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
vi
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
5.39 Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 0.65 . . . . . . . . . . . 95
5.40 Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 1.02 . . . . . . . . . . . 95
5.41 Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 1.30 . . . . . . . . . . . 96
5.42 Radial Location of Simultaneous Measurements . . . . . . . . . . . . . . . . . . . . . . 98
5.43 Spectral, Coherence & Phase Information; H/D = 1, r/D = 0.37 . . . . . . . . . . . . 99
5.44 Spectral, Coherence & Phase Information; H/D = 1, r/D = 0.65 . . . . . . . . . . . . 99
5.45 Spectral, Coherence & Phase Information; H/D = 1, r/D = 1.02 . . . . . . . . . . . . 100
5.46 Spectral, Coherence & Phase Information; H/D = 1, r/D = 1.30 . . . . . . . . . . . . 100
5.47 Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 0.37 . . . . . . . . . . . 101
5.48 Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 0.65 . . . . . . . . . . . 101
5.49 Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 1.02 . . . . . . . . . . . 102
5.50 Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 1.30 . . . . . . . . . . . 102
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5.51 Spectral, Coherence & Phase Information; H/D = 2, r/D = 0.37 . . . . . . . . . . . . 103
5.52 Spectral, Coherence & Phase Information; H/D = 2, r/D = 0.74 . . . . . . . . . . . . 103
5.53 Spectral, Coherence & Phase Information; H/D = 2, r/D = 1.02 . . . . . . . . . . . . 104
5.54 Spectral, Coherence & Phase Information; H/D = 2, r/D = 1.30 . . . . . . . . . . . . 104
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
5.62 Spectral, Coherence & Phase Information; H/D = 4, r/D = 1.02 . . . . . . . . . . . . 114
5.63 Spectral, Coherence & Phase Information; H/D = 4, r/D = 1.48 . . . . . . . . . . . . 114
5.64 Radial Location of Simultaneous Measurements; H/D = 8 . . . . . . . . . . . . . . . . 115
5.65 Spectral, Coherence & Phase Information; H/D = 8, r/D = 1.11 . . . . . . . . . . . . 116
5.66 Spectral, Coherence & Phase Information; H/D = 8, r/D = 1.86 . . . . . . . . . . . . 116
5.67 Nu Distribution & Heat Flux Spectra; 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
5.71 Spectral, Coherence & Phase Information; H/D = 2, α = 60, r/D = −1.11 . . . . . . 121
5.72 Spectral, Coherence & Phase Information; H/D = 2, α = 60, r/D = 0.37 . . . . . . . 122
5.73 Spectral, Coherence & Phase Information; H/D = 2, α = 60, r/D = 1.11 . . . . . . . 122
5.74 Radial Location of Simultaneous Measurements; H/D = 2, α = 45 . . . . . . . . . . . 123
5.75 Spectral, Coherence & Phase Information; H/D = 2, α = 45, r/D = −0.81 . . . . . . 124
5.76 Spectral, Coherence & Phase Information; H/D = 2, α = 45, r/D = 0.76 . . . . . . . 124
5.77 Spectral, Coherence & Phase Information; H/D = 2, α = 45, r/D = 1.41 . . . . . . . 125
6.1 Grinding Process Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.2 Experimental Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.3 Schematic of Test Set-up & Corresponding Heat Transfer Distribution . . . . . . . . . 134
6.4 Particle Image Velocimetry Measurement Set-up . . . . . . . . . . . . . . . . . . . . . 134
6.5 Flow Entrained by Grinding Wheel; Vs = 20m/s . . . . . . . . . . . . . . . . . . . . . 136
6.6 Wheel & Impinging Jet; 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
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6.14 Other Wheel and Impinging Jet Heat Transfer Distributions . . . . . . . . . . . . . . . 145
6.15 Schematic of High Speed Impinging Jet Set-up . . . . . . . . . . . . . . . . . . . . . . 147
6.16 Wheel and High Speed Impinging Jet Heat Transfer Distributions . . . . . . . . . . . 148
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.
5.2.1 Normally 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.
5.2.2 Obliquely Impinging Jet
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.
5.3.1 Normally Impinging Jet
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
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 5.22: 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.
