Recent Advances in Mechanical Engineering: Select Proceedings of ERCAM 2021 (Lecture Notes in Mechanical Engineering) 9811913870, 9789811913877

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Lecture Notes in Mechanical Engineering

S. Narendranth P. G. Mukunda U. K. Saha   Editors

Recent Advances in Mechanical Engineering Select Proceedings of ERCAM 2021

Lecture Notes in Mechanical Engineering Series Editors Francisco Cavas-Martínez , Departamento de Estructuras, Construcción y Expresión Gráfica Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesca di Mare, Institute of Energy Technology, Ruhr-Universität Bochum, Bochum, Nordrhein-Westfalen, Germany Francesco Gherardini , Dipartimento di Ingegneria “Enzo Ferrari”, 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, Machines 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

Lecture Notes in Mechanical Engineering (LNME) publishes the latest developments in Mechanical Engineering—quickly, informally and with high quality. Original research reported in proceedings and post-proceedings represents the core of LNME. Volumes published in LNME embrace all aspects, subfields and new challenges of mechanical engineering. Topics in the series include: • • • • • • • • • • • • • • • • •

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S. Narendranth · P. G. Mukunda · U. K. Saha Editors

Recent Advances in Mechanical Engineering Select Proceedings of ERCAM 2021

Editors S. Narendranth Department of Mechanical Engineering National Institute of Technology Karnataka (NITK) Surathkal, Karnataka, India

P. G. Mukunda Department of Mechanical Engineering Nitte Meenakshi Institute of Technology Bengaluru, Karnataka, India

U. K. Saha Department of Mechanical Engineering Indian Institute of Technology Guwahati, India

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-981-19-1387-7 ISBN 978-981-19-1388-4 (eBook) https://doi.org/10.1007/978-981-19-1388-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed 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

Preface

Multidisciplinary Emerging Research has become critical in the creation of a wide range of materials, technical processes, and systems in today’s world. Civil, aeronautical, and mechanical engineering have long been recognised as important contributors to the country’s economy and societal development. Advanced Materials, Mechanics of Engineering Components, Engineering Structures and Systems, and other disciplines are attracting the attention of researchers all around the world in the development of a wide range of engineering technologies. The International Conference, ERCAM-2021, is intended to bring together experts and practitioners from various industries, R&D institutes, and academicians from around the world, providing a forum for knowledge exchange on Emerging Research and Recent Trends in Major Sectors of Materials, Processes, and Systems pertaining to Civil, Aeronautical, and Mechanical Engineering with a focus on Civil, Aeronautical, and Mechanical Engineering. The ERCAM-2021 International Conference aims to bring together experts and practitioners from various industries, R&D institutes, and academicians from around the world, providing a forum for knowledge exchange on Emerging Research and recent trends in major sectors of materials, processes, and systems pertaining to Civil, Aeronautical, and Mechanical Engineering with multi-disciplinary approaches. The Third International Conference ERCAM-2021 focuses on a variety of topics including Materials, Mechanics, Structures, Systems, and Sustainability, and topics of interest for research paper submissions encompass all these disciplines but are not limited to them. Leading academicians, scientists, researchers, and industry experts in the disciplines of interest will attend the conference from all over the world. University Putra Malaysia, Gazi University, and North Dakota State University are all active participants in ERCAM-2021. This conference was a huge success in terms of offering a strong platform for scholars from all over the world to exchange their knowledge, experiences, and various aspects of growing technologies in Civil, Aeronautical, and Mechanical Engineering. The proceedings cover a wide range of issues that are relevant to industry’s current demands. An experienced technical review committee comprised of professionals in the field from all over the world thoroughly assessed all of the papers submitted for the ERCAM-2021 conference on all aspects of emphasis areas. We’d v

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like to convey our gratitude to the authors for amending their articles in response to the reviewers’ comments and suggestions. We owe a huge debt of gratitude to all the organisers and members of the Program Committee for their tireless efforts in ensuring that the proceedings were of the highest possible quality. The management and faculty of NMIT, as well as the Advisory Committee, have provided invaluable counsel and assistance. We appreciate the support of all of our sponsors. Despite numerous hurdles, we are grateful for the cooperation of various colleagues from academia and industry who offered to assess papers and deliver plenary talks. The ERCAM-2021 proceedings are collected in a single volume. We anticipate that the ERCAM-2021 proceedings will serve as a valuable intellectual resource for academics in Civil, Aeronautical, and Mechanical Engineering, pushing these disciplines forward and facilitating improved collaboration and sharing of ideas. Surathkal, India Bengaluru, India Guwahati, India

S. Narendranth P. G. Mukunda U. K. Saha

Contents

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Preliminary Design Approach for Sub-Scale Rocket Motor Thrust Stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harshit Shukla, Umang Jain, and Deepak Kumar Numerical Investigation of the Effect of Liquid Temperature on Supercavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ramanakanthan Rajkumar, Kumar Gaurav, Ashish Karn, Vipin Kumar, and Harshit Shukla Smoke-Based Visualization of Jet Flow from a Cruciform Nozzle of Unit Aspect Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Rajesh Kumar, Kaavya Ramachandran, and B. T. Kannan Aerodynamic Design and Numerical Analysis of Bi-cambered Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sashant Kapoor, Vipin Kumar, Harshit Shukla, Kumar Gaurav, and Dalbir Singh A Qualitative Comparison of the Effect of Exit Ramps and Coaxial Subsonic Jet on Primary Supersonic Jet . . . . . . . . . . . . . P. Sivakumar, R. Suthan, and B. T. N. Sridhar DSC and TGA Investigation on Ammonium Nitrate-Based Solid Propellant Doped with Ammonium Dichromate for Gas Generator Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. Suthan, P. Sivakumar, S. Ganesan, and B. T. N. Sridhar Experimental Investigation of Thin-Walled Multi-Cell GFRP Structure on Energy Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Sridhar, V. Praveen Kumar, Gokul Haricharan, V. Dilip, V. Amin Himamshu, and R. Suthan

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Study of Regression Rate in Hybrid Rockets Using Vortex Injector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. K. Dash and G. Ram Vishal

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Designing of a Long-Range Autonomous Multirotor on a Custom-Built Carbon Fiber Frame . . . . . . . . . . . . . . . . . . . . . . . . . Prashant Manvi, P. K. Siddalingappa, and Santosh Hosur

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10 Abrasive Wear Behaviour of Camphor Soot Filled Coir/Palmyra Fibre Reinforced Nylon Composites . . . . . . . . . . . . . . . T. Raghavendra and K. Panneerselvam

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11 Impact of Viscosity and Heat Source Variance on the Onset Convection in a Fluid Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 S. Kiran, Y. H. Gangadharaiah, and H. Nagarathnamma 12 Design and Analysis of Longitudinal Butt Joints Using an Excel/VBA Computational Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Raghav Agarwal, Priyanshu Dwivedi, Rohit Mahawar, and Ashish Karn 13 Effective Computational Tools for Teaching and Learning of Heat Transfer Through Extended Surfaces . . . . . . . . . . . . . . . . . . . . 131 Ayush Dwivedi, Gorakh Sawant, Ayush Vyas, and Ashish Karn 14 Optimization of Tribological Properties of Microparticulate-Reinforced ZA-27 Composites . . . . . . . . . . . . . . . 141 G. R. Gurunagendra, B. R. Raju, C. Ravi Keerthi, Vijayakumar Pujar, D. P. Girish, and H. S. Siddesha 15 Study of Characterization, Mechanical Properties, and Tribological Behavior of Magnesium-Silver Alloy . . . . . . . . . . . . 157 Pradeep V. Badiger, M. Vinyas, T. Ram Prabhu, N. V. Naveen Kumar, Nikhil B. Nargund, and P. K. Ramesh Gouda 16 Peristaltic Flow and Heat Transfer Through a Prandtl Fluid in Vertical Annulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Indira Ramarao, Priyanka N. Basavaraju, and Jagadeesha Seethappa 17 Effect of Variable Diffusivity on Solute Transfer with Reference to Stent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Jagadeesha Seethappa, Indira Ramarao, and Madhura Keshavamurthy 18 Prediction of Thermal Conductivity for Al6061 Reinforced with Silicon Carbide and Graphite Using Statistical Approach . . . . . 201 S. Vijay Kumar, M. Girish Prasad, S. Basavaraj, L. Avinash, B. A. Praveen, Shiv Prathap Singh Yadav, K. R. Varadaraj, and Arpith Chacko

About the Editors

Dr. S. Narendranth is working as a Professor in the Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal since November 1995. He has 25 years of academic experience and 1 year of experience in the industry. He completed his Bachelors in Mechanical Engineering from Govt. BDT College of Engineering Davanagere, Karnataka, India; MTech (PEST) from university BDT College of Engineering Davanagere, Karnataka and PhD (Materials) from IIT Kharagpur, West Bengal, India. His areas of interests are advanced manufacturing and technology, non-traditional machining of advanced materials, severe plastic deformation, shape memory alloy, and welding technology. He has more than 150 publications in peer-reviewed journals and conferences. He is a member of a number of professional bodies such as Indian Society of Technical Education (ISTE), Metrology Society of India (MSI), the Institution of Engineers (IE) and the Indian Institute of Metals (IIM). He has successfully guided 17 PhDs and 4 more are in the process of completion. Also, 29 MTech students and 26 engineering students have successfully completed their projects under his guidance. Two copyrights have been granted under his name such as “Flipping Type-ECAP Die” and “Slant type taper fixture-WEDM”. He has completed a number of administrative roles such as heading the Department of Mechanical Engg, NITK Surathkal, Professor in-charge for Hostel affairs, Finance warden, Secretary DRPC and to name a few. The funded projects handled under him were “Investigation of machining characteristic of NiTi based shape memory alloys using WEDM” and “Study the corrosion behaviour of Wrought Mg Alloys processed by Severe Plastic Deformation for Naval Applications”. Dr. P. G. Mukunda is working as a Professor in the Department of Mechanical Engineering, NITTE Meenakshi Institute of Technology, Bangalore since 2005. He is a former Retd. Professor of IIT Kharagpur. He has a vast teaching/research experience of more than 40 years in the Department of Metallurgy and Materials Engineering, IIT Kharagpur. He obtained his BSc (Hons) in Chemistry from Mysore University, DIISc (Metallurgy) from Indian Institute of Science, Bangalore and MTech and PhD (Powder Metallurgy) from IIT Kharagpur. Dr. P. G. Mukunda has published more than 100 papers in peer-reviewed journals and conferences and has won several merit ix

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prizes and awards for the achievement of academic excellence in the university. He is a recipient of “Kamani gold medal” for the best research paper. He has worked as a Guest Professor at the University of Germany, Karlsruhe during 1974–1975 under Professor Tumbler in the area of Metallurgical Engineering. Dr. P. G. Mukunda has an expertise in the areas of Metal Matrix Composites, solidification, metallurgical engineering, advanced materials, heat treatment, powders and materials’ processing. His thrust areas in research include investigation on sintering behaviour of copper-tin and iron-graphite antifriction materials, studying the mechanism of structure formation in the alloying copper-tin and iron-graphite during sintering, sintering of silicon carbide powders, polytypes in SiC, production of SiC from rice husks, machinability and tribological properties of aluminium-silicon, modelling of centrifugal casting. Dr. U. K. Saha is working as a professor in the Department of Mechanical Engineering at IIT Guwahati since 2012. He worked at NERIST, Silchar as an assistant professor before joining IIT Guwahati. He completed his PhD in Aerospace Engineering from IIT Bombay; postgraduation in space engineering and rocketry; and bachelors in aerospace engineering. He has an abundance of experience in the field of turbomachinery, propulsion, wind energy conversion, and internal combustion engines. As a dedicated faculty of mechanical engineering in IIT Guwahati, he contributed sizable number of research and publications in field of aerospace and mechanical engineering. He has 82 journal articles, 3 chapters in book, 56 conference proceedings, 5 review articles, and 1 letter. He has 820 citations in 2020 and this year he reached to 348 citations till date. He has both academic and research excellency. He has carried out sizable numbers of funded research and presently he is working on three research projects. A number of students from graduate, postgraduate, and doctoral thesis have completed under his guidance in IIT Guwahati and NIT Silchar. Not only research but he also contributed significantly to academic improvements. Majority of his published papers are in peer-reviewed Scopus indexed and SCIE journals. Most of his journal papers are also indexed in Google Scholar and Microsoft Academic Research.

Chapter 1

Preliminary Design Approach for Sub-Scale Rocket Motor Thrust Stand Harshit Shukla, Umang Jain, and Deepak Kumar

Nomenclature SRM HRM LRM AMFS CC HTPB CF k Pc Pe Pa Ae At Ac Mt ve g R Dc Dt

Solid rocket motor Hybrid rocket motor Liquid rocket motor Axial force measurement system Combustion chamber Hydroxyl-terminated polybutadiene Thrust coefficient Specific heat ratio Combustion chamber pressure, kPa Nozzle exit pressure, kPa Atmospheric pressure, kPa Nozzle exit area, m2 Throat area, m2 Chamber cross-section area, m2 Mach at the throat Exit velocity, m/sec Gravitational constant m/sec2 Universal gas constant, 8314 J/kg. K Chamber diameter, cm Diameter of throat, cm

H. Shukla (B) · D. Kumar Department of Aerospace Engineering, University of Petroleum and Energy Studies, Dehradun 248007, Uttarakhand, India U. Jain Department of Space Engineering and Rocketry, Birla Institute of Technology, Ranchi 835215, Jharkhand, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_1

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De Dp a Tc ρ M lcone L Lc

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Nozzle exit diameter, cm Port diameter, cm Speed of sound, m/sec Chamber temperature, K Density of propellant, g/cm2 Molecular weight of propellant, gm Length of the diverging section, cm Length of propellant grain, cm Length of the combustion chamber, cm

Introduction While designing a rocket engine it’s better to know the performance characteristics such as specific impulse, net thrust, nozzle discharge coefficient, pressure v/s time, specific fuel consumption, etc. which varies with the selected fuel/oxidizer combination. To evaluate these performances a system is required which is generally known as thrust stand. Thrust stand is of great importance in the field of Professional engineering and Amateur Rocketry. With the advancement in technology the frequency of space missions in the last decade has gone high and cost become an important criterion for the mission. More Research and development are required to meet the needs of the mission nowadays. Thrust stand helps to cut the development time and cost. As we know it is very important to test the engine of rockets because of its complexity. Engine is very destructive so full power testing is necessary. Here thrust stand comes into picture which helps in knowing the performance characteristics at the designing stage of engine. In the recent research [1, 2] presented a scale force measurement system made to measure the side forces with a 2-axis component. In his study the overall thrust is measured using an on-axis load cell and found that thrust stand was very helpful in evaluating the performances at the design stage. So here our objective to design a thrust stand to evaluate the performances like net thrust, specific impulse, specific fuel consumption, etc.

Methods to Test the Thrust The thrust stand differs mainly in size and type of rocket motor to be used. Usually, the chemical rocket is categorized into three types based upon their propellant phase, i.e., Solid Rocket Motor, Hybrid Rocket Motor, and Liquid Rocket Motor. Liquid rocket motor requires much more safety and instrumentation, as compared to SRM and HRM because of additional piping for the flow of O/F with control over flow rate and ignition system additionally great care, should be taken for storage of the Oxidizer and Fuel. Working with SRM and HRM is easy as compared to LRM. The

1 Preliminary Design Approach for Sub-Scale Rocket …

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test stand structure for both remains the same only some piping and valve are required for HRM which are attached to the motor only for the reason that the oxidizer is in the gaseous or liquid phase without influencing the stand. Details about SRM and HRM can be found later in the report. The main function of the thrust stand is to hold the motor while measuring forces to define the thrust vector. With various force measurement systems available to determine thrust namely scale force measurement, momentum balance, and calculations using nozzle coefficient or component stacking method [3]. In the scale force measurement system, the rocket motor is attached to the frame, it becomes a complete free body and the summation of the forces acting on the free body provides the gross thrust and the engine net thrust. The momentum balance method measures the internal forces generated by the working fluid as it exits the engine to determine the gross thrust and engine net thrust. The component performance stacking method solely depends upon the computational method and accounts for mass, momentum, and energy of working fluid as it passes through each section of the test article. Choosing a particular thrust measurement system strongly depends upon several factors: (1)

(2)

(3)

Shape and size of the engine: The size of the rocket engine can vary according to the requirement and test to be performed. Our study is based upon a small rocket engine test with a range of up to 200 N. This range can easily be calculated with a scale force measurement system. Measurement Uncertainty: All the component error and system error when taken into consideration gives an uncertainty in a result that should be as minimum as possible. Since our system is not that big-scale force measurement is effective in delivering results. Limitation of the program: This factor includes the funds and test time available to design and develops an accurate system.

Predominantly, the momentum balance and component performance methods are used in an air-breathing engine (Figs. 1.1, 1.2, and 1.3).

Fig. 1.1 Component performance stacking method

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Fig. 1.2 Scale force measurement system

Fig. 1.3 Momentum Balance method

Solid Rocket Motor Solid rocket motor uses oxidizer and fuel in solid form. Generally classified based on usage, i.e., large booster second stage motors, High altitude motors, Tactical missiles, Ballistic missile defense, and Gas generator. All these classifications are based upon propellant characteristics, applications, and motor design. Solid propellant being highly dense requires a small volume motor that why it is preferred mostly for booster stage (first stage) in various launches. SRM is simple, safe, reproducible, low-cost, and low-hazard manufacturing. Having a disadvantage of once ignited can’t be stopped. SRM uses a solid O/F mixture that is packed into the motor having a hole in the middle throughout the length of the motor which acts as a combustion chamber. The igniter is placed inside the motor at the head end to ensure uniform burning on the whole surface. The pressure inside the combustion chamber is directly proportional to the burning surface area. Different grain configuration gives different pressure vs. time graph which is the main parameter that can be easily calculated through thrust stand.

Test Bed Type Our system is based on the scale force measurement system that uses the axial direction to determine thrust. It is an elementary system in terms of designing, manufacturing, maintenance, and delivers a satisfactory result. Since a free body has 6 degrees of freedom with different forces and moment generating on motor because of self-weight, inertial forces, and dynamic environment. The basic principle of the Axial (scale) force measurement system is to restrain the rocket motor from the other

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two directions. So, that thrust vector will not deviate from the geometric axis of the motor. In this way, the measurement of side force is not required and the complexity of the system reduces. Also, AMFS is further divided into on-axis and off-axis. This division is based upon the location of the load cell [4]. When load cell is attached on the axis of the rocket motor central line as shown in Fig. 1.4 is known as on-axis configuration. The Off-axis configuration has a load cell placed out of the line but parallels to the centerline axis as shown in Fig. 1.5. We have used a scale force measurement system that measures the force in the axial direction with an off-axis configuration. The one advantage of off-axis configuration is that the engine can easily be removed and replaced without disturbing the stand. On-axis is preferred for large rocket motors. Fig. 1.4 On-axis

Fig. 1.5 Off-axis

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Components in a Thrust Stand This section of the thrust stand focuses on instruments and components used to evaluate the desired parameter from the rocket motor. Since we aim to get the measurement data as accurate as possible, this depends entirely upon the quality of the data acquired. Proper alignment and use of components reflect the satisfactory result. (a)

(b)

(c)

(d)

Load cell: It works on the principle of conversion of energy from one form to another. With various types of load cells available in the market like Strain gauge, pneumatic, hydraulic, and others. The strain gauge is ideal in all 3types as it is highly accurate, versatile, and cost-effective. It consists of very fine wires or foil set up in a grid form called strain gauge which on compression or tension generates a change in electrical resistance to produce the value of load applied. It is very sensitive and can account for minute change as well. It is further divided into several other types for specific applications, i.e., Bending beam, pancake, single point shear beam load cell, double-ended shear beam, canister load cell, S-type load cell, etc. For our design, S-type and canister type are best suited since the motor bed is generating a compressive force. Pressure sensor: It is a device that senses the pressure of liquid or gas by the forced fluid generated on the sensor. It also converts one form of energy to others. A thin flexible film called the diaphragm inside the sensor allows the pressure effect is generated due to the moving fluid to pass through it but not the fluid. The effect generates an electrical signal in terms of voltage and then converted to force per unit area which is pressure. This sensor is attached to the combustion chamber boundary to read the correct pressure inside CC. Silicone gel is poured inside the sensor to resist the diaphragm from hot gases. Thermocouple: It is used to measure the temperature. It is made up of two wires with different metals and welded together to form a junction on the other side leaving one end with two wires. When a change in temperature occurs, it creates a voltage which then resolves to measure the temperature this effect is also called a thermoelectric effect. In our design, it will be placed just outside the nozzle to measure exit gas temperature. Indicator system: It is used to collect all the values from different hardware equipment and convert them to the digital numeric value that can be manipulated by a computer.

Stand Design The thrust stand is exorbitant and can take as long as a while to configuration, create, introduce, and confirm for testing. With all the data available on the internet it has been found that sub-scale stand for educational and experimental purpose is not complex and almost have the same structure. Our design in Fig. 1.6 is easy and stable for experimental work. The motor bed (1) as shown is where the rocket motor

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Fig. 1.6 Thrust stand design

will be placed and set for test firing. The L-shape is the stand base (2) is attached to the ground using the secure brackets (4). Triangular support (5) is used to give ancillary to both the pieces of the L-shape. Spring steel (3) being flexible is responsible for the movement of the motor bed but possesses enough elasticity to come back in its original shape. Rivets are used to attach the spring steel to the motor bed and stand base. The firing of the motor makes the motor bed move forward toward (7) where the load is placed and this axial movement deflection is sensed by a load cell and an output is generated in the form of force. The thrust stand design is composed of three units: Base stand, motor bed, spring steel support. Base stand: Two hollow rectangular metallic bars are welded in an ‘L’ configuration to form the base of the test bed. Two triangular metallic plates are attached at the joint to provide support and strength to the joint. And the material used for both these, base bar and triangular support is ‘Mild Steel’. Rivet is used to fix the base to ground, which restrains any linear moment of the base stand. The securing brackets are made of cast iron. Both mild steel and cast iron have high resistance to breakage. Motor bed: High strength to weight ratio and ease of fabrication are two important parameters considered while choosing the material. The motor bed is manufactured using a stainless/mild steel rectangular bar. Spring steel support: Spring steel is a flexible material having high resistance to deformation and high yield strength. Spring steel support provides the required deflection needed for the thrust measurement. It is attached to the base stand and motor bed via ‘L’ brackets, which are riveted to give better support.

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Harshit et al. [5] has presented a study on MEMS Pyrotechnic Thruster for Micro Propulsion Applications and has shown how important the thrust stand is during the development of these kinds of applications.

Structural Analysis Structural analysis is key to test the design as it evaluates whether a specific structural design will be able to withstand external and internal stresses and forces. The structural analysis helps to determine the cause of structural failure before manufacturing the entire system. The main components on which the accuracy and reliability of the thrust stand depend are the vertical thin column that supports the motor bed and moves horizontally by exhaust gas velocity. The material of the vertical rods must be flexible enough to sustain the forward thrust, weight of the rocket motor, maintain ease in calibration for load cell, and come back to its original shape. High carbon steel columns are best for this purpose. The materials selected for the vertical column are Spring Steel, Austenite. Austenitic steel is non-magnetic stainless steel that contains high levels of chromium and nickel and low carbon. Known for its formability and resistance to corrosion, austenitic steel is the most widely used grade of stainless steel. Spring steel is also high carbon steel used widely in the manufacturing of spring due to its property of coming back to its original shape and size after getting deformed. Considering the cad model shown in Fig. 1.6 L-shape bar is fixed on the ground, vertical support column lower end and the upper end is fixed on L-shape bar and motor bed, respectively, making it movable in only one direction. The thrust of 150 N in form of the load is applied in the negative X-axis direction with the motor weight of 30 N is applied in the negative Y-axis direction to get the deformation and stress in the vertical support column. For Austenitic The above Fig. 1.7 shows the analysis results of Austenitic steel. The blue region is a safe region or region with minimum/least deformation, while the red region demonstrates the higher risk areas (Figs. 1.8 and 1.9). The graphs show the variation of deformation with different thrust force and variation of maximum stress developed in the column with the different thrust force. The Deformation and stress curve obtained in Austenite material is linear with the thrust. Selecting a reference point on the graph will lead to a better picture of deformation. At 150 N of thrust, deformation is 0.145 mm. This deflection is very small so required a sensitive load cell to measure it accurately. For Spring Steel The above Fig. 1.10 shows the analysis results of Spring steel. The blue region is a safe region or region with minimum/least deformation, while the red region demonstrates the higher risk areas (Figs. 1.11 and 1.12).

1 Preliminary Design Approach for Sub-Scale Rocket …

Fig. 1.7 Static structural analysis of austenitic steel

Fig. 1.8 Deformation versus thrust curve for austenitic steel

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Fig. 1.9 Max. stress versus thrust curve for austenitic steel

Fig. 1.10 Static structural analysis of spring steel

Similarly, the above graphs are obtained for spring steel. The deformation curve obtained in spring steel material is also linear with the thrust. At 150 N of thrust, the deformation obtained is 110 mm. This deformation value is very large as compared to austenite. From these two it’s not quite clear which material to be used for the column. So, in view to select a suitable material an alternative option is considered which is the availability and sensitive load cell. For example, for highly sensitive load

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Fig. 1.11 Deformation versus thrust curve for spring steel

Fig. 1.12 Max. stress versus thrust curve for spring steel

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12 Table 1.1 Pre-required quantities

H. Shukla et al. Ammonium perchlorate

70%

HTBP/curative

15%

Aluminum

15%

Propellant density

1.7256 g/cm2

Propellant mass

250 g

Combustion temperature  k = C p Cv

3170 K

Molecular weight of the mixture

25.038 gm

Desired thrust

1000 N

1.1834

Chamber pressure

5000 kPa

Chamber temperature

3154.992 K

Exit pressure

101,325 Pa

cell, even a slight deflection of the column can give appropriate readings, which means even austenitic steel is a good option. On the other hand, for load cells having lower sensitivity one may have to use spring steel due to its higher deflection to get appropriate readings. Again, load cell sensitivity depends upon its quality, the costlier the load cell better the sensitivity (Table 1.1).

Rocket Motor Design A Rocket motor is made up of two parts: A combustion chamber and nozzle. Designing a motor appropriately is not an easy task as it varies with the type of propellant used based on the propellant combustion temperature chamber material is selected. Propellant chemical characteristics such as combined density, combustion temperature, specific heat ratio, desired thrust, the molecular weight of the mixture, chamber pressure, etc. must be known before carrying out the calculation of the motor. For the calculation the propellant selected is based on Ammonium perchlorate with Ammonium perchlorate (70%), HTPB (15%), Aluminum (15%). The combustion chamber pressure is taken 725psi with optimum expansion (exit pressure equals to ambient pressure). All these values with the calculation are shown below. Before going for calculation several assumptions are made to simplify the calculation maximum efficiency.

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13

Calculation The below-mentioned ideal conditions are considered during the following design calculation [6] (1) (2) (3) (4) (5) (6)

Complete combustion of the propellant. Perfect gas law is obeyed. Adiabatic flow and combustion in nozzle and chamber. No shocks and discontinuity in the expansion process. One-dimensional and non-rotational flow through the nozzle. Burning is normal to the surface of the propellant.

Step 1: Finding the thrust coefficient.        k−1  2k 2  2  k+1 k−1 Pe k Pe − Pa Ae  CF = 1− + k−1 k+1 Pc Pc At

(1.1)

The highlighted part of the equation adds very little and can be neglected. Now, Pe = 101325 Pa Pc = 5000 k Pa     0.1834   2(1.1834)2  2  2.1834 0.1834 1.1834 101325 1− = 1.56 CF =  0.1834 2.1834 5000000

(1.2)

Step 2: Fixing the area ratio of the chamber to the throat. Ac =9 At

(1.3)

Step 3: Finding cross-sectional area of the throat (At ). CF = At =

F Pc At

F 1000 = 0.000128116 m 2 = C F Pc 1.56 × 5000000

Diameter of the throat,

(1.4)

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Dt =

4 At = π



4 × 0.000128116 = 1.277 cm 3.14

(1.5)

Step 4: Cross-sectional area of the combustion chamber. Using the area ratio, Ac = 9At = 9 × 0.000128116 = 0.001153044 m 2

Dc =

4 Ac = π



4 × 0.001153044 = 3.8355 cm 3.14

(1.6)

Step 5: Exit velocity      k−1  2k Pe k  ve = RTc 1 − k−1 Pc

=

(1.7)

2 × 1.1834 8134 × × 3154.99 × 0.45 = 2478.03 m/s 0.1834 25

Step 6: Speed of sound a=

√

k RT =

1.1834 ×

8314 × 3154.99 = 1114.29 m/s 25

(1.8)

ve = 2.223 a

(1.9)

Step 7: Mach at exit Me =

Step 8: Nozzle exit area expansion ratio. At = Ae  =

2.1834 2



1   0.1834

k+1 2

1   k−1

  1k      k−1 k Pe  k + 1 P e  1− Pc k−1 Pc

(1.10)

  1   1.1834  0.1834   2.1834  1.1834 101325 101325  = 0.1390 1− 500000 0.1834 500000 Ae = 7.193 At

1 Preliminary Design Approach for Sub-Scale Rocket …

15

Ae = 7.193 × 0.000128166 = 0.000921555 m 2 Step 9: Exit diameter

De =

4 Ae = 3.426 cm π

(1.11)

Step 10: Length of the diverging section. Half angle, α = 15o , of diverging section. l cone =

r2 − r t tan α

(1.12)

r 2 = r e = Rad i us o f nozzl e exi t r t = Rad i us o f nozzl e t hr oat l cone

  1 3.426 − 1.277 = 4 cm = 2 tan 15

The converging section half-angle is 30°. The length of the converging section can easily be obtained from the CAD model by setting the throat and diverging diameter with a half-angle. Step 11: Finding chamber length and chamber volume. Mass of propellant = 250 g. Density of propellant = 1.7256 g\cm3 . Volume of propellant = M/V = 144.877 cm3 . Since the propellant grain is tubular, the port diameter (D p ) should be calculated accordingly. Port diameter should be at least 1.6 times the throat diameter, V =

π 2 Dc − D 2p L 4

(1.13)

144.877 × 4  = 3.8352 − 22 L 3.14 Pr opellantgrainlength = L = 17.2 cm +2 cm can be added to make the head end cap fit properly. Therefore, the total length of the combustion chamber (Lc ) is approx. = 19cm (Figs. 1.13 and 1.14).

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Fig. 1.13 2D representation of chamber

Fig. 1.14 2D representation of nozzle

Kumar et al. [7] has shown the study on impact of fluidic injection angle on thrust vectoring using CFD analysis and presented how shock vectoring is a major option of thrust vector control and presented a CFD study using convergent-divergent nozzle.

Conclusion The design of the sub-scale thrust stand for solid rocket motor is sophisticated with the fulfillment of greater accuracy for the measurement of the forces acting on a rocket motor. Various factors are responsible to design a thrust stand considering the application of the rocket motor, transmitting signals in fractions of time from load cell to transducer, and ease of fabrication. Different thrust losses are also recognized while performing analysis and by practically firing the rocket motor. The natural frequency must be smaller in small components of thrust stand which means smaller deflection under thrust will occur. Considering the thrust loss, all the potential tare of the forces must be identified and understood for data correction. Calibrations are done frequently for the satisfactory operations of the thrust stand. Design criteria are extremely important and the weight of the components must be given for the

1 Preliminary Design Approach for Sub-Scale Rocket …

17

ease of calibration. Economic factors must be kept in mind before manufacturing the thrust stand as to attain the best accuracy of thrust stand, alloy material and certified electronic components with less tolerance value must be selected. Talking about the motor design an ideal approach is selected to simplify the calculation and get the best result out of it. With some rule of thumb approach in amateur rocketry had been made in last 3–4 decades through a number of testing and experimental data collected which give a very satisfactory result [8]. Some rules of thumb: (1) (2) (3) (4)

The area ratio of the combustion chamber to the throat section should be 9. The angle of the converging section and diverging section should be 30 degrees and 15 degrees, respectively. The cross-sectional area of the nozzle exit should be 7–8 times the crosssectional area of the throat. If the propellant grain is tubular (hollow cylindrical) in shape, then the port diameter (inside diameter of grain) should be 1.6 times the throat diameter. This point is important as the burning surface area decides the mass flow rate of the propellant.

Pressure in the combustion chamber decides the throat area cross-section which again depends upon the propellant selected. Calculating all the required parameters for various propellants is a laborious task, to avoid this an excel sheet can be made to save time. In addition to SRM, this stand also serves the same for the HRM only difference in HRM and the solid motor is the additional pipeline of oxidizer. This sub-scale thrust stand setup is best for educational purposes for introducing the students to the concepts of the rocket motor and propulsion system at the college level[9].

References 1. Rezende RN, Alves LR, Mishra A, Shukla H Varshney H, Dhawan H, Kapoor S, Jain U, Mendonsa R (2021) AIAA propulsion and energy 2021 forum 2. Jain U, Shukla H, Kapoor S, Pandey A, Nirwal H (2020) Design and analysis of 2-axis rocket motor stand for thrust vectoring. In: AIAA propulsion and energy 2020 forum 3. Smith R, Wehofer S (1982) Measurement of engine thrust altitude ground test facilities. In: 12th Aerodynamics testing conference. https://doi.org/10.2514/6.1982-572 4. Runyan R Jr, Rynd J, Seely J (1992) Thrust Stand Design Principles. In 17th Aerospace ground testing conference. https://doi.org/10.2514/6.1992-3976 5. Shukla H, Nandan GRS, Shukla P, Kumar V, Varma M (2017) Ignition and combustion characteristics of a micro-electromechanical system (MEMS) pyrotechnic thruster for micro propulsion applications. Int J Energet Mater Chem Propuls 16(2) 6. Rocket manual for amateurs—By Capt. Bertrand R. Brinley (Ballantine Books—1960) 385s 7. Kumar V, Shukla H, Yadav R, Kumar G (2021) Fluidic injection angle impact on thrust vectoring using computational fluid dynamics analysis. Int J Fluid Mech Res 48(3):41–53 8. http://www.nakka-rocketry.net/th_prope.html 9. Sutton GP, Biblarz O (1949) Rocket propulsion element. Wiley, Hoboken (N.Y.).

Chapter 2

Numerical Investigation of the Effect of Liquid Temperature on Supercavitation Ramanakanthan Rajkumar, Kumar Gaurav, Ashish Karn, Vipin Kumar, and Harshit Shukla

Nomenclature Dmax dc L/2 Pv P∞ U∞ Cc , Cv pv p T

Maximum diameter of the supercavity Diameter of the cavitator Half-length of the supercavity Vapor pressure Freestream static pressure Freestream velocity Coefficients for cavitation model Vapor pressure of the liquid Static pressure of the liquid Static temperature of the liquid

Greek Letters σ ρ σ∞

Cavitation number Density of the liquid Unbounded cavitation number

R. Rajkumar · K. Gaurav (B) · V. Kumar · H. Shukla Department of Aerospace Engineering, University of Petroleum and Energy Studies, Dehradun, India A. Karn Department of Mechanical Engineering, University of Petroleum and Energy Studies, Dehradun, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_2

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Introduction Supercavitation is the process where the cavity formed underwater is large enough to envelop the whole surface of the body. Supercavitation may be broadly divided into two major categories, i.e., natural and ventilated supercavitation [2]. Natural supercavitation forms due to the generation of water vapor due to high velocity, whereas artificial cavitation forms due to injection of non-condensable gas through the cavitators [4]. In the case of natural supercavitation, high velocity results in the decrease of static pressure on the cavitators surface. When the static pressure becomes equals to the vapor pressure of water, then the water starts to change its phase to gas which results in the production of water vapor [7]. Natural supercavitation has been employed in various practical applications such as torpedoes, underwater transport, wastewater treatment, and desalination [9]. In the desalination process, the rate of production depends largely on the amount of steam generation and hence the supercavity size [5]. Various research has been conducted on supercavitation size enhancement in the past [10]. The cavitators shape plays a crucial role in the supercavity geometry, a cone cavitators can form the supercavity at much lower velocity but forms a smaller cavity as compared to disk cavitators [3]. Cavitator shape can be optimized to achieve a balance between the supercavity size and drag can be experienced by the cavitator [1]. The mounting strut also plays a role in the supercavitation experiments, researchers have suggested adopting a forward-facing mounting system for studies related to entrainment rate whereas backward-facing mounting systems for studies related to supercavity geometry and closure modes [8]. Despite a prominent amount of research in this area, the effect of liquid temperature on the supercavity geometry has not been investigated. This paper presents the effect of the fluid temperature on the vapor generation rate and supercavity geometry. Section Computational Methodology describes the computational methodology adopted in the present work. This section includes the details of the computational model, governing equations, meshing, boundary, and operating conditions. Section Validation of Computational Method presents the validation of the computational method with the analytical results. Section Result and Discussion presents the computation results and related discussions. The conclusion of the present study is described finally in Sect. Conclusion.

Computational Methodology Computational Model In the present study, numerical simulations are carried out using ANSYS Fluent version 2021 R1 on a disk cavitator of diameter 30 mm and thickness 8 mm. The length and height of the computational domain are 1200 mm and 95 mm, respectively.

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21

a) Inlet

Cavitator

b)

Outlet

Farfield

Axis

Freestream Velocity Direction

Front wall

Rear Wall

Cavitator

Fig. 2.1 Geometrical details of a computational domain and b cavitator

Axisymmetry conditions are also incorporated in the simulation by considering the lowermost edge of the domain as the axis of rotation. The complete domain and closeup view of the cavitator geometry are shown in Fig. 2.1a, b, respectively.

