Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation (Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart) [1st ed. 2021] 365833438X, 9783658334383

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Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart

Chenyi Zhang

Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation

Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart Reihe herausgegeben von Michael Bargende, Stuttgart, Deutschland Hans-Christian Reuss, Stuttgart, Deutschland Jochen Wiedemann, Stuttgart, Deutschland

Das Institut für Fahrzeugtechnik Stuttgart (IFS) an der Universität Stuttgart erforscht, entwickelt, appliziert und erprobt, in enger Zusammenarbeit mit der Industrie, Elemente bzw. Technologien aus dem Bereich moderner Fahrzeugkonzepte. Das Institut gliedert sich in die drei Bereiche Kraftfahrwesen, Fahrzeugantriebe und Kraftfahrzeug-Mechatronik. Aufgabe dieser Bereiche ist die Ausarbeitung des Themengebietes im Prüfstandsbetrieb, in Theorie und Simulation. Schwerpunkte des Kraftfahrwesens sind hierbei die Aerodynamik, Akustik (NVH), Fahrdynamik und Fahrermodellierung, Leichtbau, Sicherheit, Kraftübertragung sowie Energie und Thermomanagement – auch in Verbindung mit hybriden und batterieelektrischen Fahrzeugkonzepten. Der Bereich Fahrzeugantriebe widmet sich den Themen Brennverfahrensentwicklung einschließlich Regelungs- und Steuerungskonzeptionen bei zugleich minimierten Emissionen, komplexe Abgasnachbehandlung, Aufladesysteme und -strategien, Hybridsysteme und Betriebsstrategien sowie mechanisch-akustischen Fragestellungen. Themen der Kraftfahrzeug-Mechatronik sind die Antriebsstrangregelung/Hybride, Elektromobilität, Bordnetz und Energiemanagement, Funktions- und Softwareentwicklung sowie Test und Diagnose. Die Erfüllung dieser Aufgaben wird prüfstandsseitig neben vielem anderen unterstützt durch 19 Motorenprüfstände, zwei Rollenprüfstände, einen 1:1-Fahrsimulator, einen Antriebsstrangprüfstand, einen Thermowindkanal sowie einen 1:1-Aeroakustikwindkanal. Die wissenschaftliche Reihe „Fahrzeugtechnik Universität Stuttgart“ präsentiert über die am Institut entstandenen Promotionen die hervorragenden Arbeitsergebnisse der Forschungstätigkeiten am IFS. Reihe herausgegeben von Prof. Dr.-Ing. Michael Bargende Lehrstuhl Fahrzeugantriebe Institut für Fahrzeugtechnik Stuttgart Universität Stuttgart Stuttgart, Deutschland

Prof. Dr.-Ing. Hans-Christian Reuss Lehrstuhl Kraftfahrzeugmechatronik Institut für Fahrzeugtechnik Stuttgart Universität Stuttgart Stuttgart, Deutschland

Prof. Dr.-Ing. Jochen Wiedemann Lehrstuhl Kraftfahrwesen Institut für Fahrzeugtechnik Stuttgart Universität Stuttgart Stuttgart, Deutschland

Weitere Bände in der Reihe http://www.springer.com/series/13535

Chenyi Zhang

Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation

Chenyi Zhang Institute of Automotive Engineering (IFS), Chair in Automotive Engineering University of Stuttgart Stuttgart, Germany Zugl.: Dissertation Universität Stuttgart, 2020 D93

ISSN 2567-0042 ISSN 2567-0352  (electronic) Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart ISBN 978-3-658-33438-3 ISBN 978-3-658-33439-0  (eBook) https://doi.org/10.1007/978-3-658-33439-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 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 Vieweg imprint is published by the registered company Springer Fachmedien Wiesbaden GmbH part of Springer Nature. The registered company address is: Abraham-Lincoln-Str. 46, 65189 Wiesbaden, Germany

Preface This Ph.D. thesis contains the results of research undertaken at the Institute for Automotive Engineering Stuttgart (IFS). This research project was conducted and financed by IFS. I am especially indebted to my doctoral adviser Prof. Dr.-Ing. Jochen Wiedemann. I offer my sincerest gratitude for his trust into me and the constant readiness for mentoring my work. He helped me constantly and stimulated my research, always showing great interest in the progress of my work. He gave me a lot of advices which are always helpful even in my future career life. I am grateful to Dr. Timo Kuthada for his kind guidance, committed support, and supervision through the years. Thanks for the countless useful discussions, comments, suggestions and his trust in me. Many thanks to Dr. Felix Wittmeier for his comments, suggestions, and continuous support on the model scale wind tunnel tests as well as useful advices on my research work. Many thanks to Nils Widdecke for his comments, advices and suggestions on my research work and publications. Thanks for taking the time to discuss scientific problems with me. Sincere thanks also to my fellow researchers and friends at the department and the staff of the MWK. I really enjoyed the daily exchange of ideas and thoughts as well as the funny moments with them. I wish to thank all the other people who worked with me over the years on not only my Ph.D. project but also other industrial projects. Many thanks also to the coauthors of my published papers. Finally, special thanks to my family members especially my mother for her tireless encouragement, motivation and support during the years. Chenyi Zhang

Contents Preface............................................................................................. V List of Figures ................................................................................ XI List of Tables .............................................................................. XIX Formula Symbols ........................................................................ XXI List of Abbreviations ................................................................ XXV Zusammenfassung ...................................................................XXVII Abstract .................................................................................... XXXI 1

2

Introduction ............................................................................. 1 1.1

Motivation ....................................................................................... 1

1.2

Research Objectives ........................................................................ 3

Basic Theories and State of the Art ....................................... 5 2.1

2.2

Basic Theories ................................................................................. 5 2.1.1

Boundary Layer Theories ................................................... 5

2.1.2

Ground Effect ..................................................................... 9

2.1.3

Aerodynamic Forces of a Ground Vehicle ......................10

State of the Art...............................................................................14 2.2.1

Previous Investigations on Vehicle Geometric Parameters ........................................................................14

3

2.2.2

Ground Simulation Technology in Wind Tunnels ...........23

2.2.3

Influence of the Moving Ground Simulation ...................25

Research Methods and Models............................................. 29 3.1

Experimental Method ....................................................................29 3.1.1

IFS Model Scale Wind Tunnel .........................................29

Contents

VIII 3.1.2 3.2

3.3

4

Test Setup .........................................................................31

Numerical Method .........................................................................31 3.2.1

Simulation Software .........................................................32

3.2.2

Boundary Conditions of the Simulations .........................35

Research Models ...........................................................................38 3.3.1

DrivAer Model .................................................................38

3.3.2

AeroSUV Model...............................................................39

Results of the DrivAer Model ............................................... 41 4.1

Baseline Results with Fixed and Moving Ground Simulation .....41

4.2

Investigated Parameters.................................................................44

4.3

Parameters at the Vehicle Front ....................................................45

4.4

4.5

4.6

4.3.1

Geometry Variations at the Vehicle Front .......................45

4.3.2

Engine Hood Slope Angle ................................................46

4.3.3

Engine Hood Height .........................................................48

4.3.4

Front Windscreen Slant Angle .........................................50

4.3.5

Sweep Angle.....................................................................51

Parameters at the Vehicle Cabin ...................................................52 4.4.1

Geometry Variations at the Vehicle Cabin ......................52

4.4.2

Roof Curvature .................................................................53

4.4.3

Camber .............................................................................54

Parameters at the Vehicle Rear End ..............................................55 4.5.1

Geometry Variations at the Vehicle Rear End .................56

4.5.2

Trunk Lid Slope Angle .....................................................56

4.5.3

Trunk Length ....................................................................57

4.5.4

Trunk Height ....................................................................59

4.5.5

Rear Screen Slant Angle ..................................................60

Underbody Parameters ..................................................................62 4.6.1

Geometry Variations at the Vehicle Underbody ..............62

4.6.2

Front Underbody Slope Angle .........................................63

Contents

4.7

5

6

IX 4.6.3

Wheel Track .....................................................................64

4.6.4

Rear Diffuser Angle .........................................................66

Attitude Parameters .......................................................................69 4.7.1

Variations of the Attitude Parameters ..............................69

4.7.2

Ride Height.......................................................................70

4.7.3

Pitch Angle .......................................................................72

4.8

Influence on the Cooling Air Flow ...............................................73

4.9

Conclusions ...................................................................................75

Statistical Analysis of the Parameters ................................. 77 5.1

Sensitivity Rating of the Parameters .............................................77

5.2

Interaction between the Parameters ..............................................82

5.3

Conclusions ...................................................................................89

Transferability Study on the SUV Model ............................ 91 6.1

Comparison of the Baseline Results between Fixed and Moving Ground Simulation....................................................91

7

6.2

Investigated Parameters on the AeroSUV Model .........................92

6.3

Results of the Parametric Study ....................................................94 6.3.1

Trunk Lid Slope Angle .....................................................94

6.3.2

Trunk Height ....................................................................95

6.3.3

Rear Screen Slant Angle ..................................................96

6.3.4

Rear Diffuser Angle .........................................................97

6.3.5

Ride Height.......................................................................98

6.4

Influence on the Cooling Air Flow ...............................................99

6.5

Conclusions .................................................................................102

Overall Conclusions............................................................. 103

Bibliography................................................................................. 107

List of Figures Figure 1.1:

Different basic shape of the electric vehicles [1, 2, 3, 4] ..........................................................................1

Figure 2.1:

Boundary layer development along a plate.......................6

Figure 2.2:

Flow seperation in the boundary layer near a wall ...........7

Figure 2.3:

Induced boundary layer of an airfoil with a positive angle of attack, the induced boundary layer increases with the reduced ground clearance hmin from far away from the ground a) to close to the ground d) (Courtesy Beese [13]) ........................................................................8

Figure 2.4:

Induced boundary layer of an airfoil with a negative angle of attack, a) the larger angle results in an increased separation area at the ground compared to the smaller angle as shown in b) (Courtesy Beese [13]) ...................................................................................8

Figure 2.5:

Principle of the ground effect............................................9

Figure 2.6:

Different distributions to the aerodynamic drag of the vehicle [15] ..................................................................... 11

Figure 2.7:

Tip vortex of the airfoil .................................................. 12

Figure 2.8:

Flow deflection by an airfoil and the induced drag ....... 12

Figure 2.9:

The formation of a pair of edge vortex due to the rolled up shear layers on rear edges (bottom) and the pressure distribution on the sloping surface (top) .......... 14

Figure 2.10:

Variation of the vehicle front shape and its resulting drag change [24] ............................................................. 15

Figure 2.11:

Drag change ∆cW∙A (top) and drag coefficient change ∆cW (bottom) over the roof curvature ar/lr [24].............. 16

Figure 2.12:

Drag change over the camber yM/a, a) results based on the Audi 100 models [23], b) results based on the Volkswagen research vehicle [24] ................................. 17

Figure 2.13:

Variation of the rear screen slant angle of the VW Polo I and corresponding drag coefficient [28] ............. 19

XII

List of Figures

Figure 2.14:

Measured total pressure change in wake (50 mm behind the vehicle rear end) with notchback (top) and estate back (bottom), with fixed ground (left) and moving ground simulation (right) [30] .......................... 20

Figure 2.15:

Lift and drag change with variation of the rear diffuser angle with two different diffuser length, a) longer diffuser length La, b) shorter diffuser length Lb [31]............................................................................. 21

Figure 2.16:

The layout of the 5-belt test section with different boundary layer control systems in the full-scale wind tunnel of University of Stuttgart [46]............................. 24

Figure 2.17:

Boundary layer profile at different positions in the test section [46] .............................................................. 26

Figure 3.1:

Test section layout with the different boundary layer control systems and the rolling road system (top view) [64] ....................................................................... 30

Figure 3.2:

The AeroSUV model positioned in the test section of the model scale wind tunnel at IFS University of Stuttgart [11]................................................................... 31

Figure 3.3:

Discretization of the simulation region in PowerFLOW: the surface elements (surfels, shown with red lines) are derived by the overlapping between the fluid elements (voxels, shown with the black grid) and the surface mesh of the geometry (facets, shown as the blue lines) [7] ............................... 33

Figure 3.4:

The reflection of the particle on the wall for friction less walls, by which the normal velocity vn is inverted but the tangential velocity component vt remains identical (left) and friction wall, by which both vn and vt are inverted (right) [7] ................................................ 33

Figure 3.5:

Calculation grids for the vehicle on the middle plane y=0 m (top) and horizontal plane z=0 m (bottom) ........ 34

Figure 3.6:

Simulation area (top) and the boundary conditions for the moving ground (bottom) .......................................... 36

List of Figures

XIII

Figure 3.7:

DrivAer model with the notchback (left), the fastback and the estate back (upper right), the underbody geometry of the DrivAer (lower right)........................... 38

Figure 3.8:

AeroSUV model with the notchback (left), the fastback and the estate back (upper right), the underbody geometry of the AeroSUV (lower right)...... 39

Figure 3.9:

Comparison of the outline contours of the AeroSUV and the DrivAer in 25 % scale ....................................... 40

Figure 4.1:

Drag and lift difference (moving ground – fixed ground) of the DrivAer notchback and estate back with closed cooling......................................................... 42

Figure 4.2:

CFD simulated wake structure of the DrivAer notchback (top) and estate back (bottom) on the symmetrical plane with fixed ground (red streamlines) and moving ground simulation (blue streamlines) ........ 43

Figure 4.3:

Investigated geometric parameters on the DrivAermodel .............................................................................. 44

Figure 4.4:

Geometry variations at the vehicle front, a) engine hood slope angle αM, b) engine hood height hM, c) front windscreen slant angle δ, d) sweep angle αP..... 46

Figure 4.5:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the engine hood slope angle αM, with fixed ground and moving ground .......... 47

Figure 4.6:

Front and rear lift change over the engine hood slope angle αM, with fixed ground and moving ground .......... 48

Figure 4.7:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the engine hood height variation ∆hM, with fixed ground and moving ground (Measures in 25 % scale) ..................................................................... 49

Figure 4.8:

Front and rear lift change over the engine hood height variation ∆hM, with fixed ground and moving ground (Measures in 25 % scale) ............................................... 49

Figure 4.9:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the front windscreen slant angle δ, with fixed ground and moving ground........................... 50

XIV

List of Figures

Figure 4.10:

Front and rear lift change over the front windscreen slant angle δ, with fixed ground and moving ground .... 51

Figure 4.11:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the sweep angle ∆αP, with fixed ground and moving ground......................................................... 51

Figure 4.12:

Geometry variations at the vehicle top head, a) roof curvature ar, b) camber yW ............................................. 52

Figure 4.13:

Drag coefficient change ∆cD (left) and ∆(cD∙A) (right) over the normalized roof curvature ar/lr, with fixed ground and moving ground ............................................ 53

Figure 4.14:

Lift coefficient change ∆cL over the normalized roof curvature ar/lr, with fixed ground and moving ground............................................................................. 54

Figure 4.15:

Drag coefficient change ∆cD (left) and ∆(cD∙A) (right) over the normalized camber yW/a, with fixed ground and moving ground......................................................... 54

Figure 4.16:

Lift coefficient change ∆cL over the normalized camber yW/a, with fixed ground and moving ground .... 55

Figure 4.17:

Geometry variations at the vehicle rear end, a) trunk lid slope angle αH, b) trunk length lH, c) trunk height hH, d) rear screen slant angle φ ........................... 56

Figure 4.18:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH, with moving ground and fixed ground........................... 57

Figure 4.19:

Drag coefficient change ∆cD (top left), front lift coefficient change ∆cLF (bottom left) and rear lift coefficient change ∆cLR (bottom right) over the trunk length variation ∆lH, with moving ground and fixed ground ............................................................................. 58

Figure 4.20:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk height h H, with moving ground and fixed ground ................................................ 59

Figure 4.21:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the rear screen slant angle φ, with moving ground and fixed ground ................................... 60

List of Figures

XV

Figure 4.22:

Comparison of the velocity distribution between fixed ground and moving ground in the center plane (top) and above the roof (bottom) of the DrivAer estate back with a rear screen slant angle of 32°................................................................................... 61

Figure 4.23:

Comparison of the static pressure distribution on the surface of the DrivAer estate back with the rear screen slant of 32° between fixed ground and moving ground ............................................................................. 62

Figure 4.24:

Geometry variations at the vehicle underbody, a) front underbody slope angle αB, b) wheel track bS, c) rear diffuser angle αD ..................................................... 63

Figure 4.25:

Drag coefficient change ∆cD (top left), lift change ∆cL (top right), front lift change ∆cLF (bottom left) and rear lift change ∆cLR (bottom right) over the front underbody slope angle αB, with moving ground and fixed ground ................................................................... 64

Figure 4.26:

The measured drag coefficient cD of the DrivAer notchback with different front- and rear wheel track combinations (bSF and bSR), with moving ground simulation (top) and fixed ground (bottom)................... 65

Figure 4.27:

The drag difference ∆cD (moving ground – fixed ground) of the DrivAer notchback with different front- and rear wheel track combinations (bSF and bSR)............................................................................... 66

Figure 4.28:

CAD details of the diffuser add-on parts under the DrivAer ........................................................................... 67

Figure 4.29:

Comparison of the drag value with different diffuser angles between fixed ground and moving ground for the DrivAer notchback (left) and the estate back (right) ..................................................................... 67

Figure 4.30:

Comparison of the rear lift value with different diffuser angles between fixed ground and moving ground for the DrivAer notchback (left) and the estate back (right) ..................................................................... 68

XVI

List of Figures

Figure 4.31:

Comparison of the isosurface of cp,total İ 0 in the wake of the DrivAer notchback between fixed ground and moving ground with the rear diffuser angle of 12° .................................................................... 69

Figure 4.32:

Attitude parameters a) ride height e, b) pitch angle αA .......................................................................... 70

Figure 4.33:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the normalized ride height e/h, with moving ground and fixed ground ................................... 71

Figure 4.34:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the pitch angle αA, with moving ground and fixed ground............................................................. 72

Figure 4.35:

Schematic 3 cooling air flow outlets of the DrviAer, illustrated with the blue arrows ...................................... 73

Figure 4.36:

Experimental results of the drag coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends .......................................... 74

Figure 4.37:

Experimental results of the front lift coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends .......................................... 74

Figure 4.38:

Experimental results of the rear lift coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends .......................................... 75

Figure 5.1:

Sensitivity ranking of the drag change to the investigated parameters with fixed ground .................... 78

Figure 5.2:

Sensitivity ranking of the drag change to the investigated parameters with moving ground simulation ....................................................................... 79

Figure 5.3:

Sensitivity ranking of the lift change to different parameters with fixed ground ........................................ 80

