fluid flow and heat transfer of an impinging …home.eps.hw.ac.uk/~tso1/thesis.pdf · fluid flow...

FLUID FLOW AND HEAT TRANSFER OF AN

IMPINGING AIR JET

by

Tadhg S. O’Donovan

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

Declaration

I, Tadhg S. O’Donovan, 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. O’DonovanMarch, 2005

ii

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, α 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 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Jet Impingement 42.1 Fluid Flow Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Jet Flow Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Vortex Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.3 Energy Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Heat Transfer Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Stagnation Point Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Heat Transfer Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Enhancement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Nozzle Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3.2 Jet Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.3 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 . . . . . . . . . . . . . . . . . . . . . . . 253.1.2 Set-up for Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Jet Flow Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.1 Air Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.2 Seeding for Laser Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.4 Laser Doppler Anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Heat Transfer Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 Thermocouple Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Micro-Foilr Heat Flux Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.3 Hot Film Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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

iv

3.4.1 DAQ Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4.2 DAQ Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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

4 Accuracy & Calibration of Measurement Systems 394.1 Fluid Flow Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1.1 Laser Doppler Anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.2 Particle Image Velocimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1.3 Air Flow Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Heat Transfer Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.1 Thermocouple Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.2 Micro-Foilr Heat Flux Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.3 Hot Film Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

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

5 Results & Discussion 545.1 PIV Flow Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.1 Free Jet Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1.2 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.1.3 Obliquely Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Heat Transfer Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.1 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.2 Obliquely Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Heat Transfer & Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 775.3.1 Normally Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.3.2 Obliquely Impinging Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.4 Fluctuating Fluid Flow & Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 815.4.1 Free Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.2 Stagnation Point for Normal Impingement . . . . . . . . . . . . . . . . . . . . . 845.4.3 Wall Jet for Normal Impingement . . . . . . . . . . . . . . . . . . . . . . . . . 905.4.4 Wall Jet for Oblique Impingement . . . . . . . . . . . . . . . . . . . . . . . . . 118

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

6 Jet Impingement Heat Transfer in a Grinding Configuration 1276.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1286.2 Impingement Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1326.3 Fluid Flow in a Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 135

6.3.1 Rotating Wheel Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1356.3.2 Rotating Wheel with Low Speed Impinging Air Jet . . . . . . . . . . . . . . . . 136

6.4 Heat Transfer in a Grinding Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 1396.4.1 Preliminary Heat Transfer Data . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.4.2 Low Speed Jet Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1426.4.3 High Speed Jet Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

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

7 Conclusions 1517.1 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-Foilr Thermocouple Calibration Data . . . . . . . . . . . . . . . . . . . . . . . 44

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

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

4.5 Micro-Foilr 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, α = 90 . . . . . . . . . . . . . . . . . . . . . 65

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

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

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

5.16 Obliquely Impinging Jet Nu Distributions; Re = 10000 . . . . . . . . . . . . . . . . . 71

5.17 Obliquely Impinging Jet Nu′ Distributions; Re = 10000 . . . . . . . . . . . . . . . . . 73

5.18 Obliquely Impinging Jet Nu Distributions; α = 45 . . . . . . . . . . . . . . . . . . . . 74

5.19 Obliquely Impinging Jet Nu′ Distributions; α = 45 . . . . . . . . . . . . . . . . . . . 75

5.20 Fluctuating & Time Averaged Nusselt Number Distributions; Re = 10000, α = 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, α = 45 . . . . . . . . . . . . . 81

5.25 Flow Velocity & Heat Transfer; Re = 10000,H/D = 2, α = 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



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

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

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

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


5.72 Spectral, Coherence & Phase Information; H/D = 2, α = 60, r/D = 0.37 . . . . . . . 122


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




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; α = 30,H = 101mm, Vs = 10m/s, Vj = 10m/s . . . . . . . . 137

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

6.8 Wheel and Impinging Jet; α = 15, Vs = −10m/s, Vj = 10m/s . . . . . . . . . . . . . . 138

6.9 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

viii

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

ix

List of Tables

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

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

x

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 guidance

within 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.

xi

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]

Pr Prandtl number, ν/κ [−]

q rate of heat transfer [W ]

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

q heat flux [W/m2]

xii

Q volume flow rate [m3/s]

r radial distance from geometric centre [m]

R resistance [Ω]

Re jet Reynolds number, ρUD/µ [−]

S energy separation factor [−]

St Strouhal number, fD/U [−]

Sw degree of swirl [−]

Sxy standard deviation [−]

∆t time interval [s]

T temperature [K]

Tu 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

Greek Symbols

Symbol Description Units

α angle of impingement []

κ thermal diffusivity [m2/s]

δ sensor thickness [m]

θ angle between LDA beams []

λ wavelength of laser beams [m]

µ viscosity [kg/ms]

ν kinematic viscosity [m2/s]

ρ density [kg/m3]

τ sensor response time [s]

φ swirl angle []

ω vorticity [1/s]

Subscripts

Symbol Description

ad adiabatic

d doppler

c cold

e exit

eff effective

h hot

i in

j jet

max maximum

o out

stag stagnation point

w wall

xiv

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 not

been answered by the available literature and outlines the objectives of the current

investigation.

1

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

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 vortex

development 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.

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 and

Akfirat [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

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 spread

radially. 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

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 schematic

the 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

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 level

in 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

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 Development

In 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 determined

by the turbulence level of the jet. A flow visualisation of the vortex pairing process is

presented in figure 2.4 by Anthoine [39].

9

VortexPairing

PairedVortex

VortexRoll−Up

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]

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 low H/D, the vortices breakup following impingement on the surface at some

radial location due to separation from the impingement surface. Increasing Reynolds

number has been shown to decrease the vortex period.

11

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. Energy

separation 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 T ej 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 Reynolds

number.

S =Tj,total − T e

j,total

T ej,total

(2.1)

where

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

and

Tj,dynamic =U2

j

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

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 the

initiation 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 number

of vortices produced, increasing the energy separation. Overall the energy separation

is conserved throughout the range of Reynolds numbers presented.

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 distribution

to 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 thermal

boundary 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 |(Tw−Tad)| >> |(Tad−Tj)|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.

14

2.2.1 Stagnation Point Heat Transfer

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

ber (Nustag) 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 is

relatively 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 Numax 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 higher H/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/D ≤ 4. This is

not the case for a jet that has high mainstream turbulence (≥ 5 %), where the peak in

the 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 low

nozzle to surface spacings (H/D ≤ 2), large spacings (H/D > 2) and jets that impinge

obliquely.

15

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 transfer

distributions. 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 maxima

are 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. The

secondary 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

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, c and n are constants and Nu is the local Nusselt number averaged over an

area from r = 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 increasing

radial distance beyond r/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.

Nu

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 between

the 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.

17

Nu

Re0.7= ae−(b+c cos α)(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 α 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 low H/D a 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 the

downhill 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 transfer

to 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,

18

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 25 − 55 %

and 50 − 70 % with respect to the fully developed pipe jet and the contoured nozzle

respectively, at low H/D = 2. This enhancement is attributed to the higher turbulence

intensity of the orifice jets.

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

19

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 < 2 the pressure is reported to

be sub-atmospheric between 0.6 < r/D < 2.2. Results are similar to those of Lee and

Lee [62] that show that the exit contour has enhanced the overall heat transfer to the

impinging air jet.

Swirl

One possible technique to enhance the overall heat transfer distribution to an impinging

air jet is the introduction of jet swirl. A swirling jet flow would have very different

flow characteristics than a plain jet flow. Swirl affects the jet spread, the turbulence

characteristics and the entrainment of ambient fluid. Lee et al. [63] installed a swirl

generator on the exit of the long pipe nozzle that generated a jet that impinged on a

heated surface. The swirl generator consisted of guide vanes that guided the flow from

the nozzle so that it spiraled towards the impingement surface. The degree to which

the flow swirled is defined by equation 2.10.

Sw =2

3

[1−

(ri

ro

)3

/l −(

ri

ro

)2]

tan φ (2.10)

where l is the length of the swirl generator, ri and ro are the inner and outer radii

respectively and φ is the angle between the swirl vane and the vane axis. In this case,

Nustag was found to be enhanced slightly for low swirl values, Sw < 0.21, however

at large swirl values (Sw ≈ 0.77) the heat transfer at the stagnation point is almost

halved in comparison to the absence of a generator. This is for a range of nozzle to

impingement surface heights from 2 to 10 diameters. The radial distribution of the

heat transfer reveals that the swirl generator has resulted in a local minimum at the

stagnation point. This is thought to be due to a blockage formed by the generator at

the centre of the nozzle. Lee et al. [63] also showed that the area averaged heat transfer

from the impingement surface could be enhanced by up to 34 % at H/D = 2. This

enhancement was at a relatively low degree of swirl (Sw = 0.21), which was the best

case scenario as the combination of the interaction of multiple jets and swirl combined

favorably to enhance the heat transfer. At larger heights of H/D = 6 and 10 the

20

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 tabs

reduces 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 the

surface. This is the most recent enhancement technique investigated by researchers.

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

21

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 − Uo

Ui + 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

22

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 1kHz and 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 that

a particular excitation has. Finally, Yu et al. [66] have shown for a heated plane jet

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

23

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 20Hz to 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 Goppert 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.

24

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.

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 the

ability 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

26

ImpingementSurfaceCarriage

NozzleCarriage

Nozzle Compressed Air 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 volume flow rate and temperature

are monitored before the air enters a long straight pipe from which the air jet issues.

The jet nozzle consists of a brass pipe of 13.4mm internal diameter. The pipe is 20

diameters long and a 45 chamfer is machined at the nozzle lip to create a sharp edge

to minimise entrainment. The desired flow condition is one of a hydrodynamically

fully developed turbulent jet. Analysis of the actual jet flow condition is presented

in Chapter 5. The nozzle is clamped on a carriage in an arrangement that allows its

height above the impingement surface and its angle of impingement to be varied. The

height of the nozzle can be varied from 0.5 to 10 diameters above the impingement

27

Nozzle

Flow Meter

Valve

HeatExchanger

PlenumChamber

Filter

Filter

PistonCompressor

Screw Compressor

ImpingementSurface

Figure 3.2: Air Flow Conditioning System

surface and the jet can be set at oblique angles ranging from 15, in 15 increments,

up to the normal angle of impingement (90).

The impingement surface is a flat composite plate, measuring 425mm × 550mm,

that consists of three main layers mounted on a carriage. The top surface is a 5mm

thick copper plate. A silicon rubber heater mat, approximately 1.1mm thick, is fixed to

the underside of the copper plate with a thin layer of adhesive. It has a power rating

of 15kW/m2 and a voltage rating of 230V . The voltage is varied using a variable

transformer that controls the heat supplied to the copper plate. A thick layer of

insulation prevents heat loss from the heating element other than through the copper.

The plate assembly is such that it approximates a uniform wall temperature boundary

condition, operating typically at a surface temperature of 60C.

Grooves are machined in the impingement surface to allow the flush mounting of

the heat flow sensors. These are positioned in a central location and, together with the

nozzle and plate carriage arrangement, allow for heat transfer measurements beyond

20 diameters from the geometric centre of the jet. For the present study, testing has

only been concerned with a region extending to 6 diameters from the geometric centre;

thus, the impingement surface can be considered as semi-infinite and edge effects can

be neglected.

28

3.1.2 Set-up for Grinding Configuration

The experimental set-up for the grinding configuration is very similar to that used in the

fundamental research. The same heated and instrumented surface is used to simulate

the workpiece in a grinding process. There are obvious inconsistencies between this set-

up and that of an actual grinding process. In particular the uniform wall temperature

boundary condition is very different to that in an actual grinding process in which heat

is generated in a localised spot that moves with the feed rate of the workpiece. This

isothermal boundary condition was necessary, however, to accurately measure the heat

transfer coefficient along the grinding plane.

(a) Grinding Wheel & Heated Surface (b) Nozzle for High Speed Jet

Figure 3.3: Grinding Configuration

A grinding wheel is suspended approximately 0.5mm above the surface and is driven

with an AC Motor. Its rotational speed is controlled using a frequency inverter. A

picture of the experimental set-up is presented in figure 3.3 (a). Contact is not made

between the grinding wheel and the surface; this is to ensure that the sensors are not

damaged by the rotating wheel.

The grinding wheel is an aluminium oxide wheel of diameter 180mm and thickness

19mm. Two nozzle types are used in this investigation. The first is identical to that

used in the fundamental research and has a diameter of 13.4mm. This can be seen

in figure 3.3 (a). The second has a much smaller diameter of 2.6mm and is shown in

figure 3.3 (b). This nozzle is used to create a high speed jet that can approach sonic

velocities and has been used for impingement jet cooling of an actual grinding process,

as described by Babic et al. [3].

29

3.2 Jet Flow Measurements

A number of techniques have been employed for measurement of the jet flow character-

istics. Necessary flow information includes the air volume flow rate supplied to the jet

nozzle, the time averaged mean and rms velocity flow fields and the temporal variation

of the flow velocity at specific locations. The instrumentation used to provide this flow

information is described in this section.

3.2.1 Air Flow Meter

An Alicat Scientific Inc. Precision Gas Flow Meter was installed on the compressed air

line to monitor the air volume flow rate. Real time acquisition of the air volume flow

rate allows for accurate setting of the jet exit Reynolds number, by varying a needle

control valve also installed on the line, just prior to the flow meter. The flow meter

forces the air flow through a streamline flow element which ensures that the flow is

laminar. The pressure drop across the element is measured and because the flow is

laminar the Poiseuille equation 3.1 can be used to determine the volumetric flow rate:

Q =(Pi − Po)πr4

8µL(3.1)

where r and L are the radius and length of the pipes in the flow element respectively.

The flow meter can display the pressure, volume flow rate and temperature in an LED

display. The flow meter also produces an analogue output signal proportional to the

flow rate.

3.2.2 Seeding for Laser Techniques

Laser techniques, such as Particle Image Velocimetry and Laser Doppler Anemometry,

are non-intrusive methods of measuring flow velocities. Seeding particles are added

to a flow to reflect laser light, allowing the visualisation of the flow. In order for any

laser technique to work effectively and non-intrusively, the seeding particles must be

large enough to scatter sufficient light but also small enough to ensure that they follow

the flow faithfully. In this investigation a fog generator is used to create the seeding

particles. Food grade polyfunctional alcohol liquid is diluted with water, heated in the

fog generator and then vaporised to form a fog of seeding particles, typically 1 to 50µm

in diameter.

30

Seeding Particles Unseeded

Air Flow

Seeded Air Flow

Figure 3.4: Venturi Seeding Injection

For the impinging jet flow study it is necessary to seed the entire flow field, which

includes both the jet flow and the ambient air. A venturi seeder, as depicted in figure 3.4

was placed in the air flow line before the nozzle. Flow entering the venturi is forced

through a contraction and, upon expansion, a low pressure zone exists. The suction

resulting from this low pressure draws seeding particles from a reservoir of particles

into the jet flow.

3.2.3 Particle Image Velocimetry

Particle Image Velocimetry is a planar flow measurement technique that acquires a

series of images of a cross-section of a flow and calculates a vector flow field from a pair

of such images. As shown in figure 3.5 the PIV system consists of a double pulse laser

that passes a coherent light beam through a cylindrical lens, creating a laser sheet.

This configuration illuminates a 2 dimensional plane across a seeded flow in two short

pulses. A CCD (Charge Coupled Device) camera records the illuminated images of the

flow field.

The short time interval between the images (∆t) allows the seeding particles to be

displaced from one image to the next. Once the images have been acquired they are

processed to output vector fields of the flow. The images are divided into interrogation

areas, and velocity vectors are extracted for each region by performing mathematical

correlation analysis on the cluster of seeding particles within each area between the

two frames. This produces a signal peak that identifies the common particle displace-

ment (∆x). The velocity vector for an interrogation area is easily calculated by using

equation 3.2.

31

LaserSheet

CCD Camera

Dual PulsedLaser

ImpingementSurface

Jet Nozzle

Figure 3.5: Particle Image Velocimetry Measurement Set-up

U =∆x

∆t(3.2)

The Particle Image Velocimetry system used in this investigation is a 15mJ New Wave

Solo PIV Double Pulse Laser that illuminates the flow. Images are captured with a

double shutter PCO Sensicam camera that has a resolution of 1280× 1024 pixels.

3.2.4 Laser Doppler Anemometry

Laser Doppler Anemometry is a method of measuring flow velocity and turbulence

intensity at a point. This method has high spatial and temporal resolution. The

LDA system consists of a laser beam that enters a bragg cell or beam splitter. The

bragg cell has the function of splitting the beam into two beams of equal intensities

but at different frequencies, fo and fshift. Two beams leave the bragg cell through

separate fiber optic cables that connect to a probe. The probe houses both the beam

transmitting and receiving optics. The parallel beams that enter the probe are focused

at some angle by the transmitting optics so that the beams intersect at a distance from

the probe. The LDA set-up is shown in figure 3.6. The intersection of the beams create

a measurement volume, as illustrated in figure 3.7, that is approximately 2.6mm long

and 0.4mm maximum width. The beams create planes of high light intensity, known

32

as fringes. The distance between the fringes is proportional to the angle between the

beams (θ) and the beam’s wavelength (λ), as defined in equation 3.3.

Jet Nozzle

ImpingementSurface

LDA Head &Receiving Optics

MeasurementVolume

Figure 3.6: Laser Doppler Anemometry Measurement Set-up

Figure 3.7: LDA Measurement Volume Fringes

df =λ

2 sin( θ2)

(3.3)

33

Seeding particles pass through the measurement volume and reflect high intensity

light at the doppler frequency (fd), as they pass through the fringes. The reflected

light is received by the optics in the probe and transmitted to a photo detector that

transmits the doppler frequency to a signal processor. The processor uses equation 3.4

to calculate the resulting instantaneous velocity of the flow.

U = df × fd =λ

2 sin( θ2)× fd (3.4)

The Laser Doppler Anemometry system is based on a Reliant 500mW Continuous Wave

laser from Laser Physics. This is a two component system and therefore the laser is split

into 2 pairs of beams, that have wavelengths of 514.5nm (green) and 488nm (blue),

to measure the velocity in orthogonal directions at the same point location. The four

beams, each of diameter 1.35mm, are focused on a point 250mm from the laser head.

The system works in backscatter mode and a Base Spectrum Analyser (BSA) acquires

and processes the signal to compute the velocity.

3.3 Heat Transfer Measurements

Two sensors are flush mounted on the heated impingement surface as illustrated in

figures 3.8 and 3.9. These are an RdF Micro-Foilr heat flux sensor and a Senflexr Hot

Film Sensor. Thermocouples are also placed on the instrumented plate in the vicinity

of the two heat flux sensors to measure the surface temperature locally. Finally, a

thermocouple is placed in the jet flow line at the flow meter and another in the ambient

air near the nozzle exit to monitor the entrained air temperature. It is necessary to

monitor the ambient air temperature because an investigation by Striegl and Diller [72]

revealed an effect of entrained ambient air on the heat transfer from the impingement

surface. A significant difference in the heat transfer coefficient was determined if the

entrained air temperature was varied from the jet temperature to the impingement

surface temperature. In this investigation the difference in temperature between the

jet and the impingement surface is maintained at approximately 40C. Therefore

allowing the temperature difference between the ambient air and the jet to be 0.5C

should eliminate this parameter as an influence on heat transfer. The specifications of

the three types of measurement device are detailed in this section.

34

RdF Micro−Foil Heat Flux Sensor

Jet Nozzle

Senflex Hot Film Sensor

Reflection

Figure 3.8: Mounted Heat Flux Sensors

ThermocoupleJunction

DifferentialThermopile

Copper ConnectingLeads

Nickel Hot FilmElement

(a) Micro-Foilr Heat Flux Sensor (b) Hot Film Sensor

Figure 3.9: Individual Heat Flux Sensors

35

3.3.1 Thermocouple Type

The thermocouples used in this study are T-type. A T-type thermocouple junction

consists of a positive copper wire and a negative constantan wire, where constantan is a

copper - nickel alloy. The junction produces a voltage proportional to the temperature

difference between the thermocouple junction (Th) and the temperature of the cold

junction (Tc).

V ∝ (Th − Tc) (3.5)

The measurement temperature range for a T-Type thermocouple is from −25C to

100C and the typical sensitivity is 46µV/C. Response time is not an issue for the

temperature measurements as they are used to obtain time averaged data only so

thermocouples of different sizes are used at the different locations. The thermocouple

wires ranged in diameter from 0.01 to 1mm.

3.3.2 Micro-Foilr Heat Flux Sensor

An RdF Micro-Foilr Heat Flux Sensor is flush mounted on the heated surface. This

sensor contains a differential thermopile, as indicated in figure 3.9 (a), that measures

the temperature above and below a known thermal barrier. The heat flux through the

sensor is therefore defined by equation 3.6.

q = k4T

δ(3.6)

where k is the thermal conductivity of the barrier (kapton) and ∆T is the temperature

difference across the thickness (δ) of the barrier. A thermopile consists of a number

of thermocouple junctions above and below the thermal barrier. Although just one

pair of thermocouple junctions is necessary to measure the differential temperature, 5

pairs are used to increase the signal magnitude and resolution. For the specific sensor

thickness used the characteristic 62 % response to a step function is 0.02s. This is

approximated by equation 3.7.

