is used in the same manner. Non-conservative quantities like displacement, temperature and stress are transferred using this algorithm in ANSYS Workbench [9], which makes this approach of profile preserving nature, see Fig. 7. It is used to transfer data from structure domain to fluid domain.

4 Model Generation Fluid-Structure Interaction is required to contain two geometrical domains, fluid and solid. Geometry for the CFD analysis includes the flow domain around the wing and FEM includes the internal structure of the wing. For validation two available experimental studies were selected, aero-elastic analysis of laminated graphite/epoxy flat plate wing (small aspect ratio wing, AR=9.2) by Landsberger et al. [4] and another of a high-aspect ratio wing, AR=17.7, by Tang and Dowell [11].

4.1 Flat Composite Plate Wing Divergence Study The cantilevered flat plate wing was designed based on the geometrical parameters used by [4–6], half span s = 0.305 m; chord c = 0.076 m, and thickness t = 0.000804 m (six layers of graphite/epoxy), as shown in Fig. 8a. The structural geometry was created using the ANSYS ACP (Pre), a composite pre-post software, consisting six layers with different composite lamina or fiber ply orientation, θF , as shown in Fig. 9. Total of four different composite plate configurations were created for this validation, [+302 /0]s , [−152 /0]s , [−302 /0]s , and

Fig. 7 Smart Bucket algorithm

Aero-elastic Analysis of High Aspect Ratio UAV …

(a) Flat plate composite wing.

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(b) Large AR wing.

Fig. 8 Schematic of geometry

Fig. 9 Fiber orientation of composite flat plate wing for a stack of six composite ply layers

(a) Flat plate composite wing.

(b) Large AR wing.

Fig. 10 CFD domain

[−452 /0]s . For validation, the zero sweep wing data has been taken form [4]. CFD domain was created around the wing, where domain walls were kept far away from the model to avoid boundary effects, Fig. 10a.

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4.2 Large AR Wing Divergence Study Based on the wing specifications used by Tang and Dowell [11], wing model was created with half span s = 0.4508 m; chord c = 0.0508 m. The slender body at the tip of the wing was created, see Fig. 8b. The wing was modeled with uniform NACA 0012 airfoil cross-section, without ribs and spar as opposed to the referred literature [11]. The actual wing used in the literature [11] was created using steel spar, aluminum ribs and balsa wood blocks fitted in-between the ribs. Modeling these elements in FEM framework is complex, time consuming and computationally costly, as the nonlinearities will creep in due to contact elements, which have to be used to couple the balsa wood blocks, aluminum ribs and steel spar. And upon careful modeling all the elements, the properties are not guaranteed to match the actual wind tunnel model. Hence recourse to above method is adopted, which gives the advantages of simplistic modeling and advantage of less computational cost. The stiffness, mass and torsional rigidity parameters are mapped using custom an-isotropic material properties, see Tables 1 and 4. But, this method could not match the properties one to one, as there were discrepancies in the elastic axis and center of gravity location of the modeled wing and the wind tunnel tested model wing [11], see Fig. 11.

Table 1 Cross-sectional properties of experimental wing setup [11] and FEM wing model Parameter Value Span, b Chord, c Flap bending rigidity, EIx Chordwise bending rigidity, EI y Torsional rigidity, GJ Ix x I yy Torsional constant, J Mass per unit length Spanwise elastic axis Center of gravity

Tang and Dowell [11] 0.4508 m 0.0508 m 0.4186 Nm2 0.1844 × 102 Nm2 0.9539 Nm2 – – – 0.2351 kg/m 50 % chord 49 % chord

Present study 0.4508 m 0.0508 m 0.4186 Nm2 0.1844 × 102 Nm2 0.9539 Nm2 4.53317 × 10−10 m4 3.02209 × 10−8 m4 1.80227 × 10−9 m4 0.2351 kg/m 44.79 % chord 41.81 % chord

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Fig. 11 Difference between the elastic axis and center of gravity location in present study and experimental study [11] (not to the scale)

5 Mesh and Boundary Conditions 5.1 Finite Elements Analysis Structural mesh/grid for the present study was generated using ANSYS Meshing. For flat composite plate wing divergence study, geometry was very simple and gives us freedom to mesh it with mapped elements. ANSYS Workbench provides automatic FEM element assigning capabilities, thus SOLID185 elements were used to discretize this geometry. SOLID185 element has eight nodes where each node has three degrees of freedom, translations in nodal x, y, and z directions [12]. As for large A R wing divergence study geometry, mapped meshing was not possible due to airfoil cross-section, thus meshed with paved hexahedral elements with sweeping along the span. SOLID186 elements were used to discretize this geometry, as they are well suited for irregular meshes where elements may have any spatial orientation. SOLID186 element has 20 nodes where each node has three degrees of freedom, translations in nodal x, y, and z direction [12]. Root of the wing is fixed in all the directions for displacement; gravitational acceleration was applied in the negative x direction for flat composite plate wing divergence study (similar to the experimental setup) and for the next study in negative y direction (Fig. 13).

5.2 Computational Fluid Dynamics ANSYS ICEM CFD software was used to discretized the CFD domain into small tetrahedron control volumes and triangular surface elements. Smooth variation of element size is maintained from near the wing to outer boundaries with a growth rate of 1.1, see Fig. 12. In order to capture near wall effects, prism layers were created based on a nondimensional turbulence quantity known as wall y + , which is the function of first layer height of mesh layer around the body, wall shear stress and local flow velocity. It needs to be closer to 1 for resolving the boundary layer gradients, leading to accurate calculation of wall forces. Prism layers were created using first layer thickness and

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(a) Flat plate composite wing.

(b) Large AR wing.

Fig. 12 Mesh for CFD analysis

(a) Flat plate composite wing.

(b) Large AR wing.

Fig. 13 Near wall mesh on wing surface

growth ratio. The first layer thickness was chosen based on the grid independence study, 0.00001 m, which was providing wall y + ≈ 1, excellent to resolve boundary layer accurately using Spallart-Allmaras turbulence model. CFD domain faces were named as inlet, outlet, symmetry and wing, as shown in Fig. 10. Inlet was considered as velocity-inlet with velocity vector defined by magnitude and direction specification method for root angle of attack, αr . Outlet was considered to be at standard sea level atmospheric pressure using pressure-outlet boundary condition. Symmetry was specified to maintain the flow symmetry for the half wing model. Wing was specified as no-slip wall boundary as well as system-coupling interface using dynamic meshing. Volumetric elements were specified to be deforming using diffusion-based smoothing and remeshing algorithms to maintain the acceptable mesh quality while absorbing and adjusting the abrupt changes due to wing-boundary displacement [13].

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6 Solver Setup 6.1 Computational Fluid Dynamics (CFD) Fluid flow and transport phenomena are governed by the conservation of mass, momentum and energy. These governing equations are solved based on the method known as Finite Volume Method (FVM), which includes dividing the CFD domain into small control volumes, integration of governing equations over the control volumes of the domain, discretization of resulting integral governing equations to obtain a set of algebraic equations and finally solution of these algebraic equations by an iterative method. For present study, three-dimensional Navier-Stokes equations with one equation Spalart-Allmaras turbulence model available in ANSYS Fluent is selected. A brief outline of the background procedure is given below [13]: Decomposing the instantaneous Navier-Stokes equations into mean and fluctuating quantities (vector and scalar) and taking time average, results in the ensembleaverage momentum equations known as Reynolds-Average Navier-Stokes (RANS) equations given as: ∂ ∂ρ + ( ρu i ) = 0 (3) ∂t ∂ xi ∂ ∂ ( ρu i ) + ( ρu i u j ) ∂t ∂ xi    ∂u j ∂u i ∂ ∂p ∂ 2 ∂u l μ + =− + + − δi j ( −ρu i u j ) ∂ xi ∂x j ∂x j ∂ xi 3 ∂ xl ∂x j

(4)

where, the last term in Eq. (5) represents the turbulence effect and Reynolds stresses, ( −ρu i u j ) , are required to be modeled towards the first step in turbulence modeling. Which is formulated based on Boussineq hypothesis [13]. From the various turbulence models available in ANSYS Fluent, Sparlart-Allmaras model was selected in order to solve kinematic eddy viscosity, for which the transport equation of the turbulent kinematic viscosity, ν˜ , is given by: ∂ ∂ ( ρ ν) ˜ + ( ρ νu ˜ i) ∂t ∂ xi       ∂ ν˜ 1 ∂ ∂ ν˜ 2 ( μ + ρ ν) ˜ + Cb2 ρ − Yν + Sν˜ = Gν + σν˜ ∂ x j ∂x j ∂x j

(5)

where, G ν is the production of turbulent viscosity, Yν is the turbulent viscosity destruction which occurs because of the viscous damping and wall blocking at the near-wall region, ν is molecular kinematic viscosity, Sν˜ is source term, and σν˜ and Cb2 are the constants. The setup of steady state in-compressible flow simulation (for static

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aero-elasticity) is established by discretized CFD domain using ANSYS Fluent see Fig. 12. ANSYS Fluent solves the RANS equations and the transport equation based on Finite Volume Method (FVM). Where second-order upwind spatial discretization scheme was selected along with SIMPLE algorithm; developed by Patankar and Spalding [14], to formulate pressure-velocity coupling. Convergence was achieved till the residuals reached below sixth order decimal place or the forces are converged.

6.2 Finite Element Method (FEM) Finite Element Method (FEM) is based on the finite element idealization, the structural model is discretized into elements (discrete regions) with connectivity at the nodes to each other. Current static structural analysis was performed using ANSYS Mechanical APDL. The equilibrium equations of a structural static analysis are: [ K ] {u} = {F a } + {F r }

(6)

N [ K e ] is global stiffness matrix, where, {F r } is reaction load vector, [ K ] = m=1 {u} is nodal displacement vector, [ K e ] is element stiffness matrix, and {F a } is the total applied load vector, formulated as: {F a } = {F nd } + {F ac } +

N



{Feth } + {Fepr }

 (7)

m=1

N where, {F r } = −[ M] {ac } is acceleration load vector, [ M] = m=1 [ Me ] is total mass matrix, [ Me ] is element mass matrix, {ac } is total acceleration vector, {Fet h} is p element thermal load vector, and {Fe r } is element pressure load vector. The above derived structural models linear equilibrium equations can be solved by one of the type of solvers available in ANSYS Mechanical APDL, which are direct and iterative solvers. For current FEM analysis direct solver has been selected, which uses a direct elimination process known as Gaussian elimination approach to solve the unknown vector, {u}, by employing LU decomposition [15].

6.3 System Coupling Once the setup for ANSYS Mechanical APDL and ANSYS Fluent was complete, ANSYS Coupling Service available in ANSYS Workbench was used to setup the two-way coupling between the two domains (FEM-CFD) [9]. For system coupling, 10 coupling steps were selected, each with maximum 5 iterations, where at each iteration Mechanical APDL and Fluent perform analysis, in a sequential manner, till convergence is achieved, data transfers were established in-between the two domains

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with RMS convergence criteria of each data transfer equal to 0.01 which was achieved at each coupling step. By default, ANSYS Workbench [9] selects the data mapping algorithms as General Grid Interface (GGI) for force transfer from Fluent to Mechanical APDL, and Smart Bucket Algorithm displacement transfer from Mechanical APDL to Fluent. Once the simulation is updated to proceed towards the solution, it will follow the process as described in Fig. 5.

6.4 Input Parameters Current study was performed with following fluid flow properties, air density, ρ, and dynamic viscosity, ν, at various freestream air velocities, U∞ , and root angles of attack, αr , for CFD solver, see Table 2. Material properties for the flat plate composite wing are taken from the experimental study performed by Landsberger et al. [4], are given in Table 3. Material properties for simplified geometry for large A R wing divergence study were calculated based on the flap bending rigidity, chordwise bending rigidity, torsional rigidity, and mass per unit length, by Tang and Dowell [11], see Tables 1 and 4.

Table 2 Input properties—computational fluid dynamics Parameter Value Air density, ρ Dynamic viscosity, ν Flat composite plate wing divergence study Freestream velocity, U∞ Root angle of attack, αr Large AR wing divergence study Freestream velocity, U∞ Root angle of attack, αr

1.225 kg/m3 1.7894 kg/ms 1.75, 5, 6.25, 8.25, and 11.5 m/s 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20◦ 10–35 m/s 2.2◦

Table 3 Material properties of Hercules ASI/3501-6 graphite/epoxy Parameter Value Young’s modulus in lateral direction, E L Young’s modulus in transverse direction, E T Poission’s ratio, νLT Shear modulus, G LT Ply thickness Density

130 × 109 Pa 10.5 × 109 Pa 0.28 6.0 × 109 Pa 1.34 × 10−6 m 1520 kg/m3

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Table 4 Material properties of custom material Parameter Value Young’s modulus in x-direction, E x Young’s modulus in x-direction, E y Young’s modulus in x-direction, E z Poission’s ratio, νx y Poission’s ratio, ν yz Poission’s ratio, νx z Shear modulus, G x y Shear modulus, G yz Shear modulus, G x z Density

9.2342 × 108 Pa 6.1 × 108 Pa 9.2342 × 108 Pa 0.33 0.33 0.33 5.2923 × 108 Pa 2.0333 × 108 Pa 3.0781 × 108 Pa 1108.2 kg/m3

7 Results and Discussion 7.1 Grid Independence Study To select the grid for FSI analysis, the grid independence study was performed on the geometry of flat composite plate wing, Fig. 8a. First, for the finite element analysis four grids were generated with increasing number of nodes, see Table 5. Static structural analysis was performed with uniform force applied on the top and bottom surface of the flat plate wing and wing twist was plotted along the span of the wing, as shown in Fig. 14a. Based on the FEM grid independence study, it is clear that the change in the wing twist is significantly small with average percentage of 0.004 in between FEM Grid 3 and FEM Grid 4 as well as in between FEM Grid 2 and FEM Grid 3 with 0.02 % but in order to have excellent data mapping fine mesh is required, therefore FEM Grid 3 was selected for the further studies. For CFD, another four grids were generated, details are given in Table 5. Using the FEM Grid 3 and four CFD grids, four FSI simulations were carried out and wing twist was calculated along the span of the wing, see Fig. 14b. Average difference in between CFD Grid 3 and CFD Grid

Table 5 Grid size details Grid ID Grid 1 Grid 2 Grid 3 Grid 4

Number of elements For FEM 2,706 22,692 138,624 249,084

For CFD 3,145,030 3,913,983 5,461,031 6,644,600

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(a) Finite Element Analysis.

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(b) Fluid-Structure Interaction.

Fig. 14 Grid independence study

4 was found to be of 0.56 % while in between CFD Grid 2 and CFD Grid 3 was 1.43 %, thus CFD Grid 3 with approximately 5.4 million elements was selected for present study. For other wing models, similar grid resolution was maintained in all the three directions while maintaining wall y + ≈ 1 for CFD analysis in order to resolve boundary layer gradient.

8 Validation Present study is based on the static two-way fluid-structure interaction analysis using ANSYS Workbench involving the CFD and FEM solvers. In order to validate the current methodology, two experimental studies were selected and the static two-way FSI analysis was performed and observations are presented below:

8.1 Flat Composite Plate Wing Divergence Study Two-way FSI analysis was performed for the static aeroelasticity based on the composite flat plate wing tested by Landsberger et al. [4]. Static deflections for composite wing of configuration [+302 /0]s , the wing tip flap wise displacement and the wing tip twist, are presented in Fig. 15. It was found that the wing tip flap wise displacement obtained from current method and the experiment performed by [4] are found to be in very good agreement for free stream velocities, U∞ = 5 and 11.5 m/s. Whereas, the wing tip twist was found to be having similar trends as of the experimental study, while over predicting the twist similar to the analytical method adopted by Landsberger et al. [4]. Divergence dynamic pressure and speed was calculated by putting 1/θ = 0 in Eq. (2) for each wing configuration using wing tip twist at different freestream velocities, same equations for each wing configuration can be seen in Table 6, which were

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(a) Flap wise tip displacement.

(b) Tip twist.

Fig. 15 Static aeroelastic deflection of Landsberger et al. [4] versus present FSI analysis for composite flat plate wing of configuration [+302 /s]s Table 6 Divergence speed calculation for present FSI analysis Plate # Equation of fitted straight line [ −452 /0] s [ −302 /0] s [ −152 /0] s [ +302 /0] s

1/θ 1/θ 1/θ 1/θ

(a) Calculation.

= 29.091/q − 0.2127 = 26.750/q − 0.2089 = 34.928/q − 0.1895 = −50.27/q − 0.2143

(b) Comparison.

Fig. 16 Divergence speed; Landsberger et al. [4] versus present FSI analysis for composite flat plate wings

obtained from Fig. 16a. The comparison of the divergence speed is presented in Table 7 and Fig. 16b, where it can be seen that the current method of two-way aero-elasticity is in excellent agreement with experimental results for two wing configurations, [−152 /0]s and [−302 /0]s , providing better prediction then the analytical RayleighRitz method. Whereas, for wing configuration, [−452 /0]s , divergence dynamic speed was over-predicted with a deviation of 10.35 %, this offset is similar to the RayleighRitz method adopted by [4]. The reason for which was found to be the use of only

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Table 7 Divergence speed, Landsberger et al. [4] versus present FSI analysis Plate # Divergence speed, UD

[ −452 /0] s [ −302 /0] s [ −152 /0] s [ +302 /0] s

Landsberger et al. [4] Exp. Ritz 13.480 m/s 14.090 m/s 14.575 m/s 14.068 m/s 17.238 m/s 17.990 m/s N/A N/A

(a) Wash-out of [−302 /0]s .

Present FSI 14.944 m/s 14.460 m/s 17.298 m/s N/A

Error %, w.r.t Exp. 10.35 0.12 0.08 –

Ritz 6.06 2.79 3.84 –

(b) Wash-out of [+302 /0]s .

Fig. 17 Static aero-elastic deflection at U∞ = 8.25 m/s and αr = 4◦ illustrating the wash-out and wash-in effect

in-plane properties to define overall material properties of the model, leading to a different torsion-bending coupling as compared to the experimental setup. From the fitted straight line equation for wing configuration, [+302 /0]s , it was found that the divergence dynamic pressure for this particular case is negative, thus the divergence speed cannot be calculated, results to the conclusion that this wing configuration with positive ply fiber orientation will not diverge owing to its wash-in effect as founded by Landsberger et al. [4]. The wash-in and wash-out of the wing can been seen in Fig. 17. Overall, it is sufficiently clear that the two-way FSI method is in good agreement with the composite flat plate wing experimental results [4].

8.2 Large AR Wing Divergence Study Another experimental study [11], performed on the high-aspect ratio wing was replicated with a simplified wing model and static two-way FSI analysis was performed and static aero-elasticity deflections were obtained for αr = 2.2◦ with respect to freestream velocities, see Fig. 18.

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(a) Flapwise tip displacement.

(b) Tip twist.

Fig. 18 Static aero-elastic deflections by Tang and Dowell [11] Versus Present Fsi Analysis at αr = 2.2◦

(a) U∞ = 10.0 m/s.

(b) U∞ = 25.0 m/s.

(c) U∞ = 28.0 m/s.

(d) U∞ = 35.0 m/s.

Fig. 19 Static aero-elastic displacement contours of large A R wing

Wing tip flap wise displacement obtained from two-way FSI analysis as compared to the experimental study of Tang and Dowell [11], was found to be following the same trend although under predicting the finds for freestream velocities greater the 30 m/s. Whereas, wing tip twist deviates from the experimental results as two-way FSI over-predicts the twist for freestream velocities 24 m/s and over-predicts for freestream velocities above 24 m/s, which is the effect of elastic axis location as it is at 44.79 % chord for present study whereas, it is at 50 % chord for experimental study. Which creates shorter moment arm between the center of pressure and elastic axis resulting the torsion-bending coupling to mismatch with experimental setup. With more detailed availability of material properties in the literature developing and performing the validation would be excellent. Figure 19 illustrates the displacement contours on large A R wing at various airspeeds. It is clear from the contours how lift influences the wing behavior and develops to overcome the gravity force to balance the wing in-between U∞ = 25.0 and 28.0 m/s.

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9 Conclusion Object of the present study was to create baseline for aero-elastic analysis using ANSYS solver package. Which was successfully executed with following observations: 1. Two-way FSI analysis with linear structural model and non-linear fluid model was efficiently able to obtain the static aero-elastic properties of a composite wing while capturing the effect of composite materials unidirectional properties with maximum 10.35 % deviation in divergence speed as compared to experimental results by Landsberger et al. [11]. 2. Whereas for Large A R Wing Divergence Study, wing tip twist over wide range of freestream velocities found to be out of trend due to the mismatch in elastic axis and center of gravity in between experimental wing model and simplified FEM model as well as insufficient material properties. Wing tip flap displacement was found to be following the trend of experimental study by Tang and Dowell [11] with acceptable agreement. 3. From Large A R Wing Divergence Study, it was clear that the exact material properties are required in order to predict the results of a real wing, which makes the two-way FSI analysis method susceptible to the measurement of wing material properties and section properties. 4. As the flat plate composite wing geometry was of low-aspect ratio, the present linear structural model was sufficient to obtain the static deflections. Although Large/High A R Wing Divergence Study performed well but it sure will provide more insight when geometric non-linearities will be included into the FEM model. Overall, the two performed validations create a strong baseline for aero-elastic analysis based on partitioned static two-way Fluid-Structure Interaction analysis using ANSYS package, which will be used to extend to the dynamic aero-elasticity analysis (flutter with and without active control, LCO, etc.), and validate reduced order models against these benchmark results.

References 1. Gundlach J (2012) Designing Unmanned Aircraft Systems a comprehensive approach. AIAA Education series 2. Afonso F, Vale J, Oliveira E, Lau F, Suleman A (2017) A review on non-linear aeroelasticity of high aspect-ratio wings. Prog Aerosp Sci 89(2017):40–57 3. Bennett RM, Edwards JW (1998). An overview of recent developments in computational aeroelasticity by aeroelasticity branch, structures division. AIAA J 4. Landsberger BJ, Dugundji J (1985) Experimental aeroelastic behavior of un-swept and forwardswept cantilever graphite/epoxy wings. J Aircraft 22(8):679–686 5. Chen G, Dugundji J (1987) Experimental aeroelastic behavior of forward-swept graphite/epoxy wings with rigid-body freedom. J Aircraft 24(7):454–462 https://doi.org/10.2514/3.45501 6. Hollowell SJ, Dungundji J (1984) Aeroelastic flutter and divergence of stiffness coupled, graphite/epoxy cantilevered plates. J Aircraft 21(1):69–76

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7. Hodges D, Pierce G (2011) Intorduction to structural dynamics and aeroelasticity, 2nd edn. Cambridge University Press, Cambridge 8. Blair M, Weisshaar Ta (1982) Swept composite wing aeroelastic divergence experiments. J Aircraft 19(11):1019–1024 9. ANSYS Workbench User s Guide (2017) (April) 10. Raja RS (2012) Coupled fluid structure interaction analysis on a cylinder exposed to ocean wave loading. Chalmers University of Technology, Masters thesis 2012, p 55 11. Tang D, Dowell EH (2001) Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings 39(8) 12. ANSYS Mechanical APDL Element Reference (2017) (April) 13. ANSYS Fluent Theory Guide (2017) (April) 14. Patankar SV, Spalding DB (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int J Heat Mass Transfer 15:1787–1806 15. ANSYS Mechanical APDL Theory Reference (2017) (April)

Numerical Study of Effect of Adjacent Blades Oscillation in a Compressor Cascade Shubham, M. C. Keerthi, and Abhijit Kushari

Abstract The present numerical study deals with the steady and unsteady aerodynamics of an airfoil in a cascade with oscillating neighboring blades. The motivation for the study arises from aeroelastic studies of turbomachinery blades, where the unsteady forces acting on a blade due to different sources is examined. In order to identify the root cause of the various phenomena affecting the aeroelastic stability, it is necessary to observe the effect of only one source of disturbance and isolate the others. The cascade comprises of five blades with zero stagger and low incidence. The two adjacent blades to central one are oscillated with a fixed frequency and phase difference, with the rest of the blades remaining stationary, covering a range of frequencies and phase difference angles. The primary objective is to look at the variation of global parameters on central blade with reduced frequency. The moment and drag are estimated numerically and compared with experimental results which shows good agreement. The hysteresis loops of lift and moment coefficient with angular displacement are used to understand the effect of reduced frequency. A laminar separation bubble is observed to be formed during part of the oscillation cycle and its size is related to the unsteady forces on the blade. The behavior is also a function of reduced frequency to some extent. Such an understanding of the effect of oscillating blades in a blade row is essential for the modeling of the aerodynamic forces in an aeroelastic problem. Keywords Aeroelasticity · Unsteady aerodynamics · Linear cascade

1 Introduction Due to the ever-increasing need to increase the thrust to weight ratio and efficiency of turbomachines, their blades are designed to be highly loaded and are done so with minimal mass. This results in blades that are thinner, which are also subjected to large aerodynamic loading. Specifically, due to the unsteady nature of the loads, this Shubham · M. C. Keerthi · A. Kushari (B) Indian Institute of Technology Kanpur, Uttar Pradesh, Kanpur 208016, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_5

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has led to increased aeroelastic issues in blades. Aeroelastic instability prediction methods are greatly needed as modern jet engines require blade designs close to the stability boundaries of the performance map. There have been extensive undertakings in the theoretical, experimental and computational understanding of the significant physical components and to enhance the predictive ability of turbomachinery blade flutter [1, 2]. However, even today, the understanding is not well enough to address aeroelastic issues at the design phase of an engine development program. Hence, more studies are required to investigate all aspects of the problem. One aspect of the research is in the unsteady aerodynamics of oscillating blades in a cascade. This is to address the requirements for modeling the unsteady aerodynamics, which is particularly challenging in a turbomachine environment. These issues start to some extent from an inability to model the unsteady aerodynamic behavior of cascades. Additionally, these models must be computationally efficient in the event that they are to be a part of a useful design framework. Of late, several investigators [3–6] have developed time-accurate Euler and Navier–Stokes solvers for analyzing unsteady flows in turbomachinery. These models can provide for small and large disturbances unstable flows in cascades. Atassi [7] developed a linearized analytical theory for oscillating cascades in uniform incompressible flows. Verdon and Caspar [4, 8] and Verdon and Usab [9, 10] developed a linearized theory for solving oscillating cascade unsteady loads imposed on a steady-state solution. Ekaterinaris and Menter [11] assessed the capacity of one-and two-equation turbulence models in predicting hysteresis effects of unsteady fully turbulent flow over oscillating airfoils. The Baldwin-Barth [12], the Spalart-Allamaras [13], and the SST k−ω [14] models demonstrate a noteworthy change over standard twocondition models. The SST k−ω model gave good predictions for the attached and the light-stall cases. For a bladerow whose aeroelastic stability is being assessed, the aerodynamic damping of a blade is of paramount importance, as a large negative value can lead to large-amplitude vibrations. It is known that the aerodynamic damping of a blade at a given inlet condition is influenced by the vibration of all blades in the bladerow including itself. In reality, it is only the immediate neighbors that significantly affect, with the blades further apart having a diminishing influence. For the most part, therefore, the aerodynamic influence of the motion of two adjacent blades and the blade itself will determine the aeroelastic stability of the blade. The present study focuses on the aerodynamic effects caused on a blade by the oscillating adjacent blades. The effects considered are the global parameters such as lift, drag and moment, as well as local effects like flow separation in the vicinity of the leading edge will be investigated. The unsteady pressure gradient at the leading edge plays a critical role in the formation of leading edge separation bubble [15]. An important application of the present analysis is to use the detailed distribution of the pressure obtained particularly close to the leading edge area for analyzing the onset of boundary layer separation that eventually could lead to separation. This study is performed to recreate the linear oscillating cascade experiment whose details can be found here [16]. Experiments enable us to obtain data only at discrete points and usually with poor spatial resolution. To have a complete flow field of

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oscillating cascade aerodynamics, numerical computation fills the crucial missing gap. The cascade of five airfoils has been modeled as a two-dimensional numerical model to reduce computation costs. The analysis has been performed for a fixed incidence angle, four different frequency (6, 9, 12, 15 Hz) with varying phase difference angles. The results have been compared for different reduced frequency and phase difference angles. The phase difference (PD) used in this study is an essential parameter, as it effectively simulates the inter-blade phase angle that is present in a real vibrating turbomachine blade row. The inter-blade phase angle is a result of the excitation of one or more nodal diameters of the rotating bladed-disk.

2 Numerical Setup The setup for numerical analysis is kept same as that of experiment so as compare the behavior and variation of parameters. Figure 1 represents the computational domain with boundary and initial condition mentioned in the figure itself. The cascade is modeled numerically by employing a commercial solver ANSYS CFX using a full-scale time-marching model. The model extends over five blades with walls on both sides. The chord of the blade is 152 mm and the upstream and downstream domain length after blade is also same as chord. The airfoil for the blade used is EPFL standard test configuration 1. The cascade is at zero stagger, incidence of 6° and amplitude of oscillation is 3°. The blades are oscillated for three cycles. The simulations are conducted using a standard SST turbulence model with wall functions. The motion of the oscillating blade is described by a set of equations and imposed as moving mesh boundary condition, deforming the mesh around the reference blade in each time step. Blade oscillation is thereafter introduced first after having the flow

Fig. 1 Computational domain

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field reaching a steady state. An inflow velocity of 29 m/s with a turbulent intensity of 5% is specified at the upstream boundary. Airfoils are specified to be the wall with no slip. Pressure is specified at the outlet boundary to be atmospheric pressure (101.325 kPa). The governing equations are solved in a stationary reference frame. Convection terms are discretized with second order upwind schemes. Convergence criteria for absolute error of all variables used are 1 × 10−5 . Table 1 shows the values for grid independence study. The study has been performed for three meshes namely low, medium and high. The low density corresponds to 0.1 million nodes, medium 0.2 million nodes and high 0.4 million nodes. It can be clearly observed that medium mesh density (Fig. 2) can be used for our further study as the percentage change in lift and drag values are very small. For validation, experimental data [17] obtained from a linear cascade with five blades is used. In the experiment, the central blade has surface pressure taps at the mid-span for unsteady pressure measurement, with the total span being 300 mm. The flow conditions used are identical to those used for the validation case. It has to be noted that numerical setup used above simulates the effect of side walls present in the experimental setup, but does not account for any possible flow variations in the out-ofplane direction due to the effect of end walls. The experimental measurements were sampled at 500 samples per second for a duration of 10 s, resulting in about 100 cycles of oscillation. Such a large sample size was necessary to ensure low uncertainties in the phase-averaged results for the experiment. However, the numerical solution Table 1 Grid independence study Mesh density

No. of elements

Drag (N)

Lift (N)

% change drag

% change lift

Low

104,290

0.00554

0.08510

–

–

Medium

207,680

0.00548

0.08403

1.09

1.27

High

481,670

0.00543

0.08329

0.92

0.88

Fig. 2 A portion of the structured mesh

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showed flow variables fluctuating with good periodicity and hence only about three to four cycles are used to avoid excessive computing time.

3 Results and Discussion 3.1 Validation The validation has been shown for steady-state and unsteady blade surface pressure. Figure 3a shows steady static pressure coefficient variation with the non-dimensional chord length. The negative x/c values represent suction surface from −1 to 0 and positive x/c values corresponds to pressure surface location from 0 to 1. The slight acceleration on the suction surface followed by a deceleration can be seen from Fig. 3 Steady pressure coefficient and pressure time history for numerical and experimental case

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Fig. 4 Motion of adjacent airfoils at PD = 90°

the change in slope for negative x/c values. The presence of the accelerating region implies adverse pressure gradient and a possibility of flow separation, although none was observed for this case where all blades were stationary. The agreement between numerical and experimental values is good. The numerical value for suction surface follows closely with experimental ones while there is slight under-prediction for pressure surface values so is the suction surface values near the leading edge. Figure 3b shows unsteady pressure coefficient along the chord for numerical and experimental case. The trend of variation seems to be similar in both of them. The experimental case seems to have the presence of higher frequency components which are partly due to flow unsteadiness and measurement uncertainty. This highfrequency component is not captured in the present numerical solution. In the study of aeroelasticity in turbomachines, it is usually that the fundamental frequency of the blade will contribute to most of the aeroelastic stability, with the contribution diminishing from the higher harmonics. As a result, the numerical scheme, which appears to cut off the high-frequency phenomena, is considered to be adequate for the purposes of this study. The lift, drag, moment coefficient data predicted by the numerical simulation is comparable to the experimental values obtained by Babu [16]. Figure 4 shows the time series of the angular displacement of blades -1 and +1 when the value of PD is 90°.

3.2 Effect of Reduced Frequency The reduced frequency and interblade phase angle both are the most important parameters for aeroelastic studies. The interblade phase angle represents the structural

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response of the system while reduced frequency is related to the flow field around the blade. The reduced frequency can be defined as the ratio of time taken by a fluid particle to travel a chord length to time period of oscillation. k=

c/U∞ ωc = 2π U∞ T

where c = chord; U ∞ = freestream velocity; ω = Angular frequency of oscillation; T = time period of oscillation. In this paper, the effect of reduced frequency on the behavior of forces on the blades is numerically investigated. The validation is already been established in the previous section. Figures 5 and 6 represents the variation of moment coefficient with time for four reduced frequencies at PD = 0° and 180°. The time axis has been normalized between 0 and 1, which is within the range total time for three cycles, in order to compare the different frequency cases. The plots have been shown for two PD values. These two specific phase differences are chosen as they represents blades moving exactly in phase and out of phase with each other. The plot at PD = 0° shows little variation with reduced frequency but for PD = 180°, the variations are getting a little offset with change in reduced frequency. This is mainly due to the presence of higher frequency components as confirmed from their Fourier amplitude spectra. There is also a reduction in amplitude as the reduced frequency is decreased. The lift coefficients plots are also similar to moment plots only varying by a scale factor. Figures 7 and 8 show similar plots for drag coefficient against normalized time. The amplitude of drag remains the same across both phase difference and reduced frequencies discussed. There is a presence of higher frequency component in reduced frequencies variation at PD = 180°. The drag coefficient for reduced frequency of Fig. 5 Moment coefficient versus time variation for reduced frequencies at PD = 0°

66 Fig. 6 Moment coefficient versus time variation for reduced frequencies at PD = 180°

Fig. 7 Drag coefficient versus time variation for reduced frequencies at PD = 0°

Fig. 8 Drag coefficient versus time variation for reduced frequencies at PD = 180°

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0.19 is varying slightly different than others at both PDs. The reasons seems to be more significant presence of higher frequency components at PD = 180° than earlier and at PD = 0°, this presence of higher frequency is introduced at this reduced frequency itself. This low frequency forced response has introduced this unique attribute for lower phase differences. It can be seen from the variation of the drag forces that the amplitude is low compared to the lift and its variation across PDs and reduced frequencies are similar. This is suggestive of the fact that the phenomena causing the amplitude change and non-linearity is affecting the transverse force more than the axial force. There is also strong correlation between lift and moment is likely due to the flow phenomena on the surface of the blade that is close to the leading and trailing edges. This also explains the reduced effect on drag, as the pressure drag component is more influenced by the regions upstream and downstream of the blade than the lateral surfaces. Figure 9 shows the hysteresis behavior of blade forces in a cycle of motion. Two important distinctions between this analysis and the hysteresis plots in typical dynamic stall studies of isolated airfoil are to be noted: firstly, in the present study the force and moment measured is on a static blade whereas dynamic stall studies reference the force and moment measurements to the same blade which is oscillating; secondly, the present oscillation amplitude (3°) is below the limits required to cause the typical sequence of events of dynamic stall including the formation and spillage of leading edge vortex followed by a massive suction-side separation and the interaction with the trailing edge vortex [18]. It is clear that even with a small amplitude oscillations of the adjacent blades is sufficient to qualitatively change the behavior of the static blade. The plots thus far establish that the reduced frequency is weakly affecting the blade force responses as compared to interblade phase differences. The hysteresis loop area is increasing with increase in reduced frequency. Though the increase is very low it can be established that reduced frequency is affecting the hysteresis. The mechanism for an oscillating blade to affect the pressure field of the adjacent blade is now explored. To do this, the pressure field contours around blade 0 Fig. 9 Variation of area of hysteresis loop

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is compared at different instances of time period fraction (t/τ) within one oscillation. Figure 10a, b show a grid of the pressure contours for all PD values presented as a vertical columns with time fractions as horizontal rows. First, considering the PD = 0° case, we can see a substantial variation of the pressure field on the pressure and suction surface sides throughout the cycle. In particular, the leading edge stagnation point is characterized by different values of pressure and location. The lift and moment acting on the airfoil is significantly affected by the location of the leading edge stagnation point, as it lies in the region of maximum pressure acting on the airfoil surface. Additionally, a dark region corresponding to very low pressure can be seen on the suction surface near the leading edge. It is interesting to note that although the low pressure region of the suction surface varies throughout a cycle, its phase within a cycle does not vary with PD. As can be seen from combined phase lag plots, the variation is not affected much with change in reduced frequency. If we compare the PD = 0° and 180°, the differences can be observed. This is due to the fact that that the field on the pressure surface side of blade 0 where the leading edge stagnation point region occurs is influenced by the blade closest to it, namely blade +1, whose displacement within a cycle shown is dependent on PD.

3.3 Effect of Stagnation Point Location on Reattachment Length It is usually recognized that the prediction of separated flows using RANS is challenging. However, presently, the trends of variation of parameters such as reattachment length are of interest. As they are consistent with the trends in variation of the global forces such as lift, it is believed that the present choice of solver and its parameters is capable of supporting the proposed conclusions. In this section, separation of flow on the suction surface of airfoil is discussed along with length of reattachment. The reattachment length is the size of the separation bubble present on the suction surface of the blade at a given time. Figure 11 shows the formation of separation bubble, length of reattachment and location of stagnation point on the central and both adjacent oscillating airfoils. The oscillating blades show a much larger reattachment length compared to the non-oscillating central blade. The oscillating airfoils have a separation bubble on their suction surface. This figure at PD = 0° and t/T = 6/8 is for representation of flow features for further reference in the discussion. Figures 12 and 13 shows reattachment length on blade 0 with time at PD = 0° and 180°. There is a significant decrease in size of reattachment length when PD is changed from 0° to 180°. The bubble sizes at PD = 0° is similar for all the reduced frequency value discussed whereas for PD = 0°, a monotonic increase is seen with an increase in frequency. Figures 14, 15 and 16 show the maximum size of the separation bubble (or reattachment length) for the three airfoils for all cases. Noting the vertical axis scales,

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Fig. 10 Phase-log plot of pressure contour a PD = 0°, b PD = 180°

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Fig. 11 Nomenclature and description of separation bubble and reattachment length

Fig. 12 Reattachment length on blade 0 with time at PD = 0°

it can be seen that the moving blades have a larger separation bubble compared to the stationary one. However, despite the small size, its variation within the range of PDs is considerable and is probably the most dominant contributor to the nature of variation in the unsteady forces on the central blade. The reason for reduction in moment amplitude (Figs. 5 and 6) and a slight reduction in drag amplitude (Figs. 7

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Fig. 13 Reattachment length on blade 0 with time at PD = 180°

Fig. 14 Variation of the maximum reattachment length on Airfoil −1 with phase difference

and 8) at PD = 180° can now be explained by noting the dip in separation bubble size from Fig. 15. In particular, when the stagnation point is further downstream from the leading edge of the airfoil’s suction surface, the maximum size of the separation bubble within the cycle is smaller and thus the load amplitude is smaller. This is a consequence of the flow field when the adjacent blades are oscillating out of phase. For a given PD, the change in reattachment length due to different reduced frequency is small, although it can be seen that the lower reduced frequency reduces the separation bubble size. Although small, the size of the separation bubble is significant for the central blade. This shows how the separation characteristics and the forces on a stationary

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Fig. 15 Variation of the maximum reattachment length on Airfoil 0 with phase difference

Fig. 16 Variation of the maximum reattachment length on Airfoil +1 with phase difference

blade can be affected by the motion of neighboring blades. The minimum value of reattachment length corresponds to values near PD = 180°, implying this is related to the formation of lift whose amplitude also is maximum around PD = 180°. It is possible that this influence on the central airfoil is brought about due to the changes in the local incidence near the leading edge of blade 0. This change in incidence will invariably have an effect on the location of the leading edge stagnation point, which is examined subsequently. Noting that the local flow incidence will directly affect the location of the leading edge stagnation point, it can be said that the influence of the oscillating blades

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is manifested through the pressure field to ultimately result in a local change in incidence of blade 0.

4 Conclusions The oscillating cascade has been studied for four different frequencies and various interblade phase angles. After benchmarking with experimental results, efforts has been made to understand the pressure variation and lags in the domain by varying the parameters. The variation of moment and lift with reduced frequency showed a small increase. The drag coefficients variation is much smaller. The change with phase difference is more considerable than reduced frequency. Further, size of reattachment bubble on central blade at phase difference 180° is increasing with increase in frequency. For the range of reduced frequencies considered, the influence on the unsteady pressure variation on the central blade was seen to be smaller compared to phase difference of the motion of adjacent blades at a given frequency.

References 1. Fleeter S (1979) Aeroelasticity research for turbomachine applications. J Aircraft 16(5):320– 326 2. Cinnella P, De Palma P, Pascazio G, Napolitano M (2004) A numerical method for turbomachinery aeroelasticity. J Turbomach 126(2):310–316 3. Hall KC, Clark WS (1993) Linearized Euler predictions of unsteady aerodynamic loads in cascades. AIAA J 1(3):540–550 4. Verdon JM, Caspar JR (1980) Subsonic flow past an oscillating cascade with finite mean flow deflection. AIAA J 18(5):540–548 5. He L (1990) An Euler solution for unsteady flows around oscillating blades. J Turbomach 112(4):714–722 6. Hall KC, Lorence CB (1993) Calculation of three-dimensional unsteady flows in turbomachinery using the linearized harmonic Euler equations. J Turbomach 115(4):800–809 7. Atassi H, Akai T (1980) Aerodynamic and aeroelastic characteristics of oscillating loaded cascades at low mach number—part I: pressure distribution, forces, and moments. J Eng Power 102(2):344–351 8. Verdon JM, Caspar JR (1982) Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades. AIAA J 20(9):1259–1267 9. Usab W, Verdon J (1991) Advances in the numerical analysis of linearized unsteady cascade flows. J Turbomach 113(4):633–643 10. Verdon JM, Usab W Jr (1986) Application of a linearized unsteady aerodynamic analysis to standard cascade configurations 11. Ekaterinaris JA, Menter FR (1994) Computation of oscillating airfoil flows with one- and two-equation turbulence models. AIAA J 32(12):2359–2365 12. Baldwin B, Barth T (1990) A one-equation turbulence transport model for high reynolds number wall-bounded flows. NASA TM 102847 13. Spalart PR, Allmaras SR (1992) A one equation turbulence model for aerodynamic flows. AIAA J 94

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14. Menter FR (1992) Improved two-equation k-omega turbulence models for aerodynamic flows. NASA STI/Recon Technical Report No. 93 15. Watanabe T, Aotsuka M (2005) Unsteady aerodynamic characteristics of oscillating cascade with separation bubble in high subsonic flow. In: ASME turbo expo 2005: power for land, sea, and air. American Society of Mechanical Engineers 16. Babu KN (2008) Experimental investigation of the forced response of a cascade blade subjected to transverse periodic aerodynamic loading. IIT Kanpur 17. Keerthi MC, Kushari A (2015) Effect of adjacent blade oscillation on the forces on a blade of a compressor cascade. In: National propulsion conference, Mumbai 18. McCroskey WJ (1981) The phenomenon of dynamic stall. NASA TM-81264

Effect of Incoming Wakes on Losses of a Low-Pressure Turbine of a Gas Turbine Engine Vishal Tandon, Gopalan Jagadeesh, and S. V. Ramana Murty

Abstract Modern civil aircraft engines are known for their high bypass ratio fans that are powered by many low-pressure turbine (LPT) stages (Mahallati et al. in J Turbomach 135/011010, [1]). LPT can contribute as much as 30% of the weight of an aero engine (Sondergaard et al. in Toward the expansion of low-pressure turbine airfoil design space, [2]; Curtis et al. in J Turbomach 119(3), [3]). Aerofoils of modern LPT blades are subjected to increasingly stronger pressure gradients as designers require higher blade loading in an effort to reduce weight and costly number of LPT blades of an engine, which leads to better reliability and maintainability. This decrease in number of LPT blades results in increase of thrust/weight ratio, thus reducing the fuel consumption. But highly loaded aerofoils can reduce aerodynamic performance, and its influences can be seen more in unsteady environment. Hence, reduction of losses in unsteady environment, improves the turbine performance which is a challenging task. Therefore, there are persistent efforts towards the generation of “high-lift” blade profiles. As a result, industry and research communities are motivated for further deep research efforts in LPT aerodynamics (Sarkar in J Turbomach ASME 131, [4]). In this paper, the effect of the incoming wakes shed from the upstream HPT blade on the downstream highly loaded transonic LPT vane are studied to better understand the LPT flow physics. In this paper, wakes shed from upstream HPT blade are simulated by cylinders of three different radius which are of the order of actual HPT rotor blade trailing edge radius ~0.8 mm, so that only the influence of wakes on vane losses can be studied. From these three cases, it is observed that incoming wakes does not always lead to increase in vane loss coefficient. For some cases, it is observed that the loss coefficient is 12.64% lower than the vane without any incoming wakes. Keywords Unsteady fluid flow · Incoming wakes · Navier–stokes equations · LP turbine vane · Pressure loss coefficient · Mach number · Strouhal number V. Tandon (B) · S. V. Ramana Murty Gas Turbine Research Establishment (GTRE), Bangalore, India e-mail: [email protected] G. Jagadeesh Indian Institute of Science, Bangalore, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_6

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Nomenclature St U P τ μ M SST ω Tu Yp y ξ

Strouhal number Flow velocity Total pressure Shear stress Dynamic viscosity Mach number Shear stress transport Specific dissipation rate Turbulence intensity Pressure loss coefficient Stagger angle Zweifel Loading

1 Introduction The flow processes that occur in turbine stages are always very complicated. The flow is three dimensional, viscous, and unsteady in nature. The flow may be incompressible or compressible and may have subsonic, transonic, and supersonic regimes that may be present concurrently in different regions. The primary flow is mainly through the blade passages, in addition to that there are secondary flows which force the fluid to move across the passages under the action of centrifugal and Coriolis forces, blade loading effects results in causing incidence and deviation, flow short circuit between the moving tips and the stationary shroud, boundary layer growth and wakes shedding, and for transonic and supersonic blades, shock waves and shockboundary layer interaction in the blade passage and at the trailing edges. Another class is unsteady effects, generated mainly by the interaction of adjacent blade rows [5–7]. There is continued enhancement of LPT efficiency and performance. This has resulted in intensified LPT aerodynamics research efforts by the research communities and industry. As a result, wide variety of different research approaches were adopted. Research activities, e.g., steady and unsteady cascade aerodynamics research and rotating turbine research, were undertaken. These research efforts have contributed in better insight into the LPT flow physics. As a result, a modern LPT design with a reduced number of blades was possible with marginal sacrifice of the efficiency. This reduction in number of blades means increase in thrust/weight ratio and results in decreasing the fuel consumption [8, 9]. In this research work, the effect of wakes shedded from the upstream blade on the downstream low-pressure vane in a turbine stage is studied to better understand the low-pressure turbine flow physics. In low-pressure turbines, the dominant source of unsteadiness is produced by the wakes of the upstream blade rows. One of the

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significant consequences is the interaction of the wakes shed by upstream vane with the downstream rotor blade suction side boundary layer. This boundary layer is often laminar along most of its surface. The free stream turbulence also has some effect on separation, but its role is less important to the wake effect [10, 11]. The transition behavior of the flow can also be influenced by periodic and random disturbances [12– 16] and in some cases may reduce the risk of laminar boundary layer separation at low Reynolds numbers [11]. In the last years, computational fluid dynamics (CFD) has contributed to get a better understanding on the physics of flow separation, transition, and reattachment under unsteady flow conditions [17, 18]. The effects of incoming wakes on the transition behavior at different flux coefficients and Strouhal numbers were investigated by a numerical URANS approach by Schwarze and Niehuis [19]. Meyer has done pioneer work in explaining the kinematics of wake convection through a cascade passage [4, 20]. A substantial progress has been made over the past 3 decades in understanding the detailed influence of unsteady wakes on separated boundary layers [21–28]. Initial open literature-based research on the aerodynamics of more highly loaded low-pressure turbines appears to have been based on the family of T104–T106 cascade aerofoils developed by Hoheisel et al. [2, 29]. Most of the high-lift work presented in the open literature is cascade-based. The non-dimensional Zweifel coefficient is approximately 1.04–1.07 for the T104–T106 family which includes aerofoils with both front and aft loading. These and other related aerofoils have been used in several cascade investigations by the research groups of both Hodson [30] and Fottner [2, 31].

2 Description of the Problem For the study of effect of incoming wakes on losses of a low-pressure turbine stator vane, a highly loaded vane 2D aerofoil is selected. The vane aerofoil is designed using Prichard 11 [32] parameter method, and the details are shown in Table 1. Wakes shed from upstream high-pressure rotor blade are simulated by a cylinder, so that we can study the influence of only wakes on the vane losses. Hence, upstream of vane only cylinder is modeled not the whole high-pressure rotor blade. Also since a unsteady simulation was planned which demands huge computational resources and takes days sometimes even months to finish a single case, it is decided to carry out first a 2D simulation and then later a 3D simulation can be taken up. Typical trailing edge radius of high-pressure rotor blade is of the order of 0.8 mm. Trailing edge Table 1 Non-dimensional parameters of LP Turbine vane

Parameter

Value

Chord (C)

63 mm

Stagger angle (y)

39.75°

Pitch/chord ratio

0.74

Zweifel loading (ξ )

0.89

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V. Tandon et al. Case 1

Upstream cylinder radius 0.65 mm

Case 2

Upstream cylinder radius 1.0 mm

Case 3

Upstream cylinder radius 1.3 mm

needs to accommodate cooling holes for cooling of the high-pressure rotor blade, and also, a lower trailing edge radius is not feasible from casting manufacturing point of view. Hence, one radii below and two radii above the baseline radius were selected for the current study as shown in Table 2.

3 Computational Methodology The analysis is carried out by using the commercial ANSYS Fluent-14.5 [33] on an IBM DX 360 parallel computing system. ANSYS Fluent is a three-dimensional, multi-block and parallel fluid flow solver. The unsteady Reynolds averaged Navier–Stokes (URANS) equations are solved. The governing equations are discretized using finite volume method. The solution algorithm is based on an implicit scheme coupled with multi-grid acceleration techniques. k–ω SST turbulence model is selected to model the turbulence effects. It is a two-equation turbulence model, and it is capable of correctly predicting the wall shear stresses in flows where adverse pressure gradient is present similar to the present study, and also, it is robust for complex flows.

4 Grid Generation ICEMCFD 14.5 software has been used to generate the computational grid for this study [34]. Structured grids are created using O, C, and H grids. The grids are multi-block. For stator grid, first an O grid is placed around the airfoil. Around the leading edge of stator and passage, a C grid is used and H grid has been used in the trailing edge of the stator. For cylinder grid, also first an O grid is placed around the cylinder, whereas H grid is used in the cylinder passage. The grids are joined periodically in a many-to-one fashion in pitch direction. No overlaps are used while attaching grids of non-moving stator and moving rotor grids. In unsteady simulation, transient sliding interface option has been used which moves the cylinder grid to the next relative location w.r.t the stator for each time step, which represents the true physical position of the cylinder w.r.t stator for every time step. Flow parameters are exchanged between the two grids by using a flux conservative algorithm. It is a second-order interpolation algorithm. For steady state simulations, one stator and one cylinder grids are modeled, whereas for frozen and unsteady simulations, one stator and two cylinder grids are modeled.

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Fig. 1 2D computational grid

For grid independence study, grids of 0.5 million (coarse), 2 million (medium) and 4 million (fine) cells were considered. Same boundary conditions were used for these three simulations. Grid independence was observed for 4 million mesh but it is observed that for this mesh size the wakes are not properly resolved. When the element size is reduced to 0.03 mm wakes were comfortably resolved as shown in Fig. 3 but the cell count has become 8 million. Hence, the simulations were run with this mesh size. Hence, the finalized stator grid size is 6 million and for cylinder grid size is 2 million. In order to resolve boundary layer, properly enough nodes are kept close to the airfoil surfaces. For the finalized stator and rotor grids, y+ values are kept lower than 1, so that all flow features are captured in the boundary layer and no flow approximations are used. Grids skew angles are kept between 25° and 155°. Aspect ratio is maintained less than 100. Expansion ratio is kept less than 1.2. There is no abrupt change in mesh density. 2D computational grid of the simulation is shown in Fig. 1.

5 Boundary Conditions At the inlet boundary of the cylinder grid, uniform total pressure and total temperature are used as inlet boundary condition. Whereas at exit of the LPNGV, average

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static pressure has been used as exit boundary condition by matching the LP turbine vane exit conditions. Walls of the stator and cylinders are considered as smooth and adiabatic. Also for the walls, no-slip boundary condition is enforced. Free stream turbulence intensity is assumed to be 5%. 10% of the inlet is taken as eddy length scale. Flow is considered as fully turbulent. In blade-to blade plane, periodic boundary condition is applied.

6 Computational Time and Convergence The simulations are carried out on IBM DX 360 parallel computing system using 8 parallel processors. For the convergence of the steady stage and frozen rotor simulations, the calculations were carried out until the max residuals drop below 10–4 . Difference between inlet and outlet mass flow values is less than 0.02%. First simulations were ran using coarse grids, and then the results of these simulation are given as interpolated guess for the steady and frozen rotor simulations which took approximately 20 h to converge. Converged frozen rotor simulation results were given as initial guess for starting of the unsteady simulation. In order to simulate properly the alternate wake shedding phenomena from the upstream cylinders, the time step was calculated from Stouhal formula fL = St U

(1)

where f is the wake shedding frequency, L is the characteristic dimension, U is the flow velocity, and St is the Strouhal number. For a typical case, the frequency was calculated as 16807 Hz. Hence, the time period is 5.65E−5. It is divided by 25 time steps so that we have enough time steps to capture the wake shedding phenomena. Hence, the time step used in the simulation for this case was 2.26E−6. For convergence in each time step which represent orientation of the cylinder grid w.r.t stator grid different from the last time step, a maximum of 20 inner loop iterations are used as converged results from frozen rotor simulation are supplied to the unsteady simulation. The simulation was made to run until a periodic repetition of lift on vane surface is obtained which is taken as convergence criteria of the simulation as shown in Fig. 2.

7 Results and Discussion Figure 3 shows the contours of the vorticity magnitude at a particular time step, for the case where the upstream cylinder radius is 1 mm. For grid cell size of 0.03 mm, we were able to resolve the alternate shedding of the wakes from the upstream cylinder,

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Fig. 2 Convergence criteria for the simulations

as can be seen from the figure there are two wakes one from top end and other from the bottom end of the cylinder being shed alternatively. For this time step, the wake from the bottom end of the cylinder is impinging on the leading edge of the LP vane, whereas wakes from the top end are getting convected along the suction surface. Figure 4 shows that after some time steps are over a new wake is going to impinge on the leading edge and the older wake has diffused. Figure 5 shows the variation in LP vane pressure loss coefficient for different time steps. As can be seen the vane loss coefficient is having a cyclic behavior, it increases then reaches a maximum value and then starts decreasing and after reaching a minimum value start increasing again. We can observe the repeating pattern for vane loss coefficient. The vane pressure loss coefficient without any incoming wakes subjected to same boundary conditions as these cases is found to be 0.144. When the wakes are impinging on the leading edge the loss coefficient calculated is 0.151, an increase of 4.9% and in subsequent time steps, the vane loss coefficient starts decreasing and reaches the base value of 0.144 by this time the wake is fully convicted from the leading edge towards the rear surface of the vane. After this time step again, the vane loss coefficient start increasing as a new wake start approaching the leading edge of the vane. Figure 6 shows the variation in LP vane exit angle for different time steps. Here also the same repeating trend is observed. Figure 7 shows the position of the cylinder for which the wakes from upper

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Fig. 3 Vorticity magnitude contours

cylinder are going towards pressure surface of vane and does not impinge on the leading edge as in the previous case. Vane loss coefficient for different time steps after the solution has converged is plotted in Fig. 8. The maximum vane loss coefficient 0.149 is observed an increase of 3.62% from base value of 0.144. The vane loss coefficient then starts deceasing and reaches minimum value of 0.126 a decrease of 12.64% from base value, which is even lower than the LP vane loss coefficient without any incoming wakes. Similar trends are observed for vane exit angle. Figure 9 shows the variation in LP vane exit angle for different time steps for the new position of the cylinder. Figure 10 shows the position of the cylinder for which the wakes from upper cylinder are passing over the suction surface of vane unlike the previous case where the wakes were going towards the pressure surface of the LP vane. The maximum vane loss coefficient 0.156 is observed an increase of 7.92% from base value of 0.144. The vane loss coefficient then starts deceasing and reaches minimum value of 0.149. Similar trends are observed for vane exit angle. Similar trends were observed for the case where the cylinder radius is 1.3 mm. The wake size is increasing which on one side results in increased vane loss coefficient but on other side the minimum loss coefficient is even much lower than the base vane loss coefficient.

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Fig. 4 New wake about to impinge on the leading edge of the vane

Vane Loss Coefficient PLot

0.152

Pressure loss coefficient

0.151 0.15 0.149 0.148 0.147 0.146 0.145 0.144 0.143 860

870

880

890

900

910

920

Time Steps

Fig. 5 Variation of pressure loss coefficient for different time steps

8 Conclusions From the above three simulations, it is observed that incoming wakes does not always lead to increase in vane loss coefficient. For the case for which wakes are passing

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Vane Exit Angle Plot Time steps

-67.41 860

870

880

890

-67.42

Vane exit angle

-67.43 -67.44 -67.45 -67.46 -67.47 -67.48 -67.49

Fig. 6 Variation of vane exit angle for different time steps

Fig. 7 Wakes passing towards pressure surface of the vane

900

910

920

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Vane Loss Coefficient Plot 0.155

Pressure loss coefficient

0.15 0.145 0.14 0.135 0.13 0.125 0.12 1220

1230

1240

1250

1260

1270

1280

1290

1270

1280

Time steps

Fig. 8 Variation of pressure loss coefficient for different time steps

Vane Exit Angle Plot -67.3 1210

1220

1230

1240

1250

1260

Vane exit angle

-67.35 -67.4 -67.45 -67.5 -67.55 -67.6

Time steps

Fig. 9 Variation of vane exit angle for different time steps

through the pressure surface of the vane, the vane loss coefficient is lower than the vane loss coefficient without any effects of incoming wakes. Also with increase in upstream cylinder size, the wake size is increasing which on one side results in increased vane loss coefficient but on other side the minimum loss coefficient is even much lower than the base vane loss coefficient. But this needs a further detailed analysis like LES or DES to understand this behavior.

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Fig. 10 Wakes passing over the suction surface of the vane

Acknowledgements The authors thank Director, GTRE for giving permission to present this work.

