ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES … · 2019-05-10 · INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA Supervisor Year : Prof. Dr

ÇUKUROVA UNIVERSITY

INSTITUTE OF NATURAL AND APPLIED SCIENCES

PhD THESIS

Cahit GÜRLEK

STUDY OF THE FLOW AROUND A BUS MODEL

DEPARTMENT OF MECHANICAL ENGINEERING

ADANA, 2008

Not: Bu tezde kullanılan özgün ve başka kaynaktan yapılan bildirişlerin, çizelge, şekil ve fotoğrafların kaynak gösterilmeden kullanımı, 5846 sayılı Fikir ve Sanat Eserleri Kanunundaki hükümlere tabidir

ÇUKUROVA ÜNİVERSİTESİ

FEN BİLİMLERİ ENSTİTÜSÜ


Cahit GÜRLEK

DOKTORA TEZİ

MAKİNA MÜHENDİSLİĞİ ANABİLİM DALI

Bu Tez ..../..../2008 Tarihinde Aşağıdaki Jüri Üyeleri Tarafından

Oybirliği/Oyçokluğu İle Kabul Edilmiştir.

İmza: …………………… İmza: …………………………. İmza: …………………………

Prof. Dr. Beşir ŞAHİN Prof. Dr. Recep YURTAL Doç. Dr. Ahmet PINARBAŞI

DANIŞMAN ÜYE ÜYE

İmza: ………………………

İmza: …………………

Doç. Dr. Hüseyin AKILLI Doç. Dr. Muammer ÖZGÖREN

ÜYE ÜYE

Bu Tez Enstitümüz Makina Mühendisliği Anabilim Dalında Hazırlanmıştır.

Kod No:

Prof. Dr. Aziz ERTUNÇ Enstitü Müdürü

Bu çalışma Çukurova Üniversitesi Bilimsel Araştırma Projeleri Birimi tarafından desteklenmiştir. Proje No: MMF2006D32.

I

ABSTRACT

PhD THESIS


Cahit GÜRLEK

DEPARTMENT OF MECHANICAL ENGINEERING INSTITUTE OF NATURAL AND APPLIED SCIENCES

UNIVERSITY OF ÇUKUROVA

Supervisor

Year

: Prof. Dr. Beşir ŞAHİN

: 2008, Pages: 145

Jury : Prof. Dr. Beşir ŞAHİN

Prof. Dr. Recep YURTAL

Doç. Dr. Ahmet PINARBAŞI

Doç. Dr. Hüseyin AKILLI

Doç. Dr. Muammer ÖZGÖREN.

Land transportation is the most widely used passenger and freight transportation in Turkey. It is known that a 10% drag reduction leads to approximately a 5% reduction of the fuel consumption of a bus at a common highway speed. An estimated total savings of $100 million per year can be recognized in Turkey alone for just a 5% reduction in fuel use in intercity passenger transportation by buses. Detailed knowledge of the aerodynamic characteristics of passenger vehicles could lead to find out new solutions to reduce fuel consumption and emissions and improving the vehicle performance and passenger comfort.

In this study, flow structures around a rectangular body and two different bus models are analyzed using both particle image velocimetry (PIV) and flow visualization techniques. Measurements were performed at several planes which were selected to highlight the aerodynamic characteristics of the models. The instantaneous and time-averaged velocity vector maps, vorticity contours, streamline topology and turbulence characteristics of flow fields are presented.

Keywords:

Vehicle aerodynamics, Rectangular body, Flow separation, Particle image velocimetry

II

ÖZ

DOKTORA TEZİ

BİR OTOBÜS MODELİ ETRAFINDAKİ AKIŞIN İNCELENMESİ

Cahit GÜRLEK

ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ

MAKİNA MÜHENDİSLİĞİ ANABİLİM DALI

Danışman Yıl

: Prof. Dr. Beşir ŞAHİN : 2008, Sayfa: 145

Jüri : Prof. Dr. Beşir ŞAHİN

Prof. Dr. Recep YURTAL

Doç. Dr. Ahmet PINARBAŞI

Doç. Dr. Hüseyin AKILLI

Doç. Dr. Muammer ÖZGÖREN Karayolu taşımacılığı Türkiye’de en yaygın kullanılan yolcu ve yük

taşımacılığı şeklidir. Normal otoyol seyir hızında, otobüslerde aerodinamik direncin %10 azaltılmasıyla %5 oranında yakıt tasarrufu sağlandığı bilinmektedir. Türkiye’de sadece otobüslerle yapılan şehirlerarası yolcu taşımacılığında %5’lik yakıt tasarrufuyla yıllık yaklaşık olarak 100 milyon dolarlık bir kazanç sağlanabilmektedir. Araçların aerodinamik yapıları hakkında elde edilen detaylı bilgiler, yakıt tüketiminin, yakıt emisyonlarının azaltılıp, araç performansının ve yolcu konforunun artırılması için yeni çözümlerin bulunmasına öncülük edebilir.

Bu çalışmada bir dikdörtgensel cisim ve farklı iki otobüs modeli etrafındaki akış yapıları, parçacık görüntülemeli hız ölçme yöntemi (PIV) ve boya deneyleri kullanılarak incelenmiştir. Ölçümler, modellerin aerodinamik karakteristiklerini vurgulamak amacıyla seçilen çeşitli eksenlerde gerçekleştirilmiştir. Akış alanlarına ait anlık ve zaman-ortalama hız vektörleri, girdap konturları, akım çizgileri ve türbülans karakteristikleri sunulmuştur.

Anahtar Kelimeler: Araç aerodinamiği, Dikdörtgensel cisim, Akış ayrılması, Parçacık görüntülemeli hız ölçme tekniği

III

ACKNOWLEDGEMENTS

I am truly grateful to my research supervisor, Prof. Dr. Beşir ŞAHİN, for

his invaluable guidance and support throughout the preparation of this thesis.

I would like to express my special thanks to Assoc. Prof. Dr. Hüseyin

AKILLI, for his advices and supports.

I would like to thank all of my research assistant friends at our Mechanical

Engineering Department, especially Ahmet Fertelli for his friendship and support.

Special thanks to Coşkun Özalp for his great cooperation and assistance

during the experimental works.

Last but not the least; I have my deepest appreciation to my beloved family

for their many sacrifices during the development of this research. Without their love,

encouragement, understanding and support, this thesis would not have been possible

to complete.

IV

NOMENCLATURE

H : Height of the model

L : Length of the model

W : Width of the model

Hw : Depth of the water in the channel

ReH : Reynolds number based on model height

u : Streamwise velocity component

urms : Root-mean square value of streamvise velocity component

v : Spanwise velocity component

vrms : Root-mean square value of spanwise velocity component

w : Cross-stream velocity component

wrms : Root-mean square value of cross-stream velocity component

u´v´ : Reynolds stresses

x : Coordinate in streamvise direction

y : Coordinate in spanwise direction

z : Coordinate in cross-stream direction

N : Frame number

U : Free stream velocity

∆t : Time interval

ψ : Instantaneous streamline

<ψ> : Time-averaged streamline

ω : Vorticity magnitude

<ω> : Time-averaged vorticity

∆<ω> : Increment of the time-averaged vorticity

<ωmax> : Maximum vorticity value

<ωmin> : Minimum vorticity value

S : Saddle point

Sab : Saddle point of attachment

F : Foci

V

Na : Node of attachment

Ld : Line of divergence

α :Yaw angle

Su : Spectra of streamwise velocity fluctuations

f : Sampling frequency

CD : Drag coefficient

VI

TABLE OF CONTENTS

PAGE

ABSTRACT.…………………………………………...…………………....... I

ÖZ …………………………………………………………………................. II

ACKNOWLEDGEMENTS………………………………………………...… III

NOMENCLATURE……………………………………………….................. IV

TABLE OF CONTENTS…………………………………………………....... VI

LIST OF FIGURES…………………………………………………………... VIII

1. INTRODUCTION……………………………………………………….. 1

1.1. Bluff Body Aerodynamics………………...................................... 1

1.2. Objectives of Present Investigation………………........................ 3

1.3. Outline of Dissertation ………………........................................... 4

2. LITERATURE SURVEY........................................................................... 5

2.1. Flow structure around a rectangular body...................................... 5

2.2. Flow structure around a ground vehicle......................................... 11

2.2.1. Experimental Studies …………………………………... 11

2.2.2. Numerical Studies ….…………………………………... 22

3. MATERIAL AND METHOD.................................................................... 26

3.1. Measurement Techniques ……………………………………….. 26

3.1.1. Particle Image Velocimetry (PIV)…................................ 26

3.1.1.1. Principles of PIV Technique …...…………… 28

3.1.1.1.(1). Seeding ………………………... 30

3.1.1.1.(2). Illumination .…………………... 31

3.1.1.1.(3). Image Capturing…...…………... 32

3.1.1.1.(4). Correlation Processing …...…… 33

3.1.2. Dye Visualization ……………………………………… 35

3.1.3. Drag Measurements ………………………………......... 36

3.2. Flow System ……………...……………………………………… 38

3.3. Experimental Apparatus and PIV Instrumentation ……………… 40

3.3.1. Experimental Models …………...…................................ 40

3.3.2. PIV Instrumentation …………...….................................. 44

VII

3.4. Post-Processing ………...…………………………...…………… 45

4. RESULTS AND DISCUSSION................................................................. 52

4.1. Flow Around a Rectangular Body ……………………................. 52

4.1.1. Flow Around a Rectangular Body With Zero Yawing

Angle ……………………………………………………

52

4.1.1.1. Time-Averaged Velocity Field ………..……… 54

4.1.1.2. Instantaneous Velocity Field and Flow

Visualization ……………………..………..………

71

4.1.2. Flow Around a Rectangular Body With 10 Degree Yaw

Angle ……........................................................................

80

4.1.2.1. Time-Averaged Velocity Field ………..……… 81

4.1.2.2. Instantaneous Velocity Field and Flow

Visualization ……………………..………..………

81

4.2. Flow Structures Around Bus Model I ……………….................... 87

4.2.1. Time-Averaged Velocity Field …………………...……. 88

4.2.2. Instantaneous Velocity Field …………………......……. 101

4.3. Flow Structures Around Bus Model II ……………....................... 106

4.3.1. Time-Averaged Velocity Field …………………...……. 107

4.3.2. Instantaneous Velocity Field …………………......……. 113

5. CONCLUSIONS AND RECOMMENDATIONS..................................... 119

5.1. Rectangular Body ….………………………………….…………. 119

5.2. Model I ……………………………………………………........... 120

5.3. Model II …………………………………………………………. 121

5.3. Recommendations for future works …..…………………………. 122

REFERENCES…………………………………………………….................. 123

CURRICULUM VITAE……………………………………………………… 132

APPENDIX ….…………………………………………………………......... 133

APPENDIX A: Vorticity Evaluation …….………………………………......... 133

APPENDIX B: Bilinear Interpolation ….…….………………………………... 135

APPENDIX C: Averaged Flow Structure ...….………………………………... 137

APPENDIX D: ADDITIONAL IMAGES ...….…………..………………………... 139

VIII

LIST OF FIGURES PAGE Figure 2.1. Schematic representation of the flow around a wall-mounted

cube ……………………………………………………..……

6

Figure 2.2. Flow around a wall-mounted cube ………………………………… 7

Figure 2.3. History of drag coefficient cD ……………………………….. 12

Figure 2.4. Schematic of the Ahmed model ……...………………..…….. 13

Figure 2.5. Flow structure behind the Ahmed model ……...…………….. 14

Figure 2.6. High-decker bus designed by Fachhochschule,Hamburg …… 18

Figure 2.7. Touring coach design study ……..…………………………... 18

Figure 2.8. The instantaneous streamlines behind a bus model …………. 23

Figure 2.9. Schematic representation of the time-averaged flow behind a

bus model …………………………………………………….

24

Figure 3.1. Basic PIV analysis process …………………………………... 29

Figure 3.2. Seeding particles ……………………….……………………. 30

Figure 3.3. Cross-correlation in PIV …………………………………….. 34

Figure 3.4. Drag measurements in the wind tunnel (Side view) ………… 37

Figure 3.5. Three component balance system and model …...…………… 37

Figure 3.6. Schematic representation of water channel and bus

model-plate arrangement ………..………….………………...

39

Figure 3.7. Schematic representations of the rectangular body…...……… 41

Figure 3.8. Location of the rectangular body in the water channel

(side view)…...………………………………………………..

41

Figure 3.9. Schematic representations of the bus model I………...……… 42

Figure 3.10. Location of the bus model I in the water channel

(side view) ......………………………………………………..

42

Figure 3.11. Schematic representations of the bus model II ….…...……… 43

Figure 3.12. Location of the bus model II in the water channel

(side view) ......………………………………………………..

43

Figure 3.13. Schematic representation of the experimental setup and PIV

system ………………..……………………………………….

47

IX

Figure 3.14. Orientations of laser sheet and camera position for side view

plane ………………………………………………………….

48

Figure 3.15. Orientations of laser sheet and camera position for plan view

planes ……………………………………...…………………

49

Figure 3.16. Orientations of laser sheet and camera position for end view

planes ……………………...…………………...…………….

50

Figure 3.17. Velocity vector map (raw data) of instantaneous flow field in

the wake region of the bus Model II …………………………

51

Figure 3.18. Velocity vector map of the instantaneous flow field in the

wake region of the bus Model II after post-processing ………

51

Figure 4.1.1. PIV measurement planes …………………………………….. 53

Figure 4.1.2.

Patterns of time-averaged velocity vector maps <v>,

streamlines <ψ> and vorticity contours <ω> in the vertical

symmetry plane z=0. Minimum and incremental values of

vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1 …………………

55

Figure 4.1.3. Velocity profiles of the flow in the vertical symmetry plane

z=0 in the wake region. [a] Dimensionless streamwise

velocity component <u/U>, [b] Dimensionless spanwise

velocity component <v/U> …………………………………...

57

Figure 4.1.4. Profiles of turbulence properties in the vertical symmetry

plane z=0 in the wake region. [a] Root mean square of

streamwise velocity fluctuations <urms>/U, [b] spanwise

velocity fluctuations <vrms>/U, [c] Reynolds stress

correlations <u′v′>/U2 ……………………………………….

59

Figure 4.1.5. Contours of streamwise velocity fluctuations <urms>/U,

spanwise velocity fluctuations <vrms>/U, and Reynolds

stress correlations <u′v′>/U2 in the vertical symmetry plane

z=0 in the wake region. Minimum and incremental values of

rms of velocity components are [<urms>/U]min=0.0075,

∆[<urms>/U]=0.0075, [<vrms>/U]min=0.0075,

X

∆[<vrms>/U]=0.0075 and Reynolds stresses correlations are

[<u′v′>/U2]min=±0.00075, ∆[<u′v′>/U2]=0.00075………….

60

Figure 4.1.6. Patterns of time averaged velocity vector maps <v>,

streamlines <ψ> and vorticity contours <ω> in the horizontal

xz-plane for y/H=0.5. Minimum and incremental values of

vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1 …………………..

62

Figure 4.1.7. Velocity profiles of the flow in the horizontal xz-plane for

y/H=0.5 in the wake region. [a] Dimensionless streamwise

velocity component <u/U>, [b] Dimensionless cross-stream

velocity component <w/U> …………………………………..

63

Figure 4.1.8. Profiles of turbulence properties in the horizontal xz-plane

for y/H=0.5 in the wake region. [a] Root mean square of

streamwise velocity fluctuations <urms>/U, [b] cross-stream

velocity fluctuations <wrms>/U, [c] Reynolds stress

correlations <u′w′>/U2 …………………………....................

64

Figure 4.1.9. Contours of streamwise velocity fluctuations <urms>/U, and

Reynolds stress correlations <u′v′>/U2 in the horizontal xz-

plane for y/H=0.5 in the wake region. Minimum and

incremental values of rms of velocity components are

[<urms>/U]min=0.01, ∆[<urms>/U]=0.01, and Reynolds

stresses correlations are [<u′w′>/U2]min=±0.0005,

∆[<u′w′>/U2]=0.0005 ………………………………………..

65

Figure 4.1.10. Patterns of the time averaged velocity vector maps <v> in the

horizontal xz-plane for different y/H levels in the wake

region ………………………………………………………...

68

Figure 4.1.11. Patterns of the time averaged streamlines <ψ> in the


region ………………………………………………………...

69

XI

Figure 4.1.12. Patterns of time averaged vorticity contours <ω>, in the


region. Minimum and incremental values of vorticity are

<ωmin>=±2s-1 and ∆<ω>=2s-1 ………………………...............

70

Figure 4.1.13. Patterns of instantaneous velocity vectors v, streamlines ψ

and vorticity contours ω in the vertical symmetry plane z=0

on the roof of the model. Minimum and incremental values of

vorticity are ωmin=±2s-1 and ∆ω=2s-1 ………………………...

73

Figure 4.1.14. Patterns of instantaneous velocity vectors v, streamlines ψ

and vorticity contours ω, in the vertical symmetry plane z=0

in the wake region. Minimum and incremental values of


74

Figure 4.1.15. Patterns of instantaneous velocity vectors v and

streamlines ψ in the horizontal xz-plane for y/H=0.5 in the

wake region …………………………………………………..

75

Figure 4.1.16. The spectrum of streamwise velocity fluctuations for selected

points downstream of the model ………………………..........

76


points in the horizontal xz-plane for y/H=0.5 in the wake

region ………………………………………………………...

77

Figure 4.1.18. Dye flow visualizations [a] on the model roof in the vertical

symmetry plane z=0. [b] on the lateral vertical side in the

horizontal xz-plane for y/H=0.5 ………………………...........

79

Figure 4.1.19. Dye flow visualization in the vertical symmetry plane z=0 in

the wake region ………………………………………………

79

Figure 4.1.20. Drag versus yaw of different vehicle types ………………….. 80

Figure 4.1.21. Patterns of time averaged streamlines <ψ> and vorticity

contours <ω> in the horizontal xz-plane for y/H=0.5.

Minimum and incremental values of vorticity are

<ωmin>=±4s-1 and ∆<ω>=2s-1 ……………………………….

83

XII

Figure 4.1.22. Patterns of instantaneous streamlines ψ in the horizontal xz-

plane for y/H=0.5 …………………………………………….

84

Figure 4.1.23. Patterns of instantaneous streamlines ψ in the horizontal xz-

plane for y/H=0.5 in the wake region ………………………..

85

Figure 4.1.24. Dye flow visualization on the lateral vertical side in the

horizontal xz-plane for y/H=0.5 ……………………………..

86


Figure 4.2.2. Patterns of time-averaged velocity vector maps <V>,



vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1………………….

89




velocity component <v/U> ………………………………….

91





correlations <u′v′>/U2 ............................................................

92


spanwise velocity fluctuations <vrms>/U, and Reynolds stress

correlations <u′v′>/U2 in the vertical symmetry plane z=0 in

the wake region. Minimum and incremental values of rms of

velocity components are [<urms>/U]min=0.0075,

∆[<urms>/U]=0.0075, [<vrms>/U]min=0.0075,


[<u′v′>/U2]min=±0.00075, ∆[<u′v′>/U2]=0.00075 …………...