Governing Equations In the present computational study, the steady axisymmetric isothermal supercavitation phenomenon is modeled in Ansys Fluent. Owing to the negligible relative motion between the phases, the mass and momentum conservation equation can be simplified as shown in Eqs. (2.1) and (2.2): ∂ρ + ∇.(ρU ) = 0 ∂t

(2.1)

∂(ρu) + ∇.(ρU ∗ U ) = −∇ p + ∇τ + F ∂t

(2.2)

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Due to the comparatively lower volume fraction of the secondary phase, the mixture multiphase model is adapted. The production and condensation rate of the secondary phase was calculated using Schnerr–Sauer cavitation model as shown in Eqs. (2.3) and (2.4). m+ = Cc

m− = CV

ρv ρl 3 αv (1 − αv ) (2/3)(( p − pv )/ρt ) for P > Pv . ρ R

ρv ρl 3 αv (1 − αv ) (2/3)(( pv − p)/ρt ) for P < Pv . ρ R

(2.3)

(2.4)

SST K-ε turbulence model in conjunction with enhanced wall treatment is employed to capture the turbulence. The method is used to since the coarser grid can be used with enhanced wall treatment which in turn reduces the computational time. The further results have proved that the results obtained are close to the validated paper. The velocity and pressure in the present computation are coupled using the SIMPLEC scheme. Pressure and convective terms are discretized using PRESTO and second-order upwind scheme respectively.

Mesh, Boundary Conditions, and Operating Conditions The computational domain was discretized by structured mesh for better accuracy with around 500,000 elements. To optimize the computational power, the mesh is biased in such a way that it is comparatively finer near the cavitator and gradually becomes coarser as moves away from the cavitator. The minimum element sizing is estimated based on the y+ value, the element size is increased with a bias factor of 20. The growth rate is 20 as defined by the bias factor. Figure 2.2 shows the zoomed-in view of the mesh near the cavitator. In the present study, all the simulations are carried out at a cavitation number of 0.21 which corresponds to a velocity of 10.7 m/s based on operational parameters. The operating pressure for all the cases was considered to be constant with a value of 15 kPa. The operating pressure is fixed based on the experimental setup referenced for validating. The inlet is taken as velocity inlet, whereas the outlet was considered as pressure outlet. The inlet velocity was set to 10.7 m/s and the outlet is provided with a static pressure value of 101,325 Pa. The turbulence intensity based on the literature review of similar studies was taken as 0.3%. To account for the effect of temperature on supercavity geometry, six different cases at operating liquid temperatures of 22 °C, 30 °C, 35 °C, 40 °C, 45 °C, and 50 °C are simulated.

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Fig. 2.2 Zoomed-in view of the mesh near the cavitator

Validation of Computational Method The computational model was validated with the empirical relation proposed by Logvinovich for the non-dimensional maximum diameter of supercavity [6].  (2.5) Dmax /dc = (0.82(1 + σ∞ )/0.96σ∞ For better reliability of the validation, the data was validated at four different cavitation numbers, i.e., 0.21, 0.25, 0.27, and 0.33, which based on operational condition corresponds to the freestream velocity of 10.7 m/s. 10 m/s, 9.5 m/s, and 8.7 m/s, respectively. Table 2.1 presents the comparison of numerical Dmax /dc obtained from present computation with the analytical value of Dmax /dc calculated from Eq. (2.3). It is evident from the comparison that the numerical method adopted can predict complex multi-physics of the two-phase flow very well. The results obtained from the numerical simulation have an error in the range of 8–13%. The discrepancy in the numerical and analytical solutions is due to the assumption of the axisymmetric Table 2.1 Comparison of present computational data with analytical data [6] Cavitation number

Freestream velocity (m/s)

Analytical (Dmax /dc )

Present computation (Dmax /dc )

Error percentage

0.33

8.7

1.84

1.68

8.58

0.27

9.5

1.99

1.73

13.11

0.247

10

2.07

1.87

9.66

0.21

10.7

2.21

1.95

12.01

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condition rather than complete three-dimensional analysis. Moreover, the inevitable occurrence of inherent errors such as discretization error, numerical error, computational error, etc., also contributed to the overall error. Owing to the simplicity in the numerical study provided by the above-stated assumptions, the error range can be accepted. Cavitation number is a dimensionless number used in flow calculations. It describes the relation between local absolute pressure from the vapour pressure and kinetic energy per volume. Cavitation number characterizes the potential of the flow to generate cavitation.

Result and Discussion The simulations are held at an operational liquid temperature of 22 °C, 30 °C, 35 °C, 40 °C, 45 °C, and 50 °C to account for the effect of liquid temperature on supercavitation. Figure 2.3 shows the contour of the volume fraction of vapor at various temperatures. The contour can also be useful in the prediction of the supercavity geometry. It is found that the amount of vapor generation increases with an increase in the operational temperature of the liquid. This is due to the increase in the vapor pressure of the liquid at a higher temperature. Higher vapor pressure of the liquid enables the supercavity formation at a comparatively lower speed since the decrease in freestream static pressure requirement reduces. The simulation images obtained are processed to extract the dimensions of supercavity. The changes in the ratio of supercavity maximum diameter to the cavitator diameter with temperature are plotted. Figure 2.4 depicts a linear dependence of supercavity maximum diameter on the temperature of the operational liquid. On application of curve fitting to the data, a mathematical relation (Eq. 2.6) is formed between supercavity maximum diameter and operational liquid temperature. Dmax /dc = 0.035T + 1.15

(2.6)

The supercavity length is also increased with an increase in operational liquid temperature. The length of supercavity obtained from the image processing is plotted with temperature in Fig. 2.5. It is found from the plot that the supercavity length increases approximately in a parabolic manner with operational liquid temperature. The quadratic curve fits quite accurately to the data with the R-squared value of 0.99. The mathematical relation obtained from the curve fitting is shown in Eq.(7). (L/2)/dc = 0.0081T 2 − 0.346T + 5.34

(2.7)

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Fig. 2.3 Volume fraction contour of water vapor at a 22C, b 30C, c 35C, d 40C, e 45C, and f 50C

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Fig. 2.4 Variation of maximum cavitation diameter with temperature

Conclusion The effect of the temperature of the operating liquid on the phenomenon of natural supercavitation is numerically studied. The geometrical parameters of the supercavity, i.e., Dmax and L/2 has been investigated and plotted for the temperature change. It was found that the increase in temperature has a considerable effect on the physics of supercavitation formation. The maximum diameter and the half-length of the supercavity increase prominently with the increase in liquid temperature. When the liquid temperature is increased to 50 °C, a maximum increment of 53% in the supercavity diameter is recorded in the present study.

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Fig. 2.5 Variation of the non-dimensional half-length of supercavity with temperature

References 1. Choi JH, Penmetsa RC, Grandhi RV (2005 Feb 1) Shape optimization of the cavitator for a supercavitating torpedo. Struct Multidiscip Optim 29(2):159–167 2. Epshtein L (1973) Characteristics of ventilated cavities and some scale effects. In: Proceedings of the international symposium IUTAM, unsteady water flow with high velocities, pp 173–185. Nauka 3. Javadpour SM, Farahat S, Ajam H, Salari M, Nezhad AH (2017 May 1) Experimental and numerical study of ventilated supercavitation around a cone cavitator. Heat Mass Transf 53(5):1491–1502 4. Karn A, Rosiejka B (2016) Air entrainment characteristics of artificial supercavities for free and constrained closure models. Exp Thermal Fluid Sci. https://doi.org/10.1016/j.expthermf lusci.2016.10.003 5. Likhachev DS, Li F, Kulagin VA (2014 Nov) Experimental study on the performance of a rotational supercavitating evaporator for desalination. Sci China Technol Sci 57(11):2115–2130 6. Logvinovich GV (1973) Hydrodynamics of free-boundary flows. Halsted Press 7. Savchenko YN (2001) Modeling the supercavitation processes. Int J Fluid Mech Res 28(5) 8. Shao S, Balakrishna A, Yoon K, Li J, Liu Y, Hong J (2020) Effect of mounting strut and cavitator shape on the ventilation demand for ventilated supercavitation. Exp Therm Fluid Sci 1(118):110173 9. Wosnik M, Schauer T, Arndt R (2003) Experimental study of a ventilated supercavitating vehicle 10. Wu Y, Liu Y, Shao S, Hong J (2019) On the internal flow of a ventilated supercavity. J Fluid Mech 862:1135–1165. https://doi.org/10.1017/jfm.2018.1006

Chapter 3

Smoke-Based Visualization of Jet Flow from a Cruciform Nozzle of Unit Aspect Ratio S. Rajesh Kumar, Kaavya Ramachandran, and B. T. Kannan

Introduction The cruciform nozzle/orifice has many applications, such as air diffusion orifice, HVAC (Heating Ventilation and Air conditioning) systems, fuel injectors in combustors, injectors in chemical reactions, thrust augmentation devices, slot in a solid propellant grain, and impinging jet studies related to heat transfer and acoustics. The cruciform geometry is simple in design and easy to manufacture. The usage of cruciform nozzle has increased in recent researches due to its mixing characteristics. Studies pertaining to non-circular cross section were carried out by researchers both numerically and in experimentation. The numerical study of isothermal jet flow of the cruciform nozzle were studied [1], using RANS standard k-ε turbulence model. The above paper indicates the evolution of jet flow from cruciform to circular shape. The values of mean flow quantities were compared with experimental work [2] and turbulent flow quantities such as turbulent viscosity, shear stress were captured as contour plots in 3D. The experimental work on cross shaped lobed orifice used for HVAC can be found [3] to improve air diffusion in room interiors of a building. The volumetric flow rates, streamwise variation of flow area, and centerline velocity of both circular and lobed jet were compared. They concluded that self-induction occurs at the periphery of jet, similar to circular jet with same exit conditions. The simulation work of turbulent jet flow coming out of a daisy-shaped orifice [4] was done for two turbulence models, viz. k-ε and k-ω. The simulation work shows that k-ω SST is an effective tool for analyzing lobed orifice design. The use of k-ε R model gives the same effect but displays reduced transverse velocities. Streamwise

S. Rajesh Kumar · K. Ramachandran · B. T. Kannan (B) Department of Aerospace Engineering, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_3

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velocity fields, half velocity widths, and evolution of momentum thickness were better reproduced using k-ω SST. The isothermal flow through cruciform nozzle using LES was simulated [5], and vortices were captured by vertical contours along plane perpendicular to axis of the nozzle. The flow field evolution of jet and its vertical development were reported in simulated work. Wall shear rate and stagnation mass transfer of impinging jets coming out of convergent nozzle and cross-shaped nozzle were studied experimentally [6]. Their study says that wall shear rate and mass transfer were higher in the impingement region for cross-shaped nozzle than circular nozzle. Then K-H (Kelvin–Helmholtz vortices are smaller and discontinuous to promote jet mixing in case of cross-shaped nozzle. The K-H vortices are large and disappear at downstream in case of circular jet. The aspect ratio of cruciform nozzle has an effect on the potential core length of the jet [7]. The experiment was conducted for four different aspect ratios, say, 3, 5, 12.5, and 50. The potential core length is higher for aspect ratio 12.5 and also higher in comparison to 2D and axisymmetric jets. The results of experiment says that inward secondary flow along span wise and normal direction (y and z axes) varies with aspect ratio. The secondary flow is found to restrict the jet from spreading outward leading to higher potential core length. The 3D cruciform nozzle with high aspect ratio was used for studying mean flow properties [8]. The jet is coming out of the nozzle into the still air. The jet is symmetric and maintains crisscross shape even at the downstream of x/d = 150. In upstream region, the velocity profile in z = 0 slice and y = 0 slice exhibits saddle back shape. The velocity decay rate is smaller in x-direction as compared to 2D and axisymmetric jets. The scales were found to be increasing in slices y = z and z = 0. The development of length scale is slower on comparison with 2D and axisymmetric jets. The current paper deals only with the flow visualization of jet originating from a cruciform nozzle having unit aspect ratio. Smoke-based flow visualization is done using a LASER and glass rod setup, similar to one used by [9]. The evolution of vortices from nozzle opening to downstream is captured along streamwise and transverse directions. The jet impinging facility [10] is modified to produce flow in horizontal direction through cruciform nozzle and images are captured. The cruciform jet visualization can be used to understand the flow and turbulence characteristics. Further, the scope can be extended to understanding the jet flow acoustics.

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Fig. 3.1 Jet impingement facility

Experimental Methodology Test Setup and Nozzle The jet impingement test facility [10] available in the aerodynamics laboratory is used for the experiment work. The setup is shown below Fig. 3.1. The cruciform nozzle was modeled in CATIA and 3D printed to final form as shown in Fig. 3.2. Figure 3.1 shows the experimental setup. The cruciform nozzle having unit aspect ratio is fitted to the setup. The flow direction of jet is kept horizontal. Although the experimental setup has nine step speed control, the flow velocity is kept at 0.58 m/s. The objective is to carryout flow visualization of jet evolving from a cruciform nozzle, so the jet flow is maintained at lowest speed possible by the setup. The fan used is a three-blade axial type with 2400 rpm, tilt angle 20 degree made up of plastic, needs a current of 0.57A and power 30 W[10]. The dimensions of the cruciform nozzle is shown in Fig. 3.3. The smoke was generated using an incense material. The smoke produced will be drawn by the fan, after passing through the settling chamber will come out of the nozzle.

LASER Illumination and Flow Visualization A purple color LASER of 405 nm is sent through a cylindrical glass rod to produce a divergent beam of light. The beam of light will cut the various planes of the jet flow.

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Fig. 3.2 3D printed cruciform nozzle

Fig. 3.3 Geometry of cruciform nozzle

The laser beam will illuminate the jet because of the smoke particle in the jet flow. The planes considered were along (i) the streamwise direction and (ii) the transverse direction (plane perpendicular to streamwise direction). The illuminated planes of jet flow are captured as videos by a camera. The visualization stills have been captured from the recorded video. The still images were processed and produced for better visualization.

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Results and Discussion The smoke-based flow visualization was done along two directions, say (i) streamwise direction and (ii) transverse direction. Figures 3.4 and 3.5 are taken along Streamwise direction. Two streamwise plane were considered say, minor Plane (mP) and Major Plane (MP) as shown in Fig. 3.3. Figure 3.4 shows the evolution of jet coming of the cruciform shape. The plane considered here is minor plane (mP). The vortices can be seen in the jet flow. These vortices are periodic and shedding in regular interval. The vortices loses its energy and gets dissipated as it moves downstream. One can see the potential core, which is of uniform velocity. Figure 3.5 show the flow visualization image in MP along streamwise direction. One can observe from the image, that vortices are formed, moves downstream and gets dissipated.

Fig. 3.4 Instantaneous flow visualization of jet along streamwise direction in minor plane

Fig. 3.5 Instantaneous flow visualization of jet along Streamwise direction in Major plane

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The primary difference between mP and MP is that, the vortices are formed near to the exit in mP and a little farther in MP. The vortices are smaller in size and closer to exit in mP, whereas larger and farther to exit in MP. The reason for large and farther vortices in MP, is because of the top edges of the cruciform. The smaller and near vortices are due to the corners of the cruciform. Figure 3.6 shows the flow visualization at different cross section along the axial direction. Figure 3.6a shows the flow exiting from the nozzle. Figure 3.6b is for x/De = 0.08, shows that flow is coming out and having a cruciform shape. Figure 3.6c shows the cruciform shape starts evolving into distorted quadrilateral [1]. Figure 3.6d

Fig. 3.6 Instantaneous flow visualization of jet at different axial locations in transverse direction, say a at x/De = 0, b at x/De = 0.08, c at x/De = 0.4, d at x/De = 0.8, e at x/De = 1.2, f at x/De = 1.6, g at x/De = 2.0, h at x/De = 2.8, i at x/De = 3.6

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shows a quadrilateral with lobes coming out. There were totally eight lobes, four at corners and four at midpoint of the edges of the quadrilateral. Figure 3.6e and f shows the eight lobes starts increasing in size and the quadrilateral shape starts becoming circular. Figure 3.6g shows the lobes being detached and the cross section is almost circular. Figure 3.6h and i shows no lobes and the jet becomes feeble.

Conclusion The flow visualization was done using a smoke-based jet impinging facility with cruciform nozzle attached to it. The aspect ratio of the cruciform nozzle is one. A purple color LASER passed through a cylindrical glass rod to produce the plane of light. This plane of monochromatic light is used to illuminate the jet flow plane along the streamwise and transverse directions. The flow visualization along the streamwise direction shows larger and father vortices in MP and smaller and nearer vortices in mP. The vortices are being shed and are visible in both minor and major planes. The transvers plane shows the evolution jet and lobes in the cross section of plane of jet. The flow starts as cruciform shape initially, then distorted quadrilateral and circular. There were eight lobes visible in the distorted quadrilateral, four lobes at corners and four lobes at mid-edges. As flow moves downstream, the quadrilateral shape becomes circular and lobes vanishes. Thus, flow visualization was done for the nozzle. Acknowledgements The corresponding author expresses acknowledgement to the Flow visualization facility and Advanced Computing Lab. The author also acknowledges the assistance provided by lab supervisor and assistants of hangar in providing proper equipment. The low-cost jet impinging facility was designed by the corresponding author and fabricated by his former student (Abdul Hamid Rather).

References 1. Kannan BT, Senthilkumar S (2017) Numerical simulation of isothermal cruciform jet flow. Lect Notes Mech Eng 595–604 2. Quinn WR, Azad M (2013) Mean flow and turbulence measurements in a turbulent free cruciform jet. Flow Turbul Combust 91:773–804 3. Nastase I, Meslem A (2008) Lobed jets for improving air diffusion performance in buildings. In: Air infiltration and ventilation centre conference—2008, AIVC Conference proceedings (International Network for Information on Ventilation and Energy Performance, Belgium, 2008), pp 113–118 4. Meslem A, El-Hassan M, Candane R, Nastase I (2010) Numerical simulation of a turbulent jet flow issued from a daisy-shaped orifice. In: HEFAT 2010, 7th International conference on heat transfer fluid mechanics and thermodynamics (Antalya, Turkey, 19–21 July 2010) 5. Kannan BT, Ssheshan P, Senthilkumar S (2016) Large Eddy simulation of isothermal cruciform jet flow: preliminary results. Perspect Sci 8:10–12

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6. Meslem A, Kristiawan M, Nastase I, Sobolik V (2012) Wall Shear rates and stagnation Mass transfer on a plate in axisymmetric and cross impinging jets. In: Eurotherm—2012, 6th European thermal sciences conference, J Phys Conf Ser 395 (Poitiers, France, 2012) 7. Fujita S, Osaka H (1992) Effect of aspect ratios on potential core length for cruciform jet. Exp Thermal Fluid Sci 5:332–337 8. Fujita S, Osaka H (1985) Three dimensional jet issuing from the cruciform nozzle. Bull JSME 28:1062–1068 9. Balachander A, Alase A, Adithya Menon K, Mahendra Perumal G, Kannan BT (2020) Smoke based visualization of turbulent swirl jet flow. In: ICAME—2020, IOP Conf Ser Mater Sci Eng 912 10. Rather AH, Kannan BT (2020) Design and development of impinging jet facility for flow visualization studies. In: ICAME—2020, IOP Conf Ser Mater Sci Eng 912

Chapter 4

Aerodynamic Design and Numerical Analysis of Bi-cambered Airfoil Sashant Kapoor, Vipin Kumar, Harshit Shukla, Kumar Gaurav, and Dalbir Singh

Introduction Till present time basic airfoil is designed with only a single maximum camber at 25% of chord for subsonic aircraft and 50% of chord for supersonic aircraft, so to retain the flow streamlined over the airfoil profile study of boundary layer interaction with the outer flow field must be a purpose of research. Boundary layer effects can be aggravated mainly at high speeds, as shock waves’ presence can be seen after the local pocket of supersonic flow over the lifting surface on the airfoil. For the last few decades, a major subject to research in aerodynamics is flow control techniques over an aircraft. As modern civilian aircraft’s cruise velocity is limited for fuel efficiency because of the drag penalty which occurs due to shock waves, which is technically termed as wave drag. To mark an additional improvement in fuel consumption, the flow control method tends to achieve an increment in the lift to drag ratio, which can be achieved by a decrement in the drag related to the shock waves in cruising flight conditions. Since there are numerous flow control methods which had been researched and practiced achieving accurate results, such flow control methods are passive control of flow at the foot of the shock by applying porous surface, a bump on airfoil surface near the shock, and active control flow control method by using mass suction or blowing of hot air [1]. Most conventional flow control methods are suction/blowing of air and contour bumps on the airfoil’s upper surface. Stanewsky et al. [3] said that the most effective way to reduce wave drag on an airfoil is a contour bump at the shock region. The contour bump is beneficial as it replaces the isentropic compression from the normal transonic shock S. Kapoor · V. Kumar (B) · H. Shukla · K. Gaurav Department of Aerospace Engineering, University of Petroleum and Energy Studies, Dehradun, India D. Singh School of Aeronautical Sciences, Hindustan Institute of Technology and Science, Chennai, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_4

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or would break down it into numerous weaker shocks [1]. Moreover, to control flow over an airfoil, additional energy input does not need for contour bump but in the case of suction/blowing of hot air additional energy is needed to reduce the wave drag [3]. In past, there are numerous studies had been performed about the suction/blowing of hot air for improvement in the existing airfoil performance at subsonic speeds [4]. Near the rigid surface, the boundary layer keeps growing along the surface as long as the pressure gradient remains zero. For an adverse pressure gradient, static pressure increases in the flow direction which is a drastic increase in the thickness of the boundary layer. The effect of viscous force and adverse pressure gradient reduces airflow boundary layer region momentum, and effectiveness of these will follow for some considerable length on the airfoil surface and will create a halt in boundary layer growth and this would be termed as flow separation. If the airfoil is being avoided from flow separation near the trailing edge, the boundary layer remains attached to the surface and hence pressure drop is being eliminated near the airfoil trailing edge, and thus drag force will be decreased [2]. The main objective is to control the boundary layer over an airfoil which would result in an increment of lift force and decrease the drag force, and hence it will enhance the aerodynamic performance of the airfoil by delaying the stall and increasing the lift-to-drag ratio. In this current paper, we analyzed and performed a study that is associated with bicamber airfoil raised protuberance and concave section that is avoided as it generally impacts to reduce the aerodynamic performance. During this study, two control mechanisms named contour bump and injection/blowing of hot air are examined to reduce the effect shock wave and hence decrement of total drag on the airfoil. It may also adversely affects other design parameters of an airfoil to get improved fluid mechanics performance by using such flow control methods [5]. To optimize the aerodynamic performance for bi-camber on different parameters, some crucial parameters were decided such as maximum camber, cord length, maximum thickness, and the crest position for two ridges on airfoil upper surface and ridges location, and angles on which two ridges were designed. The ridges can be found symmetrical or asymmetrical as it depends on the location of the upper surface ridges on the airfoil. However, an efficient method that is based on the optimization technique of the pressure gradient, this method is used to optimize the parameters of contour bump and the steady suction/blowing of hot air. These optimizations were carried out by CFD fluent solver. Since various airfoil profiles have been designed to support aerodynamic performance by inducing flow transition at an early stage of separation which leads to energizing the flow near the boundary so that it gives benefit to delay the flow separation. For example, a reduction in drag can be attained when airfoil stall performance is yielded, which leads to results an increment in lift force, but at the cost profile drag increment. Stall performance of an airfoil can be enhanced, which dually affects the drag and lift performance, but general performance characteristics can be improved for some angles of attacks or some Reynolds number, but at the same time accepting reduced performance for other angles of attacks [6]. To reduce the drag disadvantage, bi-camber airfoil is designed smoothly along with using flow control methods. This type of profile could be useful in normal aircraft applications such as the use of trim tabs to fly aircraft at high angle of attack

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or flaps or any other applications like rotorcrafts and wind turbines where airfoils operated at a wide range of flight conditions, the advantage of bi-cambered airfoil would become more noticeable.

Methodology Since there are very little research data available on bi-camber airfoil design we re-mapped airfoil using paper and designed an optimized flat base bi-camber airfoil with two ridges on the upper surface. Frederick et al. [7] suggested an innovative design of a bi-camber airfoil that records a stable performance parameter of the airfoil such as efficiency and high angle of attack. This airfoil is providing a design condition for favorable and adverse pressure gradients in between two ridges and maximizing flow to be attached further to the trailing edge and minimizing flow separation. To illustrate the basic design of bi-camber airfoil author describes some basic design characteristics in Fig. 4.1. Figure 4.1 demonstrates the profile of a bi-camber airfoil section 1 with leading-edge at 12, trailing edge at 13, and chord line at 14. Upper surface demonstrates a section divided into some major fractions 1,2,5,6,7,8,3. Leading-edge front section I (slope 1,2) and trailing edge rear section III (slope 3). The front and rear slopes are separated by a central section II comprised of slope segments 5,6,7,8 and with a minimum thickness in central Sect. 10. The central section slopes are divided into two convex and two concave sections; rearfacing convex and concave division 5 and 6, forward-facing concave and convex Sects. 7 and 8. The divisions’ combination consists of forward-facing slope 5,6 and rear-facing slope 7,8 and the two ridges with front and rear end maximum thickness 9,11. Using this type of front and rear slopes on the upper surface defined it as a bi-cambered airfoil surface. The four separated slopes on the upper surface of this airfoil incorporate pressure gradient in respect to fluid flow at zero degrees of angle of attack. The convex and concave slope of the first ridge or section I results in a favorable pressure gradient and the front slope of a rear camber i.e., 5,6 results in us an adverse pressure gradient. For second elevation curve consists of a forward-facing slope, 7–8 which is responsible for favorable pressure gradient at the rear end, and a

Fig. 4.1 Descriptive view of Bi-camber airfoil

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rear-facing slope or section III results in a final adverse pressure gradient. The lower surface is a flat surface that only has a single convex section for the entire length of the lower surface and resulting, in a favorable pressure gradient at the first half section of the airfoil, and resulting in an adverse pressure gradient, to the rest of the section. The lower surface contains only a single raised curve 4. Using Q-blade software, the author designed the bi-camber airfoil in the preliminary phase. Q-blade is based on Blade Element Momentum (BEM) method. To design a specific definition for such airfoil, a scalar objective function does not have any need but some expertise must be required to identify the potential problems So, during the preliminary design of the bi-camber airfoil, the author adopts two methods i.e., direct method and inverse method. The direct design method implies direct airfoil designing which involves the geometric section specification, pressure calculation, and performance of airfoil. The inverse methods which author adapts to further design and analysis of an airfoil. As inverse design can be explained with the help of an example, a thin airfoil theory can be used to solve for the shape of the camber line that produces a specified pressure difference on an airfoil in potential flow and design problem starts when an author has somehow defined an objective for the airfoil design. So, using the inverse method author re-mapped the existing bi-camber and analyzed the airfoil which is then compared with commonly known airfoils. Further, the author used ANSYS fluent software to analyze the flow over a bicamber airfoil. According to the requirement and outcome author reviewed some research on various turbulence models. RNG K-ε model: RNG k-epsilon model is developed using mathematical methods known as Re-Normalization Group which take account of turbulent motion at different existence scales. This method is generally used in the simulation of flows in rotating cavities. Equation (4.1)—Turbulent kinetic energy k   ∂ρku i ∂ μt ∂k ∂ρk + 2μt EijEij − ρε + = ∂t ∂ xi ∂ x j σk ∂ x j

(4.1)

Equation (4.2)—dissipation ε   ε ∂ μt ∂ε ε2 ∂ρε ∂ρεu i + + C1ε 2μt Ei j Ei j − C2ερ = ∂t ∂ xi ∂ x j σk ∂ x j k k

(4.2)

K-ω turbulence model: It is similar to the k-epsilon model, but the k-omega model uses turbulent energy dissipation rate instead of dissipation equation. Using this model k determines energy turbulence and omega determines characteristic linear turbulence scale. This model is most sensitive to the boundary conditions in external flow and initial conditions of the turbulence level i.e., why it describes well near-wall flows, including with large eddy currents.

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   ∂ρu j k ∂ρk ρk ∂k ∂ μ + σk (4.3) + = ρ P − β ∗ ρωk + ∂t ∂x j ∂x j ω ∂x j    ∂ρω ∂ρu j ω ∂ ρk ∂k αω ρσd ∂k ∂ω + P − βρω2 + = μ + σk + ∂t ∂x j k ∂x j ω ∂x j ω ∂x j ∂x j (4.4) SST K-omega turbulence model: SST k-omega model is a shear stress transport turbulent model. This model consists of a combination of two models; one is kepsilon which works away from the wall and another is k-omega near the surface region of a test article. This model outputs good results in mixing layers at medium pressure gradient. Equation (4.5)—Kinematic Eddy Viscosity υT =

a1 k max(a1 ω, S F2 )

(4.5)

Equation (4.6)—Turbulence Kinetic Energy   ∂k ∂ ∂k ∂k + Uj = Pk − β ∗ kω + (υ + σk υT ) ∂t ∂x j ∂x j ∂x j

(4.6)

Equation (4.7)—Specific Dissipation Rate   ∂ω ∂ω ∂ ∂ω 2 + Uj = αS − βω2 + (υ + σω υT ) ∂t ∂x j ∂x j ∂x j 1 ∂k ∂ω + 2(1 − F1)σω2 ω ∂ xi ∂ xi

(4.7)

Analysis shows that turbulence model SST k-omega outputs the best results in the calculation of flows over an airfoil at a high angle to attack [8]. Geometry and Grid Generation: The airfoil considered in this study is a Bi-camber airfoil with 18 cm of chord length. A C-type domain that follows the uniform pattern of structured mesh over a bi-cambered airfoil is created in ICEM CFD (version 15.0) with far-field boundaries measured from the trailing edge is 12.5 chords away in all directions Fig. 4.2. Structured mesh is organized in numerical blocks in which each numerical polygon with at least 4 corners which mark as 4 block sides that are pairwise opposite to each other and a grid which is generated in ICEM-CFD with at least 430,000 nodes [8, 9]. Flow around the bi-cambered airfoil between two ridges is complex enough due to the convex and concave surface, which leads to a high-intensity pressure gradient between those two bumps. Hence, the far-field cell growth ratio is considered as 1.05. Wall y + values along the airfoil surface are kept

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Fig. 4.2 C-Type mesh over a Bi-camber airfoil

1 to account for the low Reynolds number flow regime. The boundary layer between two ridges of the bi-camber airfoil is shown in Fig. 4.3. Flow domain Boundary Conditions and Fluent Solver Settings: The boundary conditions assigned to the flow domain around an airfoil as sidewall assigned with the no-slip condition while the inlet boundary condition is defined as velocity inlet and outlet boundary condition is defined as pressure outlet condition. For numerical solution implicit scheme has been usually used to solve steady flow problems and flow properties have been taken as second-order upwind and Mach number less than 0.1907. However, the assumption had been taken as incompressible flow with 1.81 × 10–5 kg/m-s as dynamic viscosity of air and 1.225 kg/m3 as constant density and temperature is 298 K. To solve residual equations a convergence criterion is given as 10–5 for all the residuals is satisfied.

Fig. 4.3 Meshing between two ridges of Bi-camber airfoil

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Turbulence Modeling: Previous studies show that the SST K-omega model is proposed to give better separation prediction for external aerodynamic applications; this model gives better agreement with experiments of mild separated flow. This model also includes a viscosity limiter. SST k-omega turbulence model consists of two governing equations, which are based on the eddy viscosity model; this turbulence model is mainly used in aerodynamics applications. This turbulence model is a type of hybrid model that is formed by a combination of Wilcox K-epsilon model and K-omega model, therefore to simulate away from the wall K-epsilon model is used and to operate near the near-wall Wilcox model is being used at low Reynolds number of 2.1 × 106 . The use of this effective feature using this model mainly depends on appropriate treatment. The performance of an airfoil is validated with an 18 cm chord length.

Results Grid sensitivity test results: The grid sensitivity test is a tool to find the optimum number of nodes that do not affect the solver results even if there is any further increment in the number of nodes, thus using this test we can get optimal grid conditions for fluent analysis studies [9]. Table 4.1 gives the result of the mesh independence test. The table represents data of the number of nodes vs drag coefficient. The table shows that at approx. 430–470k the coefficient of drag is constant; this implies that at 430k the mesh is suitable for the given design of airfoil. Lift and drag coefficients: Figure 4.4a represents a graph variation between drag coefficient and angle of attack of an airfoil, which represents comparative data between various airfoils that are bi-camber airfoil, NACA 2412, NACA 63(2)215Mod-b, Clark Y. As represented in graph drag bucket value on a bi-camber airfoil Table 4.1 Table of grid independency test

Number of nodes

Coefficient of drag (Cd )

58,320

0.011148483

131,730

0.009135839

234,640

0.007189258

304,840

0.003457691

348,420

0.002794558

379,420

0.002163941

401,830

0.001342873

438,740

0.001104262

443,345

0.001104387

458,420

0.001104432

469,420

0.001104452

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Fig. 4.4 Graph between a coefficient of lift (Cl ) versus angle of attack (AOA). b Coefficient of drag (Cd ) versus angle of attack (AOA). c Cl/Cd versus angle of attack

is less than that of NACA 63(2)-215 MOD-b which implies drag is less on bi-camber airfoil as compared to NACA 63(2)-215 MOD-b because in bi-camber flow separates at half chord which reattaches after certain interval over the airfoil. Figure 4.4b represents a graph variation between lift coefficient and angle of attack of an airfoil, which represents comparative data between various airfoils that are bi-camber airfoil, NACA 2412, NACA 63(2)-215Mod-b, Clark Y. As represented in graph lift coefficient value on a bi-camber airfoil is more than that of NACA 63(2)-215 MOD-b which implies lift is more on bi-camber airfoil as compared to NACA 63(2)215 MOD-b because in bi-camber flow separates at half chord which reattaches after certain interval over the airfoil. Figure 4.4c represents the aerodynamic efficiency of various airfoils at different angles of attack. As represented in the graph, aerodynamic efficiency is significantly more for bi-camber airfoil at all angles of attack which

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shows the superiority of bi-camber airfoil design over other conventional airfoil designs. Validation of bi-camber airfoil data by wind tunnel: The author has performed the wind tunnel model validation with the following wind tunnel specifications. • Test Section size: 600 mm × 600 mm × 2000 mm with side windows opening on either side of test section and top opening. • Wind tunnel Maximum Speed: 60 m/s. • Contraction ratio: 9–10. • Honeycomb L/D: 7–9. • Wind tunnel Maximum Length: 14 m. The wind tunnel test has been performed on a bi-camber airfoil at a velocity of 28 m/s, Reynolds number as 2 × 106 , and at room temperature. Pressure Contour: Figure 4.5 shows the pressure contour over a bi-camber airfoil. Blue curves over the upper surface represent the negative pressure which implies that the generate lift after the first ridge also (Fig. 4.6).

Fig. 4.5 Graph representation of CFD results validation from wind tunnel data. a Coefficient of lift (Cl ) versus angle of attack (AOA). b Coefficient of drag (Cd ) versus angle of attack (AOA)

Fig. 4.6 Static pressure contour over Bi-camber airfoil at 4 deg AOA

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Conclusion The results obtained show how bi-camber airfoil acts in low Reynolds number flow conditions. The flow separation occurs as the angle of attack increases on the upper surface of the airfoil but is delayed which results in a drop in lift force coefficient, and a simultaneous increment in drag force coefficient. However, in the low turbulent flow region, flow is reattached due to the second camber, which gives lift at a high angle of attack also, which is superior in aerodynamic performance over the conventional airfoil. The CFD analysis results are also validated using the wind tunnel, which reflects similar results as CFD results i.e., at a higher angle of attack lift is high. Thus, we can conclude that bi-camber airfoil results in higher lift force and lower drag force, hence, increase the lift by drag ratio. Hence, an airfoil with a bi-camber profile is more effective than any other conventional airfoil profile.

Future Work The currently proposed airfoil design can be altered to both the upper and lower surface of an airfoil, which could increase the efficiency for the positive and negative angle of attack. However, this research is limited to design and analysis prospects only, and this research can be further carried out to get more insights. The first and the foremost usage and development of the bi-camber can be put into the manufacturing state and can be manufactured for various commercial, military, and training aircraft. The aircraft with bi-camber airfoil will not only improve liftdrag ratio but will also work upon saving fuel and improving the speed and hence the overall efficiency of the aircraft can be improved and enhanced. The second usage is concerned with the automotive industry where the bi-camber design can make a huge impact on the vehicles industry. All the sports and hybrid cars use the traditional single-camber streamline body design which has its disadvantages. Acknowledgements We would also like to extend our gratitude toward the Department of Aerospace and Department of Research and Development, University of Petroleum and Energy Studies, Dehradun, for their valuable support throughout the work. This paper is meant to design and analyze a software-based airfoil to spread theoretical and practical knowledge among the researchers. This analysis on the bi-camber airfoil profile helps students to pursue their interests and will bring ease to both the institute and students to explore different possibilities in aerodynamics.