References 1. Mahallati A, Sjolander SA, Praisner TJ (2013) Aerodynamics of a low-pressure turbine airfoil at low reynolds numbers—part I: steady flow measurements. J Turbomach 135/011010 2. Sondergaard R, Sjolander SA, Praisner TJ (2013) Toward the expansion of low-pressure-turbine airfoil design space. In: Proceedings of ASME Turbo Expo 2008: power for land, sea and air, GT2008 9–13 June 2008 3. Curtis EM, Hodson HP, Banieghbal MR, Denton JD, Howell RJ (1997) Development of blade profiles for low pressure turbine applications. J Turbomach 119(3) 4. Sarkar S (2009) Influence of wake structure on unsteady flow in a low pressure turbine blade passage. J Turbomach ASME 131 5. Yang X (2003) Aerodynamic loss modelling in transonic turbines (M.Sc. thesis), Concordia University, Canada 6. Cohen R, Saravanamuttoo (2008) Gas turbine theory, chap 7, 6th edn 7. Paniagua G, Rivir RB (ed) (2006) Advances in turbomachinery aero-thermo-mechanical design analysis. Von Karman Institute for fluid dynamics, lecture series 2007-02, Nov 2006, Rhode Saint Genese 8. Ozturk B, Schobeiri MT (2007) Effect of turbulence intensity and periodic unsteady wake flow condition on boundary layer development, separation, and reattachment along the suction surface of a low-press turbine. J Fluids Eng ASME 129

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9. Moustapha H, Zelesky MF, Baines NC, Japikse D Axial and radial turbines 10. Ciorciari R, Kirik I, Niehuis R (2014) Effects of unsteady wakes on the secondary flows in the linear T106 turbine cascade. J Turbomach ASME 136 11. Volino RJ (2012) Effect of unsteady wakes on boundary layer separationon a very high lift low pressure turbine airfoil. J Turbomach ASME 134 12. Acton P (1998) Untersuchungen des Grenzschichtumschlages an einemhochbelastetenTurbinengitterunterinhomogenen und instationearenZustreombedingungen, Ph.D. thesis, Universitat der BundeswehrMunchen,Munchen, Germany. 13. Stadtmuller, P., (2002), “Grenzschichtentwicklung und Verlustverhalten vonhochbelastetenTurbinengitternunterEinflußperiodischinstationarerZustreomung,” Ph.D. thesis, Universiteat der BundeswehrMunchen, Munchen, Germany 14. Hodson HP, Howell RJ (2005) Blade row interactions, transition, and high-lift aerfoils in low-pressure turbines. Annu Rev Fluid Mech 37:71–98 15. Schobeiri MT, Ozturk B, Ashpis DE (2003) On the physics of the flow separation along a low pressure turbine blade under unsteady flow conditions. J Fluid Eng ASME 127 16. Schobeiri MT, Ozturk B (2004) Experimental study of the effect of periodic unsteady wake flow on boundary layer development, separation,and re-attachment along the surface of a low pressure turbine blade. J Turbomach ASME 26(4) 17. Ibrahim MB, Vinci S, Kartuzova O, Volino RJ (2012) CFD simulations of unsteady wakes on a highly loaded low pressure turbine airfoil (L1A). In: Proceedings of ASME turbo expo 2012: power for land, sea and air, GT2012 11–15 June 2012 18. Nessler CA, Marks C, Sondergaard R, Wolff M, Sanders DD, O’Brien WF, Polanka MD (2010) A CFD and experimental investigation of unsteady wake effects on a highly loaded low pressure turbine blade at low reynolds number. In: Proceedings of ASME turbo expo 2010: power for land, sea and air, GT2010 Oct 2010 19. Schwarze M, Niehuis R (2010) Numerical simulation of a highly loaded LPT cascade with strong suction side separation under periodically unsteady inflow conditions. In: Proceedings of ASME turbo expo 2010: power for land, sea and air, GT2010 Oct 2010 20. Meyer RX (1958) The effects of wakes on the transient pressure and velocity distributions in turbomachines. ASME J Basic Eng 80 21. Mayle RE (1991) The role of laminar turbulent transition in gas turbine engines. J Turbomach ASME 22. Walker GJ (1993) The role of laminar turbulent transition in gas turbine engines: a discussion. J Turbomach ASME 115(2) 23. Halstead DE, Wisler DC, Okiishi TH, Walker GJ, Hodson HP, Shin H-W, (1997) Boundary layer development in axial compressors and turbines—part 1: composite picture. J Turbomach ASME 119(1) 24. Halstead DE, Wisler DC, Okiishi TH, Walker GJ, Hodson HP, Shin H-W (1997) Boundary layer development in axial compressors and turbines—part 2: compressors. In: Proceedings of ASME turbo expo 2010: power for land, sea and air, GT-462, vol 1 25. Halstead DE, Wisler DC, Okiishi TH, Walker GJ, Hodson HP, Shin H-W (1997) Boundary layer development in axial compressors and turbines—part 3: LP turbines. J Turbomach ASME 119(2) 26. Halstead DE, Wisler DC, Okiishi TH, Walker GJ, Hodson HP, Shin H-W (1997) Boundary layer development in axial compressors and turbines—part 4: computations and analyses. J Turbomach ASME 119(1) 27. Wu X, Jacobs RG, Hunt JRC, Durbin PA (1999) Simulation of boundary layer transition induced by periodically passing wakes. J Fluid Mech 398 28. Wu X, Durbin PA (2001) Evidence of longitudinal vortices evolved from distorted wakes in turbine passage. J Fluid Mech 446 29. Hoheisel H, Kiock R, Lichtfuss HJ, Fottner L (1987) Influence of free-stream turbulence and blade pressure gradient on boundary layer and loss behaviour of turbine cascades. J Turbomach ASME 1 86-GT-234

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30. Howell RJ, Ramesh ON, Hodson HP, Harvey NW, Schulte V (2004) High lift and aft loaded profiles for low pressure turbines. J Turbomach ASME 3 GT-0261 31. Ladwig M, Fottner L (1993) Experimental investigations of the influence of incoming wakes on the losses of a linear turbine cascade. J Turbomach ASME 3C GT-394 32. Pritchard LJ (1985) An eleven parameter axial turbine aerofoil geometry model. J Turbomach ASME 1 GT-219 33. ANSYS FLUENT User Guide, Release 14.5 34. ICEMCFD User Guide, Release 14.5

Effect of Axial Location on the Performance of a Control Jet in a Supersonic Cross Flow Raj Kiran Grandhi and Arnab Roy

Abstract Control jets injected into a supersonic flow cause a significant region of separated flow over the parent vehicle in the vicinity of injection. This altered external flow contributes to an additional force on the vehicle in addition to the jet thrust thereby effecting its performance. In this study, numerical simulations were carried out to estimate the effect of injection location and body attitude on the overall performance of a Reaction Control System jet in producing a control force. Commercial CFD software was used to solve the 3D RANS equations using the SSTkω turbulence model. It is seen that favourable interaction results from injection at rearward locations and positive angles of attack whereas injection from forward locations and negative angles of attack results in an adverse interaction. Keywords Reaction control systems · Supersonic flow · CFD

1 Introduction Launch vehicles incorporate Reaction Control Systems (RCS) for attitude control. These systems offer significant advantages over aerodynamic surfaces such as fins through their ability to be used during the low dynamic pressure regimes of flight— either at low velocities or at high altitudes as well as by not incurring a drag penalty when not operative. Control forces are generated by RCS by expelling high pressure gas through nozzles located at the peripheral regions of a flight vehicle. When the vehicle is travelling at supersonic speeds, these jets act as a barrier to the external flow over the vehicle and result in a complex flow field around the injection which R. Kiran Grandhi (B) Advanced Systems Laboratory, Defence Research and Development Organisation, Hyderabad 500058, India e-mail: [email protected] A. Roy Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur 721302, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_7

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consists of several shocks and vortical structures. The external flow is thus subjected to a severe disruption in the presence of these control jets. This altered flow field causes a corresponding change in the pressure distribution around the vehicle and consequently in the aerodynamic forces acting on the vehicle. The interaction flow field corresponding to the injection of a side jet into a supersonic cross flow is a subject of much interest to the aerospace community. These interactions arise not only in RCS systems where they influence the effectiveness of the jet in producing control forces by disrupting the flow field, but also in SCRAMJET engines where they affect the penetration, mixing and combustion [1] of the injected fuel. These interactions also appear in Secondary Injection Thrust Vector Control (SITVC) systems where again they affect the control forces produced by the nozzle [2]. The complex flow structure resulting from this interaction [3] is shown in Fig. 1 where the expanding jet is enclosed in a barrel shock and acts as a barrier to the incoming external flow. This causes a bow shock to form upstream of the injection, and this shock wraps itself around the injected jet. The boundary layer of the cross flow separates upstream of the injection and forms a horse shoe vortex around the jet. This is a characteristic feature of the interaction structure. The shock structure resulting from this interaction creates a region of high pressure upstream of the injection and a region of low pressure downstream of the injection [4].

LARGE-SCALE STRUCTURES M>1

BOW SHOCK BARREL SHOCK MACH DISK

BOUNDARY LAYER SEPARATED REGION

SIDE JET

RECIRCULATION ZONE Fig. 1 Schematic of the jet interaction flow field [3]

RECIRCULATION ZONE

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In an earlier study, [5] have studied the effect of a number of parameters, such as the jet pressure ratio (Po,jet /P∞ ), injection Mach number, parent body attitude with respect to the external flow and the presence of a flare on the effectiveness of the injected control jet. The present study focusses on the effect of injection location on the aerodynamic force due to jet interaction.

2 Methodology The simulations were carried out using a commercial CFD software for a typical cone-cylinder configuration. The cylindrical section has a diameter D = 40 mm and a length of 6.2D. The length of the conical section was 2.8D. The lateral jet was injected from the cylindrical section, and four different models were made which correspond to different locations of this injected jet. The three dimensional RANS equations were solved on a hexahedral grid consisting of about 7 lakh cells using the shear-stress transport (SST) k − ω turbulence model. A second order upwind scheme was employed in all the simulations. The pressure distribution obtained from the simulations was integrated to obtain the aerodynamic force acting on the vehicle. A summary of the simulation cases is shown in Table 1. The cross flow parameters (P∞ = 16,400 Pa, T∞ = 100 K, M∞ = 3.0), the injection Mach number (Minj = 1) and the jet stagnation temperature (280 K) were unchanged in all the simulations. The effectiveness of the control jet can be defined as the ratio of the total side force generated when the jet is operated to the jet thrust. In the presence of an angle of attack, the total side force includes a component due to the attitude which is accounted for in calculating the effectiveness by running a reference simulation with the jet “off” and subtracting the corresponding forces from the simulation with the jet “on”. The jet reaction can be computed using the rocket thrust equation: Fjet = m˙ jet Ve + (Pe − P∞ ) ∗ Ae

(1)

The additional force acting on the body due to the interaction can be computed as: Fi = Faero − Fref

Table 1 Summary of simulation cases Parameter Injection Mach number Injection location (from nosetip) Angle of attack

Variation 1.0, no injection 3.3D, 4.3D, 6.0D, 8.5D −15◦ , 0◦ , +15◦

(2)

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And the effectiveness of the control jet is thus computed as: E jet = 1 +

Fi Fjet

(3)

If the additional force due to jet interaction is negligible, then Faero ≈ Fref and the jet effectiveness is close to unity. Depending on whether the jet interaction force is in the direction of jet reaction or opposite to it, the jet effectiveness is respectively greater than or less than unity.

3 Validation and Grid Independence Study The simulation methodology was validated using experimental pressure measurements on a similar configuration reported by [6]. The geometry considered for validation purpose and the associated computational grid are shown in Fig. 2. This geometry is nearly identical to the model described in the preceding section. The only difference is that in this model, there is a flare extending from 6.0D to 9.0D with an end diameter of 1.66D. The side jet is injected from an orifice located on the cylindrical surface at a distance of 4.3D from the nose tip. The flow structure and surface pressure distribution as obtained from the simulation are shown in Fig. 3. In order to establish grid independence of the obtained results simulations were run on coarse, medium and fine meshes consisting of about 3.3 lakh, 7.7 lakh and 15.7 lakh cells respectively. A comparision of the pressure variation along the upper centre line of the model for these different grids along with the experimental values

Injection orifice 0.1D at X = 4.3 D

0mm

D=4 2.8D 3.2D

Fig. 2 The hexahedral grid used for the validation studies

3.0D

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Pathlines coloured by velocity (m/s)

Deflected RCS jet

Horse-shoe vortex

Pressure distribution on surface (kPa)

Region of separation

Region of low pressure in the wake

Fig. 3 Flow structure and surface pressure distribution

Fig. 4 Variation of pressure along the centre-line

is shown in Fig. 4. The components of the normal force coefficient due to the jet, the interaction flow field and the overall effectiveness along with the Grid Convergence Index (GCI) as proposed by [7] using a factor of safety of 1.25 for the present threegrid study are shown in Table 2. The GCI was found to be less than 1%, and thus the solution may be considered to be grid-independent.

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Table 2 Variation of the force components with grid size Size (Million) CN,total CN,jet CN,i 0.33 0.77 1.57 GCI (%)

−0.246 −0.257 −0.259 0.329

−0.396 −0.396 −0.395 0.027

0.150 0.138 0.136 0.824

E jet 0.621 0.650 0.657 0.416

4 Results The overall effectiveness of the control jet depends on several features of the complex flow interaction structure around the injected jet as well as the body attitude with respect to the incoming flow. Some of these features are: • • • •

The conical shock emanating from the tip of the vehicle. The bow shock ahead of the injected jet. The barrel shock around the expanding jet. The horse shoe vortex forming around the jet and trailing downstream alongside the vehicle. • Leeward vortices generated by the separation and roll up of boundary layer due to an angle of attack. Depending upon the angle of attack and location of the injected jet, interaction among the above is also possible. For example, at negative angles of attack or for injection from the fore-regions, the conical shock can interact with the bow shock. Similarly, the lee vortices forming due to an angle of attack can interact with the horse shoe vortex. The surface pressure distribution over the vehicle is thus dependant on all the above features and their interactions.

4.1 Shock Structures The shock structures of the interaction are shown in Figs. 5, 6 and 7 wherein contours of Mach numbers on the symmetry plane and pressure coefficient on the body surface are depicted for injection from different locations at various angles of attack. For a negative angle of attack, the conical shock emanating from the tip of the vehicle impinges on the bow shock ahead of the injection as seen in Fig. 5. This impingement exists for all the injection locations except for the aft-most. For zero angle of attack, as seen in Fig. 6, this impingement is seen only for the fore-most injection and to a lesser extent, injection at 4.3D. For positive angles of attack, shown in Fig. 7, there is no impingement whatsoever as the shock is present only on the side opposite that of the injected jet.

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Cp

Mach number

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 5 Mach number and Cp contours for injection at different locations (α = −15◦ )

Cp

Mach number

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 6 Mach number and Cp contours for injection at different locations (α = 0◦ )

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Cp

Mach number

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 7 Mach number and Cp contours for injection at different locations (α = 15◦ )

Cp

Mach number

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 8 Flow pathlines for injection at different locations (α = −15◦ )

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Cp

Mach number

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 9 Flow pathlines for injection at different locations (α = 15◦ )

4.2 Vortex Structures Flow pathlines around the body and from the injected jet are shown in Figs. 8 and 9. The bow shock ahead of the injection causes the boundary layer to separate, creating a vortex in the region of separation. This vortex curves around the barrel shock resulting in the horse-shoe vortex that is a characteristic feature of the jet interaction. The incoming flow also deflects the injected jet aligning it parallel to the flow. At negative angles of attack, this deflected jet lies close towards the body and at positive angles of attack it is deflected further away from the body. In addition, when the body is at an of attack, the boundary layer on the lee side of the body separates and rolls up into a pair of vortices that trail downstream along the body. These vortices interact with the horse shoe vortex, further altering the flow structure around the vehicle.

4.3 Surface Pressure Distribution The effectiveness of the injected jet depends on the surface pressure distribution which is strongly influenced by the shock and vortical structures described in the preceding sections. Figures 10, 11 and 12 highlight the key aspects of the effect of these structures on the surface pressures. In these figures, numerical oilflow patterns are shown over plots of the differential pressure coefficient obtained by subtracting the pressure distribution of the reference simulation (without jet) from the surface pressure distribution. For the cases without an angle of attack, shown in Fig. 11, the basic features of the interaction such as separation of the boundary layer upstream of the injection

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ΔCp

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 10 Surface flow for injection at different locations (α = −15◦ )

ΔCp

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 11 Surface flow for injection at different locations (α = 0◦ )

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ΔCp

(a) Xinj = 3.3D

(b) Xinj = 4.3D

(c) Xinj = 6.0D

(d) Xinj = 8.5D

Fig. 12 Surface flow for injection at different locations (α = 15◦ )

followed by the high pressure region, the region of suction in the wake of the injected jet and reattachment further downstream of the injection location can all be clearly seen. Also, the basic structure of the oilflow pattern and intensity of the pressure distribution is nearly independent of the injection location. For the fore-most injection case (X inj = 3.3D), the separation region upstream of the injection extends all the way to the bottom of the body. This is because of the lowered pressure of the incoming flow just after the expansion corner at the interface between the conical and cylindrical sections. For injection from the more downstream locations, the incoming flow on the bottom side is effected to a lesser and lesser extent. For the cases with an angle of attack, shown in Figs. 10 and 12, the strong interaction of the separation vortices with the injection flow structure can clearly be seen. For these cases, the separation of the boundary layer due to the angle of attack occurs about about 30◦ towards the lee side. These separation lines are clearly seen for injection from all but the fore-most location in these figures. For a negative angle of attack, the suction in the wake of the jet that has been deflected close to the body is significantly stronger than in the case of a positive angle of attack for which the effect of suction is rather diminished.

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4.4 Force and Moment Due to Interaction The differential surface pressure distributions over the body were integrated to obtain the variation of force and moment along the vehicle. These force and moment distributions are shown in Figs. 13, 14 and 15. Since these forces and moments were based on the pressure distribution obtained after subtracting the reference pressure, the absence of any interaction with the external flow would dictate that these are both zero. Thus, these figures depict only the effect of interaction excluding the effect of body attitude. The raw values of force and moment were non-dimensionalised using Fjet and Fjet × D as the scaling factors for force and moment respectively. The moment was computed about the injection location with pitch-up moment considered as positive. Force acting in the direction of jet thrust was considered positive. Thus, for force, positive region of the graphs corresponds to favourable interaction and negative region corresponds to adverse interaction. In the absence of an angle of attack, as seen in Fig. 14, the only significant change in the force distribution is a geometric shift that corresponds to the change in injection location. As discussed in the preceding section, the interaction pattern is relatively independent of the injection location for zero angle of attack and the force distribution reflects the same. In the presence of an angle of attack, however, the changes in the extent and intensity of the regions of suction in the jet wake coupled with the interaction of the separation vortices with the injected jet results in more significant changes to the corresponding force variations (Fig. 15).

(a) Force per unit length

(b) Cumulative force

(c) Moment per unit length

(d) Cumulative moment

Fig. 13 Non-dimensional force and moment due to interaction (α = −15◦ )

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(a) Force per unit length

(b) Cumulative force

(c) Moment per unit length

(d) Cumulative moment

Fig. 14 Non-dimensional force and moment due to interaction (α = 0◦ )

(a) Force per unit length

(b) Cumulative force

(c) Moment per unit length

(d) Cumulative moment

Fig. 15 Non-dimensional force and moment due to interaction (α = 15◦ )

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4.5 Jet Effectiveness The variation of jet effectiveness in producing the desired normal force with injection location for different angles of attack is shown in Fig. 16. For all angles of attack, it is seen that injection from the aft-most location is most favourable as it results in an amplification of the jet thrust. For injection from other locations, the effectiveness is relatively independent of the injection location in the absence of an angle of attack. Further, while a positive angle of attack results in a favourable interaction force, a negative angle of attack results in adverse interaction and injection from progressively upstream locations result in progressively worse effectiveness. The non-dimensionalized moment about the injection location can be thought of as a shift of the injection location caused by the interaction flow field, an effective moment arm, that is given by: X i =

Mi Fjet

Like the jet effectiveness, X i is zero if there is no moment developed about the injection location due to the interaction. It is negative for a pitch-down moment and positive for a pitch-up moment. The variation of this effective moment arm is shown in Fig. 17. It is seen that for all the cases, the overall effect of the interaction is to cause a pitch-down moment about the injection location. Like the jet effectiveness for force, this effective moment arm is greatest for a negative angle and for injection from the fore-most location. For other cases, it is more modest and lies within 0.5D.

Fig. 16 Variation of jet effectiveness with location (Normal force)

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Fig. 17 Variation of jet effectiveness with location (Moment)

5 Conclusion Numerical simulations were carried out to study the effect of location and attitude on the control characteristics of a side jet injected from an axi-symmetric parent body consisting of a sharp cone followed by a cylinder. The methodology was validated with published experimental data and a grid independence study was performed to establish the accuracy. The effect of injection location was studied by creating four models each corresponding to injection of the side jet from a distinct location on the cylindrical region. The effect of body attitude was also studied by varying the angle of attack. The results indicate that both injection location as well as the angle of attack strongly influence the effectiveness of the injected jet in producing the desired control force. Injection from aft locations as well as positive angles of attack contribute favourably to the force amplification while injection from forward locations and negative angles of attack contribute negatively.

References 1. Kawai S, Lele SK (2010) Large-eddy simulation of jet mixing in supersonic crossflows. AIAA J 48(9). https://doi.org/10.2514/1.J050282 2. George R, Krishna JM, Grandhi RK, Gupta RK (2011) Flow-field analysis of SITVC in a contoured nozzle. In: Fifth symposium on applied aerodynamics and design of aerospace vehicles 3. Ben-Yakar A (2000) Experimental investigation of mixing and ignition of transverse jets in supersonic crossflows. PhD thesis, Stanford University 4. Viti V, Neel R, Schetz JA (2009) Detailed flow physics of the supersonic jet interaction flow field. Phys Fluids 21(4):046101. https://doi.org/10.1063/1.3112736 5. Grandhi RK, Roy A (2017) Effectiveness of a reaction control system jet in a supersonic crossflow. J Spacecraft Rockets 54(4):883–891. URL https://doi.org/10.2514/1.a33770

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6. Stahl B, Esch H, Glhan A (2008) Experimental investigation of side jet interaction with a supersonic cross flow. Aerosp Sci Technol12(4):269–275. https://doi.org/10.1016/j.ast.2007. 01.009 7. Roache PJ (2003) Error bars for CFD. In: 41st aerospace sciences meeting and exhibit. https://doi.org/10.2514.6,2003-408

Effect of Chord Variation on Subsonic Aerodynamics of Grid Fins Manish Tripathi , Mahesh M. Sucheendran, and Ajay Misra

Abstract Current paper deliberated the impact of gap-to-chord ratio (g/c) variation on grid fin subsonic flow characteristics through chord modifications while retaining the same gap and aspect ratio to explicitly decipher the role of chord on grid fin aerodynamics through numerical analysis. Solver validation is followed by comprehensive examination of the pertinent aerodynamic coefficient results associated with different grid fin chord variants. The study establishes enhanced maximum lift coefficient at the expense of reduced aerodynamic efficiency in the most operable angle of attack region for higher g/c (lower chord). Efficiency reduction is attributed to increase in drag for higher g/c emanating due to increased pressure drag applicable for a blunt compact geometry. Stall angle undergoes minimal deviation for different g/c when chord is the varying parameter. However, deviations associated with grid fin aerodynamic efficiency for varying chord were found to be appreciably significant. The study categorically deduces the impact of chord in the g/c parameter, and hence can be helpful for grid fin designers while selecting the optimum chord value for enhanced aerodynamic efficiency and lift requirements. This study in conjunction with analysis carried out for gap variation can help achieve an efficient grid fin design with respect to delayed stall angle and increased aerodynamic efficiency. Keywords Grid fins · Cascade fins · Gap-to-chord ratio · Chord variation · Aerodynamic efficiency · CFD++

M. Tripathi (B) · A. Misra Department of Aerospace Engineering, Defence Institute of Advanced Technology (DU), Girinagar, Pune, Maharashtra, India e-mail: [email protected] A. Misra e-mail: [email protected] M. M. Sucheendran Department of Mechanical and Aerospace Engineering, Indian Institute of Technology, Hyderabad, Telangana, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_8

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Nomenculture AR b, c, th bFP , cFP CD CFD CFL CL C Lα CL /CD CLmax CP e0 g/c M NS p Re SA t uj U∞ , P∞ , T∞ xj x/c

aspect ratio of horizontal members span, chord and thickness of members, m span and chord of planar fin, m coefficient of drag Computational fluid dynamics Courant-Friedrichs-Lewy number Coefficient of lift Lift slope, deg −1 Aerodynamic efficiency Maximum lift coefficient Pressure coefficient Total energy Gap-to-chord ratio Mach number Navier-Stokes equations Pressure, Pa Reynolds number Spalart-Allmaras turbulence model Time, s jth component of velocity vector Freestream pressure (Pa), temperature (K ) and velocity (m/s) jth component of position vector Non-dimensional chordwise distance

Greek letters α ρ

Angle of attack, ◦ Density of flow, kg/m3

1 Introduction Missiles and unmanned aerial vehicles are unmanned warhead delivery vehicle systems comprising of numerous sub-systems like guidance and control, propulsion, and warhead (payload) systems. Optimizing their guidance and control system is imperative to achieving the desired mission objective. Control system consists of external aerodynamic surfaces called control surfaces, which generate the required aerodynamic forces by virtue of angular deflections to execute a desired manoeuvre. Deliberating the aerodynamic forces generated by these surfaces, and the inherent

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Fig. 1 Missile with grid fins

aerodynamic efficiency plays a critical role in evaluating the most optimum geometry. Grid fins also termed as lattice fins are a recent advancement in the control surface aero-mechanical technology. Grid fins have been globally recognized as unconventional control surfaces ascribed to its unique structural characteristics consisting of numerous intersecting planar surfaces encompassed by a thin outer frame to provide rigidity (Fig. 1). This interlacing of multiple lifting surfaces leads to the formation of multiple cells which act as individual lifting surfaces. Unlike conventional planar fins, these fins are aligned transverse to the freestream flow with the air being allowed to pass through these cells. These fins have been implemented on a multitude of aerospace applications. For instance, these were implemented as control surfaces on numerous Soviet (now called Russia) supersonic missiles (Adder AA-12, SS-12 ‘Scaleboard’ etc.) in the late1950s [1], as stability and air drag devices on the Soyuz TM-22 Launch Escape Spacecraft, as maneuvering device on the USA based Massive Ordinance Air Blast (MOAB) bomb [2], and as hypersonic control and stability surface on reusable launch vehicle named Falcon 9, developed by SpaceX [3]. Most recently, these were implemented on the North Korean Intercontinental ‘Musudan’ cruise missile [4]. Owing to their unique structural and aerodynamic characteristics, these are also being explored for under-water launched missiles and munitions as well as interstellar space exploration spacecrafts [5, 6]. Recent upsurge in its world wide application has been attributed to its unique structural and aerodynamic characteristics leading to significant utility based advantages compared to conventional fins. The most favorable advantage pertains to augmented lift capability at high angles of attack and across wider Mach number (M) regimes (subsonic and high supersonic). In-fact these have been credited with delayed stalling even up to angle of attack (α) = 50◦ in some cases. Due to the shock waves getting swallowed within the cells, grid fins display superior control characteristics at high supersonic speeds [7]. Smaller chord enables significant hinge moment curtailment leading to salient control surface actuator weight requirements [8, 9]. Due to the reduced impact of curvature on grid fin aerodynamics, these possess superior folding capabilities [10]. Some additional advantages including improved roll control due

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to attenuated body vortex interference [11], high strength-to-weight ratio, as well as increased target area and reduced miss distance due to their elevated manoeuvrability [12]: further increase their utility potential. In-spite of these advantages, limited usage during their advent was linked to higher drag especially in the transonic regime (originating due to the flow choking phenomena [7]), increased radar cross-section area [8, 13], and complex manufacturing process. A plethora of research has been carried out historically to contemplate the underlying rudimentary flow-physics linked to its unique aerodynamic characteristics in comparison to planar fins. These studies involved experimental observations [8, 10, 11, 13–17], theoretical analysis through the application of Vortex Lattice Theory [18– 21] and Prandtl-Meyer’s shock expansion theory [22]. A theoretical study involving missile body and grid fin integration was carried out by Ledlow et al. using preexisting theoretical methods and a missile aerodynamic prediction tool. The study also carried out grid fin geometry optimization using a modified ant colony optimization technique [12]. Additional investigations by carrying out dynamic characterization using the small perturbation theory [23] was accomplished to analyze the control characteristics of grid fin control surfaces. With the advancement of computational power, several numerical examinations were carried out to decipher the grid fin’s aerodynamic [9, 24–34], thermal [35], and aeroelastic properties [36]. Significant research oriented around comprehending the flow-physics linked to these fins had been carried out to mitigate drag as well as improve its transonic performance. These studies incorporated a number of geometrical modifications like altered frame cross-section leading to 25% drag reduction [8], and local sweeping [37] for drag reduction of around 38% in the supersonic regime. Drag mitigation in transonic domain was achieved through implementation of: (1) swept-back grid fin [38, 39], (2) combination of sharp leading edges and swept grid fins [40, 41], (3) single cell leading edge variations with a delta configuration [42], amounting to a drag reduction of ≈12–13, 25–30, and 40%, respectively. An investigation pertaining to incorporating an optimized Busemann profile cross-section for the grid fin cells suggested significant drag reduction in the supersonic regime due to the wave cancellation effect [33]. Thus, drag reduction had been the main approach towards grid fin performance enhancement. As per the authors’ knowledge, hitherto study related to aerodynamic efficiency enhancement has been scarce. In 2009, Misra et al. suggested a simplified grid fin variant called as cascade fins (hereinafter referred as grid fins only). These consisted of a cascade of horizontal lifting members (termed as planar members) placed parallel to each other and supported by end plate members to provide rigidity (Fig. 2). Removal of cross-members lead to reduced drag, and hence enhanced aerodynamic efficiency. These simplified grid fins had been extensively utilized in subsonic flow to comprehend the impact of different geometrical parameters like number of lifting members, gap between the members, and cross-section of the members through experimental [43, 44], and theoretical [45, 46] analysis. These studies established enhanced high α performance for grid fins, delayed stall angle along with lowered lifting characteristics for lower gap grid fins as well as the fact that grid fins possess lower aerodynamic efficiency compared to planar fins. Current research aims at carrying out numerical analysis to decipher flow-

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Fig. 2 Cascade fin (simplified grid fin variant)

physics involving the impact of different grid fin geometrical parameters, and hence suggest the most optimum grid fin geometry for enhanced aerodynamic efficiency and delayed stall characteristics. Subsequently, validated numerical evaluations pertaining to gap-to-chord ratio (g/c) variation through gap alterations, number of planar member modifications, and cross-section variation were carried out by the authors in Refs. [47–49] to underscore the rudimentary flow-physics associated with these geometrical modifications. Current paper ventures up on explicitly evaluating the effect of chord variation on grid fin subsonic flow characteristics at different angles of attack through a sequence of numerical simulations performed at different g/c values where, g is gap between the members which remains constant and c (variable analyzed) is chord of the planar members pertaining to different grid fin variants. Moreover, span is also varied along with c such that aspect ratio ( A R) remained constant. The following section (Sect. 2) describes the numerical methodology adopted to carry out the pertinent steady state numerical simulations, followed by the results and discussions section. Conclusions drawn out from this section deliberating the effect of chord variation on grid fin aerodynamics have been discussed in Sect. 4.

2 Numerical Methodology Aerodynamic analysis in the present study was accomplished using computational fluid dynamics (CFD). Details related to the pertinent geometry being simulated, simulated flow conditions, mesh configuration, boundary conditions, and solver specifications are described in the succeeding section.

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2.1 Geometry The simulations make use of grid fins consisting of three rectangular cross-section planar members placed parallel to each other (Fig. 3a) with the following geometrical specifications: • • • •

Gap between the members (g): 0.05 m Thickness of the members (th): 2.5 × 10−3 m gap-to-chord ratio (g/c): 0.3 to 1.3 at increments of 0.1, and 2.0. Aspect ratio (AR): 2.0

Thus, planar member chord was varied to obtain the particular g/c and span (b) was varied such that A R was maintained at 2.0 with the respective values given in Fig. 4a. Consequently, surface area varied according to these specifications as shown in Fig. 4b. Notably, the variant pertaining to g/c = 0.5, was used for solver validation by comparing experimental results obtained for the same geometry as given in Ref. [44]. The same geometry shall be taken as baseline geometry to compare the impact of increasing or decreasing g/c on grid fin aerodynamics. Further confirmation with respect to validity of the current numerical results was obtained by carrying out simulations for a single planar member with the geometrical specifications as given in Fig. 5. Values pertaining to the different geometrical

(a) Isometric view of grid fin

(b) Top and side cross-section cut views

Fig. 3 Model view of the tested grid fin variant (*variable) 0.06

Chord variation (c) Span variation (b)

0.3

0.05 2

Projected area (in m )

Chord and span variation (in m)

0.35

0.25 0.2 0.15 0.1

0.03 0.02 0.01

0.05 0 0

0.04

0.5

1

1.5

2

gap to chord ratio, g/c

(a) Span and chord for different g/c and constant AR Fig. 4 Geometrical variations at different g/c

0 0

0.5

1

1.5

gap to chord ratio, g/c

(b) Projected area variation

2

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Fig. 5 Flat plate geometry for validation

Fig. 6 Computational mesh configuration

parameters were bFP = 0.02 m, cFP = 0.1 m, and same th as that of the grid fin members mentioned earlier. The numerical results pertaining to this geometry were compared against the experimental results obtained for the same geometry by Misra in Ref. [43]. The study implemented cylindrical computational domain across all the simulations pertaining to different grid fin variants. Its radius was adjusted such that the frontal area of the respective geometry was less than 5% of the computational domain frontal area (Fig. 6a). Moreover, the domain length was taken as 5 × c and 20 × c in the upstream and downstream directions respectively (Fig. 6b). Angle of attack (α) was simulated by rotating the domain and keeping the geometry fixed on the axis. Additionally, it was rotated to be aligned within 5◦ of the flow direction to efficiently capture wake region variations at different angles of attack.

2.2 Mesh and Boundary Conditions Meshing in the current setup was carried out using MIME software (also known as IMIME Mesher) developed by Metacomp Technologies [50]. Mesh implemented a hybrid mesh configuration comprising of structured prism layers close to the walls and tetrahedral cells (characterized as unstructured mesh) away from the walls. Prism layers enable efficient flow capturing in the wall-adjacent boundary layer region

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(Fig. 6c). Moreover, to optimally reduce the mesh cell size and increase efficiency, mesh implemented a multi-block meshing environment wherein, mesh was finer close to the walls and coarser towards the far-field boundaries (Fig. 6a, b). Meshing was carried out for one half of the domain taking advantage of symmetry about the midspan location as seen earlier in Fig. 3a. The total number of cells depending on the geometry varied between 2.0 million cells for g/c = 0.3, and 0.75 million cells for g/c = 2.0. Mesh pertaining to grid fins with g/c ranging between 0.3 and 2.0 were segregated as 56–90% tetrahedral, and 40–7% triangular prisms away from the walls, 3.1–2.0% hexahedral, and remaining pyramids within the prismatic layers. Height of the first layer pertaining to the prismatic layer is quantified by considering the y + value. It is a non-dimensional number signifying the first layer height away from the walls with respect to the turbulent boundary layer. It is analogous to Reynolds number (Re) with a lower value corresponding to first layer residing in the viscous sub-layer and a higher value corresponding to placement in the fully turbulent flow region. Hence, it delineates which part of the turbulent boundary layer the first layer resides in. Selection of y + value also depends on the turbulent model being used for simulations. Based on the analysis carried out in the present research, the best results were presented by the Spalart-Allmaras model (SA), which produces the most accurate results when the mesh is refined up to the viscous sub-layer. Thus, prismatic layer was refined up to y + ≈ 1 leading to a first layer height of 3.616 × 10−5 m and a growth factor of 0.8. In order to cater for the accuracy hampering high aspect ratio cells originating at sharp corners of the grid fin geometry, mesh incorporated a sharp turn blending feature (Fig. 6c) leading to the creation of degenerate prismatic elements projected from geometry corners and edges. This enabled efficient meshing within sections corresponding to high geometric curvature (Fig. 7). The study utilized characteristic based boundary conditions for inlet, outlet and farfield boundaries. This boundary condition is characterized by assigning flow related M and direction values to a cell by using data supplied to an approximate Riemann solver. Walls were assigned the adiabatic no-slip boundary condition, which necessitated the presence of zero velocity along the wall surfaces. Symmetry boundary condition was assigned for the symmetry plane described earlier.

Fig. 7 Degenerate mesh cells at grid fin corners pertaining to prism layers

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2.3 Mathematical Model Numeral analyses were carried out by solving a set of 3D Navier-Stokes equations (NS) which are a set of time (t) dependent non-linear, coupled differential equations consisting of one mass conservation equation (Eq. 1), three momentum conservation equations (Eq. 2), and an energy conservation equation (Eq. 3). These equations are solved together to obtain the values of different flow parameters namely, velocity components (u j , jth component of velocity vector) and pressure (p) in the different directions [49].  ∂ρ ∂  + ρu j = 0 ∂t ∂x j

(1)

 ∂ ∂  ρu i u j + pδi j − τ ji = 0, i = 1, 2, 3 (ρu i ) + ∂t ∂x j

(2)

 ∂ ∂  ρu j e0 + u j p + q j − u i τi j = 0 (ρe0 ) + ∂t ∂x j

(3)

Here, x j , ρ, τ ji , e0 , and q j are jth component of position vector, density, viscous shear stress, total energy, and heat flux respectively. δi j = 1 for i = j, and zero otherwise These coupled equations in the current numerical setup were solved using the Reynolds-Averaged Navier-Stokes equations (RANS), which are derived from the original NS equations by replacing the flow variables (signified by Φ in Eq. 4) with the sum of their respective mean (Φ) and fluctuating components (Φ  ) as seen in Eq. 4. These equations are time averaged to obtain the final set of RANS equations (Eq. 5). Φ = Φ + Φ  1 Φ≡ Φ(t)dt T T

(4) (5)

As a consequence of this averaging process, new additional terms are introduced called the Reynolds stresses (τi j ) which are solved using additional equations called the turbulence model equations. Turbulence closure problem (mentioned earlier in Sect. 2.2) in the current study was accomplished by using the one-equation SpalartAllmaras (SA) turbulence model which relates the eddy viscosity parameter and length scale specifications through a one transport differential equation. This model originally developed for external aerodynamic flows [51] has been deliberated to be robust and computationally less expensive compared to other turbulence models. It has been delineated to generate accurate results for external aerodynamic flow problems including low Re wall-bounded flows, flows involving adverse pressure gradient

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and rotation [38, 51–53]. In the current research, a systematic comparison with results obtained using other turbulence models also reaffirmed its higher accuracy. A brief mathematical description of this turbulence model is elaborated in Ref. [49].

2.3.1

CFD++ Solver Specifications

Numerical simulations were performed using the commercial CFD++ solver developed by Metacomp Technologies [54] which is a three-dimensional finite volume method based solver adopting a hybrid mesh configuration. In the current numerical setup, it utilized a second order space discretization method along-with an implicit time integration method for steady state evaluations. It incorporated a preconditioned based method which is favorable for low speed flows. This method applies a preconditioning operator on the time derivatives of the NS equations and mitigates the eigen value spread alleviating the numerical diffusion (characteristic of low speed simulations), and hence accelerate the rate of convergence towards steady state solutions. A multidimensional Total Variation Diminishing (TVD) interpolation scheme was adopted by the solver to avoid spurious numerical oscillations linked with second or higher order numerical schemes. A local wave-model solution based approximate Riemann solver was used to evaluate inter-cell fluxes which leads to correct signal propagation for the inviscid flow terms. Moreover, a multigrid algorithm had been incorporated to enhance convergence acceleration and provide solution grid independence [55]. Simulations were computed in parallel on Linux based machines consisting of 12–24 processors (based on the mesh size) and a double precision solver at the Parallel Computation (PARC) facility located in the Department of Aerospace Engineering, at the Defence Institute of Advanced Technology, Pune. In order to achieve faster convergence and adapt according to the forthcoming transients related to a flow like sudden changes in the flow direction, the Courant-Friedrichs-Lewy (CFL) number was ramped from 1 to 40. Normalized flow residuals were iteratively tracked, and the solution was deemed converged when these stabilized and acquired values less than 5 orders of magnitude.

2.4 Flow Conditions Simulation conditions were based on the conditions as mentioned in Ref. [44] that is, low subsonic speeds with M = 0.1176, and Re = 2.855×105 (based on chord length of the baseline model) which amounts to a freestream velocity of 40 m/s. Freestream was assigned standard sea level conditions that is, ambient pressure (P∞ ) = 101,325 Pa, and Temperature (T∞ ) = 288 K. Flow variation pertaining to varying α was obtained by rotating the domain about the x-axis (Fig. 3a) and keeping the geometry fixed. For g/c = 0.3 to 1.0, and 2.0, α was varied between 0◦ to 50◦ at an increment of 5◦ with an additional simulation at 53◦ . Moreover, for comparative purposes, simulations pertaining to g/c = 1.1, 1.2, and 1.3 were performed for 0◦ to

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15◦ only, at intervals of 5◦ . Notably due to the varying c values, Re for the various geometries varied between 7.1 × 104 for g/c = 2.0 to 4.76 × 105 for g/c = 0.3, which are typically below the critical Re value for flow over a flat plate. Hence, the results can be considered to be corresponding to qualitatively similar flow conditions. Non-dimensionalization of the forces related to a particular geometry was carried out by using chord length, and single planar member projected area of the respective variant as the reference length and reference area, respectively.

3 Results and Discussions 3.1 CFD++ Validation Validity of the numerical results for the particular flow conditions was ascertained through comparison between the aerodynamic coefficient data obtained experimentally [43] and the numerically obtained data. This comparison was carried out between the data corresponding to: 1. grid fin of g/c = 0.5 (baseline model) 2. planar fin of A R = 2.0 (Fig. 5). Notations used for data corresponding to the respective variants are described in Table 1. Deviation between the experimental and numerical results were evaluated by taking angle-wise difference between the lift and drag coefficient values, and dividing them by the maximum value of the experimentally obtained result for the specific force coefficient. Further clarification related to this method can be obtained from [47]. As seen in Fig. 8a, coefficient of lift (CL ) results were within 11% for the GF_GC0.5 case, whereas it was found to be within 15% for the PF case. The larger value for PF can be associated with the lower maximum value of CL . Stall angle is also found to be efficiently captured by the numerical solutions. In the case of drag coefficient (CD ), error was within 9 and 7% for GF_GC0.5 and PF cases, respectively. Reasons pertinent for the palpable deviation between the numerical and experimental results can be attributed to:

Table 1 Validation plot notations Symbol Notated value GF_GC0.5Exp GF_GC0.5Sim PFExp PFSim

Experimental results for grid fin with g/c = 0.5 Simulation results for grid fin with g/c = 0.5 Experimental results for planar fin Simulation results for planar fin

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2

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Exp

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GF_GC0.5

Exp

GF_GC0.5Sim

Coefficient of drag, CD

Coefficient of lift, CL

Exp

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(a) Lift coefficient comparison with experimental value

1.5

GF_GC0.5Sim PF

Exp

PFSim 1

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0 0

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50 40 30 20 Angle of attack, α (in deg)

60

(b) Drag coefficient comparison with experimental value

Fig. 8 Solver validation by comparison with experimental results [44]

• Differences arising due to smoothness of the simulated geometry compared to the rough surface of the tested model • Numerical inaccuracies related to space and time based mathematical modeling of real continuum flows. • Lack of transition model for laminar to turbulent flow transition • Imposition of the symmetry boundary condition. . Despite these differences, the numerical results were within acceptable deviations for the two geometries. Hence, the same mesh and solver configurations were appreciated to be valid for carrying out simulations for similar geometries with the same flow conditions, and within the particular α range. Before proceeding on to the analysis pertaining to comparison between grid fins of different g/c, Fig. 8a, b have been used to draw a preliminary comparison between the aerodynamic performance of grid fins and planar fins. Lift is found to be higher for grid fin at all angles due to its multi-planar geometry (Fig. 8a). Moreover, stall angle is significantly higher at α = 30◦ compared to the planar fin (α = 20◦ ). Additionally, post-stall drop in lift is smoother for grid fin compared to the conventional fins. Thus, grid fins present a tangible improvement in its high α lifting characteristics, establishing their ability to provide elevated manoeuvrability to a flight vehicle they get affixed upon. Notably, the smooth stall characteristic of planar fin in Fig. 8a can be linked to its smaller span leading to alleviated flow separation due to the presence of increased influence of wing-tip vortices for lower A R [56]. Drag (Fig. 8b) is significantly higher for grid fin due to higher skin friction drag and pressure drag linked to increased number of plates and leading edge flow separation, respectively. Thus, increased lift at higher angles and improved stall performance for grid fins are acquired at the cost of drag advancement. This reasserted the need to carry out further analysis to alleviate this shortcoming, and hence improve its applicability.

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5 4

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Fig. 9 Aerodynamic efficiency comparison of grid fin against planar fin

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Based on these coefficients, a concerted comparison between the aerodynamic efficiency (CL /CD ) of planar and grid fins carried out in Fig. 9 displayed an average decrement of ≈15% through all the angles for grid fin. In-fact this reduction was calculated to be ≈24.3% within the most operable α (α = 5◦ − 15◦ ) region. This efficiency reduction can be linked to the higher drag values for grid fins observed earlier. However, at higher angles, efficiency displays tangible convergence for the two variants. Thus, aerodynamic efficiency of grid fins remain comparable to planar fins alongside improved stall angle. Notwithstanding the better performance at high angles of attack, reduced aerodynamic efficiency of grid fins in the most operable α region, establishes the need to study the impact of different geometrical parameters on grid fin efficiency, which would assist in accomplishing an optimum grid fin geometry based on lift, stall angle, and aerodynamic efficiency requirements. As a part of the same study, analyzing the aerodynamic impacts of chord variation while keeping the gap constant has been carried out in this paper, discussed in the succeeding sections. This parameter has been non-dimensionalized by using the g/c parameter (commonly employed for the analysis of such geometry [47]). It is noteworthy that, span (b) was also varied along-with c such that, A R retained the same value of 2.0 for all grid fin variants.

3.2 Aerodynamic Coefficient Comparison for Different g/c As elaborated earlier, current study carries out numerical evaluations for different g/c variations by varying the chord and retaining the same A R (A R=2.0) and compares them against a planar fin (PF) of A R = 2.0. Lift coefficient and stall angle are found to be higher for all grid fin variants compared to PF. CL is seen to be increasing as g/c increases (chord reduces). Difference

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between the successive g/c variant reduces at lower chords. The trend linked to g/c = 2.0 displaying a sudden dip in lift at α = 10◦ leading to lower lifting forces compared to g/c = 0.6 − 1.0 up to 40◦ is due to the same trend. Thus, after a certain g/c value, this increase seizes, and hence we achieve reduced lifting performance for higher g/c. Interestingly, stall angle is similar for all the variants. This is contrary to the results as obtained by the authors in Ref. [47], wherein, it had been established that lower g/c attained by reducing gap and retaining the same chord leads to reduced lift but delayed stalling. Thus, it can be established that, chord variation has minimal impact on the stall angle of the grid fins. Moreover, post-stall behavior relating to gradual drop in lift is also similar for all the variants. Although, minimal improvement can be asserted for higher g/c. Thus, high α lifting characteristics remain similar for different chord variants. However, lift availability increases as chord reduces. The flow-physics associated with these trends shall be addressed in a later section, while describing the pressure coefficient and the flow field visualisation results. Comparison in Fig. 10b, presents higher CD for higher g/c. It is to be noted that, span variation to retain the same A R leads to lower span for higher g/c. Thus, the grid fin with the lower chord (greater g/c) and narrower span presents higher drag force. Thus, a more compact geometry, in-spite of its smaller surface area, presents higher drag. It is noteworthy that, drag at such low Re is attributed to the presence of skin friction and pressure drag. Moreover, it has been established [57] that, for a blunt geometry, drag is mainly effected by pressure drag related to flow separation. Thus, higher g/c variant leads to higher pressure drag, and hence the higher CD values for the compact variant. This inference shall be backed up by pressure coefficient analysis and flow visualisation study later in the paper. The ratio of lift and drag coefficients is seen to be lower for higher g/c. Thus, the increase in drag is more compared to lift advancement for higher g/c leading to reduced efficiency for higher g/c. Moreover, efficiency of the grid fins approach that of the PF as g/c lowers. It is noteworthy that, the impact of g/c variation on the overall aerodynamic efficiency is found to be significantly high when chord is the varying parameter, whereas the deviation was subtle when gap was the varying parameter in Ref. [47]. Thus, this study establishes the significant impact of chord on the overall aerodynamic efficiency, and hence can be a very helpful tool for a control surface designer while selecting the final c value for optimising efficiency and maximum lift. Diligent comparison of the lift versus α curve slope (CLα ) can provide qualitative information about the aerodynamics of control surfaces, and hence has been used as a tool to compare the control performance of different grid fin variants. In Fig. 11a, the same has been evaluated for different g/c variants below α = 10◦ (assuming linear variation). Notably, additional evaluations were carried out for g/c = 1.1, 1.2, and 1.3 for α = 0◦ to 15◦ in order to comprehensively compare their slopes within this range. This was carried out to validate the trend associated with the sudden dip in C L for g/c = 2.0 observed earlier. The results present increase in slope as g/c increases. However, a sudden dip in the slope can be discerned beyond g/c = 1.0. Thus, CLα enhancement by virtue of chord reduction is delimited up to g/c = 1.0, after which

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Fig. 10 Variation of aerodynamic coefficients with angle of attack for different g/c

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(b) Variation of aerodynamic efficiency with different g/c for different angles of attack

Fig. 11 Variation of lift slope and aerodynamic efficiency for different g/c at several angles of attack

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it starts reducing. This analysis can be a useful tool for grid fin designers based on the limiting range of chord reduction for lift enhancement. Following inferences can be established by analyzing the aerodynamic efficiency at angles of attack 5◦ , 10◦ , and 15◦ for different g/c presented in Fig. 11b: • Efficiency reduces as g/c increases (chord reduces), which was observed earlier in Fig. 10c due to drag advancement. • Maximum efficiency is found to be present at α = 10◦ , and hence can be considered the best operating angle. • Efficiency is found to be lowest at α = 5◦ for g/c = 0.5 and beyond, which reaffirms aerodynamic performance deterioration for lower chords even at such lower angles of attack.

3.3 Aerodynamic Performance Deviation for Different g/c in Relation to the Baseline Model To further assess the effect of varying chord over the performance of grid fins, a concise comparison was carried out by comparing the gain in maximum lift coefficient (Fig. 12a), and average efficiency deviation (Fig. 12b) for different g/c grid fin variants against the baseline model (GF_GC0.5) which is indicated by the dot dashed line in these figures. The figure tangibly illustrates gain in maximum lift and reduction in the efficiency as chord reduces. Appropriate diligence of these results can further comprehend the application based constraints on chord variation for grid fins. Lift slope at lower angles which would govern the controllability of the control surface increases for the lower chord variant at the expense of aerodynamic efficiency reduction.

Fig. 12 Variation of maximum lift coefficient and aerodynamic efficiency with different g/c

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Thus, a grid fin with wider span and chord geometry would present a more efficient design with regards to the aerodynamic efficiency parameter, which can lead to reduced fuel consumption or increased payload carrying capacity. This would lead to increased application based advantages for a wider chord grid fin. However, a wider chord control surface necessarily dictates elevated hinge moment requirements. Hence, chord selection requires further optimization based on aerodynamic efficiency, lift availability as well as the hinge moment constraints. In order to qualitatively assess the underlying flow-physics related to the aforementioned trends, further analysis using the pressure coefficient (CP ) plots and flow field visualisation using the velocity contour distribution was carried out in the succeeding sections.

3.4 Pressure Coefficient Comparison An approach towards elucidating the underlying flow-physics involves examination of the CP distribution. Since, the flow involved is a subsonic flow, wherein the contribution of pressure drag is found to be significantly higher compared to the skin-friction drag, this approach can greatly assist us in comprehending the physics leading to drag and lift variations. Since, M corresponding to the flow being examined resides in the low subsonic speed regime (M < 0.2), the flow can conveniently be considered an incompressible flow. Hence, formula for calculating CP is given by Eq. 6. CP =

p − P∞ 1 2 ρU∞ 2

(6)

Here, p is the local static pressure, P∞ is the freestream static pressure, ρ and U∞ are the freestream density and velocity values, respectively (described earlier). In Fig. 13, CP has been plotted along the chord length of different planar members (also called as simply ‘members’) at the midspan location (Fig. 3a) for α = 5◦ , 15◦ , and 20◦ . Distance along the chord was non-dimensionalized (x/c) by dividing the chordwise distance (x) by the respective variants chord (c) value. The naming scheme implemented to describe the associated results follows the terminology described in Table 2. For instance, L1_g/c = 0.4 notates, distribution along the lower surface of Member 1 for the grid fin of g/c = 0.4. The member surfaces can be categorized as cascaded surfaces and non-cascaded surfaces. Cascaded surfaces (L1, U2, L2, U3) are the ones surrounded by neighboring members, whereas non-cascaded surfaces (U1 and L2) are exposed to the freestream flow. Flow corresponding to α = 5◦ , is characterised by lowered flow separation for all the members. Although, bluntness of the leading edges lead to leading edge flow separation for all the members (Fig. 13a–c). This is indicated by the instant lowering of CP for all the surfaces at their leading edges. Apparently, bluntness leads to the formation of wake region behind the leading edges leading to reverse flow, and hence the lowered pressure value. The lowering is mitigated for lower surfaces

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Fig. 13 Pressure coefficient distribution comparison across different members of varying g/c at several angles of attack Table 2 Naming scheme for pressure distribution plots Naming scheme Description of the naming scheme A P_g/c = X X

A symbolizes the upper and lower surfaces of the respective members by L and U, respectively P is the number corresponding to the member varying as 1,2 or 3 according to the Member number shown in Fig. 2 g/c = X X represents the g/c variant with X X representing the g/c value

indicating reduced leading edge separation which is in-sync with the known physics. Although, as flow approaches further downstream, separation region reduces, leading to increase in pressure. However, CP increment for upper surfaces of all the members is found to be slower for g/c = 0.7. Thus, higher g/c amounts to reduction in the rate of leading edge flow separation deterioration. Hence, the reduced increment of pressure for higher g/c variant would emphasize its increased drag value at lower angle, which was established earlier in Fig. 10b. Despite these variations, due to meagre differences with respect to flow separation at such low angles, the underlying deviations for different g/c at such low angles is considerably small.

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As α increases to 15◦ , Fig. 13d–f demonstrate absence of leading edge flow separation over the lower surfaces. However, flow separation is higher on the upper surfaces due to the enhanced wake region close to the leading edge corners. In-fact for non-cascaded upper surface (U1) as seen in Fig. 13d, flow becomes fully separated, which is indicated by the presence of constant chordwise pressure distribution. A fully separated flow leads to the formation of a wake across the whole chord leading to the main flow becoming independent of the freestream flow. This leads to the formation of a near constant negative pressure distribution along the upper surface. Notably, this angle is close to the stall angle of conventional fins. Hence, due to the lack of cascading, the uppermost member stalls indicated by the presence of constant CP distribution along its surface. Notably, CP distribution for non-cascaded surfaces is comparable for both the g/c variants. However, CP distribution along the cascaded lower surfaces (Fig. 13e, f) display increased reduction of CP along x/c for lower g/c. This indicates the higher velocity acceleration for lower g/c (increased c value). The trend associated with gradual CP increment for lower g/c along x/c for the upper surface flow (as observed earlier for α = 5◦ ) was discernible at this angle also. The elevated reduction in lower surface CP and the steeper increment in CP over the upper surfaces of lower g/c grid fins lead to reduction in the overall pressure differential, and hence the lowering of lift for lower g/c grid fins (as observed earlier in Sect. 3.2). Similarly, the gradual CP recovery for the higher g/c variant indicates higher pressure drag. This accounts for the elevated drag level for higher g/c as established in Fig. 10b. Similar deviation with respect to steeper decrement in CP values along x/c for the cascaded lower surfaces (Fig. 13h) in comparison to non-cascaded lower surface (Fig. 13i) can be delineated at α = 20◦ also . Moreover, CP advancement was again slower for higher g/c. Thus, these plots explain the reasons leading to increased lift and drag for higher g/c. It is also to be observed that, deviation between the two variants for the lowermost member U3 is less prominent compared to the differences related to CP distribution over U2. It has been established earlier by the authors in Ref. [49], that this member stalls second after stalling of the uppermost member, which ultimately determines the overall stall angle of the grid fin. Hence, the presence of similar CP variation for the lowermost member of different chord, accounts for their similar stall angle and post-stall behaviour.

3.5 Flow Field Visualization Using Velocity Contours Qualitative understanding with respect to the aforementioned flow-physics can be accomplished through implementation of flow-field visualisation methods. In this section, the same was carried out by comparing the contours pertaining to the longitudinal velocity component across grid fins at their respective mid-span locations in Fig. 14 for different angles of attack and g/c. Assessment of the magnitude of this component eventually indicates the amount of flow separation across a lifting mem-

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Fig. 14 Velocity contour distribution for different g/c variants at midspan location for various angles of attack

ber. It is noteworthy that, flow separation region using this method can be recognised by the presence of a region consisting of negative velocity distribution. Bluntness of the planar members lead to flow separation at the leading edges for all the members of all g/c variants (Fig. 14a–l). Moreover, for a particular g/c variant, the amount of flow separation increases as α increases. This separation is maximum for the uppermost member, indicating its first-most tendency to stall. Although, for the lower members, flow separation region is significantly smaller at higher angles compared to the uppermost member. This results in the delayed stall characteristic of grid fins. Differences between the various variants at low angles of attack is small (Fig. 14a, d, g, j). Although, as α increases, disparity associated with flow between the planar members becomes more appreciable. This is indicated by the reduction in velocity between the members for higher g/c variants (Compare Figs. 14b, e, h, k or 14c, f, i, l). This again indicates the presence of higher drag between the members

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for the grid fin with higher g/c leading to reduced velocity between their members. This leads to increased drag values for higher g/c as mentioned earlier. It was also noted that, size of the separation bubble remained similar for the lifting members at same angles for various variants. This again explains the similar stall angle and post-stall characteristic for different g/c variants (when c is the varying parameter). This analysis further reaffirmed the presence of higher drag values for higher g/c when chord is the varying parameter. Furthermore, stall angle similarity was also affirmed through this analysis. Lowering of aerodynamic efficiency alongside increase in the maximum lift coefficient for increased g/c were the main observations during this study. Hence, chord selection would require optimization based on lift, efficiency requirements, and the associated hinge moment liabilities.

4 Conclusions The paper discusses the impact of gap-to-chord ratio (g/c) variation on the flowdynamics of grid fins by virtue of chord variation while retaining the same aspect ratio. The analysis is carried out by performing steady state numerical simulations in the subsonic regime for high angles of attack. Some of the prominent inferences drawn out from the study were as follows: • The solver has been validated against experimental results available in the literature for similar flow conditions and same angle of attack (α) range. • Chord reduction (increasing g/c) leads to increase in the lifting performance up to a certain bounded g/c, beyond which the lift starts reducing as g/c increases. • Aerodynamic efficiency reduces as the g/c increases due to drag increment. Thus, a more compact geometry with smaller chord and span would generate greater drag forces leading to efficiency reduction. • Variation of g/c by virtue of chord alterations, has minimal impact on the stall angle, and a more significant impact on the maximum lifting force and aerodynamic efficiency of the fins. • Through elaborate comparison carried out for pressure coefficient distribution and velocity contour plots across the different planar members of grid fins, the underlying rudimentary flow-physics associated with these trends were explained. • A grid fin designer can use this analysis for chord selection based on aerodynamic efficiency requirement and lift availability. Additional consideration with respect to hinge moment requirement would also be a criteria for chord selection. • Further research pertaining to detailed comparison between gap and chord variation impacts would lead to a greater understanding with respect to their role on grid fin aerodynamics. This can be collated with studies related to other geometrical parameters like aspect ratio, etc. to determine the most optimum grid fin geometry based on maximum lift, stall angle and aerodynamic efficiency requirements.

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Numerical Investigation on the Effect of Propeller Slipstream on the Performance of Wing at Low Reynolds Numbers K. Shruti and M. Sivapragasam

Abstract The flow over a flat plate airfoil with 5-to-1 elliptical leading and trailing edge at Re = 80,000 and for different angles of attack (0°–15°) is numerically investigated by solving the Reynolds-averaged Navier–Stokes equations. The k − ω shear stress transport equation, γ − Reθ turbulent transition model is used to address the effect of laminar-turbulent transition. The present computed aerodynamic forces are compared with the available experimental data for validation. Large flow separation and a single recirculation zone is found at higher angles of attack. The study is extended to investigate the laminar separation bubble effect on a three-dimensional Zimmerman wing planform for Re = 50,000; 100,000 and 150,000 at different angles of attack. The present results agree well with the available experimental and computational data. The influence of propeller on the aerodynamic performance of a Zimmerman wing planform is investigated. The results show that the wing with propeller configuration has lower C D values compared to wing alone case. The results presented in this paper show the importance of modelling the propeller slipstream effects on the aerodynamic characteristics of low aspect ratio wing. Keywords Micro air vehicles · Low Reynolds numbers · Aerodynamic characteristics · Propeller slipstream

K. Shruti (B) · M. Sivapragasam Department of Automotive and Aeronautical Engineering, Faculty of Engineering and Technology, M. S. Ramaiah University of Applied Sciences, Bangalore 560058, India e-mail: [email protected] M. Sivapragasam e-mail: [email protected] K. Shruti Centre for Civil Aircraft Design and Development, CSIR-National Aerospace Laboratories, Bangalore 560017, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_9

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1 Introduction Micro air vehicles (MAVs) are asserting their impact in the modern aerospace industry due to their wide range of applications. The recent interest in micro air vehicles has motivated to study the aerodynamic performance of MAVs operate at Reynolds numbers ranging from 104 to 105 . The key parameters of MAV are maximum dimension less than 15 cm, operating range of 10 km and average endurance of about 30 min [1]. At such low Reynolds numbers, the viscous effect dominate the flow and has a tendency to separate even at mild adverse pressure gradients leading to laminar flow separation, transition and perhaps reattachment, leading to the formation of a laminar separation bubble. Due to this phenomenon the aerodynamic characteristics are deteriorated. Experiments on the aerodynamic characteristics of flat plate with 5-to-1 elliptical leading and trailing edge and on low aspect ratio wings at the low Reynolds numbers were done by Pelletier and Mueller [2]. Only a few experimental studies have been conducted on the LSBs with 3D characteristics, while experiments on the 2D wing section with the endplates have been investigated by many researches. Lain and Shyy [3], indicated the transition can occur at Re > 104 , and therefore a transition model is essential to capture detailed flow features. However, very little data exist on the investigation of Laminar Separation Bubble (LSB) for fixed low-aspect-ratio wings in this Reynolds numbers range. Brandt and Selig [4], had performed many experiments on series of propeller performances and characteristics. Propeller slipstream influence on wing aerodynamics at Re = 40,000 was studied experimentally by Makino and Nagai [5]. Sudhakar et al. [6], had performed surface flow topology on the surface of MAV wing at propeller-on and off condition. At propeller-off condition, the symmetry flow patterns was observed on the wing. More recently, experimental studies on propeller effects on wings at Re = 50,000–300,000 were presented by Ananda et al. [7]. However, data for low aspect ratio (AR) wings relevant to MAVs are sparse in the literature. Thus the study of aerodynamics at low Reynolds numbers becomes pertinent and this is the main inspiration to carry out the present work. In this paper, the aerodynamic characteristics of a flat plate airfoil with 5-to-1 elliptical leading and trailing edge with thickness-to-chord ratio 1.93% is numerically computed at Reynolds number (Re = 80,000) for different angles of attack (α = 0°– 15°), and the study is extended to three-dimensional Zimmerman wing planform with AR = 2. Later a propeller is attached ahead of the Zimmerman wing planform to study the aerodynamic characteristics. The choice of the flat plate, wing planform and the study at these Reynolds numbers, angle of attack was motivated by the availability of the published results. The 3D computations are performed for Re = 50,000; 100,000 and 150,000 at various angles of attack (α = 0°, 4° and 8°). The comparison between wing alone and wing with propeller configuration is studied to understand the propeller slipstream effect on the aerodynamic characteristics, flow behavior and span wise lift distribution. These factors alter the performance of MAVs and these are key factors to design a MAV.

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Fig. 1 Cross-section of flat plate airfoil

2 Geometric Details and Numerical Model 2.1 Geometric Details For current numerical investigations, a thin flat plate airfoil is selected as shown in Fig. 1. Geometric details are inferred from the available experiments of Pelletier and Mueller [2]. The flat plate was designed to have a 5-to-1 elliptical leading and trailing edge, chord of 100 mm, thickness-to-chord ratio 1.93%. The Re based on freestream velocity and chord length was 80,000.

2.2 Numerical Model The Reynolds-averaged Navier Stokes equation are solved numerically using commercial finite-volume method based ANSYS FLUENT software. An approach to determine laminar-turbulent transition is to use transition SST model which is available in FLUENT. Menter’s k − ω shear stress transport (SST) model is used for the turbulence closure with the γ − Reθ transition model. The model consists two additional transport equations, intermittency (γ ) and momentum thickness Reynolds number (Reθt ). γ − Reθ model typically correlates the transition momentum thickness Reynolds number to local freestream conditions such as freestream turbulence intensity and pressure gradient [8]. Default model constants are used for all the computations, as they are capable of capturing the transition. Spatial discretization was done using second order upwind scheme. The pressure–velocity coupling was achieved by coupled scheme. All computations were performed in double-precision arithmetic.

2.3 Mesh Details ANSYS ICEM-CFD software is used to generate a structured mesh around the flat plate airfoil and wing planform. To minimize the far field boundary condition effects, the domain is set at 10c upstream, 20c downstream, upper and lower boundaries are placed at 10c, with all the distance considered from airfoil leading edge, where c is the airfoil chord length. Total number of grid points used for computations are

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15

0.04

10

0.02

y/c

y/c

5 0

0 -0.02 -5 -0.04 -10 -10

-5

0

5

10

15

20

-0.04

-0.02

0

x/c

x/c

(a)

(b)

0.02

0.04

Fig. 2 Mesh around flat plate airfoil and near the leading edge

42,412. Enough care is taken while generating the mesh and it is ensured for the application of transition model, the average y+ value should be of the order 1. The mesh around the flat-plate airfoil and mesh near leading edge is shown in Fig. 2.

2.4 Boundary Conditions Velocity inlet and pressure outlet boundary conditions are applied at the domain upstream and downstream respectively. The wall boundary condition was imposed on airfoil upper and lower surfaces which enforces no-slip, no-penetration of the fluid on the airfoil surfaces. At the domain inlet, velocity was calculated using corresponding to Re = 80,000. The turbulence intensity of 0.05% was used for this investigation.

