FLUID FLOW AND HEAT TRANSFER OF AN IMPINGING AIR JET

8/11/2019 FLUID FLOW AND HEAT TRANSFER OF AN IMPINGING AIR JET

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FLUID FLOW AND HEAT TRANSFER OF AN

IMPINGING AIR JET

by

Tadhg S. ODonovan

A thesis submitted to the University of Dublin for the degree of Doctor of Philosophy.

Department of Mechanical & Manufacturing Engineering, Trinity College, Dublin 2.

March, 2005


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Declaration

I, Tadhg S. ODonovan, declare that this thesis has not been submitted as an exercisefor a degree at any other university and that the thesis is entirely my own work.

I agree that the library may lend a copy of this thesis.

Tadhg S. ODonovanMarch, 2005

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Abstract

Convective heat transfer to an impinging air jet is known to yield high local and area

averaged heat transfer coefficients. The current research is concerned with the mea-

surement of heat transfer to an impinging air jet over a wide range of test parameters.

These include Reynolds Numbers, Re, from 10000 to 30000, nozzle to impingement

surface distance, H/D, from 0.5 to 8 and angle of impingement, from 30

to 90

(normal impingement). Both mean and fluctuating surface heat transfer distributions

up to 6 diameters from the geometric centre of the jet are reported. The time averaged

heat transfer distributions are qualitatively compared to velocity flow fields. Simul-

taneous velocity and heat flux measurements are reported at various locations on the

impingement surface to investigate the temporal nature of the convective heat transfer.

At low nozzle to impingement surface spacings the heat transfer distributions ex-

hibit peaks at a radial location that varies with both Reynolds number and H/D. It

is shown that fluctuations in the velocity normal to the impingement surface have a

greater influence on the heat transfer than fluctuations parallel to the impingement sur-

face. At certain test configurations vortices that initiate in the shear layer impinge on

the surface and move along the wall jet before being broken down into smaller scale tur-

bulence. The effects of these vortical flow structures on the heat transfer characteristics

in an impinging jet flow are also presented. Specific stages of the vortex development

are shown to enhance vertical fluctuations and hence increase heat transfer to the jet

flow, resulting in secondary peaks in the radial distribution.

Air jet cooling of a grinding process has been investigated as large quantities of

heat must be dissipated to avoid high temperatures that have an adverse effect on the

workpiece and the grinding wheel itself. Convective heat transfer distributions along

the axis of cut are compared to local flow characteristics for a range of jet and grinding

wheel configurations. It has been shown that the jet velocity must be significantly

higher than the tangential velocity of the grinding wheel in order to penetrate the

grinding wheel boundary layer and effectively cool the arc of cut.

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Table of Contents

Abstract iii

Table of Contents iv

List of Figures vi

List of Tables x

Acknowledgements xi

Nomenclature xii

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Research Ob jectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Jet Impingement 4

2.1 Fluid Flow Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Jet Flow Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Vortex Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.3 Energy Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Heat Transfer Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Stagnation Point Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Heat Transfer Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Enhancement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Nozzle Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.2 Jet Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.3 Other Enhancement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Experimental Rig & Measurement Techniques 253.1 Experimental Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.1 Set-up for Fundamental Investigation . . . . . . . . . . . . . . . . . . . . . . . 25

3.1.2 Set-up for Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Jet Flow Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Air Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.2 Seeding for Laser Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.3 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.4 Laser Doppler Anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Heat Transfer Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.1 Thermocouple Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Micro-Foil Heat Flux Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.3 Hot Film Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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3.4.1 DAQ Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.4.2 DAQ Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Accuracy & Calibration of Measurement Systems 39

4.1 Fluid Flow Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1.1 Laser Doppler Anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.2 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1.3 Air Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Heat Transfer Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.1 Thermocouple Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.2 Micro-Foil Heat Flux Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.3 Hot Film Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5 Results & Discussion 54

5.1 PIV Flow Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.1 Free Jet Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1.2 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.1.3 Obliquely Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Heat Transfer Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2.1 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64


5.3 Heat Transfer & Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.3.1 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77


5.4 Fluctuating Fluid Flow & Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.4.1 Free Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.2 Stagnation Point for Normal Impingement . . . . . . . . . . . . . . . . . . . . . 84

5.4.3 Wall Jet for Normal Impingement . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.4.4 Wall Jet for Oblique Impingement . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6 Jet Impingement Heat Transfer in a Grinding Configuration 127

6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.2 Impingement Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.3 Fluid Flow in a Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.3.1 Rotating Wheel Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.3.2 Rotating Wheel with Low Speed Impinging Air Jet . . . . . . . . . . . . . . . . 1366.4 Heat Transfer in a Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.4.1 Preliminary Heat Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . 139

6.4.2 Low Speed Jet Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.4.3 High Speed Jet Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7 Conclusions 151

7.1 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

A Calibration Certificates 154

Bibliography 158

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List of Figures

2.1 Impinging Jet Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Obliquely Impinging Jet Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Schematic of Vortex Breakdown Process according to Hussain [38] . . . . . . . . . . . 8

2.4 Example of Vortex Pairing by Anthoine [39] . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Vortex Interactions presented by Schadow and Gutmark [40] . . . . . . . . . . . . . . 9

3.1 Fundamental Rig Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Air Flow Conditioning System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Venturi Seeding Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5 Particle Image Velocimetry Measurement Set-up . . . . . . . . . . . . . . . . . . . . . 31

3.6 Laser Doppler Anemometry Measurement Set-up . . . . . . . . . . . . . . . . . . . . . 32

3.7 LDA Measurement Volume Fringes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.8 Mounted Heat Flux Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.9 Individual Heat Flux Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1 Ambient Air Thermocouple Calibration Data . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Micro-Foil Thermocouple Calibration Data . . . . . . . . . . . . . . . . . . . . . . . 44

4.3 Hot Film Thermocouple Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Jet Air Thermocouple Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.5 Micro-Foil Heat Flux Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.6 Constant Temperature Anemometer Circuitry . . . . . . . . . . . . . . . . . . . . . . . 49

4.7 Hot Film Resistance Calibration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Free Jet Flow Field; Re = 10000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.2 Free Jet Centreline Velocity & Turbulence Intensity;Re = 10000 . . . . . . . . . . . . 56

5.3 Free Jet Velocity and Turbulence Intensity Profiles;Re = 10000 . . . . . . . . . . . . . 57

5.4 Impinging Jet Full Field Flow Measurement;Re = 10000,H/D= 2 . . . . . . . . . . . 58

5.5 Comparison of a Free Jet Flow to an Impinging Jet Flow;Re = 10000,H/D= 2 . . . 59

5.6 Centreline Similarity of Free and Impinging Jet Flows;Re = 10000,H/D= 2 . . . . . 59

5.7 Impinging Jet Full Field Flow Velocity & Turbulence Intensity;Re = 10000 . . . . . . 61

5.8 Impinging Jet Flow Visualisation;Re= 10000,H/D= 2 . . . . . . . . . . . . . . . . . 61

5.9 Impinging Jet Full Field Flow Vorticity;Re= 10000 . . . . . . . . . . . . . . . . . . . 62

5.10 Oblique Impingement Velocity Flow Fields;Re = 10000,H/D= 6 . . . . . . . . . . . 63

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5.11 Displacement of Stagnation Point from Geometric Centre . . . . . . . . . . . . . . . . 63

5.12 Heat Transfer Distributions;Re = 30000, = 90 . . . . . . . . . . . . . . . . . . . . . 65

5.13 Time Averaged Nusselt Number Distributions; = 90 . . . . . . . . . . . . . . . . . 67

5.14 Fluctuating Nusselt Number Distributions; = 90 . . . . . . . . . . . . . . . . . . . . 68

5.15 Nu Distributions;Re = 10000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.16 Obliquely Impinging JetN u Distributions; Re = 10000 . . . . . . . . . . . . . . . . . 71

