1. AN EXPERIMENTAL INVESTIGATION INTO
THE ROUTES TO BYPASS TRANSITION
Author
Domhnaill Hernon
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
COLLEGE OF ENGINEERING, UNIVERSITY OF LIMERICK, IRELAND
Supervisor
Dr. Edmond Walsh
Submitted to the University of Limerick, November 2007
2. The substance of this thesis is the original work of the author and due ref-
erence and acknowledgement has been made, when necessary, to the work
of others. No part of this thesis has previously been accepted for any degree
nor has it been submitted for any other award.
Domhnaill Hernon Candidate
The substance of this thesis is the original work of the author and due ref-
erence and acknowledgement has been made, when necessary, to the work
of others. No part of this thesis has previously been accepted for any degree
nor has it been submitted for any other award.
Dr. Edmond Walsh Principal Adviser
This thesis was defended on the 5/10/2007.
Examination Committee
Chairman Dr. John Jarvis Univeristy of Limerick
External Examiner Prof. Terrence W. Simon University of Minnesota
Internal Examiner Dr. David Newport Univeristy of Limerick
ii
3. ABSTRACT
This report documents an experimental investigation into the bypass route to transition
for zero-pressure gradient laminar boundary layer flow when under the influence of ele-
vated freestream turbulence (FST). A complete understanding of how disturbances from
the freestream enter the boundary layer and their subsequent evolution towards turbulent
flow has been the source of intense investigation for some time, both experimentally and
numerically. However, the breakdown process is still not fully understood and it is the main
objective of this investigation to give some experimental insight into the pre-transitional
flow characteristics that initiate the transition from a laminar to a turbulent state. What
follows is a summary of the main results of this doctoral thesis.
Through thermal anemometry a measure of the change in receptivity of the laminar
boundary layer with increased FST level was achieved by examining the wall-normal pro-
files of the skewness distribution. The location of peak negative skewness was used as a
measure of the penetration depth of disturbances into the boundary layer and was shown
to demonstrate the same parameter dependence as theory, i.e., the penetration depth scaled
with the Reynolds number, the frequency of the largest freestream eddies and the shear
stress. Furthermore, a relationship is presented that predicts the wall-normal location in the
boundary layer where the most intense negative spike activity is observed and this location
is considered to represent the most probable wall-normal location of turbulent spot produc-
tion. These relationships represent the first attempt at predicting the wall normal location
of breakdown.
Taking mean statistics is not sufficient in fully explaining the routes to bypass tran-
sition. By examining profiles of the maximum positive and negative of the streamwise
fluctuation velocity it was demonstrated that the peak disturbance magnitudes of the low-
and high-speed streaks far exceed those presented in RMS terms, i.e., the Klebanoff mode
disturbance profiles. In this investigation, at transition onset, the peak disturbance associ-
ated with the negative fluctuation velocity was approximately 40% of the freestream ve-
locity for all turbulence intensities considered, and this was always greater than the peak
positive value. Furthermore, the location of the peak negative disturbance moved towards
the boundary layer edge and the location of the peak positive disturbance moved towards
the wall as the location of transition onset approached. Due to the higher disturbance am-
plitudes associated with the peak negative fluctuation velocities it can be inferred that the
breakdown to turbulence most likely occurs on the low-speed regions that are lifted to the
upper portion of the boundary layer. Simultaneous measurements between a hotwire probe
traversed throughout the boundary layer thickness and hotfilm probes placed at the wall
demonstrated that high-frequency structures with negative fluctuation velocity are observed
away from the wall before any near-wall turbulent spots are formed and an estimate of the
leading edge overhang size is gained. These results lend further support to the boundary
layer edge breakdown concept under naturally occurring disturbance conditions. A num-
ber of relationships are presented that allow for accurate prediction of the new parameters
measured.
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4. Acknowledgments
First and foremost I would like to thank my supervisor Dr. Edmond Walsh for always being
there to answer my questions and to engage in conversation on all aspects of engineering.