2.5 Grid Independence Study Grid Independence Study was done for both 2D and 3D case. Enough care was taken in generating a good quality mesh. The number of grid points for computations was selected after careful grid independence study. For a 2D case, this study was done at Re = 80,000 at α = 4° with three grids g1 with 19,754 (fine grid), g2 with 42,414 (medium grid) and g3 with 82,854 (coarse grid) grid points. The Grid Convergence Index (GCI) was calculated for Cl and Cd , the results are summarized in Table 1. g2 grid had reasonably low value of discretization error and the same was used for all the present computations.

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Table 1 Grid independence study Re = 80,000 at α = 4° Grid

No. of grid points

Cl

GCI for Cl

Cd

GCI for Cd

g1

19,754

0.4243

0.039

0.0346

4.048

g2

42,414

0.4204

g3

82,854

0.4203

0.0306 0.002

0.0298

1.007

Fig. 3 Comparison of Cl and Cd with experiment data

2.6 Aerodynamic Coefficients A series of 2D simulations were carried out for a flat plate airfoil. The lift and drag coefficients at Re = 80,000 at different angles of attack (α = 0°–15°) respectively. The 2D simulations are compared with the experiment data of Pelletier and Mueller [2]. The numerical results show good agreement with the experimental data until α = 8°. The aerodynamic coefficients are shown in Fig. 3. At higher angles of attack, aerodynamic coefficients are slightly low when compared to experimental data. This is because during experiment at the 2D sectional wing, Pelletier and Muller [2] found that endplates can lead to an increase in Cd . Menter’s transition SST model is not able to capture the flow behavior at higher angles of attack. However, the computational values are within the uncertainty range which was provided by Pelletier and Mueller [2].

2.7 Flow Structure Over Flat Plate At α = 0°, the flow remains attached on both the upper and lower surfaces of the airfoil. In the low α range, α = 2° the flow structure is dominated by leading edge

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separation, which enlarges gradually as the angle of attack increases. At α = 4°, a very small separation region is present near the leading edge. At α = 6° the leading edge separation bubble dominates the flow structure. At higher angles of attack α = 10°–15°, a large recirculation zone is seen on the airfoil upper surface. At α = 15°, the single very large recirculation zone is formed on the airfoil upper surface. The streamlines over the airfoil at α = 0°–15° is shown in Fig. 4. The numerical results of flat plate airfoil presented in this section provided confidence with the numerical simulation methodology to handle complex flow problems

α = 0°

α = 2°

α = 4°

α = 6°

α = 8°

α = 10°

α = 12° Fig. 4 Streamlines over the airfoil at α = 0°–15°

α = 15°

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involving LSB. In the next section, the numerical computations on the wing alone and wing with propeller configuration are presented to understand the aerodynamic characteristics and behaviour of flow.

3 3D Computations 3.1 Geometric and Mesh Details The Zimmerman wing geometric details are inferred from the experimental studies of Torres and Mueller [9]. The wing section profile remains same as in the 2D study. The wing has zero camber, thickness-to-chord ratio (t/c) of 1.96%, root chord of 0.25 m, wing span of 0.44 m and mean aerodynamic chord of 0.189 m. The Re selected for the present computations was 100,000. For the same planform an APC Slow-Flyer propeller was installed. Based on the experiments conducted by Brandt and Selig [4], the APC Slow-Flyer had good performance characteristics and a 10 × 4 [10] propeller was selected for the present computations. This propeller was installed 0.044 m ahead of the wing leading edge, with the disk enclosing the propeller of diameter 0.212 m. Propeller rotates in anti-clock wise direction when viewed from front. For the present investigation, the rotational speed of propeller is set from 540 rad/s (10,000 rpm) to 1626 rad/s (15,527 rpm). ANSYS ICEM-CFD is used to generate structured grid. The C-H mesh topology is used for 3D grid generation. For wing with propeller configuration a multi-block strategy was employed. This structured mesh contains two domains, a circular domain which encloses the propeller and a C-H outer domain containing the wing. Total number of grid points used for computations for wing alone case was 1,630,438 (for half wing) and for wing with propeller configuration was 3,767,830. Figure 5 shows the mesh on the wing alone and on wing propeller configuration.

3.2 Boundary Conditions The wall and farfield boundary conditions are similar with the 2D case as mentioned earlier. To minimize far field boundary effects, the far field domain is set at 10c upstream, 20c downstream, upper and lower boundaries are placed at 10c, with all the distances being from the wing leading edge. Here c is the mean aerodynamic chord. Along the span wise direction the domain extent was set at one span length. A symmetry boundary condition is imposed at the wing root, simulating the wing with an AR = 2. At the symmetry plane, 3D mesh resembles the mesh which was generated for the 2D case. For the wing with propeller combination, boundary conditions remain same as that discussed for wing alone case. However, symmetry boundary condition cannot be

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Fig. 5 Mesh on the wing

applied due to the presence of the propeller. The full wing planform was simulated. Interface boundary condition was imposed on the disk surrounding the propeller. Wall boundary condition was applied on the propeller blades.

3.3 Grid Independence Study Grid independence study was performed at α = 4° for Re = 100,000. For grid independence study three grids G1 with 820,480 points, G2 with 1,630,438 points and G3 with 3,138,842 cells were used. The Grid Convergence Index (GCI) was calculated for C L and C D , and the results are summarized in Table 2. G2 grid had the reasonably low value of discretization error and the same was used for all present computations. The wall y+ value was ensured to be less than 1 for all the computations.

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Table 2 Summary of GIS Re = 100,000 α = 4° Grid

No. of Grid Points

CL

GCI for C L

CD

GCI for C D

G1 G2

820,480

0.1701

0.1501

0.0166

1.1643

1,630,438

0.1717

G3

3,138,842

0.1719

0.0165 0.0171

0.0164

0.7520

3.4 Results and Discussion 3.4.1

Aerodynamic Coefficients

Numerical computations for Zimmerman wing alone and wing with propeller configuration were carried out for Re = 50,000; 100,000 and 150,000. The study is performed at α = 0◦ , 4◦ and 8◦ . The present computational results agree well with experimental data of Torres and Mueller [9] and an excellent agreement with the computational data of Chen [11]. The results are shown in Fig. 6. The present computational results are within the experiment uncertainty range (10% for lift and drag) [2]. The aerodynamic performances in terms of C L and C D at various angles of attack is computed for three different Reynolds numbers. Typical results are presented for Re = 50,000 and shown in Fig. 7. Figure 7a, shows the lift coefficients of both wing alone and wing with propeller. The lift coefficient is higher for wing-alone case when compared to wing-with propeller at a given α. The lift coefficient for wing at α = 4° is 0.1689 and for wing-with propeller it is 0.1060. This is because in the wing-alone case, larger LSB occupies the upper surface of the wing which contributes to C L enhancement. In wing-with propeller case, the LSB is washed out due to propeller slipstream effect.

Fig. 6 Comparison of C L and C D with experiment data, Re = 100,000

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Fig. 7 Comparison of aerodynamic coefficients for wing alone and wing with propeller configuration, Re = 50,000

Figure 7b, shows the drag coefficient. The propeller slipstream effect has a large impact on the C D values. At α = 4°, the wing-alone has C D = 0.0186 and for wing-with propeller is 0.0297, which is 111 drag counts higher.

3.5 Pressure Distribution The pressure contours on the wing alone and wing with propeller is shown in Fig. 8. The pressure distribution is different for wing alone and wing with propeller configurations. The flow field is symmetric about the x–y plane for the wing alone case. However, for wing with propeller, asymmetric flow behavior is observed due to the effect of propeller slipstream. The pressure is more on the right-side wing due to the direction of the propeller blade rotation. The bubble is reduced with the wing

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Y X

Y

Z

X Z

Cp:

-1.27 -0.805 -0.34

0.125

0.59

Fig. 8 Pressure contours for wing alone and wing with propeller configuration

propeller case, due to the propeller flow and the bubble becomes asymmetric which triggers a side force. Figure 9 show the C p distribution at z/b = 0.2 for wing alone and wing with propeller case at α = 4° for Re = 50,000. The peak suction pressure is low for wing alone case and higher for wing with propeller. Due to propeller slipstream effect the wing with propeller configuration produces negative lift coefficients from z/b = (0 to −0.2). The separation region is found to be more for the wing alone when compared to wing with propeller. -4

Fig. 9 C p distribution at z/b = 0.2, α = 4° for wing alone and wing with propeller

Wing alone Wing with propeller

-3 -2

Cp

-1 0 1 2 3 4

0

0.2

0.4

x/c

0.6

0.8

1

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3.6 Flow Structure on Wing Planform The 3D flow becomes very complicated and it needs a better understanding than 2D flow structures. As per the topological rules by Tobak and Peake [12] we assume that the body is simply connected and immersed in a flow that is uniform far upstream. The topological rule is given by Eq. 1.  N − S = 2

(1)

where N = Nodal points. S = Sadal points. A detailed flow topology analysis is performed and the critical points on the wing surface were identified and were found to satisfy Eq. 1. The flow structure on the wing differs when compared between wing alone and wing with propeller case. However, both the flow structure satisfy the topological criteria of Tobak and Peake [12]. The flow structure on the upper surface of wing alone and wing with propeller is shown in Fig. 10.

Fig. 10 Flow structure on the upper surface on the wing alone and wing with propeller

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4 Conclusion Numerical computation was carried out for a flat plate with 5-to-1 elliptical leading and trailing edge at Re = 80,000, for different angles of attack. The behaviour of aerodynamic characteristics were evaluated. The numerical results were compared with the experimental data of Pelletier and Mueller [2]. The laminar separation bubble (LSB) formation on the airfoil were investigated. As α increases the LSB increases in both length and thickness on the airfoil upper surface. Different flow modes were captured for different angles of attack and a large recirculation zone was observed at higher angles of attack. Zimmerman wing alone computations were performed for various Reynolds number and for several angles of attack. The computational results are validated with the experiment data of Torres and Mueller [9] and with the computational data of Chen [11]. The Zimmerman wing has better aerodynamic coefficients. The flow structure on the upper and lower surface of the wing is qualitatively represented and the parameters of flow topology were discussed. The Zimmerman wing with the propeller combination is computed to study the effect of propeller slipstream on the wing. LSB is formed on the upper surface of the wing, due to propeller slipstream effect the aerodynamic coefficients are altered. This leads to decrease in C L and increase the C D . Propeller rotation alters the sectional Cl distribution this leads to negative lift coefficient from z/b = (0 to −0.2). The present study was based on the Zimmerman planform since many MAVs employ this wing. It would be of fundamental and practical value to also study the aerodynamic characteristics for other planforms as well. Further, in the present paper we noticed that the propeller slipstream had some benefits in C D . However, the lift-todrag ratio of wing with propeller configuration was poorer. This fact would motivate one to perform an optimization study including the propeller slipstream effects to achieve enhanced aerodynamic characteristics for the objective functions.

References 1. Mueller TJ, DeLaurier JD (2003) Aerodynamics of small vehicles. Ann Rev Fluid Mech 35:89– 111 2. Pelletier A, Mueller TJ (2000) Low Reynolds number aerodynamic of low-aspect ratio, thin/flat/cambered-plate wings. J Aircr 37(5):825–832. https://doi.org/10.2514/2.2676 3. Shyy W, Lain Y, Tang J, Viieru D, Liu H (2008) Aerodynamics of low reynolds number flyers. Cambridge University Press, New York 4. Brandt JB, Seling MS (2011) Propeller performance data of low Reynolds numbers, 49th AIAA aerospace sciences meeting, pp 1–8 5. Makino F, Nagai H (2014) Propeller slipstream interference with wing aerodynamic characteristics of mars airplane at low reynolds number. In: AIAA, 52nd aerospace sciences meeting 6. Sudhakar S, Chandankumar A, Venkatakrishnan L (2017) Influence of propeller slipstream on vortex flow field over a typical micro air vehicle. Aeronaut J 121:95–113. https://doi.org/10. 107/aer.2016.114

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7. Ananda GK, Selig MS (2018) Experiments of propeller-induced flow effects on a low-reynoldsnumber wing. AIAA J 8. Menter FR, Langtry RB, Likki SR, Suzen YB, Huang PG, Volker S (2003) A correlation-based transition model using local variables-part 1: model formulation. J Turbomach 128(3):413–422. https://doi.org/10.1115/1.2184352 9. Torres GE, Mueller TJ (2004) Low-aspect ratio wing aerodynamics at low reynolds numbers. J Aircr 43(5):865–873. https://doi.org/10.2514/1.439 10. Deshpande MD, Sivapragasam M, Umesh S (2014) Air suction system for chemical senor for MAV applications. In: Compendium on advances in micro air vehicles in India, National Design and Research Forum 11. Chen ZJ (2014) Micro air vehicle design for aerodynamic performance and flight stability, Ph.D. Thesis, The University of Sheffield, UK 12. Tobak M, Peake DJ (1982) Topology of three-dimensional separated flows. Annu Rev Fluid Mech 14:61–85

Theoretical Design and Performance Evaluation of a Two-Ramp and a Three-Ramp Rectangular Mixed Compression Intake in the Mach Range of 2–4 Subrat Partha Sarathi Pattnaik

and N. K. S. Rajan

Abstract The present study focuses on the design and performance evaluation of a rectangular mixed compression intake for ducted rocket ramjet applications. For the theoretical design stage, a 1D optimization criterion has been used to fix the ramp angles for theoretical maximum total pressure recovery (TPR), at on-design M 2.9 (shock-on-lip). Two different ramp designs (two and three ramps) have been considered for optimization, to find their effect on the overall performance. The throat height has been fixed using the practical self-starting contraction ratio (CR), (i) for the on-design Mach number of 2.9 and (ii) for the low off-design Mach number of 2. The throat length used is about six times the throat height for the required supercritical margin as well as to contain the shock train and the subsonic diffuser divergence angle is about 6°. The viscous flow field has been obtained by solving Favre averaged Navier-Stokes (FANS) equations with two-equation SST k-ω model. The analysis shows that, for the two-ramp and three-ramp design with self-starting contraction ratio at M 2.9, the on-design critical TPR is 0.645 and 0.67, and the critical mass flow ratio (MFR) is 1 and 0.99, respectively. The performance at low off-design M 2 shows, the MFR of both designs reduces to 0.51 and 0.47, respectively, and improves to a value of 0.6 for the two-ramp configuration with self-starting CR at M 2. This indicates that the two-ramp design has a better low off-design Mach number performance. Keywords Mixed compression intake · Supercritical margin · Compressible flow · Shock wave turbulent boundary layer interaction (SWBLI) · CFD

S. P. S. Pattnaik (B) · N. K. S. Rajan CGPL, Indian Institute of Science, Bangalore 560012, India e-mail: [email protected] N. K. S. Rajan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_10

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Nomenclature α β θ θd Ac A∞ Mj m˙ p0 P¯0 f P0 f max P0 f min MFR Re

Angle of attack (AoA) Ramp/flow deflection angle of the jth shock the shock wave angle of the jth shock The lower wall divergence angle of the subsonic diffuser Maximum capture area Freestream capture area Mach number after jth station Captured mass flow rate Total pressure Area weighted average total pressure at combustor face Maximum total pressure at the exit of intake Minimum total pressure at the exit of intake Mass flow ratio Reynolds number

TPR

Total pressure recovery =

DI

Distortion index =

P¯0 f P0∞ P0 f max −P0 f min P¯0 f

SWBLI Shock wave boundary layer interaction FANS Favre averaged Navier–Stokes equations  Throttling degree/ exit blockage ratio (EBR)

Subscripts 0 ∞ c t 1, 2, 3 f

Stagnation/total condition Freestream condition Cowl Throat entrance Ramp upstream station Intake exit/combustor entrance station

1 Introduction In the recent years, ducted rocket ramjet engines are becoming popular for long range air-to-air missile applications [1]. Here, the oxygen required for combustion is taken from the atmosphere through an intake system and the missile carries only the solid/liquid fuel. These missiles commonly use a fixed geometry rectangular or axisymmetric side intake. Designing such air intake systems is of key importance as it

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145

Fig. 1 Schematic of a rectangular side intake

affects the overall performance of the engine. Their basic functions are to (i) capture the required mass of air from the freestream at high velocity and compress it to low velocity and high pressure before supplying it to the combustor, (ii) maximize the static/total pressure recovery (TPR), (iii) provide a flow with good homogeneity (low pressure distortion) and stability for each flight conditions (subcritical buzz stability limit), (iv) operate efficiently with the pressure fluctuations due to combustion at a range of F/A ratios and off-design conditions. The major parts of a ramjet intake are a supersonic diffuser, throat and a subsonic diffuser. For a rectangular intake, the supersonic diffuser can further be divided as ramp, cowl and side plates as shown in Fig. 1. As the flow enters the intake, it goes through a series of oblique shocks in the supersonic diffuser, a terminal normal shock at the throat and the subsonic flow after the normal shock is compressed further in the subsonic diffuser to the required combustor Mach number at the exit. In this process, the flow incurs stagnation pressure loss across the shocks, viscous boundary layer and their interactions. A better explanation of this flow field can be found from the work of Saha et al. [2]. Hence, designing an intake involves selecting the different geometric components and optimizing them to minimize the losses or to maximize the performance in terms of total pressure recovery and mass capture as well as to have minimal drag and flow field distortion at the exit. Several studies have been reported in the literature on supersonic intake, (i) theoretical design approach [3–5], (ii) experimental and numerical performance evaluation, focusing on the effect of various geometric concepts [6–9], (iii) intake unstart [10, 11] as well as (iv) subcritical oscillating flow behavior (buzz) [12–14]. A detailed review of literature shows, the supersonic compression structure, internal contraction ratio and throat length are the major source of performance loss in an intake and their selection is operational range dependent. Hence, the objective of the current study is to design and evaluate the performance of a two-ramp and a three-ramp mixed compression rectangular intake at Mach 2.9, considering the self-starting contraction ratio at the on-design Mach number of 2.9 and the lower off-design Mach number of 2. Consequent to this introductory note, the paper has been organized as follows: Section 2 describes a theoretical design methodology, for fixing the ramp angles

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and other geometric dimensions of intake. Section 3 describes the numerical simulation procedure to find the viscous flow field. And in the final section, a detailed comparison of performance parameters for different geometric designs is presented. The maximum on-design TPR for the two-ramp design is close to 0.645 and that of three-ramp design is 0.67. Here, only the results of 2D simulation are presented. The 3D effect and complete off-design performance analysis will be considered for further studies.

2 Modes of Operation The operation of ramjet air intakes can be divided into three different modes, characterized by the position of the terminal normal shock/shock train in the intake. These are sub-critical, critical and supercritical modes of operation and are primarily the function of engine demand or downstream combustor pressure condition. At low downstream pressure, the flow at the throat expands after the cowl shock and forms a normal shock downstream (of throat) at a higher Mach number, resulting in higher stagnation pressure loss or low stagnation pressure recovery is known as the supercritical mode of operation. As the downstream pressure increases, the normal shock structure moves upstream towards the throat and gradually weakens. The maximum recovery is achieved when the terminal shock stands at the throat, known as critical operation. With further increase in downstream pressure, the normal shock moves upstream of the throat resulting in large flow separation and then moves outside the cowl, leading to unstart. This process is called as the subcritical operation. In this case, the ramp oblique shocks and normal shock interact outside the cowl, to form a bowed/curved shock ahead of it. And, a series of slip planes/vortex sheets are produced at the point of interaction. Here, as the shock stands ahead of the cowl, the MFR decreases compared to the critical operation (because of mass spillage) as well as the total pressure recovery decreases based on the losses across the shocks [15]. Usually, it is observed that till a certain range of subcritical operation, the flow field remains stable known as stability margin. And below the stable subcritical operation, flow field (Shock system) starts to oscillate, resulting in fluctuations in pressure recovery and mass flow capture. This unstable condition is known as buzz [14]. In order to avoid this unstable condition during the actual operation, all intakes are conventionally designed with a supercritical margin, where the intake operates at a supercritical mode, and as the back pressure increases, the shock system adjusts to have a critical operation. Hence, the subcritical operation is avoided [15]. These modes of operation of the intake are conventionally represented through an inlet characteristic diagram, as shown in Fig. 2. This shows the variation of total pressure recovery and mass flow ratio (defined as the ratio of actual freestream mass captured to the maximum possible mass capture) for different modes of operation.

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Fig. 2 Example of inlet characteristic diagram

3 Theoretical Design The theoretical design stage of the intake involves selection of the different internal geometric concepts that is the selection of supersonic compression structure, throat length and subsonic diffuser divergence angle to maximize the performance. For the current application, the intake has been designed at an on-design Mach number of 2.9. Hence, in order to have a compromise between length, weight, external drag and internal boundary layer effects, a mixed compression intake configuration has been selected which is considered to be efficient above a design Mach number of 2.5 [16].

3.1 Selection of Supersonic Compression Structure As mentioned earlier, to achieve the subsonic flow at the exit of the intake, the flow gets compressed through a series of oblique shocks and a terminal normal shock. Hence, for the supersonic compression geometry, higher the number of ramps for a fixed freestream Mach number, higher is the total pressure recovery that can be achieved. This is graphically represented in Fig. 3. But higher number of ramps leads to increase in geometric length, weight, viscous boundary layer losses and cowl drag, in addition the low off-design Mach number performance decreases. Hence, going for higher and higher number of ramps or isentropic ramp is not always useful. So, for the present study, two ramp designs, (i) a two-ramp and (ii) a three-ramp design, have been considered to find their effect on the overall performance of the intake. For fixing the ramp angles, a 1D optimization criterion is used. The process aims at maximizing the TPR or minimizing the total pressure loss for a system of oblique

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Fig. 3 Shock pressure recovery for freestream Mach number and number of oblique shocks [4]

Fig. 4 Schematic of theoretical shock system in the designed intake

shocks, a terminating normal shock and the subsonic diffuser, as pictorially summarized in Fig. 4. The optimization closely follows the method used by Benson [3] and Ran et al. [4], for which the oblique shock relations at ramp and cowl shocks, normal shock relations [17], Oswatitsch criterion (1944) for planar shocks and empirical relation for subsonic diffuser pressure loss [5] have been solved combinedly for a freestream Mach number of 2.9 using MATLAB. The optimization process for a five-shock (four oblique shock, one normal shock) system has been described below. Let the freestream Mach number is M∞ . The shock angle and ramp angle at the different ramp stations be θ1 ,β1 , θ2 ,β2 , θ3 ,β3 and at cowl be θ4 ,β4 . The Mach number at each ramp be M1 , M2 , M3 , M4 and after the terminal normal shock be M5 . The Mach number at the end of subsonic diffuser be M6 , which is fixed by the combustor design requirement. Here, all the angles mentioned are measured from the flow direction, just before the particular station, considering an angle of attack of α. The equations relating the Mach number, ramp angle, shock angle are as follows: (1) Oblique shock relations at the ramp and cowl (Eqs. 1–8)

Theoretical Design and Performance Evaluation …

(γ + 1)M 2 cot β1 = tan θ1 [  2 2 ∞  − 1] 2 M0 sin θ1 − 1     M02 (γ + 1)ε1 + (γ − 1) − 2 ε12 − 1 2   M1 = ε1 (γ − 1)ε1 + (γ + 1) where ε1 =

P1 P0

=

149

(1)

(2)

2γ M02 sin2 θ1 −(γ −1) (γ +1)

 (γ + 1)M12  −1 cot β2 = tan θ2  2 2 2 M1 sin θ2 − 1     M12 (γ + 1)ε2 + (γ − 1) − 2 ε22 − 1 2   M2 = ε2 (γ − 1)ε2 + (γ + 1) 

where ε2 =

P2 P1

=

(3)

(4)

2γ M12 sin2 θ2 −(γ −1) (γ +1)

 (γ + 1)M22  −1 cot β3 = tan θ3  2 2 2 M2 sin θ3 − 1     M22 (γ + 1)ε2 + (γ − 1) − 2 ε22 − 1 2   M3 = ε2 (γ − 1)ε2 + (γ + 1) 

where ε3 =

P3 P2

=

(5)

(6)

2γ M22 sin2 θ3 −(γ −1) (γ +1)

 (γ + 1)M32  −1 cot β4 = tan θ4  2 2 2 M3 sin θ4 − 1     M32 (γ + 1)ε + (γ − 1) − 2 ε2 − 1 2   M4 = ε (γ − 1)ε + (γ + 1) 

where ε4 =

P4 P3

=

(7)

(8)

2γ M32 sin2 θ4 −(γ −1) (γ +1)

(2) As per Oswatitsch (1944) criteria [4], to obtain maximum pressure recovery for a system of planar oblique shocks and a normal shock, the shock strength should be equal that is the Mach number perpendicular to the individual shocks is equal. Hence, the oblique shock angles can be related as

M0 sin θ1 = M1 sin θ2

(9)

M1 sin θ2 = M2 sin θ3

(10)

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M2 sin θ3 = M3 sin θ4

(11)

(2) From the normal shock relations, the Mach number across it can be related as

M52 =

(γ − 1)M42 + 2 2γ M42 − (γ − 1)

Hence, the number of unknown variables in the shock system is 13 and number of equations relating them is 12. As the number of unknowns is less than that of number of equations, to solve the system, any one of the variables that is Mach number before the normal shock (M4 ) or the shock angle θ1 can be assumed and solved for the remaining variables for a fixed inlet Mach number. Now, with the known shock angles, the total pressure recovery for the system can be found as described below. Calculation of total pressure recovery. The following stagnation pressure recovery (PR) relations have been used at different sections of the intake to obtain the total pressure recovery. (a) PR across the oblique shock γ  −1 Pti (γ + 1)εi + (γ − 1) γ −1 = ∗ εiγ −1 PRi = Pti−1 (γ − 1)εi + (γ + 1)

(13)

where i = 1,2,3,4 (b) PR across the normal shock  PR5 =

 1 (γ + 1) (γ + 1)M42 γ γ−1 ] ] γ −1 2γ M42 − (γ − 1) (γ − 1)M42 + 2

(14)

(c) PR across the subsonic diffuser The flow in the subsonic diffuser happens across an adverse pressure gradient. So, if the pressure gradient is high, the flow can separate from the wall resulting in a stagnation pressure loss. It mainly depends on the divergence angle, length to height ratio, upstream Mach number as well as the flow condition (boundarylayer separation) at the throat. In the literature, a number of empirical relations can be found formulating the pressure loss across the subsonic diffuser, of which the relation provided by Bridges [5] using the experimental data of Nicolai has been used here. This can be defined as below:

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The stagnation pressure recovery, in the subsonic diffuser is given by: ⎤

⎡ ⎢ PR6 = 1 − κ(M)⎣1 − 1+

1 γ −1 M52 2

⎥  γ γ−1 ⎦

(15)

where the diffuser loss co-efficient, κ(M) is: κ(M) = 0.2867M − 0.0875 Now, the total pressure recovery in the intake is given by TPR =

6 

PRi

(16)

i=1

Optimized ramp angles. The above process has been repeated by assuming a range of Mach number upstream of the normal shock (M4 ), from which the shock/ramp angles that produce the maximum total pressure recovery are obtained by plotting the TPR with the Mach number upstream of the normal shock. The result of 1D optimization for the two-ramp and three-ramp system is as shown in Fig. 5. The ramp angles corresponding to maximum TPR have been used for designing the geometry. Table 1 shows the summary of optimized ramp angles for both the designs. The theoretical TPR and the cowl angle obtained for the two-ramp case is about 0.83 and 8.5°, respectively, and that for the three-ramp case is about 0.86 and 16°, respectively.

3.2 Throat Design For a mixed compression supersonic intake, the throat height and length are important design variables as they affect the overall performance of intake. The concepts that have been used to fix these variables are explained below. Throat height. Usually, the cowl lip height of an intake is fixed by the overall system or drag requirement. From the cowl lip height and the optimized ramp angles, the inlet area can be known. Now for the fixed inlet/cowl area, the throat area or the throat bottom surface can be found out using the “self-starting contraction ratio limit” for the design Mach number. It is defined as the ratio of cowl area to the throat area, above which complete incoming mass cannot be captured in the intake, resulting in the formation of a bow shock or normal shock ahead of cowl to allow mass spillage. And the operation of the intake is said to be unstarted. In the literature, there are several studies aiming to find the self-starting contraction ratio limit with upstream Mach number for different geometries, starting from the

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Fig. 5 Result of 1D optimization for a two-ramp, b three-ramp intake

Table 1 Ramp angles and theoretical performance for different ramp designs Ramp structure

M0

β1

θ1

M1

P1 /P0

β2

θ2

M2

P2 /P1

Two-ramp

2.9

10.5

28.5

2.4

2.08

12.5

35.5

1.9

2.08

26.4

2.51

1.773

9.1

Three-ramp

8.05

β3

θ3

M3

P3 /P2

14.5

46.3

1.383

2.08

10.3

37.13

1.75

1.773

31

2.13

1.773

β4

θ4

M4

P4 /P3

M5 0.747

0.82

11.5

49

1.34

1.773

0.786

0.861

TPR

theoretical work of Kantrowitz [10]. Sun and Zhang [11] have recently compiled all the data from literature and provided the practical limit of self-starting contraction ratio with upstream Mach number. This practical limit has been used here for the selection of the contraction ratio. For the present study, two different contraction ratios are used for both two-ramp and three-ramp designs. These are (i) A ratio of 1.316, which is the self-starting contraction ratio for the internal compression, for the 2-ramp design. And a ratio of 1.282, which is the selfstarting contraction ratio for the internal compression, for the three-ramp design at a freestream Mach number of 2.9.

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(ii) A contraction ratio of 1.111, which is the self-starting contraction ratio at offdesign freestream Mach of 2 for both two- and three-ramp design. Throat length. At the critical mode of operation in the ramjet intake, the supersonic flow terminates with a normal shock at the throat. But practically, instead of a single terminal normal shock, usually a normal shock train is formed because of the SWBLIs, depending on the upstream flow condition [18]. The structure of shock train and the different parameters affecting it can be found from the earlier studies in the literature. Hence, the length of throat should be such that, it should completely contain the shock train within to achieve the maximum performance at the intake exit in terms of flow uniformity and low subsonic Mach number. In the present design, as a first iteration, a fixed throat length of 80 mm has been used which is about six times the throat height for both two-ramp and three-ramp design.

3.3 Subsonic Diffuser Design The subsonic diffuser lower wall divergence angle affects the axial adverse pressure gradient across which the flow occurs, hence is an important design variable. As per the literature, an angle of 4–10° is usually preferred for this subsonic diffuser lower wall angle of divergence. Thus, to have minimal flow separation, for the present case, a 6°-divergence angle has been used.

3.4 Comparison of Inlet Dimensions Boundary layer correction. The 1D optimization procedure used here to obtain the ramp angles does not consider the viscous effects. Thus, in order to achieve shockon-lip condition considering viscous boundary layer effects, the ramp angles need to be corrected to take care of displacement thickness. As the supersonic boundary layer thickness is small, here a simple method has been used instead of going for exact boundary layer displacement thickness correction. To take care of this, all the ramp angles have been reduced by 0.5° each. As will be shown from the CFD simulation, this is good enough to keep the streamlines within the cowl lip. Geometric dimensions. The corrected ramp angles have been used to obtain the geometric dimensions for the intake, with a fixed cowl tip height of 40 mm. Here, the oblique shocks generated by the three ramps are designed to focus on the cowl leading edge. The throat and subsonic diffuser dimensions are then fixed as explained before. The major geometric dimensions of the intake are presented in Table 2.

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Table 2 Geometric dimensions (mm)

Total length Cowl angle Throat height Throat length Subsonic diffuser length

Two-ramp

400

Three-ramp 406.7

8.5°

15.2

16°

13.5

Fixed 80

250

4 Computational Methodology To evaluate the performance of the initial design considering viscous effects and shock wave turbulent boundary layer interactions, 2D CFD analysis has been carried out. The numerical methodology adopted for the analysis is explained in this section.

4.1 Geometry Details and Grid Generation The intake geometry obtained from the theoretical analysis has been used for the numerical study. To simulate the different modes of operation, a downstream throttle has been used to vary the back pressure by varying the throat area. The computational domain used for the study is as shown in Fig. 6a. The top and bottom external geometry heights are about 15 and 5 times the cowl height, respectively. This large outer domain has been considered to avoid any influence of freestream at angle of attack simulation. The computational domain has been meshed with complete hexahedral cells as shown in Fig. 6b using ICEM CFD [19].

4.2 Numerical Details To solve the flow through the intake, which is compressible and turbulent, Favre averaged Navier–Stokes (FANS) equations with two-equation SST k-ω turbulence model have been employed [20]. The governing equations are integrated using finite volume technique and solved using commercial CFD software: CFX-17. Even though the flow field in the intake is completely three-dimensional, to optimize the length and the geometry of subsonic diffuser, only a quasi 2D simulation has been carried out, which considers a single cell in the 3D direction. The fluid properties like specific heat capacity (C p ), thermal conductivity (K) and viscosity are modelled as a function of temperature, where viscosity is modelled using the model provided by Sutherland [1893], obtained from kinetic theory for dilute gases. The specific heat variation with temperature has been modelled using a curve fit. And the thermal conductivity of air has been modelled using the modified Euken Model (2001) [20]. Boundary condition. The boundary conditions applied for the domain are as shown in Fig. 6a. All the solid walls are modelled as stationary and no-slip adiabatic

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Fig. 6 Schematic of the computational a domain with applied BC, b grid used

boundary. At the inlet to the supersonic intake, all the freestream conditions are applied as a supersonic velocity inlet boundary, i.e. static pressure, static temperature and velocity are specified. The turbulence quantities at the inlet are specified in terms of eddy viscosity ratio and turbulence intensity. The outlet boundary in the outer regions above the cowl and below the ramp is assigned with subsonic outlet where static pressure is specified. And the outlet after the downstream throttle has been modelled as supersonic outlet. Convergence metrics. The point of convergence of the numerical simulations has been identified by considering the overall mass, momentum, energy balance in the domain, with a criterion of residuals below 10−5 and the flow property monitors getting stabilized.

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Validation studies. To ensure the effect of turbulence model and boundary condition uncertainties, the numerical methodology has been validated with the intake experimental data of Emami et al. [21]. For this, a 2D dual-mode ramjet inlet geometry has been considered for the simulation. The geometry consists of a supersonic diffuser, an isolator followed by an expanding section which acts as a subsonic diffuser in the ramjet mode of operation. The supersonic diffuser includes a 11° compression ramp, cowl and side plates with leading-edge radius of 0.005 in. each. The isolator section considered is a constant rectangular area of length to throat height ratio (L/Ht ) of 4.7, where Ht is 0.4 in., followed by a rectangular 6° expanding section of length 4.25 in. The subsonic diffuser considered has a lower wall divergence angle of 20°. For this validation study, both 2D and 3D simulations considering the effect of side walls have been carried out. Figure 7 shows the ramp and cowl wall static pressure variation obtained from 2D simulations. A closer look at the points of pressure rise clearly indicates, the separation regions due to the shock wave boundary interactions are not captured well but the pressure peaks and the trend of shock structure are predicted quite accurately in the 2D simulation. The similar results of 3D simulation are shown in Fig. 8. It can be seen that, here the effect of side plate shock and the separation regions is predicted better. Hence, the overall favourable agreement between the predicted results with the data demonstrate

Fig. 7 Comparison of predicted non-dimensional wall static pressure from 2D simulation, along a ramp wall, b cowl wall with experiment [21]; M ∞ − 4.0

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Fig. 8 Comparison of predicted non-dimensional wall static pressure from 3D simulation along, a ramp wall, b cowl wall midplane with experiment [21]; M∞ − 4.0

that this numerical methodology can be used for the preliminary design optimization of the intake before final experimentation.

4.3 Grid Independence Study To have a mesh with optimal number of cells, three sets of grids have been considered for the simulation and the wall static pressure has been compared. The grids are systematically refined and have a resolution as given in Table 3. Figure 9 shows the variations of ramp and cowl wall static pressure distribution for all the three grids. Table 3 2D mesh resolution

Level of resolution

Cells (millions)

First cell distance y (mm)

Maximum wall y+

Coarse

0.094

0.01

11

Intermediate

0.148

0.001

1.5

Fine

0.181

0.0008

3δ) gap on both sides of the FFS to avoid the effect of the side wall boundary layer on SWBLI [4].

2.2 Particle Image Velocimetry Particle image velocimetry (PIV) is a flow visualization technique primarily used in the present study. In this work, we used two-dimensional two-component (2D2C) particle image velocimetry (PIV) system from Dantec Dynamics, Denmark. It comprises of a New Wave 120 mJ energy, 532 nm dual cavity Nd-YAG laser, 1.92 Megapixel (1600×1200 pixel resolution) CCD sensor camera, timer card for synchronization, grabber card for image acquisition, beam to sheet converter (convex and concave lens assembly) and PIV software DynamicStudio. Laser beam was made in to a sheet using a spherical convex and cylindrical concave lens assembly, with adjustments possible for the laser sheet thickness. For the present experiments laser sheet thickness was kept approximately at 1.5 mm. The camera used had a minimum inter frame time of 0.3 µs when operated in the double exposure mode. In the present experiments, an inter frame time of 0.5–1.0 µs was used. Nikon Micro-N60 mm f/2.8 D and 105 mm f/2.8 G lens were used with the camera. During PIV experiments, the surface of the model was painted with black color which helped in reducing the laser reflection from the surface. The flow was seeded with olive oil particles for PIV (Melling 1997). Olive oil particles were produced using in-house built Laskin nozzle based seeder. Oil particles from this were injected into the settling chamber perpendicular to the flow direction 1 m upstream of the test section. Oil particles after mixing with the incoming flow passed through a coarse mesh, honey comb and a series of fine meshes. Two vertical side plates 2 mm thickness were welded inside the settling chamber upstream of the honeycomb to minimize smearing of oil particles on the Perspex window of the test section. This helped in getting clear PIV images and also reduced the need for cleaning of the test section windows between runs.

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3 Results and Discussion The PIV flow visualization in the cross-stream plane (x-y) were done separately both upstream and downstream of the forward-facing step of height, h/δ = 2.0 (δ is the oncoming boundary layer thickness). The PIV velocity field results obtained from these measurements, both upstream and downstream were processed separately and then time-averaged. The time-averaged fields from both upstream and downstream cases were then stitched into a single velocity vector field, shown in Fig. 2. It is observed from the mean velocity vector field figure, the incoming boundary layer deflects approximately at a distance 4h upstream of the step. A continuous straight line is drawn to represent the sharp change in the flow deflection which is called as separation shock. The flow separating at x/ h = −4 forms a large separation bubble (recirculation region) upstream of the step. The flow after the separation bubble turns around the top corner of the step, through a series of expansion waves. The series of expansion waves at the top step corner is marked as dotted straight line. The zero mean streamwise velocity contour line (u = 0) is drawn in the Fig. 2 as a dotted curved line. The mean separation shock location (xs ) is found by locating velocity field points far away from the wall (outside the boundary layer), where the mean flow is deflected, as shown schematically in Fig. 2. Mean separation shock location (xs ) at a particular wall-normal location (y) is found by locating the streamwise (x) position where the flow is deflected by greater than 6.5◦ ; this threshold deflection criteria being one-half of the mean flow deflection angle. This method is followed at different wall-normal locations from y = 1.5h to 2.1 h and flow deflection streamwise locations are marked as solid circles (•) in Fig. 2. A continuous straight line is fitted through these solid

Fig. 2 Mean velocity vector field obtained after averaging approximately 800 instantaneous vector fields over forward-facing step of h/δ = 2. Downstream of the separation shock and upstream of the step face, a separation bubble (reverse flow region represented as curved dotted line, u = 0) exists. For visibility, every fourth and third velocity vector is shown in streamwise and wall-normal directions, respectively

Observation of Low-Frequency Shock Oscillation Over …

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circles (•) using least square method (shown as solid line through the solid circles) and it is extended up to the bottom wall, shown by the dotted line, to locate the mean separation shock location (xs , ). It should be noted that this mean separation shock location (xs , ) is about 4h upstream of the step, and represents the mean location of the separation shock as measured in the bulk flow outside the boundary layer. This may be compared with the separation location on the surface determined from surface oil flow, both being approximately close to 4h for the h = 2δ case [2]. Figure 3 shows two sample instantaneous velocity fields upstream of the forwardfacing step. Figure shows the sample instantaneous velocity fields with the separation shock (dotted straight line) and the zero streamwise velocity contour (dotted curved line) representing the reverse flow region shown in both cases. Figure 3a shows a small reverse flow region with the separation shock closer to the step face, while in Fig. 3b, the reverse flow region is much larger with separation shock being pushed further upstream. Clearly, the flow field is highly unsteady with large-scale shock oscillations. From every instantaneous velocity vector field in the cross-stream plane, we extract incoming boundary layer velocity field as upstream parameter and separation region or reverse flow region as downstream parameter. The relation of these

Fig. 3 Instantaneous velocity vector plot showing a small and b big reverse flow region (u = 0). Dotted straight line represents separation shock and dotted curved line represents zero streamwise velocity contour (u = 0). For visibility, every third velocity vector is shown in the streamwise and wall-normal directions

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parameters with the corresponding instantaneous shock location obtained from the velocity field is studied. The upstream parameter is obtained as the line-averaged streamwise velocity at a wall-normal location of y = 0.5δ (=0.25h) over a distance of 2δ, which is equivalent to the step height (h). Similarly, downstream parameter is obtained as the area of the reverse flow region (hereafter called as separation region). The angle formed by the mean separation shock wave (solid line) with the wall is the shock wave angle represented as βs . Similarly instantaneous separation shock angle (βs ) is also defined based on flow well outside the boundary layer (as shown in [3]) for all the instantaneous velocity fields. The variation of these parameters along with the shock location is shown in Figs. 4, 5, 6 and 7. The instantaneous separation shock location and separation shock angle is found out by following the same procedure followed to locate the mean separation shock location and shock angle. Figure 4 shows the variation of the line-averaged streamwise velocity fluctuations measured between streamwise location of x/h = −6 to −5 upstream of the step for each one of the 800 measured instantaneous velocity fields. The line-averaged streamwise velocity fluctuation varies from −50 to 50 m/s. The positive line-averaged streamwise velocity fluctuation implies that the incoming boundary layer is thinner

50

25

u′ (m/s)

Fig. 4 Estimated values of the line-averaged streamwise velocity fluctuations measured between x/ h = −6 to −5 upstream of the step for each one of the 800 measured instantaneous velocity fields. The velocity fluctuations varies from −50 to 50 m/s

0

-25

-50

0

200

400

600

800

600

800

PIV Image 400

300

A (mm2)

Fig. 5 Estimated values of the reverse flow or separation region for each one of the 800 measured instantaneous velocity fields. It varies from no separation to separated region of bubble size approximately 300 mm2

200

100

0

0

200

400

PIV Image

Observation of Low-Frequency Shock Oscillation Over … -3

-4

xS/h

Fig. 6 Estimated values of the instantaneous shock location normalized using step height for each one of the 800 measured instantaneous velocity fields. It varies from −3.5 to −5h

225

-5

-6

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200

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800

600

800

PIV Image

Fig. 7 Estimated values of the separation shock angle for each one of the 800 measured instantaneous velocity fields. It varies from 28 to 40◦

45

βS

40

35

30

25

0

200

400

PIV Image

and negative line-averaged streamwise velocity fluctuation implies that the incoming boundary layer is thicker. Figure 5 shows the reverse flow or separation region for each one of the 800 measured instantaneous velocity fields. The separation bubble varies from almost small size to big size of approximately 300 mm2 . When the bubble size is big, we can observe from Fig. 5, that separation shock is far from the step. Similarly, when the bubble size is smaller, the separation shock is closer to the step. Figures 6 and 7 shows separation shock location and shock angle for each one of the 800 measured instantaneous velocity fields, respectively. The separation shock location varies approximately from −3.5 to −5h upstream of the step. Separation shock oscillates approximately 1.5 h. The separation shock angle varies from 28 to 40◦ . It is observed from the cross correlation between the separation shock location and incoming streamwise boundary layer velocity fluctuation that the separation shock is weakly correlated to the incoming streamwise boundary layer velocity fluctuation. At the same time, there is strong correlation between separation shock and separa-

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tion bubble or reverse flow region. Based on this, we conclude that the separation shock foot motion is correlated to incoming boundary layer velocity fluctuations and separation shock oscillation is correlated to reverse flow or separation region.

4 Conclusions Shock wave boundary layer interaction was studied over a forward-facing step of step height equals two times the incoming boundary layer. Particle image velocimetry is the primary methodology used to study the interaction between shock wave and boundary layer. The purpose of using step height greater than the boundary layer thickness is to obtain bigger separation bubble downstream of the separation shock wave. Instantaneous PIV measurements shows separation shock oscillates over a distance of step height about the mean separation shock position. Similarly, instantaneous PIV vector fields show for large separation bubble separation shock is far from the step face and for smaller separation bubble, separation shock is near to the step face. In general, correlation of separation shock with incoming boundary layer velocity fluctuations and reverse flow regions shows that separation shock foot is more related to reverse flow region.

References 1. Dolling, David S (2001) Fifty years of shock-wave/boundary-layer interaction research: what next? AIAA J 39(8):1517–1531 2. Clemens NT, Narayanaswamy V (2014) Low frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu Rev Fluid Mech 46:469–492 3. Zukoski EE (1967) Turbulent boundary-layer separation in front OFA forward-facing step. AIAAJ 39(8):1746–1753 4. Murugan J, Govardhan R (2016) Shock-wave/boundary layer interaction in supersonic flow over a forward-facing step. J Fluid Mech 807:258–302

RANS Computations of Hypersonic Interference Heating on Flat Surface with Protuberances M. Mahendhran and C. Balaji

Abstract RANS computations are performed for M ∞ = 8.2, Re∞ /m = 9.35 × 106 flow past a flat surface with protuberance of size of the same order as that of the boundary layer. The local intensification of heat transfer rates in the vicinity of the protuberance is considered as the main focus of the study. The effect of separated and unseparated boundary layer is considered by varying the protuberance angle. The results are compared with available experimental data. The maximum heat transfer rate, a major design parameter, is found to be fairly predicted by computations. However, accurate prediction of parameters such as upstream separation length and heat flux distribution requires further research and calibration of available turbulence models. Keywords Hypersonic flow · Flat surface with protuberance · CFD++

1 Introduction Protuberances in the form of rivet heads, screws, etc., present on the surfaces of missiles and other aero-vehicles traveling at hypersonic speeds interfere with the otherwise undisturbed flow past these surfaces and result in the appearance of shock waves around them, altering the evolution of the boundary layer and intensifying local heat transfer rates to the vehicle’s surface [1]. Estruch et al. [2] have performed experiments involving hypersonic flow past protuberances with finite span and height of the order of the boundary layer thickness in order to characterize the augmentation in heat transfer to the vehicle’s surface and, depending on the configuration of the protuberance, the location where the maximum heat transfer rates can be expected. The complex interaction between M. Mahendhran (B) · C. Balaji Metacomp Technologies Pvt. Ltd, #14, 3rd Cross St., Karpagam Gardens, Adayar, Chennai 600020, India e-mail: [email protected] C. Balaji e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_17

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the shock wave and boundary layer at hypersonic speeds makes this localized heat transfer dependent on many parameters, including the protuberance deflection angle, the state of boundary layer, flow Reynolds and Mach numbers. Computing such flow fields involving shock wave/boundary layer interactions at hypersonic speeds and predicting the augmentation in heat transfer rates and its location in the vicinity of protuberances is a challenging task. In this paper, the hypersonic flow past a protuberance considered by Estruch et al. [2] is computed using the CFD software suite, CFD++ [3]. Computations are performed for both unseparated and separated boundary layer ahead of the protuberance by varying the protuberance angle (α), and the results are compared with experimental data.

2 Geometry and Mesh The protuberance is a wedge of height 5 mm and width 13.5 mm. It protrudes from a flat plate of length 255 mm, width 155 mm and thickness 6 mm and is located at 175 mm from the leading edge of the plate (x le ), and it extends up to 80 mm downstream (see Fig. 1). The surface mesh is generated using triangles and quadrilaterals, and the near wall and core regions are constructed with prism layers and hexahedral elements, respectively. Prism layers are constructed such that the wall y+ for the first layer is less than one in most regions of the domain and reaches a maximum value of 2.5 at the side edge corner of the protuberance. In the volume regions that are marked with constant mesh size, hexahedral cells resembling a structured mesh are employed (see Fig. 2). Pyramids and tetrahedral cells are used as required to bridge the near-wall prismatic cells and the surface mesh with the core hexahedral cells. The total mesh size of this 3D hybrid unstructured mesh is ≈20 million cells. A cut section through the mid-span of a representative mesh employed for this study is shown in Fig. 2.

175

80 5

All dimensions are in mm

30° wedge angle

Fig. 1 Plate with protuberance in side view showing important dimensions

6

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Fig. 2 Unstructured computational mesh in the vicinity of the protuberance

3 Computational Details The fluid flow is modeled using the 3D compressible Navier–Stokes equations with due consideration of viscous heating in the energy balance. The working fluid, air, is treated as real gas, with the consideration of specific heat variation with respect to temperature. Its material properties—viscosity, thermal conductivity and their dependence on temperature—are modeled using Sutherland’s law. Considering the complexity of the flow field and the uncertainty of the best suited turbulence model to simulate turbulence in such flow fields, three different turbulence models are employed in this study, viz., the one-equation Goldberg Rt model [4], the two-equation SST model and the two-equation nonlinear cubic k-ε model [5] with variable Prandtl number treatment [6]. A second-order spatial discretization is employed along with a continuous-type slope limiter in order to avoid spurious numerical oscillations across sharp variations in solution variables [7]. Partial blending from the first-order discretization (up to 20%) is required to support stability and improve convergence while employing cubic

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k-ε model for computations involving protuberance with boundary layer separation (α ≥ 45°). Pressure switches [7] are used to control additional diffusion only at locations of sharp variation in pressure, ensuring stability with minimal penalty on the computation accuracy. An implicit iterative advancement of the solution coupled with an implicit treatment of boundary conditions and an algebraic agglomeration multi-grid helps in achieving rapid convergence toward the steady-state flow field. Vortex generators (VGs) are employed by Estruch et al. [2] to trip the boundary layer. The VGs are located 20 mm from the leading edge, and vortex breakdown is reported to occur at about 100 mm from the leading edge. In an attempt to transition the boundary layer to turbulent, numerical trip wires are placed 100 mm from the leading edge [7].

4 Results Unless otherwise stated, computations are performed for M ∞ = 8.2, Re∞ /m = 9.35 × 106 . The walls are kept at 295 K, as in experiment. The near-wall shear stresses and heat transfer rates are directly computed using a solve-to-wall approach without resorting to wall functions. Tables 1 and 2 summarize the boundary layer height and heat transfer rates, respectively, obtained for an undisturbed boundary layer flow past the plate (without protuberance). The results include the measurement of boundary layer height and heat transfer to the plate at x le = 175 mm, both in the presence and absence of boundary layer trip. Table 1 Boundary layer height at x le = 175 mm for an undisturbed boundary layer BL trip

BL height (mm) Exp.

CFD++ Rt

SST

Cubic k-ε

No

2.25–2.75

2.58

2.54

2.61

Yes

4.5–5.5

5.51

2.53

2.64

Table 2 Heat transfer rate at x le = 175 mm for an undisturbed boundary layer BL trip

Heat transfer rate (W/cm2 ) Exp.

CFD++ Rt

SST

Cubic k-ε

No

1.62–1.98

1.9

1.74

1.35

Yes

5.31–6.49

5.85

2.39

1.35

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In the absence of a boundary layer trip, the boundary layer height predicted by all the models lies within the experimental range. The corresponding heat transfer rates predicted by Rt and SST models lie within the experimental range, whereas it is underpredicted by 15% from the mean value when the cubic k-ε model is employed. Only the Rt model is observed to respond to the placement of numerical trip wires, turning the boundary layer into a turbulent state with a corresponding increase in boundary layer height and with heat transfer rates that lie within or very close to experimental range. The presence of turbulent dissipation rates in the SST and cubic k-ε model makes the flow relaminarize rapidly after the numerical trip. The boundary layer state remains laminar for these models and is found to have a profound impact on the evolution of flow field (see Fig. 3) and the resulting heat transfer that occurs in the vicinity of the protuberance (see Figs. 4, 5, 6, 7 and 8). The presence of the protuberance increases the local heat transfer rate in its vicinity (see Fig. 4) and induces a separation shock ahead of it, whose intense adverse pressure gradient causes the boundary layer to separate, resulting in a recirculation zone ahead of the protuberance (see Fig. 5). The maximum heat transfer rate in the vicinity of the protuberance—a significant parameter for engineering design requirements—is predicted to a fair extent by

Fig. 3 Mach number contours in the protuberance region for α = 90° case

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50 45

exp

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Stmax x 10-3

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Cubic k-eps

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α (°) Fig. 4 Comparison of maximum heat flux variation with respect to α

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RL x 104

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separation shock

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SST Cubic k-eps

30 20 10 0

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105

α (°) Fig. 5 Non-dimensional separation length ahead of protuberance for different α

computations, up to α = 90°, see Fig. 4. For α = 135°, heat transfer rates in the vicinity of protuberance converged to a constant value for the Rt model, whereas oscillations are noted for SST and cubic k-ε, with notably large amplitudes for the cubic k-ε model. This could possibly indicate the presence of a large-scale structures

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14

flow

num, α=30° exp, α=45°

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xk

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num, α=90° 4 2 0 -30

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Rex x 104 Fig. 6 Comparison of heat flux distribution, obtained using Rt turbulence model ahead of the protuberance along the centerline for different α

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exp, α=45°

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exp, α=90°

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exp, α=30°

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0

Rex x 104 Fig. 7 Comparison of heat flux distribution, obtained using SST turbulence model, ahead of the protuberance along the centerline for different α

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flow

num, α=30° exp, α=45°

α

12

xk

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num, α=45° exp, α=60°

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exp, α=90°

St x 10-3

14 exp, α=30°

num, α=90° 4 2 0 -30

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0

Rex x 104 Fig. 8 Comparison of heat flux distribution, obtained using Cubic k-ε turbulence model, ahead of the protuberance along the centerline for different α

in the vicinity of protuberance possibly caused by a laminar boundary layer ahead of the protuberance at these angles. Figure 5 shows the variation of separation length ahead of the protuberance from the computations. It is underpredicted by Rt model and is overpredicted by SST and cubic k-ε. The primary reason for overprediction by SST and cubic k-ε is the failure of the numerical trips to transition the boundary layer to a turbulent state, leaving the laminar boundary layer to be influenced to a greater extent by the adverse pressure gradient introduced by the separation shock. This also affects the heat transfer rates ahead of the protuberance as seen in Figs. 6, 7 and 8. As expected, the Rt model with a turbulent oncoming boundary layer (Fig. 6) fares better than the SST (Fig. 7) and cubic k-ε (Fig. 8) models, with oncoming laminar boundary layers, wherein a general underprediction in heat transfer rates is noted. Considering the fair representation of the flow field by the Rt model, further analyses are performed using this model, for α = 90° unless otherwise stated explicitly. This includes the dependence of results on the type of mesh employed (unstructured or structured), mesh resolution and the location of numerical trip. The structured mesh with similar mesh resolution as in the unstructured mesh was prepared. The heat transfer parameters such as the maximum heat transfer rate in the vicinity of the protuberance (a major design parameter), the heat transfer distribution ahead of the protuberance and along the centerline obtained from the unstructured and structured meshes are compared in Table 3, Figs. 9 and 10, respectively. Table 4

RANS Computations of Hypersonic Interference Heating … Table 3 Comparison of maximum heat transfer ahead of protuberance between unstructured and structured meshes for α = 90° case employing Rt turbulence model

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Case

Maximum heat flux ahead of protuberance (Stmax × 10–3 )

Experiment

11.022

Unstructured

10.593

Structured

10.579

Fig. 9 Heat flux distribution around the protuberance for α = 90° base case

12 unstructured mesh

10

structured mesh

6

St x 10-3

8

4 2 0 -30

-25

-20

-15

-10

-5

0

Rex x 104 Fig. 10 Comparison of heat flux ahead of protuberance along centerline between unstructured and structured meshes for α = 90° case employing Rt turbulence model

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Table 4 Comparison of separation distance ahead of protuberance between unstructured and structured meshes for α = 90° case employing Rt turbulence model

Mesh type

Separation distance (ReL × 104 )

Experiment

21.638

Unstructured

12.479

Structured

13.522

compares the non-dimensional separation length ahead of the protuberance obtained from unstructured and structured meshes. Only a marginal difference in results is noted because of the change in the type of mesh employed in the computations. The unstructured mesh with the hex-core feature prepared using IMIME [8] produces results that compare very closely with its structured mesh counterpart. Further analyses are performed only using hex-core unstructured mesh unless otherwise stated explicitly. Computations are repeated by refining the mesh in the shock/boundary layer interaction region ahead of the protuberance and by locating the numerical trip to an upstream location, 20 mm from the leading edge. The mesh count for the refined mesh is almost doubled from the base case. The mesh is refined in the region ahead of the protuberance to predict the separation shock’s location and strength more accurately. The placement of the numerical trip at an upstream location is expected to change the momentum of the boundary layer. Figure 11 compares the heat flux distribution ahead of the protuberance for these cases. Mesh refinement has increased the upstream heating marginally and has 14 exp base case

12

fine mesh

10 8 6 4 2 0

-30

-25

-20

-15

-10

-5

Rex x 104 Fig. 11 Heat flux ahead of protuberance along centerline for α = 90° case

0

St x 10-3

upstream trip

RANS Computations of Hypersonic Interference Heating … Table 5 Separation distance ahead of protuberance for α = 90° case

Table 6 Maximum heat flux ahead of protuberance for α = 90° case

Case

Separation distance (ReL × 104 )

Experiment

21.638

Base case

12.479

Fine mesh

13.540

Upstream trip

13.885

237

Case

Maximum heat flux ahead of protuberance (Stmax × 10–3 )

Experiment

11.022

Base case

10.593

Fine mesh

10.518

Upstream trip

7.700

resulted in corresponding increase in separation distance, see Table 5. The upstream trip placement has resulted in similar increase in separation distance; however, it has resulted in much lower heat transfer to the plate. Maximum heat flux obtained for these cases is summarized in Table 6. The base and refined mesh results fall within the experimental error of 10%; however, the upstream trip case underpredicts the maximum heat flux significantly.

5 Summary and Conclusion Hypersonic flow past wedge-shaped protuberances whose dimensions are of the same order as that of the boundary layer height are computed using three turbulence models, viz. Rt, SST and cubic k-ε models, and salient results are compared with experimental data. Initially, an undisturbed boundary layer flow over the flat plate is computed. All the models fare well in the absence of boundary layer transition and the heat flux and boundary layer height showed a very good match with the experimental results. Numerical trip wires are employed in the computations to transition the boundary layer to turbulent state as in experiments. Only Rt model is observed to respond to numerical trip placement and shows very good comparison of boundary layer height and heat transfer rates. Under the flow conditions considered, the numerical trips are essentially ineffective in the case of the SST and cubic k-ε models. This is likely due to the turbulence dissipation rate determined from the second transport equation in both these models. Subsequently, the flow past wedge-shaped protuberances are computed for both attached and separated boundary layers, obtained by varying the wedge angle.

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Computations predict the maximum heat flux with reasonable accuracy, and this is found not to depend much on the state of boundary layer. However, the state of the boundary layer has a profound impact on the separation distance and the spatial extent of upstream heat transfer. The Rt model with a turbulent boundary layer is found to underpredict the separation distance, whereas the SST and cubic k-ε models with laminar boundary layer overpredict the separation distance. This suggests that the physical boundary layer, post-trip, has insufficient time to become fully developed and remains transitional. Heat transfer distribution ahead of the protuberance is represented reasonably well by the Rt model, but with severe underprediction noted for SST and cubic k-ε models. In concurrence with the experimental findings [2], the computations indicate that the state of the oncoming boundary layer plays an important role in the flow field evolution in the vicinity of the protuberance. Further research is required to sensitize models with length scale determining transport equations (SST and cubic k-ε) to numerical trip placement, to conduct studies involving boundary layer transition, and subsequently to evaluate their performance with models that lack a free-stream turbulence decay mechanism (e.g., Rt).

References 1. Guoliang M, Guiqing J (2004) Comprehensive analysis and estimation system on thermal environment, heat protection and thermal structure of spacecraft. Acta Astron 54(5):347–356 2. Estruch D, MacManus DG, Stollery JL, Lawson NJ, Garry KP (2010) Hypersonic interference heating in the vicinity of surface protuberances. Exp Fluids 49:683–699 3. Metacomp Technologies Inc. Homepage. https://www.metacomptech.com. Last accessed 2018/09/26 4. Goldberg U (2003) Turbulence closure with a topography-parameter-free single equation model. IJCFD 17(1):27–38 5. Palaniswamy S, Goldberg U, Peroomian O, Chakravarthy S (2001) Predictions of axial and transverse injection into supersonic flow. Turbul Combust 66:37–55 6. Goldberg UC, Palaniswamy S, Batten P, Gupta V (2010) Variable turbulent Schmidt and Prandtl number modeling. Eng Appl Comput Fluid Mech 4(4):511–520 7. ICFD++ theory manual, Metacomp Technologies Inc. 8. IMIME theory manual, Metacomp Technologies Inc.

Multi-fidelity Aerodynamic Optimization of an Airfoil at a Transitional Low Reynolds Number R. Priyanka, M. Sivapragasam , and H. K. Narahari

Abstract Aerodynamic shape optimization is carried out for (a) maximizing lift coefficient, C l and (b) maximizing endurance factor (C l 3/2 /C d ) of an airfoil at a transitional low Reynolds number (Re = 5 × 104 ) using surrogate-based optimization technique. Bezier curves are used to parameterize the airfoil. Latin hypercube sampling (LHS) technique is used to sample the initial set of samples. The aerodynamic response is estimated using low- and high-fidelity datasets. A co-krigingbased multi-fidelity surrogate is built using these datasets, and the response surface is used in the optimization procedure for the search of optima. Expected improvement strategy is used to update the surrogate at every iteration, and optimization is terminated once the convergence criterion is met. The objective function improvement for maximizing C l and maximizing (C l 3/2 /C d ) is 18.08% and 38.70%, respectively. Keywords Low Reynolds number · Laminar separation bubble · Co-kriging · Aerodynamic optimization

1 Introduction Micro air vehicles (MAV) find widespread use in many civilian and military applications. These small-sized vehicles typically cruise at a Reynolds number (Re) of the order of 105 based on the flight speed and chord length. In the low Reynolds number regime, viscous forces have a significant effect on the aerodynamic characteristics.

R. Priyanka (B) · M. Sivapragasam · H. K. Narahari Department of Automotive and Aeronautical Engineering, Faculty of Engineering and Technology, M.S. Ramaiah University of Applied Sciences, Bangalore, India e-mail: [email protected] M. Sivapragasam e-mail: [email protected] H. K. Narahari e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_18

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The flow properties in this regime have significant effects on the aerodynamic performance of MAVs. Hence, the understanding of aerodynamics at low Reynolds number regime becomes important. In low Reynolds number regime, the flow is very sensitive to small changes in flow parameters such as airfoil geometry, Reynolds number, freestream turbulence and angle of attack. In this regime, the airfoil often encounters laminar boundary layer separation, transition to turbulence and reattachment on the suction surface which forms a laminar separation bubble (LSB) on the airfoil. The LSB on the suction surface deteriorates the aerodynamic performance of the MAV [1]. Optimization techniques are useful in improving the aerodynamic performance. The application of such formal optimization methods is sparse in the literature involving transitional low Re. In the present paper, a surrogate-based optimization methodology is formulated to achieve enhanced aerodynamic performance characteristics. Optimization is performed for two different objective functions: (a) maximizing lift coefficient, C l and (b) maximizing endurance factor (C l 3/2 /C d ), at Re = 5 × 104 . For each of these objective functions, multi-fidelity surrogate models are constructed, and genetic algorithm is employed for optimization.