5.17 Obliquely Impinging JetN u Distributions;Re = 10000 . . . . . . . . . . . . . . . . . 73

5.18 Obliquely Impinging JetN u Distributions; = 45 . . . . . . . . . . . . . . . . . . . . 74

5.19 Obliquely Impinging JetN u Distributions; = 45 . . . . . . . . . . . . . . . . . . . 75

5.20 Fluctuating & Time Averaged Nusselt Number Distributions;Re = 10000, = 45 . . 76

5.21 Flow Velocity & Heat Transfer;Re = 10000,H/D= 1 . . . . . . . . . . . . . . . . . . 78

5.22 Flow Velocity & Heat Transfer;Re = 10000,H/D= 8 . . . . . . . . . . . . . . . . . . 79

5.23 Location of Heat Transfer Maxima & Maximum Turbulence Intensity . . . . . . . . . 79

5.24 Flow Velocity & Heat Transfer;Re = 10000,H/D= 2, = 45 . . . . . . . . . . . . . 81

5.25 Flow Velocity & Heat Transfer;Re = 10000,H/D= 2, = 60 . . . . . . . . . . . . . 82

5.26 Free Jet Velocity Spectra;x/D = 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.27 Stagnation Velocity Variation with Nozzle Height;Re = 10000 . . . . . . . . . . . . . 85

5.28 Stagnation Heat Transfer Variation with Nozzle Height: Effect of Reynolds Number . 85

5.29 Stagnation Point Turbulence Intensity;Re = 10000 . . . . . . . . . . . . . . . . . . . . 86

5.30 Stagnation Point Intensity of Heat Transfer Fluctuations . . . . . . . . . . . . . . . . . 86

5.31 Stagnation Point Spectral Data;H/D= 0.5, Re= 10000 . . . . . . . . . . . . . . . . . 88

5.32 Stagnation Point Spectral Data;H/D= 4, Re= 10000 . . . . . . . . . . . . . . . . . . 89

5.33 Stagnation Point Spectral Data;H/D= 2.0, Re= 10000 . . . . . . . . . . . . . . . . . 90

5.34 Nu Distribution & Heat Flux Spectra; Re = 30000,H/D = 1.5 . . . . . . . . . . . . . 91

5.35 Heat Transfer Spectra;H/D= 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.36 Normally Impinging Jet; H/D= 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.37 Radial Location of Simultaneous Measurements;H/D= 0.5 . . . . . . . . . . . . . . . 94

5.38 Spectral, Coherence & Phase Information; H/D= 0.5,r/D= 0.37 . . . . . . . . . . . 94




5.42 Radial Location of Simultaneous Measurements . . . . . . . . . . . . . . . . . . . . . . 98

5.43 Spectral, Coherence & Phase Information; H/D= 1,r/D= 0.37 . . . . . . . . . . . . 99








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5.55 Mean & Fluctuating Nusselt Number Distributions;Re = 10000 . . . . . . . . . . . . 107

5.56 Mean Velocity Distributions;Re = 10000 . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.57 RMS Velocity Distributions;Re = 10000 . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.58 Nu Distribution & Heat Flux Spectra; Re = 30000,H/D = 3 . . . . . . . . . . . . . . 111

5.59 Nu Distribution & Heat Flux Spectra; Re = 30000,H/D = 8 . . . . . . . . . . . . . . 112

5.60 Heat Transfer Spectra;r/D= 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.61 Radial Location of Simultaneous Measurements;H/D= 4 . . . . . . . . . . . . . . . . 113



5.64 Radial Location of Simultaneous Measurements;H/D= 8 . . . . . . . . . . . . . . . . 115

5.65 Spectral, Coherence & Phase Information; H/D= 8, r/D= 1.11 . . . . . . . . . . . . 116

5.66 Spectral, Coherence & Phase Information; H/D= 8, r/D= 1.86 . . . . . . . . . . . . 116

5.67 Nu Distribution & Heat Flux Spectra; = 30, Re= 10000,H/D= 2 . . . . . . . . . 118

5.68 Nu Distribution and Heat Flux Spectra; = 75, Re= 10000,H/D= 2 . . . . . . . . 119

5.69 Radial Location of Simultaneous Measurements;H/D= 2, = 60 . . . . . . . . . . . 120

5.70 Spectral, Coherence & Phase Information; H/D= 2, = 60,r/D= 1.30 . . . . . . 1215.71 Spectral, Coherence & Phase Information; H/D= 2, = 60,r/D= 1.11 . . . . . . 121

5.72 Spectral, Coherence & Phase Information; H/D= 2, = 60

,r/D= 0.37 . . . . . . . 122

5.73 Spectral, Coherence & Phase Information; H/D= 2, = 60,r/D= 1.11 . . . . . . . 122

5.74 Radial Location of Simultaneous Measurements;H/D= 2, = 45 . . . . . . . . . . . 123

5.75 Spectral, Coherence & Phase Information; H/D= 2, = 45,r/D= 0.81 . . . . . . 1245.76 Spectral, Coherence & Phase Information; H/D= 2, = 45,r/D= 0.76 . . . . . . . 124

5.77 Spectral, Coherence & Phase Information; H/D= 2, = 45,r/D= 1.41 . . . . . . . 125

6.1 Grinding Process Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.3 Schematic of Test Set-up & Corresponding Heat Transfer Distribution . . . . . . . . . 134

6.4 Particle Image Velocimetry Measurement Set-up . . . . . . . . . . . . . . . . . . . . . 134

6.5 Flow Entrained by Grinding Wheel; Vs= 20m/s . . . . . . . . . . . . . . . . . . . . . 136

6.6 Wheel & Impinging Jet; = 30, H= 101mm,Vs= 10m/s,Vj = 10m/s . . . . . . . . 137

6.7 Wheel & Impinging Jet;H= 101mm,= 15, Vs= 10m/s,Vj = 10m/s . . . . . . . . 138

6.8 Wheel and Impinging Jet; = 15, Vs= 10m/s,Vj = 10m/s . . . . . . . . . . . . . . 1386.9 Heat Transfer to Grinding Wheel Boundary Layer . . . . . . . . . . . . . . . . . . . . 139

6.10 Heat Transfer Distributions to Obliquely Impinging Jets . . . . . . . . . . . . . . . . . 141

6.11 Schematic of Jet Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6.12 Wheel and Impinging Jet Heat Transfer Distributions,Vw =Vj . . . . . . . . . . . . . 143

6.13 Wheel and Impinging Jet Heat Transfer Distributions;Vw = Vj . . . . . . . . . . . . 144

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6.14 Other Wheel and Impinging Jet Heat Transfer Distributions . . . . . . . . . . . . . . . 145

6.15 Schematic of High Speed Impinging Jet Set-up . . . . . . . . . . . . . . . . . . . . . . 147

6.16 Wheel and High Speed Impinging Jet Heat Transfer Distributions . . . . . . . . . . . 148

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List of Tables

4.1 Contributory Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 Summary of Experimental Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 53

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Acknowledgements

I have been very fortunate to receive a great deal of support throughout the course

of my research and I wish to express my gratitude for the help given by the following

people:

My supervisor, Professor Darina. B. Murray for her invaluable help and guidance

throughout. Also, I would like to thanks Professor Andrew Torrance for his guidancewithin the research group.

Technical support provided by Alan Reid, Tom Havernon, Gabriel Nicholson, J. J.

Ryan, John Gaynor, Paul Normoyle, and in particular Gerry Byrne is much appreci-

ated.