93

XIII

Figure 4.2.6. Patterns of time averaged velocity vector maps <V>,

streamlines <ψ> and vorticity contours <ω> in the horizontal

xz-plane for y/H=0.5. Minimum and incremental values of

vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1 …………………..

97

Figure 4.2.7. Velocity profiles of the flow in the horizontal xz-plane for

y/H=0.5 in the wake region. [a] Dimensionless streamwise

velocity component <u/U>, [b] Dimensionless cross-stream

velocity component <w/U> …………………………………..

98

Figure 4.2.8. Profiles of turbulence properties in the horizontal xz-plane

for y/H=0.5 in the wake region. [a] Root mean square of

streamwise velocity fluctuations <urms>/U, [b] cross-stream

velocity fluctuations <wrms>/U, [c] Reynolds stress

correlations <u′w′>/U2 ………………………………………

99



correlations <u′v′>/U2 in the horizontal xz-plane for y/H=0.5

in the wake region. Minimum and incremental values of rms

of velocity components are [<urms>/U]min=0.01,

∆[<urms>/U]=0.01, [<vrms>/U]min=0.01, ∆[<vrms>/U]=0.01 and

Reynolds stresses correlations are [<u′v′>/U2]min=±0.0005,

∆[<u′v′>/U2]=0.0005 …………………………………………

100

Figure 4.2.10. Patterns of instantaneous velocity vectors V, streamlines ψ




103


points in the vertical symmetry plane z=0 in the

wake region …………………………………………………..

104

XIV


points in the horizontal xz-plane for y/H=0.5 in the wake

region ………………………………………………………...

105


Figure 4.3.2. Patterns of time-averaged velocity vector maps <V>,



vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1………………….

108




velocity component <v/U> ………………………………….

109





correlations <u′v′>/U2 ............................................................

111



correlations <u′v′>/U2 in the vertical symmetry plane z=0 in

the wake region. Minimum and incremental values of rms of

velocity components are [<urms>/U]min=0.0075,

∆[<urms>/U]=0.0075, [<vrms>/U]min=0.0075,


[<u′v′>/U2]min=±0.00075, ∆[<u′v′>/U2]=0.00075 …………...

112

Figure 4.3.6. Patterns of time averaged velocity vector maps <V>,

streamlines <ψ> and vorticity contours <ω> in the cross-

planes for x/H=0.23 and x/H=0.53. Minimum and

incremental values of vorticity are <ωmin>=±0.5s-1 and

∆<ω>=0.5s-1 ………………………………………………….

115

XV

Figure 4.3.7. Patterns of instantaneous velocity vectors V, streamlines ψ




116

Figure 4.3.8. Instantaneous velocity field in two cross-planes x/H=0.23 and

x/H=0.53 …………………………………………..................

117


points in the vertical symmetry plane z=0 in the

wake region …………………………………………………..

118

Figure D.1. Patterns of time-averaged velocity vector maps <V> around

rectangular body (a), bus model I (b) and bus model II (c) in

the vertical symmetry plane z=0 ……………………………..

140

Figure D.2. Patterns of time averaged streamlines <ψ> around


the vertical symmetry plane z=0 ………………………..........

141

Figure D.3. Patterns of time-averaged vorticity contours <ω> around


the vertical symmetry plane z=0. Minimum and incremental

values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1 ………...

142

Figure D.4. Patterns of time-averaged velocity vector maps <V> around

rectangular body (a) and bus model I (b) in the horizontal xz-

plane for x/H=0.5 …………………………………………….

143

Figure D.5. Patterns of time averaged streamlines <ψ> around


plane for x/H=0.5 …………………………………………….

144

Figure D.6. Patterns of time-averaged vorticity contours <ω> around


plane for x/H=0.5. Minimum and incremental values of

vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1 ………………......

145

INTRODUCTION Cahit GÜRLEK

1

1. INTRODUCTION

1.1 Bluff Body Aerodynamics

Aerodynamics is the study of a solid body moving through the atmosphere and the

interaction which takes places between the body surfaces and the surrounding air with

varying relative speeds and wind direction. Motor vehicle aerodynamics is a complex

subject because of the interaction between the air flow and the ground, and the complicated

geometrical shapes that are involved. Aerodynamics is important because it affects both

vehicle stability and fuel consumption.

The flow around a vehicle is responsible for its directional stability as well: straight

line stability, dynamic passive steering, and response to crosswind depend on the external

flow field. Further more, the outer flow should be tuned to prevent droplets of rain water from

accumulating on windows and outside mirrors, to keep headlights free of dirt, to reduce wind

noise, to prevent the windshield wipers from lifting off, and to cool the engine’s oil pan, muffler

and brakes, etc. The internal flow has to accommodate the heat losses of the engine. It must

ensure that this wasted heat is carried away under all driving conditions. Finally, another internal

flow system has to provide a comfortable climate inside the passenger compartment. In both

cases the related temperature fields have to be considered as well. All in all, aerodynamics has a

strong influence on the design of a vehicle and requires a good understanding of the flow

around the vehicle including unsteady and turbulent flow phenomena (Hucho, 1998).

As noted by Hucho (1998) road vehicle aerodynamics has specific differentiating

features compared to other aerodynamic problems:

i) Body geometries used for road vehicles are "bluff bodies" in aerodynamic terms.

Drag is primarily due to the pressure distribution on the body, with only a small contribution to

the drag due to skin friction. Road vehicles are characterized by flow separation in the back

of the vehicle and the formation of recirculation regions in the near wake, which in turn

result in a lower pressure on the back surfaces. Hence, the difference between the pressure

acting on the front of the vehicle and on the back increases. The skin friction drag is due to

the viscous shear forces acting on the surfaces of the vehicle. The contribution of pressure


2

drag to the overall drag of a typical ground vehicle is estimated to be between 70 and 90%

depending on the particular design of the vehicle.

ii) Another important differentiating feature of road vehicle aerodynamics is the

complexity and coupled nature of the flow. Many aerodynamic problems can be analyzed in

terms of the flow about several components uncoupled from each other. The performance of

the system is optimized by improving the performance of each component with only small

corrections needed to account for component interaction effects. This is not the case for most

road vehicles which are fully coupled flow systems. For example the flow at the base of the

vehicle is strongly influenced by the flow around the front of the car.

iii) The road surface alters the aerodynamic performance of the vehicles and must be

taken into account.

An important feature of a bluff body is that very strong interactions take place between

viscous and inviscid regions of its flow field. Usually, bluff bodies induce flow separation at

positions where the velocity at the edge of the boundary layer is higher than the free stream

velocity. This results in a high rate of shedding of circulation which in turn leads to a high time-

mean drag which is experienced primarily as a difference in pressure between the windward

and leeward faces of the body. Flow separation from bluff bodies may occur either from sharp

edges or from continuous surfaces. The prediction of separation position from a continuous

surface is particularly difficult because it depends on both the characteristics of the upstream

boundary layer and on the structure of the region of flow just downstream of the body

known as the near wake (Bearman, 1997).

The flow around three-dimensional bluff bodies is characterized by separated shear

layers formed at the top, bottom and side edges of the body. In some complex three-

dimensional bluff bodies, these shear layers may interact with the body or with other shear

layers. The wake of a three-dimensional bluff body is far more complex than that of a two-

dimensional one and is often dominated by streamwise vortices rather than transverse ones.

These vortices originate from various features of the upstream body and may interact with each

other both around the body and in the near wake. The wake behind these bodies exhibits

large recirculation regions and its unsteady nature can affect aerodynamic forces acting on the

body. If the frequency of these forces matches the natural frequency of the body, it can

induce noise and vibrations which could seriously affect the driver's or passengers'


3

comfort (Al-Garni, 2003). Until relatively recently the instantaneous structure of such wake

flows has been very difficult to measure but with the advent of techniques such as PIV much

more detailed information can now be obtained.

1.2 Objectives of Present Investigation

Land transportation is the most widely used passenger and freight

transportation in Turkey and 95% of total of passenger transport performed by road.

It is known that a 10% drag reduction leads to approximately a 5% reduction of the

fuel consumption of a bus at a common highway speed (Hucho 1998). An estimated

total savings of $100 million per year can be recognized in Turkey alone for just a

5% reduction in fuel use in intercity passenger transportation by buses. Detailed

knowledge of the aerodynamic characteristics of passenger vehicles could lead to

find out new solutions to reduce fuel consumption and emissions and improving the

vehicle performance and passenger comfort.

The time-averaged flow around ground vehicles is fairly well known and

understood. In contrast, the instantaneous flow has until recently been unstudied and

still remains unexplored. The aerodynamic properties of the vehicles, such as drag,

lift, stability, wind noise and the accumulation of water and dirt on the surface of the

vehicles are result of transient motions of the flow. Understanding of these processes

could lead to better design of the aerodynamics (Krajnovic and Davidson, 2003).

The validation of turbulence models requires the availability of detailed

experimental data. These quantitative data should cover the most critical flow

regions around a bluff vehicle-shaped body and they should give physical quantities

that can directly be correlated to the results of numerical simulations (Lienhart and

Becker, 2003).

In the present study, flow structure around two different rear end shaped bus

models are analyzed using the particle image velocimetry (PIV) technique and flow

visualization studies. A much simplifier bluff body (rectangular body) is also

investigated in order to identify similarities and differences compared to the flow

around the bus models. The main goal of the present research is to provide the better


4

understanding of the aerodynamics of bus models that exhibit both time-averaged

and unsteady flow features. A secondary but also important goal is to obtain

quantitative data sets for validation of numerical simulations of the flow around these

geometries for comparison of different CFD models against experimental results.

1.3 Outline of Dissertation

This thesis is structured in five chapters. The background and objectives of

the present investigation have been presented in Chapter 1.

Chapter 2 summarizes the literature survey conducted for the rectangular

body and ground vehicle aerodynamics.

Chapter 3 describes the experimental system and measurement techniques.

Results and discussion of the PIV results of the rectangular body and two

different rear end shaped bus models are presented in Chapter 4.

Chapter 5 summarizes the main findings and conclusion of the present work

and provides recommendation for further investigations as a future work.

2. LITERATURE SURVEY Cahit GÜRLEK

5

2. LITERATURE SURVEY

2.1. Flow structure around a rectangular body

Flow around a wall mounted rectangular cylinder in a channel represents a

general engineering configuration that is relevant in many applications. Owing to

simple geometry but with complex vertical structures and generic flow phenomena

associated with a turbulent flow, this configuration has attracted increasing attention

from researchers and has been used for the bench-marking purposes to validate

turbulent models and numerical methods.

Before the 1990s, measurements of three-dimensional flows around wall-

mounted cubical obstacles were unavailable. Instead any understanding of the major

global features of flow patterns were based on flow visualization studies. The first

published measurements of the turbulent velocity field, energy balance and heat

transfer around a surface-mounted cube begun to appear in the 1990s. Several

experimental works have been performed on a flow around a single wall-mounted

cube in a developed turbulent channel flow (Martunizzi and Tropea 1993; Hussein

and Martinuzzi 1996; Mills et al. 2003; Wang and et al. 2004; Depardon et al. 2005).

Results showed that this flow is characterized by the appearance of a horseshoe-type

vortex at the windward face, an arc-shaped vortex in the wake of the cube, flow

separation at the top and side face of the cube and vortex shedding. The flow features

and experimental data for time-averaged flow quantities have been well documented

in Martinuzzi and Tropea (1993) and Hussein and Martinuzzi (1996). They carried

out flow visualization and LDV measurement of a wall mounted cube in a fully

developed channel flow. A reattachment region is formed downstream of the cube by

the downwash shear flow originating at the top leading edge. The horseshoe vortex is

drawn towards the plane of symmetry up to the reattachment region, and then

dispersed outwards by the downwash flow. Figure 2.1 shows the schematic

representation of the flow around a wall-mounted cube by Martinuzzi and Tropea

(1993). Further, the studies included a detailed description of the Reynolds stresses

and higher order moments. It was found that the horseshoe vortex region was


6

unstable but non-periodic which caused bimodal velocity distributions. Vortex

shedding was detected in the wake of the cubical obstacle.

Figure 2.1. Schematic representation of the flow around a wall-mounted cube (Martinuzzi and Tropea, 1993)

The ability to perform these measurements aroused great interest in numerical

simulation of these flows. Most numerical studies were performed by using the

Reynolds-averaged Navier–Stokes (RANS) method with different turbulent models

(Lakehal and Rodi, 1997; Iaccarino et al., 2003) and large-eddy simulations (LES)

(Rodi et al., 1997; Shah and Ferziger, 1997; Krajnovic´ and Davidson, 1999, 2001;

Niceno et al., 2002). Figure 2.2 shows the flow around a wall-mounted cube by

Krajnovic and Davidson (2001). RANS approach could not reproduce the details of

the complex fluid structure near the wall, e.g. the converging–diverging horseshoe

vortex and separation of the boundary layer in front of the cube, nor the separation

length behind the cube. It is commonly believed that this inability is due to the

disregard of unsteady effects such as vortex shedding. In contrast, global flow

features and characteristics predicted by LES and more recently by unsteady RANS-

based modeling (Iaccarino et al., 2003) showed good agreement with experimental

data. In spite of previous investigations, many aspects of the flow structure around a

finite-length prism have yet to be better understood. For example, how is the flow

dependent upon H/d? How do the tip, spanwise and base vortices interact with each

other?


7

Figure 2.2. Flow around a wall-mounted cube (Krajnovic and Davidson, 2001)

Bearman et al. (1984) investigated the corner radius effect on the hydro-

dynamic forces on cylindrical bluff bodies subjected to an oscillatory flow in which

the Keulegan Carpenter (KC) number ranged from 1 to 100. They found that the drag

coefficient, CD, was sensitive to the corner radius in a steady flow and even more so

in an oscillatory flow. Tamura et al. (1998) and Tamura and Miyagi (1999)

investigated numerically and experimentally the aerodynamic forces on square

cylinders and observed a decrease in the wake width as well as Cd with the corner

chamfered or rounded. Zheng and Dalton (1999) studied numerically the corner

effect in an oscillatory flow and argued that vortex attachment occurred at irregular

high frequency modes when KC>3 for a square cylinder with rounded corners. The

calculated drag and inertia coefficients were in good agreement with the

experimental data of Bearman et al. (1984). Recently, Dalton and Zheng (2003)

presented numerical results for a uniform approach flow past square and diamond

cylinders, with and without corner modifications at Re=250 and 1,000. They noted

that rounding corners of the bluff bodies produced a noticeable decrease in

the calculated drag and lift coefficients. Similar studies emphasizing corner effects

were also conducted by Delany and Sorensen (1953), Naudascher et al. (1981) and

Okamoto and Uemura (1991). These investigations largely focused on the effect of


8

corner radii on the aerodynamic or hydrodynamic characteristics, such as drag/lift

forces and shedding frequency, of bluff bodies.

Previous investigations, e.g., Cantwell and Coles (1983), Hussain and

Hayakawa (1987), Kiya and Matsumura (1988), Matsumura and Antonia (1993) and

Zhou and Antonia (1993, 1994a), characterized the flow structure based on

conditionally averaged hotwire data. However, due to the large fluctuations of

velocities in the near wake, it is difficult to deploy the hotwire technique to measure

reliably fluctuating velocities at a station smaller than 10d downstream of a cylinder.

Particle-image velocimetry (PIV) provides an alternative solution, in which the flow

field, including the immediate vicinity of a cylinder, can be visualized and quantified

in terms of instantaneous images of the velocity field.

An understanding of the flow around a bluff body close to a ground is very

important in automobile, aeronautical and wind engineering fields because of

aerodynamic characteristic and instability resulting from flow separation. It has been

reported that the traffic accidents such as overturning or slipping induced by the

abrupt cross-wind at tunnel exit of highway and on the long bridge. Under such

strong cross-wind conditions, it is noteworthy that vortex shedding past bluff shape

vehicles such as sports utility vehicles, articulated lorries, large buses etc. The

separation from bluff bodies produces a strong loss of pressure recovery and vortex-

induced oscillation, which result in the increase of the aerodynamic drag and

instability. Therefore, it is necessary to evaluate aerodynamic characteristics at the

conceptual design state of a ground vehicle near the ground. In general, the charac-

teristics of this type of flow are governed not only by the Reynolds number, Re but

also by the gap ratio i.e., the ratio of the gap distance between the bluff body and the

plane boundary, S, to the cylinder diameter D. However, the details of the effects of

S/D or ground effect are still far from being fully understood due to the existence of

other influencing factors, such as the state of the boundary layer formed on the plane

boundary, the aspect ratio of the bluff body, and the spanwise-end condition of the

bluff body.

Bluff body flow in close proximity of a stationary wall has drawn the interest

of several authors in recent years, namely, Bearmen and Zdravkovich (1978), Bosch


9

and Rodi (1996), Lei et al. (1999) and Zovatto and Pedrizzetti (2001). The stationary

wall induces a shear in the incoming velocity profile and the flow differs from its

unbounded counterpart. A shear layer with negative vorticity forms along the

stationary wall. This negative vorticity interacts with the vorticity, which originates

from the lower side of the bluff body. It has been found that vortex shedding

suppression occurs beyond a critical gap height between the bluff body and the

stationary wall (Bearmen and Zdravkovich (1978)). For smaller values of the gap

height, the vortex shedding process from the bluff body is different from that of a

cylinder placed in a free stream (Zovatto and Pedrizzetti (2001)). The mechanisms

that cause the suppression of vortex shedding are complex and not yet fully

understood. Many authors have hypothesized that suppression is simply due to

vorticity generated along the wall cancelling opposite sign vorticity in the lower

shear layer of the cylinder. By this hypothesis, the strength of the lower shear layer is

thought to weaken to the point where it can no longer couple with the upper shear

layer, thereby yielding a stationary flow field. It is thus suggested that the

suppression of vortex shedding is an abrupt process, i.e. when sufficient vorticity is

cancelled from the lower shear layer, the flow becomes stationary. The laser Doppler

velocimetry (LDV) study of Durao et al. (1991) suggests that vortex shedding is

suppressed abruptly at S/D= 0.35, however, other experiments by Bosch and Rodi

(1996) and Tamiguchi et al. (1983) describe organized events (shedding) interspersed

with periods of random (turbulent) fluctuations. Furthermore, recent LDV studies by

Wu and Martinuzzi (1997), Bailey (2001) and Bailey et al. (2001) reported that for

small S/D, organized shedding events were observed 6D downstream of the cylinder,

while only random activity was observed in the immediate vicinity of the cylinder.

These studies all indicate that for S/D>1, the strength of vortex shedding is

similar to the no-wall case of Lyn et al. (1995) and decreases for smaller gap heights.

Durao et al. (1991) concluded that vorticity destruction and entrainment of turbulent

eddies from the boundary layer reduce the strength of the shear layer closest to the

wall and prevent shedding. However, Bosch et al. (1996) observed that the influence

of the wall resulted in a thinning of the lower shear layer (closest to wall) and a

thickening of the upper shear layer (furthest from wall), when compared to the no-


10

wall case. Bailey et al. (2002) observed that the strength of the upper shear layer

increased for S/D<0.5 while the lower shear layer decreased in strength. Their LDV

measurements in the base region indicated that this was due to the straightening of

the lower shear layer. They concluded that suppression of periodic shedding occurs

because of the increasingly different strengths of the shear layers for decreasing gap

heights so that the lower shear layer is eventually too weak to couple with the upper

one.

