THE PERFORMANCE OF A THERMAL TRANSIENT ANEMOMETER (TTA) FOR

NONUNIFORM VELOCITY MEASUREMENTS

By

Sarah Plant

A THESIS

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Mechanical Engineering – Master of Science

2020

ABSTRACT

THE PERFORMANCE OF A THERMAL TRANSIENT ANEMOMETER (TTA) FOR

NONUNIFORM VELOCITY MEASUREMENTS

By

Sarah Plant

A thermal transient anemometer (TTA) is a device used to measure fluid flow over a planar

cross-sectional area. The TTA system includes a frame containing several cells arranged in a

grid and an electronic control unit. Each cell contains a sensing wire which provides an area-

averaged velocity measurement. The measuring strategy relies on the transient convection

and the temperature decay of the sensing wire, which is correlated with the magnitude of

the velocity. The relationship between the temperature decay and the velocity is determined

by calibrating the TTA with a set of known uniform velocities.

The performance of the TTA under uniform and nonuniform flow conditions has been

evaluated through numerical analysis and experimentation. Following the calibration of the

TTA, a numerical model was developed to simulate the sensing wire in a TTA cell when ex-

posed to a given velocity field. The model was used to investigate how linear velocity profiles

affect the convective heat transfer and resulting temperature response of the sensing wire.

Dimensionless velocity gradients ranging from 0 to 1.9 with corresponding mean velocities

ranging from 0.1 to 15 m/s were evaluated. The temperature decay with velocity gradients

exceeding 0.5 was slower than that of the uniform decay, due to strong axial conduction

effects. This contributed to error in the mean velocity measurement from 1% with gradients

of 0.4 to 24% with gradients of 1.9. A nonuniform flow correction scheme was developed

using the numerical simulations that can reduce the mean velocity measurement error to
within ±1% in the presence of large velocity gradients (≥ 0.4). The correction scheme was
validated by experimental measurements using the TTA. The TTA was used to evaluate the

distribution of flow exiting an automotive radiator for various installation configurations.

The correction scheme was utilized in the presence of strong velocity gradients.

ACKNOWLEDGEMENTS

Special thanks to Dr. Foss and Dr. Klausner for the opportunity to work on this project. I’m

lucky to have such knowledgeable advisors to guide and encourage me during my graduate

studies. I’m appreciative of their patience and their adaptability during this time period.

I’d also like to thank my thesis committee, consisting of my two advisors and Dr. Pe-

trasch, for their feedback and support.

To the doctorate and post-doctorate students I’ve met, thanks for the continuous aca-

demic (and emotional) support. I wish them the best of luck with their academic careers

and future endeavors.

Finally, I’d like to collectively thank the faculty and staff within the Mechanical Engi-

neering Department. Whether it was staying late during class office hours or offering advice

for my research, I’m appreciative of my professors for always finding time in their busy

schedules to help me.

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF ABBREVIATIONS AND SYMBOLS . . . . . . . . . . . . . . . . . . . . . xvii

CHAPTER 1

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 The Present TTA Description . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Prior Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
3
3
4
5

CHAPTER 2 EXPERIMENTAL FACILITY AND MEASUREMENT TECHNIQUES 6
6
8
9
9

2.1 The Test Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Measurement Techniques and DAQ . . . . . . . . . . . . . . . . . . . . . . .
2.3 The Force Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 The Slit-Jet and its Discharge Coefficient . . . . . . . . . . . . . . . .
2.3.2 Computational Fluid Dynamics (CFD) Analysis on the Discharge

Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Procedure for Calibration . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Final Notes on the Force Transducers . . . . . . . . . . . . . . . . . .
2.4 Hot-wire Anemometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Procedure for Calibration . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 3 CALIBRATION OF TTA . . . . . . . . . . . . . . . . . . . . . . .
3.1 Procedure for Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
14
15
15
16

19
19
20
22

4.1 Model and Assumptions

23
CHAPTER 4 NUMERICAL SIMULATIONS . . . . . . . . . . . . . . . . . . . . .
23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
4.1.1 Thermophysical Properties . . . . . . . . . . . . . . . . . . . . . . . .
26
4.1.2
Sensing Wire Resistance . . . . . . . . . . . . . . . . . . . . . . . . .
26
4.1.3 Air Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
4.2 Simulation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Nusselt Number Determination . . . . . . . . . . . . . . . . . . . . .
28
4.2.2 Numerical and Analytical Methods for Determining the Time Constant 29
4.2.3 Natural and Forced Convection . . . . . . . . . . . . . . . . . . . . .
31

CHAPTER 5 PERFORMANCE OF TTA WITH LINEAR VELOCITY GRADIENTS 33
33

5.1 Defining the Velocity Gradient . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

. . . . . . . . . . . . . . . . . . . . .
5.2 Simulating a Linear Velocity Gradient
5.3 Simulating a Linear Velocity Gradient Along the Height of the TTA Cell
. .
5.4 Correction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implementing the Correction Scheme . . . . . . . . . . . . . . . . . .
5.5 Experimental Response of the TTA Cell with an Imposed Velocity Gradient
5.5.1 Determining the Velocity Profile . . . . . . . . . . . . . . . . . . . . .
5.5.2 Procedure and Results of Experimental Evaluation . . . . . . . . . .

5.4.1

CHAPTER 6 NONUNIFORM VELOCITY DISTRIBUTION AT THE EXIT PLANE
OF A RADIATOR . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Experimental Setup and Procedure . . . . . . . . . . . . . . . . . . . . . . .
6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Horizontal Position . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inclined Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2
6.2.3
Inclined Configuration with Shroud Attached . . . . . . . . . . . . .

CHAPTER 7 SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . .

34
43
48
50
50
51
54

57
57
60
61
64
69

75

77
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
APPENDIX A CALIBRATION OF TTA . . . . . . . . . . . . . . . . . . . . .
APPENDIX B DERIVATION OF EQUATIONS . . . . . . . . . . . . . . . . .
93
APPENDIX C TESTING WITH RADIATOR . . . . . . . . . . . . . . . . . . 101

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

v

LIST OF TABLES

Table 3.1: Calibration uncertainty for each cell

. . . . . . . . . . . . . . . . . . . . .

Table 4.1: Constant properties used in simulation . . . . . . . . . . . . . . . . . . . .

Table 4.2: Constants in Nusselt correlation for cells 13 - 15 . . . . . . . . . . . . . .

Table 5.1: Time constants and computed velocities for uniform and nonuniform cases

Table 5.2: Correction constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 5.3: Results from gradient validation after correction scheme is applied for all

three cells and mean velocities tested . . . . . . . . . . . . . . . . . . . .

Table 6.1: Percentage of inclined data points within the 95% confidence intervals . .

Table A.1: Calibration constants for TTA cells

. . . . . . . . . . . . . . . . . . . . .

22

25

29

37

48

56

68

90

Table C.1: Standard deviation of percent difference for each inlet velocity in the

horizontal configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Table C.2: Standard Deviation of percent difference for each inlet velocity in the

inclined configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

vi

LIST OF FIGURES

Figure 1.1:

Images of TTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.1: Axial Fan Research and Development facility . . . . . . . . . . . . . . . .

Figure 2.2: Schematic representation of the net moment of momentum flux measur-

ing apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.3: Slit-jet nozzle mounted at AFRD inlet for calibration of force transducers

Figure 2.4: CFD model of slit-jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

6

7

10

11

Figure 2.5: Discharge coefficient calculated using Fluent for various maximum velocities 12

Figure 2.6: Hot-wire setup for CFD validation of discharge coefficient . . . . . . . . .

Figure 2.7: Comparison of hot-wire and Fluent velocity vertical survey . . . . . . . .

Figure 2.8: North and south force transducer calibration . . . . . . . . . . . . . . . .

Figure 2.9: Hot-wire probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.10: Hot-wire calibration facility . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 2.11: Sample hot-wire calibration curve . . . . . . . . . . . . . . . . . . . . . .

Figure 3.1: TTA calibration setup at inlet of AFRD facility . . . . . . . . . . . . . .

Figure 3.2: TTA cell number assignments . . . . . . . . . . . . . . . . . . . . . . . .

Figure 3.3: TTA calibration curve for cell 1 . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.1: Schematic representation of a TTA cell . . . . . . . . . . . . . . . . . . .

Figure 4.2: Cell 13 experimental and simulated calibration . . . . . . . . . . . . . . .

Figure 4.3: Comparison of numerical and analytical methods of solving for the time

constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.4: Richardson number for velocities ranging from 0 m/s to 15 m/s

. . . . .

Figure 5.1: Schematic of linear velocity profile imposed on the TTA cell

. . . . . . .

13

13

14

16

17

18

20

21

21

24

29

30

32

34

vii

Figure 5.2: Resistance decay of wire with and without various gradients for mean

velocities of 1, 5, and 10 m/s . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.3: Temperature distribution along wire at subsequent time steps for various

mean velocities and gradients

. . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.4: Percent difference in TTA measurements for various mean velocities and

gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.5: Resistivity along wire as it convectively cools for a mean velocity of 5

m/s with various velocity gradients . . . . . . . . . . . . . . . . . . . . .

Figure 5.6: Schematic representation of linear velocity profile imposed on the TTA

cell (varying along the height) . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.7: Velocity along the sensing wire for a mean velocity of 10 m/s and gra-

dient of 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.8: Percent difference in TTA measurements for various mean velocities and

vertical gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.9: Temperature distribution along wire at subsequent time steps for various

mean velocities and gradients

. . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.10: Percent difference in TTA measurements with and without the correc-

tion for cell 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

39

40

42

43

44

45

47

49

Figure 5.11: Mesh used to impose a linear velocity profile (uniform horizontal gradient) 51

Figure 5.12: Fluent analysis of velocity contour 2.08 cm downstream of mesh . . . . .

52

Figure 5.13: Fluent analysis of velocity magnitude 2.08 cm downstream (vertical dis-

tance at midpoint height)

. . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.14: Setup for mesh velocity profile measurements using pitot tube . . . . . .

Figure 5.15: Pitot tube determined mesh velocity profile at different distances down-

stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5.16: TTA with mesh mounted 2.08 cm above tested cell

. . . . . . . . . . . .

Figure 5.17: Velocity profiles with mesh used for validation of TTA correction scheme

Figure 6.1: Radiator and TTA frame installation . . . . . . . . . . . . . . . . . . . .

viii

52

53

54

55

55

58

Figure 6.2: 8◦ inclination inlet channel . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.3: Radiator with shroud attached with a view looking up from AFRD

upper receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.4: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 0.26 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.5: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 5.04 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.6: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 9.57 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.7: Standard deviation of velocity distribution in horizontal configuration . .

Figure 6.8: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 0.26 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.9: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 4.93 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.10: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 9.28 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.11: Standard deviation of velocity distribution in inclined configuration . . .

Figure 6.12: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 1 . .

Figure 6.13: Change in percent difference by row . . . . . . . . . . . . . . . . . . . . .

Figure 6.14: Schematic representation of TTA frame position with respect to the

shroud opening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.15: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 8.85 m/s . . . . . . . . . . . . . . . .

Figure 6.16: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 1.03 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.17: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 8.29 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 6.18: Kinetic energy flux with and without the shroud attached . . . . . . . .

59

60

62

62

63

63

64

65

65

66

67

69

70

71

72

72

73

ix

Figure 6.19: Difference between kinetic energy flux with and without the shroud . . .

Figure A.1: TTA calibration curve for cell 1 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.2: TTA calibration curve for cell 2 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.3: TTA calibration curve for cell 3 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.4: TTA calibration curve for cell 4 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.5: TTA calibration curve for cell 5 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.6: TTA calibration curve for cell 6 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.7: TTA calibration curve for cell 7 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.8: TTA calibration curve for cell 8 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.9: TTA calibration curve for cell 9 . . . . . . . . . . . . . . . . . . . . . . .

Figure A.10:TTA calibration curve for cell 10 . . . . . . . . . . . . . . . . . . . . . .

Figure A.11:TTA calibration curve for cell 11 . . . . . . . . . . . . . . . . . . . . . .

Figure A.12:TTA calibration curve for cell 12 . . . . . . . . . . . . . . . . . . . . . .

Figure A.13:TTA calibration curve for cell 13 . . . . . . . . . . . . . . . . . . . . . .

Figure A.14:TTA calibration curve for cell 14 . . . . . . . . . . . . . . . . . . . . . .

Figure A.15:TTA calibration curve for cell 15 . . . . . . . . . . . . . . . . . . . . . .

Figure A.16:TTA calibration curve for cell 16 . . . . . . . . . . . . . . . . . . . . . .

Figure A.17:TTA calibration curve for cell 17 . . . . . . . . . . . . . . . . . . . . . .

Figure A.18:TTA calibration curve for cell 18 . . . . . . . . . . . . . . . . . . . . . .

Figure A.19:TTA calibration curve for cell 19 . . . . . . . . . . . . . . . . . . . . . .

Figure A.20:TTA calibration curve for cell 20 . . . . . . . . . . . . . . . . . . . . . .

Figure A.21:TTA calibration curve for cell 21 . . . . . . . . . . . . . . . . . . . . . .

Figure A.22:TTA calibration curve for cell 22 . . . . . . . . . . . . . . . . . . . . . .

74

78

79

79

80

80

81

81

82

82

83

83

84

84

85

85

86

86

87

87

88

88

89

x

Figure A.23:TTA calibration curve for cell 23 . . . . . . . . . . . . . . . . . . . . . .

Figure A.24:Cell 13 experimental and simulated calibration . . . . . . . . . . . . . . .

Figure A.25:Cell 14 experimental and simulated calibration . . . . . . . . . . . . . . .

Figure A.26:Cell 15 experimental and simulated calibration . . . . . . . . . . . . . . .