τ =4(Xδ)2ρCp

π2k(3.7)

36

where X in this equation is the cover layer factor of the sensor. The sensor calibration

certificate rates the output of the sensor at 44.41nV/(W/m2). This rating is dependent

on the operating temperature of the sensor as the thermal properties of the thermal

barrier will change with temperature. A further multiplication factor is supplied in the

calibration certificate in Appendix A to compensate for the difference due to operating

temperature. This signal is amplified by a factor of 1000 by an Omega Omni-Amp

amplifier, to further increase the signal magnitude and resolution. The physical size

of the measurement region of the sensor is of the order of 1mm × 4mm. This spatial

resolution is sufficient considering the region of interest extends over 6 nozzle diameters,

where D = 13.4mm. A single pole thermocouple is also embedded in this sensor to

measure the surface temperature locally.

3.3.3 Hot Film Sensor

A Senflexr Hot Film Sensor operates in conjunction with a Constant Temperature

Anemometer to measure the fluctuating heat flux to the impinging jet. This sensor

is also flush mounted on the heated impingement surface in a central location. As

indicated in figure 3.9 (b), the sensor consists of a nickel sensor element that is electron

beam deposited onto a 0.051mm thick Upilex S polyimide film. The hot film element

has a thickness of < 0.2µm and covers an area of approximately 0.1mm×1.4mm. The

typical cold resistance of the sensor is between 6 and 8 Ohms. Copper leads are also

deposited on the film to provide terminals for connection to the CTA. The leads have

a resistance of approximately 0.002Ω/mm.

A TSI Model 1053B Constant Temperature Anemometer is used to control the

temperature of the hot film. It maintains the temperature of the film at a slight

overheat (≈ 5C) above the heated surface. The power required to maintain this

temperature is equal to the heat dissipated from the film. A CTA is essentially a

Wheatstone bridge where the probe, or hot film in this case, forms one arm of the

bridge. The resistance of the film varies with temperature and therefore, by varying a

decade resistance that forms another arm of the bridge, the temperature of the film is

controlled. The decade resistance has a resolution of 0.1Ω and the bridge has a ratio

of 5 : 1. This enables the hot film temperature to be set to within 0.5C. The voltage

required to maintain the temperature of the film constant is proportional to the heat

transfer to the air jet as described in equation 3.8.

37

qdissipated ∝ E2out

R(3.8)

While this equation accurately estimates the heat dissipated from the hot film sensor

there are several corrections made to determine the actual convective heat transfer to

the impinging air jet. These will be discussed in Chapter 4.

3.4 Data Acquisition

Real time acquisition is used to set-up and monitor the stabilisation of the various

signals. The acquisition hardware and software are described in this section.

3.4.1 DAQ Card

The data acquisition card is a National Instruments PCI 6036E. This card can acquire

200kS/s and has 16 Bit resolution. The card can acquire 16 referenced single ended

signals or 8 differential signals. The card works in conjunction with a National Instru-

ments SCB-68 breakout board. This is a shielded Input/Output connector block. The

screw terminals are in a metal enclosure to protect the signals from noise corruption.

The breakout board also has a temperature sensor for the cold junction compensation

of thermocouple readings.

3.4.2 DAQ Software

LabVIEWTMsoftware is used for the acquisition of data. The acquisition software

enables the real-time acquisition of all signals. This real-time acquisition is used to

set-up individual tests. During the set-up phase, all flow rate and temperature settings

are monitored at a frequency of 100Hz. Once temperatures stabilise and flow rates

are set correctly a 4 to 8 second acquisition is triggered and saved to file. Recorded

signals are normally acquired at 8192Hz which is more than twice the peak frequency

of interest in this investigation.

38

3.5 Summary

The experimental set-up described in this chapter facilitates the testing of an impinging

air jet configuration. It allows for a fundamental investigation of the impinging jet flow

on a flat surface. The set-up has also been modified to simulate a grinding process.

Various techniques have been employed to measure both the fluid flow and heat transfer.

The operating principles, of the measurement techniques used have been detailed in

this chapter. The calibration of the instrumentation is described in Chapter 4.

Chapter 4

Accuracy & Calibration ofMeasurement Systems

The measurement techniques employed in this study have been described in Chapter 3;

this chapter details the calibration of those measurement systems and techniques. The

uncertainty associated with each measurement technique is reported with a 95 % con-

fidence level in accordance with the ASME Journal of Heat Transfer policy on un-

certainty [73]. The uncertainty interval (±U) is the band about the reported result

within which the true value is expected to lie with 95 % confidence. The uncertainty is

a combination of the estimated bias limit (B) and the precision limit (P ) in accordance

with equation 4.1:

U =√

B2 + P 2 (4.1)

The bias limit is the magnitude of a fixed or constant error in the sensor measure-

ment technique. This is typically small as calibration against a reference will reduce

this. The uncertainty in the calibration reference measurement is considered generally

as the bias limit. The precision limit is defined as 2 times the standard deviation of a

measurement based on at least 30 samples. This chapter has been divided into two sec-

tions that deal with the methods of measuring fluid flow and heat transfer respectively

and a third section that summarises the calculated uncertainties.

4.1 Fluid Flow Measurements

As detailed in Chapter 3, three methods are employed to measure the impinging air jet

flow characteristics. These methods are Laser Doppler Anemometry for point velocity

measurements, Particle Image Velocimetry for determining the flow field and an air

flow meter to set the required Reynolds Number.

39

40

4.1.1 Laser Doppler Anemometry

Although LDA is often assumed to be an absolute velocity measurement technique

there are aspects of the technique that introduce uncertainty into the measurements.

Angle bias is defined as a bias towards the velocity of a seeding particle that enters the

measurement volume perpendicular to the fringes. In the case where a particle passes

through the volume at an angle to the fringe pattern it may not pass through enough

fringes to generate a velocity signal. Phase bias occurs in the case where multiple

seeding particles pass through the measurement volume at the same time. Reflections

from the individual seeding particles mix before being received by the receiving optics.

The mixed reflection will correspond to an error in the velocity measurement. A velocity

bias occurs due to the fact that in any given measurement, higher velocity particles

will pass through the measurement volume more frequently than low velocity particles.

Therefore when it comes to calculating the average velocity it is biased towards higher

magnitudes. Light from other sources such as ambient lighting and reflections can

register as a signal through the receiving optics. This error is termed shot noise and can

be significantly reduced by operating in a dark environment and blackening surfaces in

the line of the laser beams. In each case careful experimental procedures with regard

to lighting and seeding densities ensured that the measurement error remained low.

The acquisition of velocity measurement is dependent on a seeding particle passing

through the interrogation zone and therefore the velocity is randomly sampled at an

irregular time interval. To process the data the signal must be re-sampled at a regular

time step and this introduces an error in the signal. There are several methods of

re-sampling such as Sample and Hold, Slotting, Decimation, Spline Interpolation etc.

In this investigation the signal has been re-sampled using Sample and Hold and a

correction for error is preformed according to Fitzpatrick and Simon [74]. Overall the

velocity measurements acquired using LDA are considered to be very accurate, the

mean velocities being consistent with flow rates measured by the air flow meter.

4.1.2 Particle Image Velocimetry

Particle Image Velocimetry is another laser based technique that can provide good

accuracy in many flow situations. Processing of the PIV images is a statistical technique

and therefore many approximations are used to eliminate “bad” vectors etc. The DaVis

PIV processing software controls the acquisition process and data processing. The

41

camera has a resolution of 1280×1024 pixels. The images are divided into interrogation

regions that are initially 32 × 32 pixels and reduce to 8 × 8 pixels with successive

correlation calculations. The overlap of the individual cells is 50%. Filtering of the

resultant vectors is carried out after each pass, eliminating vectors that are not within

two times the root-mean-square of neighboring vectors. The acquisition of the images

however is dependent on the test set-up. In general a cross-section of the jet diameter is

examined. The laser sheet thickness is approximately 1mm and therefore this provides

measurements which are averaged across a significant percentage of the jet diameter.

Background noise or reflections have been subtracted from each test image to ensure

that a clean signal is acquired. The PIV technique is accurate in the main flow regions

however in zones where a wide range of flow velocities are investigated the system is

less accurate. This is because setting the time between frames is dependent on the

velocities being measured and so measuring a flow from 0 to 10m/s, for example, is

difficult and will lead to inaccuracies. The function of the PIV measurements in this

investigation is to determine the general flow characteristics and to identify regions of

interest. To this end the technique is considered sufficiently accurate.

4.1.3 Air Flow Meter

The Alicat air flow meter has been calibrated by the manufacturer up to a limit of 400

standard liters per minute (SLPM). This flow meter measures the volumetric flow rate

that is supplied to the jet nozzle. From this, the jet Reynolds number is calculated

using equation 4.2.

Re =4Qρ

πµD(4.2)

The uncertainty in fluid property values is dependent entirely on the uncertainty in

the jet temperature measurement. According to the manufacturer’s specification the

volume flow rate has an uncertainty of 1 % of the full scale deflection of the meter.

According to Coleman and Steele [75], in the case where a measurement, r, is a function

of various other measurements, as in equation 4.3, the uncertainty of the measurement,

Ur, is a combination of the uncertainties of the constituent measurements as described

by equation 4.4. The uncertainty in the Reynolds number therefore, results from

a combination of the uncertainties of the volume flow rate, jet diameter and fluid

properties. This described by equation 4.5.

42

r = r(X1, X2, . . . , XJ) (4.3)

U2r

r2=

(X1

r

∂r

∂X1

)2 (UX1

X1

)2

+

(X2

r

∂r

∂X2

)2 (UX2

X2

)2

+ . . . +

(XJ

r

∂r

∂XJ

)2 (UXJ

XJ

)2

(4.4)

URe

Re=

√(UQ

Q

)2

+

(UD

D

)2

+

(Uρ

ρ

)2

+

(Uµ

µ

)2

(4.5)

On this basis the uncertainty in the Reynolds number is calculated to be 4.18 % for

the lowest Reynolds number studied in this investigation (10000). This is the worst

case uncertainty in Reynolds number. The calibration certificate for the flow meter is

included in Appendix A.

4.2 Heat Transfer Measurements

As described in Chapter 3, three types of sensor are used to measure heat transfer.

Firstly, four thermocouples are used for measuring the temperatures of the air jet,

the ambient air, and the plate temperature at two locations respectively. Secondly an

RdF Micro-Foilr sensor is flush mounted on the impingement surface to acquire time

averaged heat transfer data. Finally, a Senflex hot film sensor is also flush mounted

on the heated impingement surface to acquire heat transfer measurements with greater

temporal resolution than the Micro-Foilr sensor. The uncertainty of many of the

parameters calibrated in this section varies with temperature; the uncertainty reported

will be at the typical operating temperature of the sensor.

4.2.1 Thermocouple Sensors

A Resistance Temperature Detector (RTD) is used as a reference for the calibration

of all the thermocouples in this section. This probe is calibrated by the manufacturer

and its certificate of calibration is included in Appendix A. The uncertainty of this

reference temperature is 0.2C at 100C; this constitutes the bias limit for all ther-

mocouples calibrated with the RTD as a reference. The ambient air temperature and

the Micro-Foilr sensor and hot film sensor temperatures are all measured using ther-

mocouples that are wired directly into the acquisition system, which has cold junction

43

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Ambient Air Temperature [°C]

RT

D [° C

]

DataTrendline

Figure 4.1: Ambient Air Thermocouple Calibration Data

compensation capability. Calibration of the thermocouple for measurement of the am-

bient air involved the submersion of both the RTD and the thermocouple in a constant

temperature bath. The bath temperature was varied from 20C to 80C. The resulting

calibration graph is presented in figure 4.1. A linear regression is fit to the calibration

data and equation 4.6 describes the linear fit.

TRTD = 0.997TAmbientAir − 0.75 (4.6)

The two surface thermocouples were calibrated in situ. A bath of water was installed

on the impingement surface above the thermocouples. The temperature of the bath

was varied from 20C to 85C and time was allowed for the set-up to reach steady

state. The reference RTD was submerged in the bath and the resulting calibration

graphs for the two thermocouples are illustrated in figures 4.2 and 4.3. Again a linear

regression was fit to the calibration data. Equations 4.7 and 4.8 describe the linear fit

to the calibration data.

TRTD = 1.011TMicro−Foilr − 1.12 (4.7)

TRTD = 0.993THotF ilm − 1.06 (4.8)

44

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Micro−Foil Sensor Temperature [°C]

RT

D [° C

]

DataTrendline

Figure 4.2: Micro-Foilr Thermocouple Calibration Data

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Hot Film Temperature [°C]

RT

D [° C

]

DataTrendline

Figure 4.3: Hot Film Thermocouple Calibration Data

45

10 15 20 25 30 35 40 45 5010

15

20

25

30

35

40

45

50

Jet Air Temperature [°C]

RT

D [° C

]

DataTrendline

Figure 4.4: Jet Air Thermocouple Calibration Data

TRTD = 1.119TJetAir − 1.5468 (4.9)

Finally the temperature of the air measured at the air flow meter is calibrated against

the reference RTD. The RTD is placed within the jet nozzle and the temperature of

the air jet is varied by controlling the heat added to the compressed air in the heat ex-

changer. The range of measurements is limited in this calibration as the heat exchanger

has limited effectiveness. Despite this, however, the range far exceeds the expected

range during measurements as the jet temperature is maintained within 0.5C of the

entrained ambient air temperature during testing. Figure 4.4 depicts the calibration

data and the linear regression. Equation 4.9 describes the regression fit.

Bendat and Piersol [76] defined the standard deviation, Sxy of calibration data from

the associated linear regression as shown in equation 4.10. To achieve 95 % confidence

limits the uncertainty in the measurement is defined as twice the standard deviation

as in equation 4.11.

Sxy =

[1

N − 2

(N∑

i=1

(yi − y)2 − [∑N

i=1 (xi − x)(yi − y)]2∑Ni=1 (xi − x)2

)]1/2

(4.10)

46

Umeasurement = 2× Sxy (4.11)

There is also an uncertainty in the regression fit. This is defined by Bendat and

Piersol [76] and is shown in equation 4.12:

URegression = Sxyt

[1

N+

(x0 − x)2

∑Ni=1 (xi − x)2

]1/2

(4.12)

where t is a factor defined by the number of data points plotted, (N), and the confi-

dence level required. xi and yi are defined as arbitrary values within the range of the

calibration data. x and y are the mean of the respective x and y components of the

data. The uncertainty of the regression curve is a minimum at the middle of the range

tested. Therefore, all of the measurement techniques have been tested far beyond the

typical measured value. Table 4.1 details both the uncertainties of the regression fit

and the uncertainty of a particular measurement.

Temperature Typical Operating Regression MeasurementMeasurement Temperature, [C] Uncertainty % Uncertainty %Ambient Air 20 0.06 0.23

Jet Air 20 0.04 0.22Micro-Foilr 65 0.05 0.24Hot Film 65 0.01 0.07

Table 4.1: Contributory Uncertainties

The uncertainties of the regression curve in all four cases is small (< 0.1 %). This

is small also with respect to the measurement uncertainties and is therefore neglected

in subsequent calculations presented in this chapter.

4.2.2 Micro-Foilr Heat Flux Sensor

The Micro-Foilr heat flux sensor is used to measure the convective heat flux from the

impingement surface. This sensor has a relatively poor response time and therefore is

limited to time averaged heat transfer measurements. The principle of operation of this

sensor is described in Chapter 3. The voltage produced by the sensor is proportional

to the heat flux through the sensor which is indicative of the convective heat transfer

from the surface. The signal is amplified by 1000 to increase the signal to noise ratio.

47

The stagnation point heat transfer was used as a reference for the calibration of the

Micro-Foilr sensor. Shadlesky [77] produced a theoretical model that estimated that

the heat transfer at the stagnation point of an impinging air jet is constant and inde-

pendent of the nozzle to impingement surface spacing. Several experimental studies,

including one by Liu and Sullivan [6], have shown this to be untrue. Liu and Sullivan [6]

however have shown that at low H/D (< 2) the convective heat transfer coefficient is

constant and independent of nozzle height above the impingement surface. This has

also been confirmed in the present study. For H/D < 2 the following correlation,

equation 4.13, has been shown to hold true.

0.585 =Nustag

Pr0.4Re0.5(4.13)

The voltage produced by the Micro-Foilr heat flux sensor was recorded when the sensor

was placed at the stagnation point under the impinging jet. The height of the nozzle

above the heated impingement surface was 0.75D. The Reynolds number was varied

from 10000 to 30000. The Nusselt number calculated from equation 4.13 was combined

with the measured surface to jet temperature difference to calculate the surface heat

flux as defined by equations 4.14 to 4.16.

Nu =hD

k(4.14)

q = h∆T (4.15)

q =0.585Pr0.4Re0.5k∆T

D(4.16)

This calculated heat flux was plotted against the voltage produced under the test

conditions. The resulting calibration graph is presented in figure 4.5. The uncertainty

of the linear regression is also plotted, however, this is calculated to be just 1.03 %

of the measurement. The relationship between the heat flux and the voltage is linear

and a regression curve was fitted to the calibration data. Equation 4.17 describes this

linear relationship.

q = 2.17× 107V − 1.09× 103 (4.17)

48

2.6 2.8 3 3.2 3.4 3.6 3.8

x 10−4

4000

4500

5000

5500

6000

6500

7000

Voltage [V]

q [W

/m2 ]

DataTrendlineRegression Uncertainty

Figure 4.5: Micro-Foilr Heat Flux Calibration Data

The slope of the graph is comparable to the calibration constant supplied by the man-

ufacturer that is also included in Appendix A. This constant was 2.25× 107 W/m2

Vand

the intercept value is comparable to the voltage under a zero flow condition which is

the heat transfer due to natural convection and radiation to the surroundings. The

uncertainty in the heat flux measurement is calculated to be approximately 4.2 %.

Heat transfer measurements are presented in the dimensionless form of the Nusselt

number. The associated uncertainty of the Nusselt number is the combination of the

uncertainties of the heat flux, the jet temperature and the surface temperature. Again

based on the jet being at 20C and the impingement surface at 65C the uncertainty

is calculated to be 5.67 % of the Nusselt number measurement.

4.2.3 Hot Film Sensor

As described in Chapter 3 the hot film operates in conjunction with a constant temper-

ature anemometer. The hot film probe is a resister that forms one arm of a Wheatstone

bridge, as indicated in figure 4.6. As a current passes through the hot film element

heat is generated because of the sensor resistance. The resistance of the sensor in-

creases with temperature and the circuitry will find equilibrium when the resistance of

49

Rt1 + Rprobe equals the resistance of the other side of the bridge, (Rt2 + Rdecade). The

decade resistance is the control resistor and therefore by varying Rdecade, the tempera-

ture of the film can be controlled. The output voltage from the bridge, E, is monitored

by the computer data acquisition system. This is related to the heat dissipated from

the film, as indicated by equations 4.18 to 4.21.

Figure 4.6: Constant Temperature Anemometer Circuitry

qdissipated = Rfilm × I2 (4.18)

where

I =E

Rt1 + Rprobe

(4.19)

and

Rprobe = Rfilm + Rcable (4.20)

therefore

qdissipated =Rfilm

(Rt1 + Rprobe)2× E2 (4.21)

In order to produce a significant output from the hot film sensor, the film is maintained

at a slight overheat above the surface temperature. As a result of this, some of the heat

dissipated from the sensor is conducted to the surface. Therefore to evaluate the heat

convected to the fluid the output voltage is measured first under a zero flow condition.

50

Under a zero flow condition the output voltage is a combination of conduction to

the surface, natural convection and radiation from the sensor to the surroundings.

The acquired output voltage with zero flow, (E0) is subtracted from the voltage for

subsequent forced convection conditions. Therefore the convective heat flux is defined

by equation 4.22.

qconvection =Rfilm

(Rt1 + Rprobe)2× (E2 − E2

0) (4.22)

There are two stages to the calibration of the hot film sensor. Firstly the variation

of the hot film resistance with temperature is evaluated. This is done so that the

temperature of the film can be accurately set by the decade resistance. Calibration

was conducted after the film was flush mounted on the heated surface. A copper block

was placed on top of the sensor and in contact with the surface. Insulation was placed

around the whole system to ensure that the temperatures above and below the sensor

were equal. The entire system was then heated to temperatures from 24C to 93C and

the resistance of the probe was measured at regular intervals. To eliminate a possible

systematic error, associated with the resistance measurement technique and the decade

resistance settings, the resistance of the film was measured through the CTA. At each

temperature setting the decade resistance was varied until the bridge was balanced.