References 1. Yagiz B, Kandil O, Pehlivanoglu Y (2012) Drag minimization using active and passive flow control techniques. Aerosp Sci Technol 17(1):21–31 2. Moghaddam T, Neishabouri N (2017) On the active and passive flow separation control techniques over airfoils. IOP Conf Ser Mater Sci Eng 248:012009

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3. Stanewsky E, Delery J, Fulker J, Matteis P (2013) Drag reduction by shock and boundary layer control. Springer, Berlin, Heidelberg 4. Chng T, Zhang J, Tsai H (2008) A novel method of flow injection and suction for lift enhancement. In: 46th AIAA Aerospace sciences meeting and exhibit 5. Meunier M (2007) Simulation and optimization of flow control strategies for novel high-lift configurations. In: 25th AIAA applied aerodynamics conference 6. Shamim MM (2013) Analysis of the effectiveness of an airfoil with a bi-camber surface. Int J Eng Technol 3:569–577 7. Felix FF (1995) Airfoil with bicambered surface U.S. Patent No.5,395,071 (7 March 1995) 8. Bulat MP, Bulat PV (2013) Comparison of turbulence models in the calculation of supersonic separated flows. World Appl Sci J 27(10):1263–1266 9. Krishnaswamy S, Jain S, Sitaram N (2014) Grid and turbulence model based exhaustive analysis of NACA 0012 airfoil. J Adv Res Appl Mech Comput Fluid Dyn 1(1):13–18

Chapter 5

A Qualitative Comparison of the Effect of Exit Ramps and Coaxial Subsonic Jet on Primary Supersonic Jet P. Sivakumar, R. Suthan, and B. T. N. Sridhar

Introduction A high-speed supersonic jet issued from a convergent-divergent (CD) nozzle is having varied applications in engineering. The fields of applications are propulsion units for the flying vehicles, rocket engines, high-speed burner and combustion, etc. Properties of supersonic flows are the main research criteria. Generally, the performance of those applications is mainly associated with the jet flow characteristics, i.e., exit pressure decay, potential core length and shock cell dimensions. Many studies have been performed to expose the important characteristics of high-speed supersonic jet, which are related to the pressure ratio of the nozzle jet. Karthikeyan and Sridhar [1] had investigated the geometry of the primary central jet, and the effect on the mixing characteristics with two different shapes of circular and triangular nozzles was analyzed. It proved that the triangular primary jets showed a high spreading rate compared to the circular primary jet. Sharma et al. [2] studied supersonic convergent and divergent nozzles with M = 1.43 and M = 2, and the effect of co-flow with the subsonic and sonic stream on the primary supersonic jet with circular cross section was compared. The primary jet nozzles were surrounded coaxially by a nozzle with a convergent cross section for co-flow. The study was P. Sivakumar (B) Department of Aeronautical Engineering, Sri Ramakrishna Engineering College, Coimbatore 641022, India R. Suthan Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore 560064, India e-mail: [email protected] B. T. N. Sridhar Department of Aerospace Engineering, Madras Institute of Technology, Chennai 600044, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_5

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conducted to analyze the contribution of co-flow on the primary jet shock structure of an over-expanded nozzle under different backpressure conditions. Murakami and Papamoschu [3] studied the salient features of single-stream and dual compressible jets. It proved substantial enhancement in mixing over the coaxial jet and rate of entrainment comparable between the single primary jet while the thickness of the secondary flow jet is small. Thus, it concludes that a secondary coaxial flow jet gives 20% more improvement in potential core length than the single primary jet. Papamoschoua and Johnsonb [4] analyzed the flow exiting a CD nozzle with different over-expanded conditions. The shock wave inside the nozzle exhibits severe instability that causes mixing enhancement of the flow. A systematic study of the phenomenon reveals that the shock-induced nozzle flow separation leads to instability. Srinivasarao et al. [5] worked on jets issued from a primary nozzle coaxially surrounded by a co-flow. The influence of lip thickness of the central nozzle on the characteristics of the co-flow jet had been studied. Enhancement in the mixing of the jet was achieved in the jet of a nozzle with thick-lip thickness compared to that of a jet issued from a nozzle with thin-lip thickness. Schomberg et al. [11] find in this experimental study proving that low deflection angles couldn’t influence the effective area of an annular supersonic nozzle. De Satyajit and Rathakrishnan [6] worked to investigate the behavior of a primary jet having M = 2, in the presence of an annular co-flow with M = 1.6. Both the nozzles were held at the nozzle with the same nozzle pressure ratio. The distribution of pressure along the centerline of the jet was examined. The primary supersonic jet potential core length was monitored adding and without adding the co-flow at all pressure ratios. Images of the jet with and without co-flow were captured by using Shadowgraph techniques and it reveals that the shock waves formed in the core jet are strongly influenced and affected by the co-flow. Swaroopini et al. [7] have done the simulation work with Convergent-Divergent nozzles having different divergence angles and with constant inputs. The study was to show the best Nozzle Pressure ratio (NPR), Nozzle Area Ratio(NAR), and Expansion ratio for the maximum thrust. Pandey and Sakthivel [8] proposed various advanced techniques in scramjet fuel injector. One among them is the ramp injector. This study resulted as the expansion ramps had reached their maximum combustion efficiency than compression ramp. Xiao et al. [9] were involved to investigate separation phenomena of a supersonic flow which is in a planar CD nozzle with a moderate expansion ratio. The computation study reveals the possible non-symmetric flow structure of the jet. The computationally obtained non-symmetric flow structures are compromised with the flow visualization captured experimentally. This study provides new facts on the flow wave structure relevant to the separated flow instability in CD nozzles with a moderate expansion ratio. Seung-CheolBaek et al. [10] investigated the characteristics of dual jets as supersonic jet with a coaxial jet issued from a supersonic nozzle and outer nozzles, respectively, with different angles of ejection. There are three important features, such as pressure ratios for both the primary and co-flow nozzles and ejection angles are chosen for a better description of the jet structure. It was proven that the highly under-expanded outer jet emanates an oblique shock wave. This oblique shock complicates the primary jet structure, and the outer ejection angle

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of the jet relatively affects the inner jet structure lesser than the pressure ratio of the outer nozzle. Ezhilmaran et al. [12] have found that jet with slanted perforations decays faster than uncontrolled nozzle and jet with straight perforation tab. Ilakkiya and Sridhar [13], in this experimental work, investigated the effect of square grooves on the structure of a supersonic jet emanating from a circular nozzle and proved that higher groove effectiveness is associated with smaller values of supersonic core length.

Design and Fabrication of CD Nozzle For Each supersonic jet, a separate convergent-divergent nozzle had been designed (one rectangular nozzle without a ramp and three rectangular nozzles with different ramp angles, i.e., 5°, 10° and 15° are considered.). A Rectangular nozzle with ramps of different angles is modeled by using the Pro-E design tool (Fig. 5.1).

Fig. 5.1 Design of convergent-divergent nozzle having rectangular exit with expansion ramps

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Fig. 5.2 a Rectangular nozzle and b Rectangular nozzle with 15° ramps

For all nozzles, Throat area, Exit area, Inlet area and Converging length are kept constant and the area ratio and pressure ratio are 1.44 and 5.746, respectively. Stainless Steel 304 material is used to fabricate the nozzles (Fig. 5.2).

Co-flow Chamber Aluminium-made Co-flow duct is a straight annular duct that is designed to give nearly uniform flow at the exit. This co-flow chamber issues subsonic flow coaxial to the primary nozzle exit flow (Fig. 5.3). Fig. 5.3 Co-flow chamber

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Fig. 5.4 Comparison of centerline total pressure decay for rectangular nozzles with 5°,10° and15° ramps (Poi = 600 kPa) with co-flow (Poi = 300 kPa)

Experimentation In this study, two different studies were conducted (i) Centerline pressure measurements of the jet and (ii) the Schlieren visualization.

Centerline Pressure Measurements of the Jet The experiments were done on the rectangular nozzles for free jets with different angles of ramps (5°, 10° and 15°) with a total inlet pressure of 600 kPa. For co-flow, experiments were conducted with an inlet pressure of 300 kPa. The total pressure is measured along the jet axis from the exit face of the rectangular nozzle using a 16-channel intelligent pressure scanner system which was connected with a traverse mechanism through a pitot probe (Fig. 5.4).

Schlieren Visualization A twin mirror Schlieren system was used to capture the shock pattern to compare the influence of ramps on potential core length (Fig. 5.5).

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Fig. 5.5 a Shock pattern captured using Schlieren visualization on CD nozzle and b Shock pattern captured using the Schlieren visualization CD nozzle with ramps

3 bar 5 bar 7 bar 9 bar

Fig. 5.6 Rectangular jet with different inlet total pressures

Comparison of Rectangular Jet Shock Patterns for Different Inlet Pressures See Fig. 5.6.

Comparison of Rectangular Jets (Poi = 600 kPa) with Induced Vortices and Co-flow (Poi = 300 kPa). See Fig. 5.7.

5 A Qualitative Comparison of the Effect of Exit Ramps …

55

Rectangular jet

(a)

Rectangular jet with coflow

(b)

Rectangular jet with 5° ramp & coflow Rectangular jet with 10° ramp & coflow Rectangular jet with 15° ramp & coflow

(c)

(d)

(e)

Fig. 5.7 a Rectangular Jet, b Rectangular jet with co-flow, c Rectangular jet with 5° ramp and co-flow, d Rectangular jet with 10° ramp and co-flow and e Rectangular jet with 15° ramp and co-flow

Results and Conclusions From these experimental results shown in Fig. 5.4, it is evident that the coaxial jet is having a decay rate of total pressure than the free jet. This tendency is inferred due to the increase in mass intrusion with the primary supersonic jet. This change in mass potentially increases the mixing and increases the decay rate of total pressure. That is rectangular jet with co-flow has total pressure decay of 9.34% than the single free jet. The same way rectangular jets with induced vortices and co-flow have a total pressure decay rate of 14.2% than the rectangular free jet. It is also inferred from Fig. 5.4 that optimum angle for the expansion ramp at the rectangular exit of the CD nozzle for in pressure decay rate would lie between 10° and 15°, i.e., in comparison with 5°ramp angle, the nozzle with 10° and 15° ramp angles shows pressure decay happening in advance along the jet axis. From Fig. 5.6, there must be a noticeable increment in the spreading nature and length of exit shock cell in a CD nozzle while the inlet total pressure increases gradually. The Schlieren image patterns showed with qualitative length scale in Fig. 5.7 clearly prove the issuing of co-flow and induced vortices influencing the primary jet at the early stage itself and mitigate the length and width of shock cell formation at the exit of the under-expanded nozzle. The length scale on the image substantiates

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this. It means that the non-circular jet along with co-flow would certainly improve the pressure decay and thereby mixing. Acknowledgements The authors acknowledge and thank the Department of Aerospace Engineering, Madras Institute of Technology, Chennai, for providing the experimental facilities for the project during the course of study and Mr.Vaibhav Durgasi (ME- Aerospace 2012-14) for his valuable suggestions for the manuscript.

References 1. Karthikeyan N, Sridhar BTN (2011) Studies on effect of jet shapes in the coaxial supersonic jet spreading rates. Int J Mech Eng Appl Res 2(2), Aug–Dec 2. Sharma H, Vashishtha A, Pinnam L, Rathakrishnan E (2008) Characteristics of sonic and supersonic co-flow jets. In 2nd International conference on recent advances in experimental fluid mechanics, 3–6 March 3. Murakami E, Papamoschou D. Mixing layer characteristics of coaxial supersonic jets. AIAA Paper-2000–2060 4. Papamoschoua D, Johnsonb AD (2010) Mixing enhancement from severely overexpanded nozzles. Int J Aerosp Innov 5. Srinivasarao T, Dakshina Murthy I, Lovaraju P, Rathakrishnan E (2017) Effect of inner nozzle lip thickness on co-flow jet characteristics. J Int J Turbo Jet-Engines 6. Satyajit D, Rathakrishnan E (2018) Experimental study of supersonic co-flowing jet. In Proceedings of the institution of mechanical engineers, Part G: Journal of aerospace engineering 7. Shanthi Swaroopini A,Ganesh Kumar M, Naveen Kumar T (2015) Numerical simulation and optimization of high performance supersonic nozzle at different conical angles. Int J Res Eng Technol 8. Pandey KM, Sivasakthivel T (2010) Recent advances in scramjet fuel injection—A review. Int J Chem Eng Appl 9. Xiao Q, Tsai HM, Papamoschou D (2012) Numerical investigation of supersonic nozzle flow separation. AIAA J 10. Seung-Cheol Baek, Soon-Bum Kwon, Byeong-Eun Lee (2003) An experimental study of supersonic dual coaxial free jet. J Mech Sci Technol 11. Schomberg K, Olsen J, Doig G (2015) Analysis of a low-angle annular expander nozzle. Shock Vibr 12. Ezhilmaran G, Chandra Khandai S, Kumar Sinha Y, Thanigaiarasu S (2019) Numerical simulation of supersonic jet control by tabs with slanted perforation. Int J Turbo Jet-Engines 13. Ilakkiya S, Sridhar BTN (2018) An experimental study on the effect of square grooves on decay characteristics of a supersonic jet from a circular nozzle. J Mech Sci Technol 32(10), Oct

Chapter 6

DSC and TGA Investigation on Ammonium Nitrate-Based Solid Propellant Doped with Ammonium Dichromate for Gas Generator Applications R. Suthan, P. Sivakumar, S. Ganesan, and B. T. N. Sridhar

Introduction The Ammonium nitrate-based propellants are environmentally benign and have a low flame temperature. So, it can be well suited for various gas generator applications such as rocket engine driving power for turbo pump, auxiliary power systems or emergency power systems, inflation of air bags, cavities pressurization, spin start turbo pump rockets, power drive for turbine in turbo machines, fuel and oxidizer source for rocket engine, pressurization of hydraulic systems, light sources (flares) and smoke generators. [1, 2]. Gas generator propellant compositions are mixtures of oxidizers, fuel-binder ingredients, coolants and special additives which permit the tailoring of the hot gas temperature, to produce gas products with moderate level flame temperatures to low. The typical flame temperatures value ranges from 800 °C to a maximum of 1650 °C (1472 °F to 3002 °F). Ammonium nitrate can be useful to slow down the burning rate. Since it has a low flame temperature and produces high gas, Ammonium nitrate is suitable for gas propellants. It needs a higher amount R. Suthan (B) Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore 560064, India P. Sivakumar Department of Aeronautical Engineering, Sri Ramakrishna Engineering College, Coimbatore 641022, India S. Ganesan Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science & Technology, Chennai 600062, India B. T. N. Sridhar Department of Aerospace Engineering, Madras Institute of Technology, Chennai 600044, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_6

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of fuel-binder to make it castable. Ammonium nitrate has no toxic and no solid elements, by decomposition, it is not producing solids. Since it is a high-energy and also a non-polluting fuel, it can be used as a more eco-friendly solid propellant [3]. The burning characteristics of AN-based propellants prepared with HTPB as fuel/binder, ADC as catalyst and TDI as a curing agent. They proved that the theoretical performance of an AN-based propellant was improved by the addition of ADC. As the mass ratio of ADC to AN is increased, the burning rate of propellant was enhanced and the pressure deflagration limit becomes lower. The burning rate of the AN/ADC propellant increases as the mass ratio of AN/ADC to AN propellant around 5–6% changes, and beyond this value of the mass ratio, the slope decreases which shows the burning rate response to the changes of mass ratio. The optimal mass ratio of ADC to AN for increasing the burning rate was found to be 6% [4, 5]. The specific impulse and adiabatic flame temperature of an AN-based propellant theoretically escalate with an increase in the proportion of Polytetrahydrofuran (PTHF) in the HTPB/PTHF blend. With an AN/HTPB propellant, a solid residue was left on the burning surface of the propellant, and the contour of this residue was similar to that of the propellant. The burning rates of the AN/HTPB/PTHF propellant were not significantly different from those AN/HTPB propellants, since a few of the liquefied HTPB/PTHF binder in the constitution cover the burning surface and impede decomposition and combustion. They proved that the burning rates of an AN/HTPB/PTHF propellant with catalyst are higher than those of an AN/HTPB propellant doped with a catalyst [6]. The objective of the present study is to improve an AN-based gas generator propellant for chlorine-free exhaust for air bag applications. To enhance thermal stability, burning performance and low flame temperature for gas generator propellants, GN and ADC were added and investigated using DSC and TG analysis.

Methodology The following propellant samples are prepared as per mass composition in Table 6.1, HTPB and Dioctyladipate are weighed and mixed, then AN, ADC (catalyst) and GN were pulverized into a fine powder to ensure the required particle size (50–70 µm) Table 6.1 Composition of propellant Sample

HTPB %

DOA %

TDI %

AN %

ADC %

GN %

1

12

2.25

0.75

81

2

2

2

12

2.25

0.75

77

4

4

3

12

2.25

0.75

73

6

6

4

12

2.25

0.75

69

8

8

5

12

2.25

0.75

65

10

10

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59

using a pneumatic pulverizer with a pressure of 7 bar and mixed for 1 h. After 1 h, Toluene Isocyanate (TDI) was added and again mixing was carried out for another 60 min. Finally, the mixture was cast in cylindrical mold and cured in an oven at 60 °C for a week. After curing, the specimen was cut into the required size for testing and then prepared samples were stored in desiccators [7]. Simultaneous Thermal Analyzer was done and intended to study the thermal decomposition of the prepared sample under an inert condition that undergoes phase transformation. The DSC and TGA experiments are the precise methods to evaluate the thermal behavior of sample materials. In DSC, the difference in the amount of heat flow observed between sample and reference material is measured as a function of temperature. NETZSCH STA 449C equipment was used and experiments were carried out using alumina crucible under inert conditions (The flow rate of argon gas is 60 ml/min). Throughout the experiment, heating rates were maintained at about 27 K/min. 20 mg sample mass was placed in the alumina crucible pan, then both the sample and reference materials were maintained at nearly the same operating conditions. These measurement results provide information both qualitatively and quantitatively about the physical changes and chemical changes or changes in heat capacity. DSC curve is plotted with heat flux against time or temperature which is used to determine the specific heat (Cp), enthalpy, etc. Using TGA, samples were characterized that are exhibiting weight loss or weight gain due to oxidation and decomposition. The flow of purge gas across the balance creates an inert atmosphere such as helium, argon or nitrogen; oxidizing i.e., such as oxygen or air or reducing such as forming gas (8–10% hydrogen in nitrogen). From TGA, the thermal stability, oxidative stability, decomposition kinetics and volatiles and moisture content of the materials, reactive or corrosive atmospheres effect on materials, multi-component systems composition and product lifetime estimation can be found [8–10] (Fig. 6.1). Fig. 6.1 NETZSCH simultaneous thermal analyzer 449C

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Results and Discussion The solid propellant decomposes upon ignition at the burning surface and it recedes in a direction perpendicular to the surface. The decomposition behaviors and grain configuration of the propellants are important to analyze the burning characteristics. The DSC and TG analysis for five sample propellant compositions were done with a Simultaneous thermal analyzer (STA) setup. In this analysis, a sample mass of propellant (about 20 mg) is taken in an alumina (Al2 O3 ) crucible and was allowed to heat in the range of 30–600 °C at a heating rate of 27 K/min in an inert gas (Argon) environment. The variation of heat flow transfer of the sample with respect to a reference empty crucible is plotted as a DSC curve and shown in Fig. 6.2. TGA curve shows the mass loss (%) with respect to the temperature increase which is plotted and shown in Fig. 6.3. As the temperature is increased, the mass percentage decreases due to up to high reactions taking place with increasing the temperature. In the TGA curve, it can be seen that as the temperature is increasing, there is a decrease in mass % due to phase change and exothermic reaction. Thus, showing that mass is changing continuously due to thermal treatment. In TGA curve, the first decomposition starts at a lower temperature and continues till a temperature with a change in weight percentage. The mass loss or mass gain of the propellant samples due to the decomposition, degradation, phase change and oxidation can be determined. Figures 6.2 and 6.3 exhibit the stages of the decomposition process of samples to the response of temperature. As the temperature increases from 30 °C at the heating rate of 27 K/min during the STA experiment, sample mass undergoes the reaction.

Fig. 6.2 DSC versus temperature curve

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Fig. 6.3 TG versus temperature curve

When the temperature reaches 150 °C, there was a two endothermic peak due to phase transition and melting of the sample. Beyond 200 °C, it starts to decompose slowly and reached peak condition due to exothermic reaction, then it falls back to the initial value. Decomposition temperature and exothermic peak temperatures are given in Table 6.2 for the samples, and it was altered due to the concentration of ADC and GN. Sample 3 shows the maximum exothermic peak due to energy release and decomposition behavior among other samples. During TG analysis, the sample starts to decompose and lose its mass as temperature increases at a constant heating rate. Further, no changes are observed in heat flux even if the temperature is increased. It was observed that addition of ADC & GN increases in samples, initiation of thermal decomposition were started early and consuming whole mass with in temperature difference of 5 °C. Among the five propellant samples given in Table 6.1, the third sample had possessed a low decomposition temperature and a high exothermic peak due to high energy release which had 6% of ADC and GN in composition. The adiabatic flame temperature for five samples was found from C PROP-SHELL software where ingredients of propellants were given as input at constant chamber Table 6.2 Stage of decomposition and peak values

Sample

Decomposition temperature (°C)

Exothermic peak temperature (°C)

1

209.28

214.30

2

253.97

258.97

3

214.17

219.67

4

224.22

229.21

5

254.22

264.22

62 Table 6.3 Adiabatic flame temperature

R. Suthan et al. Sample

Adiabatic flame temperature (°C)

1

1473.62

2

1429.94

3

1638.41

4

1307.22

5

1245.45

pressure. For the chamber pressure of 40 bar, the adiabatic flame temperature was determined and formulated in Table 6.3. Sample 3 shows high adiabatic flame due to the addition of 6% of ADC and 6% of GN among other samples. It shows that the oxidization content increasing in the propellants to a certain extent will increase the adiabatic flame temperature. Then, beyond this composition, an increase in ADC and GN in the sample causes a decrease in adiabatic flame temperature.

Conclusion The burning characteristics and thermal decomposition behavior of AN propellants doped with ADC and GN were investigated. From the DSC and TGA investigation, the following observation was made for AN-based solid propellant with the addition of ADC and GN. The decomposition temperature, exothermic peak temperature and endothermic peak condition were obtained for all samples, and the addition of ammonium dichromate in the propellant has initiated the decomposition early. It was found that the adiabatic flame temperature also will increase up to a certain extent of ADC and GN in the propellant composition. Among all propellant samples, 6% of ADC and 6% of GN in composition had possessed early decomposition and attained exothermic peak due to high energy release. Acknowledgements The authors acknowledge and thank the Department of Aerospace Engineering, Madras Institute of Technology, Chennai, for providing the experimental facilities for the completion of work.

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References 1. Jos J, Mathew S (2017) Ammonium nitrate as an eco-friendly oxidizer for composite solid propellants: promises and challenges. Crit Rev Solid State Mater Sci 42(6):470–498. https:// doi.org/10.1080/10408436.2016.1244642 2. Sutton ES, Vriesen CW (1979) Gas generator propellants for aerospace applications. AIAA Paper. https://doi.org/10.2514/6.1979-1325 3. Oommen C, Jain SR (1999) Ammonium nitrate: a promising rocket propellant oxidizer. J Hazard Mater 67(3):253–281. https://doi.org/10.1016/S0304-3894(99)00039-4 4. Kohga M, Nishino S (2009) Burning characteristics of ammonium nitrate-based composite propellants supplemented with ammonium dichromate. Propellants Explos Pyrotech 34(4):340–346. https://doi.org/10.1002/prep.200800060 5. Kumar P, Kumar M, Lakra R (2018) Effect of catalysts on the burning rate of phase stabilized ammonium nitrate based composite propellants. IOP Conf Ser Mater Sci Eng 455(1). https:// doi.org/10.1088/1757-899X/455/1/012022 6. Kohga M, Naya T, Okamoto K (2012) Burning characteristics of ammonium-nitrate-based composite propellants with a hydroxyl-terminated polybutadiene/polytetrahydrofuran blend binder. Int J Aerosp Eng 2012:1–10. https://doi.org/10.1155/2012/378483 7. Ganesan S, Sridhar B (2014) Thermal decomposition characteristics of ammonium nitratebased energetic materials. Int J Mech Mechatron 4:110–115. http://scholar.google.com/ scholar?hl=en&btnG=Search&q=intitle:Thermal+Decomposition+Characteristics+of+Amm onium+Nitrate-Based+Energetic+Materials#0 8. Kohga M, Togo S (2018) Influence of iron oxide on thermal decomposition behavior and burning characteristics of ammonium nitrate/ammonium perchlorate-based composite propellants. Combust Flame 192:10–24. https://doi.org/10.1016/j.combustflame.2018.01.040 9. Wang Y, Song X, Li F (2019) Thermal behavior and decomposition mechanism of ammonium perchlorate and ammonium nitrate in the presence of nanometer triaminoguanidine nitrate. ACS Omega 4(1):214–225. https://doi.org/10.1021/acsomega.8b02515 10. Xu ZX, Fu XQ, Wang Q (2016) Phase stability of ammonium nitrate with organic potassium salts. Cent Eur J Energ Mater 13(3):736–754. https://doi.org/10.22211/cejem/65013

Chapter 7

Experimental Investigation of Thin-Walled Multi-Cell GFRP Structure on Energy Absorption K. Sridhar, V. Praveen Kumar, Gokul Haricharan, V. Dilip, V. Amin Himamshu, and R. Suthan

Introduction Multi-cell structures are thin-walled structures having multiple closed cavities in them. They are found to be good at absorbing energy when subjected to high axial compressive loads or crush loads. They are also cost0effective to produce. The energy-absorbing capability of the multi-cell is important for aerospace applications in which the aircraft is subjected to dynamic loads due to impact with foreign objects, for example, bird strikes. Another example is the deceleration pulse generated at the passenger seats in the aircraft during a hard landing. Thus, multi-cell structures have to be lightweight, cost-effective and have a long fatigue life. Bending collapse is also another important aspect as it is observed in components such as wing box due to gusts and other air loads. These beams can also be used to withstand high crush loading; thus, they can be used as stiffeners, longerons or any other structural members that are used under axial loading conditions. In automobile, thin-walled structures have been used to improve the safety of the vehicle in order to avoid severe injuries of the passengers and damages of the vehicle due to road accidents. Glass Fiber Reinforced Polymers (GFRP) are lightweight materials and their usage is prominent in the automobile industry and as well as aerospace industry because of their excellent mechanical properties and high specific energy absorption over metal structures [1–3]. In order to enhance the metallic thin-

K. Sridhar (B) · V. Praveen Kumar · G. Haricharan · V. Dilip · V. Amin Himamshu · R. Suthan Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bangalore 560064, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_7

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walled structures’ crashworthiness performance, multi-cell section configurations have been used, but for the fiber reinforced structures with design concepts, their results are still under study [4, 5]. As a result, the thin-walled reinforced polymers are widely used in the automobile industry as well as in the aerospace industry because the structural weight is less and at the same time crashworthiness capability is also improved, which meets the modern-day design requirements [6]. It was observed that the analytical model was able to predict the SEA values of different configurations within the margin of error, and also for any given configuration, the SEA was directly proportional to the number of corners and sides of that configuration [7, 8]. Multi-Cell structures have higher energy absorption characteristics when compared to single-celled structures. The oblique angle of the load plays an important factor in EA and Peak Loading for all tubular sections [9]. As the cell number increases, the peak load and the energy absorbed also increase for axial loading. Increasing the thickness of the walls, punch radius and speed of loading increased the SEA under transverse loads [10–12]. It was found that for reducing the thickness gradient factor, the peak load of functionally graded multi-cell was slightly less than the peak load of uniform thickness multi-cell. The converse was also possible. SEA increased by 30–35% [13]. From the past research, a lot of work had been done for the CFRP tubes with different configurations subjected to crushing under quasi-static loadings. But, there has not been much focus on the crashworthiness of GFRP multi-cell structures [14–19]. Thus, the aim of the study is to know the crashworthiness of Multi-cell GFRP tubes under axial compression and transverse load. This study’s focus is to design, analyze, fabricate and test the different configurations (Square-1 cell, Square-2 cell and Square-4 cell) using Glass Fiber Reinforced Polymers (GFRP). CATIA was used to design the multi-cell section with different configurations and the models were imported to LS-DYNA and ANSYS software to simulate the compressive loads on the section. The vacuum bag techniques have been used for manufacturing the multi-cell configured model. In the testing phase, the crushing behavior of all the configurations of multi-cell was determined. To estimate the SEA, the specimen was subjected to axial compressive load using a Universal Testing Machine (UTM).

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Methodology

Selection of Configuration for Fabrication

Modelling and Simulation

Procurement of Raw Materials

Finalization of Standards

Fabrication

Testing and Result Validation

Determination of Material Property The specimen is prepared by vacuum bag technique by using following materials such as 200 GSM Glass fiber and Lapox L-12 with K6 Hardener, and it is cut to the required dimension as per the ASTM D3036 standard for tensile test. The test is carried out for the standard gauge length of the model using UTM. The model is tested for the tensile properties and then the results are used to calculate the remaining properties of the glass fiber for analysis purposes. Results are then imported to analyzing software and the required analysis is carried out.

Design and Analysis The compressive test simulation or analysis was conducted in an open-source FEM software LS-DYNA. The first step is to design the model for compression within LS-DYNA Pre-Post. Figure 7.1 shows the modeling of multi-cell model with the rigid plate.

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Fig. 7.1 Four-cell model with rigid plate

Analysis Once the modeling phase is done, the parameters necessary for the analysis are entered. The first step in this phase is to define the curve for the displacement of the rigid body. The next step is to define all the implicit keywords necessary for the simulation and the termination time. Finally, all the required parameters to be measured are selected and then the file is saved in a ‘.k’ format which is then imported to LS-RUN. The following mesh and element details have been used for the analysis and it is shown in Table 7.1 Based on the Analysis results, Energy absorption, specific Energy absorption and Peak Crushing force have been calculated and tabulated in Table 7.2. Figure 7.2 shows the top view of one-cell, two-cell and four-cell after compression. From Table 7.2, it can be observed that SEA increased by 11.88% and PCF increased by 45.29% when comparing one-cell and two-cell and 20.66% increase in SEA and 62.80% increase in PCF when comparing one-cell and four-cell. Similarly, when comparing two-cell and four-cell, the SEA is increased by 9.96% and PCF is increased by 30.40%. Table 7.1 Solution details for compression simulation

Table 7.2 Results from compressive test simulation

Experiment type

Mesh size (mm)

No. of elements

Time to solve

1-Cell compression

1.4

2520

40 min

2-Cell compression

1.4

6250

1 h 5 min

4-Cell compression

1.4

7500

1 h 30 min

Experiment type

EA (J)

SEA (J/g)

PCF (N)

1-Cell compression

77.38

4.30

9300.00

2-Cell compression

107.38

4.88

17,400.00

4-Cell compression

141.00

5.42

25,000.00

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Fig. 7.2 Top view of models after compression

Fabrication of Multi-cell Structure After analyzing the theoretical results, the multi-cell structure has been fabricated using the following steps and also single-cell model is shown in Fig. 7.3. Step 1: Mandrel Preparation Step 2: Fibre Preparation Step 3: Matrix Preparation Step 4: Resin Application Step 5: Wrapping of the wetted fibre Step 6: Peel Ply and Breather Step 7: Preparation of Vacuum Bag Step 8: Curing Step 9: Mandrel and Breather Removal

Fig. 7.3 Single-cell model for testing

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Fig. 7.4 Compression test setup in UTM

Fig. 7.5 Tested specimen

Testing Testing was carried out for compression using a 100kN Computerized Universal Testing Machine (UTM). For the compression test, the model was cut to a length of 70 mm as per ASTM D690-15 standard. The test specimen was placed between the chucks of the UTM and loaded at a rate of 5 mm/min until the total Cross Head Travel (CHT) was 9 mm as shown in Fig. 7.4. This process was repeated for three samples for each configuration and tested specimens are shown in Fig. 7.5

Results and Discussion Using the experimental values of loads vs deflections for all the models, the averaged EA, SEA, PCF, MCF and CFE for each configuration under compression are shown in Table 7.3.

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Table 7.3 Averaged values of EA, SEA, MCF, PCF, CFE and Weight Experiment type

Final deformation (m)

EA (J)

SEA (J/g)

1-Cell compression

0.009

64.76

3.65

2-Cell compression

0.009

125.45

4-Cell compression

0.009

181.99

MCF (N)

PCF(N)

CFE

Weight (g)

7195.37

11,400.00

63.80

17.67

5.72

13,938.89

19,150.00

73.19

22.00

6.81

20,221.30

25,816.67

78.44

26.67

From Table 7.3, it is observed that moving from a single-cell configuration to a two-cell configuration increased the SEA by 36.18%, and PCF is increased by 40.46%. On further increase to a four-cell configuration, a 46.40% increase in SEA and 55.84% increase in PCF compared to a single-cell configuration and 16.00% increase in SEA and 25.82% increase in PCF compared to a two-cell configuration can be seen. This trend supports the hypothesis of a declining return in benefits as cell size is increased for a fixed cross-sectional dimension. Therefore, the ideal number of cells for a given structure will depend on the cross-sectional dimension of the structure. From the study of designing and fabricating multi-cell of different configurations, the following things could be inferred from the analytical and experimental results. From the study in LS-DYNA, it was observed that the model which had Young’s Modulus of 1.4GPa underwent crushing at loads as low as 9.3kN for singlecell, 17.4kN for two-cell and 25kN for four-cell beams. The model started to get compressed such that the center position of the beam bulged and underwent folding. As the loading progressed, the folding took place laterally and not in the center. For loading the model until complete crushing, it was observed that the geometry was completely distorted at the end. The same was observed for the two-cell and four-cell beams, the only difference being the peak load. This shows us that higher numbered cell configuration has more strength than the lower numbered one, i.e., four-cell strength > two-cell strength > one-cell strength. Also, four-celled beams were found to have a higher energy absorption value when compared to the two-cell and single-cell beams because of the aforementioned reason. Note that the analysis was conducted keeping displacement of the loading body (Rigid body) constant, because of which a higher celled beam will be able to bear a higher peak load is shown in Fig. 7.6.

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Fig. 7.6 Comparison of experimental and theoretical curves of three different configured cells

In Table 7.4, both the theoretical and the experimental values for compression are shown, and also the percentage error has been calculated for EA, SEA and PCF for one-cell, two-cell and four-cell compression. The EA, SEA and PCF values are nearly the same when calculated and experimentally tested but there is some error occurring due to the difference in material properties theoretically calculated and experimentally tested. This is due to the manufacturing errors, impurities in the Table 7.4 Error percentage between theoretical and experimental values for compression Model

EA The

Exp

% Error

The

SEA Exp

% Error

PCF The

Exp

% Error

1-Cell compression

77.38

75.40

2.55

4.30

3.97

7.68

9300.00

10,850.00

14.28

2-Cell compression

107.39

110.40

2.81

4.88

5.49

12.46

17,400.00

17,250.00

0.86

4-Cell compression

141.00

157.00

11.35

5.42

6.31

14.10

25,000.00

27,350.00

9.40

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manufacturing atmosphere, moisture, manufacturing process and calibration error of the testing machine. These add up to the experimental values due to which there are error values when compared to the theoretical values.

Conclusion Experimental results of the testing conducted in the UTM showed a good resemblance with the analytical values. The slight variation in load values of the three consecutive models is a result of minor variation of thickness among the models due to small flaws during fabrication. When the testing was done in the UTM, it was observed that as the loading progressed, the folding took place in the outward direction from the edges, slowly tearing apart the material. After loading the model until complete crushing, it was observed that the geometry was completely distorted at the end. The same was observed for the two-cell and four-cell beams, the only difference being the peak load. This shows us that the higher numbered cell configuration has more strength than the lower numbered one, i.e., four-cell strength > two-cell strength > one-cell strength. The results showed that the energy absorption increased by increasing the number of cells in the beam on being subjected to high crush loads. Thus, the fourcelled beams had higher energy absorption, Specific energy absorption and Peak crushing force than the other configuration. The multi-cell was found to have a CFE range of 60–82% with models whose CFE is greater than 80%, showing more promising results. Our research further emphasizes that multi-cell structures can be used in place of solid beams for various applications. Acknowledgements The authors acknowledge and thank the Karnataka State Council for Science and Technology (KSCST) for funding this project and thank the Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, for providing the support and experimental facilities for the completion of work.