I would like also to especially thank my girlfriend Lisa for all of her love and support
and for always being there for me.
My parents have always been a major influence in my life and it is fair to say that
without their encouragement and support I would not have had the confidence to do a PhD.
I would like to thank all of the lads that joined SRI at the same time as myself for their
friendship and for the good fun we had. Thank you Colin, Dave, John (big thanks to John
for letting me crash at his place) Mike, and Magali. Thanks also to my house mates Ronan
and Lisa for the good company over the last number of years. I would especially like to
thank Cian for his help with the SED programme, Dave for his help with Matlab and Kevin
for his help with Adobe illustrator.
I would also like to thank the technical staff at the University. Pat Kelly, Paddy O’Donnell,
Ken Harris and especially John Cunningham and Paddy O’Regan. Dr. Philip Griffin gave
me his Wavelet code that was donated to the group by Prof. Ralph Volino and for this I
must thank both of them.
I must also thank Dr. Marc Hodes and Dr. Alan Lyons who were instrumental in
getting me a position with Bell Labs Ireland and also for allowing me the time to complete
my thesis.
I wish to give thanks to Prof. Donald McEligot for all of his engaging comments and for
sharing his vast experience with me throughout our manuscript draft process. Also thanks
to his wife Julie for taking the time to help with our correspondence over the last few years.
I would like to thank Science Foundation Ireland (SFI) and the H.T Hallowell Jr Grad-
uate Scholarship for their financial support over the three years.
iv
7. 4.7.1 Deviation from Blasius . . . . . . . . . . . . . . . . . . . . . . . . 78
4.7.2 Measure of Increased Energy Dissipation Rates . . . . . . . . . . . 79
4.8 The Change in Flow Structure from the Wall to the Freestream During the
Early Stages of Turbulent Spot Development . . . . . . . . . . . . . . . . . 82
5 The Route to Bypass Transition: Part 1-The Receptivity of the Boundary
Layer to Freestream Disturbances 88
5.1 Normalised Skewness Profiles and Signal Level Probability . . . . . . . . . 88
5.2 On the Significance of the Skewness and PDF Results . . . . . . . . . . . . 96
5.3 Parameter Dependence for Penetration Depth (PD) Measure Using Peak
Skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 The Route to Bypass Transition: Part 2-Disturbance Growth and Breakdown 110
6.1 Instantaneous Velocity Fluctuation Profiles . . . . . . . . . . . . . . . . . . 110
6.1.1 Maximum Positive and Negative Fluctuations Scaled with the
Freestream Velocity . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.1.2 Maximum Positive and Negative Fluctuations Scaled with the Lo-
cal Mean Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2 A New Method To Predict the Location of Transition Onset Based on Local
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.3 Simultaneous Hotwire and Hotfilm Measurements . . . . . . . . . . . . . . 129
7 Conclusions and Recommendations for Future Work 147
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography 154
A MATLAB Code 163
B Example of Uncertainty Estimation 170
C Published Work 171
vii
8. List of Tables
2.1 Geometric description of turbulence grids and range of turbulence charac-
teristics available. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Tabulated results for each measured test condition presented in figure 4.2,
where the leading edge distance downstream of the turbulence grid is ∆L. . 65
4.2 Comparison between the current measurements and the proposed transition
onset models of Brandt et al. (2004). . . . . . . . . . . . . . . . . . . . . 73
5.1 Summary of the average locations for the peak negative skewness values. . 96