2 Airfoil Parametrization The choice of a suitable parametrization technique is important in optimization. Two important points have to be kept in mind while parametrizing a given geometry: Firstly, the parametrization technique must be capable of representing the given geometry very accurately, and secondly, it must do this by utilizing a minimum number of control variables for ease in optimization. In the present study, NACA 0012 airfoil is chosen as the baseline and is parametrized using Bezier curves. The airfoil is represented by 12 control points with six each on upper and lower surfaces of the airfoil. Among the 12 control points, six control points are fixed to maintain the leading edge continuity and trailing edge closure. The remaining six control points were allowed to participate in the design process. The control points are allowed to move in y-direction. The bounds on the design variables were set to 50% of their initial values on either side of the control point [2]. Figure 1 shows the Bezier approximation of NACA 0012 airfoil along with the control points and their bounds.

3 Co-kriging-Based Surrogate Modeling In the present study, co-kriging-based surrogate modeling was employed. A large set of cheap data was coupled with a comparatively smaller set of expensive data build the surrogate. Co-kriging-based surrogate model takes advantage over standard kriging model by constructing an accurate model with a fewer high-fidelity evaluations. In

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Fig. 1 Bezier approximation of NACA 0012 airfoil also showing the control points and their bounds

the present study, high-fidelity evaluations were done in ANSYS FLUENT, and lowfidelity evaluations were done in XFLR5. High-fidelity solutions are more accurate and expensive, but low-fidelity solutions are less accurate and cheap. Co-kriging model was built by combining the set of data from high-fidelity and low-fidelity evaluations as follows: ⎡ (1)  ⎤ ⎡ ⎤ yc x c x (1) c ⎢ ⎥ .. ⎢ . ⎥ ⎢ ⎥ . ⎢ .. ⎥ ⎢

⎥ ⎥ (n ⎢ ⎥     ⎢ c) ⎢ (n c ) ⎥ ⎢ yc x c ⎥ Y c (xc ) Xc ⎢ xc ⎥ ⎢ ⎥

 (1) = ⎢ (1) ⎥ and y = =⎢ x= (1) ⎥ ⎢ xe ⎥ Y e (xe ) Xe ye x e ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ .. ⎢ .. ⎥ ⎢ ⎥ ⎣ . ⎦ ⎣ . ⎦ (n c ) (n e) xe ye x e where X denotes a vector of design variables, X c and X e denotes the sampling plan of the cheap and expensive dataset, respectively. Y c and Y e represents the corresponding functional values at these training points. The expensive code using the auto-regression model of Kennedy and O’Hagan [3] is expressed as Z e (x) = γ Z c (x) + Z d (x)

(2)

where Z c (x) and Z e (x) denotes the local features of cheap and expensive codes, respectively, while Z d (x) denotes a Gaussian process which represents the difference between the γ Z c (x) and Z e (x). γ denotes the scaling parameter. The covariance matrix with both high- and low-fidelity dataset is given as

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ργc2 ψc (X c , X e ) γc2 ψc (X c , X c ) C= 2 2 2 ργc ψc (X e , X c ) ρ γc ψc (X e , X e ) + γd2 ψd (X e , X e )

 (3)

ψc (X c , X e ) represents the correlation matrix between the data X c and X e . There are two correlation and four hyper-parameters to be determined because of the usage of two datasets. For the given data and the values of estimated hyper-parameters, the co-kriging predictor is given as. Forrester et al. [4] can be referred for more detailed information.

 y e (x) = μˆ + cT C −1 y − 1μˆ



(4)

4 Computational Procedure and Grid The high-fidelity computations are performed using ANSYS FLUENT. The two dimensional, steady and incompressible Navier–Stokes equations in Eq. 5 are solved numerically. ∇ · u = 0 1 u · ∇ u = − ∇ p + ν∇ 2 u − u i u j ρ

(5)

Transition SST k-ω model is used here for computations. The transition γ −Reθ model is coupled with SST k-ω model where is turbulence kinetic energy and is specific dissipation rate, is intermittency, Reθ is Re based on momentum thickness. Spatial discretization was done by using a formally second-order accurate discretization scheme, and double-precision arithmetic solver is used for calculations. Boundary conditions applied are velocity inlet and pressure outlet at the domain upstream and domain downstream, respectively. Velocity inlet boundary condition, calculated based on the required Re, is imposed on the upper and lower boundaries. The no-slip boundary condition is imposed on the airfoil. The convergence of the residuals was 10–6 . The sample airfoil geometries are constructed using CATIA. Structured mesh of C-grid topology is generated around airfoil using ANSYS ICEM-CFD. The domain is extended 10c upstream, above and below the airfoil and 20c downstream from the leading edge, where c is airfoil chord length. Mesh generation is automated using script file in ANSYS ICEM-CFD. Figure 2a shows the mesh in the computational domain and (b) shows the grid around the airfoil. The computational domain had 24,500 grid points which was chosen after a careful grid independence study. Grid independence study is performed to ensure that the results are independent of the number of grid points. Three different meshes are

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Fig. 2 a Mesh in the computational domain. b Grid around airfoil

created with different number of grid points (fine mesh, medium mesh, coarse mesh). To perform grid independence study, CFD simulations are carried out at Re = 5 × 104 , Tu = 0.3% and α = 6°. Table 1 shows the values of C l and C d for different number of grid points. The grid convergence index (GCI) between G2 and G3 is less when compared between G1 and G2 . From the grid independence study, grid G2 is selected for the further computations. Y + is maintained 0.6 for all the computations. The present computational results were validated with the experimental results of Kim et al. [5] at Re = 4.8 × 104 , Tu = 0.3% and α = 6˚. Figure 3 shows the comparison of C p distribution with experimental results. A good agreement was seen validating the present computational procedure.

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Table 1 Grid independence study α = 6° Grid

No. of grid points

Cl

GCI for Cl

Cd

GCI for Cd

G1

11,712

0.5629

1.41180

0.0332

2.29432

G2

24,500

0.5814

0.0312 0.35175

G3

49,200

0.47963

0.5933

Fig. 3 Comparison of C p distribution with experimental result

0.0308

-2 Present CFD Expt. (Kim et al., 2011)

-1.5

Cp

-1

-0.5

0

0.5

1

0

0.2

0.4

0.6

0.8

1

x/c

5 Optimization Methodology In the present work, surrogate-based multi-fidelity optimization was performed. Cokriging-based multi-fidelity surrogate was built using low- and high-fidelity datasets. Latin hypercube sampling (LHS) technique [4] is used to sample the design space. The sample points given by LHS are converted into the actual coordinates of the design variables based the upper and the lower limits in the y-direction. A sample of 150 airfoils is generated using LHS technique, and the objective functions were evaluated using XFLR5. Thirty airfoil samples were randomly chosen from the set of 150 airfoils, and the objective function is evaluated using FLUENT. The sample geometries were constructed using CATIA. Automated mesh generation was done using script files in ICEM-CFD. Co-kriging surrogate model was constructed using these 150 cheap and 30 expensive datasets. The surrogate model was subjected to genetic algorithm toolbox in MATLAB. Expected improvement infill technique [4] was used to update the surrogate. Expensive evaluations were carried out for the optimal geometry identified by the GA, and it was used to update and reconstruct the surrogate. The procedure was repeated until the convergence criterion is met. The

Multi-fidelity Aerodynamic Optimization … Fig. 4 Quality of multi-fidelity surrogate

245

0.6

MFS prediction

0.55

0.5

r2 = 0.757

0.45

0.4 0.4

0.45

0.5

0.55

0.6

Independent data set

  ∗  ≤ 10–3 where f k∗ is current objective function convergence criteria are  f k∗ − f k−1 ∗ pervious objective function value. Figure 5 shows the flowchart of value and f k−1 the expected improvement-based optimization process. A co-kriging-based multi-fidelity surrogate model was built using 150 low-fidelity and 30 high-fidelity datasets. The quality of this surrogate model was estimated by obtaining the model predictions and comparing with an independent high-fidelity dataset as shown in Fig. 4. This independent high-fidelity dataset was obtained from a separate study [2]. The correlation coefficient, r 2 , between the two sets of data, was 0.757. It is important to note that this value of r 2 is only for the initial build of the surrogate. In the iterative process described in the previous paragraph and illustrated in Fig. 5, high-fidelity infill point, evaluated from the expected improvement method, is used to update the surrogate model at every iteration, and thereby, the quality of the model improves subsequently.

6 Results and discussion The objective procedure was carried out as detailed in Sect. 5. The convergence of the objective function with iterations for both the objective functions is shown in Fig. 6. It can be seen that the objective function converges in about eight iterations. The optimal airfoil geometries for both the objective functions are shown in Fig. 7. The optimal airfoils had camber and a reduced thickness. The maximum t/c for optimal geometry is 12.6% at 30% chord, and the maximum camber of the optimal airfoil is 0.4% occurring at 19% chord for maximizing C l . The maximum t/c for

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Objective function

Design variables

Design

Constraints

Design of experiments

Expensive evaluation

Cheap evaluation

Multi-fidelity surrogate

Genetic algorithm

CFD

No

Convergence

Yes Optimal geometry Fig. 5 Flowchart of multi-fidelity optimization procedure

Multi-fidelity Aerodynamic Optimization … Fig. 6 Convergence of objective function for a maximizing C l and b maximizing (C l 3/2 /C d )

247

0.6

0.5

Cl

0.4

0.3

0.2

0.1

0

0

2

4

6

8

6

8

Itrerations

(a) 20

3/2 Cl /Cd

18

16

14

0

2

4

Itrerations

(b)

optimal geometry is 9.2% at 40% chord, and the maximum camber of the optimal airfoil is 1.6% occurring at 17% chord for maximizing (C l 3/2 /Cd ). The streamlines over the optimal airfoils are shown in Fig. 8. A prominent LSB was observed on the upper surfaces of the optimal airfoils. The separation, transition and reattachment locations and the length of the LSB were evaluated from C f distribution on the upper surface of the airfoils shown in Fig. 9. They are tabulated in Table 2. There was early separation and early reattachment resulting in a reduced bubble length for the optimal airfoil for maximizing C l case. However, for

248

Optimalgeometry Baseline 0.05

y/c

Fig. 7 Comparison of optimal and baseline geometry for a maximizing C l and b maximizing (C l 3/2 /C d )

R. Priyanka et al.

0

-0.05 0

0.2

0.4

x/c

0.6

0.8

1

(a) Optimalgeometry Baseline

y/c

0.05

0

-0.05 0

0.2

0.4

0.6

x/c

(b) Fig. 8 Streamlines over the optimal geometry for a maximizing C l and b maximizing (C l 3/2 /C d )

0.8

1

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0.03

Fig. 9 C f distribution on the upper surface of the optimal geometry for a maximizing C l and b maximizing C l 3/2 /C d

Cf

0.02

0.01

0

0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

x/c

-0.01

(a)

0.03

Cf

0.02

0.01

0

0

0.2

0.4

x/c

(b)

-0.01

Table 2 Comparison of LSB of optimal and baseline airfoil for a maximizing C l . b maximizing C l 3/2 /C d (a) (x/c)s

(x/c)t

(x/c)r

LLSB

Baseline

0.23

0.66

0.79

0.56

Optima

0.21

0.61

0.69

0.48

Baseline

0.23

0.66

0.79

0.56

Optima

0.19

0.67

0.78

0.59

(b)

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the optimal airfoil for maximizing (C l 3/2 /C d ) case, there was early separation, but the reattachment location was only slightly early. This resulted in the little longer bubble length compared to the baseline airfoil. Figure 10a shows the pressure distribution over the optimal and baseline airfoils for maximizing C l case. From C p plot, we can see that the change in pressure distribution on the upper and lower surfaces of the airfoil contributes to C l improvement. However, the pressure distribution on the upper surface of optimal airfoil for maximizing (C l 3/2 /C d ) case was nearly the same as the baseline airfoil. This is due to the fact that the upper surface of both baseline and optimal airfoils had similar Fig. 10 Pressure distributions over optimal and baseline airfoil for a Maximizing C l , b Maximizing (C l 3/2 /C d )

-2

-1.5

Optimal geometry Baseline

Cp

-1

-0.5

0

0.5

1

0

0.2

0.4

x/c

0.6

0.8

1

(a) -2

-1.5

Optimal geometry Baseline

Cp

-1

-0.5

0

0.5

1

0

0.2

0.4

x/c

(b)

0.6

0.8

1

Multi-fidelity Aerodynamic Optimization … Table 3 Aerodynamic coefficients for the baseline and optimal geometries for a maximizing, C l b maximizing (C l 3/2 /C d )

251

(a) Cl Baseline

0.459

Optimal

0.542

(b) Cl

(C l 3/2 /C d )

Cd

Baseline

0.459

0.0258

12.04

Optimal

0.552

0.0245

16.70

geometry; see Fig. 7b. Much of the C l improvement was brought about by the lower surface and the C d improvement is due to the reduced thickness. The aerodynamic coefficient of the baseline and optimal airfoils for both the objective functions is listed in Table 3. The optimal geometry for maximizing C l has 18.08% improvement compared to the baseline. The optimal geometry for maximizing endurance factor (C l 3/2 /Cd ) has 38.70% improvement compared to the baseline. It is interesting to note that C l for maximizing (C l 3/2 /C d ) objective function is slightly more than that achieved by the maximizing C l objective function. To see why this happens, we plotted the camber distribution of the optimal airfoils in Fig. 11. It is observed that the optimal airfoil for (C l 3/2 /C d ) objective function had picked up larger camber than the other optimal airfoil. The maximum camber was about 1.6% occurring at 17% chord. This higher camber leads to higher C l . Fig. 11 Camber distribution for the optimal airfoils

0.035 0.030 Camber for max. Cl 0.025

Camber for max. (C3/2 l / Cd )

0.020

y/c

0.015 0.010 0.005 0.000 -0.005 -0.010

0

0.2

0.4

0.6

x/c

0.8

1

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7 Conclusion Aerodynamic shape optimization of an airfoil was carried out to obtain optimal airfoil shapes at a transitional low Reynolds number. Parameterization of the airfoil was done using Bezier curve. The Bezier control points were the design variables. Latin hypercube sampling technique was used to sample the design space. Simulations were carried out at Re = 5 × 104 , α = 4° and Tu = 0.3%, using a laminar–turbulent transition model. Optimization was performed for two objective functions: (a) maximizing C l and (b) maximizing (C l 3/2 /Cd ). Co-kriging-based surrogate models were built using multi-fidelity datasets. The surrogate models were subjected to genetic algorithm to obtain the optima. The optimal airfoil for both the objective functions had camber. The objective function improvement for maximizing C l and maximizing (C l 3/2 /C d ) was 18.08 and 38.70%, respectively, compared with the baseline NACA 0012 airfoil.

References 1. Shyy W, Lian Y, Tang J, Viieru D, Liu H (2011) Aerodynamics of low Reynolds number flyers. Cambridge University Press, Cambridge 2. Pranesh C, Sivapragasam M, Narahari H (2019) Multi-fidelity aerodynamic shape optimization of an airfoil at transitional low Reynolds number. In: Ncmdao.org. https://www.ncmdao.org/ docs/NCMDAO2018_Schedule.pdf. Accessed 30 Aug 2019 3. Kennedy M, O’Hagan A (2000) Predicting the output from a complex computer code when fast approximations are available. Biometrika 87:1–13. https://doi.org/10.1093/biomet/87.1.1 4. Forrester A, Sobester, A, Keane A (2019) Engineering design via surrogate modelling: a practical guide (eBook, 2008) [WorldCat.org]. In: Worldcat.org. https://www.worldcat.org/title/eng ineering-design-via-surrogate-modelling-a-practical-guide/oclc/264714649. Accessed 30 Aug 2019 5. Kim D, Chang J, Chung J (2011) Low-Reynolds-number effect on aerodynamic characteristics of a NACA 0012 airfoil. J Aircraft 48:1212–1215. https://doi.org/10.2514/1.c031223

Aerodynamic Optimization of Transonic Wing for Light Jet Aircraft K. Sathyandra Rao, M. Sivapragasam , H. K. Narahari, and Aneash V. Bharadwaj

Abstract Light jet aircraft capable of carrying 6–10 passengers over short and medium ranges find great demand in the present and future civil aviation market. Light jets often cruise at high subsonic Mach numbers enabling greater range. Consequently, the drawback associated with high Mach number flight is that it leads to the deterioration of the aircraft’s aerodynamic characteristics. Aerodynamic optimization of a typical transonic wing was performed to reduce the wing cruise drag coefficient at a fixed Mach number and lift coefficient. A surrogate-based 2D optimization of wing sections was performed. Objective function values were obtained by solving Reynolds-averaged Navier–Stokes equations. The optimal baseline wing was constructed using the optimal airfoil sections obtained from the 2D optimization. Subsequently, parametric studies were conducted using vortex lattice method to arrive at an optimal wing by varying the wing twist distribution. The optimal airfoils showed 2% and 4% reduction in drag coefficient compared to the corresponding baseline airfoils. The optimal wing showed about 4% reduction in drag coefficient compared to the baseline wing. Keywords Transonic regime · Light business jets · Supercritical airfoil · Aerodynamic optimization

K. S. Rao (B) · M. Sivapragasam · H. K. Narahari Department of Automotive and Aeronautical Engineering, Faculty of Engineering and Technology, M.S. Ramaiah University of Applied Sciences, Bangalore, India e-mail: [email protected] M. Sivapragasam e-mail: [email protected] H. K. Narahari e-mail: [email protected] A. V. Bharadwaj Genser Aerospace & IT Pvt. Ltd, Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_19

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Abbreviations c Cd CD Cp C L /C D Cl CL M∞ t/c α

Chord length (m) Airfoil drag coefficient Wing drag coefficient Coefficient of pressure Lift to drag ratio Airfoil lift coefficient Wing lift coefficient Freestream Mach number Thickness to chord ratio Angle of attack (°)

1 Introduction Transport aircraft capable of flying at high subsonic and transonic speeds have dominated the civil aviation market since the 1950s [1]. Light jet aircraft, capable of carrying 6–10 passengers operate over various ranges. There has been an increasing demand for such class of aircraft. These aircraft cruise in the transonic regime where the wing’s aerodynamic performance is limited by the presence of shock waves leading to wave drag penalty. This led to the development of supercritical airfoils which had higher drag divergence Mach number compared to other conventional airfoil designs [2]. The aft lower section of the supercritical airfoil has a concave shape, which contributes to the overall C l , thereby reducing the loading on the upper surface of the airfoil. This leads to a weaker terminal shock wave on the upper surface and hence, a lower wave drag. There is a possibility of further drag reduction of a supercritical airfoil to improve its performance in transonic flight regime through optimization methods. In the present study, a transonic wing was optimized which cruises at a Mach number of 0.79, at a C L of 0.30. The baseline wing consisted of 12% and 10% t/c supercritical airfoils at the root and tip sections, respectively. A family of NASA supercritical airfoils were represented using a set of geometrically orthogonal basis functions. The weighting coefficients of the basis functions were the design variables. A high-fidelity surrogate model was constructed in the design space. Genetic algorithm was applied on the surrogate model to obtain optimal airfoil shapes for minimizing C d . The optimal airfoils were used to construct a swept, cranked-wing whose twist distribution was tweaked to arrive at an optimal wing. The aerodynamic characteristics were evaluated.

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2 Methods 2.1 Computational Procedure NASA SC(2)-0714 airfoil was chosen for validation studies. O-grid topology was used to generate the grid around the airfoil in ANSYS ICEM-CFD. The domain size was chosen after carrying out domain independence study. Boundary influence from the far-field domain was found to be prominent even when the pressure far-field boundary condition was imposed. The domain boundaries were fixed at a distance of 10c from the leading edge of the airfoil in the upstream, upward and downward directions of the airfoil. The downstream boundary was fixed at a distance of 20c from the airfoil leading edge. This type of domain configuration will be represented as 10/20c henceforth. Here c stands for the chord length of the airfoil. The drag coefficient (C d ) was obtained from RANS simulation. Similarly, computations were performed with domains of 20/40c, 30/60c, 40/80c, and 50/100c dimensions. When this study was performed, the grid around the airfoil in 10/20c domain was unchanged while moving towards 20/40c. Similarly, this was applied during generating grids for subsequent larger domains. This is a systematic way of performing a domain independence study, without the grid affecting the variation in flow simulation results. From this study, 50/100c domain was chosen to be suitable for the present study as the change in C d between 50/100c and 40/80c domains was only 1.72%. Also, the computational cost estimated for the optimization process influenced the selection of 50/100c domain. A grid-independence study was performed using the 50/100c domain, to choose a computational grid containing about 2.5 × 105 cells for the present study. The steadystate, compressible Reynolds-averaged Navier–Stokes equations were solved using the finite-volume flow solver ANSYS Fluent. An implicit density-based solver using the Roe-FDS was employed. Spatial discretization was done using the Green-Gauss node based second order upwind scheme. Turbulence closure was achieved by using Menter’s SST k-ω model. Pressure far-field boundary condition was imposed on the domain extents and no-slip boundary condition on the airfoil. Computations were performed for the conditions corresponding to the experiments of [3]. The pressure distributions over the airfoil at C n = 0.8715 obtained from experiment and present computation are compared in Fig. 1. Figure 2 shows a comparison between the computational and experimental drag polar. A good agreement is seen validating the computational procedure.

2.2 Airfoil Optimization The airfoils to be used in construction of the transonic wing were optimized for minimizing C d, at a fixed C l . To realize the effects of the optimized airfoil over the wing, pressure distribution transformation is required. Hence, the cosine rule was

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Fig. 1 Comparison of C p distribution

Fig. 2 Drag polar comparison

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257

employed based on the half chord sweep location of the wing [4]. In this transformation, the C l , airfoil thickness to chord ratio (t/c) and effective Mach number from the wing case were transformed for optimizing the 2D airfoil case. The transformed values on the airfoil corresponding to the wing requirements were: • • • •

C l = 0.43 M ∞ = 0.72 t/c at root = 13.22% t/c at tip = 11.019%

Based on these considerations the optimization problem can be formally stated as follows: Minimize: Cd Subject to: Cl = 0.43 M∞ = 0.72 In the present study a set of orthogonal basis functions were used to represent the airfoil geometry. A series of select supercritical airfoils were represented by a linear combination of basis functions as: j Zi

=

n 

j

bk Z ik

(1)

j

j

k=1

that best fitted the selected airfoils [5, 6]. Here, Z i are basis function coordinates, bk the weighting coefficients and n the number of basis functions. In the present study n was chosen to be 2 and the weighting coefficients b1 and b2 represent maximum t/c and camber, respectively. The two basis functions are represented in Fig. 3 derived by fitting the mean of the source airfoils with the NASA SC(2)-0412 airfoil. The limits on the t/c of the airfoils were: 0.75 ≤ b1 ≤ 1.2 −1.5 ≤ b2 ≤ 1.5 corresponding to maximum t/c bounds of 9% ≤ t/c ≤ 14%. Latin Hypercube Sampling technique [7] was used for sampling the design space. The number of initial samples generally required to represent the design space well is about 10 times the number of design variables. Since two design variables were considered in the present study, the number of samples generated was 20. The aerodynamic properties of the sampled airfoils were evaluated using ANSYS Fluent at a fixed C l = 0.43, M ∞ = 0.72 and Re = 10 × 106 . The constraint of fixed C l made the evaluation of the objective functions expensive, as a minimum of three CFD simulations were necessary to arrive at the required C l . A Kriging-based surrogate

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Fig. 3 Basis functions

model [7] was constructed using these responses. The objective function landscape of the surrogate model is shown in Fig. 4. The coordinate values of design variables b1 and b2 are non-dimensionalized based on the maximum t/c bounds. The quality of this surrogate model was estimated using the leave-one-out crossvalidation method [7]. The root-mean-square error was calculated to be 4.4 × 10–3 %.

Fig. 4 Objective function landscape

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Fig. 5 Comparison of optimal and baseline airfoils. a Wing root, b wing tip

The surrogate model was subjected to genetic algorithm which resulted in optimal airfoils at required t/c values. The optimal airfoil obtained for the root section is shown in Fig. 5a along with the 14% t/c baseline airfoil. The optimal airfoil for the root section had a C d value which was about 2% lower than the baseline airfoil. The optimal airfoil for the tip section had about 4% lower C d than the 12% t/c baseline airfoil. The optimal airfoil obtained for the tip section is shown in Fig. 5b along with the 12% t/c baseline airfoil. The suction peak in the C p distribution was found to be lower in the optimal airfoils, subsequently, a reduced shock strength.

3 Results and Discussion Initially, the baseline wing was constructed using the 12 and 10% t/c baseline airfoils at root and tip of the wing, respectively. A structured grid with 3.0 million cells was generated for the computations. Computations were performed for the wing made of baseline airfoils at C L = 0.3, M ∞ = 0.72 and Re = 10 × 106 . Later, the optimal airfoils obtained from the 2D optimization study were transformed to the corresponding t/c required on the wing. Computations were performed for the wing made of optimal airfoils for the same flow conditions. A parametric study was performed over the optimal baseline wing (wing made of optimal airfoils). The parameter studied here was the wing twist distribution. This was done for wing with optimal airfoil profiles in order to enhance its aerodynamic performance further. The twist distribution was decided based on the spanwise lift distribution on the wing. At the location of the trailing edge kink there was a sudden dip in the load distribution. Hence, it was necessary to obtain higher lift at the kink location, so that the span efficiency factor ‘e’ can be improved by driving towards the ideal elliptic loading. This parametric study was performed in the low-fidelity flow solver OpenVSP [8]. In the present study, vortex lattice method was used to

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simulate the flow over the wing. Before performing the parametric study, the results from the OpenVSP were compared with that of high-fidelity CFD data obtained from ANSYS Fluent. The comparison of drag polar is shown in Fig. 6. The data from the low-fidelity flow solver, OpenVSP was able to match the high-fidelity data. An optimal wing configuration was achieved through the study, which had a washin of 3.5° from the root to the kink location and a wash-out of 3.5° from the kink to the tip of the wing. The comparison of the three wing configurations is shown in Table 1. The shock strength listed in Table 1 is a ratio of increase in static pressure across a shock wave to the freestream static pressure. A comparison of the C P contours over the upper surface of the baseline and optimal wings is shown in Fig. 7. The C P contour lines are more closely spaced near

Fig. 6 Comparison of drag polar from Fluent and OpenVSP

Table 1 Comparison of the three wings Wing

α˚

CL

CD

% Reduction in C D

CL /C D

% Increase in C L /C D

Shock strength

% Reduction in shock strength

Baseline

1.10

0.3

0.01378

–

21.78

–

1.51

Optimal baseline

−0.19

0.3

0.01327

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22.60

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21.19

–

Optimal

−2.19

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0.01327

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22.60

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1.24

17.88

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Fig. 7 C p contour on upper surface. a Baseline wing, b optimal wing

the leading edge of the wing on the outboard sections of the baseline wing indicating shock occurrence. This is not incurred in the optimal wing. The Mach number contours over the upper surfaces of the baseline and optimal wing are compared in Fig. 8. The maximum Mach number has reduced from 1.20 to 1.10 for the case of optimal wing. Consequently, the shock strength has reduced to 1.24 for the optimal wing when compared to 1.51 for the baseline wing. The wing was divided into 20 equidistant stations along its span. The C P distributions at various spanwise stations are plotted in Fig. 9. The critical C P is also plotted in these figures to indicate the occurrence and strength of the shock wave generated over the wing sections. The C P plot comparisons at various spanwise stations show a reduced peak Mach number for the optimal baseline and optimal wings. As seen from Fig. 9e a favorable upper surface platform pressure gradient is observed in the optimal baseline and optimal wings. This helps in attaining required C L at lower drag due to a weaker shock. The shock strength is also reduced for the optimal and optimal baseline wings as seen from the maximum C P above the C P critical line. Computations were extended for a range of angles of attack at Mach number of 0.79 for the three wings. The aerodynamic performances of the three wings are compared in Fig. 10. There is an upward vertical shift observed in the C L versus α curve, for the case of optimal wing compared to both the baseline and optimal baseline wings. This indicates that a lower angle of attack is required by the optimal wing to achieve the same C L . This aids in reducing the wing setting angle which

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Fig. 8 Mach number contour on upper surface. a Baseline wing, b optimal wing

has an advantage of lower form drag for the aircraft. The maximum C L attained by the optimal baseline wing is higher than the baseline wing. The optimal wing is found to have lower values of C D at more negative angles of attack compared to the other two wings. This is mainly because the C L obtained at a given angle of attack is higher for the optimal wing case. Hence, the associated induced drag component is higher, which shows up in the total value of C D . The drag polar of the optimal and the optimal baseline wings have a leftward shift at higher values of C L as seen in Fig. 10c. This indicates that the drag acting on the wings for a given value of C L is lower compared to the baseline wing. The C L /C D curve shifts more towards lower values of α for the optimal wing case. The optimal wing performs better than the baseline wing by achieving the same C L /C D at a much lower angle of attack. Also, the maximum C L /C D achieved by the optimal wing is higher than the baseline wing by 3.8%. The spanwise lift distribution of the optimal wing is plotted in Fig. 11 along with the equivalent elliptic loading. The optimal wing has a lift distribution much closer to the equivalent elliptic loading at a C L of 0.3. This helps to minimize the induced drag component of the wing. Hence, the optimal wing performs better even at higher C L ranges.

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Fig. 10 Comparison of: a C L versus α, b C D versus α, c drag polar, d C L /C D versus α

4 Conclusion A surrogate-based optimization procedure was employed to obtain optimal airfoils for minimizing C d . The optimal airfoils had about 2% and 4% lower C d compared to corresponding baseline airfoils at the root and tip sections, respectively. Optimal baseline wing was constructed using the optimal airfoils. The optimal baseline wing was tweaked to obtain an improved spanwise lift distribution, by varying the wing twist angle. The spanwise lift distribution was found to be close to the equivalent elliptic lift distribution in the optimal wing as against the baseline wing. The optimal wing had about 4% lesser C D than its baseline counterpart. An increase in the Oswald span efficiency factor of around 0.4% was obtained for the optimal wing as against the baseline. The aerodynamic advantages gained by the optimal wing over the baseline wing makes it a good contender for medium/long range transonic flights.

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Fig. 11 Spanwise C L distribution of optimal wing

References 1. Vos R, Farokhi S (2015) Introduction to transonic aerodynamics. Springer, London 2. Whitcomb RT, Clark LR (1965) An airfoil shape for efficient flight at supercritical Mach numbers. NASA-TM-X-1109, L-4517. NASA, Washington 3. Jenkins R, Hill A, Ray E (1988) Aerodynamic performance and pressure distributions for a NASA SC(2)-0714 airfoil tested in the Langley 0.3-meter transonic cryogenic tunnel. NASA Technical Memorandum 4044 4. Zhao T, Zhang Y, Chen H et al (2016) Supercritical wing design based on airfoil optimization and 2.75D transformation. Aerosp Sci Technol 56:168–182. https://doi.org/10.1016/j.ast.2016. 07.010 5. Robinson GM, Keane AJ (2001) Concise orthogonal representation of supercritical airfoils. J Aircraft 38:580–583. https://doi.org/10.2514/2.2803 6. Keane AJ, Nair PB (2005) Computational approaches for aerospace design: the pursuit of excellence. Wiley, Chichester, pp 429–479 7. Forrester AIJ, Keane AJ, Sobester A (2008) Engineering design via surrogate modelling: a practical guide. Wiley, Chichester 8. OpenVSP (2018) https://openvsp.org/wiki/doku.php?id=start

Non-adiabatic Wall Effects on Transonic Shock/Boundary Layer Interaction Sahil Bhola

and Tapan K. Sengupta

Abstract Direct simulations are carried out to investigate the influence of unsteady heat flux transfer on transonic shock-boundary layer interaction; for flow past SHM-1 airfoil at a free-stream Mach number M∞ = 0.72 and angle of attack α = 0.38◦ . Flux is added in a periodic manner through a region (8−18% of the chord ) located on the suction side of the airfoil, with multiple values of exciter time period (Te = 2, 4) considered for our simulation. We show that addition of unsteady heat flux delayed shock formation, along with significant modifications in it’s structure. The time-averaged Cp distributions revealed a shift in the shock towards the aft, by approximately 5% of the chord; along with an increased lift near the trailing edge, suggesting a nose-down stabilizing influence. Primarily, it is noted that the additional heat flux resulted in an overall increase of the aerodynamic efficiency (lift to drag ratio) by approximately 10%. Keywords DNS · SBLI · Transonic flow

1 Introduction The phenomenon of shock-wave boundary layer interaction (SBLI) in transonic flow regime has significant influence on the aerodynamic and the thermodynamic design through substantial modifications of the flow field. It involves several repercussions, such as alteration of the wall pressure, modification of the highly viscous boundary layer, flow unsteadiness, increased drag etc. An adequate understanding of this highly time dependent phenomenon, by solving the compressible Navier-Stokes equations S. Bhola (B) Thapar Institute of Engineering and Technology, Patiala, India e-mail: [email protected] T. K. Sengupta High Performance Computing Laboratory, Department of Aerospace Engineering, IIT Kanpur, Kanpur, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_20

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(NSE) is required to predict critical design factors such as shock location, aerodynamic forces, along with efficient techniques for it’s control. Several studies[1–4] have been carried out to understand the interaction of shock wave (SW) with boundary layer (BL), however all these works implemented the adiabatic wall boundary conditions. Direct numerical simulations (DNS) to investigate the influence of wall temperature on the shock wave and turbulent boundary layer interaction for a wedge reflected shock, has been carried by Bernardini et al. [5] at a free stream Mach number M∞ = 2.28 and wall-recovery temperature values (Tw /Tr ) of 0.5, 0.75, 1.0, 1.4, 1.9. It was reported that in case of cooling (Tw /Tr 1). Numerical simulations to investigate the effect of steady heat transfer on transonic flows over NACA0012 airfoil using the thin-layer NSE with Baldwin-Lomax turbulence model were reported by Raghunathan and Mitchell [6] , where surface cooling resulted in decrease of the drag coefficients along with a fuller velocity profile, as compared to the adiabatic wall case. Qualitative understanding of the control of the periodic shock motion through heat transfer on a 14% bi-convex airfoil at a transonic Mach number M∞ = 0.83, Re = 9 × 106 , α = 0◦ were reported by Raghunathan et al. [7] , where transfer of energy from the mainstream to boundary layer (cold wall) made the boundary layer more resistant to separation and reduced the amplitude of shock oscillation. Prior scientific work pertaining to SBLI and it’s control through heat transfer addresses the case of steady heat flux transfer across the wall and to our knowledge, no high-fidelity simulations have been carried out to investigate the effect of unsteady heat flux transfer across the wall on SBLI. The authors report DNS results to investigate the influence of unsteady heat flux transfer on SBLI, across a natural-laminar-flow (NLF) airfoil, the SHM-1 [8] profile. Several numerical schemes [9–14] have been proposed to accurately capture the dynamics of shock wave in a compressible flow, and for the present work to attain near spectral accuracy using relatively compact stencils, we use the dispersion relation preserving (DRP), optimized upwind compact schemes [15–17]. It was shown by Sengupta et al. [18] that these compact schemes which were originally developed for direct simulation of incompressible flows, could be used to clearly capture the SBLI in case of compressible transonic flows. Computational validation for flow past SHM-1 without the unsteady flux transfer across the airfoil surface is done through the experimental data reported by Fujino et al. [8] for the two dimensional transonic wind-tunnel testing. Although, problems related to two-dimensional testing in transonic wind tunnels [19, 20] such as wall interference, three-dimensional effects in two-dimensional tests might affect the reliability of the data. The manuscript is organized as follows. Followed by the introduction, the numerical strategy and the flow conditions of the simulations are described in Sect. 2 and the results of the DNS are presented in Sect. 3. Concluding remarks drawn from the obtained results are finally provided in Sect. 4.

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2 Computational Setup 2.1 Flow Solver To investigate the highly time dependent phenomenon of SBLI, the two-dimensional (2D) NSE is solved in strong conservation form for a perfect compressible gas, with the application of Prandtl analogy for thermal conductivity and Sutherland’s law to compute the dynamic viscosity. Molecular heat conductivity in the flow has been evaluated using the Fourier heat law, and Newtonian viscous stress components have been used to compute the shear stress in the flow. The governing equations have been discretized on a transformed curvilinear coordinate system (ξ, η) by introducing a transformation [ξ = ξ(x, y), η = η(x, y)], using an in-house developed solver based on finite-difference schemes, which has been previously validated by Sengupta et al. [18] to compute 2D transonic flows over NACA0012 and SHM-1 airfoils. Convective flux derivatives were evaluated through high accuracy optimized, implicit upwind compact scheme [21] OUCS3 and its symmetrized version S-OUCS in the η and ξ directions, respectively. These implicit schemes are highly robust, have superior stability, DRP [15, 16, 22] properties and provide near-spectral accuracy by optimizing the numerical dispersion and dissipation in the spectral plane [17, 23]. To provide closure at the boundary and the near boundary points, explicit schemes have been used, as proposed by Sengupta et al. [15]. Derivatives in the isotropic viscous flux terms are evaluated using the second order central differencing (CD2) scheme in self-adjoint form, preserving isotropic nature. The schemes are used in parallel computing framework using Message Passing Interface (MPI) libraries, by domain decomposition technique [24, 25] , which require overlap of the sub-domains to attenuate non-physical growth near the sub-domain boundaries. Time integration has been performed using a third-order, low-storage, explicit Runge-Kutta scheme [26]. The governing equation in non dimensional, strong conservation form in the physical (x, y)-plane is given by ˆ ∂ Eˆ ∂ Fˆ ∂ Eˆv ∂ Fˆv ∂Q + + = + ∂t ∂x ∂y ∂x ∂y where the conservative variables are ˆ = [ρ, ρu, ρv, ρet ]T Q The convective flux vectors, Eˆ and Fˆ are Eˆ = [ρu, ρu2 + p, ρuv, (ρet + p)u]T Fˆ = [ρv, ρuv, ρv 2 + p, (ρet + p)v]T and the viscous flux vectors Eˆv and Fˆv are given by

(1)

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Eˆv = [0, τxx , τxy , (uτxx + vτxy − qx )]T Fˆv = [0, τyx , τyy , (uτyx + vτyy − qy )]T In Eq. (1), the variables ρ, u, v, et , p represent the non-dimensional density, Cartesian velocity components, total specific energy, and pressure. All the terms were non-dimensionalized√with scales such as the free stream density (ρ∞ ), free stream velocity (U∞ = M∞ γ RT∞ ), free stream temperature (T∞ ), free stream dynamic viscosity (μ∞ ), Length scale (L = c) and (c/U∞ ) for time; where γ denotes the heat capacity ratio (1.4 for air). Stokes hypothesis (3λ + 2μ = 0), where λ and μ are the Lame’s coefficient has been assumed, thereby neglecting the effect of molecular bulk viscosity while computing the viscous flux components. The heat conduction terms involved are given by ∂T μ 2 ∂x PrRe∞ (γ − 1)M∞ ∂T μ qy = − 2 PrRe∞ (γ − 1)M∞ ∂y qx = −

μ ReM 2 γ RT

and are non-dimensionalized using ( ∞ L∞∞ ∞ ) scale. Governing equations in the transformed curvilinear coordinate system, written in strong conservation form, preferred for suitable capturing of shocks [16] is given by ∂F ∂Ev ∂Fv ∂Q ∂E + + = + ∂t ∂ξ ∂η ∂ξ ∂η where the corresponding state variables and flux vectors are given by ˆ Q = Q/J ˆ E = (ξx Eˆ + ξy F)/J ˆ F = (ηx Eˆ + ηy F)/J Ev = (ξx Eˆv + ξy Fˆv )/J Fv = (ηx Eˆv + ηy Fˆv )/J

where J is defined as the Jacobian of the transformation and is given by J =

1 xξ yη − xη yξ

The grid metrics terms ξx , ξy , ηx , ηy are computed as ξx = Jyη ; ξy = −Jxη ; ηx = −Jyξ ; ηy = Jxξ

(2)

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Heat conduction terms in the transformed plane are given by μ (ξx Tξ + ηx Tη ) 2 PrRe∞ (γ − 1)M∞ μ qy = − (ξy Tξ + ηy Tη ) 2 PrRe∞ (γ − 1)M∞ qx = −

While performing the reported computations, we have not used any model for transition and/or turbulence. However, to eliminate the spurious high wavenumber (k) components, which may lead to numerical instability, we have used explicit twodimensional filters [16, 27] in the whole domain. The two-dimensional filter stencil is given by, uˆ i,j + α2 (ˆui−1,j + uˆ i+1,j + uˆ i,j−1 + uˆ i,j+1 ) =

m  an n=0

2

(ui±n,j + ui,j±n )

where as per convention, 2 m represents the ‘order’ of filter and α2 is the twodimensional filter coefficient, which ranges from −0.25 to 0.25; where α2 = 0.25 indicates no filtering of the solution. To attenuate the numerical errors and the possible Gibbs’ phenomenon while computing high wavenumber components, a transfer function [16] (Ti,j ) (defined in the k-plane) was chosen. This is given by T(ki hi ,kj hj ) =

 a0 + m i=1 ai [cos(mki hi ) + cos(mkj hj )] 1 + 2α2 [cos(ki hi ) + cos(kj hj )]

In the present computations, we have used a ’Sixth’ order filter to represent the filtered quantities (ˆu) in terms of unfiltered variables (u) in an explicit manner. For moderate filtering of the solution, filter coefficient (α2 ) has been taken as 0.2. Data filtering has been performed at the final stage of each ORK3 time-integration step and to obtain the filtered physical quantities, the iterative technique of BI-CGSTAB [28] have been used till the residue converges to 1 × 10−6 .

2.2 Flow Conditions and Computational Arrangement Flow past the SHM-1 airfoil is computed using an orthogonal, body-conforming O-grid topology which is generated using hyperbolic grid generation technique [17, 29] , with 959 points in azimuthal (ξ ) direction and 500 points in the wall-normal (η) direction. This required the introduction of a mathematical cut-(ξ -direction) in the computational domain, along which periodicity of flow variables is used. The mapping from the physical plane to the transformed plane is one-to-one, with uniform grid spacing in the transformed plane ( ξ = η = 1).

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Fig. 1 Computational domain and boundary segments

A schematic view of the flow configuration investigated is shown in Fig. 1, which shows a non-adiabatic region along the top surface of the airfoil, placed between 0.08c (ξi = 100) to 0.18c (ξf = 150). Location of this non-adiabatic region is chosen so that it lies a head of the supersonic pocket developed in case of the completely adiabatic wall; thereby, locally accelerating the flow, according to the ideal Rayleigh flow. Exchange of heat flux in the non-adiabatic region takes place along the wallnormal direction, and to avoid it’s discontinuity along the airfoil surface, a Gaussian function is prescribed for the wall-normal heat flux (qη ) in the transformed plane as ξ −ξo 2 ∂q = qη = A(t)[exp( 10 ) ] ∂η

(3)

where, ξo corresponds to the location of maximum flux transfer in the transformed plane and A(t) is the time-varying periodic amplitude given by A(t) = 1.01 × 10

−6

  2π t π + 4.95 × 10 sin − Te 2 −7

(4)

This spatio-temporal dependence of wall normal heat flux function ensure the flux expenditure remained in the physical limits, with a mean transfer rate of approximately 422 W m−2 (Te = 2) and 217 W m−2 (Te = 4). This is a small perturbation. The heat conduction terms in the non-adiabatic region are given by qx = qη ηx qy = qη ηy

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and for the adiabatic wall region, there is no transfer of heat flux qx = 0 qy = 0 On the airfoil surface, no-slip boundary condition is imposed in terms of velocity components, given by u=v=0 Assuming one dimensionality of the flow (in η-direction) at the far field, nonreflective characteristic-like boundary conditions [30, 31] , based on the onedimensional Euler equations are enforced. Depending upon the sign of eigenvalues, of the linearized 1-D Euler equations, flow at the inflow or at the outflow could either be subsonic or supersonic. Characteristic variables are used to enforce the boundary conditions at the free stream, where any information entering the computational domain is set to it’s free stream values and the information leaving the computation domain, is extrapolated using the interior flow variables. The outer boundary of the computational domain is located at approximately 22c from the airfoil surface, for accurate implementation of the far-field boundary conditions and to avoid contamination of the flow-field from the acoustic wave reflection at the boundaries. Numerical simulations have been carried out at values of Te = 2, 4 and for a completely adiabatic wall (without exciter); which and are labeled as SBLI-T2, SBLI-T4, SBLI-U, respectively. For all the cases free-stream initial conditions are implemented on all the flow variables, with free-stream Mach number M∞ = 0.72 , Re = 16.2 × 106 , α = 0.38◦ , T∞ = 222.36 K and ρ∞ = 1.101552 kg m−3 .

3 Results and Discussion This section presents the results of the simulations with adiabatic wall conditions, essentially validated with the flight test data reported by Fujino et al. [8] and also computations carried out with the added unsteady heat flux. The instantaneous flow field analysis along with time-averaged data analysis have been done to underline the salient features of the transonic SBLI.

3.1 Validation of Methodologies for Compressible Flow Calculation and Shock Capturing For transonic flow past SHM-1 airfoil, without any unsteady flux transfer across the wall (SBLI-U), numerically obtained pressure coefficients are compared with

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Fig. 2 Comparison of computed and experimental Cp -distribution for flow around SHM-1 airfoil, without exciter(SBLI-U). Averaging is done over t = 50–80

reference experimental values, and are shown in Fig. 2. To obtain a clear view of the transonic compressible flow, we have time-averaged the computed solution over meaningful intervals, removing the initial transient state resulting from introducing the airfoil into the computational domain. A good agreement is observed between the experimental and computed time-averaged pressure coefficients, with a slight deviation in shock location, which could be accounted through an error of 5% [4] in experimentally determined inflow Mach number. As reported by Sengupta et al. [18] , these flows show significant time-dependent behavior prior to the formation of the shock and such unsteadiness are augmented with shock formation, due to the physical dispersion of high wavenumber components. Discontinuities of physical variables across the shock excites wide spectrum of physical variables, consequentially one could notice from Fig. 3, the downstream convection of pressure pulses which originated near the shock. It is to be further noted, that we did not observe any spurious upstream propagating q-waves [16], which is in agreement that such unsteadiness for high wave numbers is due to physical dispersion and not numerical dispassion [18]. Instantaneous numerical Schlieren pictures for the selected flow conditions are shown in Fig. 4. In this case, Robert’s cross edge detector model [32] is used as a methodology to numerically visualize the strong density gradients developing within the flow field. From the instantaneous Schlieren images, we note a self-sustained oscillatory motion of the shock wave with varying amplitude, on the suction side of the airfoil. Lee et al. [33] identified this 2D transonic buffeting as a closed loop mechanism based on the coupling between the shock and the trailing edge, through pressure waves. Due to the physical dispersion at the shock discontinuity, pressure pulses are generated at regular intervals, which propagate downstream within the boundary layer. At the trailing edge, these pressure waves diffract and cause wake deflection, consequentially generating upstream propagating pressure waves, termed as Kutta waves [34].

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Fig. 3 Comparison of computed instantaneous Cp -distribution with experimental values for flow around SHM-1 airfoil, without exciter (SBLI-U)

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Fig. 4 Visualization of Kutta-wave generation at the trailing edge by Robert’s cross edge detector model for flow around SHM-1 airfoil, without exciter (SBLI-U). The red line denotes the sonic line

These Kutta waves propagate outside the boundary layer, and while moving upstream exhibit non-linear interaction with one another, adding on to their strength. Further upstream, these waves merge into the shock-wave, resulting in an unsteady shock motion and strength modulation [4, 33]. For a thermodynamic systems where the → total enthalpy is conserved, generation of vorticity (− ω ) is an indication of the presence of entropy gradients across any streamline, as given by the Crocco’s theorem [35], RT dp0 T dS − → =− ω = u dη up0 dη

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where S is the entropy and p0 is the stagnation pressure. Such physical gradients of entropy are inherently created in cases of shock formation, consequentially we did notice the creation of rotational effects within the shear layer in the proximity of shock foot as shown in Fig. 4. Generally, it is not possible to numerically capture these phenomena as these excite a wide spectrum of spatial and temporal scales, however the use of high fidelity numerical methods with near-spectral accuracy and superior dispersion properties enable us to capture these with good resolution. For the SHM-1 airfoil used, a spatial resolution of sη = 2.702 × 10−5 has been used to provide near spectral accuracy for the employed compact scheme [15, 16]. Computations have been carried out at a temporal resolution of t = 2.5 × 10−6 , which has been used to accurately capture the wide spectrum of spatial and temporal scales, by providing better DRP properties and numerical stability [16] for the employed space-time discretization schemes.

3.2 Influence of Unsteady Heat Flux To provide an overview of the flow organization and a qualitative perception of the influence of unsteady heat flux on SBLI, we report in Fig. 5, contours of mean Mach number and density. It is to be noted that irrespective of addition of heat flux we could observe the typical characteristics of transonic SBLI, identified by it’s mixed flow nature, i.e presence of locally supersonic region ahead of the shock and a subsonic region downstream of it. Furthermore, it could be observed that addition of heat flux resulted in a marked dilation of the supersonic region along with a shift in the shock location by approximately 5% of the chord further downstream, as also noted from the time averaged Cp distributions reported in Fig. 6. It is evident from these visualizations that the shock structure has been significantly modified, with a much smoother pressure recovery observed, as compared with the SBLI-U case. The Gaussian function imposed on the wall-normal heat flux is revealed in Fig. 6, where the flow experiences a stronger favorable pressure gradient, and is locally accelerated as a consequence of increase in kinetic energy, which is derived from the surge in internal energy due to flux addition. Use of a smooth Gaussian function for flux transfer could be clearly elucidated with the fact that we do not observe any sudden discontinuity in the physical variables at the boundary of the non-adiabatic region, which could potentially be sites for Gibbs’ phenomenon. At the aft region of the airfoil, we could note that there is an increase in suction, whereas the pressure distribution on the bottom surface showed minimal variations. These pressure distributions suggested that under the same flow parameters, addition of unsteady heat flux resulted in an increased lift near the trailing edge of the airfoil in conjunction with a stabilizing pitch-down moment. By performing time-accurate simulation we are able to capture the unsteady nature of flow separation and the formation of the laminar separation bubble at the shock foot due to the fluctuations in longitudinal pressure

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Fig. 5 a Computed mean Mach contours, b computed mean density contours for M∞ = 0.72, Re = 16.2 × 106 , α = 0.38◦ . Time averaging is done over t = 50–80

gradients. These pressure variations over the airfoil surface resulted in the formation of multiple separation points, which are broadly identified in the near vicinity of the shock foot and the trailing edge, as depicted through instantaneous Cf variations in Fig. 7. The flux amplitude function A(t), as given by Eq. (4) has been chosen, such that there is continuous heat flux addition from across the airfoil surface to the flow. The periodic nature of the amplitude function could be reflected through the distribution of instantaneous wall temperature (Tw ) on the suction side of the airfoil as reported in Fig. 8. Physically, the maximum flux transfer rate peaked to approximately 1772 W m−2 (SBLI-T2) and 886 W m−2 (SBLI-T4), as a consequence of which we could note strong amplifications in the wall temperature distribution. However, it was further noted that due to the strong convection of heat energy ( ξ dominated ), these fluctuations were not of periodic nature themselves and could reach a maximum value of 2223.6 K approximately at around 13% of chord. As previously discussed, there exists a self sustaining closed feedback mechanism for shock oscillation on the surface of the airfoil due to which the pressure and shear forces become highly

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Fig. 6 Comparison of computed and experimental Cp -distribution for flow around SHM-1 airfoil. Averaging is done over t = 50–80

time-dependent. Impulsively introducing the airfoil into the computational domain with a uniform initial flow condition excites a wide band of spectrum in the spectral plane and produces results that are physically not relevant. In most cases, it took about t  20 for the flow to develop into a meaningful viscous state. Hence, in order to evaluate the time evolution of the loads acting on the airfoil we show the computational results from t = 20 to t = 80 which physically correspond to a time duration of 0.278 s. The coefficient of lift (Cl ) and drag (Cd ) are computed by integrating the static pressure and shear stress over the airfoil surface. Addition of unsteady heat flux introduces a time scale into the flow which alters the pressure and shear force distribution over the airfoil, as one could observe through Figs. 9a, 10a and 11a, which report the instantaneous Cl , Cd and Cf excursions, respectively. To bring out the contrast between the load distribution signature, corresponding fast Fourier transformation (FFT) are shown in Fig. 9b, 10b, 11b. These FFT reveal additional heat flux modulated the natural frequency of the signal, as marked in the figures. Slight variations could be noted in case of Cl and Cd spectrum, however in the case of Cf , we observe a surge in amplitude of the dominant frequency. These variations suggest that the major effect of heat flux on drag is through skin friction variation, which is a function of dynamic viscosity (temperature dependent). Table 1 shows the consolidated mean load values along with the lift to drag ratios, to comprehend the influence of heat flux on pressure and shear forces. We do notice that there is a significant increment in the mean lift coefficient (C¯ l ) by approximately 26% (SBLI-T2) and 26.8% (SBLI-T4), as we could also observe through the Cp distributions reported in Fig. 6. Overall, an increment in the lift to drag ratio was noted by approximately 8.9% (SBLI-T2) and 10% (SBLI-T4), as compared to the completely adiabatic wall case, indicating an increase in the aerodynamic efficiency of the control surface.

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Fig. 7 Instantaneous skin friction coefficient distribution on the suction side

4 Summary and Conclusion The present paper has presented first-time results from a simulations of unsteady heat flux transfer from an airfoil at M∞ = 0.72, α = 0.38◦ , Re = 16.2 × 106 . The objective is to augment the knowledge on transonic Shock-wave boundary layer interaction (SBLI) by performing high-resolution, high-accuracy simulations to capture the phenomenon involved in a transonic flow over the SHM-1 airfoil. First, computations are performed with the adiabatic wall boundary condition, which have shown good agreement of Cp distribution with flight test data [8] , with a slight underestimation in the shock location. The instantaneous flow field analysis reveals a self sustaining closed feedback mechanism of shock oscillation, as a consequence of physical dispersion and wake deflection. Typically, these highly time-dependent phenomenon are difficult to resolve as they excite large spectrum of spatial and temporal scales, however with the usage of compact schemes with near-spectral accuracy and good DRP properties, these are captured nicely. Moreover, presented computations do not require any model for transition and turbulence, except the two-dimensional

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Fig. 8 Instantaneous wall temperature Tw distribution for flow around SHM-1 airfoil

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Fig. 9 a Instantaneous Cl distribution and b FFT for flow around SHM-1 airfoil. t = 20–80

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Fig. 10 a Instantaneous Cd distribution and b FFT for flow around SHM-1 airfoil. t = 20–80

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Fig. 11 a Instantaneous Cf distribution and b FFT for flow around SHM-1 airfoil. t = 20–80

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Table 1 Computed mean loads for viscous flow past SHM-1 airfoil. Averaging is done over t = 20–80 Case Lift-drag C¯ l C¯ d C¯ f ratio (C¯ l /C¯ d ) SBLI-U SBLI-T2 SBLI-T4

0.2092 0.2634 0.2654

6.671 ×10−3 7.710 ×10−3 7.707 ×10−3

8.724 ×10−4 9.134 ×10−4 9.148 ×10−4

31.35 34.16 34.43

Pad´e filters to remove the spurious high wavenumber components that might lead to numerical instability. Computations performed with the unsteady heat flux transfer (SBLI-T2 and SBLIT4) reveal significant dilation of the supersonic region along with a shift in the shock location by approximately 5% of the chord, downstream. The time averaged Cp distribution further suggested a higher lift near the trailing edge, which provides a nose-down stabilizing influence on the airfoil surface. By computing time-accurate flow, we are able to capture the longitudinal pressure variations, which are responsible for the creation of multiple sites of unsteady separation near the shock foot and at the trailing edge of the airfoil. It is noted that primarily unsteady heat flux influences the airfoil drag, through variation in the skin friction, which further depends on the dynamic viscosity of the fluid medium. Overall, we are able to increase the lift to drag ratio of the control surface by approximately 8.9% (SBLI-T2) and 10% (SBLI-T4), reflecting a significant increment in the aerodynamic efficiency. Hence, these computations lay down the groundwork to study the influence of rapid unsteady heat rejection across a control surface on transonic SBLI. Typically, they could be used to study the load fluctuations and the delay in shock formation across a control surface in a stabilized altitude vehicle. Primarily, modifications in the shock structure is studied by placing a non-adiabatic region on the airfoil surface; in the subsonic flow regime ahead of the supersonic pocket. Since energy conservation remains the primary objective of the aerospace industry, it is necessary to study the flow control using minimal energy input. Further investigations are required to study transonic SBLI using different duty cycles for the heat flux, unlike the sinusoidal cycles used here which resulted in continuous addition of heat flux into the flow. Additionally, multiple magnitudes of flux transfer rates and exciter location should be considered to augment our knowledge on the outcomes of unsteady heat flux transfer on SBLI.

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References 1. Toure PSR, Schuelein E (2018) Numerical and experimental study of nominal 2-D shockwave/turbulent boundary layer interactions. In: AIAA 2018-3395, fluid dynamics conference, 3395 2. Gross A, Lee S (2018) Numerical analysis of laminar and turbulent shock-wave boundary layer interactions. In: AIAA 2018-4033, fluid dynamics conference , 4033 3. Quadros R, Bernardini M (2018) Numerical investigation of transitional shock-wave/boundarylayer interaction in supersonic regime. AIAA J 56:2712–2724 4. Hermes V, Klioutchnikov I, Olivier H (2013) Numerical investigation of unsteady wave phenomena for transonic airfoil flow. Aerosp Sci Technol 25(1):224–233 5. Bernardini M, Asproulias I, Larsson J, Pirozzoli S, Grasso F (2016) Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions. Phys Rev Fluids 1(8):084403 6. Raghunathan S, Mitchell D (1995) Computed effects of heat transfer on the transonic flow over an aerofoil. AIAA J 33(11):2120–2127 7. Raghunathan S, Early JM, Tulita C, Benard E (2008) Periodic transonic flow and control. Aeronaut J 112(1127):1–16 8. Fujino M, Yoshizak Y, Kawamura Y (2003) Natural-laminar-flow airfoil development for a lightweight business jet. J Aircr 40(4):609–615 9. Chakravarthy S, Harten A, Osher S (1986) Essentially non-oscillatory shock-capturing schemes of arbitrarily-high accuracy. In: AIAA 1986-339, 24th aerospace sciences meeting, 339 10. Ha Y, Kim CH, Lee YJ, Yoon J (2013) An improved weighted essentially non-oscillatory scheme with a new smoothness indicator. J Comput Phys 232(1):68–86 11. Allaneau Y, Jameson A (2009) Direct numerical simulations of a two-dimensional viscous flow in a shocktube using a kinetic energy preserving scheme. In: 19th AIAA computational fluid dynamics, 3797 12. Chiu EKY, Wang Q, Jameson A (2011) A conservative meshless scheme: general order formulation and application to Euler equations. In: 49th AIAA aerospace sciences meeting, 651 13. Ohwada T, Shibata Y, Kato T, Nakamura T (2018) A simple, robust and efficient high-order accurate shock-capturing scheme for compressible flows: towards minimalism. J Comput Phys 362:131–162 14. Borges R, Carmona M, Costa B, Don WS (2008) An improved weighted essentially nonoscillatory scheme for hyperbolic conservation laws. J Comput Phys 227(6):3191–3211 15. Sengupta TK, Ganeriwal G, De S (2003) Analysis of central and upwind compact schemes. J Comput Phys 192(2):677–694 16. Sengupta TK (2013) High accuracy computing methods: fluid flows and wave phenomena. Cambridge University Press 17. Sengupta TK (2004) Fundamentals of computational fluid dynamics. Universities Press, Hyderabad, India 18. Sengupta TK, Bhole A, Sreejith NA (2013) Direct numerical simulation of 2D transonic flows around airfoils. Comput Fluids 88:19–37 19. Garbaruk A, Shur M, Strelets M (2003) Numerical study of wind-tunnel walls effects on transonic airfoil flow. AIAA J 41(6):1046–1054 20. Binnion TW (1979) Limitations of available data. AGARD-AR 138 21. Dipankar A, Sengupta TK (2006) Symmetrized compact scheme for receptivity study of 2D transitional channel flow. J Comput Phys 215(1):245–273 22. Sengupta TK, Ganerwal G, Dipankar A (2004) High accuracy compact schemes and Gibbs’ phenomenon. J Sci Comput 21(3):253–268 23. Sengupta TK, Dipankar A, Sagaut P (2007) Error dynamics: beyond von Neumann analysis. J Comput Phys 226(2):1211–1218 24. Sengupta TK, Dipankar A, Rao AK (2007) A new compact scheme for parallel computing using domain decomposition. J Comput Phys 220(2):654–677

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25. Dolean V, Lanteri S, Nataf F (2002) Optimized interface conditions for domain decomposition methods in fluid dynamics. Int J Numer Methods Fluids 40(12):1539–1550 26. Rajpoot MK, Sengupta TK, Dutt PK (2010) Optimal time advancing dispersion relation preserving schemes. J Comput Phys 229(10):3623–3651 27. Sengupta TK, Bhumkar YG (2010) New explicit two-dimensional higher order filters. Comput Fluids 39(10):1848–1863 28. Van Der Vorst HA (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13(2):631–644 29. Bagade PM, Bhumkar YG, Sengupta TK (2014) An improved orthogonal grid generation method for solving flows past highly cambered aerofoils with and without roughness elements. Comput Fluids 103:275–289 30. Hoffmann KA, Chiang ST (1993) Computational fluid dynamics for engineers, vol 2. Engineering Education System Wichita, KS 31. Pulliam TH (1986) Solution methods in computational fluid dynamics. In: Notes for the von Kármán institute for fluid dynamics lecture series 32. Samtaney R, Morris RD, Cheeseman P, Sunelyansky V, Maluf D, Wolf D (2000) Visualization, extraction and quantification of discontinuities in compressible flows. In: International conference on computer vision and pattern recognition (2000) 33. Lee BHK, Murty H, Jiang H (1994) Role of Kutta waves on oscillatory shock motion on an airfoil. AIAA J 32(4):789–796 34. Tijdeman H (1977) Investigations of the transonic flow around oscillating airfoils. Nationaal Lucht-en Ruimtevaartlaboratorium 35. Liepmann HW, Roshko A (1957) Elements of gasdynamics. Courier Corporation

An Adjoint Approach for Accurate Shape Sensitivities in 3D Compressible Flows Srikanth Sathyanarayana, Anil Nemili, Ashish Bhole, and Praveen Chandrashekar

Abstract This paper presents the development of a robust discrete adjoint approach for accurate computation of shape sensitivities in three-dimensional inviscid compressible flows. The adjoint Euler solver is generated by applying algorithmic differentiation techniques to the underlying primal solver. The novelty of the proposed framework is that the geometry subroutine that computes cell volumes, surface areas and normals is integrated to the subroutine that performs the primal fixed point scheme so that the adjoint code directly yields the desired shape sensitivities. The applicability of the developed adjoint approach is demonstrated on ONERA-M6 wing test case. The consistency and accuracy of the adjoint solver are assessed by comparing the adjoint shape sensitivities with the values from finite differences and tangent linear code. Numerical results show that the adjoint residual inherits the asymptotic rate of convergence of the primal residual. Keywords Aerodynamic optimisation · Shape sensitivities · Discrete adjoints · Algorithmic differentiation · Compressible flows

S. Sathyanarayana (B) · A. Nemili Department of Mathematics, BITS-Pilani, Hyderabad Campus, Hyderabad 500078, India e-mail: [email protected] A. Nemili e-mail: [email protected] A. Bhole Université de Nice Sophia-Antipolis, C.N.R.S. U.M.R. & Inria Sophia-Antipolis, Biot, France e-mail: [email protected] P. Chandrashekar TIFR Centre for Applicable Mathematics, Bengaluru 560065, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_21

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1 Introduction Aerodynamic shape optimisation has been a subject of intense research for almost three decades. Typically, these problems are characterised by a large number of shape variables, also known as design or control variables. An efficient way of finding the optimal set of control variables is by employing the gradient-based optimisation algorithms. Central to the success of gradient algorithms is the accurate and efficient computation of the sensitivity gradients of an objective function with respect to shape variables. This information is then used in finding a descent direction that changes the initial shape such that there will be an improvement in the design. This process is then repeated until we achieve the desired optimal solution. One way of computing the sensitivities is by using the finite differences [10] or the Complex Taylor Series Expansion (CTSE) method [19]. These methods provide a simple and flexible means of evaluating the desired sensitivities. However, both these methods are not practical as the computational costs increase linearly with the number of shape variables. Alternatively, control theory based techniques [13] can be employed to compute the sensitivities by solving the continuous [11] or the discrete adjoint equations [4]. An advantage of the adjoint approach is that the computational cost of solving the adjoint equations and thus evaluating the sensitivities is bounded and also independent of the number of shape variables. In continuous adjoint methods, the adjoint versions of the governing (primal) PDEs and the boundary conditions are first derived. The adjoint PDEs are then discretised and solved numerically. However, deriving adjoint equations for high-fidelity simulation models can be mathematically very challenging. Another drawback is that the sensitivities based on continuous adjoints may not be consistent with the values obtained from primal numerical simulations [2]. On the other hand, in discrete adjoint methods, the primal PDEs are first discretised. The adjoint equations and then the adjoint solver are constructed by linearising the non-linear discretised residuals. The linearisation can be performed either manually or by employing Algorithmic Differentiation (AD) techniques [6]. An advantage of AD is that it performs the exact linearisation of the residuals. This results in an adjoint solver that is always consistent to the corresponding primal solver and therefore yields accurate shape sensitivities. However, the computational cost of AD based discrete adjoint solver is more than the continuous adjoint solver. Furthermore, these costs vary depending on the way AD is employed. In earlier works [5, 14], AD is used selectively to minimise the CPU and memory requirements as black-box application of AD can lead to very poor performance of the adjoint code. In this approach, AD is used to linearise the discrete residuals and to construct the Jacobian matrix of the adjoint linear system. A lot of hand coding was still required in the development of discrete adjoint codes. This is a laborious process and is prone to errors. In fact, developing adjoint versions of industry standard CFD codes by hand may take several years and their maintenance can become a tedious task. With significant progress in the development of AD tools and their performance, another line of research has gained considerable acceptance [18]. In this approach,

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as a first step, the adjoint codes are constructed by applying AD directly to the underlying primal codes. This results in an adjoint solver that is always consistent to the primal and therefore yields accurate sensitivities. Since the differentiation is performed in a black-box fashion, the adjoint code demands substantial amount of memory and run-time. In the second stage, the computational efficiency is enhanced by employing various advanced techniques of AD like reverse accumulation and checkpointing [6]. Computationally, these adjoint codes are still found to be more expensive than the hand-discrete codes. Numerical experiments have shown that the run-time of fully AD based adjoint codes is around 4–10 times more than their primal codes. However, the lack of computational efficiency of AD based adjoint solvers is well compensated by robustness, easy maintenance of adjoint codes and availability of affordable computational resources. In fact, this approach has matured to the level of applying to industry standard CFD codes to generate accurate and efficient adjoint codes. [1, 9, 15]. It should be noted that any further enhancement in the computational efficiency may require better understanding of the primal solver and also the underlying AD tools. At times, a re-organisation of the primal code structure may result in more efficient adjoint codes. In this paper, we pursue the development of a robust and accurate discrete adjoint solver for accurate computation of shape sensitivities in three-dimensional inviscid compressible flows. The primal Euler code is organised in such a way that AD results in an efficient discrete adjoint Euler code that directly yields shape sensitivities. This paper is organised as follows. Section 2 presents the governing inviscid fluid flow equations. Section 3 presents the details pertaining to the primal numerical solver. Section 4 presents the development of an adjoint approach for accurate shape sensitivities. Numerical results to validate the performance of the adjoint solver are shown in Sect. 5. Finally, conclusions are drawn in Sect. 6.