References 1. Sun G, Xu F, Li G, Li Q (2014) Crashing analysis and multiobjective optimization for thinwalled structures with functionally graded thickness. Int J Impact Eng 64:62–74. https://doi. org/10.1016/j.ijimpeng.2013.10.004 ´ 2. Urbaniak M, Swiniarski J, Czapski P, Kubiak T (2016) Experimental investigations of thinwalled GFRP beams subjected to pure bending. Thin-Walled Struct 107:397–404. https://doi. org/10.1016/j.tws.2016.06.022 Oct 3. Xiao Y, Wen XD, Liang D (2012) Failure modes and energy absorption mechanism of CFRP Thin-walled square beams filled with aluminum honeycomb under dynamic impact. Compos Struct 271, Sep. https://doi.org/10.1016/j.compstruct.2021.114159

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4. Fang J, Gao Y, Sun G, Zheng G, Li Q (2015) Dynamic crashing behavior of new extrudable multi-cell tubes with a functionally graded thickness. Int J Mech Sci 103:63–73. https://doi. org/10.1016/j.ijmecsci.2015.08.029 Nov 5. Alavi Nia A, Parsapour M (2014) Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections. Thin-Walled Struct 74:155–165. https://doi.org/10.1016/j.tws.2013.10.005 6. Fang J, Gao Y, Sun G, Qiu N, Li Q (2015) On design of multi-cell tubes under axial and oblique impact loads. Thin-Walled Struct 95:115–126. https://doi.org/10.1016/j.tws.2015.07.002 Jul 7. Bai Z, Guo H, Jiang B, Zhu F, Cao L (2014) A study on the mean crushing strength of hexagonal multi-cell thin-walled structures. Thin-Walled Struct 80:38–45. https://doi.org/10.1016/j.tws. 2014.02.024 8. Czechowski L, Gliszczy´nski A, Bienia´s J, Jakubczak P, Majerski K (2017) Failure of GFRP channel section beams subjected to bending—Numerical and experimental investigations. Compos Part B Eng 111:112–123. https://doi.org/10.1016/j.compositesb.2016.11.057 Feb 9. Baroutaji A, Sajjia M, Olabi AG. On the crashworthiness performance of thin-walled energy absorbers: recent advances and future developments 10. Gliszczy´nski A, Kubiak T (2017) Load-carrying capacity of thin-walled composite beams subjected to pure bending. Thin-Walled Struct 115:76–85. https://doi.org/10.1016/j.tws.2017. 02.009 Jun 11. Ahmed S, Ayub S (2015) Failure analysis of composite thin walled multi-cell closed cross section beams with multi-tapered configuration. Appl Mech Mater 789–790:382–388. https:// doi.org/10.4028/www.scientific.net/amm.789-790.382 Sep 12. Zhu G, Sun G, Yu H, Li S, Li Q (2018) Energy absorption of metal, composite and metal/composite hybrid structures under oblique crushing loading. Int J Mech Sci 135:458–483. https://doi.org/10.1016/j.ijmecsci.2017.11.017 Jan 13. Wang Z, Li Z, Zhang X (2016) Bending resistance of thin-walled multi-cell square tubes. Thin-Walled Struct 107:287–299. https://doi.org/10.1016/j.tws.2016.06.017 Oct 14. Zhu G, Sun G, Li G, Cheng A, Li Q (2018) Modeling for CFRP structures subjected to quasistatic crushing. Compos Struct 184:41–55. https://doi.org/10.1016/j.compstruct.2017.09.001 Jan 15. Qiu N, Gao Y, Fang J, Feng Z, Sun G, Li Q (2015) Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases. Finite Elem Anal Des 104:89–101. https://doi.org/10.1016/j.finel.2015.06.004 Jul 16. Kim JS, Yoon HJ, Shin KB (2011) A study on crushing behaviors of composite circular tubes with different reinforcing fibers. Int J Impact Eng 38(4):198–207. https://doi.org/10.1016/j.iji mpeng.2010.11.007 Apr 17. Zhang Y, Ge P, Lu M, Lai X (2018) Crashworthiness study for multi-cell composite filling structures. Int J Crashworthiness 23(1):32–46. https://doi.org/10.1080/13588265.2017.1304169 Jan 18. Liu Q, Fu J,Ma Y, Zhang Y, Li Q (2020) Crushing responses and energy absorption behaviors of multi-cell CFRP tubes. Thin-Walled Struct. 155, Oct. https://doi.org/10.1016/j.tws.2020. 106930 19. Huang Z, Li Y, Zhang X, Chen W, Fang D (2021) A comparative study on the energy absorption mechanism of aluminum/CFRP hybrid beams under quasi-static and dynamic bending. ThinWalled Struct 163, Jun. https://doi.org/10.1016/j.tws.2021.107772

Chapter 8

Study of Regression Rate in Hybrid Rockets Using Vortex Injector P. K. Dash and G. Ram Vishal

Nomenclature a m˙ B Cp D fm G h H k K ox L Le n

Regression rate coefficient Mass flow rate per unit length Mass transfer number Specific heat of gas Diameter Fuel-air rate Free stream mass flux Enthalpy Heat of combustion Thermal conductivity Oxidizer mass fraction Length of fuel grain Lewis number Flux index

P. K. Dash (B) · G. Ram Vishal Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bengaluru, Karnataka, India e-mail: [email protected] G. Ram Vishal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_8

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Introduction Rockets are incredible feats of human ingenuity with origins in past science and technology. A rocket propulsion system is assigned a name according to the source of energy. Depending upon the physical state of the stored propellant prior to combustion, chemical propulsion systems can be classified as liquid rockets, solid rockets, and hybrid rockets. A hybrid propellant rocket engine combines the advantages of a solid and a liquid propellant rocket engine. A hybrid’s fundamental architecture consists of a combustion chamber tube filled with a solid chemical, generally the fuel, similar to regular solid-fueled rockets. Bartel and Rannie [1] presented a hybrid combustion model connecting the fuel in the form of a tube through which a onedimensional and turbulent airflow was studied in the early 1950s. The rate-controlling component was believed to be the diffusion or transfer of oxygen through the gas layer to the surface, but no assumptions about the flame’s position or structure were made. Marxman and Gilbert [2] conducted a thorough investigation on hybrid combustion. According to this theory, the boundary layer is separated into two zones: one above the fire, where the temperature and velocity gradients are in opposite directions, and one below the fire, where they are in opposite directions. The zone under the fire is believed to create an effective boundary layer for heat transfer to the wall, while the two zones together form a boundary layer for momentum transfer. The combustion behaviour of a PVC plasticized hybrid fuel in a gaseous oxygen oxidizer stream was investigated by Chatterjee and Joshi [3]. The effect of fuel port grain length and port size on local regression rate, mean regression rate, and mass consumption rate was also investigated. The engine is securely placed in the test stand, and the oxygen gas line is connected to the adapter at the entrance to the oxidizer compartment. The oxidant injection pressure is controlled using a dome regulator at the desired amount of 600 psi, and ignition is initiated by turning on the ignition current. When the igniter lit, oxygen gas was supplied, and the combustion was halted by shutting off the oxidizer supply after a specific period of time had passed. Each grain of fuel burns for three seconds. The fuel pellets are removed from the combustion chamber after each fire test and cut along in four places with a sharp stick for visual inspection and measurement of the thickness of the unburned mesh along the fuel grain. The fuel pellets are weighed after the fire to determine the rate of mass consumption. The local regression rate was estimated by measuring the thickness of the unburned strip using a micrometer at each cm interval. Band thickness was measured four times around the periphery of each station and the average value was used to calculate the station’s local regression rate. The mass consumption rate is calculated using the difference in weight before and after the fire, assuming a constant consumption rate. The mean regression rate was obtained by means of the local regression rate data and the average unburned band thickness.

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Experimental Setup The current research was carried out at the hybrid rocket test facility. A testing stand, a control room, a storage building, and a protection wall make up the test facility. An oxidizer compartment, an injector, an ignition compartment, and a nozzle made up the hybrid test motor. A showerhead injector has been used at the end of the motor head, which has been made up of a stainless-steel plate having seven holes out of which six holes have been drilled at the same p.c.d. and one hole has been drilled at the centre. A vortex tube has been introduced from the nozzle end to study the effect of vortex injection, while oxygen gas has also been introduced from the head end injector. At the nozzle end, the injector was used in the motor made of a stainlesssteel cylindrical tube. This injector tube has two configurations, namely two holes vortex injector and multi-perforated vortex injector. In the first configuration, two holes were made at a 180° pattern, while the second configuration includes four holes each at a 90° pattern, both having different lengths. A length of 30 mm of vortex injector was kept for the post-combustion chamber and injector retainer ring, while the remaining length was kept inside the fuel grain. A combustion chamber made of mild steel having a hollow cylindrical shape was used for the test motor. A hole was drilled and threaded at the end of the head side to a pressure transducer to find the combustion compartment pressure. The nozzle used was made from graphite for use in the present investigation. The nozzle was held in place with the combustion chamber by a mild steel nozzle retention ring. Figure 8.1 depicts the arrangement. Due to its superior mechanical and chemical properties, ease of handling, accessibility, and wide range of applications in the propellant industry, PVC plastisol is used as a binder in solid propellants and as a fuel in hybrid propellants. The correct amount of PVC and DBP are combined in a horizontal sigma blade mixer. In an aluminium mould and mandrel, the fuel mixture was cast. To start the fuel combustion, a pyrotechnic shellac igniter was employed. Bolts and nuts were used to secure the showerhead injector and oxidizer chamber at the chamber’s head end. The vortex injector tube was introduced into the fuel grain from the downstream end of the combustion chamber for the vortex hybrid rocket case after being placed in the vortex injector retention ring. After the injector retention ring, a nozzle retaining ring was used to secure the nozzle.

Fig. 8.1 Schematic of vortex hybrid rocket motor

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Test Procedure The oxygen fuel line became linked to the adaptor on the oxidizer chambers intake, and the motor became firmly mounted to take a look at the bed. The oxidizer injection stress became regulated to the best quantity with the assistance of a dome regulator, and the combustion became initiated with the aid of turn valve at the ignition current. The neighbourhood regression fee became envisioned with the aid of using measuring the un-burnt internal thickness, the use of a micrometer at every cm interval. The mass intake fee became calculated by the use of the distinction in weights earlier than and after the fire, assuming a steady fee of intake. The common regression fee became received with the aid of averaging the neighbourhood regression fee records and taking the common of the unburnt Internal thickness.

Results and Discussion In this study, work was carried out to study the regression rate of PVC-DBP fuel with three compositions using two different configurations of constant injection pressure vortex injectors. The fuel regression rate was also determined using the showerhead injector and the data were compared with the two vortex injectors. a.

Local Regression Rate The values in all the cases of showerhead injectors as well as of vortex injectors for cylindrical port configuration of solid fuel grains have been plotted in Fig. 8.2. All the local regression rate curves for showerhead injectors, as apparent in Fig. 8.2, have a similar trend. The regression rate has been found highest at the head end from where it decreases to a minimum at about ten diameters and then increases slightly until the nozzle end. In the case of vortex injector 1, the trend was found to be similar to that of the shower head where the regression velocity was maximum at the head end and continued to decrease towards the nozzle tip. The scheme is slightly different for the 60P and 65P vortex 2 injector configurations, since the regression rate is practically uniform across the grain length of the solid fuel in this situation, but the trend for the 50P is the same as for injectors with a shower head. The greatest regression rate in a showerhead injector can be assigned to high oxidizer concentrations and heterogeneous chemical reactions caused by direct oxygen impingement at the fuel intake port. Due to the proximity of the flame zone to the grain port, the head tip regression rate is expected to be high. GOX is depleted and reduced along the grain of the solid fuel. Mass flow, on the other hand, continues to increase throughout. The oxygen quality at the site, which allows sufficient oxygen diffusion in the flame zone, and the total mass flow, which is responsible for the heat transfer to the fuel surface for pyrolysis and hence regression, can both affect the velocity. Regression at each position can be controlled in the fuel grain. The heat feedback from the flame to the

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Fig. 8.2 Local RR along the length of solid fuel grain using showerhead and vortex injectors in cylindrical port

solid fuel surface contributes to and controls the rate of regression. The flame zone, on the other hand, moves away from the fuel surface while the boundary layer develops along the fuel grains. As a result, heat feedback from the flame zone to the fuel surface decreases with time, as does the rate of regression. The minimum regression rate at the nozzle tip, where it shows a minimum value before regrowth, can be caused by the boundary layer merging into the flow, causing the flow to become turbulent. Except for 60P and 65P in vortex injector 2 configurations, where the regression rate has been found out of a lower value and is almost uniform throughout the length of the solid fuel grain, the local regression rate curves in the cases of vortex injectors appear like the showerhead injectors, with the highest value at the head end and decreasing towards the nozzle end continuously. Only a slight decrement of regression rate can be seen in these cases. The trend for local regression rate data is the same for 50P and 60P, suggesting that vortex injector 1 does not play a major role in determining local regression rate as a function of length. There is a trend of greater regression rate values in the case of vortex

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injectors, which might be due to direct oxygen impingement at the fuel input port, and the flame zone is near to the grain port, resulting in a larger regression rate at the head end. As the distance along the solid fuel increases, GOX decreases as it reacts, and the intensity of the heterogeneous reaction decreases. But again, after about 6–9 diameters, the vortex injector generates more GOX and thus tries to keep the oxidant concentration in the port. An extra supply of oxidizer at this port allows solid fuel grains to recoil almost evenly after the butt end. The mass flow is also very high towards the nozzle tip and the flame zone will not be as close to the solid fuel surface as it is at the head tip. The decrease in regression rate is due to a decrease in heat feedback from the flame zone to the fuel surface. While in the case of 60P and 65P in vortex injector 2 configurations, the regression rate is almost uniform throughout the length of the solid fuel grain. When seen more accurately, there is a slight increase in the regression rate at the nozzle end which may be due to the boundary layer, making the flow turbulent. b.

Effect of Vortex Injectors In Fig. 8.3, various injector designs were used to compare the local regression rate of solid fuel grain for 50P composition. The showerhead injector as well as the vortex 1 injector configuration has a similar type of decrement in the regression rate values. There is a slight increment of regression rate in the showerhead injector towards the nozzle end from its minimum value. While in vortex 2 injector although regression rate values are dropping, the rate of decrease is extremely little in this situation. In Fig. 8.4, a comparison has been made for 60P fuel grains. In this figure, compared to showerhead injectors, the

Fig. 8.3 Comparison of local RR in different motor configurations for 50P fuel grain

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Fig. 8.4 Comparison of local RR in different motor configurations for 60P fuel grain

entire injector design exhibits a very uniform regression rate. From this figure, the vortex injector contributes to the uniform combustion of solid fuel grains in the 60P case. The vortex injector 2 configuration shows a nearly uniform regression rate.

Fig. 8.5 Comparison of local RR in different motor configurations for 65P fuel grain

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Fig. 8.6 Comparison of average RR in all fuel combinations for all motor configurations

In Fig. 8.5, comparison has been made in 65P fuel grain. The showerhead injector and vortex 1 injector show a totally different nature of regression rate from the other configurations. c.

Average Regression Rate In Fig. 8.6, the average regression rate was shown against various motor setups and injectors. In all combinations of solid fuel grains, the average regression rate values are shown to be greater for vortex 2 injector. The lowest average regression rate value was observed in vortex 1 injector, implying that vortex 1 injector does not contribute to average regression rate values.

Conclusion The problem of non-uniform solid fuel combustion in hybrid rocket motors is addressed in this study. Three different injectors were tested for regression rates in the cylindrical port: shower head, vortex injector 1, and vortex injector 2. On the basis of fuel grain composition as well as injector designs, the regression rates of all of these setups were compared. During the research, certain major findings might be drawn. Except for a few instances when the regression rate increased somewhat towards the nozzle end, local regression rates were found to be higher at the head end, followed by a decrease in values along the entire grain length. Regression was found to be nearly uniform in the vortex injector configuration compared to the showerhead injector system. In the vortex injector 2 configuration, the uniformity of the regression rate is excellent.

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In all cases, the exhaust plume was brilliant with a yellowish flame, indicating full combustion. Smoke was determined to be nearly non-existent. In the case of vortex hybrid rockets, soot formed on the nozzle and the showerhead injector plate has been found to be practically non-existent. When compared to other systems, the vortex hybrid system has a higher fuel mass consumption rate.

References 1. Bartel HR, Rannie WD (1946) Solid fuel combustion as applied to ramjets. Progress Report 3–12, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, Sep 2. Marxmann GA, Gilbert M (1963) Turbulent boundary layer combustion in the hybrid rocket. Academic Press, New York, Ninth International Symposium on Combustion, pp 371–372 3. Chatterjee AK, Joshi PC (1980) Length and port size effect on combustion of PVC plastisol hybrid fuel. Propellant Explos J 15:163–167

Chapter 9

Designing of a Long-Range Autonomous Multirotor on a Custom-Built Carbon Fiber Frame Prashant Manvi, P. K. Siddalingappa, and Santosh Hosur

Introduction Unmanned aerial vehicles or un-crewed aerial vehicles are commonly called drones; they are machines that fly without human pilots inside the vehicle and are controlled by remote control or a computer. The modern UAVs have come so far from the past with great technologies with high capability of Autonomous missions with high success rate in the missions. Nowadays, the modern UAVs are most widely used in military applications, surveying purposes, and inspection. In the present scenario due to pandemics, most of the delivery companies are leaning toward UAV Technology for safe and secure delivery of goods to the customer. The frame is the mechanical structure of a multirotor. It is the structure that joins the motors to the rest and strength of the multirotor. The frame should carry all the electronics and wires from the circuit battery. The frame is also connected to the landing gear, for the safety of the electronics present in the frame. The Electric motors are the main parts of the drone with which the propeller produces thrust by spinning in its axis to lift the drone; it is the propulsion system of a drone. The flight controller (FC) is the Brain of a Drone, containing various types of sensors to know the current dynamics and information of the present physical quantity information such as pressure and temperature of the surroundings.

P. Manvi (B) · P. K. Siddalingappa · S. Hosur Department of Aeronautical Engineering, Nitte Meenakshi Institute of Technology, Bengaluru, Karnataka, India e-mail: [email protected] P. K. Siddalingappa e-mail: [email protected] S. Hosur e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_9

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A propeller is a body with rotating hubs and pitched blades attached which transforms the rotational power to linear thrust. There are different kinds of propellers depending on the number of fans (rotors) present and the pitch of the propeller. ESC is a device that interprets the signals from the flight controller and the power from the battery and translates those signals to phased electrical pulses to determine and set the RPM of the motor. The batteries are the powerhouse of a drone and are selected properly to achieve a balance in performance and flight time. There are various types of batteries like LiPo battery, nickel–cadmium battery, Li-ion battery, load cells, etc.; among these, the vastly used batteries are the LiPo batteries because of their high energy density and high discharge rate. The FPV camera is the key component of the drone that allows the pilot to view the first-person perspective view of the drone onboard; these cameras would be streaming the real-time video of the drone to the pilot who is piloting it. These cameras are used for a wide dynamic range and low latency. There is a set of transmitters placed in the drone to transmit the real-time images and the controls to and from the receiver [1]. The transmitters are the Video transmitter also called VTX which transmits the video to the goggles, or the monitor, and the transmission happens at 5.8 GHz, and the Receiver receives the information sent by the pilot to steer and commands to the airborne drone. Javir et al. [2] discussed the designing process with thrust calculation and decided on compatible avionics that was selected for custom-built and analyzed frame. By analyzing the model in appropriate software’s for better approximation of design for thrust calculation and decided on compatible avionics that was selected for custom-built and analyzed frame. Mahaveer et al. examined an approach to optimize the design of quadcopter and to build custom quadcopter using 3D printing technology; a safe static structural frame has been fabricated using 3D printing technology with a reduction in cost and type of fabrication and can reduce cost and time of fabrication; also, production waste can be reduced by using this additive manufacturing technology. Endrowednes Kanata et al. demonstrated the difference between the propeller with the duct and the propeller with the duct using CFD, and propellers of the given size can be optimized by adding ducts around them but keeping the weight adding of ducts below a certain range. Inman et al. investigated the aerodynamic behavior of ducts and studied the flow control techniques. New models for flow control techniques are studied such as flow separation technique at duct lip, and synthetic piezoelectric jet blowing is used in flow control techniques; these flow control concepts proved themselves to be successful in producing aerodynamic forces and moments on a ducted fan. It is evident that both ducted fans and synthetic jets are good at controlling the flow, and these can increase efficiency at a certain amount of power. Hunter Gossett [3] presents an indoor autonomous drone system using a self-assembled drone that uses a companion computer as well as external sensors for autonomous flight and electronics supporting the autopilot system.

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Fig. 1 a Flow simulation and vortex formation for the rotor, without duct, b Velocity profile for the rotor, without duct, and flow over the propeller

Flow Simulation for Thrust Determination The rotor (without duct) analysis is done to know the thrust produced by the propeller (Jumpfan-5 ) model when the propeller is rotating at 24,000 RPM and inlet velocity of 18 m/s to know the flow trajectory (Fig. 1). Due to the pressure between the upper and lower surfaces of the propeller, thrust is produced in the direction above the propeller. The flow over the propeller is responsible for the generation of thrust. The total force in the z-direction is considered for the thrust force. From the simulation, the total thrust produced by the rotor at 24,000 RPM (100% throttle) is obtained as 8.001 N.

Designing of Duct In the case of a ducted rotor, the shape of the diffuser determines the change in the area of the air or the slipstream outside the duct [4]. The slipstream can be forced to either keep a consistent cross-sectional region or to increase the region by utilizing a cylindrical diffuser. So, this allows the air which moves out the diffuser expansions in pressing factor and reducing the power requirements for activities [5]. Similarly, as an open rotor, the energy hypothesis can be utilized for the main request expectation of the exhibition, yet the solitary distinction is the slipstream that has extended back to typical air pressure at the leave plane (Fig. 2). For the present research work, the following dimensions are considered while designing the duct (Fig. 3): δtip = 0.1%Dt i. Lip radius γtip = 13% Dt ◦ ii. Angle of diffuser = 72

(9.1)

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Fig. 2 Duct parameters

Fig. 3 Duct dimensions

iii. Diffuser Length = 40% Dt

(9.2)

Dt = 0.1%Dt + D + 0.1%Dt Dt = 0.2%Dt + 0.12954 [Propeller diameter D = 0.12954 m] Dt = 0.129799 m δtip = 0.1%Dt 0.1 ∗ 0.12979 = 100 = 0.000129799m of the rotor disk: A=

π 2 D 4

(9.3)

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π 0.129542 4 = 0.01317 m2

(9.4)

π 2 Dt 4 π = 0.1297992 4 = 0.01323 m2

(9.5)

=

Diffuser exit area: Ae =

Diffuser Expansion Ratio (σd ): σd = Ae/A 0.01323 = 0.01317 = 1.00455

(9.6)

Lip radius: γtip = 13% Dt =

13 (0.12799) 100 = 0.01687m

(9.7)

Ld = 40% Dt 40 = (0.129799) 100 = 0.05191m

(9.8)

Diffuser Length:

Angle of Diffuser: 7◦ 2 = 3.5◦

θd =

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Fig. 4 a Von Mises stress for the frame, b total deformation analysis for the frame

Result and Discussion Static Analysis of the Frame The structural analysis of the quadcopter was carried out in ANSYS (Static structural workbench) by considering the thrust produced by each rotor and the total mass of the drone. The total thrust (Upward force) acting on the drone is set to 39.2 N (9.8*4). The results shown are the stresses acting on the from and total deformation due to the weight of the frame including electronics and the thrust produced by the rotor. The Von Mises stress contours show a maximum value of 1.1*107 Pa, minimum value of 1.7*10+5 Pa, maximum total deformation of 9.8588*10−5 m, and minimum total deformation of 6.2109*10−6 m (Fig. 4).

Flow Behavior The CFD analysis is used to know the performance of the quadcopter with and without the duct and to know which one produces more thrust and its efficiency. The analysis was carried out taking some of the conditions specified in the thrust for a given motor. The figure shows the velocity profile over the duct. From the above analysis for the open rotor, there is a vortex formation at the tip of the propeller which reduces the net thrust produced; installing a duct around the propeller would increase the net thrust. As there is a small gap between the rotor and the duct wall, this would reduce the vortex formation. The total thrust produced due to Propeller is 4.947 N and Duct is 3.552 N. The cumulative thrust is 8.498 N, compared to that of thrust produced by the rotor without duct of 8.001 N. It has been observed from that from the analysis rotor with duct is more efficient for design considerations (Table 1; Fig. 5).

9 Designing of a Long-Range Autonomous Multirotor … Table 1 The details of test cases

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Parameters

Values

Propeller rotating direction

Clockwise

Propeller rotation

24,000 RPM

Gravity

9.8 m/s2

Air density

1.225 kg/m3

Diameter of propeller

0.12954 m

Diameter of duct

0.129799 m

Turbulence parameters

Intensity—0.1%

Fig. 5 a Flow simulation and vortex formation for the rotor, with duct b Velocity profile for the rotor, with duct, and flow over the propeller

Design The process of designing the frame is to calculate the total thrust by considering the total weight of the model (Electronics and frame) and finding a suitable motor and its suitable propeller. According to the calculation, the motor (T motor VELOX V2 2306 2400 kV) produces a thrust of 979gm when a propeller of 5 is attached to it. The configuration of the drone is noted (X or plus configuration), and the length of the arm is adjusted accordingly. The base frame is made up of 2 plates that sandwich the arms in between them. These plates are placed opposite to each other to get the required length for placing the electronics on these plates [6]. This type of setup will increase the resistance on impact while landing; there are sufficient holes given for the placement of electronics and the attachment of other structures. The top plate is a single plate that is identical to the top view of base plates. The top plate holds the battery and other electronics. The distance between both the top and bottom plate is 40 (mm); this gap relates to a standoff made of brass and is placed at each corner and the places where the structure seems to get compressed. There is a total of 8 standoffs placed in our model. There is a soft foam added in the base of the frame to cushion while landing. The frames are

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Fig. 6 a CATIA model of drone, b 3D Model of rotor with duct

made up of carbon fiber material and other component accessories are 3D printed, and a brass standoff was used in fabricating the model (Fig. 6).

Materials Used The carbon fiber which contains the fiber which contains at least 92 of weight % of carbon composition. They can either be short or continuous fibers [7]. The high modulus of the carbon fiber coupled with its lower weight makes it an ideal material to be used in aerospace applications. The mold of the part which has to be made is placed inside the vacuum bag and sealant tape is used to close the bag around the mold and the part. The vacuum pump is switched on and the vacuum controller is set to 20% of vacuum. The vacuum bag is positioned and controlled in such a way that there is no bridging of the film on any of the corners, and the film is fully pressed into all details and contours of the mold. Once the part is fully cured without any air voids, it is then removed from the mold (Fig. 7).

Fig. 7 a Carbon fiber plate after processing. b Carbon fiber plates after cutting

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Autonomous Autonomous Platform An autonomous mission typically uses a global positioning system (GPS) for its flight to act as an autopilot system. It takes the GPS coordinate and has the capability to travel without any pilot input. There are numerous open-source software that are available and can be used for coding and controlling the drone [8]. INAV is a unique software that is highly focused upon the GPS feature for both planes and drones. It supports RTH, position hold, altitude hold, way-point missions, and many other features. This software has a wide range of support on numerous flight controllers. The software is user-friendly to configure, hence for the current research work INAV is used as primary software. Tekko32 F3 4in1 ESC comes with an F3 MCU which provides smooth operation and better response time. The PCB in the ESC uses a design where the drive circuit and control circuit are separated. HGLRC M81 GPS comes with an M810 chip onboard and also has a built-in compass module, thereby reducing the space taken by the GPS.

Fail-Safe/Return to Home If a quadcopter loses the signal at any point, then the pre-defined FAIL_SAFE configuration will come into action and collects the data from the GPS of the initial take-off position and comes back to that position (Fig. 8).

Fig. 8 a Fail-safe configuration though INAV. b Return to home sequence

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Fig. 9 Waypoints given in INAV platform

Waypoint Mission The initial waypoints are defined in the INAV platform, then these positions are loaded onto the flight controller. Then when the command is given to the mission; it takes the input from the pre-defined waypoints and completes the mission Autonomously and carries the mission without any pilot controls [9]. A pre-defined altitude is set in the INAV platform and is stored in flight controller. While the drone is in motion if the pilot gives the command of altitude hold, the drone executes the given command and stays on the altitude which was given (Fig. 9).

Conclusion The structural and computational fluid dynamics analysis was carried out for rotor, with duct and without duct; it was observed that the thrust is increased by 6.2% for the rotor with duct as well as aerodynamic efficiency was improved. This design has undergone static structural analysis, and it has been found that 3 mm thickness for carbon fiber is the efficient option to keep the model light and strong. The best feasible design for the frame is the X configuration quadcopter of the micro-level vehicle. The developed UAV has been installed with autonomous enabled firmware of the open-source INAV platform which has filled the drone with autonomous features of altitude hold, GPS lock, return to home, etc. The flight test of the UAV has been carried out with the autonomous features in it which are suitable for long-range missions with the installation of a first-person view camera for a live and recorded feed of the surveillance under the drone.

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Conflict of Interest The authors confirm that there is no conflict of interest to declare for this publication.

References 1. Kardasz P, Doskocz J, Hejduk M, Wiejkut P. Drones and possibilities of their using lower silesia accelerator technology and innovation Nowodworska, Wrocław, Poland 2. Javir AV, Pawar K, Dhudum S, Patale N, Patil S. Design, analysis and fabrication of quadcopter. ISSN: 2208–2379 3. Chao HY, Cao YC, Chen YQ (2010) Autopilots for small unmanned aerial vehicles: a survey. Int J Control, Autom Syst 4. Rejane Cavalcante Sa Instituto Federal de Educação, Ciência e Tecnologia do Ceará Guilherme A. Barreto Universidad Federal do Ceará Design and construction of a quadrotor-type unmanned aerial vehicle: preliminary results conference paper, May 2012 5. Quadcopter thrust optimisation with ducted propeller. In MATEC web of conferences, January 2017. https://doi.org/10.1051/matecconf/201712601002 6. Balakrishnan S (2016) Master Thesis in engineering design. Duct fan shielding design for quadrotors, July 7. Modh H (2014) Quadrotor—An unmanned aerial vehicle. J IJEDR 2(1):1299–1303 8. Besada JA, Bergesio L, Campaña I, Vaquero-Melchor D. Drone mission definition and implementation for automated infrastructure inspection using airborne sensors madrid, Spain 9. Park D, Lee J, Paek J (2017) An empirical measurement study on UAV controller Communication NSL@CAU Technical report

Chapter 10

Abrasive Wear Behaviour of Camphor Soot Filled Coir/Palmyra Fibre Reinforced Nylon Composites T. Raghavendra and K. Panneerselvam

Introduction Abrasive wear is a commonly faced situation in applications like gears, vanes, pumps handling fluids, bearings subjected to higher temperatures, chute linings abraded by mineral ores, coal, coke, etc. [1]. Abrasive wear depends on the particle size of the abrasive, applied load, velocity of sliding, chemical composition of the material, and wear mechanisms accruing during friction. Polymers are soft, though they have very good abrasive wear resistance compared to some soft metals. The higher performance of plastics is mainly due to the inability to its fracture the tenacities and gives rise to sharp edges [2]. Abrasive wear takes place when softer material is worn out from the surface by a harder one, leaving debris among two surfaces. Usually, abrasive wear happens mainly with two circumstances namely two-body abrasion and three-body abrasion [3]. Circumstance abrasion encompasses scratching away of small pieces of material which makes hardness and tensile strength the important factors to be considered. In comparison to metals, polymers having relatively low mechanical, wear, and thermal properties compels researchers to look for suitable reinforcing materials and fillers to reinforce virgin polymers to enhance their mechanical, tribological, and thermal properties [4, 5]. In recent days, growing attention towards lignocellulosic fibre reinforced polymer composites are mainly recommended as counterparts over synthetic fibre reinforced composites due to various benefits such as availability, mere density, biodegradability, lower cost, moderate T. Raghavendra (B) Departmentof mechanical engineering, National institute of engineering, Mysuru, Karnataka 570008, India e-mail: [email protected] K. Panneerselvam Departmentof production engineering, National institute of technology, Tiruchirapalli, Tamil Nadu 620015, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_10

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mechanical properties, and good abrasive resistance [6–8]. Usually, natural fibres have problems like moisture absorption from the surrounding which results in lesser bonding with polymer matrices due to the presence of components in natural fibre like cellulose, hemicellulose, pectin, lignin, and some waxy materials [9]. Alternative methods to enhance compatibility are alteration of natural fibres interracially with the aid of various chemical treatments which improve bonding between fibre and polymer surfaces [10]. Coir fibres are rough and dense and are taken from the shell of fruit of coconut tree, found abundantly in Asian countries like India, Srilanka, Thailand, Indonesia, Vietnam, and Malaysia. Coir fibres are used to make a range of floor finishing materials like yarns, brushes, mattresses, rugs, boats, and insulation panels. Due to its remarkable properties owing to its durable quality, are great stiffness, considerable sound resistance, resistive to fungi and bacterial degradation, is non-flammable, with extra resistance to humidity than other natural fibres, and being steady in high temperature and saline water [11, 12]. Among all the natural fibres, palmyra fibres have the lowest density (0.7/g/cm3 ). This property accounts for its lightweight. The fibres have resist heat and friction and can withstand chemicals and solvents [13]. Nylon has higher wear properties, good lubricating material, and decent mechanical properties owing to its hydrogen bond and van der walls force present between its molecular chains [14]. Camphor (C6 H16 O) is a new nanomaterial supplier extracted from the cinnamomum tree which consists of both sp2 and sp3 covalent bonds with carbon. 0.1 g of carbon nanotubes can be extracted from the 0.5 g of camphor, and hence it is the effective means for carbon nanomaterials that are nontoxic and eco-friendly [15]. The aim of the present work is to alter coir and palmyra fibres interracially by reinforcing the camphor soot particles into the fibres through osmosis process as these are highly porous. Further, camphor soot reinforced coir and palmyra fibres are reinforced with varying fibre loads into nylon-6 using a twin screw extruder tailed by injection moulding to obtain nylon-coir and nylon-palmyra composites, respectively. The obtained nylon-coir and nylon-palmyra composites are characterised for two-body abrasive wear behaviour, mainly focussing on the influence of load, sliding distance, and fibre loading, on the abrasive wear performance, with SiC abrasive paper. Further, the morphology of abraded surfaces observed with the help of scanning electron microscope is discussed.

Experimental Details Materials Coir fibres were supplied by SKT textile services India Pvt. Ltd. The density of coir fibres was 0.79 gm/cm3 . Palmyra fibres were supplied by Chinmayi traders, Jangareddigudem, Andra Pradesh with a density of 0.7–1.0 g/cm3 , camphor was collected from local sources and camphor soot was manufactured by vaporising camphor tablets and gathering the soot on a glass substrate. The approximate density

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of camphor soot was around 0.3 g/cm3 . Nylon-6 was supplied in the form of pellets by Colam merchants, Coimbatore with a density of 1.13 g/cm3 .

Coir and Palmyra Fiber Processing and Composites Preparation The raw coir and palmyra fibres were pre-splashed with distilled water to eliminate impurities like dust and mud and kept in a hot-air oven for 2 h at 60 °C to remove moisture content. Then coir and palmyra fibres were chopped into around 1 mm pieces. Further, the chopped fibres were immersed into varying camphor soot water solutions (0.5, 1.0, 1.5 wt.%) for different temperature and time intervals (30–50 °C) and (4, 8, 12 h), respectively. Experiments were carried out based on L9 orthogonal array for both coir and palm fibres separately. The influence of parameters was validated using main effect plots and ANOVA analysis. ANOVA analysis revealed that the optimised parameters were time 12 h, camphor soot concentration 1 wt.%, and temperature of 50 °C whereas osmosis rate was higher for these parameters. A detailed discussion regarding coir and palm fibre processing with camphor soot and coir fibre reinforced nylon composites was discussed in the papers [16–18]. Coir and palmyra fibres are made of a bunch of microfibrils (around 200–250) named elementary fibres which are hollow (20 µm) having a lacuna at the centre (80 µm) which makes them highly porous. When the chopped coir and palmyra fibres are immersed in camphor soot solution, osmosis takes place where camphor soot particles will diffuse into coir and palmyra fibres as the size of the particles is 100–300 nm approximately. Coir and palmyra fibres act as semipermeable tissues and camphor soot moves from a higher concentration to a lower concentration filling the porosity of coir and palmyra fibres. Further, the modified fibres were removed from the camphor soot solution and subsequently dried in a hot-air oven for 60 °C to remove humidity. Modified coir and palmyra fibres filled with camphor soot protect the fibres from thermal degradation while processing with nylon-6 which has a higher processing temperature of around 260 °C. Hence, the thermal stability of coir and palmyra fibres was enhanced considerably. As camphor soot is hydrophobic in nature it enables compatibility with the nylon matrix. The manufacturing of CCFNCs and CPFNCs was carried out using a twin screw extruder with the L/D ratio of 40. Nylon-6 pellets and modified coir and palmyra fibres were kept in a hot-air oven at 80 °C for around three hours to remove moisture as nylon has greater moisture absorbing capacity. The modified coir and palmyra fibres were infused in nylon-6 in various proportions (0, 3, 6, 9 wt.%) in a temperature range of 200–260 °C in the extruder and further injection molded at a temperature of 240 °C in accordance with ASTM standards.

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Test Details Abrasive sliding wear examinations were completed using pin on disc type equipment to examine abrasive wear. The diagram of the test apparatus is shown in Fig. 10.1. Waterproof SiC emery papers of grade 600 were used. The emery sheet was rigidly attached to the steel disc by ethyl cyanoacrylate type of adhesive. Square samples of 6 × 6 mm and 29 mm long dimensions were used for the experiment. To measure the Frictional force, a force transducer is used fixed on the loading arm. This transducer was used to illustrate the linear wear of the pins during the experiment. Variation in dimensions of the pin and frictional force was measured continuously and data was stored in data storage system. The two-body abrasive wear study was carried out according to ASTM-G99 using pin on disc equipment (dry sliding wear) in ambient conditions and under dry contact conditions for varying weight percentages of modified coir and palmyra fibre loads (0, 3, 6, 9 wt.%). Mass was taken as a function of the constant sliding velocity of 5 m/s for loads of 10, 15, and 20 N and varying sliding distances of 200, 300, 400 m. using 600 grit SiC abrasive papers. The initial and final mass of the pins was recorded afore and after the test using an electronic balance with an accuracy of 0.1 mg. Further, the average values of the measured frictional force, mass loss, and wear were used for future analysis. The probable mechanism involved in sliding abrasive wear is illustrated in Fig. 10.2.

Fig. 10.1 The illustration of the pin on disc test equipment

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Fig. 10.2 The abrasive wear mechanism in between nylon composite pin and SiC abrasive paper

Results and Discussion Coefficient of Friction The deviations in the coefficient of friction (COF) as a function of camphor soot reinforced coir and palmyra fibre content at 5 m/s sliding velocities for CCFNCs and CPFNCs is shown in Figs. 10.3 and 10.4, respectively. COF µ, is the proportion of the friction force among two bodies and the force pressing them together which is a dimensionless scalar value. Friction can be reduced by using a lubricant.

Fig. 10.3 COF for CCFNCs at a constant velocity of 5 m/s for varying load and sliding distances

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Fig. 10.4 COF for CPFNCs at a constant velocity of 5 m/s for varying load and sliding distances

The mechanisms include the creation of transfer film on the counterpart when two bodies rub each other [19]. During high loads and frequency, there is a chance for the formation of the compact film which helps to improve high load carrying capacity and good wear resistance [20, 21]. COF declines with an increase in camphor soot reinforced fibre content. During dry sliding, nylon comes into contact with the abrasive paper which abrades the pure nylon and higher COF can be observed as the load increases. Meanwhile, in CCFNCs and CPFNCs, COF is reduced as modified fibre content increases, which shows that as nylon composite come into contact with abrasive paper coir and palmyra fibres are exposed to abrasive paper. At the same time, camphor soot also comes into contact with the abrasive paper which acts as a lubricant and reduces COF predominantly. As camphor soot is made of graphite and stacked in layers it acts as a lubricant. Also, COF is increased with an increase in normal load. Similar tendencies are seen at different sliding distances in this study.