Recently, Straatman and Martinuzzi (2002, 2003) presented a combination of

numerical and experimental results for turbulent vortex shedding from a square

cylinder in close proximity to a wall. Their results attempted to quantify changes in

the shedding frequency and the lift and drag coefficients over a range of cylinder to

wall gaps that spanned unobstructed shedding through to complete suppression of

periodic motions. A key finding of the study is the observations that the structure of

the wake changes significantly as the gap between the cylinder and wall is reduced.

For large gaps, the shedding pattern is distorted, but vortices are shed in the near

wake and periodic pressure modulations are observed on the cylinder faces.

However, for sufficiently small cylinder to wall gaps, the wake extends and periodic

structures are only observed downstream of the cylinder. For even smaller gaps, the

periodic structures are seen to be entirely suppressed, as reported in earlier literature.

The transition of the wake occurs when the lower shear layer on the cylinder is

deflected towards the wall away from the upper shear layer. As such, coupling of the

shear layers occurs further downstream, leading to an extension of the wake. This

transition has important implications in terms of the forces on the cylinder and the

mixing activity in the wake.

When the wall is considered to be moving horizontally, the classical

boundary layer on the wall is absent and the flow mechanism is different from that of

the stationary wall. There are only a small number of theoretical studies published in

the open literature. Bearmen (1980) reviewed earlier studies on bluff body flows that

are relevant to the understanding of vehicle flows. There he predicted that the

velocity profile may overshoot in the gap flow between the lower surface of the

cylinder and the moving wall. The bluff body close to the moving wall may


11

experience a downward force. Arnal et al. (1991) performed a numerical simulation

of square cylinder under the condition of the free-stream, fixed and sliding wall

conditions with changes in the Reynolds number. Arnal et al. (1991) pointed out that

the positive vortex that forms in the downstream lower corner of the square cylinder

is much weaker when the downstream wall is fixed than when it is moving. They

claimed that the presence of the fixed wall reduced the Strouhal number where the

periodic vortex shedding occurred. In contrast, the sliding wall at the free-stream

velocity resulted in vortex shedding which was extremely periodic. Kumarasamy and

Barlow (1997) studied the flow over a half-cylinder close to a moving wall. Kim and

Geropp (1998) investigated flow around some two dimensional bluff bodies with

wind tunnel experiments equipped by moving-belt and reported that a larger lift

forces and longer wakes was apparent with decreasing clearance. An experimental

study for three-dimensional flow with free-stream turbulence past an aerodynamic

body placed near a moving ground was conducted by Senior and Zhang (2001). They

found that the flow remains symmetric about the centre plane of the diffuser and the

suction level at the diffuser inlet continues to rise as the ride height is reduced.

2.2. Flow structure around a ground vehicle

2.2.1. Experimental Studies

Historically, aerodynamics has not been a big concern in the vehicle design

process. Increasing fuel prices and environmental pollution have made aerodynamics

more important in the last half of the 20 th century. First improvement was

accomplished by moving from a carriage-like body to a three-volume body (pontoon)

with reduction of the drag coefficient from cD=0,8 to cD=0,45. The next development

in drag reduction started at the begging of the 1970s. The first oil crisis during the

winter of 1973-74 made the automobile industry ready to accept arguments from

aerodynamicists and so a trend to lower drag became rather pronounced. Presently,

an average mid-size car has cD=0,35 value and it is believed chat this value still can


12

be improved by applying basic aerodynamic principles. Figure 2.3 shows the history

of drag coefficient CD of passenger cars.

Figure 2.3. History of drag coefficient, cD (Hucho, 1998)

Shapes of real ground vehicles are too complex to be used for detailed flow studies

in experiments and numerical simulations. Although these shapes are used in the ground

vehicle industry to determine global quantities such as drag or lift, they are not amenable to

learn about the interaction of the flow features around the vehicle responsible for its

aerodynamic properties. Therefore, the aerodynamics of the ground vehicles has

frequently been studied in the simplified vehicle models, that can produce flow similar

to that around a real ground vehicle. A review of early work in this area can be found in

Hucho (1998). In general, there are two common bluff body geometries that have been used

as a benchmark case in the early automotive aerodynamics literature. The first generic bluff

body case for ground vehicle aerodynamics was introduced by Morel (1978), and then

Ahmed et al. (1984) modified this geometry and published similar bluff body study. Both

geometries are almost the same size and shape, except the first one is slightly longer than the

second. However, detailed geometry definition and easy manufacturability made Ahmed

Body the first choice for most bluff body studies in ground the vehicle aerodynamics.

CD

Year


13

The Ahmed reference model was originally developed for a time-averaged vehicle

wake investigation (Ahmed et al. 1984). Figure 2.4 shows schematic of the Ahmed model. It

is a car-like bluff body with a curved fore body, straight centre section and an angled rear

end, representing a highly simplified one-fourth-scale, lower-medium-size hatchback

vehicle. The specific angle of the back end can be altered between 0° and 40°, in 5°

increments (the angle of the slanted back zero is making this body a generic bus rather than a

car). The model’s major dimensions are 1044 mm x 389 mm x 288 mm. The Ahmed body

was designed to have a fully attached flow over the front, and to exhibit many of the flow

features of an automobile with its nine interchangeable rear ends. This variation in backlight

geometry provides a range of flow characteristics over the back end of the model. The

geometry of this bluff body was designed to be such that an experiment could be conducted

with reference to only one significant aerodynamic feature, namely the flow over the slanted

rear end, as flow was expected to remain attached over the other sections. A simple

geometric body that retains the main flow features, specially the vortex wake flow

where most part of the drag is concentrated is a good candidate to be used as a

numerical test for CFD code development. In this sense Ahmed body model has

these characteristics and for this reason it has been used as the benchmark test in this

kind of applications.

Figure 2.4. Schematic of the Ahmed model (Ahmed et al., 1984)

It has been shown that the flow over the angled back section is dependent on the

specific backlight angle being investigated (Ahmed et al. 1984). There have been found to be

two critical angles, at which the flow structure changes significantly. Below 12.5°


14

(first critical angle) airflow over the angled back end remains fully attached before separating

from the model when it reaches the vertical back-end. The flow from the angled section and

the side walls produces a pair of counter-rotating vortices, which continue down-stream. For

backlight angles between 12.5° and 30° (second critical angle) the flow over the angled

section becomes highly three-dimensional. Two counter-rotating lateral vortices are again

shed from the sides of the angled back section, but are larger than were formed below 12.5°.

This increased vortex size affects the flow over the whole backlight, causing the three-

dimensional flow. These vortices are also responsible for maintaining attached flow over a

section of the backlight up to an angle of 30° and have been shown to extend more than

0.48 L beyond the model trailing edge. Close to the second critical angle a separation bubble

is formed over the backlight. The flow separates from the body, but re-attaches before

reaching the vertical back section. At this point, the flow again separates from the model.

Above 30°, flow over the angled section is fully separated. There remains though a weak

tendency of the flow to turn around the side edge of the model, a result of the relative

separation positions of the flow over model top and that over the backlight side edges. When

the flow is in this state a near constant pressure is found across the backlight. Figure 2.5

shows the flow structure behind the Ahmed model by Ahmed et al. (1984).

Figure 2.5. Flow structure behind the Ahmed model (Ahmed et al., 1984)


15

Duell and George (1999) investigated the unsteady near wake bus-like body

using hot wire anemometry and an unsteady pressure measurement system. A three

dimensional bluff body model was used to simulate the time dependent three

dimensional near wake flow field generated by trucks, buses, and automobiles.

Spectral analysis of the velocity and pressure signals was used to identify periodic

wake flow structures. The shape of the model used in this study was chosen to

generate the near wake structure of a typical ground vehicle and was based on the

work of Ahmed et al. (1984). The Reynolds number based on model length was

7,5x105. Velocity measurements were performed with constant temperature

anemometers and single hot wire anemometer probes. Mean pressure measurements

were made using differential pressure transducers and a multiport pressure

measurement system mounted inside the model. They concluded that the near wake

contains a large, ring-type vortex in the recirculation region between the free

stagnation point and the model base. They explained the unequal strength of the

upper and lower parts of the vortex by the presence of the bound leg of a trailing

horseshoe vortex. They reported two periodic processes in the wake corresponding to the

dimensionless frequencies at Strouhal numbers 0.069 and 1.16. The lower value was

attributed to the periodic interaction of the upper and lower partitions of the ring vortex in the

near wake. The higher value was found to be associated to the vortex shedding process in the

shear layer. They have also investigated the effects of base cavities on the unsteady

pressure in the near wake. The mean base pressure increases with increasing cavity

depth. The unsteady near wake is shifted downstream and the recirculation length is

increased when the cavity is in place.

Using the same idealized geometry, Sims-Williams (2001) conducted a

detailed study on the time-averaged and unsteady flow structures associated with the

critical geometry. Using a smoke flow visualization technique, Sims-Williams (2001)

demonstrated the sensitivity of the flow pattern near this critical backlight angle.

When the tunnel was started up from rest, the flow would be in the low drag state,

and then it would switch to the high drag state after several minutes and persist

indefinitely. The lower the freestream speed, the longer that the low drag flow state

would exist. Sims-Williams (2001) also found that, in their time-averaged form,


16

results agreed with those obtained by Ahmed et al. (1984) in that the flow structure

was dominated by the two C-pillar vortices, which are drawn down towards the

ground. Time-accurate data showed that high levels of unsteadiness also existed in

the wake, with the highest levels located around the periphery of the C-pillar

vortices. It was revealed that these regions of high unsteadiness were associated with

a distinct shedding frequency, giving a Strouhal number of about 0.35 (based on

square-root of the frontal area). However, due to limitations associated with

instrumentation, Sims-Williams was unable to investigate the flow field very close to

the model surface (i.e. regions of large flow angles), and therefore, was unable to

completely describe the complex behaviour in the near-wake.

In a more recent study, Spohn and Gillieron (2002) were also able to show

the complex flow phenomena occurring around the Ahmed model shape via an off-

body flow visualization water tunnel based technique. Although their work was

focused solely on the 250 backlight angle configuration, they too found that the near-

wake was dominated by a set of counter-rotating (lifting) trailing vortices, which

bounded a central separation bubble that enclosed a flow reversal region. However,

unlike the work of Ahmed et al. (1984) they showed that the detached flow region on

the slant did not reattach prior to reaching the vertical rear base of the model, but

mixed with the flow in the wake. Within this separated region above the slant existed

two radiating foci (one on each side of the model) situated near the top corners of the

slanted edge, which caused the reverse flows inside the bubble to take a radiating

path back toward the foci origins. This result helps explain the hypothesized skin

friction patterns of Ahmed et al. (1984), who showed a similar result through surface

flow visualization, although were unable to show the existence of the stable focus.

Vino et all. (2004) have studied the time-averaged and time-dependant nature

of the wake of a simplified passenger vehicle (Ahmed model) experimentally. A

1/4 scale Ahmed model geometry was used in this investigation, with the rear slant

angle held constant at 30 degrees. Time-averaged and time-varying surface pressure

measurements were measured with a Dynamic Pressure Measurement System

(DPMS). Tests were conducted at a range of speeds between 20 and 35 m/s. In

order to obtain a more complete representation of the flow field, off-body flow


17

measurements were taken at three downstream transverse planes in the wake of the

model. Time-dependant analysis revealed that the shedding behind the model is

analogous to vortex shedding behind simple bluff bodies, with most of the

fluctuations confined to the axial and vertical directions. In addition, the shedding

characteristics on the slant showed very similar behaviour to the vertical base,

indicating strong turbulent mixing between the two regions, emphasizing time-

averaged findings and complementing the proposed flow topology. They concluded

that the separated flow region over the slanted edge does not fully reattach further

down the slant, but instead mixes with the large separated region behind the vertical

base. The two regions consequently exhibit similar time-dependant behaviour.

Spectral characteristics of surface pressure signals also revealed that the recirculation

bubbles found behind the vertical base could be seen as analogous to longitudinal

vortices in a Von Karman vortex street.

Strachan et all. (2007) was presented Laser Doppler anemometry (LDA) data

for an Ahmed reference model employing various backlight angles in the presence of

a moving ground. LDA velocity measurements were taken in a number of planes

around and downstream of the model at a free-stream velocity of 25 m s-1. During the

testing a rolling road provided ground simulation and six-component force data were

recorded. It was found that the inclusion of the ground simulation and the consequent

supporting strut produces a reduction in the size and strength of the vortices shed

from the back end of the Ahmed model when compared with previous analysis. It

was further concluded this effect is primarily a result of the overhead strut, and that

the rolling road has little effect on these upper vortices. In addition, vortices shed

from the underside of the model, not reported in previous experimental work, was

found and analyzed.

A number of aerodynamic solutions have been realized in a research project

for high-decker buses by the Fachhochschule, Hamburg. The smooth airflow pattern

around this bus is shown in Figure 2.6. Drag coefficient, CD of this bus is reduced to

0.3 from 0.6. This large drag reduction of about 50% reduces fuel consumption at 80

km/h by 15% and at 100 km/h by more than 20%. Figure 2.7 shows an imaginative


18

front-end design for a low-drag bus. The entrance door has been moved to the front

to make possible sloping the front contours and arching the windshield Hucho (1998).

Figure 2.6. High-decker bus designed by Fachhochschule, Hamburg (Hucho, 1998)

Figure 2.7. Touring coach design study (Hucho, 1998)

Nouzawa et al. (1992) extended an earlier investigation with an unsteady

analysis of a notchback vehicle shape. They observed that an arch vortex (initially

found on the rear window and deck-lid of an earlier study) exhibited significant

unsteady characteristics. Through hot-wire and surface pressure measurements, they

found that the arch vortex sheds from the model at a frequency of 20–30 Hz


19

(corresponding to a Strouhal number, also based on square-root of the frontal area, of

about 0.37–0.55) in an alternate fashion from each side of the rear window. This

characteristic frequency compared well to fluctuations observed in drag

measurements, indicating that this vortex structure governs much of the aerodynamic

characteristics.

Through the use of PIV, Wang et al. (1996) were able to illustrate the

significant differences between time-averaged and unsteady flow structures in the

wake of a fastback vehicle shape. For a transverse plane taken behind the model,

they found that the instantaneous flow field consisted of several ‘small’ vortices

quite evenly distributed throughout the traversing plane, while the time-averaged

counterpart appeared to have ‘diffused’ much of the small pockets of vorticity and

consisted of mainly two large contra-rotating trailing vortices.

Bearman (1997) studied the formation of streamwise vortices in the near

wake of a l/8th-scale car model. He used PIV measurements to determine the

instantaneous flow on cross-sectional planes normal to the freestream direction in the

near wake. The results show that although in the mean there is a well-defined

counter-rotating vortex pair, instantaneous images show randomly located vortical

structures. These data suggest that the concept of a road vehicle wake consisting of a

pair of persistent counter-rotating vortices is not correct. Instead, the results show

that the wake of a road vehicle consists of compact small scale vortex structures

located randomly in space and time and, consequently, the near wake dynamics

appears to be much more complicated than the classical high-aspect-ratio-wing wake

problem.

Kozaka and et al. (2004) investigated turbulent structure of flow behind a

model car with local velocity measurements with emphasis on large structures and

their relevance to aerodynamic forces. The experiments were performed on a

replicated 1:8 scale model of a Fiat Brava, a hatchback car in an open-circuit

subsonic wind tunnel. By adjusting the tunnel speed, the model was exposed to the

approach velocities U∞= 18, 28 and 38ms-1 with the corresponding Reynolds

numbers Re∞=0.20x106, 0.31x106 and 0.42x106, respectively. A constant temperature

hot-wire anemometer was used. They showed that two counter-rotating helical


20

vortices, which are formed within the inner wake region, play a key role in

determining the flux of kinetic energy. The turbulence was generated within the

outermost shear layers due to the instabilities, which also seem to be the basic drive

for these relatively organized structures. The measured terms of the turbulent kinetic

energy production, which are only part of the full expression, indicate that vortex

centers act similar to the manifolds draining the energy in the streamwise direction.

As the approach velocity increases, the streamwise convection becomes the dominant

means of turbulent transport and, thus, the acquisition of turbulence by relatively

non-turbulent flow around the wake region is suppressed.

Ozdemir et al. (2004) examined a full kinematic map of turbulent wake flow

behind a model car exposed to crosswind by local measurements of velocity. Results

showed that the wake flow becomes highly asymmetric with the crosswind which

introduces a rotation to the in-plane velocity field and tilts the system of counter-

rotating helical vortices appearing on both sides of the centerline. The vortex

formation plays an important role in the transport and re-distribution of the turbulent

kinetic energy produced by the crosswind. And that the turbulent energy is partly

regained back to the streamwise mean flow through the vortex centers. As a result,

the turbulence produced by the crosswind cannot induce a significant additional drag.

One of the first investigations of the influence of the moving floor on the

flow around a road vehicle was done by Bearman et al. (1989), who studied flows

around a typical 1:3-scale car and around a generic car shape with stationary and

moving belt floors. They measured drag and lift coefficients and found that the floor

movement reduced drag by about 8% and lift by 30% for a 1:3-scale car. The effect

on lift is more pronounced when the vehicle is yawed to the flow. The generic car

bodies were equipped with an adjustable, rear-end underbody diffuser, and the

influence of the floor motions on different diffuser angles was studied. An influence

of the moving floor on lift was found for diffuser angles up to 250 while drag was

affected by this motion for all diffuser angles.

Howell (1994) used a generic car similar to the Ahmed body (Ahmed et al.

1984) to study the influence of floor motion on lift and drag forces. The model was

equipped with an adjustable, slanted, rear upper surface and rear-ends underbody


21

diffusers. Their experiments showed that, in comparison with a stationary floor, the

moving floor produced higher drag and lower lift for almost all combinations of

angles of upper slanted and diffuser surfaces. One exception is the case of a 00

diffuser and angle of the upper slanted surface of 250. It is interesting to note that

they found reduced lift and no change in drag with floor motion for this case.

Lajos et al. (1986) measured the flow around bus models with a moving belt

and a stationary floor. The bus models had underbody up-sweep at the rear. They

found a large influence on the wake flow caused by floor movements.

Essentially, the road resistance of a motor vehicle consists of a mechanical

and an aerodynamic part. At high speeds the aerodynamic component dominates,

whereby the aerodynamic pressure drag is predominant. As is the case with all bluff

bodies, the pressure drag is due to separation effects which induce intensive turbulent

vortex structures with high dissipation. To reduce the drag, the pressure drag and

more specifically the structure of the wake region must be changed. Although a

variety of techniques are currently used to reduce drag many have a limited range of

application. Passive processes can be used to control the flow such as attaching long

splitter-plates to the rear side as shown by Apelt et al. (1973) or by realizing boat-

tailing. These measures are however exhausted for stylistic and safety-related

reasons, which underline the need for more active processes such as modifying the

dead water using suction and/or blowing. Geropp and Odenthal (2000) constructed a

test facility to realistically simulate the flow around a two dimensional car shaped

body in a wind tunnel. A moving belt simulator was employed to generate the

relative motion between model and ground. In a first step, the aerodynamic

coefficients CL and CD of the model was determined using static pressure and force

measurements. LDA-measurements behind the model showed the large vortex and

turbulence structures of the near and far wake. In a second step, the ambient flow

around the model was modified by way of an active flow control which uses the

Coanda effect, whereby the base-pressure increases by nearly 50% and the total drag

can be reduced by 10%. The recirculating region was completely eliminated.