The resulting calibration data are presented in figure 4.7. The relationship between

the resistance of the film and the temperature is linear and the equation of the linear

fit is given in equation 4.23.

Rprobe = 0.0258T + 7.022 (4.23)

The typical operating temperature of the film is 70C and the corresponding uncer-

tainty at this temperature is 0.0135Ω. The probe resistance includes both the resistance

of the film and the resistance of the connecting cables as shown in equation 4.20. Heat

dissipated by the film was generated by the film resistance alone, therefore it is im-

portant to subtract the cable resistance in the calculations. The cable resistance was

also measured through the CTA by shorting the connecting cables close to the hot

film. The resistance of the cable was 0.60 Ω. The resulting uncertainty in the probe

resistance is a combination of the uncertainty in the film and cable resistances and is

51

20 30 40 50 60 70 80 90 1007.5

8

8.5

9

9.5

Temperature [°C]

Rpr

obe [Ω

]

DataTrendline

Figure 4.7: Hot Film Resistance Calibration Data

0.05 Ω at 70C. This is approximately 0.54 % of the film resistance.

In order to calculate the convective heat transfer coefficient it was necessary to

determine the effective surface area of the hot film sensor, as indicated by equation 4.24.

In an investigation by Beasley and Figliola [78] the effective surface area was shown

to vary significantly from the geometric surface area. This was attributed to lateral

conduction from the sensor element to the thin coating on the sensor. The effective

surface area of a similar sensor to the one used in this investigation has been shown

by Scholten [79] to be approximately twice the geometric surface area of the film.

Therefore the second part of the hot film calibration was concerned with comparing

correlated heat transfer data with measured data to calculate the effective surface area

of the hot film sensor. The correlation described by equation 4.13 and used to calibrate

the Micro-Foilr heat flux sensor is used also to calibrate the effective surface area of

the hot film. By combining equations 4.22, 4.24 and 4.13, the effective surface area

can be calculated and is given by equation 4.25.

q = hAeff (Tfilm − Tjet) (4.24)

Aeff =Rfilm(E2 − E2

0)D

0.585(Rprobe + Rt1)2(Tfilm − Tjet)kPr0.4Re0.5(4.25)

52

To evaluate the effective surface area measurements have been taken at the stagnation

point for a jet nozzle to plate spacing of 0.75 jet diameters and Reynolds numbers

of 10000, 15000, 20000, 25000, 30000. This was repeated ten times for each Reynolds

Number. The calibration procedure has shown that the effective surface area is 2.97×10−7 m2. According to the manufacturer’s specifications the geometric surface area,

Ageometric ≈ 1.471 × 10−7 m2. Therefore the effective surface area was found to be

approximately a factor of two times greater than the geometric surface area. This is

consistent with the study by Scholten [79] in which a Dantec hot film was calibrated.

There was a relatively large degree of scatter in the calibration data and therefore the

measurement uncertainty is 18.79 % of the effective surface area.

In another investigation by Scholten and Murray [80] the effect of the hot film

overheat has been investigated. Essentially the higher temperature of the hot film

constitutes discontinuity in the isothermal boundary condition and the magnitude of

the overheat determines the extent of the deviation in the thermal boundary condition.

It would therefore be favorable to reduce the hot film overheat to a negligible level. A

small overheat, however, has the effect of reducing the sensor sensitivity. A correction

for the overheat has been established by Scholten and Murray [80] and this is presented

in equation 4.26.

qconvective |Tsensor = Tsurface= qsensor |Tsensor = Tsurface + Toverheat

−qshear |Tsensor = Toverheat + Tambient(4.26)

This correction was made for the application of heat transfer measurements from

a cylinder in cross-flow. It was found that the correction is only valid for the range

where the flow does not separate from the cylinder. In this investigation, the range

of validity of equation 4.26 is much smaller so a new approach was required. Thus,

equation 4.27 has been shown to hold true when the overheat is small. This relationship

has been used by Liu and Sullivan [6] and it has been shown that at small overheats

the fluctuating part of the hot film measurement is unaffected.

q′ = 2CEE ′ (4.27)

53

where

C =Rfilm

Aeff (Rprobe + Rt1)2(4.28)

E =

√qconvection

C(4.29)

Therefore the mean qconvection, which is estimated from the Micro-Foilr heat flux sen-

sor, is used to evaluate the corresponding E value. This is then substituted into

equation 4.27 to calculate the value of the fluctuating component of the heat flux. q′

is then used to calculate the fluctuating Nusselt number. This leads to an uncertainty

of approximately 30 % in the magnitude of Nu′.

4.3 Summary

This chapter has outlined the values of all uncertainties with a 95 % confidence level.

The calibration techniques have been detailed for the experimental equipment and the

results presented together with calibration charts. A summary of the uncertainties in

the measurement techniques used is given in table 4.2.

Measurement Units Uncertainty %Re − 4.18q W/m2 4.53

Nu − 5.67Rf Ω 0.59

Aeff m2 18.79E V 9.67

Nu′ − 30.05

Table 4.2: Summary of Experimental Uncertainties

Chapter 5

Results & Discussion

The results from fluid flow and heat transfer measurements of an impinging air jet are

presented and analysed in this chapter. The fluid flow measurements include velocity,

turbulence intensity and vorticity of a free jet and of a jet in an impingement config-

uration. The heat transfer measurements consist mainly of heat transfer distributions

over the impingement surface subject to the jet. Results are analysed on both a time

averaged and temporal basis.

There are many parameters that affect the heat transfer to an impinging jet. These

parameters include confinement, submergence, nozzle geometry, non-dimensionalised

nozzle to impingement surface spacing (H/D), jet exit Reynolds number (Re) and

angle of impingement (α). In the current investigation the influence of confine-

ment, submergence and nozzle geometry have not been investigated. Results are pre-

sented for an unconfined air jet issuing from a long pipe for three Reynolds numbers

(Re = 10000, 20000, 30000) and eleven different spacings above the impingement sur-

face, (H/D = 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8). This range of spacings gives good pre-

cision at low spacings and extends beyond the potential core length of the jet at the

highest Reynolds number. Data acquired for an obliquely impinging jet are presented

for angles that range from 30, in 15 increments, to the normal impinging jet (90).

Correlating the fluid flow to the heat transfer has been conducted on a qualitative

basis for the time averaged data. The time averaged data also revealed particular lo-

cations of interest for further investigation. Investigation of the time varying nature of

the heat transfer and fluid flow in these locations involved the simultaneous measure-

ment of local fluid velocity and heat transfer. A quantitative comparison of the heat

transfer and the fluid flow in these locations has given an insight into the convective

heat transfer mechanisms of an impinging jet.

54

55

5.1 PIV Flow Field Data

The flow field of interest in this investigation is a cross-section through the centreline

of the jet. The PIV (Particle Image Velocimetry) system described in Chapter 3 was

employed to take full field flow measurements of the free jet and of the jet in various

impingement configurations. The PIV images were used to calculate the mean velocity,

turbulence intensity and vorticity of the flow field.

Measurements of the free jet are presented to ensure that the desired flow condi-

tion is achieved. The free jet is of interest also because, in a study by Gardon and

Akfirat [20], the free jet flow characteristics are used to interpret the heat transfer

corresponding to a similar jet in an impingement configuration. Although it was found

by Gardon and Akfirat [20] that there is reasonable agreement between the free jet

flow characteristics and the heat transfer to the impinging jet the impingement surface

does influence the fluid flow. Therefore, to make a more relevant comparison, flow

measurements for the impinging jet are presented and analysed.

5.1.1 Free Jet Configuration

The standard jet flow investigated in impinging jet heat transfer studies is a hydro-

dynamically fully developed turbulent jet. The turbulence of such a jet is defined

by the jet Reynolds number and the nozzle diameter. For this reason, heat transfer

correlations are, in general, independent of a turbulence intensity term. However, var-

ious nozzle geometries and turbulence promoters have been researched in an attempt

to enhance the resultant heat transfer between the jet and the impingement surface.

The nozzle used in this investigation was chosen to approximate the standard jet flow

condition.

The fundamental structure of a free jet flow is well established and the experimental

flow field data obtained at a Reynolds number of 10000 and presented in figure 5.1

provide a reasonable approximation of the desired flow. The jet spreads as ambient

fluid is entrained. The width of the mixing region increases with distance from the

nozzle. The maximum jet velocity occurs at the centreline and this remains constant

until the mixing layer eventually penetrates to the centreline of the jet. The turbulence

intensity is defined in equation 5.1 to be the local rms velocity as a percentage of the

mean jet exit velocity. The maximum turbulence intensity occurs in the mixing region

of the jet and the minimum is experienced within the jet core.

56

Figure 5.1: Free Jet Flow Field; Re = 10000

Tu =U ′

Ujet,exit

× 100 (5.1)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.8

0.85

0.9

0.95

1

U/U

max

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20

Tur

bule

nce

Inte

nsity

, %

y/D

Figure 5.2: Free Jet Centreline Velocity & Turbulence Intensity; Re = 10000

Jet profiles were extracted from the colour maps that are presented in figure 5.1,

in order to take a closer look at the jet structure. The variation of mean velocity and

turbulence intensity along the centreline of the jet is illustrated in figure 5.2 and radial

distributions of these parameters are presented in figure 5.3 for various axial locations.

The jet exit flow profile approximates a top hat shape. The potential core of the jet

is the region in which the jet exit velocity is conserved and for Re = 10000, the core

57

0 0.5 1

−1

−0.5

0

0.5

1

y/D = 1

x/D

0 0.5 1y/D = 2

0 0.5 1y/D = 3

Mean Velocity, U/Uexit

0 0.5 1y/D = 4

0 0.5 1y/D = 5

0 10 20

−1

−0.5

0

0.5

1

y/D = 1

x/D

0 10 20y/D = 2

0 10 20y/D = 3

Turbulence Intensity, %

0 10 20y/D = 4

0 10 20y/D = 5

Figure 5.3: Free Jet Velocity and Turbulence Intensity Profiles; Re = 10000

length is 3.5 diameters based on 95 % of the jet exit velocity. The centreline turbulence

intensity is low, but does rise gradually within the potential core. Beyond the core

however, there is a sharp rise in the centreline turbulence intensity. In general, the

desired hydrodynamically fully developed turbulent jet flow condition is approximated.

ω =dv

dx− du

dy(5.2)

The vorticity field is calculated from the mean flow velocity field and is defined as

the local component of rotation in the flow as in equation 5.2. This parameter is

useful as it identifies regions within the jet flow that encourage the growth of coherent

rotating flow structures. It is apparent from the vorticity flow field of figure 5.1 that a

flow structure rolls up or initiates at the lip of the jet nozzle. From there it convects

58

downstream and is responsible for the entrainment of ambient fluid and the spread

of the jet. The vorticity is positive on the left side of the jet centreline and negative

on the right side. This is the cross-section through a three dimensional vortex ring

where clockwise motion is defined as positive vorticity. It is also apparent that the flow

structure diminishes in strength (or coherence) with distance from the nozzle.

5.1.2 Normally Impinging Jet

Figure 5.4 shows an example of PIV results for a normally impinging jet at H/D = 2.

In this case the impingement surface is located within the potential core of the jet.

The stagnation zone includes a stagnation point where the local fluid velocity is zero

and the surrounding flow is deflected into the wall jet.

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

The turbulence intensity flow field, also presented in figure 5.4, depicts the outer

edge of the shear layer as the line of maximum turbulence intensity. The impingement

surface forces the flow to stagnate at the geometric centre and to accelerate as it moves

radially. Beyond the stagnation region it is also apparent that regions of locally high

turbulence exist in the wall jet flow.

According to Gardon and Akfirat [20], the free jet is largely unaffected beyond 1.5

diameters from the impingement surface. The similarity (as defined in equation 5.3)

between the free jet up to 2 diameters from the nozzle exit and an impinging jet flow,

(H/D = 2) is presented in figure 5.5.

Similarity, [%] =Uimpingingjet

Ufreejet

× 100 (5.3)

59

(a) Impinging Jet (b) Free Jet (c) Similarity

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

0.5 1 1.5 20

20

40

60

80

100

120

x/D

Sim

ilarit

y, %

Centreline Similarity

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

60

Figure 5.6 shows that the centreline velocity is largely unaffected beyond 1 diameter

from the impingement surface. It is notable however that the similarity is greater than

100 % at the largest radial distances presented in figure 5.5. This indicates that in the

impingement configuration the jet spreads further than the free jet. This is evident

for the entirety of the interrogation region and so, although it might appear at first

that the impingement surface has no effect on the free jet zone, it does in fact have an

influence on the jet spread far beyond the stagnation zone.

Of particular interest in this investigation of surface heat transfer is the flow field

in the vicinity of the stagnation zone and the wall jet. Data have been acquired for

the eleven different heights of nozzle above the impingement surface. The flow field

in the region, from 0 to 0.75 diameters from the impingement surface, is presented in

figure 5.7 for each nozzle to plate spacing. The impinging jet flow varies significantly

with H/D. With increasing distance of the nozzle from the impingement surface the

jet develops further. At low H/D (≤ 2) the free jet applies a downward pressure on

the expanding wall jet. It is this downward pressure that suppresses the turbulence

within the stagnation region. As the jet is allowed to develop further, however, the

centreline velocity is appreciably reduced and this results in the arrival velocity being

much more uniform across the profile of the jet.

The turbulence intensity in the flow field is also presented in figure 5.7. The regions

of high turbulence indicate the limits of the shear layer and as such clearly show the

spread of the impinging jet flow. The shear layer impacts upon the surface at greater

and greater radial distances with increasing H/D. Once again at low H/D it is obvious

that the stagnation region remains a zone of particularly low turbulence. At larger

H/D, however, the turbulence at the stagnation point is relatively high locally.

In addition to the quantitative the results from the PIV measurements described to

date, the impinging jet flow has been seeded and illuminated to allow the visualisation

of the flow. Figure 5.8 contains two examples of the flow visualisation, where in one

case the main jet flow is seeded and the ambient fluid is seeded in the other. In both

cases the vortex roll up, as discussed in section 5.1.1, is evident.

Some of the more recent research in impinging jet heat transfer has been concerned

with the enhancement associated with artificial excitation of the jet. As discussed in

Chapter 2 there are many ways of achieving this, from novel nozzle design to acoustic

excitation. The effect that the acoustically excited flow structure has on the surface

heat transfer has been established by Liu and Sullivan [6], and will be discussed in

61

Figure 5.7: Impinging Jet Full Field Flow Velocity & Turbulence Intensity;Re = 10000

Figure 5.8: Impinging Jet Flow Visualisation; Re = 10000, H/D = 2

greater detail in section 5.4.3. The vorticity flow field for the impinging jet is therefore

of great significance. Figure 5.9 presents the vorticity flow field for normally impinging

jets at various heights ranging from H/D = 0.5 to 8. Much like the free jet vorticity

field, with increasing distance from the jet nozzle the flow structure breaks down into

random turbulence. The vorticity in the flow field at large distances from the nozzle is

spread over a wide area and is much diminished in magnitude. Therefore, the natural

frequency of the jet has less significance for heat transfer at large nozzle to impingement

surface spacing.

62

Figure 5.9: Impinging Jet Full Field Flow Vorticity; Re = 10000

5.1.3 Obliquely Impinging Jet

Data have also been acquired for obliquely impinging jets, although the range of param-

eters is not as extensive. Two nozzle to plate spacings of H/D = 2 and 6 were chosen

to correspond to within and just beyond the potential core for the jet Reynolds number

of 10000. The range of angles considered is from α = 30 to 90, in 15 increments.

Figure 5.10 presents time averaged velocity flow fields for various angles of im-

pingement. The green and red circles indicate the location of the geometric centre

and stagnation point respectively. As the angle made with the impingement surface

becomes more acute the stagnation point moves further from the geometric centre in

the uphill direction. The variation in location of the stagnation point with respect to

the geometric centre has been observed for H/D = 2 also and is plotted in figure 5.11

(a).

63

Figure 5.10: Oblique Impingement Velocity Flow Fields; Re = 10000, H/D = 6

30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

Angle of Impingement α, [°]

Sta

gnat

ion

Poi

nt D

ispl

acem

ent,

[D]

H/D = 2H/D = 6

30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

Angle of Impingement α, [°]

Sta

gnat

ion

Poi

nt D

ispl

acem

ent,

[D]

H/D = 4H/D = 6H/D = 10

(a) PIV Data (b) Goldstein & Franchett [58]

Figure 5.11: Displacement of Stagnation Point from Geometric Centre

It is clear that the stagnation point location is dependent on the angle of impinge-

ment; however the height of the jet above the plate appears to have negligible influence.

In a paper by Goldstein and Franchett [58] the displacement of the stagnation point

from the geometric centre is investigated. In their investigation the stagnation point

is located by the peak in the heat transfer distribution, rather than from direct ve-

locity measurements. Although the variation of the stagnation point displacement is

not discussed by Goldstein and Franchett [58] in detail, an empirical equation that

correlates their experimental data shows a dependence on the nozzle to impingement

surface spacing. This variation of stagnation point displacement from the geomet-

ric centre is illustrated in figure 5.11 (b). In an investigation reported by Beitelmal

64

et al. [60], the displacement of the stagnation point was found to be independent of

Reynolds number and varied up to 3 diameters from the geometric centre. Although

the location of the stagnation point reported in the current investigation is not entirely

consistent with the literature it is the case that nozzle geometry has a significant effect

on all jet impingement studies and differences in the nozzle geometry may explain the

inconsistencies reported here.

5.2 Heat Transfer Distributions

The time averaged surface heat transfer data include mean and root-mean-square Nus-

selt number distributions for the various jet impingement configurations. Nu is based

on the heat flux (q) and the temperature difference (∆T ) between the jet temperature

at the nozzle exit and the impingement surface. Nu′ is based on the same temperature

difference and the fluctuating heat flux (q′) is as defined in Chapter 4. Heat transfer

data are presented for a zone extending from the geometric centre to a radial distance

of 6 diameters.

The three dominant influences on convective heat transfer for the impinging air

jet are the local fluid velocity, turbulence intensity and surface to fluid temperature

difference. The magnitude of the fluctuations in the Nusselt number are an indication

of the instability of the flow velocity and temperature and as such provide some insight

into the heat transfer mechanisms that occur along the impingement surface.

In this section the characteristic heat transfer distributions are presented and de-

scribed. Variations in the mean heat transfer distributions are presented in conjunction

with the time averaged fluctuating component. Results are broken down into two cat-

egories, the normally impinging jet and the obliquely impinging jet.


The measured heat transfer distributions vary considerably with H/D. Distributions

for two different heights (H/D = 0.5; 6.0) are presented in figure 5.12. These two

heights correspond respectively to well within the potential core (H/D = 0.5) where

the jet exit velocity is conserved across the entirety of the profile, and to a height where

the impingement surface is beyond the potential core (H/D = 6.0). In the latter case

the shear layer has penetrated to the centreline of the jet, resulting in a diminished

centreline velocity and in a centreline turbulence intensity which is relatively high.

65

0 1 2 3 4 5 60

50

100

150

Nu

H/D = 0.5H/D = 6

0 1 2 3 4 5 60

5

10

15

r/D

Nu′

Figure 5.12: Heat Transfer Distributions; Re = 30000, α = 90

For the range of parameters tested the Nusselt number distributions exhibit a max-

imum at the stagnation point. The flow at the stagnation point is not truly stagnant in

that velocity fluctuations in the radial direction occur, but can be considered stagnant

on a time averaged basis. Since the flow is not actually stagnant the mixing that occurs

results in the continued introduction of cold fluid, maintaining a high local temperature

difference. Therefore the combined effects of a high instantaneous velocity and large

temperature difference results in a heat transfer peak at the stagnation point. At H/D

of 0.5 the Nusselt number distribution decreases from this maximum at the geometric

centre but rises again to give a peak at a radial location that is both Reynolds number

and H/D dependent. Beyond this peak the heat transfer distribution decays with in-

creasing radial distance from the stagnation point. It is thought that these secondary

peaks are a result of transition of the wall jet boundary layer, that develops from the

stagnation point, to fully turbulent flow.

The fluctuating heat transfer distribution is an indication of the instability in the

flow along the impingement surface. At H/D = 0.5, the free jet exerts pressure on the

wall jet within the stagnation zone. This maintains the heat transfer fluctuations low

and constant. As the wall jet escapes from the effects of the free jet, it is free to undergo

transition to turbulent flow and the combination of high local velocity and turbulence

66

intensity lead to peaks in both the time averaged and fluctuating Nusselt number

distributions. However the ever increasing local air temperature and the decreasing

local fluid velocity eventually negate the effects of high turbulence in the wall jet and

the Nusselt number falls off with increasing radial distance. The fluctuations in the

heat transfer also decrease in magnitude as the local fluid velocity decreases.