2 Governing Equations The equations that govern the 3D inviscid compressible flows are given by ∂Fy ∂Fx ∂Fz ∂U + + + =0 ∂t ∂x ∂y ∂z

(1)

Here, U is the vector of conserved variables, Fx , Fy and Fz are the flux vectors along the coordinate directions x, y and z directions respectively. These quantities are defined by ⎡

⎡ ⎡ ⎡ ⎤ ⎤ ⎤ ⎤ ρ ρu1 ρu2 ρu3 ⎢ρu1 ⎥ ⎢ p + ρu2 ⎥ ⎢ ρu1 u2 ⎥ ⎢ ρu1 u3 ⎥ 1 ⎥ ⎢ ⎢ ⎢ ⎢ ⎥ ⎥ ⎥ ⎢ ⎥ , Fy = ⎢ p + ρu2 ⎥ , Fz = ⎢ ρu2 u3 ⎥ ⎥ ρu u U = ⎢ρu2 ⎥ , Fx = ⎢ 1 2 2 ⎥ ⎢ ⎢ ⎢ ⎥ ⎥ ⎣ρu3 ⎦ ⎣ ρu1 u3 ⎦ ⎣ ρu2 u3 ⎦ ⎣ p + ρu32 ⎦ ρe (p + ρe) u1 (p + ρe) u2 (p + ρe) u3 (2)

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Here, ρ is density, p is pressure, u1 , u2 , u3 are the components of fluid velocity along the coordinate directions x, y, z respectively. e is the total energy per unit mass, given by 1 2 p + u1 + u22 + u32 (3) e= ρ (γ − 1) 2

3 Primal Numerical Solver The UG3 code is based on a finite volume method for the compressible Euler and Navier-Stokes equations on hybrid, unstructured grids. It is capable of operating on a mesh comprised of tetrahedra, pyramids, prisms and hexahedra. The discretization is based on vertex-centered scheme which means that all solution variables are stored at the vertices of the mesh, also called the primary mesh. A dual mesh is constructed from the primary mesh on which the conservation law is satisfied. The main task is to estimate the inviscid and viscous fluxes across the faces of the dual mesh. For inviscid fluxes, we make use of Riemann solver type fluxes and also those based on central schemes. The viscous fluxes are computed in a central manner with a compact stencil consisting of only the first neighbours of any vertex, similar to a P1 Galerkin method. To achieve high order accuracy, a linear reconstruction of some primitive variables is performed in combination with limiters in case of discontinuous solutions. Edgebased MUSCL-type limiters and multi-dimensional limiters of Barth-Jesperson and Venkatakrishnan are available in the code. The code is essentially 3D but can also solve 2D problems by extruding a 2D mesh in the third direction and using periodic boundary conditions in the third direction.

3.1 Grid and Cell Topology The grid is composed of non-overlapping polyhedral cells like tetrahedra, pyramid, triangular prism and hexahedra, which will be referred to as the primary cells. The unknowns are stored at the vertices of the mesh around which a dual cell is constructed. The dual cell is obtained by joining the mid-point of edges with the average points of faces and cells. Within each primary cell, the geometric entities comprising the cell like vertices, edges and faces have a local numbering which is based on the convention in Gmsh and helps us to compute various geometric quantities required in the finite volume method. The dual cell is obtained by joining the arithmetic center of each cell, face and edge as shown in Fig. 1. Note that the faces of dual cells are comprised of triangular surfaces. Let

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Fig. 1 Definition of faces of dual cells

N (i) = {all vertices j connected to vertex i by an edge} C(i) = {all primary cells containing vertex i} F(i, c) = {all interior dual faces of vertex i inside primary cell c} B(i) = {all boundary dual faces containing vertex i} Each element of F(i, c) and B(i) is a triangular face as shown in Fig. 1. For a tetrahedral grid, we also define G(i, c) = {face of cell c opposite to vertex i}

3.2 Numerical Scheme The finite volume scheme is based on satisfying the conservation laws on each control volume, which in our case are the dual cells constructed around each vertex. The semi-discrete finite volume scheme can be written as Vi





dU i ˆ f Sf + ˜ f Sf + G G Fˆ ij Sij + F˜ f Sf = dt j∈N (i) c∈C(i) f∈B(i) f ∈B(i)

(4)

f ∈F(i,c)

The second term on the left is the inviscid flux across interior faces while the third term contains boundary fluxes. The numerical approximation of differential operators on unstructured grids is described in [7], see also [12]. The inviscid flux Fˆ ij is computed using a numerical flux function ˆ ij , Qji , nij ) Fˆ ij = F(Q where Qij , Qji are primitive variables at the middle of the edge ij obtained by some reconstruction scheme. The primitive variables are taken to be Q = [u1 , u2 , u3 , ρ, p]

(5)

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In the code we have a variety of MUSCL type reconstruction schemes along with limiters for computing flows with shocks and other discontinuities. The reconstruction process required the knowledge of the gradient of primitive variables at the vertices which is obtained by applying the divergence theorem over the dual cell in a very careful manner to account for hybrid grids leading to a scheme which is exact for linear functions even on hybrid grids. The above equations resulting from the semi-discrete finite volume method are a system of non-linear ordinary differential equations. For a time accurate solution, we integrate these equations using a RungeKutta schemes which are strong stability preserving while for steady state solutions, we use local time stepping to accelerate convergence to steady state.

4 A Discrete Adjoint Approach for Shape Sensitivities Consider the problem of finding an optimal shape that maximises or minimises an objective function of particular interest in aerodynamic applications. This amounts to a PDE-constrained optimisation problem. A general formulation of this problem can be given as max/min J (U, α) (6) subject to C (U, α) = 0 where J is the objective function, U is the conserved vector, α is the vector of control variables comprising the shape coordinates (x, y, z). In the present work, C (U, α) = 0 represents the inviscid Euler equations in Eq. (1) along with boundary conditions. In the semi-discrete form, the constraints can be written as dU + Rs (U, α) = 0 dt

(7)

Here, Rs (U, α) is the discrete residual vector obtained after the finite volume discretisation of the spatial derivatives in the governing equations. Approximating the temporal derivative using the first order forward difference formula, the state-update formula can be written as U n+1 = U n − tRs (U, α)

(8)

Since we are interested in the steady state solution, at each pseudo-time iteration n, the residual equations are solved for the solution of the state vector U using a fixed point formula  (9) U n+1 = G U n , α Here, G represents an iteration of the finite volume scheme employed for the numerical solution of the 3D Euler equations. The above fixed point iteration converges to the steady state solution U, given by

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U = G (U, α)

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(10)

In the discrete form, the optimisation problem defined in Eq. (6) can then be written as max/min J (U, α) (11) subject to U = G (U, α) The Lagrangian functional associated with the above constrained optimisation problem is given by (12) L = J (U, α) −  T {U − G (U, α)} Here  is the adjoint state vector or the Lagrangian multiplier. The first order necessary conditions (KKT conditions) for optimality of the Lagrangian function are given by ∂L =0 ∂ ∂L =0 ∂U ∂L =0 ∂α

(State equations)

(13a)

(Adjoint equations)

(13b)

(Control equation)

(13c)

From Eq. (13b), the discrete adjoint equations can be derived in the fixed point form as   ∂G ∂J  n+1 = T n + T (14) ∂U ∂U From this equation, it is clear that the adjoint iterative scheme requires the converged flow solution U to evaluate G and J . Therefore, to solve the adjoint equations the primal solution should be available a priori. A general notation for the adjoint fixed point iterative scheme can be written as   n+1 = G  n , U, α

(15)

where G represents a pseudo-time iteration of the discrete adjoint solver for 3D Euler equations. The above fixed point iteration converges to the adjoint solution , given by (16)  = G (, U, α) The solution of the adjoint equations is then substituted in Eq. (13c) to evaluate the sensitivities of the objective functional with respect to the shape variables as ∂J ∂G dL = + T dα ∂α ∂α

(17)

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From Eqs. (14) and (17), it is clear that accurate computation of the shape sensitivities require the exact differentiation of J and G. Note that the primal fixed point iterator G consists of discrete residuals due to higher order convective scheme and limiters. The exact differentiation of these terms by hand is laborious and prone to errors. Any approximation made by neglecting the differentiation of these terms will result in inaccurate computation of sensitivities [17]. One way to circumvent this difficulty is by employing Algorithmic Differentiation (AD) techniques. An advantage of AD is that it performs the exact differentiation of these terms with much ease. In the present work, at the first step, AD is applied in a black-box fashion to differentiate the computer code that represents the primal 3D Euler solver with respect to the vector of shape variables α. Since all terms in the primal solver are differentiated exactly, the adjoint solver is always consistent to the primal solver and therefore gives accurate sensitivities at any residual level achieved by the primal solver. A major drawback of the black-box AD approach is that the discrete adjoint code demands expensive memory and computational time. Therefore, adjoint calculations on practical configurations involving millions of grid points can become an infeasible task. Algorithms 1 and 2 show the general structure of the primal Euler solver and the corresponding black-box AD based discrete adjoint Euler solver. From Algorithm 2, it is clear that the excessive demand for computational resources is due to the blackbox application of AD to the primal fixed point iterative solver. In this approach, the adjoint code stores the primal solutions U n for all N iterations that yield a desired accuracy and convergence. The stored solutions are then used to compute the adjoints in the reverse sweep. Note that for large values of N , the storage costs can become significant. One way to circumvent the storage of primal solutions is by employing the reverse accumulation technique [3]. This approach makes use of the iterative structure of the adjoint fixed point scheme in Eq. (15). From this equation, it is clear that the adjoint solver requires only the converged primal solution U. The structure of an efficient adjoint solver based on this technique is shown in Algorithm 3. Here, M represents the number of pseudo-time iterations required for the convergence of adjoint solution. In [16], this approach has been successfully employed in accurate computation of sensitivities in flows governed by incompressible URANS equations. In the present work, the discrete adjoint Euler code UG3A is developed by algorithmically differentiating the primal UG3 code using the AD tool Tapenade [8]. The resulting adjoint solver precisely performs the adjoint fixed point scheme shown in Algorithm 3. The novelty of the present approach is that the geometry subroutine that computes cell volumes, surface areas and normals is integrated to the subroutine that performs the primal fixed point scheme so that AD generated adjoint code directly yields the desired shape sensitivities. To enhance the computational efficiency, the primal code is organised in such a way that the computational requirements of the adjoint code are as minimum as possible. Numerical investigations have shown that the run time of the adjoint code is around a factor of 5 compared to the primal code. The performance of the discrete adjoint Euler code in accurate computation of shape sensitivities is demonstrated in numerical results.

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Algorithm 1: Primal Euler Solver Initialize U 0 for n ← 1 to n ≤ N do perform the primal iteration U n+1 = G(U n , α) end return Objective function J n (U n , α)

Algorithm 2: Black-box AD based adjoint Euler solver Initialize U 0 for n ← 1 to n ≤ N do store (U n ) perform the primal iteration U n+1 = G(U n , α) end compute the objective function J n (U n , α) Initialize  N for n ← N to n ≥ 1 do perform the adjoint iteration  n−1 = G( n , U n , α) retrieve (U n ) end ∂J + T ∂G return Shape sensitivities ddLα = ∂α ∂α

Algorithm 3: Adjoint Euler solver based on reverse accumulation Initialize U 0 for n ← 1 to n ≤ N do perform the primal iteration U n+1 = G(U n , α) end compute the objective function J n (U n , α) Initialize  N for n ← 1 to n ≤ M do perform the adjoint iteration  n+1 = G( n , U, α) end ∂J return Shape sensitivities ddLα = ∂α + T ∂G ∂α

5 Numerical Results In this section, we present the numerical results to demonstrate the performance of the discrete adjoint solver in accurate computation of shape sensitivities. The test case under investigation is the transonic flow past ONERA-M6 wing with Mach number M = 0.84 and angle of attack AoA = 3.06◦ . The computational domain consists of an unstructured grid with 72,791 points. The wall boundary is resolved with 30,635 grid points. For the discrete optimisation problem, the objective functions are defined as the minimisation of inviscid aerodynamic drag coefficient and total

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Table 1 Sensitivities of the drag coefficient with respect to the shape variable x Index Finite differences Tangent linear code Discrete adjoint code 160 170 1524 25,930

7.92357672529942E–05 –8.07455664830758E–05 7.33930052149167E–04 4.82636153265048E–05

7.92366912337142E–05 –8.07444484751142E–05 7.33931859299297E–04 4.82641982087865E–05

7.92366912337503E–05 –8.07444484751254E–05 7.33931859299497E–04 4.82641982087881E–05

The bold values signify the accuracy of the values from discrete adjoint solver (third column) with respect to the first and second column. It shows the extent till which the third column values match with the first and second columns Table 2 Sensitivities of the drag coefficient with respect to the shape variable y Index Finite differences Tangent linear code Discrete adjoint code 160 170 1524 25,930

7.00035862610803E–05 8.08812392061320E–05 –5.81716619318939E–04 1.06139865993504E–03

7.00033454518258E–05 8.08812570771250E–05 –5.81716715574034E–04 1.06136000617902E–03

7.00033454517270E–05 8.08812570771694E–05 –5.81716715573846E–04 1.06136000617888E–03

The bold values signify the accuracy of the values from discrete adjoint solver (third column) with respect to the first and second column. It shows the extent till which the third column values match with the first and second columns Table 3 Sensitivities of the drag coefficient with respect to the shape variable z Index Finite differences Tangent linear code Discrete adjoint code 160 170 1524 25,930

7.72512453312002E–04 8.47840010004263E–04 –4.33925430309845E–04 –6.35399718951212E–06

7.72514007628485E–04 8.47838916150582E–04 –4.33924914359014E–04 –6.35426243142565E–06

7.72514007628787E–04 8.47838916150576E–04 –4.33924914358905E–04 –6.35426243142373E–06

The bold values signify the accuracy of the values from discrete adjoint solver (third column) with respect to the first and second column. It shows the extent till which the third column values match with the first and second columns

entropy produced in the computational domain. The control variables are the shape coordinates that define the surface of the wing. This implies that at each wall point, we have sensitivities due to x, y and z coordinates. In total, this results in 91,905 control variables. Tables 1, 2 and 3 show a comparison of drag sensitivities obtained with finite differences and AD based tangent linear and discrete adjoint solvers at 4 randomly selected wall points. The point 160 is near the leading edge of the wing tip and the point 170 is near the trailing edge of the wing tip. The point 1524 is located near the leading edge of the midsection and 25,930 is near the trailing edge of the midsection. Note that the tangent linear code gives accurate sensitivity information with respect to only one control variable. Obviously, for large number of control variables this approach is practically not feasible as the computational costs grow linearly with the number of control variables. However, the tangent code is very useful in building and validating the adjoint code.

An Adjoint Approach for Accurate Shape Sensitivities in 3D Compressible Flows 2

2

0

0

-2

-2

Residue

Residue

Entropy sensitivty

-4 -6

-6 -8

-10

-10

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1000 2000 3000 4000 5000 6000 7000 8000 9000

Iterations

Cd sensitivty

-4

-8

-12

299

-12

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Iterations

Fig. 2 Transonic flow past ONERA-M6 wing. Comparison of the convergence histories of primal and discrete adjoint residuals

From these tables it can be clearly seen that the shape sensitivities based on the discrete adjoint code are in excellent agreement with the values obtained from the second order finite differences with a step size of δ = 10−7 . Furthermore, the adjoint sensitivities match even better with the values obtained from the tangent linear code. It has been observed that the percentage error in sensitivities due to finite differences and discrete adjoint approach is found to be varying between 10−3 and 10−4 . On the other hand, the error in sensitivities based on the adjoint and tangent codes is less than 10−11 , which is an outcome of the exact differentiation of the primal fixed point iterator G. Fig. 2 shows a comparison of primal and adjoint residual convergence history. It can be observed that the residues continue to decrease to machine zero. Furthermore, the adjoint residual inherits the asymptotic rate of convergence of the primal residual. Figure 3 shows the convergence of the objective function Cd and its sensitivity with respect to the shape coordinate y at the point 25,930. Figure 4 shows the corresponding plots for the total entropy. From these plots we can argue that the convergence of sensitivity gradients may require more number of iterations compared to the objective function. The pressure contours in Fig. 5 clearly show the λ-shock structure on the upper surface of the wing. The contours of the sensitivities of the drag coefficient with respect to the y coordinates of the shape are shown in Fig. 6. From the sensitivities plot, it is clear that the maximum positive sensitivities occur at the trailing edge close to the root of the wing. We can also observe mild negative sensitivities in the λ-shock region. Figure 7 shows the contours of entropy produced on the wing surface. These contours show that the maximum entropy production on this grid resolution occurs near the leading edge close to the root of the wing. Figure 8 shows the contours of the magnitude of the total entropy sensitivities. From this plot, it can be observed that the dominant sensitivities occur near the leading edge region from midspan to the tip of the wing. We can also observe mild sensitivities in the λ-shock region.

S. Sathyanarayana et al. 0.2

0.0015

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0.001

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Cd

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1000 2000 3000 4000 5000 6000 7000 8000 9000

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Fig. 3 Transonic flow past ONERA-M6 wing. a Convergence history of the objective function Cd . b Convergence history of the sensitivity of Cd with respect to the shape coordinate y at wall point 25,930 150

Total entropy sensitivty w.r.t y

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1000 2000 3000 4000 5000 6000 7000 8000 9000

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Fig. 4 Transonic flow past ONERA-M6 wing. a Convergence history of the objective function total entropy. b Convergence history of the sensitivity of total entropy with respect to the shape coordinate y at wall point 25,930 Fig. 5 Transonic flow past ONERA-M6 wing. Pressure contours on the upper surface of the wing

An Adjoint Approach for Accurate Shape Sensitivities in 3D Compressible Flows Fig. 6 Transonic flow past ONERA-M6 wing. Sensitivities of the drag coefficient with respect to the shape coordinate y on the upper surface of the wing

Fig. 7 Transonic flow past ONERA-M6 wing. Entropy contours on the upper surface of the wing

Fig. 8 Transonic flow past ONERA-M6 wing. Magnitude of the total entropy sensitivities on the upper surface of the wing

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6 Conclusions In this paper, we presented the development of a discrete adjoint approach for accurate computation of shape sensitivities in inviscid compressible flows. The threedimensional discrete adjoint code was developed by algorithmically differentiating an unstructured grid-based finite volume Euler code. The performance of the adjoint solver in accurate computation of sensitivities of the drag coefficient and total entropy with respect to the shape variables was assessed. Numerical results for the ONERAM6 wing test case have shown that the sensitivities based on the discrete adjoint code were in excellent agreement with the values obtained from the tangent linear code and second order finite differences. The run-time of the adjoint code is found to be around a factor of 5 compared to the primal code. In future, we want to extend the discrete adjoint solver to turbulent flows governed by Reynolds-averaged Navier Stokes (RANS) equations. Research will also focus on further enhancement in the computational efficiency of the adjoint solver. Acknowledgements The authors gratefully acknowledge the financial support from the Science and Engineering Research Board, Department of Science and Technology, Government of India, under the project number EMR/2016/003182.

References 1. Albring T, Sagebaum M, Gauger N (2016) A consistent and robust discrete adjoint solver for the Stanford University Unstructured (SU2) framework—Validation and application. Notes Numer Fluid Mech Multidiscip Des 132:77–86 2. Carnarius A, Thiele F, Özkaya E, Nemili A, Gauger N (2013) Optimal control of unsteady flows using a discrete and a continuous adjoint approach. IFIP Adv Inf Commun Technol 391:318–327 3. Christianson B (1994) Reverse accumulation of attractive fixed points. Optim Methods Softw 3:311–326 4. Elliott J, Peraire J (1997) Practical three-dimensional aerodynamic design and optimization using unstructured meshes. AIAA J 35(9):1479–1485 5. Giles M, Ghate D, Duta M (2008) Using automatic differentiation for adjoint CFD code development. CFD J 16(4):434–443 6. Griewank A, Walther A (2008) Evaluating derivatives: principles and techniques of algorithmic differentiation. SIAM 7. Ham F, Mattsson K, Iaccarino G (2006) Accurate and stable finite volume operators for unstructured flow solvers. Annual Research Brief, Centre for Turbulence Research, Stanford University 8. Hascoët L, Pascual V (2013) The Tapenade automatic differentiation tool: principles, model, and specification. ACM Trans Math Softw 39(3). https://doi.org/10.1145/2450153.2450158 9. Hay JA, Özkaya E, Gauger N, Schönwald N (2016) Application of an adjoint CAA solver for design optimization of acoustic liners. In: AIAA paper 2016–2775 10. Hicks RM, Henne PA (1978) Wing design by numerical optimization. J Aircr 15(7):407–412 11. Jameson A (1988) Aerodynamic design via control theory. J Sci Comput 3:233–260 12. Khalighi Y, Ham F, Nichols J, Lele S, Moin P (2015). Unstructured large eddy simulation for prediction of noise issued from turbulent jets in various configurations. Am Inst Aeronaut Astronaut. https://doi.org/10.2514/6.2011-2886

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13. Lions J (1971) Optimal control of systems governed by partial differential equations. Grundlehren der mathematischen Wissenschaften. Springer. http://books.google.nl/books? id=1TYgWwbmFGMC 14. Mohammadi B (1997) A new optimal shape design procedure for inviscid and viscous turbulent flows. Int J Numer Meth Fluids 25(2):183–203 15. Nemili A, Özkaya E, Gauger N, Cramer F, Höll T, Thiele F (2014) Optimal design of active flow control for a complex high-lift configuration. In: AIAA paper 2014–2515 16. Nemili A, Özkaya E, Gauger NR, Kramer F, Thiele F (2017) Accurate discrete adjoint approach for optimal active separation control. AIAA J 55(9):3016–3026 17. Nielsen EJ, Anderson WK (1999) Aerodynamic design optimization on unstructured meshes using the Navier-Stokes equations. AIAA J 37(11):185–191 18. Özkaya E, Gauger N (2010) Automatic transition from simulation to one-shot shape optimization with Navier-Stokes equations. GAMM-Mitteilungen 33(2):133–147 19. Squire S, Trapp G (1998) Using complex variables to estimate derivatives of real functions. SIAM Rev 40(1):110–112

Robust Flutter Prediction of an Airfoil Including Uncertainties A. Arun Kumar

and Amit Kumar Onkar

Abstract This work presents the robust stability analysis of 2DoF airfoil by including various uncertainties. These uncertainties arise due to several factors such as modeling and manufacturing errors as well as disturbances in the flight conditions. The approach adopted to study the uncertain aeroelastic system is based on the structured singular value (μ-method). In this approach, the aeroelastic system is formulated in a robust stability framework by parameterizing around dynamic pressure and introducing uncertainties in the system parameters to account for errors and disturbances. This results in the perturbed aeroelastic system which is then represented using Linear Fractional Transformation (LFT). Then, the nominal and robust stability analysis of the perturbed aeroelastic system is carried out using μ method. In this work, first the validation of μ method is done for 2DoF airfoil with quasisteady aerodynamics having uncertainties in the structural and aerodynamic properties. Further, the robust flutter boundary of 2DoF airfoil with Theodorsen’s unsteady aerodynamics is studied using μ method in the presence of stiffness, damping, and aerodynamic uncertainties. Keywords 2DoF airfoil · Uncertainty · LFT · μ-method · Robust flutter

1 Introduction Aeroelastic stability is one of the important criteria for the safety of flight vehicles. Since the aeroelastic phenomena such as flutter and LCO can result in catastrophic structural failure of the aircraft, these instabilities should be avoided in the whole operational envelope. In order to predict these instabilities accurately, it is necessary to consider uncertainties that arise due to the differences between the model A. A. Kumar · A. K. Onkar (B) CSIR-National Aerospace Laboratories, Bangalore 560 017, India e-mail: [email protected] A. A. Kumar e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_22

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and the actual flight vehicle, in the conventional aeroelastic analysis. In general, this is handled by carrying out various parametric studies by enumerating all possible combinations of uncertainties. This approach is relatively simple but can take enormous computational hours and also possibility of omitting the worst-case situation [1]. Recently, the concept of robustness from the control theory is introduced into the aeroelastic analysis to study the flutter margins in the presence of uncertainties. In this technique, the flutter analysis considering various uncertainties can be treated as the robust stability problem under the perturbation of uncertainty set. This stability problem can be solved by the structured singular value μ-method and proves as an effective tool for robust aeroelastic studies [1].

2 Objectives The objective of this work is to find the robust flutter boundary of 2DoF airfoil with various structural and aerodynamic uncertainties. For this purpose, a statespace model of 2DoF airfoil system is built along with perturbation in the system parameters considered for uncertainties. Then, this is represented in LFT form as a feedback interconnection between the perturbation in uncertainties and the nominal state-space model. First, the present μ method is validated for 2DoF airfoil system with quasi-steady aerodynamics having structural and aerodynamic uncertainties. Further, the robust flutter boundary of 2DoF airfoil system is studied using μ method with Theodorsen’s unsteady aerodynamics in the presence of various uncertainties.

3 Problem Formulation In this study, a 2DoF airfoil system considered for the robust stability analysis is shown in Fig. 1. Here, b represents the half-chord length, ba is the dimensional distance between the centerline and the elastic axis, bx α is the dimensional distance between the elastic axis and the center of gravity of the airfoil. The governing equations of motion of 2DoF airfoil system having heave (h) and pitch (α) degrees of freedom can be expressed as [2]:     [M] X¨ + [C] X˙ + [K ]{X } = {Q}

(1)

where [M], [C], [K] are the mass, stiffness and damping matrices respectively, and {X} is the displacement vector whose components are given as:  [M] =

       Ch 0 Kh 0 h m mxα b , [C] = , [K ] = , {X } = mxα b Iα 0 Cα 0 Kα α

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b

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b bxcg ba

V∞

α

Z

h

M

L

c.g.

Kα Cα

Kh

X

bxα

Ch

Fig. 1 A typical 2DoF airfoil system

Here m, I α , K h , K α , C h and C α are mass, mass moment of inertia about elastic axis, heave stiffness, pitch stiffness, heave damping and pitch damping respectively. The expression for unsteady aerodynamic load vector in matrix form is given as [3]:         {Q} = q [A1 ] X¨ + [A2 ] X˙ + C(k)[R] [S1 ] X˙ + [S2 ]{X }

(2)

where C(k) is the Theodorsen’s function, k = ωb/U is the reduced frequency and q is the dynamic pressure. Here, ω and U are the frequency and freestream velocity, respectively. Further, the matrices [A1 ], [A2 ], [S1 ], [S2 ] and [R] are defined as:     bS −π S 0 π ba −π b  = , ] [A 2 U 2 π ba −π b2 0.125 + a 2 U 0 −π b2 (0.5 − a)       S 1 b(0.5 − a) 01 −clα 0 , [S1 ] = , [S2 ] = S [R] = 0 cmα 0b U b b2 (0.5 − a)

[A1 ] =

where clα = 2π and cmα = 2π(0.5 + a). In the present study, the following approximation is used for Theodorsen function as given in [4]: C(k) = 1 −

0.165 0.335 − for k < 0.5 0.045 1 − 0.3 i 1− k i k

(3)

The above expression of Theodorsen’s function which is in reduced frequency domain is converted to time domain by using Laplace transform. Here, aerodynamic state variables are introduced resulting in additional aerodynamic degrees of freedom. The final form of unsteady aerodynamic load vector is:         {Q} = q [A1 ] X¨ + [A2 ] X˙ + [R] [A3 ] X˙ + [A4 ]{X } + [A S ]{X }a

(4)

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where [A3 ] =

      S 1 b(0.5 − a) S 01 S Ub c2 c1 . , = = , [A ] ] [A 4 S 2U b b2 (0.5 − a) 2 0b b U c2 c1 b

The governing equation of aerodynamic state variables resulted from the Laplace transformation of the Theodorsen’s function is:     X˙ a = [B1 ]{X }a + [B2 ] X˙ + [B3 ]{X }

(5)

where

[B1 ] =

     0 1 0 0 0 0  U 2 U , [B2 ] = , [B3 ] = . 1 b(0.5 − a) 0U − b c4 − b c3

The values of c1 , c2 , c3 and c4 are 0.10805, 0.006825, 0.3455 and 0.01365, respectively. Substituting Eq. (4) in Eq. (1), the aeroelastic equation of motion is written as:     [M] X¨ + [C] X˙ + [K ]{X }         = q [A1 ] X¨ + [A2 ] X˙ + [R] [A3 ] X˙ + [A4 ]{X } + [A S ]{X }a

(6)

4 Flutter Analysis Using μ Method In this work, the nominal and robust stability of 2DoF system is solved by μ method [2]. Here, the stability of nominal/robust aeroelastic system (P) having a set of unity norm bounded uncertainties  ={ : ∞ ≤ 1} is measured by structured singular value μ(P) defined as [2]: μ(P) = 1 min{σ () : det(I − P) = 0} ∈

(7)

If there is no  ∈  that causes det(I − P) = 0, then μ = 0. If μ(P) < 1, then the system is robustly stable under all unity norm bounded uncertainties. The importance of μ method is that it results in less conservative stability margin for systems having structured uncertainty descriptions when compared to analyzing stability using small gain theorem [5].

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4.1 Nominal Flutter Analysis Initially, the nominal flutter analysis of 2DoF airfoil system is carried out using the nominal (or mean) values of the structural and aerodynamic properties. Many methods such as k-method, p-k method, p-method and μ-method are available for nominal flutter analysis. In the current work, μ-method is chosen since it can be directly extended to carry out robust stability analysis including various uncertainties. In the μ method for nominal flutter analysis, the state-space model of the aeroelastic governing equation is derived by introducing perturbation in the dynamic pressure [2]. Then, this is represented in LFT form to perform nominal stability analysis using μ method. Here, the μ analysis treats dynamic pressure as uncertain parameter and searches for the minimum perturbation in this uncertainty that causes instability. This minimum perturbation corresponds to the required minimum dynamic pressure change that may result in aeroelastic instability. Following the procedure described in [2], the total dynamic pressure q is defined by considering an additive perturbation, δ q , on the nominal dynamic pressure, q0 as: q = q0 + δq

(8)

Equation (8) is then substituted in Eq. (6) and after appropriate simplifications and grouping results in:   −1   −1 

−1

−1 X¨ = M C X˙ + M K {X } + M q0 [R][A S ]{X }a + M {w}q (9) where





 M = [M] − q0 [A1 ], C = q0 ([A2 ] + [R][A3 ]) − [C], K = q0 [R][A4 ] − [K ] The feedback input {w}q to the dynamic pressure perturbation block is given by: {w}q = δq {z}q

(10)

where 



−1  C + [A2 ]  ˙  [A1 ] M X +[R][A3 ]  

−1

−1 (11) + [A1 ] M q0 [R][A S ] + [A S ] {X }a + [A1 ] M {w}q

 

−1  {z}q = [A1 ] M K + [R][A4 ] {X } +

The LFT representation of the aeroelastic system state-space model [P] along with the dynamic pressure perturbation is shown in Fig. 2.

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Fig. 2 LFT representation of the nominal aeroelastic system

4.2 Robust Flutter Analysis The robust flutter analysis of 2DoF airfoil system is carried out by considering uncertainties in the damping and stiffness of the structural system as well as in the aerodynamic coefficient matrix [R]. Following the similar derivation in the previous section for nominal flutter analysis, the governing equations for robust flutter analysis are presented. Consider the uncertainties in damping, stiffness and aerodynamic coefficients matrices as [2]: [C] = [C0 ] + [WC ][C ], [K ] = [K 0 ] + [W K ][ K ], [R] = [R0 ] + [W R ][ R ] (12) where subscript 0 represents nominal values of the respective structural and aerodynamic matrices; ([C ], [ K ], [ R ]) ∈ R2×2 represents the unity norm bounded uncertainty operators and ([WC ], [W K ], [W R ]) ∈ R2×2 represents the weighting matrices. For a given uncertain parameter, the weighting matrix along with its associated uncertainty operator [] with ∞ ≤ 1 defines a range of values that should be considered in the stability analysis [2]. Substituting these uncertainties (Eq. 12) in Eq. (9) and grouping the feedback terms appropriately, after simplifications results in:

−1   −1   −1  C X˙ + M K {X } + M q0 [R0 ][A S ]{X }a X¨ = M

−1

−1

−1

−1 + M {w}q + M q0 {w} R − M {w}C − M {w} K

(13)

The feedback inputs {w}q , {w} R , {w}C , and {w} K to the uncertainty block  are given respectively as:

 {w}q = δq {z}q , {w} R = [ R ]{z} R {w}C = [C ]{z}C , {w} K = [ K ]{z} K

(14)

where  

−1  {z}q = [A1 ] M K + [R0 ][A4 ] {X } +





−1  C + [A2 ]  ˙  [A1 ] M X +[R0 ][A3 ]

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Fig. 3 LFT representation of the aeroelastic system including uncertainties

 

−1

−1 + [A1 ] M q0 [R0 ][A S ] + [R0 ][A S ] {X }a + [A1 ] M {w}q  

−1

−1

−1 + [A1 ] M q0 + [I ] {w} R − [A1 ] M {w}C − [A1 ] M {w} K    {z} R = [W R ] [A3 ] X˙ + [A4 ]{X } + [As ]{X }a   {z}C = [WC ] X˙ , {z} K = [W K ]{X } (15) The LFT representation of the aeroelastic system state-space model [P] including perturbation in the dynamic pressure, structural, and aerodynamic uncertainties is shown in Fig. 3.

5 Results and Discussions First, the nominal and robust flutter velocities obtained from the present approach are validated with those given in [6] for 2DoF airfoil considering quasi-steady aerodynamics. The input data considered for the analysis are [2]: m = 12.387 kg; I α = 0.065 kg m2 , b = 0.135 m, bx α = 0.033291 m, K h = 2844.4 N/m, K α = 3.525 Nm/rad, C h = 27.43 kg/ s, C α = 0.036 kg m2 /s and ba = 0.0675 m. The uncertainties considered in the airfoil system for robust flutter analysis are: plunge damping (C h ) = 5 kg/ s, pitch stiffness (K α ) = 0.35 Nm/rad, lift coefficient (clα ) = 0.1 and moment coefficient (cmα ) = 0.1. The nominal and robust flutter analysis are conducted at U = 6 m/ s and ρ = 1.225 kg/ m3 . Table 1 gives the comparison of nominal and robust flutter dynamic pressures as well as frequencies for 2DoF airfoil obtained from the present approach with the literature [6]. It is observed that there exists a good agreement between the two Table 1 Comparison of flutter dynamic pressure and frequency for 2DoF airfoil system using quasi-steady aerodynamics Present results

Reference [6]

q (Pa)

ω (Hz)

q(Pa)

ω (Hz)

Nominal flutter

55.256

1.524

55.3

1.52

Robust flutter

41.693

1.415

41.8

1.41

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q = 62.05 Pa q = 41.69 Pa q = 32.05 Pa

1.5

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0

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4

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10

12

14

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(rad/s) Fig. 4 Variation of structured singular values (μ) with frequency (ω) at different dynamic pressures for 2DoF airfoil system under quasi-steady aerodynamics with various uncertainties

results. The variation of structured singular value (μ) with frequency (ω) at various dynamic pressures is also shown in Fig. 4. It can be observed that μ ≈ 1 is found at q = 41.693 Pa with ω = 8.891 rad/s indicating the minimum destabilizing perturbation. Next, the robust flutter boundary of 2DoF airfoil system due to uncertainties in the stiffness, damping, and aerodynamic coefficients is studied based on Theodorsen’s unsteady aerodynamic theory. Here, the nominal input data considered for the analysis are same as defined earlier except the position of elastic axis which is assumed to be ba = −0.081 m and U = 12 m/s. The uncertainties in the stiffness (K α ) and damping (C h ) are assumed to be 10% and 20% respectively [2]. The uncertainties in the lift and moment coefficients (clα and cmα ) are assumed to be 5% and 10%, respectively [7]. Table 2 shows the converged nominal and robust dynamic pressure of 2DoF airfoil system based on unsteady aerodynamics. It can be observed that the worst flutter dynamic pressure due to uncertainty in the aeroelastic system is about 17% lower than the nominal flutter. The variation of μ with ω for different dynamic pressures is also shown in Fig. 5. At q = 89.502 Pa, the value of μ is approximately 1 corresponding to the frequency of 11 rad/s. Thus, the smallest perturbation in q to make the 2DoF airfoil system unstable under the given set of parametric uncertainties is qr ob = 89.502 Pa. Table 2 Flutter dynamic pressure and frequency of 2DoF airfoil system using unsteady aerodynamics

Present approach Nominal flutter Robust flutter

q(Pa)

ω (Hz)

107.518

1.959

89.502

1.752

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q = 107.518 Pa q = 89.502 Pa q = 74.212 Pa

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32

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(rad/s) Fig. 5 Variation of structured singular value (μ) with frequency (ω) at different dynamic pressures for 2DoF airfoil system under unsteady aerodynamics including various uncertainties

6 Conclusions In this paper, the robust stability analysis of an airfoil is carried out considering uncertainties in the aeroelastic system using structured singular value (μ) method. First, the validation of μ method is carried out for 2DoF airfoil by considering uncertainties in stiffness, damping and aerodynamic coefficients under quasi-steady aerodynamics. The results obtained from the present approach agree well with those given in the literature. Further, the method is extended by incorporating Theodorsen’s unsteady aerodynamics to study the robust flutter characteristics of 2DoF airfoil system with parametric uncertainties in stiffness, damping and aerodynamic coefficients. It is observed that there is a reduction of 17% in the flutter dynamic pressure due to uncertainties considered in the aeroelastic system.

References 1. Zhigang W, Chao Y (2008) A new approach for aeroelastic robust stability analysis. Chin J Aeronaut 21:417–422 2. Lind R, Brenner M (1999) Robust aeroservoelastic stability analysis—flight test applications, 1st edn. Springer, London 3. Bisplinghoff RL, Ashley H, Halfman RL (1955) Aeroelasticity. Addison-Wesley, Cambridge 4. Fung YC (1955) An Introduction to the theory of aeroelasticity. Wiley, NewYork 5. Lind R, Brenner M (1998) Incorporating flight data into a robust aeroelastic model. J Aircraft 35(3):470–477

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6. Akmese A, Comert, MD, Platin BE (2004) Aeroservoelastic analysis of missile control surfaces via robust control methods. In: IFAC automatic control in aerospace. Elsevier IFAC publications, Saint-Petersburg, Russia, pp 719–723 7. Sadraey M (2009) Robust nonlinear controller design for a complete UAV mission. VDM Publishing

Effect of Vortex Generator on Flow in a Serpentine Air Intake Duct B. B. Shivakumar, H. K. Narahari, and Padmanabhan Jayasimha

Abstract Low Radar Cross Section (RCS) is one of the important requirements of aircraft design for stealth. Rotating engine face components are one of the major sources of radar reflection and hence need special attention. To this end, present day aircraft air intake ducts are designed to hide the rotating components from the radar signal by incorporating multiple bends. This type of intake ducts ensures that there is no direct line of sight from the entrance of the duct to engine face components and are generally called as Serpentine Ducts. Design of serpentine duct, therefore involves sharp bends that are likely to cause flow separation and consequent instability and distortion in the flow. In order to realize optimal performance from the engine, it is necessary to reduce the losses and minimize distortion at the Aerodynamic Interface Plane (AIP) that is near the outlet of the duct. This requires use of flow control techniques to alleviate the effects of flow separation. A Serpentine duct described in (Hamstra et al. in Active inlet flow control technology demonstration. ICAS, 2000 [1]) was selected for the present study, as the geometry details and experimental results were reported in the paper. Based on this, a duct was created and CFD flow simulations were performed. Results so obtained were compared with the test results in order to establish a baseline duct. Subsequently, passive vortex generators of trapezoidal shape were introduced and CFD simulations were carried out. The results, in comparison with the base design, indicate an enhancement in the flow uniformity at the AIP although with a 3% reduction in the pressure recovery. Further course of study is also indicated. Keywords Serpentine intake duct · Trapezoidal vortex generator · Passive flow control B. B. Shivakumar (B) M.S. Ramaiah University of Applied Sciences, Bangalore 560 054, India e-mail: [email protected] H. K. Narahari Department of Automobile and Aeronautical Engineering, Faculty of Engineering and Technology, M.S. Ramaiah University of Applied Sciences, Bangalore 560 054, India P. Jayasimha HAL-ARDC, Bangalore, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_23

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Abbreviations AIP CFD DC VG Pto PtAIP qAIP Ps Pt

Aerodynamic interface plane Computational fluid dynamics Distortion coefficient Vortex generator Free stream total pressure Total pressure at AIP Dynamic pressure at AIP Static pressure Total pressure

1 Introduction Research and development is an ongoing activity in the aerospace industry as new requirements are continuously evolving. Contemporary advanced capabilities are expected based on changing technological scenario. Extreme performance and lowered detectability are of primary importance to Fifth Generation of combat aircraft. These aircraft are characterized by high thrust-to-weight ratio and improved stealth characteristics without compromising the performance qualities. Major reduction in the radar signal reflection is achieved by hiding the rotating parts of the engine, since they are a main source of returning radar signal. These rotating components are hidden from the radar signal by a multiple curvature duct so that there is no direct line of contact from the entrance of the duct. Further, the radar signals that enter the duct get reflected on to the duct walls and are absorbed by Radar Absorbing Structure (RAS) specially designed for this purpose. This prevents reflection of the radar signal from the intake. Air intake duct is an important component of the aircraft propulsion system. Principle objective of the intake duct is to ensure uniform airflow to the engine at all operating conditions with maximum pressure recovery. However, the geometry of the duct plays a major role in the quality of flow that ensues. Flow in serpentine duct is complex in nature due to the effect of sharp bends between the inlet of duct and the aerodynamic interface plane (AIP), which may be construed as the outlet of the duct. As the flow moves towards a bend, there is a velocity difference in the transverse direction due to the centrifugal forces acting on the flow, causing the outer surface flow to accelerate and the inner surface flow to decelerate. After the bend, the decelerated flow may not be able to overcome the adverse pressure gradient, leading to flow separation. However, the separation bubble may close downstream. A similar situation would exist at the second bend. If the AIP is close to be bend, the separation bubble may not close leading to regions of low total pressure and consequently high distortion index and low pressure recovery.

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A significant body of work already exists where a host of flow control devices and techniques have been explored. Researchers have studied both active flow control impinging micro-jets, and passive devices like guide vanes and vortex generator (VG) attached to the duct wall. Encouraging results in the form of improved flow quality at the AIP have been reported. Present study is to explore trapezoidal VG as a passive flow control method mounted upstream of the bends to reduce the formation of secondary flow. A few positions and orientations of the VG have been studied and presented in this paper. It is proposed to continue the study further to optimize the shape, size, location and orientation of VG.

2 Literature Review Serpentine duct and vortex generators have been studied extensively, both in wind tunnel and CFD. The results have been presented in [1] by Hamstra et al. Since the base duct geometry and experimental results were available in this reference, it has been selected as a basis for comparison in the present research work reported in this paper. Effect of active flow controls such as micro-vane effectors and micro-jet effectors has been reported. Logdberg [2] has clearly explained the effect of vortex generator on the turbulent boundary layer and concluded that they were effective in controlling the separation, albeit with increase in the drag. Experimental studies of flow in S-Ducts have been reported in [3]. A parametric study of the vortex generator on a flat plate, airfoil, and diffuser has been reported in [4]. It has been inferred that flow mixing is accentuated by the formation of vortices due to VG. Chima et al. [5] have analyzed through CFD, the Versatile Integrated Inlet Propulsion Aerodynamic Rig (VIIPAR) located at NASA Glenn Research Centre. The rig consisted of serpentine inlet, rake assembly, fan stage, exit rakes or probes and exhaust nozzle. Experimental investigations have been done and pressure recovery measurements compared with results from CFD-codes. The conflicts and compromises during the design of fighter aircraft intakes have been explained in [6].

3 Geometry of the Serpentine Duct A serpentine duct was designed by Lockheed Martin Aeronautics Company and tested in NASA Glenn Research Centre for unmanned vehicle applications [1]. It featured 2 bends of approximately 45° each, biconvex inlet shape with a ratio 4:1 (major axis of 490 mm and minor axis of 124 mm), a circular outlet of 254 mm diameter and a total length of 632 mm. Based on that, a similar serpentine duct was designed for the present research using CATIA, a commercial CAD software. Figure 1 shows the baseline duct used for the present study. Since all the dimensions were not available from [1], appropriate assumptions had to be made and therefore the two ducts may not be identical.

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Fig. 1 Baseline duct

4 Grid Independence Study The initial step, for CFD simulation, was to discretize the domain using hexahedral or tetrahedral elements. Accuracy of results obtained from finite volume method of CFD depended to a large extent on the number of grids in the domain. Therefore, it was necessary to carry out the grid sensitivity study to confirm that the grid size selected for the given model was adequate to capture the flow physics with minimum error. In grid sensitivity study, a series of grids were created starting with coarse elements followed by systematic enrichment in x, y and z-directions. For each of these grids, CFD simulation was performed and results tabulated. When results from two successive grids did not vary by greater than 5%, the coarser of the two grids was chosen for further computations. Present study started with a hexahedral grid topology consisting of 90 elements along the circumference () of the outlet, 63 elements along the diameter (D) and 158 elements along the axis (L) of the flow. Nature of the flow inside the duct being complex, with zones of separated and secondary flows due to the bends, it was important to capture the flow near the wall region. The often quoted standard parameter to assess proper resolution of boundary layer flows is Y + . Mach number for the present research was 0.65 and using corresponding density, frictional factor and shear stress values, Y + computed turned out to be 5. Hexahedral grids were generated using ANSYS-ICEM-CFD for the baseline serpentine duct without Vortex Generators (VG), as shown in the Fig. 2. Table 1 lists different grids used for simulation, giving details of grid size along each coordinate, first layer thickness and total grids used for grid dependence study.

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Fig. 2 Baseline duct without Vortex generator

Table 1 Grid sensitivity criteria

Case

Grid size

First layer thickness

Total number of grids

G1

, D, L

4.00E−06

507,232

G2

, 2D, L

4.00E−06

1,173,216

G3

2, D, L

4.00E−06

1,277,760

G4

2, 2D, L

4.00E−06

3,066,624

G5

2, 2D, 2L

4.00E−06

5,068,800

Compressible flow simulation was carried out for the inlet total pressure 101,325 Pa and temperature 288.15 K. The outlet static pressure was varied till the obtained inlet Mach number was 0.65. For the grid sensitivity study, K-ε standard turbulence model was used. Since the objective of the study was to improve the flow at AIP, pressure recovery and distortion coefficient (DC) were calculated for all 5 grids and compared. Pressure recovery was defined as the ratio of total pressure at AIP to the free stream total pressure. Distortion coefficient was defined as the ratio of average total pressure at AIP minus 60° sector minimum average of the total pressure at AIP to the average dynamic pressure at AIP. Sector could be selected as 45°, 60° and 90° for the DC calculation and based on the selection of sector angle, the index of distortion coefficient is defined as DC-45, DC-60 and DC-90. For the present work, sector of 60° was selected for DC-60 calculation. For discretization, 36 circumferential locations, at 10° interval, were defined. For each circumferential location, 19 equidistance radial points were created as stated in [1]. Total 684 points were created to measure the distortion coefficient. Figure 3 shows the points created for the calculation of DC-60.

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Fig. 3 684 points at AIP for DC-60 calculation

Table 2 Grid independent study results Results-Grid Independent Study Coefficient

G1

G2

G3

G4

G5

DC-60 (%)

21.97

21.04

24.69

17.96

17.78

Pressure recovery

0.97156

0.97115

0.97081

0.97160

0.97157

Equations used for the calculation of pressure recovery, DC-60 and static pressure ratio were as follows: Pressure recovery: PtAIP /Pt0 Distortion Index: DC-60: ((PtAIP − Pt. min 60 avg)/qAIP ) ∗ 100 Static pressure ratio: Ps /Pt0 Pressure recovery and DC-60 values were calculated for different grids, and compared in Table 2. From the grid sensitivity study, G4 (180 grid points along tangential direction, 126 grid points along the radial direction and 158 grid points along the flow direction)was selected as adequate for the study.

5 Turbulence Model Study Among the various turbulence models available in the commercial code ANSYSFLUENT, four models were selected for this study. Models chosen were SpalartAllamaras (SA) one equation model, Standard K-ω two equation model, Shear Stress

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Transport(SST) K-ω two equation model and Realizable K-ε two equation model. Figures 4 and 5 show the static pressure ratio on the center plane of top and bottom surface of the duct for all 4 turbulence models compared with the experimental

Fig. 4 Static pressure ratio on the center plane of top surface

Fig. 5 Static pressure ratio on the center plane of the bottom surface

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Table 3 CFD simulation results and comparison with [1] for different turbulence model Coefficient Spalart-Allamaras K-Omega-standard SST-K-Omega Realizable Experimental K-Epsilon results [1] DC-60 [%] Pressure recovery

24.35 0.967

29.67 0.956

24.93 0.963

58.84 0.952

38.00 0.910

results. Experimental results of [1] were compared with CFD results for different turbulence models in Table 3. When the simulation results were compared with the experimental results, it was observed that there were significant deviations in the simulation results. Similar deviations were observed in [1] between CFD and experiment. Commenting on the delayed prediction of flow separation on both top and bottom surfaces, the authors have concluded that it is mainly attributed to the inadequacy of turbulence models. Therefore, it was decided that the selection of the turbulence model would be based on the closeness to the experimental results. Accordingly, it was decided to choose the K-Omega Standard turbulence model for further study. It may also be noted that the top contour could be different from the experimental contour as adequate geometric information was not available for construction. Sensitivity to this factor would be studied later.

6 Vortex Generator Study From the baseline duct simulation, flow separation was noticed on the bottom surface after the first bend and the top surface after the second bend. Initial studies indicated a boundary layer thickness around 2.5 mm near the first bend. Hence VG dimensions were chosen such that they are not submerged inside the boundary layer. The trapezoidal VG of leading edge height 4 mm, trailing edge height 20 mm, length of 40 mm, thickness of 1 mm were the dimensions considered for the design of VGs for the study. Figure 6 shows the VG dimension and geometry considered for the study. Once the VG design was finalized, it was necessary to decide on the position of the VG inside the duct. Since flow separation is noticed after the turning at the bend, it was decided to place the VGs exactly at the beginning of the first bend. Six possible locations and orientations of VGs have been studied, as indicated in Figs. 7, 8, 9, 10, 11 and 12. Figure 7 shows D1 design with a pair of 2 VGs located on top of the serpentine duct equally positioned at a distance of 80 mm from the center axis. Figure 8 shows the D2 design, which is similar to D1, but with VG placed at the bottom surface. Figure 9 shows the D3 design with 3 pairs of VGs at the bottom surface of the serpentine duct at throat. One pair of VG was placed exactly at the center and remaining 2 pairs were equally positioned at a distance of 120 mm from the center axis. Figure 10 shows the D4 design with 6 VGs and their orientation at

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Fig. 6 Vortex generator geometry

Fig. 7 D1-serpentine duct with 2 pair of VGs at the top surface of the throat

the bottom surface of the serpentine duct at throat. Figure 11 shows the D5 design which was similar to D4 but with VGs on the top surface of the duct. Figure 12 shows the D6 design with 6 VGs and their orientation at the top and bottom surface of the serpentine duct at throat. For all 6 design cases, G4 type hexahedral grids were generated using ANSYSICEM-CFD commercial code. Compressible flow simulation was carried out for an entry Mach number of 0.65.

7 Results and Discussion A comparison of pressure recovery and DC-60 values between baseline duct and all the 6 design case is shown in Table 4. Placing two pairs of contra rotating VG on the top surface at the entry plane (D1) indicated marginally higher distortion and a little lower pressure recovery compared to the baseline duct without VG. Introducing

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Fig. 8 D2-serpentine duct with 2 pair of VGs at the bottom surface of the throat

Fig. 9 D3-serpentine duct with 3 pair of VGs at the bottom surface of the throat

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Fig. 10 D4-serpentine duct with 6 VGs at the bottom surface of the throat

Fig. 11 D5-serpentine duct with 6 VGs at the top surface of the throat

the same pair on the bottom surface (D2) made the distortion higher and pressure recovery lower compared to the top position (D1). Adding one more pair, at the center plane on the bottom surface (D3), again lowered level of distortion, but also lowered pressure recovery in comparison with the baseline duct. In the next configuration, three VG on either side (D4), with the leading edge towards the center line, showed further lower levels of distortion, about 9% lower than baseline, and the pressure recovery better than D3, but lower than the baseline by 2.7%. Next configuration

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Fig. 12 D6-serpentine duct with 6 VGs at the top and bottom surface of the throat

Table 4 CFD results and comparison with experiment result Parameters

S-duct, without VG

D1-top surface, VG-2

D2-bottom surface, VG-2

D3-bottom surface, VG-3

DC-60 [%]

29.67

30.94

33.12

23.55

Pressure recovery

0.956

0.950

0.918

0.917

Parameters

D4-Bottom surface, 6 VGs-oneside oriented

D5-Top surface, 6 VGs-Oneside oriented

D6-Bottom and Top surface, 6 VGs-Oneside oriented

DC-60 [%]

20.71

31.28

44.67

Pressure recovery

0.929

0.949

0.895

D5 tried was with six VG, similar to D4, but on the top side. The results were not encouraging. So D6 configuration with 12 VG, six on top and six on the bottom side, was tried. This led to substantially higher distortion and substantially lower pressure recovery. Obviously configuration D4 appears the best among the six configurations tried. Further study would be around this configuration, with the effect of VG geometric parameters varied. The static pressure ratio along the centerline is presented in Figs. 13 and 14. From the graphs it can be seen that, VGs placed on the top surface of the duct (D1, D5) had no impact on the flow inside the duct. Surprisingly, when the VG were placed at the bottom side of the inlet, the static pressure distributions seemed to match better with the experimental data. This requires to be studied in greater detail. For example, in the case of D4, the point of separation on the bottom side very closely matched with the experimental data. However, the differences observed on the top side could be due to geometric differences between the experimental model and the CFD model. Small changes to be geometry would be tried to verify this aspect at a later stage. Figures 15 and 16 show the stream line plots inside the duct for baseline duct and

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Fig. 13 Static pressure ratio on top of the mid surface of the duct

Fig. 14 Static pressure ratio on bottom of the mid surface of the duct

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Fig. 15 Streamline plot for baseline duct

Fig. 16 Streamline plot for duct for D4 VG design

duct with D4 VG design. Figures 17 and 18 show the static pressure plot at the center plane for both baseline duct and duct with D4 VG. Figure 19 shows the velocity at the AIP for baseline duct and duct with D4 VG. Further study is required to understand the reason for the reduction in DC60.

Fig. 17 Static pressure plot for baseline duct

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Fig. 18 Static pressure plot for the D4 VG design

Baseline duct

D4 VG design

Fig. 19 Velocity plot at AIP for base design duct and D4 VG design

8 Conclusion A CFD study of Serpentine duct was conducted to evaluate the effect of Vortex Generators to improve the flow characteristics. A duct, as described in a reference paper, was modeled using CATIA software. ANSYS-ICEM-CFD was used to generate the grid and RANS option of ANSYS-FLUENT was used to solve the flow problem. Grid independence study was conducted and it was established that for the given problem, G4 grids (180 grid points along tangential direction, 126 grid points along the radial direction and 158 grid points along the flow direction) was adequate. Various turbulence model options in the software were tried out and it was found that Standard K-Omega turbulence model was the best suitable for the present study. Flow characteristics through CFD of a baseline duct were compared with experimental data. As the trends from CFD were similar to those presented in the reference

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paper, with the deviations from experiments following same pattern, it was decided to accept the baseline duct as the best match possible with the experiment for this study. Six different configurations of VG were tried out and it was found that D4 configuration (six of them on the bottom surface—three co-rotating on either side of centerline at the entry section) gave the best results. There was a substantial reduction of Distortion Index DC60 from nearly 30% in baseline to 21%, even though the pressure recovery had reduced by nearly 2.7%. The static pressure ratios on the centerline for the D4 configuration matched better with the experimental trend. The difference in pressure recovery between experiment and CFD could also be due to the type of bell mouth used in the experiment. There could be a pre-entry loss that is missing in CFD, as the flow was assumed to enter the duct with no loss in Total pressure at the inlet. Further work is planned to reconcile the major differences noticed between CFD and the experiment. After that, effect of placing VG on the top surface at the second bend and the effect of changing the geometry of VG would be studied.