Zhdanov and Papenfuss (2003) investigated the influence of thin plates and

dimples arranged ever the upper surface of an IVECO Euroclass HD-380 bus on base


22

pressure variations, turbulent wake characteristics and body drag. They found that

the near-wake structure, base pressure and model aerodynamic drag could be

governed by weak disturbances applied to the restricted region of the boundary layer.

2.2.2. Numerical Studies

To meet consumer demand effectively and to stay competitive, automobile

manufacturers today must develop more economical, safer and more comfortable

vehicles at an increasingly rapid pace. Using solely the traditional wind tunnel and

road test techniques, the long development cycle times are proving to be a serious

impediment in this situation. Due to this, interest has been steadily growing in using

computers and computational fluid dynamics (CFD) methods to simulate the wind

tunnel tests. Consequently, CFD is slowly emerging as an additional basic tool in

aerodynamics design.

Flow field around the simplified ground vehicles are investigated by a large

number of numerical studies to validate CFD technique using different RANS and

LES turbulent models. Numerical studies such as those made by Han (1989) and

described in Manceau and Bonnet (2000) are used to validate the CFD technique

(often RANS simulation). Large number of RANS simulations (using different

turbulence models) and one large eddy simulation (LES) of the flow around body

defined by Ahmed et al (1984) are presented by Manceau and Bonnet (2000). Only

two angles of the rear slanted surface, 25o and 35o, were considered in these

simulations. The results of these simulations were compared with the experimental

data produced by Lienhart and Becker (2003). The main conclusion from these

simulations was that while the simulations were relatively successful in prediction of

the 35o case, they were unsuccessful in the 25o case.

Kapadia and Roy (2003) have reported a Spalart-Allamaras based detached

eddy simulation hybrid model and numerical results for the Ahmed reference car

model with 25o base slant angle. Highly three-dimensional and unsteady wake flow

behavior was documented by showing velocity vectors in the trailing region. One-

equation RANS model was also used for the same simulation. Both techniques were


23

compared by showing the capability of each technique in capturing the minor flow

details and in predicting the coefficient of drag (CD). Finally, unsteady behavior of

CD was studied in both cases. Average value of CD was calculated and validated with

the reported experimental data of Ahmed et al. (1984) and numerical results.

Comparison the RANS model with DES results shows the ability of DES in

capturing unsteady structure of the flow with minor flow details than RANS.

Krajnovic and Davidson (2003) analyzed the flow around a simplified bus

using large-eddy simulation (LES). Mechanisms of the formation of flow structures,

instantaneous and time-averaged flow features were verified with the previous

experimental results. The computed aerodynamic forces and their time history were

used to reveal the characteristic frequencies of the flow motion around the body.

They found large differences between time-averaged flow containing only small

number of three-dimensional vortices and the instantaneous flow containing large

number of three-dimensional vortices at different position and size. They also

reported that at the Reynolds number of 0.21x106, based on the model height and the

incoming velocity, the flow produced features and aerodynamic forces relevant for

the higher Reynolds numbers. Figure 2.8 and 2.9 shows the instantaneous and time-

averaged flow structures behind a bus model respectively.

Figure 2.8. The instantaneous streamlines behind a bus model. (Krajnovic and Davidson, 2003)


24

Figure 2.9. Schematic representation of the time-averaged flow behind a bus model. (Krajnovic and Davidson, 2003)

Krajnovic and Davidson (2004) investigated the flow around a simplified car

model using large-eddy simulation. It was tested a hypothesis of using lower

Reynolds number large eddy simulation (LES) to simulate the flow around ground

vehicle at higher Reynolds number. The Reynolds number, based on the incoming

velocity U∞ and the car height H, was Re = 2x105. They concluded that the external

vehicle flow at high Reynolds number becomes insensitive to the Reynolds number.

It seems that the geometry rather than the viscosity dictates the character of the flow

(attached or detached) and the position of flow separations. Using lower Reynolds

number in their LES they resolved the near-wall energy-carrying coherent structures

and predicted the flow accurately. This observation raises hope that flow around real

cars can be simulated with LES at reduced Reynolds numbers.

Liu and Moser (2003) presented airflow over the Ahmed body by means of

transient RANS turbulence models. They showed that the unsteady wake comprises

two vortices behind the rear with the larger one in the higher part, and the smaller

one in the lower part. It was found that the peak value of turbulent kinetic energy k

was located in the center of the small vortex downstream of the body, as observed in

the experiments. They found that Durbin’s k-ε-v2 model was more accurate than the


25

other turbulence models for the wall-bounded cases with separation and

reattachment.

Murad et al.(2004) simulated a simplified vehicle model with rectangular and

slanted A-pillar geometry to replicate flow behind a vehicle A-pillar region using

computational Fluid Dynamics (CFD). Investigations were carried out at velocities of

60, 100 and 140km/h and at 0, 5, 10 and 15-degree yaw angle. Results showed that

for the rectangular model, the A-pillar vortex generated was bigger in size when

compared to the slanted edge model at 00 yaw but with less intensity. Results for the

rectangular at various yaw angles showed that at the windward side, the A-pillar

vortex generated had more intensity than the leeward side but was smaller in size.

Results for the slanted edge model from various yaw angles showed that at the

leeward side, the A-pillar vortex generated had a higher intensity and in size when

compared to the A-pillar vortex in the windward side. Results for both model was

greatly influenced by the yaw angles and also by the A-pillar geometry.

The effect of a moving floor on the flow around a simplified car with typical

fastback geometry was investigated by Krajnovic and Davidson (2005). Two large-

eddy simulations of the flows with stationary and moving floors was made and both

instantaneous and time-averaged results was compared. It was found that the floor

motion reduces drag by 8% and lift by 16%. The wake flow was found to be

relatively insensitive to the floor movement, in agreement with previous

experimental observations. The periodicity of the flow events was found to be

dependent on whether the floor was moving. Power spectral density of both the lift

and the drag contain only one dominant frequency peak when the moving floor was

adopted as compared to scattered spectra in the stationary floor case. They concluded

that changes in the qualitative picture of the flow were limited to the flow near the

floor and on the slanted surface of the body. However, changes in the surface

pressure on the body and the history of the flow showed the need of a moving floor

in experimental and numerical simulations.

3. MATERIAL AND METHOD Cahit GÜRLEK

26

3. MATERIAL AND METHOD

3.1. Measurement Techniques

3.1.1. Particle Image Velocimetry (PIV)

Measurement of velocity fields is of critical importance in aerodynamic

studies in order to both verify the flow field and also to determine the performance of

components/systems in the flow field. Quantitative flow field measurements were

initially obtained in aerodynamic studies using Pitot static probes, which were

suitable for measuring the time-average or low frequency response flow field

properties at a single point in the flow. Hot wire anemometry proved to be a

significant improvement over pitot probes by providing high frequency response

velocity measurements. Adding more wires enabled multi-component flow

measurements. Similar to pitot probes, hot wire anemometers were invasive and

disturbed the flow field under study. The first non-invasive point velocity

measurement technique was Laser Doppler Velocimetry (LDV), which used a

crossed pair of laser beams to measure the velocity of seed particles entrained in the

flow. Additional advantages of the LDV technique were the high frequency response

and high measurement accuracy.

Planar velocity measurement techniques were a significant improvement over

point based velocity measurement techniques such as LDV. Although very accurate,

point based Velocimetry measurements required sophisticated traversing system to

move the probe volume through the desired measurement range of the flow field.

Mapping planes or volumes of the flow required many hours of facility run time,

which could prove quite costly. The advantage offered by planar velocity

measurement techniques was the ability to capture the instantaneous, planar cross

sections of unsteady flow structures which was not possible using point based

techniques. Particle Image Velocimetry (PIV) is a technique for measuring the in-

plane two or three-component velocity field of a flow seeded with tracer particles

small enough to accurately follow the flow (Mercer, 2003).


27

Most of the velocity-measuring techniques such as LDV, hot wire

anemometry, or measurements with the Pitot-static tube have the disadvantages of

collecting values at one point or position at a time. Thus the determination of the

velocity and turbulence characteristics of a whole flow field turns out to be a very

time-consuming task. PIV technique overcomes this shortfall (Hucho, 1998).

The measurement of the overall flow field properties, such as velocity and

vorticity is one of the most challenging problems. Coherent structures in shear flows

or wake flows are extremely unsteady. So, in this type of flow both spatial and

temporal information of the entire flow field are required in order to capture

instantaneous flow fields and thus to allow the detection of spatial structures in

unsteady flows quantitatively, which is not possible with other experimental

techniques. For this type of flow measurements, PIV technique is extremely

convenient. This technique has the ability to achieve higher accuracy, higher spatial

and temporal resolution and larger observation areas and volumes of experimental

data (Raffel et al., 1998).

PIV can be considered one of the most important achievements of flow

diagnostic technologies in the modern history of the fluid mechanics (Smits and Lim,

2003). Many researchers became interested in PIV because it offered a new and high

promising means of studying the structure of turbulent flow. This goal strongly

influenced the choices made in the development of the method (Adrian, 2005). The

origin of the PIV technique goes back to traditional qualitative particle flow

visualizations; however the early work of Meynard (1983) established the

foundations of its present form. The theory of PIV was introduced by Adrian (1988)

in the late 1980s with the first experimental implementations following shortly

afterwards (Keane and Adrian, 1990, 1991). At that stage, due to hardware

limitations, a single photographic frame was multiple exposed and analyzed using an

auto-correlation technique. However, improved speed of photographic recording

soon allowed images to be captured on separate frames for analysis by cross-

correlation (Keane and Adrian, 1992). One of the most important changes in the PIV

technique was the move from photographic to videographic recording. This change

profoundly influenced the usability and, hence, the popularity of PIV. The


28

introduction of digital camera technology to PIV enabled the direct recording of

particle images (Willert and Gharib, 1991), at the expense of reduced resolution,

resulting in the development of digital PIV (Westerweel, 1997). As well as these

hardware advances, many new algorithms have been developed in the past decade,

increasing the accuracy and the speed of PIV analysis. Comprehensive reviews of

PIV techniques were given by Rockwell and Lin (1993), Rockwell et al. (1993), and

Adrian (1986, 1991, 2005).

3.1.1.1. Principles of PIV Technique

PIV is a powerful method of quantitative flow visualization and has become

the method of choice for the investigation of unsteady separated flows. It provides

high spatial resolution and accuracy ever an entire plan at an instant of time. A

theoretical description of PIV involves many different disciplines, such as fluid

mechanics, optics, image processing and signal analysis. Each of these subsequent

steps has influence on the representation of the fluid motion with respect to the

observed images.

The experimental set-up of a system typically consists of several sub systems.

In most applications tracer particles have to be added to the flow. These particles

have to be illuminated in a plane of the flow at least twice with a short time interval.

The light scattered by the particles has to be recorded either on a single frame or on a

sequence of frames. The displacement of the particle images between the light pulses

has to be determined through evaluation of the PIV recordings. In order to be able to

handle the great amount of data which can be collected employing the PIV

technique, sophisticated post processing is required. Figure 3.1 briefly explains a

typical set up for PIV recording. Small tracer particles are added to the flow. A plane

(light sheet) within the flow is illuminated twice by means of laser (the time delay

between pulses depending on the mean flow velocity and the magnification at

imaging). It is assumed that the tracer particles move with local flow velocity

between the two illuminations. The light scattered by the tracer particles is recorded

on a special cross correlation CCD sensor. The output of the CCD sensor is stored in


29

real time in the memory of a computer directly. For evaluation the PIV recording is

divided in small sub areas called “interrogation areas”. The local displacement vector

for the images of the tracer particles of the first and second illumination is

determined for each interrogation area by means of statistical methods (auto-and

cross-correlation). It is assumed that all particles within one interrogation area have

moved homogenously between the two illuminations. The projection of the vector of

the local flow velocity into the plane of the light sheet is calculated taking into

account the time delay between the two illuminations and the magnification at

imaging. The process of interrogation is repeated for all interrogation area of the PIV

recording (Raffel et al., 1998).

The details of the PIV technique are presented and reviewed in the following

section.

From the basic principles the following main topics of PIV emerge:

• Seeding

• Illuminating

• Image Capturing

• Image Evaluation

• Correlation

Figure 3.1. Basic PIV analysis process


30

3.1.1.1.(1). Seeding

In PIV it is not actually the velocity of the flow that is measured, but the

velocity of particles suspended in the flow. Instead, the velocity of small tracer

particles entrained in the flow is measured. In this respect these seeding particles can

be considered to be the actual velocity probes, and seeding considerations are thus

important in PIV. The seeding particles can be seen in Figure 3.2.

Figure 3.2. Seeding particles

For water, fluorescent, polystyrene, silver-coated particles or other highly

reflective particles must be used to seed the flow; while olive oil or alcohol droplets

are generally used for wind tunnels. The choice of seeding depends on a number of

parameters. Primarily the seeding material should be chosen considering the flow

that is to be measured, and the illumination system available. Depending on the

nature of the flow, seeding particles used for PIV measurements usually have particle

diameters ranging from 0.1 to 50 µm. In general seeding particles should be chosen

as large as possible in order to scatter the most light, but the particle size is limited,

since too large particles will not track the flow properly. In general the maximum

allowable particle size decrease with increasing flow velocity, turbulence and

velocity gradients.

The camera images of seeding particles should have a diameter of at least 2

pixels, preferably 3 pixels or more. This will allow the system to estimate particle


31

positions and displacements to subpixel accuracy, effectively increasing the

resolution of the technique.

Ideally the seeding material should also be chosen, so the seeding particles

are neutrally buoyant in the carrying fluid, but in many flows this is a secondary

consideration.

Water flows are often implemented using water in a closed circuit, and here

commercial seeding particles such as latex beads or pine pollen can be used. Air

flows on the other hand are usually not recirculated, and thus require the seeding to

be generated at the inlet and disposed of at the outlet. Two approaches to flow

seeding are commonly used, depending on the mass flow rate of the experiment, or

whether the seeded flow field is recirculating: localized seed injection and global

seeding. If the physical properties of the flow field/experiment permit, then global

seeding is the most desirable, since this typically leads to the most uniform

distribution of the seed particles.

3.1.1.1.(2). Illumination

In the PIV technique, the light scattered by seeding particles moving in the

flow field provides a signal when it is recorded on a camera. Both the initial and final

positions of the seeding particles are to be captured so the displacement between

them can be measured. Thus, the PIV illumination method should fulfill the

following basic criteria:

• the light budget should be sufficiently high to ensure the intensity of scattered

light from the seeding particles is such that images of them can be recorded

on the PIV camera, above the optical noise level of the system

• the duration of the light pulse should be such that the particle does not move

significantly during its exposure to the light-pulse

• the time between successive light pulses should be such that the flow field

does not move significantly

• the location and dimensions of the measurement plane should be well-

defined.


32

The PIV technique can use any light source to illuminate the flow field under

study, provided that the pulses are of sufficient energy, are close enough together in

time and that the pulse duration is short enough to provide unblurred images of the

particles in the fluid. The light source does not have to be coherent or

monochromatic. The range of potential light sources includes: continuous wave

lasers, pulsed lasers, laser diodes and Xenon flash lamps. Lasers are widely used in

PIV, because of their ability to emit monochromatic light with high energy density,

which can easily be bundled into thin light sheets for illuminating and recording the

tracer particles without chromatic aberrations. Nd:YAG (Neodymium-Doped

Yttrium Aluminum Garnet) is the most widely used in PIV due to the high output

energy (25 to 400 mJ/pulse), short pulse duration (6 to 10 ns) and 532 nm emission.

The nominal pulse repetition rate of Nd:YAG lasers is 10 to 15 Hz.

3.1.1.1.(3). Image Capturing

In the PIV technique a pair of single exposure image frames is required to

enable data processing. The purpose of the camera is to capture the initial and final

positions of seeding particles in the flow fields and from these particle positions the

displacement vector can be proceed. In the PIV systems, CCD cameras are used

since these provide an instantaneous digital signal of the image map of seeding

particle positions. Historically, photographic film has been used also.

The term CCD stands for charge-coupled device. A CCD camera comprises

an array of detectors called pixels. Each pixel is a capacitor, being charged by

converting incident photons of light into electrons, like in photodiode. The cells are

isolated from each other by potential wells, created by the doping of the silicon chip

and by applying voltages to a grid of transparent metallic electrodes deposited on the

CCD surface. Light falling on a pixel is thus converted in to an electronic charge.

The charge falling on the individual pixels is transformed to a voltage during rear-out

of the CCD chip and the value of the voltage is seen as a grey scale distribution on

the PIV image map. Ideally, images should have a high charge i.e. appear white and

the background noise level of the CCD chip should be i.e. appear dark.


33

There are several types of CCD cameras with differing layout/architecture of

the CCD array. Basically, the architecture of the CCD array influences whether the

particular camera can be used for auto- or cross-correlation image capture.

Historically, auto-correlation has been the most commonly used method of image

capture in PIV initially because photographic film was used as an image capturing

medium. Thereafter, CCD camera frames could not be advanced quickly enough to

record images with a short time interval between them. Now, cameras are available

which can have a very short time between double frames so cross-correlation image

capture is now possible. In cross-correlation, the initial positions of the seeding

images in the flow field are recorded on the first frame of the camera, the camera

frame is advanced, and the final positions are recorded on the second camera frame.

The two images can then be processed, using cross-correlation algorithms, to obtain

a velocity vector map of the imaged flow field. Directional velocity information is

unambiguously obtained since it is known which is the first and which is the second

frame.

3.1.1.1.(4). Correlation Processing

PIV processing basically determines the distance that the particles have

moved in the time between laser illuminations in photographic based or laser pulses

in digital PIV. There are three general types of data reduction techniques used to

process PIV image data: auto-correlation, cross-correlation and particle tracking. The

choice of a processing technique depends primarily on the available equipment used

to record the particle image data and the seed particle concentration. Correlation

based processing techniques produce spatially averaged velocity estimates. The

recorded image frame is divided into small subregions, each containing particle

images. By processing the image over a regular grid of small subregions, a velocity

vector map is generated. Both auto and cross-correlation operations are implemented

using Fast Fourier Transforms (FFT), since this technique is more efficient than the

direct numerical computation of the correlation.


34

Auto-correlation processing is the oldest of the PIV processing techniques,

essentially due to the fact that film based recording systems were incapable of

recording independent particle image records at two closely spaced instances in time.

In the auto-correlation technique a single image frame is exposed multiple times and

processed over a regular grid of small subregions.