At H/D = 6 (also shown in figure 5.12) the heat transfer decreases from a peak

at the geometric centre with increasing radial distance. At this distance of the nozzle

above the plate, the shear layer has penetrated to the centre of the jet and therefore the

flow at the geometric centre is highly turbulent. The fluctuations in heat transfer are

also a maximum at the stagnation point. The flow velocity along the plate increases

from zero at the geometric centre, as the free jet joins the wall jet flow. With further

increasing radial distance the wall jet velocity decays as the flow spreads radially.

Also at greater radial distances the fluctuations in the flow decrease and the local air

temperature increases. The combination of these flow characteristics result in the heat

transfer distribution decaying from a maximum at the geometric centre with increasing

radial distance. The fluctuating heat transfer distribution exhibits a subtle secondary

peak (at r/D ≈ 3) even at this large H/D, indicating that the free jet remains an

influence on the wall jet beyond the potential core length. This is not sufficient to

overcome the effects of decreasing radial velocity and decreasing local temperature

difference, however, so that the time averaged Nusselt number continues to fall.

Studies by Goldstein and Behbahani [32], and others have shown the Nusselt number

at the stagnation point to be a local minimum. This is the case where the Reynolds

number is extremely high and/or the nozzle to plate spacing is extremely low and this

is the case for a low turbulence jet only. In these circumstances the flow genuinely does

stagnate and therefore the heat transfer is low. The flow condition and heat transfer

at the stagnation point is examined in greater detail in section 5.4.2.

Time averaged and fluctuating heat transfer distributions for a much wider range

of parameters are plotted in figures 5.13 and 5.14 respectively. In general, the area

averaged heat transfer is greater for higher Re. It is also apparent that as the height

of the jet above the plate increases the secondary peaks decrease in magnitude until

they eventually disappear. Secondary peaks occur at low H/D in both Nu and Nu′

distributions, however the highest spacing at which they occur is Reynolds Number

dependent. This is, in part, due to the elongation of the potential core at larger jet

exit velocities.

67

0 1 2 3 4 5 60

50

100

150

r/D

Nu

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(a) Re = 10000

0 1 2 3 4 5 60

50

100

150

r/D

Nu

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(b) Re = 20000

0 1 2 3 4 5 60

50

100

150

r/D

Nu

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(c) Re = 30000

Figure 5.13: Time Averaged Nusselt Number Distributions; α = 90

68

0 1 2 3 4 5 60

5

10

15

r/D

Nu′

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(a) Re = 10000

0 1 2 3 4 5 60

5

10

15

r/D

Nu′

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(b) Re = 20000

0 1 2 3 4 5 60

5

10

15

r/D

Nu′

H/D = 0.5H/D = 2H/D = 4H/D = 6H/D = 8

(c) Re = 30000

Figure 5.14: Fluctuating Nusselt Number Distributions; α = 90

69

0 1 2 3 4 5 60

2

4

6

Nu′

H/D = 1

0 1 2 3 4 5 60

2

4

6N

u′

H/D = 3

0 1 2 3 4 5 60

2

4

6

r/D

Nu′

H/D = 6

PotentialCore

Shear Layer

Figure 5.15: Nu′ Distributions; Re = 10000

The area averaged Nu′ also increases with Re. The distribution, however, has

three distinct patterns that are dependent on H/D. An example of each distribution is

presented in figure 5.15, together with a schematic representation of its location within

the free jet. At very low H/D, as discussed previously, the heat transfer fluctuations

are low within the stagnation zone, increasing to a peak and then decreasing as the jet

spreads radially. The axial velocity is high and therefore suppresses the fluctuations in

the stagnation region. The spread of the jet is also small and therefore once the wall

jet has escaped the lip of the jet the heat transfer fluctuations increase rapidly.

At intermediate heights (2 < H/D < 4) the fluctuations remain low at the stag-

nation point, however two peaks are evident in the Nu′ distribution. In this case the

width of the potential core is less and the suppressive nature of the free jet flow is

mainly felt across this reduced area. The first peak is located within the shear layer

of the free jet and is due to the high turbulence injected into the wall jet flow upon

impingement. This peak is much smaller at lower H/D because the shear layer is much

narrower. With increasing height this peak moves towards the geometric centre as the

70

shear layer penetrates the core of the jet. The second peak is once again attributed to

the wall jet escaping beyond the constraining effect of the free jet flow. The jet has

spread further at greater H/D and therefore the location of this secondary peak moves

further from the geometric centre.

The final trend is evident at large H/D, where the potential core width has de-

creased to zero as evident in figure 5.15 for H/D = 6. At this stage the inner peak in

the Nu′ distribution has reached the geometric centre. This corresponds to the shear

layer penetrating to the centreline of the jet. The outer peak has decreased significantly

in magnitude at this stage as the axial velocity of the free jet is reduced, lowering the

suppressive force exerted on the wall jet flow. In this case the Nu′ distribution simply

decays from a peak at the stagnation point with increasing radial distance. Evidence

in support of this explanation is presented in section 5.3 where the local flow velocities

are qualitatively compared to the heat transfer distributions.


Heat transfer distributions to a jet impinging at an oblique angle to the surface are

presented in figure 5.16. The asymmetry of the profile is apparent for each test con-

figuration and the differences between the uphill and downhill direction are more pro-

nounced as the angle of impingement deviates further from normal impingement. Both

figures 5.16 (a) and (b) show that the peak heat transfer no longer occurs at the

geometric centre but at a location displaced from the geometric centre in the uphill

direction. This displacement increases as the angle made between the jet and the sur-

face decreases. This is consistent with the displacement of the stagnation point from

the geometric centre at various angles of impingement, presented in section 5.1.3.

The shape of the heat transfer distributions indicate that the heat transfer decreases

slowly in the downhill direction and quickly in the uphill direction. Once again, the

difference is more pronounced at more acute angles of impingement. At the lower

H/D of 2 presented in figure 5.16 (a) secondary peaks are appreciable at certain radial

locations. These peaks occur in each profile in the downhill direction but only occur in

the uphill direction when the jet impinges at angles approaching normal impingement.

The majority of the jet flow forms the wall jet that flows in the downhill direction.

Therefore the development of the wall jet boundary layer follows the usual pattern in

this direction. In the case where the jet impinges at small angles, the wall jet flow

in the uphill direction is greatly reduced and therefore the heat transfer will approach

71

−4 −2 0 2 4 60

20

40

60

80

100

120

Nu

r/D

α = 30°

α = 45°

α = 60°

α = 75°

α = 90°

(a) H/D = 2

−4 −2 0 2 4 60

20

40

60

80

100

120

Nu

r/D

α = 30°

α = 45°

α = 60°

α = 75°

α = 90°

(b) H/D = 6

Figure 5.16: Obliquely Impinging Jet Nu Distributions; Re = 10000

72

zero at short radial distances from the stagnation point. This does not allow for the

development of a boundary layer that would result in a secondary peak. In general the

peak heat transfer that occurs at the stagnation point increases with decreasing angle

of impingement at H/D = 2, as shown in figure 5.16 (a). Figure 5.16 (b) however

shows that the opposite is true for H/D = 6.

The distribution of the fluctuating Nusselt number is presented in figure 5.17. These

distributions exhibit many characteristics which are similar to the mean Nusselt number

distributions. The peak in the magnitude of the fluctuations occurs at the stagnation

point, somewhat displaced from the geometric centre. Again secondary peaks at radial

locations are evident in the profiles for H/D = 2. These peaks occur in the uphill direc-

tion to a greater extent than is observed from the mean Nusselt number distribution.

This indicates that while a boundary layer does develop in the uphill direction, the

mean volume flow rate in this direction is low and therefore the increased magnitude

of the fluctuations does not correspond to an increase in the mean heat transfer.

The heat transfer distributions to a jet impinging at an oblique angle of 45 are

presented in figure 5.18. The heat transfer distributions for three different Reynolds

numbers are broadly similar. As in the case of a normally impinging jet, the peaks in the

heat transfer distribution are more evident for larger Reynolds numbers. The primary

peak in the heat transfer distribution occurs in the same location, indicating that

the stagnation point location is independent of the Reynolds number. The secondary

peaks that occur at low H/D, as depicted in figure 5.18 (a), occur at increasing radial

distances as Re increases. This was also evident for the normally impinging jet and is

attributed to the development of the jet being delayed for the larger Re. Thus, at a

specific H/D the heat transfer distribution will differ as it is not in a self similar position

within the jet flow. This explains why, secondary peaks are evident in figure 5.18 (b),

where H/D = 6, for Re = 30000 that do not occur at Re = 10000. Figure 5.19, presents

the distribution of Nu′ for the same range of parameters. In this case the secondary

peak in the uphill direction is especially evident at higher Reynolds numbers and at

H/D = 2. These peaks correspond in location (r/D ≈ −1.5) to a subtle change in

slope in the mean Nusselt number distributions presented in figure 5.18 (a).

Results for a more extensive range of heights, an angle of impingement of 45 and

a Reynolds number of 10000 are presented in figure 5.20. Figure 5.20 (a) shows that

the magnitude of the peak heat transfer decreases with increasing nozzle to surface

distance for this angle of impingement. Peak fluctuations in heat transfer are shown in

73

−4 −2 0 2 4 60

2

4

6

8

10

12

Nu′

r/D

α = 30°

α = 45°

α = 60°

α = 75°

α = 90°

(a) H/D = 2

−4 −2 0 2 4 60

2

4

6

8

10

12

Nu′

r/D

α = 30°

α = 45°

α = 60°

α = 75°

α = 90°

(b) H/D = 6

Figure 5.17: Obliquely Impinging Jet Nu′ Distributions; Re = 10000

74

−4 −2 0 2 4 60

50

100

150

Nu

r/D

Re = 10000Re = 20000Re = 30000

(a) H/D = 2

−4 −2 0 2 4 60

50

100

150

Nu

r/D

Re = 10000Re = 20000Re = 30000

(b) H/D = 6

Figure 5.18: Obliquely Impinging Jet Nu Distributions; α = 45

75

−4 −2 0 2 4 60

2

4

6

8

10

12

Nu′

r/D

Re = 10000Re = 20000Re = 30000

(a) H/D = 2

−4 −2 0 2 4 60

2

4

6

8

10

12

Nu′

r/D

Re = 10000Re = 20000Re = 30000

(b) H/D = 6

Figure 5.19: Obliquely Impinging Jet Nu′ Distributions; α = 45

76

−4 −2 0 2 4 60

10

20

30

40

50

60

70

80

90

100

Nu

r/D

H/D = 2H/D = 4H/D = 6H/D = 8

(a) Nu Distribution

−4 −2 0 2 4 60

1

2

3

4

5

6

7

8

9

10

Nu′

r/D

H/D = 2H/D = 4H/D = 6H/D = 8

(b) Nu′ Distribution

Figure 5.20: Fluctuating & Time Averaged Nusselt Number Distributions;Re = 10000, α = 45

77

figure 5.20 (b) to be greatest for low H/D. The location of the peak in both the mean

and fluctuating Nusselt number distributions does not vary with H/D.

5.3 Heat Transfer & Velocity Measurements

This section is dedicated to the qualitative comparison of time averaged heat transfer

distributions with local velocity data obtained using LDA and is broken down into

analysis of the normally impinging jet and a jet impinging at oblique angles. Thus

peaks and troughs in the Nu and Nu′ distributions are linked to regions of high local

fluid velocity and turbulence intensity.


While the PIV measurements provided an overall picture of the flow field, the LDA

technique was used to measure in more detail the flow velocity close to the impingement

surface. In general, the PIV results presented in figure 5.7 have shown that quite a

severe velocity gradient exists at low nozzle to impingement surface spacing (H/D ≤ 2).

This contrasts to the gradual changes in velocity and turbulence intensity in the flow

field for the larger spacings (H/D > 2).

Figures 5.21 and 5.22 compare the flow velocities near the impingement surface to

the heat transfer from the surface with a normally impinging jet at H/D of 1 and 8

respectively. Both the axial and the radial velocity components (perpendicular and

parallel to the impingement surface respectively) are presented. These measurements

were made at a location of 3mm from the impingement surface which was the closest

possible given experimental constraints. The abrupt changes in velocity evident in

figure 5.21 contribute to the non-monotonic decay of the Nusselt number from a peak

at the stagnation point. The axial velocity is a maximum in the stagnation zone. This

is often termed the arrival velocity. With increasing radial distance from the stagnation

point the axial velocity decreases and may even turn negative (i.e. in a direction away

from the impingement surface). The radial velocity is zero at the centreline of the

jet which corresponds to the stagnation point. This velocity increases with increasing

distance from the stagnation point but peaks at a radial location beyond the lip of the

jet as the jet spreads radially.

Figure 5.21 demonstrates that at low H/D the axial velocity profile is more uniform

within r/D < 0.5 than in the case where H/D = 8, which is presented in figure 5.22.

78

−50

15Mean Axial VelocityMean Radial Velocity

0

5

Vel

ocity

, [m

/s]

RMS Axial VelocityRMS Radial Velocity

0

50

Nu

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

r/D

Nu′

Figure 5.21: Flow Velocity & Heat Transfer; Re = 10000,H/D = 1

This indicates that the deflection of the jet to a radial flow occurs much further from

the impingement surface for the larger H/D case. It is the high axial velocity of the free

jet that suppresses the development of the wall jet flow. The effect of the mean and rms

velocities on the mean and fluctuating heat transfer is also apparent in both figures.

At H/D = 1 the axial velocity magnitude decays sharply beyond r/D = 0.5 and once

this axial velocity has decreased sufficiently the wall jet flow is less constrained and

undergoes transition to a highly turbulent flow. Both the radial and axial velocities

exhibit peaks in their rms velocities at radial locations where the axial velocity is

low. These peaks in rms velocity, for the axial velocity in particular, correspond in

location to peaks in both the mean and fluctuating heat transfer distributions as seen

in figure 5.21. At larger H/D, as indicated in figure 5.22, the axial velocity has a

much smaller magnitude in the region r/D < 1 and therefore does not have the same

suppressive effect on the development of the wall jet flow. As a result the entire profile

has a more uniform turbulence level and peaks are not evident in either the mean or

fluctuating heat transfer distributions.

From figure 5.21 the secondary peak in the Nu distribution at H/D = 1 occurs at

79

−50


0

5

Vel

ocity

, [m

/s]


0

50

Nu

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

r/D

Nu′

Figure 5.22: Flow Velocity & Heat Transfer; Re = 10000,H/D = 8

0 1 2 30

1

2

3

4

5

6

r/D

H/D

Re = 10000Re = 20000Re = 30000

0 1 2 30

1

2

3

4

5

6

r/D

H/D

Re = 10000Re = 20000Re = 30000

0 1 2 30

1

2

3

4

5

6

r/D

H/D

Axial RMS VelocityRadial RMS Velocity

(a) Peak Nu (b) Peak Nu′(c) Peak Turbulence

(Re = 10000)

Figure 5.23: Location of Heat Transfer Maxima & Maximum Turbulence In-tensity

80

the same radial location as the peak in the Nu′ distribution. Figure 5.23 depicts the

location of the peaks in both the Nu and Nu′ distributions for a range of jet to plate

spacings and jet Reynolds numbers and compares them to the location of the peaks in

both rms axial and radial velocities. As was shown in figure 5.13, the Nusselt number

distributions continue to exhibit secondary peaks up to a nozzle to plate spacing which

depends on the jet Reynolds number. The radial location of the peak, however, is

independent of the Reynolds number but moves in the positive radial direction as H/D

increases. A similar trend is evident for the peak locations in the Nu′ distributions, as

shown in figure 5.14. The fact that the peaks occur at the same location for both Nu

and Nu′ distributions may indicate that the heat transfer fluctuations have a positive

influence on the mean heat transfer. In general, however, fluctuations in the local

flow velocity will have the effect of enhancing both the mean and the fluctuating heat

transfer. Also, the peaks in the Nu′ distribution are evident at nozzle to plate spacings

for which there are no peaks in the mean Nusselt number distribution, indicating that

other factors must influence the mean heat transfer.

As the location of the heat transfer peaks moves radially outwards with increasing

H/D it is hypothesised that this is due to the spreading of the free jet flow. Previous

studies by Gardon and Akfirat [20] have related the flow characteristics of a free jet to

the resulting heat transfer to a similar jet in an impingement configuration. A more

relevant comparison has been achieved in this study with the use of the local fluid

velocities along the surface subject to an impinging jet. The location of the peak in

the local turbulence intensity is presented in figure 5.23 (c). As the height of the nozzle

above the impingement surface increases a divergence between the locations of the peak

radial and axial velocity fluctuations is realised. The peak in Nusselt number occurs

close to the peak in the axial velocity fluctuation and therefore it is surmised that

the heat transfer is dependent primarily on the magnitude of fluctuations in velocity

normal to the surface. This dependence will be discussed further in section 5.4.


Velocity and heat transfer distributions are presented and compared in figures 5.24

and 5.25 for jets impinging at angles of 45 and 60 respectively. In each case it is

apparent that the velocity is much greater in the downhill direction. As in the normally

impinging case the radial velocity increases from zero at the stagnation point. The

location of the stagnation point is indicated in the figures at approximately r/D = −1

81

and −0.9 for α = 45 and 60 respectively. By comparing figures 5.24 and 5.25, it can

be seen that the peak radial velocity occurs at greater radial distances as the angle

of impingement decreases. The comparison of the fluid flow velocity with the heat

transfer confirms that the maximum heat transfer occurs at the stagnation point. Also

the secondary peaks in the heat transfer distributions can be attributed to the regions

of high local velocity fluctuations. At r/D = 1.5 and 2 for α = 45 and 60 respectively,

the mean axial velocity is negative or in a direction away from the surface. At these

locations the suppressive force of the free jet no longer affects the wall jet boundary

layer development. In effect, the flow lifts from the surface at such locations. This flow

velocity away from the impingement surface encourages the transition of the wall jet

boundary layer to fully turbulent flow.

−50


0

5

Vel

ocity

, [m

/s]


0

50

100

Nu

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

r/D

Nu′

DownhillUphill

Stagnation Point

Figure 5.24: Flow Velocity & Heat Transfer; Re = 10000,H/D = 2, α = 45

5.4 Fluctuating Fluid Flow & Heat Transfer

The PIV technique enabled the rapid acquisition of full velocity flow fields for several

impinging jet configurations, but the results obtained lack both temporal and spacial

resolution, particularly close to the impingement surface. Thus, the PIV data have

82

−50


0

5RMS Axial VelocityRMS Radial Velocity

0

50

100

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

r/D

Vel

ocity

, [m

/s]

Nu

Nu′

Uphill Downhill

Stagnation Point

Figure 5.25: Flow Velocity & Heat Transfer; Re = 10000,H/D = 2, α = 60

been used to identify regions for investigation in further detail with the LDA system.

These areas include the lip of the jet nozzle, the stagnation point and various locations

within the wall jet flow. The difference between the jet exit temperature and the local

surface temperature is used in the calculation of the heat transfer coefficient; thus data

have not been acquired for the local temperature difference between the impingement

surface and the fluid, nonetheless the influence on heat transfer of decreasing local

temperature difference as the wall jet develops is discussed. This section presents

spectral data of the velocity and heat flux signals measured. The local velocity and

heat flux have, in certain cases, been measured simultaneously. In these cases coherence

and phase information between the velocity and heat flux signals are also presented.

5.4.1 Free Jet

The vorticity of the free jet flow field was shown in figure 5.1. The vorticity is a

maximum in the shear layer close to the nozzle exit. Vorticity is the measure of the

velocity gradients in the flow field and a free jet flow encourages the initiation of a

vortical flow. At greater distances from the nozzle exit the velocity gradients are lower

83

and therefore so too is the vorticity. It is also apparent that the turbulence intensity

of the free jet increases with increasing distance from the nozzle exit as the coherent

vortical flow is broken down into smaller scale turbulence. Local instantaneous velocity

measurements have been acquired in both axial and radial directions across the profile

of the jet at a distance of 0.5D from the jet exit. It has been shown from the PIV

measurements that a vortex ring rolls up at the lip of the jet nozzle. It has also been

shown by Liu and Sullivan [6] that the frequency associated with such flow structures

has an influence on the area averaged heat transfer distribution. It is for this reason

that temporal fluid flow measurements are presented in this section. The frequency

(f) of velocity fluctuations is presented in the non-dimensional form of the Strouhal

number, defined in equation 5.4:

St =fD

Ujet

(5.4)

where Ujet is the jet exit velocity

The velocity spectra at the centreline of the jet and in the shear layer are presented

in figure 5.26. In both the centreline and shear layer flow the spectral power density is

lower for the radial velocity component. This indicates that the velocity fluctuations

are greatest in the main jet flow direction. Overall, however, the spectral power is far

greater in the shear flow as this is a location of high turbulence. It is apparent that no

dominant frequency appears in the jet centreline flow and that the velocity fluctuations

reflect random small scale turbulence. In the shear layer, however, three dominant

peaks in the power spectrum are evident at Strouhal numbers of approximately 0.6, 1.1

and 1.6 respectively. Schadow and Gutmark [40] reported similar frequencies that

occur at the exit of their jet. The highest of the three frequencies was attributed to

the frequency at which vortices roll up in the shear layer. The lower frequencies are

attributed to the frequencies at which vortices pass following merging processes. In an

investigation by Han and Goldstein [45], two peaks were found in the velocity spectra.