References 1. Hamstra JW, Miller DN, Truax PP (2000) Active inlet flow control technology demonstration. ICAS 2. Logdberg O (2006) Vortex generators and turbulent boundary layer separation control. Technical Report, Royal Institute of Technology, Stockholm, Sweden, Oct 2006 3. Wellborn SR, Reichert BA, Okiishi TH (1992) An experimental investigation of the flow in a diffusing S-duct. NASA Technical Memorandum, AIAA-92-3622 4. Computational studies of Passive Vortex generators for Flow control. Technical Report, Royal Institute of Technology, Stockholm, Sweden, Dec 2009 5. Chima RV, Arend DJ, Castner RS, Slater JW (2010) CFD models of a serpentine inlet, fan and nozzle. In: AIAA 2010, 33 Jan 2010 6. Sobester A (2007) Tradeoffs in jet inlet design, a historical perspective. J Aircraft 44(3), June 2007

Supersonic Flow Behavior in Cartridge Starter Ritesh Gaur, Suparna Pal, Vimala Narayanan, D. Kishore Prasad, and N. Balamurali Krishnan

Abstract Hot flow analysis was undertaken in a cartridge starter using NUMECA software. Cartridge starter provides high temperature gases with kinetic energy which impinges on to the rotor blades of the turbine at the initial stage of starting a gas turbine engine which sets gas turbine to rotate. Other starting mechanisms which can be used are air starter, electric motor or a small gas turbine engine. The cartridge starter assembly consists of gas generator section with perforated central core, vertical tube/pipe which bifurcates into two pipe lines, called short arm and long arm, which provide high velocity hot gases to the high pressure turbine rotor blades. These two pipelines form convergent–divergent nozzles. Computational fluid dynamics (CFD) analyses were carried out for nine operating points for the inlet pressure ranging from 90 to 157 bar. Analyses considered the cartridge starter gas flow domain only and burning model is not considered. Hexahedral cells are generated with cut cell approach using fine Hexpress software. The problem is considered as threedimensional, steady, compressible with turbulent flow for the flow analysis. The aim of the project is to determine the mass flow rate, its distribution in two arms and the total pressure loss. Spalart–Allmaras turbulence model with extended wall function was chosen for this analysis. First analysis showed that the flow was unsteady at the exit plane of nozzle. Therefore, analysis was carried out by considering unsteadiness in the flow and averaged quantities are derived. Flow is found to diffuse in the divergent nozzle after a normal shock. Mass flow rate has reduced due to the formation of shock. It is also found that the total pressure loss has reduced near the perforated central core of cartridge starter. Keywords Cartridge starter · HPT rotor blade · Starting mechanism

R. Gaur (B) · S. Pal · V. Narayanan · D. Kishore Prasad · N. Balamurali Krishnan Gas Turbine Research Establishment, CV Raman Nagar, Bangalore 93, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_24

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1 Introduction The use of small gas turbine engines as propulsion sources for cruise missiles and UAVs is based on the ability to realize the engine including its peripheral systems at low cost and offer high reliability. The starting system being a critical peripheral system is required to provide the initial cranking of the gas turbine engine followed by initiation of combustion in the combustor till the propulsion system takes over. Hence, two common steps in the engine starting sequence include cranking and ignition. The selection of the cranking device, also called as the starter, depends on many factors like the engine configuration, operating comfort, engine stat time requirements, safety and reliability. Among the various alternatives available to start a small turbo fan engine, cartridge type of starter is found suitable for initial cranking of small expendable engines owing to its simple, compact design which is independent of any other source, high torque to weight ratio, high reliability and ability to meet lower starting time requirement. The purpose of a starter is to transmit the required starting torque to the engine rotating assembly such that it is able to accelerate the engine to enable light up and taking over by turbine such that the starter assistance can be removed. A typical starting cycle is shown in Fig. 1 indicating different speed requirements with time for starting of a typical gas turbine engine. Cartridge starter discussed in the current paper is sized to supply torque to overcome the drag torque of the engine such that it is used to accelerate the engine to the required speed. The cartridge starter discussed in the current work comprises of a solid propellant based gas generator. The cartridge starter is initiated through supply of electrical voltage to an pyro cartridge. Upon activation, the starter generates high temperature and high pressure gases that impinge on the HP turbine rotor assembly and provide the initial torque. Starting nozzles are used at the exit of the cartridge starter to maximize the exit velocities and hence the momentum for the given mass flow rate of gases. The high acceleration rate of the turbine helps to ensure lower exposure time of the turbine blades to the high temperature gases. Anil and Balamuralikrishan [2] have described the approach for sizing and configuring pyro-based starting system. They explained the challenges involved in attaining light up speed for establishing sustained combustion. It deals with high acceleration of spool and the assessment of all inertia loads. They have detailed the starting process and developed a torque model which can predict the achievable spool speed using pyro gas. In the work presented, hot flow analysis was undertaken for a cartridge starter using NUMECA software. Cartridge starter provides high temperature gases with kinetic energy which impinges on to the rotor blades of the turbine at the initial stage of starting a gas turbine engine which sets gas turbine to rotate. Other starting mechanisms which can be used are air starter, electric motor or a small gas turbine engine. The cartridge starter assembly consists of gas generator with perforated central core, vertical tube/pipe which bifurcates into two pipe lines which provide

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Fig. 1 Starting cycle [1]

high velocity hot gases to the high pressure turbine rotor blades. These two pipelines form convergent–divergent nozzles.

2 Modeling and Grid Generation Grid generation is a process of dividing the domain of observation into a set of small control volumes, which are associated to several flow variables (e.g., velocity, pressure, temperature, etc.). The generated grid has an impact on the accuracy of the results, which shows the importance of this process. The grid was generated using the software named Hexpress [3] which is an unstructured hexahedral grid generation software designed to automatically generate meshes for the discretization of complex 2D and 3D geometries using cut cell approach. This gives the advantage of structural mesh in the accuracy of solver and flexibility of an unstructured grid for capturing the details of the domain. It starts its mesh generation process from

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an initial mesh which encompasses the whole computational domain. An initial mesh is automatically proposed which corresponds to an isotropic subdivision of the computational domain bounding box. The next step consists of two major actions, refinement and trimming. Grid refinement is a process in which cells are successively subdivided such that specific geometrical criteria (to make grid adapt the shape of the geometry) are satisfied. Number of refinements can be decided using following formula:   n=

ln

D di

ln(2)

(1)

where ‘n’ is number of refinements, ‘D’ size of the initial cell in xyz direction and di minimum cell size required to capture the smallest detail of geometry. To capture the geometry, it is required to define the refinement level for different surface. This refinement level ensures that the smallest detail of the geometry is captured. Trimming involves two operations viz. snapping and optimization. The trimming step removes all the cells intersecting or located outside of the geometry. Software automatically finds the cells located inside the computational domain as both domain coordinates and cell coordinates are known. At the end of the process, a staircase mesh is obtained including all the interior cells. Finally, the mesh is smoothed by moving outer grid points on the surfaces and in the volume in order to obtain a mesh with a good but not guaranteed quality. The mesh obtained after the snapping action may involve poor quality cells usually located close to corners and curves. Some of these cells can be concave, twisted or may even present a negative volume. Software uses specific algorithms to convert concave cells to convex ones by slightly displacing their vertices. A novel approach is also implemented to improve the orthogonality of convex cells and hence the quality of overall grid based on the preset criteria. The convex cells are important to ensure the stability and the robustness of a flow solver. The grid generated at the end of this step can be used for Euler solver. Software uses a very specific approach for the insertion of layers of large aspect ratio cells to accurately resolve boundary layers. The technique is based on successive subdivisions of the cells connected to the walls; this contrasts with other techniques which insert layers by extrusion. This refinement technique has the advantage of robustness and speed. Besides, the inflation algorithm improves the mesh quality in viscous layers. Once optimized grid is available, the software asks for the boundary layer refinements for different surfaces. This is where first cell width can be specified and can also be calculated for a required Y+ using the following equation: ywall = (

Vref −7 L ref 1 + )8( ) 8 y1 v 2

(2)

Y+ distribution over the entire domain for the plain passing through the center of long leg is shown in Fig. 2. Depending upon the flow reference velocity, reference length and kinematic viscosity, the grid with close to desired Y+ is generated. Since

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Fig. 2 Y+ details of the generated grid

Y+ is close to 40, turbulence model with extended wall function is used. The focus was to generate a good quality grid for the domain particularly for the long and short nozzles. The grid size for the entire domain is 1.23 million without any negative, concave or twisted cells. Grid quality is not relaxed for any domain. Other grid quality details are presented in Table 1. Figure 3 is showing the arrangement of cartridge starter with details of CFD domain’s inlet and outlet.

3 Governing Equations The well-known Navier–Stokes equations of motion describe the mechanism of flow and associated energy transfer for any fluid. Although the fluid considered is incompressible, the generalized equations are shown which are applicable for both incompressible and compressible flows. The general Navier–Stokes equations written in a Cartesian frame can be expressed as: ∂ ∂t



 U d + 

x

 S − F.d

 s

− →  G.d S =

 ST d 

(3)



where  is the control volume, S is the control surface, and U is the set of conservative variables:

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Fig. 3 Arrangement of cartridge starter with details of CFD domain’s inlet and outlet

⎡

⎤ ρ ⎢ ρu ⎥ ⎢ ⎥ ⎢ ⎥ U = ⎢ ρv ⎥ ⎢ ⎥ ⎣ ρw ⎦ ρE

(4)

− → − → and F and G are the advective and diffusive part of the fluxes, respectively, also can be denoted as inviscid and viscous fluxes. When U is taken as ρ (density) and the diffusive part of the flux is zero (as mass cannot diffuse) along with source term (as mass neither can be created nor can be destroyed), it represents the mass conservation equation, popularly known as continuity equation. Next three values of U (ρu, ρv,ρw) represent the momentum equation and are popularly known as Navier–Stokes equations. When U is taken as ρ E (internal energy), it represents the energy equation.

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⎛⎡

⎤⎞ ⎤ ⎡ ⎤ ⎡ ρu ρw ρv ⎜⎢ ρu 2 + p ⎥ ⎢ ρuv ⎥ ⎢ ρuw ⎥⎟ ⎢ ⎥⎟ ⎥ ⎢ ⎥ ⎢ − → ⎜ ⎜⎢ ⎥⎟ ⎥ ⎢ ⎥ ⎢ F = ⎜⎢ ρuv ⎥, ⎢ ρv 2 + p ⎥, ⎢ ρvw ⎥⎟ ⎜⎢ ⎥⎟ ⎥ ⎢ ⎥ ⎢ ⎝⎣ ρuw ⎦ ⎣ ρvw ⎦ ⎣ ρw 2 + p ⎦⎠ ρw H ρv H ρu H

(5)

where H is the total enthalpy per unit mass: H = E + p/ρ ⎛⎡ ⎜⎢ ⎜⎢ ⎢ − → ⎜ ⎢ G =⎜ ⎜⎢ ⎜⎢ ⎝⎣

0 τx x τx y τx z uτx x + vτx y + wτx z − q x

⎤ ⎡ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥, ⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣

0 τ yx τ yy τ yz uτ yx + vτ yy + wτ yz − q y

(6) ⎤ ⎡

0 τzx τzy

⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥, ⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣

τzz

⎤⎞ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎥⎟ ⎦⎠

(7)

uτzx + vτzy + wτzz − qz

As only Newtonian fluids are considered (which is the case for most gases and common liquids), the stress tensor is a linear function of the shear rate as shown in the equation.    2 − →− − →→ − → → − → →T ∇ .→ v I + ζ ∇ .− τ =μ ∇ ⊗− − v v + ∇ ⊗− v 3

(8)

→ where μ is the dynamic molecular viscosity, − v is velocity vector and I represents Identity (unit) tensor. The heat flux vector is defined by Fourier’s law: − →  − → q = −k ∇ T

(9)

where T is the static temperature and k is the molecular thermal conductivity. ⎞ 0 ⎜ρf ⎟ ⎜ ex ⎟ ⎟ ⎜ ST contains the source terms : ST = ⎜ ρ f ey ⎟ ⎟ ⎜ ⎝ ρ f ez ⎠ wf ⎛

(10)

− → with the vector f e expressing the effects of external forces and W f , the work performed by those external forces is accounted as − → → v W f = ρ f e .−

(11)

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The Spalart–Allmaras turbulence model is one equation turbulence model which estimates the kinematic turbulent viscosity based upon the value specified in the boundary conditions. Details regarding all the terms and coefficients of the effective turbulence eddy viscosity can be found in manual of FINE-Open [4].

4 Computational Details CFD analyses were carried out for nine operating points for the inlet pressure ranging from 90 to 157 bar. Analyses considered the cartridge starter gas flow domain only and burning model is not considered. Air is considered as perfect gas with static pressure and temperature values at the inlet as reference values for property definition. The problem is considered as three-dimensional unsteady, compressible with turbulent flow for the flow analysis. The aim of the analysis is to determine the mass flow rate, its distribution in two arms and the total pressure loss. Spalart–Allmaras turbulence model with extended wall function was chosen for this analysis. Since the flow was unsteady at the exit plane of nozzle, unsteady computation was carried out. Secondorder central difference scheme is employed in space for discretizing the variables in the governing equations (Navier–Stokes equations) using commercial software package FINE-Open [4]. The minimum convergence criterion of 10–6 is defined for the governing equations.

5 Results The computational results are extracted and relevant performance indicators are derived to assess the performance of the cartridge started under various operating conditions. Computations are carried out for nine different operating conditions from 80 to 160 bar as inlet total pressure value. Flow is found to diffuse in the divergent nozzle after a normal shock. Mass flow rate has reduced due to the formation of shock. It is also found that the total pressure loss has reduced near the perforated central core of cartridge starter and maximum loss is associated with the shocks in the CD nozzles. The variation of pressure loss in two arms of the cartridge starter is presented in Fig. 4. Pressure loss in the short arm remained almost constant. Pressure loss in the long arm is slightly more for most of the cases. For 80 bar case, Mach number was found to be comparatively lesser as shown in Fig. 5, which has resulted in lesser loss. For case 120 bar, mass flow from the CD nozzle was comparatively increased for long arm, as shown in Fig. 6, and recirculation zone has reduced which resulted in lesser loss in this arm. Mach number variation at the exit of the long and short arms is shown in Fig. 5 which shows that Mach number remains almost constant from 80 to 120 bar for both

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Variation of Pressure Loss 25

Pressure loss (%)

20 15 10

Long_Arm Short_Arm

5 0 8000000

10000000

12000000

14000000

16000000

Total Pressure (Pa) Fig. 4 Variation of pressure loss with total pressure for different inlet total pressure values

VariaƟon of Mach Number with Total Pressure Long Arm

Short Arm

2.60

Mach Number

2.55 2.50 2.45 2.40 2.35 2.30 2.25

Total Pressure (Pa) Fig. 5 Mach number distribution with total pressure for different inlet total pressure values

long and short arm and then reduce and settle for lesser value after 140 bar case which indicates the higher mass flow and lower losses close to design condition.

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Total Pressure Vs Mass Flow DistribuƟon 0.70 0.60

Total Mass_Flow

Mass Flow (kg/s)

Short Arm 0.50

Long Arm

0.40 0.30 0.20 0.10 0.00

Total Pressure Fig. 6 Mass flow distribution with total pressure for different inlet total pressure values

6 Conclusion Unsteady CFD analyses are carried out for nine different operating conditions from 80 to 160 bar as inlet total pressure value. Flow is found to diffuse in the divergent nozzle after a normal shock. Mass flow rate has reduced due to the formation of shock. CFD is successfully applied for studying the supersonic flow behavior in cartridge starter. The velocity of the high pressure high temperature gas coming out from the exit of converging diverging nozzles predicted using CFD study is found to be in good agreement with the design value. Table 1 Grid quality details

Quality criteria

Value

Minimum orthogonality

13.4

Average equiangular skewness

80.7

Maximum expansion ratio

7.9

Maximum aspect ratio

6.7

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References 1. https://megiovandi.wordpress.com/tag/starting-system/ 2. Anil Kumar K, Balamuralikrishnan N (2017) Pyro assisted starting of small gas turbine engine for unmanned application. In: Proceedings of the 2017 gas turbine india conference, 7–8 Dec, Bangalore 3. User manual Hexpress version 7.2 (2018) 4. Theoretical manual FINE-Open version 7.2 (2018)

High-Speed Shadowgraph Visualization Studies of the Effectiveness of Ventilating a V-Gutter Flame Holder to Mitigate Screech Combustion Instability in an Aero-Gas Turbine Afterburner C. Rajashekar, Shambhoo , H. S. Raghukumar, R. M. Udaya Kumar, K. Ashirvadam, and J. J. Isaac Abstract Screech combustion instabilities are high frequency (>1000 Hz) transverse periodic oscillations driven by combustion and which are then manifested as large amplitude oscillations in the afterburner duct pressure, accompanied by the characteristic high-pitched audible tones. These screech instabilities which are detrimental to the engine are conventionally suppressed by embedding Helmholtz resonator arrays in the afterburner liner. This method has been found inadequate when mixed mode combustion instability oscillations occur and also when the frequencies of oscillation were lower. The design of practical Helmholtz resonator arrays is classified and so is not available in the open domain. Hence, it was necessary to evolve a robust design solution to mitigate screech combustion instabilities in an afterburner. In an afterburner, V-gutters are used as flame stabilizers. The high Reynolds number flow past a V-gutter array is dominated by the presence of vortices characterized by the Kelvin–Helmholtz instability, which is a convective flow instability related to the shear layers separating from the V-gutter lips and the Benard–von Karman instability which is related to the asymmetric vortex shedding of the flow in the flame holder wake. The shedding of von Karman vortices at non-reacting and near the blowout conditions, and the transition from a Kelvin–Helmholtz instability to that of a Bernard–von Karman instability during near flame blowout create conditions for the frequency to get locked-on to the duct transverse acoustic mode frequency; screech is triggered. Hence, a smart flame stabilization method which has the intrinsic property of preventing the lock-on between the frequency of the vortex shedding from the V-gutter and the duct transverse acoustic frequency was developed. The test rig with optically accessible critical zones around the V-gutter flame stabilizer had the capability to operate the afterburner model under simulated inlet conditions of pressure and temperatures. A FastCam SA-4 Photron high-speed camera was used in this experimental investigation and high-speed shadowgraph flow visualization studies C. Rajashekar (B) · Shambhoo · H. S. Raghukumar · R. M. Udaya Kumar · J. J. Isaac Propulsion Division, CSIR-National Aerospace Laboratories, Bengaluru, Karnataka, India e-mail: [email protected] K. Ashirvadam ABES, Gas Turbine Research Establishment, DRDO, Bengaluru, Karnataka, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_25

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were carried out to develop a comprehensive method of introducing an aerodynamic splitter plate concept through a ventilated V-gutter; mitigation of screech combustion instability has been demonstrated. Keywords Combustion instability · Ventilated V-gutter · Screech · Afterburner · Screech mitigation

List of Abbreviations CAF Compressed Air Facility CSIR-NAL Council of Scientific and Industrial Research, National Aerospace Laboratories PXI Peripheral Extended Instrumentation DAS Data Acquisition System FFT Fast Fourier Transform KH Kelvin Helmholtz B-VK Benard–von Karman

1 Introduction Afterburner combustion instability is one of the serious problems that is encountered by aero-gas turbine engineers in the development phase of advanced military engines [1, 2]. The serious detrimental effects of screech combustion instability phenomena need to be solved through a robust design solution. The occurrence of combustion instabilities is found to happen when there is coupling between the unsteady pressure oscillations and the combustion heat release, thus satisfying the Rayleigh criterion. Screech refers to an acoustic instability of resonant combustion, with the frequency and phase of the wave oscillations corresponding to those for the transverse acoustic resonance of the afterburner duct. It is essential to understand the cause of the problem when addressing it through robust and innovative solutions. Schlieren and Shadowgraphy are simple, but very effective, non-intrusive techniques used to study complex flow phenomena such as unsteady combustion in propulsion systems like the afterburner. Flow visualization studies help in understanding the flow phenomena, to evolve and verify flow models, help make theoretical predictions and also validate the computed solutions [3].

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2 Experimental Test Facility A comprehensive experimental investigation has been carried out in a specially set up versatile single V-gutter flame holder afterburner test rig (Fig. 1). The test facility consisted of an air feed line of 152.4 mm diameter with a maximum air delivery pressure of 1 MPa. This test rig was connected to the main reservoirs of the compressed air facility (CAF) available at the wind tunnel center, CSIR-NAL. The test rig consisted of a kerosene fueled slave combustor to heat up the air to simulate the afterburner inlet conditions, a settling chamber to provide stabilized uniform entry conditions to the test section and a transition duct connecting the circular outlet of the settling chamber to the rectangular section afterburner duct where the V-gutter flame holder/fuel injector was fitted. The required air mass flow, metered by an orifice plate, was allowed into the afterburner test rig model and was controlled by a motorized valve. Metered kerosene fuel was fed to the slave combustor and the afterburner using a nitrogen gas top loading method. The hot section of the test rig had a proper cooling arrangement to avoid over heating of the critical afterburner section of the test rig. The dimensions of the rectangular section afterburner were 200 mm × 70 mm, which housed the single V-gutter to generate screech combustion instability at selected frequencies. The length of the afterburner duct was around 1 m. The afterburner fuel injector was located upstream of the V-gutter and the fuel was injected transversely to the air flow through 14 nos 0.5 mm holes.

Fig. 1 Schematic and photograph of the experimental test set up

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The critical section of the afterburner test facility was appropriately modified with optical access to enable the high-speed flow visualization studies. The test section in the region of the V-gutter flame holder could be fitted with a metal cover plate or quartz glass depending on the type of experiments. Two collimating concave mirrors of diameter 300 mm and focal length 2.8 m were used for flow visualization studies. A fiber optic illuminator having a 150 W halogen bulb was used as the light source. A Photron FastCam SA 4 camera was used to capture the unsteady flow structures in the V-gutter region; camera speeds up to 13,500 frames per sec at a resolution of 512 × 464 pixels was used during the study. Figure 1 shows a schematic and photograph of the complete test set up and the conventional Z-type mirror arrangement for the flow visualization studies.

2.1 V-Gutter Configurations Considered for the Experimental Studies Figure 2a shows a CAD drawing of the flame stabilizer that was used for the experimental studies. The material used was Nimonic 263 alloy. The flame stabilizer had a rectangular slit at the center which could be varied from zero ventilation to various widths of bleed using an insert and also to use a special metal insert which could isolate the top and bottom halves of the V-gutter while completely covering the slit as shown in Fig. 2b. The V-gutter was designed in such a way that a passage was provided to channel ventilated air directly to the flame holder base to create the best vortex suppression effect. Figure 2c shows the assembly of the V-gutter inside the test rig and also the mechanical splitter plate assembled V-gutter in position.

2.2 Instrumentation Details The details of the test rig instrumentation scheme are shown in Fig. 3. The DAS included pressure (steady and unsteady), temperature and mass flow rate measurements. The pressure of air and fuel was measured using YOKOGOWA pressure transmitters. All pressure signals were calibrated and connected to the NI PXI DAS system. The temperatures at the exit of the slave combustor and at the inlet to afterburner section were measured using K-type thermocouples. The mass flow rates of air and fuel were measured using orifice and Coriolis mass flow meters, respectively. The dynamic pressure measurements were carried out using Kulite unsteady pressure sensors mounted in the afterburner section of the test rig. The other critical parameters that were monitored during the experiments were the afterburner inlet temperature, inlet pressure and overall afterburner equivalence ratio.

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Fig. 2 a Dimensions of the V-gutter flame stabilser. b V-Gutter hardware. c Assembly of ventilated V-gutter flame stabilizer in afterburner duct, and V-gutter with mechanical splitter plate

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Fig. 2 (continued)

Fig. 3 Instrumentation scheme of the test rig

2.3 Experimental Procedure Experiments were conducted to generate a specified controlled and sustained screech frequency of 2000 Hz by a special technique at afterburner inlet temperatures of around 600 K. The duct pressures were maintained around 150 kPa bar, abs. The air flow to the afterburner test rig was controlled from a 152.4 mm diameter motorized valve and the required air flow and pressure was regulated in the test rig for smooth ignition of the slave combustor. After ignition of the slave combustor, the fuel flow and the line air pressure were controlled to get the required pre-set afterburner inlet pressure and temperature. The afterburner fuel flow was carefully regulated, and after the ignition of the afterburner and stable operating conditions attained, the afterburner

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fuel flow was carefully further increased until screech was observed. The occurrence of screech was noted from the distinct high frequency audible tone. Simultaneously, the FFT of the fundamental mode and the overtones were observed on the control room DAS monitor. The raw data and the derived data during the entire test run were acquired in the DAS. Simultaneously, the shadowgraph images were captured by the monochrome high-speed video camera and color flame pictures by a Nikon D 800 still camera. The following sets of experiments were conducted during the investigation: 1. V-gutter with zero ventilation 2. V-gutter with a mechanical splitter plate 3. V-gutter with an aerodynamic splitter plate by inserting three selected metal inserts with ventilation of width 42 mm and gap height of 10, 14 and 16 mm as shown in Fig. 2a.

3 Results and Discussion Figure 4 shows a high-speed shadowgraph of the flame holder wake at different operating conditions. Figure 4a shows a high-speed shadowgraph of the flame holder wake when the afterburner (A/B) was off, while the main combustor was kept on and the AB inlet temperature was maintained at around 600 K. Corresponding pressure signals measured with a dynamic pressure transducer are shown in Fig. 5a. At A/B off conditions, fluctuations in pressure signals were very small and were of random nature. The Kelvin–Helmholtz (K-H) instability was observed in the separating shear layers originating from the V-gutter tips, when afterburner was lit at low equivalence ratios Fig. 4b. Pressure signal fluctuations had increased as compared to A/B off condition but still small and random in nature. At higher equivalence ratios this K-H instability changed into a Benard–von Karman (B-VK) instability, which was characterized by the presence of periodic asymmetric vortex shedding behind the flame holder as shown in Fig. 4c. Pressure signals, at this condition (afterburner on, high equivalence ratio), exhibited large fluctuations with definite periodicity in the pressure variation in the duct. From the trace of the vortex evolution, extracted from high-speed video shadowgraphy, the vortex shedding frequency was found to be 1930 Hz, which was very close to the frequency obtained from the FFT of measured dynamic pressure as shown in Fig. 6, first mode:2000 Hz). Interestingly, this frequency (~2000 Hz) is not the expected Strouhal frequency. Here, the vortex shedding frequency had ‘locked-on’ to duct resonant acoustic transverse mode frequency (first mode). Asymmetric vortex shedding, large pressure oscillation, ‘lock-on’ of vortex shedding frequency to the duct acoustic frequency indicated that the root cause of the screech combustion instability was vortex shedding behind the flame holder. Suppression of this vortex shedding could be the key in eliminating the screech combustion instability [4–6].

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(b) Afterburner on; no ventilation, (a) Main combustor-on and afterburner-off with inlet temperature overall equivalence ratio ~ 0.35 (Kelvin-Helmholtz instability), of ~ 600 K No screech

(c) Afterburner on; no ventilation, equivalence ratio ~0.45 (Benard-Von Karman instability), Screech Fig. 4 High-speed shadowgraph images in the V-gutter region

Vortex shedding can be suppressed by introducing a mechanical splitter plate in the wake behind the flame holder, which suppressed formation of any large-scale shedding vortex structure in the flame holder wake. Experiments were conducted using the V-gutter with a mechanical splitter plate as shown in Fig. 2b under similar afterburner inlet conditions that were maintained for the V-gutter with zero ventilation. Figure 7a, b shows high-speed shadowgraphs of flame holder wakes showing the effect of mechanical splitter at afterburner inlet temperature of 600 K. Mechanical splitter plate was successful in suppressing the formation of large-scale shedding vortex structure at low equivalence ratio (up to ~Ø = 0.7) which is better than an earlier result (without splitter plate case where screech was observed at Ø = 0.45), but at higher equivalence ratio (Ø > 0.7), screech was observed. Figure 7c shows

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Fig. 5 Unsteady pressure signal measured behind the flame holder for different operating condition a Afterburner off; main combustor on, afterburner inlet temperature ~ 600 K. b Afterburner on; no ventilation, overall equivalence ratios ~0.35, No screech (c) Afterburner on; no ventilation, equivalence ratios ~0.45, screech

Fig. 6 Typical test result showing the screech frequency of 2000 Hz for an inlet pressure of 150 kPa abs and inlet temperature ~600 K and equivalence ratio ~0.45

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a

b

Fig. 7 a, bHigh-speed shadowgraphs of flame holder wakes showing the effect of the mechanical splitter plate. c Screech frequency of 2000 Hz for an inlet pressure of 1.5 bar abs and inlet temperature of ~600 K and equivalence ratio of ~0.85

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the FFT of the unsteady pressure signal. The pressure excursion over the duct mean pressure was found to be around 14%. At low equivalence ratio, feedback energy from heat release fluctuation was small to the acoustic field, which was easily dampened by the presence of a mechanical plate. As the equivalence ratio increased, feedback energy also increased, and due to fluid–structure interaction, the plate started to oscillate. Finally, the vortex shedding got locked-on to the duct acoustic resonance frequency. Relative strength of the plate and strength of feedback energy play an important role in determining the operating condition at which screech might be triggered. A very heavy and strong plate might be required to suppress the screech over a wide range of operating condition. This will add a weight penalty to the system, notwithstanding the plate cooling difficulties, which is not desirable in aero-systems. Hence, an innovative design was adopted to create the same effect, as a mechanical splitter plate, over a wider range of operating condition, but without weight or cooling penalty. A passage was provided to channel ventilated air directly to the flame holder base to create the best vortex suppression effect. If the channel was not provided, due to a Coanda effect, the ventilated air would move along the inside V-gutter face and would also experience bi-stability and wake asymmetry. The ventilation coefficient ‘v’ is defined as the ratio of the ventilation slit gap width (h) to the V-gutter base height (H). Figure 8a shows the effect of ventilation at an afterburner inlet temperature ~600 K. The center jet from the V-gutter (for v = 10.6%) successfully eliminated any largescale shedding vortex structure, and no screech was observed at all operating conditions for this ventilation coefficient value. While in other cases (for v = 6.67%), low strength of the center jet allowed shedding vortex structure and screech combustion instability was observed at such a low ventilation coefficient (low bleed). Figure 8b shows the FFT of dynamic pressure measured for different ventilation coefficient (0%, 6.6%, 9.3%, 10.6%). As the ventilation coefficient increased, the strength of the central jet increased which suppressed the formation of large-scale shedding vortex structure and hence the amplitude of screech combustion instability decreased as shown in Fig. 9. At v = 10.6%, screech combustion instability had been completely suppressed. High-speed shadowgraphs as shown in Fig. 7 and FFT of dynamic pressure signal as shown in Fig. 8 both confirmed the suppression of screech at all operating conditions. Figure 10 shows the afterburner flame photographs at similar operating test conditions. With no bleed condition, the screech was found to occur at an equivalence ratio ~0.45, whereas with 16 mm (v = 10.6%) bleed, it was possible to go to higher equivalence ratios of the order 0.7. The intensity of the flame also clearly indicated that it was possible to test at higher equivalence ratios without encountering any screech combustion instability problems. It clearly indicated that the concept of aerodynamic bleed was successful in breaking the communication between the top and bottom halves of the V-gutter, suppressing the vortex shedding getting locked-on to the duct acoustic frequency and thus mitigating screech.

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Fig. 8 a High-speed shadowgraphs of flame holder wakes showing the effect of ventilation. Afterburner inlet temperature ~600 K. b FFT showing the effect of ventilation on the intensity of screech combustion instability, afterburner inlet temperature ~600 K, equivalence ratios ~0.5

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Fig. 9 Variation of screech amplitude with ventilation coefficient. Afterburner inlet temperature ~600 K, equivalence ratio ~0.8 (Screech frequency—2000 Hz)

4 Conclusions A method of enabling controlled screech has been evolved. Using this, a technique of incorporating an aerodynamic splitter plate using ventilation in the V-gutter flame holder base has been successfully developed to mitigate screech in a model aerogas turbine afterburner. High-speed shadowgraphy has been shown to be a powerful technique of studying V-gutter flame holder wake structures when screech combustion was present. The transition from a Kelvin–Helmholtz to a Benard–von Karman instability characterized the onset of screech combustion instability. For the chosen operating conditions of pressure of 1.5 bar abs and temperature of ~600 K, ventilation coefficient of atleast 10.6% was found to give good screech mitigation.

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Fig. 10 Comparison of afterburner flame structure with aerodynamic splitter plate and with bleed ventilation of 16 mm (v = 10.6%)

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Acknowledgements The authors thank the Director, Gas Turbine Research Establishment, DRDO for sponsoring this project under the Gas Turbine Enabling Technology (GATET) scheme. The authors thank the Director, NAL and the Head, Propulsion Division for granting permission to take up this project. They would also like to thank Mr Fakruddin Goususab Agadi, Technician-1 Propulsion Division for his technical support.

References 1. Sotheran A (1987) High performance turbofan afterburner systems. In: AIAA-87–1830 AIAA/SAE/ASEE 23rd joint propulsion conference, 29 June–2 July 1987 2. Houshang E (2006) Overview of gas turbine augmentor design, operation, and combustion oscillation. In: AIAA-2006–4916 AIAA/SAE/ASEE, 42nd joint propulsion conference, 9–12 July 2, 2006 3. Culick FEC (1988) Combustion instabilities in liquid-fueled propulsion systems—an overview. AGARD 72B PEP meeting, Bath, England 4. Briones A, Sekar MB (2012) Effect of von Karman vortex shedding on regular and open slit V-gutter stabilized turbulent premixed flames. Spring Technical meeting of the Central States Section of the Combustion Institute 5. Yiqing Du, Qian R, Peng S (2016) Coherent structure in flow over a slitted bluff body. Commun Nonlinear Sci Numer Simul 11(3):391–412 6. Jing T, Chang W, Go L (1994) Flame stabilization in the wake flow behind a slit V-gutter. Combust Flame 99(2):288–294

Passive Reduction of Aerodynamic Rolling Moment for a Launch Vehicle Pankaj Priyadarshi, Amit Sachdeva, and Leya Joseph

Abstract Aerodynamic rolling moment on a core-alone launch vehicle due to the presence of a wire tunnel and the associated roll dynamics has been studied. Computational Fluid Dynamics (CFD) simulations across the roll angles from φ = 0◦ to 180◦ and across the Mach number range indicated the wire tunnel to be the major cause of the rolling moment. A passive means of roll moment reduction has been proposed by adding dummy wire tunnels symmetrically around the vehicle. It was found that adding one dummy wire tunnel diagonally opposite to the existing wire tunnel did not reduce the peak rolling moment as the leeward wire tunnel is ineffective. However, adding two dummy wire tunnels reduced the rolling moment substantially. Addition of the third dummy wire tunnel was also helpful in reducing the rolling moment further, though marginally. In addition to the CFD studies, the maximum roll rates and roll errors of the different configurations have been compared through roll dynamic simulations. A novel linear superposition methodology has been proposed and validated to obtain the rolling moment coefficient for multiple wire tunnel configurations. Keywords Aerodynamic rolling moment · Roll dynamics · Wire tunnels · Core-alone launch vehicle · CFD · SU2

P. Priyadarshi (B) · A. Sachdeva · L. Joseph Vikram Sarabhai Space Centre, Thiruvananthapuram, India e-mail: [email protected] A. Sachdeva e-mail: [email protected] L. Joseph e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_26

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Abbreviations M Mach number φ Roll angle CRM Rolling moment coefficient CN Normal force coefficient α Angle of Attack t Time φ˙ Roll rate Izz Second moment of inertial about the roll axis C Moment generated by the control system R Aerodynamic rolling moment q Dynamic pressure S Reference area d Reference length Cmax Amplitude of moment generated by control system K φ Gain associated with roll error K φ˙ Gain associated with roll rate φ Roll error S Sigmoid function

1 Introduction Attitude angles of a launch vehicle need to be controlled to ensure that a nearnominal trajectory is achieved with acceptable peak angular rates for the survival of the vehicle’s instrumentation and payload. At high angular rates, the gyro sensors can lose their reference and become inaccurate. Launch vehicles, especially corealone vehicles, have low inertia about the roll axis and are susceptible to large roll rates and roll angle errors due to aerodynamic rolling moments. Hence, either the inherent rolling moment has to be reduced or appropriate roll control system to counter the disturbing rolling moments has to be incorporated. Typically, launch vehicles employ aerodynamic control surfaces such as fins and propulsive systems like Reaction Control System (RCS) to control the roll rates and roll angle errors. Pure hydrazine based roll control thrusters are used in European launch vehicles like Ariane 5 and VEGA [1]. In this work, a passive technique for rolling moment reduction for a core-alone launch vehicle configuration is presented. Asymmetry introduced by the wire tunnel, in the one-wire tunnel configuration, is the major source of rolling moment when the vehicle is at an angle of attack. RCS sizing studies on a single wire tunnel configuration indicated large roll-control demand. The current proposal is based on a detailed study on how the rolling moment, roll rate and roll error can be reduced in a passive manner. This is investigated by progressively adding dummy wire tunnels

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to induce symmetry about the roll axis such that the rolling moment generated by the overall system is significantly reduced. Such a technique would also significantly bring down the roll control demand. The rolling moment demand due to CG offset and thrust offset are easily corrected by the pitch and yaw thrust vector control of the vehicle and do not cause any rolling moment on the vehicle. The methodology adopted in the aerodynamic and roll dynamic studies is presented in Sect. 2. Results of CFD simulations are presented in Sect. 3.1. The applicability of various techniques presented in Sect. 2 has been validated in the same section. Sect. 3.2 presents the results of the roll dynamics studies. Conclusions are presented in Sect. 4.

2 Methodology This section presents the methodology followed for the study. Section 2.1 presents the approach used to characterize the aerodynamic rolling moment coefficients across various Mach numbers and roll angles. This includes the proposed linear superposition based method to obtain rolling moment coefficients for multiple wire tunnel configurations by employing data from single wire tunnel simulations. Section 2.2 presents the methodology adopted in the roll dynamics studies to assess the maximum roll rates and roll angle errors for various configurations.

2.1 Characterization of Aerodynamic Rolling Moment First the methodology for the Computational Fluid Dynamics (CFD) simulations is presented. Thereafter, the proposed approach employing linear superposition to compute rolling moment for two, three and four wire tunnel configurations, by employing results from single wire tunnel configuration, is presented. It is followed by description of the scaling approach to obtain variation of rolling moment with roll angle across Mach numbers.

2.1.1

CFD Studies

An initial database of rolling moment has been derived using CFD simulations on a one wire tunnel configuration of the core-alone launch vehicle at Mach number 1.6 and roll angles ranging between 0◦ and 180◦ , at an angle of attack of 4◦ . The simulations have been carried out using the in-house CFD software, PARallel Aerodynamic Simulator-3 Dimensional (PARAS-3D) [2]. The solver is based on rectangular adaptive Cartesian mesh and can solve both compressible Euler equation and Reynolds Averaged Navier-Stokes (RANS) equations. The solver utilizes finite volume technique with explicit time marching. Primitive Variable Riemann Solver (PVRS) is

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(a) Initial grid

(b) Grid after final refinement

Fig. 1 Grid used for CFD simulations

used to evaluate inviscid fluxes, whereas central difference scheme is used for viscous fluxes. The solver also has utility to refine the grid at any stage based on flow gradients. In this study, RANS equation and k- turbulence model have been used for simulations. The domain considered for CFD simulations extends across −50 to +50 D in the longitudinal direction, and from −40 to +40 D in the lateral directions, where D is the diameter of the configuration. D and its associated circular area are the reference length and reference area used in computation of aerodynamic coefficients respectively. Adaptive grid refinement has been carried out at sufficient iteration intervals. Figure 1 shows the initial Cartesian grid and the final grid after a sequence of flow refinements till convergence in rolling moment coefficient has been achieved. Figure 2 shows typical convergence plots for vehicle normal force coefficient (CN ) and rolling moment coefficient (CRM ). The grid is refined based on gradients in the flow field at user specified iterations. Thus, after each refinement, the number of cells in the grid increases as seen in Fig. 2. The convergence is measured across the solutions before and after the last refinement, which are essentially the solutions from two different grids. The CFD results had convergence in CRM within 0.8%. Limited CFD simulations have been also carried out for other Mach numbers and configurations with one and four wire tunnels to validate the PARAS results and linear superposition explained in subsequent subsections. These simulations have been carried out in the open-source CFD code, SU2 [3] using the body fitted grid generated in Pointwise [4]. SU2 is capable of high-fidelity analysis solving compressible and incompressible Euler, Navier-Stokes, and RANS solvers, along with optimal shape design and adaptive grid refinement [5].

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0.3 0.25 0.2 0.15 0

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(a) Variation of normal force coefficient with iterations

0.0035

No of Cells(in million)

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Fig. 2 Convergence plots for normal force and rolling moment coefficients

2.1.2

The Proposed Linear Superposition Approach to Obtain Rolling Moment Coefficients for Non-simulated Wire Tunnel Configurations

As discussed earlier, most of CFD simulations have been carried out on a single wire tunnel configuration. The rolling moment coefficients for configurations with multiple wire tunnels were derived from the CFD results of single wire tunnel configuration using the principle of linear superposition. The simulated core-alone launch vehicle configuration has very low CRM , which is primarily contributed by the wire tunnel. The rolling moment contribution of the wire tunnel and the protrusions was extracted from the single wire tunnel CFD simulations. Then, these result were used to construct the rolling moment for the multiple wire tunnel configurations using the principle of linear superposition. The linear superposition of CRM is justifiable when the separation between the wire tunnels is significantly high so as to avoid interference effects between the tunnels, and when the wire tunnel diameter is very small in comparison to the launch vehicle diameter. The validation studies for this approach have been presented in Sect. 3.1. Consider a modified configuration of the core-alone vehicle with an additional wire tunnel placed diametrically opposite to the already existing wire tunnel. The modified configuration has an additional wire tunnel at a phase difference of 180◦ from the wire tunnel in the single wire tunnel configuration. The contribution from the two wire tunnels can be captured as a linear superposition of two single wire tunnel cases at a phase difference of 180◦ . The linear superposition is schematically shown in Fig. 3a and can be mathematically expressed for a given roll angle φ and Mach number M as follows: (2) (1) (1) CRM (φ, M) = CRM (φ, M) + CRM (φ + 180◦ , M)

(1)

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(1) (2) where CRM and CRM represent rolling moment coefficients of one and two wire tunnel configurations in the absence of protrusions respectively. Similarly, the CRM for three and four wire tunnel configurations are obtained through linear superposition of individual wire tunnel contributions as follows: (3) (1) (1) (1) CRM (φ, M) = CRM (φ, M) + CRM (φ + 120◦ , M) + CRM (φ + 240◦ , M) (2)

(4) (1) (1) (1) CRM (φ, M) = CRM (φ, M) + CRM (φ + 90◦ , M) + CRM (φ + 180◦ , M) (1) + CRM (φ + 270◦ , M)

(3)

(3) (4) where CRM and CRM represent rolling moment coefficients of three and four wire tunnel configurations in the absence of protrusions respectively. The schematic representations for three and four wire tunnel configurations are shown in Fig. 3b, c respectively. The contribution of protrusions to CRM is also linearly superposed as follows: (n+prot)

CRM

(prot)

(n) (φ, M) = CRM (φ, M) + CRM (φ, M) , n = 1 . . . 4

(n+prot)

(4)

(prot)

where CRM and CRM represent the CRM of the configuration with n wire tunnels in the presence of protrusions and the CRM due to protrusions respectively.

2.1.3

Rolling Moment Coefficients at Non-simulated Mach Numbers

Rolling moment variation with roll angle (φ) has been characterized extensively for the single wire tunnel configuration at Mach 1.6. However, roll dynamics studies require aerodynamic moments at time-varying Mach number across the vehicle’s trajectory. Thus, to derive the CRM variation with roll angles at a range of Mach numbers (M = 0.8, 0.95, 1.05, 1.2, 2 and 4), available CFD simulation results at φ = 45◦ [6] at these Mach numbers were made use of. The variation of CRM with φ captured from Mach 1.6 simulations are scaled to other Mach numbers using the CRM data at φ = 45◦ at these Mach numbers. (1+prot)

CRM

(1+ pr ot)

(φ, M) =

CRM

(45◦ , M)

CRM

(45◦ , 1.6)

(1+prot)

(1+prot)

× CRM

(φ, 1.6)

(5)

2.2 Roll Dynamic Studies The roll dynamics of the launch vehicle in presence of aerodynamic disturbances was studied through 1-DOF simulations governed by the following equations of motion.

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Fig. 3 Schematic representation of linear superposition of CRM for various configurations

˙ + R (t) C(φ, φ) d φ˙ = dt Izz (t)

(6)

dφ = φ˙ dt

(7)

˙ C and R represent roll angle, roll rate, moment generated by control where φ, φ, system and aerodynamic rolling moment respectively. Aerodynamic rolling moment is obtained as,

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R (t) = S d q(t) CRM (M, φ)

(8)

where q, S and d represents dynamic pressure, reference area and reference length respectively. A 1-DOF code was written in Octave [7] and was used to carry out analysis of the vehicle’s roll dynamics in the presence of aerodynamic moments alone, i.e., with ˙ = 0. Also simulations with a PI controller with rate feedback and with the C(φ, φ) rolling moment modeled as a sigmoid function, were carried out. Moment generated by control system is modeled using sigmoid function as follows:   ˙ φ C (t) = (−2Cmax ) × S φ,

(9)

  ˙ φ is given by, where the sigmoid function S φ, ⎞ ⎛   1 ˙ Δφ = ⎝   − 0.5⎠ S φ, ˙ 1 + e−K φ˙ φ(t)−K φ φ(t)

(10)

Cmax and φ represent maximum moment that can be produced by the control system and the deviation from initial roll angle respectively. K φ and K φ˙ represent the   ˙ φ PI controller gains associated with roll error and roll rate respectively. As S φ, varies from 0 to 1, C (t) varies from −Cmax to Cmax . The system of differential equations Eqs. (6) and (7) can be solved with the appropriate initial conditions on roll angle and roll rate as follows: φ (0) = φ0

(11)

φ˙ (0) = φ˙ 0

(12)

where φ0 and φ˙ 0 represent the initial values of roll angle and roll rate respectively. The assumptions involved in the roll dynamics simulations are as follows: – All simulations have been carried out with α = 4◦ throughout the flight for conservative estimates. The variation of CRM corresponding to φ and M is considered. – Off-nominal aerodynamic rolling moment data have been considered with 100% dispersion for conservative estimates. – Upper bound trajectory has been used for variation in Mach number and dynamic pressure with time. – Aerodynamic damping has been neglected. – Sources of rolling moment other than aerodynamics, have not been considered. – Nominal variation of moment of inertia about the roll axis has been accounted as a function of time. – Ideal control without any delay is considered. – Control has been modeled using a sigmoid function. – Wind plane azimuth is considered to remain invariant throughout the flight.

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– Pitch-yaw coupling has been neglected. – CRM variation with φ at Mach 1.6 has been scaled to other Mach numbers using φ = 45◦ data at the respective Mach numbers. – Linear superposition has been used to obtain CRM for two, three and four wire tunnel configurations.

3 Results Section 3.1 presents the rolling moment characterization for the core-alone vehicle at different M and φ. The validation studies for the linear superposition method has been discussed in the same section. Section 3.2 presents the results of the 1-DOF simulations and compares the one, two, three and four wire tunnel configurations based on the maximum roll rates and roll angle errors.

3.1 Characterization of Aerodynamic Rolling Moment CFD simulations in PARAS-3D were carried out on the one wire tunnel configuration of the vehicle at Mach 1.6, when the vehicle encounters peak dynamic pressure. Figure 4 shows the variation of CRM with roll angle at this Mach number. As can be observed from the plot, the peak aerodynamic rolling moment is generated when the vehicle with one wire tunnel is at a roll angle around 67.5◦ and 292.5◦ . It can also be observed that CRM is very low for φ in the roll angle range [120◦ , 240◦ ], when the wire tunnel is on the leeward side. Figure 4 also compares the CRM values obtained from PARAS-3D and SU2 . The values are fairly closely matching, thus giving confidence on the CFD results especially when the wire tunnel is on the windward side.

Fig. 4 CRM variation with φ for one wire tunnel launch vehicle configuration at M = 1.6

0.003

PARAS-3D SU2

0.002

CRM

0.001 0 -0.001 -0.002 -0.003 0

45

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180 φ (deg)

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Rolling moment coefficients for two, three and four wire tunnel configurations as obtained from the linear superposition of results from one wire tunnel configuration are shown in Fig. 5a. The maximum value of CRM remains similar for both one and two wire tunnel configurations. This is due to the low rolling moment generation by the wire tunnel on the leeward side, due to which the moment generated by the wire tunnel on the windward side is not significantly reduced. Three and four wire tunnel configurations have been simulated and both of them are found to be attractive. The configurations with three and four wire tunnels leads to substantially lower CRM as compared to one and two wire tunnel configurations at M = 1.6 (Fig. 5). The phase difference between the wire tunnels is such that the rolling moment contributions add up to provide very low net CRM . This is clearly seen from Fig. 5b where the contribution from each wire tunnel is plotted along with the sum of contribution from all wire tunnels for the three wire tunnel case. The contribution from the protrusion is also plotted and is linearly superposed to obtain the final results. Figure 6 shows the CRM variation with roll angle for one wire tunnel configuration at various Mach numbers obtained by scaling the results at M = 1.6. A similar approach has been applied on the linearly superimposed CRM of 2, 3 and 4 wire tunnel cases.

3.1.1

Validation Studies

CFD simulation of the four wire tunnel configuration was carried out in SU2 and was compared with the results from linear superposition. The maximum CRM for the single wire tunnel case is 0.00267 which gets reduced by 80.5% to 0.0005 when computed using linear superposition. Computational Fluid Dynamics (CFD) simulations using SU2 show that the value reduces by 85% to 0.0004, which is very close considering the small magnitude of CRM .

3.2 Roll Dynamics Studies Time evolution of roll angle and roll rate obtained from 1-DOF simulations in the absence of control, with initial roll angles varying from 0◦ to 180◦ are shown in Fig. 7. As mentioned earlier, simulations were carried out using 100% dispersion in CRM and considering an angle of attack of 4◦ throughout the trajectory. The initial roll rate is considered to be zero for all simulations. As can be observed from results for single wire tunnel configuration in Fig. 7a and Table 1, the system tries to achieve the nearest roll trim point with a maximum roll rate of 15.2◦ /s. However, for most of the cases, the system has non-zero roll rates at the end of simulation along with significant roll errors. The reduction in roll rate with the addition of dummy wire tunnels are evident from Fig. 7b–d. However, it is also observed from these figures that in the absence of control, the roll angle errors are lesser in the configurations with two and three additional wire tunnels as compared to the one wire tunnel configuration. Three and

Passive Reduction of Aerodynamic Rolling Moment for a Launch Vehicle Fig. 5 CRM variation with φ for one, two, three and four wire tunnel configurations at M = 1.6

0.004

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N = 1 (CFD) N = 2 (LS)

0.003

N = 3 (LS) N = 4 (LS)

CRM

0.002 0.001 0 -0.001 -0.002 -0.003 0

50

100 150 200 250 300 350 400 Roll angle (deg)

(a) CRM variation with φ for 1,2,3, and 4 wire tunnel configurations 0.004

3-WT Config. Contribution: WT 1 Contribution: WT 2

0.003

Contribution: WT 3 Contr.: Protrusions

CRM

0.002 0.001 0 -0.001 -0.002 -0.003 0

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100

150

200

250

300

350

Roll Angle (deg)

(b) CRM variation with φ for three wire tunnel configuration. The contribution from each wire tunnel have been superimposed

Fig. 6 CRM variation with φ and M for one wire tunnel configuration

0.004

M = 0.8 M = .95 M = 1.05 M = 1.2 M = 1.6 M = 2.0 M = 4.0

0.003 0.002

CRM

0.001 0 -0.001 -0.002 -0.003 -0.004 0

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150 200 250 Roll angle (deg)

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(a) Results for single wire tunnel configuration

(b) Results for two wire tunnel configuration

(c) Results for three wire tunnel configuration

(d) Results for four wire tunnel configuration

Fig. 7 Roll error and roll rate evolution with time obtained from simulations without control

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Table 1 Maximum roll rate and roll angle errors from simulations in the absence and presence of control No. of wire Without control With 400 Nm control tunnels φmax φmax φ˙ max φ˙ max 1 2 3 4

444.7 790.7 387.2 390.0

15.2 13.2 6.0 5.2

267.8 137.3 40.4 16.6

13.0 11.5 2.1 0.7

four wire tunnel configurations have fairly low maximum roll rate and roll error as compared to one and two wire tunnel configurations (Table 1). 1-DOF simulations in the presence of roll control with varying maximum roll control capability have been carried out. Results of studies with a maximum control capability of 400 Nm are shown in Table 1. In these studies, initial roll angle is varied from 0◦ to 180◦ . Similar to the observation in the absence of control, the maximum roll rates of 3 and 4 wire tunnel configurations are significantly low as compared to the 1 and 2 wire tunnel configurations, and are ≈2.1◦ /s and ≈0.7◦ /s respectively. The evolution of roll rate and roll angle for various configurations with time in the presence of 400 Nm control are shown in Fig. 8. As observed from Fig. 8c, d, the maximum roll rates are significantly low for three and four wire tunnel configurations. All the configurations tend to return to the initial roll angles in the presence of control. As mentioned earlier, the three and four wire tunnel configurations experience very low deviation from the initial roll orientation and this is clearly evident from Fig. 8c, d. As can be observed from Fig. 9a, b, one wire tunnel configuration experiences the highest roll rate and roll error. Even with a control of 400 Nm capability, the maximum roll angle error and roll rate are significant; the values being ≈268◦ and ≈13◦ /s respectively in comparison to ≈445◦ /s and ≈15.2◦ /s in the absence of control. The addition of wire tunnels imparts symmetry to the system and hence is a passive technique for rolling moment reduction. The two wire tunnel configuration has a marginal decrease in maximum CRM (2.8%), which translates to a marginal decrease in maximum roll rate. Even with a control of 400 Nm capability, the maximum roll angle error and roll rate for the configuration are ≈137◦ and ≈11.5◦ /s respectively. Inclusion of two additional wire tunnels reduces the CRM by 77%. The three wire tunnel configuration thus enables significant reduction in roll rate and roll angle error. Further, a reduction in maximum roll angle error from ≈387.2◦ in the absence of control to ≈40.4◦ in the presence of 400 Nm control is possible. The roll rate also reduces from ≈6◦ /s to ≈2.1◦ . The four wire tunnel configuration has the least aerodynamic rolling moment compared to the other three configurations. CRM reduces by ≈80% with the inclusion of three dummy wire tunnels. The configuration has a maximum roll angle error and roll rate of ≈390◦ and ≈5.2◦ /s in the absence of control. It is to be noted that the maximum roll rate is significantly lower than that achievable with 400 Nm control

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(a) Results for single wire tunnel configuration

(b) Results for two wire tunnel configuration

(c) Results for three wire tunnel configuration

(d) Results for four wire tunnel configuration

Fig. 8 Results of One Degree of Freedom (1-DOF) Simulations with 400 Nm control

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100 Nm 200 Nm 300 Nm 400 Nm 500 Nm

300 250 Max. Δ φ(deg)

Fig. 9 Comparison of configuration with different number of wire tunnels and different maximum control moments

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200 150 100 50 0 1

2 3 Number of wire tunnels

4

(a) Maximum roll angle error 16

100 Nm 200 Nm 300 Nm 400 Nm 500 Nm

14

. Max. φ (deg/s)

12 10 8 6 4 2 0 1

2 3 Number of wire tunnels

4

(b) Maximum roll rates

in case of a single wire tunnel configuration. With a 400 Nm control, the maximum roll angle error and roll rate further reduces to ≈16.6◦ and ≈0.7◦ /s respectively. As observed from Fig. 9a, b, the maximum roll rate and roll angle error reduces with the increase in control moment for all the configurations.

4 Conclusions CFD studies carried out on the single wire tunnel configuration of the core-alone launch vehicle indicated that the wire tunnel is the major source of asymmetry, and hence the major source of aerodynamic rolling moment. The results also showed significant rolling moment when the wire tunnel was positioned in the windward side. A passive mode of CRM reduction has been attempted by adding dummy wire tunnels

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to impart symmetry to the configuration. Addition of a wire tunnel diametrically opposite to the existing wire tunnel turned out to be of minor consequence, as the wire tunnel positioned in the leeward side couldn’t oppose the rolling moment of the windward wire tunnel efficiently. However, the addition of two and three dummy wire tunnels reduced the CRM of the system by ≈77% and ≈80% respectively. A new, linear superposition based method has been proposed to estimate the CRM for two, three and four wire tunnel configurations. First we extract the rolling moment contribution of the wire tunnel and the protrusions from the CFD simulations on a single wire tunnel configuration at various roll angles. These are linearly superposed to predict CRM for two, three and four wire tunnel configurations. The method has been validated by carrying out CFD simulations on the four wire tunnel configuration. Roll dynamics simulations have been carried out to compare the maximum roll rates and roll errors for the 4 configurations in presence of only aerodynamic rolling moments as the source of perturbation. Conservative studies assuming upper bound trajectory and α = 4◦ throughout the trajectory have been carried out. The results indicate that the maximum roll rate in the absence of control is around 15.2◦ /s for single wire tunnel and 13.2◦ /s for two wire tunnel configuration. The same reduces to 6◦ /s with three wire tunnels and to a mere 5.2◦ /s with three wire tunnels. It is however not recommended to rely on aerodynamics alone (without the use of any roll control system). This is because the roll errors are found to persist throughout the region of prominent atmosphere and the system doesn’t settle to the roll trim points within this regime for many of the initial conditions used for simulations. However, with the application of control, it is found that the maximum roll errors can be reduced. The maximum roll rates are also found to decrease tremendously with the application of control. With a 400 Nm control, the maximum roll rates for one, two, three and four wire tunnel configurations are 13.0, 11.5, 2.1 and 0.7 respectively. The dummy wire tunnels add to the efficiency and reliability to the launch vehicle due to their simplicity, lower mass and passive nature. Therefore, provision of a minimum of two dummy wire tunnels provides an elegant and passive aerodynamic solution to the problem of rolling moments generated by the single wire tunnel configuration. The proposed design solution is likely to add to the reliability and efficiency of the launch vehicle due to its passive nature, simplicity, ease and cost of implementation, and likely to have a lower mass penalty.

References 1. Ulrich G, Stephan K, Dietmar W, Daniel F, Pierre M, Christian D, Santiago C, Bastian G, Rainer K (2015) Development and test of a 3D printed hydrogen peroxide flight control thruster. In: 51st AIAA, SAE, ASEE joint propulsion conference, 27–29 July 2015, Orlando. Florida, USA 2. Kumaravel G, Gopalsamy M (2011) PARAS 3D user’s manual, version 4.1.0, VSSC/ARD/GN/01/2011 3. Palacios F, Colonno MR, Aranake AC, Campos A, Copeland SR, Economon TD, Lonkar AK, Lukaczyk TW, Taylor TWR, Alonso JJ (2013) Stanford University Unstructured (SU2): an open-source integrated computational environment for multi-physics simulation and design. In:

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AIAA paper 2013–0287, 51st AIAA aerospace sciences meeting and exhibit, 7th–10th Jan 2013. Grapevine, Texas, USA Pointwise user manual V18 Economon TD, Palacios F, Copeland SR, Lukaczyk TW, Alonso JJ (2016) AIAA J 54(3):828– 846 Sreenivasulu J, Saha SK (2018) Analysis of rolling moment coefficients for SSLV configuration. VSSC/ACD/TM/006/2018 Eaton JW, Bateman D, Hauberg S, Wehbring R (2014) GNU octave version 3.8.1 manual: a highlevel interactive language for numerical computations. CreateSpace Independent Publishing Platform. ISBN 1441413006, http://www.gnu.org/software/octave/doc/interpreter

Design and Development of Miniature Mass Flow Control Unit for Air-Intake Characterization D. B. Singh, P. Vinay Raya, Buddhadeb Nath, N. Srinivasan, Anju Sharma, and B. Sampath Rao

Abstract Wind tunnel tests on high-speed air-intake configuration needs an accurate simulation of mass flow through the intake ducts. This leads to the requirement of miniature mass flow control device which provides linear variation in the throat area. Here, an attempt has been made to design and develop new miniature mass flow control device to characterize the air-intake model in the 1.2 m wind tunnel. This paper describes the design and development aspect of miniature mass flow control unit, drive electronics and its utility in wind tunnel testing of air-intake models. Emphasis is placed on experimental results obtained from an electrically actuated plug which controls the critical flow area at the downstream end of the intake model. Keywords Mass flow control unit · Air intake · Plug controls · Mass flow calibration

1 Introduction Simulating the required mass flow in wind tunnel experiments is a challenging problem. The air flow through the model has to be accurately simulated during the wind tunnel tests to assess the intake performance parameters like total pressure recovery, engine face total pressure distortion and the intake instability/buzz phenomenon [1, 2]. Mass Flow Control Unit (MFCU) is used for controlling the mass flow through the air-intake duct. It is required to calibrate the airflow passing through the MFCU for various axial positions of the plug by simulating the pressure ratios across the MFCU as observed during the wind tunnel tests. The effective throat area for various MFCU plug positions is established through detailed calibration tests. Figure 1 shows the schematic view of the typical air-intake model. It was proposed to have intake studies on missile model. The dimensions of the wind tunnel model were finalised according to the standard procedure to suite 1.2 m Trisonic wind tunnel of NTAF, D. B. Singh (B) · P. Vinay Raya · B. Nath · N. Srinivasan · A. Sharma · B. Sampath Rao National Aerospace Laboratories, CSIR, Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_27

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Fig. 1 Schematic view of the typical air intake model with Y duct

CSIR-NAL [3]. According to the approved model, duct size available is of diameter 60 mm. The existing mass flow controller Unit (MFCU) is bigger and cannot be used for simulating required mass flow. Hence it was decided to make a new miniature mass flow control unit with LabVIEW based control. The developed unit is miniature and it can be used for duct size of 50 to 150 mm with traverse length of 10–60 mm. The unit is robust in design and having a backlash-free driving mechanism. Higher motor torque availability with planetary gear mechanism of the gear ratio of 1:62, this makes it more accurate and allows to cater for higher torque required during wind tunnel testing. High-resolution encoder makes the system more readable regarding the position of the conical plug. System electronics developed based on digital logic and complete control and data acquisition system is realised on National Instrument cDAQ based hardware and LabVIEW based software. Most of the components (Motor, gear, encoder and clock buffer circuitry) are housed inside the protective casing preventing uncertainties during the wind tunnel tests.

2 Experimental Setup Present tests are conducted using two independent systems, one system used for controlling the MFCU unit and another system used for data acquisition. Both the systems are tightly synchronised. Tests were conducted in continuous/step mode, here at every step with fixed free stream condition rake data and plug position was acquired and processed using LabVIEW based programs. Pressure probes and thermocouple placed near orifice plate to calculate the primary mass flow. 40 probe total pressure rake followed by MFCU unit were placed downstream to the model. The pressurised

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chamber uses to simulate the tunnel pressure was made to check the amount of air entering into the duct with and without ejector in place for different upstream pressures ranging from 16 to 45 psig. Pressure regulating valve place in upstream of the experimental setup for precise control of the pressure in the chamber.

3 Mass Flow Control Unit (MFCU) The Schematic view of MFCU plug unit is shown in Fig. 2 The unit is fixed at the downstream end of the intake model. It consists of a plug whose shape is contoured having a radius of curvature of 288 mm. The movement of the plug axial and is controlled through a drive motor. A geared DC motor, drives the plug and the plug position is obtained using incremental optical encoder mounted on the motor shaft at the rear extension. The encoder provides 500 pulses per rotation. An interface unit has been built to provide an integrated pulse counting with 7 segment LED (Light Emitting Diode) display and buffered TTL (Transistor-Transistor logic) equivalent data to the associated data acquisition system for the position of the plug. The total traverse length of the MFCU is 60 mm which corresponds to 80,000 counts in the controller. At different axial locations, different throat areas are formed between the plug and the insert ring. This indicates the area that controls the mass flow through the intake model for a given upstream condition. The flow-through (throat) area varies from a maximum to a minimum value (non-zero) at the two extreme traverse limits. Figure 3 shows the block diagram of the MFCU unit. The developed unit provides local mode operation/controls for forward/reverse drive of the plug and for resetting the counter to zero at the fully open condition. The unit offers an interface for remote operations from the PC for a programmed control operations. PC based control is developed using NI cDAQ 9188 chassis with NI 9401 module to acquire

Fig. 2 Schematic view of a designed MFCU plug unit

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Fig. 3 Block diagram of developed MFCU control unit

Fig. 4 Photograph of MFCU setup

20 bit digital information (5 digit plug position), NI 9401 for directly reading clock and other handshake signals, NI 9205 to acquire analog input from pressure sensor which is plotted against plug counts/area to detect the occurrence of buzz. Provision has been made to reverse the plug manually in case of buzz occurrence. Figure 4 shows the photograph of the complete system.