Figure B.1: Thermal conductivity fit . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure B.2: Specific heat fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure B.3: Kinematic viscosity fit . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure B.4: Prandtl number fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

91

92

92

95

96

97

97

Figure C.1: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 0.26 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure C.2: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 0.57 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure C.3: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 0.80 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure C.4: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 1.06 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure C.5: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 1.51 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure C.6: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 2.02 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure C.7: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 2.81 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Figure C.8: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 3.66 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Figure C.9: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 4.16 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure C.10: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 5.04 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xi

Figure C.11: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 5.90 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure C.12: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 6.71 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure C.13: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 7.18/ m/s . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure C.14: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 7.76 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure C.15: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 8.68 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure C.16: Radiator exit plane flow distribution in the horizontal configuration with

inlet velocity of 9.57 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure C.17: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 0.26 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure C.18: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 0.56 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Figure C.19: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 0.79 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Figure C.20: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 1.04 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Figure C.21: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 1.49 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure C.22: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 2.00 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure C.23: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 2.78 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure C.24: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 3.61 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure C.25: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 4.09 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

xii

Figure C.26: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 4.93 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Figure C.27: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 5.72 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure C.28: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 6.63 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Figure C.29: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 7.04 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure C.30: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 7.59 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Figure C.31: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 8.43 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Figure C.32: Radiator exit plane flow distribution in the inclined configuration with

inlet velocity of 9.28 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Figure C.33: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 1 . . 119

Figure C.34: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 2 . . 120

Figure C.35: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 3 . . 120

Figure C.36: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 4 . . 121

Figure C.37: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 5 . . 121

Figure C.38: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 6 . . 122

Figure C.39: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 7 . . 122

Figure C.40: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 8 . . 123

Figure C.41: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 9 . . 123

Figure C.42: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 10 . 124

Figure C.43: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 11 . 124

Figure C.44: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 12 . 125

xiii

Figure C.45: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 13 . 125

Figure C.46: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 14 . 126

Figure C.47: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 15 . 126

Figure C.48: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 16 . 127

Figure C.49: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 17 . 127

Figure C.50: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 18 . 128

Figure C.51: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 19 . 128

Figure C.52: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 20 . 129

Figure C.53: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 21 . 129

Figure C.54: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 22 . 130

Figure C.55: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 23 . 130

Figure C.56: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 6.40 m/s . . . . . . . . . . . . . . . . 131

Figure C.57: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 6.47 m/s . . . . . . . . . . . . . . . . 131

Figure C.58: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 7.11 m/s . . . . . . . . . . . . . . . . 132

Figure C.59: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 7.51 m/s . . . . . . . . . . . . . . . . 132

Figure C.60: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 7.95 m/s . . . . . . . . . . . . . . . . 133

Figure C.61: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 8.29 m/s . . . . . . . . . . . . . . . . 133

Figure C.62: Radiator exit plane flow distribution with shroud attached before and

after correction for inlet velocity of 8.85 m/s . . . . . . . . . . . . . . . . 134

Figure C.63: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 0.26 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

xiv

Figure C.64: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 0.74 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Figure C.65: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 1.03 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Figure C.66: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 1.28 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Figure C.67: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 1.64 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Figure C.68: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 1.83 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Figure C.69: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 2.12 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Figure C.70: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 2.80 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Figure C.71: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 3.47 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Figure C.72: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 4.67 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Figure C.73: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 5.41 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Figure C.74: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 6.40 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Figure C.75: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 6.47 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Figure C.76: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 7.11 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Figure C.77: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 7.51 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Figure C.78: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 7.95 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

xv

Figure C.79: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 8.29 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Figure C.80: Radiator exit plane flow distribution with shroud attached and inlet

velocity of 8.85 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

xvi

LIST OF ABBREVIATIONS AND SYMBOLS

Abbreviations

Description

AF RD

CF D

CT A

T T A

Coordinate Systems
x − y − z
x − y − s − φ

Axial Fan and Research Development (facility)

Computational Fluid Dynamics

Constant Temperature Anemometer

Thermal Transient Anemometer

Description

Spatial coordinate system

Spatial coordinate system (of TTA cell)

Greek Symbols

Description

γ

∆

κ

ν

ξ

ρ

σ

τ

θ

ζ

Resistivity (Ωm)

Percent difference
Sum of U 3 for all TTA cells (∝ kinetic energy flux)

Kinematic viscosity (kg/ms)

Gradient (horizontal or vertical orientation)

Density (kg/m3)

Standard deviation

Time constant (s)

Angle
Temperature coefficient of resistance (1/◦C)

xvii

Roman Symbols

A

CD

Cp

D
dU∗/dx∗

dU∗/dy∗

E

(cid:126)F

Gr

h

H

I

k

L

˙m

M

ˆn

N

N u

P

Description

Area (m2)

Discharge coefficient

Specific heat (J/kgK)

Diameter (m)

Uniform horizontal velocity gradient (imposed along
the length of a TTA cell)

Uniform vertical velocity gradient (imposed along
the height of a TTA cell)

Voltage (V )

Force vector (N)

Grashof number

Heat convection coefficient (W/m2K)

Height of cell (m)

Current (A)

Thermal conductivity (W/mK)

Length of cell (m)

Mass flow rate (kg/s)

Moment (N m)

Normal vector (m)

Number of samples

Nusselt number

Pressure (P a)

xviii

P r

˙q

(cid:126)r

R
R∗

Re

t

T

U

(cid:126)U

w

Prandtl number

Heat transfer over wire segment (kg/s3)

Position vector (m)

Resistance (Ω)

Dimensionless resistance

Reynolds number

Time (s)
Temperature (◦C)

Velocity (m/s)

Velocity vector (m/s)

Width of slit-jet opening (m)

Subscripts and Superscripts Description

0

a

in

max

mean

min

n

ref

u

w

Initial condition

Ambient property

Inlet condition

Maximum

Mean/average

Minimum

Nonuniform

Reference property

Uniform

Wire property

xix

CHAPTER 1

INTRODUCTION

1.1 Background

The thermal transient anemometer (TTA) is an instrument that measures mass or volume

flow over a discrete region. For uniform density with a fixed cross section, the mean velocity

is also determined. The TTA frame, which includes multiple interrogation cells, provides a

detailed mapping of the flow distribution spanning the interrogation region. The TTA frame

described here is applied for flow conditions in which the velocity is normal to the area of

interest. The TTA in this work is shown in Figure 1.1.

(a) TTA frame mounted on automobile radiator

(b) Individual TTA cell

Figure 1.1: Images of TTA

The TTA is intended to measure the mass flow rate distribution for applications with

large cross-sections, such as heat exchangers, gas turbine inlets, wind turbines, and pipe

conduits, among others. Most instruments used to measure velocity are intended to provide

a single-point measurement, and they need to be traversed over many points to resolve the

flow field over a cross-section, which may be tedious or impractical. In contrast, the TTA

1

frame is specifically designed to resolve the flow distribution over a large cross-section.

The TTA is comprised of two parts; the frame with individual cells and an electronic

control unit. The frame is subdivided into a grid containing several cells. The size of the

frame and its corresponding cells are determined based on the area of interest and the desired

length scale over which the velocity distribution needs to be resolved. Each cell contains a

sensing wire used to measure the total temperature dependent resistance when subjected to

the flow field. The sensing wire is strung in a multi-X pattern to recover an area-average

flow rate measurement.

The electronic control unit provides a heating current to elevate the temperature of the

sensing wire until it reaches a preset threshold resistance, RT . Then the heating current is
switched to a sensing current of 10 mA to record the resistance of the wire while it is allowed

to convectively cool by flow field. The resistance of the wire exhibits an exponential decay

[8],

R∗ =

R(t) − Ra
R0 − Ra

= e−t/τ

(1.1)

where R denotes the resistance of the wire, subscripts a and 0 refer to respective ambient

and initial (when the sensing current starts) resistances, and τ denotes the time constant

for resistance decay (proportional to temperature decay). The sensing wire resistance decay
is observed until the dimensionless resistance reaches a value of R∗ = e−1. The duration of
resistance decay to this point defines the time constant.

The TTA is typically calibrated by measuring the time constants for a set of uniform

velocities. The mean velocity and measured time constant are related by the calibration

equation [8],

= A ∗ U B + C

1
τ

(1.2)

where A, B, and C are calibration constants. Once a TTA cell is calibrated, the spatially

averaged velocity, U, can be inferred from the measured time constant, τ. Using this strat-

egy, the average velocity over each cell is evaluated, providing a comprehensive velocity

distribution over the area of the frame.

2

1.2 Motivation

Internal combustion engines are found in transportation vehicles such as automobiles.

They are used to convert chemical energy (through combustion of a fuel and oxidizer) to

work. These engines produce heat from the combustion process, but require a controlled

temperature environment to avoid damage and maintain a high-performance level.

In automobiles, the excess heat is addressed with the cooling system. Generally, a liquid

is circulated through the engine, carrying the excess heat from the engine to the radiator

assembly. This assembly consists of the radiator with an attached shroud and fan. As air

passes through the radiator, fins are used to assist in the convective dissipation of heat from

the liquid to ambient air. The cooled liquid is then returned to the engine. Often, vehicles are

moving at fast enough speeds to provide a sufficient amount of airflow through the radiator

to dissipate heat from the coolant. However, at high ambient temperature conditions or low

vehicle speeds, a fan is used to draw in excess air through the radiator.

Knowing the magnitude and distribution of airflow through the radiator is necessary for

analyzing the cooling performance. One method for improving the cooling system is to opti-

mize the design of the fan or shroud to create more homogeneous airflow at the appropriate

operating condition. This requires a detailed understanding of the air passing through the

radiator. The TTA is an instrument well suited to measure the airflow distribution through

a radiator with and without a shroud. The thin frame of the TTA fits between the exit plane

of the radiator and shroud with minimal blockage of the radiator flow area. In doing so, the

exiting flow is minimally disrupted.

1.3 The Present TTA Description

The TTA frame used in this work is designed to span the area occupied by a stock

automobile radiator. The frame is fabricated from stainless steel with outer dimensions of

0.698 m x 0.981 m. This area is subdivided into a 6 x 4 grid containing 23 cells (the top

left cell is omitted for mounting purposes) to provide a detailed survey. Each cell has inner

3

length and height dimensions of 154 mm x 166 mm. The sensing element is a 1.6 m long,

0.2 mm diameter tungsten wire, chosen for its high temperature coefficient of resistance,

making it sensitive to temperature changes. Garolite rods serve as tether points to secure

the sensing wire to the edge of the frame and provide electrical and thermal insulation from

the stainless steel. The garolite rods measure 4.5 mm in diameter and are placed 36 mm

apart. Teflon spacers measuring 6.5 mm in diameter are added where the wire crossed at

the ‘X’, to prevent radial conduction. Terminal blocks are used to connect the endpoints of

the sensing wire to the electrical wires.

The electrical control unit is supplied by Sakor Technologies Inc. It is used to supply the

heating current to the sensing wires and to record the transient resistance. Upon operation

of the TTA, the control unit supplies a heating current of 2 A to the sensing wire for a

specified duration of time, called the pulse time. The current is then switched to the 10 mA

sensing current to record the resistance during the decay period. The time constant, τ, is

determined within the program based on Equation 1.1 at the end of the cooling period.

The control unit is accessed through a LabView program installed on the PC. From the

program, the user can specify the specific row(s) of interest and adjust the pulse time and/or

duration of the cooling period. The resulting data in the form of the time constant, velocity,

and/or temperature can be recorded from within the program.

1.4 Prior Work

The TTA was first introduced by Foss et al [8]. A later publication, Foss et al [7], explored

the ambient temperature and free stream turbulence effects on the TTA. The calibration
(with ambient temperature, Ta = 30◦C) was used to determine the mean velocity when the
TTA was subjected to elevated ambient temperatures for measurements (Ta,cal ≤ Ta,meas).
It was found that the room temperature calibration could be used to adequately measure the
velocity magnitude when the free stream temperatures of Ta,meas = 50◦C, 70◦C, 100◦C were
present. Based on results from the ambient temperature exploration, Foss also concluded

4

that the radiation effects did not influence the heat transfer of the TTA. The freestream

turbulence was evaluated with controlled disturbance levels. It was found that the TTA was

insensitive to disturbances in the approaching flow. In these conditions, the TTA was found

to maintain the 1/τ = f (U ) relationship established after calibration.

In the M.S. thesis by Leung [11], the radiator in application was studied using the TTA.

During this stage the present TTA was fabricated. Leung introduced the question of how

the TTA would perform under nonuniform flow distributions. This thesis attempts to build

upon that framework to answer the question.

1.5 Objectives

Previous investigations have demonstrated confidence in the TTA as a measuring tool

when free stream turbulence and radiation effects are present, but have not addressed con-

cerns when the velocity distribution is nonuniform. Practical applications suggest the pos-

sibilities of nonuniform velocity distributions in the flow fields of interest. The present in-

vestigation establishes a parameter space in which the TTA can accurately measure uniform

and nonuniform flow using the uniform calibration.

5

CHAPTER 2

EXPERIMENTAL FACILITY AND MEASUREMENT TECHNIQUES

2.1 The Test Facility

The present investigation is conducted in the Axial Fan Research and Development

(AFRD) facility at Michigan State University. This vertical wind tunnel provides a con-

stant, uniform velocity flowing in the downward direction. In previous investigations, the

facility was utilized to study axial fans, but the design accommodates a wide variety of ge-

ometries. The large inlet allows for convenient mounting of the TTA and radiator in the

various installation conditions. Features of the AFRD facility are outlined in Figure 2.1.

(a) Schematic of interior

(b) Image of exterior

Figure 2.1: Axial Fan Research and Development facility

The vertical wind tunnel transports air from above the AFRD into the upper receiver,

via the inlet. The air is driven by the auxiliary fan, with an adjustable throttle plate (F) to

control the mass flow rate. Air enters the upper receiver and is directed to the lower receiver

through the nozzles (A) on the north and south end of the facility. After passing through

6

(cid:88)

(cid:90)

(cid:16)

(cid:17)(cid:16)(cid:126)U · ˆn
(cid:17)

the nozzles, turning vanes (B) direct the air back to the inlet of the fan (B). The two turning

vanes are used to measure the net moment of momentum flux using force transducers (C).

A vertical shaft within the upper receiver (E) can be used to mount axial fans. Morris et al

[13] provide a detailed description of the AFRD facility.

The AFRD introduces a unique measurement system for the mass flow rate, using the

net moment of momentum flux. The incoming air passes through the nozzles and undergoes
a 90◦ turn across the turning vanes. The turning vanes are supported by a knife-edge pivot
to provide the net moment of momentum flux [13],

M = (cid:126)r × (cid:126)F =

(cid:126)r × (cid:126)U

ρ

(2.1)

where (cid:126)r represents the radius from a point on the pivot, (cid:126)F represents the measured force, (cid:126)U

represents the fluid velocity, ˆn represents the normal vector, and CS is the control surface.

CS

Features of the system are shown in Figure 2.2.

Figure 2.2: Schematic representation of the net moment of momentum flux measuring ap-
paratus

The force transducers, located on the opposite edge of the turning vanes, measure the

force from the incoming air, which is proportional to the mass flow rate.

7

2.2 Measurement Techniques and DAQ

Several measurement techniques are available to measure the mean velocity or mass flow

rate. While the thermal transient anemometer is one such method, another independent

measurement is needed for the calibration of the TTA and for reference. Other measuring

techniques utilized in the present study include: (i) the force transducers in the AFRD for

a mass flow rate measurement, (ii) a hot-wire anemometer for local velocity measurements,

and (iii) a pitot probe for local velocity measurements. Methods (i) and (ii) are discussed

in Sections 2.3 - 2.4, as they require an instructive calibration process. The pitot tube in

combination with a pressure transducer or manometer does not require such calibration and
is accurate within ±0.3% [14].

It is noted that only the force transducers provide a direct mass flow rate measurement,

and the mean velocity can be inferred with knowledge of the cross-sectional area and density.

The pitot probe and hot-wire anemometer provide a direct local velocity measurement.

The air density is acquired using the barometric pressure and temperature (converted to

density using P = ρRT ). The barometric pressure is acquired through the Lansing airport

(LAN) hourly pressure readings. The altitude in the test facility is understood to be the

same as that of the airport, making it a reasonable source for the barometric pressure. The
temperature is based on ambient conditions (typically 24◦C ≤ Ta ≤ 26◦C). The pressure is
measured using an MKS Baratron capacitance manometer, with an uncertainty of ±0.25%
in a 10 V signal range.

Data is acquired using the LabJack Pro T7 board. The board has a 16-bit analog to digital
conversion with a ±10 V range and is controlled through a program installed on the PC.
The LabJack Pro is utilized for data acquisition (DAQ) in which the pressure transducer,

strain gauges (north and south), and CTA anemometer (for hot-wire measurements) are

connected. Data acquired with the board is taken over a time period (typically between

30 – 60 seconds) at a scan rate of 20 Hz, then averaged in post-processing to provide a

time-averaged measurement.