To all those who advised and worked with me, Dr. Ludovic Chatellier, Dr. John

Cater, Dr. David Hann, Dr. Victor Chan, Orla Power, Meaghan Mathews and Darko

Babic, I owe a sincere depth of gratitude for their invaluable assistance.

Finally, I would like to thank my family and friends for their unlimited moral

support and welcome social distraction.

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Nomenclature

Symbol Description Units

a correlation constant []A area [m2]

b correlation constant []c correlation constant []C calibration constant []Cp specific heat [J/kgK]

df distance between LDA interference fringes [m]

D diameter [m]

E electro motive force [V]

E root-mean-square electro motive force [V]

f frequency [Hz]

h convective heat transfer coefficient [W/m2K]

H height of nozzle above impingement surface [m]

I electrical current [A]

k thermal conductivity [W/mK]

l length of swirl generator [m]

L length of flow meter element [m]

n correlation constant []N number of variables []Nu Nusselt number, hD/k []Nu root-mean-square Nusselt number []P pressure [N/m2]

P r Prandtl number, / []q rate of heat transfer [W]

q root-mean-square heat transfer rate [W]

q heat flux [W/m2]

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Q volume flow rate [m3/s]

r radial distance from geometric centre [m]

R resistance []

Re jet Reynolds number, UD/ []S energy separation factor []St Strouhal number, fD/U []Sw degree of swirl []Sxy standard deviation []t time interval [s]

T temperature [K]

T u turbulence intensity [%]

U velocity [m/s]

u, v streamwise and radial velocity components [m/s]

V voltage [V]

V r velocity ratio of coaxial jet []x displacement [m]

X sensor cover layer factor [V]

x, y streamwise and radial directions [

]

xiii


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Greek Symbols

Symbol Description Units

angle of impingement []

thermal diffusivity [m2/s]

sensor thickness [m]

angle between LDA beams []

wavelength of laser beams [m]

viscosity [kg/ms]

kinematic viscosity [m2/s]

density [kg/m3]

sensor response time [s]

swirl angle []

vorticity [1/s]

Subscripts

Symbol Description

ad adiabatic

d doppler

c cold

e exit

ef f effective

h hot

i in

j jet

max maximum

o out

stag stagnation point

w wall

xiv


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Chapter 1

Introduction

This research is a fundamental investigation of heat transfer to an impinging air jet.

Impinging jets are known as a method of achieving particularly high heat transfer

coefficients and are therefore employed in many engineering applications. For this

reason, jet impingement heat transfer has attracted much research. Research into

the flow characteristics alone for the free and impinging jet configurations is a broad

area of interest. Independent investigations of heat transfer to an impinging jet have

reported a wide variation in heat transfer coefficients for similar testing parameters.

Thus, it has been realised that small changes in nozzle geometry and in confinement

arrangement can have a major influence on the heat transfer distributions. In recent

times the specific flow characteristics are related to the measured heat transfer in most

impinging jet heat transfer investigations.

Grinding is a widely employed machining process used to achieve good geometri-

cal form and dimensional accuracy with excellent surface finish and surface integrity.

Grinding however produces heat which must be dissipated as high temperatures have

an adverse effect on the metallurgical composition, the surface finish and the geomet-

rical accuracy of the workpiece. Convective heat transfer to an impinging air jet is

known to yield high local and area averaged heat transfer and as such is employed for

the cooling of a grinding process. The current research is concerned with the use of

an air jet in the place of traditional methods that use a mixture of oil and water. The

motivation for this change is both an economic and environmental one.

This chapter has been divided into two sections. The first is a brief summary of

the research conducted in the areas of jet impingement heat transfer and temperatures

in a grinding zone. The second section details some of the questions that have notbeen answered by the available literature and outlines the objectives of the current

investigation.

1


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2

1.1 Background

Impinging jets have been used to transfer heat in diverse applications, which include

the drying of paper, the cooling of turbine blades and the cooling of a grinding process.

Hollworth and Durbin [1], investigated the impingement cooling of electronics. Roy et

al. [2] investigated the jet impingement heat transfer on the inside of a vehicle wind-

screen and Babic et al. [3] used jet impingement for the cooling of a grinding process. In

these, and in other cases, research has been conducted specifically with an application

in mind but there have also been many fundamental investigations into the fluid flow

and heat transfer. These have led to the identification of several parameters which have

significance for the enhancement of heat transfer on the impingement surface. Thus,

the main variables for jet impingement heat transfer are the angle of impingement, the

jet Reynolds number and the height of the nozzle above the impingement surface. The

current investigation is concerned with heat transfer to a submerged impinging axially

symmetric air jet as this is the case of most relevance for jet cooling of a grinding

process.

In more recent times control of the jet vortex flow has attracted much research

interest as the latest parameter identified to have a role to play in the heat transfer

mechanisms. Hussain and Zaman [4], Ho and Huang [5] and others have reported on

the methods of controlling the vortex flow of a free jet. Liu and Sullivan [6] have

shown that when the jet is exited acoustically at certain frequencies, the heat transfer

to the jet can be enhanced. Hwang et al. [7] employed different methods to control the

vortex roll-up in the jet flow and investigated the resulting effect on the heat transfer.

Hwang and Cho [8] continued this research for a wider range of test parameters. While

the research to date has shown possible enhancement of the mean heat transfer at

various excitation frequencies, much of this has been attributed to changes in the

arrival velocities. The effect of the vortical flow structure on the local heat transfer

has not been reported in depth.

The current research is concerned with the fundamental heat transfer mechanisms

that occur in an impinging jet flow and with the application of air jet cooling to a

grinding process. Much research effort has been directed towards the cooling of a

grinding process. Several numerical models have been proposed by Lavine and Jen [9],[10], Jen and Lavine [11], [12] and Liao et al. [13] that investigate the heat generation

and dissipation in the arc of cut of a grinding process. Experimental measurements of


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3

the grinding temperatures have been reported by Rowe et al. [14], Ebbrell et al. [15]

and Babic et al. [16], [3]. To date however, little has been reported on the convective

heat transfer distributions along the workpiece.

1.2 Research Objectives

The current research investigates the fluid flow and heat transfer for a submerged, un-

confined axially symmetric impinging air jet, for a range of impingement parameters.

Mean and fluctuating heat transfer distributions are compared with local velocity mea-

surements. Of particular interest to the current investigation are the secondary peaks

that occur in the mean heat transfer distribution when the jet nozzle is placed within 2

diameters of the impingement surface. An important objective of the current research

is to reveal the convective heat transfer mechanisms that influence the magnitude and

location of these peaks.

Control of the vortex development in the shear layer of the free jet and its influence

on heat transfer has been a major area of interest in this field in recent years. It has

been shown that by exciting the jet, acoustically or otherwise, the vortex development

can be controlled and this has a consequence for heat transfer. Another objective

of this research is to understand the influence that various stages within the vortexdevelopment have on the convective heat transfer in the wall jet.

One important application of jet impingement is the cooling of a grinding process.

To date this has been achieved using flood cooling with a traditional coolant such as

an oil and water mixture. For both environmental and economic reasons, it would

be preferable to cool the process using air. The final objective of this research is to

investigate the convective heat transfer mechanisms that occur in an air cooled grinding

process, with a view to determining an optimal jet set-up.