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3.1 Salient Features of the Newly Developed MFCU System Guide Shaft: The guide shaft is designed in such a way that it caters the simple supported structure for a respective ball-screw rod this makes evenly load distribution on the driving pins during operation. Pitch of the MFCU can be adjusted with different ball screw to get different traverse speed. Photograph of the developed system is shown in Fig. 5 Ball Screw and Nut assembly: Provision has been made to use two ball screws with a pitch of 2 and 4 mm, this will operate the plug to and fro 60 mm (2 mm pitch) and 50 mm (4 mm pitch) length in 26–12 s respectively. With the ball-screw arrangement, the system has increased positional accuracy and ware and tare that may occur due to the long run. As all the parts lead screw, nut and balls of the ball screw assembly are hardened; there will be very negligible ware in the long run. As Ball-screw is placed with the simple support system, it experiences only axial load acting on the plug, keeping frictional loads minimum and frictional loss negligible. Web: Web is the structure designed to keep the MFCU in the centre of the duct/ MFCU casing. The web is designed to take all the loads acting on MFCU, it has three arms place at 120◦ apart evenly. The web has two bearings on which coupling are placed; this will act as an intermediate part between the drive and driven mechanism of the MFCU. It is necessary to keep the web diameter lesser than the maximum plug diameter to have a proper choking effect only at throat region. It is recommended to have an area greater than 120% of area available between casing and web region concerning that of throat area in fully opened condition. Drive and Feedback mechanism: Drive mechanism has two major components; DC motor and planetary gearbox, as mentioned above. The appropriate motor has been selected to provide necessary torque in smaller form factor. To achieve the required

Fig. 5 Schematic view of a designed MFCU plug unit

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Fig. 6 Figure shows the logic implementation of MFCU control and motor drive logic

Fig. 7 MFCU continuous and step mode operation response

torque appropriate gearbox with 1:62 gear ratio is selected for the current design. The unit contains the feedback device (encoder) having 500 pulses per rotation. Drive circuit designed with latest digital logic circuitry as shown in Fig. 6. Motor drive circuit implemented using H-bridge concept. Safety for ball-screw and motor is taken care during design. Figure 7 shows the response of MFCU in continuous and in step mode of operation, the system maintains linearity. In step mode system response has been checked for the step size varying from 2000 to 10,000. Counts have checked repeatability in full span of the traverse and by physical measurement of distance traveled and found good repeatability in the traverse of the plug.

4 Plug Control for Air Intake Experiments LabVIEW based data acquisition and control programs are developed and used for controlling and acquiring position data of mass flow control plug. Here plug position feedback is acquired through attached encoder giving 500 pulses per rotation. As it required transmitting clock signal from the model to control situated 30 m away, the clock signal was buffered onboard. Clock output is used for electronic counting of up/down motion of plug. The local display is provided using five-digit seven segment display. Further, position information is converted to BCD (5 digits, 20 bit) and made available for three PCs used for acquiring model steady pressure data and for model unsteady pressure data. With the developed program, it was ensured that all the system, i.e. Steady pressure data acquisition, unsteady pressure data acquisition and plug control PC are tightly synchronised. In plug control PC provision has been made to display any of models Kulite pressure sensor output against the plug counts

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Fig. 8 Screenshot of LabVIEW based plug control GUI

or plug area, this makes real-time monitoring of buzz onset and control of the plug motion. Figure 8 shows a screenshot of LabVIEW based GUI used for plug motion control and coordinating the data acquisition events on other systems. MFCU control algorithm represented through flow-chart shown in Fig. 9.

5 Discussion of Test Results Improved mass flow control unit with listed specification in Table 1 has been designed and developed at CSIR-NAL Bangalore; the system is tested rigorously at bench level and at high-speed flow facility. System performance matched as per design specification. The developed system was calibrated at high-speed test rig; typical result presented in Fig. 10. Many repeat tests were conducted and found an excellent match in calibration data.

6 Conclusion Improved MFCU has been developed and tested at high-speed flow facility. The system is extensively checked for its load capability, accuracy, repeatability and positional resolution. The system developed based on the latest electronic circuitry and tested with portable NI data acquisition and control. Complete system performance in continuous and step mode was established during mass flow calibration. Many repeat tests were conducted and found an excellent match at similar conditions.

384 Fig. 9 MFCU operational flow-chart

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Start MFCU Unit

Enter parameters and press Enter (For remote operation)

Enable Reverse motion: Local/System

Reverse limit reached ?

no

yes Enable Reset: Local/System

Enable Forward motion: Local/System (till reach initial position)

Enable forward motion with Po estd.

no

Forward limit switch reached or Keyboard hit ?

yes Enable reverse motion: Local/System

Is Count = 5000 ?

yes Stop MFCU Unit

no

Design and Development of Miniature Mass Flow . . . Table 1 Specification of the developed MFCU unit Precision ball screw Pitch 4 mm and shaft diameter 10 mm Precision ball screw Pitch 2 mm and shaft diameter 10 mm Length of screw rod 95 mm Traverse length 59 mm Motor outer diameter 32 mm Motor type DC motor 24 V Torque required 2.5 Nm Motor length 60 mm Planetary gear box 1:62 Encoder details 500 PPR Limit switches details Micro switch Bearing type Ball bearing Outer diameter 47 mm Inner diameter 25 mm Model no. and make SKF 6005 Z (2 no.s)

Fig. 10 Plot shows a typical calibration result of MFCU unit

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Acknowledgements The authors are thankful to Shri. Rajeev G, Head, NTAF for his support and guidance. The author would like to appreciate the support of the vendor Yottec, Bangalore for realising the hardware of MFCU. Help of Design office and 1.2m wind tunnel staff acknowledge with thanks.

References 1. Chidananda MS et al. Development of an ejector for ADA intake model tests. Project Document, NAL PD PR 8805 2. Jaganatha Rao B et al. Static tests and mass flow calibration of 1:7 scale PV2GE air intake model. Project Document, NAL PD PR0501 3. Narayan G et al. Instrumentation, control and data acquisition system for the LCA Kaveri air intake model tests in NAL 1.2 m trisonic wind tunnel. Project Document, NAL PD NT 0007

The Effect of Variable Inlet Guide Vanes on the Performance of Military Engine Fan Baljeet Kaur, Reza Abbas, and Ajay Pratap

Abstract This paper discusses the effect of variable inlet guide vanes (VIGV) on the performance of military engine fan. The variable inlet guide vanes (VIGV) are necessary in order to safely start up multi-stage axial compressors. It not only improves surge margin at off-design condition but also gives nearly flat efficiency for wider speed range. The present fan design is a transonic three-stage axial flow compressor without inlet guide vanes. The aerodynamic performance of fan was limited by issues of lower stability range at part speeds, and blade flutter was observed in engine testing. So, it was proposed to redesign the fan with VIGV for addressing the abovementioned design issues. Fixed-flapping type variable inlet guide vanes are designed to improve the performance of present fan. The design concept of VIGV itself will be a new design and development in our country. As a result of introducing VIGV, aerodynamic performance of redesigned fan is improved in terms of better surge margin at speeds lower than 95% due to reduced inlet incidence on rotor—stage1. The baseline fan was having stall flutter at part speed 80–85%; it is expected to get eliminated due to reduced incidence and improved stall margin. Keywords Fan · Variable inlet guide vane design · Inlet flow angle · Aerodynamic performance · Surge margin

B. Kaur (B) · R. Abbas · A. Pratap Gas Turbine Research Establishment, Bangalore, Karnataka, India e-mail: [email protected] R. Abbas e-mail: [email protected] A. Pratap e-mail: [email protected] Defence Research & Development Organisation, Ministry of Defence, New Delhi, India © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_28

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1 Introduction Axial flow compressors are one of the most critical components in a gas turbine engine pertaining to its operation in an adverse pressure gradient. To satisfy the demands of high thrust to weight ratio, reduced fuel consumption and performance in a modern day gas turbine, compressors are being pushed towards operating in the transonic regime. The current research in aero-compressor field is devoted towards designing compact and high performance compressors with characteristics such as high blade loading, greater tip speeds, fewer stages and lesser axial gap between stages [1]. The challenges associated with off-design operation of transonic compressors lies in a mismatch of the incidence angle with that of the design conditions. This increases the risk of blade stall leading to compressor surge, in addition to low efficiency and surge margin of the compressor [2]. One method of countering the above problem is multispooling, wherein the compressor stages are divided into two or more spools termed as low-pressure and high-pressure spools that are coupled to respective turbines through separate shafts. This enables us to rotate the low-pressure and high-pressure compressor at different speeds, thus matching the design point incidence angle. In many cases, variable inlet guide vanes (VIGV) are necessary in order to safely start up multi-stage axial compressors. It not only improves surge margin at off-design condition but also gives nearly flat efficiency for wider speed range. Alternative method is to implement bleed control system but that causes loss to the engine performance. Inlet guide vanes work as a regulating valve by adjusting the stagger angle of each airfoil. It will lead to turn of the blades around a radial axis, so that inflow to the following rotor is influenced in a positive way. As a result, the high incidences on following rotor blades and correspondingly higher aerodynamic loadings can be avoided [3]. Depending on the interface restriction and other engine requirements, both the above methods are used at the discretion of the designer. For example, GE F110 has a fan pressure ratio of 3.2:1 is equipped with VIGV, while Eurojet EJ200 employs the multiple spool configuration with three stages of low-pressure and five stages of high-pressure compressor. There have been many works dedicated towards establishing the performance characteristics of centrifugal compressors equipped with variable guide vanes. Simon et al. [4] reported the improvement in performance of centrifugal compressor by simultaneously adjusting the inlet guide vanes and diffuser vanes. Experimental determination of closure schedule for simultaneous adjustment of guide vane and diffuser vanes was carried out in accordance with the required performance characteristics. Rodgers [5] carried out compressor rig testing in a single-stage centrifugal compressor, with moderately high specific speed and high inducer Mach number. Testing showed that the surge margin increased with IGV regulation. The maximum static pressure recovery and highest work done factor of the impeller occurred near the stall conditions. Similar research has been carried out that investigates the causes and effects of off-design operation in axial flow compressors. Stephenson [6] highlighted that the surging in axial flow compressor happens due to operation in condition far from

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design point. Limitation in the pressure ratio of the compressor and mass flow rate is analysed. Handel et al. [7] investigated the transition and separation phenomenon on inlet guide vane with symmetric profile used in an axial flow compressor. Experimental investigation at different stagger angle and Reynolds number was carried out. Results indicated that for acute stagger angles the flow separation occurred on the pressure side trailing edge. Shaw et al. [8] experimentally investigated and validated using CFD, the effects of inlet guide vanes in performance characteristics of transonic compressor. The experimental tests were conducted for both clean inlet flow and distorted flow with and without IGV. The results indicated the accuracy of CFD methods in predicting the flow characteristics in a transonic compressor with inlet distortion. The maximum pressure and mass flow rate at stall were found to be within 2% and 3% of the measured values, respectively. The VIGV showed a positive effect on the performance of the fan when the swirl angle upstream of the rotor was found to be more uniform. Broichhausen et al. [9] conducted experiments using static wall pressure taps and semi-conductor pressure transducers, pneumatic hole probes with incorporated pressure transducers to establish the off-design performance of supersonic compressors with fixed and variable geometry. Semi-empirical models were integrated with the through-flow algorithm to estimate in detail the losses and deviation of the compressor performance in off-design condition. Williams et al. [10] used an open-loop flow control algorithm to induce swirl in the flow downstream to IGV using smart inlet guide vanes. Unlike mechanically actuated IGV, smart IGV uses Coanda effect negating the need of articulating mechanism. The experiments conducted demonstrated the ability of the guide vane to regulate the flow by 14° at 85% corrected RPM. From the above discussion, it can be concluded that there have been significant research carried out regarding the usage on inlet guide vanes and variable diffuser vane in centrifugal compressors. In the case of axial flow compressors, there have been many experimental works carried out to establish the effects of off-design operation on the performance of transonic compressors. The effects of inlet distortion and IGV articulation have been verified experimentally, which require sophisticated test rigs and measuring probes to determine the compressor performance. However, there is very less work that focuses on utilising numerical tools to verify the effect that inlet guide vane actuation with varying compressor speed would have effect on the surge margin and compressor stability. The present fan design is a three stage transonic axial compressor without inlet guide vanes. The aerodynamic performance of fan was limited by lower stall margin at part speed, and blade flutter was observed at part speed in engine testing [11]. So, it was proposed to redesign the fan with application of variable inlet guide vanes (VIGV) to address the above-mentioned performance issues. Fixed-flapping type variable inlet guide vanes are designed to improve the performance of present fan. The design concept of VIGV itself will be a new design and development in our country.

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Table 1 Fan aerodynamic performance at design point (ISA-SLS)

Normalised parameter Design intent

Achieved

Mass flow

1.0

1.0154

Pressure ratio

1.0

0.994

Isentropic efficiency (%)

85

86

Flutter

Flutter free

Flutter in rotor 1 at NLR of 83% [13]

2 Fan–Baseline Fan module consists of fan inlet casing and three stage transonic fan. Inlet casing has eleven fixed struts inlet casing which has met requirement of uniform flow to the inlet of fan and minimum loss. The gradients of velocity and static pressure in radial direction are less than 1%, and total pressure loss is ~0.5% [12]. The aerodynamic features of fan are given as below Table 1.

3 Variable Inlet Guide Vane (VIGV) Design The VIGV system is capable of improving the compressor performance with the turning of the vanes leading to an increase in vane incidence angle. This can cause separations in the VIGV which reduces the desired flow deflection and produce additional losses. The classical configuration of IGVs consists of un-cambered or slightly cambered profiles that are staggered. This configuration produces disadvantageous flow physics, which cause comparatively large flow losses for small stagger angles. A better configuration for IGVs consists of profiles with mechanical flaps as shown in Fig. 1. VIGVs with mechanical flaps are applied in some military aircraft engines for many years.

Inflow

Fig. 1 VIGV configuration consisting of profiles with flaps

Outflow

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3.1 Design Configuration of VIGV The objective of incorporating VIGV was to assess relative improvement in flutter and operability margins of fan which is presently integrated with gas turbine engine. The fan axial length and tip diameter for are constraints from the baseline design fan module. Keeping the inlet casing length same as baseline engine, available axial length for VIGV is 160 mm. Considering tip solidity as one, 15 number of vanes was decided for VIGV. Design Trial 1 Initial design for VIGV was configured with chord-wise fixed to flapping part ratio 1:1. VIGV aerofoil considered is of symmetrical design as there is no preswirl at design condition. The strength requirement of the inlet casing is same as the baseline design. So, NACA0008 aerofoil is used for hub and tip section of IGV with keeping the wetted area same. The above-mentioned configuration was analysed using ANSYS CFX. It was found that maximum normalised mass flow of 0.977 was passing through the inlet casing. Choking was occurred in the hub region, where solidity was as high as 2.5. Distribution of swirl angle was not uniform also at the hub locations, flow turning was very high. After this initial trial, it was decided that hub chord to be reduced. Design Trial 2 To address design problem from trial 1, the hub chord of VIGV reduced from 160 to 130 mm, which resulted in reduced hub solidity of 2. This design changes nearly restored mass flow rate with pressure loss of 1%. But non-uniformity in the swirl angle all most remains the same as baseline configuration of VIGV. Design Trial 3 The objective of this trial was to have uniform swirl angle variation from hub to tip. This can be done by increasing the chord-wise fixed to flapping part ratio at tip location and reducing the same at hub location of VIGV. Numerous designs iterations and analyses were carried out to finalise the split ratio. The final design of the VIGV is described as given in Table 2. Final configuration of the inlet casing with VIGV was analysed. This design has the capacity to handle intended mass flow rate with a pressure loss of less than 1% Table 2 Design parameters of VIGV

Parameters

Hub section aerofoil Tip section aerofoil

Aerofoil series

NACA0008

NACA0006

Chord (mm)

130

160

Fixed part length (mm)

78

64

Flapping part length 52 (mm)

96

392 Table 3 Aero design parameters of VIGV

B. Kaur et al. Flap angle (º)

Flow angle (º)

IGV pressure loss (%)

0

0

0.6

19

17.8

0.7

30

25.3

1.7

Fig. 2 Swirl angle distribution from hub to tip

with meeting the flow angle requirements of the fan at part speeds. It has swirl angle variation of ±2° from hub to tip. The detailed result of the VIGV is given in Table 3. Swirl angle distribution from hub to tip and flow filed around VIGV is shown in Figs. 2 and 3, respectively.

4 Numerical Modelling and CFD Reynolds averaged Navier-Stokes equation modified for turbomachinery calculations along with shear stress transport turbulence model [14] are used to numerically simulate the axial flow compressor. CFX (ANSYS 17.0) is a pressure-based finite volume solver with multi-block grid facility. In turbomachinery applications, conservation of mass is an important parameter for judging the accuracy of the numerical model [15], and for the same reason, finite volume model was used.

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Fig. 3 Flow field around IGV

4.1 Geometry and Grid Generation The various inlet guide vane configurations with different vane angles were generated by importing the co-ordinate files of the vanes, hub and the shroud. ANSYS turbo grid 17 was used for the grid generation. The machine type is chosen as an axial compressor with the principal axis of rotation as the X-axis. There are 15 vanes in this system. For the hub, shroud and the vane, the B-spline curve type is used as it generates a smooth curve obtained by interpolating the points provided in the coordinate files. Initially, there are two layers: at the hub (span = 0) and at the shroud (span = 1). In addition to that, three more layers are generated at spans of 0.25, 0.5 and 0.75. These layers project the topology onto a given span and improve the quality of the mesh by creating a curve for the mesh to follow from the hub to the shroud. Following this step, the 3D mesh is generated, and refinements are made to improve the mesh quality. After the refinement, the mesh quality parameters are ascertained, and necessary changes are made. The above steps were followed for generating grid of all the rotor and stator configurations. The topology of ’O’ grid close to surface and ’H’ grid in the blade to blade passage with rotors mesh size of varying from 90,000 to 70,000 elements, and for stators, varying from of 70,000 to 50,000 elements were used in decreasing order from first stage to third stage, respectively; along with IGV, mesh size of 70,000 elements was used. Rotor tip clearance of 0.5 mm was considered during meshing. A 3D model of fan is shown in Fig. 4.

4.2 Pre-processing and Boundary Conditions In the preprocessor, a turbomachinery simulation file is set-up. An axial compressor is chosen as the machine type with X-axis as the rotational axis, and the analysis type is chosen as steady state. Rotor–stator interface is defined by a stage model which

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Fig. 4 3D view of the fan showing rotating and stationary stage

uses span-wise variation of pitch averages of all properties and redistributes mass, momentum and energy based on pitch differences between the rows. The meshes of the next stage rotors and stators are imported in a sequential order and integrated with the meshes generated for the different vane angles. The rpms are varied from 100% (design condition) for the fully open configuration of the vane to 70% for the fully closed configuration. There are three boundary conditions available in the ANSYS CFX-Pre 17 module, namely: • P-Total Inlet P-Static Outlet Here, the total pressure and the total temperature values at the inlet along with the static pressure at the outlet need to be specified for evaluation of the problem. • P-Total Inlet Mass Flow Outlet In this condition, the total pressure and the total temperature at the inlet along with the mass flow rate at the outlet are specified. • Mass Flow Inlet and P-Static Outlet In this condition, the mass flow rate and the total temperature at the inlet along with the static pressure at the outlet are specified. The boundary condition used for the analysis under consideration is the P-total inlet P-static outlet. The inlet total pressure and the total temperature values are found at ISA-SLS conditions which are 101.325 kPa and 288 K, respectively. The flow was initialised with a velocity of 220 m/s. A high-resolution advection scheme is used, and the number of iterations for each back pressure is set to 400. For convergence control, the RMS value limit is set to 1E-6. Two user-defined expressions are created to monitor the mass flow rate at the inlet and outlet conditions throughout the entire solving phase. After completing the entire set-up, the preprocessor file is converted into a ’.def’ file and used as the solver input.

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4.3 Solver The solver runs for either the total number of iterations as specified by the user or for the convergence criteria set by the user, whichever is satisfied first [14]. Following the completion of the run for starting back pressure, the static pressure at the outlet is increased by 10 kPa and evaluated again using the previous run’s output as the initial input for the next file. After the completion of each run, total pressure ratio and the isentropic efficiency were evaluated, and subsequently, the next run file was set-up. The above steps are repeated till the total pressure ratio starts to drop for a particular back pressure.

4.4 Post-processor The pressure and temperature variables at the inlet and outlet for the entire fan components were extracted. Along with this, we extract the mass flow rate at the inlet and outlet, velocities and Mach numbers at various spans of the blades. These variables were to assess the performance of each component as well as plotting the compressor maps.

4.5 CFD Model Validation The present CFD model was validated by comparing the model with other similar analysis published by the AGARD researchers [15]. In turbomachinery applications, the commercial CFD codes under predict the efficiency of the rotor due to over prediction of the tip leakage losses. Also there is an error in the pressure ratio prediction due to the negligence of corner stall in the leading edge of the rotor blades [12]. Simoes et al. [16] used the similar CFD model and verified the suitability of the three available turbulence models viz. k-ε, k-ω and shear stress transport model in turbomachinery applications. Shear stress transport is the most suitable turbulence model as it is confirmed with the fan analysis.

5 Performance Analysis 5.1 Characteristic Maps The compressor maps are collective plots of the pressure ratio and efficiency vs. the corrected mass flow rate at constant speeds. The pressure values and the mass flow rates were taken from CFD post for each case of analysis. The isentropic efficiency

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is calculated from the following equation:  η=

P2 P1

γ −1 γ

 −1 (1)

T2 T1

P and T denote total pressure and total temperature, respectively. Subscript 1 refers to inlet, and Subscript 2 refers to outlet. γ denotes ratio of specific heats for air equal to 1.4. The surge margin is given by the following equation [17]:  surge margin(%) =

(Pr/m)surge (Pr/m)opearting



 − 1 ∗ 100

Pr and m denote total pressure ratio and total mass flow rate, respectively. Subscript surge refers to stall point, and operating refers to design point.

5.2 Redesigned Fan with VIGV Performance Results The 3D analysis was carried to estimate aerodynamic performance at all speeds. The variability of inlet guide vane (IGV) has been introduced at off-design speeds to lower the incidence on rotor 1 to enhance performance. This involved carrying out the analysis at each of the lower speed with several iterations of different rotational setting of the inlet guide vane to optimise the final choice of rotational setting for the inlet guide vane to have satisfactory aerodynamic performance for that speed. Inlet guide vane (IGV) is having a symmetrical aerofoil throughout with increasing chord from hub to tip. For the variability of IGV, 40% of rear hub section was rotated through desired angle at a particular speed; while at the tip, 60% rear section was rotated. This configuration for rotational movement for IGV was chosen through various iterations from the initial guess of configuration based on earlier experience and the literature available regarding the same kind of fans and on the basis of configuration suitable for mechanical design point of view. The optimised closure schedule followed for variability of VIGV and stator at various speeds arrived through analysis is mentioned below and shown in Fig. 5 (Table 4). The performance analysis with optimised closure schedule for inlet guide vane at design speed (10,312 rpm) and at low speeds, i.e. (100, 90, 85, 80 and 75%) was carried out. The characteristics plots (overall pressure ratio vs. corrected mass flow rate and overall efficiency vs. corrected mass flow) are shown in Fig. 6.

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Fig. 5 VIGV closure schedule

Table 4 Variable inlet guide vane (VIGV) closure schedule

NLR %

VIGV flow an2008014gle (°)

100 and 95

0

90

5

80

15

85

25

75

35 (constant for speeds below 75% NLR)

5.3 Surge Margin Improvement The surge margin improvement is listed below from the baseline fan to redesigned fan with VIGV [18]. The change is surge margin was defined with respect to fan operating line arrived after engine component matching vis compressor, combuster, turbine, etc. (Table 5). Characteristics at 75% Querypart speed were not obtained due to software solution divergence as flow separation was very high in first rotor itself.

6 Results and Conclusion The performance comparison of baseline fan and redesigned fan with VIGV is shown in Figs. 7 and 8. The effect on aerodynamic performance of fan with introduction of VIGV is summed up as given below.

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Fig. 6 Characteristics plots—fan with VIGV Table 5 Surge margin comparison Change in surge margin with mod 2 Ncorrected (%) + VIGV Estimate

100

95

90

85

80

75

−0.6

1.5

2.6

0.4

1.7

–

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Fig. 7 Comparison characteristics plot (overall pressure ratio vs. corrected mass flow rate)

Fig. 8 Comparison characteristics plot (overall efficiency vs. corrected mass flow rate)

• The number of vanes are increased to 15 in count for VIGV as compared to that earlier inlet casing was having 11 number of struts. As a result of more blocked inlet area, the corrected mass flow at design point is reduced by 0.3 kg/s and subsequently affected the operating point at lower speeds. • It was observed that considerable reduction in the inlet Mach numbers, showing that there is a corresponding reduction in shock losses by employing VIGV.

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• At speeds lower than 95%, characteristics are shifted to lower mass flow rate due to VIGV closure but stalling pressure has not changed significantly. • The surge margin is improved at speeds lower than 90% due to reduced inlet incidence on rotor—stage 1. • The efficiency of redesigned Fan was improved at off design conditions as rotor incidences were brought down at operating line and mass flow rate from choke to stall got extended. • The baseline Fan was having stall flutter at part speed 80–85%. With the incorporation of VIGV, it is expected to get eliminated due to reduced incidence and improved stall margin. • Part speed stall witnessed at high altitude low Mach No. during engine restart accelerating is expected to get alleviated due to reduced fan mass flow and Fan rotor 1 blade incidences.

References 1. Sanders AJ, Fleeter S (2000) Experimental investigation of rotor-inlet guide vane interactions in transonic axial-flow compressor. J Propul Power 16:421–430 2. Kerrobrock JL (1981) Flow in transonic compressors, AIAA 80–0124R. AIAA J 19:4–19 3. Farokhi S (2014) Aircraft propulsion, 2nd edn. Wiley, West Sassex, United Kingdom 4. Simon H, Wallmann T, Monk T (1987) Improvements in performance characteristics of singlestage and multistage centrifugal compressors by simultaneous adjustments if inlet guide vanes and diffuser vanes. J Turbomach 109:41–47 5. Rodgers C (1991) Centrifugal compressor inlet guide vanes for increased surge margin. J Turbomach 113:696–702 6. Stephenson JM (1981) A solution of stall problem in axial-flow compressors. Readers Forum 67–69 7. Handel D, Rockstroh U, Niehuis R (2014) Experimental investigation of transition and seperation phenomenon on an inlet guide vane with symmetric profile at different stagger angles and Reynolds Number. In: 15th international symposium on transport phenomenon and dynamics of rotating machinery, pp 1–9 8. Shaw MJ, Heilel P, Tucker PG (2014) The effect of inlet guide vanes on inlet flow distortion transfer and transonic fan stability. J Turbomach 136 9. Broichhausen KD, Gallus HE, Monig R (1988) Off-design performance of supersonic compressors with fixed and variable geometry. J Turbomach 110:312–321 10. Williams DR, Cornelius D, Acharya M, James D, Marshall T (2006) Smart inlet guide vanes for active flow vectoring in an axial compressor. In: 3rd AIAA flow control conference, 1–7. 11. Compressor Group, Gas dynamic stability of fan and compressor module. Report No. 0002 00 03 00 06 004 056, Gas Turbine Research Establishment, Bangalore 12. Compressor Group, Design of K9+ LP compressor. Report No. 0001 00 02 09 00 002 019, Gas Turbine Research Establishment, Bangalore 13. Compressor Group, Aeromechanical testing of MOD II fan with casing treatment. Report No. DRDO-GTRE-CPR-FSR-020–2012, Gas Turbine Research Establishment, Bangalore 14. User & Theory Documentation, CFX-ANSYS 17.0, ANSYS Inc. 15. Dumhan J (1988) CFD validation for propulsion system components. AGARD Advisory Report 355, AGARD, France

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16. Simoes MR, Montojos BG, Moura NR, Sujian JS (2009) Validation of turbulance models for simulation of axial flow compressor. In: 20th international congress of mechanical engineering, 1–9 17. Cohen H, Rogers GFC, Saravanamutoo HIH (1996) Gas Turbine Theory, 4th edn. Longman Group Limited, Essex, England 18. Compressor Group, Aerodynamic design of new fan with high inlet pressure distortion tolerance. DRDO-GTRE-CPR-FSR-141–2015, Gas Turbine Research Establishment, Bangalore

Transition Prediction for Flow Over a MAV Wing Using the Correlation Based Model M. B. Subrahmanya and B. N. Rajani

Abstract In this work, a low aspect ratio MAV fixed wing at a relatively low Reynolds number wherein the flow undergoes transition is analysed. The effectiveness of the correlation based transition model γ -Reθ SST proposed by Menter and Langtry (Correlation based transition modeling for unstuctured parallelized computational fluid dynamics codes. AIAA J 47:2894–2906 [7]) is brought out by making vis-a-vis comparison with the pure turbulence model SST (Turbulence, heat and mass transfer vol 4. Begell House Inc., pp 625–626 [6]). The transition model is able to handle separated flow transition and gives more insight to flow than the turbulence model. Some of the results depicting the transitional flows are presented and the superiority of the transitional model over the pure turbulence model is demonstrated. Keywords γ -Reθ SST Transition model · Low Re · Laminar separation bubble · Transition onset · Pressure based finite volume method

1 Introduction The aircraft industry in the last couple of decades has seen a rapid growth in the miniaturised and unmanned aerial vehicles like the MAVs which find application for both military and civil purposes. MAVs are designed based on specific missions they are meant to accomplish. These are low aspect ratio vehicles with high lift thin wings either fixed or flexible or flapping and flying at low speeds and are usually made of light weight composites to enhance their range and/or duration of flight. The flow is very complex and transition plays a significant role because of low Reynolds number and low aspect ratio thin wing sections. Owing to their dimensions and flight Supported by CSIR-NAL M. B. Subrahmanya (B) · B. N. Rajani CSIR-NAL, Bengaluru 560017, India e-mail: [email protected] B. N. Rajani e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_29

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speeds they pose lot of challenges to the designers and especially to the computational fluid dynamics (CFD) research community. Therefore to design an efficient MAV, a thorough research in multiple disciplines is needed. This has led to lot of innovations and research in small and more efficient motors and batteries, light weight airframe structures and high lift generating surfaces, highly efficient propellers, light-weight and efficient autopilots and control systems, light weight sensors and cameras and so on. The stability of the vehicle is another important factor due to its dimensions and weight. The fixed wing MAVs are known to be more stable compared to the flexible and flapping wings. Now looking at the fluid dynamics point of view, the flow regime of MAVs is 104 < Re < 105 where transition, separation and reattachment are very predominant features. Further in this regime, the flow tends to become unsteady even at lower angles of attack. Even today the transitional flows are not fully understood and lot of research is still on going in the area of CFD to explore this grey area. The behaviour and the underlying aerodynamics of MAVs is quite different and more complex from conventional aircrafts which are their larger counterparts. The flow over MAV wings are predominantly transitional leading to the formation of the laminar separation bubble (LSB) and we lack a proper understanding of these complex flows coupled to their geometrical complexities. There are few approaches to handle transitional flows numerically. One can use either a simple empirical method or a more sophisticated approach like the direct numerical simulation (DNS). But from the designers point of view, a viable tool like RANS is most desirable since this approach greatly reduces the computational cost and time compared to the much complicated DNS while an acceptable accurate mean quantities are still possible to compute. Several researchers have developed RANS based approaches to handle transitional flows. Some of them are, Abhu-Ghannam and Shaw correlation based model coupled to turbulence models, low Reynolds number versions of turbulence model, point transition approach and transport equation based transition models viz. kT -kL -ω model and γ -Reθ SST transition model. The transport equations based transition model is one of the recent approach to model transition. Here additional transport equations are solved to handle the effects of transition. A correlation based transition model γ -Reθ SST was proposed by Menter and Langtry [7] using local variables based on his SST turbulence model. Along with the original SST model transport equations, this model uses additional two transport equations. One of the equation is for the intermittency (γ ) and the other for the momentum thickness based Reynolds number (Reθ ) inorder to calculate the location of transition onset. The current work is on a 300 mm class fixed wing MAV where flow is transitional because of the flight speed and its physical dimensions. The γ -Reθ SST transition model has been used to model the transitional flow. The effects of transition modelling is brought out by comparing results with the results of base turbulence model SST. The flow solution code used is 3D-PURLES (3D Pressure based Unsteady RANS LES solver) which is an in-house developed URANS and LES code equipped with various turbulence and transition models [10]. This code is extensively used for both external and internal aerodynamics problems. The γ -Reθ transition model recently implemented in 3D-PURLES is validated for the ERCOFTAC flat plate test cases and SD7003 airfoil [5].

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2 Mathematical Formulation Three-dimensional incompressible flow simulation is carried out by numerical solving of the Navier Stokes (NS) equations. The numerical simulation of the NS equation needs an appropriate mathematical model to handle the geometrical complexities and the physical complexities.

2.1 Governing Equation The Reynolds averaged Navier Stokes equations for unsteady incompressible flow in the coordinate-free form: Mass conservation: .ρU = 0 (1) Momentum conservation: Dt ρU = −  P + .((μ + μt )(U + t U ))

(2)

where μ and ρ are fluid viscosity and density, p and U are the pressure and velocity vector, respectively. The eddy viscosity μt is evaluated through turbulence/transition models. The γ -Reθ SST model implemented in 3D-PURLES uses the constants, damping function, etc. as given by Menter [7] except for the two correlation functions viz. ReθC and Flength which are adopted from Malan et al. [4]. However, the ReθC correlation has been suitably modified as given below based on our validation study carried out for the flat plate T3A test case [5].   ˜ θt + 66.5, Re ˜ θt ReθC = min 0.665 Re

(3)

2.2 Flow Solution Procedure The simulations are carried out using the in-house multi-block finite volume flow solution code 3D-PURLES [3, 10]. This code uses the SIMPLE algorithm to solve the three-dimensional unsteady incompressible Navier Stokes equation in nonorthogonal curvilinear coordinates using the collocated variable arrangement. The SIMPLE algorithm is suitably modified for the collocated variable arrangement [2] to avoid the checkerboard oscillations of the flow variables. The system of linear equations derived from the finite volume procedure is solved in a decoupled manner for the velocity components, pressure correction and turbulence scalars using the

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strongly implicit procedure of Stone [11]. The effect of turbulence and transition is modelled either using different eddy viscosity based Reynolds averaged Navier Stokes (RANS) models or Large Eddy Simulation (LES).

3 Results and Discussion The transition prediction capability of the γ -Reθ SST model for different angles of attack is analysed for the 300 mm MAV wing at Re = 1.7 × 105 based on the mean chord (C) of the root section.

3.1 Computational Details The MAV considered for this study is a modified cropped delta wing with modified Eppler-61 as its cross-section. The wing semispan is 0.625C having a planform area of 0.5140C 2 . H-H grid topology consisting of 12 blocks is generated for the semi span MAV wing using the in-house grid generation code. The computational domain, boundary conditions and grid used for the present simulation are shown in Fig. 1. At the farfield boundary, depending on the sign of the convective flux either an inlet boundary condition is applied for the velocity components and turbulent scalars or an outflow boundary is applied where the normal gradients of the velocity components and turbulent scalars are made zero. At the wing surface, no slip condition (U = 0, V = 0 and W = 0) is specified. At the block boundary, one overlap control volume is provided on the either side of the block interface boundary for appropriate transfer of the solution from the neighbouring block. The near wall boundary conditions for the turbulence scalars (k, ω γ and Reθ ) have been appropriately used depending on the model used. The turbulence intensity (Tu) at the inlet is assumed to be 1% of the freestream velocity.

3.2 Effect of Grid Refinement The MAV wing analysis using the in-house flow solution code 3D-PURLES is carried up to the stall angle using a coarser grid (193 × 126 × 97) having a near wall y + ranging between 11 to 15. The effect of grid refinement on the aerodynamic characteristics of the wing is studied using the SST turbulence model. For the grid refinement study, a finer grid of size 295 × 166 × 129 with near wall y + < 1 is generated and simulations are carried at three typical angles of attack (low, middle and high). The aerodynamic coefficients obtained using the coarse and finer grid are compared with the NAL wind tunnel measurement data [1] and is shown in Fig. 2. It is quite evident from this figure that refining the grid has not brought in a

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Fig. 1 Boundary conditions and H-H grid used in the present simulation

(a) Boundary conditions Y X Z

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significant improvement in aerodynamic coefficients indicating that the coarser grid will suffice. It is further observed that, a reasonable good match with the measurement data is obtained for the drag coefficient (Cd ) and moment coefficient (Cm ). However the present computation has underpredicted the lift coefficient with the measurement predicting a very early stall (α = 16◦ ). This early stall behaviour is not observed in the measurements [8, 12] for similar class of low aspect ratio (AR) wings (AR < 3) where the stall in general is obtained around α = 22◦ .

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3.3 Effect of Transition Model The coarser grid is used to simulate the effect of modelling the transition in the RANS framework. The γ -Reθ transition model implemented in the in-house code 3D-PULRES is used for this simulation and its performance is asserted by comparing with fully turbulent SST results. The flow characteristics obtained by γ -Reθ transition model is compared with SST in detail for α = 12◦ along with the aerodynamic characteristics. The surface pressure coefficient (−Cp ) and skin friction coefficient (Cf ) distribution at three spanwise locations (root, mid and near tip) on the wing surface obtained by the transition and turbulence model for α = 12◦ are shown in Fig. 3. The Cp distributions predicted by the transition model as well as the

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turbulence model at the three locations are very similar. However, a notable difference is observed in the Cf distribution with the difference increasing as we move from the root to tip which may be due to the difference in the turbulence level obtained by the two models. The eddy viscosity ratio (μt /μ) contours on the cross planes (Fig. 4) obtained by γ -Reθ model for α = 12◦ indicate that the flow is laminar almost upto the mid wing. The γ -Reθ model has predicted a small negative Cf on the tip section close to the leading edge (0.264 ≤ x/c ≤ 0.28) of the wing which indicates that there is a flow separation which is also evident in the surface streamlines (Fig. 4a). The separation is laminar since the flow becomes turbulent at this span location beyond x/c = 0.35 as indicated in the Reynolds shear stress contours (Fig. 5a). The Reynolds shear stress (τx z ) contours for α = 12◦ at different planes along the wingspan are shown in Fig. 5. The dashed line shown in Fig. 5a is the indicative transition onset line drawn based on the shear stress criteria [9]. In this criteria, the onset location is determined wherever the Reynolds shear stress (τx z ) exceeds more than 0.001 of the mean kinetic energy and a clear visible rise is observed. The τx z contours obtained by the SST turbulence model (Fig. 5b) clearly indicate that the flow is turbulent right from the leading edge of the wing. The shift of transition onset location with angle of attack is captured by the γ -Reθ model as depicted by eddy viscosity ratio contours at different cross planes (Fig. 6) and τx z contours predicted at different spanwise planes (Fig. 7). The trend of the transition onset shifting upstream with increase in angle is captured by the present computation. The level of turbulence is observed to be greatly enhanced at the higher angle leading to an early transition when compared to the lower angle of attack.

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(a) γ-Reθ SST model

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Fig. 4 Surface streamlines and eddy viscosity ratio contours on the different cross planes α = 12◦ , Re = 1.7 × 105

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Fig. 5 Reynolds shear stress contours at different planes across the wingspan at α = 12◦ , Re = 1.7 × 105 (dashed line: indicative transition onset)

The transition onset line shown in Fig. 7 indicates that at α = 4◦ the onset at root of the wing occurs at x/c = 0.3 and moves slightly downstream at wing tip (x/c = 0.42) whereas for α = 28◦ the onset occurs close to the leading edge of the wing (x/c = 0.25) and remains almost constant along the wingspan. The surface streamlines indicate that at α = 4◦ (Fig. 6a) and α = 12◦ (Fig. 4a) the flow is smooth with the formation of the separation line at the tip of the wing which eventually forms the tip vortex. Whereas, at α = 28◦ (Fig. 6b) the flow is complex with separation occurring at the root itself. The volume streamlines at three different angles of attack are shown in Fig. 8 which clearly indicate the formation of the tip vortex and its strength increases with angle of attack.

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The aerodynamic coefficient predicted by γ -Reθ SST model using the two grids are compared with the present SST results and NAL measurement and is shown in Fig. 9. Inspite of the difference observed in the flow features predicted by the transition model and SST turbulence model the aerodynamic coefficients are almost identical in the linear regime. However the transition model has predicted the stall early by 2 degree. Simulations using the finner grid are also carried out at few angles of attack. Similar to the SST turbulence model, no significant improvement in the aerodynamic coefficients was obtained for the γ -Reθ transition model by using the finer grid.

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(a) α = 4◦

(b) α = 12◦

(c) α = 24◦ Fig. 8 Volume streamlines obtained at different angles of attack at Re = 1.7 × 105

4 Concluding Remarks The transitional flow analysis past a 300 mm class fixed wing of a MAV is carried out. The simulation done within the RANS framework has shown the significance of modelling the transition while comparing the results of base turbulence model. The γ -Reθ SST transition model is able to capture the separated flow transition. Thus an engineering approach to handle the transitional flows past an aerodynamic configuration like MAV is demonstrated.

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References 1. Arivoli D, Ravi D, Roshan A, Suraj CS, Ramesh G, Sajeer A (2011) Experimental studies on a propelled micro air vehicle. In: 29th AIAA applied aerodynamics conference, Honolulu, Hawaii, 2011-3656, pp 1–10 2. Majumdar S (1988) Role of underrelaxation in momentum interpolation for calculation of flow with non-staggered grids. Numer Heat Transf 13:125–132 3. Majumdar S, Rajani BN, Kulkarni DS, Mohan S (2003) RANS computation of low speed turbulent flow in complex configuration. In: Symposium on state of the art and future trends of CFD. NAL SP0301. NAL, Bangalore, pp 31–48 4. Malan P, Suluksna K, Juntasaro E (2009) Calibrating the γ -Reθ transition model for commercial CFD. In: 47th AIAA aerospace sciences meeting, Orlando, Florida, 2009-1142 5. Manu YC, Rajesh A, Subrahmanya MB, Kulkarni DS, Rajani BN (2015) Simulations using transition models within the framework of RANS. In: Sengupta TK et al (eds) Advances

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7. 8. 9. 10. 11. 12.

M. B. Subrahmanya and B. N. Rajani in computaion. Modeling and control of transitional and turbulent flows. World Scientific, Singapore Menter FR, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. In: Hanjaliac K, Tummers M (eds) Turbulence, heat and mass transfer vol 4. Begell House Inc., pp 625–626 Menter FR, Langtry R (2009) Correlation based transition modeling for unstuctured parallelized computational fluid dynamics codes. AIAA J 47:2894–2906 Mizoguchi M, Itoh H (2013) Effect of aspect ratio on aerodynamic characteristics at low Reynolds number. AIAA J 51(7):1631–1639 Radespiel R, Windte J, Scholz U (2007) Numerical & experimental flow analysis of moving airfoils with laminar separation bubbles. AIAA J 45:1346–1356 Shetty P, Subrahmanya MB, Kulkarni DS, Rajani BN (2013) CFD simulation of flow past MAV wings. Int J Aerosp Innov 5(1):19–27 Stone HL (1968) Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J Numer Anal 5:530–530 Torres, Gabriel E, Thomas JM (2004) Low-aspect-ratio wing aerodynamics at low Reynolds numbers. AIAA J 42:865–873

Rotor Flow Analysis in the Presence of Fuselage Using Unsteady Panel Method K. R. Srilatha, Premalatha, and Vidyadhar Y. Mudkavi

Abstract Panel methods are known to be simple yet effective during initial design stages. With the advent of advanced CFD methods and high speed computers, there is a feeling that these methods are no longer needed. On the contrary, experience with many practical problems shows that their utility is significant. There are also some problems where panel methods may be even superior to CFD approaches. One such problem is that of flow field analysis of rotors in the presence of stationary fuselage. In this paper we make use of an unsteady panel method which is a simple extension of a steady panel method to assess the effect of presence of fuselage on the rotor wake. Another significant advantage an unsteady panel method offers is that it is particularly easy to ‘fly’ the rotor in the presence of fuselage and assess the wake. Typical flight scenarios include hover, forward flight, ascent and descent flights. Some specific applications include assessment of wake flow for weapon separation from helicopters and estimates of noise due to unsteady rotor loading. Keywords Unsteady panel method · Rotor · Fuselage

1 Introduction Panel methods [1, 2] are lowest in the hierarchy of flow analysis tools and are generally not classified as mainstream CFD. Notwithstanding this, they played significant role in aircraft design and development. Almost every design house made use of panel methods during initial design stages. More recently, there is a perception that these K. R. Srilatha (B) · Premalatha CTFD Division, CSIR NAL, Bangalore, India e-mail: [email protected] Premalatha e-mail: [email protected] V. Y. Mudkavi CSIR Fourth Paradigm Institute, Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_30

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methods can be dispensed with owing to advances in CFD and availability of significant computing power. However, this perception is misplaced as they still continue to play major role in several areas. In fact, when flow regimes are genuinely linear, these methods are as good as any advanced CFD method, provided there are no flow separations and compressibility effects are small. It should, however, be noted that in aerospace applications, flow separations still remain challenging to CFD methods and when separations do occur, the flow is generally nonlinear. Some of the applications where panel methods are still effective include rotor flows [3], both unsteady and steady, rotor noise (as the noise in this case is due to fluctuating loads) [4], fluid-structure interaction, simultaneous analysis of stationary and moving parts such as rotor and fuselage interaction studies. At CSIR National Aerospace Laboratories (CSIR-NAL), panel methods have been used for a variety of problems. Wind turbine analysis and marine propeller [5, 6] analyses were carried out with success assuming steady flow. Propeller performance degradation for light transport aircraft in pusher configuration was estimated combining panel method under quasi-steady assumption with Euler solution for a live project [7, 8]. Recently the capability of the panel method was extended to include unsteady effects and applied to pitching wing and interaction of helicopter main and tail rotor wakes. In this paper we describe an attempt to study the interaction of helicopter main rotor and fuselage flow which has applications in stores separation from helicopter platforms.

2 Methodology Panel method solves the linearised potential flow equation, also known as the PrandtlGlauert equation. The basic assumptions are that the flow is linear (small perturbations), irrotational and inviscid. The Prandtl-Glauert equation is transformed into the Laplace equation which, in turn, is converted into an integral equation over the bounding surfaces. This reduces the three-dimensional problem by one order and makes it possible to obtain flow solutions about completely arbitrary configurations with little effort. The integral equation is solved by discretization of the configuration surface into plane panels and distributing singularities such as sources and doublets whose strengths are determined subject to boundary conditions. The mathematical formulation is described briefly here [1, 2]. With respect to the body fixed frame of reference, the body surface is denoted by Sb (r ) = 0.

(1)

where r is the radial coordinate and the subscript b denotes the body. The governing equation for the velocity potential  is the Laplace equation ∇ 2 (r, t) = 0.

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In panel method analysis, this potential is split into potential at infinity ∞ which represents uniform undisturbed flow U∞ and a disturbance potential ϕ. Then (r, t) = ∞ + ϕ(r, t),

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where the second integral is carried out over the wake w. As noted before, the body being analysed is discretised into plane polygonal (normally quadrilateral) panels and closed form expressions for ϕ and induced velocities for a planar polygonal element with constant distribution of source [1, 2] are used to cast this problem into a matrix problem. The numerical procedure consists of dividing the wing and mean surface into a number of small polygonal (quadrilateral, in practice) planar surfaces. Only constant sources, whose strengths are unknown at the moment, are distributed on each of the surface panels. Vortex panels which are equivalent to the doublet distribution are placed on mean camber surface of lifting components much like a collection of horse-shoe elements forming a number of columns. The vortex elements leave the trailing edges where one Kutta panel is placed for each horse-shoe column. Assuming that the strength of doublet elements are proportional to the local thickness of the lifting element, one needs to only determine the constant of proportionality per Kutta panel by applying Kutta condition. The application of boundary condition leads to a system of linear equations which is easily solved for singularity strengths from which one can calculate other flow parameters. This part of the procedure is common to both steady and unsteady panel methods. When the flow is unsteady [3], the procedure is as follows. At time t = 0, the body is impulsively started from rest at a given initial position. At this instant there is no wake. The singularity (sources and doublets) strengths are determined by solving a linear system as described above. Using these singularities, the induced velocities at the downstream corner point of the Kutta panel are evaluated. A straight vortex element of known strength is released from the downstream points of each Kutta panel. The ends of this vortex element is moved with the induced velocities and other movement of the body, if any. Now this forms the next configuration at time t + t where t is the time step. Once a vortex element (or equivalently a doublet

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element) enters the wake, its strength is kept constant. For the next time step, the new system of equations with wake elements is solved. With each time step the vortex panels in the wake grows and are never removed from the computations. At each time step the potential and induced velocities at all the control points is evaluated from the known singularity distributions. The pressure coefficient at a control point is evaluated by unsteady Bernoulli’s equation  cp = 1 −

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2.1 Non-dimensionalization For the purpose of non-dimensionalization, we prescribe U∞ in terms of its components Vx , Vy , Vz in m/s and use it as reference velocity. However, when U∞ is zero, as in the case of hover, the reference velocity is taken as the rotor tip speed.

3 Results and Discussion We present the results for a representative rotor with 4 blades fixed atop ROBIN fuselage [9] (without the pylon). Four flight cases are considered, viz., vertical climb, forward climb, hover and forward motion. Results with and without the presence of fuselage are compared to assess the effect of the presence of the fuselage on the flow. The fuselage is represented using 400 panels while each blade is represented using 301 panels. The time steps are coarse for these studies mainly because one is interested in a quick assessment. The paneling is shown in Fig. 1. We use body fixed coordinate system where x is along the fuselage positive from tail to nose, z is positive vertically up and y is positive towards portside of the fuselage.

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3.1 Vertical and Forward Climb For the case of vertical climb, vertical velocity of Vz = 1 m/s is prescribed and the analysis is carried out for two rotor revolutions. Time step corresponds to increment of azimuthal angle by 15◦ . Thus, 48 time steps are required to complete two revolutions. For the case of forward climb, an additional forward velocity of Vx = 1 m/s is prescribed over and above vertical climb of 1 m/s. The time step is the same as for vertical climb. Figures 2 and 3 shows the results. Here, CA is the coefficient of force along z, CW is the force coefficient along x. Thus, CA is akin to lift while CW is akin to drag. CM represents the pitching moment about y. For the rotor alone case, the force and moment coefficients do not exhibit much variations. There are mild oscillations whose period coincides with rotor motion. However, the addition of fuselage shows that the force and moment coefficients are significantly modified. The flow is characteristically different. In the case of combined forward and climb motion, there is a significant variation in CA and CW . This is expected because the rotor will undergo significant change in angle of attack due to rotation and forward motion. The periodicity is same as that of rotor motion. While CA and CW are nearly symmetric over one rotation, CM exhibits asymmetry which is also as expected. The most interesting feature in contrast to climb alone case is that the addition of fuselage has very little effect on CA and CW while there is reasonable modification to CM .

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3.2 Hover and Forward Flight Next we consider hover and forward flight. The panelling is the same as the previous case. We also retain the same time step and perform simulations for two revolutions of the rotor. The results are shown in Figs. 4 and 5.

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For the case of hover, we observe very little difference between case with and without fuselage. Essentially, hover is very close to steady state and the fuselage shows insignificant changes. The periodicity is maintained in both the cases. For the forward flight, we specify forward velocity of Vx = 1 m/s. We note that there is a characteristic difference in CW and CM . The effect of CA is much less.

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4 Concluding Remarks Applications of an unsteady panel method for complex problem of rotor flow field analysis in the presence of fuselage are carried out. Though panel methods suffer from several theoretical limitations, these applications indicate that essential features of flow phenomenon can be extracted. The results show the effect of fuselage is enhanced in some flight conditions like vertical climb and forward flight while in

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other cases effects are minimal. The method is useful in understanding qualitative flow features while it may be as yet difficult to ascertain accuracy of results for such complex flows unlike when the flow conditions are genuinely linear. It may be possible to enhance their utility by performing computations for a much better resolved geometry and associated smaller time steps. The flow features for the present calculations, however, exhibit sufficient smoothness.

References 1. Hess JL, Smith AMO (1962) Calculation of non-lifting potential flow about arbitrary threedimensional bodies. Technical report E. S. 40622. Douglas Aircraft Company, USA 2. Hess JL (1972) Calculation of potential flow about arbitrary three-dimensional lifting bodies. Technical report MDC J5679-01. Douglas Aircraft Company, USA 3. Ahmed SR, Vidjaja VT (1994) Numerical simulation of subsonic unsteady flow around wings and rotors. In: AIAA applied aerodynamics conference. No. AIAA-94-1943-CP, pp 938–950 4. Yin JP, Ahmed SR (1999) Aerodynamics and aeroacoustics of helicopter main rotor/tail rotor interaction. In: AIAA applied aerodynamics conference. No AIAA99-1929, A99-27283. pp 834–844 5. Narayana CL (1998) Panel method calculations for the DTMB P4119 propeller. In: ITTC propulsion committee propeller RANS/Panel method workshop, Grenoble, France 6. Narayana CL (2002) Analysis of propeller by panel method. In: NRB seminar on marine hydrodynamics. NSTL, Visakhapatnam, India 7. Narayana CL, Srilatha KR (2004) Aerodynamic analysis of Saras propeller by a panel method. CSIR-NAL Project Document CF 0403. CSIR National Aerospace Laboratories, Bangalore, India 8. Srilatha KR, Narayana CL, Premalatha, Mudkavi VY (2007) Performance analysis of Aft mounted propeller for a light transport aircraft. In: 7th Asian computational fluid dynamics (ACFD7) conference, Bangalore, India. pp 107–115 9. Schweitzer S (1999)Computational simulation of flow around helicopter fuselages. Masters thesis, The Pennsylvania State University, USA

Numerical Analysis of High Reynolds Number Effects on the Performance of GAW-1 Airfoil D. S. Kulkarni and B. N. Rajani

Abstract The aerodynamic behaviour of the GAW-1 airfoil at high Reynolds number is analysed numerically using the Spalart-Allmaras (SA) turbulence model. Initially an inter-code comparison is carried out at Re = 6 × 106 and the aerodynamics characteristics obtained using the in-house flow solution code 3D-PURLES and the open source CFD tools SU2 and OpenFOAM are validated with the available measurement data. Based on this validation exercise, 3D-PURLES is used to study the effect of increasing Reynolds number (1, 3, 6, 9, 12 millions) on the aerodynamic characteristics. Keywords Spalart Allmaras turbulence model · Aerodynamic characteristics · Drag count · SU2 · OpenFOAM · 3D-PURLES

1 Introduction The GAW-1 is a 17% thick airfoil which has been designed for general aviation applications. Detailed measurements for this airfoil was conducted by McGhee and Beasley [1] for a range of Mach number (0.1 ≤ M ≤ 0.28) and Reynolds number (2 × 106 ≤ Re ≤ 2 × 107 ) at different angles of attack (−10◦ ≤ α ≤ 24◦ ). The performance of the wing is greatly influenced by the airfoil characteristics. Therefore it becomes important to understand the effect of Reynolds number on airfoil characteristics. The Clmax and Cdmin are two important parameters [2] to characterize the airfoil especially at high Reynolds number. The high Reynolds number flows are usually encountered in wind turbines [3, 4] and transport aircrafts [5]. In the present study, numerical simulation of GAW-1 airfoil is initially carried out using three flow solution codes viz. in-house 3D-PURLES (3D Pressure based Unsteady RANS LES D. S. Kulkarni · B. N. Rajani (B) CSIR-NAL, Bengaluru 560017, India e-mail: [email protected] D. S. Kulkarni e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_31

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solver), OpenFOAM and SU2 which is validated against the measurement data [1] at Mach number 0.2 and Reynolds number 6 × 106 . On the basis of this validation exercise, the in-house flow code 3D-PURLES is used to analyze the effect of high Reynolds number on the aerodynamic performance of GAW-1 airfoil.

2 Methodology The in-house grid generation code [6] is used to generate the 2D grid around GAW1 airfoil. This 2D grid generation code is based on simple differential-algebraic hybrid procedure to generate boundary-orthogonal body fitted grids. All the flow computations are carried out using the Spalart-Allmaras (SA) turbulence model [7] on the C-grid having a grid size of 527 × 101 with the farfield placed at 15 times the airfoil chord ( C ). The near wall grid spacing is adjusted by stretching the grids along the normal direction in order to obtain the desired near wall y + < 1. The boundary conditions and grid used for present simulation are shown in Fig. 1. At the wall boundary, no slip condition is applied for the velocity and the turbulent scalar ν˜ is set to zero. The turbulence intensity at the far field is prescribed as 1% of the freestream velocity for all the computations. The convergence criteria has been fixed to be 10−5 for all the three solvers. The details of the solvers are described briefly below.

2.1 3D-PURLES—In-House Incompressible Flow Solver 3D-PURLES [8] is an in-house flow solution code to solve the unsteady turbulent incompressible flows. The code is based on SIMPLE algorithm modified for

Wall

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(a) C-grid (527 × 101) for GAW-1 airfoil

(b) Boundary condition

Fig. 1 Grid and boundary condition used for airfoil simulations

Farfield

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collocated variable arrangement [9]. The system of linear equations derived from the finite volume procedure is solved in a decoupled manner for the velocity components, pressure correction and turbulence scalars using the strongly implicit procedure of Stone [10]. For the present study, 3D-PURLES computations are carried out using QUICK scheme for spatial discretization of convective flux of the momentum equations. The upwind spatial discretization scheme is used to the compute the convective flux of the turbulent scalar equation. Whereas, the diffusion (viscous) flux is computed using the central difference scheme. The farfield boundary is treated either as an inflow (flow is prescribed) or as an outflow (zero gradient) depending on the sign of the convective flux on the relevant face. For the inflow condition, uniform velocity, the turbulent viscosity (μt ) equal to the laminar viscosity (μ) and the turbulent scalar ν˜ = μρ are prescribed.

2.2 OpenFOAM—Open Source Incompressible Flow Solver OpenFOAM is a free open source CFD software developed in C++. This software package is capable of simulating a wide variety of fluid flow processes. The package has over 80 solver modules, to handle incompressible turbulent flows, compressible turbulent flows, chemically reacting flows, porous medium, multiphase physics, heat transfer, acoustics and fluid structure interactions. In the present study, OpenFOAM computations are carried out using simpleFoam coupled to the second order linear upwind scheme for the convective flux of the momentum equation and the central difference scheme for the viscous flux. The convective flux of the turbulent equation is discretized using the upwind scheme. At the farfield, freestream boundary condition is applied which switches between fixed (inlet) value and zero gradient based on the sign of the flux. For the inlet condition, uniform velocity, μt = μ and ν˜ = μρ are prescribed.

2.3 SU2—Open Source Compressible Flow Solver The Stanford University Unstructured (SU2) open source software suite was developed for solving partial differential equations (PDE) and PDE constrained optimization problems. The core suite is a RANS solver capable of simulating the compressible, turbulent engineering problems. The SU2 computations are carried out for M = 0.2 using the second order Roe scheme for spatial discretization of convective flux with Venkatakrishnan’s limiter for the primitive variables. The convective flux of the turbulent scalar and the viscous flux is calculated using upwind scheme and corrected average gradient method respectively. Implicit local time-stepping has been used to obtain the steady-state solution, and the linear system is solved using

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the GMRES method. The characteristic based farfield boundary condition is applied to the outer domain and adiabatic wall condition is enforced on the airfoil surface. At the inlet, uniform velocity is prescribed. μt = 10μ and ν˜ = 3 μρ are fixed in the code.

3 Results and Discussion 3.1 CFD Code Validation at Re = 6 × 106 The aerodynamic coefficients obtained for GAW-1 airfoil at Re = 6 × 106 using the three flow solution codes are shown in Fig. 2 and is observed to closely follow the measurement data [1]. The variation of drag polar obtained by OpenFOAM and 3DPURLES are almost identically and closer to the measurement when compared to the SU2. However all the three codes have consistently predicted a higher drag coefficient (Cd ) when compared to the measurement. On the other hand, all the three codes have underpredicted the pitching moment coefficient (Cm ) with 3D-PURLES and SU2 being closer to the measurement. Table 1 compares the aerodynamic performance parameters obtained by the three flow codes. Stall angle (αstall ) predicted by the 3D-PURLES and the OpenFOAM are identical and closer to the measurement data, whereas SU2 has predicted an early stall. The Clmax obtained by 3D-PURLES is observed to be closest to the measurement data. The angle of attack at which the lift coefficient (Cl ) becomes zero obtained by the three codes is observed to be slightly overpredicted when compared to the measurement with OpenFOAM having the maximum difference of 0.4◦ . The Cd at this angle of attack (Cd0 ) is also overpredicted with maximum error of 24% obtained by 3D-PURLES and SU2 whereas OpenFOAM

(a) Drag polar

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Fig. 2 Variation of aerodynamic coefficients for GAW-1 airfoil at Re = 6 × 106

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Table 1 Aerodynamic performance parameters for GAW-1 airfoil at Re = 6 × 106 Data set Clmax αstall Cd0 Cdmin 3D-PURLES

1.92

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104.7 × 10−4 , α = −2◦ 99.7 × 10−4 , α = −2◦ 105.8 × 10−4 , α = −4◦ 73.3 × 10−4 , α = −2◦

is having the minimum error of 18%. Similar to to the Cd0 , the minimum drag coefficient (Cdmin ) is also overpredicted. The overprediction of the drag coefficient may be due to the errors and ad-hoc assumptions associated with the turbulence modelling.

3.2 Effect of Reynolds Number The in-house code 3D-PURLES is used to analyze the effect of Reynolds number on the aerodynamic characteristics of GAW-1 airfoil. The variation of the aerodynamic coefficients obtained for five Reynolds numbers (1, 3, 6, 9 and 12 million) are shown in Fig 3 and has captured the expected trend [4, 11], The maximum lift and stall angle are observed to increase with Re whereas the drag coefficient reduces with Re. This effect is also reflected in the L/D plot with maximum L/D occurring at the same angle of attack (α = 8◦ ) for all the Re. The momentum coefficient (Cm ) is also found to increase with Re. The maximum difference in the aerodynamic coefficient is found between 1 million Reynolds number to 3 million Reynolds number and this difference reduces at higher Re. The difference is almost negligible between 9 and 12 million Reynolds number indicating the insensitivity of the aerodynamic characteristics beyond Re = 9 × 106 similar to the experimental results [4]. Figure 4 shows the trend of the minimum drag coefficient (Cdmin ) expressed in drag count (D.C = Cd × 104 ), maximum lift coefficient (Clmax ), maximum ((L/D)max ) and lift slope (between −4◦ and 4◦ ) with Reynolds number. A decreasing trend of the minimum drag coefficient and increasing trend of both maximum lift coefficient and maximum L/D is observed as Reynolds number increases. It is further noticed that the above trend tends to become almost constant beyond 9 million Reynolds number. On the other hand, the slope of the lift coefficient curve in the linear region obtained at different Reynolds is found to be nearly same and hence may be treated as constant over this Reynolds number range.