Figure 5.4:

Sensitivity ranking of the lift change to different parameters with moving ground simulation .................. 81

Figure 5.5:

Combined variation of geometric parameters, variation of the trunk height hH and the diffuser angle

List of Figures

XVII αD on the notchback (left), variation of the rear screen angle and the diffuser on the estate back (right) ............ 82

Figure 5.6:

Response surface for the drag coefficient of the DrivAer notchback with delta trunk height ∆h H and diffuser angle αD, with moving ground (top) and fixed ground (bottom) .................................................... 84

Figure 5.7:

Response surface of the rear lift coefficient of the DrivAer notchback with delta trunk height ∆hH and diffuser angle αD, with moving ground (top) and fixed ground (bottom) .................................................... 85

Figure 5.8:

Response surface of the drag coefficient of the DrivAer estate back with different rear screen slant angle φ and diffuser angle α D, with moving ground (top) and fixed ground (bottom) ........................ 87

Figure 5.9:

Response surface of the rear lift coefficient of the DrivAer estate back with different rear screen slant angle φ and diffuser sangle α D, with moving ground (top) and fixed ground (bottom) ........................ 88

Figure 6.1:

Drag and lift difference (moving ground – fixed ground) of the AeroSUV fastback and estate back with closed cooling......................................................... 92

Figure 6.2:

Investigated geometric parameters on the AeroSUVmodel, a) trunk lid slope angle αH, b) trunk height hH, c) rear screen slant angle φ, d) rear diffuser angle αD, e) ride height e ................................................................ 93

Figure 6.3:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH of the AeroSUV notchback, with moving ground and fixed ground ............................................................................. 94

Figure 6.4:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH of the AeroSUV notchback, with moving ground and fixed ground ............................................................................. 95

Figure 6.5:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the rear screen slant angle φ of the

XVIII

List of Figures AeroSUV estate back, with moving ground and fixed ground ............................................................................. 96

Figure 6.6:

Comparison of the drag value with different diffuser angles between fixed ground and moving ground for the AeroSUV fastback (left) and the estate back (right) ..................................................................... 97

Figure 6.7:

Comparison of the rear lift value with different diffuser angles between fixed ground and moving ground for the AeroSUV fastback (left) and the estate back (right) ..................................................................... 98

Figure 6.8:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the normalized ride height e/h of the AeroSUV estate back, with moving ground and fixed ground ............................................................................. 99

Figure 6.9:

Experimental results of the drag coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends ..................................... 100

Figure 6.10:

Experimental results of the front lift coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends ..................................... 101

Figure 6.11:

Experimental results of the rear lift coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends ..................................... 101

List of Tables Table 3.1:

Flow properties in the simulations ................................. 37

Table 4.1:

Experimental results of the DrivAer model (baseline, closed-cooling) with moving ground simulation ........... 41

Table 6.1:

Experimental results of the AeroSUV model (baseline, closed-cooling) with moving ground simulation ....................................................................... 91

Formula Symbols A

Projection area

[m2]

a

Wheelbase

[m]

ar

Height of the roof curve

[m]

ar/lr

Roof curvature

AW

Wing area

[m2]

b

Ground clearance according to Pfadenhauer

[mm]

b0

Basic ground clearance according to Pfadenhauer

[mm]

bL

Wingspan

[m]

bS

Wheel track

[m]

bSF

Front wheel track

[m]

bSR

Rear wheel track

[m]

cA

Lift coefficient in German

-

cAH

Rear lift coefficient in German

-

cD

Drag coefficient

-

cL

Lift coefficient

-

cLF

Front lift coefficient

-

cLR

Rear lift coefficient

-

cM

Pitching moment coefficient

-

cp,stat

Static pressure coefficient

-

cp,total

Total pressure coefficient

-

cW

Drag coefficient in German

-

-

Formula Symbols

XXII e

Ride height

[m]

FD,i

Induced drag

[N]

FL

Lift

[N]

h

Vehicle height

[m]

hH

Trunk height

[m]

hM

Engine hood height

[m]

hmin

Ground clearance of the airfoil according to E. Beese

[m]

k

Wing shape coefficient

k

Turbulent kinetic energy

La

Shorter diffuser length

[m]

Lb

Longer diffuser length

[m]

lH

Trunk length

[m]

lr

Roof length

[m]

P

Points in the rating method

p∞

Environmental pressure

[Pa]

pi

Parameter combination

-

Re

Reynolds number

-

U(y)

Local flow velocity

[m/s]

ഥ (y) 

Averaged local flow velocity

[m/s]

U∞

Incoming flow velocity

[m/s]

v

Flow velocity

[m/s]

vA

Incoming flow velocity

[m/s]

vn

Particle normal velocity

[m/s]

[m2/s2]

-

Formula Symbols

XXIII

vt

Particle tangential velocity

[m/s]

w

Downstream flow velocity

[m/s]

x

Length in tangential direction

xU

Length of the laminar area

[m]

y

Height in vertical direction

-

yM

Camber

yM/a

Normalized roof curvature

z

Trunk height

[m]

ZS

Height of the stagnation point

[m]

ZV

Vehicle height according to R. Buchheim et al.

[m]

α

Pitch angle

[e]

αA

Angle of attack

[e]

αB

Front underbody slope angle

[e]

αD

Diffuser angle

[e]

αeff

Effective angle of attack

[e]

αH

Trunk lid slope angle

[e]

αi

Induced angle of attack

[e]

αM

Enginge hood slope angle

[e]

αP

Sweep angle

[e]

αW

Rear diffuser angle

[e]

δ

Front screen angle

[e]

δb

Thickness of the boundary layer

[mm]

ε

Energy dissipation rate

[m2/s3]

-

[m] -

Formula Symbols

XXIV Λ

Span-chord ratio

τ

Local effective relaxation time

φ

Rear screen slant angle

ߥ

Kinematic viscosity

[s] [e] [m2/s]

List of Abbreviations CAD CB CBTB CFD DOE DS DWT

FKFS IFS LBM MWK NRCC OCDA OFAT PBLPS RNG RSM SBLPS SUV TT ULH WLTP

Computer-Aided Design Center Belt Center Belt Tangential Blower Computational Fluid Dynamics Design of Experiment Distributed Suction Standard Digital Wind Tunnel provided by PowerFLOW without wind tunnel interference effects (box with low blockage ratio) Research Institute of Automotive Engineering and Vehicle Engines Stuttgart Institute for Automotive Engineering Stuttgart Lattice-Boltzmann Method Model Scale Wind Tunnel at IFS University of Stuttgart National Research Council of Canada Open Cooling DrivAer Model One Factor at a Time Primary Boundary Layer Pre-Suction Re-Normalization-Group Response Surface Method Secondary Boundary Layer Pre-Suction Sport Utility Vehicle Turn Table Uniform Latin Hypercube Worldwide harmonized Light Vehicles Test Procedures

Zusammenfassung Die meisten klassischen aerodynamischen Untersuchungen zur Fahrzeuggrundform wurden in konventionellen Windkanälen nur mit stehendem Boden durchgeführt, bei denen die Mängel bei der Simulation der Strömung auf der Oberfläche einer realistischen bewegenden Fahrbahn und des Strömungs-feldes rotierender Räder aufweisen. Mit der Entwicklung der Messtechnik sind die modernen Windkanäle der Automobilindustrie heutzutage standardmäßig mit Bodensimulationssystemen - einschließlich sich bewegender Fahrbahn, Grenzschichtvorabsaugung und rotierender Radeinheiten - ausgestattet. Das Strömungsfeld kann in modernen Windkanälen viel realitätsnaher simuliert werden. Seit der Einführung des WLTP (Worldwide Harmonized Lightweight Vehicle Test Procedure) sind moderne Bodensimulationssysteme sogar als obligatorische Anforderungen für die Windkanalmessungen im offiziellen Fahrzeugzertifizierungsprozess geworden. Die meisten Ergebnisse in den Lehrbüchern basieren jedoch auf den klassischen Untersuchungen mit nur stehendem Boden. Bisher gibt es nur wenige Untersuchungen, bei denen die Geometrieparameter unter Berücksichtigung der Bodensimulation systematisch variiert wurden. Die Wirkung aerodynamischer Maßnahmen an der Fahrzeuggrundform können in Abhängigkeit von Bodensimulationstechnologien von einer Optimierung nach dem herkömmlichen Verfahren abweichen. Das Ziel dieser Arbeit ist es daher, die Ergebnisse der parametrischen Untersuchungen in Bezug auf ihre Gültigkeit bei Verwendung der Bodensimulation zu überprüfen. Der grundlegende physikalische Mechanismus, der für die Grenzschicht-Theorien und den Bodeneffekt relevant ist, wurde dargestellt. Diese Theorien wurden verwendet, um die Einflüsse der Bodensimulation auf den Fahrzeugnachlauf und die Unterbodenströmung zu erklären. Außerdem wurde die Aufteilung zum Luftwiderstand des Fahrzeugs eingeführt, unter denen der induzierte Widerstand durch den Nachlauf und die Unterbodenströmung beeinflusst werden kann. Diese grundlegenden Theorien bildeten die theoretischen Grundlagen der vorliegenden Forschung. Zusätzlich wurde eine kurze Zusammenfassung der historischen Parameterstudien zur Fahrzeugform und zum Einfluss der Bodensimulation in Windkanälen angeführt, die eine Referenz für die vorliegende Forschung bildeten.

XXVIII

Zusammenfassung

In der Forschung wurden sowohl experimentelle als auch numerische Methoden verwendet. Die Messungen wurden im Modellwindkanal der IFS Universität Stuttgart (MWK) durchgeführt. Der MWK ist mit einem realen 5-BandStraßenfahrt-Simulationssystem ausgestattet und kann eine Windgeschwindigkeit von bis zu 288 km/h erreichen. Die numerischen Simulationen erfolgten mit dem 3D-CFD-Programm PowerFLOW, das auf der Lattice-Boltzmann-Methode basiert. Die untersuchten Modelle waren das DrivAer-Modell und das AeroSUV-Modell im Maßstab 25 %. Die Simulationsergebnisse zeigen eine gute Übereinstimmung mit den experimentellen Ergebnissen. Zunächst wurden eine Reihe von Vergleichsuntersuchungen zwischen dem stehenden Boden und dem beweglichen Bodensimulation am DrivAer-Basismodell mit drei Heckaufsätzen - Stufenheck, Fließheck und Kombiheck durchgeführt. Der Auftrieb des DrivAer mit jedem Heck wurde durch die Bodensimulation reduziert aufgrund des vergrößerten Strömungsimpulses und des verkleinerten statischen Drucks am Unterboden. Das Stufenheck und das Fließheck zeigten jedoch aufgrund der Bodensimulation eine entgegengesetzte Widerstandsänderung als das Kombiheck. Der physikalische Mechanismus wurde mit Hilfe der grundlegenden Theorien dargestellt. Darüber hinaus wurden parametrische Untersuchungen am DrivAer mit stehendem Boden und beweglichem Bodensimulation mit Hilfe von dem statistischen Ansatz „One-Factor-at-a-Time“ (OFAT) durchgeführt. Die untersuchten geometrischen Parameter des DrivAer decken die Bereiche Vorderwagen, Fahrzeugmitte, Hinterwagen und Unterboden ab. Die Einflüsse der Lageparameter der Fahrzeugkarosserie und des Kühlluftstroms wurden ebenfalls untersucht. Für die Variation der einzelnen Parameter wurden die Einflüsse der Bodensimulation mit einer Sensitivitätsanalyse untersucht. Darüber hinaus wurde die Wechselwirkung zwischen den geometrischen Parametern am Heck mit der Response-Surface-Methode (RSM) untersucht. Abgesehen davon, dass die Simulation des sich bewegenden Bodens zu einer Reduzierung des Auftriebs führt, wurden Unterschiede im Verlauf des Luftwiderstands oder der Auftriebsänderung in den Geometrievariationen am Unterboden und am Fahrzeugheck festgestellt. Anschließend wurden Untersuchungen zur Übertragbarkeit der Ergebnisse auf das AeroSUV-Modell durchgeführt, die unterschiedliche qualitative Ergebnisse liefern. Bei den geometrischen Parametern wie dem Neigungswinkel des Kofferraumdeckels und der Kofferraumhöhe wurde der Unterschied des Luftwiderstands, der von der Bodensimulation verursacht wird, verkleinert. Grund

Zusammenfassung

XXIX

dafür ist die größere Bodenfreiheit des AeroSUV im Vergleich zum DrivAer. Das Optimum des Heckscheibenwinkels und des Diffusorwinkels war jedoch immer noch empfindlich zu den Bedingungen der Bodensimulation. Die Ergebnisse geben einen Einblick in den Einfluss der Bodensimulation und zeigen Unterschiede in Bezug auf Luftwiderstand und Auftrieb bei Variation der Geometrieparameter, was eine entscheidende Ergänzung zu den historischen Untersuchungen darstellt.

Abstract Most of the aerodynamic studies on the vehicle basic shape have been carried out in the wind tunnels with only stationary ground condition, which have shortages in simulating the air flow on the surface of a real moving road and the flow field of rotating wheels. With the development of the wind tunnel test technology, the modern ground simulation systems – including moving belts, boundary layer suction and rotating wheel units – have been widely adopted in the modern wind tunnels in automobile industry nowadays. The flow field can be simulated much closer to the reality in modern wind tunnels. Since the introduction of the WLTP (Worldwide Harmonized Lightweight Vehicle Test Procedure), modern ground simulation systems even become mandatory requirements for the wind tunnel tests in the official vehicle certification process. However, the most results in the textbooks are based on the classical investigations with only stationary ground condition. There exist so far, only few investigations, which have systematically varied the geometry parameters with respect to ground simulation. Aerodynamic optimizations on the vehicle basic shape could differ with the modern ground simulation technology compared to an optimization based on fixed ground. Therefore, the aim of this research is to review the previous results with respect to ground simulation. The basic physical mechanism relavant to the boundary layer theories and ground effect was depicted. These theories were used to explain the influences of moving ground simulation on the vehicle wake and underbody flow. Besides, different distributions to the aerodynamic drag of the vehicle were introduced, among which the induced drag can be influenced by the wake and underbody flow. These basic theories constituted the theoretical fundamentals of the present research. In addition, a brief summary of the historical parametric studies on the vehicle shape and the influence of the moving ground simulation in wind tunnels was summarized, which formed a reference for the present research. Both experimental and numerical methods were used in the research. The experiments were performed in the model scale wind tunnel at IFS, University of Stuttgart (MWK). It is equipped with a 5-belt real road simulation system and can reach wind speeds up to 288 km/h. The simulations were conducted with the CFD-program PowerFLOW, which is based on the Lattice-Boltzmann-Method. The investigated models were the DrivAer model and the

XXXII

Abstract

AeroSUV model in 25 % scale. The simulation results show a good correlation to the experimental results. Firstly, a set of comparative investigations between fixed ground and moving ground simulation were conducted on the basic DrivAer model with three rear ends - notchback, fastback and estate back. The lift of the DrivAer with each rear end was reduced by the moving ground simulation due to the larger flow momentum and lower static pressure at underbody. But the notchback and the fastback showed an opposite drag change as the estate back due to the moving ground simulation. The physical mechanism was depicted with the help of the basic theories. Futhermore, parametric investigations were conducted on the DrivAer with fixed ground and moving ground simulation using the statistical approach “One-Factor-at-a-Time” (OFAT). The investigated geometric parameters cover the areas of the vehicle front, cabin, rear end and underbody. The influence of the attitude parameters of the vehicle body and the cooling air flow were also reviewed. For the variation of each parameter, the interaction with the ground simulation was investigated with the sensitivity study. Moving ground simulation results usually a reduction of lift. However, differences on the trend of the drag or lift change were found in the geometry variations at underbody and rear end. Based on the findings derived from the OFAT-investigations, the interaction between the geometric parameters at rear end were investigated with the response surface method (RSM). Thereafter, transferability studies were carried out to apply the findings on SUV like vehicles, which reveal different qualitative results. For geometric parameters, such as the trunk lid slope angle and the trunk height, the difference of the drag resulted from moving ground simulation was weakened because of the larger ride height of the AeroSUV compared with the DrivAer. But the optimums of rear screen angle and the diffuser angle were still sensitive to ground simulation conditions. The results give an insight into the influence of ground simulation and show different results in drag and lift for the varied the geometry parameters, which offers a decisive complement to the historical investigations.

1 Introduction The basic properties of a ground vehicle are influenced by aerodynamics. First of all, the energy consumption together with the emission and the top-speed of the car are all related to the aerodynamic drag. For the vehicles with new energy powertrains, although the emission is no longer an issue, the aerodynamic drag is still critical to the energy consumption and the range. In addition, vehicle aerodynamics also plays a vital role in the driving dynamics, which have an impact on the driving comfort and stability, especially in the field of sports cars and race cars. Therefore, the reduction of aerodynamic drag and the improvement of the driving dynamics are two main tasks for aerodynamicists in automobile industry.

1.1

Motivation

The automotive market today is being divided into more detailed segments than before to meet the diverse demand of customers. Correspondingly, the vehicle basic shape becomes more numerous. Another reason which affects the vehicle packaging is the electrification. Due to the diversity of the new energy powertrain, the structure as well as the geometric parameters of the car body can be different to the vehicles with conventional powertrains. Some manufacturers have given an image of the prospective vehicle concepts, as illustrated in Figure 1.1.

Figure 1.1:

Different basic shape of the electric vehicles [1, 2, 3, 4]

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_1

2

1 Introduction

At the vehicle front, the engine hood and the front windscreen have a flat slope angle. In the cabin region, the roof curvature and the camber of the cabin are varied to improve the comfort. As for the vehicle rear end, some new concepts are designed from a combination of the three classic rear end shapes – notchback, fastback and squareback. The rear screen angle and the trunk shape vary by the vehicle models. They differ much for the three typical rear end shapes. For the underbody area, some sport cars are equipped with rear diffusers to improve the vehicle road behavior. Within the last years, Sports Utility Vehilces (SUV) obtain the most increasing share in the global market in addition to the other classes of passenger cars. The typical characteristic of an SUV is its large ride height, approach, ramp and departure angle, which enables an improved off-road ability. In addition to that, the SUVs have a larger cross-sectional area than sedans. All those geometric variations have an impact on vehicle aerodynamics. In the vehicle aerodynamic development process, a variety of methods are used to investigate and to improve the vehicle aerodynamic properties. In the early years before 1980s, only road tests and wind tunnel tests were applied in the vehicle aerodynamic development [5]. Since the 1980s, computational fluid dynamics (CFD) was widely adopted in the vehicle aerodynamic development process [6, 7]. With the increasing computing capacity and the developed mathematical models in the calculation codes, the agreement between the CFD simulations and the wind tunnel tests have been improved. Nowadays, CFD simulation is a widely used tool in the vehicle aerodynamic research. Parallel to the development of the numerical tools, the experimental method, e. g. the wind tunnel test technology has also been improved. However, the most of the classic aerodynamic investigations on the vehicle basic shape in the past decades were predominantly carried out in conventional wind tunnels with fixed ground and stationary wheels. With the ongoing development of wind tunnel testing techniques – e.g. road simulation with moving belts, boundary layer suction systems and wheel rotation units – the flow field around a vehicle can be simulated much closer to reality. It has been shown that the optimization of the vehicle shape using a wind tunnel with ground simulation can differ significantly from the optimization results in wind tunnel with fixed ground [8, 9]. Nevertheless, only few investigations exist that vary the vehicle basic shape systematically and consider the influence of the chosen ground simulation technique.