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Chapter 2

Jet Impingement

Impinging jets have attracted much research from the viewpoint of the fluid flow char-

acteristics and their influence on heat transfer. The jet flow characteristics are highly

complex and consequently the heat transfer from a surface subject to such a flow is

highly variable. Numerous jet configurations have been studied and numerous experi-

mental parameters exist that influence both the fluid flow and the heat transfer. The

overall objective of the current research is to conduct a fundamental investigation of

the heat transfer mechanisms for an impinging air jet. Much of the research presented

in this chapter has been conducted as independent investigations into jet impingement

fluid flow and impinging jet heat transfer. This chapter has been divided into four

sections. The first section details the research concerned with the jet fluid flow charac-

teristics. This includes all the aspects of the flow that have been shown to influence the

heat transfer. The second section describes the research conducted into heat transfer to

an impinging jet. The variation of the heat transfer with various test parameters is dis-

cussed and related to what is known of the fluid flow. A third section summarises some

of the novel techniques that have been employed to enhance the heat transfer to an

impinging air jet. Finally some concluding remarks are made that identify some gaps

in the available literature that have influenced the path of the current investigation.

2.1 Fluid Flow Characteristics

Comprehensive studies of the mean fluid flow characteristics of both a free and an axi-

ally symmetric impinging air jet have been presented by Donaldson and Snedeker [17],

Beltaos [18] and Martin [19]. In many investigations, including one by Gardon andAkfirat [20], the heat transfer to an impinging jet has been correlated with what is

often termed the arrival flow condition. This is the flow condition at an equivalent

4


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5

location in a free jet. Details of the flow characteristics of the jet used in the current

research are presented in Chapter 5 and the flow is compared to previous investigations.

Jet flow characteristics are highly complex and can be influenced easily by varying flow

rate, nozzle geometry, etc. Impinging jet flow characteristics are even more complicated

with additional variables affecting the flow such as angle of impingement, distance from

impingement surface, etc. This section presents some of the latest research on imping-

ing jet fluid flows that has a consequence for heat transfer and has not been presented

in the previous reviews of mean characteristics of jet flow.

2.1.1 Jet Flow Characteristics

Figure 2.1: Impinging Jet Zones

Three zones can be identified in an impinging jet flow. These are illustrated in

figure 2.1. Firstly there is the free jet zone, which is the region that is largely unaffected

by the presence of the impingement surface; this exists beyond approximately 1.5

diameters from the impingement surface. A potential core exists within the free jet

region, within which the jet exit velocity is conserved and the turbulence intensity

level is relatively low. A shear layer exists between the potential core and the ambient

fluid where the turbulence is relatively high and the mean velocity is lower than the

jet exit velocity. The shear layer entrains ambient fluid and causes the jet to spreadradially. Beyond the potential core the shear layer has spread to the point where it has

penetrated to the centreline of the jet. At this stage the centreline velocity decreases


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6

and the turbulence intensity increases. Figure 2.1 also identifies a stagnation zone that

extends to a radial location defined by the spread of the jet. The stagnation zone

includes the stagnation point where the mean velocity is zero and within this zone the

free jet is deflected into the wall jet flow. Finally, the wall jet zone extends beyond the

radial limits of the stagnation zone.

The effects of nozzle geometry on the potential core length were in investigated by

Ashforth-Frost and Jambunathan [21]. Four jet exit conditions were studied, namely

flat and fully developed flow for unconfined and semi-confined jets. It is shown that

the potential core length can be elongated by up to 7 % for the fully developed flow

case. This is attributed to the existence of higher shear in the flat velocity profile,

leading to more entrainment of ambient fluid and therefore earlier penetration of the

mixing shear layer to the centre of the jet. Semi-confinement has the effect of reducing

entrainment and by applying the same principle this also elongates the potential core

length by up to 20 %.

Figure 2.2: Obliquely Impinging Jet Schematic

Figure 2.2 defines some of the terms used in an obliquely impinging jet configuration.

The geometric centre (G.C.) is the centre about which the jet nozzle pivots. The uphill

direction is towards the acute angle that the jet makes with the impingement surface.

Consequently the downhill direction is the direction of the main flow. In this schematicthe stagnation point is displaced in the uphill direction from the geometric centre.

In a study by Foss and Kleis [22], the mean flow properties of a jet impinging


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7

obliquely were investigated. The stagnation point for a jet impinging at an angle of 9

is shown to be displaced from the geometric centre in the uphill direction. The stag-

nation point however is further displaced from the geometric centre than the location

of maximum static pressure. In further investigation by Foss [23], results for a larger

angle of impingement (45) were presented. In this case the location of maximum static

pressure and stagnation coincide.

Several investigations varied the jet fluid to include water, oil, air and others.

Womac et al. [24] investigated heat transfer to water and a fluorocarbon coolant.

Garimella and Rice [25] experimented with similar submerged coolants. Their study

was followed by a more thorough investigation for various impingement set-ups by

Garimella and Nenaydykh [26]. In this case, submergence was investigated as another

parameter that affected the impinging jet flow and hence the heat transfer. In two in-

vestigations by Ma et al. [27], [28], heat transfer to liquids with large Prandtl numbers

liquids such as transformer oil, was studied. Gabour and Lienhard V [29] investigated

a free surface (not submerged) liquid jet for a range of Prandtl numbers. Stevens et

al. [30] and Pan et al. [31] investigated the effect of nozzle geometry on the turbulence

characteristics with respect to the heat transfer for a free surface impinging liquid jet.

For many applications, confinement has been shown to have an influence on the

heat transfer to an impinging jet. In the case where a jet issues from a nozzle plate

the impingement configuration is semi-confined. Further restrictions of the wall jet at

radial locations increases the confinement of the impingement configuration. In the

cooling of electronics, confinement is inevitable due to the small space in which cooling

occurs. Arrays of impinging jets, rather than a single jet, have also been investigated

for the cooling of electronics. Confinement introduces cross-flow as another parameter

for consideration. Goldstein and Behbahani [32] presented heat transfer results for a jet

with and without cross-flow and Goldstein and Timmers [33] investigated heat transfer

to arrays of impinging jets. The degree of confinement determines the magnitude and

direction of cross-flow in arrays of impinging jets. Obot and Trabold [34] investigated

the effects of cross-flow as a result of confinement on the heat transfer to an array of

impinging jets.

As stated previously, nozzle geometry has a very significant influence on the heat

transfer. This is due primarily to the influence the nozzle has on the turbulence levelin the main jet flow. In addition to this, however, the nozzle geometry influences

the entrainment of ambient fluid, the spread of the shear layer and the length of the


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8

potential core. Colucci and Viskanta [35], Garimella and Nenaydykh [26], Brignono

and Garimella [36] investigated the effect of nozzle geometry on the heat transfer to

jets for an otherwise similar range of parameters.

2.1.2 Vortex DevelopmentIn a jet flow, vortices initiate in the shear layer due to Kelvin Helmholtz instabilities. As

the vortices move downstream of the jet nozzle each vortex can be wrapped and develop

into a three dimensional structure due to secondary instabilities. These secondary

instabilities can lead to the cut and connect process as described by Hui et al. [37]

and Hussain [38] which breaks the toroidal vortices down into smaller scale motions,

generating high turbulence. A schematic of the breakdown process of toroidal vortices

in an axially symmetric jet flow is presented in figure 2.3.

Figure 2.3: Schematic of Vortex Breakdown Process according to Hussain [38]

Vortices, depending on their size and strength, affect the jet spread, the potential

core length and the entrainment of ambient fluid. In certain cases jet vortices can

pair, forming larger but weaker vortices. With distance from the jet nozzle the vortices

break down into random small scale turbulence. In the vortex pairing case, the vortices

initiate in the shear layer at a certain frequency. These vortices pass in the shear

layer of the jet at the same frequency as the frequency at which they roll up. As

the vortices pair off the passing frequency halves. In general, turbulent jets have a

fundamental frequency at which the pairing process stabilises and this is determinedby the turbulence level of the jet. A flow visualisation of the vortex pairing process is

presented in figure 2.4 by Anthoine [39].