Influence of Load and Sliding Distance on the Weight Loss for CCFNC’s and CPFNC’s The graphs of weight loss as a function of modified coir fibre content (0, 3, 6, 9 wt.%) at varying normal loads (10, 15, and 20 N) and sliding distances (200, 300, 400 m) for CCFNC’s are shown in Fig. 10.5a–c. All the figures show that weight

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Fig. 10.5 Weight loss as a function of camphor soot reinforced coir fibre content in nylon at different sliding distances and varying loads, a 10 N, b 15 N, c 20 N

loss declines with increased fibre content of up to 6 wt.% and increased marginally in the case of 9 wt.%. Weight loss increased with increased sliding distance as it is clearly seen that at 400 m maximum weight loss is observed. Similarly in CPFNC the same trend can be seen from Figs. 10.6a–c, where for coir fibre reinforced nylon composites for the same parameters, have minimum weight loss at 6 wt.% which increased at 9 wt.%, due to the agglomeration of the fibres. Excellent wear properties in the case of 6 wt.% in both CCFNC’s and CPFNC’s was attributed to uniformly distributed modified coir and palmyra fibres in the nylon decreased wear loss due to good wear resistant properties of coir and palmyra fibres and also attributed to the existence of camphor soot in the fibres which acts as a lubricant and reduces weight loss in composites with respect to neat nylon. The camphor soot consists of crystalline graphite where carbon atoms are organised hexagonally in a condensed ring. The graphite layers are arranged parallel to each other with weak wander walls forces while the atoms within the rings are connected with strong covalent bonds. This enables graphite to move in two dissimilar crystallographic directions. The facility of camphor soot to form a dense film lubricant may be due to the chemical bonds. On the other hand, weak wander Waal’s forces between separate layers fail with small forces resulting in the sliding of graphite layers one above the other making it a good lubricant reducing wear loss. In CCFNCs and CPFNCs, wear debris consists of deformed nylon, camphor soot, broken coir, palmyra fibres, and some SiC particles,

Fig. 10.6 Weight loss as a function of camphor soot reinforced palmyra fibre content in nylon at different sliding distances and varying loads, a 10 N, b 15 N, c 20 N

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respectively. These particles can either be lost from the contact surface or continue there providing the cushioning effect for the counterpart.

Specific Wear Rate Figure 10.7a–c depicts the dependence of the SWR on camphor soot reinforced coir fibre content in nylon composites. It is clear from the plots that increase of modified coir fibre content from 0 to 9 wt.% decreased specific wear rate of up to 6 wt.% of fibre load which slightly increased in the case of 9 wt.%. This shows that best wear properties are observed at 6 wt.% fibre load and also that specific wear rate declined with increased sliding distance. Lower specific wear rate is observed at 400 m irrespective of the applied loads. The same trend can be seen in Fig. 10.8a–c as for palmyra fibre reinforced nylon composites for the same set of parameters. Again minimum specific wear rate is observed at 6 wt.% and slightly increased at 9 wt.% due to the agglomeration of the fibres. Wear of CCFNCs and CPFNC consists of two wear approaches polymer matrix wear, which constitutes plastic deformation of nylon and cracks induced due to the ploughing action of the SiC particles in the abrasive paper, fibre rupture, fibre cracking, and pulverisation of coir and palmyra fibres. The reduced specific wear rate with increased camphor soot reinforced coir and palmyra

Fig. 10.7 SWR as a function of camphor soot reinforced coir fibre content in nylon at different sliding distances and varying loads, a 10 N, b 15 N, c 20 N

Fig. 10.8 SWR as a function of camphor soot reinforced palmyra fibre content at different sliding distances and varying loads, a 10 N, b 15 N, c 20 N

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fibres is due to fibres which have very good wear resistance. Camphor soot mainly consists of graphite which acts as a solid lubricant. During sliding, the lubricating action of camphor soot reduces the sticking of polymer to abrasive paper. At the start of sliding, the polymer pin and abrasive paper are in interact with each other, and as shear forces develop, the nylon matrix starts to deform, resulting in the protrusion of modified fibres from the sample surface. As sliding distance increases, wear rate decreases due to an increase in load. Interface temperature increases causing both coir and palmyra fibre to fracture. The resulting debris of coir and palmyra fibres trap camphor soot causing further wear by third body abrasion preventing fibres which act as a lubricant reducing specific wear rate.

Worn Surface Morphology Figure 10.9a–f shows the worn surfaces of neat nylon and 6 wt.% modified palmyra fibre reinforced nylon composites abraded against 600 git SiC paper at a load of 20 N and 200 m sliding distance. The black arrow indicates the direction of abrasion. From SEM micrographs, it is clear that Fig. 10.9a depicts ploughing action on the surface, and as the matrix is softer uniform damage is observed. Nylon debris and silicon particles are seen clearly due to the sticking action caused by the increase in temperature. On the other hand, Fig. 10.9b–f displays the worn surface of the modified palmyra fibre reinforced nylon composites, where exposed fibres are seen. These exposed palmyra fibres tend to break and get detached from the surface of the

Fig. 10.9 a–f SEM pictures of worn surface of neat nylon and 6 wt.% CPFNC’s abraded against 600 grit SiC paper at 20 N and sliding distance of 200 m

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composites. Camphor soot is also exposed. The matrix is greatly scratched by the cutting and ploughing action of some larger SiC particles at 200 m sliding distance. Firstly, the fibre failure starts with microcracking followed by breaking as the palmyra fibres are already in a brittle condition due to processing at a higher temperature in the twin screw extruder and injection moulding. Over all surface topography for composites indicates more fibre maceration, more fibre breaking, and less fibre matrix deboning. Also, the micrographs indicate deterioration of the fibre matrix bond due to repetitive stress caused by the SiC particles and fibre pull-out from the matrix. Figure 10.10a–f show the worn surfaces of the 6 wt.% CCFNC’s abraded against 600 grit SiC paper at a load of 20 N and 200 m sliding distance with the black arrows indicating the direction of the abrasion. From SEM images, it is evident that Fig. 10.10a shows the coir fibre embedded in the nylon matrix starting to protrude as sliding progresses. Figure 10.10b, c shows the section of the coir fibre protruding while camphor soot is also seen. Figure 10.10d, e shows the ploughing marks in the matrix is also the fibre rupture. Figure 10.10f shows broken fibre particles sticking to the nylon and debris of nylon particles together.

Fig. 10.10 a–f SEM pictures of worn surface of 6 wt.% CCFNC’s abraded against 600 grit SiC paper at 20 N and sliding distance of 200 m

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Conclusion The main purpose of this work is to examine the abrasive wear behaviour of camphor soot reinforced coir and palmyra fibre nylon composites. An investigational study of the wear behaviour of CCFNCs and CPFNCs at constant sliding velocity and varying load and sliding distances on 600 grit SiC paper discloses the following. • Increase in load and sliding distance, increased weight loss in CCFNC’s and CPFNC’s composites but excellent wear properties were observed in 6 wt.% fibre loads compared to neat and 9 wt.% fibre loaded nylon composites. • In contrast, specific wear rate decreased with an enhancement in sliding distance and load. Better wear properties were noticed in 6 wt.% fibre loaded composites compared to neat and 9 wt.% fibre loaded nylon composites. • The worn surface in neat nylon revealed greater damage compared to CCFNC’s and CPFNC’s, as nylon is softer and experienced more cutting and plaguing action. There is a sticking action in the nylon debris due to an increase in temperature. On the other hand, CCFNCs and CPFNC experienced fibre breakage due to repeated loads exerted by the SiC particles, they also experienced the pull-out of some fibres from the surface of the composites and exposed camphor soot which acts as a lubricant which greatly influenced the decrease in wear rate.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Harsha AP, Tewari US (2002) Polym Test 21:697–709 Batchelor AW, Stachowiak GW (1995) J Mater Process Technol 48(1–4):503–515 Suresha B, Seetharamu S, Sampath Kumaran P (2009) Wear 267(9):1405–1414 Unal H, Mimaroglu A, Arda T (2006) Appl Surf Sci 252(23):8139–8146 Sudhir Kumar KP (2015) J Mater Sci Mech Eng 2(6):24–28 Deo C, Acharya SK (2010) Ind J Mater Sci 17:219–223 Reis PNB, Ferreira JAM, Antunes FV, Costa JDM (2007) Compos Part A: App Sci Manuf 38(6):1612–1620 Ba P, Shetty P, B, HV S, Singh Yadav SP (2020) Advances in materials and processing technologies, pp 1–16 Doan TTL, Gao SL, Mäder E (2006) Compos Sci Technol 66(7–8):952–963 Gill NS, Yousif BF (2009) Proceedings of the institution of mechanical engineers. Part J: J Eng Tribol 223(2):183–194 Ayrilmis N, Jarusombuti S, Fueangviva V, Bauchongkol P, RH (2011) Fibers Polym 12(7):919– 926 Mohanty AK, Misra M, Hinrichsen G (2000) Macromol Mater Eng 276(1):1–24 Tran LQN, Minh TN, Fuentes CA, Chi TT, Van Vuure AW, Verpoest I (2015) Ind crops Prod 65:437 Xing Y, Zhang G, Ma K, Chen T, Zhao X (2009) Polym-Plast Technol 48(6):633–638 Kumar M, Ando Y (2003) Diamond Relat Mater 12:998–1002 Raghavendra T, Kavan P (2018) Fiber Polym 19(7):1567–1575 Raghavendra T, Panneerselvam K (2020) Fibers Polym 21(11):2569–2578 Raghavendra T, Panneerselvam K (2020) Surf Rev Lett 27(2):1950104

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19. Hager AM, Davies M (1993) Compos Mater Ser 8:107–157 20. Ye Y, Chen J, Zhou H (2009) Wear 266(7–8):859–864 21. Cho MH, Bahadur S (2005) Wear 258(5–6):835–845

Chapter 11

Impact of Viscosity and Heat Source Variance on the Onset Convection in a Fluid Layer S. Kiran, Y. H. Gangadharaiah, and H. Nagarathnamma

Introduction The study of convective instability in a thin layer of fluid heated from below and free at the upper surface has numerous applications in domains such as material science engineering, chemical engineering, insulating oils, and geothermal engineering. These liquids have the ability to act as a cooler, a diagnostic medium, and an electrical insulator, among other things [1, 2]. Straughan and Rionero [3] have used the linear stability technique to explore convective motion with a changeable internal heat source with gravity variance in a porous matrix. Mahabaleshwar [4] and Ananda et al. [5] examined convective motion in changeable heat source and gravity vector. Gangadharaiah et al. [6] addressed three different internal heating patterns on porous matrix. Suma et al. [7] examined the penetrative convection problem in a composite layer with throughflow. Shivakumara et al. [8] investigate the heating effects in an anisotropic medium with surface tension effects. Internal heating in a composite layer system was examined by Gangadharaiah [9]. Bhadauria [10] investigates the penetrative convective motion with the Soret effect. Very recently, the impact of variable heating patterns on Darcy–Brinkman terms effects in an anisotropic porous matrix is examined by Gangadharaiah et al. [11]. The internal friction of every liquid is related to its viscosity. The Boussinesq approximation, which states that fluid viscosity is temperature dependent, was S. Kiran (B) Department of Mathematics, Nitte Meenakshi Institute of Technology, Bangalore, India e-mail: [email protected] Y. H. Gangadharaiah Department of Mathematics, RV Institute of Technology and Management, Bangalore, India H. Nagarathnamma Department of Mathematics, Dr. Ambedekar Institute of Technology, Bangalore, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_11

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assumed in most publications on convective motion. Because of the thermorheological features of various fluids, the subject of convection in variable viscosity liquids has gotten its own focus. Fluid viscosity is a physical attribute. The liquid viscosity is assumed to be constant in the majority of the study. However, there are only a few examples of fluids in nature that have this feature. The fluid viscosity may not have to be constant in certain conditions. The temperature distribution within the system is not uniform in many thermal transport systems; therefore, the fluid viscosity may alter substantially if a large temperature variance occurs in the system. As a result, it is critical to account for temperature-dependent viscosity in both the momentum and energy equations. The impact of changeable viscosity in convection problems has been considered by many researchers in recent years Lam and Bayazitoglu [12], Gangadharaiah and Ananda [13], Chaya and Gangadharaiah [14] Stengel et al. [15], Gangadharaiah and Suma [16], Booker [17] Gangadharaiah, and Ananda [18]. The goal of this work is to study the convective motion in a horizontal fluid layer with a variable internal heat source; we use exponential type to represent the viscosity. The perturbation technique is used to find out the analytical expression for the critical Rayleigh number Rc as a function of heat source constant N s and viscosity parameter B.

Mathematical Formulation The schematic of flow configuration consists of an endless horizontal fluid layer of thickness d. The following are the mathematical governing relationships: − → ∇ · V =0  ρ0

 ∂ V   + V · ∇ V ∂t

(11.1)

 = − ∇ p + ρ0 g[1 − α(T − T0 )]    +2∇ · μ ∇ · V + ∇ · V T

∂ T − →  + V · ∇ T = k ∇ 2 T + Q(z) ∂t

(11.2) (11.3)

where μ = μ0 exp[−A(T − T0 )] In the above equations, Q(z) is the variable heat source, p is the pressure, T is the temperature, and κ is the thermal diffusivity. The basic state is of the form

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(u, v, w, p, T ) = [0, 0, W0 , pb (z), Tb (z)]

(11.4)

It is supposed that the basic state of being time-independent and of the form u = 0, v = 0, w = w0 , p = pb (z) &T = Tb (z)

(11.5)

Then Eq. (11.3) can be written for basic temperature Tb as 1 d 2 Tb − Q(z) = 0 dz 2 κ

(11.6)

On Integrating and applying the boundary conditions, we obtain −1 Tb (z) = κ

 z ξ Q(λ)dλ dξ − C z + Tl , 0

(11.7)

0

where 1 1 C = (Tl − Tu ) − d κd

d ξ Q(λ)dλ dξ. 0

0

The dimensionless disturbance equations are given by(after linearization)

∂ f˜ ∂w ∂ 2 f˜ 2 1 ∂ 2 ∇ w = f˜ ∇ 4 w + 2 ∇ 2 + 2 ∇ w − 2∇h2 w + R∇h2 pr ∂t ∂z ∂z ∂z  ∂ 2 − ∇ T = −(1 + N s N (z)) w ∂t

(11.8) (11.9)

where R = αg(T0 − Tu )d 3 /ν κ is the Rayleigh number and  



 f˜ = exp B z − 21 , B = ννmax temperature dependence of viscosity. min Normal mode analysis (w, T ) = [W (z), (z)] exp[i(lx + my)]

(11.10)

Simply using Eq. (11.10) into Eqs. (11.8) and (11.9), we arrive

2



f˜ D 2 − a 2 W + 2D f˜ D 2 − a 2 DW + D 2 f˜ D 2 + a 2 = Ra 2

D 2 − a 2 = −(1 + N s N (z)) W

(11.11) (11.12)

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The boundary conditions take the form W = DW = D = 0

at z = 0, 1

(11.13)

Method of Solution Accordingly, the control variables are expanded in powers of a 2 in the form (W, ) =

N  2 i a (Wi , i )

(11.14)

i=0

f˜ D 4 W0 + 2D f˜ D 3 W0 + D 2 f˜ D 2 W0 = 0

(11.15)

D 2 θ0 = −(1 + N s N (z))W0

(11.16)

W0 = DW0 = D 0 = 0

(11.17)

Then responses to the above equations are W0 = 0

and

0 = 1

(11.18)

First-order equations are D 4 W1 − 2B D 3 W1 + B 2 D 2 W1 = R E x p[B(z − 1/2)] D 2 1 = 1 − (1 + N s N (z)).

(11.19) (11.20)

The general solution of (19) is   z 2 B(z−1/2) e W1 = R A1 + A2 z + A3 e Bz + A4 ze Bz + 2B 2

(11.21)

the solvability condition, obtained by 1 {(1 + N s N (z))} W1 dz = 1 0

Finally, the critical Rayleigh number is calculated as follows:

(11.22)

11 Impact of Viscosity and Heat Source Variance …

Rc (linear) =

K l1

Rc (Parabolic) =

Rc (cubic) =

1 2

+

Ns 6



1

B + K l1 e − 1 − N s 4e B − 1 + K l3

113

(11.23)

1



3B B K p1 e e − 1 − N s + K p2 N s 4e2B − N s + K p3 (11.24)



K c1 N s 4e B − 1 23 +

Ns 4



1

+ K c2 e B (1 + N s) − 1 4 + K c3 (11.25)

where  e B/2 2 − 2e B + B + Be B , 2B 2 e2B − B 2 e B − 1  eB − B − 1 e B/2 , K l2 = 2 2B 1 + e2B − 2e B − B 2 e B

 1 K l3 = 3 (2B − 2)e B/2 + N s (2 − 2B)e−B/2 , 2B   e−B/2 3e B + B 2 e B eB − B2 − 1 , , K p2 = = 2B 2 eB − 1 e2B − 2e B − B 2 e B

 1 = 3 N s 1 − B + B 2 e−B/2 2B   2 − B2 B2 e B/2 e−B/2 , , K c2 = = 2 2B 2B e + B 2 e B − 1 6B 2 e−2B + 2B 2 e B  1 = 4 2B 2 e B/2 + N se−B/2 . 2B K l1 =

K p1 K p3 K c1 K c3

From Eqs. (11.23), (11.24), to (11.25), we found that for constant viscosity (i.e.,B → 0), and lack of internal heating (i.e N s → 0),Rc → 720, which is the exact value that is known [19].

Results and Discussion The combined effect of viscosity variance on the onset of convection with variable internal heating patterns is examined. The perturbation approach is performed to solve the resulting eigenvalue problem (Fig. 11.1). Figures 11.2, 11.3, and 11.4 illustrate the variation of Rc verses B for three heat source parameters for all three types of heating patterns. From these plots, for N s = 0, it is emphasized that the Rc increases at first reaches a maximum and subsequently drops with further increase in the value of viscosity parameter (see Stengel et al. [15]).

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Fig. 11.1 Rc versus B for three values of heat source constant for case (i) heat variation

Fig. 11.2 Rc versus B for three values of heat source constant for case (ii) heat variation

It is also noted, from these estimates, that the effects in the value of heat variance constant N s cause an inconsistent effect on the system. In addition, the convection is indicated to be more unstable for the linear type heat source and more stable for the cubic type heat source strength (see Fig. 11.4). Figures 11.5, 11.6, and 11.7 depicts the velocity disturbance W versus normalized height Z for various values of B for heat source parameter N s = 2. It has been noticed the freshly developed sub-appearance layer’s, which first occur at the maximum Rc with B, after that, continues to show themselves, becoming dominant at the critical level. For higher viscosity parameter, The viscously inhibitory impact of the system above reduce the thickness of the sub-layer, thus Rc declines as B increases. As a result, towards the bottom of the fluid layer, the vertical velocity disappears. Further

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Fig. 11.3 Rc versus B for three values of heat source constant for case (iii) heat variation

Fig. 11.4 Rc versus B for all three types of heat variation with N s = 2

noted that the convection is more unstable for the linear type heat source and more stable for the cubic type heat source strength.

Conclusions In appearance of a fluctuating heat source with an exponential temperature-dependent viscosity fluctuation, an analytical analysis of convective motion in a system is performed. The following are the main findings of the linear stability research: • The velocity disturbance flow disappears at the bottom of the fluid layer for the larger values of viscosity parameter.

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Fig. 11.5 Velocity disturbance W versus normalized height Z for three values of B with N s = 2 for case (i) heat variation

Fig. 11.6 Velocity disturbance W versus normalized height Z for three values of B with N s = 2 for case (ii) heat variation

• In the absence of N s, the Rc rises at first, reaches a peak, and then falls as the value of the viscosity parameter is enhanced further; however, in the existence of heating pattern, the critical Rayleigh number lowers as the value of the viscosity parameter is increased further. • The cubic type heat source variation is the most stable compared to linear and parabolic heat strength variation in the fluid layer.

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Fig. 11.7 Velocity disturbance W versus normalized height Z for three values of B with N s = 2 for case (iii) heat variation

References 1. Straughan B (2004) The energy method, stability, and nonlinear convection. In: Applied mathematical sciences. Springer, New York 2. Nield DA, Bejan A (2006) Convection in porous media, 3rd edn. Springer, New York 3. Rionero S, Straughan B (1990) Convection in a porous medium with internal heat source and variable gravity effects. Int J Eng Sci 28:497–503 4. Mahabaleshwar US, Basavaraja D, Wang S, Lorenzini G, Lorenzini E (2017) Convection in a porous medium with variable internal heat source and variable gravity. Int J Heat Mass Transfer 111:651–656 5. Ananda K, Gangadharaiah YH, Nagarathnamma H (2020) Combined impact of variable internal heat source and variable viscosity onset of convection motion in a porous layer. Malaya J Matematik 8:915–919 6. Gangadharaiah YH, Kiran S, Nagarathnamma H, Ananda K (2021) Effect of variable heat source on the onset of darcy-brinkman convection in an anisotropic porous medium. Adv Mech Eng Lect Notes Mech Eng. https://doi.org/10.1007/978-981-16-0942-8_40 7. Suma SP, Gangadharaiah YH, Indira R, Shivakumara IS (2012) Throughflow effects on penetrative convection in superposed fluid and porous layers. Transp Porous Med 95:91–110 8. Shivakumara IS, Suma SP, Indira R, Gangadharaiah YH (2012) Effect of internal heat generation on the onset of Marangoni convection in a fluid layer overlying a layer of an anisotropic porous medium. Transp Porous Media 92:727–743 9. Gangadharaiah YH (2016) Onset of Benard-Marangoni convection in a composite layers with anisotropic porous material. J Appl Fluid Mech 9:1551–1558 10. Nouri-Borujerdi A, Noghrehabadi AR, Rees DAS (2007) Onset of convection in a horizontal porous channel with uniform heat generation using a thermal non-equilibrium model. Transp Porous Med 69:343–357 11. Gangadharaiah YH, Kiran S, Nagarathnamma H, Ananda K (2021) Effect of variable heat source on the onset of darcy-brinkman convection in an anisotropic porous medium. In: Advances in mechanical engineering. Lecture notes in mechanical engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-0942-8_40 12. Lam TT, Bayazitoglu Y (1987) Effect of internal heat generation and variable viscosity on Marangoni convection. Numer Heat Trans 165–182

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13. Gangadharaiah YH, Ananda K (2020) Influence of viscosity variation on surface driven convection in a composite layer with a boundary slab of finite thickness and finite thermal conductivity. JP J Heat Mass Trans 19:269–288 14. Chaya, Gangadharaiah YH (2020) Combined impact of internal heating and variable viscosity on the onset of Benard-Marangoni double-diffusive convection in a binary fluid layer. Int J Mech Prod Eng Res Dev 10(2):385–396 15. Stengel KC, Oliver DS, Booker JR (1982) Onset of convection in a variable viscosity fluid. J Fluid Mech 120:411–431 16. Gangadharaiah YH, Suma SP (2013) Effects of internal heat generation and variable viscosity on onset of Rayleigh-Benard convection. Int J Comput Technol 5(3):200–213 17. Booker JR (1976) Thermal convection with strongly temperature-dependent viscosity. J Fluid Mech 76(1):741–754 18. Gangadharaiah YH, Ananda K (2018) Effects of temperature-dependent viscosity on penetrative convection in a fluid layer bounded by slabs of finite thermal conductivity and finite thickness. Int J Sci Res Math Stat Sci 5(5):41–50 19. Nield DA (1987) Throughflow effects on the Rayleigh-Benard convective instability problem. J Fluid Mech 185:353–360

Chapter 12

Design and Analysis of Longitudinal Butt Joints Using an Excel/VBA Computational Tool Raghav Agarwal, Priyanshu Dwivedi, Rohit Mahawar, and Ashish Karn

Introduction Undergraduate mechanical engineering curriculum can broadly be divided into thermal, design, manufacturing, and industrial engineering. Among these, the design of machine elements is an integral part of the “design” division of the mechanical engineering. Design of rivets constitute a topic within the course of design of machine elements. The study and design of rivets is crucial since rivets provide strength over welded joints to make the structure stand erect and withstand enormous load. In the industry, one can see boilers which are joined using rivets where these are designed for its thickness and type of riveting with a view to minimize cost and maximize strength. Similarly, a number of rivets can be observed underneath a railway bridge where these are impinged on its surface to make the structure unbreakable. The rivets used seen in different applications, however, differ in their dimensions. The rivets of an appropriate dimensions are required to be chosen for a specific engineering application and there exists a standard procedure to make the right selections. Even though there are some formulae to provide some cues into the design and selection of rivets, but if the problems are dynamic in nature and have some modifications incorporated, it is not always possible to use the standard formulae. This makes the teaching and learning of this topic somewhat challenging, as far as the real-life problem-solving is concerned. There are other reasons why understanding the principles of design becomes cumbersome for the students: the subject involves the usage of advanced mathematics. Not only the design but also many undergraduate problems involve the large iterations and tedious calculations. The work of Tuttle [1], Engeda [2], Sachis et al. R. Agarwal · P. Dwivedi · R. Mahawar · A. Karn (B) Department of Mechanical Engineering, School of Engineering, University of Petroleum and Energy Studies, Energy Acres, Bidholi, Dehradun, Uttarakhand 248007, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_12

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[3], and Tay et al. [4] clearly shows that the computational tools help you analyze and understand the concept of engineering mathematics, thermodynamics, turbomachinery, and mechanics of materials, respectively, in a better way. Solutions to these problem are generally obtained by sophisticated experiments and complicated computations that are difficult to understand. The traditional teaching methods fall far short of the mark in communicating these complex procedures such as iterative calculations required in design calculations. More so, resorting only to the conventional pen-and-paper methodology of solving such challenging engineering problems is not only cumbersome but also reveals a clear disjoint between the concurrent industrial practice and the engineering pedagogy. Evidently, there is a need for a suitable technological intervention to bridge this gap and to enable students to see the integration of computers in engineering and its practical utility in solving challenging engineering assignments. Those who know the antecedents will admit that it is very difficult for any undergraduate to deal with understanding concepts in engineering. As far as computational frameworks are concerned, there are a variety of software/computer languages, both commercial and open-source which can be amicably employed in the solution of pipe flow problems and the visualization of the data involved, such as Python, SciLab, Matlab, Wolfram Mathematica, Pyro, Cycle pad, etc. In fact, there are software tools available to different disciplines like CFD tools, CATIA, SOLIDWORKS, etc., but for Design application there is none. Having seen this drawback we found it necessary to develop some tools to bridge the gap of understanding and who knows we get to understand rivets while walking over it. Many other platforms are available for us to do so and we decided to choose the one which has a widespread accessibility and availability. Hence, MS Excel/VBA platform was selected for the development of a computational solver because of its user-friendly nature, low cost, and easy availability. Excel VBA helps an engineering learner to solve critical equations, scale live graphs, to learn new concepts just by changing the parameters without worrying about the errors. It can be equally utilized to stage unique engineering demonstrations and animations. The programming language of VBA allows the user to access functions beyond what is available in other Microsoft applications [5]. Users can use the application of VBA to customize applications according to the need, such as creating user-defined functions, etc., and because of its very friendly nature and a wide variety of specifications, it can also be used to create computerized tools [6]. Considering the user-friendly nature of Excel/VBA, it helps to solve critical equations, scale live graphs, to learn new concepts just by changing the parameters without worrying about the errors. For the calculation of the design parameters, an Excel workbook program has been designed that allows the user to calculate parameters as per the requirements. This tool was utilized for teaching and learning in an undergraduate classroom and the student responses have been collected in the form of an online survey. The results have been collated and statistical analysis have been conducted to gauge the effectiveness of such a computational tool on the overall teaching–learning process.

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Longitudinal Butt Joint for Boilers The use of temporary joints have proven to be useful than permanent joints as nowadays we see a greater use of alloys in industries. As mentioned in Adeyeri [7] riveted joints are of prime importance to engineering application and making a safe and reliable design is itself a challenge. There are two types of riveted joints in cylindrical boiler shell. These are longitudinal butt joints and circumferential lap joints. Boilers and pressure vessels are subjected to high steam pressures. These should be made leak-proof and must be capable to withstand such high pressures. The plate of boiler shell is bent to form a ring and the edges of plate are joined by longitudinal butt joints. The rings are connected to each other by circumferential lap joints and provide the required length of the boiler shell.

Methodology The methods and equations adopted for the design of longitudinal butt joint is laid out in standard texts [8] and these steps are transformed into a flow chart explaining the algorithm for the Excel/VBA program. The following procedure has been adopted for the design of longitudinal butt joint for boiler shell as shown in the Fig. 12.1.

Design Equations The design of riveted joint for boiler shell is very important task from industry point of view. A small fault in design can lead to many problems as well as failure. Therefore, proper steps should be followed with proper assumptions. The rivet design comprises Fig. 12.1 This figure shows longitudinal butt joint with zigzag riveting

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of various elements like diameter of rivet, thickness of boiler shell as well as straps, strength of plate, and efficiency. And these can be calculated as follows. Thickness of boiler shell (t)—The cylindrical shell subjected to internal pressure (Pi ), thickness is given by t=

Pi ∗ Di 2σt η

(12.1)

where Pi is internal pressure (N/mm2 ); Di is inner diameter of cylinder (mm); σt is permissible tensile strength for cylinder material (N/mm2 ); η is efficiency of riveted joint. The wall of the heater shell is exposed to corrosion which leads to the thinning of wall, thus reducing life of the shell. An arrangement must be made by an appropriate increment in the wall thickness to make up for the thinning because of corrosion. Corrosion allowance (CA) is basically the additional thickness which is provided to compensate corrosion. Minimum corrosion allowance thickness is 1.5–2 mm. t=

Pi ∗ Di +CA 2σt η

(12.2)

Figure 12.2 shows the range of standard efficiencies for commercial butt joints. As the figure shows, for the single riveting, the efficiency lies in the range of 50–60%, whereas for the double riveting, it falls within the range of 70–83%. The efficiency increases for tripe riveting to 80–90% and for quadruple riveting, it attains a value as high as 85–94%. According to Clause of Indian Boiler the ultimate shear strength and tensile strength of rivets and steel plates are 21 and 26 tons per square inch, respectively. Therefore, S ut = 401 N/mm2 and S us = 324 N/mm2 . As factor of safety for boiler shell varies from 4.5 to 4.75. Therefore for safe practice it is assumed to be 5. Fig. 12.2 The range of standard efficiencies for commercial butt joints

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The permissible tensile and shear stress are given by σt =

Sut Sus ≈ 80 N/mm2 ; τ = ≈ 65 N/mm2 5 5

There is no method for calculating compressive stress in Boiler Regulations. Assuming σc = 1.5 ∗ 120 = 80 N/mm2 Diameter of Rivet (d)—Design engineers suggested empirical relationship to find diameter as Indian Boiler Regulations doesn’t have formula to calculate rivet diameter: √ d=6 t

(12.3)

where d is the diameter of rivet in mm; t is the thickness of boiler shell. Number of Rivets (n)—It is determined keeping in mind of two cases. They are: • Case 1—when the inner and outer straps are of unequal width In this case, n = n 1 + n 2 , where n1 = number of rivets subjected to single shear per pitch; n2 = number of rivets subjected to double shear per pitch. • Case 2—when the inner and outer straps are of equal width In this case, all the rivets are subjected to double shear. Pitch of Rivet (p)—The pitch is calculated by equating tensile strength with shear strength, we get p=

(n 1 + 1.875n 2 )π d 2 τ +d 4tσt

(12.4)

The pitch obtained from the above equation has some minimum and maximum values. According to Indian Boiler Regulation (IBR): • To enable the forming of rivet head the pitch of the rivets should not be less than 2d, pmin = 2d. • The maximum pitch is to provide leak proof joint, pmax = Ct + 41.28. The value of C in the above equation depends on number of rivets per pitch (nr ). For single-strap butt joints, the value of C is 1.53, 3.06, and 4.05 for nr = 1, 2, and 3, respectively. For double-strap butt joints, these values are 1.75, 3.5, 4.63, 5.52, and 60 for nr = 1, 2, 3, 4, and 5, respectively. Transverse Pitch (pt )—According to Clause 184 of Indian Boiler Regulation, the distance between two rows of rivets or transverse pitch is specified.

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For chain riveting, pt = 2d. For zigzag riveting, pt = 0.2 p + 1.15d. Margin (m)—The distance from edge of the plate to center of rivet hole is called margin. The minimum margin is given by m = 1.5d. Thickness of straps (t 1 )—According to Clause 182 of Indian Boiler Regulation, the thickness of straps for butt joint is calculated: For unequal width, t1 = 0.75d. p−d . For equal width, t1 = 0.625d p−2d Efficiency of Joint (η)—The efficiency of joint is given by η=

Minof(Pt , Pc , Ps ) ptσt

(12.5)

where Pt = ( p − d)tσt

(12.6)

Pc = (n 1 + n 2 )dtσt

(12.7)

Ps =

(n 1 + 1.875n 2 )π d 2 τ 4

(12.8)

Figure 12.3 shows the step-by-step algorithm behind the design of the computational tool on the longitudinal butt joints (/rivets) as available from Bhandari [8]. In the succeeding section, a sample problem from Bhandari [8] on the rivet joints is being solved using the computational tool.

Flow Chart Algorithm for Rivet Design in Excel/VBA See Fig. 12.3.

Sample Problem A cylindrical pressure vessel with a 1.5 m inside diameter is subjected to internal steam pressure of 1.5 MPa. It is made from steel plate by triple-riveted double-strap longitudinal butt joint with equal straps. The pitch of the rivets in the outer row is twice of the pitch of the rivets in the inner rows. The rivets are arranged in a zigzag pattern. The efficiency of the riveted joint should be at least 80%. The permissible stresses for the plate and rivets in tension, shear, and compression are 80, 60, and 120 N/mm2 ,

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Fig. 12.3 Shows the algorithm of the computational tool on riveting joints

respectively. Design the joint and calculate thickness of the plate, diameter of rivets, pitch of rivets, diameter between the rows of rivets, margin, thickness of the strap, and efficiency of the joint with a neat diagram [8].

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Solution Using Excel/VBA • All the input values are entered in the Excel/VBA user interface and the result can be seen in Fig. 12.4. • The user also has the freedom to choose the type of riveting from the drop down box as shown in Fig. 12.5a. • The user can also select the type of strap from the drop down box as shown in Fig. 12.5b. • The last thing that the user needs to select is the pattern of riveting, i.e., either zigzag or chain as shown in Fig. 12.4a. • As per the selection from above dropdown boxes, we will get the picture of the selected riveted joint automatically as shown in Fig. 12.6a. This will help the students to visualize the designed joint and they can select the type of riveted joint according to their weird imagination. • After selecting the type of riveted joint, the user needs to know whether their weird imagination is possible or it’s just an imagination. If the calculated efficiency (as shown in Fig. 12.4b) is less than the required efficiency (as compared to Fig. 12.2), then a message box is popped (as shown in Fig. 12.6b).

Fig. 12.4 This figure shows the input parameters a and output results, b calculated using Excel/VBA. The figure (b) also shows the important standard parameters that are used for calculating results

Fig. 12.5 User have freedom to choose the type of riveting a and type of strap, b from the dropdown menu. This gives user an idea why a particular type of riveting can or cannot be used

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Fig. 12.6 Figure a shows the diagram of the riveted joint according to selected parameters and b shows a dialog box of whether the joint is safe or not

Hypothesis Testing Finally, we will test the effectiveness of our tools by doing the hypothesis testing. The hypothesis testing is away to determine whether our assumption about the tools are correct or not. This will give us a clue whether our tools are widely accepted or not. This is done by considering a reverse hypothesis or also called null hypothesis. We have provided the computational tool to students as well as teachers on the webpage: https://www.drkarnteaching.com/machine-element-des ign-tools. Next, their detailed reviews and responses about the tools and the usefulness of the tools was collected. We’ve done statistical analysis on the review provided by the students and calculated the p-value of each responses using solver tool in Excel. The responses were collected on a scale of 1–5 where 1 represents “don’t like” and 5 represents “appreciate greatly”. The responses of the users were juxtaposed against a null and alternate hypothesis, where the rejection of the null hypothesis (for p-value < 0.05) affirmed the efficacy of the developed computational tool in that particular aspect. The questions and the reviews on the different expects of teaching and learning are shown below.

Student’s Perception on Learning The next four questions were on student’s perception in learning and the various areas it can be helpful. The responses are recorded and shown in a bar graph as shown in Fig. 12.7a. The various areas were quality improvement, sustaining interest, cooperative learning, and difficulty reduction. For all the areas discussed above, more than 60% of students claims that they greatly appreciate the effort of the computational tools and will help in learning the concepts of design of machine elements in an easy way. Some students remarks the computational tool as “good work”. It can be seen

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Fig. 12.7 This figure shows the responses of students on different, a student perceptions of learning, and (b) and learning ways

through the graph that a very few are neutral or remarks as “somewhat like” for the developed computational tools.

Student’s Perception on Learning Ways The next questions was on the perception of the new learning way and was again categorized into four areas, namely, computer integration, real-life application, lecture demonstration, and hones problem-solving, and the results are shown in the bar graph in Fig. 12.7b. Here, also it can be seen through the bar graph that majority of the users appreciate the work of the computational tools and think that it can help in greater learning, problem-solving, and give a perception on real-life applications. They also says that it is a good way of computer integration and helps in greater learning. There are some who rate us four on the scale of 5 and remarks us as “good work”. A few are neutral about the tools or somewhat like the tools. It can be that they need more time with the tools to understand its usefulness.

Overall Acceptance of New Method The first question asked to the students was on the overall acceptance of the computational tool in enhancing teaching and learning experience and the responses are shown in a pie chart in Fig. 12.8a. It can be seen that 81% of the users greatly appreciate the concept of computational tool and says that our tool help in boosting interactive teaching and learning, while 16% remarks us with “good work”. Around

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Fig. 12.8 Figure shows the overall acceptance of this new method, a whereas figure b shows the p-value chart which shows that we can accept the hypothesis

3% of the responses were neutral regarding the computational tools. The interesting thing is that no one dislikes the new concept of teaching through computational.

p-Value for Different Hypotheses There are many tests that can be done for hypothesis testing. Out of these several test, the t-test is considered to be most suitable for the present population. Thus, we have performed the t-test on our responses for all our ten questions and calculated the p-value using solver tab in Excel for one-tailed and two-tailed tests and plotted the graph as shown in Fig. 12.8b. We can accept our hypothesis that this tool helps in interactive teaching and learning off the subject as the by value calculated is less than 0.05. That means our hypothesis is correct and can help students in learning the subject in an effective way.