In cross-correlation of PIV, two single exposure image frames must be

recorded. The cross-correlation operation is similar to auto-correlation where again

the image frames are divided into small subregions. However, now a subregion from

image 1 (recorded at the first laser pulse) is cross-correlated with a subregion from

image 2 (recorded at the second laser pulse). The resulting output on the correlation

plane is a single-peaked function, where the peak represents the average

displacement of the particles across the subregion between the two laser pulses. The

direction of the displacement is determined unambiguously because the images from

exposures 1 and 2 are recorded separately. Figure 3.3 shows principles of cross-

correlation process of the PIV technique.

Figure 3.3. Cross-correlation in PIV


35

3.1.2. Dye Visualization

The observation of fluid motion using dye is one of the oldest visualization

techniques in fluid mechanics, dating back to the time of Leonardo da Vinci. The

technique is inexpensive and easy to implement. Above all, it offers significant

insight into the phenomena occurring in complex fluid flows. In fact, some of the

major discoveries in fluid phenomena were made using this simple technique. A

classic example is the experiment by Osborne Reynolds in which dye injection

method was used to show the transition from a laminar flow to turbulent flow in a

pipe.

Of all the flow visualization techniques, dye flow visualization is perhaps the

easiest to carry out. Most often, food dye is used because it is safe to handle. Under

normal lighting a dilute fluorescent dye solution appears almost transparent, but

when illuminated with a laser light source of an appropriate wavelength the dye

fluoresces strongly. This unique property has attracted many to use it to visualize the

internal structures of fluid flow by illuminating it with a thin sheet of laser light.

Some of the common fluorescent dyes used in flow visualization include

Fluorescein, Rhodamine-B and Rhodamine-6G.

There are various methods of introducing dye into the flow. Most commonly,

it is released through a dye probe which is usually fabricated using either a

hypodermic needle or stainless steel tubing of 1.5 to 2.0 mm in diameter. The

advantage of this technique is that the probe can be moved easily within the flow and

the dye can be released at the location of interest. However, its greatest drawback is

the disturbance that the probe may cause to the flow field. To minimize this effect,

the probe is often located some distance upstream from the point of observation. The

dye is usually supplied to the probe by either a gravity-feed or a pressurized

reservoir. In either case, the dye exit velocity must be equal to the local flow velocity

in order to minimize the disturbance of the flow. When the exit velocity is too high, a

jet like flow is produced which generates mushroom-like structures. Similarly, when

the exit velocity is too low, wake structures are formed which appear as a series of


36

interconnecting vortex loops. When a correct exit velocity is reached the dye should

appear as a smooth filament.

Qualitative flow visualization experiments were performed by injecting

fluorescence dye Rhodamine-B from the leading edge of the model using home made

mechanisms. Measurement were performed in the vertical symmetry plane z=0 and

horizontal xz-plane y/H=0.5H at the geometrical center of the model.

Measurements planes were illuminated by a double-pulsed Nd:YAG

(Neodymium: Yttrium-Aluminum-Garnet crystals) laser unit of New Wave Research

at a wavelength of 532nm, with a maximum energy output of 120mj/pulse. The

SONY DCR-TRV355E camera was used to capture the instantaneous video images

of flow field. The images were analyzed with frame grabber and enhanced using

Adobe Photoshop software.

3.1.3. Drag Measurements

Measurements of drag of bus models were conducted with the Plint Three

Component Balance system (Plint and Partners Ltd.) in a wind tunnel made by Plint

and Partners Ltd. model TE44 without ground effect (Figure 3.4, and 3.5). The wind

tunnel is an open-circuit blower type subsonic wind tunnel, and is able to generate

flow speeds of up to 33 m/s. The test section is 457mm x 457 mm cross-section and

1200 mm length. Measurements were conducted at a flow speed of 25m/s.

The balance was constructed mainly in the aluminum alloy and its main

framework comprises a mounting plate which was secured to the wind tunnel

working section and carries a triangular force plate. The force plate and mounting

plate were connected by three supporting legs, disposed at the corners of the force

plate. Each leg was attached to the force plate and mounting plate by spherical

universal joints. The effect of this was to constrain the force plate to move in a plane

parallel to the mounting plate, while leaving it free to rotate about a horizontal axis;

the necessary three degrees of freedom was thus provided.


37

Figure 3.4. Drag measurements in the wind tunnel (Side view)

Figure 3.5. Three component balance system and model


38

Models are provided with a 12 mm diameter mounting stem and this was

inserted in the bore of the model support and secured by a collet tightened by the

model clamp. The model support was graduated on the periphery and was free to

rotate in the force plate for adjustment of the angle of incidence of the model, while

its position may be locked by means of an incidence clamp.

The forces acting on the force plate was transmitted by way of flexible cables

to strain gauge load cells which measure respectively the fore and lift forces and the

drag force. The drag cable, which lies horizontally, acts on a line through the centre

of the model support, while the two lift cables act vertically through points disposed

equidistant from the centre of the model support and in the same horizontal plane as

the support. The sum of the forces on the fore and aft lift tapes thus gives the lift on

the model. A drag balance spring acts on the force plate to apply pre-load to the drag

load cell.

The output from each load cell was taken to a strain gauge amplifier carried

on the mounting plate and thence via a flexible cable to a display unit comprising a

set of three electronic voltmeters showing the output from the respective load cell

circuits. Lift and drag forces were calculated directly in Newtons.

3.2. Flow System

Experiments were conducted in a recirculating, open surface water channel

located in the Çukurova University Fluid Mechanics Laboratory shown in Figure 3.6.

The water channel test section has a width of 1000 mm, a depth of 750 mm, and a

length of 8000 mm. Side and bottom walls of the test section were equipped with 15

mm thick Plexiglas for optical access. The flow was driven by a 15 kW centrifugal

pump having a variable speed controller. Before entering the test chamber, the flow

passes through a settling reservoir, a honeycomb and a 2:1 contraction. The mean

velocity is uniform and average turbulent intensity is less than 0.5% in an empty test

section. The flow speeds vary linearly according to free stream velocity ranging from

0 to 297mm/sec and are calibrated for a test section water depth, Hw= 400mm.


39

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40

The experiments were performed at a free stream velocity of U=183 mm/s which

corresponds to the Reynolds number ReH=1.2x104 based on the model height.

The velocity profile and boundary conditions between the real road and the

wind tunnel conditions looks different and modifies the flow field around a vehicle.

One of the approaches to reproducing or simulating the road is to equip the wind

tunnel with an elevated ground plate that creates a much thinner boundary layer than

the wind tunnel floor (Hucho, 1998). For the present experiments, a 2 m long ground

plate mounted 0.1 m above the bottom wall of the test section was used to simulate

ground effects (Figure 3.6). The ground plate spans the cross section of the tunnel

and has a rounded leading edge to avoid flow separation. During the experiments all

bus models were fixed to the ground plate. The gap between the ground plate and the

bottom surface of the model was 9mm.

3.3. Experimental Apparatus and PIV Instrumentation

3.3.1. Experimental Models

In the present experiment three different bus models were studied. First

model was taken as a rectangular prism with square corners. This model was taken

for the purpose of comparison with other two models. The overall dimensions of the

model are; length, L=175mm, height, H=66mm and width, W=56mm. Figure 3.7

shows the layout of the model with the relevant dimensions. Figure 3.8 shows the

location of the model in the water channel. Figure 3.9 shows the bus model I

geometry. The length of the model L=175mm, the height, H=66 mm and the width

L=56 mm. Figure 3.10 shows schematically the location of the bus model I in the

water channel. Figure 3.11 depicts bus model II schematically. The front of the bus

model II is the same as the bus model I shown in the Figure 3.9. The bus model II

has the same overall dimensions as the bus model I. Figure 3.12 shows the water

channel with the bus model II installed.


41

Figure 3.7. Schematic representation of the rectangular body

Figure 3.8. Location of the rectangular body in the water channel (side view)


42

Figure 3.9. Schematic representation of the bus model I

Figure 3.10. Location of the bus model I in the water channel (side view)


43

Figure 3.11. Schematic representation of the bus model II

Figure 3.12. Location of the bus model II in the water channel (side view)


44

3.3.2. PIV Instrumentation

The velocity fields were measured by Dantec PIV system which consisted of

a dual-head Nd:YAG laser, a high resolution CCD camera, a synchronizer and

optics. Schematic of the PIV system used in this study is shown in Figure 3.13. The

measuring planes were illuminated by a thin and intense laser sheet by using a pair of

double-pulsed Nd:YAG laser units each having a maximum energy output of 120

mJ/pulse at 532 wavelength. The time interval between pulses was 1.2 ms. The

thickness of the laser sheet was approximately 2 mm. The time interval and the laser

sheet thickness were selected such that the maximum amount of particle

displacement in the interrogation window was obtained.

PIV measurements were performed at several vertical, horizontal and cross

planes which were selected to highlight the aerodynamic characteristics of the

models. Location of the laser sheet and the view of camera for measurement planes

as well as the coordinate system are shown in Figures 3.14, 15 and 16. In our

coordinate system x, y and z are respectively the streamwise, vertical and spanwise

directions. The origin of this system was located in the symmetry plane and

downstream bottom edge of the models. For the side view, the laser sheet was

oriented vertically, parallel to the flow direction through the center of the models

(Figure 3.14). For the plan view, the laser sheet was parallel to the bottom surface of

the water channel and the axis of the camera lens has a right angle intersection with

the laser sheet (Figure 3.15). For the end view, the laser sheet was oriented

perpendicular to the flow direction, and a surface mirror was installed downstream of

the models to reflect the image of the end view laser sheet to the recording CCD

camera. The angle between the mirror and the free-stream was 450. The distance

between the model’s base and the front edge of the mirror was kept approximately

8.5 H to eliminate the interference with the near-wake of the models (Figure 3.16).

The image capturing was performed by a Model MEGAPLUS ES 1.0 8-bit

cross-correlation CCD camera having a spatial resolution of 1024x1024 pixels with a

maximum frame rate of 15 frames per second. The camera was equipped with a

Nikon AF Micro 60 f/2.8D lens of a focal length of 60 mm. The Nd:YAG laser


45

andCCD camera were connected using a Dantec FlowMap Processor synchronizer to

control the timing of data acquisition.

The flow was seeded with silver-coated spherical particles of 12 μm in

average diameter. These particles are very close to being neutrally buoyant. The

silver coated hollow particles were mixed in a container and poured in to the water

channel. Then, the water channel was run at maximum speed for a period of several

minutes in order to ensure that particles were uniformly dispersed through the water.

Instantaneous velocity vector fields were generated using a cross-correlation

technique between successive particle images. A cross-correlation technique was

employed to determine the velocity vector for each interrogation area. The

dimensions of the interrogation area employed throughout were 32x32 pixels with

50% overlap providing 3844 velocity vectors over the entire field of view plane. To

determine the time-averaged mean flow structure, 300 instantaneous velocity fields

were measured. These instantaneous velocity fields were averaged to obtain the

corresponding time-averaged patterns of vorticity <ω> and streamline <ψ> topology.

3.4. Post-Processing

The post-processing of the raw velocity field involves vector validation,

removal of spurious vectors, replacement of the removed vectors, and data

smoothing and filtering.

In PIV, particle images are correlated to obtain vector displacement

information. Since the particle images themselves are random functions, the resulting

correlation functions have random components which create a finite probability of

having erroneous measurements which must be removed before the dataset can be

used. After the velocity field was calculated, the vectors were validated using

CleanVec (CleanVec is a PIV vector validation program written by Ron Adrian's

group in Theoretical and Applied Mechanics at the University of Illinois). Following

the process of removing incorrect vectors, a bilinear least-square fit technique was

used to fill in the areas of missing vectors, scale the image field to the actual flow

field, and compute the vorticity distribution. The resulting velocity field was also


46

smoothed by using a Gaussian-weighted technique based on the work Landreth and

Adrian (1989). A suggested smoothing parameter of 1.3 was used for the results of

this study.

The resulting vector field and streamline topology are obtained from

TECPLOT (Amtec Engineering Inc., 2003). The out-of-plane vorticity contours are

generated and displayed using SURFER (Golden Software Inc., 2002). Figure 3.17

and 3.18 shows the velocity vector map (raw data) of instantaneous flow field in the

wake region of the bus Model II and velocity vector map of the instantaneous flow

field in the wake region of the bus Model II after post-processing, respectively.


47

Figure 3.13. Schematic representation of the experimental setup and PIV system


48

Figure 3.14. Orientations of laser sheet and camera position for side view plane


49

Figure 3.15. Orientations of laser sheet and camera position for plan view planes


50

Figure 3.16. Orientations of laser sheet and camera position for end view planes


51

Figure 3.17. Velocity vector map (raw data) of instantaneous flow field in the wake region of the bus Model II

Figure 3.18. Velocity vector map of the instantaneous flow field in the wake region of the bus Model II after post-processing

4. RESULTS AND DISCUSSIONS Cahit GÜRLEK

52

4. RESULTS AND DISCUSSIONS

In this study, flow around a rectangular body and two different rear end

shaped bus models are analyzed using both particle image velocimetry (PIV) and

flow visualization techniques. The Reynolds number based on the model heights, H

and the free stream velocity, U was about ReH=1.2x104. Rodi et al. (1997) presented

the simulation of flows around the surface cube at two different Reynolds numbers,

3000 and 40.000, based on the incoming velocity and cube height. They found a

great similarity in the results for these two flows. The time-averaged coherent

structures had almost identical shapes and sizes in the two flows. Thus it seems likely

that the qualitative knowledge about flow around three-dimensional bluff bodies

(such as a car) can be extracted from the flow at lower Reynolds number. This

observation is not new and has long been used for experimental studies (Ahmed, et

al. 1984, Duel and George, 1999). Note, however that the choice of the lower

Reynolds number, which is high enough to produce a flow similar to that around a

full-scale vehicle is not trivial (Krajnovic and Davidson, 2003).

In the present study PIV measurements were performed at several vertical,

horizontal and cross planes which were selected to highlight the aerodynamic

characteristics of the models. The PIV technique provided instantaneous and time-

averaged velocity vector maps, vorticity contours, streamline topology and

turbulence characteristics.

4.1. Flow Around a Rectangular Body

4.1.1 Flow Around a Rectangular Body With Zero Yaw Angle

Flow around a three-dimensional rectangular body located in close proximity

to the ground board has been investigated by using the particle image velocimetry

technique. In this part of study, the rectangular body is set with zero degree of yaw

angle to the main flow direction. The flow Reynolds number based on the

rectangular body height, H and the free stream velocity, U was about ReH=1.2x104.


53

PIV measurements were performed in the vertical symmetry plane (side-view plane)

at z=0 and six different horizontal xz-planes (plan-view planes) at elevations of

y/H=-0.1, y=0, y/H=0.19, y/H=0.34, y/H=0.5 and y/H=0.8. Figure 4.1.1 shows the

PIV measurement planes. Detailed flow structures and characteristics were obtained

by averaging over 300 instantaneous velocity maps. In addition to the PIV

measurements, flow visualization studies were also carried out.

Figure 4.1.1. PIV measurement planes


54

4.1.1.1 Time-Averaged Velocity Field

Figure 4.1.2 presents the time-averaged velocity vector maps, <v>, the

patterns of streamlines, <ψ> and the corresponding vorticity contours, <ω> along the

rectangular body in the vertical symmetry plane, z=0. The minimum and incremental

values of the vorticity contours are <ωmin> =±2s-1 and <∆ω>=2s-1, respectively.

Contours of positive (clockwise) and negative (counterclockwise) vorticity are

indicated by solid and dashed lines, respectively. As the free-stream flow approaches

to the model, the speed of the flow particularly along the central axis deteriorates

gradually and hence a stagnation point appears at the central point of the model. The

time-averaged patterns of streamlines are diverged rapidly as the free-stream flow

takes place in close region of the front surface of the model and hence the

approaching flow is further divided into two main flows. The division starts from the

half-saddle point of attachment, Sab indicated by a small arrow in Figure 4.1.2,

located on the upstream surface of the model. One part of the flow is oriented

towards the bottom surface and the other part is oriented towards the roof surface of

the model. Animations of 300 instantaneous images indicate that, this saddle point of

attachment Sab moves upward and downward directions in random motion. As soon

as the flow passes the sharp corners, the flow begins to separate rapidly. The upper

part of flow is separated starting from the sharp leading top edge and hence a large

reverse flow region is formed. The leading–edge shear layer is reattached to the

model roof surface as indicated by a half-node of attachment, Na. Here, the centers of

the foci, saddle points, the node of attachment and the line of divergence designated

as F, S, Na and Ld, respectively. The distance of the reattachment point to the leading

edge is x/H=1.3 which corresponds to 48% of the model length. This shear layer

reattachment directly influences the drag on the model (Higuchi, 2006). Patterns of

streamlines, <ψ> along the vertical symmetry plane indicates that a well defined

focus, F1 occurs on the roof surface of the model. The distance of the focus, F1 to the

leading edge of the model is x/H=0.66. Downstream of the model, separation occurs

and two shear layers are developed which interact with each other in the near wake

region. Regions of positive and negative vorticity contours are created by the


55

Figure 4.1.2. Patterns of time-averaged velocity vector maps <v>, streamlines <ψ> and vorticity contours <ω> in the vertical symmetry plane z=0. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


56

upperbody shear layer and the underbody shear layer, respectively. The length of the

underbody shear layer is shorter than the length of the upperbody shear layer as a

result of the ground effect. Jet like flow emerging from the narrow gap between the

lower wall of the model and ground surface creates the base corner vortex. In the

wake region, two circulatory bubbles are observed, one located above the other, and

they rotate in the sense of opposite directions. The bubble rotating in clockwise

direction interacts with the upper region of the vertical base of the model, while the

lower bubble, which rotates in the opposite direction, covers the bottom surface. The

upsweep flow in the circulatory region is clearly identifiable. The saddle point, S1

defines the size of the wake region. The time-averaged velocity vector, <v> map and

the corresponding patterns of streamline, <ψ> clearly indicate the location of the

saddle point which is far from the model base with a distance of x/H=1.07 which

corresponds to 40% of the model length. Between nodal point of attachment, Na and

saddle point, S1, a line of divergence, Ld takes place. A pair of foci F2 and F3 are

observed near the bottom and upper edges of the model with distances of x/H=0.11

and 0.48, respectively. Nodal point of attachment, Na is also evident as seen in

Figure 4.1.2.