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9

VortexPairing

PairedVortex

VortexRollUp

Figure 2.4: Example of Vortex Pairing by Anthoine [39]

Vortex Merging

Collective Interaction

Figure 2.5: Vortex Interactions presented by Schadow and Gutmark [40]


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10

Results will be presented in the current investigation for a jet that is formed from

a fully developed pipe flow. In this case instabilities in the boundary layer of the flow

within the nozzle form vortices once the jet exhausts from the nozzle. These vortices

are typically small and initiate at high frequencies. The vortices grow and merge as

they are convected downstream to form larger scale vortices in a process similar to

the pairing mentioned previously. This process has been illustrated by Schadow and

Gutmark [40] and is presented in figure 2.5. This decreases the eventual frequency

substantially. Again the jet will have a natural frequency at which the formed vortices

will pass.

In an investigation by Schadow et al. [41] several peaks in the velocity spectra near

the jet lip are reported. The lowest frequency was normalised with the jet diameter

to calculate a jet Strouhal number of approximately 0.27. The second or intermediate

frequency peak was attributed to the first vortex merging frequency. The highest

frequency peak was identified as the preferred frequency mode at which instabilities

in the nozzle boundary layer form vortices at the jet exit. This frequency value is

normalised as a Strouhal number with the boundary layer thickness as the characteristic

length. Finally another lower frequency exists in the velocity spectrum at the end of

the potential core and this is due to jet column instability according to Crow and

Champagne [42]. This frequency is typically a second or third subharmonic of the

initial highest frequency of the shear layer instabilities.

Fleischer et al. [43] employed a smoke wire technique to visualise the initiation and

development of vortices in an impinging jet flow. The effect of Reynolds number and

jet to surface spacing on the vortex initiation distance and vortex breakup distance

was investigated. The vortex breakup location indicates a transition to turbulent flow

that cannot sustain large scale flow structures. Two methods of vortex breakup were

identified. At large H/D the vortices breakup as they reach the end of the potential

core before impinging on the surface. This occurs following a vortex merging process

where the size of the vortex increases but the strength decreases. Vortices merge

because the vortex does not move fast enough to prevent being entrained by the fluid

flow. At lowH/D, the vortices breakup following impingement on the surface at someradial location due to separation from the impingement surface. Increasing Reynolds

number has been shown to decrease the vortex period.


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2.1.3 Energy Separation

It is known that fluids in motion can separate into regions of high and low temperature

and this phenomenon is termed energy separation. Energy separation involves the

re-distribution of total energy in a fluid flow without external work or heating. Energyseparation can be initiated within the jet nozzle boundary layer flow and is enhanced

later with the onset of vorticity. Because of this the naturally occurring vortex struc-

tures of an impinging jet have been the focus of much research. An energy separation

factor is defined by equation 2.1, where Tej is the temperature at the jet exit. This

equation indicates that energy separation is independent of jet Reynolds number. How-

ever this has been shown by Seol and Goldstein [44] not to hold true within the region

(0.3 < x/D < 4), where the energy separation, S increases with increasing Reynoldsnumber.

S=Tj,total Tej,total

Tej,total(2.1)

where

Tj,total = Tj,static+ Tj,dynamic (2.2)

and

Tj,dynamic =U2j

2Cp(2.3)

Seol and Goldstein [44] have shown that the energy separation process begins to be

affected by vortices at approximately 0.3D from the nozzle exit. At shorter distances

from the nozzle the energy separation parameter is negative. At this distance from

the nozzle (0.3D), part of the energy separation distribution is positive indicating

an intensification of energy separation. With increasing distance from the nozzle the

area across which energy separation has been measured, increases as the size of the

vortical structures increases. The maximum energy separation peaks at approximately

H/D = 0.5 where the strength of the vortex is a maximum. Beyond this, at about

H/D= 1 the maximum energy separation decreases until it is no longer discernable at

H/D= 14.

Han and Goldstein [45], [46] have investigated instantaneous energy separation in a


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12

free jet. In the first part of this two part investigation by Han and Goldstein [45], the

fluid flow measurements are presented. A hot wire is used to measure the motion of

the coherent structure and a schlieren technique is used to visualise the jet flow. For

the free jet at a relatively low Reynolds number of 8000 there is no coherent structure

before H/D 1. Just beyond this (H/D = 2) the flow visualisation identifies theinitiation of a vortex ring. The spectrum of the hot wire also reveals a peak at a

Strouhal number of 0.65. This peak has been attributed to the passing frequency of

the coherent structure. At a further distance from the nozzle exit ( H/D= 3) a second

peak occurs in the spectrum (St = 0.4); this is due to the frequency of the vortical

structure. At this stage the structure has been shown to grow in size. This frequency

peak becomes the dominant frequency at H/D = 4 as the spectral density of the

passing frequency decreases. This was attributed to vortex merging or to the growing

of the vortices by viscous diffusion.

In the second part of this investigation of energy separation in jet flows, Han and

Goldstein [46] measured the energy separation factor across the profile of the jet at

various axial locations. Energy separation was observed to occur in the shear layer of

the free jet with the maximum energy separation occurring at larger radial distances

than the maximum turbulence intensity. It was confirmed that the energy separation

in the free jet is caused by the motion of coherent vortical structures in the free jet

flow as the dominant frequencies of total temperature fluctuation coincide with the

velocity fluctuations. It was shown that the energy is distributed so that the centre of

the vortex has a minimum energy and therefore is coolest.

Further investigations by Han et al. [47] were conducted for jets with Reynolds

numbers ranging from 100 to 1000. In this numerical analysis pressure fluctuations

were induced by the roll up and transport of vortices in the shear layer. It was shown

that the pressure fluctuations are responsible for the energy separation. It was also

shown that increasing the Reynolds number has the effect of increasing turbulence

mixing between regions of energy separation, which counteracts the effect of overall

energy separation. However, increasing the Reynolds number also increases the numberof vortices produced, increasing the energy separation. Overall the energy separation

is conserved throughout the range of Reynolds numbers presented.


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13

2.2 Heat Transfer Characteristics

Comprehensive reviews of the heat transfer to impinging jets have been presented by

Martin [19], Jambunathan et al. [48] and Polat et al. [49]. The heat transfer distributionto an impinging jet varies significantly in shape and magnitude with the various test

parameters. Experimental results for the heat transfer distribution to an impinging

air jet are presented in some detail in Chapter 5 and therefore this section focuses

primarily on differences between various investigations available in the literature. This

includes the effects of some parameters that have not been considered in the current

research. In general the heat transfer distribution is presented as the variation of the

local Nusselt number (as defined by equation 4.14) with radial position.

Nu=hD

k (2.4)

Depending on the measurement technique and thermal boundary condition, the heat

transfer coefficient may be defined by either equation 2.5 or equation 2.6. The first

definition of the convective heat transfer coefficient can be used when the thermalboundary condition is one of uniform heat flux only whereas equation 2.6 can be used

for either uniform wall flux or uniform wall temperature boundary conditions. Tad is

the adiabatic wall temperature, i.e. the steady state temperature of the wall under a

zero flow condition.

h= q

(Tw Tad) (2.5)

h= q

(Tw Tj) (2.6)

Goldstein and Behbahani [32] presented results using both definitions of the convective

heat transfer coefficient and concluded that in the case where |(TwTad)| >> |(TadTj)|

the Nusselt number calculated based on each temperature difference will be similar.Otherwise, when equation 2.5 defines the convective heat transfer coefficient, the Nus-

selt number will be lower in the stagnation zone.