1.2 Research Objectives

1.2

3

Research Objectives

As depicted in the above section, the improvement of the wind tunnel testing technology with the ground simulation techniques enables the on-road simulation in the wind tunnels much closer to the reality. Despite the numerous investigations on the vehicle basic shape, these classic results need to be reviewed with the moving ground simulation. In order to obtain a good understanding into the differences between the two ground simulation techniques on the vehicle aerodynamic characteristics, three questions are solved in the present research: „

The geometric parameters are figured out, by which the moving ground simulation causes differences in the results compared with the fixed ground. To answer this question, a number of parameter investigations are carried out and analyzed by the means of a sensitivity study.

„

Furthermore, the correlations between the geometric variations and the results are reviewed with the moving ground simulation. It is investigated, how the classic results are changed by the altering of the ground simulation techniques.

„

The physical mechanism is analysed.

The results of the present research provide a complement to the historical investigations on the vehicle basic shape with respect to a more sophisticated ground simulation. The parametric investigations on the vehicle basic shape are carried out on two generic vehicle models – the DrivAer [10] and the AeroSUV [11, 12]. These two generic vehicle models represent typical mid-class passenger cars in the automotive market nowadays. The transferability of the findings on the DrivAer model was reviewed on the AeroSUV model, so that the results are able to provide a comprehensive reference for the aerodynamic research.

2 Basic Theories and State of the Art The relevant physical theories are described in the following, which give a basic understanding of the physical mechanism behind the aerodynamic forces of the vehicle and their interaction with the ground simulation. In addition, the aerodynamic investigations on the vehicle basic shape from literature are reviewed.

2.1

Basic Theories

Subsequent, the fundamentals of vehicle aerodynamics are described. The basic theories of boundary layer and ground effect are set forth in detail. To analyze the interaction between the ground simulation and the aerodynamic forces of a vehicle, the mechanisms of the drag and the lift as well as the ground simulation in wind tunnels are depicted. These fundamentals give a reference to the investigations in the following sections and explain the basic flow characteristics of the vehicle. 2.1.1

Boundary Layer Theories

In the following, the physical mechanism of laminar and turbulent boundary layers and the equations are introduced for estimating the thickness of the boundary layers. Due to the flow viscosity and the velocity difference between the physical boundary of an object and the flow, boundary layer exists close to the solid surface of the object. The thickness of the boundary layer grows downstream while the flow status in it alters from laminar to turbulent. Though the thickness of the boundary layer is only several millimetres at the beginning, the behaviors of the flow involving friction determine the flow downstream near the solid boundary considerably. The flow structure and its development in the boundary layer along a plate are illustrated in Figure 2.1. Assume that flow velocity U∞, kinematic viscosity 𝜈 and pressure p∞ in the far field are constant, the flow in the boundary layer © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_2

2 Basic Theories and State of the Art

6

passes through two stages sequentially, which are the laminar and the turbulent stage.

Figure 2.1:

Boundary layer development along a plate

In the laminar area, the thickness of the boundary layer δb is described with ଵ

ߥޚ ଶ Ɂୠ~ ൬ ൰ ஶ

Eq. 2.1

In the transition region, the flow status changes from laminar to turbulent status, where the Reynolds number is

ܴ݁୶ ୳ =

ஶ ή š୳ ൌ ͷ ή ͳͲହ ߥ

Eq. 2.2

in which š୳ is the length of the laminar flow length. This equation applies only to the case without pressure gradient since the pressure gradient influences the transition position. In the turbulent area, the thickness of the boundary layer is defined as ଵ

ߥ ହ ସ Ɂୠ~ ൬ ൰ ή š ହ ஶ

Eq. 2.3

2.1 Basic Theories

7

The laminar and turbulent boundary layer flow depends much on the pressure gradient in the flow field. By streamwise pressure increase, the flow near the solid boundary is decelerated and even reverse flow appears. This flow behavior is defined as flow separation and is illustrated in Figure 2.2. The streamline at the separation point, marked with point A in Figure 2.2, leaves the solid boundary.

Figure 2.2:

Flow seperation in the boundary layer near a wall

In the boundary layer, the flow is decelerated due to the viscous force. On the other side, the pressure will be increased if the cross-sectional area of the flow is enlarged due to the reduced flow speed. At point A, the curved solid surface forms an enlarged cross-sectional area for the flow, where adverse pressure gradient appears. The momentum in the flow is reduced by the viscous force in the boundary layer and cannot support the flow still along streamwise to move. As a result, the flow is further decelerated and its velocity in the direction along the wall becomes zero. Behind point A, the velocity component is negativ and characterizes a reverse flow due to adverse pressure gradient. When a body moves above the ground with a small ground clearance, an interaction between the body and the ground occurs, which is charachterized by a noticeable boundary layer. Beese [13] has explained this interaction through the investigations on the airfoil near the moving ground. In his research, the airfoil with different ground clearance hmin and angle of attack was tested in the wind tunnel with moving ground simulation. Firstly, the ground effect of an airfoil with a positive angle of attack is presented in Figure 2.3.

2 Basic Theories and State of the Art

8

a)

c)

b) hmin = 0(l)

U∞

U∞ U∞

hmin → ∞ U∞

Figure 2.3:

d) hmin = 0(l) hmin → 0 U∞ U∞

U∞

hmin → 0

U∞

Induced boundary layer of an airfoil with a positive angle of attack, the induced boundary layer increases with the reduced ground clearance hmin from far away from the ground a) to close to the ground d) (Courtesy Beese [13])

With sufficient large ground clearance, the boundary layer is formed only around the airfoil, as illustrated in Figure 2.3 a). When the ground clearance is reduced, the flow between the airfoil and the ground is also influenced. The airfoil induces a boundary layer on the ground, as presented in Figure 2.3 b). With a further reduced ground clearance close to zero, as shown in Figure 2.3 c) and d), this effect is strengthened. The flow between the airfoil and the ground will eventually be blocked [13]. a)

b)

U∞

U∞

U∞

Figure 2.4:

U∞

Induced boundary layer of an airfoil with a negative angle of attack, a) the larger angle results in an increased separation area at the ground compared to the smaller angle as shown in b) (Courtesy Beese [13])

In the case of a negative angle of attack, the induced boundary layer of an airfoil is presented schematically in Figure 2.4. Similarly, a boundary layer appears on the ground. But differently, the airfoil with a steeper negative angle causes a recirculation near the ground because of the reduced pressure under

2.1 Basic Theories

9

the airfoil rear, as illustrated in Figure 2.4 a). The recirculation is weakened with a smaller negative angle, as presented in Figure 2.4 b) [13]. These theories give an understanding of the flow mechanism in the boundary layer. The thickness of the boundary layer can be estimated with the help of equation 2.3. The analysis on the interferences between the moving ground and the airfoil provides basic fundamentals to the present research. An analogy analysis on the ground vehicles is performed based on these theories.

2.1.2

Ground Effect

The principle of the ground effect can be described as the combination of the road surface and the vehicle underfloor forming a venturi-tunnel (venturi effect), depicted in Figure 2.5.

Figure 2.5:

Principle of the ground effect

The front underbody slope and the surface of the ground shape a duct. Due to the smaller ground clearance at position 2, the underbody flow is accelerated. At position 3, the flow is decelerated by the diffuser. The pressure reduction and the resulting down force depends on the ratio of cross sections at the diffuser and the duct. The basic aerodynamic characteristics of a ground vehicle is comparable to that of a bluff body near the ground. The flow field between the vehicle body and the ground is not only influenced by the underbody geometric parameters discussed above, but also strongly affected by the attitude parameters, e.g. the

10

2 Basic Theories and State of the Art

ground clearance. The lift force of the vehicle is directly affected by the ground clearance. In addition, it has an indirect effect on the drag force. Pfadenhauer has investigated the correlations between the aerodynamic coefficients of a bluff body and the ground clearance [14]. In the results, three curves – drag, lift and pitching moment coefficient (c D, cL and cM) over the ground clearance b were plotted. The investigated bluff body with its basic ground clearance b0 features a cD value of about 0.21. In the range of 0.5 – 1.5 b0, the cD value changed linearly with the ground clearance. The lowest drag coefficient attained a figure of about 0.19. Out of this range, the c D value remained constant with different ground clearances. Compared with the drag coefficient curve, the lift and the pitching moment coefficient curves reveal more obvious changes. The bluff body has positive lift coefficient with small ground clearance (b < 0.3 b0), because the flow rate is reduced so that the pressure on the underside is raised. With the increasing ground clearance, a down force is caused by the Venturi effect, which gives rise to a negative lift coefficient. But it increases again when the ground clearance is further enlarged. This lift recovery is caused by the reduction of the underbody flow velocity with a larger ground clearance. The pitching moment coefficient shows a similar trend, which indicates more down force at the rear of the bluff body.

2.1.3

Aerodynamic Forces of a Ground Vehicle

The aerodynamic drag of a vehicle is the sum of the pressure and the friction forces which act on the vehicle. It is important to note, that friction forces account for almost 90 % of the total aerodynamic drag of a sedan car. The local contributions to the aerodynamic drag of a vechicle are divided into the contributions from the basic shape, the roughness of the add-on parts, the cooling air and the interference between the add-on parts and the body. A typical distribution of each type of the drag is illustrated in Figure 2.6 [15], among which the form drag and the roughness drag caused by wheels, underbody parts and mirrors account for the majority.

2.1 Basic Theories

Figure 2.6:

11

Different distributions to the aerodynamic drag of the vehicle [15]

As indicated by Figure 2.6, the drag resulting from the basic shape accounts for the majority of the total aerodynamic drag. This part of the drag is determined substantially by the basic shape of the vehicle, which considers only the exterior shape of the bodywork without wheels, cooling flow and underbody geometries. The pressure difference between the vehicle front and rear end along with the skin friction of the bodywork surface build the form drag [15]. It is important to point out that the induced drag is part of the vehicle’s pressure drag, which is affected by the lift of the vehicle [16]. The induced drag results from the change in pressure distribution due to a pair of edge vortices at the vehicle rear end. The mechanism of the induced drag and its correlation to the lift are interpreted in the airfoil theories [17]. Due to the non-symmetrical pressure distribution on the upper and the under side of the airfoil, a pair of tip vortices are produced to compensate the pressure difference, as illustrated in Figure 2.7. The vortex intensity depends on the pressure difference. As a result, the flow in the middle of the wingspan is deflected, namely the downwash or the upwash.

2 Basic Theories and State of the Art

12

Figure 2.7:

Tip vortex of the airfoil

With respect to the overall effect, the flow deflection is caused by the airfoil while the reaction force from the flow acts on the airfoil. This force is deconstructed as lift in the vertical direction and induced drag in the horizontal direction, presented as A and Wi in Figure 2.8. The skin friction is here ignored.

Figure 2.8:

Flow deflection by an airfoil and the induced drag

The correlation between the flow velocity U∞, the vertical velocity component behind the airfoil w and the deflection angle αi can be depicted by the following equation [17]:

2.1 Basic Theories

13

–ƒ Ƚ୧ ≈ Ƚ୧ ൌ

™ ʹ ή ஶ

Eq. 2.4

Therefore, the induced drag is derived from its correlation to the lift:

ୈ౟ = ୐ ή –ƒ Ƚ୧ ൌ ୐ ή

™ ʹ ή ஶ

Eq. 2.5

஠

The distance between the two tip vortexes is „୐, where bL is the wingspan. ସ

Thus, the induced drag coefficient of the airfoil can be described as:

…ୈ౟ = k∙

where Ȧ=

ୠై మ ୅

…୐ ଶ ɎήȦ

Eq. 2.6

, A is the wing area, cDi is the induced drag coefficient, cL is the

lift coefficient and k is a constant dependent on the wing shape [18, 19]. The principle for calculating the induced drag of the ground vehicle can be derived from the airfoil theories [20]. However, for the application of the equation 2.6 to ground vehicles, the wing area A has to be recast to the frontal area of the vehicle [21]. Compared to the airfoil, the ground vehicle is a bluff body which moves close to the ground. Although it has a flow separation area in the wake and interferences between the ground and the underbody, the typical vortex-pair exists also in the wake of the ground vehicle. As presented in Figure 2.9 (bottom), the rear shape of the bluff body is similar to a vehicle rear end. The shear layers on the rear edges of the bluff body are rolled up and formed a pair of edge vortex. The edge vortex can result in a decrease of the total force acted on the rear surface due to the lower pressure in the vortex center, as the pressure distribution cp presented in Figure 2.9 (top). The longitudinal component of the force forms the induced drag and contributes to the aerodynamic drag.

2 Basic Theories and State of the Art

14

Figure 2.9:

2.2

The formation of a pair of edge vortex due to the rolled up shear layers on rear edges (bottom) and the pressure distribution on the sloping surface (top)

State of the Art

Subsequently, the literature dealing with aerodynamic investigations on the vehicle basic shape is introduced. In addition, the ground simulation technology in wind tunnels and the research on the influence of the moving ground simulation is presented.

2.2.1

Previous Investigations on Vehicle Geometric Parameters

The investigated vehicle shape parameters in the previous literature can principally be be sorted in four regions of the car body, which are the vehicle front, the cabin, the rear end and the underbody. In addition to the shape parameters,

2.2 State of the Art

15

there exist a number of investigations dealing with the attitude parameter of the vehicle body. At the vehicle front, Carr has investigated the influence of the engine hood slope angle on the drag coefficient [22]. In his investigation, the engine hood slope angle was varied from 0° (horizontal position) to 10° from the horizontal position. A curve of the drag coefficient of the test vehicle with different engine hood slope angle was plotted in his result. It indicates a reduced drag with an increasing engine hood slope angle from 0° to 5°. The drag may be reduced by the decreasing stagnation area at the front end. But in the range from 5° to 10°, the drag coefficient curve shows nearly the constant trend. The investigations on the front windscreen angle were carried out by Buchheim et al. [23]. Their research reveals a correlation between the front windscreen slant angle and the drag coefficient. The investigations were performed on a Audi 100 model. The front windscreen angle was defined as the angle from the front wind screen to vertical direction. A larger angle corresponds to a more flat front windscreen. In their research, the angle was varied from 55° to 61°, which corresponded to the front windscreen angles of the two generations of Audi 100 (II and III). All the drag coefficients of these variations were plotted in a drag curve. Their results indicated that a more flat front windscreen reduced the drag coefficient. From 55° to 61°, the drag coefficient was reduced of nearly 0.01. Moreover, the drag coefficient was reduced rapidly from 55° to 59°. After that, it droped slower with the enlarged front windscreen angle. In addition to the front windscreen slope angle, Buchheim et al. have also investigated the vehicle front shape, as presented in Figure 2.10. Serie

0.020 ΔcD

ZS

ZV

0.010

e 0.000 -0.010

Figure 2.10:

0.1

0.3 ZS = Height of the stagnation point 0.2 ZS/ZV ZV = Vehicle height e = Ride height

Variation of the vehicle front shape and its resulting drag change [24]

2 Basic Theories and State of the Art

16

They varied the front-end geometry to build different height of the stagnation point ZS [24]. The height of the stagnation point was non-dimensionalized with the vehicle height ZV. The illustration in Figure 2.10 indicates that the front underbody slant angle and the engine hood shape were simultaneously varied with the height of the stagnation point. The drag coefficient reaches a lower and a higher value with the increasing height of the stagnation point, as presented in the diagram in Figure 2.10. The influence of the front underbody slant angle is investigated separately in the present thesis. Similar investigations on the vehicle front end shape were performed by Hucho et al. [25]. In addition to the variation of the front-end shape, they added a front spoiler, which reduced the drag and the front lift coefficient. In the cabin area, the roof curvature was varied by Buchheim et al. [24]. The diagrams in Figure 2.11 show the correlations of ∆cD∙A and ∆cD over the dimensionless roof curvature ar/lr.Although the drag coefficient was reduced for more than 0.01, as shown in Figure 2.11 (bottom), the total aerodynamic drag increased, which can be represented by ∆cD∙A, as illustrated in Figure 2.11 (top).

ΔcW∙A in m² 0.040 0.030 0.020

0.010

lr 0.02 0.04 0.06 0.08 0.10 Dachwölbung ar/lr

ar

-0.010 ΔcW -0.020 Figure 2.11:

Drag change ∆cW∙A (top) and drag coefficient change ∆cW (bottom) over the roof curvature ar/lr [24]

2.2 State of the Art

17

In the middle part of the vehicle, Buchheim et al. have investigated the influences of the camber on the drag in their investigations [23, 24]. The results and the geometry variations are presented in Figure 2.12. The camber yM was non-dimensionalized with the wheelbase. The results based on the Audi 100, as shown in Figure 2.12 a), indicates that the drag coefficient decreases with the camber. But the drag force increases at first and decreases despite the enlarged frontal area. Similar trend of the drag coefficient change can be found on the Volkswagen research vehicle, as shown in Figure 2.12 b). However, the drag force increases first with the enlarged camber. It begins to decrease when the dimensionless camber y M/a is larger than 0.03. a) 0.00 ΔcW -0.010

yM/a 0.01

0.02

b)

0.02

yM/a 0.04

0.06

0.02

0.04

0.06

ΔcW

-0.010

-0.020 -0.030

-0.020 -0.030

0.010 0.000

0.010

-0.010 -0.020 Δ(cW∙A) -0.030

0.000 Δ(cW∙A) -0.010 a yM

Figure 2.12:

Drag change over the camber yM/a, a) results based on the Audi 100 models [23], b) results based on the Volkswagen research vehicle [24]

For the geometric parameters in the vehicle rear end, a number of investigations were carried out in the past decades. These results provide substantial references for the investigations in the present thesis.