Figure 4.1.3 shows the time-averaged normalized velocity profiles in the

wake region downstream of the model at the selected locations in the vertical

symmetry plane, z=0. Here, velocity components are normalized with the free stream

velocity, U. Figure 4.1.3.a shows the streamwise velocity profiles, /U at different

locations downstream of the model. The wake flow downstream of the model is

reversed causing a negative velocity in between x/H=0.11 and x/H=1.07. The

maximum reversed velocity in the recirculatory flow region is approximately one-

fifth of the free stream velocity, U. The location of the maximum reversed velocity

coincides with the midsection of the model. In the first measuring plane at a station

of x/H=0.11, streamwise velocity component takes negative values between y/H=0.2

and y/H=1 which corresponds to the boundaries of the model. Because of the jet flow

occurring between the ground and the bottom surface of the model, the value of

streamwise velocity increases in this region. The rate of increase in the streamwise

velocity across the shear layer at the upper part of the model is due to the


57

Figure 4.1.3. Velocity profiles of the flow in the vertical symmetry plane z=0 in the wake region. [a] Dimensionless streamwise velocity component U, [b] Dimensionless spanwise velocity component <v/>U


58

entrainment of wake and the core flow regions. The jet flow emanating from the

narrow gap between the ground board and the bottom surface of the model travels

towards the mid-section of the model and later interacts with the reversed flow

arising from the upper trailing edge and loses its strength rapidly. As a result of this

interaction, a negative velocity region occurs below the level of y/H=0.8 at the

measuring section of x/H=0.48. Since the third measuring section, x/H=1.07

correspond to the saddle point, streamwise velocity distribution in the spanwise

direction does not indicate any negative velocity value. Figure 4.1.3.b displays the

time-averaged spanwise velocity profiles, <v>/U in the symmetry plane. Rapid

changes in velocity profiles occur along the lateral directions of shear layers. These

velocity profiles reveal that there is an intense shear throughout the velocity field.

Positive spanwise velocity in the near wake indicates the upsweep flow. The

maximum upsweep velocity is 0.07 times the free stream velocity, U. The velocity

field viewing both distributions of the velocity components, u and v present that, the

flow field is not symmetric due to the ground effect.

Figure 4.1.4 presents the profiles of the root mean square of streamwise and

spanwise velocity components, <urms>/U and <vrms>/U normalized by the free stream

velocity, U and Reynolds stress correlation, <u′v′>/U2 normalized by the square of

the free stream velocity in the central region of vertical plane. The locations of peak

values of <urms>/U and <vrms>/U take place along the upperbody and underbody

shear layers. The magnitude of the root mean square of streamwise velocity

fluctuations, <urms>/U shown in Figure 4.1.4.a are higher in the upperbody shear

layer emanating from the upper trailing edge than that of in the underbody shear

layer emanating from the lower trailing edge as a result of the ground effect. The

peak value of <urms>/U in the upperbody shear layer is approximately 0.16 at

x/H=1.5. The root mean square of spanwise velocity components, <vrms>/U

presented in Figure 4.1.4.b shows a similar trend. The maximum value of <vrms>/U is

approximately 0.12 at x/H=1.07 which is smaller than the corresponding value of

<urms>/U at the same location. Profiles of the Reynolds stress correlation, <u′v′>/U2

are shown in Figure 4.1.4.c. The maximum value of Reynolds stress correlation,

<u′v′>/U2 appears along the upperbody shear layer with a magnitude of 0.011


59

Figure 4.1.4. Profiles of turbulence properties in the vertical symmetry plane z=0 in the wake region. [a] Root mean square of streamwise velocity fluctuations <urms>/U, [b] spanwise velocity fluctuations <vrms>/U, [c] Reynolds stress correlations <u′v′>/U2


60

Figure 4.1.5. Contours of streamwise velocity fluctuations <urms>/U, spanwise velocity fluctuations <vrms>/U, and Reynolds stress correlations <u′v′>/U2 in the vertical symmetry plane z=0 in the wake region. Minimum and incremental values of rms of velocity components are [<urms>/U]min=0.0075, ∆[<urms>/U]=0.0075, [<vrms>/U]min=0.0075, ∆[<vrms>/U]=0.0075 and Reynolds stresses correlations are [<u′v′>/U2]min=±0.00075, ∆[<u′v′>/U2]=0.00075


61

at x/H=1.07. Magnitude of Reynolds stress correlations, <u′v′>/U2 along the

underbody shear layer are smaller comparing to the upperbody shear layer.

Figure 4.1.5 shows the contours of streamwise velocity fluctuations <urms>/U,

spanwise velocity fluctuations <vrms>/U, and Reynolds stress correlations <u′v′>/U2

in the vertical symmetry plane z=0 in the wake region.

The time-averaged velocity vectors map, <v> the patterns of streamlines,

<ψ> and the corresponding vorticity contours, <ω> in the horizontal xz-plane at the

geometrical center of the model is exhibited in Figure 4.1.6. The main features of the

flow in this plane are two shear layers originating from the sharp leading side edges

of the model, and the reversed flow region downstream of the model. As the

bifurcating streamlines of the incoming flow approaching to the front surface of the

model, a half-saddle point of attachment, Sab appears on the front surface of the

model. The flow is separated from the vertical side edges and formed two

recirculatory flow regions on both side walls of the model. The separating and

reattaching shear layers and the circulating flow within the separation bubbles are

clearly seen from the stream line patterns in Figure 4.1.6. Regions of high vorticity

contours define the side wall shear layers. The distance of the reattachment points to

the leading edge of the model is about x/H=1.06. A well defined pair of foci, F1 and

F2 are observed near the side walls of the model which are far from the leading edge

with distances of x/H=0.74. In the wake region at the rear part of the model, a pair of

similarly sized recirculation region is identified. These two shear layers extend

approximately to the same downstream location. A pair of identical foci F3 and F4

and a saddle point, S1 are observed in the wake region. The distances of these points,

F3, F4 and S1 to the vertical model base are x/H=0.45, 0.45 and 1.13, respectively.

Figure 4.1.7 presents the time-averaged velocity profiles of the near wake of

the model in the horizontal xz-plane at y/H=0.5. The streamwise velocity profiles,

/U are shown in Figure 4.1.7.a. Similar to the vertical symmetry plane data

shown in Figure 4.1.3.a, the reversed flow region occurs resulting in a negative

streamwise velocity, u beginning from the rare surface of the model up to a point

with a distance of x/H= 1.07. The maximum upstream velocity in the wake region is

0.16 times the free stream velocity, U. The maximum values of lateral velocity


62

Figure 4.1.6. Patterns of time averaged velocity vector maps <v>, streamlines <ψ> and vorticity contours <ω> in the horizontal xz-plane for y/H=0.5. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


63

Figure 4.1.7. Velocity profiles of the flow in the horizontal xz-plane for y/H=0.5 in the wake region. [a] Dimensionless streamwise velocity component U, [b] Dimensionless cross-stream velocity component <w>/U


64

Figure 4.1.8. Profiles of turbulence properties in the horizontal xz-plane for y/H=0.5 in the wake region. [a] Root mean square of streamwise velocity fluctuations <urms>/U, [b] cross-stream velocity fluctuations <wrms>/U, [c] Reynolds stress correlations <u′w′>/U2


65

Figure 4.1.9. Contours of streamwise velocity fluctuations <urms>/U, and Reynolds stress correlations <u′v′>/U2 in the horizontal xz-plane for y/H=0.5 in the wake region. Minimum and incremental values of rms of velocity components are [<urms>/U]min=0.01, ∆[<urms>/U]=0.01, and Reynolds stresses correlations are [<u′w′>/U2]min=±0.0005, ∆[<u′w′>/U2]=0.0005


66

component, <w/U> take places in the inner regions of the shear layers at x/H=0.11.

The difference of the lateral velocity component, <w/U> between locations situated

on both sides of the central axis is attenuated at x/H=0.48. Figure 4.1.8 shows the

profiles of the root mean square of streamwise velocity component, <urms>/U, and

cross-stream velocity component, <wrms>/U and the corresponding Reynolds stress

correlations, <u′w′>/U2 in the horizontal xz-plane at y/H=0.5. The distributions of

the root mean square of streamwise velocity fluctuations, <urms>/U shown in

Figure 4.1.8.a indicate two maxima at two different locations along the lateral

direction which correspond to the edge shear layers and have a symmetrical

structure. The fluctuations of the cross-stream velocity components, <wrms>/U in the

lateral direction shown in Figure 4.1.8.b reveal that the values of <wrms>/U in

upperbody shear layers are bigger than that of in underbody shear layer. Profiles of

the Reynolds stress correlation, <u′w′>/U2 shown in Figure 4.1.8.c indicate that the

peak values of the Reynolds stress correlations, <u′w′>/U2 occur along the shear

layers emerging from the both sides of the trailing edges. Figure 4.1.9 shows the

contours of streamwise velocity fluctuations <urms>/U, and Reynolds stress

correlations <u′v′>/U2 in the vertical symmetry plane z=0 in the wake region.

The time-averaged velocity vector maps, <v>, the streamline patterns, <ψ>

and the corresponding vorticity contours, <ω> in the wake region downstream of the

rectangular body in the horizontal xz-plane for different six levels such as y/H=-0.1,

y/H=0, y/H=0.19, y/H=0.34, y/H=0.5 and y/H=0.8 are shown in Figures 4.1.10,

4.1.11 and 4.1.12, respectively. It is evident that these images correspond to a

symmetrical pattern of flow field. In all y/H levels a pair of counter-rotating flows

can be easily observed downstream of the rectangular body as indicated by the time-

averaged streamline patterns, <ψ> presented in Figure 4.1.11. At y/H=-0.1 and

y/H=0, a flow field which is oriented in the downstream direction, exists along the

gap region between the model base and saddle point, S2. This region disappears at

other levels and reverse flow occupies the whole region between the model base and

saddle point, S1. Close to the ground board at y/H=-0.1 a reverse flow takes place in

between saddle points, S2 at x/H=0.22 and S1 at x/H=1.13 and two main foci, F1 and


67

F2 appear downstream of the saddle point S2. For the case of y/H=0, the saddle point

S2 observed further downstream of the model base at x/H=0.37. The reverse flow

region shrinks in size compared to the results obtained from other measuring-sections

and takes place between S2 at x/H=0.37 and S1 at x/H=0.97. Two main foci, F1 and

F2 appear close to the saddle point, S2. At levels of y/H=-0.1 and y/H=0 the time-

averaged streamline topology downstream of the model involving critical points S1,

S2, F1 and F2 takes on a form known as an owl face of the first kind. For levels of

elevations, y/H=0.19, y/H=0.34 and y/H=0.5 similar flow behaviors are observed.

The circulation regions between the rear wall of the model and saddle point S1

extend up to approximately 1.13 of the model height. For the case of y/H=0.8, the

size of the reverse flow region is reduced and saddle point, S1 takes place at

x/H=0.55. Two main foci, F1 and F2 displaced upstream of the saddle point, S1. The

present results indicate that the flow structure in the wake region downstream of the

rectangular body vary significantly with the elevation level.

The size of the wake region is smallest at an elevations of y/H=-0.1 and

y/H=0 indicated by the velocity vectors map, <v> and the corresponding patterns of

streamline, <ψ> presented in Figures 4.1.10 and 4.1.11 respectively. Particularly at

an elevation of y/H=-0.1 the saddle point, S2 is developed at a location close to the

base of the model due to the entrainment caused by the flow emerging on the trailing

edge of the model. A cluster of vorticity takes place along the shear layers emerging

on both sides of the model.


68

Figure 4.1.10. Patterns of the time averaged velocity vector maps <v> in the horizontal xz-plane for different y/H levels in the wake region


69

Figure 4.1.11. Patterns of the time averaged streamlines <ψ> in the horizontal xz-plane for different y/H levels in the wake region


70

Figure 4.1.12. Patterns of time averaged vorticity contours <ω>, in the horizontal xz-plane for different y/H levels in the wake region. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


71

4.1.1.2 Instantaneous Velocity Field and Flow Visualization

This section presents the instantaneous flow fields and flow visualization

images in the vertical symmetry plane (side-view plane) at z=0 and the horizontal

xz-plane (plan-view plane) at an elevation of y/H=0.5 at the central axis of the model

to illustrate the instantaneous structure of the flow around the rectangular body.

Figure 4.1.13 presents the instantaneous flow patterns along the top roof of the model

on the vertical symmetry plane obtained by the PIV technique. The instantaneous

velocity vectors map, v and the corresponding stream lines, ψ clearly presents that

the large-scale swirling patterns of velocity vectors are evident near the roof surface

of the model. These circulatory flow patterns interact severely with the surface of the

model in random mode. The time-averaged flow data presented in Figure 4.1.2

indicates that reattachment occurs at x/H=-1.3. On the other hand animation of 300

instantaneous velocity vector fields reveals that, the location of the reattachment

point moves in forward and backward directions in an unsteady manner. The

instantaneous flow structures along the roof of the model present the generation of

additional vortices comparing to the time-averaged flow data. The instantaneous

velocity vectors map, v and the patterns of stream lines, ψ present three different

vortices. Combination of these vortices creates a well defined single vortex

occupying the whole area of the wake flow region with an expansion in the flow

direction at frame numbers N=57, 59, 61 and 66. Contours of vorticity, ω show that

the concentration of vortices occurs along the shear layer. As soon as the wake

region expands in the flow direction with a single focus, the vortex elongates in the

flow direction along the shear layers. This unsteady flow structure, for example,

having vortices close to the surface of the model may cause vibration and noise due

to the strong interactions. The strength of these vortices depends on the sharp

(square) corners. It is commonly known that rounding these sharp corners degrades

the level of the vorticity strengths.

The instantaneous flow structure in the wake region downstream of the model

on the vertical symmetry plane (side-view plane) shown in Figure 4.1.14 indicates

that, swirling patterns of velocity vectors take place along the inner regions of the


72

upperbody shear layer. On the other hand, well defined large-scale swirling patterns

of velocity vectors are evident on the bottom edge of the vertical base of the model.

The positive vortex induced in the under body shear layer grows in size, elongates

and loses its strength as shown in the first three frames. The point of attachment on

the ground surface travels forward and backward in the flow direction in unsteady

mode. Shear layers emanating from the upperbody and lowerbody surfaces cause

complex flow field which consists of a number of vortices that move randomly in

time and space. At N=14 the distributions of velocity vectors, v the patterns of

streamlines, ψ and the corresponding vorticity contours, ω clearly show that a small

size vortex (F1 or V1) is developed on the lower side of the rear wall of the model.

On the other hand primary vortex (F2 or V2) takes place along the inner face of the

shear layer emanating from the top trailing edge of the model. As soon as focus, F2

or vortex V2 enlarges in size this vortex moves upward in vertical direction along the

vertical wall of the model. Focus F2 or vortex V2 attenuates and moves away from

the close region of the model travels further downstream. In the last column of

Figure 4.1.14 the patterns of vorticity, ω which has elongated shape and designated

as V2 changes the path in downward and upward directions. When this upper vortex,

V2 moves upward the other vortex in the lower part of the image expands in size and

occupy a larger wake region. The wake flow covers a larger region under this

combination. Figure 4.1.15 shows the instantaneous flow field downstream of the

model in the horizontal xz-plane (plan-view plane) at an elevation of y/H=0.5. The

generations of additional vortices are clearly visible. Circulatory flow motions which

increase the rate of entrainment between the wake and the main flow regions take

place along the both shear layer. Namely, well defined Kelvin-Helmholtz vortices

occur. These vortices on both side of the wake flow region combine together to

create a well defined cluster of vorticity. Topology of the flow structure clearly

shows that the size of the wake flow region changes randomly.


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Figure 4.1.13. Patterns of instantaneous velocity vectors v, streamlines ψ and vorticity contours ω in the vertical symmetry plane z=0 on the roof of the model. Minimum and incremental values of vorticity are ωmin=±2s-1 and ∆ω=2s-1


74

Figure 4.1.14. Patterns of instantaneous velocity vectors v, streamlines ψ and vorticity contours ω, in the vertical symmetry plane z=0 in the wake region. Minimum and incremental values of vorticity are ωmin=±2s-1 and ∆ω=2s-1


75

Figure 4.1.15. Patterns of instantaneous velocity vectors v and streamlines ψ in the horizontal xz-plane for y/H=0.5 in the wake region


76

The spectra of streamwise velocity fluctuations obtained using FFT analysis

for three selected points in the vertical symmetry plane (side-view plane) are shown

in Figure 4.1.16. The location of these selected points are in the lower shear layer

taken as point 1 at x/H=0.25, y/H=0.4, in the upper shear layer taken as point 2 at

x/H=0.22, y/H=1.09 and close to the saddle point, S1 taken as point 3 at x/H=0.99,

y/H=0.25 in the wake region. The dominant frequency of 0.414 at the third point

close to the saddle point corresponds to the Strouhal number St=fH/U=0.153 (based

on the model height H and the free steam velocity U) and is consistent with the

experimental results of Duell and George (1999) and numerical results of Krajnovic

and Davidson (2001a) around bus like ground vehicle body. Duell and George

(1999) measured St=0.155 at the point close to the free stagnation point and they

concluded that this peak indicates the vortex pairing close to the free stagnation

point. Figure 4.1.17 shows the spectra of streamwise velocity fluctuations evaluated

at various locations in the horizontal xz-plane y/H=0.5 in the wake region

downstream of the model. The spectra taken from the upstream locations of the

model do not show a dominant frequency.

Figure 4.1.16. The spectrum of streamwise velocity fluctuations for selected points in the vertical symmetry plane z=0 in the wake region


77

Figure 4.1.17. The spectrum of streamwise velocity fluctuations for selected points in the horizontal xz-plane for y/H=0.5 in the wake region


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The dye flow visualization of separating shear layers on the upper surface of

the model (in the vertical symmetry plane at z=0) and on the lateral side wall (in the

horizontal xz-plane at y/H=0.5) are shown in Figures 4.1.18.a and b, respectively.

Shear layer instabilities were clearly identifiable both in vertical and horizontal

planes. Flow visualization both on the roof of the model and around the vertical side

wall displays identical flow structures due to the geometrical similarity. Quantitative

data obtained by PIV shown in Figure 4.1.13 and qualitative flow data obtained by

dye flow visualization presented in Figure 4.1.18.a are in good agreement with each

other. In both cases, a well defined vortex appears as soon as separation starts and

expands in size while revolving further downstream. Figure 4.1.19 presents the dye

flow visualization in the wake region on the vertical symmetry plane. A well-defined

ring type vortex clearly appears on the lower side of the rear wall of the model due to

the jet like flow immerging underbody of the model.


79

Figure4.1.18. Dye flow visualizations [a] on the model roof in the vertical symmetry plane z=0. [b] on the lateral vertical side in the horizontal xz-plane for y/H=0.5

Figure 4.1.19. Dye flow visualization in the vertical symmetry plane z=0 in the wake

region


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4.1.2 Flow Around a Rectangular Body With 10 Degree Yaw Angle

In this part of study the rectangular body is set with 10 degrees of yawing

angle to the flow direction. The flow around a rectangular body with off-set angle

has been studied, because the obstacle has a certain angle to the flow in many actual

situations. The drag coefficient at zero yaw angle, equivalent to driving in still air,

gives insufficient indication of aerodynamic characteristics in real operation, where

tangential force coefficient CT (due to yaw) must be taken into account. All vehicle

types show a considerable increase in CT with increasing yaw angle (Hucho, 1998).

Figure 4.1.20 shows drag versus yaw of different vehicle types.

The flow field analyzed both using PIV and flow visualization techniques.

The PIV technique provided instantaneous and time-averaged vorticity contours, and

streamline topology around the rectangular body. Measurements were performed in

horizontal xz-plane at an elevation of y/H=0.5.