6.1 Summary of the peak locations for the high-speed streaks (hs) and the low-
speed streaks (ls) when scaled with U∞ and Umean . . . . . . . . . . . . . . 125
viii
9. List of Figures
1.1 Smoke flow visualisation of streamwise streaks, streamwise wiggles and
turbulent spots (Matsubara and Alfredsson, 2001). . . . . . . . . . . . . . . 5
1.2 Sketch of the bypass transition process adapted from Zaki and Durbin (2006). 12
2.1 Sketches of constant temperature anemometer probes (DantecDynamics,
2006). (a) Hotwire probe. (b) Hotfilm probe. . . . . . . . . . . . . . . . . . 18
2.2 Simple schematic of Wheatstone bridge used to maintain probes in constant
temperature mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Hotwire calibration using King’s law. , Measured data points. ——,
Trend line fit to data points. The equation of the trend line gives the co-
efficients in King’s law with A = −0.83 and B = 7.075 and n = 0.45. . . . 21
2.4 Picture of the hot wire traverse mechanism (O’Donnell, 2000). . . . . . . . 23
2.5 Illustration of the hotfilm array. (a) Zoomed in picture of the hotfilm el-
ements courtesy of Kevin Nolan. (b) Schematic of Senflex 9101 hotfilm
elements at 180◦ orientation compared to (a). . . . . . . . . . . . . . . . . 24
2.6 Frequency response of the hotwire probe (Lomas, 1986). . . . . . . . . . . 25
2.7 Photograph of experimental facility. (a) (1) Controller unit; (2) AN-1005
CTA system; (3) Data acquisition computer; (4) DSPACE stepper motor
controller; (5) Test section; (6) Diffuser; (7) Contraction. (b) (8) Flat plate;
(9) Hotwire and stepper motor support; (10) Stepper motor; (11) Hotwire
support; (12) Turbulence grid. . . . . . . . . . . . . . . . . . . . . . . . . 28
2.8 Sketch of the three flat plate designs (not to scale). (a) Roach and Brierley
(1990). (b) Jonas et al. (1999). (c) Becker et al. (2002). . . . . . . . . . . . 30
ix
10. 2.9 Illustration of experimental arrangement (not to scale). ∆L is the plate
leading edge distance downstream of the grids. . . . . . . . . . . . . . . . 31
2.10 Flow visualisation demonstrating the flow characteristics on the flat plate
test surface with the flap angles set to zero, maximum (approximately
+40 degrees) and -15 degrees using the oil and powder mixture at Rex =
1, 500, 000. The left hand figure is a full view of the plate with the flap at
zero degrees and the pictures at the right hand side are of zoomed in regions
of the plate with the flap at different settings. . . . . . . . . . . . . . . . . . 32
2.11 Flow visualisation demonstrating the flow characteristics on the flat plate
test surface with various flap angles using the shear sensitive liquid crystal
mixture at Rex = 1, 500, 000. (a) zero degrees. (b) maximum (approxi-
mately +40 degrees). (c) -15 degrees. . . . . . . . . . . . . . . . . . . . . 33
2.12 (a) Measured velocity profiles compared to theoretical Blasius velocity pro-
file. ◦, (Reθ , T u) =(178, 0.2%); , (Reθ , T u)= (303, 0.2%); , (Reθ , T u)=
(351, 0.2%); +, (Reθ , T u)= (410, 1.3%); , (Reθ , T u)= (442, 1.3%); ——,
Blasius profile. (b) The velocity distribution over the plate. . . . . . . . . . 35
2.13 Sketch of PP turbulence grid. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.14 Turbulence decay for all three grids. , PP1, Red = 6000; , PP1, Red =
2600; ◦, PP2, Red = 760; , PP2, Red = 1310, +, SMR, Red = 100, ,
SMR, Red = 430. ——, Eqn. 2.5; - - -, Eqn 2.6. . . . . . . . . . . . . . . . 38
2.15 Examples of the non-dimensional autocorrelation function R(T). , Xgrid =
0.456 mm, Red = 6000. ; Xgrid =0.456 mm, Red =2600; ; Xgrid =0.456
mm, Red = 2600. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.16 Integral and dissipation time scale estimation from the autocorrelation func-
tion, (R(T)) at T u = 1.3%. ——, R(T). . . . . . . . . . . . . . . . . . . . . 40