The higher frequency peak was attributed to the roll-up or passing frequency of the

vortex. The lower frequency peak, however, only occurs at larger distances from the

nozzle exit and was attributed to vortex pairing. In the current investigation it is

thought that vortex pairing occurs earlier due to the relatively high turbulence at the

jet exit.

84

0 0.5 1 1.5 2

10−4

10−3

10−2

St

Pow

er S

pect

rum

Mag

nitu

de

Axial Velocity SpectrumRadial Velocity Spectrum

0 0.5 1 1.5 2

10−4

10−3

10−2

St

Pow

er S

pect

rum

Mag

nitu

de

Axial Velocity SpectrumRadial Velocity Spectrum

(a) Centreline, r/D = 0 (b) Shear Layer, r/D = 0.35

Figure 5.26: Free Jet Velocity Spectra; x/D = 0.5

5.4.2 Stagnation Point for Normal Impingement

A theoretical model by Shadlesky [77] presented results that showed that the heat

transfer at the stagnation point is independent of the height of the nozzle above the

impingement surface. This is contrary to much published experimental data, including

the current research. This discrepancy may result from the fact that in experimental

studies the point referred to as the stagnation point actually experiences a velocity

which fluctuates around zero. Thus the average velocity at this location is zero and it

is termed a time averaged stagnation point. The heat transfer at the stagnation point

is dependent on the instantaneous fluid velocity and the local temperature difference.

In this section, results describing the variation of the heat transfer with flow velocity

are presented for the stagnation point of a normally impinging air jet.

The flow velocity in both the radial and axial directions is measured 3mm above

the stagnation point with the two component LDA system as this was the closest the

85

measurement volume could be positioned to the impingement surface. Figure 5.27

presents both the mean and rms velocities at this location for a jet Reynolds number

of 10000. As expected the mean radial velocity is zero at this location for the range of

heights investigated. The arrival axial velocity is relatively constant at approximately

47 % of the jet exit velocity for H/D < 5. At greater nozzle heights, however, the

axial velocity decreases with distance beyond the end of the jet core. The arrival rms

velocity is low and almost constant up to H/D = 3. Beyond this the rms velocity

in both the axial and radial directions increases sharply to a peak at approximately

7.5D. The rms velocity in the axial direction is greater across the range tested by

approximately 2 % of the jet exit velocity.

0 1 2 3 4 5 6 7 8−10

0

10

20

30

40

50

60

H/D

U/U

exit, [

%]

Mean Radial VelocityMean Axial Velcoity

0 1 2 3 4 5 6 7 82

4

6

8

10

12

14

16

U′/U

exit, [

%]

H/D

RMS Radial VelocityRMS Axial Velcoity

(a) Mean Velocity (b) Fluctuating Velocity

Figure 5.27: Stagnation Velocity Variation with Nozzle Height; Re = 10000

0 1 2 3 4 5 6 7 850

60

70

80

90

100

110

120

Nu st

ag

H/D

Re = 10000Re = 20000Re = 30000

0 1 2 3 4 5 6 7 82

3

4

5

6

7

8

9

10

Nu′

stag

H/D

Re = 10000Re = 20000Re = 30000

(a) Mean Nusselt Number (b) Fluctuating Nusselt Number

Figure 5.28: Stagnation Heat Transfer Variation with Nozzle Height: Effect ofReynolds Number

86

For the range of tests conducted the heat transfer is a maximum at the stagna-

tion point, as was shown in figure 5.13. A more detailed display of the variation of

Nustag with nozzle to plate spacing is presented in figure 5.28. It is apparent from

the data displayed that at H/D < 3 both Nu and Nu′ are low and almost constant,

although strongly dependent on Reynolds number. With increasing distance of the

nozzle from the impingement surface, however, both the mean and the fluctuating heat

transfer at the stagnation point increase. The mean Nusselt number reaches a peak at

H/D ≈ 5.5, 6.5 and 7.5 for Re = 10000, 20000 and 30000 respectively. This location is

representative of the potential core length which increases with increasing jet Reynolds

number. The rms Nusselt number varies in accordance with the local fluctuations in

velocity. Nu′ is low and rising gradually within the potential core. Before the end of

the potential core the fluctuations increase rapidly and for a Reynolds number of 10000

the peak rms Nusselt number occurs at approximately 7.5D. Again this peak occurs

at higher H/D for the larger jet Reynolds numbers. The peak in the mean Nusselt

number is therefore a result of a combination of high arrival rms and mean velocity.

0 1 2 3 4 5 6 7 80

10

20

30

40

50

Tur

bule

nce

Inte

nsity

, [%

]

H/D

Axial DirectionRadial Direction

Figure 5.29: Stagnation Point Turbulence Intensity; Re = 10000

0 1 2 3 4 5 6 7 82

4

6

8

10

12

(Nu′

/Nu)

stag

, [%

]

H/D

Re = 10000Re = 20000Re = 30000

Figure 5.30: Stagnation Point Intensity of Heat Transfer Fluctuations

87

The variation of the turbulence intensity at the stagnation point has significance

for the stagnation point heat transfer. In this instance, however, the axial and radial

components of the turbulence intensity are defined by equation 5.5, to be the fluctuating

component as a percentage of the mean velocity close to the stagnation point. In

figure 5.27 the rms velocity was normalised by the jet exit velocity instead. This

definition of the turbulence intensity (equation 5.5) facilitates comparison with the

intensity of heat transfer fluctuations, defined in a similar manner.

TI, [%] =U ′

Ulocal

× 100 (5.5)

Figure 5.29 presents the relationship between the turbulence intensity at the stagnation

point for a jet exit Reynolds number of 10000 and the dimensionless nozzle to plate

spacing. The turbulence intensity at the stagnation point shows a similar trend as the

intensity of heat transfer fluctuations at the stagnation point presented in figure 5.30.

The turbulence intensity is low and constant at low H/D and then increases almost

linearly beyond the potential core. This is true for both the axial and radial component

of the turbulence intensity, however the magnitude of the fluctuations are greater in

the radial direction. The Nusselt number fluctuations normalised by the mean Nusselt

number are also low within the core of the jet and increase sharply beyond the end of

the potential core. A similar trend is also evident for the larger Reynolds numbers of

20000 and 30000.

Simultaneous measurements of the heat transfer and fluid flow 3mm above the

surface at the stagnation point reveal the extent to which the heat transfer depends

on the local fluid flow. A trigger mechanism ensured the simultaneous acquisition of

both fluid velocity and heat transfer signals. Figure 5.31 depicts the power spectrum

of both the surface heat transfer and the axial fluid velocity for H/D = 0.5. At the low

height of H/D = 0.5, there are no dominant frequency peaks evident in either the axial

velocity or the heat transfer spectrum. Despite this there is reasonably high coherence

between the two signals, reaching 0.6 at low frequencies. The convection velocity (Uc)

of the flow between the velocity and heat flux measurement locations can be calculated

from the phase difference between the two signals as indicated in equations 5.6 to 5.8.

Uc =2πδf

Φ(5.6)

88

where δ is the distance between the velocity and heat flux measurement points, f is the

frequency at which the convection velocity is calculated and Φ is the phase difference

between the two signals. The slope of the phase difference with respect to frequency

is defined as follows:

m =Φ

f(5.7)

Therefore the convection velocity is defined by equation 5.8.

Uc =2πδ

m(5.8)

The phase difference between the signals decreases approximately linearly, from zero,

with increasing frequency within the range where the coherence is high. The convection

velocity is calculated to be approximately 3.5m/s. At higher frequencies corresponding

to a Strouhal number of 1.5 the phase information is less accurate due to the low

coherence between the two signals at high frequencies.

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

St

Pow

er S

pect

rum

Mag

nitu

de

Axial VelocityHeat Flux

0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce

0 1 2−12

−10

−8

−6

−4

−2

0

St

Pha

se

Figure 5.31: Stagnation Point Spectral Data; H/D = 0.5, Re = 10000

89

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

St

Pow

er S

pect

rum

Mag

nitu

de

Axial VelocityHeat Flux

0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce

0 1 2−16

−14

−12

−10

−8

−6

−4

−2

0

St

Pha

se

Figure 5.32: Stagnation Point Spectral Data; H/D = 4, Re = 10000

At greater nozzle to impingement surface spacings the coherence between the two

signals is much lower as depicted in figure 5.32. The axial velocity spectrum exhibits a

slight peak at a Strouhal number of around 0.6. Although there is no peak evident in the

heat transfer spectrum the coherence is a maximum at this frequency, which is higher

than the frequency at which the maximum coherence is achieved for H/D = 0.5. This

Strouhal number of 0.6 corresponds to the expected frequency for the column instability

that occurs near the end of the jet core. Crow and Champagne [42] reported on orderly

modes of axisymmetric flow (column instability), where the whole jet flow oscillates at

a frequency dependent on the jet Reynolds number. In this case the phase difference

between the two signals also decays from zero with increasing frequency. The slope of

the phase is greater than for the low H/D and the lower convection velocity of 2.1m/s

corresponds well with the lower arrival velocity that occurs at H/D = 4.

For the range of heights tested from H/D = 0.5 to 8, the coherence between the

heat flux and the radial velocity is extremely low, as shown in figure 5.33 for H/D

if 2. The coherence between the radial velocity and the heat flux remains less than

0.1 across the Strouhal number range. The phase in this case is highly inaccurate due

to the low level of coherence. It can therefore be concluded that the heat transfer

at the stagnation point is determined mainly by the arrival velocity normal to the

90

impingement surface and is influenced less by the parallel fluctuating flow.

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

St

Pow

er S

pect

rum

Mag

nitu

de

Radial VelocityHeat Flux

0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce

0 1 2−8

−7

−6

−5

−4

−3

−2

−1

0

1

2

St

Pha

se

Figure 5.33: Stagnation Point Spectral Data; H/D = 2.0, Re = 10000

5.4.3 Wall Jet for Normal Impingement

The radial distribution of mean heat transfer for a jet impinging at low nozzle to

plate spacings is quite different to that of a jet impinging at a large spacing, as shown

in section 5.2. This has been linked in section 5.3.1 to the variation in local fluid

turbulence intensity for the different nozzle to plate spacings. In this section the

characteristics of both the local heat transfer and fluid flow fluctuations in the wall

jet are presented. This section has been divided into two further subsections that deal

with the small and large nozzle to plate spacings separately.

Nozzle to Plate Spacing (H/D ≤ 2)

The heat transfer distribution to an impinging air jet has been shown to exhibit a

secondary peak, at low nozzle to plate spacings. The location of the trough and peak

in the heat transfer distribution is linked to the development of the wall jet boundary

layer. As discussed in section 5.2, this secondary peak is associated with development

of the wall jet and the transition to turbulence within the wall jet.

Figure 5.34 presents both the mean and fluctuating Nusselt number distributions

and identifies the location in the boundary layer at which spectral analysis is performed

91

on the heat flux signal. The spectrum at the stagnation point exhibits no dominant

frequency peak and decays to a low turbulence level. At a location approaching the

trough in the heat transfer distributions (r/D = 1.1) a dominant frequency peak occurs

in the spectrum at a Strouhal number of approximately 0.6. This Strouhal number

corresponds to the frequency of the resulting vortex following the merging process of

higher frequency vortices evident at the exit of the free jet. Beyond this radial distance,

however, the vortex begins to be broken down as the wall jet flow undergoes transition

to a fully turbulent flow where only small scale flow structures survive. At r/D = 1.5

the power dissipated at high frequencies is increased substantially relative to the shorter

radial distances considered. This is a further indication that the coherent vortical flow

structure is being broken down into small scale, higher frequency random turbulence.

0 2 4 60

20

40

60

80

100

120

r/D

Nu

0 0.5 1 1.5 210

−2

10−1

100

101

102

103

St

Pow

er S

pect

rum

Mag

nitu

der/D = 0r/D = 1.1r/D = 1.5

Nu

Nu’

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

The heat transfer spectrum has been investigated for the entire range of parameters

studied. It has been found that at low H/D and at specific locations along the im-

pingement surface there are dominant frequencies at which the heat transfer fluctuates.

Figure 5.35 shows a characteristic variation in heat transfer spectrum with both radial

distance and Reynolds number for a normally impinging jet with H/D = 1.5.

92

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

Pow

er S

pect

rum

Mag

nitu

de

r/D = 0

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

r/D = 1.1

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

r/D = 1.5

Re = 10000Re = 20000Re = 30000

Figure 5.35: Heat Transfer Spectra; H/D = 1.5

0 1 2 3 4 5 60

20

40

60

80

100

120

r/D

Nus

selt

No.

0 0.005 0.01 0.015 0.0235

40

45

50

55

60

65

Time, [s]

Nus

selt

No.

Re = 10000Re = 20000Re = 30000

(a) Nu Distribution (b) Nu Time-trace

Figure 5.36: Normally Impinging Jet; H/D = 1.5

93

The frequency peak occurs in the spectrum of the heat flux signal at a radial location

which depends on Reynolds number and on nozzle to impingement surface spacing. It

is most pronounced at locations approaching the trough in the mean Nusselt number

distribution. The effects of the vortex are also evident at smaller radial distances but to

a lesser extent, and as the structure moves along the wall jet it eventually breaks down

into smaller scale turbulence. The Reynolds number has been varied by varying the jet

exit velocity. The peak in the heat transfer spectrum occurs at a higher frequency with

increasing Re, as evident from the plotted spectra of figure 5.35. The time trace of the

Nusselt number signal presented in figure 5.36 (b) also shows the effect of Reynolds

number on the frequency of heat transfer fluctuations. Figure 5.36 (a) identifies the

location (with green markers) on the mean heat transfer distribution to which the

time trace corresponds. It is clear that the frequency of the heat transfer fluctuations

increases significantly with increasing Reynolds number. The specific frequencies are

depicted in the spectra of figure 5.35. The frequency of the peak is directly proportional

to the jet Reynolds number as expected.

The local fluid velocity and heat transfer spectra were calculated from simultaneous

measurements and the coherence and phase difference between the two velocity signals

and the heat flux were also calculated for a range of parameters: heights, H/D =

0.5, 1.0, 1.5, 2.0; radial distance, 0 < r/D < 3 and a Reynolds number, Re = 10000.

Both the axial and radial velocity components 3mm above the plate exhibit many of

the characteristics of the surface heat transfer, although the influence of the fluctuating

velocities on the heat flux varies with the location on the impingement surface. At low

H/D the dependence on radial location is very significant due to the velocity gradients

involved in this particular jet set-up. It has been shown in section 5.4.2 that the heat

transfer at the stagnation point is largely dependent on the axial velocity. This is also

found to be true for any radial location within the stagnation zone.

In figure 5.37 the locations at which simultaneous measurements were made are

marked on the velocity and heat transfer distributions. The coherence between the

heat flux and the velocity perpendicular to the surface (axial velocity) is illustrated

in figure 5.38 to be significant at 0.37D from the stagnation point. The coherence

decreases from a value of 0.5 with increasing frequency. The gradient with frequency

of the phase difference between the axial velocity and the heat flux has been used

to determine that the convection velocity normal to the impingement surface is ap-

proximately 9.8m/s. At this radial location within the stagnation zone, the coherence

94

−5

0

15

U, [

m/s

]

Mean Axial VelocityMean Radial Velocity

0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80

Nu

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

Figure 5.37: Radial Location of Simultaneous Measurements; H/D = 0.5

between the heat flux and the radial velocity is less than 0.1 and consequently the

phase difference between the two signals is of no significance. The dependence of the

heat flux on the axial velocity fluctuations is understandable as the axial fluctuations

are greater in magnitude than those parallel to the surface.

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de

Axial VelocityRadial VelocityHeat Flux

0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce

Axial VelocityRadial Velocity

0 1 2−7

−6

−5

−4

−3

−2

−1

0

1

2

3

St

Pha

se


Figure 5.38: Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 0.37

At the greater radial distance of r/D = 0.65, presented in figure 5.39, the frequencies

that initiated at the jet exit are reflected in both velocity signals and consequently have

an influence on the surface heat flux. Thus, the two frequency peaks that occur in each

spectrum, to a lesser or greater extent, are similar to two of those that occur in the jet

95

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−18

−16

−14

−12

−10

−8

−6

−4

−2

0

2

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−8

−6

−4

−2

0

2

4

St

Pha

se



96

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−5

−4

−3

−2

−1

0

1

2

3

St

Pha

se



exit velocity spectra. The Strouhal number of 1.6 corresponds to the frequency at which

vortices roll up at the jet exit. The lower Strouhal number of 1.1 relates to passing

frequency of a larger vortex that has developed following a merging process. The

velocity spectra indicate that the two frequency peaks have quite similar magnitudes

suggesting that the vortex merging process is in progress. The heat flux spectrum is

clearly influenced by both velocity signals. The coherence between the heat flux and

both axial and radial velocities is higher at this larger radial distance, particularly in

the frequency range associated with the coherent flow structure that impinges upon

the surface at this location. While the radial velocity component has more of an

influence on the heat flux at this radial location than in the stagnation zone, the higher

coherence values suggest that the axial velocity remains the main influence on surface

heat flux. With regard to the phase difference, the convection velocity has increased,

with the greater radial distance, to approximately 13.5m/s. The coherence between

the radial velocity and the heat flux signal is sufficient to get good phase information

in the middle frequency range. However, the slope of the phase difference between the

radial velocity and heat flux signals is very different to that between the axial velocity

and the heat flux at this radial location. Effectively the radial convection velocity is

much lower than the axial convection velocity. The difference can be attributed to the

97

location of the heat flux measurement point with respect to the velocity component

being measured. The axial convection velocity is in line with the axial flow velocity

and fluctuations in the flow in this direction convect directly towards the heat flux

sensor. The radial convection velocity is measured perpendicular to the direction of

the radial velocity. Therefore fluctuations in the radial direction convect at a lower

rate towards the heat flux sensor. Consequently the radial convection velocity is lower

than the axial convection velocity throughout the range of tests presented.

Simultaneous velocity and heat flux measurements at even greater radial locations

for H/D = 0.5 are presented in figures 5.40 and 5.41. Similar to previous velocity and

heat flux spectra, dominant frequency peaks occur. At these larger distances from the

geometric centre the lower Strouhal number of 1.1 exhibits the slightly larger peak in

the velocity and heat flux spectra. This indicates that vortices continue to merge within

the wall jet. The radial velocity spectrum indicates that the vortex merging process is

at a more advanced stage than the axial velocity suggests. One possible explanation

for this is given by the findings of Orlandi and Verzicco [81] who investigated vortex

rings impinging on a wall. In this computational investigation it has been shown that

merging vortices present as one large vortex in the radial direction, while remaining

separate entities in the axial direction. At the location of r/D = 1.02 the coherence

between the velocity signals and the heat flux is greater than for any other radial

location investigated. Again the axial velocity has slightly higher coherence with the

heat flux than the radial velocity, even though the magnitude of the fluctuations in

the both the axial and radial directions is similar, as shown in figure 5.37. This is

understandable as temperature gradients normal to the surface are greater than parallel

to the surface. Beyond this radial distance the peaks in all spectra reduce in size as can

be seen at r/D = 1.30. In this region the turbulence in the wall jet increases, breaking

the coherent vortex down into random small scale velocity fluctuations. The phase

information indicates that the convection velocity in the axial direction has decreased

once again and this is most likely due to the decreased mean velocity in this direction.

The axial convection velocities are calculated to be 18.7m/s and 7.3m/s for r/D = 1.02

and 1.30 respectively.

A similar analysis of simultaneous velocity and heat flux measurements is conducted

for a jet impinging at nozzle to plate spacings of H/D = 1.0, 1.5 and 2.0. Figure 5.42

indicates the radial locations where simultaneous measurements are made for each case.