Figure 4.1.20. Drag versus yaw of different vehicle types (Hucho, 1998)


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4.1.2.1 Time-Averaged Velocity Field

Figure 4.1.21 presents the time-averaged patterns of streamlines, <ψ> and the

corresponding vorticity contours, <ω> along the model in the horizontal xz-plane at

an elevation of y/H=0.5 having yaw angle of α=100. The minimum and incremental

values of the vorticity contours are <ωmin> =±4s-1 and <∆ω>=2s-1, respectively. The

approaching flow on the upstream of the model is decelerated and divided into

upward and downward flows at a half-nodal point of attachment, Sab on the front face

of the model. The bifurcation streamline, <ψ> attaches to the surface of the model at

the lower side. The approaching flow is separated from the corner A of the

rectangular body. Then, the shear layers and recirculating flows are observed around

corner A of the model. The circulation region on the upper face of the model (corner

A) is larger than the lower one in the side-view plane. Regions of high negative and

positive vorticity contours define the side wall shear layers. A well defined focus, F1

is observed in the upper circulating flow region (corner A). In the wake region at the

downstream of the model, an asymmetric large circulating flow region is identified.

A well defined corner vortex and a focus, F2 are observed near the upper corner of

the model in the wake region.

4.1.2.2 Instantaneous Velocity Field and Flow Visualization

The instantaneous streamline topology on the lateral upper face of the model

is shown in Figure 4.1.22. The results indicate that some small-scale vortices are

visualized in the main flow over the separation line. These small-scale vortices

coalesce to form larger-scale vortices. The vortex street stands along the shear layer,

and the size of the vortex becomes larger further downstream. Animation of these

instantaneous flow data reveals that the size of the wake region expands and shrinks

in size in random motion. The point of a half nodal point of attachment, Sab moves

side to side. The size of this separated flow region increases when the yaw angle

increases. Around the corner B separation occurs rarely because of the direction of

the incoming flow. Figure 4.1.23 depicts the instantaneous flow structure in the wake


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region downstream of the rectangular body. Instantaneous flow data shows that

multiple vortices are formed along the side wall shear layers in the wake region. The

instantaneous streamline patterns clearly indicate that the size of vortices gradually

increases in the downstream. The animation of 300 instantaneous patterns of

streamlines demonstrated that the vertical flow structure is sometimes dominant

along the lower shear layer, while sometimes dominant along the upper shear layer.

Significant differences between the time-averaged and the instantaneous flow

structures can be clearly seen. Small-scale vortices which are visualized in the

instantaneous streamline topology are not recognized in the time-averaged flow field.

In summary wake region occupies the region around corner C and downstream of the

model. Variation of this wake region as a size occurs unsteadily. Examining

Figures 4.1.21 and 4.1.22 together demonstrates that separated flow region starting

from the corner A covers the whole wall up to the corner C because of the yaw angle.

Flow visualization of the flow structure is shown in Figure 4.1.24. Kelvin-

Helmholtz vortices can be identified clearly along the shear layer. Small-scale

turbulent structures were found which is due to the earlier shedding of the Kelvin-

Helmholtz vortices from the leading upper edge of the rectangular body. The pairing

and combining of the Kelvin-Helmholtz vortices conducted in the downstream flow

field of the leading edge. Further downstream, well defined Kelvin-Helmholtz

vortices were found to break down into many small-scale vortices which yield the

fluctuation to a higher level. Because of yaw angle α=100 wake flow region takes

place starting from the leading edge up to the trailing edge of the model. The

instantaneous flow structure is well defined both by PIV and flow visualization

techniques.


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Figure 4.1.21. Patterns of time averaged streamlines <ψ> and vorticity contours <ω> in the horizontal xz-plane for y/H=0.5. Minimum and incremental values of vorticity are <ωmin>=±4s-1 and ∆<ω>=2s-1


84

Figure 4.1.22. Patterns of instantaneous streamlines ψ in the horizontal xz-plane for y/H=0.5


85

Figure 4.1.23. Patterns of instantaneous streamlines ψ in the horizontal xz-plane for y/H=0.5 in the wake region


86

Figure 4.1.24. Dye flow visualization on the lateral vertical side in the horizontal xz-plane for y/H=0.5


87

4.2. Flow Structures Around Bus Model I

In this section, flow around a three-dimensional bus model (Model I) has

been investigated by using the particle image velocimetry technique. The Reynolds

number based on the model height, H and the free-stream velocity, U was about

ReH=1.2x104. PIV measurements were performed in the vertical symmetry plane z=0

and horizontal xz-plane at the geometrical center of the model at an elevation of

y/H=0.5. Figure 4.1.1 shows the PIV measurement planes. Detailed flow structures

and characteristics were obtained by averaging over 300 instantaneous velocity

maps. The PIV results provided instantaneous and time-averaged velocity vector

maps, vorticity contours, streamline topology and turbulence characteristics.

Figure 4.2.1. PIV measurement planes


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4.2.1 Time-Averaged Velocity Field

Figure 4.2.2 presents the time-averaged velocity vector maps, <V>, the

patterns of streamlines, <ψ> and the corresponding vorticity contours, <ω> along the

bus Model I in the vertical symmetry plane z=0. The minimum and incremental



indicated by solid and dashed lines, respectively. On the upstream surface the flow is

divided in to an upperbody and underbody flow region from the front stagnation

point, Sab and one part of the flow is oriented towards the bottom surface and the

other part is oriented towards the roof surface. The size of the leading edge radii has

a substantial influence on the drag of a bus. The generation of the separation regions

with recirculating flow close to the leading edges influences the wind generated

noise and the accumulation of water and dirt on the surface of vehicle (Hucho, 1998).

As shown in Figure 4.2.2 detachment does not occur on the front part of the model

roof due to the adequate rounded leading edge. At the rear, the flow separated and an

asymmetric double vortex is observed. There is a large circulatory flow region

rotating in anticlockwise direction at the rear of the model. The length of the wake

region is approximately 0.99 times the height of the model. The main focus F1 is

found with coordinates x/H=0.18 and y/H=0.31. There is also a smaller circulatory

flow region rotating in clockwise direction which is located along the upperbody

shear layer. The focus F2 is approximately placed at x/H=0.52 and y/H=0.95.

Figure 4.2.2.c shows the underbody shear layer which has positive vortex, and

upperbody shear layer which has negative vortex in the wake region. The negative

vortex originating from the upper shear layer moves along the horizontal direction

while the positive vortex emerging from the beneath of the model tends to move

towards the wake center.


wake region downstream of the model at selected locations such as x/H=0.11,

x/H=0.48, x/H=1.07 and x/H=1.2 in the flow direction, on the other hand, in vertical

symmetry plane z is equal to zero. Here, velocity components are normalized with


89

Figure 4.2.2. Patterns of time-averaged velocity vector maps <V>, streamlines <ψ> and vorticity contours <ω> in the vertical symmetry plane z=0. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


90

the free stream velocity, U. Figure 4.2.3.a shows the streamwise velocity profiles,

<u/U> at x/H=0.11 downstream of the bus model. Here, in the lower part of the

velocity profile the positive velocity field is evident corresponding to the jet flow

emanating between the ground board and the bottom surface of the model. The

maximum positive velocity is 0.28 times the free stream velocity, U. In the middle

part of the velocity profile there is a negative velocity field located in between

y/H=0.36 and y/H=0.96 which indicates the reverse flow that happen downstream of

the bus model. The maximum negative velocity is approximately 0.05 times the free

stream velocity, U. At the second measuring section, x/H=0.48 significant reverse

flow at the rear side of the model can be clearly seen which is located in between

y/H=0.48 and y/H=0.93. The maximum reverse velocity in this profile is located at

y/H=0.75 and approximately 0.08 times the free stream velocity, U. Positive

streamwise velocity values, <u/U> are identified in the third and fourth measuring

sections x/H=1.07 and x/H=1.5. Figure 4.2.3.b displays the time-averaged spanwise

velocity profiles, <v/U> at the selected locations downstream of the bus model on

vertical symmetry plane, z=0. At x/H=0.11, near the base of the model, the spanwise

velocity is positive in the lower part of the velocity profile whereas in the middle

part, spanwise velocity takes a negative value. The spanwise velocity is mostly

positive for x/H=0.48 and x/H=1.07. The maximum positive spanwise velocity is

0.13 times the free stream velocity, U at x/H=0.48. Both distributions of the velocity

components, <u/U> and <v/U> indicate that, the wake flow is not symmetric due to

the ground effect.


spanwise velocity components, <urms/U> and <vrms/U> normalized by the free stream

velocity, U and Reynolds stress correlation, <u′v′/U2> normalized by the square of

the free stream velocity in vertical symmetry plane z=0. The locations of peak values

of <urms/U> and <vrms/U> take place along the shear layers. The magnitude of the

root mean square of streamwise velocity fluctuations, <urms/U> shown in

Figure 4.2.4.a are higher in the upperbody shear layer than that of in the underbody

shear layer. The maximum value of <urms/U> in the upperbody shear layer is

approximately 0.23 at y/H= 1.09 in the fourth measurement section, x/H=1.5.


91

Figure 4.2.3. Velocity profiles of the flow in the vertical symmetry plane z=0 in the wake region. [a] Dimensionless streamwise velocity component <u/U>, [b] Dimensionless spanwise velocity component <v/U>


92



93



94

The root mean square of cross stream velocity components, <vrms/U> presented in

Figure 4.2.4.b shows a similar trend. The maximum value of <vrms/U> is

approximately 0.07 at x/H=1.07 which is smaller than the corresponding value of

<urms/U> at the same location. Profiles of the Reynolds stress correlation, <u′v′/U2>


<u′v′/U2> appears along the upperbody shear layer with a magnitude of 0.01 at

x/H=1.5. Magnitude of Reynolds stress correlations, <u′v′>/U2> along the underbody

shear layer are smaller comparing to the upperbody shear layer. Figure 4.2.5 shows

the contours of streamwise velocity fluctuations <urms>/U, spanwise velocity

fluctuations <vrms>/U, and Reynolds stress correlations <u′v′>/U2 in the vertical

symmetry plane z=0 in the wake region.

Figure 4.2.6 presents the time-averaged velocity vector maps <V>, the

patterns of streamlines <ψ> and the corresponding vorticity contours <ω> along the

Model I in the horizontal xz-plane at an elevation of y/H=0.5 at the geometrical

center of the model. The minimum and incremental values of the vorticity contours

are <ωmin> =±2s-1 and <∆ω>=2s-1, respectively. Because of the geometrical

similarity, just one side of the front part of the model is presented for velocity vectors

map, <V> and the patterns of streamlines, <ψ>. There are two shear layers

originating from the leading edge on both sides of the model, and the reversed flow

region downstream of the model is present. Although the side walls of the Model I

have rounded leading edges, the flow is separated at the front lateral edges of the

body and formed two circulating regions on each side of the model. The separating

and reattaching shear layers and the circulating flow within the separation bubbles

are clearly evident from the stream line patterns presented in Figure 4.2.6.b. The

separated flow reattaches to the side wall surface at the nodal point of attachment, Na

with a distance of x=0.6 H. The circulating flow region close to the leading edge

generates noise. In the wake region downstream of the model the mean flow is

symmetric with respect to the geometrical symmetry plane and a pair of recirculating

region with similar size is identified. A pair of identical foci F2 and F3 at x/H=0.35,

z/H=±0.24 and a saddle point S1 at x/H=0.95 are developed in the wake region. The


95

saddle point, S1 shown in Figure 4.2.6.b indicates the merging of shear layers

emenating both sides of the bus model. Comparison of streamwise velocity

component shown in Figure 4.2.6.a indicate that developing flow regions extends

further downstream starting from the saddle point, S1. Regions of negative and

positive vorticity contours in Figure 4.2.6.c define the side wall shear layers. These

two shear layers extend approximately to the same downstream locations in the flow

direction.

Figure 4.2.7 presents the time-averaged velocity profiles on the horizontal

xz-plane at an elevation of y/H=0.5 in the wake region downstream of the Model I.

The streamwise velocity profiles, <u/U> are shown in Figure 4.2.7.a. The reverse

flow region occurs resulting in a negative streamwise velocity, u beginning from the

rare surface of the model up to a point with a distance of x/H= 1.07. The maximum

negative velocity in the wake region is 0.067 times the free stream velocity, U. The

flow characteristics are symmetric about the centerline of the model. Dimensionless

cross-stream velocity component <w/U> shown in Figure 4.2.7.b shows that the

maximum value of <w/U> occurs at x/H=1.07 indicating that the maximum mixing

fluids happen around this location. At firs station, x/H=0.11 the magnitude of

dimensionless cross-stream velocity components, <w/U> are smallest, but increases

gradually until x/H=1.07. Starting from this station, the level of the dimensionless

cross-stream velocity component, <w/U> decays down gradually. The distance

between maximum values of dimensionless cross-stream velocity component,

<w/U> is maximum at x/H=0.11, but this distance is minimum at x/H=0.15.

Dimensionless velocity components <u/U> and <w/U> show that minimum velocity

occurs at the central axis of measuring planes.

Figure 4.2.8 shows profiles of the root mean square of streamwise and

cross-stream velocity components, <urms/U>, <wrms/U> and the corresponding

Reynolds stress correlations, <u′w′/U2> in the central region of the horizontal plane.

The distributions of the root mean square of streamwise velocity fluctuations,

<urms/U> shown in Figure 4.2.8.a indicate two maxima at two different locations

along the lateral direction which correspond to the edge shear layers and have a

symmetrical structure. The fluctuations of the cross-stream velocity components,


96

<wrms>/U in the lateral direction shown in Figure 4.2.8.b reveal that the values of

<wrms>/U in upperbody shear layers are bigger than that of in underbody shear layer.

Profiles of the Reynolds stress correlation, <u′w′>/U2 shown in Figure 4.2.8.c

indicate that the peak values of the Reynolds stress correlations, <u′w′/U2> occur

along the shear layers emerging from the both sides of the trailing edges. It is clear

that all statistical curves are symmetric about the centerline. Profiles of turbulence

properties show that maximum fluctuations appear just downstream of the saddle

point, S1 at a location of x/H=1.07 due to the high rate of mixing flows. Figure 4.2.9

shows the contours of streamwise velocity fluctuations <urms>/U, spanwise velocity

fluctuations <vrms>/U, and Reynolds stress correlations <u′v′>/U2 in the vertical

symmetry plane z=0 in the wake region.


97

Figure 4.2.6. Patterns of time averaged velocity vector maps <V>, streamlines <ψ> and vorticity contours <ω> in the horizontal xz-plane for y/H=0.5. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


98

Figure 4.2.7. Velocity profiles of the flow in the horizontal xz-plane for y/H=0.5 in the wake region. [a] Dimensionless streamwise velocity component <u/U>, [b] Dimensionless cross-stream velocity component <w/U>


99

Figure 4.2.8. Profiles of turbulence properties in the horizontal xz-plane for y/H=0.5 in the wake region. [a] Root mean square of streamwise velocity fluctuations <urms>/U, [b] cross-stream velocity fluctuations <wrms>/U, [c] Reynolds stress correlations <u′w′>/U2


100

Figure 4.2.9. Contours of streamwise velocity fluctuations <urms>/U, spanwise velocity fluctuations <vrms>/U, and Reynolds stress correlations <u′v′>/U2 in the horizontal xz-plane for y/H=0.5 in the wake region. Minimum and incremental values of rms of velocity components are [<urms>/U]min=0.01, ∆[<urms>/U]=0.01, [<vrms>/U]min=0.01, ∆[<vrms>/U]=0.01 and Reynolds stresses correlations are [<u′v′>/U2]min=±0.0005, ∆[<u′v′>/U2]=0.0005


101

4.2.2. Instantaneous velocity field

The instantaneous flow structures in the wake region downstream of the

Model I on the vertical symmetry plane z=0 are shown in Figure 4.2.10.

Comparisons of the instantaneous flow structures reveal that additional vortices are

generated. Swirling patterns of velocity vectors take place along the upperbody shear

layer. On the other hand, well defined large-scale swirling patterns of velocity

vectors are evident in the lower part of the near wake region. The corresponding

pattern of instantaneous vorticity contours show that the positive vortex induced in

the underbody shear layer grows in size elongates and moves towards the model base

while the negative vortex originating from the upperbody shear layer moves almost

along the horizontal direction. In the separated shear layers bounding the upper and

lower part of the wake region, concentrations of vorticty are evident. Shear layers

emanating from the upperbody and underbody surfaces cause complex flow field

which consists of a number of vortices that move randomly in time and space.

Through the observation of an animation of 300 instantaneous images, it was seen

that the point of attachments on the ground surface travels forward and backward in

the flow direction in an unsteady mode.

Upper and lower trailing edges of the bus model I fairly expanded in the

vertical direction. For example, upper trailing edge of the bus model I conveys the

emerging shear layers in horizontal plane. Vortices occur along the upper shear layer

and travels in the flow directions and layer disappear. Jet-like flow emanating under

body of the bus model I creates counter clockwise vortex. This vortex occupies the

region around the lower part of rear side of the bus model I. Flow data show that the

wake flow occupies a larger region comparing to the rectangular shaped bus model

due to the geometry of the trailing edges of the bus model I. Patterns of vorticity <ω>

show that elongated vortices take place along the shear layer caused by the upper

trailing edges of the bus model I. At the lower part of the bus model a low level of

vortex occurs due to the shape of the lower part of the trailing edges comparing to

the rectangular body. These vortices are broken into pieces.


102

Figure 4.2.11 and 4.2.12 show the spectra of streamwise velocity fluctuations

evaluated at various locations in the vertical symmetry plane (side-view plane) and in

the horizontal xz-plane (plan view plane) for y/H=0.5 in the wake region downstream

of the model. The spectra taken from the upstream locations of the model do not

show a dominant frequency.


103

Figure 4.2.10. Patterns of instantaneous velocity vectors V, streamlines ψ and vorticity contours ω, in the vertical symmetry plane z=0 in the wake region. Minimum and incremental values of vorticity are ωmin=±2s-1 and ∆ω=2s-1


104



105

Figure 4.2.12. The spectrum of streamwise velocity fluctuations for selected points in the horizontal xz-plane for y/H=0.5 in the wake region


106

4.3. Flow Structures Around Bus Models II

In this section, flow around a three-dimensional bus model (Model II) has

been investigated by using a particle image velocimetry technique. The Reynolds

number based on the rectangular body height, H and the free stream velocity, U was

about ReH=1.2x104. PIV measurements were performed in the vertical symmetry

plane z=0 and two different cross-planes (end view planes) at locations in the flow

direction x/H=0.23 and x/H=0.53. Figure 4.3.1 shows the PIV measurement planes.

Detailed flow structures and characteristics were obtained by averaging over 300

instantaneous velocity maps. The PIV results provided instantaneous and time-

averaged velocity vector maps, vorticity contours, streamline topology and

turbulence characteristics.