Conclusion The current manuscript hopes to bridge the gaps involved in the teaching and learning of an important concept of design of riveting joints in the “Design of Machine elements” course of the Mechanical Engineering curriculum. The computational tool was developed, hosted on a website, and used in the teaching learning process. Next, the responses of the students regarding the overall acceptance and the usefulness of the tool were solicited. The responses of the users show that that the tool can be used in solving different expects of riveting and can help in creative thinking and effective teaching. This can help in getting rid of the tedious long calculations and helps student in participate in interactive sessions. This tool can help teachers to deliver better lectures with demonstration and helps student to regain the lost interest

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in the subject and reduces the difficulty of the course. With the iterative property of excel, we can perform large iterations and solve real-life problems sitting in a classroom. This computational tool doesn’t require any add-ons or large computer space, nor does it require any computational knowledge to operate. This paper also shows the statistical analysis of the user responses and p-values were computed for different hypotheses regarding the efficacy in teaching and learning methodology. The ten hypothesis questions centered around students’ perceptions on learning, the usefulness of this new method of teaching and learning, overall acceptance of the new method of learning, and recommendation for other courses. Since the p-values for all the hypothesis are well below 0.05, the null hypotheses can be rejected. This clearly establishes the immense usefulness and efficacy of these tools in terms of improvement in design pedagogy.

References 1. Tuttle KL (1998) Computer models using spreadsheets to study heat engine thermodynamics. In: ASEE annual conference proceedings,pp 1–7 2. Engeda A (2010) Spreadsheet as a data acquisition tool in turbomachinery. In: Proceedings of ASME turbo expo 2010: power for land, sea and air, pp 1–7 3. Sanchis EJ, Alcaraz JG, Borrell JMG, Vañó JM (2011) An application of an optimization tool to solve problems of mechanics of materials. In: Spreadsheets in education (eJSiE), pp 1–12 4. Tay KG, Kek SL, Kahar RA (2012) A spreadsheet solution of a system of ordinary differential equations using the fourth-order Runge-Kutta method. In: Spreadsheets in education (eJSiE)), pp 1–12 5. Mahawar R, Dwivedi P, Agarwal R, Karn A (2020) Computational tool for teaching learning velocity triangle of hydraulic turbines. OSF Preprints 6. El-Bahrawy AN (1997) A spreadsheet teaching tool for analysis of pipe network. Eng J Univ Qatar 33–50 7. Adeyeri MK (2016) Development of software for riveted joints design. J Multidiscip Eng Sci Technol (JMEST) 1–11 8. Bhandari VB (2010) Design of machine elements. Tata McGraw-Hill Education

Chapter 13

Effective Computational Tools for Teaching and Learning of Heat Transfer Through Extended Surfaces Ayush Dwivedi, Gorakh Sawant, Ayush Vyas, and Ashish Karn

Introduction Engineering applications related to heat transfer are frequently encountered by engineer professionals of several disciplines, such as aerospace, mechanical, civil, petroleum, environmental or biological engineering. To facilitate the understanding of working principles, students should have complete practical knowledge of them. Heat transfer is widely taught in the undergraduate and post-graduate curricula. Interactive computer simulations that visualize heat transfer and temperature distribution may provide a straightforward way. These concepts are taught and learned. Extended external surface processes often have the involvement of partial differential equations which in a normal way solving may require hard calculations and if we analytical solutions of these then we have to use the mathematical method model. This paper includes different heat transfer concept that incorporates, analytical, numerical and experimental analyses to enhance student’s understanding of extended heat transfer surfaces. Our goal is to develop a free interactive computational tool that can provide students a powerful tool to learn the concepts of heat transfer. Modern teaching requires software which is powerful, capable of stimulating industrial process that cannot be performed in a laboratory. Extended surfaces heat transfer is a topic that is to be covered in undergraduate heat transfer class with utmost importance, and solution to these types of A. Dwivedi · G. Sawant · A. Vyas · A. Karn (B) MultiPhase Flows Laboratory, Department of Mechanical Engineering, School of Engineering, University of Petroleum and Energy Studies, Dehradun, India e-mail: [email protected] A. Dwivedi e-mail: [email protected] A. Vyas e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_13

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the problem requires the use of complicated mathematical analysis or approximate numerical methods beyond the scope of a majority students [1]. The heat generated in a system such as refrigerators, boilers, transformers, air-cooled engines, compressors and electronic components must be dissipated to its surroundings to maintain the system functionality [2]. Fin technology is the most important method which helped in enhancement of the heat sink performance since fins are a part of heat transfer systems that are mostly encountered by mechanical engineering students. Thermophysical storage of thermal energy can be realized as sensible or latent energy through cooling or heating a bulk of the material. The energy is then made available when the reverse process is applied. Fusible materials, also known as phase-change materials (PCMs), are widely utilized for thermal energy storage at a fixed temperature by taking advantage of their heat of fusion (latent heat) during phase transition [3]. Thermal Energy Storage systems offer the possibility to store high amounts of thermal energy, especially the latent heat thermal energy storage (LHTES) system at a constant or near-constant temperature depends on the temperature difference of the phase-change material (PCM). The applications embedded in the PCM, such as longitudinal, circular/annular, plate and pin fins, represent the base of most extended surface or fin heat transfer enhancement techniques, especially the techniques based on plate finned heat exchangers, pin fin heat sinks and tree-shaped fins [4]. PCMs have the potential of storing large a amount of energy, interestingly, within a smaller range of temperature in comparison with prevalent sensible thermal storage materials. Likewise, the huge thermal storage capacity of latent heat storage materials and also their isothermal behaviour during charging (liquefying) and discharging (solidifying) processes have caused to utilize them in many applications. The applications of PCM have soared in various industries including the solar applications, space industry, air-conditioning, electronic industry, photovoltaic electricity systems, agricultural industries and so forth [5]. Therefore, it becomes clear that mechanical engineering students need to have strong foundation knowledge in extended heat transfer surfaces. In this article, we are presenting a powerful and versatile tool to simulate heat transfer in extended surfaces that takes the minimum time and gives the result with the best precision. As technology advances, the conventional methods fall short of conveying the idea. With the help of a computational tool following problems can be solved: • • • • •

Inability to make this course interesting. Inability to involve a student who is unable to attend classes. Lack of teaching aids to explain concepts. Shortage of time. Inability in giving a practical application of the concept

To facilitate the student’s learning in this topic, two tools have been developed. The first tool is a spreadsheet that allows the student to calculate Fin heat transfer rate and temperature at a different location along the fin using three different boundary conditions: Adiabatic fin tip, Very long fin, Convection at fin tip. This allows the student to get a hand on experience of the fins, variations in temperature along the fin. The second tool is also a spreadsheet which allows the student to compare heat

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transfer rate, effectiveness and temperature of different location along the length for various materials. This allows the student to gather foundational knowledge of fins through comparison between various materials. The virtual learning environment and computational tools help in promoting analytical thinking skills in students and provide a major change in usual teaching methodologies. As mentioned above, it is evident that computational tools help in providing teaching–learning processes, and even more in subjects whose approach is theoretical-practical such as heat transfer. Considering the user-friendly nature of Excel/VBA, it helps in providing solutions to critical problems, to plot live graphs, to learn new concepts just by changing the input parameters. For the heat transfer rate calculations in the fin, an excel workbook program has been developed that allows users to calculate, compare and plot graphs as per the requirement. Finally, this tool was utilized for teaching and learning in an undergraduate Fluid Mechanics classroom, and the student responses have been collected in the form of an online survey. The results have been collated and statistical analysis has been conducted to gauge the effectiveness of such a computational tool on the overall teaching–learning process.

Background Fins that we use as extended surfaces over a body when the heat transfer coefficient between the fin and the surroundings (h) is low, as is often the case with cooling processes in air, which mainly comes in free convection conditions. Electronic devices, condenser tubes of home refrigerators and cylinders of small aircooled motorcycles use fins that enhance their cooling process. The temperature distribution over a particular fin, which is obtained by solving out the governing non-lineal differential equation (subjecting it to proper boundary conditions), shows the heat transfer rate from the fin and its efficiency, and effectiveness [6]. The tool we have developed focuses on calculating the fin heat transfer rate and variation of temperature along the length of the fin. Normally, to solve problems based on extended heat transfer surfaces, a student had to go through a very timeconsuming series of repetitive calculations. This tool allows the student to analyse and solve the problem in a fraction of seconds. Normally, the calculations of the heat transfer rate and temperature at any point of the fin can be done with the help of information that includes the distance from the base end (x), the temperature at location x (T), the ambient temperature (Ta), the base temperature (Tb), the corrected fin length (Lc), the cross-sectional area (Ac), the parameter (P), the diameter of the fin (Dfin), the convection heat transfer coefficient (h), the conduction heat transfer coefficient (k), the length of the fin (L). The value of parameter and area of fin can be given as P = π D f in andAc√= π D f in 2 /4. Now for √ further calculations the following equations will help us m = h P/k Ac andM = h Pk Ac . The value of corrected fin length is given asL c = L + D f in /4. If the fin falls under the condition of very log fin the equations that will be used are (T −Ta )/(Tb −Ta ) = e−mx andQ f in = M(Tb −Ta ).

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If the condition of adiabatic fin is present then the equations that will be used are (T − Ta )/(Tb − Ta ) = cosh[m(L − x)]/coshm L andQ f in = M(Tb − Ta )tanhm L. If convection is taking place at the fin tip then the equations that will be used are (T −Ta )/(Tb −Ta ) = cosh[m(L c − x)]/coshm L c andQ f in = M(Tb − Ta )tanhm L c , where x is the distance from the base end, T is the temperature at location x, Ta is the ambient temperature, Tb is the base temperature, L c is the corrected fin length, Ac is the cross-sectional area, P is the parameter, D f in is the fin diameter, h is the convection heat transfer coefficient, k is the conduction heat transfer coefficient, L is the length of the fin. Figure 13.1 presents the schematic view of the heat transfer through extended surfaces system showing key parameters involved in the calculation such as base temperature, T b , the temperature of fluid passing, T ∞, fin length, L, fin width, W, fin thickness t. The figure also shows that both heat conduction and convection are involved when we discuss the heat transfer through extended surfaces, which increases the complexity in manual solutions. To find out the heat transfer and the temperature at different locations equations containing terms of all heat transfer ways, i.e. conduction, convection and radiation have to be solved. In addition, design problems can come handy if the computational tools are suitably designed and implemented, and also facilitate the instructors to better equip their students with skills to solve such problems and to make their classrooms more demonstrative. Hence, the current study proposes two computational tools for this purpose: first is fin analysis using different boundary conditions, and second, consideration in fin material selection. Both the tools are supplemented with demonstrative plots which demonstrate the comparison between the different conditions chosen at the click of a button. Fig. 13.1. A schematic view of the heat transfer through fins showing key parameters involved in the calculation

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Description of the Developed Computational Tool As mentioned in the previous section, two distinct computational solver tools have been developed using VBA/Excel on fin analysis. The first is fin analysis using different boundary condition solver can which can be downloaded from https://www. drkarnteaching.com/heat-transfer-tools by the engineering students, instructors or professionals, as shown in the figure below, the user can seek six inputs: length of the fin, the radius of the fin, fin material, boundary condition at fin tip, hot surface temperature and ambient temperature. Boundary conditions can easily be selected from the drop-down menu which offers users three boundary conditions: convection at fin tip, very longfin, adiabatic fin tip. In addition, a table in the tool provides a range of thermal conductivity(k) for a variety of materials so the user may easily select and enter the right values in the input column (Fig. 13.2). Upon feeding these desired inputs, a solver button is also inserted in the spreadsheet that on clicking gives the result that is ‘Fin heat transfer rate’ and plots temperature vs distance graph, which is presented in the form of a table. As shown in the figure below, a table is provided that gives the variation of temperature along the length of the fin along with a graphical plot. The plot shows blue dots which denote the temperature at a given distance. The tool does not merely compute the fin heat transfer rate but also help in visualizing the change of temperature with distance at selected boundary condition (Fig. 13.3). Next Fig. 13.5 presents the consideration in fin material selection solver. A spreadsheet is provided where the user can seek the seven inputs: Hot surface temperature, ambient temperature, the diameter of long cylindrical fins, heat transfer coefficient,

Fig. 13.2. Input section of the tool for calculating heat transfer rate of fin

Fig. 13.3. Output section of the tool

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Fig. 13.4. Graphical representation of temperature variation

thermal conductivity for material 1, thermal conductivity for material 2, thermal conductivity for material 3. In addition, for the selection of material drop-down boxes is presented which provide a range of thermal conductivity(k) for a variety of materials so the user may easily select and enter the right values in the input column for each material. The tool calculates the heat transfer rate and effectiveness of all the three materials selected and presents them in a tabular form as shown in Fig. 13.6. The tool does not merely calculate the heat transfer rate and effectiveness but also helps in visualizing the variations of temperature with the distance of all three. At the bottom of the spreadsheet, a table is provided that gives the variation of temperature along the length of the fin of all the three materials selected along with graphical representation. Fig. 13.6 shows the comparison of temperature vs distance and plots of all the three materials selected in (Fig. 13.7). Figure 13.8 demonstrates a flowchart depicting the typical algorithm behind the complicated solution of the fin analysis using different boundary conditions problems. As the figure shows, the strategy begins with seeking the inputs from the user such as r, L and t as well as the base temperature and the ambient temperature. However, any solution for the heat transfer rate and temperature at various locations using different equations can’t proceed further without the area and parameter calculations. Paradoxically, however, the calculation of m and M, both of which depend

Fig. 13.5. Input section of the tool that compares the fin properties for different materials

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Fig. 13.6. Output section of the tool

Fig. 13.7. Graphical variation of temperature comparison for different fin materials

upon the value of conduction heat transfer rate. Hence, the solution must proceed by finding out the material selected for the fin and the fin boundary condition. However, to solve the equation to find out the temperature at various locations along the fin length, a set of repetitive and circular calculations must be done. Hence, the calculation must proceed by the assigned value of the loop variable so that the conditions of the loop can be checked. And hence, the iterations must continue with incremental changes in the loop variable till a value of the loop variable greater than the condition is attained. Although the algorithm of this repeated iterative procedure may look somewhat involved, its actual implementation within the MS Excel/VBA is rather quite straightforward and simple. In fact, its extremely user-friendly front graphical interface with a very simplistic backend coding in Visual Basic is one of those distinguishing features that makes it truly unique and attractive for developing applications that are easy to develop and use. Actually, this iterative and tedious computation can be very easily carried out in MS Excel with its ‘For loop feature’.

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Fig. 13.8. Flowchart showing the algorithm behind the computation for a very long fin case

Users Surveys and Results Finally, to test the efficacy of the developed computational tool in enhancing the teaching and learning of heat transfer through extended surfaces problems in undergraduate Heat Transfer course has been tested by taking sample surveys of a variety of users and the resulting data has been analysed using hypothesis testing principles, to arrive at some substantive conclusions. In order to collect the data, the developed tool was uploaded on the course website https://www.drkarnteaching.com/heat-tra nsfer-tools and it was given access to the second year B.Tech Mechanical Engineering, Mechatronics Engineering and Automotive Design Engineering students who have studied the Heat Transfer course. The tool was also open for review from the B.Tech third-year students as well as the faculty/ research scholars who wished to provide the data and feedback for the innovative tool. The users provided feedback on the efficacy of the tool in enhancing the overall teaching–learning process, how the tools inspired the students to do quality work, to retain and interest in the course, how it helped in assisted peer-learning, on whether it reduced the difficulty level of the course, on whether it helped them to see the integration of computers in

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engineering education, helps in applying theoretical concepts to real-life problems, etc. The survey also highlighted the other side of these tools—one from a pedagogical perspective and it was seen that the tool is a great lecture demonstration to aid students’ learning, is helpful in problem-solving skills and gets a firsthand recommendation for such implementation in other engineering courses. Overall, there was an overwhelmingly positive response from all the users who affirmed the immense usefulness of the computational tool.

Conclusions A helpful, versatile and computational program has been developed to make network models of heat transfer processes in simple fins which, otherwise, can be numerically simulated with adequate computer code. The approach developed in this paper for solving extended surfaces heat transfer problems provides a reliable, efficient means of explicitly determining a variety of design, operating and calibration parameters for fins. Manual solutions to these types of problems require time and is a difficult process as it involves solving of complex equations. This approach also provides an efficient technique to enhance real-time modelling, which requires the reliable, fast calculation of many of the parameters discussed in this paper. The paper demonstrates the use of spreadsheets as an educational tool in the area of analysis of heat fins. Certain features like IF statements, FOR loop, inherent to spreadsheets were used to improve the efficiency of the solution, like the macros used to automate the solution steps. We have also provided the tool on a self-created open-source website freely to be used by the students and engineering instructors alike. Not only we have designed, but we have described the exact methodology, using which anyone can design such a tool for himself. We have provided also the tool on a self-created open-source website freely to be used by the students and engineering instructors alike. This paper presents solutions to the temperature at different locations from the base via numerical and graphical presentation and solutions to heat flux generated by implementing spreadsheet programs along with VBA functions. To satisfy industrial demand, that is, usable and economic, determining the optimum fin profile is the topmost priority of the researchers [7].

References 1. Somerton CW, Schroeder JB, Lacin F, Harrier R (2003) Alternative approaches to teaching extended surface heat transfer. ASEE Annu Conf Proc pp. 1699–1718. https://doi.org/10.18260/ 1-2-12299 2. Nagarani N, Mayilsamy K, Murugesan A, Kumar GS (2014) Review of utilization of extended surfaces in heat transfer problems. Renew Sustain Energy Rev 29:604–613. https://doi.org/10. 1016/j.rser.2013.08.068

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3. Dhaidan NS, Khodadadi JM (2017) Improved performance of latent heat energy storage systems utilizing high thermal conductivity fins: a review. J Renew Sustain Energy 9(3). https://doi.org/ 10.1063/1.4989738 4. Abdulateef AM, Mat S, Abdulateef J, Sopian K, Al-Abidi AA (2018) Geometric and design parameters of fins employed for enhancing thermal energy storage systems: a review. Renew Sustain Energy Rev 82:1620–1635. https://doi.org/10.1016/j.rser.2017.07.009 5. Bazri S, Badruddin IA, Naghavi MS, Bahiraei M (2018) A review of numerical studies on solar collectors integrated with latent heat storage systems employing fins or nanoparticles. Renew Energy 118:761–778. https://doi.org/10.1016/j.renene.2017.11.030 6. Del Cerro Velázquez F., Gómez-Lopera SA, Alhama F (2008) A powerful and versatile educational software to simulate transient heat transfer processes in simple fins. Comput Appl Eng Educ 16(1):72–82. https://doi.org/10.1002/cae.20159 7. Maji A, Choubey G (2020) Improvement of heat transfer through fins: A brief review of recent developments. Heat Transf 49(3):1658–1685. https://doi.org/10.1002/htj.21684

Chapter 14

Optimization of Tribological Properties of Microparticulate-Reinforced ZA-27 Composites G. R. Gurunagendra , B. R. Raju , C. Ravi Keerthi , Vijayakumar Pujar , D. P. Girish, and H. S. Siddesha

Introduction Metals and alloys have found to be versatile engineering materials in various applications. In the last two decades, there is a significant interest on the fabrication and use of composites in niche applications of structures and machine members of automotive and aerospace assemblies. Composites are made of two different constituent materials, i.e., matrix and reinforcement phases. The matrix material holds the reinforcement material in a composite. This makes the composite material stronger than the individual phases. However, they are found to exist separately when mixed because of their chemical and physical differences. ZA-27 alloys are commercially proven bearing materials. In spite of excellent mechanical properties, wear resistance and machinability ZA-27 alloy lose the dimension at temperature greater than100° C. Heat treatment processes like T4 and T6 and addition of reinforcement into ZA-27 alloy with synthetic ceramic particles and whiskers like Alumina, Silicon carbide, titanium carbide, boron carbide, graphite [1–6] and organic waste like rice husk ash, groundnut shell ash and industrial waste like quarry dust, fly ash etc. to achieve better mechanical, wear characteristics [7–10].

G. R. Gurunagendra (B) · C. R. Keerthi · V. Pujar Department of Mechanical Engineering, Global Academy of Technology, VTU, Bangalore 560098, India B. R. Raju Department of Automobile Engineering, TOCE, VTU, Bangalore 560068, India D. P. Girish Department of Mechanical Engineering, GEC Ramanagar, VTU, Bangalore 562159, India H. S. Siddesha Department of Mechanical Engineering„ ACS College of Engineering, VTU, Bangalore 560074, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_14

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Fig. 14.1 a ZA27 alloy billets as procured b Zircon sand as procured [4]

Table 14.1 Composition of ZA-27 alloy (ASTM B669-82) Al

Mg

Cu

Fe

Silicon

Zinc

25.60%

0.07%

2.10%

0.04%

0.001

Remainder

Table 14.2 Composition of Zircon sand

Zircon oxide + hafnium

Silica

Traces of elements

65%

24%

Al2 O3 , TiO2 and Fe2 O3

Materials The matrix used in the present work is ZA-27 alloy, which is a proven bearing material. The materials in as procured condition is shown in Fig. 14.1. The chemical composition of the matrix material is shown in the Table 14.1. In this work, Zircon sand (ZrsiO4 ) of particle size 100 mesh is used as a primary reinforcement in the matrix of ZA-27. Chemical composition of Zircon sand is shown in Table 14.2. Density of zircon sand(ρ = 4.56 g/cc) is in proximity with the density of ZA-27(ρ = 4.5 g/cc) alloy.

Fabrication of Composites by Stir Casting ZA-27 alloy is procured by FenFe Metallurgicals Bangalore in the form of ingots. 2 kg of ZA-27 alloy is placed in the furnace and heated to 400 °C till it reaches molten state. Stainless steel blade stirrer arrangement with motor and speed regulator is placed in the furnace containing melt. Stirring is performed at 300 rpm for 3 min. A known weight of zircon sand at different weight proportions of 1.5wt. %, 3.0wt. %, 4.5wt. % and 6.0wt. % is preheated and added to the molten metal slowly with continued stirring. Borax powder of 20 g is added as wetting agent to obtain a good

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Fig. 14.2 a Solidification of casting b Cast samples

interface between ZA-27 and Zircon sand. The melt is poured in preheated cast-iron dies and after solidification cast samples are obtained as shown in Fig 14.2.

Microstructure Studies The cast samples are cut, and surface is prepared for microstructure examination using emery sheets of different grit sizes and polished to reveal the morphology of the samples in Fig. 14.3. SEM/EDAX instruments are used for microstructure and distribution of reinforcement particles in ZA-27 matrix alloy as well as chemical composition.

Fig. 14.3 Specimens for microstructure studies

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Fig. 14.4 Pin on disc tester [11]

Wear Test The main parts of a pin on disc tester include LVDT, lever arm with pin holder, steel disc driven by a motor, weighing arrangement and data acquisition system as shown in Fig. 14.4. LVDT will measure the linear displacement. As the wear of the specimen occurs the load on the pan push, the lever arm to contact the disc resulting in the movement of LVDT plunger generating the signals continuously during the test that is acquired and analyzed for understanding wear and frictional behavior. Weight loss method is used to compute the wear loss by measuring the weight of specimen before and after conducting wear test.

Design of Experiments A statistical method of design of experiments (DOE) is used to optimize the wear behavior of the composites produced for different process parameters and their levels specified by Orthogonal array using Taguchi method. Planning, conduction and analysis are the three phases in DOE. The main purpose of this method is to find the wear loss using the combination of factors and its levels. Dry sliding wear test is conducted with three parameters applied load, sliding speed and sliding distance and varying them for four levels. L16 Orthogonal array (OA) consisting of 16 rows and 3 columns was selected as shown in Table 14.3 is used in the present work. The selection of Orthogonal array depends on three items in order of priority, viz., the number of factors and their interactions, number of levels for the factors and cost limitations. Sixteen experiments in total were performed based on the run order

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Table 14.3 Process parameters used in the test Process parameters Zircon sand (wt. %)

A

1

2

3

4

1.5

3.0

4.5

6.0

Load(N)

B

15

30

45

60

Sliding velocity (m/s)

C

0.25

0.5

1.0

1.5

generated by the Taguchi model. The response for the model is weight loss. In this OA, a column is assigned to wt. % reinforcement, applied load and sliding velocity and the remaining columns are assigned to their interactions [11]. Signal to noise ratio (S–N) is used in the analysis phase of the design of experiment for finding the optimum process parameter especially in dry sliding wear experiments. Rank of process parameters is obtained, and the level of significance of influencing factor and their interactions is obtained for the wear loss with smaller the better characteristic. Minitab 17 is used for conducting Taguchi analysis.

Results and Discussion Microstructure The SEM analysis of reinforcement is shown in Fig. 14.5. The microstructure of ZA-27 alloy with zircon sand as primary reinforcement is shown in Fig. 14.6b. The scanning electron micrograph of the zircon particles and the conformation of zircon and silicate are shown in Fig. 14.6a as procured. Zinc rich and aluminum grains along with grain boundaries are revealed in SEM with particles adhering to grain boundaries. The scan area confirms the reinforcement of zircon sand dispersed in ZA-27 matrix in EDAX spectrum. Agglomerations and porosity are observed in the SEM.

Tribological Behavior Dry sliding wear tests are performed on the cast samples of ZA-27-zircon sand composites by pin on disc tribometer as per ASTM G99-95 standards. Samples of size 12 mm diameter and 25 mm length are machined to fabricate pins. The pin surface is made flat to have proper contact on the counter face disc The pin (stationary) is held against the rotating disk (shaft) by load applied acting as counterweight and balancing the pin, mimicking the bearing applications where the bearing (pin) is stationary supporting the rotating shaft (disc). The disc is 160 mm diameter and 10 mm thickness and made of hardened steel of 65 HRC. The track diameter is fixed

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Fig. 14.5 a SEM of Zircon. b EDAX of Zircon sand

to 100 mm in the experiment, while the Reinforcement content (wt. %), Load (N), sliding speed (m/s) is varied in the test as shown in Table 14.3. Initially, weight of test samples is found using electronic balance of accuracy 0.0001 g. Weight loss of material due to wear is measured after the test and tabulated. The tests are performed by varying the process parameters at room temperature. Weight loss the simple measurement of wear loss is found by conducting the experiment as per L16 OA by combination of factors using Minitab v17 and results are tab-ulated as shown in Tables 14.4 and 14.5.

ANOVA Test The influence of process parameters like weight percentage of reinforcement applied load and sliding speed on the response of wear of ZA-27 matrix reinforced with 1.5wt. % to 6 wt. % in the space of 1.5wt. % is studied using ANOVA performed in Minitab v17. Analysis was carried out at confidence limit of 95% with a level of significance of 5%. P-values less than 0.05 are said to be statistically significant affecting the

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Fig. 14.6 a SEM image of cast ZA-27 MMC. b SEM image of cast ZA-27 MMC at different weight percentages of zircon sand. c EDAX of ZA-27 MMC [6]

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Table 14.4 Result of wear test Test run

Wt. % Zircon sand

Load(N)

Sliding velocity (m/s)

Weight loss (mg)

SNRA4

1

1.5

15

0.25

2.3

−7.2346

2

1.5

30

0.5

4.76

−13.5521

3

1.5

45

1

11.9

−21.5109

4

1.5

60

1.5

50.8

−34.1173

5

3.0

15

0.5

2.2

−6.8485

6

3.0

30

0.25

1

0.0000

7

3.0

45

1.5

53.7

−34.5995

8

3.0

60

1

24.2

−27.6763

9

4.5

15

1

14.7

−23.3463

10

4.5

30

1.5

33

−30.3703

11

4.5

45

0.25

5.1

−14.1514

12

4.5

60

0.5

2

−6.0206

13

6.0

15

1.5

11.3

−21.0616

14

6.0

30

1

8.3

−18.3816

15

6.0

45

0.5

4.7

−13.4420

16

6.0

60

0.25

1.6

−4.0824

Table 14.5 Response for signal to noise ratios smaller is better

Level Zircon sand (wt. %) Load (N) Sliding velocity (m/s) 1

−19.104

−14.623

−6.367

2

−17.281

−15.576

−9.966

3

−18.472

−20.926

−22.729

4

−14.242

−17.974

−30.037

Delta 4.862

6.303

23.670

Rank

2

1

3

wear loss. Percentage of contribution indicates the degree of influence on the result. Sliding velocity is most significant followed by wt. zircon sand and load as shown in Table 14.6.

Regression Analysis A linear regression relationship is established using the Minitab v17 software between the control parameters of wt. % reinforcement, load sliding speed and weight loss. The equation also establishes the correlation with ANOVA results in terms of significant factors and interactions if any.

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Table 14.6 Analysis of variance Source Zircon sand (wt. %)

DF Seq SS Contribution (%) Adj SS Adj MS 3

428.1

9.66

428.1

Load

3

400.8

9.05

400.8

Sliding speed

3

3129.0

70.62

3129.0

Error

6

472.6

10.67

472.6

Total

15

F-Value p-Value

142.71

1.81

0.245

133.58

1.70

0.266

1042.99 13.24

0.005

78.7

100

R-sq-89.33% R-sq (adj)-73.33%

Regression Equation (R2 = 81%). weight loss mg = − 9.25 − 2.63 wt. % Reinforcement + 0.288 Load (N) + 28.06 Sliding velocity (m/s)

(14.1)

The effect of load, sliding velocity and wt. % reinforcement was studied for weight loss of the specimens subjected to pin on disc test. The main aim of the experiment is to study the influencing factor among combinations of parameters for obtaining smaller weight loss. From Table 14.6 based on response for means and signal to noise ratio, it is observed that sliding speed and wt. % reinforcement are affecting the weight loss with smaller the better characteristic followed by load. 6 wt. % zircon, 15 N load and 0.25 sliding velocity give the least weight loss. This is also confirmed by Fig. 14.7a and b by main effect plots by the large inclinations of sliding speed and wt. % reinforcement. The interaction plot shown in Fig. 14.9 reveals the strong interaction of process parameters affecting the weight loss of the ZA27 composites. Figure 14.8 shows the surface plot of variation of weight loss vs load, wt. % reinforcement and sliding velocity. Weight loss, the major response factor in tribological applications, is found to increase with increase in process parameters, i.e., load and sliding velocity but reduces as wt. % reinforcement increases. The surface plot bulges indicating interactions with the process parameters. The interactions plot shown in Fig. 14.9 reveal the interactions of the process parameters.

Wear Mechanisms Microstructure studies using SEM are carried out to understand the wear behavior of ZA-27/Zircon sand composites by sectioning the pin near the worn surface. The SEM images of worn pin contact surfaces reveal the wear tracks on the material in the form of ploughs, cracks, pits or groves and spread of debris of wear particles as shown in Fig. 10a and b. The SEM pictures demonstrate the wear scars in the sliding motion. Mild wear regime, moderate wear regime and severe wear regime are noticed in the pin surface

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Main Effects Plot for SN ratios Data Means Load(N)

wt. % reinforcement

Sliding velocity(m/s)

-5

Mean of SN ratios

-10

-15

-20

-25

-30 1.5

3.0

4.5

6.0

15

Signal-to-noise: Smaller is better

30

45

60

0.25

0.50

1.00

1.50

(a) Main Effects Plot for Means Data Means

wt. % Reinforcement

Sliding velocity(m/s)

Load(N)

40

Mean of Means

30

20

10

0 1.5

3.0

4.5

6.0

15

30

45

60

0.25

0.50

1.00

1.50

(b) Fig. 14.7 a Main effect plots of S–N ratio. b Main effect for means

after the test. Both adhesive wear and abrasive wear are seen to exist in the pin. Since there exist asperities on the surfaces, scratches and groves are seen due to ploughing action [12, 13]. Abrasion is seen at high loads due to excessive plastic deformation of material. Non-uniform dispersion of particles also leads to abrasion at low load. Delamination of particle with continuous presence of crack on the pin is noticed, which is regarded as severe wear regime due to higher sliding speed. Since at high

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Fig. 14.8 Surface plot showing the variation of response weight loss (mg) versus process parameters

Interaction Plot for weight loss(mg) Data Means 15

30

45

60

wt. % Reinforcement 1.5 3.0 4.5 6.0

40

20

wt. % Reinforcement

0

40

Load(N)

20

Load(N) 15 30 45 60

0

40

Sliding velocity(m/s)

20

0 1.5

3.0

4.5

6.0

0.25

0.50

1.00

Sliding velocity(m/s) 0.25 0.50 1.00 1.50

1.50

Fig. 14.9 Interaction plot of process parameters with weight loss of ZA-27 composites

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Fig. 14.10 a SEM image of worn pin surfaces at high load for 3wt. % of ZA-27/zircon sand composites at low load. b SEM image of worn pin surfaces at high load for 6wt. % of ZA-27/zircon sand composites at high load

sliding velocity, zircon particles come out of the matrix bonding leading to ploughing and crack formation [14, 15]. The EDAX spectrum obtained at different scanning points of worn surface indicates the peaks of elements like zinc, aluminum, zircon oxygen, carbon and iron as shown in Fig. 14.11. The presence of elements indicates oxide layer formation on the worn surface due to heat generated and environment creating high temperature at the worn surface during sliding action. The presence of iron oxides is confirmed due to peaks of iron and oxygen. This is due to the erosion of counterface steel disc eroded by zircon sand-reinforced composite pins.

14 Optimization of Tribological Properties of Microparticulate Reinforced …

Base(342)(292)(639)_p t1 Base(342)(292)(639)_p t2

153

CK

OK

AlK

FeK

ZnK

ZrL

0.7 9

8.4 7

13.8 0 19.3 9

16.0 0

60.9 3 79.6 2

0.0 0 0.9 9

Fig. 14.11 EDAX spectrum of worn surface and elemental peaks on worn surface

Confirmation Test The last step of the design of experiment is using optimal control factors. S–N ratios of experimental values are predicted values of the table and are tabulated in Table 14.7. Table 14.7 Results of the test Sl no

(Wt.%) reinforcement

Load (N)

Sliding speed (m/s)

Experimental value

Predicted value

% error

1

3

60

1.0

−27.673

−26.510

4.05

2

6

30

1.0

−18.316

−17.671

3.85

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The experimental values and predicted values of S–N ratio are compared, and error is minimum that indicated the effectiveness of regression model for weight loss prediction using L16 Orthogonal array.

Conclusion ZA-27 MMC was successfully fabricated using stir casting process using appropriate stirring parameters. The cast samples were subjected to microstructure studies revealing a dispersion of zircon particles in the ZA-27 matrix, and EDAX confirmed the elemental composition. ZA-27 MMC as cast samples were machined to obtain pins and subjected to pin on disc test to evaluate the tribological behavior of composites. The obtained results were optimized using Latin square 16 Orthogonal array by Taguchi method. 6wt. % zircon sand reinforcement, load of 15 N and sliding velocity of 0.25 m/s gave the lowest weight loss. Sliding velocity was the significant factor followed by load and reinforcement. Wear micrographs of pin showed the presence of mild and severe wear as the load and sliding velocity increased.