(d) Coefficient of pitching moment

(c) Lift to drag ratio

Fig. 3 Variation of aerodynamic coefficients with the angle of attack for different Reynolds numbers

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Fig. 4 Variation of aerodynamic parameters with Reynolds number

4 Concluding Remarks The flow simulations with SA turbulence model were carried out for GAW-1 airfoil at Re = 6 × 106 using the two incompressible flow solvers viz., 3D-PURLES, OpenFOAM and the compressible flow solver SU2. The results indicate that the stall angle and Clmax obtained by 3D-PURLES were closer to the measurement data but has overpredicted the drag coefficient when compared to OpenFOAM. Based on this code validation study, the in-house code 3D-PURLES was successfully used to study the effect of high Reynolds numbers (1, 3, 6, 9 and 12 million) on the aerodynamic performance of GAW-1 airfoil. This study has captured the expected trend with lift coefficient increasing and drag coefficient decreasing with Reynolds number. The Cdmin was found to decrease with Reynolds number where as an increasing trend was obtained for Clmax , stall angle and (L/D)max . The maximum difference in the aerodynamic coefficient was obtained between 1 and 3 million Reynolds numbers and this difference was found to reduce at higher Reynolds numbers. Further, this

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difference was observed to be quite negligible for Reynolds number between 9 and 12 million indicating the insensitivity of the aerodynamic coefficient beyond 9 million Reynolds number. The slope of the lift curve in the linear regime was found to be almost same for all the five Reynolds numbers. Acknowledgements The authors acknowledge the Director, CSIR-NAL, Bangalore and Head, CTFD Division, CSIR-NAL, Bangalore for giving us the opportunity to carry out this work and permitting us to publish. We sincerely thank Dr. V. Ramesh Jt. Head CTFD Division, CSIRNAL, Bangalore for his support and fruitful discussion. We wish to express our special thanks to Mr. K. Madhu Babu Scientist CTFD Division, CSIR-NAL, Bangalore for providing the airfoil geometry data.

References 1. McGhee RJ, Beasley WD (1973) NASA TN D-7428 2. Yamauchi GK (1983) Trends of Reynolds number effects on Two-dimensional airfoil characteristics for helicopter rotor analyses. Technical report TM 84363, NASA 3. Kang S, Li J, Fan Z (2009) In: Inaugural US-EU-China thermophysics conference-renewable energy 2009 (UECTC 2009 proceedings 4. Pires O, Munduate X, Ceyhan O, Jacobs M, Snel H (2016) J Phys : Conf Ser 753:1 5. Clark PW, Pelkman RA (2001) In: 39th AIAA aerospace meeting and exhibit. Reno, NV 6. Fathima A, Baldawa NS, Pal S, Majumdar S (1994) Grid generation for arbitrary 2D configurations using a differential algebraic hybrid method. Technical report PD CF 9461. National Aerospace Laboratories, Bangalore 7. Spalart PR, Allamaras SR (1992) In: AIAA paper 92–0439 8. Shetty P, Subrahmanya MB, Kulkarni DS, Rajani BN (2013) Int J Aerosp Innov 5(1):19 9. Majumdar S (1988) Numer Heat Transfer 13:125 10. Stone HL (1968) SIAM J Numer Anal 5:530 11. Abbott HI, Doenhoff AEV (1949) Theory of wing sections. Dover Publications Inc., New York

Investigation of the Effect of Booster Attachment Scheme on the Rolling Moment Characteristics of an Asymmetric Vehicle Using CFD P. K. Sinha, Munish Kumar Ralh, Naveed Ali, R. Krishnamohan Rao, and G. Balu Abstract The rolling moment characteristics of a launch vehicle (LV) arising out of joining an air-breathing cruise vehicle (CV) and a booster is investigated through CFD to explain experimental observed behaviour. The launch vehicle has a stabilising fin at the rear and is placed on bearing to have free roll with respect to body. The basic and control rolling moment of LV (without stabilising fin, to mimic freely rolling fin), obtained experimentally, is compared with the corresponding experimental data for CV and found that the values differ, contrary to that observed in literature. CFD is used to investigate the reason for this difference. Investigation in two representative Mach numbers 0.8 (subsonic) and 2.0 (supersonic), has revealed that the interstage flare in LV, has significant effect in modifying the rolling moment contribution of the CV fin. Apart from that, the booster attachment arm, launch shoes are also having some impact in modifying the rolling moment. It is evident that for a canard controlled vehicle, even if the stabilising fin is freely rolling, the after-body geometry has significant effect in dictating the aerodynamic characteristics, especially rolling moment. Keywords Asymmetric vehicle · Rolling moment · Booster attachment · Experiment · CFD

Abbreviations LV CV RF CRM CN Cm

Launch Vehicle Cruise Vehicle Rolling Fin Coefficient of Rolling Moment Coefficient of Normal Force Coefficient of pitching moment

P. K. Sinha (B) · M. K. Ralh · N. Ali · R. Krishnamohan Rao · G. Balu Defence Research and Development Laboratory, Hyderabad 500 058, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_32

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Roll orientation Angle of attack Fin deflection Mach number Length of vehicle

1 Introduction Aerodynamics of an asymmetric vehicles, like the one shown in Fig. 1, is very challenging. The vehicle, called CV, is basically an air-breathing vehicle having two side mounted intakes. The configuration, in consideration, has intakes in closed condition. It has four control fins in cruciform position at the rear end, for vehicle control. The length behind the fins are very small ~0.38 d where d is the smallest diameter. It can be seen from Fig. 1 that the configuration is symmetric about pitch plane but it is asymmetric about yaw plane. Due to these geometric features, the longitudinal characteristics show a non-linear variation with angle of attack [1] due to cross-coupling and also the characteristics vary with roll orientation. The longitudinal characteristics of the vehicle and comparison of CFD with experimental data is already discussed in Ref. [1]. The lateral characteristics for this vehicle are also asymmetric with roll orientation [2], in contrast to the behaviour observed in case of symmetric configurations. In fact it is seen that, in intake closed condition, beyond α ~7° the rolling moment keeps on increasing very fast because of the cross coupling. Hence, it is desirable that the vehicle roll orientation is maintained around the view shown in Fig. 1, defined as ϕ = 0 orientation where the intakes are in the windward side and also the angle of attack is kept low. Any deviation from ϕ = 0 orientation or any asymmetric disturbance also makes the body vulnerable to roll. Hence, a tight control on the vehicle roll is desired from vehicle performance point of view. Proper estimates of lateral characteristics especially rolling moment, both basic and control, is very important for these kind of vehicles as they play an important role in vehicle performance and control. It is also required to have a good understanding of the

Actuator cover 1.5°Flare

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factors which affect their values. Though experiment is the only reliable means of estimating the characteristics, it may not be cost-effective to understand the factors responsible for the values through experiments. In such cases, a validated CFD code can throw sufficient light on those aspects. Though the vehicle is designed for air launch, to prove certain technology, ground launch is preferred. For ground launch, booster with a specified diameter, (almost twice that of CV) is attached at the rear end of the CV. Ground booster is used to boost the vehicle to a desired Mach number and altitude from where the CV can be brought to required air launch condition. CV and LV are connected through a flare at the interstage due to diameter difference between the two. Also, the interstage length is restricted in order to restrict the overall length of LV which has increased the flare angle. The interstage length is kept at 1.62d, where, d is the smallest diameter of LV. Integrated vehicle termed as Launch Vehicle or LV, shown in Fig. 2, is designed to meet the vehicle stability and the control requirement. Since, pitch/yaw control is not effective in boost phase, it was decided to make the vehicle sufficiently stable so that pitch/yaw control can be avoided. To maintain the roll orientation and control vehicle roll rate, only roll control using CV fin is used in this phase. Vehicle stability is achieved by placing stabilising fin on booster. During the initial studies using CFD, it was observed that a huge roll rate is developed if the stabilising fin is fixed and an acceptable fin misalignment is considered. The roll control effectiveness of the control fin, which is part of the CV, is unable to keep the roll rate within allowable limit due to induced rolling moment on the stabilising fin. In order to decouple the induced rolling moment on the stabilising fins, the fins are placed on a bearing as suggested by Auman and Kreegar [3]. This makes the fin free to rotate and the rolling moment contribution from the booster fin do not get transferred to the body. As a result, it is expected that the rolling moment characteristics will be governed mostly by that of CV. Auman and Kreegar [3] has shown experimentally, that for the body with single diameter, the rolling characteristics of the vehicle are nearly same with rolling tail fin and without tail fin. Hence, it is expected that when only cylindrical booster (without any protrusions) is attached to the CV, the rolling characteristics of LV will be same as that of CV. But in LV configuration, CV is attached to booster through some attachment scheme using a flare configuration, as mentioned earlier. Though the stabilising fin is on bearing, the presence of other portrusions viz. launch shoes, booster attachment arms may have influence on the rolling moment characteristics of LV. Further, though rolling moment due to stabilising fin is decoupled, the yawing moment and pitching moment contribution of these fins will be present during roll control and has to

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be considered for LV characterization. This is because it becomes equivalent to canard controlled vehicle having lifting surface and the vehicle characteristics are governed by CV fin downwash effect on the portrusions and the stabilising fin. In order to characterize LV aerodynamics, experiments are performed for the LV configuration [4]. To validate the findings of Auman and Kreegar [3], the rolling moment characteristics of LV, viz basic and control, are compared with that of CV obtained from separate test [2]. A difference in rolling moment values is observed which will be discussed in detail in the subsequent sections. In order to understand the reason for the difference, CFD simulations are performed. In this paper, the experimental observations in respect of rolling moment will be discussed and the CFD based explanations to justify the difference will be dealt with in detail.

2 Experimental Observation The effect of booster attachment scheme on rolling moment characteristics of LV, is estimated through wind tunnel tests. The tests are performed in 0.6 m × 0.6 m tunnel of NTAF, NAL for configuration without stabilising fin [4] which will be equivalent to that with fin sitting on a free bearing as the rolling moment contribution from booster fin is removed in both the cases. The CV characteristics are also obtained from wind tunnel tests, carried out in 1.2 m × 1.2 m tunnel of NTAF, NAL [2]. To confirm the findings of Auman and Kreegar [3], on rolling moment characteristics, the corresponding data (both basic and control) of LV and CV were compared. Typical comparison of basic rolling moment for CV and LV (without booster fin) are made in Fig. 3a, b respectively for M = 0.8 and M = 2.0 at roll orientation, ϕ = 22.5 (non-zero roll orientation is selected for better comparison). It is observed that for α > 5°, the basic rolling moment of LV is lower than that of CV (by maximum 15%) at M = 0.8 whereas at M = 2.0, the difference is much less. Similarly, the comparison of rolling moment with control deflection 10° (in roll sense) for CV and LV is presented in Fig. 4a, b respectively for M = 0.8 and 2.0. It is found that control rolling moment is lower for LV in comparison to CV. The difference is found to be more at lower angle of attack and less at higher angle of attack for both Mach = 0.8 and 2.0. The difference is found to be more (maximum ~20%) in M = 0.8 (transonic Mach numbers) and CRM Vs. Alpha,Phi=22.5 deg.,M=0.8

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Fig. 4 Comparison of Rolling moment for CV and LV from experiment at Droll = 10° a M = 0.8, b M = 2.0

comparatively less (~10%) at M = 2.0 (supersonic Mach numbers). It is expected that at supersonic Mach numbers, as the disturbance from the flare will be insignificant, the difference in rolling moment should be negligible. But experiment showed a difference, especially for δ(Droll) = 10°. Understanding the cause of this difference in rolling moment characteristics through experiment is not cost effective. Though it is known that predicting rolling moment values through CFD is very challenging, it is planned to be investigated numerically with a view that it will be possible to obtain the relative difference in the values and the reason for it.

3 CFD Simulations To understand the experimentally observed rolling moment characteristics, CFD simulations are carried out for both LV (without booster fin) and CV to obtain basic rolling moment and control rolling moment at conditions identical to experiment i.e. M = 0.8 and 2.0, δ = 0° and 10° (roll sense).

3.1 Details of Solver and Grid Generator Commercial CFD software, HEXPRESS [5] is used for grid generation and Fluent15 [6] is used for flow simulation. The grid generator generates a hybrid grid and the flow solver solves 3-D Reynolds Averaged Navier Stokes (RANS) equation on unstructured grid based on finite volume approach. It also solves one of the following turbulence models viz. k-ε, k-ω or SST turbulence model, etc. along with the RANS equations. The computational domain for the subsonic flow simulation of CV is selected with boundaries located sufficiently far from the body as shown in Fig. 5, where, L being the length of the vehicle, whereas for supersonic flow simulation boundaries

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Fig. 5 Typical computational domain for CV

5L 1.5L

4L

Subsonic Domain 5L

Fig. 6 Typical surface grid for CV

are placed at a maximum distance of 2L from the body. Typical surface grid for CV is shown in Fig. 6. It can be seen that grids are sufficiently refined in the region of intake entry, wire tunnel, launch shoes and fins. Typical grid size for CV is about 17 Million. At inflow boundary, uniform conditions of Mach number, static pressure and static temperature are imposed. At outlet boundary, the supersonic outflow boundary condition is imposed. No-slip and adiabatic wall boundary conditions are prescribed at the solid wall. Second-order scheme for mass, momentum and energy and firstorder scheme for turbulence quantities are used for solution. A log normalized rms residue of about 1e–04 has been set as the convergence criteria. Same philosophy is followed in domain selection and grid generation for LV. Typical surface grid for LV (zoomed around interstage) is shown in Fig. 7. The final grid size selected for simulation is about 18 Million.

3.2 Validation of Longitudinal Characteristics for CV and LV The CFD computation for CV and LV is carried out according to the solution methodology described above. The longitudinal characteristics especially the normal force

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coefficient CN and pitching moment coefficient Cm are compared for CV in Fig. 8 and for LV in Fig. 9. Good match of the values are observed. The rolling moment coefficient obtained from the same simulations are compared in subsequent sections.

3.3 Comparison of Rolling Moment The basic rolling moment coefficient (CRM) data for LV and CV, obtained from CFD is first validated with experiment at ϕ = 22.5°. Typical comparison of computed basic rolling moment for LV (without booster fin) and CV at ϕ = 22.5° with experiment, is presented in Fig. 3a, b for M = 0.8 and 2.0, respectively. It is observed from the

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comparison that in case of CFD also, at α = 5° the CRM of both LV and CV is nearly same as in experiment but at α = 10°, the basic rolling moment for LV is lower than CV. The trend is same at both the Mach numbers i.e. M = 0.8 and M = 2.0. It may be observed from Fig. 3a, b that at α = 10°, the relative difference in CRM values is more at M = 0.8 (~20%) than at M = 2.0 where it is ~10% as observed in experiment. It may be further observed that though CFD is unable to capture absolute values of CRM, it is able to capture well the trend of CRM variation. At supersonic Mach numbers, the variation of relative difference in CRM between CV and LV with angle of attack could not be captured through CFD. Similarly, the comparison of control rolling moment between experiment and CFD is shown in Fig. 4a, b for the same Mach number and angle of attack conditions as above. In this case also, the CFD is unable to capture the absolute values of CRM, but once again, it has predicted lower CRM for LV in comparison to CV as in the case of experiment. Though CFD data is able to capture the angle of attack effect on the relative difference of CRM between CV and LV for M = 0.8, it has failed to capture the effect in M = 2.0. The variation of computed CRM of LV (without booster fin) for 10° deflection of fins (in roll sense), with Mach number is plotted against that from experiment for LV in Fig. 10a, b for α = 5° and 10° respectively. It CFD Vs. Expt.

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is observed that CFD is able to predict the experimental trend of CRM variation with Mach number well for α = 5°, but for α = 10° the difference between experiment and computation is high at supersonic Mach number. As both experiment and CFD are showing lower rolling moment for LV, in comparison to CV, with and without roll control deflections, it is necessary to understand the reason for it. Since, CFD is not able to capture the experimental trend of CRM variation for M = 2.0, the analysis is restricted to M = 0.8.

3.4 Discussions and Analysis In this case, CFD data has been used for analysis, where component wise contribution to CRM can be obtained. Component wise contribution of major roll producing components of LV are plotted in comparison to CV for α = 5° and 10° for M = 0.8 in Fig. 11. It is found that at M = 0.8, there is significant reduction in CV fin contribution for LV. In addition, the four arms, that attaches CV to the booster, generate an opposing rolling moment. Because of the presence of the interstage flare and attachment components, the pressure distribution on fin, intakes and actuators are getting altered in LV case in comparison to CV case. The pressure contours for the CV fin with and without booster attachment are compared in Fig. 12. It clearly brings out the effect of booster attachment in altering the fin pressure distribution Component contribuƟon to CRM, M=0.8,A=10 Deg.,D=10 Deg.

Component contribuƟon to CRM, M=0.8,A=5 Deg.,D=10deg. AƩachment

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Fig. 12 Pressure distribution at Fin TE a CV b LV (with booster) for M = 0.8, α = 10° and δ roll = 10°

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around trailing edges (TE) which is responsible in reducing the fin contribution to rolling moment. As a result, their contribution is reducing. But, in case of M = 2.0, reasons are not very clear which is causing the lower value of rolling moment in case of LV. In summary, it can be stated that the reason for the difference in rolling moment between LV and CV is mainly due to reduction in fin contribution apart from contribution from intake fairing, actuator and attachment arms in subsonic/transonic Mach numbers. It brings that after body has significant effect on the rolling moment characteristics with canard controlled fin geometry.

4 Conclusions The effect of booster attachment scheme on the rolling moment characteristics are investigated both experimentally and numerically. It is found from the experimental data, obtained from wind tunnel tests, that the rolling moment (both basic and control) of Launch vehicle is lower than that of Cruise Vehicle. The difference in values decreases with angle of attack. Two Mach numbers viz. M = 0.8 and 2.0 are selected for analysis which represents subsonic and supersonic Mach number regime. It is found from experiment that the relative difference in values are more at subsonic Mach number. To understand the reason for this difference, CFD computations are performed. CFD code is first validated for the longitudinal characteristics of the configurations and the detail analysis has been made in respect of rolling moment. It is found that computed rolling moment values differ considerably from experiment. However, it is able to capture the experimental trend, in respect of LV values lower than that of CV. It also captured the trend of the effect of angle of attack on rolling moment difference between CV and LV for M = 0.8, but it failed to capture the trend for M = 2.0. The analysis showed that the CV fin has the maximum effect in reducing the rolling moment for LV. Actually, booster flare has significant effect in altering the pressure in fin trailing edge region which is responsible in bringing down fin contribution to rolling moment. Apart from control fin, booster attachment components are also having marginal contribution in reducing the rolling moment of launch vehicle. It may be noticed that in the literature, the free-spinning tail was on the same diameter as the canard fin and was effective in eliminating roll coupling and reducing other out of plane forces and moments. But in this case, though the tail fin is free to roll, the rolling moment is affected as the tail fin and canard fin are placed on two different diameters. It may be concluded that even if the tail fin is freely rolling, the control fin after-body has significant effect in altering the rolling moment characteristics of a canard controlled vehicle. Acknowledgements The authors would like to acknowledge the support and encouragement of Director, DRDL and Project Director for their constant support and encouragement in their activity of characterizing one of most complex aerodynamic configuration. The support of Ms. Ankita Jain, Contract engineer, in mesh generation and CFD simulation is highly acknowledged.

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References 1. Ralh MK, Sinha PK, Theerthamalai P (2017) Aerodynamic characteristics of an Aerospace vehicle with side mounted air-intake in closed condition at subsonic and supersonic flow. In: Proceedings NCWT-05, MIT, Chennai, Mar 2017 2. Nath B, Sreenivasan N, Sampath Rao B Force measurement on a 1:3.56 scale model of SFDR configuration. Doc. No. PD-NTF/2016/1011 3. Auman LM, Kreegar RE Aerodynamic characteristics of a canard controlled missile with a free spinning tail. AIAA-1998–0410 4. Sreenivasan N, Nath B, Joshi K, Sampath Rao B Force measurement on 1:10.2 scale model of SFDR with ground booster configuration. Doc. No. PD-NTF/2017/1014 5. User’s Manual for NUMECA-FINE/Hexa V2.10–4”, Numeca International, Brussels, Belgium 6. Ansys Fluent-14.5 theory and users guide-Ansys inc, India (2013)

Multi-objective Optimization Approach for Low RCS Aerodynamic Design of Aerospace Structures P. S. Shibu, Sandeep, Balamati Choudhury, and R. U. Nair

Abstract This paper presents a multidisciplinary, multi-objective optimization approach towards low Radar Cross section (RCS) aerodynamic design of aerospace structures. As a typical example, design and analysis of aircraft intake duct for stealth behavior by integrating computational fluid dynamics (CFD) and computational Electromagnetics (CEM) has been demonstrated. The design constraints (inlet area, throat area, exit area, and diameter) are calculated based on the RAE M2129 diffuser and subsonic flow condition with Mach number 0.8 is considered at the Indian standard atmospheric conditions (ISA_SL + 15). Inlet shaping parameters for intake are modified based on super ellipse equation by retaining the area as constant. Shaping parameter samples have been generated by limiting major axis to maximum length and minor axis to minimum length using MATLAB code. Based on each curvature parameter, three geometries were opted and CAD models are generated from sample space. For these geometries, CFD and CEM analysis has been performed and corresponding pressure recovery and RCS at 10 GHz (X-band) has been estimated. The CFD-CEM performance analysis has been presented for the optimized intake duct geometry. Particle swarm optimization (PSO) in-conjunction with CFD solver and CEM developed indigenous RCS solver has been used for optimization of the designed duct towards stealth characteristics. Keywords CFD-CEM optimization · Radar stealth · Intake duct · RCS reduction

1 Introduction Stealth technology is one of the most important requirements for the next-generation combat aircraft. Most of the stealth aircraft design focuses on low radar signature to P. S. Shibu · Sandeep · B. Choudhury (B) · R. U. Nair Centre for Electromagnetics, CSIR—NAL, Bangalore 560017, India e-mail: [email protected] P. S. Shibu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_33

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reduce the detection possibility. Stealth technology allows the aircraft to enter into the enemy territory without being detected by enemy radars. Across the world, only few successful aircrafts are flying which are stealthier in nature. The stealth aircraft design with low radar signature depends on the nature of mission. The fighter aircraft which take part in air to air battle is designed for reduced front and back radar cross section, whereas in bombers design, even side and bottom RCS reductions are also considered. Cavities such as intake, exhaust, landing gear gates, air breath sensors, etc., are the main RCS hotspots. The best way to reduce RCS is by removing or hiding the RCS contributing portions from the enemy radar vicinity. Some of the components which cannot be avoided have to be redesigned for low radar signature characteristic. Design of stealth aircraft involves the disciplines like computational fluid dynamics, structural and computational electromagnetics. An integrated approach has to be considered for the stealth design process. The shape feature of the aircraft is most important in the improvement of the stealth characteristics to avoid detection from radars. There are two kinds of radar systems, one is ground based radar detection system and other is air to air radar detection systems. Both radar system works on same principle, i.e., transmitting the signal and receiving the reflected waves. Based on the incoming wave characteristics, the RCS will be calculated for the object. RCS contributions from the cavities like intake, exhaust, landing gear gates, air breath sensors, etc., contribute more due to accumulation of electromagnetic energy. In order to avoid this high contribution, these cavities need to be designed to achieve the requirement of low radar signature. Air intake duct is considered for the analysis of the aerodynamic and electromagnetics characteristics. Intakes are designed for suction of air from the atmosphere to fulfill the requirement of engine. Reduced pressure loss is desirable across the duct while retaining the distortion levels to adequate for the best performance of the engine and to avoid instabilities. As aerospace platforms are always multidisciplinary in nature, the design optimization also should follow an integrated approach to achieve the goal. The optimization problem of an inlet shape of duct for minimum pressure loss and low radar signature with maximum mass flow rate has been discussed in this paper.

2 Objective The design of advanced fighter aircraft intake ducts leans to compact nature due to its stealth factor. This leads to the unsteady in aerodynamic performance. As a result, there should be a need for a compromise between aerodynamic attributes and radar signature. Understanding of flow physics and electromagnetic scattering mechanism of duct to predict the unsteady aerodynamics and assess of radar signature has a great significance for stealth design. The present work attempts to use Computational Fluid Dynamics—Computational Electromagnetics (CFD-CEM) integrated framework to optimize the inlet shape of duct to ensure the maximum mass flow rate with minimum pressure loss and radar signature. This would have a positive influence on the ability

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to improve association between low observability and aerodynamic effect on the designed structures. These two domains have been analyzed integrally to design a stealthier intake duct.

3 Approach and Literature To design optimal intake duct with stealth characteristics, needs an integrated research of an aerodynamic and electromagnetic characteristic of aircraft intake duct. Initially to understand the flow physics RAE M2129 S-shaped diffuser model of Royal Aircraft Establishment has been identified for the computational fluid dynamic simulation and compared with experimental results that are available for assessment [2]. The geometry of M2129 S-shaped diffuser is shown in Fig. 1. The dimension of the duct are: Dthroat (0.1288 m) is the throat diameter, Dc (0.1440 m) is cowl diameter, DEF (0.1524 m) is engine face diameter and L (0.4572 m) is the duct length. Intake duct scattering characteristic depends on the shape of the duct longitudinally as well as inlet opening and it should meet the aerodynamic performance. Longitudinal shape variation of air intake duct has strong impact on the radar cross-section and aerodynamic performance. A straight cylindrical-shaped duct (Fig. 2a) has been designed based on the design criteria values that mention in Fig. 1. Straight cylindrical duct design has mean RCS contribution of −8.7629 dBsm with the 97.6189% pressure recovery. Inside RCS contribution without cowl was estimated based on inhouse MATLAB code. Aerodynamically it meets good performance but with high radar signature. Intake duct shape has altered to single curved nature through longitudinally as shown in Fig. 2b which leads to mean RCS contribution of −25.0767 dBsm and 96.79% of pressure recovery. Radar signature has lowered while pressure recovery has slightly reduced. The duct shape has further changed to double curve nature through longitudinally as shown in Fig. 2c. The mean RCS of −42.1962 dBsm Fig. 1 RAE M2129 diffuser geometry

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Fig. 2 Intake ducts a Straight. b Single curved. c Double curved. d Co-centric single curved

and 92.4044% pressure recovery is achieved. Radar signature is reduced considerably but the aerodynamic performance has drastically degraded which leads to aerodynamically instable structure. Further, the design criteria have been shifted by retaining the single curve nature of the duct longitudinally and altering the inlet shape in which the open end cavity space should not visible to the engine face. The design is shown in the following Fig. 2d. Mean RCS of −30.0253 dBsm and 96.2873% of pressure recovery was observed. Co-centric single curved duct radar signature was further lowered when compared to the single curved duct and the pressure recovery is approximately similar. It can be observed that the inlet shape change has an impact on the radar signature. Hence, the problem of optimization of an inlet shape of duct for minimum pressure loss and radar cross-section with maximum mass flow rate is of great importance. The super ellipse equation is considered to design inlet shape of air intake duct. Super ellipse is a closed curve analogous to the ellipse [1]. The generalized twodimensional cartesian form of super ellipse is represented as  x n  y m       +  =1 a b

(1)

where ‘a’ and ‘b’ are the semi diameters of the curve, while ‘n’ and ‘m’ are curvature factor. Different combination of ‘n’ and ‘m’ is capable of generating number of diverse shapes having range of symmetries. Variation of such shapes are shown in Fig. 3. Curvature factor m = n is assigned to retain the symmetry nature. To design the inlet shape of air intake duct the following equation is considered. Variation of such shapes are shown in Fig. 4.  x  n  y n       +  =1 a b

(2)

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Fig. 3 Super ellipse shape variations with a = 2, b = 1, n = 1–5 with step size of 1, m = 0.5–2 wit step size of 0.5

Fig. 4 Super ellipse shape variations with a = 2, b = 1, n = 1–5 with step size of 0.5

To design optimal intake duct with stealth characteristics needs an integrated research of aerodynamic and electromagnetic characteristic of aircraft intake duct. The conceptual design and analysis approach of cavity structure such as intake duct of aircraft is shown in Fig. 5.

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Fig. 5 Intake duct conceptual design using CFD-CEM integrated approach

4 Intake Duct Design 4.1 Design (Super Ellipse) Based on Eq. (2), three variable parameters alter the shape in two dimension. Curvature factor ‘n’ influences the shape of the curve, while semi major axis ‘a’ and semi minor axis ‘b’ has an impact on the dimension of the shape. An algorithm was developed in MATLAB to determine the ‘a’ and ‘b’ values based on the constrained area of 13029.31575 mm2 . The variables ‘a’, ‘b’ and ‘n’ has certain dimension limitations. The range of ‘a’ confined between 50 and 300 mm, while ‘b’ bounded to 30–300 mm. The range of ‘n’ varies from 1 to 5 with step size of 0.5. Based on these limits, 154 samples are generated. For each ‘n’ we opted three combinations based on the limiting ‘a’ and ‘b’ ranges into three sections. The limitation of each section of ‘a’ and ‘b’ depends on the ‘n’ value. Each section is termed as set 1, set 2 and set 3. For a particular ‘n’ three combinations of ‘a’ and ‘b’ values are opted. Twenty-seven combinations are chosen to study integrated analysis of aerodynamic and electromagnetic characteristics of the inlet shape of duct. Designed ducts with respective ‘n’, ‘a’ and ‘b’ are shown below (Table 1).

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Table 1 Inlet shape configurations Case

Set 1

Set 2

Set 3

n = 1, a = 81.13 mm b = 80.299 mm

n = 1, a = 130.94 mm b = 49.753 mm

n = 1, a = 199.83 mm b = 32.601 mm

n = 1.5, a = 71.13 mm b = 66.905 mm

n = 1.5, a = 116.14 mm b = 40.976 mm

n = 1.5, a = 142.26 mm b = 33.4525 mm

n = 2, a = 70.00 mm b = 59.248 mm

n = 2, a = 105.80 mm b = 39.20 mm

n = 2, a = 133.65 mm b = 31.0315 mm

n = 2.5, a = 66.18 mm b = 58.2315 mm

n = 2.5, a = 91.33 mm b = 42.196 mm

n = 2.5, a = 120.56 mm b = 31.9655 mm

n = 3, a = 62.05 mm b = 59.4295 mm

n = 3, a = 90.61 mm b = 40.6975 mm

n = 3, a = 117.99 mm b = 31.2535 mm

1

2

3

4

5

6

(continued)

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Table 1 (continued) Case

Set 1

Set 2

Set 3

n = 3.5, a = 69.30 mm b = 51.7105 mm

n = 3.5, a = 70.83 mm b = 50.5935 mm

n = 3.5, a = 112.43 mm b = 31.8735 mm

n = 4, a = 63.81 mm b = 55.065 mm

n = 4, a = 92.36 mm b = 38.0435 mm

n = 4, a = 110.13 mm b = 31.905 mm

n = 4.5, a = 73.72 mm b = 46.994 mm

n = 4.5, a = 88.65 mm b = 39.0795 mm

n = 4.5, a = 106.34 mm b = 32.5785 mm

n = 5, a = 61.29 mm b = 55.9345 mm

n = 5, a = 89.35 mm b = 38.3685 mm

n = 5, a = 95.81 mm b = 35.7815 mm

7

8

9

4.2 Computational Fluid Dynamics The aerodynamic design constraints have been calculated based on the Indian Reference Atmospheric (IRA = ISA_SL + 15) conditions. The duct has been designed for subsonic flow condition with 0.8 Mach number. Accordingly, the inlet velocity is set to 272 m/s with mass flow rate of 3 kg/s. The throat dimension is calculated to allow maximum mass flow rate through duct. Accordingly, 27 designs have been modeled using available CAD software. The aerodynamic flow analysis has been performed using steady-state flow equations solved in 3D field. In solver the flow field parameters have been computed based on Reynolds Averaged Navier Stokes (RANS) equations, Ideal gas flow equation along with SST K-omega turbulence model has been used. The results such as mass flow rate, pressure recovery, and total pressure loss coefficient have been estimated at the engine face.

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4.3 Computational Electromagnetics Monostatic RCS analysis is carried out at 10 GHz (X-band). High-frequency ray tracing Geometric Optic (GO) method is used to estimate RCS in FEKO software. The scattering energy is observed at azimuth = 0 with an elevation variation of −10 to 10.

5 Results The variation of curvature factor with pressure recovery values of the inlet designs are shown in Fig. 6. It depicts that pressure recovery for all the design are greater than 97% which makes the structure aerodynamically feasible. Similarly variation of semi-major axis (a) and semi-minor axis (b) with pressure recovery values of the inlet design are represented in (Figs. 7 and 8). From Fig.6 it portrays that set 1 contribution has good pressure recovery when compared to set 2 and set 3. Figure 9 shows the mean RCS contribution of the ducts over the curvature factor. It depicts that the set 3 has low radar signature contribution when compared to the set 1 and set 2. Similarly, the mean RCS distribution over semi-major and semi-minor axis is shown in Figs. 10 and 11. To design a low radar signature duct, shaping parameter samples has to be opted by selecting the major axis to maximum length and minor axis to minimum length. A nature based optimization technique namely particle swarm optimization technique has been used in conjunction with CFD and CEM solvers. Particle swarm optimization is based on

Fig. 6 Pressure recovery variations over curvature factor (n) of all duct inlet models

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Fig. 7 Pressure recovery variation over semi-major axis (a) of all duct inlet models

Fig. 8 Pressure recovery variation over semi-minor axis (b) of all duct inlet models

swarm intelligence for collection of high density food in the field and has been implemented here as a multiobjective optimization technique to select the best design with maximum mass flow and minimum RCS [6]. The optimized design (a: 95.81 mm, b: 32.57 mm and n: 4.5) that has been obtained using PSO provides a mean RCS of -3.1431 dBsm and a pressure recovery of 98%.

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Fig. 9 Mean RCS (elevation = −10 to 10, Azimuth = 0) variation over curvature factor (n) of all duct inlet models at 10 GHz Horizontal polarization

Fig. 10 Mean RCS (elevation = −10 to 10, Azimuth = 0) variation over semi-major axis (a) of all duct inlet models at 10 GHz Horizontal polarization

6 Conclusion This paper provides an insight to CFD-CEM integration approach in conjunction with nature base optimization techniques towards design of a low RCS air intake duct for aerospace applications. Inlet shape optimization of an air intake duct for

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Fig. 11 Mean RCS (elevation = −10 to 10, Azimuth = 0) variation over semi-minor axis (b) of all duct inlet models at 10 GHz Horizontal polarization

maximum mass flow rate with minimum pressure recovery loss and radar cross section has been carried out with simulation of adequate models based on CFD-CEM integration approach in conjunction with multi-objective algorithm. Twenty-seven intake ducts have been evaluated for flow analysis and electromagnetic scattering mechanism. Based on these performance values multi-objective design optimization has been employed to design an optimized inlet of an intake duct which provides a mean RCS of −3.14 dBsm with 98% pressure recovery. The results suggest that the multi-objective design optimization can help for the design of the intake duct inlet in CFD-CEM integrated approach with best compromise performance.

References 1. Gridgeman NT (1970) Lamé Ovals. Math Gaz 54:31–37 2. Berens TM, Delot A, Chevalier M, Muijden JV, Waaijer RA, Tattersall P (2012) GARTEUR AD/AG-43 application of CFD high offset intake diffusers, garteur final report, ARTEUR TP173, pp 18–24, Oct 2012 3. Kumar I (2015) 6th generation stealth aircraft. Int J Res Sci Eng 1(2):7–12 4. Richardson D (2001) Stealth warplanes: deception. Evasion and Concealment in the Air. MBI Publishing Company, New York 5. Raymer DP (1989) Aircraft design: A conceptual approach, 5th edn. AIAA Publishers, Washington 6. Balamati C, Jha RM (2015) Soft computing in electromagnetics: methods and applications. Cambridge University Press, Cambridge, CB2 8BS UK, USA, (ISBN: 9781107122482), p 215

Analysis of Propeller by Panel Method for Transport Aircraft Premalatha, K. R. Srilatha, and Vidyadhar Y. Mudkavi

Abstract The new aviation policy in place has given much impetus to local connectivity that has been re-emphasized with the launch of UDAN program. Certainly, this program will propel introduction of a significant number of propeller-driven aircraft suitable for short hauls. It is also well known that propeller-driven aircraft can be far more fuel efficient. In this context, CSIR-NAL initiated development of 14-seat Saras, a twin engine propeller-driven aircraft in pusher configuration. Being essentially an ab-initio design, one needs to understand complex aerodynamics that results from a pusher configuration. There are a number of technical issues such as propeller-fuselage interaction, propeller induced noise, power-on drag that need to be understood for design inputs. It is also known that full blown CFD methods for such analysis are still not very mature. Even if they are, they consume enormous computing power and clock-time to provide meaningful design inputs. In this paper, we present application of NAL’s unsteady Panel Code (Unsteady panel method analysis. PD-CTFD/2016/1009, CSIR National Aerospace Laboratories, Bangalore [1]) for the analysis of Hartzel propeller for a combination blade setting and advance ratios. This is an initial step towards more complex analysis wherein fuselage and other components can also be added in a much simpler fashion. Results indicate that there is a good confidence in this approach and as such one can generate significant design data at initial design stage. Keywords Panel method · Propeller · Transport aircraft

Premalatha (B) · K. R. Srilatha CTFD Division, CSIR NAL, Bangalore, India e-mail: [email protected] K. R. Srilatha e-mail: [email protected] V. Y. Mudkavi CSIR Fourth Paradigm Institute, Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_34

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1 Introduction With UDAN program set to boost regional transport, a need will soon be felt to introduce turbo-prop aircraft as they are far more efficient when compared to jet equivalents. Towards this, CSIR National Aerospace Laboratories (CSIR-NAL) had initiated development of turbo-prop regional transport aircraft. Much earlier, NAL also began development of 14-seat Saras in pusher prop configuration keeping NorthEast segment in mind. Such developments require quick and robust propeller flow analysis methods. It is well known that full blown CFD methods require high end computing systems and long turn around time to produce reasonable solutions needed for initial design studies. It is interesting to note that panel methods continue to play a useful role in analysis of propeller flow fields, in spite of their complexity, requiring very little compute power and extremely short turn around times to generate design data. In this paper, we present validation of in-house developed unsteady panel code for propeller flows. We consider five-bladed propeller used for powering NAL developed Saras. We analyze the flow for free propeller at various flow conditions defined by blade setting angles (β). Flow quantities such as thrust and torque coefficients are compared with experimental results. For inviscid, incompressible and irrotational flow past an arbitrary threedimensional body, we have (1) ∇ 2 (r, t) = 0 where  is the velocity potential, r is the position vector, and t is the time. We can decompose the velocity potential as (r, t) = ∞ + φ(r, t)

(2)

where ∞ is the velocity potential in the absence of the body and φ(r, t) is the perturbation potential due to the presence of the body. Usually, this perturbation is regarded as small. Assuming that the undisturbed flow U∞ = ∇∞ is uniform and steady, Eq. (1) reduces to (3) ∇ 2 φ(r, t) = 0 Since the flow disturbances are assumed to decay at infinity and that body is impermiable, the boundary conditions become v = ∇φ → 0

as r → ∞

(U∞ + v) · n = 0 where n is the unit normal on the boundary surface.

(4)

(5)

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From Green’s theorem [2], it follows that any solution of Laplace equation can be expressed as an integral given by   φ P (r, t) = body



+ wake

 σ (S, t) ∂  1  μ(S, t) dS + r (S, P) ∂n r (S, P)

∂  1  μ(S, t) dS ∂n r (P, q)

(6)

where σ and μ are the strengths of the source and doublet singularities, respectively. r (S, P) is the distance from the integration point to the field point P where the potential is being evaluated. n is the normal along the surface S. The source singularity is used to take into account the thickness effects, and the doublet singularity is used to account for the lifting effects. As the velocity induced by constant doublet distribution has the same magnitude as the vortex line of same strength situated around the perimeter of the panel, the doublet distribution on quadrilateral panels is replaced by vortex rings around the same panel. This enables one to use Biot–Savart law for the calculation of velocities at any point due to quadrilateral vortex ring. This method is well-established [3].

1.1 Numerical Procedure The numerical procedure consists of dividing the lifting body such as wing and its mean surface into a number of quadrilateral planar surfaces. Only constant sources whose strengths are unknown are distributed on each of the surface panels. The camber surface is also panelled similar to surface panelling. The vortex panels are placed on camber surface from leading to trailing edge. The chordwise panels on each column are grouped together, and only constant doublets proportional to section thickness are distributed. The boundary condition is set on Kutta panel downstream of trailing edge. Imposing the condition Eq. (6) in Eq. (5) results in a system of algebraic equation of the form, Ax = b (7) where A is known as the influence coefficient matrix, x is the vector of unknowns consisting of source and doublet strengths, and b is the known vector that accounts for boundary conditions. The solution of this system gives the strengths of σ and μ at each instant of time. If the flow is steady, then A is constant and the solution is simple [4, 5]. However, if the flow is unsteady, as in the present case, then we proceed as follows. At time t = 0, there is no wake when the body is started impulsively from rest. With the solution of Eq. (7), the strengths of the singularities are determined. Next the induced velocity at the downstream corner point of Kutta panels for lifting surfaces

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is evaluated, and a straight vortex element is released whose length is the distance traversed by local velocity in that time interval. This row of vortex filaments forms the first increment of wake. The vortex strength of this row remains same for all subsequent calculations. For the next time step, Eq. (7) is solved taking into account all the body bound singularities and the induction due to first row of wake panels. Repeating the procedure, this results in the second wake row. The process continues for subsequent time steps yielding unsteady wake as it develops. Figure 1 shows the model of the blade surface and the development of the wake on it. In order to calculate other parameters such as thrust and torque, we need pressure coefficient Cp which is calculated using the following unsteady Bernoulli’s equation  Cp = 1.0 −

|V | VRef

2 −

2 ∂φ 2 ∂t VRef

(8)

where V is the total velocity and VRef is any reference velocity. The time derivative of potential in Eq. (8) is evaluated using ∂φ ϕ(t + t) − ϕ(t) = ∂t t

(9)

W

Fig. 1 Panelling strategy adopted for lifting surfaces. Doublets are distributed on the mean surface, accounting for lift, while sources are distributed on the actual surface, accounting for thickness. Panels are generated by taking sections span-wise and chordwise. A Kutta panel is inserted which is an extension of the mean surface. Wake panels are introduced beyond the Kutta panel

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Once the pressure coefficient acting at all panels is calculated, the forces and moments acting on individual panels and the configuration as a whole are easily obtained at every time instant [1]. In what follows, we present an application of this technique to the five-bladed Saras propeller for various flow conditions.

2 Results and Discussion Figure 2 shows the propeller configuration and their panel discretization. The propeller was first analysed for five blade angle settings of β = 20◦ , 22.5◦ , 25◦ , 27.5◦ and 30◦ . These were compared with the values provided by the design team. Subsequently, results were generated for four more blades angles β = 19◦ , 23◦ , 27◦ and 31◦ . We primarily are interested in the thrust coefficient CT defined by CT =

T 1 2 S ρU∞ 2

=

T ρn 2 D 4

(10)

where T is the magnitude of the thrust calculated as the axial component of the aerodynamic force, U∞ is the reference velocity which is the undisturbed flow at infinity, S is the propeller swept area, n is the revolutions per second (rps) of the propeller, ρ is the density, and D is the diameter of the propeller. The torque coefficient CQ is defined by CQ =

Q ρn 2 D 5

(11)

where Q is the magnitude of the torque. Figure 3 shows the comparison of thrust coefficient as a function of advance ratio with NAL experiments for different blade setting angles. For all cases, it is clear that the trend is extremely well-captured except for a near constant shift. This may be attributed to the fact that the blade setting angle measured on actual propeller blade, and the simulations may have some differences. It is also not clear if the blade setting angle is taken at 70% of the propeller centerline or from the edge of the hub. However, for design purposes, these results can be used with confidence if the blade setting angle correction is added. A simple exercise shows that the difference in the results, i.e., a constant shift, can be accounted for by adding 5◦ to the blade setting angle. This is shown as a composite plot in Fig. 4. Here Rtip refers to propeller blade radius. Even though the method is simple in nature, the wake can get fairly complex as time evolves. Since the wake is significant and has major effect on moments and forces, it is important to assess the convergence of these quantities. Figures 5 and 6 show evolution of thrust coefficient with time for different blade setting angles

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Z

X Y

Fig. 2 Five-bladed Saras propeller showing the panelling. The blade geometry was obtained by physically scanning the propeller blade. For the purpose of these calculations, data was cleaned before panelling

for axial velocity of 70 m/s and 100 m/s, respectively. In about 1 time unit (nondimensional), the propeller would have executed about half a revolution. It is clear that thrust coefficient converges smoothly rapidly in about one propeller revolution that corresponds to about 2 time units. The convergence is a little slower for smaller blade setting angles. The blade setting angles examined were provided by the design team. Similarly, Fig. 7 shows the convergence history of thrust coefficient for blade setting angle of β = 31◦ for various axial velocity values. It is again clear that convergence is smooth and rapid. Next we examine behaviour of torque coefficient. Figure 8 shows the variation with respect to advance ratio for various blade setting angles. Figure 9 shows the variation with axial velocity. The trends are right. Also, it is notable that variations are smooth. However, it should be noted that the results may not be reliable for lower advance ratio as the method does not account for any separation which is likely to occur for lower values. As mentioned earlier, wake is developed as part of the solution that may get fairly complex. For this purpose, we examine the physical structure of the wake for a qualitative assessment. Figures 10 and 11 show the wake structure for axial velocity of 40 m/s and 90 m/s, respectively. The structure for axial velocity of 40 m/s is

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0.4

o

0.4

Panel Expt.

Panel Expt. 0.3

CT

CT

0.3

0.2

0.1

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shown for about two revolutions while that for 90 m/s is for about one revolution. The helical structure is well-maintained and is expected when the wake is nearby to the propeller. Wake distortions are expected to happen far downstream. It is also clear that wake expands after about one revolution. In Fig. 12, we examine wake structure for different blade setting angles. While the structure is in general smooth and well-organized, a close examination shows that for higher blade angle the wake distortion is initiated. However, this is not of any consequence since relevant design quantities are already converged.

3 Conclusions A modified panel method to account for unsteady flows is applied for Saras fivebladed propeller. Convergence of thrust and torque coefficients, relevant for initial design, is examined. Results converge smoothly and rapidly. Wake structure is also examined, and it shows that the picture is qualitatively meaningful. Wake distortions are expected to happen much later. However, this is not of consequence as the results are already converged within about one propeller revolution. The results are compared with NAL experiments and show that but for a near constant shift, the match is excellent. The shift in computation and experimental result may be attributed to the fact that the blade setting angle measured on actual propeller blade and the simulations may be different. However on adjusting the blade setting angle by about 5◦ , the method yields results that can be used for all practical design calculations.

References 1. Srilatha KR, Premalatha, Ahmed SR, Narayana CL, Mudkavi VY (2016) Unsteady panel method analysis. PD-CTFD/2016/1009, CSIR National Aerospace Laboratories, Bangalore 2. Lamb H (1932) Hydrodynamics. Dover Publications, New York 3. Ahmed SR, Vidjaja VT (1994) Numerical simulation of subsonic unsteady flow around wings and rotors. AIAA-1994-1943, A94-30939 10-02 938-951 4. Narayana CL, Srilatha KR (2004) Aerodynamic analysis of SARAS propeller by a panel method, NAL PD CF 0403. CSIR National Aerospace Laboratories, Bangalore 5. Srilatha KR, Narayana CL, Premalatha, Mudkavi V (2007) Performance analysis of AFT mounted propeller for a light transport aircraft. In: Proceedings, 7th Asian CFD conference, pp 107-115

Effect of Reynolds Number on Typical Civil Transport Aircraft Vishal S. Shirbhate, K. Siva Kumar, and K. Madhu Babu

Abstract Reynolds Averaged Navier–Stokes (RANS) simulations have been performed over a civil transport aircraft at Mach number 0.17. The present work aims to understand the effect of various Reynolds number on the aerodynamic performance of aircraft since the Reynolds number is considered as a most important parameter in fluid dynamics. The current study also helps to identify the various hot spots for higher drag so that the design team can focus on these specific areas to minimise the total drag. The present CFD solver uses a Roe scheme for convective flux discretisation and Spallart-Allmaras turbulence model for eddy viscosity computations. Calculations showed that with an increase in Reynolds number, the maximum lift coefficient increases and minimum drag coefficient decreases. The paper also highlights the sectional Cp plots and pressure contours along with the velocity streamlines at different span-wise stations of an aircraft wing. The strength of vortex over a midboard flap gradually decreases with the increase in Reynolds number. The drag of various aircraft components is also shown in the form of Pie chart so that the major drag contributing parts can be identified. Keywords RANS · Wind-tunnel · Reynolds number · Civil transport aircraft · Vortex

V. S. Shirbhate (B) · K. Siva Kumar · K. Madhu Babu Computational and Theoretical Fluid Dynamics Division, Council of Scientific and Industrial Research—National Aerospace Laboratories, Bangalore, Karnataka 560017, India e-mail: [email protected] K. Siva Kumar e-mail: [email protected] K. Madhu Babu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_35

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1 Introduction Today, the regional civil transport aircraft market has a huge potential in India. The government is also very keen on the regional connectivity program for tier-II and tier-III cities since India’s civil aviation industry is on a high-growth trajectory [1]. India aims to become the third largest aviation market by 2020 and largest by 2030 as per the report posted by India Brand Foundation Equity website. According to the latest market analysis, turbo-propeller aircraft is going to share the 24% of market share in an Asia–Pacific region. Towards this, smaller passenger aircraft segment of around 14–40 seater aircraft will play a vital role to fulfil the market demand. In the view of the above context, the current paper focuses on the computational aerodynamic studies performed on a typical civil transport aircraft. The Reynolds number plays a vital role in determining the aerodynamic coefficients and type of fluid flow (laminar or turbulent). The effect of various Reynolds number over aerofoil has been studied experimentally [2]. The authors observed from the experiment that the minimum drag decreases and the maximum lift increase on the aerofoil with the increase in Reynolds numbers. The extensive work has also been performed to determine the effect of Reynolds number for applications like smaller MAVs and UAVs [3–6]. However, such investigations are not much helpful at civil aircraft level. Therefore, an attempt has been made to perform the RANS simulations over a typical civil transport aircraft for different Reynolds numbers 1.0 million, 5.0 million and 10.0 million at a freestream Mach number of 0.17. The stall behaviour for all the three Reynolds number has been studied and the flow characteristics at corresponding region are thoroughly assessed and reported.

2 Methodology 2.1 Grid Generation The unstructured grid is recommended for complex geometries like full aircraft configuration integrated with engine and nacelle. An unstructured tetrahedral grid has been generated using Pointwise software for present aircraft configuration as shown in Fig. 1. The present grid consists of 2 million elements on the surface and 68 million volume elements. A cylindrical domain is used for a far-field boundary which is placed at 10 body-lengths from the nose and tip of the wing and the 20 body lengths behind the aircraft. The prismatic layer is created using a special technique called T-Rex (anisotropic tetrahedral extrusion). The first grid cell spacing of the mesh is 1.5e–05 and the y + considered for the present computations is less than 1.0 on the lifting surfaces. The drag prediction workshop guidelines have been followed for building a mesh.

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Fig. 1 Unstructured grid generated over aircraft

2.2 Solver Details Three-dimensional steady RANS computations [7, 8, 10] have been performed using a commercial CFD package ANSYS Fluent. This solver is the most powerful and flexible general-purpose tool used to model flow, turbulence, heat transfer and reactions for many aerospace applications. All present CFD simulation uses Roe [9] scheme for convective flux discretisation and Spallart-Allmaras turbulence model for eddy viscosity computations. A special initialisation technique called Full MultiGrid (FMG) initialisation has been used for better initial guess values and accelerating the convergence. FMG solves the flow problem on a sequence of coarser meshes using Euler equations before transferring the solution onto the actual mesh [11]. FMG initialisation is useful for complex flow problems involving large pressure gradients on finer meshes. The computations have been performed on ICE cluster super-computing facility of CSIR-4PI.

3 Results and Discussion The lift coefficient comparison between CFD computations for three different Reynolds numbers; 1.0 million, 5.0 million and 10.0 million and wind tunnel experiment are shown in Fig. 2. The wind tunnel data shows a slow and gradual stall pattern compared to sudden stall pattern predicted by CFD results. The computations have

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Fig. 2 CL versus AoA comparison between CFD and WT

predicted a similar stall behaviour for all the three Reynolds number whereas experiment data slightly varies in the same region. It is observed from the CFD results that the maximum lift coefficient (CL) increases with increasing Reynolds number. The lift coefficient at 0° angle of attack remains nearly equal for all the Reynolds number. The best comparison can be observed for Re = 1.0 million which also corresponds to the wind tunnel data. The drag coefficient versus angle of attack comparison between computations and wind tunnel data is plotted in Fig. 3. The numerical results have predicted a lower drag than the wind tunnel data. It is also seen that the drag coefficient decreases with the increase in Reynolds number. Figure 4 shows the lift versus

Fig. 3 CD versus AoA comparison between CFD and WT

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Fig. 4 CL versus CD comparison between CFD and WT

drag plot and it is depicted that the CFD computations have predicted a lower drag as compared to the experimental data till the stall region. The zero lift drag coefficient (CD0 ) reduces as the Reynolds number increases. The drag polar trend for 5.0 and 10.0 million Reynolds numbers is identical in nature until the stall region. It has also been observed that for a Re = 1.0 million, the drag prediction is slightly higher than the other two Reynolds number cases and lower than wind tunnel data. The lift versus pitching moment coefficient comparison is depicted in Fig. 5. It is seen that the pitching moment slope is negative for a range of alpha sweep and the slope remains almost constant till it reaches to stall angle. The computations under-predict

Fig. 5 CL versus Cm comparison between CFD and WT

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the pitching moment at zero lift compared to experiments for all the three Reynolds numbers. At the stall angle, the sectional Cp plots and Cp contours along with streamlines on different spanwise sections are shown in the Figs. 6, 7 and 8. It is understood from the figures that a vortex forms over a trailing edge of the midboard flap and also in the gap between main wing and inboard aileron. It can also be noticed in the corresponding sectional Cp plots that the pressure distribution is slightly disturbed near that region. The same vortex becomes stronger as it moves towards the midboard aileron region. This phenomenon finally results in a wing stall. The strength of vortex over a midboard flap gradually decreases with the increase in Reynolds number as depicted in figures. The above flow characteristics are clearly visible in the zoomed view of all pressure contour pictures. The Cp plots illustrate that the peak of negative pressure coefficient is maximum at the highest Reynolds

Fig. 6 Sectional Cp plot (left), Cp contours along with streamlines (full view: middle, zoomed view: right) at Re = 1.0 million: mid-board flap, inboard aileron, and midboard aileron

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Fig. 7 Sectional Cp plot (left), Cp contours along with streamlines (full view: middle, zoomed view: right) at Re = 5.0 million: mid-board flap, inboard aileron, and midboard aileron

number. Since experimental data is not available for sectional Cp plots, results are presented only for computations. The zero lift drag coefficient (CD0 ) for various aircraft components at different Reynolds numbers are shown in Fig. 9. It is presented in the form of Pie charts so that the major drag generating areas can be easily identified. The Pie charts clear that the wing drag contribution is maximum to the total drag of aircraft, followed by fuselage and engine nacelle. The percentage of zero lift drag increases on a wing and decreases slightly on the fuselage with the increase in Reynolds number. (HT-Horizontal Tail, VT-Vertical Tail, N&SW-Nacelle & Stub-Wing, VF-Ventral Fin).

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Fig. 8 Sectional Cp plot (left), Cp contours along with streamlines (full view: middle, zoomed view: right) at Re = 10.0 million: mid-board flap, inboard aileron, and midboard aileron

4 Conclusion The present CFD study is carried out over a civil transport aircraft for various Reynolds number and it has been observed that the sudden stall pattern remains similar for all the Reynolds number. The maximum lift coefficient increases and the minimum drag coefficient decreases with the increase in Reynolds number. It is also noted that a vortex is observed between the main wing and aileron region which causes a massive flow separation. It is also seen that the strength of vortex over a midboard flap gradually decreases with the increase in Reynolds number. It can be concluded that the stall pattern and corresponding flow characteristics are well captured by current CFD methodology and can be helpful in future design modifications.

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Fig. 9 Contributions of various aircraft components (shown in %) to drag coefficient at α = 0o

Acknowledgements The authors would like to thank Dr. J.S. Mathur, Head and Dr. V. Ramesh Jt. Head, CTFD Division and Director, CSIR-NAL for their kind support. The authors also wish to thank Dr. V.Y. Mudkavi, Head, CSIR-4PI for arranging reservation of nodes on CSIR-4PI ICE HPC facility.

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References 1. Flight Global Flight Fleet, Forecast Executive Summary (2017) 2. Pires O, Munduate X, Ceyhan O, Jacobs M, Snel H (2016) Analysis of high Reynolds numbers effects on a wind turbine airfoil using 2D wind tunnel test data. J Phy. https://doi.org/10.1088/ 1742-6596/753/2/022047 3. Mueller TJ, Batill SM (1982) Experimental studies of separation on a two-dimensional the airfoil at low Reynolds numbers. AIAA J 20(4):457–463 4. Selig MS, Donovan JF, Fraser DB (1989) Airfoils at low speeds. Soartech 8, Soartech Publications, Virginia Beach, Va, USA 5. Brown L, Filippone A (2003) Aerofoil at low speeds with Gurney flaps. Aeronautical J 107(1075):539–546 6. Traub LW, Agarwal G (2008) Aerodynamic characteristics of a gurney/jet flap at low Reynolds numbers. J Aircraft 45(2):424–429 7. CTFD Division, CSIR-NAL (2014) Bangalore, IIT Kanpur: Aerodynamic analysis of dornier 228 aircraft with and without external antennae 8. Shirbhate VS (2012) Reynolds averaged navier-stokes analysis for civil transport air aircraft using structured and unstructured grids. In: Proceedings, 14th annual CFD Symposium, Indian Institute of Science, Bangalore, CP-054 9. Shirbhate VS, Sonil S (2012) Viscous computations for 4 and 5 abreast NCA configuration using HiFUN code: results and discussions. NCAD/AE-02/0001/2012 10. Mathur JS, Dhanalakshmi K, Ramesh V, Chakrabarty SK (2008) Aerodynamic design and analysis of SARAS aircraft. Comput Fluid Dyn J 16(3):320–334 11. ANSYS Fluent https://www.ansys.com/Products/Fluids/ANSYS-Fluent

Prediction of MultiStore Separation from a Fighter Aircraft Using In-House Code—WISe S. Karthik, Jishnu Suresh, P. Karthikeya, S. Rajkumar, Mano Prakash, Sashi Kiran, and D. Narayan

Abstract An efficient and economical in-house code WISe (Weapon Integration and Separation) has been developed to predict the trajectory of stores (1000 lb bomb and 250 kg bomb) released from an Indian fighter aircraft. First the stores are released in isolated mode and validated with a commercial code CFD++ and flight test data. After successful validation, the in-house code is extended to predict the trajectory of 1000 lb bombs when they are mounted on the mid-board and inboard stations on either sides of the Fighter Aircraft. The bombs are released in the following sequence— mid-board (left) followed by mid-board (right) followed by inboard (left) followed by inboard (right). Time interval considered between subsequent releases is 100 ms. A heavy-duty ejector release unit (ERU) has been used for inboard bombs whereas for mid-board bombs a light duty ejector has been used. The histories of store positions, orientation and miss distance are presented.

1 Introduction During operational firing from a fighter aircraft, number of bombs are required to be dropped simultaneously or with minimum time interval between two subsequent releases. Accurately simulating the trajectory of the bombs dropped from the parent aircraft is a challenging task, especially when they are jettisoned simultaneously or within very short interval of time. The problem becomes more complex when their ejection force is not same for all the stations. In the event of multi-store jettison the store separation engineers are to define operational release envelope of the stores by working out safe release sequence and minimum time interval between two subsequent releases. Hence the adopted store separation techniques should be robust in terms of complexity of configuration and range of flight conditions. Also S. Karthik (B) · J. Suresh · P. Karthikeya · S. Rajkumar · M. Prakash · S. Kiran · D. Narayan Aeronautical Development Agency, Bangalore, India e-mail: [email protected] J. Suresh e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. K. Kumar et al. (eds.), Design and Development of Aerospace Vehicles and Propulsion Systems, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9601-8_36

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Fig. 1 Schematic view of bombs

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the technique should be capable of providing accurate results with low turnaround time. In the present study, to predict the trajectory of stores, an in-house code WISe (Weapon Integration and Separation) has been developed. The code works based on decay factorization sheme [2]. Trajectories of two different type of bombs—1000 lb and 250 kg (shown in Fig. 1) released from an Indian fighter aircraft have been predicted using WISe code and validated with a commercial code CFD++ [1] and flight test data. The bombs are released from mid-board station in presence of a fuel tank at inboard station in isolated mode. After successful validation, the in-house methodology is extended to predict the trajectory of 1000 lb bomb when they are mounted on the mid-board and inboard stations on either sides of the Fighter Aircraft. The bombs are released in following sequence—mid-board (left) followed by mid-board (right) followed by inboard (left) followed by inboard (right). Time interval considered between subsequent releases is 100 ms.

2 Methodology Any store trajectory prediction program consists mainly of two distinct modules: (i) an aerodynamic prediction module that computes the forces and moments acting on the store and (ii) a 6-DOF time integration module that generates the trajectory of a store using the forces and moments acting on the store and its inertial properties, such as mass and moments of inertia. During the trajectory prediction process the aerodynamic forces and moments may be generated from wind tunnel tests or through CFD approaches.

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2.1 In-House Code—WISe The WISe code computes store aerodynamic forces and moments using two basic sets of aerodynamic data—(i) carriage loads when the stores are attached to the aircraft (ii) free-stream data base as a function of attitudes. The variation of store aerodynamic load from installed to the freestream is described by a decay-function which is assumed to be dependent on store’s vertical displacement. A linear decay function [2] is used to compute the store aerodynamic coefficients from carriage flight to its free-stream value when it is away from the carriage location. The decay function is defined as follows:     Z (t) (1) d_fact = max 0, 1 − (abs D ∗ R1 where D = diameter of store. R1 = constant. Z = vertical distance of store w.r.t. aircraft which is function of time (t). This decay factorization system has to be tuned by matching with flight tests results. The tuned and approved mathematical model then can be used to define the safe separation envelope. In the present study, the required data base is generated using a CFD approach. A Cartesian grid based Euler code—PARAS [3] is used to generate the required installed load and free-stream data base. The viscous crossflow terms are calculated based on empirical relation given by Jorgensen [4] and added to the inviscid aerodynamic coefficients. The code can also compute store dynamic derivatives from store sectional loads2 and added to the above aerodynamic coefficients. This store aerodynamic prediction module is integrated with 6-DOF module. The store force and moment data apart from other parameters are fed into the 6-DOF module to predict the store’s new location and orientation.

2.2 Commercial Code—CFD++ In CFD++ the flow field over the parent aircraft and stores are simulated using unsteady RANS calculation. Flow is assumed to be turbulent, the effects of which are computed in terms of eddy viscosity using Spalart-Allmaras model. The computational domains are discretized with unstructured hybrid grids using Ansys ICEM CFD [5]. The grids comprise of prism cells in near wall zones and tetrahedrons in the remaining flow domains. The first layer height is fixed to be 0.0012 mm in grid over the bomb as well as in the aircraft grid. The bomb grid was constructed with a smaller domain and is merged with the background aircraft grid to form a single set after concatenation of the overlapping grids using the overset mesh technique in CFD++. The near wall resolution in grids resulted in average first layer y+