8

2.3 The Force Transducers

The force transducers are constructed with a proving ring, each containing four strain

gauges fastened to create a Wheatstone bridge circuit. The force transducers are utilized

for the mass flow rate measurements within the AFRD facility. The established relationship

between the measured force (as a voltage) and the mass flow rate is determined after cali-
bration. The uncertainty in the strain gauges is ±0.5% and ±0.4% for the north and south
strain gauges respectively [13].

2.3.1 The Slit-Jet and its Discharge Coefficient

The calibration of the strain gauges require a slit-jet orifice for proper measurement. The air

passing through the slit-jet resembles a nominally steady, incompressible, inviscid flow (in an

otherwise viscous flow), wherein the Bernoulli equation can be utilized for the determination

of velocity [14]. That is,

U =

(cid:115)

2∆P

ρ

(2.2)

where ∆P is change the pressure (from atmosphere to upper receiver) and ρ is the density

of the air.

The slit-jet consists of two identical nozzle plates, of length L, in planar position with

the opening or ‘slit’, of width w. The nozzles are placed a distance of w apart such that
L/w (cid:29) 1. The thickness of the nozzle is very small in proportion to its length, so as to
maintain two-dimensional flow characteristics.

The vena contracta describes the point of maximum velocity and occurs downstream of

the slit opening. For air, this distance is approximately 1.5w downstream of the opening.

The calculated velocity in Equation 2.2 refers to the vena contracta velocity.

Potential flow analysis suggests that the discharge coefficient, CD – the ratio which
compares the mass flow rate at the end of the nozzle to the mass flow rate of an ideal nozzle
– is a value of ≈ 0.611. The discharge coefficient is of interest for mass flow rate calculations

9

in nozzles particularly, where the mass flow rate is then given by [14],

˙m = ρU ACD

(2.3)

where U refers to the velocity calculated using Equation 2.2 and A is the area of the slit-jet

opening.

The slit-jet used in calibration is comprised of two sets of nozzles fabricated from 1.5

mm (nominally 1/16”) thick stainless steel plates with L x w to be 14 cm x 100 cm. The

nozzles are supported by thin (1.5 mm wide, 12.7 mm deep) ribs spaced 2.54 cm apart at the

separation lip to ensure the required planar condition. The nozzles rest on a piece of 1.25

m x 1.25 m medium-density fiberboard (MDF), with a cutout to clear the nozzles and ribs.

Two pieces of 35 cm x 1.25 m sheet metal are placed vertically on either side of the slit-jet

as guidance rails, to ensure incoming air only in the y-direction. Two pieces of 14 cm x 100

cm sheet metal are placed to cover the remainder of the MDF for smooth airflow transition.

The slit-jet setup for the force transducer calibration is in Figure 2.3.

(a) Schematic of setup

(b) Image of setup

Figure 2.3: Slit-jet nozzle mounted at AFRD inlet for calibration of force transducers

2.3.2 Computational Fluid Dynamics (CFD) Analysis on the Discharge Coeffi-

cient

Although close, the slit-jet utilized in calibration does not provide perfectly inviscid flow.

Attempts to quantify the expected discharge coefficient for mass flow rate calculations are

done using computational software. Ansys Fluent software is utilized for CFD analysis.

10

The Fluent model consists of a two-dimensional geometry (simplified to two dimensions

due to uniform flow in the x-direction) matching the dimensions of the fabricated slit-jet.

The length, L, is 1 m, with a thickness of 1.5 mm. The slit width, w is 140 mm. The induced

air coming from the atmosphere, is assumed to come uniformly from all sides, thus modeled

by a semi-circle (radius equivalent to 1.07 m). The exit is made far enough away so as to

analyze the jet profile downstream (3 m away downstream of slit-jet). The modeled slit-jet

is shown in Figure 2.4. Note that the velocity flows ‘downward’ in the z-direction.

Figure 2.4: CFD model of slit-jet

No-slip boundary conditions are implemented at the walls and slit-jet. The velocity is

defined incoming in the normal direction from the semi-circular ‘atmosphere’. This creates

a sink around the opening of the slit-jet.

The discharge coefficient, CD, is calculated based on the following equation,

CD =

πDUin
2Umaxw

(2.4)

where D is the diameter of the ‘atmosphere’ (semicircle representative of atmosphere), Uin is
the inlet velocity (normal to semicircle as defined within Fluent), and Umax is the maximum
or vena contracta velocity (determined from Fluent solution). The discharge coefficients

calculated are a function of velocity are shown in Figure 2.5.

11

Figure 2.5: Discharge coefficient calculated using Fluent for various maximum velocities

The inability of the streamline to make abrupt turns is a distinguishable trait which is

visible in the CFD results, following proper setup. As the flow approaches the opening,

the velocity should gradually increase as a result from the interfering nozzles. For this

reason, a vertical (z-direction) velocity field is modeled in Fluent and compared to hot-wire

measurements for validation of the Fluent analysis.

For the supporting measurements, the hot-wire is mounted on a digital height gauge to

take a vertical survey of the flow in 1 mm increments. The height gauge is positioned out

of the jet path so as to not disrupt hot-wire readings. At a distance of approximately 2

mm away from the edge of the nozzle (laterally), the vertical survey is taken to assess the

profile of the turning flow. Starting at a vertical height approximately parallel to that of
the slit-jet (± 0.5 mm), the hot-wire is traversed upward a distance of 7 mm for a total of 8
measurements. This process is repeated for two different flow conditions with corresponding

maximum velocities, Umax. Note that only one nozzle is evaluated, as it can be assumed
that the velocity profile is the same for the other nozzle due to symmetry. The setup is

illustrated in Figure 2.6.

12

05101520250.60.640.680.72(a) Hot-wire placed 2 mm
away from slit-jet nozzle

(b) Hot-wire mounted on dig-
ital height gauge

Figure 2.6: Hot-wire setup for CFD validation of discharge coefficient

The vertical velocity component is extracted from the Fluent simulation and compared

to the hot-wire measurements in Figure 2.7. For the two inlet settings (20 and 23 m/s)

with respective maximum velocities, the hot-wire results from the vertical survey are in

reasonable agreement with the Fluent analysis so as to proceed with the determined discharge

coefficients.

(a) Inlet condition with maximum velocity of 20
m/s

(b) Inlet condition with maximum velocity of 23
m/s

Figure 2.7: Comparison of hot-wire and Fluent velocity vertical survey

13

00.511.50.50.60.70.80.9100.511.50.50.60.70.80.912.3.3 Procedure for Calibration

After confirming the discharge coefficients as determined in Fluent, the force transducers are

calibrated. The relationship between the voltage of the strain gauges (proportional to the

force) and the mass flow rate is established during the calibration.

Fifteen inlet conditions (inlet flow rates) are measured in the calibration process. The

pressure drop, barometric pressure, temperature, and voltages as measured by the north and

south strain gauges, are recorded for each inlet condition. This process is repeated for each

inlet condition.

Equation 2.3 is utilized for the mass flow rate calculation. The area of the slit-jet is 0.14
m2, while the respective velocity is determined from the Bernoulli Equation (Equation 2.2)

based on the pressure drop between atmosphere and upper receiver. For the calibration, it

can be assumed that the mass flow rate is split evenly between the north and south strain

gauges – that is each strain gauge measures half of the mass flow rate passing through the

AFRD. The calibration curve for the strain gauges is shown in Figure 2.8.

Figure 2.8: North and south force transducer calibration

14

0.511.522.533.544.500.511.522.52.3.4 Final Notes on the Force Transducers

The unique measuring strategy of the force transducers provides a mass flow rate measure-
ment following calibration. The calibration is limited within 0.08 kg/s ≤ ˙m ≤ 4.27 kg/s.
This equates to a velocity of roughly 40 m/s for the nozzle area (0.14 m2) and 5 m/s for the
experimental inlet area (0.68 m2). Therefore the maximum mass flow rate measured with

the experimental inlet (approximately 8 kg/s) cannot be precisely evaluated using the force
transducers, as it exceeds the calibration range. Additionally, at high mass flow rates (∼4
kg/s), the uncertainty in the measurements is approximately ±0.5 V or ±10% error in mass
flow rate.

Presumably, the force transducers in the AFRD favor a smaller inlet area in combination
with lower mass flow rates ( ˙m ≤ 4 kg/s) for accurate measurements. For this reason, it
is decided to measure the reference velocity using other techniques. To preserve the strain

gauges, a block is placed underneath the turning vanes to prevent deformation at high mass

flow rates.

2.4 Hot-wire Anemometry

A Dantec MiniCTA (constant temperature anemometer) control unit is utilized to pro-

vide a constant temperature to the hot-wire probe to measure the velocity. The operating

principle of a hot-wire anemometer is similar to that of the TTA – it measures the convective

heat transfer of the wire related to the fluid velocity.

The hot-wire probe is shown in Figure 2.9. The probe consists of prongs holding a 5

µm diameter wire with a resistance of 0.4 Ω. The thin wire allows the hot-wire to measure

velocity fluctuations at fine scales.

15

(a) View of probe sensor

(b) Entire probe

Figure 2.9: Hot-wire probe

2.4.1 Procedure for Calibration

Standard experimental techniques require the hot-wire to be calibrated each time before

measurements. The calibration is good for about 3-4 hours, after which it should be re-

calibrated again. The relationship between the hot-wire voltage and the velocity follows the

hot-wire calibration equation [12],

E2 = A + BU 0.43

(2.5)

where E is the voltage and A and B are constants established after the calibration process.

The hot-wire is calibrated in the facility illustrated in Figure 2.10. The facility includes

a blower, to provide an inlet base condition and slit-jet exit, where the hot-wire is placed.

The blower provides velocities at the inlet via an adjustable throttle plate.

16

(a) View of facility and blower

(b) View of slit-jet exit

Figure 2.10: Hot-wire calibration facility

After powering on the CTA and waiting 30 minutes to warm up, the hot-wire sensor is

placed in the calibration facility at a distance of approximately x/w = 1.5 away from the

slit jet. This is to ensure the hot-wire measures the velocity directly related to the plenum

pressure (see Equation 2.2). The sensor is mounted in the same orientation with respect
to the flow (0◦ or 90◦). The throttle on the blower is adjusted to vary the inlet velocity.
Selected inlet velocities (between 8 - 16 velocities) well within the range of expected velocities

(typically between 1 to 25 m/s) are used. Measurements for both the hot-wire and plenum

pressure are taken over a 30 second period and recorded with the LabJack Pro for each inlet

velocity. A least-squares curve-fit is fit to the data to follow Equation 2.5.

It is important to note that while the slit-jet and its discharge coefficients are necessary in

determining the mass flow rate for the strain gauge calibration in Section 2.3, the discharge

coefficient is not necessary in the hot-wire calibration. This is because the hot-wire mea-

sures the velocity instead of the mass flow rate, which can be computed using the Bernoulli

equation (Equation 2.2).

An example calibration is shown in Figure 2.5. Note, that the hot-wire calibration curve

varies slightly with each new calibration. For the calibration illustrated, the constants A and

17

B are 1.73 and 1.09 respectively.

Figure 2.11: Sample hot-wire calibration curve

18

11.522.533.5433.544.555.566.5CHAPTER 3

CALIBRATION OF TTA

The TTA is calibrated in the AFRD facility. The calibration is used to establish a relationship

between the time constant for resistance decay, τ, and the passing velocity, U, for each cell,

as noted in Equation 1.2. Once calibrated, the TTA can be used to infer a velocity based

on the measured time constant, τ.

Measurements using the TTA rely on an accurate and robust calibration. It is suggested

that the entire TTA frame be calibrated every few months when not in use. This is due

to the sensitivity of the sensing wires and connectors that can experience small changes in

ambient resistance over time.

3.1 Procedure for Calibration

During calibration the TTA is supported by a piece of medium-density fiberboard (MDF).

The MDF is placed at the inlet of the AFRD and a hole is cut to redefine the inlet area

to match the dimensions of the TTA (excluding the outer frame), that is 0.96 m x 0.68 m.

The outer frame of the TTA then rests on the MDF. Quarter-rounds are placed around the

perimeter of the TTA to uniformly guide air to the TTA. A hot-wire is used to measure the

velocity. The hot-wire sensor is placed 5.08 cm (2”) above the TTA sensing wire. In this

position, the hot-wire measures the velocity of the approaching flow to the sensing wire. The

setup is shown in Figure 3.1.

The throttle plate on the AFRD is adjusted to vary the inlet velocity between 0.1 to

13.1 m/s. Seventeen measurements (between 15-20 measurements is recommended) spaced

evenly within this range are used for the calibration. At each velocity, ten measurements are

taken with the TTA (pulse time of 0.3 seconds, duration of 3 seconds). The average of the

ten measurements (excluding any outlying data) is determined in post processing.

19

(a) TTA placed on MDF with quarter-rounds at inlet

(b) Hot-wire probe sensor placed 5.08 cm
above the plane of the TTA sensor wires

Figure 3.1: TTA calibration setup at inlet of AFRD facility

3.2 Calibration

Since each of the 23 cells in the TTA frame has a unique calibration curve, each cell is

assigned a number for reference. The number assignments for the TTA cells is shown in

Figure 3.2. Note that the dimensions of the frame and cells are not to scale.

20

Figure 3.2: TTA cell number assignments

Using the hot-wire velocity measurements the TTA is calibrated according to Equation
1.2 (1/τ = A∗ U B + C). The calibration constants A, B, and C for each cell are determined
using a least-squares curve-fit for the time constant data points. The calibration curve for

cell 1 is shown in Figure 3.3 (See Appendix A for all cell calibration curves). The calibration

constants for each cell are listed in Table A.1 in Appendix A.

Figure 3.3: TTA calibration curve for cell 1

21

02468101201234563.3 Uncertainty

The standard deviation between the calibration fit and the data points is used to estimate

the measurement uncertainty. The standard deviation, σ, is defined as [7],

(3.1)

(cid:118)(cid:117)(cid:117)(cid:116) 1

σ =

N(cid:88)
(Ucalc − Umeas)2

i

N − 1

i

where N is the number of samples (N = 17, for the total velocity samples taken).

The uncertainty for all the cells is shown in Table 3.1.

Cell Number Uncertainty (m/s)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

0.3317
0.2290
0.3176
0.4597
0.3797
0.0656
0.1251
0.0812
0.1410
0.1794
0.1004
0.1055
0.1721
0.1324
0.1040
0.1121
0.1855
0.1340
0.3656
0.1926
0.2141
0.1687
0.1624

Table 3.1: Calibration uncertainty for each cell

22

CHAPTER 4

NUMERICAL SIMULATIONS

A significant portion of the TTA investigation includes computational analysis and simula-

tion of the sensing wire, later supported by experimentation (see Chapter 5). The compu-

tational simulation is utilized to study the convective heat transfer effects of uniform and

nonuniform velocity profiles on the response of a TTA cell. A TTA cell is calibrated with a

uniform velocity field and thus the temperature and thermophysical properties of the sens-

ing wire are uniform. A concern arises when the TTA cell is subjected to a nonuniform

velocity field, since the sensing wire temperature and thermophysical properties will also be

nonuniform along the length of the wire. When measuring mean velocity in the presence

of a nonuniform velocity field, it is of interest to understand the error introduced by tem-

perature and thermophysical property nonuniformities. This understanding is garnered by

solving a transient energy model for the sensing wire that is developed within a MATLAB

computational platform.

4.1 Model and Assumptions

A schematic depiction of a TTA cell is shown in Figure 4.1. Each cell consists of a single

sensing wire, strung across the entire cell in a multi-X pattern; therefore the wire position,

s, is defined with respect to the spatial coordinates (x, y, φ) of the cell.