References 1. Babi´c M, Ninkovi´c R (2004) Zn-Al alloys as tribomaterials. Tribol Ind 26:3–7 2. Babi´c M, Ninkovi´c R, Mitrovi´c S, Bobi´c I (2007) Influence of heat treatment on tribological behavior of Zn-Al alloys. Tribol Ind 29:23–31 3. Kiran TS, Prasanna Kumar M, Basavarajappa S, Viswanatha BM (2014) Dry sliding wear behavior of heat treated hybrid metal matrix composite using Taguchi techniques. Mater Des 63:294–304. https://doi.org/10.1016/j.matdes.2014.06.007 4. Gurunagendra GR, Bharat V, Raju BR, Amith DG, Pujar V, Keerthi CR (2021) Microstructure, dislocation density and thermal expansion behavior using thermo elastic models of zircon sand reinforced as cast ZA-27 composites. J Miner Mater Charact Eng 09:100–115. https://doi.org/ 10.4236/jmmce.2021.91008 5. Pujar V, Devarajaiah RM, Suresha B, Bharat V (2021) A review on mechanical and wear properties of fiber-reinforced thermoset composites with ceramic and lubricating fillers. In: Materials today: proceedings. https://doi.org/10.1016/j.matpr.2021.02.214 6. Gurunagendra GR, Raju BR, Pujar V, Amith DG, Hanumantharaju HG, Angadi S (2021) Investigations on microstructure and tensile properties of as-cast ZA-27 metal matrix composite reinforced with zircon sand. Mater Today Proc 46:7618–7623. https://doi.org/10.1016/J.MATPR. 2021.01.896 7. Alaneme KK, Fatile BO, Borode JO (2014) Mechanical and corrosion behaviour of Zn-27Al based composites reinforced with groundnut shell ash and silicon carbide. Tribol Ind 36:195– 203 8. Alaneme KK, Bodunrin MO, Awe AA (2018) Microstructure, mechanical and fracture properties of groundnut shell ash and silicon carbide dispersion strengthened aluminium matrix composites. J King Saud Univ - Eng Sci 30:96–103. https://doi.org/10.1016/j.jksues.2016. 01.001. 9. Fatile BO, Adewuyi BO, Owoyemi HT (2017) Synthesis and characterization of ZA-27 alloy matrix composites reinforced with zinc oxide nanoparticles. Eng Sci Technol Int J 20:1147– 1154. https://doi.org/10.1016/j.jestch.2017.01.001

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10. Gurunagendra GR, Raju BR, Pujar V, Amith DG, Poornachandra Siddesha HS (2021) Mechanical, wear and corrosion properties of micro particulates reinforced ZA-27 hybrid MMC by stir casting: a review. Mater Today Proc 46:7602–7607. https://doi.org/10.1016/J.MATPR.2021. 01.892 11. Marigoudar RN, Sadashivappa K (2013) Effect of reinforcement percentage on wear behavior of SiCp reinforced ZA43 alloy metal matrix composites. Sci Eng Compos Mater 20:311–317. https://doi.org/10.1515/secm-2013-0024 12. Hariharasakthisudhan P, Rajan BS, Sathickbasha K (2022) Inspiration of reinforcements, manufacturing methods, and microstructural changes on wear behavior of metal matrix composites - a recent review. Mater Res Express 7. https://doi.org/10.1088/2053-1591/ab6918 13. Lakshmikanthan A, Prabhu TR, Babu US, Koppad PG, Gupta M, Krishna M, Bontha S (2020) The effect of heat treatment on the mechanical and tribological properties of dual size SiC reinforced A357 matrix composites. J Mater Res Technol 9:6434–6452. https://doi.org/10. 1016/J.JMRT.2020.04.027 14. Reddy AP, Krishna PV, Rao RN (2017) Dry sliding wear behaviour of ultrasonically-processed AA6061/SiCp nanocomposites. Int J Automot Mech Eng 14:4747–4768. https://doi.org/10. 15282/ijame.14.4.2017.12.0373 15. Lakshmikanthan A, Bontha S, Krishna M, Koppad PG, Ramprabhu T (2019) Microstructure, mechanical and wear properties of the A357 composites reinforced with dual sized SiC particles. J Alloys Compd 786:570–580. https://doi.org/10.1016/J.JALLCOM.2019.01.382

Chapter 15

Study of Characterization, Mechanical Properties, and Tribological Behavior of Magnesium-Silver Alloy Pradeep V. Badiger, M. Vinyas, T. Ram Prabhu, N. V. Naveen Kumar, Nikhil B. Nargund, and P. K. Ramesh Gouda

Introduction In the present engineering material stream, magnesium alloy is considered to be one of the best alloys. It is the lightest structural metal with the highest specific strength and stiffness in comparison to any other structural metal [1]. Magnesium alloys are now majorly being used in the aerospace, automobile, and electronics sectors [2] due to their low density, high specific strength, good damping characteristics, high specific stiffness, and brilliant machinability [3]. To improve the mechanical properties of magnesium alloys, researchers have refined the grains using plastic deformation techniques such as extrusion, rolling, and equal channel angular pressing [4], of which heat treatment and solidification have been used in this paper to improve the mechanical properties of magnesium alloys. Because of its use and efficacy in enhancing heat conductivity in wood and wood composites, Saivash Bayani et al. used silver nano-suspension [5, 6]. Silver has a low wear rate and wear contact resistance [7], and thus is added to magnesium to avail a better version of the material used in this paper. SEM and XRD were carried out for checking the microstructural stability [8], characterization and finding the nature of the Mg-Ag material [9]. From SEM, the material quality and composition [10] were found while the XRD intensity graphs showed the crystallinity and deviation of P. V. Badiger (B) · N. V. N. Kumar · N. B. Nargund · P. K. R. Gouda Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology, Bengaluru 560064, India M. Vinyas Department of Mechanical Engineering, NIT, Silchar 788010, India Department of Mechanical Engineering and Aeronautics, City, University of London, London EC1V 0HB, UK T. R. Prabhu Joint Director, DRDO Bengaluru, Bengaluru, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_15

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Mg-Ag from pure Mg material [11]. The tensile test was carried out on a dumb-bellshaped Mg-Ag sample until it got fractured [12] at ASTM E8. Stress-strain graph was plotted from which the tensile strength, % elongation, yield point, and break stress [13] were obtained. Vickers hardness test was carried out at three different locations to determine the surface resistance to indentation [14] at ASTM E92 with a 2 kg load and holding time of 15 s. Wear is one of the most common problems being faced in engineering applications such as bearings, engine parts, and movable items and even in the mechanical industries. It is basically a surface phenomenon, but it can completely subvert the mechanical functioning of engineering parts. The statical approach in this paper used Taguchi L9 array and the ANOVA techniques to estimate the impact of each parameter on the variance of wear loss of Mg-Ag alloy, i.e., analysis of the Mg-Ag alloy for the wear process. Mathematical modeling was developed with process variables and wear behavior [15]. For the trial and validation of cutting force during machining of red brass, M. Hanief and colleagues coupled regression and ANN modeling, with ANN outperforming regression in terms of accuracy [16]; similarly in this paper, regression and ANN modeling have been combined to predict the results. Based on the literature survey, it was evident that Mg alloys have enormous qualities, wherein their poor resistance toward corrosion remains a major drawback, whereas Ag particles possess excellent corrosion resistance. It was also observed that despite these contrasting properties research on Mg-Ag alloy was minimal. Hence, in the current work, properties of Mg-Ag alloy are examined, starting from characterization by SEM and XRD and understanding its probable effects on mechanical properties of the material. Mechanical properties of the alloy were determined using tensile and hardness tests. Tribological behavior was assessed using a pin-on-disk wear testing machine. Later, the effect of each input characteristic on output features was analyzed using ANOVA. Finally, regression and ANN models were developed to predict the outcomes.

Materials and Methodology Magnesium-Silver alloy has been chosen for the current project (Mg-Ag). The alloy consists of 9% Ag and 91% Mg. Microstructure analysis of the specimen was done using SEM and XRD. The MgAg Sem analysis was carried out on an ESEM Quanta200 FEI equipment, which is equipped with a solid-state backscattered electron detector and an ultrathin window EDS system with a resolution of 20 kV in vacuum at room temperature. For the analysis, a cylindrical solid specimen of 25 mm in height and 15 mm in diameter was used. When electrons interact with the surface of the specimen, surface signals are generated, which are collected by detectors and stored as pictures. Empyrean III (it is the 3rd generation X-ray diffractor) was used for the microstructural analysis of Mg-Ag Alloy. It can measure from powders to thin films, from nanomaterials to solid objects. X-ray powder diffraction (XRD) is a quick analytical

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159

Fig. 15.1 Mg-Ag tensile test specimen (ASTM E8)

technique that can provide information on unit cell dimensions and is commonly used to identify the phase of crystalline materials. The sharp XRD peaks indicate that the metal is crystalline, whereas the non-sharp peaks indicate that the metal is amorphous. Tensile testing is a destructive test that involves applying force to the ends of a specimen until it breaks, in order to ascertain its ultimate tensile strength. The MgAg alloy was tensile tested following the ASTM E8 standard using a Tinius Olsen model 5OST machine. The geometrical views of the conventional round tensile test specimen are shown in Fig. 15.1 (dog-bone shaped). The following are the standard dimensions: Gauge length is 50 mm, the diameter is 12.5 mm, Fillet Radius = 10 mm, and Reduction Section Length is 60 mm. The hardness of the Mg-Ag alloy was determined using the Vickers-Buehler method. The Vickers hardness test was performed with a weight of 2 kg and a holding time of 15 s, using an average of three trials. The Vickers hardness test was carried out according to the ASTM E92 standard. The following are the dimensions that were used: H = 1.5D, and the specimen’s height should be less than 1.5 times its diameter. Table 15.1 shows how an orthogonal array was created after defining the control elements, their levels, and responses. This experiment has three variables, each with three levels. A complete factorial experiment would require (33) = 27 trials. Instead of executing all potential combinations, the Taguchi technique is used to construct the experiment for wear study in order to acquire optimal results with the least number of tests in order to save time, money, and resources [9, 17]. We developed a Taguchi L9 orthogonal array for our experimental circumstances, which included 9 tests, 3 variables, and 3 levels. The analysis considers many aspects such as speed, load, and sliding distance. Under dry sliding conditions in ambient air at room temperature, the DUCOM pin-on-disk tester was used to investigate the tribological properties of Mg-Ag alloy. Smooth polished ends with a diameter of 12 mm and a length of 25 mm were put to a cylindrical specimen for the wear test. The specimen’s surface was rubbed first with Emery Paper Grit P400, then with Emery Paper Grit P800 for a super fine finish. The specimen is clamped and held against an EN31 abrasive disk during the testing. The

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Table. 15.1 Wear results Trial Speed Load Sliding Results (Rpm) (N) distance volume (m) wear (mm3 ) 50

500

S/N ratio

Wear S/N rate ratio (mm3 /m)

11.9352 −21.5366 0.0239

Wear Loss (mg)

S/N Ratio

1

500

32.4428 0.0208 33.6387

2

500

75

750

21.8108 −26.7734 0.0291

30.7278 0.0352 29.0692

3

500

100

1000

32.5381 −30.2478 0.0325

29.7522 0.0452 26.8972

4

1000

50

750

13.0695 −22.3252 0.0174

35.1761 0.0150 36.4782

5

1000

75

1000

12.2801 −21.7840 0.0123

38.2160 0.0253 31.9376

6

1000

100

500

9.5126 −19.5660 0.0190

34.4134 0.0134 37.4579

7

1500

50

1000

11.0948 −20.9024 0.0111

39.0976 0.0152 36.3631

8

1500

75

500

9.7671 −19.7953 0.0195

34.1841 0.0124 38.1316

9

1500

100

750

9.3056 −19.3749 0.0124

38.1263 0.0220 33.1516

weight is applied to the specimen by a cantilever mechanism with a track diameter of 100 mm. During the test, weight loss was seen for the variables of speed, load, and sliding distance. The full factorial design was utilized for the design and analysis of trials in this study. Different levels of trials for input variables such as speed, load, and sliding distance are conducted using the L9 orthogonal design, and the findings are listed in Table 15.1. The association between input parameters and output responses is established using a quadratic mathematical regression model in regression analysis. The mathematical regression model is used to predict the outcomes of the 27 experimental combinations. The desirability approach for the minimization function is used to perform multi-objective optimization for output responses (smaller is better). Training, testing, and validation are the three processes of ANN modeling. The training parameters suggested by Badiger et al. [6] were used to construct ANN modeling. The “Trainlm” learning rate training process of the MATLAB neural network toolbox was used to train the ANNs for the combinations of 27 tests (MathWorks Incorporation 2015). Figure 15.2 shows how a trial-and-error process and repetitive training simulation are used to determine the number of neurons in the hidden layer and the learning parameters. By introducing 27 input process parameter combinations to the trained ANN network, the results for error and accuracy were predicted. The anticipated volume wear, wear rate, and wear loss for each input training combination are compared to the experimental findings. The ANN model’s predicted data was found to be quite close to the experimental data.

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Fig. 15.2 Architecture of ANN

Result and Discussion Characterization Figure 15.3a–d shows the morphological images of Mg-Ag alloy obtained by SEM. From Fig. 15.3a, it can be observed that there is a uniform and homogeneous dispersion of Ag particles in the Mg-Ag alloy. Figure 15.3a–d represents the image of Mg-Ag alloy at 100x, 200x, 500x, and 1000x magnification, respectively. The presence of silver particles can be clearly observed in Fig. 15.3d. The dark region in the image depicts the Ag particles, whereas the lighter regions represent the Mg particles. The presence of Ag particles accounts for the strengthening of the alloy. The mechanical properties of the alloy are expected to improve due to the inclusion of Ag particles. The composition of Ag in Mg-Ag can be estimated to be 9% after the morphological analysis of the alloy. With the help of ImageJ software, the average grain length was found to be ~46.8 micron [15]. The phase purity and crystallinity of Magnesium-Silver Alloy were investigated using the X-ray diffraction technique, as shown in Fig. 15.4 (XRD). Because the crystallites in Mg-Ag are so small, none of them diffract at the same angle, resulting in the typical graph seen above [10]. Strong diffraction peaks between 30 and 40 degrees can be seen in XRD patterns. Peak height will vary depending on the selected crystal orientation; however, peaks will be low if the crystals are arranged randomly. The graph (Fig. 15.4) shows a similar intensity between Mg-Ag alloy and Mg when

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Fig. 15.3 a–d Represents the surface morphology of alloy at 100x, 200x, 500x, and 1000x magnification, respectively

Fig. 15.4 XRD results of Mg-Ag Alloy

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the highest peak is taken into consideration, while the individuals (i.e., Mg-Ag, Mg, and Ag) show the same peaks at the range of 45–50° angle. Mg-Ag alloy with 6.26 percent and 8.51% sliver was used by Zhidan Liu et al. Mg-Ag alloys exhibited a significantly stronger antibacterial activity than pure Mg, according to the findings. To obtain a lower deterioration rate, the microstructure was modified using solution treatment (T4), which included XRD. The deterioration rate in Mg-Ag alloys must be high if there are many precipitates [18].

Mechanical Properties Figure 15.5 shows the stress versus strain curve of Mg-Ag alloy. 0.2% Proof stress was found to be 204 MPa with the ultimate tensile strength of 278 MPa. Referring to Fig. 15.5, the fracture point of Mg-Ag alloy occurs at 276 MPa and 6.71 percent elongation which shows a higher ductile and toughness as compared to the pure Mg comprising a tensile strength of 151 MPa, yield strength of 84.5 MPa, and % elongation of 3 percent, thus proving Mg-Ag alloy better with nearly twice higher values than pure Mg. D. Steglich et al. used AZ31 (Mg + 3 percent Al + 1 percent Zn) and ZE10 (Mg + 1 percent Zn + 0.3 percent Ce-based misc metal) magnesium rolled sheets and extruded products and conducted tensile and compression tests at room temperature. Tensile test was also validated against the hydraulic bulge and cruciform specimen tests, and it was found to produce good results [19]. I.

Ulacia et al. told that AZ31B had the potential to achieve larger elongations for AZ31B at high strain rates at room temperature [20], with elongation about 15 percent but in Mg-Ag the elongation was absorbed in 5.96%.

On the basis of the above information, magnesium alloy and tensile test were considered for this paper.

Fig. 15.5 Tensile test results of Mg-Ag alloy

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Fig. 15.6 Hardness Trace of Mg-Ag

Figure 15.6 shows the hardness trace of Mg-Ag alloy. Three trials were taken with a regular interval of 0.1 mm distance. Out of 3 trials, the maximum hardness was found to be 88.2 whereas the minimum hardness was 85.1. Average of three trial, i.e., 87.1HV with a standard deviation of 1.8 was considered. 87.1HV 2—{87.1 Hardness value; HV as per Vickers; test load of 2kgf (19.6133 N)} A considerable decrease in grain size of the alloy is observed due to the addition of Ag, due to which there is an increase in the hardness of the material. The hardness of Mg-Ag is comparatively higher than that of pure Mg (275 MPa).

Wear Analysis The software MINITAB 18, which is designed for the design of experiment (DOE) applications, was used to conduct a statistical analysis of volume wear, wear rate, and wear loss. L9 orthogonal array test conditions and output results are presented, and the respective S/N ratios are presented in Table 15.1 [15]. It can be observed that the frictional force is directly proportional to the load applied, hence a major amount of wear loss can be seen in trail 3 (speed = 500 rpm, load = 100 N, sliding distance = 1000 m). With an increase in speed, the abrasive particle tends to smoothen up and hence least amount of wear loss can be seen in trial 8 (speed = 1500 rpm, load = 75 N, sliding distance = 500 m). The specimens’ worn-out surfaces were examined using an Olympus (BX53M) optical microscope. Figure 15.7a–i shows a micrograph of the Mg-Ag specimens’ worn-out surfaces. The groove in the microscopic image depicts the wearing of the surface due to abrasion, whereas the pit and cracks are the results of adhesive and fatigued ear. Abrasive wear is characterized by the following characteristics: Hard asperities on the steel counterface, or hard particles between the pin and the disk, plow or cut

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Fig. 15.7 a–i Micrograph of worn-out surface of Mg-Ag alloy a 500 rpm, 50 N, 500 m; b 500 rpm, 75 N, 750 m; c 500 rpm, 100 N, 1000 m; d 1000 rpm, 50 N, 750 m; e 1000 rpm, 75 N, 1000 m; f 1000 rpm, 100 N, 500 m; g 1500 rpm, 50 N, 1000 m; h 1500 rpm, 75 N, 500 m; i 1500 rpm, 100 N, 750 m

into the pin, removing small fragments or ribbon-like strips of material, and creating wear [21]. Harder materials, according to ARCHARD [22], are better at resisting abrasion wear. Variations in sliding speed result in varying degrees of grooving, as seen in Fig. 15.7a–i. At greater speeds, well-defined deep grooves change to shallower scratches, whereas at lower speeds, shallower grooves turn into well-defined deep grooves. Deeper grooves imply more penetration by strong asperities, which, along with minor material displacement on both sides of the grooves, indicates a predominantly cutting mode of abrasion at lower speeds. As the speed of the pin rises, frictional heating causes the temperature of the pin surface to rise. As a result, enhanced matrix plastic deformation at higher sliding speeds enhances the transition from cutting to plowing or wedge formation during abrasion. Plowing is the removal of material from both sides of an abrasion groove without disturbing the groove itself. This could explain the smaller scratches and lower wear rates as the sliding speed increases. This finding supports Archard’s theory that a material’s wear rate is inversely related to its hardness in the case of abrasive wear. As the sliding speed was raised, frictional heating generated a gradual softening of the pin surface, resulting in more extensive adhesion between the pin and the disk. As a result of frictional heat, the active slip planes increase, generating plastic deformation and adhesive

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wear [23]. According to the post-wear study of the worn-out surface, abrasive wear decreases with increasing speed, resulting in a drop in wear rate, volume wear, and wear loss of the specimen.

Regression Analysis The S/N ratio was calculated for the volume wear, wear rate, and wear loss of the material as the reaction, taking into account the various aspects. The S/N ratio is recommended by Taguchi; this will represent the performance of quality characteristics. In the current work, Taguchi L9 array “smaller-the-better” quality characteristics are used [17]. The S/N ratio is calculated using the following formula: S/N = −10 log 10(1/n) (yi)2

(15.1)

The number of times the experimental combination has been performed is n, and the quality characteristic value measured for the ith trial is yi . Figure 15.8a–c illustrates the S/N ratios and responses for each factor against each of its levels, with the smaller-the-better condition for volume wear, wear rate, and wear loss, respectively. Analysis of Variance (ANOVA) To determine the contribution of each process parameter to the specified performance characteristic, a statistical analysis of variance was used in conjunction with the Taguchi technique. This study was conducted in order to determine a 95 percent confidence level. Sources having a p-value of less than 0.05 were deemed statistically significant contributors to the performance measures. It can be observed that Speed has the highest influence on the wear rate, volume wear, and wear loss with 65.56 percent, 45.47%, and 45.21% contribution, respectively. Load and sliding distance contribute less to volume wear, wear rate, and wear loss, with (8.11%, 4.88%, and 14.88%) and (21.26%, 1.54%, and 25.96%), respectively. As a result, during the wear test of Mg-Ag alloy, speed is a critical factor to consider, followed by load and sliding distance.

Regression Analysis A multiple linear regression model was used to determine the relationship between the wear parameters speed, load, and sliding distance with volume wear, wear rate, and wear loss.

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Fig. 15.8 Main Effect plots for Means and SN Ratio a Volume wear b Wear rate c Wear loss

  Volume Wear mm3 = 11.3 + 0.0292 Speed (rpm) + 0.018 Load (N) − 0.0354 Sliding distance (m) −0.000422 Speed (rpm) × Load (N) −0.000007 Speed (rpm) × Sliding distance (m) +0.000650 Load (N) × Sliding distance (m) (15.2)   Wear Rate mm3 / m = 0.0346 + 0.000027 Speed (rpm) + 0.000032 Load (N) −0.000057 Sliding distance (m) − 0.000000 Speed (rpm) × Load (N) −0.000000 Speed (rpm) × Sliding distance (m) + 0.000001 Load (N) × Sliding distance (m) (15.3)

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Wear Loss (mg) = 0.0389 − 0.000004 Speed (rpm) − 0.000316 Load (N) −0.000033 Sliding distance (m) − 0.000000 Speed (rpm) × Load (N) −0.000000 Speed (rpm) × Sliding distance (m) + 0.000001 Load (N) × Sliding distance (m) (15.4) Equations 15.2, 15.3, and 15.4 are the regression equations obtained for volume wear, wear rate, and wear loss, respectively.

Confirmation Experiments Mathematical models for the volume wear, wear rate, and wear loss were developed for the Mg-Ag alloy using ANN and mathematical regression models. A predictive analysis was carried out to test the trained ANN and the regression model. From the results of Table 15.2, it can be observed that volume wear, wear rate, and wear loss decrease with an increase in Speed and decrease in load and sliding distance. Considering these results, ANN and Regression models were tested for the following test experiments as shown in Table 15.3. Because regression models can only predict outcomes within specific constraints (border limits), ANN models were developed to predict outcomes outside of those bounds [6]. Table 15.3 shows the outcomes of the test experiments. It can be seen that neither the regression nor the ANN model exhibits any substantial deviation, and the values of both prediction models are near to 1, implying that the produced models are appropriate.

Conclusion • Microstructural analysis (SEM) and phase analysis (XRD) were carried out on a selected specimen constructed of Mg-Ag alloy, and it was discovered that the grain size of the alloy had been reduced due to the insertion of Ag, which could be attributed to the material’s improved mechanical capabilities. • Tensile and Vickers hardness tests on the material revealed a significant increase in tensile strength (almost twice that of pure Mg) as well as a substantial increase in the alloy’s hardness number when compared to pure Mg. • When the wear findings were analyzed using L9 Taguchi and ANOVA, it was discovered that the speeds had a significant impact on the wear rate, volume wear, and wear loss of the material, with these qualities tending to decrease as the speed increases. In contrast, when the load and sliding distance rise, the wear rates, wear loss, and volume wear increase.

0.000417

0.000902

Wear loss

0.000080

0.000041 6

6

6 2

2

2

Residual

Regression

Residual

32.98

Regression

445.17

Degrees of freedom

Sum of Square

Wear rate

Volume wear

Response

Table 15.2 ANOVA result summary of Mg-Ag alloy

0.000902

0.000069

32.980

Regression

Mean square

0.000040

0.000021

16.4899

Residual

3.78

3.36

4.50

F ratio

0.224

0.247

0.193

p*

0.9190

0.9096

0.9096

CoD(R2 )

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1250

3

80

60

850

650 0.023

0.021

0.010

750

2

800

1600

1

40

Regression

Sliding distance

Speed

Trial

Load

Wear Loss (mg)

Test Experiments

Table 15.3 Results of test experiment

0.028

0.024

0.009

ANN

13.2170

13.9527

14.6850

Regression

13.1135

14.1223

13.98850

ANN

Volume Wear (mm3 )

0.0155

0.0220

0.0186

Regression

0.0140

0.0201

0.0173

ANN

Wear Rate (mm3 / m)

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• A predictive analysis conducted using ANN and Regression mathematical models implied that both regression and ANN models does not show any significant deviation and the values of both predictive models are close to 1, hence it can be predicted that the developed models are adequate. Acknowledgements The financial support by The Royal Society, London, through Newton International Fellowship (NIF\R1\212432) is sincerely acknowledged by the author Vinyas Mahesh. The rest of the authors are obliged to IISc Bangalore, NITK Surathkal, SIT Tumkur, and REVA Bangalore for providing us with the essential facilities.

References 1. Hasan M, Begum L (2015) Semi-continuous casting of magnesium alloy AZ91 using a filtered melt delivery system. J Magnes Alloy 3(4):283–301. https://doi.org/10.1016/j.jma.2015.11.005 2. Abbassi F, Srinivasan M, Loganathan C, Narayanasamy R, Gupta M (2016) Experimental and numerical analyses of magnesium alloy hot workability. J Magnes Alloy 4(4):295–301. https:// doi.org/10.1016/j.jma.2016.10.004 3. Hao, H (2011) Casting technology and quality improvement of magnesium alloys. In special issues on magnesium alloys (pp. 1-24) IntechOpen. https://doi.org/10.5772/19877 4. Xu T, Yang Y, Peng X, Song J, Pan F (2019) Overview of advancement and development trend on magnesium alloy. J Magnes Alloy 7(3); National Eng Rea Center Magnes Alloys 536–544. https://doi.org/10.1016/j.jma.2019.08.001 5. Bayani S, Taghiyari HR, Papadopoulos AN (2019) Physical and mechanical properties of thermally- modified beech wood impregnated with silver nano-suspension and their relationship with the crystallinity of cellulose. Polymers 11(10). https://doi.org/10.3390/polym11101538 6. Badiger Pv, Desai V, Ramesh MR, Prajwala BK, Raveendra K (2019) Cutting forces, surface roughness and tool wear quality assessment using ANN and PSO approach during machining of MDN431 with TiN/AlN-coated cutting tool. Arab J Sci Eng 44(9):7465–7477. https://doi. org/10.1007/s13369-019-03783-0 7. Stappers L, Ngoy CN, Zhang W, Toben M, Fransaer J (2013) Electrodeposition of silver-carbon coatings with low contact resistance and wear rate. J Electrochem Soc 160(4):D137–D145. https://doi.org/10.1149/2.039304jes 8. De M, Pereira-Da-Silva A, Ferri FA (2017) 1 - scanning electron microscopy. https://doi.org/ 10.1016/B978- 0-323-49778-7/00001-1 9. Narain R (2020) Polymer science and nanotechnology fundamentals and applications. Elsevier 10. Methods for assessing surface cleanliness. Developments in surface contamination and cleaning, vol 12. Elsevier (2019), pp 23–105. https://doi.org/10.1016/b978-0-12-816081-7. 00003-6 11. Regi M (2007) Synthesis, characterization and application of carbon nanotubes: the case of aerospace engineering. In: Nanofibers and nanotechnology in textiles. Elsevier Ltd, pp 113– 193. https://doi.org/10.1533/9781845693732.2.113 12. Lewis PR, Gagg C (2010). Examination and analysis of failed components. In: Forensic polymer engineering, Elsevier, pp 42–88. https://doi.org/10.1533/9781845697808.42 13. Saba N, Jawaid M,. Sultan MTH (2018) An overview of mechanical and physical testing of composite materials. In: Mechanical and physical testing of biocomposites, fibre-reinforced composites and hybrid composites, Elsevier, pp 1–12. https://doi.org/10.1016/B978-0-08-102 292-4.00001-1 14. Metallic Materials for Piping Components

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15. Serrao P, Prabhu R, Chiranth B, Mohammed Y (2016) Application of Taguchi method to predict the abrasive wear behavior of CP titanium surface mechanical attrition treatment view project severe plastic deformation (SPD) of Mg alloy view project application of taguchi method to predict the abrasive wear behavior of CP titanium. J Mech Eng Autom 6(5A):13–17. https:// doi.org/10.5923/c.jmea.201601.03 16. Hanief M, Wani MF, Charoo MS (2017) Modeling and prediction of cutting forces during the turning of red brass (C23000) using ANN and regression analysis. Eng Sci Technol Int J 20(3):1220–1226. https://doi.org/10.1016/j.jestch.2016.10.019 17. Badiger Pv, Desai V, Ramesh MR (2018) Performance of Ti-multilayer coated tool during machining of MDN431 alloyed steel. In: AIP conference proceedings, vol. 1943. https://doi. org/10.1063/1.5029640 18. Liu Z et al (2017) Influence of the microstructure and silver content on degradation, cytocompatibility, and antibacterial properties of magnesium-silver alloys in vitro. Oxidative Med Cell Longev. https://doi.org/10.1155/2017/8091265 19. Steglich D, Tian X, Bohlen J, Kuwabara T (2014) Mechanical testing of thin sheet magnesium alloys in biaxial tension and uniaxial compression. Exp Mech 54(7):1247–1258. https://doi. org/10.1007/s11340-014-9892-0 20. Ulacia I, Salisbury CP, Hurtado I, Worswick MJ (2011) Tensile characterization and constitutive modeling of AZ31B magnesium alloy sheet over wide range of strain rates and temperatures. J Mater Process Technol 211(5):830–839. https://doi.org/10.1016/j.jmatprotec.2010.09.010 21. Srinivasan M, Loganathan C, Kamaraj M, Nguyen QB, Gupta M, Narayanasamy R (2012) Sliding wear behaviour of AZ31B magnesium alloy and nano-composite. Trans Nonferrous Metals Soc China (Engl Ed) 22(1):60–65. https://doi.org/10.1016/S1003-6326(11)61140-0 22. Archard JF (1953) Contact and rubbing of flat surfaces. J Appl Phys 24(8):981–988. https:// doi.org/10.1063/1.1721448 23. Hokkirigawa K, Kato K (1988) An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear

Chapter 16

Peristaltic Flow and Heat Transfer Through a Prandtl Fluid in Vertical Annulus Indira Ramarao, Priyanka N. Basavaraju, and Jagadeesha Seethappa

Introduction In the case of many physiological situations like in the esophagus, anus, intestine, etc., the flow of semi-solid bolus will reduce to contraction and expansion of the wall generating a waveform. This type of motion is called peristaltic flow, which has a lot of industrial and biological importance. There has been a lot of research in this field and still there is scope for further analysis. Latham [1], Shapiro et al. [2] have conducted and obtained experimental results using Newtonian fluid. The mechanism of peristaltic flow can be adapted to transport slurries in the industry (see Pozrikidis [3]). Li et al. [4] conducted a study on Newtonian fluid under unsteady peristaltic flow using tubes of finite length. A steady frame of reference was used. Shukla et al. [5] considered micro-organism movement modeling with peristalsis to understand the transport of spermatozoa. The flow of bolus of food in the esophagus was studied by Mishra et al. [6]. The effect of heat transfer was considered relevant because of oxygenation in a process like a hemodialysis (see Radhakrishnamacharya et al. [7]). It was speculated that the water transport from roots to an upper part tree is due to peristalsis and some researchers studied this (see Aikman et al. [8] and Canny et al. [9]). Radhakrishna Murthy et al. [10] have considered the effect of heat transfer on peristaltic flow in porous vertical tubes. The peristaltic flow was considered to understand fluid mechanic effects by Mishra et al. [11]. Vajravelu et al. [12] have considered the flow of Herschel–Bulkley fluid. Newtonian fluid flow was considered in an asymmetric inclined channel with non-linear peristalsis by Kothandapani et al. [13]. Vajravelu I. Ramarao · J. Seethappa (B) Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, Karnataka 560064, India P. N. Basavaraju Department of Mathematics, ATME College of Engineering, Mysuru, Karnataka 570028, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_16

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et al. [14] have analyzed peristaltic pumping in vertical porous annulus. An application to the endoscope is considered by Hayat et al. [15] and Nadeem et al. [16] by considering different non-Newtonian fluids. Mekheimer et al. [17] and Ellahi [18] have considered the effect of magnetic field on peristalsis and heat transfer. Nadeem et al. [19] have investigated the peristaltic flow involving Prandtl fluid. Nabil et al. [20] have studied the peristaltic flow of non-Newtonian fluid in the vertical channel. Recently, [21, 22] have analyzed the peristaltic motion of couple stress fluid. In the present study, an attempt is made to understand the process of flow of Prandtl fluid subjected to peristalsis and heat transfer with application to a situation like an endoscope creating a concentric annular region. The pressure gradient and friction are obtained and graphically depicted.

Mathematical Formulation An endoscope is inserted into the esophagus creating an annular region where the outer wall represents the wall of the esophagus which can contract and expand. Inner tube represents rigid endoscope. A sinusoidal wave travels along the outer tube wall as shown in Fig. 16.1. Hence, the following equations define wall motion: R 1 = a1 ,  R2 = a2 + b sin

  2π  z − ct . λ

(16.1) (16.2)

Governing equations are ∇ · V = 0, ρ

dv − → =∇ ·τ +ρ F, dt τ = −P I + S,

ρc f

dT = K c ∇ 2 T, dt

(16.3) (16.4) (16.5) (16.6)

− → → where − v is the velocity, τ is the stress tensor, F is the body force, ρ is the density of the fluid, ρc f is the heat capacity, T is the temperature, and φ is the mass. A moving frame is introduced with a velocity of a wave being C by using r = R, z = Z − ct, u = V, and w = W − C.

16 Peristaltic Flow and Heat Transfer …

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Fig. 16.1 Physical configuration

The resulting governing equations are non-dimensionalized using the following parameters: r∗ =

T − T0 r ∗ Z λu ∗ w a2 P ∗ ct , Z = , u∗ = , w = , P∗ = ,t = ,θ = a λ ac c λμc λ T1 − T0

s∗ =

λ ρgαa 2 (T1 − T0 ) as r1 ρca , δ = , r1∗ = , Re = , Gr = . μc a a2 μ μc

(16.7)

The flow is considered under the influence of low Reynolds number “Re” and longwavelength approximation, hence δ → 0. Using this, the final forms of governing equations along with suitable boundary conditions are

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−

∂p = 0, ∂r

1 ∂ ∂p + Gr θ, (r Sr z ) = r ∂r ∂z   ∂w 3 ∂w Sr z = α +β , ∂r ∂r   1 ∂ ∂θ r = 0, r ∂r ∂r

(16.8) (16.9)

(16.10) (16.11)

where Gr is the Grashof number. θ = 0 atr = r1 , θ = 1 at r = r2 ,

(16.12)

w = −1 atr = r1 and r = r2 ,

(16.13)

where r1 is the radius of inner cylinder and r2 is the radius of outer cylinder, which is given by r2 = 1 + ϕsin(2π z),

(16.14)

where φ = ab2 . Solving for the temperature θ and using the boundary conditions given in Eq. (16.12), the solution is given by  θ=

log log

r r1

 . r2 r1

(16.15)

To obtain velocity and pressure, a regular perturbation method is employed by using f = f 0 + β f 1 + β 2 f 2 + . . . for velocity.

(16.16)

The governing equations for zeroth- and first-order perturbation become 1 ∂ α r ∂r

and



∂w0 ∂r



  ∂p Gr r  log = + , r2 ∂z r 1 log r1

(16.17)

16 Peristaltic Flow and Heat Transfer …

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     ∂w1 1 ∂ 1 ∂ ∂w0 3 r + α = 0, r r ∂r ∂r r ∂r ∂r

(16.18)

subject to boundary conditions w0 = −1 at r = r1 and r = r2 ,

(16.19)

w1 = 0 at r = r1 and r = r2 .

(16.20)

The velocity profile is obtained in the form ⎡   ⎤  2 2  − r r 1 ∂ p ⎣ 2 r ⎦ w0 = − r1 − r 2 + 2  1 log r 4α ∂z r1 log r21 ⎤ ⎡ ,       2 2     2 r − r Gr r r  ⎣ r − r22 log − 2  1 log − r 2 + r12 ⎦ − 1 + r2 r2 r r 1 1 αlog r1 log r1 (16.21) 



1 1 [φ(r2 ) − φ(r1 )] r  , w1 = − [φ(r ) − φ(r1 )] + log r2 α α r 1 log

(16.22)

r1

where φ(r ) = a11 r 4 + ar122 + a13 r 3 + a14 logr +   3   2 +a17 r 4 log rr1 + a18 r 4 log rr1     +a19 r 4 log rr1 + a22 r 3 log rr1 − 1 ,

a15 r

  2 + a16 log rr1

the constants are listed in the Appendix. The rate of flow is obtained and pressure gradient is evaluated as given below: Mean flow rate is given by F = F0 + β F1 + . . .

(16.23)

r2 r2 where F0 = r w0 dr andF1 = r w1 dr. r1

r1

The flow rate is given by Q=F+

  φ2 1 1+ − ε2 2 2

(16.24)

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where ε = aa21 = r1 . The pressure gradient is obtained as F0 + a21 ∂p = a20 ∂z 4α

(16.25)

where the constants a20 , a21 are listed in appendix. The rise in pressure between the walls p is calculated as 1 p =

dp dz. dz

(16.26)

0

The frictions at inner wall and outer wall are as follows: 1 F = 0

  dp dz r12 − dz

(16.27)

  dp dz. r22 − dz

(16.28)

0

and 1 F = 1

0

The velocity, pressure gradient, rise in temperature, and friction are numerically evaluated and graphically depicted in the next section.

Results and Discussion The present study brings out essential features of the peristaltic flow of a Prandtl fluid in the annular region created by inserting an endoscope in the esophagus or annal region. The flow characteristics like velocity, rise in pressure, etc. are evaluated for different values of flow rate Q, Grashof number Gr , α, β, etc. are available in the literature. The axial velocity profile in the radial direction is plotted in Figs. 16.2, 16.3, 16.4, and 16.5. Figure 16.2 shows a variation of the Grashof number Gr . The Grashof number gets introduced as a result of the heat transfer effect being enhanced. Gr = 0 corresponds to the absence of heat transfer, which shows maximum velocity. As Gr increases, initially there is a decrease in velocity due to an increase in buoyancy force but later there is a decrease in velocity. The effect is dominant in the mid of the annular region than near the wall, where the viscous force will be dominant.

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Fig. 16.2 Axial velocity profile in radial direction (φ = 0.1, α = 1, β = 0.002, r1 = 0.1, Q = 4.0)

Fig. 16.3 Axial velocity profile in radial direction (φ = 0.1, α = 1, Gr = 0.2, r1 = 0.1, Q = 4.0)

Fig. 16.4 Axial velocity profile in radial direction (φ = 0.1, α = 1, Gr = 0.2, r1 = 0.1, Q = 4.0)

Figure 16.3 shows the effect of β, which is a parameter indicating the effect of the non-Newtonian nature of the fluid. As β increases, the velocity decreases due to an increase in resistance to flow and dominance of the non-linear term in the equation. Figure 16.4 shows the effect of amplitude φ on the velocity profile which is not very significant.