The results for each nozzle to plate spacing have many of the same attributes as the

98

−5

0

15U

, [m

/s]


0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80

Nu

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

(a) H/D = 1.0

−5

0

15

U, [

m/s

]


0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80N

u

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

(b) H/D = 1.5

−5

0

15

U, [

m/s

]


0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80

Nu

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

(c) H/D = 2.0

Figure 5.42: Radial Location of Simultaneous Measurements

99

0 1 210

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10−8

10−7

10−6

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10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−5

0

5

10

15

20

St

Pha

se


Figure 5.43: Spectral, Coherence & Phase Information; H/D = 1, r/D = 0.37

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−12

−10

−8

−6

−4

−2

0

2

St

Pha

se



100

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−5

−4

−3

−2

−1

0

1

2

3

4

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−5

−4

−3

−2

−1

0

1

2

3

St

Pha

se



101

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−6

−4

−2

0

2

4

6

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−6

−4

−2

0

2

4

6

St

Pha

se



102

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−12

−10

−8

−6

−4

−2

0

2

4

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−4

−3

−2

−1

0

1

2

3

St

Pha

se



103

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−14

−12

−10

−8

−6

−4

−2

0

2

4

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−8

−6

−4

−2

0

2

4

St

Pha

se



104

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−10

−5

0

5

10

15

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−5

−4

−3

−2

−1

0

1

2

3

4

St

Pha

se



105

H/D = 0.5 case and only significant differences are discussed.

Spectral, coherence and phase information for the velocity and heat flux signals at

various radial locations for a jet impinging at H/D = 1.0 are presented in figures 5.43

to 5.46. Within the stagnation region (r/D = 0.37) a sharp peak in the coherence at a

Strouhal number of approximately 0.6 coincides with evidence of a subtle peak in the

velocity signal. This Strouhal number is associated with the jet column instability due

to the merged vortices that had originally rolled up at a Strouhal number of 1.6. This

is in agreement with Crow and Champagne [42], as it occurs in the second to third

subharmonic range. At locations where the vortices in the flow are more coherent

(r/D = 0.65, 1.02), the dominant frequency peaks occur at Strouhal numbers of 0.6

and 1.1. Also, a slight peak is evident at St = 1.6. It is apparent that the vortices which

rolled up at the jet nozzle have merged to form larger vortices at a lower frequency.

This new vortex is also undergoing a second merging process and this results in a peak

at the low Strouhal number of 0.6. The coherence between the velocity signals and the

heat flux is greatest at r/D = 1.02 which is once again consistent with the location

where the vortex impinges on the surface. The radial velocity spectrum indicates that

the two frequency peaks have similar magnitudes suggesting that the second vortex

merging process is in progress. The axial velocity spectrum however, shows the peak

at the higher frequency to have the greater magnitude, suggesting that this vortex

merging is in its initial stages. At r/D = 1.30 the coherence between the individual

velocity signals and the heat flux is similar. The Strouhal number of 1.6 is no longer

evident in the spectra suggesting that the initial merging process is complete.

Figures 5.47 to 5.54 detail spectral, coherence and phase difference information

for the heat flux and local fluid velocity for H/D = 1.5 and 2 for a similar range of

radial locations. At these larger nozzle to impingement surface spacings the vortices

have grown in size due to the vortex merging process. The frequency at which the

resulting vortices pass is now evident even within the stagnation region as can be seen

in figure 5.47 and to a lesser extent in figure 5.51. The large scale vortices pass at

this lower frequency and determine the frequency of the jet column instability to be

St = 0.6. At greater radial distances the effect of the vortices on the velocity and

heat flux spectra is more obvious. For H/D = 1.5 two dominant peaks are evident in

the individual spectra at St = 0.6 and 1.1 (figures 5.48 and 5.49). In general the two

peaks have similar magnitudes indicating that the second vortex merging process is

in progress. Once again, the spectrum of the radial velocity indicates that the vortex

106

merging process is further advanced as the peak at the lower Strouhal number of 0.6

has the greater magnitude. Also, the coherence between the radial velocity and the

heat flux is low at the higher Strouhal number (St = 1.1). Once again the influence

on heat transfer of velocity fluctuations normal to the impingement surface is shown

to be more significant.

Finally, at H/D = 2 only one dominant peak remains in all three spectra, at

a Strouhal number of 0.6. The vortex that passes at this frequency is appreciable

across the range of radial locations, but once again is most coherent at r/D = 1.02 as

shown in figure 5.53. At this stage it is apparent that the second merging process has

completed to form one large vortex that passes at a Strouhal number of approximately

St = 0.6. According to Broze and Hussain [82], this Strouhal number is consistent

with the natural frequency that is expected for a jet that issues with a turbulence level

of approximately 30 %.

In general, for a normally impinging jet with H/D ≤ 2 the heat flux exhibits

a significant dependence on velocity fluctuations normal to the impingement surface.

Even in cases where velocity fluctuations parallel to the surface are greater than normal

to the surface, the heat transfer relies substantially on the axial fluctuations. The

variation of H/D from 0.5 to 2 has seen vortices at different stages of their development

impinge upon the heated surface. At H/D = 0.5 the vortices are strong and initiate

and pass at high frequencies. At larger H/D the vortices merge, and pass along the

wall jet at lower and lower frequencies.

By taking another look at the mean velocity and heat transfer distributions at dif-

ferent stages within the vortex development, a fuller understanding of the influence of

the vortices can be achieved. Figure 5.55 presents the mean heat transfer distributions

at low nozzle to impingement surface spacings. It is apparent that the mean and fluc-

tuating Nusselt number distributions merge in the stagnation zone (r/D < 1) and in

the fully developed wall jet region (r/D > 2.5). Figure 5.56 presents the mean velocity

distributions for the four different heights. There is no significant difference between

the radial velocity distributions, however a slight difference can be appreciated for the

mean axial velocity distributions. At the lower H/D, at the first stage of the vortex

development, the axial velocity is more negative in the location corresponding to the

vortex impinging on the wall jet. It has been shown, by Didden and Ho [83], that

strong vortices in the wall jet have the effect of inducing flow separation. The axial

velocity distributions are consistent with this. Otherwise the axial velocity distribu-

107

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

r/D

Nu

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

0 1 2 3 4 5 60

1

2

3

4

5

6

r/D

Nu′

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

Figure 5.55: Mean & Fluctuating Nusselt Number Distributions; Re = 10000

108

0 0.5 1 1.5 2 2.5−2

−1

0

1

2

3

4

5

6

7

r/D

Mea

n A

xial

Vel

ocity

, [m

/s]

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

0 0.5 1 1.5 2 2.50

2

4

6

8

10

12

14

r/D

Mea

n R

adia

l Vel

ocity

, [m

/s]

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

Figure 5.56: Mean Velocity Distributions; Re = 10000

109

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

r/D

RM

S A

xial

Vel

ocity

, [m

/s]

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

r/D

RM

S R

adia

l Vel

ocity

, [m

/s]

H/D = 0.5H/D = 1H/D = 1.5H/D = 2

Figure 5.57: RMS Velocity Distributions; Re = 10000

110

tions coalesce in the same location as the Nusselt number distributions. Finally the

distribution of the rms velocity are presented in figure 5.57. The magnitude of the

fluctuations in the radial velocity has been influenced slightly by the various stages

of the vortex development. It has been shown to date that fluctuations in the radial

direction have less of an influence on the heat transfer than the fluctuation normal

to the impingement surface. At the different nozzle heights above the impingement

surface the velocity fluctuations normal to the impingement surface have changed sig-

nificantly. Since the mean velocity distributions are relatively unchanged the variation

in the velocity fluctuations is attributed to the variation in the vortical nature of the

impinging jet flow. Axial fluctuations have been shown to have the greatest influence

on the heat transfer.

Although vortices delay the transition to a fully turbulent flow in the wall jet, the

eventual breakup of vortices induce velocity fluctuations normal to the impingement

surface that increase surface heat transfer. In general, when a vortex impinges at the

early stage of its development, it is strong and maintains the low turbulence in the wall

jet. Breakup of this strong vortex, however, results in large axial velocity fluctuations

that enhance the mean surface heat transfer. When the vortex impinges on the surface

at later stages of its development, its effects are less pronounced. The breakup of this

weaker vortex results in lower magnitude axial velocity fluctuations and therefore does

not increase the surface heat transfer to the same extent.

111

Nozzle to Plate Spacing (H/D > 2)

At large H/D (> 2) secondary peaks in the mean heat transfer profile may still exist,

however no dominant frequency can be seen in the heat transfer spectrum for jet to plate

spacings from 2D to 8D. Figure 5.58 depicts the heat transfer spectra as calculated

from the heat transfer signal acquired at three radial locations, (r/D = 0.0, 1.2 and 1.7)

for H/D = 3.0 and a Reynolds number of 30000. Only a very subtle peak is evident at

r/D = 1.7. This is for a normally impinging jet with a large Reynolds number and in

this case the potential core is extended further than with lower Reynolds number jets.

0 2 4 60

20

40

60

80

100

120

r/D

Nu

0 0.5 1 1.5 210

−2

10−1

100

101

102

103

St

Pow

er S

pect

rum

Mag

nitu

de

r/D = 0r/D = 1.2r/D = 1.7

Nu

Nu’

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

Figure 5.59 presents similar data for the case where H/D = 8. At this nozzle height

the secondary peak in the mean Nusselt number distribution is no longer evident. This

has been shown to be due to the uniformity of turbulence across the impingement

surface. The rms velocity in both axial and radial directions, presented in figure 5.22,

is an indication of the uniformity of the wall jet turbulence levels. The heat transfer

spectra at the indicated radial locations of r/D = 0, 1.2 and 1.7, suggest that no

coherent flow structure is affecting the heat transfer, which reflects the turbulence

levels along the impingement surface.

112

0 2 4 60

20

40

60

80

100

120

140

r/D

Nu

0 0.5 1 1.5 210

−1

100

101

102

103

St

Pow

er S

pect

rum

Mag

nitu

de

r/D = 0r/D = 1.2r/D = 1.7

Nu

Nu’

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

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

Pow

er S

pect

rum

Mag

nitu

de

H/D = 3

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

H/D = 5

0 1000 2000 300010

−2

10−1

100

101

102

Frequency, [Hz]

H/D = 8

Re = 10000Re = 20000Re = 30000

SubtlePeak

Figure 5.60: Heat Transfer Spectra; r/D = 1.2

113

The variation in core length of the jet with nozzle to plate spacing and with Reynolds

number can be inferred from the heat transfer spectra presented in figure 5.60. In this

figure heat transfer spectra at a radial distance of 1.2D from the stagnation point are

plotted for three different Reynolds numbers and for H/D = 3, 5 and 8. While a subtle

peak may be evident in the heat transfer spectra at H/D = 3 this is most notable for

the larger Re value. With increasing H/D and decreasing Re the peaks are no longer

evident. The delayed development of the jet at higher Reynolds numbers is responsible

for the differences in the heat transfer spectra. With increasing distance from the jet

nozzle the vortices that occur in the shear layer of the jet flow are broken down into

smaller scale turbulence. At higher Reynolds numbers this development of the jet is

delayed and thus the frequencies associated with the vortices can be seen in the heat

transfer spectrum for larger H/D than is the case at lower Reynolds numbers.

Simultaneous velocity and heat transfer signals have been acquired at various radial

locations on the impingement surface for H/D = 4 and 8. The spectrum of and the

coherence and phase difference between the heat flux and the velocity both normal

and parallel to the surface are presented in this section. At these nozzle distances it

can be seen from figure 5.61, for example, that the mean and rms velocity gradients in

both the axial and radial components are small in comparison to lower H/D set-ups

(as shown in figure 5.21 where H/D = 1). At H/D = 4 a secondary peak in the mean

Nu′ distribution still occurs at approximately 2.3 diameters from the stagnation point,

as shown in figure 5.61, and so too does the suppression of the wall jet development,

albeit to a lesser extent than for H/D ≤ 2.

−5

0

15

U, [

m/s

]


0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80

Nu

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

Figure 5.61: Radial Location of Simultaneous Measurements; H/D = 4

114

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−10

−8

−6

−4

−2

0

2

4

6

8

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−20

−15

−10

−5

0

5

St

Pha

se



115

Figure 5.61 indicates the location on the heat transfer and velocity distributions at

which measurements are acquired simultaneously for H/D of 4. At the radial location

of r/D = 1.02 no dominant frequency peak is evident in the velocity and heat flux

spectra presented in figure 5.62. While the coherence is quite low at all frequencies,

it does have a peak at the Strouhal number (St = 0.6) equivalent to the jet column

instability. This peak is more evident between the axial velocity and the heat flux and

indicates that even at this large distance from the jet exit some features of the vortical

flow remain. It is also noteworthy that at this radial location the axial mean and rms

velocity magnitudes are low but still have an appreciable influence on the heat flux, as

reflected by the coherence levels. Figure 5.63 presents data for a location 1.48D from

the stagnation point. Again the velocity and heat flux spectra contain no dominant

frequency peaks but the coherence levels in the range associated with vortex merging

provide some evidence for the existence of the flow structure at this location. In this

case the coherence level is similar for the two velocity directions, indicating that even

small fluctuations in the axial direction have the same influence on the heat flux as

large fluctuations in the radial direction. The gradients of the phase information are

consistent with the decline in the mean velocities with increasing radial distance.

−5

0

15

U, [

m/s

]


0 0.5 1 1.5 2 2.5 30

2

4

r/D

U, [

m/s

]


0

20

40

60

80

Nu

0 0.5 1 1.5 2 2.5 30

2

4

6

8

r/D

Nu′

Figure 5.64: Radial Location of Simultaneous Measurements; H/D = 8

116

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−6

−4

−2

0

2

4

6

8

St

Pha

se



0 1 210

−9

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

St

Pow

er S

pect

rum

Mag

nitu

de


0 1 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−30

−25

−20

−15

−10

−5

0

5

10

15

20

St

Pha

se



117

Finally, for the largest distance of the nozzle above the impingement surface in-

vestigated, H/D = 8, figure 5.64 indicates the locations at which spectral data of

the various signals are presented in figures 5.65 and 5.66. Both the velocity and heat

flux distributions are reasonably constant across the distribution. Again at this nozzle

height above the impingement surface the spectra exhibit no dominant frequency. At

a nozzle height of H/D = 8 the jet flow is fully developed; the vortices have not only

merged but have also been broken down into small scale random turbulence. Coherence

between the velocities and the heat flux is low generally although the axial velocity

exhibits higher coherence with the heat flux in the low frequency range.

In certain instances the phase information between the flow velocities and heat

flux has been poor due to the relatively low levels of coherence between the individ-

ual signals. In these cases, the calculated magnitude of the convection velocities are

unreliable. Nonetheless, some trends can be reported. The convection velocity normal

to the impingement surface is small in the stagnation zone. It increases with radial

distance, reaching a peak velocity and then decreases at even greater radial distances.

Overall the convection velocity decreases as H/D increases, as a direct result of the

decreased mean flow velocities.

118

5.4.4 Wall Jet for Oblique Impingement

The spectrum of the heat flux signal is presented in this section. It differs from the

normally impinging case because of the asymmetry between the uphill and downhill

directions.

−4 −2 0 2 4 60

20

40

60

80

100

120

r/D

Nu

0 0.5 1 1.5 210

−2

10−1

100

101

102

103

St

Pow

er S

pect

rum

Mag

nitu

de

r/D = −1.71r/D = −0.07r/D = 1.04

Nu

Nu’

Downhill Uphill

Figure 5.67: Nu Distribution & Heat Flux Spectra; α = 30, Re =10000,H/D = 2

Figure 5.67 depicts both the fluctuating and mean Nusselt number distribution for a

jet impinging at an angle of 30. Three spectra of the heat flux signal are also presented

in this figure at three radial locations. It is apparent that while a flow structure exists

that affects the heat flux at particular radial locations in the downhill direction, this is

not the case in the uphill direction. For the range of heat transfer measurements in the

uphill direction, no peak in the heat transfer spectra was found. An example of one

such spectrum is presented for a radial location of r/D = −1.71. The power spectrum

simply decreases to the noise level with increasing frequency. This is due to the small

distance between the jet nozzle and the impingement surface at the side of the acute

angle made between the jet and the surface. Because of this small distance, there is

insufficient space for a vortex to develop. The volume flow rate in the uphill direction

119

−4 −2 0 2 4 60

10

20

30

40

50

60

70

r/D

Nu

0 0.5 1 1.5 210

−2

10−1

100

101

102

St

Pow

er S

pect

rum

Mag

nitu

de

r/D = −1.26r/D = 0.74r/D = 1.34

Downhill Uphill

Nu

Nu’

Figure 5.68: Nu Distribution and Heat Flux Spectra; α = 75, Re =10000,H/D = 2

is also small and therefore the velocity gradient in this region is small, leading to low

vorticity.

Figure 5.68 presents similar results for a larger angle of impingement, α = 75.

Although the same effects are apparent, in this case they occur to a lesser extent. The

asymmetry to the heat transfer profile is less pronounced and the heat flux spectra

in both the uphill and downhill directions are more similar. A peak in the heat flux

signal is apparent at a radial location in the downhill direction. This is clearly defined

thus the vortex at this location appears to be a strongly coherent structure. In the

uphill direction, the effect of a vortex on the heat flux signal is also apparent, but to a

lesser extent. The distance between the lip of the jet and the surface at the apex of the

acute angle is now sufficiently large that a vortical flow structure has time and space

to develop, yet by changing direction it is apparent that the coherence of the structure

has been affected and the turbulence level is much greater at r/D = −1.26.

Simultaneous measurements of velocity and heat flux have been obtained for the

obliquely impinging jet also. Figure 5.69 indicates the locations on both Nusselt number

120

−5

0

15

U, [

m/s

]


−2 −1 0 1 2 3 4 50

2

4

r/D

U, [

m/s

]


Downhill

Stagnation Point

Uphill

0

20

40

60

80

Nu

−2 −1 0 1 2 3 4 50

2

4

6

8

r/D

Nu′

DownhillUphill

Stagnation Point

Figure 5.69: Radial Location of Simultaneous Measurements; H/D = 2, α =60

and velocity distributions at which spectral, coherence and phase information of the

simultaneously measured signals are presented. Figures 5.70 and 5.71 indicate that a

vortex passes in the uphill direction at a Strouhal number of 0.6. This vortex is weak

however as the relative magnitude of the peak in each spectrum is small. The coherence

between the individual velocity signals and the heat flux is low also. Figures 5.72

and 5.73 present data in the downhill direction of the wall jet jet flow. It is apparent

that the vortices that pass in this direction are stronger and have more of an influence

on the heat flux. At a radial location of 0.37D from the geometric centre, peaks in all

three spectra are evident at a Strouhal number of 0.6. At r/D = 1.11 however, this

peak is only evident in the velocity normal to the surface and in the heat flux signal.

This radial location highlights the effect that relatively small fluctuations in the axial

direction can have on the heat flux. The subsequent breakup of this strong vortex, at a

greater radial distance (r/D ≈ 2.2) from the stagnation point enhances the local heat

transfer to a secondary peak in the downhill direction.

121

0 1 210

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10−8

10−7

10−6

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0 1 20

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0.2

0.3

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0.7

0.8

0.9

1

St

Coh

eren

ce


0 1 2−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

St

Pha

se


Figure 5.70: Spectral, Coherence & Phase Information; H/D = 2, α =60, r/D = −1.30

0 1 210

−9

10−8

10−7

10−6

10−5

10−4

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1

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Coh

eren

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0 1 2−12

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0

2

4

6

St

Pha

se



122

0 1 210

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10−8

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0 1 20

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0.9

1

St

Coh

eren

ce


0 1 2−25

−20

−15

−10

−5

0

5

St

Pha

se


Figure 5.72: Spectral, Coherence & Phase Information; H/D = 2, α =60, r/D = 0.37

0 1 210

−9

10−8

10−7

10−6

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0 1 2−10

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5

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Pha

se



123

−5

0

15

U, [

m/s

]


−2 −1 0 1 2 3 4 50

2

4

r/D

U, [

m/s

]


Downhill

Stagnation Point

Uphill

0

50

100

Nu

−2 −1 0 1 2 3 4 50

5

10

r/D

Nu′

Downhill

Stagnation Point

Uphill

Figure 5.74: Radial Location of Simultaneous Measurements; H/D = 2, α =45

Similar data are presented for a jet impinging at an oblique angle of 45. Once

again the locations at which the spectral, coherence and phase information is analysed

are detailed in figure 5.74. The simultaneous data exhibit many of the characteris-

tics discussed earlier for α = 60. However, at r/D = −0.81 each spectrum exhibits

peaks at Strouhal numbers of 0.6 and 1.1. It has been shown previously for normal

jet impingement that these frequencies only occur at low nozzle to plate spacings i.e.

H/D ≤ 1.5. Therefore it is concluded that these peaks occur in the uphill direction

because the lip of the jet is closest to the surface in the uphill direction. The devel-

opment of the vortices and the merging process is not complete and so both peaks are

evident on the uphill side.

At locations in the downhill direction of the geometric centre, one dominant fre-

quency peak appears in the spectra. This can be seen in figures 5.76 and 5.77. This

peak occurs at a Strouhal number of 0.6 and therefore it is clear that the vortex merging

process has been completed. At r/D = 1.41 the coherence between the axial velocity

and the heat flux is particularly high, indicating the influence that fluctuations normal

to the surface have on the heat flux.