A transient heat transfer model is used to compute the temperature distributions along

the sensing wire for various flow conditions. The thermal energy conservation equation for

the wire is [11],

1

∂k(s, t)

∂Tw(s, t)

ρCp

∂s

∂s

+

k(s, t)
ρCp

∂2Tw(s, t)

∂s2

− 4h(s, t)
ρCpD

(Tw(s, t) − Ta) + 16

=

I2γ(s, t)
ρCpπ2D4
∂Tw(s, t)

∂t

(4.1)

where s is the position along the wire (see Figure 4.1) and Tw is the temperature of the wire.

23

Figure 4.1: Schematic representation of a TTA cell

The derivation of the energy equation is in Appendix B.1.

The transient model is used to simulate the transient variation of temperature during two

different time periods. The first period is the heating period, in which a controller is used

to pass 2 A of current through the wire for heating. The resistance and temperature of the

wire are computed at each time step (∆s=1 ms). Once the resistance reaches the threshold

resistance at RT = 5Ω, the current is switched to a sensing level of 10 mA and the second
period begins. The temperature of the wire decays due to convection by the passing air

flow. This period is referred to as the cooling period and continues until the wire reaches a
dimensionless resistance (defined by Equation 1.1) of R∗ = e−1. The time during the second
period for R∗ to reach e−1 is the time constant. Computational methods for determining
the time constant are discussed in Section 4.2.2.

For both time periods, Equation 4.1 is solved explicitly with a forward marching scheme

in time and space. The spatial step, ∆s, is a value of 1 mm (∆s/D = 5) and the time step,

∆t is a value of 1 ms; these increments are selected to maintain stability. The MacCormack

predictor-corrector method [2] is used to obtain second order accuracy. The following as-

sumptions are inherent in the model. Heat conduction is neglected in the radial direction.

This is justified due to the very low Biot number. Thermal expansion and contraction of

24

the wire is neglected since the wire temperature does not exceed 250◦C. Heat exchange with
the garolite rods, Teflon spacers, and electrical connectors is neglected. The endpoints of

the wire are assigned adiabatic boundary conditions. The initial condition sets the wire

temperature to that of the ambient.

4.1.1 Thermophysical Properties

The temperature of the wire, calculated from Equation 4.1, depends on several temperature

dependent thermophysical properties of the air and the tungsten wire. The variables ρ, Cp,
D, and I – the density (of the tungsten wire), specific heat (of wire), diameter (of wire), and

electrical current respectively are taken to be constant. The density and specific heat can

be taken as constants since there is little variation over the temperature range of interest
(20◦C ≤ Tw ≤ 250◦C). These values are listed in Table 4.1. The remaining properties in
Equation 4.1 such as k (thermal conductivity of tungsten), h (heat convection coefficient),

γ (resistivity of tungsten) are taken to be temperature dependent.

Property

Cp (tungsten)

ka (air)

Ra
Ta
Tref
γref

ρ (tungsten)

ζ

Value

2.85 Ω
24◦C
30◦C

133.15 J/kgK

25.4 ∗ 10−3 W/mK

5.6 ∗ 10−8 Ωm
19.3 ∗ 103 kg/m3
4.403 ∗ 10−3 1/◦C

Table 4.1: Constant properties used in simulation

The properties of the tungsten sensing wire (k, γ) are evaluated at the respective tem-

perature of the wire while the properties of air (pertaining to h) are evaluated at the film

temperature (Tf = (Ta +Tw)/2). The respective thermal properties are provided from tables
in two Heat Transfer texts [5] and [10]. The tables of properties are used to create a best-

fit equation for each property to describe it as a function of temperature. This is done in

25

lieu of interpolation. The relations for air and tungsten properties (specific heat, kinematic

viscosity, Prandtl number, and thermal conductivity) are shown in Appendix B.2.

4.1.2 Sensing Wire Resistance

The sensing wire resistivity is evaluated locally at the wire temperature Tw(s, t). The resis-
tivity of tungsten characterizes the material response to the electrical current. It is used in

the heat generation term in the energy equation (Equation 4.1) and for determining the resis-

tance (see Equation 1.1). The resistivity varies linearly with temperature and is represented

as,

γ(s, t) = γref

(cid:2)1 + ζ(Tw(s, t) − Tref )(cid:3)

(4.2)

where ζ is the temperature coefficient of resistance. The value of ζ is shown in Table 4.1.

The resistance of the tungsten wire is an integral quantity over the length. The wire

resistance is computed as [11],

(cid:90) L

γ(s, t)ds

R(t) =

0

A

(4.3)

where A refers to the cross-sectional area of the wire, that is A = πD2/4.

Best-fit polynomial equations based on the tables for tungsten [10] are utilized for the

thermal conductivity and specific heat computations. A 6th order polynomial is fit to the

thermal conductivity scheme while an 8th order polynomial is fit to the specific heat of

tungsten. Note that the specific heat of tungsten is a constant value based on the ambient

temperature and the best-fit polynomial is utilized to determine that condition, whereas

thermal conductivity is not a constant value. The exact equations and fits are shown in

Appendix B.2.

4.1.3 Air Characteristics

The properties of air are computed at the film temperature. The boundary layer temperature

of the air passing over the wire during convection can be assumed as the average of the

26

ambient and wire temperatures, Tf = (Ta + Tw)/2.

The convective heat transfer coefficient over the wire is,

h(s, t) =

kaN u(s, t)

D

(4.4)

where ka refers to the thermal conductivity (of air) at ambient conditions and N u refers to
the Nusselt number.

The Nusselt number is characteristic of the subject geometry and convection method.

Several correlations exist to describe forced convection over a wire (or a long, thin cylinder).

The chosen correlation used in the simulations is a modified version of the Hilpert correlation

[5] for flow over a cylinder. The Hilpert correlation suggests different values for c and m

in Equation 4.5 based on the Reynolds number regime during operation. However, the

suggested constants are slightly modified to fit the TTA calibration (see Section 4.2.1). The

Nusselt number is,

N u(s, t) = cRe(s, t)mP r(s, t)1/3

(4.5)

where c and m are the constants defined by the Reynolds number regime. Re and P r are

the Reynolds and Prandtl numbers respectively. See Section 4.2.1 for determination of the

constants c and m.

The Reynolds number for flow over the sensing wire is defined as,

Re(s, t) =

U (s, t)D

ν(s, t)

(4.6)

where ν is the kinematic viscosity of the fluid at the film temperature.

After combining Equations 4.5 and 4.6, the heat convection coefficient is rewritten as,

h(s, t) =

kacU (s, t)mDm−1P r(s, t)1/3

ν(s, t)m

.

(4.7)

Best-fit polynomials based on tables [5] for kinematic viscosity and Prandtl number are

used to describe the air properties. The corresponding equations and fits are shown in

Appendix B.2.

27

4.2 Simulation Considerations

4.2.1 Nusselt Number Determination

For the numerical simulations, the constants in the Nusselt number equation, c and m are

modified to fit the TTA calibration for selected cells (cells 13 - 15). These cells are selected

because they are used in experimentation with the velocity gradient (see Chapter 5.5). The
Reynolds regime of the modified Nusselt number is valid for 1 ≤ Re ≤ 185.

The determination of the constants is done through an iterative process. The initial

guess is based off the analytical time constant for uniform flow (see Appendix B.3 for the

derivation),

1/τ = ln (cRem) = m ln(Re) + ln(c).

(4.8)

The calibration provides both the time constant and the uniform velocity (thus the

corresponding Reynolds number). Plotting the inverse time constant against the natural

log of the corresponding Reynolds numbers determines the initial values for c and m as the

slope and intercept. The iterative process then continues until there is reasonable agreement

between the calibration fit and numerical simulation.

The simulated calibration curve along with the TTA fit and data for cell 13 is shown in

Figure 4.2 (see Appendix A for cells 14 - 15). The constants for cells 13 - 15 along with the

calculated uncertainty (determined using Equation 3.1) are shown in Table 4.2.

28

Figure 4.2: Cell 13 experimental and simulated calibration

Cell Number

c

m

Uncertainty (m/s)

13
14
15

0.778
0.784
0.785

0.425
0.422
0.424

0.1579
0.1202
0.1897

Table 4.2: Constants in Nusselt correlation for cells 13 - 15

4.2.2 Numerical and Analytical Methods for Determining the Time Constant

Two methods for computing the time constant are available; numerical and analytical. In

the numerical approach, the dimensionless resistance from Equation 1.1 is used to compute
the time constant. This process involves plotting the dimensionless resistance, R∗, as a
function of time, to identify the rate of decay as the time constant (likewise the slope in the
evaluation of log(R∗) is also characteristic of the time constant). In the analytical approach,
the governing equation (Equation 4.1) is used to write the thermal properties as a function

of the time constant to directly solve for the time constant, τ.

29

0246810120123456For the simulations, the numerical approach is utilized to compute the time constant.

However, the validation of the simulation is done by computing the time constant for uniform

flow both numerically and analytically to ensure they are equivalent.

In uniform flow, the thermophysical properties along the wire are approximately constant,

thus the governing equation simplifies to,

1/τ = ln

(cid:18) 4h(t)

(cid:19)

ρCpD

.

(4.9)

The derivation of Equation 4.9 is in Appendix B.3.

Uniform velocities ranging from 0.1 to 15 m/s are simulated and the time constants

are determined numerically and analytically. This is shown in Figure 4.3. The calculated
percent difference between the numerical and analytical computations is nominally ±0.5%.
The small difference is due to the analytical time constant being evaluated at the final instant

only. The agreement in the numerical and analytical solutions serves as a validation of the

simulation.

Figure 4.3: Comparison of numerical and analytical methods of solving for the time constant

30

051015012345674.2.3 Natural and Forced Convection

Traditional heat transfer classifies convection as either natural (also referred to as free) or

forced, based on how the fluid motion is initiated. In forced convection the fluid motion is

initiated by an outside source such as a pump, moving body, etc. In the case of the TTA,

the velocity passing over from an outside source is forced. Natural convection is driven by

outside factors such as buoyancy (hot fluid rising while cooler fluids fall). Natural convection

is always present when there is a temperature gradient, however it is often neglected in the

presence of the more dominant forced convection. Cengel and Ghajar [5] suggest that natural

convection can be neglected when Gr/Re2 < 0.1, where Gr and Re represents the Grashof

and Reynolds number. This ratio, Gr/Re2, is referred to as the Richardson number.

The Richardson number for the TTA with velocities ranging from 0 to 15 m/s is shown

in Figure 4.4, where the threshold Richardson number for consideration of free convection
effects (Gr/Re2 = 0.1) is noted. For velocities ≤ 0.06 m/s, the Richardson number suggests
that both natural and forced convection should be considered. However, since the range of

interest for the TTA is between 0.1 m/s to 15 m/s, the effects of free convection are neglected

in the simulation.

31

Figure 4.4: Richardson number for velocities ranging from 0 m/s to 15 m/s

32

10-210-110010110-610-510-410-310-210-1100101PERFORMANCE OF TTA WITH LINEAR VELOCITY GRADIENTS

CHAPTER 5

The response of the sensing wire in a TTA cell when exposed to a linear velocity profile

(uniform gradient) is evaluated through numerical simulations and experimentation. The

TTA is calibrated with a set of uniform velocities, in which the temperature and thermal

properties along the wire are approximately uniform. With the imposition of a linear velocity

profile, the temperature and thermal properties along the wire are nonuniform, impacting

the temporal response of the sensing wire to the nonuniform flow. It is of interest to study

whether the TTA device subjected to nonuniform flow will return the correct mean velocity

using the uniform velocity calibration. The performance of the TTA device is characterized

by the error between the mean velocity it measures and that which is imposed, with and

without a velocity gradient.

5.1 Defining the Velocity Gradient

It is expected that nonuniformities in the flow will be more impactful on the TTA response

at low mean velocities than at higher mean velocities. Thus, it is of interest to scale the

velocity gradient to obtain a dimensionless parameter to reflect the relative strength of

the gradient. A linear velocity profile is considered such that there is some minimum and

maximum velocity at either end of the cell, with some mean velocity (Umean = (Umin +
Umax)/2). This mean velocity is compared to the inferred velocity provided by the TTA
measurement. The dimensionless uniform velocity gradient, dU∗/dx∗, is defined as,

dU∗
dx∗ =

Umax − Umin

Umean

.

(5.1)

The derivation of the gradient is shown in Appendix B.4.1. For the present TTA frame,

each cell contains the same length sensing wire, of 1.6 m. A schematic of the linear velocity

profile is shown in Figure 5.1. Note that the velocity profile varies uniformly in the x-

33

direction; there is no variation in the y-direction. Therefore, the portion of the wire which

is strung vertically does not vary in velocity magnitude.

Figure 5.1: Schematic of linear velocity profile imposed on the TTA cell

Mean velocities ranging from 0.1 to 15 m/s with dimensionless gradients ranging from 0

to 1.9 are simulated for cells 13 - 15. The range of gradients simulated correspond with the

measurement capabilities of the TTA; reverse or negative flow is not considered since the

TTA cannot determine the flow direction. It should be noted that dimensionless gradients

exceeding 1.0 are considered extreme and are not expected to be encountered in typical

applications.

5.2 Simulating a Linear Velocity Gradient

The effects of the linear velocity gradient are explored for cells 13 - 15, but for illustration

purposes the figures presented in this section are representative of cell 13.

To observe how the gradient affects the resistance decay and time constant, mean veloc-

34

ities of 1, 5, and 10 m/s with and without gradients of 0.5, 1.0, and 1.9 are simulated. The

temperature decay for the following scenarios is shown in Figure 5.2. For a gradient of 0.5

(Figure 5.2a), the wire decay is slightly faster with a gradient than without. As the strength

of the gradient increases to 1.0 and 1.9, the wire starts to decay at a slower rate (Figures

5.2b - 5.2c). This is most evident with the gradient of 1.9 in Figure 5.2c. This generally

holds true regardless of mean velocity.

The computed time constants, inferred velocities, and percent differences for the simu-

lated flow conditions in Figure 5.2 are listed in Table 5.1. The percent difference refers to the

difference between the inferred velocity from the TTA calibration (from the time constant

and Equation 1.2) and the mean velocity imposed in the simulation.

In the existence of smaller gradients (demonstrated by a gradient of 0.5), the inferred

mean velocity is nominally 1.25% higher than the simulated mean velocity for the cases of
1, 5, and 10 m/s. With the existence of larger gradients (dU∗/dx∗ ≥ 0.5), the percent
difference approaches 13% due to the under-prediction of the mean velocity. The higher

mean velocities are most affected by the strong gradient, as noted by the percent difference.

The percent difference ranges from 10.10% for the mean velocity of 1 m/s to 12.30% for the

mean velocity of 10 m/s.