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Fig. 16.5 Axial velocity profile in radial direction (φ = 0.1, α = 1, Gr = 0.2, r1 = 0.1, β = 0.002)

Figure 16.5 shows the effect of the rate of flow of Q. As Q increases, the velocity shows the increasing pattern. Near the inner wall, there is an initial decrease in the velocity as Q increases but at the middle of the annulus, velocity increases. Q increases from 3 to 4, velocity initially decreases but increases in the middle of the annulus. But as it increases from 4 to 5, there is a decrease between 0.1 and 0.4 closer to the inner wall but later the difference is small. The flow characteristic is due to the decrease in pressure rise with increasing flow rate as shown in Fig. 16.10a. Figures 16.6, 16.7, and 16.8 depict pressure gradient in the axial direction for different parameters. Figure 16.6 compares the effect of the Grashof number. The effect of the Grashof number Gr is to increase the pressure gradient. As Gr increases, pressure gradient increases and, on the contrary, the magnitude of pressure gradient is negative. The effect is due to the decrease in viscous force compared decreases as dp dz to buoyancy force near the inner wall as the values are taken near r = r1 . Figure 16.7 shows the effect of the volume rate of flow on the pressure gradient. As Q increases, the pressure gradient decreases and the effect is predominant near the exit than the entrance of the cylinders. As Q increases from 2 to 4, the pressure gradient significantly decreases but as it increases from 4 to 6, the curve is exactly

Fig. 16.6 Axial pressure gradient (φ = 0.1, α = 1, β = 0.002, r1 = 0.1, Q = 4.0)

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Fig. 16.7 Axial pressure gradient (φ = 0.1, α = 1, Gr = 0.2, r1 = 0.1, β = 0.002)

Fig. 16.8 Axial pressure gradient (φ = 0.1, α = 1, Gr = 0.2, r1 = 0.1, Q = 4.0)

between the other two curves. The effect was similar on velocity also. As Q increases between 4 and 6, the flow characteristics reverse their behavior. Figure 16.8 shows the effect of amplitude on the pressure gradient. As φ increases, the amplitude of pressure also increases showing the different nature of the wave. Figures 16.9, 16.10, and 16.11 show pressure rise p, friction at inner and outer walls for different parameters. As Gr increases, pressure rises for all amplitudes. p in Fig. 16.9 shows pressure rise against the amplitude φ. As φ increases, pressure rise p decreases, and beyond 0.4 the decrease is faster. Effect of heat transfer is visible in presence of Gr which results in increase of pressure. This increase is due to maintaining a constant volume flow rate for a given velocity. Figure 16.10a shows p versus Q the volume flow rate. As Q increases p falls sharply. The effect of Gr is again to increase p. Figure 16.11a shows the effect of Q on the curve showing p versus Gr . p increases steadily with increasing Gr and effect is same for all values of Q and φ. The friction at lower as well as upper wall shows the same type of variation. Fig. 16.9b, c shows friction plotted against φ. F 0 and F 1 both increase with an increase in amplitude. The effect of increase in Gr is to decrease the friction due to reduction in viscosity and this is more dominant on outer wall. Increase of friction

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Fig. 16.9 a Pressure rise versus amplitude. b Friction at inner wall versus amplitude. c Friction at outer wall versus amplitude (φ = 0.1, α = 1, β = 0.002, r1 = 0.1, Q = 4.0)

Fig. 16.10 a Pressure rise versus flow rate. b Friction at inner wall versus flow rate. c Friction at outer wall versus flow rate (φ = 0.1, α = 1, β = 0.002, r1 = 0.1, Q = 4.0)

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Fig. 16.11 a Pressure rise versus Grashof number. b Friction at inner wall versus Grashof number. c Friction at outer wall versus Grashof number (α = 1, β = 0.002, r1 = 0.1)

Table 16.1 Comparison with exact solution obtained for β = 0, Gr = 0, Br = 0, ϕ = 0

Q

p (perturbation solution)

p (exact solution)

−2.0

6.136

6.137

−1.0

3.1585

3.1538

0.0

0.000646

0.000646

1.0

−3.1575

−3.1575

2.0

−6.3156

−6.3156

with increase in Q is more linear and steadier. The effect of Gr is same as the previous figure. Last two figures show that effect of increase in Gr decreases friction at the walls steadily. The effect of φ is not so significant as Q. Table 16.1 compares the values of the present study in the limiting case Gr → 0, β → 0 with the exact solution obtained in absence of heat transfer and non-linear terms. The values are in good agreement.

Conclusions The friction at the inner and outer walls shows similar nature of decrease almost linearly with increasing Gr and a linear increase with increasing volume rate Q. Increase in Gr signified the enhanced heat transfer and the effect is to reduce friction at both walls.

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The values obtained by the perturbation method and exact method for β → 0 (Newtonian) in absence of heat and mass transfer for different values of volume flow rate show that results are in good agreement. The values of the present study reduce the absence of heat transfer for Gr → 0, and the results of Nadeem et al. [19] can be obtained.

Appendix a1 = − a2 =

a3 =

1 , 4α

r22 − r12  , log rr21 Gr  , αlog rr21

b1 = −2a1 − a3 , b2 = a1 a2 − a3r22 − a2 a3 , b3 = 2a3 , a11 =

3b3 3b2 b3 3b1 b2 b13 − 3 − 2 + 4 128 16 32, a12 = − a13 =

b23 , 2

3b12 b2 , 2

a14 = 3b1 b22 , a15 = 3b2 b3 , a16 =

3b22 b3 , 2

a17 =

b34 , 4

16 Peristaltic Flow and Heat Transfer …

a18 = a19 =

185

3b3 3b1 b3 − 3, 4 16

3b33 3b2 b3 3b1 b3 + 1 − , 32 4 8

2b1 b2 b3 , 3  2 2    2 2 r2 − r12 r2 − r12 r22 r22 − r12  −  , a20 = + 4 2log rr21 4log rr21

      2 r2 − r12 r22 r22 − r12 r2 Gr r22  − log − − = 2 r1 16 4 αlog r2 a22 =

a21

r1

   ⎤  2   r2 − r12 r22 r22 r12 1 + 2r22 ⎦ r2  − log + − . 2 r1 2 4 log rr21

References 1. Latham TW (1966) Fluid motion in a peristaltic pump. MS Thesis, Massachusetts Institute of Technology Cambridge MA 2. Shapiro AH, Jaffrin MY, Wienberg SL (1969) Peristaltic pumping with long wavelengths at low Reynolds number. J Fluid Mech 37:799–825 3. Pozrikidis C (1987) A study of peristaltic flow. J Fluid Mech 180:515–527 4. Li M, Brasseur JG (1993) Non-steady peristaltic transport in finite-length tubes. J Fluid Mech 248:129–151 5. Shukla JB, Chandra P, Sharma R, Radhakrishnamacharya G (1988) Effects of peristaltic and longitudinal wave motion of the channel wall on movement of micro-organisms: application to spermatozoa transport. J Biomech 21(11):947–954 6. Misra JC, Pandey SK (2001) A mathematical model for oesophageal swallowing of a foodbolus. Math Comput Model 33(8–9):997–1009 7. Radhakrishnamacharya G, Radhakrishna Murthy V (1994) Long wavelength approxomation to peristalsis with heat transfer. Proc Nat Acad Sci 64:345 8. Aikman DP, Anderson WP (1971) A quantitative investigation of a peristaltic model for phloem translocation. Ann Bot 35:761–772 9. Canny MJ, Phillips OM (1963) Quantitative aspects of a theory of transloaction. Ann Bot 27:379–402 10. Radhakrishna Murthy V, Radhakrishnamacharya, G (1995) Flow through a vertical porous tube with peristalsis and heat transfer. In: Advances in physiological fluid dynamics, pp 147 11. Mishra M, Ramachandra Rao A (2003) Peristaltic transport of a Newtonian fluid in an asymmetric channel. ZAMP 54(3):532–550 12. Vajravelu K, Sreenadh S, Ramesh Babu V (2005) Peristaltic pumping of Herschel-Bulkley fluid in a channel, Appl Math Comput 169:726–735

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13. Kothandapani M, Srinivas S (2008) Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium. Phys Lett A 372(8):1265–1276 14. Vajravelu K, Radhakrishnamacharya G, Radhakrishna Murthy V (2007) Peristaltic flow and heat transfer in a vertical porous annulus with long wave approximation. Int J Non-Linear Mech 42:754–759 15. Hayat T, Ali N, Asghar S, Siddiqui AM (2006) Exact peristaltic flow in tubes with an endoscope. Appl Math Comput 182(1):359–368 16. Nadeem S, Akbar NS (2010) Influence of temperature dependent viscosity on peristaltic transport of a newtonian fluid: application of an endoscope. Appl Math Comput 216:3606–3619 17. Mekheimer K, Elmaboud YA (2008) The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus application of an endoscope. Phys Lett A 372(10):1657–1665 18. Ellahi R (2014) The thermodynamics, stability, applications and techniques of differential type a review. Rev Theor Sci 2(8):116–123 19. Ellahi R, Riaz A, Nadeem S (2014) A theoretical study of Prandtl nanofluid in a rectangular duct through peristaltic transport, vol 4, pp 753–760 20. Nabil TM, Mohammed YA, Yasmeen MY (2017) Magnetohydrodynamic peristaltic flow of Jeffry nanofluid with heat transfer through a porous medium in a verticle tube. Appl Math Inf Sci 11(4):1097–1103 21. Indira R, Sreegowrav KR, Dinesh PA (2018) Effects of heat transfer on peristaltic flow of couple-stress fluid in oesophagus. IJPAM 120:871–879 22. Rashmi KR, Indira R, Jagadeesha S (2021) Peristaltic flow of couple-stress fluid in doubly connected region with reference to endoscope. Palest J Math 10:1–5

Chapter 17

Effect of Variable Diffusivity on Solute Transfer with Reference to Stent Jagadeesha Seethappa, Indira Ramarao, and Madhura Keshavamurthy

Introduction A drug delivery system refers to a device that introduces the drug or the agent used for therapy into the body by different means by controlling time, place, and rate. The drug release involves transport across a semi-permeable membrane, dissolution of coating, the in vitro release of therapeutic agent by different means. Gene therapy also can fall into this category. Drugs are administrated through different routes such as Rectal, Oral, Subcutaneous injection, Gastrointestinal, Intravenous and Arterial injection, buccal cavity through mucus membrane, pulmonary by inhalation, etc. The topic of current interest is cardiovascular drug delivery. The vascular system carries oxygen, nutrients as well as other solutes from and to different organs. Drugs can directly be injected into the cardiovascular system or devices like catheters, stents, etc., can be introduced. The above-said aspects have led to the development of new systems and devices sustained release is referred to as the long-acting, slow release of the drug. DDS can be localized, sustained, rapid, targeted, controlled release on a time scale, etc. Catheters are used to deliver drugs. Particles ranging from up to can be proposed for drug targeting. DDS require constant redesigning and cost reduction. There has been exhaustive work carried out on drug delivery systems and drug release. As early as 1980, Langer has reviewed control release of the drug, highlighting applications of polymeric systems giving a lot of clinical, environmental, biological, and pharmaceutical uses considering diffusion, swelling, etc. [1] have modeled receptors consisting of binding, trafficking, and signaling. In the year 2008, J. Seethappa (B) · I. Ramarao Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, Karnataka 560064, India M. Keshavamurthy Department of Mathematics, Sai Vidya Institute of Technology, Bengaluru, Karnataka 560064, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_17

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[2] have developed a mathematical model. Reference [3] have given a model mathematically describing transient diffusion of solute across the cornea. In 2010, many authors have published their work in this field. Significant are following, [4] have developed a model assuming wall as a multi-layer system which is made up of porous material in case of drug-eluting stents. They used one-dimensional coupled partial differential equations to describe diffusion. Restenosis can be cured by placing a stent in the affected region. The release of the drug depends on coating geometry, chemical, and physical properties, diffusivity, solubility, etc., (see [5]) predicting drug delivery requires mathematical models. Concentration should act for a prolonged time [6]. References [7] and [8] have concluded that the effect due to convective flow due to pressure drop is important. A purely diffusive model is developed by [9]. Initial studies explained the retention of the drug at the arterial wall. References [8] and [10] have focused on effects due to laminar flow. Reference [11] have modeled drug release from a stent assuming diffusion and drug dissolution as an important process occurring in the matrix. They have also considered surface erosion. In 2011, [12] have used PLDA as a biodegradable polymer. They have studied release mechanisms. Reference [13] have estimated elution rate, effects mediated by receptor and drug deposition and validated their results with porcine coronary artery. Another dissolution-based model has been discussed by Ref. [14]. The importance of solubility is highlighted. Reference [15] have developed a model mathematically for the stent-eluted transport of drugs in a region of smooth muscle cells. Reference [16] has reviewed the process of elution of drug from the stent and the models developed in the year 2014. He has elaborately discussed models which describe drug transport, coupled drug release, and uptake giving possible future directions. Reference [17] has highlighted the physical phenomena responsible for the drug distribution through a model for the transport of drugs eluted from the implanted stent in the arterial wall. Reference [18] have proposed a general model for drug delivery system considering the release of the drug, transport to tissue region, and absorption by the tissue. They have taken polymer matrix for drug release, assuming time-dependent onedimensional coupled PDE with flux conditions at interphase. In 2017, [19] have developed a numerical simulation for a two-phase model considering a mass transfer from the stent. A convection–diffusion equation for drug release and diffusion equation for transport is considered. Reference [20] have extensively worked on drug release relative to the drugeluting stent. [21] has published a paper analyzing the coronary stent and its design. They have conducted a numerical study to investigate strength and temperature analysis. [22] have studied drug transport assuming the wall of the artery as porous material in which stent is implanted, Darcy flow is assumed. A two-dimensional model assuming diffusion convection equation is considered. They have analyzed the effect of the Peclet number.

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Reference [23] have conducted a computational study to understand the transport of drugs with an arterial wall assuming a three-phase model. Their results showcase the effect of binding on transport. Reference [20] have designed a model to understand the kinetics of drug release, transport of drug to and within the wall, and retention of the same assuming time-dependent model. Recently, [24] have demonstrated that luminal flow is an important factor in enhancing drug delivery near bifurcations. Numerical simulations have been carried out. In view of all the above facts, the problem considered by Ref. [9] is revisited by taking variable diffusivity coefficient and adopting regular perturbation technique to solve the resulting nonlinear equations in the present study.

Mathematical Formulation A physical configuration is presented in Fig. 17.1. A stent strut of thickness ‘L 1 ’ filled with a drug is embedded in the porous wall of thickness ‘L 2 ’. Mass transfer is in the radial direction. Initially, the drug is present in the stent region and drug concentration is zero in the wall region. The governing equation for the stent region is given by   ∂c1 ∂c1 ∂ D(c1 ) , = ∂t ∂x ∂x

(17.1)

Similarly, convective diffusive transfer in the wall is given by   ∂c2 ∂ ∂c2 ∂c2 + 2δ = D(c2 ) − βc2 , ∂t ∂x ∂x ∂x

(17.2)

where δ is the filtration parameter, β is the drug reaction rate, D(ci ) is the diffusivity coefficient, and ci is the mass concentration for i = 1, 2. Above equations are subjected to initial and boundary conditions: D(c1 = 1)

∂c1 = 0 at x = 0, ∂x

c1 = 1, c2 = 0 at t = 0, c1 = c2 ,

(17.3) (17.4)

∂c1 ∂c2 = D(c2 ) at x = 1, ∂x ∂x

(17.5)

c2 = 0 at x = h,

(17.6)

Concentration-dependent diffusion coefficient is given by

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Fig. 17.1 Physical configuration

D(ci ) = 1 − αci .

(17.7)

Using Eq. (17.7), the Eq. (17.1) and (17.2) become,   ∂c1 2 ∂c1 ∂ 2 c1 = (1 − αc1 ) 2 − α , ∂t ∂x ∂x   ∂c2 ∂c2 ∂c2 2 ∂ 2 c2 + 2δ = (1 − αc2 ) 2 − α − βc2 . ∂t ∂x ∂x ∂x

(17.8)

(17.9)

Similarly, the boundary conditions become −(1 − αc1 )

∂c1 = 0 at x = 0, ∂x

(17.10)

17 Effect of Variable Diffusivity on Solute …

c1 = 1, c2 = 0att = 0, c1 = c2 ,

∂c1 ∂c2 = (1 − αc2 ) at x = 1, ∂x ∂x c2 = 0at x = h,

191

(17.11) (17.12) (17.13)

Concentration can be assumed as ci = c0 + αc1 + α 2 c2 + . . . .

(17.14)

Using this in Eqs. (17.8) and (17.9) and equating the coefficients of α 0 and α 1 , we get ∂c10 ∂ 2 c10 , = ∂t ∂x2

(17.15)

∂c20 ∂ 2 c20 ∂c20 + 2δ = − βc20 , ∂t ∂x ∂x2

(17.16)

and   ∂ 2 c11 ∂ 2 c10 ∂c11 ∂c10 2 = − c − , 10 ∂t ∂x2 ∂x2 ∂x   ∂c21 ∂c21 ∂ 2 c21 ∂ 2 c20 ∂c20 2 + 2δ = − c − − βc21 . 20 ∂t ∂x ∂x2 ∂x2 ∂x

(17.17)

(17.18)

Using perturbation equation, boundary and initial conditions become ∂c10 = 0 at x = 0, ∂x

(17.19)

c10 = 1, c20 = 0 at t = 0

(17.20)

c10 = c20 ,

∂c20 ∂c10 = at x = 1, ∂x ∂x

c20 = 0at x = h, and

(17.21) (17.22)

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−c10

∂c11 ∂c10 + = 0 at x = 0, ∂x ∂x

c11 = 1, c21 = 0 at t = 0, c11 = c21 , −c10

∂c11 ∂c21 ∂c10 ∂c20 + = −c20 + at x = 1, ∂x ∂x ∂x ∂x

(17.23)

(17.24) (17.25)

c21 = 0 at x = h,

(17.26)

ci j = θi j e−ωi t ,

(17.27)

Using the transformation 2

Eqs. (17.15)–(17.18) and boundary conditions (17.19)–(17.26) reduce to −ω02 θ10 =

d 2 θ10 ,. dx2

(17.28)

d 2 θ20 dθ20 = − βθ20 , (17.29) dx dx2     d 2 θ10 d 2 θ11 dθ10 2 −(2ω02 −ω12 )t 2 ω1 θ11 + = θ10 + (17.30) e dx2 dx2 dx  2   2 2 d θ d θ dθ dθ 2 2 21 21 20 20 + ω12 θ21 − 2δ − βθ21 = θ20 + e−(2ω0 −ω1 )t (17.31) dx dx2 dx2 dx −ω02 θ20 + 2δ

and ∂θ10 = 0 · at · x = 0. ∂x

(17.32)

θ10 = 1, θ20 = 0 · at · t = 0.

(17.33)

θ10 = θ20 ,

dθ20 dθ10 = · at · x = 1. dx dx

θ20 = 0 · at · x = h, . −θ 10

dθ10 −2ω02 t dθ11 −ω12 t + = 0 · at · x = 0, e e dx dx

(17.34) (17.35) (17.36)

17 Effect of Variable Diffusivity on Solute …

−θ 10

193

θ11 = 1, θ21 = 0 · at · t = 0, .

(17.37)

θ11 = θ21 x = 1,

(17.38)

dθ10 −2ω02 t dθ11 −ω12 t dθ20 −2ω02 t dθ21 −ω12 t + = −θ 20 + · at · x = 1, e e e e dx dx dx dx (17.39) θ21 = 0 · at · x = h · at · x = h.

(17.40)

Solving the ordinary differential equations given in Eqs. (17.28)–(17.31), we get the following solutions: θ10 = c1 cosω0 x + c2 sinω0 x

(17.41)

θ20 = eδx (c3 coshφ1 x + c4 sinhφ1 x), .

(17.42)

c12 ω02 2 2 e−(2ω0 +ω1 )t cos2ω0 x (17.43) 2 2 4ω0 − ω1  = eδx (b3 coshφ2 x + b4 sinhφ 2 x) + Ee2δx A1 e2φ1 x + A2 e−2φ1 x + A3 , . (17.44)

θ11 = b1 cosω1 x + b2 sinω1 x + θ21

where E = c42 e−(2ω0 +ω1 )t , 2

2

tanω0 = δ +

φ1 (1 − tanhφ1 htanhφ1 ) . tanhφ1 − tanhφ1 h

(17.45)

The constants arising in the study are listed in appendix.

Results and Discussion The drug-filled stent, which is placed in the arterial wall, starts diffusing into the wall as time progresses. The model adopts the perturbation technique to obtain concentration. The drug fraction left in the wall is also calculated as a function of time and depicted graphically. Varying reaction parameter β, perturbation parameter α, and filtration parameter δ. Figures 17.2, 17.3, and 17.4 show the plot of drug concentration in regions 1 and 2 and also the drug fraction left at the wall for different filtration parameters. As δ increases, the filtration velocity increases, and more drug gets convected faster.

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Fig. 17.2 Plot of concentration profile for different values of filtration parameter

Fig. 17.3 Plot of concentration profile for different values of filtration parameter

c1 decreases faster for a higher value of δ. c2 increases initially very fast and starts decreasing at around t = 1, and increases steadily, asymptotically, for higher values of δ. For small δ, the concentration of the wall increases steadily and slowly. The drug fraction left at the wall is initially zero and increases with time, reaching a peak value and decreasing slowly for a large time. The drug fraction left is higher for δ = 2 than δ = 1 as convection increases and more drug is transported to wall. Figures 17.5, 17.6, and 17.7 analyze the effect of the perturbation parameter α. As α increases, diffusion increases. For higher α, concentration in stent region diffuses very fast and asymptotically reaches zero for a large time, whereas concentration at the wall increases very fast initially, reaches a peak at t = 0.5, and starts decreasing asymptotically. The drug fraction left at the wall shows the same pattern as c2 .

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Fig. 17.4 Drug fraction left at the wall versus time

Fig. 17.5 Plot of concentration profile for different values of diffusivity parameter

Figures 17.8 and 17.9 show the effect of reaction parameter β, which arises due to wall degradation, which exists only in the wall region. The reaction parameter does not affect on c1 . As β increases, concentration at the wall increases and reaches a constant asymptotically. The drug fraction left at wall M also shows the same pattern. The results for small values of α are in accordance with results presented by [5] for constant coefficient.

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Fig. 17.6 Plot of concentration profile for different values of diffusivity parameter

Fig. 17.7 Drug fraction left at the wall versus time

Conclusions The study explores the possible effect of the variable diffusion coefficient on the drug transport from an embedded stent in the arterial wall to the tissue region of the wall. The transport from the stent is only by diffusion, and in the tissue by both convection and diffusion. The drug fraction left in the wall is also evaluated and graphically depicted. As time progresses, the drug fraction left at the wall increases and starts decreasing slowly after a very long time, emphasizing the fact that the method of inserting a stent prevents restenosis for a long time. The effect of the filtration parameter is to increase the concentration in the wall, thus increasing the effect of the drug. The effect of the diffusivity parameter is to decrease diffusion as an

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Fig. 17.8 Plot of concentration profile for different values of reaction parameter

Fig. 17.9 Drug fraction left at the wall versus time

increase in α signifies faster reaction and degradation. Overall, the study concludes that the insertion of a stent is effective in slowing down restenosis significantly.

Appendix φ1 =



  δ 2 − ω02 − β , φ2 = δ 2 + ω02 + β ,

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ξ1 + ξ2 + ξ3 ξ1 + ξ2 − ξ3  2 , A2 =  2  A1 =  2 4 4φ1 + 4δφ1 − ω1 + β 4 4φ1 − 4δφ1 − ω12 + β , ξ1 + ξ2 A3 = −  2 4 ω1 + β  ξ1 = −4δφ1 tanhφ1 h + 2δ 2 + φ12 tanh2 φ1 h + φ12 ,  ξ2 = −4δφ1 tanhφ1 h + φ12 1 + tanh2 φ1 h + 2δ 2 ,   ξ3 = 4δφ1 1 + tanh2 φ1 h − 4 δ 2 + φ12 tanhφ1 h, 4sinω0 , c2 = 0, c3 = −c4 tanhφ1 h, 2ω0 + sin2ω0

(−δ+φ )h (−δ+φ )  1 −e 1 s(t) e −δ+φ1 , c4 =  2φ h 2φ  e 1 −e 1 − tanφ h) − − 1)(1 + tanφ h) (1 (h 1 1 2φ1  2 2   c1 ω0 sin(2ω0 +ω1 ) sin(2ω0 −ω1 ) + 2ω0 +ω1 2ω0 −ω1 4ω02 −ω12 b1 = , b2 = 0, sin2ω1 1 + 2ω1 c1 =

b3 = −e(2ω0 −ω1 )t B1 − b4 2

b4 =

−b1 ω1 sinω1 + B2 +

2

tanhφ2 h , eδh

+ (G 1 − B3 )e−(2ω0 −ω1 )t , −(G 1 tanhφ2 h + G 2 ) c12 ω02 −2ω2 t e 0 sin2ω0 2

2

 2(δ+φ1 )h ξ1 e + ξ2 e2(δ−φ1 )h + ξ3 e2δh ,

B1 =

c42 δh 4e coshφ

B1 =

 2(δ+φ1 )h c42 ξ1 e + ξ2 e2(δ−φ1 )h + ξ3 e2δh , δh 4e coshφ2 h

2h

2

B2 = e2δ c42 (E 1 + E 2 + E 3 ), B3 =

c12 ω02 c2 (2ω0 sin2ω0 ) + 4 F1 , 2 2 4 4ω0 − ω1

E 1 = (δtanhφ1 h − φ1 )tanhφ1 h cosh2 φ1 , E 2 = (δ − φ1 tanhφ1 h) sinh2 φ1 , E 3 = (2δ − φ1 tanhφ1 h)sinhφ1 h cosh φ1 ,

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F1 = ξ1 (2δ + 2φ1 )e2δ+2φ1 + ξ2 (2δ − 2φ1 )e2δ−2φ1 + 2δξ3 e2δ , G 1 = δeδ coshφ2 + eδ φ2 sinhφ2 , G 2 = δeδ sinhφ2 + eδ φ2 coshφ2 .

References 1. Lauffenburger DA, Linderman JJ (1993) Receptors: Models for Binding, Trafficking, and Signalling. Oxford University Press 2. Siepmann J, Siepmann F (2008) Mathematical modelling of drug delivery. Int J Pharm 364:328– 343 3. Zhang WE, Prausnitz MR, Edwards AU (2004) Model of transient drug diffusion across cornea. J Control Release 99:241–258 4. Pontrelli G, Monte F (2010) A multi-layer porous wall model for coronary drug-eluting stents. Int J Heat Mass Transf 53:3629–3637 5. Sakharov DV, Kalachev LV, Rijken DC (2002) Numerical simulation of local pharmacokinetics of a drug after intravascular delivery with an eluting stent. Jour. Drug. Target. 10(6):507–513 6. Rogers CDK (2002) Drug-eluting stents: role of stent design delivery vehicle and drug selection. Rev. Cardiov. Med. 3(supp. 5):S10–S15 7. Ai, L & Vafai, K 2006, ‘A coupling model for macromolecules transport in a stenosed arterial wall’, Int. J. Heat Mass Transf ., pp. 1568–1591. 8. Hwang, CW, Wu, D & Edelman, ER 2001, “Physiological transport forces govern drug distribution for stent-based delivery”, Circulation, vol. 104), no. 5, pp. 600–605. 9. Pontrelli G, Monte F (2007) Modelling of mass convection-dffusion in stent-based drug delivery. Int J Heat Mass Transf 50:3658–3669 10. Joner M, Finn AV, Farb A, Mont EK, Kolodgie FD, Ladich E, Kutys R, Skorija K, Gold HK, Virmani R (2006) Pathology of drug-eluting stents in humans: delayed heating and late thrombotic risk. J Am Coll Cardiol 48(1):193–202 11. Formaggia L, Minisini & Zunino, P, (2010) Modeling polymeric controlled drug release and transport phenomena in the arterial tissue. Math. ModelsMethods Appl. Sci. 20(10):1759–1786 12. Fredenberg S, Reslow MHW, Axelsson A (2011) The mechanisms of drug release in poly(lacticco-glycolic acid)-based drug delivery systems - a review. Int J Pharm 415:34–52 13. Tzafriri, AR, Groothuis, A, Sylvester, PG & Edelman, ER 2012‘Stent elution rate determines drug deposition and receptor-mediated effects’, J. Control. Release, vol. 161, pp. 918–926. 14. Siepmann J, Siepmann F (2013) Mathematical modelling of drug dissolution. Int J Pharm 453:12–24 15. McGinty S, McKee S, Wadsworth RM, McCormick C (2013) ‘Modeling arterial wall drug concentrations following the insertion of a drug-eluting stent’, SIAM. J Appl Math 73:2004– 2028 16. McGinty S (2014) A decade of modelling drug release from arterial stents. Math Biosci 257:80– 90 17. Bozsak, F, Gonzalez-Rodriguez, D, Sternberger, Z, Belitz, P, Bewley, T, Chomaz, JM, & Barakat, AI 2015, ‘Optimization of drug delivery by drug-eluting stents, PLoS One, vol. 10, no. 6, e0130182. 18. McGinty S, Pontrelli G (2015) A general model of coupled drug release and tissue absorption for drug delivery devices. J Control Release 217:327–336 19. Ali A, Alias N, Al Rahmi W (2017) ‘Numerical Simulation of Two Phase Mathematical Model for Transportation of Mass and Drug from Drug Eluting Stents. Math. Model. Nat. Phenom. 12(5):162–179

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20. Saha R, Mandal PK (2018) ‘Modelling Time-dependent Release Kinetics in Stent-based Delivery. Journal of Exploratory Research in Pharmacology 3:61–70 21. Ravikumar P, Bharathiraja E, Tharani V, Yamuna R, Yamunarani T (2011) Design and analysis of coronary stent. Int J Healthc Technol Manag 12(5–6):447–456 22. Sarifuddin & Mandal, PK, (2012) Effect of diffusivity on the transport of drug eluted from drug-eluting stent. Int J Appl Comput Math 2(2):291–301 23. Mandal AP, Mandal PK (2012) Computational Modelling of Three phase Stent-based Delivery. J Explor Res Pharmacol 2(2):31–40 24. Kolachalama, VB, Levine, EG & Edelman, ER 2009, ‘Luminal flow amplifies stent-based drug deposition in arterial bifurcations’, PLoS One, vol. 4, no. 12, e8105.

Chapter 18

Prediction of Thermal Conductivity for Al6061 Reinforced with Silicon Carbide and Graphite Using Statistical Approach S. Vijay Kumar, M. Girish Prasad, S. Basavaraj, L. Avinash, B. A. Praveen, Shiv Prathap Singh Yadav, K. R. Varadaraj, and Arpith Chacko

Introduction Thermal performance of composite materials has a major role for their behavior of reinforcement materials. Therefore, thermal behaviors of Al6061 were widely explained for all the defined reinforcements for the lightweight applications. Based on the homogeneity, a negligible porosity of the reinforcements was determined using SEM and EDS analyses. Al 6061 microstructure without any reinforcements revealed that the alloying elements with fine precipitates have been dispersed in aluminum matrix. It is found that thermal conductivity of Al 6061 exhibits maximum, in which there is a decline at maximum temperature of thermal conductivity for the compositions of hybrid metal matrix at the different temperatures [1]. Thermal and electrical behaviors with different percentage compositions of reinforcements were investigated. It has been found that enthalpy, specific heat capacity, and heat flow for hybrid metal matrix composites of different compositions decrease by the addition of graphite with silicon carbide [2]. Al 6061 with SiC and Gr thermal conductivity was determined from room temperature to 300 °C. Based on the laser flash technique, it has been found that thermal conductivity decreases for hybrid MMCs at different compositions considered [3]. In case of 450–550 °C with a combinations of Al6061 with SiC and Gr at a ratio of 2:1, 3:1, and 4:1. Results revealed that extrusion S. Vijay Kumar (B) · M. Girish Prasad · L. Avinash · B. A. Praveen · S. P. S. Yadav · A. Chacko Department of Mechanical Engineering, Nitte Meenakshi Institute of Technology, Bangalore, India e-mail: [email protected] S. Basavaraj Deepthi Engineering, Bangalore, India K. R. Varadaraj Department of Mechanical Engineering, Reva University, Bangalore, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Narendranth et al. (eds.), Recent Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-19-1388-4_18

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ratio of 3:1 with a combination of Al 6061, 4% SiC, 2% Gr both thermal expansion and thermal conductivity was found to be improved compared to conventional aluminum [4]. Based on the observation, friction, wear, and mechanical characteristics increase with a maximum quantity of particulate in the alloy. However, for fracture toughness, thermal properties, and ductility, this may not be same where reinforcement with higher percentage of this property decreases [5–7]. In case of steady-state method for Al6061 with SiC particle composites, thermal conductivity of maximum 250 W/m·K was achieved. Low thermal conductivity was observed for the composites with smaller size SiC particles were measured [8]. For heat treatment with 3% and 5% of SiC composites, there was a decline in the thermal conductivity was achieved [9]. In pressure infiltration technique, for liquid aluminum with the addition of 12.2 wt.% to the Al6061, there was an increase in thermal conductivity to 532 W/m·K, whereas in case of 20–40% of silicon content, thermal conductivity declined to 372–314 W/m·K [10]. In case of silicon nitride reinforced with Al6061 composite, the uniformity dispersion of Si3N4 particles was achieved. Due to low thermal conductivity of the reinforcement, there was a decrease in thermal conductivity because thermal conductivity was higher in forged system compared to cast ones [11].

Materials and Methods In steady-state method for the measurement of temperature difference during heat flow throughout, the materials was used to determine the thermal conductivity. For the present investigations, base material of Al6061 reinforced with silicon carbide (1 and 2%) and graphite (1–7%) with an interval of 2%, respectively, was considered (Table 18.1). Finally, prepared specimen was used to machine for the required diameter and length to insert into the thermal conductivity setup and is shown in Figs. 18.1 and 18.2. Table 18.1 Compositions considered for the experimentation

Specimen

Al6061

SiC

Graphite

Al 6061

100

0

0

Al 6061 + 0% SiC + 1% Gr

99

0

1

Al 6061 + 2% SiC + 1% Gr

97

2

1

Al 6061 + 0% SiC + 3% Gr

97

0

3

Al 6061 + 2% SiC + 3% Gr

95

2

3

Al 6061 + 0% SiC + 5% Gr

95

0

5

Al 6061 + 2% SiC + 5% Gr

93

2

5

Al 6061 + 0% SiC + 7% Gr

93

0

7

Al 6061 + 2% SiC + 7% Gr

91

2

7

18 Prediction of Thermal Conductivity for Al6061 Reinforced …

203

Fig. 18.1 Thermal conductivity setup

Fig. 18.2 prepared samples of 2.5 cm diameter and 27 cm length

Experimental Investigations In the present investigation to perform the thermal conductivity, some of the accessories were used such as electrical heater, temperature indicator, dimmer state, ammeter, voltmeter, and a thermocouple was used. All the accessories were assembled and the detailed setup is shown Fig. 18.1. To measure the temperature difference during the process for thermal conductivity, an ASTM guideline C177-97 hot plate system (Standard Testing Method for obtaining Steady-State Heat Flux and Thermal Transmission Properties with the help of a Guarded Hot Plate Apparatus) was used. Figure given below shows the experimental setup, having the following elements: hot and two cold plates (one on either side of the system), a mounting system, an isolation chamber, and the compulsory devices for tuning the voltage and current to monitor the heat flow in to the system. To measure the temperature difference, the specimens were fabricated with a specification of 27 cm length, 2.5 cm diameter, and maintain a thermocouple distance of 4 cm was throughout the length of the specimen (Fig. 18.3).

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Fig. 18.3 Prepared samples with Thermocouple holes of 4 cm apart to perform temperature measurement

Results and Analysis For the determinations of thermal conductivity of the hybrid metal matrix composites, varying percentages of SiC from 0 to 2% and graphite from 1 to 7%, respectively, were used. The voltage varies from 30 to 70 V, parallel to that water inlet and outlet temperatures were monitored. For pure Al6061, the thermal conductivity was measured around 251.7 and 211.7 W/m·C for 30 V and 70 V, respectively. For 0% of SiC with 1% of graphite, the thermal conductivity was 274.63 W/m·C, whereas in case of 2% of SiC with 7% of graphite, the thermal conductivity of 116.02 W/m·C was measured for the combinations considered. The results clearly show that the average thermal conductivity for all the combinations considered is 4.25% decline compared to pure Al6061. This was achieved with the combinations Al6061 with 2% SiC and 7% of graphite which gave a maximum temperature difference of 24.75% and is shown in Fig. 18.4. To observe the normality of the experimental data sets, Kolmogorov test was used to perform the probability value. This test clearly showed that the observed values of 82% of the data sets are normally distributed on 45° line with a μ value of 180.05 and σ value of 52.78 as represented in the Fig. 18.5. Fig. 18.4 Thermal Conductivity variations with different temperatures of Al6061 reinforced with SiC and graphite combinations considered

18 Prediction of Thermal Conductivity for Al6061 Reinforced …

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Fig. 18.5 Normal probability plot of thermal conductivity

Mathematical Modeling for Thermal Conductivity of Al6061 Reinforced with Silicon Carbide and Graphite Regression and Analysis of variance (ANOVA) methods used to predict the parameters experimentally found significant factors are statistically significant. MINITAB was a powerful statistical tool to obtain or analyze the significance of factors [12–15]. In the present analysis, SiC, current, water inlet, and water outlet are the significant parameters on thermal conductivity of Al6061 reinforced with SiC and graphite with a P-value of 0.05 and the coefficient determination of 0.827. Therefore, the predicted equation is 95% of confidence interval. All the detailed results are shown in Table 18.2 and Figs. 18.6 and 18.7.

Multiple Linear Regression Analysis TC of Al6061 + SiC + Gr = −203 + 2.27 Al6061 − 15.53 SiC − 2.870 Current − 342 Voltage + Power + 5.71 Water Inlet + 6.50 Water outlet R2 = 0.827

(18.1)

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Table 18.2 ANOVA Analysis for thermal conductivity Source

DF

Adj SS

Adj MS

F-Value

P-Value

Regression

7

40,075.8

5725.11

59.81

0.000

Al6061

1

197.7

197.73

2.07

0.170

SiC

1

1611.4

1611.37

16.83

0.001

Current

1

2490.0

2489.96

26.01

0.000

Voltage

1

105.3

105.32

1.10

0.310

Power

1

129.8

129.84

1.36

0.261

Water Inlet

1

506.4

506.43

5.29

0.035

Water Outlet

1

2080.1

2080.14

21.73

0.000

Error

16

1531.6

95.73

Total

23

Fig. 18.6 Predicted versus measured thermal conductivity for the combination considered

Conclusions In the present investigations, the reinforcement varies for silicon carbide from 0 to 2% (with an interval of 2%) and graphite varies from 1 to 7% (with an interval of 3%) to the base material of Al6061. The results clearly show that the thermal conductivity of the hybrid composites decreases with an increase in graphite and silicon contents for all the combinations considered. As graphite increases to the Al6061, there is a decline in the thermal conductivity at maximum temperature. The thermal conductivity was 271.08 and 116.02 W/m·K for the combinations of Al6061 with 0% SiC and 2% graphite and 2% SiC with 7% graphite, respectively. Finally, a mathematical model was developed to determine the significant parameters on

18 Prediction of Thermal Conductivity for Al6061 Reinforced …

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Fig. 18.7 Residual plot for the predicted thermal conductivity

thermal conductivity. The results revealed that the model is statistically significant with a p-value of 0.05.

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