In the direction of the main flow, i.e. the downhill direction, the distance from

the nozzle lip where the vortices initiate to the location where the vortex impinges

on the surface is sufficient for the vortex to develop fully until one frequency peak

(St = 0.6) remains. In the uphill direction, however, the distance is less and therefore

the vortex is at an earlier stage in its development. Thus, although the heat transfer

is decreased due to a lower flow rate in this direction, it is being maximised due to the

124

0 1 210

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0 1 20

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0.9

1

St

Coh

eren

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0 1 2−25

−20

−15

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0

5

10

St

Pha

se



0 1 210

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10−8

10−7

10−6

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0 1 20

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0 1 2−20

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5

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se



125

0 1 210

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0 1 20

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0 1 2−4

−3

−2

−1

0

1

2

3

4

5

6

St

Pha

se



early stage of the vortex merging process. Unfortunately, in the downhill direction,

the potential of the large flow rate is not being realised because of the late stage of the

vortex development.

5.5 Summary

Results presented in this chapter include mean velocity, rms velocity and vorticity flow

fields for free and impinging jets at various impingement configurations. For a similar

range of parameters, both mean and fluctuating heat transfer distributions have been

presented. Regions of high heat transfer have been associated with regions of high local

fluid velocity and turbulence intensity. In particular, peaks in the heat transfer distri-

butions have been shown to coincide with locations where velocity fluctuations normal

to the impingement surface are large. Comparison of the velocity flow fields to heat

transfer distributions has revealed areas of interest that required further investigation

of a temporal nature.

Initially, the temporal nature of the velocity at the exit of the free jet was investi-

gated. This revealed three frequency peaks which have been associated with the roll-up

and merging frequency of the vortices in the shear layer. At H/D < 2 similar peaks

126

have been observed in the spectra of the heat transfer and local velocity signals in the

transitional wall jet. Simultaneous local velocity and heat flux measurements have re-

vealed that axial velocity fluctuations exhibit higher coherence with the heat transfer

signal. Again, this highlights the dependence of heat transfer on the axial velocity

fluctuations. As the height of the nozzle above the impingement surface changes from

0.5 to 2 diameters, the mean velocity in the axial and radial direction does not change

significantly. The velocity fluctuations in the transitional wall jet decrease substan-

tially however. The main difference between these heights is the stage of the vortex

development. In particular, the axial velocity fluctuations along the impingement sur-

face in the transitional wall jet have been shown to decrease substantially in the latter

stages of the vortex development. Axial fluctuations have been shown to have the

most significant influence on the heat transfer and thus a reduction in their magnitude

reduces the mean heat transfer at this location.

Having established that the early stages of the vortex development enhance the

heat transfer, the significance for oblique impingement is appreciated. In the direction

of the main flow (downhill direction), the heat transfer does not meet its potential

because the distance between the lip of the jet and the surface is sufficiently large that

the vortices have developed and thus the vertical velocity fluctuations along the surface

will be small. On the other side (uphill direction), however, the distance between the

lip of the jet and the surface is small and therefore an underdeveloped vortex flow

impinges on the surface. The flow rate in the uphill direction is low, but at least the

axial fluctuations due to the early stage of the vortex development result in higher heat

transfer.

Chapter 6

Jet Impingement Heat Transfer in aGrinding Configuration

Having explored the characteristics of jet impingement heat transfer in an idealised

laboratory set-up, the next objective was to investigate the heat transfer and fluid flow

characteristics in a set-up closer to an engineering application of interest. One potential

application of impinging jet heat transfer is the air jet cooling of a grinding process.

To this end the convective heat transfer characteristics and limited flow data have been

measured for a set-up in which a grinding wheel rotates above the instrumented test

plate. The basic experimental set-up is described in Chapter 3. While many of the

same testing parameters are relevant to this set-up, (H/D,Ujet, α), the spinning wheel

adds extra complexity.

Three main test configurations are identified. Firstly, the flow and heat transfer

due to the grinding wheel alone is investigated. The grinding wheel is mounted at

some small distance above the heated surface. A significant fluid flow is induced due

to the air entrained by the grinding wheel and this has been measured along with the

resulting convective heat transfer. The second testing configuration is with the grinding

wheel and a low speed air jet. This is the same jet for which all the fundamental heat

transfer data in Chapter 5 have been acquired. This jet, because of the relatively

large jet diameter, has a maximum exit velocity of ∼ 30m/s. This is similar to the

typical tangential velocity at which a grinding wheel operates. Finally, testing was

conducted using the rotating grinding wheel and a smaller diameter nozzle as described

in Chapter 3. The jet that issues from this nozzle can reach much higher velocities for

the same air mass flow rate. At the highest flow rate the jet approaches sonic velocity.

This chapter includes a brief review of background information relevant to the

cooling of a grinding process. Additional information on the experimental set-up is

127

128

discussed, mainly with reference to some of the approximations made and their influ-

ence on the results presented. Finally results are presented for a range of grinding

test configurations. Time averaged data have been acquired for the three test config-

urations and for a range of testing parameters. PIV measurements have been used to

characterise the fluid flow field and a flush mounted RdF Micro-Foilr heat flux sensor

has been used to measure heat transfer in the grinding configuration.

6.1 Background

This section outlines some of the fundamental characteristics of a typical set-up for

grinding. This is followed by a brief review of previous research concerned with the

cooling of a grinding process.

Vw

b

a

ds

Vs

Figure 6.1: Grinding Process Set-up

The geometric parameters of a grinding process are defined and illustrated in fig-

ure 6.1. The grinding wheel is shown to rotate in a clockwise direction with a tangential

velocity Vs. The workpiece is fed with a velocity Vw in the same direction as the wheel.

This configuration is termed down grinding. Up grinding is the case where the wheel

rotates in the opposite direction to the movement of the workpiece. The depth of cut,

a, is shown exaggerated in the diagram as this is typically around 5µm for conventional

grinding. The workpiece exerts a tangential force, Ft, on the grinding wheel. The jet

flows in the same direction as the workpiece with velocity, Vj. The power used in a

129

grinding process is dissipated as heat in the grinding zone. This heat flux is defined in

equation 6.1.

q′′total =FtVs

b√

ads

(6.1)

For a conventional grinding process with a cutting fluid the heat generated in the

grinding zone is dissipated in four ways. Some of the heat is conducted to the grinding

wheel grains and some is conducted into the workpiece. Heat is also transferred to

the cutting fluid by convection and, finally, heat is removed with the chip removal. A

simple energy balance presented in equation 6.2 defines the heat dissipation. Typically

the heat transfer to the chip is a small percentage of the overall heat generated and is

sometimes neglected in both numerical and experimental investigations.

qtotal = qworkpiece + qwheel + qfluid + qchip (6.2)

It is essential that the temperature in the grinding zone is kept low to prevent thermal

damage. Thermal damage is one reason that process times cannot be reduced as

depth of cut and feed rates cannot be increased without compromising surface quality.

Thermal damage can manifest itself in many ways. These include the softening of

the ground surface, which allows for the possibility of rehardening and embrittlement.

Thermal expansion has the effect of reducing geometrical accuracy and may leave

residual tensile stresses in the workpiece. Excessive temperatures may also have the

adverse effect of inducing accelerated wear of the grinding wheel.

Heat is generated by individual grains cutting the workpiece as they pass at high

speeds in the grinding zone. Individual grains are responsible for very localised but

intense heat generation that results in spike temperatures at the workpiece surface.

These temperatures occur for very short periods of time. The total effect of a large

number of grains cutting the slow moving workpiece surface is considered to be a

continuous band source of heat passing over the workpiece. The temperature due to

this band source is a background temperature that occurs for a substantial period of

time. Spike temperatures are not of consequence for thermal damage because thermal

damage such as re-austenitization requires time to occur. For this reason much of the

literature relates to the background temperature in a grinding process.

130

Rowe et al. [14] conducted a study of energy partitioning in a grinding process

for two different grinding wheel materials. This study was both a numerical and an

experimental investigation that measured the maximum background temperature on

the ground surface. The partition ratio is defined as the ratio of the heat transferred

to the workpiece to the total heat generated, as shown in equation 6.3.

Rpartition =qworkpiece

qtotal

(6.3)

This study assumed heat transfer to both the cutting fluid and the chip to be negligible.

Therefore the theoretical model could predict the partition ratio from the temperature

measured at the workpiece surface. The assumption that the heat removed with the

chip is small is commonly made, however the heat transfer to the cutting fluid being

considered negligible is less common. The primary role of the cutting fluid is to reduce

the generation of heat in the grinding process. The fluid is used to remove grinding

debris and to lubricate the process, thus reducing the heat generated rather than re-

moving heat from the process. In general the heat transfer to the fluid is not considered

negligible, however, unless film boiling occurs. In this case the boiling creates a vapour

barrier between the grinding zone and the rest of the coolant.

An investigation by Ebbrell et al. [15] recognised the effect of ambient air entrained

by the spinning grinding wheel. The boundary layer that forms around the spinning

grinding wheel can have the effect of preventing the liquid coolant from reaching the

grinding zone, depending on the method of coolant delivery. LDA results presented

by Ebbrell et al. [15] show a back flow that results when the grinding wheel boundary

layer comes into close proximity with the workpiece. The boundary layer flow reaches

the surface and flows away from the grinding zone. It is this back flow that inhibits the

cutting fluid from reaching the grinding zone. Ebbrell et al. [15] also present various

nozzle configurations proposed to overcome the effect of the boundary layer.

A theoretical model of heat transfer in grinding was developed by Lavine and Jen [9].

This model assumed that the heat flux to the fluid across the workpiece is uniform

and that the fluid moves at the same velocity as the tangential velocity of the wheel.

Therefore heat transfer to the fluid was approximated as conduction to the static fluid.

It was also shown that the convective heat transfer to the fluid from the grinding wheel

is small, typically 0.4 % of the heat transfer to the grinding wheel. A later model by

131

Jen and Lavine [11] addressed some of the restrictive assumptions made by the original

model, in particular by modifying the assumption of uniform heat flux to the grinding

wheel grains, fluid and workpiece. Duhamel’s theorem was used to vary the heat fluxes

with distance through the grinding zone.

In an investigation by Jen and Lavine [12], a modified model was developed to take

into account the effect of film boiling. Instead of an abrupt change from constant heat

flux to zero heat flux with the onset of film boiling, as reported in Lavine and Jen [9],

this investigation predicted the effect on workpiece temperature of the occurrence of

film boiling. Finally, in an investigation by Lavine [10], an exact solution for the surface

temperature in a grinding process was developed. In the previous models it had been

assumed that all the heat was generated at the wear flats. This is known to be untrue

as much of the heat is generated at shear planes due to plastic deformation.

A commonality between all the studies reviewed thus far is that the cutting fluid

is a liquid, typically some oil and water mixture. The function of the cutting fluid

is primarily to reduce the amount of heat generated rather than to remove heat from

the grinding process. Although it is recognised by some of the studies that heat is

transferred to the cutting fluid, this heat transfer is a small percentage of the heat

generated. This is because the cutting fluid is typically supplied at low velocities, to

the point where some of the research has been concerned with flood cooling. The

present research is concerned with the cooling of a grinding process with an impinging

air jet, a procedure which has received little attention up until now. Heat generation

in the grinding zone will not be reduced to any significant extent as an air jet is not

an effective lubricant. Thus, the convective heat transfer to the air jet will be required

to be much higher than that to the liquid cutting fluid in order to ensure against high

temperatures and thermal damage.

High speed air jet cooling of a grinding process has been investigated by Babic

et al. [16]. This investigation showed that the high speed jet can slightly reduce the

heat generated in the grinding zone by reducing the tangential force. The predomi-

nant explanation for this reduction in temperature in the grinding zone, however, is

considered to be the enhanced heat transfer convected to the impinging air jet. In

a later investigation by Babic et al. [3], a small quantity of water was injected into

the air flow before the nozzle, which generated a high speed jet mist. The use of this

jet mist in a grinding process has been shown to further reduce the tangential force

and increase the convective heat transfer. To date, convective heat transfer coefficients

132

have not been reported in the available literature. In the present study, experiments

have measured the convective heat transfer coefficient to the impinging jet flow used

by Babic et al. [3]. This is done in an attempt to explain the findings of Babic et al. [3].

Results are presented and discussed in section 6.4.3.

6.2 Impingement Geometry

The experimental rig used for the investigation of heat transfer coefficients in grind-

ing is described in Chapter 3. This section addresses the differences between this

experimental set-up and an actual grinding process. The reasons necessary for these

differences and their implications are also discussed.

Figure 6.2: Experimental Set-up

Figure 6.2 is a schematic of the test rig. A number of differences exist between this

test set-up and the typical set-up for a grinding process as illustrated in figure 6.1.

Firstly, the surface being ground is replaced with a flat surface in the heat transfer

testing. This approximation is not considered to be significant for conventional grinding

as the depth of cut is in the region of 0.005mm, however, for creep feed grinding the

depth of cut varies up to 20mm.

It was necessary to mount the grinding wheel slightly above (0.5mm) the heated

surface in order to protect the heat transfer sensors that are flush mounted on the

heated surface. This contrasts with the situation in an actual grinding process where

133

the wheel is in contact with the surface. Thus, the wheel was mounted at a height of

0.5mm above the surface. The set-up used here is similar to that of Ebbrell et al. [15]

who investigated the effect of such a gap on the pressure distribution along the grinding

plane, and on the back flow resulting from the grinding wheel boundary layer. This

gap exerts a significant influence on the flow characteristics as the peak pressure in the

distribution varies from 250Pa to 50Pa for a gap of 0.005mm to 1.5mm respectively.

The consequence of the relatively large gap used in this study is a reduction in the

magnitude of the back flow by allowing a flow under the grinding wheel surface. It

is also important to realise that the smallest gap of 0.005mm investigated by Ebrell

et al. [15] does approximate the grinding process quite accurately as the contact area

between the grinding wheel and the workpiece in the grinding zone is typically only a

few percent of the total grinding zone area.

The heat transfer experiments were conducted for a uniform wall temperature

boundary condition, which differs appreciably from the point heating that would oc-

cur in the grinding zone. This thermal boundary condition was chosen as a reference

condition to facilitate comparison with published data and to ensure that there is a

temperature difference between the air and all the points on the test surface. The main

significance of the different thermal boundary conditions is the heating of the fluid as

it moves along the isothermal test surface. The difference between the bulk or jet air

temperature and the local surface temperature is used to calculate the convective heat

transfer coefficient. Thus, the heat transfer coefficient will tend to be underestimated

in this study as the calculation is based on a larger temperature difference than actu-

ally exists locally. The location of peaks and troughs in the heat transfer distributions,

however, will not change significantly.

Many possibilities exist for the method of application of the cooling fluid. However,

in this study of impingement jet cooling the number of variables has been reduced and

the test set-up is defined here. The nozzle can be positioned at various heights and

angle of impingement; however the testing was always conducted so that the grinding

wheel was mounted with its centre directly above the geometric centre of the jet.

Therefore the minimum height of the nozzle above the impingement surface is defined

by the grinding wheel diameter and the angle of jet impingement.

Experimental data have been acquired along the centreline of the grinding plane,

as depicted in figure 6.3. In this case the jet is impinging at an angle of 15 and the

distribution of heat transfer coefficients along the plate is indicated by the red plot.

134

−150 −100 −50 0 50 100 150

0

50

100

150

200

Distance Along Workpiece, [mm]

Con

vect

ive

Hea

t Tra

nsfe

r C

oeffi

cien

t, h

[W/m

2 K]

Figure 6.3: Schematic of Test Set-up & Corresponding Heat Transfer Distribu-tion

ImpingementSurface

CCD Camera

LaserSheet

Dual PulsedLaser

Jet Nozzle

Grinding Wheel

Figure 6.4: Particle Image Velocimetry Measurement Set-up

135

Fluid flow data have been acquired along the same plane. Figure 6.4 indicates the

PIV set-up for the grinding tests. The flow field measurements are limited due to the

optical constraints imposed by the grinding wheel. Data will be presented for the three

testing configurations previously described and for a range of parameters such as jet

and wheel velocities.

6.3 Fluid Flow in a Grinding Configuration

Mean and root-mean-square velocity flow fields are presented in this section. The

flow induced by a rotating grinding wheel alone is investigated initially. Data are also

presented for the flow field with a jet impinging at various angles and heights and for

a wheel rotating in the same and opposing directions to the jet flow. The expected

effect of the flow characteristics on the heat transfer is discussed in this section also.

6.3.1 Rotating Wheel Only

The rotating grinding wheel entrains air from the surroundings and induces a flow pat-

tern with corresponding heat transfer at the surface. In an experimental investigation

by Rowe et al. [14], back flow was reported for the air entrained by the grinding wheel.

The air entrained by the wheel flows in the same direction as the wheel until it comes

into close proximity with the surface or workpiece. As the air reaches the minimum

gap between the wheel and the plate, some of the flow stagnates and, then flows back-

wards away from the grinding zone. This is confirmed by the PIV data presented in

figure 6.5 where the wheel is rotating with a tangential velocity of 20m/s. The back

flow magnitude is small and occurs far from the minimum gap, in this case, beyond

the stagnation point at x ≈ 85mm. This is understandable as the relatively large gap

between the wheel and the surface (0.5mm) allows much of the entrained air to pass

under the wheel.

This back flow is expected to have a negative impact on the cooling of a grinding

process. Ebbrell et al. [15] discussed the need to penetrate the boundary layer sur-

rounding the grinding wheel, in order to supply the grinding zone with a cooling jet

flow. The influence of this back flow on the heat transfer will be discussed in greater

detail in section 6.4. In the case of an impinging air jet with no grinding wheel, the

results presented in Chapter 5 have shown that the maximum heat transfer coefficient

occurs at the stagnation point. The results presented in figure 6.5 show only minimal

136

Figure 6.5: Flow Entrained by Grinding Wheel; Vs = 20m/s

back flow, but nonetheless the effect of the back flow is to move the stagnation point

further from the grinding zone, again having a negative consequence for the overall

cooling of the grinding process. On the positive side, peaks in the local mean and

rms velocity are evident from these PIV results, occurring near the minimum gap or

notional grinding zone. These peaks are expected to contribute to higher local heat

transfer coefficients.

6.3.2 Rotating Wheel with Low Speed Impinging Air Jet

For the tests with impinging air jet and rotating grinding wheel, the back flow is

expected to have the effect of moving the peak heat transfer coefficient further from

the geometric centre of the jet, or in this case the notional grinding zone. In figure 6.6

it can be seen that for a jet impinging on the grinding zone at an angle of 30, the

stagnation point occurs at a location of approximately 40mm from the arc of cut.

This compares to approximately 27mm from the geometric centre for an unobstructed

impinging jet.

The streamlines in the velocity flow field also indicate that some of the air flow

recirculates, and is entrained by the wheel, after it has been in contact with the heated

137

Figure 6.6: Wheel & Impinging Jet; α = 30,H = 101mm,Vs = 10m/s, Vj =10m/s

surface. The recirculation zone is indicated by an arrow in figure 6.6 and occurs

at approximately 45mm from the grinding zone. The rms velocity flow field has not

changed significantly with the addition of the impinging air jet; the turbulence remains

high in the wedge made between the grinding wheel and the surface.

Figure 6.7 presents the mean and rms velocity flow fields for a jet impinging at

15 and at a height of 101mm above the surface. It is apparent that much of the

flow entrained by the jet has come from close to the heated surface. This will have

a negative effect on the heat transfer results, as presented later in this chapter. In a

real grinding process, however, the surface temperature of the workpiece at a distance

from the grinding zone is low. Therefore the entrained air would not have increased in

temperature significantly. It is apparent that two regions of high turbulence join near

the minimum gap at approximately x = 30mm. These are attributed to the jet and to

the grinding wheel boundary layer respectively.

Figure 6.8 presents results for a grinding wheel turning in the opposite direction

to the impinging jet flow. The results show that much of the air leaving the notional

grinding zone is recirculated and re-enters the grinding zone. This will have a negative

effect on the heat transfer coefficient because the air entering this critical zone will

138

Figure 6.7: Wheel & Impinging Jet; H = 101mm,α = 15, Vs = 10m/s, Vj =10m/s

Figure 6.8: Wheel and Impinging Jet; α = 15, Vs = −10m/s, Vj = 10m/s

have an elevated temperature. The intensity of turbulence is higher in this grinding

configuration but at a large distance from the surface. The peak turbulence intensity

occurs along the stagnation zone that occurs between the two distinct flow regions.

The turbulence close to the surface, where the influence on heat transfer is greatest,

remains comparable to the case where both the jet and wheel velocities are in the

same direction. In effect this configuration will not have a favorable influence on the

convective heat transfer coefficient in the grinding zone.