35

(a) Gradient of 0.5

(b) Gradient of 1.0

Figure 5.2: Resistance decay of wire with and without various gradients for mean velocities
of 1, 5, and 10 m/s

(c) Gradient of 1.9

36

00.10.20.30.40.50.60.30.40.50.60.70.80.9100.10.20.30.40.50.60.30.40.50.60.70.80.9100.10.20.30.40.50.60.30.40.50.60.70.80.91Inverse

Time Constant

Mean Velocity

Inferred

(m/s)

Percent Difference

(%)

Mean Velocity

(m/s)

Gradient

1

5

10

0
0.5
1.0
1.9
0
0.5
1.0
1.9
0
0.5
1.0
1.9

(1/s)
1.89
1.90
1.88
1.81
3.75
3.77
3.72
3.57
5.04
5.06
4.99
4.78

1.01
0.98
0.89

5.06
4.92
4.44

-

-

-

10.12
9.80
8.77

1.34
1.90
10.10

1.28
1.54
11.24

-

-

-

1.16
1.94
12.30

Table 5.1: Time constants and computed velocities for uniform and nonuniform cases

The slow temperature decay with the existence of a velocity gradient is evident based

on the varying temperature distribution. Using the simulation, mean velocities of 1 and 5

m/s with gradients of 0.5, 1.0, and 1.5 are evaluated to observe the temperature distribution

during the cooling period. The temperature distribution along the wire at various time

steps is shown in Figure 5.3. The initial time stage (0 ms) represents the wire after it has

been heating and is about to begin the cooling process. The final time stage represents the
time at which R∗ = e−1, which varies depending on the case. Each time step is spaced
evenly apart. Areas of high relative velocity are in the ‘center’ of the wire, noted by lower

temperature values, while areas of low relative velocity are on either endpoint, noted by

higher temperature values.

In Figures 5.3a - 5.3b a gradient of 0.5 is simulated for mean velocities of 1 and 5 m/s

respectively. The effect of the dimensionless gradient is approximately the same for both

mean velocities simulated. At the initial time step, the temperature variation along the wire
(difference between maximum and minimum temperature at a given time) is 2.3◦C and 4.6◦C
for the mean velocities of 1 and 5 m/s. At the final time step, the temperature variation along
the wire for 1 and 5 m/s is 15.3◦C and 16.2◦C. At this gradient magnitude, the temperature

37

distribution along the wire takes an approximately linear profile as it cools for both mean

velocities. In Figure 5.3c, the mean velocity is 5 m/s with a gradient is 1.0. At this gradient,

the temperature takes a nonlinear distribution as it continues to cool, most evident in the
final time step. At the final stage, the temperature variation along the wire is 34.3◦C. This
effect is more pronounced as the gradient increases as shown in Figure 5.3d (mean velocity

of 5 m/s with a gradient of 1.5). The temperature distribution is immediately nonlinear,
with the final temperature variation being 57.9◦C. As the magnitude of the dimensionless
In the existence of strong
gradients increase, the total temperature variation increases.

gradients, the temperature distribution becomes nonlinear and the temperature variation

increases. This generally holds true for all mean velocities.

38

(a) Mean velocity of 1 m/s and gradient of 0.5

(b) Mean velocity of 5 m/s and gradient of 0.5

(c) Mean velocity of 5 m/s and gradient of 1.0

(d) Mean velocity of 5 m/s and gradient of 1.5

Figure 5.3: Temperature distribution along wire at subsequent time steps for various mean velocities and gradients

39

00.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.680100120140160180200220The percent error due to the uniform velocity gradient for all mean velocities (0.1 to

15 m/s) and gradients (0 to 1.9) is shown in Figure 5.4. The percent difference is noted

by the color, with blue being a low percent difference and yellow being a high percent

difference. For small gradients between 0.4 to 0.5, the percent difference is around 1% for all

mean velocities. The error increases as the strength of the gradient increases. At extreme

gradients between 1.5-1.9, the error goes from 4% to above 12%, with the higher mean

velocities having the largest error. The error starts to propagate when the dimensionless
velocity gradient surpasses a magnitude of 0.4 for most mean velocities (U ≥ 4 m/s).

Figure 5.4: Percent difference in TTA measurements for various mean velocities and gradients

The resistivity of the TTA sensing wire is temperature dependent. The resistivity varies

linearly with temperature and is used directly in the computation of resistance (Equation

4.3). For this reason, the resistivity profiles for a mean velocity of 5 m/s at various velocity

gradients (0, 0.5, 1.0, 1.5) are simulated. Contour plots of the resistivity profiles along the

wire during the cooling period are in Figure 5.5. When the velocity is perfectly uniform, the

resistivity profile is constant as observed and expected in Figure 5.5a. With a dimensionless

velocity gradient of 0.5, the resistivity profile is nominally linear, as seen in Figure 5.5b. At

40

246810121400.511.51.924681012this stage, the error is just above 1% for the mean velocity of 5 m/s. When the gradient

reaches 1.0 and 1.5, the resistivity profile is extremely nonlinear due to the imposed velocity

profile as seen in Figures 5.5c - 5.5d.

41

(a) Perfectly uniform case

(b) Gradient of 0.5

(c) Gradient of 1.0

(d) Gradient of 1.5

Figure 5.5: Resistivity along wire as it convectively cools for a mean velocity of 5 m/s with various velocity gradients

42

00.20.40.60.811.21.41.600.050.10.150.20.257.588.599.510-800.20.40.60.811.21.41.600.050.10.150.20.2577.588.599.510-800.20.40.60.811.21.41.600.050.10.150.20.2577.588.599.51010-800.20.40.60.811.21.41.600.050.10.150.20.2577.588.599.51010-85.3 Simulating a Linear Velocity Gradient Along the Height of the

TTA Cell

The velocity gradient, dU∗/dx∗, in Section 5.2, considers a velocity profile with varia-
tion along the cell length (horizontal velocity gradient). The same linear velocity profile is

considered with variation along the cell height instead of the length. This vertical velocity
gradient, dU∗/dy∗, is defined as,

dU∗
dy∗ =

(Umax − Umin)

Umean

.

(5.2)

The derivation of the vertical velocity gradient is shown in Appendix B.4.2. A schematic

of the vertical velocity gradient is shown in Figure 5.6.

Figure 5.6: Schematic representation of linear velocity profile imposed on the TTA cell
(varying along the height)

The same mean velocity and gradient range is considered (mean velocities ranging from

0.1 to 15 m/s, gradients ranging from 0 to 1.9). The velocity along the wire length, s, when

the horizontal and vertical gradients are imposed is shown in Figure 5.7 (mean velocity of

10 m/s, gradient of 0.5 simulated). Note that the maximum and minimum velocities are the

same, since the same magnitude gradient is imposed. The velocity along the wire when the

43

gradient dU∗/dy∗ is imposed, varies in accordance to the vertical positioning of the wire. It
reflects the multi-X pattern in which the wire is strung.

(a) Velocity gradient imposed along the length
of TTA cell (dU∗/dx∗)
Figure 5.7: Velocity along the sensing wire for a mean velocity of 10 m/s and gradient of 0.5

(b) Velocity gradient imposed along the height
of TTA cell (dU∗/dy∗)

Let ξ represent the gradient (in the horizontal or vertical orientation). For the TTA cell

(length of 154 mm and height of 166 mm), the relative velocity along the sensing wire varies

based on the gradient orientation. Consider a position along the sensing wire, s, such that,

0 ≤ s ≤ H

sin(φ)

(5.3)

where φ = 78.38◦. When a gradient, ξ, is imposed, the relative velocity, U, based on the
position along the wire, s, is,

Umin + ξ

Umin + ξ

U =

Umean

L

Umean

H

s cos(φ) horizontal gradient

s sin(φ)

vertical gradient

(5.4)

where the relative velocity at the position along the wire (when the gradients and mean

velocities are equivalent) is always larger when a vertical gradient is imposed than when

a horizontal gradient is. This indicates that there are larger velocity fluctuations within a

given segment of the sensing wire when a vertical gradient is imposed (see Figure 5.7). Note

that for a given mean velocity gradient, the minimum and maximum velocities across the

44

00.20.40.60.811.21.41.67891011121300.20.40.60.811.21.41.678910111213cell are equivalent for both horizontal and vertical positions. The relative velocities vary
between the minimum and maximum velocity (Umin ≤ U ≤ Umax).

The percent error due to the vertical velocity gradient for all mean velocities (0.1 to 15

m/s) and gradients (0 to 1.9) is shown in Figure 5.8. For small gradients, less than 0.4, the

percent difference is less than 1%. This error increases as the gradients increase to 1.9, where

the error approaches 24%. The percent error is higher when the velocity gradient is imposed

along the height of the TTA cell due to the pattern in which the sensing wire is strung and

the resulting velocity along the wire.

Figure 5.8: Percent difference in TTA measurements for various mean velocities and vertical
gradients

In Figures 5.9a - 5.9d horizontal and vertical gradients of 0.5 and 1.0 are simulated for

a mean velocity of 5 m/s. At a gradient of 0.5, the temperature distribution is linear for

the horizontal gradient case (as established in Section 5.2). The temperature profile for the

vertical gradient of 0.5 is nominally linear as shown in Figure 5.9b. At the final time step, the
temperature variation along the wire for the horizontal and vertical gradients are 15.3◦C and
17.5◦C respectively. As observed with the horizontal gradient, the temperature distribution

45

246810121400.511.51.904812162024starts to become nonlinear as the gradient increases. This is shown in Figure 5.9d, where the

vertical gradient is 1.0. For the horizontal and vertical gradients of 1.0, the final temperature
variation is 34.3◦C and 37.4◦C respectively. The larger temperature variation corresponds
with a higher percent difference for a given gradient and mean velocity as shown in Figure

5.8. This generally holds true for all gradients and mean velocities.

46

(a) Mean velocity of 5 m/s and horizontal gradient of 0.5

(b) Mean velocity of 5 m/s and vertical gradient of 0.5

(c) Mean velocity of 5 m/s and horizontal gradient of 1.0

(d) Mean velocity of 5 m/s and vertical gradient of 1.0

Figure 5.9: Temperature distribution along wire at subsequent time steps for various mean velocities and gradients

47

00.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.68010012014016018020022000.20.40.60.811.21.41.6801001201401601802002205.4 Correction Scheme

The imposition of a uniform velocity gradient on the TTA cell introduces error of 1% in

the mean velocity measurements when the gradient surpasses 0.4. This error reaches 24%

with a mean velocity of 15 m/s and extreme vertical gradient of 1.9.

A correction scheme, developed using the numerical simulations, is implemented to reduce

the error when large gradients are present. The nonuniform time constant can be decomposed

into a uniform component and an incremental components,

τn = τu + ∆τ

(5.5)

where subscripts n and u denote the nonuniform and uniform time constants. By quantifying

the value of the incremental component, ∆τ, the measured nonuniform component can

be used to determine the uniform component in Equation 5.5.

It is hypothesized that

incremental component, ∆τ is a function of the dimensionless gradient and mean velocity,

∆τ = f (ξ, U ). A proposed correlation scheme is,

(cid:104)
α1 ∗ U β1ξ2 + α2 ∗ U β2ξ + α3 ∗ U β3

(cid:105)−1

(5.6)

∆τ =

where constants αi and βi (i = 1, 2, 3) are dependent on the cell number. The specific
constants for the simulated cells are shown in Table 5.2. The uniform component of the time

constant can be computed as,

τu = τn − ∆τ

(5.7)

and used with the uniform calibration to determine the mean velocity within ±1%.

Cell Number Gradient Orientation

13
13
14
14
15
15

Horizontal
Vertical
Horizontal
Vertical
Horizontal
Vertical

α1

0.0491
0.0605
0.0489
0.0602
0.0496
0.0611

β1

0.4816
0.4797
0.4784
0.4782
0.4801
0.4781

α2

-0.0575
-0.0304
-0.0572
-0.0303
-0.0581
-0.0312

β2

0.4488
0.4912
0.4466
0.4916
0.4465
0.4840

α3

0.0044
0.0073
0.0042
0.0072
0.0044
0.0076

β3

0.4920
0.4951
0.5037
0.4990
0.4894
0.4772

Table 5.2: Correction constants

48

The correction scheme is applied over the entire test range of mean velocities and gradients

considered (mean velocities from 0.1 to 15 m/s and gradients from 0 to 1.9). The calculated

error with and without the correction is shown in Figure 5.10. Note the scales for the percent

difference vary (the scale without the correction goes to 12% for the horizontal gradient and

24% for the vertical gradient, while the scale with the correction only goes to 3%). With the

correction implemented, the TTA measurement error is within 1% for the majority of mean

velocities and gradients considered, with the exception of low mean velocities (0.1 to 1 m/s

with gradients exceeding 1.5) at 3%.

(a) Without correction (horizontal gradient,
dU∗/dx∗)

(b) With correction (horizontal gradient,
dU∗/dx∗)

(c) Without correction (vertical gradient,
dU∗/dy∗)

(d) With correction (vertical gradient,
dU∗/dy∗)

Figure 5.10: Percent difference in TTA measurements with and without the correction for
cell 13

49

246810121400.511.51.924681012246810121400.511.51.900.511.522.53246810121400.511.51.904812162024246810121400.511.51.900.511.522.535.4.1

Implementing the Correction Scheme

In practical applications, the TTA can be used to accurately determine the mean velocity

with the existence of large velocity gradients, using the correction scheme. The protocol for

implementing the correction scheme and determining the mean velocity is as follows:

1. Utilize the TTA frame to obtain the time constant for each cell with a specific flow

condition

2. Determine the corresponding inferred mean velocities using the calibration equation

(Equation 1.2)

3. Plot the inferred mean velocities obtained from each cell against their relative position

to estimate a horizontal or vertical gradient

4. Plug the time constant (nonuniform) into the correction scheme (Equations 5.6 - 5.7) to

determine the uniform component of the time constant based on the estimated gradient

and inferred mean velocity

5. Repeat steps 2 - 4 until the time constant converges

This is easily carried out using an iterative script.

5.5 Experimental Response of the TTA Cell with an Imposed Ve-

locity Gradient

A linear velocity profile is imposed over the length of a TTA cell to validate the correction

scheme proposed in the numerical simulation in Section 5.4. For the purpose of validation,

three TTA cells are evaluated. These cells are selected based on the following criteria: (i)

central location for ease of access and setup and (ii) excellent calibration fit, with a high
root mean square fit (R2 ≥ 0.998). The chosen cells are cells 13, 14, and 15 (refer to Figure
3.2 for cell locations). Each cell is tested at three different mean velocities with respective

horizontal gradients.

50

A thin, 3D printed mesh is used to impose a velocity profile across the TTA cell. The

mesh is designed to create a linearly increasing velocity profile across the cell. The entire

mesh is the size of a TTA cell and features several rectangular holes with corresponding areas,

A, spaced across the entire mesh. The area of each hole, A, determines the imposed velocity

upon exit of the mesh. Thus spacing the holes across the mesh in order of descending

area creates the desired linear velocity profile. The velocity distribution from the mesh

creates dimensionless gradients between 0.4 - 1.0 based on the incoming flow speed. Before

experimental testing, a model of the mesh is first designed and the profile is evaluated using

computational fluid dynamics (CFD) software. The mesh is then printed and tested in the

AFRD facility. Following the observation of an approximately linear velocity profile through

CFD evaluation and experimentation, the mesh is placed upstream of a TTA cell. An image

of the mesh is shown in Figure 5.11.

Figure 5.11: Mesh used to impose a linear velocity profile (uniform horizontal gradient)

5.5.1 Determining the Velocity Profile

Ansys Fluent is utilized for the CFD analysis. The oncoming velocity is imposed normal

to the mesh at a distance of 5.08 cm (2”) away from the mesh. The velocity profile after

passing through the mesh is observed at distances of 5.08 - 10.16 cm (2” - 4”) downstream.

51

Contours of the velocity distribution are shown in Figure 5.12. The velocity magnitude (in

the x-direction) of the mesh is shown in Figure 5.13.