18

2 Basic Theories and State of the Art

In the research from Buchheim et al. [23], investigations on different trunk height of the Audi 100 were performed. The basic trunk height of the Audi 100 was defined as the reference geometry. Based on it, the trunk height was varied in a range from -30 mm to +100 mm. The drag coefficients of these configurations were plotted in a curve, which indicated that the drag coefficient decreased when the trunk height is varied from -30 mm to +40 mm based on the reference geometry. With a further increase of the trunk height till +100 mm, little change on the drag coefficient was observed. Similar investigations were extended by Krüger and Lentzen [26]. Compared to the investigations from Buchheim et al., they continued to increase the trunk height further. Thus, the rear end was varied from notchback to squareback with a total of six geometry konfigurations (variation 1 to 6). The rear screen slant was changed correspondingly. From variantion 1 to variantion 4, the drag coefficient decreased, which is similar to the results from Buchheim et al. When the trunk height was further increased (from variation 5 to 6), the drag coefficient increased again and exceeded the drag coefficient of the variation 1 (notchback). Therefore, the squareback configuration had a larger drag coefficient than the notchback. In addition to the trunk height, the rear screen slant angle plays a vital role in building the wake structure behind the vehicle, which can affect the drag significantly. Ahmed et al. performed a set of investigations concerning the slant angle on a bluff body (the so-called Ahmed body) to simulate the influence on the drag of different rear screen slant angles [27]. The results indicate that the drag drops when the slant angle increases to values > 30°. Investigations on the rear screen angle of the VW Polo were also carried out by Janssen and Hucho [28]. Figure 2.13 illustrates the change of drag and lift due to the rear screen slant angle. The results show a similar trend when compared to the results of the Ahmed body. The critical slant angle for the drag drop is however slightly larger than 30°, while for the lift drop it is smaller than 30°.

2.2 State of the Art

Figure 2.13:

19

Variation of the rear screen slant angle of the VW Polo I and corresponding drag coefficient [28]

The investigations mentioned above were conducted in the conventional wind tunnels with fixed ground and wheels only. Different from these investigations, the research by Kuthada et al. [29, 30] compared the flow difference between the two ground simulation techniques with the notchback and the estate back. Their results revealed that the flow difference appears in the side of the vehicle in addition to the underbody flow. Figure 2.14 presents the total pressure change in the wake of the two rear ends with fixed ground and moving ground simulation. Compared to the fixed ground condition, the flow from underbody and vehicle side with moving ground simulation has lower pressure loss. With same ground simulation condition, notchback results in a larger pressure loss in the flow from these two areas. The side flow interacts with the wake. This interaction is influenced by the boat-tailing. With different rear end shapes and boat-tailings, the difference of the base pressure varies. The cooling drag is affected by the rear ends with fixed ground simulation. But with moving ground simulation, the change of the cooling drag shows less sensibility to the rear end shapes. As a result, the difference of the drag value between the vehicle rear end shapes depends on the the two ground simulation techniques.

20

Figure 2.14:

2 Basic Theories and State of the Art

Measured total pressure change in wake (50 mm behind the vehicle rear end) with notchback (top) and estate back (bottom), with fixed ground (left) and moving ground simulation (right) [30]

For the underbody region, Potthof has investigated the rear diffusor on the UNICAR [31]. The research was conducted also in the conventional wind tunnel with only fixed ground and stationary wheels. The results presented in Figure 2.15 (top) show that an obvious fall on the equivalent rear lift appears with a diffuser angle in the range of 0° to 4°. After that, the rear lift is further reduced with increasing diffuser angle. But the drop rate is smaller. With a longer diffuser length, the diffuser is more effective. As for the drag of the vehicle, it is reduced firstly with the increased diffuser angle until 3° with the langer diffuser length, as presented in Figure 2.15 (bottom). After that, the drag increases again when the diffuser angle is further enlsarged. With the shorter diffuser length, this turning point of the curve appears at 4°.

2.2 State of the Art

Figure 2.15:

21

Lift and drag change with variation of the rear diffuser angle with two different diffuser length, a) longer diffuser length La, b) shorter diffuser length Lb [31]

In addition to the investigations from Potthoff, similar research was carried out by Cooper et al. [32, 33] and Ruhrmann and Zhang [34]. They performed the investigations on a simplified bluff body with both fixed and moving ground simulation in the 10 % model scale wind tunnel of the NRCC. The mechanism of the vehicle diffuser was explained with the non-dimensional value - the area ratio. This value is defined as the ratio of the diffuser outlet area and the smallest cross-sectional area between the underfloor and the ground. The efficiency of the diffuser can be described by the area ratio. But the influence of the rotating wheel was not investigated with the simplified bluff body. The research of Zhang et al. [35] has described the mechanism of the lift reduction with a rear diffuser. Their results were obtained with moving ground simulation and revealed that, the flow topology under the diffuser is symmetrical with a small diffuser angle. When the diffuser angle is further enlarged, the flow in the middle under the diffuser begins to separate. But the flow topologie under the diffuser is still symmetrical. At this status, the diffuser results in the smallest rear lift. This flow topologie can be disturbed by an even larger separation with a further enlarged diffuser angle. After that, the rear lift begins to increase. However, their research was also conducted on a bluff body without wheels. The investigations of Marklund [36] have given a detailed analysis of the interaction between the underbody flow and the wake to explane the influence

22

2 Basic Theories and State of the Art

of the diffuser on the drag. In his research, both wind tunnel tests and CFDsimulations were conducted with moving ground condition. The results indicate that the upwash in the wake is influenced by the diffuser. Correspondingly, the flow direction of the wake is changed due to the diffuser, which has an impact on the induced drag of the vehicle. Dependent on the driving speed and conditions, the ride height and the pitch angle of the vehicles varies. The ride height affects the ground clearance. These attitude parameters of the vehicle body have large impact on the aerodynamic characteristics. In 1973, Janssen and Hucho. investigated the influences of the pitch angle and the ride height on the drag and lift coefficient [37]. Several vehicle models including VW Variant 411, VW Kastenwagen, VWPorsche 914, Audi 100, Citroen ID 19 and Wettbewerber F2-2 were compared in their research. The pitch angle of these vehicles was varied from -3° to +2° while the ride height was varied in a range from 100 mm to 350 mm. The drag and lift coefficient with different ride height and pitch angle were plotted with different curves respectively. The results indicated an increasing trend of the drag and lift coefficient with the enlarged pitch angle of the vehicle body. This finding was applicable for all the investigated vehicle models in their research. However, on the variation of the ride height, the investigated vehicle models showed different drag and lift change. The drag coefficient of the VW Kastenwagen, the VW-Porsche 914 and the Wettbewerber F2-2 increased with the enlarged ride height. Only the drag coefficient of the Citroen ID 19 was firstly reduced and then slightly increased with the enlarged ride height. The lift coefficient of this vehicle behaved also differently from the other models with different ride height. The lift coefficient also first droped down and after that it was slightly increased with the enlarged ride height. For the other investigated vehicle models, smaller changes on the cL value can be observed when the ride height was varied. However, their investigations were carried out in the wind tunnel without moving ground simulation. The similar parametric study on the vehicle ride height and the pitch angle is also conducted with the moving ground simulation in the present thesis. Similar investigations on the ride height were carried out by Coggotti [38]. In his research, different ride heights were tested in the Pininfarina wind tunnel with the fixed ground and the moving ground simulation. The results reported a lower drag coefficient for reduced ride heights. The lift coefficient has a minimum at a certain ride height. Compared to the fixed ground, usually a

2.2 State of the Art

23

lower drag coefficient at high ground clearance was measured with the moving ground simulation. The influences of the ground simulation on the cooling drag were investigated by Wickern et al [39]. In their research, different vehicle models were tested in the wind tunnel with stationary ground and moving ground simulation. An increased cooling drag with moving ground simulation was derived for most measured vehicles [40]. Based on the numerous parametric investigations as mentioned above, empiric correlations between the geometry details of the vehicle and their contributions to the drag were proposed [41, 42, 43, 44]. The first rating method for predicting the drag coefficient was raised by MIRA. The vehicle was partitioned into 9 regions by parts and listed in a 3 × 3 matrix. Each region was rated with scores P in terms of its contribution to the drag. A streamlined shape detail obtained a lower score while a stream disturbing element gained a higher score. Besides the score rating matrix, MIRA developed a chart of correlations between the scores and drag coefficient values. From the sum of the scores a drag coefficient can be evaluated by looking up the chart [41]. After that, the rating method was upgraded by Carr [42], Calkins et al [43] and Calkins and Chan [44]. They integrated the rating method into CAD development tools, so that the drag coefficient of the vehicle could be roughly evaluated in the early development phase. The aim of the rating method was to achieve a faster development process and lower development costs. However, there exist differences between the estimation and the wind tunnel tests. It is not able to replace wind tunnel tests and CFD simulations. Because the rating method is too limited to predict the drag coefficient of a modern vehicle compared to the wind tunnel tests and CFDsimulations.

2.2.2

Ground Simulation Technology in Wind Tunnels

In the conventional wind tunnels, which are equipped with only fixed ground in the test section, the boundary layer continues to grow after leaving the nozzle. In addition, the wheels of the vehicle are stationary. With the ongoing development of wind tunnel testing techniques, e.g. the moving ground simulation system, the flow field around a vehicle can be simulated much closer to reality. The application of the moving ground system is now also one of the

24

2 Basic Theories and State of the Art

requirements for the emission homologation of vehicles under the Worldwide harmonized Light Vehicles Test Procedures (WLTP) [45]. For testing the passenger vehicles, a 5-belt moving ground simulation system is widely adopted in the modern automotive wind tunnels. Figure 2.16 presents the layout of the newly upgraded 5-belt moving ground simulation system in the full-scale wind tunnel of University of Stuttgart in 2014 [46].

Figure 2.16:

The layout of the 5-belt test section with different boundary layer control systems in the full-scale wind tunnel of University of Stuttgart [46]

This 5-belt moving ground simulation system consists of the center belt, four wheel-rotation-units and the boundary control systems. These include the primary and the secondary boundary layer pre-suction, the center belt tangential blower and distributed suctions. In addition to the 5-belt system, a changeable 3-belt moving ground system was also adopted to meet with the test requirements for the race cars [47, 46]. The numerical research [48] indicated that the use of a single belt or alternatively a 3-belt system can predict lift more accurately. The IFS full-scale wind tunnel was the first wind tunnel certified to WLTP standard [49].

2.2 State of the Art

25

The present research deals with only the comparison between the fixed ground and the moving ground simulation with the 5-belt system, which is commonly applied in the production vehicle wind tunnel tests.

2.2.3

Influence of the Moving Ground Simulation

The research carried out by Wiedemann [50] indicated the irreplaceable effect of the tangential blowing in modeling the correct momentum thickness of a boundary layer on a moving wall. For the ground-effect vehicles, there is a complete change of the flow field near the ground with the moving ground simulation compared to the fixed ground. A free recirculation zone appears behind the vehicle with moving ground simulation, whereas a large separation zone exists on the stationary ground. The technical paper by Mercker and Wiedemann [51] has compared the physical mechanism of different ground simulation techniques including stationary ground, moving ground and distributed suction. It was revealed that in an automotive wind tunnel a steady turbulent boundary layer always develops along the ground. This boundary layer usually is considerably thicker than the unsteady boundary layer generated at the road under a moving car. If parts of the car penetrate into the boundary layer, the aerodynamic coefficients may be falsely measured. Furthermore, the displacement effect on a stationary ground introduces a flow angularity into the air stream which may lead to considerable errors when testing vehicles. Therefore, the moving belt, distributed suction and tangential blowing systems are necessary in reproducing an on-road flow condition in an automotive wind tunnel. During wind tunnel tests of vehicles with fixed ground and moving ground simulation, a general trend has been referred by Wickern et al. [21] that notchback vehicles typically displayed lower drag when measured with moving ground simulation, whereas estate backs show higher drag. Furthermore, they revealed the interaction between the induced drag and the ground simulation through the investigations on the rear spoiler. The moving ground simulation system is the state-of-the-art solution to simulate a real on-road flow condition of the vehicle in wind tunnels. Compared to the conventional fixed ground simulation technique, the moving ground simulation reduces the boundary layer on the ground in test sections successfully. For instance, with the application of the boundary layer presuction system in

26

2 Basic Theories and State of the Art

the full-scale wind tunnel of University of Stuttgart, the thickness of the boundary layer in the middle of the ground plate is reduced. With the activation of the full road simulation system including the tangential blowing, the flow velocity profile in the middle of the ground plate is ideal as a block form, as shown in Figure 2.17 [52].

Figure 2.17:

Boundary layer profile at different positions in the test section [46]

In addition to the boundary layer control system, the wheel rotation units enable the rotation of the wheels. Previous investigations revealed that the rotating wheels have a significant impact on the aerodynamic properties in the measurements [53, 54, 55]. In the research by Mercker et al. [53], the effect of the rotating wheels with different vehicle configurations was compared with the fixed wheels. The ride height, the wheel spoiler and the tire width of the vehicle were varied. A wakerake analysis behind the wheels was carried out in their research. In the comparison of the front wheel wakes between rotating and the fixed wheels, different total pressure distributions can be observed. The wake of the front wheel with low ride height shows a larger pressure loss at the ground with fixed wheels compared with rotating wheels. In the upper wake structure, obvious difference can be observed. The upper region of fixed wheels had smaller pressure loss than rotating wheels. It was indicated that the fixed front wheels have

2.2 State of the Art

27

more intensive tread swirl and smaller upper swirls in the wake. For the cases with high ride height, this difference in the upper wake structure was presented more obviously. Obvious difference exsits in the wake of the rear wheels as well. Rotating wheels affect the underbody and wake flow topologie. The research by Wäschle [54] revealed that the difference in the wake resulting from the rotating wheel have an impact on the optimal diffuser angle. Based on these findings, the influence due to the moving ground simulation on the alteration of the geometric optimums is studied in the present research. In open jet wind tunnels different interference effects exist between the test vehicle and the wind tunnel geometry, which include jet-expansion effect, nozzle blockage effect, jet deflection effect,collector blockage effect and horizontal buoyancy effect [56, 57, 58, 59, 60, 61]. These interferences depend on the wind tunnel and the tested vehicle geometry. They can cause a deviation on the absolute test results. Therefore, Mercker and Wiedemann have developed the correction method to correct the deviation [56]. The interferences caused by the wind tunnel geometry are not discussed in the present thesis, since they are not counted as a significant cause for the differences resulting from the ground simulation techniques. In addition, the horizontal pressure gradient is also influenced by the boundary layer condition systems in the test section [62, 63]. Based on the previous investigations, the influences on the test results caused by the moving ground simulation can be attributed to the different flow topology in the vehicle underbody region, the wake of the rotating wheels and the horizontal pressure gradient. Their impact and interactions with the vehicle geometric parameters are investigated and depicted in the present thesis.

3 Research Methods and Models In the present research, both CFD simulations and wind tunnel tests were applied, which are two common methods in aerodynamic research. Wind tunnel tests enable the fast results. Whereas CFD simulations provide a deep insight into the flow field information, e.g. the velocity and the pressure distribution at each point of the simulated area. Although the agreement between wind tunnel and CFD has been improved largely in the past dacades, both tools are unlikely to replace each other completely due to their own advantages. Both tools were used in the present research and benefited from their advantages. Especially for a number of geometry variations, the investigations were carried out by means of CFD simulations. Because more flow informations can be presented, which were difficult to be obtained in the wind tunnel tests due to the physical limitations of the existing vehicle hardware model. The parametric investigations were performed based on two generic vehicle models, which represent the typical mid class passenger cars in the automotive market. The used tools and models in the present research are introduced in this chapter.

3.1

Experimental Method

In the experiment, the geometry variations are realized with the add-on parts, which are manufactured by the 3D-printer. Due to the geometric limitations of the hardware model, not all the parameters can be tested in the wind tunnel. The test facility used in the present study and the test setup are introduced subsequently. 3.1.1

IFS Model Scale Wind Tunnel

The measurements were performed in the model scale wind tunnel of IFS University of Stuttgart (MWK). This Goettingen-type wind tunnel, operated by FKFS, has a nozzle area of 1.6 m² and is suitable for measuring models in 20 % and 25 % scale. The maximum wind velocity is 80 m/s. A state-of-the-art © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_3

30

3 Research Methods and Models

ground simulation system is installed in the test section, as presented in Figure 3.1.

Figure 3.1:

Test section layout with the different boundary layer control systems and the rolling road system (top view) [64]

It consists of a 5-belt rolling road system. The wheels are rotated by the belts of 4 wheel-rotation units. To remove the boundary layer and produce a block profile of the flow, boundary layer suction and tangential blowing is used [64].

3.2 Numerical Method 3.1.2

31

Test Setup

The use of all above described subsystems is called moving ground simulation or “FKFS Real Road Simulation”. The measurements without the use of the described subsystems are referred to as fixed ground. For each geometry configuration, both ground simulation techniques were tested to compare the difference of the results. The test speed was 50 m/s, which corresponded a Reynolds number of 2.3×106. Figure 3.2 shows the model of the AeroSUV positioned in the test section of the MWK.

Figure 3.2:

3.2

The AeroSUV model positioned in the test section of the model scale wind tunnel at IFS University of Stuttgart [11]

Numerical Method

For CFD, the vehicle geometry is modified by means of the computer-aided design (CAD) software. For some basic shape variations, the mesh of the vehicle model is transformed directly by a mesh morphing tool in the CFD software packet. The modified geometry or mesh variants are simulated in the CFD solver. The results are interpreted by the post-processing programm. Based on the simulation results, new geometry variations are created and simulated to obtain complete parametric studies. The numerical scheme including the simulation software and the setup of the boundary conditions are depicted in the following sub-sections.