5.3.2 Obliquely Impinging Jet
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
15Mean Axial VelocityMean Radial Velocity
0
5
Vel
ocity
, [m
/s]
RMS Axial VelocityRMS Radial Velocity
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
15Mean Axial VelocityMean Radial Velocity
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
]
RMS Axial VelocityRMS Radial Velocity
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
Axial VelocityRadial Velocity
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
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 2−18
−16
−14
−12
−10
−8
−6
−4
−2
0
2
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.39: Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 0.65
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 2−8
−6
−4
−2
0
2
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.40: Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 1.02
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
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 2−5
−4
−3
−2
−1
0
1
2
3
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.41: Spectral, Coherence & Phase Information; H/D = 0.5, r/D = 1.30
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]
Mean Axial VelocityMean Radial Velocity
0 0.5 1 1.5 2 2.5 30
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
]
Mean Axial VelocityMean Radial Velocity
0 0.5 1 1.5 2 2.5 30
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
]
Mean Axial VelocityMean Radial Velocity
0 0.5 1 1.5 2 2.5 30
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
−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 2−5
0
5
10
15
20
St
Pha
se
Axial VelocityRadial Velocity
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
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 2−12
−10
−8
−6
−4
−2
0
2
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.44: Spectral, Coherence & Phase Information; H/D = 1, r/D = 0.65
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
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 2−5
−4
−3
−2
−1
0
1
2
3
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.45: Spectral, Coherence & Phase Information; H/D = 1, r/D = 1.02
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 2−5
−4
−3
−2
−1
0
1
2
3
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.46: Spectral, Coherence & Phase Information; H/D = 1, r/D = 1.30
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
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 2−6
−4
−2
0
2
4
6
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.47: Spectral, Coherence & Phase Information; H/D = 1.5, 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
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 2−6
−4
−2
0
2
4
6
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.48: Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 0.65
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
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 2−12
−10
−8
−6
−4
−2
0
2
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.49: Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 1.02
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 2−4
−3
−2
−1
0
1
2
3
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.50: Spectral, Coherence & Phase Information; H/D = 1.5, r/D = 1.30
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
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 2−14
−12
−10
−8
−6
−4
−2
0
2
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.51: Spectral, Coherence & Phase Information; H/D = 2, 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
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 2−8
−6
−4
−2
0
2
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.52: Spectral, Coherence & Phase Information; H/D = 2, r/D = 0.74
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
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 2−10
−5
0
5
10
15
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.53: Spectral, Coherence & Phase Information; H/D = 2, r/D = 1.02
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 2−5
−4
−3
−2
−1
0
1
2
3
4
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.54: Spectral, Coherence & Phase Information; H/D = 2, r/D = 1.30
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
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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
]
Mean Axial VelocityMean Radial Velocity
0 0.5 1 1.5 2 2.5 30
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
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 2−10
−8
−6
−4
−2
0
2
4
6
8
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.62: Spectral, Coherence & Phase Information; H/D = 4, r/D = 1.02
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 2−20
−15
−10
−5
0
5
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.63: Spectral, Coherence & Phase Information; H/D = 4, r/D = 1.48
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
]
Mean Axial VelocityMean Radial Velocity
0 0.5 1 1.5 2 2.5 30
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
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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 2−6
−4
−2
0
2
4
6
8
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.65: Spectral, Coherence & Phase Information; H/D = 8, r/D = 1.11
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 2−30
−25
−20
−15
−10
−5
0
5
10
15
20
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.66: Spectral, Coherence & Phase Information; H/D = 8, r/D = 1.86
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
]
Mean Axial VelocityMean Radial Velocity
−2 −1 0 1 2 3 4 50
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
−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 2−50
−45
−40
−35
−30
−25
−20
−15
−10
−5
0
St
Pha
se
Axial VelocityRadial Velocity
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
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 2−12
−10
−8
−6
−4
−2
0
2
4
6
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.71: Spectral, Coherence & Phase Information; H/D = 2, α =60, r/D = −1.11
122
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 2−25
−20
−15
−10
−5
0
5
St
Pha
se
Axial VelocityRadial Velocity
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
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 2−10
−5
0
5
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.73: Spectral, Coherence & Phase Information; H/D = 2, α =60, r/D = 1.11
123
−5
0
15
U, [
m/s
]
Mean Axial VelocityMean Radial Velocity
−2 −1 0 1 2 3 4 50
2
4
r/D
U, [
m/s
]
RMS Axial VelocityRMS Radial Velocity
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
−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 2−25
−20
−15
−10
−5
0
5
10
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.75: Spectral, Coherence & Phase Information; H/D = 2, α =45, r/D = −0.81
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 2−20
−15
−10
−5
0
5
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.76: Spectral, Coherence & Phase Information; H/D = 2, α =45, r/D = 0.76
125
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 2−4
−3
−2
−1
0
1
2
3
4
5
6
St
Pha
se
Axial VelocityRadial Velocity
Figure 5.77: Spectral, Coherence & Phase Information; H/D = 2, α =45, r/D = 1.41
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
155
156
Alicat Air Flow Meter Calibration Certificate
157
Resistance Temperature Detector Calibration Certificate
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