2.17 Integral length scale evolution. , PP1, Red = 6000; ∗, PP1, Red = 2600;
◦, PP2, Red = 760; , PP2, Red = 1310, +, SMR, Red = 100, , SMR,
Red = 430; ×, estimation of Λx using Eqn. 2.10 for the SMR grid. ——,
Eqn. 2.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
x
11. 2.18 Evolution of Λx and λx downstream of turbulent grids. , PP1 grid; ,
PP2 grid; , SMR grid. Open symbols are λx . . . . . . . . . . . . . . . . . 42
2.19 Non-dimensional freestream energy spectra compared to the von Karman
one-dimensional isotropic approximation, Eqn. 2.10 (Hinze, 1975). ,
T u = 1.3%; •, T u = 4.2%. , T u = 6%. . . . . . . . . . . . . . . . . . . 43
3.1 Dual slope method for intermittency detection within the boundary layer,
Reθ = 577. +, y/δ=0.3, γ = 0.1%. . . . . . . . . . . . . . . . . . . . . . . 48
3.2 (a) Voltage trace of hotwire placed near boundary layer edge (y/δ = 0.86)
at T u = 1.3%. (b) Time derivative of the hotwire trace squared (du/dt)2 . . 49
3.3 Comparison between the magnitude of two turbulent spots at low- and
high-turbulence intensity. Complete trace. ——, T u = 1.3%, Reθ = 577,
y/δ = 0.3. ——, T u = 6%, Reθ = 165, y/δ = 0.14. . . . . . . . . . . . . 50
3.4 Full trace where the arrow signifies the the portion of the trace to be anal-
ysed. Test conditions are T u = 1.3% and Reθ = 577 . . . . . . . . . . . . 50
3.5 Typical velocity profile in wall coordinates compared to the linear law of
the wall. , Reθ =94, %T ule =7; ——, u+ =y + . (b) ——, Local rate of
energy dissipation, , calculated for square symbols case in (a). . . . . . . 52
3.6 Example of the Mexican hat wavelet transform. . . . . . . . . . . . . . . . 53
3.7 Demonstration of the advantages of wavelet over FFT analysis. . . . . . . . 55
3.8 Comparison between the energy spectrum and the time-average of the wavel-
et map, y/δ = 0.3, Reθ = 577 and %T u = 1.3. ——, Fourier spectrum. ◦,
time-averaged wavelet spectrum. . . . . . . . . . . . . . . . . . . . . . . . 56
3.9 Sample illustration showing the calculation of the 5th and 95th statistical
distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 Example of umax and umin determination. . . . . . . . . . . . . . . . . . . 58
4.1 Hotfilm detection of turbulent spot, U∞ =17 m/s and T u = 1.3%. Inlay
caption is zoomed in view of the turbulent spot. . . . . . . . . . . . . . . . 62
xi
12. 4.2 Comparison of transition onset Reynolds numbers against the transition
onset correlations of Mayle (1991) and Fransson et al. (2005). , Reθ =
442 − 577, T u = 1.3%; , Reθ = 186 − 209, T u = 3.1%; •, Reθ = 154 −
167, T u = 4.2%; , Reθ = 131 − 166, T u = 6%; +, Reθ = 123 − 139,
T u = 7%. ——, Mayle (1991) correlation, Reθ = 400T u−5/8 . - - -,
Fransson et al. (2005) correlation, Reθ = 745/T u, at γ=0.1. . . . . . . . . 64
4.3 Plot illustrating the relationship between urms,max and U τ at transition on-
set for the same Reθ values presented in figure 4.2. , T u = 1.3%; ,
T u = 3.1%; •, T u = 4.2%; , T u = 6%; +, T u = 7%. . . . . . . . . . . . 66
4.4 Non-dimensional velocity profiles over the complete range of %T u com-
pared to the linear law of the wall. ——, U + =Y + . - - - -, Blasius velocity
profile. , Reθ = 303, T u = 1.3%; , Reθ = 186, T u = 3.1%; •,
Reθ = 181, T u = 4.2%; , Reθ = 131, T u = 6%; +, Reθ = 139, T u = 7%. 67
4.5 Growth of disturbances through the laminar boundary layers investigated
at transition onset. , (Reθ , Xle , T u)= (577, 0.556m, 1.3%); , ((Reθ ,
Xle , T u)=(209, 0.195m, 3.1%); , (Reθ , Xle , T u)=(167, 0.272m, 4.2%);
•, (Reθ , Xle , T u)=(166, 0.255m, 6%); , (Reθ , Xle , T u)=(139, 0.325m,
7%). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.6 (a) Plot illustrating how urms,max varies in linear proportion to Re0.5 . (b)
x
0.5
urms,max /U∞ scaled with Rex . (c) urms,max /U∞ %T u scaled with Re0.5 .