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2.2.1 Stagnation Point Heat Transfer

Goldstein et al. [50] have presented the variation of the stagnation point Nusselt num-

ber (N ustag) with H/D. At heights of the nozzle above the impingement surface that

correspond to within the potential core length, the stagnation point heat transfer isrelatively low and constant. Nustag increases with H/D for distances beyond the po-

tential core length until it reaches a maximum at H/D= 8. This increase is attributed

to the penetration of turbulence induced mixing from the shear layer to the centreline

of the jet. The decrease beyond H/D= 8 is due to the lower arrival velocity of the jet.

Similar variation of the stagnation point Nusselt number has been reported by Lee et

al. [51] however N umax occurs at H/D = 6. The difference between the two studies

has been attributed to the different potential core lengths. Ashforth-Frost and Jam-

bunathan [21] have shown that the maximum stagnation point Nusselt number occurs

at a distance of approximately 110 % of the potential core length from the nozzle exit.

This coincides with the location where the enhanced heat transfer due to increased

turbulence intensity more than compensates for the loss of centreline velocity. Con-

finement has been shown to change the potential core length, therefore the heat transfer

can be enhanced at higherH/D for an unconfined jet by elongating the core of the jet.

Semi-confinement has been shown to reduce the stagnation point heat transfer by up

to 10 % at the optimal H/D. This is due to the reduced level of turbulence because of

reduced entrainment. Hoogendoorn [52] reported on the heat transfer distribution in

the vicinity of the stagnation point. For a jet issuing with a low turbulence intensity

(< 1 %) the stagnation point heat transfer is a local minimum for H/D4. This isnot the case for a jet that has high mainstream turbulence ( 5 %), where the peak inthe heat transfer distribution occurs at the stagnation point.

2.2.2 Heat Transfer Distribution

The shape of the radial heat transfer distribution is affected by the height of the nozzle

above the impingement surface and by the angle of impingement. To give a brief review

of the variations in heat transfer distributions to an impinging air jet, this section has

been further divided into sections that illustrate the heat transfer distribution at lownozzle to surface spacings (H/D 2), large spacings (H/D >2) and jets that impingeobliquely.


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Nozzle to Plate Spacing (H/D 2)

In studies by Baughn and Shimizu [53], Huang and El-Genk [54], Goldstein et al. [50]

and others, secondary peaks in the heat transfer distribution to an impinging air jet

have been reported. In some cases two radial peaks are present in the heat transferdistributions. Both Hoogendoorn [52] and Lytle and Webb [55] have shown that at low

H/D, the wall jet boundary layer thickness decreases with distance from the stagnation

point as the flow escapes through the minimum gap between the nozzle lip and the

impingement surface. In the case of a low turbulence jet this thinning results in a local

maximum in the distribution. With increased distance from the stagnation point the

laminar boundary layer thickness increases before transition to a fully turbulent flow.

Effectively the thickening of the laminar boundary layer decreases the rate of heat

transfer and upon transition to a fully turbulent wall jet, the heat transfer distribution

increases to a secondary peak.

Goldstein and Timmers [33] compared heat transfer distributions of a large nozzle

to plate spacing (H/D = 6) to that of a relatively small spacing (H/D = 2). This

study had a uniform wall flux thermal boundary condition and used equation 2.6 to

define the heat transfer coefficient. It was shown that while the Nusselt number decays

from a peak at the stagnation point for the large H/D, the Nusselt number is a local

minimum at the stagnation point when H/D = 2. Overall, for the same jet Reynolds

number the heat transfer coefficient is lower for the lower H/D. This is attributed

to the fact that the mixing induced in the shear layer of the jet has not penetrated

to the potential core of the jet. The flow within the potential core has relatively low

turbulence and consequently the heat transfer is lower in this case. Although not

discussed, it is apparent from the results presented by Goldstein and Timmers [33]

that subtle peaks occur at a radial position.

Goldstein et al. [50] continued research in this area, but, defined the convective

heat transfer coefficient as per equation 2.5. This investigation concentrated on a

wider range of nozzle to plate spacings (2 H/D 10) and Reynolds numbers(60000 < Re < 124000). Once again at small spacings,H/D 5, secondary maximaare evident at a radial location in the heat transfer distribution. In the case where

H/D = 2 these maxima are greater than the stagnation point Nusselt number. Thesecondary maxima occur at a radial distance of approximately 2 diameters from the

stagnation point and were attributed to entrained air caused by vortex rings in the shear


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16

layer. The heat transfer has been successfully correlated in the form of equation 2.7.

Nu

Re0.76 =

(a |H/D 7.75|)b+ c(r/D)n

(2.7)

where a, b, candn are constants and N uis the local Nusselt number averaged over an

area fromr= 0 to r = ri.

Nozzle to Plate Spacing (H/D >2)

Several investigators, including Donaldson and Snedeker [56], presented heat transfer

data for a jet impinging at large H/D. According to Mohanty and Tawfek [57] the heat

transfer rate peaks at the stagnation point and decreases exponentially with increasingradial distance beyondr/D= 0.5 for a relatively large range of nozzle to impingement

surface spacings (4 < H/D < 58). For this reason several investigators have success-

fully correlated their results. One such investigation by Goldstein and Behbahani [32]

presented equation 2.8 as a good fit to their experimental results.

N u

Re0.6 =

1

a + b(r/D)n (2.8)

Similar to the correlation presented earlier (equation 2.7), a, b and n are constants

that depend on the height of the nozzle above the impingement surface. Although

their study has a uniform wall flux boundary condition the convective heat transfer

coefficient is defined by 2.6.

Oblique Impingement

Several applications require jets to impinge at oblique angles to the surface. Thus, the

angle of impingement is another variable that has concerned investigators. Goldstein

and Franchett [58] investigated the variation of the heat transfer distribution for angles

of impingement from 30 to 90 (normal impingement). The most notable consequence

of a jet impinging obliquely is that the peak in the heat transfer distribution no longer

occurs at the geometric centre of the jet. The maximum Nusselt number occurs at the

stagnation point which is displaced in the direction of the acute angle made betweenthe jet and the surface. Data are presented for a smaller range of Reynolds numbers

(10000 Re 30000). The data were successfully correlated as shown in equation 2.9.


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17

Nu

Re0.7 =ae(b+c cos)(r/D)

n

(2.9)

Once again, a,b,c and n are constants that are specific to the impingement setup

defined by Goldstein and Franchett [58] and is the angle of impingement.

Yan and Saniei [59] also investigated the heat transfer to an obliquely impinging ax-

isymmetric air jet. The displacement of the stagnation point from the geometric centre

has been found to be sensitive to the height of the jet nozzle above the impingement

surface. Also, the heat transfer has been shown to decay rapidly in the uphill direction

and more slowly in the downhill direction. This asymmetry is more pronounced at

small angles of impingement. At lowH/Da secondary peak has been identified in the

heat transfer distribution, but only in the downhill direction. This secondary peak has

been attributed to the transition of the wall jet boundary layer.

Heat transfer to a two-dimensional air jet was investigated by Beitelmal et al. [60].

It was found that the displacement of the peak in the heat transfer distribution is

insensitive to variation in Reynolds number for the range tested, (4000 Re 12000).The heat transfer distributions for various angles of impingement have been shown to

coalesce in the uphill direction beyond the stagnation point, and to diverge in thedownhill direction.

Sparrow and Lovell [61] used a naphthalene sublimation technique to evaluate the

mass transfer from a surface subject to an obliquely impinging air jet. The correspond-

ing heat transfer coefficient was derived by the well established analogy between heat

and mass transfer. As in previous investigations the decay of the heat transfer distri-

bution was observed to be much more rapid in the uphill direction than in the downhill

direction. Also, the displacement of the stagnation point from the geometric centre is

reported. Both effects are more pronounced as the angle of impingement decreases.