Şekil 4.3.1. PIV measurement planes


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4.3.1 Time-Averaged Velocity Field

Figures 4.3.2 depicts the time-averaged velocity vector maps <V>, the

patterns of streamlines <ψ> and the corresponding vorticity contours <ω> around the

bus Model II in the vertical symmetry plane z=0. The minimum and incremental



indicated by solid and dashed lines, respectively. Figure 4.3.2 provides a clear view

of flow structures near the front face, on the roof and in the wake region of the

model II. The approaching flow on the upstream of the model decelerates

longitudinally and accelerates vertically to pass around the model. The streamlined

flow is divided into upward and downward flows from the stagnation point, Sab at the

forward face of the model. Attached flow can be clearly seen on the leading part of

the model roof due to the adequate rounded leading edge of the model. The attached

flow moves further downstream along the roof surface and is separated at the trailing

roof edge of the model. At the rear of the model a large reverse flow region is

formed. The length of this recirculation region is approximately 0.92 times the height

of the model. Foci F1 located at a location of x/H=0.23, y/H=0.37 is clearly visible.

Figure 4.3.2.c displays the upperbody and underbody wall shear layers. The

upperbody has negative vorticity while the underbody shear layer has positive and

negative vortices. The wake pattern is markedly asymmetric. The upper negative

vortex moves almost along the horizontal direction while the positive lower vortex

tends to move towards the top corner of the model. In conclusion, flow topologies

reveal a well defined circulating flow which is occupying the wake flow region

downstream of the model.


wake region downstream of the model at the selected locations on the vertical

symmetry plane. Here, velocity components are normalized with the free stream

velocity, U. Figure 4.3.3.a shows the streamwise velocity profiles, /U at different

downstream locations behind the model. The negative velocity fields in between

x/H=0.11 and x/H=1.07 represent the existence of the wake flow region downstream


108

Figure 4.3.2. Patterns of time-averaged velocity vector maps <V>, streamlines <ψ> and vorticity contours <ω> in the vertical symmetry plane z=0. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1


109

Figure 4.3.3. Velocity profiles of the flow in the vertical symmetry plane z=0 in the wake region. [a] Dimensionless streamwise velocity component <u/U>, [b] Dimensionless spanwise velocity component <v/U>


110

of the model. The maximum reversed velocity in the circulatory flow region is

approximately 0.18 times the free stream velocity, U at y/H=0.72. At the first

measuring section x/H=0.11 the streamwise velocity, /U takes positive values in

the lower part of the velocity profile because of the jet flow occurring between the

ground and the bottom surface of the model and streamwise velocity component

increases in this region. The maximum positive velocity in this region is

approximately 0.45 times the free stream velocity, U at y/H=0.03. The rate of

increase in the streamwise velocity across the positive shear layer at the upper part of

the model is due to the entrainment of wake and the core flow regions. In the middle

part of the velocity profile there is a negative velocity field in between y/H=0.43 and

y/H=0.92 which represents the reverse flow downstream of the model. The

maximum negative velocity is approximately 0.15 times the free stream velocity, U.

At the second measuring section, x/H=0.48 significant reverse flow in the

downstream region of the model can be clearly seen between y/H=0.4 and y/H=0.86.

The maximum reverse velocity in this measuring section is located at y/H=0.72 and

approximately 0.18 times the free stream velocity, U. Positive streamwise velocity

values identified in the third and fourth measuring sections x/H=1.07 and x/H=1.5,

respectively. From the distributions of the velocity components, u and v asymmetric

flow field is clearly visible.


spanwise velocity components, <urms>/U and <vrms>/U normalized by the free stream

velocity, U and Reynolds stress correlation, <u′v′>/U2 normalized by the square of

the free stream velocity in the central region of vertical plane. The peak values of

turbulence properties take place along the upperbody and underbody shear layers.

The magnitude of the root mean square of streamwise velocity fluctuations, <urms>/U

shown in Figure 4.3.4.a are higher in the upperbody shear layer than in the

underbody shear layer due to the ground effect. The peak value of <urms>/U is

approximately 0.23. The root mean square of cross stream velocity components,

<vrms>/U presented in Figure 4.3.4.b shows a similar trend. The maximum value of

<vrms>/U is approximately 0.14 which is smaller than the corresponding value of

<urms>/U at the same location. Profiles of the Reynolds stress correlation, <u′v′>/U2


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112



113


<u′v′>/U2 appears along the upperbody shear layer with a magnitude of 0.02.

Magnitude of Reynolds stress correlations, <u′v′>/U2 along the underbody shear

layer are smaller comparing to the upperbody shear layer. Figure 4.2.5 shows the

contours of streamwise velocity fluctuations <urms>/U, spanwise velocity fluctuations

<vrms>/U, and Reynolds stress correlations <u′v′>/U2 in the vertical symmetry plane

z=0 in the wake region.

Figure 4.3.6 presents the time-averaged velocity vector maps <V>, the

patterns of streamlines <ψ> and the corresponding vorticity contours <ω> in two zy

cross-sections of end-view planes for x/H=0.23 and x/H=0.53 locations. The flow

field downstream of the model at a location x/H=0.23 is dominated by a pair of

counter rotating trailing vortices (V3 and V4) originated from the bottom corners of

the model. Han (1989) found these vortices near the lower lateral edges of the

Ahmed body and concluded that they were formed due to the viscous interaction

between the body and the ground-plane boundary layer. The left (V1, V3) and right

(V2, V4) vortices rotate counterclockwise and clockwise, respectively. The upwash

flow is clearly visible between the counter rotating vortices. Further downstream at a

location x/H=0.53 two counter rotating longitudinal vortices originated from the

upper corners of the model can be clearly identified. They are stronger than the

vortices originating from the bottom corners of the model at a location x/H=0.23.

There is a strong upwash flow between the counter rotating longitudinal vortices. It

is known that the model experiences lift and the sense of rotation of the vortices is

seen to be compatible with this (Bearman, 1997).

4.3.2 Instantaneous Velocity Field

The instantaneous flow structure in the wake region downstream of the

Model II on the vertical symmetry plane z=0 is shown in Figure 4.3.7. The

instantaneous wake is different from the time-averaged flow field and comparisons

of the instantaneous flow structures reveal that additional vortices are generated.

Swirling patterns of velocity vectors take place along the upperbody shear layer. On


114

the other hand, well defined large-scale swirling patterns of velocity vectors are

evident on the bottom edge. The positive vorticity layer separating from the lower

edge of the model diverges substantially and, tends to interact with the cluster of

vorticity of the separating layer emerging from the roof surface of the model. The

negative vortex originating from the upperbody shear layer moves almost along the

horizontal direction. The point of attachment on the ground surface travels forward

and backward in the flow direction in an unsteady mode. Shear layers emanating

from the upperbody and underbody surface cause complex flow field which consists

of a number of vortices that move randomly in time and space. The intensity and

domain of vortices, ω, emanating from the bottom trailing edge of the model is

higher comparing to those vortices occur downstream of the model I.

In conclusion flow structures downstream of the model changes rapidly in

random mode. The size of the wake region of this model is smallest comparing to

other models. Hence, the drag coefficient of this model is also smallest.

Figure 4.3.8 depicts the instantaneous velocity fields in cross-planes. The

instantaneous wake in the cross-plane is different from the time-averaged one and it

was found that the mean trailing vortices form as a result of several instantaneous

vortices. The instantaneous wake region was found to consist of a substantial number

of coherent vortex structures that move randomly in time and space. The many

longitudinal vortex structures observed in the instantaneous flow field will have

originated from various features of the complex bus body.

Figure 4.3.9 shows the spectra of streamwise velocity fluctuations evaluated

at various locations in the vertical symmetry plane (side-view plane) in the wake

region downstream of the model. The spectra taken from the upstream locations of

the model do not show a dominant frequency.


115

Figure 4.3.6. Patterns of time averaged velocity vector maps <V>, streamlines <ψ> and vorticity contours <ω> in the cross-planes for x/H=0.23 and x/H=0.53. Minimum and incremental values of vorticity are <ωmin>=±0.5s-1 and ∆<ω>=0.5s-1


116

Figure 4.3.7. Patterns of instantaneous velocity vectors V, streamlines ψ and vorticity contours ω, in the vertical symmetry plane z=0 in the wake region. Minimum and incremental values of vorticity are ωmin=±2s-1 and ∆ω=2s-1


117

Figure 4.3.8. Instantaneous velocity field in two cross-planes x/H=0.23 and x/H=0.53


118


5. CONCLUSIONS AND RECOMMENDATIONS Cahit GÜRLEK

119

5. CONCLUSIONS AND RECOMMENDATIONS

An experimental investigation of the flow around a rectangular body and two

different bus models was presented. The objective of this work was to investigate the

flow around the road vehicles and obtain experimental data that can be used to

understand the time averaged and instantaneous structure of the flow field. The

principle measurement technique was particle image velocimetry (PIV), which was

supported by flow visualization technique. Experiments were conducted in a free

surface water channel at the Reynolds number ReH=1.2x104 based on the model

heights and free stream velocity. PIV measurements were performed at several

vertical, horizontal and cross planes along the models. The PIV technique provided

instantaneous and time-averaged velocity vector maps, vorticity contours, streamline

topology and turbulence characteristics.

5.1. Rectangular Body

The main conclusions of the results of the Rectangular Body are:

1. In the forward part of the rectangular body the flow is separated from the top

leading sharp edge and a large reverse flow region is formed in the vertical

symmetry plane. The length of this reverse flow region was found to be

around 1.3 times the model height.

2. In the wake region, the flow is separated from the upper and lower rear

corners of the body and two counter rotating vortices are formed a separation

bubble. The length of this recirculation region is found to be around 1.07

times the model height.

3. The shear layer with negative vorticity is originated from the roof surface of

the model while the shear layer with positive vorticity is emerged from the

lower surface of the model.

4. The maximum values of turbulence intensities are found along the upperbody

and underbody shear layers.


120

5. In the plan-view plane the flow is separated from the sharp leading edges and

formed two circulatory flow regions on both lateral walls of the model. The

length of this circulating flow region is found to be around 1.06 times the

model height.

6. In the horizontal plane across the wake flow region a pair of identical counter

rotating circulation region is identified. The length of this circulation region

was found to be around 1.13 times the model height.

7. The instantaneous flow images provide detailed information comparing to the

time-averaged flow topology in both vertical and horizontal measuring

planes. The instantaneous flow fields are consist of a substantial number of

coherent vortex structures that move randomly in time and space.

8. Flow visualization both on the roof of the model and around the vertical side

depicted shear layer instability waves. A well-defined ring type vortex is

clearly identified on the lower side of the rear wall of the model due to the jet

like flow immerging underbody of the model.

9. For the flow around a rectangular body with 10 degrees of yawing angle, the

shear layers and recirculation flows are observed on both lateral surface of

the model. The recirculation region on the upper lateral face of the model is

much larger than lower one. In the wake region, an asymmetric large

recirculation region is formed.

5.2. Model I

The main conclusions of the results of the Bus Model I are:

1. In the vertical symmetry plane in the forward part of the model roof, attached

flow is observed due to the adequate rounded leading edge.

2. At the rear, asymmetric double vortices are formed in the vertical symmetry

plane. There is a large circulatory flow region rotating in anticlockwise

direction at the rear of the model in the wake flow region. There is also a

smaller circulatory flow region rotating in clockwise direction which is


121

located along the upperbody shear layer. The length of the wake region is

found to be approximately 0.99 times the height of the model.

3. In the horizontal plane although the side walls of the Model I have rounded

leading edges, the flow is separated from the leading edges of side walls and

formed two recirculating flow regions on each lateral side of the model. The

length of this recirculating flow region was found to be around 0.6 times the

model height.

4. In the wake region a pair of recirculating flow region with a similar size is

identified. The length of the wake flow region is found to be approximately

0.95 times the height of the model.

5. The maximum values of turbulence intensities are found along the upperbody

and underbody shear layers in both vertical and horizontal measuring planes.

6. The instantaneous flow fields are consist of a substantial numbers of vortices

with a coherent structures that move randomly in time and space.

7. The drag coefficient of the Model I is found about CD =0.62.

5.3. Model II

The main conclusions of the results of the Bus Model II are:

1. Attached flow can be clearly seen on the front part of the model roof due to

the adequate rounded leading edge of the model in the vertical symmetry

plane.

2. In the wake flow region downstream of the model a large reverse flow region

is formed. The length of this recirculation region is approximately 0.92 times

the height of the model.

3. The wake pattern is markedly asymmetrical. The upper negative vortex

moves almost along the horizontal direction while the positive lower vortex

tends to move towards the top corner of the model.


122

4. The maximum values of turbulence intensities appear along the upperbody

and underbody shear layers in vertical symmetry plane.

5. In cross-planes the flow field downstream of the model is dominated by a pair

of counter rotating vortices originating from the bottom and upper corners of

the model.

6. The instantaneous wake flow characteristics are different from the time-

averaged flow data and contain not only two longitudinal vortices but a larger

number of vortices that move randomly in time and space.

7. The drag coefficient of the Model I is found about CD =0.54.

5.4. Recommendations for future works

Based on the experiments carried out in this study, the following

recommendations are made for future work.

1. Active or passive drag reduction methods should be applied to the models

and their effects on the drag can be identified using both PIV and wind tunnel

experiments.

2. Investigation of flow structures of models using computational methods and

comparisons with these experimental results will be the subject of a future

study.

3. Detailed studies of add-on devices such as mirrors can be performed using

PIV technique.

123

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132

CURRICULUM VITAE

Cahit GÜRLEK was born on October 02, 1970 in Sivas. After completing his

education in primary and high school, he enrolled in Cumhuriyet University Mechanical

Engineering Department in 1994. He had graduated from the Mechanical Engineer

Department of Cumhuriyet University with a Bachelor of Science degree in 1998. He

had obtained Master of Science degree from the Mechanical Engineer Department of

Cumhuriyet University in 2001. He had commenced the studies leading to the degree of

Doctor of Philosophy in 2002 at the Department of Mechanical Engineering, Çukurova

University. He has been working as a Research Assistant at the Mechanical Engineering

Department of Çukurova University since 2002.

133

APPENDIX A

Vorticity Evaluation

For 2-D flows, the out-of-plane component of vorticity is given by:

∂∂

−∂∂

=Ωyu

xv

21

The most common way to compute this expression numerically is to approximate the

partial derivatives with finite difference. Using central difference at an interior point to

leads to:

−−+−

−−+=Ω

yxij

jiujiujivjivδδ 2

)1,()1,(2

),1(),1(21

Any computation involving derivatives is very sensitive to noises that are the primary

reason to try to smooth out the velocity field before computation of the vorticity, strain

rate or similar gradient quantities.

Another way around the noise problem for the particular case of the computation

of vorticity is to use a self-smoothing method derived from the Stokes theorem. This is

the so-called circulation method that the user can choose to compute the vorticity.

The Stokes theorem can be formulated as:

∫∫∫→→→→→

=∇ dludsux )(

134

Assuming that the vorticity is constant all over the unit surface formed by the

four grid cells surrounding a given point, the vorticity at that point is given by:

∫→→

=Ω dluyxδδ4

1

where the integral is the circulation of the velocity around the path formed by the sides

of the unit surface.

135

APPENDIX B

Bilinear Interpolation

To fill the gaps left in the data grid by the interrogation system, a bilinear least

square fit technique is used.

Knowing the data values u1,….., un at the N nearest neighbor location of a point

where the data u is missing, the idea is to find a value for u that does not deviate too

much from these values. To realize this goal, in a least square technique, one has to

minimize the merit function:

∑=

−=

N

k

k

k

uu

1

22

σχ

u=a0+a1x+a2y

v=b0+b1x+b2y

using the 5 nearest neighbors of a missing data. The standard way to deal with the

measurement errors kσ , on each data uk, when they are not known, is to set them to 1.

The minimum of the merit function:

( )25

1210

2 ∑=

++−=k

k yaxaauχ

occurs when:

( ) ( ) ( ) 0,,,2

2

1

2

0

2

=∂∂

=∂∂

=∂∂

kkkkkk yxa

yxa

yxa

χχχ for k=1,……..,5

136

This is a linear system of 15 equations and 3 unknowns that is solved using the Singular

Value Decomposition (SVD) technique described in the Numerical Recipes books.

Gaussian Smoothing

To reduce the measurement noises in the velocity data from PIV, a local

weighted averaging technique is used. The weights used are Gaussian:

( ) ( )∑ ∑−= −=

−−=4

4

4

4m kmjkikmji y,xuwy,xu

where:

∑ ∑−= −=

= 4

4

4

4k mkm

kmkmw

ω

ω

and ( )

2

222σω

mk

km e+

=

The parameter σ is the smoothing parameter. It controls how fast the Gaussian ω is

decaying and therefore, determines the contributions of the surrounding points to the

average value.

137

APPENDIX C

Averaged Flow Structure

Calculation of the averaged quantities was performed according to the equations

listed in the flowing table. Each averaged parameter was calculated at each spatial

coordinate (x,y) by considering the average of all instantaneous values (x,y). The

terminology for each of the averaged parameters and the dimensionless equation

employed to determine the averaged parameter as follows:

<V> ≡ averaged (or mean) total velocity

)y,x(VN

VN

nn∑

=

≡><1

1

 = averaged value of streamwise component of velocity

)y,x(uN

uN

nn∑

=

≡><1

1

<v> = averaged value of transverse component of velocity

)y,x(vN

vN

nn∑

=

≡><1

1

<ω> = mean value of vorticity

)y,x(N

N

nn∑

=

≡><1

1ωω

urms = root-mean-square of u component fluctuation

[ ]2

1

1

21

><−≡><≡ ∑

=

N

nnrmsrms )y,x(u)y,x(u

Nuu

138

vrms = root-mean-square of v component fluctuation

[ ]2

1

1

21

><−≡><≡ ∑

=

N

nnrmsrms )y,x(v)y,x(v

Nvv

=>′′< vu averaged value of Reynolds stress correlation

[ ][ ]∑=

><−><−>=′′<N

nnn )y,x(v)y,x(v)y,x(u)y,x(u

Nvu

1

1

139

APPENDIX D: ADDITIONAL IMAGES

140

Figure D.1. Patterns of time-averaged velocity vector maps <V> around rectangular body (a), bus model I (b) and bus model II (c) in the vertical symmetry plane z=0

141

Figure D.2. Patterns of time averaged streamlines <ψ> around rectangular body (a), bus model I (b) and bus model II (c) in the vertical symmetry plane z=0

142

Figure D.3. Patterns of time-averaged vorticity contours <ω> around rectangular body (a), bus model I (b) and bus model II (c) in the vertical symmetry plane z=0. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1

143

Figure D.4. Patterns of time-averaged velocity vector maps <V> around rectangular body (a) and bus model I (b) in the horizontal xz-plane for x/H=0.5

144

Figure D.5. Patterns of time averaged streamlines <ψ> around rectangular body (a) and bus model I (b) in the horizontal xz-plane for x/H=0.5

145

Figure D.6. Patterns of time-averaged vorticity contours <ω> around rectangular body (a) and bus model I (b) in the horizontal xz-plane for x/H=0.5. Minimum and incremental values of vorticity are <ωmin>=±2s-1 and ∆<ω>=2s-1

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ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES … · 2019-05-10 · INSTITUTE OF NATURAL AND APPLIED SCIENCES UNIVERSITY OF ÇUKUROVA Supervisor Year : Prof. Dr