3 Research Methods and Models

32 3.2.1

Simulation Software

Numerical simulations were performed with the commercial CFD code PowerFLOW, which is widely used in the automotive industry. This CFD program is based on the Lattice-Boltzmann method (LBM). Differing from other CFD codes based on the Navier-Stokes equation, the LBM considers the fluid at a mesoscopic level with the Lattice-Boltzmann equation. The core equation of the Boltzmann equations is the distribution function, which describes the distribution of the moving molecules in a control volume [65]. The relevant macroscopic values can be derived from the distribution function. The change in the molecule count resulting from the external forces and molecule transports is balanced in the Boltzmann equations with respect to the molecule collision. The Lattice-Boltzmann equation describes the evolution of a discrete particle distribution function, which characterizes the number of particles at a time with a momentum at each node on a spatial grid (lattice). In PowerFlow the lattice is defined as the “Voxel”. The flow velocity is determined with the Lattice-Boltzmann equation on the Cartesian grids. This allows a considerable saving of the computational expenditure and a high degree of parallelization in the computation [66, 67]. Similar to the CFD codes based on the Navier-Stokes equations, the turbulence model of PowerFlow is also described by an overlap of a stationary main equation and the stochastic fluctuation. The turbulence model of PowerFlow was named k-ε-RNG model (RNG: Re-Normalization-Group), which is determined by two additional transport equations for the turbulent kinetic energy k and the dissipation ε as well as a local effective relaxation time τ. The local effective relaxation time τ is determined by the collision of the molecules in the Boltzmann-equation [68]. The wall-model of the PowerFLOW is based on the universal wall law [69]. Together with the turbulence model, the separation in the boundary layer can be well represented with relative rough grids at a large Reynolds number. The volume grids are automatically discretized by PowerFlow before simulation. The discretization principle of the grids is illustrated in Figure 3.3. The surface mesh, which is defined as “Facets” by PowerFlow (a blue line with two nodes represent a section of a facet), is cut by the voxels planes (black lines). The facets are then devided into the “Surfels” (represented by red lines

3.2 Numerical Method

33

with nodes). If a facet is positioned completely in a voxel, the entire facet is recognized as a surfel. Consequently, the resolution of the geometry details in the simulation is determined by not only the surface mesh, but also the refinement of local voxels [7].

Figure 3.3:

Discretization of the simulation region in PowerFLOW: the surface elements (surfels, shown with red lines) are derived by the overlapping between the fluid elements (voxels, shown with the black grid) and the surface mesh of the geometry (facets, shown as the blue lines) [7]

During the calculation, particles collide with the surfels and are reflected, whereby a momentum exchange between fluid and wall takes place. Figure 3.4 shows two extreme cases of the particle reflection on the wall.

Figure 3.4:

The reflection of the particle on the wall for friction less walls, by which the normal velocity v n is inverted but the tangential velocity component vt remains identical (left) and friction wall, by which both vn and vt are inverted (right) [7]

34

3 Research Methods and Models

In the case of the “Specular Reflection”, the particle is reflected like light on a mirror. The normal velocity component is inverted, while the tangential velocity component remains identical. The momentum balance during the collision results only in a normal force. This case corresponds to a frictionless wall (slip condition). A non-slip condition is achieved through the “Bounce Back Reflection” in which the tangential velocity component of the particle is also inverted by the impact. Thus, a frictional force between the fluid and the wall occurs. In order to minimize deviations of the calculation, the volume mesh near the solid body needs to be refined to ensure the precision of the simulation [7]. The mesh partition scheme was applied according to the PowerFLOW Best Practice [70]. The resolution of the region which is close to the vehicle geometry is refined to ensure a high quality of the geometry details. The resolution of the volume grids for the simulations in the present research is displayed in Figure 3.5.

Figure 3.5:

Calculation grids for the vehicle on the middle plane y=0 m (top) and horizontal plane z=0 m (bottom)

3.2 Numerical Method

35

The regions where large pressure and velocity gradient occur were refined. The grids in the regions far from the vehicle geometry is coarsed to increase the simulation efficiency. Near the geometry surface, the grid was set with the highest level of resolution to ensure the calculation precision for the boundary layer. As for the stagnation area, the grid was also refined with different levels to provide a fine resolution for a precise calculation of the velocity gradient. In the wake, the fine resolution region was extruded to cover the vortices and the flow separation area. In order to enable the efficient simulations of the vehicle models in a virtual wind tunnel, PowerFlow developed a simplified modul which is called the digital wind tunnel (DWT). The parameters of the DWT can be defined according to the real wind tunnels. The conditioning for the ground simulation, e.g. the boundary layer thickness of the ground and the center belt with the specific friction can also be adjustable.

3.2.2

Boundary Conditions of the Simulations

The simulation area, displayed in Figure 3.6 (top), was simplified as a box with a blockage ratio of 0.1 %. The overall length was approximately 12 vehicle lengths from air-inlet to outlet. It extended 5 vehicle lengths upstream and 6 vehicle lengths downstream. The vehicle model size in the simulations was 25 % scale, which corresponded to the physical model size in the MWK tests. The refinement regions of the fluid cells were adjusted based on the PowerFlow best practice [70]. In order to recreate the same moving ground conditions as in the MWK, the central moving belt and the 4 belts of the wheel-rotation units were modeled in their size and applied with the moving wall boundary condition. The tires were modeled as rotating wall and the rims of the wheels were modeled as sliding mesh. The rest of the floor was a frictionless wall, as shown in Figure 3.6 (bottom). For simulating the fixed ground, certain areas of the floor were modeled as standard wall with a specified roughness. The roughness parameters were adjusted to build a proper boundary layer thickness, which matched the boundary layer profile in the model scale wind tunnel [71, 72].

36

Figure 3.6:

3 Research Methods and Models

Simulation area (top) and the boundary conditions for the moving ground (bottom)

3.2 Numerical Method

37

The flow properties of the simulations are listed in Table 3.1, which are obtained from the actual air properties in the MWK. Table 3.1:

Flow properties in the simulations

Variable

Value

Unit

Ambient pressure

101325

Pa

Wind speed

50

m/s

Ambient temperature

20

°C

Kinematic viscosity

1.51×10-5

m2/s

Characteristic length

0.697

m

Cell number along along the characteristic length

1161

-

Gas molecular weight

28.97

kg/kmol

Constant-pressure specific heat

1007

J/(kg*K)

Turbulent length scale

1.5

mm

Wind tunnel tests and CFD-simulations were the two main tools in the present research. Depending on the complexity of the configuration change, it was investigated either in CFD or in experiment. The results of these two test environments show a good agreement, as it could be shown in [73, 74].

3 Research Methods and Models

38

3.3

Research Models

The models used for all investigations in this work were the DrivAer model [10] and the AeroSUV model [11, 12] in 25 % scale. These two generic vehicle models have a high level of geometric details, which are able to represent the typical mid-class passenger cars in the market.

3.3.1

DrivAer Model

The DrivAer model was developed by Heft et al. [10] in 2012. This vehicle model has a realistic contour and features three different rear end geometries (notchback, estate back and fastback) as well as the underfloor details. The wheels are detailed and can be rotated. This model was modified by Wittmeier and Kuthada [75], adding a generic drivetrain and cooling air system, resulting in the open-cooling DrivAer model (OCDA) [76], as illustrated in Figure 3.7. The modified model provides a production car like flow field also making it possible to investigate the cooling flow details, as all interfering geometric details are present.

Figure 3.7:

DrivAer model with the notchback (left), the fastback and the estate back (upper right), the underbody geometry of the DrivAer (lower right)

Considering the simulation costs, the influence of the moving ground simulation on the cooling flow was investigated separately on the OCDA model in the present research. The investigations on the other geometric parameters were carried out with closed-cooling.

3.3 Research Models 3.3.2

39

AeroSUV Model

In addition to the DrivAer, the AeroSUV model was investigated, which represents a mid-class SUV. The AeroSUV model was developed based on the DrivAer model by Zhang et al. [11, 12]. A considerable number of manufacturers have introduced the SUV models with the fastback rear shape into the market in addition to the square back. Mercedes-Maybach has introduced a concept SUV model with notchback rear end shape [77]. Since different rear end shapes result in different wake structures [15], the AeroSUV model was designed to carry over the three rear ends of the DrivAer. Additionally, certain components of the under-hood compartment, drivetrain and the design style of the wheels were adopted. The geometry of the AeroSUV with three rear ends and the detailed underbody is presented in Figure 3.8.

Figure 3.8:

AeroSUV model with the notchback (left), the fastback and the estate back (upper right), the underbody geometry of the AeroSUV (lower right)

Compared to the DrivAer model, the overall height of the AeroSUV is increased by 47 mm (in 25 % scale). The length and width of both models deviate only slightly. The ground clearance of the AeroSUV is increased by 13 mm. The outline of the wheels is widened by 8 mm on each side, as illustrated in Figure 3.9, all measures are in 25 % scale.

40

Figure 3.9:

3 Research Methods and Models

Comparison of the outline contours of the AeroSUV and the DrivAer in 25 % scale

This results in an increased cross-sectional area of the AeroSUV by 14 % compared to the DrivAer. In addition, the AeroSUV has a larger ride height and wheel size. The approach and departure angle are larger than those of the DrivAer [11, 12].

4 Results of the DrivAer Model In the following section, the comparison of the results on the DrivAer baseline in 25 % scale between fixed and moving ground simulation is presented first. Furthermore, the investigated geometric parameters on the DrivAer are described and their results are depicted. Lastly, conclusions to the parametric study on the DrivAer model are derived based on the presented results.

4.1

Baseline Results with Fixed and Moving Ground Simulation

The DrivAer baseline model with closed-cooling was tested in the MWK. The results with the drag coefficient cD, the front- and the rear lift coefficient c LF and cLR are presented in Table 4.1. Only small difference between the notchback and the fastback can be observed. Compared with the aerodynamic coefficients of the estate back, the drag coefficient is reduced by about 0.030 while the lift coefficient is reduced, as well. The results are comparable to the test data reported by Heft et al. [10] and others. Table 4.1:

Experimental results of the DrivAer model (baseline, closedcooling) with moving ground simulation cD

cLF

cLR

Notchback

0.271

-0.025

0.119

Fastback

0.272

-0.028

0.139

Estate back

0.298

-0.062

0.036

In addition, comparative MWK-tests with the moving ground simulation were carried out with the notchback and the estate back. Due to the similarity of the © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_4

42

4 Results of the DrivAer Model

flow properties between the notchback and fastback, only the notchback was tested in MWK. Meanwhile, these variations were simulated with PowerFlow using the simulation setup depicted in section 3.2. The differences of the drag and the lift coefficient between the two ground simulation techniques are plotted in Figure 4.1. The results with fixed ground are subtracted from the results with moving ground. The light blue bars represent the results of the notchback; the dark blue bars represent those of the estate back. The CFD results (bars with diagonal strips) show a good agreement with the experimental results (filled bars).

Figure 4.1:

Drag and lift difference (moving ground – fixed ground) of the DrivAer notchback and estate back with closed cooling

For the lift distribution, the diagram shows similar changes on the two rear end shapes. Smaller lift coefficients can be observed with moving ground. This is caused by the larger flow momentum and lower static pressure in the underbody area. However, the two rear end shapes show a different behavior of change in drag due to ground simulation. The drag of the notchback is reduced with moving ground simulation. The estate back with moving ground simulation shows a 0.005 higher drag value compared to the results with fixed ground. These results are similar to that reported by Wickern et al. [11]. This opposite change on the drag is caused by the different wake structures of the two rear ends. The CFD simulated wake structures of the two rear ends with fixed ground and

4.1 Baseline Results with Fixed and Moving Ground Simulation

43

moving ground simulation on the symmetrical plane are presented in Figure 4.2. The wake of the notchback tends to be a downwash while the estate back has an upwash in the wake. Analog to the airfoil in section 2.1.3, the flow deflection in the wake caused by the vehicle results in the induced drag. With moving ground, the underbody flow obtains larger flow rate. As a result, the flow in the underbody region with moving ground has more momentum than that with fixed ground and deflect the wake of the vehicle upwards. Consequently, the wake direction of the notchback in the case of moving ground simulation (blue streamlines) tends to be more near horizontal compared to the fixed ground (red streamlines). As a result, the induced drag on the notchback is reduced. For the estate back, the wake under the moving ground condition is further upwards deflected compared to the fixed ground. The induced drag applied on the estate back is increased. Therefore, the notchback has a reduced drag but the estate back has an increased drag with moving ground.

Figure 4.2:

CFD simulated wake structure of the DrivAer notchback (top) and estate back (bottom) on the symmetrical plane with fixed ground (red streamlines) and moving ground simulation (blue streamlines)

Based on the analysis above, it can be indicated that whether the measured drag is increased or reduced in case of moving ground simulation can be evaluated by the downstream flow direction in the wake. According to the mechanism of the induced drag, a nearly horizontal downstream flow in the wake results in the smallest induced drag, because it contributes little component in the longitudinal direction. Moving ground simulation increases the flow rate

4 Results of the DrivAer Model

44

in the underbody area. The wake flow gains more momentum from the underbody flow and deflects upwards. Therefore, for a vehicle which has upwash wake, with moving ground simulation will increase the drag. For a vehicle which has downwash wake, its drag may be reduced because the downstream flow can be deflected by moving ground simulation more nearly to the horizontal direction.

4.2

Investigated Parameters

In the following sections, different geometric parameters of the DrivAer model are investigated with respect to the two ground conditions. The investigated parameters on the DrivAer model are listed in Figure 4.3, which are sorted by the location on the vehicle. The investigated areas cover the parts in the vehicle front, cabin, rear end and underbody. In addition to those, two attitude parameters of the entire vehicle body – the ride height and the pitch angle – were also investigated in the research.

Figure 4.3:

Investigated geometric parameters on the DrivAer-model

The selection of the parameters was based on the previous investigations mentioned in section 2.2.1. Those geometric parameters characterize usually the vehicle basic shape and determine its aerodynamic properties to a large extent.

4.3 Parameters at the Vehicle Front

45

In order to evaluate the influence of each single geometric parameter, all the parameters were modified separately in chapter 4, which corresponds to the statistical approach One-Factor-at-a-Time (OFAT) [78]. The interaction between the parameters was investigated in section 5.2.

4.3

Parameters at the Vehicle Front

The investigated parameters at the vehicle front include the engine hood slope angle, the engine hood height, the front windscreen slant angle and the sweep angle of the front bumper. The variations of these geometric parameters and their results are elucidated in this chapter.

4.3.1

Geometry Variations at the Vehicle Front

The geometry variations at the vehicle front are illustrated in Figure 4.4. The engine hood slope angle αM was defined as the angle between the hood and the horizontal plane, as presented in Figure 4.4 a). The original engine hood slope angle of the DrivAer is 8°. This angle was changed from 4° to 12°. The hood height hM was varied from -10 mm to +10 mm based on the original height, as illustrated in Figure 4.4 b). The front windscreen angle was defined as the angle between the windscreen and the vertical plane, as shown in Figure 4.4 c). It was modified from 50° to 65°. Figure 4.4 d) presents the variation of the front bumper sweep angle αP. It was changed based on the original sweep angle from -10° to +10°. To analyze the influence of the moving ground, the relative value of the aerodynamic coefficient is calculated. The result of each geometry variantion is subtracted from the reference value, which is established by the aerodynamic coefficient of the baseline DrivAer. In the presented graphs, the light blue dashed lines represent the results with fixed ground while the dark blue solid lines stand for the results with moving ground. The other graphs in the following sections involving the results with these two ground simulations are also presented in this format. All given measures are in 25 % scale.

4 Results of the DrivAer Model

46

Figure 4.4:

4.3.2

Geometry variations at the vehicle front, a) engine hood slope angle αM, b) engine hood height hM, c) front windscreen slant angle δ, d) sweep angle αP

Engine Hood Slope Angle

The numerical results of the engine hood slope angle are presented in the following section. The drag and lift coefficient changes with different engine hood slope angle of the DrivAer notchback are plotted in Figure 4.5.All the aerodynamic coefficients of each geometry variation is subtracted by the coefficients of the basic DrivAer geometry with fixed ground and moving ground simulation respectively. The baseline is defined as the original DrivAer model with basic rear end shapes including notchback, fastback and estate back. Through the above-mentioned normalization, the aerodynamic coefficients of the baseline either with fixed ground or moving ground simulation will be showed as zero in the graphs. The differences in results between the baseline and other geometry variations will be presented as delta-values in the graphs. This normalization is processed in all the following charts of this thesis. The logic of this and the following charts is such, that the graphs reveal the effect

4.3 Parameters at the Vehicle Front

47

of a certain vehicle-modification, i.e. 'cD and 'cL. This is done twice, namely for fixed ground and for moving ground. Therefore, the difference between the two graphs indicates the so called ''-Effect, which means the change in predicted effectiveness of a modification due to a change in ground simulation. Comparing the difference between the fixed ground and the moving ground, the two lines show similar change trend for both drag and lift coefficients. Therefore, the moving ground simulation has little influence on the results change when the engine hood angle is variated.

Figure 4.5:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the engine hood slope angle αM, with fixed ground and moving ground

As for the aerodynamic impact of the engine hood angle variation, the drag coefficient is slightly reduced with the enlarged hood angle, which shows the same trend as the results from Carr [22]. However, the lift coefficient is increased.

4 Results of the DrivAer Model

48

Figure 4.6:

Front and rear lift change over the engine hood slope angle αM, with fixed ground and moving ground

Comparing the lift distribution on the front- and rear axle, as illustrated in Figure 4.6, an opposite change can be observed. The front lift is reduced while the rear lift is increased with the hood angle. The vehicle’s pitching moment is decreased by increasing the engine hood angle. In comparision to the results with fixed ground, the moving ground simulation shows the same trend for the front- and rear lift coefficient.

4.3.3

Engine Hood Height

The numerical results of the engine hood height on the DrivAer notchback are depicted in this section. The drag and lift coefficient change with the engine hood height variation is presented in Figure 4.7. The trend of both dashed and solid curves is similar. The ground condition shows little influence on the trend of the drag and lift when the engine hood height was variated. As for the aerodynamic effect of the hood height variation, the drag coefficient is increased by approx. 0.005 with an elevation of the engine hood for about 20 mm. The lift coefficient is reduced with the increased height of the engine hood.

4.3 Parameters at the Vehicle Front

Figure 4.7:

49

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the engine hood height variation ∆hM, with fixed ground and moving ground (Measures in 25 % scale)

The lift distribution on the front- and rear axle changes for the two ground simulation techniques are illustrated in Figure 4.8. Similar trend for both curves with fixed and moving ground can be observed.

Figure 4.8:

Front and rear lift change over the engine hood height variation ∆hM, with fixed ground and moving ground (Measures in 25 % scale)

The ground condition has also little influence on the trend of the front- and rear lift coefficients. With respect to the aerodynamic influence of the hood

4 Results of the DrivAer Model

50

height variation on the lift distribution, the front lift coefficient increases while the rear lift decreases with the hood height. Therefore, the vehicle tends to have a positive pitching angle with the elevated engine hood.

4.3.4

Front Windscreen Slant Angle

The numerical results of different front windscreen slant angle are presented in this section. The diagrams in Figure 4.9 show the drag- and the lift change with the front windscreen angle.

Figure 4.9:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the front windscreen slant angle δ, with fixed ground and moving ground

The drag value is reduced for less than 0.005 with the increasing front windscreen angle. The trend is same as the results of the Audi 100 obtained by Buchheim et al. [23]. The moving ground simulation has little influence on the trend of the drag. For the total lift, the curve with moving ground simulation shows a slight increasing trend. There exists a small difference compared to the curve with fixed ground especially for the front screen angles smaller than the baseline. On the lift distribution, a similar trend can be observed with fixed and moving ground (compared with Figure 4.10). The ground condition has little impact on the trend for different front screen angle. But the front lift is reduced while the rear lift is increased conversely with the similar magnitude. As a result, there is no obvious change in the total lift coefficient. But a negative pitching moment is applied on the vehicle body.