Both the peak and area averaged heat transfer were reported to decrease marginally

(15 to 20 %) with increasing angle of impingement.

2.3 Enhancement Techniques

Several techniques have been investigated with a view to enhancing the heat transferto an impinging air jet. These include increasing the turbulence in the jet, the addition

of swirl or artificially exciting the jet. This section identifies some of these techniques,


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explains the principles behind them and then briefly describes some of the findings of

the various research conducted.

2.3.1 Nozzle Geometry

The jet nozzle geometry is believed to have a significant effect on the heat transfer to

the impinging air jet. Several studies attribute inconsistencies between reported data

and their own research to slight differences in the nozzle geometries. For this reason

the effect of nozzle geometry on heat transfer has attracted much research. One of

the most important aspects of the nozzle geometry is confinement. A long pipe nozzle

issuing a jet into a open space is considered to be unconfined, however in many cases,

a nozzle is machined into a plate. This situation is considered to be semi-confined.

Nozzle Shape

Brignoni and Garimella [36] studied the effect of nozzle inlet chamfering, with a view

to enhancing the ratio of area averaged heat transfer coefficient to the pressure drop

across the jet nozzle. This was done by finding the optimum inlet chamfering angle.

It was concluded that while the inlet chamfer angle has a large effect on the pressure

drop across the nozzle; the effect on the heat transfer coefficient was not significant. A

chamfer angle in the vicinity of approximately 60 was shown to be the optimum set-up

as this removed a sharp corner at the inlet which reduced the effect of a vena contract

within the nozzle. Both smaller and larger angles were more similar to a sharp edged

orifice.

For a semi-confined jet orifice, Lee and Lee [62] investigated the effect of jet exit

chamfering on the heat transfer to the impinging air jet. It has been shown that for

a sharp edged orifice the maximum turbulence intensity is greater than that with less

chamfering or no chamfering (square edged). The nozzle exit chamfering has been

shown to induce more jet expansion than the sharp edged orifice. Results reported in

their investigation were also compared to previous investigations that employed both

contoured nozzles and fully developed flow from long pipe jets. All the data presented

by Lee and Lee [62] have shown enhancements in the heat transfer by 2555 %and 50 70 % with respect to the fully developed pipe jet and the contoured nozzle

respectively, at lowH/D = 2. This enhancement is attributed to the higher turbulenceintensity of the orifice jets.

An investigation by Colucci and Viskanta [35] reported the effects of a contoured


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nozzle exit geometry on the pressure distribution and on the heat transfer of an impinge-

ment surface. The nozzles investigated included a semi-confined hyperbolic shaped

nozzle, a semi-confined orifice and an unconfined jet. In general the pressure distribu-

tion along the impingement surface decreases from a maximum at the geometric centre

with increasing radial distance. However, at low H/D


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addition of swirl has the effect of reducing the overall heat transfer from the surface.

A different technique is employed by Wen and Jang [64] to develop a swirling

jet flow. Longitudinal swirling strips are fitted within the long pipe that forms the

jet nozzle. Smoke injected in the pipe flow before exiting the jet nozzle enables the

visualisation of the fluid flow. It was revealed that depending on the swirl generator,

the jet flow is divided into distinct flow streams. At a distance of 1.5D from the jet

exit however the flow streams have been shown to combine. This was also suggested

by Lee et al. [63]. Wen and Jang [64] also showed that swirl results in a local minimum

in the heat transfer distribution at the stagnation point. Despite this, swirl was found

to increase the heat transfer at the stagnation point by up to 6 %.

Vortical Augmentation

The effect of mechanical tabs that are installed on the inside of a jet nozzle on the

jet flow were investigated by Hui et al. [37]. The mechanical tabs have the effect

of instigating streamwise vortical structures. These have the effect of increasing the

secondary instabilities in the jet and therefore hasten the cut and connect process

that breaks the vortices down into small scale turbulence. Gao et al. [65] presented

heat transfer measurements for a jet issuing from a nozzle, for a range of mechanical

tab configurations, that impinged on a flat plate. Results presented show that an

enhancement in the heat transfer is achieved, for certain tab configurations, of up to

20 % in the stagnation zone at low H/D ( 4). Effectively the addition of the tabsreduces the length of the potential core of the jet. Therefore the peak heat transfer

occurs at lower H/D. The tabs however have a negative effect on the uniformity of

the heat transfer distribution. At certain radial locations the tabs block the flow and

local peaks and troughs occur at certain angular locations.

2.3.2 Jet Excitation

Jet excitation has been shown to have the potential to significantly influence heat

transfer to an impinging jet. A jet has a natural frequency at which vortices form and

develop and it is thought that this naturally occurring frequency has an effect on the

heat transfer distribution. Artificial excitation can control the development of vortices

in the jet flow and therefore has the potential to enhance the heat transfer from thesurface. This is the most recent enhancement technique investigated by researchers.

Liu and Sullivan [6] excited the impinging air jet acoustically and reported on the


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resulting flow and heat transfer distributions. It has been shown that, depending

on the frequency of excitation, the area averaged heat transfer can be enhanced or

reduced at low nozzle to impingement surface spacings. In the case where the jet

is excited at a subharmonic of the natural frequency of the jet, the heat transfer is

reduced. This frequency has the effect of strengthening the coherence of the naturally

occurring frequency. It is thought that the energy separation due to a more coherent

flow structure has an adverse affect on the heat transfer to the jet. The jet was also

excited at a frequency higher than that of the natural jet frequency. In this case

the excitation had the effect of producing intermittent vortex pairing. This results in

a break down of the naturally occurring vortex. Consequently, the effects of energy

separation are reduced and transition to small scale turbulence effectively increases the

heat transfer to the impinging air jet.

Hwang et al. [7] investigated the effect of acoustic excitation on a coaxial jet. Two

methods were employed in this research to control the vortex generation in an impinging

jet flow. In the free jet without a secondary shear flow, flow visualisation revealed that a

vortex initiates in the shear flow as a consequence of the instability in the mixing layer.

This vortex is observed to move downstream and eventually undergo a pairing process

with other vortices. In so doing the size of the vortex increases and penetrates the core

of the jet signifying the end of the potential core. Hwang et al. [7] also investigated

the effect that a shear flow had on the potential core length. For a coaxial jet flow a

velocity ratio (V r) is defined by equation 2.11 where Ui and Uo are the average nozzle

exit velocities of the main and shear flow respectively.

V r=Ui UoUi+ Uo

(2.11)

Therefore the case where V r < 1 refers to counter-flowing and V r > 1 refers to a

co-flowing arrangement.

Co-flowing has the effect of elongating the potential core and counterflow has the op-

posite effect. Beyond the potential core the centreline velocity is higher for a co-flowing

jet but decays at the same rate as other jet configurations. The flow visualisation data

presented reveals the reason for this. The co-flowing arrangement inhibits vortex pair-ing, and therefore also jet spread and the entrainment of ambient fluid. These effects

combine to elongate the potential core. The vortex control by use of an axial flow has


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only been shown to accelerate or retard the air jet development. The resulting heat

transfer distributions appear to confirm this.