(a) With mesh outline displayed

(b) Without mesh outline displayed

Figure 5.12: Fluent analysis of velocity contour 2.08 cm downstream of mesh

Figure 5.13: Fluent analysis of velocity magnitude 2.08 cm downstream (vertical distance at
midpoint height)

From the CFD analysis, the mesh exhibits a near-linear profile. The mesh is then printed

using a Prusa 3D printer (with Prusament PLA filament) and tested in the AFRD facility

without the TTA. The purpose of testing the mesh alone is to determine the optimal distance

downstream which produces the linear velocity profile.

52

00.020.040.060.080.10.120.140.16456789To test the mesh alone, MDF (medium-density fiberboard) with a cutout the size of

the mesh (155 mm x 165 mm) is placed at the inlet of the AFRD. Surrounding the mesh,

is a sectioned 10.16 cm (4”) diameter PVC pipe constructed into a quarter-round to guide

ambient air uniformly to the mesh. Underneath the mesh in the upper receiver, a pitot tube

is set up to traverse across the length of the mesh. Since the opening at the inlet is so small,

the door to the AFRD is cracked to avoid surging. The incoming air from the door did not

have an effect on the airflow passing through the mesh, as it is positioned far enough away.

The setup of the mesh and pitot tube traverse is shown in Figure 5.14.

(a) View from top of AFRD

(b) View from upper receiver of AFRD

Figure 5.14: Setup for mesh velocity profile measurements using pitot tube

Two velocity settings are tested with the mesh. That is, a high and low inlet velocity with

mean velocities of 8.2 and 4.6 m/s respectively. The two velocities are tested at distances

of 2.54 - 7.62 cm (1” - 3”) away from the mesh. The results from the survey are shown in

Figure 5.15.

53

Figure 5.15: Pitot tube determined mesh velocity profile at different distances downstream

Following the pitot tube survey, the results indicate that the mesh produces a stable and

a nominally uniform velocity gradient at a distance of 5.08 cm downstream.

5.5.2 Procedure and Results of Experimental Evaluation

For the measurements with the TTA, the setup used in calibration (Section 3.1) is used.

The mesh is placed 5.08 cm above a designated TTA cell (13, 14, or 15) with a quarter-

round to uniformly guide the air. A cardboard cutout is placed between the TTA and

mesh and any gaps are sealed to ensure mass is not lost to leakage. The pitot tube is then

placed underneath the assembly to measure the velocity and determine the gradient at the

respective inlet condition. The setup is shown in Figure 5.16. Note that the mesh is placed

above one TTA cell at a time and not all three cells simultaneously.

54

00.20.40.60.8156789101100.20.40.60.813.544.555.56Figure 5.16: TTA with mesh mounted 2.08 cm above tested cell

With the mesh placed above one of the three chosen cells (cells 13 - 15), three differ-

ent velocities (with respective gradients) are tested. At each velocity, ten successive TTA

measurements are taken for each cell. The three mean velocities tested are 3.27 m/s, 6.21

m/s, and 8.93 m/s with respective dimensionless gradients of 0.742, 0.632, and 0.707. The

velocity profiles are shown in Figure 5.17.

Figure 5.17: Velocity profiles with mesh used for validation of TTA correction scheme

The TTA gradient validation results are listed in Table 5.3. The inferred mean velocity is

55

00.050.10.15024681012calculated using the corresponding time constant and the corresponding calibration equation

(Equation 1.2) for the cell. The correction equation (Equation 5.6) is implemented due to

the large gradients observed in the three cases. The result is the corrected mean velocity

(using the uniform TTA calibration) within 1% of the mean velocity measured using the

pitot tube. The application of the correction scheme for all three cells and three different

velocity conditions demonstrates the validity of the correction scheme that was formulated

using numerical simulations.

Mean Velocity

(m/s)

Cell

Number

3.27

6.21

8.93

13
14
15
13
14
15
13
14
15

Corrected Inverse
Time Constant

(1/s)
3.09
3.09
3.18
4.07
4.06
4.16
4.78
4.77
4.87

Inferred

Mean Velocity

(m/s)
3.29
3.28
3.29
6.24
6.19
6.23
8.89
8.91
8.95

Standard

Deviation (10
measurements)

0.040
0.040
0.050
0.146
0.156
0.131
0.153
0.628
0.175

Percent
Difference

(%)
0.904
0.230
0.605
0.349
0.437
0.279
0.463
0.716
0.229

Table 5.3: Results from gradient validation after correction scheme is applied for all three
cells and mean velocities tested

56

CHAPTER 6

NONUNIFORM VELOCITY DISTRIBUTION AT THE EXIT PLANE OF A

RADIATOR

The TTA frame is utilized to interrogate the velocity distribution at the exit plane of an

automotive radiator with various installation configurations. The three installation config-
urations explored are: (i) radiator in the horizontal position, (ii) radiator inclined at 8◦
with respect to the horizontal, and (iii) radiator inclined at 8◦ with the shroud attached.
These installation configurations are tested with uniform base flow conditions provided by

the AFRD facility, ranging from 0.26 to 9.57 m/s.

The horizontal configuration is used as the reference condition. It is used to evaluate the

exit velocity distribution when the radiator is installed in a vehicle. The inclined configura-

tion is of interest since it mimics the mounting configuration for the specific vehicle in which
the radiator is installed. The packaging constraints for that vehicle require an 8◦ inclination
between the plane of the grill and the plane of the radiator. The inclined and horizontal

configurations are compared to observe and quantify the effect of tilting the radiator. For the

final configuration, the shroud is attached and the radiator is mounted in the same inclined

position. The effect of attaching the shroud is determined by comparing its results to those

of the inclined configuration without the shroud.

6.1 Experimental Setup and Procedure

The experimental setup within the AFRD is shown in Figure 6.1. The TTA frame is

attached to the back face of the radiator and secured with four 8 mm (5/16”) screws (see

Figure 1.1a for TTA attached to radiator). A metal frame constructed with 3.81 cm (1.5”)

aluminum beams is used to support the radiator and TTA frame. The frame and radiator

are positioned horizontally with respect to the inlet, facing downward. Sectioned 10.16 cm

(4”) diameter PVC piping is placed around the perimeter of the radiator as a quarter-round

57

inlet, to ensure uniform flow. Foam insulation is placed around the frame to seal any gaps

and prevent air leakage.

(a) View from on top of AFRD roof

(b) View looking up from upper receiver

Figure 6.1: Radiator and TTA frame installation

In the vehicle, the radiator is hinged along its length to create the 8◦ inclination angle.
Instead of physically inclining the radiator, an inlet channel is utilized to mimic this effect.

The inlet channel redirects the flow with respect to the desired position in the vehicle. The
central axis on the inlet channel is inclined 8◦ with respect to horizontal. A honeycomb
flow straightener with inner diameter, D, and thickness, L, such that L/D = 8 is placed

58

at the channel inlet. The distance from the honeycomb exit to the radiator (at midpoint)

inlet agree with the installation condition of the vehicle, that is a distance of 16.6 cm. The

channel design is shown in Figure 6.2.

(a) Model of inlet channel

(b) Channel mounted on top of automobile radiator

Figure 6.2: 8◦ inclination inlet channel

The shroud is attached to the back of the TTA using four screws (8 cm or 5/16”). There

is a small gap between the radiator and shroud due to the protruding TTA electrical wires.

This along with other gaps are sealed using tape to prevent any leakage. The setup with the

shroud is shown in Figure 6.3.

The AFRD fan is utilized to establish a base flow condition. This is measured using

the TTA output. For each flow rate, the TTA is used to survey the radiator plane exit

distribution. Ten TTA measurements at each velocity are taken. This procedure is repeated

for each inlet condition. The inlet velocities tested range from 0.26 m/s to 9.6 m/s, with an

emphasis on the lower velocities.

59

Figure 6.3: Radiator with shroud attached with a view looking up from AFRD upper receiver

Measurements for the horizontal and inclined configurations are taken at each inlet condi-

tion by adding and removing the inlet channel. This provides a similar set of inlet velocities

in the test range. The results with the addition of the shroud are done separately, after

mounting the shroud on the radiator.

6.2 Results

The TTA provides a velocity survey at the exit face of the radiator. The results are

analyzed for the three installation configurations (horizontal, inclined, inclined with shroud).

The addition of the inclined entry channel introduces a subtle pressure drop between the

atmosphere and honeycomb, not present in the horizontal study. This results in a small

reduction in flow rate. Likewise, measurements with the shroud are not taken with the same

base flow conditions. When comparing the measured cell velocity to the inlet mean velocity,

the difference is normalized by the mean inlet velocity to give a percent difference from the

mean as,

∆ijk =

U − Ucell

U

∗ 100

(6.1)

where the indices i,j,k refer to the row (i = 1, ..., 4), column (j = 1, ..., 6), and installation

configuration (k = 1 for horizontal, k = 2 for inclined, and k = 3 for inclined with shroud

60

attached), U is the inlet mean velocity and Ucell is the measured cell velocity. A positive
value indicates the cell velocity is higher than the inlet velocity, while a negative value

indicates the cell velocity is lower than the inlet velocity.

The standard deviation of the percent difference (∆ij) for a given installation condition,
σk reflects the variation of the distribution for a given inlet condition. The standard deviation
is calculated using,

(cid:114) 1

(cid:88)

σk =

N − 1

∆2

ijk

(6.2)

where N refers to the number of cells (N = 23). A large standard deviation indicates

large amounts of variation while a low standard deviation indicates less variation (more

homogeneous flow distribution).

6.2.1 Horizontal Position

The radiator is tested in the horizontal configuration with inlet velocities ranging from 0.26

to 9.57 m/s.

The results for the radiator exit plane survey for inlet mean velocities (0.26, 5.04, and

9.57 m/s) are shown in Figures 6.4 - 6.6. The results for the full range of velocity conditions

is shown in Appendix C.1.1. Note that in the velocity figures, blue refers to a low velocity

and yellow refers to a high velocity, while in the percent difference figures, pink refers to a

negative percent difference and yellow refers to a positive percent difference.

The cases represent the radiator at three respective inlet conditions. At low speeds (0.26

m/s), the left portion of the radiator has minimal flow, with a flow decrease of 10% up to
60%. At higher speeds (≥5 m/s) the velocity distribution in the radiator center is more
homogeneous, since most percent differences are 7% or less of the inlet velocity. At these

speeds, there are still areas of high and low velocity around the perimeter of the radiator.

Eventually (at 9.57 m/s), the areas around the perimeter of the radiator start to homogenize

as well.

61

This is also reflected in the standard deviation. The standard deviation for the range of

inlet velocities is shown in Figure 6.7 (the exact standard deviation values are shown in Table
C.1 in Appendix C.1.2). At extremely low velocities (≤ 1 m/s), there is a large amount of
variation in the flow distribution. As the inlet velocity increases from 2.02 m/s to 9.57 m/s,

the flow distribution slowly becomes more homogeneous. From Figures 6.4 - 6.6, this occurs

first in the radiator center, then outwards.

(a) Velocity

(b) Percent difference

Figure 6.4: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 0.26 m/s

(a) Velocity

(b) Percent difference

Figure 6.5: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 5.04 m/s

62

(a) Velocity

(b) Percent difference

Figure 6.6: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 9.57 m/s

Figure 6.7: Standard deviation of velocity distribution in horizontal configuration

In the horizontal configuration, the gradients are between 0 ≤ ξ ≤ 0.2. Therefore the

correction scheme is not necessary.

63

012345678910510152025306.2.2

Inclined Position

The inlet entry channel is placed on the radiator to evaluate the inclined configuration.

Sixteen velocity conditions ranging from 0.26 to 9.28 m/s are evaluated.

The results for the radiator exit plane survey for inlet velocities (0.26, 4.93, and 9.28 m/s)

are shown in Figures 6.8 - 6.10. The data for the full range of inlet conditions is shown in

Appendix C.2.1. The velocity distribution is similar to the horizontal configuration, implying
that the effect of the 8◦ inclination on the flow distribution is subtle. The standard deviation
for the range of inlet conditions is shown in Figure 6.11 (the exact standard deviation values

are shown in Table C.2 in Appendix C.2.2). The same effect observed in the horizontal

configuration (Figure 6.7) is present in the inclined configuration.

(a) Velocity

(b) Percent difference

Figure 6.8: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 0.26 m/s

64

(a) Velocity

(b) Percent difference

Figure 6.9: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 4.93 m/s

(a) Velocity

(b) Percent difference

Figure 6.10: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 9.28 m/s

65

Figure 6.11: Standard deviation of velocity distribution in inclined configuration

To validate the proposition that the inclined configuration has a minimal effect on the

flow distribution through the radiator, the horizontal cell velocity is plotted against the inlet

velocity as a linear model with 95% confidence intervals. Then the data points from the

inclined configuration are added to the plot. The results for cell 1 are shown in Figure 6.12.

The results for the rest of the cells are shown in Appendix C.2.3. All the inclined data points

are within or near the 95% confidence band over the range of inlet mean velocities tested,
implying that there is a minimal effect from inclining the radiator at 8◦. This is consistent
for all 23 cells as reflected in Table 6.1.

Table 6.1 shows the percentage of inclined data points that lie within the established 95%

confidence intervals. For the majority of cells 90-100% of the data points lie within these

intervals, with the exception of cell 13 at 81.25%. This indicates that the effect of inclining
the radiator at an 8◦ angle has a minimal influence on the radiator flow distribution.

66

01234567891051015202530Figure 6.12: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 1

67

0123456789101101234567891011Cell Number

Percent of data points

within confidence interval

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

100 %
100 %
93.75 %
93.75 %
100 %
93.75 %
93.75 %
100 %
93.75 %
100 %
100 %
93.75 %
81.25 %
93.75 %
100 %
100 %
93.75 %
100 %
100 %
100 %
100 %
100 %
93.75 %

Table 6.1: Percentage of inclined data points within the 95% confidence intervals

Another means for exploring the difference in flow distribution is by examining the change

in percent difference, ∆, between the horizontal and inclined configurations. This is given

as,

∆ij2 − ∆ij1

(6.3)

where subscripts for for k are 1 and 2 denoting the inclined and horizontal percent differences,

respectively.

Since the radiator inclination is with respect to its length (variation in the flow angle

with respect to the ‘row’), its velocity distribution is expected to vary for each row. Thus,

the change in percent difference is evaluated as the average for each row. The change percent

68

difference for five selected velocities over the range of inlet velocities tested is shown in Figure

6.13a. Regardless of the inlet velocity, the general observation is an increase in velocity for

rows 1-2 and a decrease in velocity for rows 3-4. To represent the effect of inclining the

radiator over all the inlet velocities, the average change in percent difference (for all inlet

conditions) is evaluated. This is shown in Figure 6.13b. The average change in percent

difference is marginal, ranging from -0.98% to 0.52%. For an inlet velocity of 10 m/s, a

-1.0% change in percent difference would correspond to a 0.1 m/s loss in velocity due to the

incline. The top of the radiator, row 4, is most affected with a 0.98% loss in velocity. This

is balanced out by an increase in velocity from 0-0.5% for rows 1-3.

(a) Change for selected velocities

(b) Average change for all velocities

Figure 6.13: Change in percent difference by row

Similar to that for the horizontal position, the correction scheme is not necessary due to

the low gradients (0 ≤ ξ ≤ 0.2).

6.2.3

Inclined Configuration with Shroud Attached

With the shroud attached, flow exiting the radiator is directed toward the shroud opening

(see Figure 6.3). A schematic depiction of the TTA frame position with respect to the shroud

opening is shown in Figure 6.14.