4.3 Parameters at the Vehicle Front

Figure 4.10:

4.3.5

51

Front and rear lift change over the front windscreen slant angle δ, with fixed ground and moving ground

Sweep Angle

The numerical results of the sweep angle on the DrivAer notchback are depicted in the following section. The drag and the lift coefficient changes for different sweep angle are plotted in Figure 4.11.

Figure 4.11:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the sweep angle ∆αP, with fixed ground and moving ground

4 Results of the DrivAer Model

52

For both drag and lift coefficients, the trends remain identical with fixed and moving ground simulation. Therefore, the ground condition has only little impact on the trend of the drag and the lift when the sweep angle is varied.

4.4

Parameters at the Vehicle Cabin

The investigations of the parameters at the vehicle cabin of the DrivAer notchback include the roof curvature aD and the camber yW. The geometry variations of the two parameters and their results are depicted in this section.

4.4.1

Geometry Variations at the Vehicle Cabin

The geometry variations of them are illustrated in Figure 4.12. The roof curvature ar was morphed based on the basic roof geometry in a range from 0 to 20 mm in 25 % scale, as illustrated in Figure 4.12 a). The camber was varied based on the 25 % basic DrivAer geometry in a range from 0 to 20 mm, as presented in Figure 4.12 b).

Figure 4.12:

Geometry variations at the vehicle top head, a) roof curvature ar, b) camber yW

4.4 Parameters at the Vehicle Cabin 4.4.2

53

Roof Curvature

The results of different roof curvature are presented in Figure 4.13. Due to the change on the projection area, both cD and cD∙A are plotted.

Figure 4.13:

Drag coefficient change ∆cD (left) and ∆(cD∙A) (right) over the normalized roof curvature ar/lr, with fixed ground and moving ground

The curvature aD in the diagrams is non-dimensionalized as aD/lD, where lD is the length of the roof. The drag coefficients show a reducing trend with the curvature, as illustrated in Figure 4.13 (left). However, there exists a slight increase on the cD∙A, as presented in Figure 4.13 (right). The entire aerodynamic drag force is increased. The results indicate similar trend as the findings from Buchheim et. al. [23, 24]. Compared to the results with fixed ground, the moving ground simulation has little influence on the trend of the results. The variation of the roof curvature has little impact on the lift coefficient of the DrivAer in 25 % scale. The curves with fixed ground and moving ground simulation show the similar trend, as presented in Figure 4.14. The two ground simulation techniques have little effect on the lift when varying the roof curvature.

4 Results of the DrivAer Model

54

Figure 4.14:

4.4.3

Lift coefficient change ∆cL over the normalized roof curvature ar/lr, with fixed ground and moving ground

Camber

The results of different camber are presented in Figure 4.15. The camber yW is non-dimensionalized with the wheelbase a. Since the variation of the camber results also in the change on the projection area, the drag coefficient c D as well as cD∙A over the camber are plotted in the diagrams.

Figure 4.15:

Drag coefficient change ∆cD (left) and ∆(cD∙A) (right) over the normalized camber yW/a, with fixed ground and moving ground

4.5 Parameters at the Vehicle Rear End

55

The drag coefficient is reduced with the increasing camber, as illustrated in Figure 4.15 (left). Comparing the results with fixed and moving ground simulation, same trends can be observed. The cD∙A value is also reduced with the enlarged camber, as shown in Figure 4.15 (right), which indicates a drag reduction. Similar to the drag coefficient change, the trend of c D∙A remains the same with the two ground simulation techniques.

Figure 4.16:

Lift coefficient change ∆cL over the normalized camber yW/a, with fixed ground and moving ground

With the enlarged camber, the lift of the 25 % scale DrivAer is firstly increased and then tends to be constant, as shown in Figure 4.16. Moving ground simulation has little impact on the trend of the lift coefficient change.

4.5

Parameters at the Vehicle Rear End

In the following section, the results of different rear end shape parameters of the DrivAer model with the two ground conditions are presented [79]. As mentioned in chapter 1, the rear end design differs with vehicle models. The findings from the literature, summarized in section 2.2.1, indicate that the variation of the rear end shape parameters changes the aerodynamic properties when the fixed ground is considered. Therefore, four geometric parameters – the trunk lid slope angle, the trunk length, the trunk height and the rear screen slant angle were investigated on the DrivAer model to show the influence of the moving ground on the achieved results. The investigations were performed using CFDsimulations.

4 Results of the DrivAer Model

56 4.5.1

Geometry Variations at the Vehicle Rear End

The schmatic of the geometry variations on the rear end shape in 25 % scale is illustrated in Figure 4.17. The trunk lid slope angle αH was varied based on the baseline in a range from -10° to +10°, as shown in Figure 4.17 a). The trunk length lH was morphed from -50 to 50 mm based on the baseline, as illustrated in Figure 4.17 b). In Figure 4.17 c) the variation of the trunk height is shown, which was varied in a range from -20 to +30 mm based on the baseline. The rear screen slant angle (illustrated in Figure 4.17 d)) was modificated from 20° to 50°.

Figure 4.17:

4.5.2

Geometry variations at the vehicle rear end, a) trunk lid slope angle αH, b) trunk length lH, c) trunk height hH, d) rear screen slant angle φ

Trunk Lid Slope Angle

The results of the notchback model with different trunk lid slope angles and the two ground conditions are plotted in Figure 4.18. The left diagram presents the drag change ∆cD with different trunk lid slope angle αH. Obvious change on the lift exists at the rear part of the vehicle, therefore the rear lift change ∆cLR is plotted in the right diagram.

4.5 Parameters at the Vehicle Rear End

Figure 4.18:

57

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH, with moving ground and fixed ground

For the drag coefficient, the value is increased from the baseline for both directions of the slope angle, as presented in Figure 4.18 (left). However, different positions as well as different magnitude of drag optimum can be observed for the two ground conditions. With fixed ground, the optimum slope angle is overestimated compared to the results with moving ground. The rear lift of the DrivAer is reduced with increasing trunk lid slope angle. As a result, the pitching moment tends to be positive, because there is no obvious change in the front lift. The trend of both curves is similar, as illustrated in Figure 4.18 (right). The ground condition shows only little influence on lift.

4.5.3

Trunk Length

For the variation on the trunk length of the DrivAer notchback, the results are presented in Figure 4.19. The drag is reduced with increasing trunk length. Both drag coefficient curves for the two ground conditions show a similar trend. However, the drag change with the moving ground simulation begins to remain constant with a trunk length extension longer than 25 mm. The drag value with fixed ground is further reduced, as presented in Figure 4.19 (top left).

58

Figure 4.19:

4 Results of the DrivAer Model

Drag coefficient change ∆cD (top left), front lift coefficient change ∆cLF (bottom left) and rear lift coefficient change ∆cLR (bottom right) over the trunk length variation ∆lH, with moving ground and fixed ground

There is only little change on the front lift, as plotted in Figure 4.19 (bottom left). The rear lift coefficient is reduced continously with the extension of the trunk, as illustrated in Figure 4.19 (bottom right). A trunk extension of 100 mm in 25 % scale corresponds to a rear lift reduction of 0.08. Compared to the lift coefficient curves with the fixed ground simulation, the trend of the lift coefficient curves with the moving ground simulation remain the same. Therefore, there is little difference between the two ground simulations for the lift change with different trunk length.

4.5 Parameters at the Vehicle Rear End 4.5.4

59

Trunk Height

The results for the different trunk heights are plotted in Figure 4.20. With moving ground, the lowest drag coefficient can be achieved with the baseline trunk height (0 mm). With fixed ground, the lowest drag can be achieved when the trunk height is increased by 10 mm – 20 mm. The drag increases again for a trunk height > 20 mm. This corresponds to a trunk height increase of 80 mm in full scale and correlates to the results obtained by Buchheim et al. [23]. Compared to the results with moving ground, the optimum trunk height is overestimated with a fixed ground.

Figure 4.20:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk height hH, with moving ground and fixed ground

The front lift has not been changed obviously. Therefore, only the rear lift is plotted. The rear lift decreases with increasing trunk height. Moving ground has also little influence on the tendency of the rear lift. The diagrams in Figure 4.20 show comparable trends to the results of the trunk lid slope angle in Figure 4.18. This is due to a similar influence on the wake flow resulting from the variation of the trunk lid slope angle and the trunk height. The downstream flow direction over the trunk lid is changed by the alteration of the trunk rear end shape. Based on the theories mentioned in section 2.1.3 and the research by Wickern et. al. [21], this influence on the wake flow results in an induced drag change. However, the change of the wake flow is different depending on the ground simulation conditions. Therefore, the induced drag applied on the

4 Results of the DrivAer Model

60

vehicle is different, resulting in different geometric optima for the lowest drag at moving ground and fixed ground.

4.5.5

Rear Screen Slant Angle

The results of the rear screen slant angle are plotted in Figure 4.21. The trend of the drag and the rear lift change is similar to the results reported by Ahmed [27]. The drag increases with increasing slant angle and then abruptly decreases for angles > 30°. For slant angles > 35°, an almost constant drag value can be observed. The moving ground shows little influence on the trend of both curves but the magnitude of the changes in drag is different. For the rear lift, the critical angle is reduced by about 2° with moving ground. For angles > 30°, the rear lift decreases. At a slant angle of 32°, there is a difference in rear lift-coefficient of 0.120 between the two ground conditions.

Figure 4.21:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the rear screen slant angle φ, with moving ground and fixed ground

In order to analyze the difference of the flow at the rear screen slant angle, the flow topology in the wake for the two ground simulation techniques is compared. The velocity distribution of the flow in the center plane is plotted in Figure 4.22.

4.5 Parameters at the Vehicle Rear End

Figure 4.22:

61

Comparison of the velocity distribution between fixed ground and moving ground in the center plane (top) and above the roof (bottom) of the DrivAer estate back with a rear screen slant angle of 32°

It can be observed that the separation area in the wake is longitudinally enlarged with moving ground. Compared to fixed ground, the moving ground increases the flow rate under the vehicle. The underbody flow with moving ground maintains more momentum than with fixed ground. Therefore, upwash is formed behind the car and the separation behind the rear screen area is enlarged. The flow speed above the rear roof edge is lower with moving ground compared to the fixed ground. As a result, the static pressure on the roof surface is affected. The pressure distribution on the vehicle base, shown in Figure 4.23, with fixed ground shows lower pressure, which causes the higher rear lift.

4 Results of the DrivAer Model

62

Figure 4.23:

4.6

Comparison of the static pressure distribution on the surface of the DrivAer estate back with the rear screen slant of 32° between fixed ground and moving ground

Underbody Parameters

The parametric investigations in the underbody region of the DrivAer model are presented in this section. The investigated parameters are front underbody slope angle αB, wheel track bS and rear diffuser angle αD.

4.6.1

Geometry Variations at the Vehicle Underbody

The geometric variations of them are schematically illustrated in Figure 4.24. The variation of the front underbody slope angle αB is shown in Figure 4.24 a). The original front underbody slope angle αB is 6.6° and is varied in the range from 0° to 16°. In addition, wheel track bS, as presented in Figure 4.24 b) was varied. For both front and rear wheel track, three variants are investigated. The rear diffuser angle is varied from 0° to 18°, as illustrated in Figure 4.24 c).

4.6 Underbody Parameters

Figure 4.24:

4.6.2

63

Geometry variations at the vehicle underbody, a) front underbody slope angle αB, b) wheel track bS, c) rear diffuser angle αD

Front Underbody Slope Angle

The results of the front underbody slope angle are presented in Figure 4.25 [80]. The drag coefficient is increased with the enlarged slope angle of 8° by 0.005. Compared to the drag increase, as shown in Figure 4.25 (top left), the increase on the front lift is more obvious. The front lift coefficient is increased for more than 100 counts for the same increase of the slope angle, as presented in Figure 4.25 (top left). But the rear lift is reduced of about 50 counts, as shown in Figure 4.25 (bottom right). Despite that, the total lift coefficient is increased of more than 50 counts, as presented in Figure 4.25 (top right). As for the influence of the ground conditions, the trends of both drag and lift curves are not changed. However, the optimal αB for the lowest drag with moving ground simulation is enlarged compared with the curve with fixed ground.

4 Results of the DrivAer Model

64

Figure 4.25:

4.6.3

Drag coefficient change ∆cD (top left), lift change ∆cL (top right), front lift change ∆cLF (bottom left) and rear lift change ∆cLR (bottom right) over the front underbody slope angle αB, with moving ground and fixed ground

Wheel Track

The results of the DrivAer notchback for different wheel tracks are depicted below. The original front and rear wheel track of the DrivAer model in 25 % scale is 381 mm. For each front and rear wheel track, three variations are investigated. The widest wheel track is increased based on the original wheel track for 5 mm due to the geometric limitation of the wheel house width. The smallest variation is reduced by 10 mm. The drag coefficients of the 9 combinations of the front and rear wheel tracks are presented in Figure 4.26.

4.6 Underbody Parameters

Figure 4.26:

65

The measured drag coefficient cD of the DrivAer notchback with different front- and rear wheel track combinations (bSF and bSR), with moving ground simulation (top) and fixed ground (bottom)

The diagram in Figure 4.26 on the top illustrates the results with moving ground simulation while the diagram on the bottom presents the results with fixed ground. For both ground simulation techniques, the results imply a reduced drag coefficient with narrower wheel tracks, the drag change are similar. With fixed ground, similar drag decrease can be observed with a reduction on both front and rear wheel track. However, with moving ground simulation, the magnitude of drag reduction by narrowing wheel tracks is larger than that with fixed ground.

4 Results of the DrivAer Model

66

In order to analyze the difference on the drag between the moving ground and fixed ground simulation with those wheel track variations, ∆cD (moving ground – fixed ground) is plotted in Figure 4.27.

Figure 4.27:

The drag difference ∆cD (moving ground – fixed ground) of the DrivAer notchback with different front- and rear wheel track combinations (bSF and bSR)

The results indicate that except for the case with both widened front and rear wheel track, lower drag coefficients are measured with moving ground simulation. The variation of the front wheel track has a more obvious impact on the drag difference than the variation of the rear wheel track. Especially with the smaller front wheel track of 371 mm, the measured drag coefficients with moving ground simulation are lower than with fixed ground for about 0.005.

4.6.4

Rear Diffuser Angle

For the study on the rear diffuser angle, variations from 0° to 6° were tested in the MWK. Due to the geometric limitations of the hardware model, larger diffuser angles could only be investigated with numerical simulation. For the MWK tests, some diffuser add-on parts were designed and manufactured by Rapid Prototyping. An undertray panel, shown in Figure 4.28, was designed to generate smooth flow under the diffuser. The diffuser angle can be varied

4.6 Underbody Parameters

67

with interchangeable wedge parts in a range from 0° to 6°. The maximum angle is limited by the original diffuser angle of the DrivAer.

Figure 4.28:

CAD details of the diffuser add-on parts under the DrivAer

Figure 4.29 shows the drag change for different diffuser angles. Good agreement between the numerical results and the experimental results can be observed.

Figure 4.29:

Comparison of the drag value with different diffuser angles between fixed ground and moving ground for the DrivAer notchback (left) and the estate back (right)

68

4 Results of the DrivAer Model

Different optimum diffuser angles for the lowest drag are identified between the notchback and the estate back. The optimum angle for the notchback is larger than that of the estate back. Moreover, compared to the case with moving ground, the optimum angle is overestimated with fixed ground for both rear end shapes. Due to the little change on the front lift, only the rear lift change for the different diffuser angles is plotted in Figure 4.30. The optimum diffuser angle of the lowest rear lift depends again on the rear end shape. With the notchback, a larger diffuser angle is required to reach the lowest rear lift compared to the estate back. With moving ground, the optimum angle for the notchback is reduced. However, for the rear lift of the estate back, moving ground shows only a small influence on the optimum angle.

Figure 4.30:

Comparison of the rear lift value with different diffuser angles between fixed ground and moving ground for the DrivAer notchback (left) and the estate back (right)

To analyse the reason for the reduced optimal diffuser angle caused by the moving ground, the differences in the wake structure of the notchback are compared. In Figure 4.31 the isosurface of cp,total ≤ 0 is plotted to identify regions where losses occur in the flow.

4.7 Attitude Parameters

Figure 4.31:

69

Comparison of the isosurface of cp,total ≤ 0 in the wake of the DrivAer notchback between fixed ground and moving ground with the rear diffuser angle of 12°

It can be observed that the pressure loss area behind the stationary wheels (left) is larger than that of the rotating wheels in the moving ground case (right). This larger wake, obstructs the underbody flow at the diffuser. Therefore, a larger diffuser angle is needed to achieve the same effect. This corresponds to the findings of Wäschle [54].

4.7

Attitude Parameters

The investigated attitude parameters on the 25 % DrivAer include ride height and pitch angle. The variation of the parameters and their results are elucidated in the following section.

4.7.1

Variations of the Attitude Parameters

The variations of the two attitude parameters are illustrated in Figure 4.32. The ride height e is measured from the distance between the lowest point of the underfloor and the ground, as shown in Figure 4.32 a). The ride height is varied from 16 mm to 56 mm in the simulations. The basic ride height of the 25 % DrivAer model is 36 mm. In the MWK tests, the ride height can be varied from 32 mm to 42 mm due to the geometric limitation of the hardware model.

4 Results of the DrivAer Model

70

Figure 4.32:

Attitude parameters a) ride height e, b) pitch angle αA

The pitch angle is adjusted around the center of the wheelbase, as presented in Figure 4.32 b). For the simulations, the pitch angle is varied in the range from -2° to +2°. But for the MWK tests, the range is limited from -0.66° to +0.66° because of the limited adjustment of the ride height.

4.7.2

Ride Height

With a vehicle length for 1.153 m of the 25 % DrivAer model and the kinematic viscosity of 1.51×10-5 m²/s, the boundary layer thickness at the rear underbody can be approximately estimated by Eq. 2.3, which is about 55 mm and larger than the baseline ride height. However, the boundary layer grows on both the underbody and the ground with fixed ground simulation. The flow velocity in the underbody region is much lower than in the case with moving ground simulation. The drag and the lift changes of the DrivAer notchback over different ride height are presented in Figure 4.33. Good agreement between the numerical results and the experimental results can be observed. The drag coefficient increases continually with the ride height. The lift coefficient is first reduced and

4.7 Attitude Parameters

71

again increased with the normalized ride height e/h larger than 0.13. The two ground simulation conditions show the same trend on the drag and lift changes.