Acoustic excitation was applied to the shear layer of the jet also. Two naturally

occurring frequencies were identified in the spectrum of the velocity data acquired

in the free jet. The larger occurred at approximately 1kH zand this corresponds to

the fundamental frequency of vortex generation. A subharmonic of this frequency at

500Hz is present and is due to the frequency of vortex pairing. Three shear layer

excitation frequencies were applied to the jet, (1950, 2440, 3250Hz). When the jet is

excited at a multiple of the natural jet frequency, the vortex is maintained at larger

distances downstream. This is because the excitation frequency suppresses the effects

of vortex pairing. Results have shown that while the frequency of the jet flow is

affected strongly by the acoustic excitation of the jet it has a less significant effect

on the vortex frequency. At higher excitation frequencies, the vortex frequency is

increased marginally. In general the excitation frequency has the potential to change

the potential core length, depending on whether the excitation frequency encourages or

discourages vortex pairing. Therefore the heat transfer rate can be affected by changing

the location of the impingement surface relative to the jet development stages without

changing its location relative to the nozzle exit. When the excitation frequency was

equal to, or close to being equal to, a harmonic of the natural frequency of the jet,

vortex pairing was suppressed. This elongated the potential core of the jet. Otherwise

the jet excitation facilitated vortex pairing and reduced the potential core length.

In a subsequent investigation by Hwang and Cho [8] the difference between main-

stream jet excitation and shear layer excitation was investigated. Essentially no signif-

icant difference was noted between the two excitation techniques. Hwang and Cho [8]

also considered the effect of the power level of excitation on the impinging jet fluid flow

and subsequent heat transfer. Results were presented for a range of Strouhal numbers

and for two different excitation power levels from 80dB to 100dB. Only slight differ-

ences in the jet structure are noticed to vary with excitation technique. When the main

flow was excited the potential core is reported to be slightly shorter and the turbulence

intensity to be elevated slightly. It has been shown that a significant excitation power

level ( 90dB) is required to have an appreciable effect on the jet velocity or turbulence

intensity. Once again however, the power level is a factor that amplifies the effect thata particular excitation has. Finally, Yu et al. [66] have shown for a heated plane jet

that when the excitation frequency is within 4.5Hzof the natural frequency of the jet,


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the vortices are strengthened by the excitation.

2.3.3 Other Enhancement Techniques

Several other techniques have been employed with a view to enhancing the overall heat

transfer to an impinging jet flow. Some of these techniques are described in this section.

Intermittency

An intermittent jet flow has been used by Zumbrunnen and Aziz [67] to provide en-

hancement of the convective heat transfer to a free surface water jet. Depending on

the location on the impingement surface the heat transfer could be enhanced by up

to 100 %. This is explained on the basis that the intermittent flow forces renewal

of the hydrodynamic and thermal boundary layers that form along the wall jet. An

investigation by Camci and Herr [68] presented results for another self-oscillating jet.

Results were presented for oscillation frequencies from 20Hzto 100Hz. A significant

enhancement in the heat transfer to the jet of up to 70 % was reported for the spe-

cific range of heights (H/D 24) and Reynolds number of 14000. Goppert et al. [69]investigated a different sort of nozzle geometry, that of a precessing jet. Effectively

the precessed jet motion is that of self-sustained unsteadiness. It was found that for

the range of parameters studied, however, the heat transfer to the jet was reduced.

Effectively there are two main competing effects. The first is that the interaction of

the jet with the ambient flow increases the mixing and turbulence of the flow along the

plate. However, this interaction has the consequence of reducing the arrival velocity

of the impinging jet. It is thought that the heat transfer is highly sensitive to the

amplitude and frequency of the oscillations and therefore the enhancement reported

by Camci and Herr [68] was not reported by G oppert et al. [69].

Surface Finish

The surface finish of the impingement surface is another parameter for the enhance-

ment of heat transfer to an impinging jet. In an investigation by Kanokjaruvijit and

Martinez-botas [70] an array of jets impinging on a dimpled surface was explored. In

certain cases it was found that the heat transfer could be enhanced by up to 50 %, de-pending on the cross-flow condition and on the height of the jets above the impingement

surface.


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Turbulence Promoters

In an attempt to enhance the heat transfer by increasing the turbulence in the jet

flow, Zhou and Lee [71] installed mesh screens across the nozzle exit with various mesh

solidity. The mesh screen has the effect of increasing turbulence in the stagnation zone.

It also reduced the pressure in this zone and this resulted in enhancement of the heat

transfer coefficients by up to 4 % at low H/D and a mesh screen solidity of 0.83.

2.4 Conclusions

The literature to date has shown that the heat transfer to an impinging air jet is highly

sensitive to each of the many experimental parameters that exist. The shape of the

heat transfer distribution in particular varies considerably with height of the jet nozzle

above the impingement surface. While abrupt increases in turbulence in the wall jet

are used to explain the location and magnitude of secondary peaks in heat transfer the

literature fails to provide an in depth explanation of the heat transfer mechanism that

causes this increased heat transfer.

In more recent years attention has been focused on the potential of vortices within

an impinging jet flow to enhance the heat transfer. It has been revealed that vortices

serve to enhance energy separation within the flow. Research has also shown that the

development of a vortex can be influenced by artificial excitation of the jet flow and

that, depending on the excitation frequency, the time averaged heat transfer can be

enhanced. An understanding of the heat transfer mechanisms at various stages within

the vortices development is not available however.

Finally it is apparent that the jet nozzle has a significant effect on the overall

heat transfer. Discrepancies between studies have been attributed to slight differences

between nozzle geometries. The jet exit flow condition is dependent on the nozzle shape

and therefore each investigation is nozzle specific. The current investigation presents

data for the most common nozzle type found in the literature, i.e. a hydrodynamically

fully developed jet that issues from a long pipe.


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Chapter 3

Experimental Rig & MeasurementTechniques

This chapter describes the experimental rig design and the measurement techniques

employed in this investigation of impinging jet heat transfer. Several experimental

parameters are significant in this research, including jet flow characteristics and nozzle

design, thermal boundary conditions and impingement surface geometry. The experi-

mental rig has been designed to allow for the variation of parameters beyond the scope

of this project and these are detailed in this chapter. The specifics of the fluid flow and

heat transfer measurement techniques used are also detailed in this chapter. Finally

the acquisition hardware and software are described.

3.1 Experimental Rig

The experimental rig is to be used both for a fundamental investigation of heat transfer

to an impinging air jet and for a study of the air jet cooling of a simulated grinding

process. To achieve this, the rig has been designed for the fundamental research and

later modified for the grinding configuration. The same instrumentation is employed

to acquire fluid flow and heat transfer data for both studies. This section will describe

the design considerations and the resultant rig design for the two experimental studies.

3.1.1 Set-up for Fundamental Investigation

The main elements of the experimental rig are a nozzle and an impingement surface.

Both are mounted on independent carriages that travel on orthogonal tracks. The flat

impingement surface is instrumented with two single point heat flux sensors and theability of the carriages to move in this way enables the jet to be positioned relative to

the sensors at any location in a two dimensional plane. The rig design and a photograph

25


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ImpingementSurfaceCarriage

NozzleCarriage

Nozzle CompressedAir Supply

ImpingementSurface

(a) Schematic (b) Photograph

Figure 3.1: Fundamental Rig Design

of the rig are presented in figure 3.1.

Figure 3.2 illustrates the air flow system that supplies the jet. Two compressors

operate in series to supply a pressure head of approximately 10bar to the system. An

Ingersall Rand M11 Screw compressor feeds into the pressure chamber of an Ingersall

Rand Type 30 Air-cooled Piston Compressor. The compressors work intermittently

to maintain the pressure head and this results in a fluctuating supply flow. A large

plenum chamber is installed in the air line to eliminate these fluctuations. Two filters

are also connected on the compressed air line to eliminate all trace of moisture and

impurities from the air line.

It is important that the jet exit temperature is maintained within 0.5C of the

ambient air temperature. To this end a heat exchanger is installed on the air line.

The heat exchanger consists of a controlled temperature water bath in which a series

of copper coils are placed. The air flows through the copper coils to increase the jet

exit temperature to the required setting. The air vol

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FLUID FLOW AND HEAT TRANSFER OF AN IMPINGING AIR JET