x
, T u = 1.3%; , T u = 3.1%; •, T u = 4.2%; , T u = 6%; +, T u = 7%. . 69
4.7 Streamwise energy growth of streaks as a function of Rex for various FST
levels. , T u = 1.3% (Rex has been scaled down by a factor of 10 for
visual purposes); , T u = 3.1%; •, T u = 4.2%; , T u = 6%; +, T u =
7%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.8 Energy growth on streamwise streaks. ——, Trend line fit to experimental
data, G ∝ %T u2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.9 Velocity traces from the near-wall to the freestream region at T u = 1.3%
and Reθ = 577 (near transition onset). . . . . . . . . . . . . . . . . . . . . 74
xii
13. 4.10 Energy spectra for the same conditions as figure 4.9. ×, y/δ = 0.3; +,
y/δ = 0.46; ◦, y/δ = 0.8; ——, y/δ = 3.4. . . . . . . . . . . . . . . . . . 75
4.11 Velocity traces from the near-wall to the boundary layer edge region at
T u = 3.1% and Reθ = 186 (near transition onset). (a) Select velocity
traces. (b) Close-up view of double negative spike at y/δ = 0.93. (c)
Close-up view of multiple negative spike at y/δ = 0.93. . . . . . . . . . . . 75
4.12 (a) Energy spectra for the same conditions as figure 4.11 at T u = 3.1%.
+, y/δ = 0.13; ◦, y/δ = 0.34; ×, y/δ = 0.93; ——, y/δ = 1.2. (b)
Reθ = 106. , y/δ = 1; - - -, y/δ = 1.2. . . . . . . . . . . . . . . . . . . . 76
4.13 Velocity traces from the near-wall to the boundary layer edge region at
T u = 6% and Reθ = 131 (near transition onset). . . . . . . . . . . . . . . 76
4.14 Energy spectra for the same conditions as figure 4.13. ×, y/δ = 0.13; +,
y/δ = 0.28; ◦, y/δ = 0.95; ——, y/δ = 1.2. . . . . . . . . . . . . . . . . . 77
4.15 Deviation in laminar velocity profiles due to increased FST compared to
the Blasius velocity profile. ◦, (Reθ , Xle , T u) =(178, 0.255m, 0.2%); ,
(Reθ , Xle , T u)= (442, 0.455m, 1.3%); , ((Reθ , Xle , T u)=(209, 0.195m,
3.1%); , (Reθ , Xle , T u)=(167, 0.272m, 4.2%); •, (Reθ , Xle , T u)=(166,
0.255m, 6%); , (Reθ , Xle , T u)=(139, 0.325m, 7%); ——, Blasius profile. 79
4.16 Increase in laminar dissipation coefficient, Cd , with increase in turbulence
intensity at leading edge. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.17 Variation in Cd for the measured test conditions in the current investigation
compared to Eqn. (3.11), with variation in %T u and Reθ . , T u = 1.3%;
, T u = 3.1%; •, T u = 4.2%; , T u = 6%; +, T u = 7%; ——, Expo-
nential trendline given by Eqn. (4.3); - - - -, ±10%, . . . . . . . . . . . . . 81
4.18 Development of high-frequency structures at various stages through the
boundary layer thickness at Reθ = 577 (transition onset) and T u = 1.3%.