139

6.4 Heat Transfer in a Grinding Configuration

In this section the convective heat transfer coefficient is plotted along the centreline

of the notional grinding plane. The heat transfer coefficient has been acquired from

the isothermal test surface and therefore the area under the graph is indicative of the

overall rate of heat transfer from the surface. In a grinding process, however, the heat

generation is localised, creating a hot spot at the grinding zone. Heat transfer to the

air only occurs where there is a local temperature difference between the surface and

the fluid. Therefore the overall rate of heat transfer in grinding is determined by the

heat transfer coefficient in the grinding zone.

6.4.1 Preliminary Heat Transfer Data

This section presents distributions of heat transfer coefficients for three preliminary

testing conditions. The first of these is the heat transfer associated with the entrain-

ment of ambient air by the rotating grinding wheel, as shown in figure 6.9. The second

and third cases are for the impinging jet at 15 and 30 respectively with no grinding

wheel present.

−80 −60 −40 −20 0 20 40 60 800

20

40

60

80

100

120

140

160

180

200

x, (mm)

h, (

W/m

2 K)

Vwheel

= 10 m/sV

wheel = 20 m/s

Vwheel

= 30 m/s High Mean Velocity

Entrainment of Cold Ambient Fluid

Low ∆T

High R. M. S. Velocity

Figure 6.9: Heat Transfer to Grinding Wheel Boundary Layer

Peaks in the heat transfer distribution due to the rotating grinding wheel, shown

in figure 6.9, can be explained in the following manner. From the right, a subtle peak

140

occurs at a position of x ≈ 42mm. This is due to a region of high turbulence intensity

occurring in the wedge between the grinding wheel and the surface. This is verified by

the PIV data presented in figure 6.5. The main peak in heat transfer is due to the peak

velocity at the minimum gap (x = 0). As the air moves beyond this point however, it is

thought that the heat transfer rate decreases because of the low temperature difference

between the surface and the local fluid, leading to a heat transfer minimum. As the gap

between the wheel and the surface increases again further fluid is entrained, increasing

the heat transfer rate again. Eventually, the heat transfer coefficient falls off as the

local fluid velocity decreases with distance from the grinding wheel.

The results presented in figure 6.9 can be compared to the heat transfer distributions

obtained for a jet impinging at angles of 15 and 30 respectively without a grinding

wheel, as shown in figure 6.10. The height of the jet above the surface corresponds in

each case to the minimum that would have been possible, had the grinding wheel been

in position. The most notable feature of the above results is that the flow induced by the

wheel rotating alone produces heat transfer coefficients broadly similar in magnitude to

those associated with the impinging air jet. As discussed in Chapter 5, the heat transfer

distribution for an impinging air jet with large H/D has a peak at the stagnation point.

The decay in the heat transfer is steep in the uphill direction and more subtle in the

downhill direction. This peak in heat transfer occurs closer to the geometric centre,

equivalent to the arc of cut in this case, for the larger angle of impingement.

141

−150 −100 −50 0 50 1000

20

40

60

80

100

120

140

160

180

x, (mm)

h, (

W/m

2 K)

Vjet

= 10 m/sV

jet = 20 m/s

Vjet

= 30 m/s

(a) α = 15

−150 −100 −50 0 50 1000

20

40

60

80

100

120

140

160

180

200

x, (mm)

h, (

W/m

2 K)

Vjet

= 10 m/sV

jet = 20 m/s

Vjet

= 30 m/s

(b) α = 30

Figure 6.10: Heat Transfer Distributions to Obliquely Impinging Jets

142

6.4.2 Low Speed Jet Cooling

The second set of tests were conducted with the tangential velocity of the wheel set

equal to the exit velocity of the jet. Once again tests were carried out for two different

angles of jet impingement and for three different velocities. The jet is also set at a

minimum height determined by the grinding wheel, as shown in figure 6.11.

−150 −100 −50 0 50 100 150

0

50

100

150

200

x, (mm)

y, (

mm

)

α = 15°

H = 65 mm

α = 30°

H = 100 mm

Figure 6.11: Schematic of Jet Position

Figure 6.12 presents the heat transfer distributions for this grinding configuration.

These distributions differ somewhat from those in figure 6.9 because the largest peak

is now due to the stagnation point of the flow and occurs at x = 35mm and 30mm for

α = 15 and 30 respectively. This peak has a greater magnitude for the impingement

angle of 15. From results presented in section 5.2.2 the greater magnitude of the peak

at this set-up can be attributed to both the proximity of the jet to the test surface

and to the small angle of impingement. By comparison of figures 5.16 (a) and (b), it

has been shown that for low heights of the nozzle above the impingement surface the

highest peak heat transfer coefficient occurs at small angles of impingement whereas,

at large H/D the peak heat transfer coefficient occurs for the normally impinging jet.

Given the expected proximity of the jet to the notional arc of cut in grinding, an angle

of impingement of 15 is preferable to 30.

143

−80 −60 −40 −20 0 20 40 60 800

50

100

150

200

250

x, (mm)

h, (

W/m

2 K)

Vwheel

= 10; Vjet

= 10 m/sV

wheel = 20; V

jet = 20 m/s

Vwheel

= 30; Vjet

= 30 m/s

(a) α = 15

−80 −60 −40 −20 0 20 40 60 800

20

40

60

80

100

120

140

160

180

x, (mm)

h, (

W/m

2 K)

Vwheel

= 10; Vjet

= 10 m/sV

wheel = 20; V

jet = 20 m/s

Vwheel

= 30; Vjet

= 30 m/s

(b) α = 30

Figure 6.12: Wheel and Impinging Jet Heat Transfer Distributions, Vw = Vj

144

The length of the grinding zone may vary between 1mm and 10cm for conventional

and creep feed grinding respectively. Averaging the heat transfer coefficient over each

of these areas is a suitable way of establishing whether the jet configuration is appro-

priate for a given grinding process. The current experimental set-up best reflects a

conventional grinding set-up and for this case the smaller angle provides the greatest

cooling overall as it appears that the grinding wheel tends to deflect the 30 jet from

the grinding zone. This is apparent from the jet set-up comparison depicted in fig-

ure 6.11, which shows that the 15 angle allows the jet to be positioned much closer

to the grinding zone. For this reason, further testing is confined to the one angle of

impingement, α = 15.

Much of the analysis reported in the literature, for example Lavine and Jen [9], is

based on the assumption that the cutting fluid has the same velocity as the tangential

velocity of the wheel in the grinding zone. This assumption is valid when the cutting

fluid’s primary function is to lubricate, i.e. the requirement is simply to get fluid

into the grinding zone and its velocity is determined by the grinding wheel. For the

evaluation of jet cooling effectiveness, testing was carried out where various relative

velocities between the wheel and jet were investigated.

−80 −60 −40 −20 0 20 40 60 800

50

100

150

200

250

x, (mm)

h, (

W/m

2 K)

Vwheel

= −10; Vjet

= 10 m/sV

wheel = −20; V

jet = 20 m/s

Vwheel

= −30; Vjet

= 30 m/s

Figure 6.13: Wheel and Impinging Jet Heat Transfer Distributions; Vw = −Vj

145

−80 −60 −40 −20 0 20 40 60 800

20

40

60

80

100

120

140

160

180

200

x, (mm)

h, (

W/m

2 K)

Vwheel

= −30; Vjet

= 10 m/sV

wheel = 30; V

jet = 10 m/s

(a) |Vwheel| = 3× Vjet

−80 −60 −40 −20 0 20 40 60 800

50

100

150

200

250

x, (mm)

h, (

W/m

2 K)

Vwheel

= −10; Vjet

= 30 m/sV

wheel = 10; V

jet = 30 m/s

(b) Vjet = 3× |Vwheel|

Figure 6.14: Other Wheel and Impinging Jet Heat Transfer Distributions

146

Figure 6.13 presents a test configuration where the wheel velocity is equal to but in

the opposite direction to the jet flow. The heat transfer distributions exhibit similar

peaks to the previous distributions but they occur at different locations and have altered

magnitudes. In this case the convective heat transfer coefficient is a minimum at the

notional grinding zone, (x = 0). This is due to the local flow stagnating at the location

of the minimum gap. Although the heat transfer coefficient is high at other locations,

this is an unfavourable configuration for cooling of a grinding process because of the

minimum in the critical region of the arc of cut.

A colour coded schematic indicating the wheel velocity direction is illustrated in

figure 6.14. The results presented with this schematic illustrate further the adverse

effect that opposing grinding wheel and jet directions can have on heat transfer in the

grinding zone. Here the heat transfer distribution resulting from a constant jet velocity

and a wheel turning at a much higher velocity (figure 6.14 (a)), can provide a local

maximum or minimum at the arc of cut, depending on the direction of wheel rotation.

It is clear that the wheel tangential velocity should be in the same direction as the jet.

Figure 6.14 (b) shows the effect that wheel velocity direction has on the heat transfer

from the grinding zone for the case where the jet velocity is higher than the peripheral

wheel velocity. In this case it appears that the heat transfer coefficient in the localised

grinding zone around x = 0 is higher in the case where the jet and wheel velocities are

in opposing directions. This is thought to be due to the fact that the air entering the

notional grinding zone is at a higher temperature in the co-flow than in the counter-

flow set-up, leading to a reduced convective heat transfer coefficient in the critical zone.

The local difference is small, however, and in general more heat is convected to the jet

flow when the wheel rotates in the same direction as the impinging air jet.

6.4.3 High Speed Jet Cooling

Heat transfer data were acquired for a high speed jet of diameter 2.6mm directed

towards the instrumented test plate. This jet has been used for cooling of an actual

grinding process, as described by Babic et al. [3], and has proven to be a surprisingly

effective cooling arrangement. Two different jet positions were tested in this part of the

heat transfer investigation and these are illustrated in figure 6.15. The first jet position

tested is the same as used for the previous 15 test, namely where the wheel rotates

about a point directly above the geometric centre of the jet. The second position was

chosen to counteract the effect of the wheel in blocking the jet flow; thus the jet was

147

−20 −10 0 10 20 30 40 50 60 70

0

10

20

30

40

x, (mm)

y, (

mm

)

Jet Position 2:H = 10 mm

Jet Position 1:H = 50 mm

Figure 6.15: Schematic of High Speed Impinging Jet Set-up

positioned at a minimum height above the plate but still at an angle of 15.

The distributions of heat transfer coefficient shown in figure 6.16 no longer exhibit

the same number of local maxima and minima, as the high speed of the jet has managed

to penetrate the boundary layer flow around the grinding wheel. The predominant

peak still occurs at the stagnation point of the jet (x ≈ 25mm) and the heat transfer

distribution also exhibits a more subtle change in slope at the grinding zone (x = 0mm).

The most significant change to be noted, however, is that the heat transfer is greatly

enhanced at the grinding zone in comparison with the low speed jets.

The first jet position considered is thought to be less favorable because the jet

is effectively impinging on the wheel and not on the grinding surface. In a grinding

process, cooling of the grinding wheel itself may well be an effective method of reducing

the temperature in the grinding zone. In this investigation, however, the effectiveness

of this type of cooling is not considered. For this reason, the obliquely impinging jet

was positioned so the convective heat transfer from the workpiece would be maximised

and thus the height of the jet was minimised. In this case the jet impingement position

is not directed at the minimum gap but slightly to the right of it. Heat transfer

coefficients for this jet set-up have proven to be even more favorable although the peak

heat transfer coefficient still does not occur close to the grinding zone. Despite this,

the second jet set-up shown in figure 6.15 has managed to double the heat transfer

coefficient in the grinding zone for the same flow rate of air.

148

−50 −25 0 25 500

200

400

600

800

1000

1200

x [mm]

h [W

/m2 K

]

Flow Rate = 0.003, [m3/s]Flow Rate = 0.004, [m3/s]Flow Rate = 0.005, [m3/s]

(a) Jet Position 1

−50 −25 0 25 500

200

400

600

800

1000

1200

1400

1600

1800

2000

x [mm]

h [W

/m2 K

]

Flow Rate = 0.003, [m3/s]Flow Rate = 0.004, [m3/s]Flow Rate = 0.005, [m3/s]

(b) Jet Position 2

Figure 6.16: Wheel and High Speed Impinging Jet Heat Transfer Distributions

149

6.5 Conclusions

The PIV data have illustrated some of the flow characteristics that occur when an air

jet impinges on a flat surface such as a workpiece in a grinding process. Data have been

presented for a range of test conditions and from these data, the influence of the flow

on heat transfer was inferred. Convective heat transfer coefficients have been estimated

for the air jet cooling of a typical grinding configuration. Some approximations were

made in order to measure the heat transfer distribution along the grinding plane. The

two main differences between the experimental set-up and an actual grinding process

are the thermal boundary condition and the non contact between the surface and the

wheel. The significance of these approximations has been discussed and it can be

concluded that the convective heat transfer coefficient is probably underestimated as

a result of these differences and that the overall heat transfer coefficient can only be

based on the local heat transfer coefficients in the grinding zone. However, it is likely

that the peaks in the distributions occur in the same locations.

• The rotating grinding wheel entrains a boundary layer that impinges on the grind-

ing surface. The heat transfer to this induced flow has a convection coefficient

comparable to that of an impinging air jet of similar velocity.

• In general, the boundary layer developed around the rotating grinding wheel has

a negative effect on the cooling of a grinding process as it prevents the jet flow

from reaching the grinding zone. It also has the effect of moving the stagnation

point, where the peak in heat transfer coefficient occurs, away from the grinding

zone.

• Depending on the grinding configuration, recirculations in the flow have been

revealed. These would have a negative effect on the heat transfer coefficient as

the local surface to fluid temperature difference would be reduced.

• For the conditions investigated the rms velocity or turbulence intensity is a max-

imum in the wedge made between the grinding wheel and the grinding surface.

• Findings from the fundamental investigation of heat transfer to an impinging air

jet presented in Chapter 5, are applicable to the cooling of a grinding process.

Peaks in the heat transfer distributions have been successfully linked to regions

of high fluid velocity and turbulence intensity. It has also been established that

150

an angle of impingement of 15 is preferable as the maximum peak in the heat

transfer distributions occur at this angle.

• When a counter-flow cooling configuration is tested, the heat transfer coefficient

is usually a minimum at the arc of cut. This coefficient tends to zero for low

velocities, suggesting the occurrence of an instantaneous stagnation point in the

flow. This indicates that a counter-current configuration is not appropriate for

the cooling of a grinding process.

• It has been shown that a high speed jet effectively penetrates the boundary layer

flow around the grinding wheel providing good cooling of the grinding zone.

• Positioning of the high speed jet has also been shown to be critical in enhancing

the convective heat transfer. In general the high speed jet provides more effective

cooling than the low speed jet; however if the distance of the jet from the grinding

zone is decreased, the heat transfer coefficient can be further increased by a factor

of two.

The cooling of a grinding process has many characteristics that are unique to the

specific application. However, the general fluid flow and heat transfer relationships pre-

sented in Chapter 5 are relevant. Although this investigation has been predominantly

directed towards cooling of the grinding zone itself it is worth noting that the area

surrounding the grinding zone will be at a somewhat elevated temperature also and

more of the heat transfer coefficient distribution will be utilised in the overall cooling

of a grinding process. It would also be of benefit if the impinging air jet was colder

than the ambient air or workpiece. In this case the pre-cooling of the entire workpiece

would also serve to reduce the temperature in the grinding zone.

Chapter 7

Conclusions

Results have been presented of fluid flow and heat transfer relating to an axially

symmetric impinging air jet. It has been shown that at low nozzle to impingement

surface spacings the mean heat transfer distribution exhibits peaks that occur at a

radial location. These peaks have been reported by several investigators and have been

attributed, in general, to an abrupt increase in turbulence in the wall jet boundary

layer. Results from the current investigation support this assertion. However the

fluid mechanical processes that control the development of the wall jet boundary layer

have not been well defined. It has been shown that the free jet flow has the effect of

suppressing turbulence in the jet flow, and upon ‘escaping’ from the lip of the free jet

the wall jet can undergo transition to a fully turbulent flow. The transition of the flow

to a fully turbulent condition is delayed however, and does not occur immediately

after the wall jet escapes the free jet flow.

Vortices that roll-up naturally in the shear layer of the free jet, close to the nozzle

exit, have been shown to merge forming larger yet weaker vortices, before being broken

down into smaller scale random turbulence. Stages within the merging processes have

been identified to occur at various distances from the jet nozzle. Upon impingement

the vortices move along the wall jet before being broken down. The coherence of the

vortical structures has the effect of maintaining the relatively low turbulence in the

wall jet flow. These vortices eventually do break down and the turbulence level within

the wall jet increases significantly, which in turn increases the heat transfer, leading

to a secondary peak in the heat transfer distribution.

In more recent years the enhancement of impinging jet heat transfer by various

methods of excitation has been investigated. Depending on the excitation frequency,

151

152

the merging of vortices and the eventual breakdown location can be controlled. In so

doing, the length of the potential core and the spread of the jet can also be controlled.

This in turn has the effect of moving the impingement surface to a new location with

respect to the jet flow without changing the relative geometric location. To explore this

phenomenon, an increase in Nusselt number has been achieved by changing the length

of the jet so that the impingement surface is located just beyond the core of the jet,

where maximum heat transfer coefficients have been reported by several investigators.

In contrast, reduced heat transfer rates have been reported when the jet develop-

ment is controlled so that the impingement surface is placed in an undeveloped jet flow.

The effect that the actual vortex structure has on surface heat transfer has

attracted little attention. It has been shown here that axial velocity fluctuations close

to the impingement surface have a far greater influence on the heat transfer than

fluctuations parallel to the surface. Vortices that impinge upon the surface determine

the magnitude and frequency of the fluctuations in both directions. Because of this,

the various stages of the vortex merging process influence the mean and rms Nusselt

number distributions at low H/D. When the vortices impinge upon the surface at

an early stage in their development, this promotes separation in the wall jet flow and

the subsequent breakup of these strong vortices leads to large velocity fluctuations

normal to the impingement surface. Vortices that impinge at later stages in their

development are weaker and therefore as they breakup in the wall jet, the magnitude

of the velocity fluctuations normal to the surface is reduced. This does not enhance

the heat transfer in the wall jet, to the same degree as stronger vortices do. In general,

the breakdown of strong vortices (in the early stages of the vortex development), has

a favorable effect on the heat transfer in the near wall jet. Enhancement of the heat

transfer in this region could be achieved by exciting the jet so that strong coherent

vortices impact on the heated surface.

Heat transfer to an impinging air jet in a grinding application has been investigated

and the results interpreted with reference to the fundamental heat transfer mechanisms

for an impinging air jet on a flat surface. Heat transfer coefficients have been presented

across the cutting plane of the grinding wheel for a range of jet cooling set-ups. It has

been shown that jet velocities similar to the tangential velocity of the wheel do not

significantly enhance the heat transfer in the grinding zone. It is apparent that the

153

jet will enhance the convective heat transfer of the workpiece overall as relatively high

heat transfer coefficients occur at locations distant from the grinding zone. In the

case of obliquely impinging jets, the peak heat transfer coefficient is displaced from

the geometric centre (grinding zone). The flow due to the grinding wheel boundary

layer has been shown to displace the peak heat transfer further from the grinding zone.

It has been shown that high speed jets are required to penetrate the grinding wheel

boundary layer and effectively cool the grinding zone.

7.1 Further Work

The current research on impinging jet flow has been concerned with the effect of vortices

at different stages in their development on the surface heat transfer. Recent studies

have shown that jet excitation has the potential to control the development of vortices

in a jet flow. With the knowledge gained from the current research, further work would

include the artificial excitation of the impinging jet flow. This would facilitate an in

depth investigation of the effect of the vortical jet flow on the surface heat transfer, for

a wider range of parameters to include the vortex strength, passing frequency, etc.

Secondly the measurement of local air temperatures in the wall jet boundary layer

would facilitate a greater understanding of the surface heat transfer to an impinging air

jet. Time averaged temperature measurements would go some way to explaining the

effect of the heat carrying capacity of the wall jet boundary layer flow. Investigation

of the fluctuations in temperature throughout the wall jet boundary layer would also

enhance our understanding of the influence that entrainment of ambient fluid has on the

heat transfer. The significance of thermal gradients normal to the impingement surface

has only been inferred in the current investigation. Simultaneous measurement of local

fluid velocity, temperature and heat flux would provide for a greater understanding of

the effect of these thermal gradients. Also measurements of temperature fluctuations

in the wall jet may indicate whether energy separation due to vortices within the jet

flow has an influence on the surface heat transfer.

Finally, a high speed water mist jet has been investigated by Babic et al. [3] and has

been shown to enhance the cooling of a grinding process significantly. The extent to

which the lower grinding temperatures can be attributed to enhanced convective heat

transfer coefficients for the mist jet rather than to lubrication of the process warrants

further investigation.

Appendix A

Calibration Certificates

Micro-Foilr Heat Flux Sensor Calibration Certificate

154

156

Alicat Air Flow Meter Calibration Certificate

157

Resistance Temperature Detector Calibration Certificate

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