Figure 4.33:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the normalized ride height e/h, with moving ground and fixed ground

Despite the similar development of the drag and the lift change with the two ground conditions, obvious relative differences can be observed with the normalized ride height smaller than 0.10. Compared with the results with moving ground, the drag coefficient drops more obviously with fixed ground when the ride height is reduced. The boundary layers of the underbody and the fixed ground begins to block the underbody flow. The flow rate in the underbody region decreases obviously. Therefore, obvious difference of the drag results between the two ground simulations can be observed with small ride heights. The results of the DrivAer estate back are similar to the notchback.

4 Results of the DrivAer Model

72 4.7.3

Pitch Angle

The drag and the lift change for different pitch angles of the DrivAer notchback are presented in Figure 4.34. The MWK test results show again a good agreement with the CFD results. The drag and the lift coefficient increase with the enlarged pitch angle. Every one-degree variation on the pitch angle corresponds to about 0.01 drag coefficient change. For the lift coefficient, the same variation interval causes value change of more than 0.05.

Figure 4.34:

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the pitch angle αA, with moving ground and fixed ground

With both ground simulation techniques, the trends of the curves remain the same. However, the increase on the drag coefficient with a pitch angle of +2° under fixed ground condition is larger than that with moving ground simulation. For the total lift coefficient, the value with moving ground shows a larger drop than the value with fixed ground with the -2° pitch angle. Therefore, the moving ground simulation has obvious influence on the change of the drag and the lift when the pitch angle varies.

4.8 Influence on the Cooling Air Flow

4.8

73

Influence on the Cooling Air Flow

The influence of the ground simulation on the cooling air flow is depicted in the following section. The cooling air flow outlet of the 25 % DrivAer model is schematically illustrated in Figure 4.35. The numerical result revealed that approaximate 50 % of the cooling air flow is exits through the bottom of the engine compartment. This part of the air flow merges into the underbody flow. The other 50 % exit the engine bay through the wheel houses.

Figure 4.35:

Schematic 3 cooling air flow outlets of the DrviAer, illustrated with the blue arrows

It was proved in the previous sections that the CFD results are in good agreement with the MWK results. Therefore, the MWK tests for comparing the difference between open and closed cooling of the DrivAer were carried out on three rear end variations due to the higher efficiency. Because the CFD-simulations with open cooling cost much langer calculation time. The cooling drag coefficient, which is defined as ∆cD, w. cooling – w/o. cooling for the three rear ends is presented in Figure 4.36. The variations of the rear end have little influence on the cooling drag, which accounts for a value of about 0.012. The ground simulation shows also little impact on the cooling drag.

74

Figure 4.36:

4 Results of the DrivAer Model

Experimental results of the drag coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends

The front- and rear lift changes of the 25 % DrivAer resulting from the cooling system are presented in Figure 4.37 and Figure 4.38. The front lift coefficient is increased because half of the cooling air flow is discharged straight downwards out of the engine compartment. As illustrated in Figure 4.37, the rear end shapes and the ground simulation conditions have little impact on the front lift change.

Figure 4.37:

Experimental results of the front lift coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends

The cooling air flow from the engine compartment is discharged downwards at the end of the underbody capsule. This flow is merged into the underbody

4.9 Conclusions

75

flow, which results in an impulse upwards. As a result, the front lift is increased and induces a positive pitching moment. Besides, the flow momentum under the rear underfloor is increased. Correspondingly, the static pressure is reduced, which results in the reduced rear lift.

Figure 4.38:

Experimental results of the rear lift coefficient difference resulted from the cooling system of the 25 % DrivAer with three rear ends

Different rear end shapes of the DrivAer have small influence on the rear lift change. However, with moving ground simulation a reduced rear lift due to the cooling flow can be observed.

4.9

Conclusions

In Section 4.1, the baseline results of the DrivAer notchback and estate back are presented. A good agreement between the CFD- and the MWK-results can be observed. In addition, the influence of the moving ground simulation on the DrivAer baseline is depicted. The total lift of both notchback and estate back models is reduced due to the larger flow momentum and lower static pressure at underbody. However, the drag of the two rear ends changes differently. The notchback shows a reduced drag while the estate back has an increased drag with moving ground simulation. The parametric investigations on the DrivAer are presented in Section 4.2 4.7, which deal with the geometric parameters from the vehicle front to the

76

4 Results of the DrivAer Model

attitude of the car body. The results indicate that moving ground simulation has influences on the optimums of the geometric parameters in the vehicle rear end and underbody. The optimum trunk lid slope angle and trunk height of the drag is overestimated with the fixed ground. Similar for the optimum rear screen slant angle for rear lift, which is also overestimated with the fixed ground. The optimum rear diffuser angle depends on the rear end shapes. To achieve the lowest drag and rear lift, the notchback requires a smaller diffuser angle than the estate back. The moving ground simulation reduces the optimum diffuser angle. It can be concluded that different optima caused by moving ground simulation appear by the variation on the parameters at rear end and underbody regions. This nature indicates that the interaction between the wake and the underbody flow plays a vital role. The results in section 4.8 indicate that moving ground simulation has little influence on the cooling drag of the DrivAer with the three rear ends. However, the rear lift caused by the cooling system is reduced with moving ground simulation.

5 Statistical Analysis of the Parameters The sensitivity of the DrivAer aerodynamics forces to geometric parameters in combination with the influence of ground simulations were investigated by means of statistical analysis. In addition, the interaction between some geometric parameters was also studied. The results are depicted in the following sections.

5.1

Sensitivity Rating of the Parameters

The parametric investigations mentioned in Chapter 4 were performed with OFAT experiments. The responses of the parameter variation are the drag and the lift coefficient change. The investigated geometric parameters of the 25 % DrivAer in Chapter 4 are sorted into two types, which are the length-parameters and the angle-parameters. In order to evaluate the sensitivity of the responses to the parameter changes, approximate partial derivatives were calculated. Because not all the coefficient changes in Chapter 4 show linear behaviour. The approximate partial derivative was defined as the difference of the maximum and minimum coefficients (cX, max – cX, min) divided by the dimensionless variation of the parameter ∆var./∆var.max, where ∆var. is difference between the geometric parameter levels corresponding to the two coefficients; ∆var. max is the maximal investigated range of the geometric parameter. This value represents the coefficient change slope per unit length or angle change of each geometric parameter, so that the sensitivity of the aerodynamic coefficient to the parameters change can be rated. With this method, the drag and lift response to different geometric parameters under the two ground simulation conditions can be compared. The sensitivity of the drag change to all the investigated parameters with fixed ground is presented in Figure 5.1. The data was processed with the nondimensionalization mentioned above. © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_5

78

Figure 5.1:

5 Statistical Analysis of the Parameters

Sensitivity ranking of the drag change to the investigated parameters with fixed ground

The variations on pitch angle, camber and ride height have the most obvious impact on the drag coefficient change. The most parameters of the vehicle rear end and the underbody rank thereafter. The parameters of the vehicle front rank the last. The pitch angle, the ride height and the camber are the parameters for the entire vehicle level. Their impact is more dominant compared with the variations of other geometric parameters which belong to the vehicle component level. The sensitivity ranking with moving ground simulation is illustrated in Figure 5.2. The variation on pitch angle, camber and ride height has still the most obvious impact on the drag coefficient change. With moving ground simulation, the drag change is more sensitive to the variation on wheel track compared to the case with fixed ground. The parameters of vehicle rear end and underbody rank still thereafter. But some parameters such as trunk height,

5.1 Sensitivity Rating of the Parameters

79

trunk lid slope angle and diffuser angle of the estate back have more dominant influences on the drag change compared to the cases with fixed ground. The variations of the most parameters at vehicle front still have less effect on the drag change compared to the parameters at vehicle rear end.

Figure 5.2:

Sensitivity ranking of the drag change to the investigated parameters with moving ground simulation

Similar to the ranking of the drag change, the lift-coefficient-responses to the variation of different parameters with fixed ground are ranked in Figure 5.3. The variation of pictch angle still has the most dominant effect on the lift change. Thereafter rank the parameters at the vehicle rear end and underbody, such as rear screen angle of the estate back, ride height and diffuser angle. Different from the ranking for the drag change, the variations of the cabin shape parameters including camber and roof curvature have much smaller effect on the lift change. However, the lift change becomes more sensitive to the variation of front underbody slope angle. But other parameters at the vehicle

80

5 Statistical Analysis of the Parameters

front such as front windscreen slant angle and engine hood height still have a small effect on the lift change.

Figure 5.3:

Sensitivity ranking of the lift change to different parameters with fixed ground

With moving ground simulation, the ranking of these parameters (illustrated in Figure 5.4) remains almost the same as that with fixed ground when sorted by the locations on the vehicle. The lift change is sensitive to the most parameters at the vehicle rear end and underbody while the parameters at the vehicle cabin and vehicle front have small effect on the lift change.

5.1 Sensitivity Rating of the Parameters

Figure 5.4:

81

Sensitivity ranking of the lift change to different parameters with moving ground simulation

From the sensitivity analysis above, it can be indicated that the variations of pitch angle, camber and ride height of the 25 % DrivAer has the most obvious effect on the drag change. Because these three parameters belong to the entire vehicle level and modifications of them will change the attitude or the basic shape of the entire vehicle body. The switch of the two ground simulation techniques has not changed their order in the sensitivity ranking. As for the geometric parameters of the vehicle component level, the parameters at vehicle rear end such as rear screen angle, diffuser angle and trunk height. have the largest effect on the drag change. With moving ground simulation, the ranking of these parameters has been changed compared to the fixed ground condition. The effect of rear screen angle, diffuser angle and trunk length on the drag change has been reduced compared to the fixed ground. For the lift change, the parameters at vehicle rear end and underbody have also larger influence than the parameters at cabin and vehicle front.

5 Statistical Analysis of the Parameters

82

5.2

Interaction between the Parameters

Based on the sensitivity rating of the geometric parameters of the 25 % DrivAer, the variation on the parameters at the vehicle rear end and the underbody has high sensitivity to the drag and the lift change. In addition, according to the OFAT investigations in Section 4, different optima can be found for the two different ground simulation techniques on the variation of the trunk lid slope angle, trunk height, the rear screen slant angle and the diffuser angle. The variation of those parameters changes the downstream direction of the wake flow, which results consequently in an induced drag change. Due to the two different ground simulations, the interaction between the wake flow and the underbody flow changes. Consequently, the induced drag change is different with the two ground simulations. But the parametric investigations in the above section were carried out with OFAT method. In order to investigate the interaction between the critical parameters at the vehicle rear end and the underbody, combined parameter studies were performed. The results are presented in the following section. As analyzed in Section 4.5.4, the variation of the trunk lid slope angle and the trunk height has similar results changes. Therefore, on the DrivAer notchback, the two parameters the trunk height and the rear diffuser angle were investigated in combination, as illustrated in Figure 5.5 (left). For the estate back, the rear screen angle and the diffuser angle were investigated in combined, as presented in Figure 5.5 (right).

Figure 5.5:

Combined variation of geometric parameters, variation of the trunk height hH and the diffuser angle αD on the notchback (left), variation of the rear screen angle and the diffuser on the estate back (right)

5.2 Interaction between the Parameters

83

Therefore, two-factor experimental spaces were built for the notchback and the estate back. Each parameter represents one factor. The variations of each parameter correspond to the levels of each factor. The results of these combined 2-factor variations are able to predict the interaction between the two factors by means of Response Surface Models (RSM). In order to reduce the simulation costs, the uniform latin hypercube (ULH) sampling method was applied to determine the variation. The ULH is a stochastic DOE algorithm which generates random numbers conforming to a uniform distribution [81]. These combined 2-parameter variations (illustrated in Figure 5.5) were simulated by PowerFlow. The drag and lift coefficient of these variations were used to train the response surface with the Kriging method by the statistic programm ModeFrontier. The response surfaces of cD with different diffuser angle and trunk height are presented in Figure 5.6. The illustration on the top presented the results with moving ground simulation while the illustration at the bottom represents the results with fixed ground. The black points are the seeded designs for the training of the response surface. The mean absolute error is 1.65×10 -16, which proves a good prediction of the response surface. The mean absolute errors of the other response surfaces from Figure 5.7 - Figure 5.9 are on a comparable level. Compared with the fixed ground, the response surface with moving ground shows a smaller region for a low drag coefficient. For each diffuser angle variantion, the drag coefficient drops at first and then increases again with the enlarged trunk height. The baseline configuration (∆hH = 0 mm) has the lowest drag. In case of fixed ground, the drag increase with the enlarged trunk is slower than with moving ground simulation. For each trunk height variantion, the optimal diffuser angle for the lowest drag coefficient is reduced with moving ground simulation compared with fixed ground.

5 Statistical Analysis of the Parameters

84

Moving ground Trunk height ΔhH in mm

+30

cD high

+20

hH

αD

+10 0 -10 -20

low 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD Fixed ground

Trunk height ΔhH in mm

+30

cD

high

+20

+10

0 -10 -20

low 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD

Figure 5.6:

Response surface for the drag coefficient of the DrivAer notchback with delta trunk height ∆hH and diffuser angle αD, with moving ground (top) and fixed ground (bottom)

The transformation of the rear end shape from the notchback to the estate back is equivalent to the variation of the trunk height, where the notchback has a lower trunk and the estate back has an extremely high trunk. For both ground simulation conditions, the optimal diffuser angle for the lowest drag is reduced with the enlarged trunk height. This finding corresponds to the results presented in Section 4.6.4, which indicated that the notchback has a smaller optimal diffuser angle than the estate back.

5.2 Interaction between the Parameters

85

Similar to the analysis on the drag, the interactions between these two geometric parameters on the rear lift with the two ground simulation techniques are depicted in the following. The response surfaces of the rear lift coefficient with different diffuser angle and trunk height are illustrated in Figure 5.7.

Moving ground

Trunk height ΔhH in mm

+30

cLR high

+20

hH

αD

+10 0

-10 -20

low 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD Fixed ground

Trunk height ΔhH in mm

+30

cLR high

+20

+10 0 -10 -20

low 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD

Figure 5.7:

Response surface of the rear lift coefficient of the DrivAer notchback with delta trunk height ∆hH and diffuser angle αD, with moving ground (top) and fixed ground (bottom)

86

5 Statistical Analysis of the Parameters

For each diffuser angle variantion, the trend of the rear lift change is similar. The rear lift is reduced with the increasing trunk height. Moving ground simulation has little impact on the trend. However, for each trunk height variantion, the optimal diffuser angle of the lowerst rear lift is reduced with moving ground simulation. The interactions between the rear screen slant angle and the diffuser angle of the DrivAer estate back on the drag coefficient with two ground simulation conditions are presented in Figure 5.8. For both ground simulation techniques, the vehicle has a high drag coefficient with a critical rear screen angle in the range of 30° - 32°. This critical angle results in an obvious drag increase. With moving ground simulation, this critical angle is 2° smaller than with fixed ground. The rear end shape tends to be squareback when the rear screen slant angle is further enlarged based on the critical angle. Correspondingly, with a smaller screen angle, the rear end of the DrivAer tends to be a fastback. Consequently, a small diffuser angle is required with a large rear screen slant angle for a low drag coefficient. On the contrary, the optimal diffuser angle is enlarged when the rear screen angle is reduced. With a rear screen angle from 36° to 38°, the optimal diffuser angle for the lowerst drag is reduced with moving ground simulation. The drag increases with diffuser angle larger than 6° in case of moving ground simulation. However, the drag of the same vehicle configuration has still the lowest drag with fixed ground. The response surfaces of the rear lift coefficient with the two ground simulation conditions are presented in Figure 5.9. For each diffuser angle variation, the rear lift decreases with the enlarged rear screen angle. With moving ground simulation, a smaller rear screen angle is required to achieve the same rear lift as with fixed ground.

5.2 Interaction between the Parameters

87

ɔ

Rear screen slant angle φ

Rear screen slant angle φ

αD Moving ground 38° cD 36° high 34° 32° 30° 28° 26° 24° low 22° 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD

Fixed ground 38° cD 36° high 34° 32° 30° 28° 26° 24° low 22° 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD

Figure 5.8:

Response surface of the drag coefficient of the DrivAer estate back with different rear screen slant angle φ and diffuser angle αD, with moving ground (top) and fixed ground (bottom)

5 Statistical Analysis of the Parameters

88

ɔ

αD

Rear screen slant angle φ

Moving ground 38° cLR 36° high 34° 32° 30° 28° 26° 24° low 22° 16° 18° 14° 0° 2° 4° 6° 8° 10° 12° Diffuser angle αD

Rear screen slant angle φ

Fixed ground 38° 36° 34° 32° 30° 28° 26° 24° 22°

Figure 5.9:

cLR high

low 0° 2° 4° 6° 8° 10° 12° 14° 16° 18° Diffuser angle αD

Response surface of the rear lift coefficient of the DrivAer etate back with different rear screen slant angle φ and diffuser sangle αD, with moving ground (top) and fixed ground (bottom)

5.3 Conclusions

5.3

89

Conclusions

A sensitivity analysis of each geometric parameter of the DrivAer model on the drag and lift change was carried out, which derived the sensitivity rating of the parameters. The investigated parameters were sorted in length and angle parameters. For the length parameters, the two most sensitive parameters to the drag change are the camber and the wheel track. The parameters of the rear end shape rank after them. However, the rear end parameters are sensitive to the lift change. As for the angle parameters, both drag and lift changes have sensitive reactions to the parameters at the rear end. The ground simlation has an impact on the sensitivity rankings. The interaction between the diffuser angle and the trunk height of the DrivAer notchback was studied by means of RSM. The response surface of the drag and lift with different combinations of these two parameters presented the optimal range of the parameter variation. For the drag coefficient, this optimal range is reduced with moving ground simulation compared to fixed ground. For the rear lift coefficient, the optimal diffuser angle was reduced by the moving ground simulation at each trunk height variation. On the DrivAer estate back, the interaction between the diffuser angle and the rear screen slant angle was studied. The trend of the drag and rear lift responses to the parameter variations are plotted. For the drag response to the parameter variations, the optimal range of the parameters were changed with moving ground simulation. As for the rear lift response, the optimal diffuser angle was reduced by the moving ground simulation at each rear screen angle variation.

6 Transferability Study on the SUV Model The parametric study on the AeroSUV was carried out with both numerical and experimental methods. The investigated geometric parameters and their results with the two different ground simulation techniques are depicted in the following section.