69

1234-2.5-2-1.5-1-0.500.511.522.51234-1-0.500.51Figure 6.14: Schematic representation of TTA frame position with respect to the shroud
opening

With the shroud attached, the blockage around the perimeter causes a larger variation
in flow distribution among the neighboring cells. Velocity gradients range from 0 ≤ ξ ≤ 0.4.
The gradient correction scheme from Chapter 5.4 is implemented. In instances where the
dimensionless gradient is 0.3 ≤ ξ ≤ 0.4 the correction curve is implemented. The inlet
velocities where this gradient range is observed is between 6.40 to 8.85 m/s (see Appendix

C.3.1 for all corrected velocity distributions). The velocity distributions before and after the

correction for an inlet velocity of 8.85 m/s is shown in Figure 6.15. The cells eligible for

correction are the cells blocked by the shroud in the left portion (first column) and lower

right portion of the radiator (last column). Note that there is not a large velocity change

between corrected and uncorrected velocities, even with velocity gradients between 0.3-0.4.

70

(a) Before correction

(b) After correction

Figure 6.15: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 8.85 m/s

Following the correction of selected cells, the velocity distribution and percent differences

are evaluated.

The radiator configuration including the shroud is tested at velocities ranging from 0.26

to 8.85 m/s. The results for the radiator exit plane survey for inlet velocities of 1.03 and 8.29

m/s are shown in Figures 6.16 and 6.17. The data for the full range of inlet conditions are

shown in Appendix C.3.2. For both inlet velocities shown, the region with the greatest mass

flow (largest local velocity) is in the center, near the shroud opening. Likewise, the lowest

velocities are observed in the left region of the radiator, where the shroud strongly blocks

the TTA cells. In the left column of TTA cells, the velocity is nominally 21% lower for the

inlet condition of 1.03 m/s. This velocity deficit increases as the inlet condition increases

to 8.29 m/s, where the measured cell velocity is nominally 28% lower than the mean inlet

velocity.

71

(a) Velocity

(b) Percent difference

Figure 6.16: Radiator exit plane flow distribution with shroud attached and inlet velocity of
1.03 m/s

(a) Velocity

(b) Percent difference

Figure 6.17: Radiator exit plane flow distribution with shroud attached and inlet velocity of
8.29 m/s

To evaluate the effect of the shroud on the flow distribution, the radiator and shroud are

taken to be a control volume with the exiting flow as a curved streamline. The flow kinetic

energy along the streamline (ρU 2/2) is integrated over the radiator exit control surface,

(cid:90)

(cid:16)(cid:126)U · (cid:126)n
(cid:17)

U 2
2

ρ

CS

dA.

(6.4)

The kinetic energy flux for a given cell velocity represents the pressure drop from the

atmosphere to the below the radiator over the given area. The significance of the kinetic

72

energy flux is that it is related to the fan power requirement to deliver a specified mass flux

across the radiator. The term U 3 in the kinetic energy flux is summed over all the cells and

is denoted by κ,

κ =

23(cid:88)

U 3
i

(6.5)

i=1

where κ is proportional to the kinetic energy flux. The evaluation of κ is done for the

radiator with and without the shroud (inclined configuration). The results are plotted as a

function of inlet mean velocity to illustrate the ‘cost’ of adding the shroud. These results

are in Figure 6.18. κ with the shroud is larger than without, particularly observable for inlet
velocities ≥ 5 m/s. This indicates that a larger fan power is required to provide a given mass
flow rate.

Figure 6.18: Kinetic energy flux with and without the shroud attached

The difference in κ with and without the shroud illustrates the cost of adding the shroud.
This is shown in Figure 6.19. For low inlet velocities (≤ 4 m/s), the difference is negligible.
For inlet velocities > 4 m/s the difference becomes significant, indicating the impact of the

shroud is experienced at higher velocities.

73

01234567890400080001200016000It is notable that when the vehicle is in motion, which corresponds to higher inlet ve-

locities, the radiator fan is shut off. While the nonuniform flow distribution induced by the

shroud may have an impact on the radiator heat transfer performance, the presence of the

shroud has minimal impact on the radiator fan power consumption.

Figure 6.19: Difference between kinetic energy flux with and without the shroud

74

0123456789020040060080010001200CHAPTER 7

SUMMARY AND CONCLUSIONS

The novel airflow measurement device, the thermal transient anemometer (TTA), has been

described and presented herein.

Each of the cells in the TTA were calibrated in the AFRD wind tunnel facility. The

cells were calibrated with uniform velocities ranging from 0.1 to 13 m/s as determined using

a calibrated hot-wire probe along with the TTA frame. The average uncertainty from the
calibration was ±0.19 m/s.

Numerical simulations were utilized to observe the transient convective effects of the

sensing wire in one TTA cell. The numerical simulations were adjusted to represent selected

calibrated TTA cells by adjusting the constants in the Nusselt number (see Chapter 4.2.1).

Inlet mean velocities ranging from 0.1 to 15 m/s with uniform dimensionless gradients,
dU∗/dx∗ and dU∗/dy∗, (see Sections 5.2 - 5.3) ranging from 0 to 1.9 were simulated. The
gradients were imposed along both the length and height of a TTA cell to provide a horizontal

and vertical gradient. For a given mean velocity, the wire cooled more slowly with the

existence of a velocity gradient, particularly over 0.5. This was due to the nonuniform,

nonlinear temperature distribution along the wire caused by the velocity gradient, thus

affecting the wire resistivity and resistance decay. This resulted in a difference of 1% with

a gradient of 0.4 to 13% and 24% with horizontal and vertical gradients of 1.9 respectively,

when using the uniform calibration to calculate the mean velocity. The relative effect of the

vertical velocity gradient is stronger than that of the horizontal gradient, due to the variation

in the velocity along the sensing wire.

A correction scheme was developed to address the large error observed at high gradients.

After implementing the correction scheme, the error in mean velocity was within 1% for most

gradients. The correction scheme was validated by empirical data collected with the TTA

(cells 13 - 15). Three different mean velocities (3.27, 6.21, and 8.93 m/s) with respective

75

horizontal gradients (dU∗/dx∗ of 0.742, 0.632, and 0.707) were imposed on the selected TTA
cells as determined in Chapter 5.5.

The TTA was utilized to measure the velocity distribution at the exit face of a radiator in
various installation configurations: horizontal, inclined (8◦ angle), and inclined with a shroud
attached. The following radiator configurations were tested with several inlet base conditions

(between 16 - 18) ranging from 0.26 to 9.57 m/s, as provided by the AFRD facility. In the

horizontal configuration, the velocity distribution at the exit of the radiator was extremely
nonuniform at low velocities (U ≤ 1 m/s) more than a 10% decrease in airflow in the left
portion of the radiator. As the inlet base velocity was increased, the airflow distribution

homogenizes first in the center of the radiator, then outwards. The effect of tilting the
radiator at an 8◦ angle with respect to the plane of the grill is minimal, although the top
row loses an average of 1% of flow as a result of the inclination (see Section 6.2.2). This

is balanced by a small gain in flow (0% - 0.5%) for the other rows. The addition of the

shroud blocks portions of the radiator, creating strong velocity gradients in the corners. The

correction scheme was implemented to determine the correct velocity distribution. A term

proportional to the kinetic energy flux was evaluated to observe the effect of adding the

shroud. It was found that at low inlet velocities, the cost of adding the shroud is minimal,

while at higher inlet velocities this cost is larger. This indicates that at higher inlet velocities

(> 4 m/s) it requires more work for the flow to provide the same mass flux when the shroud

is attached.

Future investigations with the TTA may include exploring the effects of different velocity

profiles or testing with another TTA geometry configuration (different frame and/or cell

dimensions with different wire).

76

APPENDICES

77

APPENDIX A

CALIBRATION OF TTA

A.1 Calibration Curves for all Cells

Figure A.1: TTA calibration curve for cell 1

78

0246810120123456Figure A.2: TTA calibration curve for cell 2

Figure A.3: TTA calibration curve for cell 3

79

02468101201234560246810120123456Figure A.4: TTA calibration curve for cell 4

Figure A.5: TTA calibration curve for cell 5

80

02468101201234560246810120123456Figure A.6: TTA calibration curve for cell 6

Figure A.7: TTA calibration curve for cell 7

81

02468101201234560246810120123456Figure A.8: TTA calibration curve for cell 8

Figure A.9: TTA calibration curve for cell 9

82

02468101201234560246810120123456Figure A.10: TTA calibration curve for cell 10

Figure A.11: TTA calibration curve for cell 11

83

02468101201234560246810120123456Figure A.12: TTA calibration curve for cell 12

Figure A.13: TTA calibration curve for cell 13

84

02468101201234560246810120123456Figure A.14: TTA calibration curve for cell 14

Figure A.15: TTA calibration curve for cell 15

85

02468101201234560246810120123456Figure A.16: TTA calibration curve for cell 16

Figure A.17: TTA calibration curve for cell 17

86

02468101201234560246810120123456Figure A.18: TTA calibration curve for cell 18

Figure A.19: TTA calibration curve for cell 19

87

02468101201234560246810120123456Figure A.20: TTA calibration curve for cell 20

Figure A.21: TTA calibration curve for cell 21

88

02468101201234560246810120123456Figure A.22: TTA calibration curve for cell 22

Figure A.23: TTA calibration curve for cell 23

89

02468101201234560246810120123456Cell Number

A

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

0.804
0.979
1.730
2.088
3.729
1.234
1.342
1.539
1.652
1.719
1.585
1.375
1.261
1.310
1.662
1.572
1.668
1.242
1.355
1.270
1.446
1.190
1.320

B

0.686
0.616
0.458
0.394
0.267
0.548
0.516
0.489
0.460
0.448
0.479
0.513
0.538
0.520
0.464
0.473
0.445
0.538
0.520
0.527
0.500
0.566
0.526

C

1.098
0.999
0.307
-0.038
-1.632
0.748
0.650
0.492
0.389
0.318
0.397
0.621
0.707
0.672
0.295
0.352
0.237
0.776
0.560
0.727
0.416
0.644
0.601

R2
0.996
0.998
0.997
0.995
0.995
1.000
0.999
0.999
0.999
0.998
0.999
0.950
0.998
0.999
0.999
0.998
0.998
0.998
0.994
0.997
0.997
0.998
0.998

Table A.1: Calibration constants for TTA cells

90

A.2 Calibration Curves with Simulation Fit

Figure A.24: Cell 13 experimental and simulated calibration

91

0246810120123456Figure A.25: Cell 14 experimental and simulated calibration

Figure A.26: Cell 15 experimental and simulated calibration

92

02468101201234560246810120123456APPENDIX B

DERIVATION OF EQUATIONS

B.1 Conservation Energy Equation

Fundamental heat transfer principles are used to evaluate a segment of the wire. The

energy moving through the control volume, CV, of the wire gives,

˙Ein − ˙Eout + ˙Egen =

˙Estored

which is written in terms of the heat,

qconduction +

˙

qconvection +

˙

qgenerated =

˙

˙qstored.

(B.1)

(B.2)

The conduction within the wire segment includes both the heat entering and exiting the wire

segment,

qconduction,in and

˙

qconduction,out,

˙

˙

qconduction,in = −k(s, t)A
(cid:20)

∂Tw(s, t)

(cid:20)

k(s, t)A

∂s
−k(s, t)A

∂Tw(s, t)

qconduction,out = −

˙

+

∂
∂s

∂s

(cid:21)(cid:21)

(B.3)

(B.4)

∂Tw(s, t)

∂s

ds

where k is the thermal conductivity of the wire, A is the cross-sectional area of the wire, and

Tw is the wire temperature. Combining Equations B.3 and B.4 characterizes the conduction
entering and leaving the control volume,

(cid:20)

(cid:20)

k(s, t)A

∂Tw(s, t)

∂s

+

∂
∂s

−k(s, t)A

∂Tw(s, t)

∂s

ds

(cid:21)(cid:21)

(B.5)

qconduction = −k(s, t)A

˙

∂Tw(s, t)

∂s

−

where k is the thermal conductivity.

The heat convection from the wire comes from the passing flow. Using Newton’s law of

cooling [10], the convection term is written as,

qconvection = −h(s, t) [Tw(s, t) − Ta] dA

˙

(B.6)

93

where h is the convective heat transfer coefficient and dA is the surface area of a wire segment.

Substituting dA = πDds into Equation B.6 simplifies the convection term to,

qconvection = −h(s, t)πD [(Tw(s, t) − Ta] ds.

˙

(B.7)

The heat in the wire comes from the electrical control unit supplying a current to the wire.

That is,

qgenerated = I2dR

˙

(B.8)

where I is the current and dR is the resistance of the wire segment ds. The change in

resistance is written in terms of the resistivity,γ, and cross-sectional area,

dR(s, t) =

γ(s, t)ds

A

.

This simplifies the heat generation term in Equation B.8 to,

qgenerated =

˙

I2γ(s, t)ds

A

.

The energy stored in the wire is,

˙qstored = mCp

∂Tw(s, t)

∂t

ds

where m represents the mass. In terms of the density and cross-sectional area is,

˙qstored = ρCpA

∂Tw(s, t)

∂t

ds.

(B.9)

(B.10)

(B.11)

(B.12)

Combining all the terms together as in Equation B.2, gives Equation 4.1 (see Chapter

4.1) as,

1
ρCp

∂k(s, t)

∂Tw(s, t)

∂s

∂s

+

k(s, t)
ρCp

∂2Tw(s, t)

∂s2

− 4h(s, t)
ρCpD

(Tw(s, t) − Ta) + 16

I2γ(s, t)
ρCpπ2D4 =

∂Tw(s, t)

∂t

.

94

B.2 Thermophysical Properties of Air and Tungsten

The thermal properties for both air and tungsten are required for the simulation. The

table for the tungsten properties is provided by the text Fundamentals of Heat and Mass

Transfer [10]. A 6th and 8th order polynomial is fit thermal conductivity and specific heat,

− 1.62 ∗ 10−18Tw(s, t)6 + 7.18 ∗ 10−15Tw(s, t)5 + 4.00 ∗ 10−12Tw(s, t)4
− 7.25 ∗ 10−8Tw(s, t)3 + 1.56 ∗ 10−4Tw(s, t)2 − 0.158Tw(s, t) + 175

(B.13)

k(s, t) =

Cp(s, t) =

− 2.02 ∗ 10−22Tw(s, t)8 + 1.44 ∗ 10−18Tw(s, t)7 − 4.08 ∗ 10−15Tw(s, t)6
+ 5.90 ∗ 10−12Tw(s, t)5 − 4.66 ∗ 10−9Tw(s, t)4 + 2.03 ∗ 10−6Tw(s, t)3
− 4.86 ∗ 10−4Tw(s, t)2 + 81.9 ∗ 10−3Tw(s, t) + 131

(B.14)

where the properties are evaluated at the local temperature of the wire Tw(s, t). The fitted
curves along with the provided data are illustrated in Figures B.1 - B.2.

Figure B.1: Thermal conductivity fit

95

-5000500100015002000250080100120140160180200220Figure B.2: Specific heat fit

A table provided by the text Heat and Mass Transfer [5] is used for the properties of air.