6.1

Comparison of the Baseline Results between Fixed and Moving Ground Simulation

The baseline geometry in this and the following sections is defined as the basic AeroSUV model with standard closed or open cooling and one of the three basic rear end configurations. The MWK results of the AeroSUV with closedcooling are presented in Table 6.1. Similar to the results of the DrivAer, there exist small differences between the notchback and the fastback. The estate back has a larger drag coefficient than the other two rear ends. The lift coefficient of the estate back is also obviously reduced. Table 6.1:

Experimental results of the AeroSUV model (baseline, closedcooling) with moving ground simulation cD

cLF

cLR

Notchback

0.278

0.037

0.078

Fastback

0.278

0.032

0.099

Estate back

0.305

0.002

0.001

The AeroSUV model with the same configurations were also tested in the MWK with fixed ground. Similar to the comparison between the two ground © The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_6

6 Transferability Study on the SUV Model

92

simulation techniques of the DrivAer, the comparison of the AeroSUV is presented in Figure 6.1. Only the results of the fast back and the estate back are showed because of the similarity between the fast back and the notchback and the popularity of the fastback on the SUV models.

Figure 6.1:

Drag and lift difference (moving ground – fixed ground) of the AeroSUV fastback and estate back with closed cooling

Different to the results of the DrivAer, the drag coefficient of the AeroSUV fastback and estate back are both slightly increased with the moving ground simulation. As for the lift coefficients, the front- and rear lift coefficients of the two rear end variations are reduced with the moving ground simulation, which shows a similar change as for the DrivAer model.

6.2

Investigated Parameters on the AeroSUV Model

As analyzed in the sections above, the most sensitive parameters to the ground simulation of the DrivAer model belong to the rear end and underbody regions. Through the variation of those parameters, different optima were observed with the two different ground simulation techniques. Consequently, in order to study the transferability of the findings derived from the DrivAer on the SUV model, four geometric parameters were investigated on the AeroSUV, as illustrated in Figure 6.2 a) – d), which are the trunk lid slope angle αH, the trunk height hH, the rear screen slant angle φ and the rear diffuser angle αD. In addition to those, due to the enlarged baseline ride height of the AeroSUV, the

6.2 Investigated Parameters on the AeroSUV Model

93

results of the variation on the ride height of the AeroSUV can be different to the results of the DrivAer. Therefore, the ride height of the AeroSUV (as shown in Figure 6.2 e)) was also varied and tested in MWK.

Figure 6.2:

Investigated geometric parameters on the AeroSUV-model, a) trunk lid slope angle αH, b) trunk height hH, c) rear screen slant angle φ, d) rear diffuser angle αD, e) ride height e

6 Transferability Study on the SUV Model

94

6.3

Results of the Parametric Study

The results of the parametric investigations on the AeroSUV are presented in the following sub-sections. Similar to the diagrams in Section 4, only relative values are presented in order to compare the difference of the trends between moving ground and fixed ground. Consequently, all the results were normalized with the results of the baseline configuration.

6.3.1

Trunk Lid Slope Angle

The results of the AeroSUV notchback with different trunk lid slope angles and the two ground conditions are plotted in Figure 6.3. The left diagram presents the drag change ∆cD with different trunk lid slope angle ∆αH. Obvious change on the lift exists at the rear part of the vehicle, therefore only the rear lift change ∆cLR is plotted in the right diagram.

Figure 6.3:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH of the AeroSUV notchback, with moving ground and fixed ground

Comparing the differences between moving ground and fixed ground, the trends of the drag and the lift changes are similar. Different to the results of the DrivAer, the optimal trunk lid slope angle for the drag coefficient remains the same for the two ground simulations. With moving ground simulation, the optimal trunk lid slope angle of the AeroSUV is also +5° based on the baseline. However, for the DrivAer model, the baseline trunk lid slope angle has already the lowest cD. The rear lift change of the AeroSUV notchback with different

6.3 Results of the Parametric Study

95

trunk lid slope angle shows a similar behavior as the results of the DrivAer notchback. The drag coefficient curve for the trunk lid angle change has less sensitivity to the two ground simulations due to the enlarged ride height. The interaction between the wake and the underbody flow is weakened.

6.3.2

Trunk Height

The results of the trunk height on the AeroSUV notchback are illustrated in Figure 6.4. The drag change is presented in the left diagram. The left diagram shows the rear lift change.

Figure 6.4:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the trunk lid slope angle αH of the AeroSUV notchback, with moving ground and fixed ground

The curves of the drag and the lift change for the AeroSUV notchback show similar trends with the two ground simulations as well as the same trunk height of the minimum drag, whereas different optimal trunk heights are shown in the results of the DrivAer (as depicted in section 4.5.4). Therefore, the alteration of the ground simulation techniques has little impact on the drag change of the AeroSUV. In addition, comparing the drag curves of the AeroSUV and the DrivAer, the relative optimal trunk height of the AeroSUV is 10 mm larger than the optimal relative trunk height of the DrivAer. As for the rear lift change, the AeroSUV

6 Transferability Study on the SUV Model

96

shows the same behavior as the DrivAer. The rear lift is reduced with the increasing trunk height. Moving ground simulation has also little impact on the rear lift trend.

6.3.3

Rear Screen Slant Angle

The results of the rear screen slant angle on the AeroSUV estate back are depicted in the following section. Similar to the diagrams of the DrivAer, the drag and rear lift changes with different rear screen angle are presented in Figure 6.5. The diagrams show the similar trends of curves with two ground simulations. However, obvious difference on the drag change can be observed at the rear screen angle of 34°, as shown in Figure 6.5 (left). The drag coefficient of the vehicle simulated with moving ground simulation drops for about 0.015 from 32° to 34°. But with the same rear screen angle varation, the result with fixed ground shows only small reduction for about 0.002. After that, obvious drag reduction appears. Therefore, the critical rear screen angle for the drag drop is reduced with the moving ground simulation. This difference was not obviously observed in the results of the DrivAer estate back.

Figure 6.5:

Drag coefficient change ∆cD (left) and rear lift change ∆cLR (right) over the rear screen slant angle φ of the AeroSUV estate back, with moving ground and fixed ground

For the rear lift of the AeroSUV estate back, a similar critical rear screen angle for the rear lift drop can be found. With moving ground simulation, this critical angle turns out to be 33°. With a further enlarged angle, the rear lift of the vehicle is quickly reduced. Compared with the results with fixed ground, the critical angle is also reduced by the moving ground simulation.

6.3 Results of the Parametric Study 6.3.4

97

Rear Diffuser Angle

The results of diffent rear diffuser angles of the AeroSUV fastback and estate back are presented in the following section. Figure 6.6 shows the drag change with the diffuser angle of the fastback (left) and the estate back (right).

Figure 6.6:

Comparison of the drag value with different diffuser angles between fixed ground and moving ground for the AeroSUV fastback (left) and the estate back (right)

Different to the results of the DrivAer, the drag coefficient change of the AeroSUV is less sensitive to the diffuser angle variation. As described in Section 2.1.2, the ground effect is less effective with the higher ride height of the AeroSUV. But different positions as well as different magnitude of drag optimum can also be observed for the two ground conditions on the AeroSUV, which is similar to the results of the DrivAer. The optimal diffuser angle is reduced with moving ground simulation compared to fixed ground. However, the results of the AeroSUV estate back with moving ground simulation show a significantly different trend to the results with fixed ground. The drag of the AeroSUV estate back with moving ground simulation increases continuiously with the diffuser angle, which behaves differently as the DrivAer. With fixed ground, the drag is reduced first and increased after a minimum at 2° with the enlarged diffuser angle. The trend of the curve is changed by moving ground simulation.

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98

As for the rear lift change curves, as presented in Figure 6.7, the results with moving ground simulation and fixed ground show the same trend.

Figure 6.7:

Comparison of the rear lift value with different diffuser angles between fixed ground and moving ground for the AeroSUV fastback (left) and the estate back (right)

Different to the results of the DrivAer, no obvious change of the optimal diffuser angle for the lowest rear lift can be observed. The influences of wheel wake are weackened because of the larger ride height of the AeroSUV.

6.3.5

Ride Height

In addition to the critical geometric parameters at the rear end, the ride height of the AeroSUV was investigated in the MWK. The results are discussed below. Figure 6.8 presents the drag and lift change for different dimensionless ride heights e/h. The drag coefficient increases with the enlarged ride height and shows the same increasing trend under both ground simulation conditions, as presented in Figure 6.8 (left). These drag curves are similar to those of the DrivAer model. Therefore, the switch from fixed ground to moving ground simulation has little impact on the drag when varing the ride height on the AeroSUV. However, different ground condition has influence on the total lift

6.4 Influence on the Cooling Air Flow

99

change. As presented in Figure 6.8 (right), the lift remains almost constant with moving ground simulation when the ride height increases. But under the fixed ground condition, the lift is first reduced and then remains constant with the increasing ride height. This drop of the lift with fixed ground may result from the complement of flow momentum in the underbody region, when the ground clearance exceeds the thickness of the boundary layers of the ground and the underfloor.

Figure 6.8:

6.4

Drag coefficient change ∆cD (left) and lift change ∆cL (right) over the normalized ride height e/h of the AeroSUV estate back, with moving ground and fixed ground

Influence on the Cooling Air Flow

The impact of the ground simulation on the cooling air flow of the AeroSUV is also investigated with experiemental method. The results are presented in the following section. The drag coefficient differences resulting from the cooling air flow of the 25 % AeroSUV with moving ground simulation and fixed ground are presented in Figure 6.9. Due to the modified air intake duct of the cooling system on the

100

6 Transferability Study on the SUV Model

AeroSUV [11], the cooling drag coefficient either with fixed ground or with moving ground is lower than 0.010 which is smaller than that of the DrivAer. The dfferent rear end shapes have only little impact on the cooling drag.

Figure 6.9:

Experimental results of the drag coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends

Compared with the results tested with fixed ground, the cooling drag coefficient with moving ground is about 0.003 smaller for the notchback and the fastback. With the estate back, the measured cooling drag coefficient with moving ground simulation is slightly larger than the value measured with fixed ground. For the AeroSUV model, the two ground simulation techniques result larger difference on the cooling drag compared to the DrivAer. The main cause is because of the different design of the air intake duct and wheel houses. The front lift difference of the AeroSUV resulting from the cooling air flow with the two ground simulation techniques is presented in Figure 6.10. Similar to the DrivAer model, the front lift is increased. According to the simulation results [11], 40 % of the entire cooling air flows downwards passing the engine and the gear box. The remaining 60 % of the cooling air exits through the opening in each wheel house. Comparing the two ground simulations, the front lift increase with moving ground simulation is less than with fixed ground. The rear end shape shows little influence on the front lift change.

6.4 Influence on the Cooling Air Flow

Figure 6.10:

101

Experimental results of the front lift coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends

Figure 6.11 shows the reduced rear lift which results from the cooling air flow. Similar to the DrivAer, the cooling air flow of the AeroSUV in the engine compartment is streamed out downwards at the end of the underbody capsule. Then, this flow is merged into the underbody flow resulting in an impulse upwards. As a result, the front lift of the vehicle is increased and induces a positive pitch moment. Consequently, the rear lift is reduced.

Figure 6.11:

Experimental results of the rear lift coefficient difference resulted from the cooling system of the 25 % AeroSUV with three rear ends

Similar to the results of the DrivAer, different rear end shapes of the AeroSUV have small influence on the rear lift change. However, a lower rear lift resulted by the cooling flow can be observed with moving ground simulation.

6 Transferability Study on the SUV Model

102

6.5

Conclusions

The transferability of the findings on the 25 % AeroSUV is investigated. First, the baseline model with moving ground and fixed ground is presented. The aerodynamic characteristics of the three rear ends can be transferred on the AeroSUV model, whereas the drag and lift coefficients of the notchback and fastback are similar. In addition, the influence of the moving ground simulation on the AeroSUV baseline is depicted. Similar to the DrivAer, the lift of both fastback and estate back models is reduced. However, the drag coefficients of the AeroSUV with these two rear ends are increased, which behave differently as the DrivAer. In addition, the results of the critical parameters at rear end of the AeroSUV are depicted. The altering on the optimal variations resulting from different ground simulations does not appear on the variation of the trunk lid slope angle and the trunk height. The main reason is because of the enlarged ride height, which reduces the interaction between the underbody flow and the wake. But the change of the critical rear screen angle for the drag and lift drop can still be observed on the AeroSUV. As for the rear diffuser angle on the AeroSUV, the results of the drag change with fixed ground show similar trend as that of the DrivAer. But with moving ground simulation, the drag coefficient of the AeroSUV estate back is increased continuiously with the enlarged diffuser angle. The two ground simulation techniques have little influence on the trends of the rear lift changes. In addition, the results of the ride height are presented. Obvious difference on the trend of the lift change can be observed when the ride height is reduced from the baseline value. Finally, the influence of the moving ground simulation on the cooling air flow is investigated. The results indicate larger differences on the cooling drag and lift compared with the DrivAer.

7 Overall Conclusions In the present work, a series of systematic investigations on geometric parameters of two types of modern vehicle models were carried out with respect to ground simulation, so that the historic results of the parametric studies could be reviewed with the state-of-the-art moving ground simulation technique. The research was performed by means of both CFD simulations and model scale testing. The numerical and experimental results show a good agreement. The One factor at a time (OFAT) parametric study was firstly carried out on the 25 % DrivAer model, which can represent a typical mid-class car with notchback, fastback and estate back rear ends. The reason for the opposite drag change on the notchback and the estate back due to the moving ground simulation is depicted: the wake direction of both rear ends is deflected upwards with moving ground simulation. Due to the different initial wake direction of the two rear ends, the extra upwards deflection of the wake caused by the moving ground simulation has an opposite effect on the induced drag of the vehicle. As a result, the notchback and the fastback show a reduced drag while the estate back has an increased drag with moving ground simulation. The lift is reduced by the moving ground simulation due to the larger flow momentum and lower static pressure at underbody. In the process of the parametric investigations on the DrivAer model, the parameters, by which ground simulation causes difference, were figured out. The correlations between the geometric variations and the results are reviewed with the moving ground simulation. The results indicate that moving ground simulation has influences on the optimums of the geometric parameters in the vehicle rear end and underbody regions. The detailed findings from the DrivAer are listed as the following: ◼

The optimal trunk lid slope angle and trunk height of the drag is overestimated with the fixed ground.

◼

The optimal rear screen slant angle of the rear lift is overestimated with the fixed ground.

◼

The optimum rear diffuser angle depends on the rear end shapes. To achieve the lowest drag and rear lift, the estate back requires a smaller

© The Author(s), under exclusive license to Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021 C. Zhang, Aerodynamic Study on the Vehicle Shape Parameters with Respect to Ground Simulation, Wissenschaftliche Reihe Fahrzeugtechnik Universität Stuttgart, https://doi.org/10.1007/978-3-658-33439-0_7

104

7 Overall Conclusions diffuser angle than the notchback. The moving ground simulation reduces the optimum diffuser angle.

The reason to the findings above can also be explained by the induced drag theory resulted from the wake deflection. The vehicle body works as an airfoil and applies force on the flow to deflect its direction. The variation on the vehicle rear end shape, e.g. trunk lid slope angle, trunk height and rear screen angle, change the downstream direction in the wake. Meanwhile, this affects the x- and z-components of the reacting force from the flow applied on the vehicle, which are counted as induced drag and lift change. By applying the moving ground simulation technique, the properties of the underbody flow and the wake of the wheels are changed by the enlarged flow rate and the rotating wheels. This effect can also cause an upwards deflection of the wake flow. Therefore, as the x- and z-components of the reacting force from the flow, the induced drag and lift are also changed which appears as a displacement of the optima on the parameters by the switch of the two ground simulation techniques. A statistical analysis was performed on the investigated parameters of the DrivAer. Varing the ride height and the pitch angle changed the drag and lift of the DrivAer most effectively because the variation of these two parameters changes the entire vehicle attitude. Among the other parameters which belong to the component level, the drag and lift changes were sensitive to the most parameters in the rear end and underbody regions. The switch of the ground simulation techniques changed the sensitivity rating of the parameters at vehicle rear end and underbody for the drag change, which again indicates that the interaction between the wake and the underbody flow plays a vital role. Based on the findings above, the interaction between the geometric parameters in the rear end and underbody regions was studied by means of response surface method (RSM). Two set of 2-factor parametric variations – trunk height versus diffuser angle on the notchback and rear screen angle versus diffuser angle on the estate back – were carried out with the two ground simulation techniques. The response surfaces of the drag and the rear lift coefficient have revealed the correlations between the optimal diffuser angle and rear end shape parameters. In addition to the parametric study on the DrivAer, some transferability investigations on the identified important geometric parameters were carried out on

7 Overall Conclusions

105

the 25 % AeroSUV, which respresents a typical mid-class SUV in the automobile market nowadays. The investigated parameters were covered mainly in rear end and underbody regions, which included trunk lid slope angle, trunk height, rear screen angle, rear diffuser angle and ride height. Compared with the DrivAer model, the AeroSUV has larger ride height, wheel houses and cross-sectional area. Consequently, different findings were derived as the following: „

The drag coefficients of the AeroSUV fastback and estate back were both increased with the moving ground simulation.

„

During the variation on the trunk lid slope angle and the trunk height of the AeroSUV notchback, the optimums were not changed by moving ground simulation compared with the results with fixed ground.

„

The displacement of the critical rear screen slant angle for the drag and the lift drop with the two ground simulation conditions could still be observed on the AeroSUV.

„

As for the results of the rear diffuser angle on the AeroSUV estate back, different trend was presented with moving ground simulation. However, the two ground simulation techniques have little influence on the trends of the rear lift changes

The reason that different findings from those of the DrivAer were derived is because of the enlarged ride height, wheels and cross-sectional area of the AeroSUV. The effect of the boundary layer on the fixed ground was weakened on the AeroSUV. Therefore, the difference of the optimums caused by the moving ground simulation was less obvious than that of the DrivAer. The results presented in this research give a decisive complement to the historical investigations. The classical results of the parametric study on the vehicle basic shapes in the textbooks for vehicle aerodynamics could be complemented with the findings of the present research. Especially for the study on parametric investigations at the vehicle rear end, the modern wind tunnel test results may indicate deviated optimums other than the classical wind tunnel test results because of different ground simulation techniques. In the vehicle development phase, potential risks for the false optimization may exist if the aerodynamic parts are developed once for a certain model and then carried over on other derivate models to save the production costs, e.g.

106

7 Overall Conclusions

the optimized rear underbody diffuser for the notchback is not applicable for the estate back. Moreover, moving ground simulation has to be considered if the optimum drag and lift values for different shape parameters is assessed with respect to providing the most efficient vehicle under real world conditions.

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