A 5th and 6th order polynomial is fit to the kinematic viscosity and Prandtl numbers,

ν(s, t) =

2.96 ∗ 10−24Tf (s, t)6 − 1.68 ∗ 10−20Tf (s, t)5 + 3.88 ∗ 10−17Tf (s, t)4
− 5.70 ∗ 10−14Tf (s, t)3 + 1.06 ∗ 10−10Tf (s, t)2 + 8.66 ∗ 10−8Tf (s, t)
+ 1.34 ∗ 10−5

(B.15)

P r(s, t) =

8.93 ∗ 10−20Tf (s, t)7 − 1.70 ∗ 10−16Tf (s, t)6 + 1.34 ∗ 10−13Tf (s, t)5
− 5.59 ∗ 10−11Tf (s, t)4 + 1.23 ∗ 10−8Tf (s, t)3 − 7.57 ∗ 10−7Tf (s, t)2
− 2.56 ∗ 10−4Tf (s, t) + 0.736

(B.16)

where the properties are evaluated at the local film temperature of the wire, Tf (s, t). The
fitted curves along with the provided data are illustrated in Figures B.3 - B.4.

96

-20002004006008001000120014008090100110120130140150160170Figure B.3: Kinematic viscosity fit

Figure B.4: Prandtl number fit

97

-2000200400600800100000.20.40.60.811.21.41.61.810-40501001502002503003504004500.690.70.710.720.730.74B.3 Analytical Time Constant for Uniform Flow

The conservation energy equation (Equation 4.1) can be simplified for uniform flow during

the cooling period. Starting with the conservation energy equation,

1
ρCp

∂k(s, t)

∂Tw(s, t)

∂s

∂s

+

k(s, t)
ρCp

∂2Tw(s, t)

∂s2

− 4h(s, t)
ρCpD

(Tw(s, t) − Ta) + 16

I2γ(s, t)
ρCpπ2D4 =

∂Tw(s, t)

∂t

.

Under uniform flow, the conduction terms are removed, since the thermophysical prop-

erties are approximately constant along the wire. During the cooling process the current is

approximately 0 (10 mA), thus removing the heat generation term. This leaves the conser-

vation equation as,

−4h(s, t)
ρCpD

(Tw(s, t) − Ta) =

∂Tw(s, t)

∂t

.

Evaluating at the initial time and rearranging gives,

− 4h(t)
ρCpD

(Tw,0 − Ta) = Tw(t) − Ta

− 4h(t)
ρCpD

=

Tw(t) − Ta
Tw,0 − Ta

.

(B.17)

(B.18)

(B.19)

The resistance varies linearly with temperature, making Equation B.19 equivalent to the

dimensionless resistance (Equation 1.1). This gives,

− 4h(t)
ρCpD

=

Tw(t) − Ta
Tw,0 − Ta

R(t) − Ra
R0 − Ra

=

= e−t/τ .

Since R∗ is evaluated when e =−1, this gives the following statement,

(B.20)

(B.21)

Solving for the time constant by taking the natural log gives the time constant,

Rewriting in terms of the heat convection coefficient (Equation 4.7) gives,

1/τ = ln

.

(B.22)

− 4h(t)
ρCpD

= e−t/τ .
(cid:19)

(cid:18) 4h(t)

.

ρCpD

1/τ = ln

(cid:32)

(cid:33)

kacRemP r1/3

ρCpD2

98

B.4 Uniform Velocity Gradients

B.4.1 Horizontal Velocity Gradient

Consider the linear velocity profile imposed along the length, L, of a TTA cell (see Figure

5.1). At either end of the TTA cell, there is some minimum and maximum velocity. For a

given horizontal position along the cell length, x, the relative velocity, U, is given by,

U = Umin +

(Umax − Umin)

L

x.

Dimensionless parameters, U∗ and x∗, are defined such that,

U∗ =

U

Umean

x∗ =

x
L

.

Substituting the dimensionless parameters U∗ and x∗ into Equation B.23,

U∗ =

Umin
Umean

+

(Umax − Umin)

Umean

x∗.

(B.23)

(B.24)

(B.25)

(B.26)

The derivative with respect to U∗ and x∗ is taken on either side of the Equation B.26,

dU∗ =

(Umax − Umin)

Umean

dx∗.

(B.27)

Dividing both sides by dx∗ gives the horizontal velocity gradient as defined in Equation

5.1,

dU∗
dx∗ =

(Umax − Umin)

Umean

.

99

B.4.2 Vertical Velocity Gradient

The derivation of the vertical velocity gradient is similar to that of the horizontal velocity

gradient. Consider the linear velocity profile imposed along the height, H, of the TTA cell

(see Figure 5.6). At either end of the TTA cell, there is some minimum and maximum

velocity. For a given vertical position along the cell height, y, the relative velocity, U, is

given by,

(Umax − Umin)

y.

(B.28)
The dimensionless parameters are U∗ and y∗, where U∗ is defined in Equation B.24 and

U = Umin +

H

y∗ is defined as,

y∗ =

y
H

.

The dimensionless parameters, U∗ and y∗, are substituted into Equation B.28,

U∗ =

Umin
Umean

+

(Umax − Umin).

Umean

y∗

(B.29)

(B.30)

Taking the derivative (with respect to U∗ and y∗) on either side of Equation B.30 and
dividing both sides by dy∗ (similar to Appendix B.4.1), gives the vertical velocity gradient
as defined in Equation 5.2,

dU∗
dy∗ =

(Umax − Umin)

.

Umean

100

APPENDIX C

TESTING WITH RADIATOR

C.1 Results with Radiator in Horizontal Position

C.1.1 Radiator exit plane distribution

(a) Velocity

(b) Percent difference

Figure C.1: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 0.26 m/s

(a) Velocity

(b) Percent difference

Figure C.2: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 0.57 m/s

101

(a) Velocity

(b) Percent difference

Figure C.3: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 0.80 m/s

(a) Velocity

(b) Percent difference

Figure C.4: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 1.06 m/s

102

(a) Velocity

(b) Percent difference

Figure C.5: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 1.51 m/s

(a) Velocity

(b) Percent difference

Figure C.6: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 2.02 m/s

103

(a) Velocity

(b) Percent difference

Figure C.7: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 2.81 m/s

(a) Velocity

(b) Percent difference

Figure C.8: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 3.66 m/s

104

(a) Velocity

(b) Percent difference

Figure C.9: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 4.16 m/s

(a) Velocity

(b) Percent difference

Figure C.10: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 5.04 m/s

105

(a) Velocity

(b) Percent difference

Figure C.11: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 5.90 m/s

(a) Velocity

(b) Percent difference

Figure C.12: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 6.71 m/s

106

(a) Velocity

(b) Percent difference

Figure C.13: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 7.18/ m/s

(a) Velocity

(b) Percent difference

Figure C.14: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 7.76 m/s

107

(a) Velocity

(b) Percent difference

Figure C.15: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 8.68 m/s

(a) Velocity

(b) Percent difference

Figure C.16: Radiator exit plane flow distribution in the horizontal configuration with inlet
velocity of 9.57 m/s

108

C.1.2 Standard Deviation of Percent Difference

Inlet Velocity

(m/s)
0.26
0.57
0.80
1.06
1.51
2.02
2.81
3.66
4.16
5.04
5.90
6.71
7.18
7.76
8.68
9.57

Standard Deviation of
Percent Difference (%)

26.23
14.02
11.97
11.73
12.46
12.74
12.29
11.32
11.03
10.03
9.41
8.14
8.21
7.10
6.14
5.84

Table C.1: Standard deviation of percent difference for each inlet velocity in the horizontal
configuration

109

C.2 Results with Radiator in Inclined Position

C.2.1 Radiator Exit Plane Distribution

(a) Velocity

(b) Percent difference

Figure C.17: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 0.26 m/s

(a) Velocity

(b) Percent difference

Figure C.18: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 0.56 m/s

110

(a) Velocity

(b) Percent difference

Figure C.19: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 0.79 m/s

(a) Velocity

(b) Percent difference

Figure C.20: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 1.04 m/s

111

(a) Velocity

(b) Percent difference

Figure C.21: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 1.49 m/s

(a) Velocity

(b) Percent difference

Figure C.22: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 2.00 m/s

112

(a) Velocity

(b) Percent difference

Figure C.23: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 2.78 m/s

(a) Velocity

(b) Percent difference

Figure C.24: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 3.61 m/s

113

(a) Velocity

(b) Percent difference

Figure C.25: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 4.09 m/s

(a) Velocity

(b) Percent difference

Figure C.26: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 4.93 m/s

114

(a) Velocity

(b) Percent difference

Figure C.27: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 5.72 m/s

(a) Velocity

(b) Percent difference

Figure C.28: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 6.63 m/s

115

(a) Velocity

(b) Percent difference

Figure C.29: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 7.04 m/s

(a) Velocity

(b) Percent difference

Figure C.30: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 7.59 m/s

116

(a) Velocity

(b) Percent difference

Figure C.31: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 8.43 m/s

(a) Velocity

(b) Percent difference

Figure C.32: Radiator exit plane flow distribution in the inclined configuration with inlet
velocity of 9.28 m/s

117

C.2.2 Standard Deviation of Percent Difference

Inlet Velocity

(m/s)
0.26
0.56
0.70
1.04
1.49
2.00
2.78
3.61
4.09
4.93
5.72
6.63
7.04
7.59
8.43
9.28

Standard Deviation of
Percent Difference (%)

27.54
13.62
12.04
12.13
12.52
12.82
12.42
11.56
11.45
10.90
9.63
9.02
8.30
7.34
6.49
6.16

Table C.2: Standard Deviation of percent difference for each inlet velocity in the inclined
configuration

118

C.2.3 Cell Velocity vs. Inlet Velocity in Horizontal and Inclined Positions with

95% Confidence Intervals

Figure C.33: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 1

119

0123456789101101234567891011Figure C.34: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 2

Figure C.35: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 3

120

01234567891011012345678910110123456789101101234567891011Figure C.36: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 4

Figure C.37: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 5

121

01234567891011012345678910110123456789101101234567891011Figure C.38: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 6

Figure C.39: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 7

122

01234567891011012345678910110123456789101101234567891011Figure C.40: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 8

Figure C.41: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 9

123

01234567891011012345678910110123456789101101234567891011Figure C.42: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 10

Figure C.43: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 11

124

01234567891011012345678910110123456789101101234567891011Figure C.44: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 12

Figure C.45: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 13

125

01234567891011012345678910110123456789101101234567891011Figure C.46: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 14

Figure C.47: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 15

126

01234567891011012345678910110123456789101101234567891011Figure C.48: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 16

Figure C.49: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 17

127

01234567891011012345678910110123456789101101234567891011Figure C.50: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 18

Figure C.51: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 19

128

01234567891011012345678910110123456789101101234567891011Figure C.52: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 20

Figure C.53: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 21

129

01234567891011012345678910110123456789101101234567891011Figure C.54: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 22

Figure C.55: Cell velocity vs. inlet velocity with 95% confidence intervals for cell 23

130

01234567891011012345678910110123456789101101234567891011C.3 Results with Radiator in Inclined Position with Shroud At-

tached

C.3.1 Radiator Exit Plane Distribution Before and After Correction

(a) Before correction

(b) After correction

Figure C.56: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 6.40 m/s

(a) Before correction

(b) After correction

Figure C.57: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 6.47 m/s

131

(a) Before correction

(b) After correction

Figure C.58: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 7.11 m/s

(a) Before correction

(b) After correction

Figure C.59: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 7.51 m/s

132

(a) Before correction

(b) After correction

Figure C.60: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 7.95 m/s

(a) Before correction

(b) After correction

Figure C.61: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 8.29 m/s

133

(a) Before correction

(b) After correction

Figure C.62: Radiator exit plane flow distribution with shroud attached before and after
correction for inlet velocity of 8.85 m/s

134

C.3.2 Corrected Radiator Exit Plane Distribution

(a) Velocity

(b) Percent difference

Figure C.63: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 0.26 m/s

(a) Velocity

(b) Percent difference

Figure C.64: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 0.74 m/s

135

(a) Velocity

(b) Percent difference

Figure C.65: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 1.03 m/s

(a) Velocity

(b) Percent difference

Figure C.66: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 1.28 m/s

136

(a) Velocity

(b) Percent difference

Figure C.67: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 1.64 m/s

(a) Velocity

(b) Percent difference

Figure C.68: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 1.83 m/s

137

(a) Velocity

(b) Percent difference

Figure C.69: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 2.12 m/s

(a) Velocity

(b) Percent difference

Figure C.70: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 2.80 m/s

138

(a) Velocity

(b) Percent difference

Figure C.71: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 3.47 m/s

(a) Velocity

(b) Percent difference

Figure C.72: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 4.67 m/s

139

(a) Velocity

(b) Percent difference

Figure C.73: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 5.41 m/s

(a) Velocity

(b) Percent difference

Figure C.74: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 6.40 m/s

140

(a) Velocity

(b) Percent difference

Figure C.75: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 6.47 m/s

(a) Velocity

(b) Percent difference

Figure C.76: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 7.11 m/s

141

(a) Velocity

(b) Percent difference

Figure C.77: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 7.51 m/s

(a) Velocity

(b) Percent difference

Figure C.78: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 7.95 m/s

142

(a) Velocity

(b) Percent difference

Figure C.79: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 8.29 m/s

(a) Velocity

(b) Percent difference

Figure C.80: Radiator exit plane flow distribution with shroud attached and inlet velocity
of 8.85 m/s

143

BIBLIOGRAPHY

144

BIBLIOGRAPHY

[1] S. Ali and J. Foss. “The Discharge Coefficient of a Planar Submerged Slit-Jet”. In:

Journal of Fluids Engineerings 125 (4 2003), pages 613–619.

[2] John Anderson. Computational Fluid Dynamics: the Basics with Applications. McGraw

Hill, 1995.

[3] David Barrent. “Controlled Diffusion Blade Axial Fan: Fluid Mechanical Mechanistic

Effects on Fan Performance”. Master’s thesis. Michigan State University, 2015.

[4] H.H. Brunn. Hot-wire Anemometry. Oxford University Press, 1955.

[5] Yunus Cengel and Afshin Ghajar. Heat and Mass Transfer: Fundamentals and Appli-

cations. 5th edition. McGraw Hill, 2015.

[6] Michael D. Dusel. “An Experimental Investigation of the Aerodynamic Shroud with an
Off-Highway Engine Cooling Fan”. Master’s thesis. Michigan State University, 2005.

[7] J. Foss, J. Peabody, M. Norconk, and A. Lawrenz. “Ambient temperature and free
stream turbulence effects on the thermal transient anemometer”. In: Measurement Sci-
ence and Technology 17.9 (2006), pages 2519–2526.

[8] J. Foss, J. Schwannecke, A. Lawrenz, M. Mets, S. Treat, and M. Dusel. “The ther-
mal transient anemometer”. In: Measurement Science and Technology 15.11 (2004),
pages 2248–2255.

[9] F. Gessner and G. Moller. “Response behaviour of hot wires in shear flow”. In: Journal

of Fluid Mechanics 47 (3 1971), pages 449–468.

[10]

Incropera, DeWitt, Bergman, and Lavine. Fundamentals of Heat and Mass Transfer.
6th edition. John Wiley & Sons, 2006.

[11] James Leung. “Nonuniform Flow over a Thermal Transient Anemometer”. Master’s

thesis. Michigan State University, 2018.

[12] S. Morris and J. Foss. “Transient thermal response of a hot-wire anemometer”. In:

Measurement Science and Technology 14.3 (2003), page 251.

[13] S. Morris, D. Neal, J. Foss, and G. Cloud. “A moment-of-momentum flux mass air flow

measurement device”. In: Measurement Science and Technology 12 (2001), N9–N13.

[14] Frank M. White. Fluid Mechanics. 7th edition. McGraw Hill, 2011.

145