The upper plots are the wavelet maps and the lower plots are the corre-
sponding fluctuation velocity/voltage traces. (a) Wall. (b) y/δ = 0.3. (c)
y/δ = 0.41. (d) y/δ = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
xiii
14. 4.19 Wavelet maps and fluctuation velocity traces at T u = 3.1% and 6% in the
near-wall and boundary layer edge regions. (a) T u = 3.1%, Reθ = 186,
y/δ = 0.13. (b) T u = 3.1%, Reθ = 186, y/δ = 1.07. (c) T u = 6%,
Reθ = 165, y/δ = 0.14. (d) T u = 6%, Reθ = 165, y/δ = 0.77. . . . . . . . 86
5.1 Skewness distribution at T u = 1.3%. , Reθ = 352; , Reθ = 392; ,
Reθ = 577. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Skewness distribution at T u = 3.1%. , Reθ = 106; , Reθ = 176; ,
Reθ = 186. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.3 Skewness distribution at T u = 4.2%. ◦, Reθ = 76; , Reθ = 107; ,
Reθ = 115; , Reθ = 181. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Skewness distribution at T u = 6%. , Reθ =83; , Reθ =107; ,
Reθ =131. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.5 Skewness distribution at T u = 7%. , Reθ =66; , Reθ =93; , Reθ =123. . 93
5.6 Probability distribution functions (PDF) for Reθ = 577 and T u = 1.3%.
♦, y/δ = 0.3; +, y/δ = 0.5; ◦, y/δ = 1. . . . . . . . . . . . . . . . . . . . 94
5.7 Probability distribution functions (PDF) for Reθ = 186 and T u = 3.1%.
♦, y/δ = 0.11; ×, y/δ = 0.48; ◦, y/δ = 0.93. . . . . . . . . . . . . . . . . 94
5.8 Probability distribution functions (PDF) for Reθ = 182 and T u = 4.2%.
♦, y/δ = 0.17; ×, y/δ = 0.51; ◦, y/δ = 0.97. . . . . . . . . . . . . . . . . 95
5.9 Probability distribution functions (PDF) for Reθ = 131 and T u = 6%. ♦,
y/δ = 0.1; ×, y/δ = 0.51; ◦, y/δ = 0.95. . . . . . . . . . . . . . . . . . . 95
5.10 Probability distribution functions (PDF) for Reθ = 123 and T u = 7%. ♦,
y/δ = 0.17; ×, y/δ = 0.5; ◦, y/δ = 0.93. . . . . . . . . . . . . . . . . . . 96
5.11 Variation in shear from the wall to the boundary layer edge. , T u = 1.3%
at Reθ = 577. , T u = 3.1% at Reθ = 186. , T u = 6% at Reθ = 131.
All measurements near transition onset. . . . . . . . . . . . . . . . . . . . 97
5.12 Variation in shear from the wall to the boundary layer edge at approxi-
mately the same Reθ . , T u = 1.3% at Reθ = 148. , T u = 3.1% at
Reθ = 176. , T u = 6% at Reθ = 131. . . . . . . . . . . . . . . . . . . . 97
xiv
15. 5.13 Basic sketch illustrating the interaction between negative jets and freestream
vortices as the boundary layer advances towards transition onset. . . . . . . 100
5.14 Variation in the maximum and minimum of the instantaneous velocities
from the wall to the boundary layer edge for T u = 1.3% ——, Average ve-
locity; , Minimum instantaneous velocities; ♦, Maximum instantaneous
velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.15 Variation in penetration depth (PD) measured from the boundary layer edge
with %T u according to table 5.1. ——, trend line fit to data points, P D ∝
0.0005%T u − 0.0005. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.16 Variation of penetration depth (PD) measured from the boundary layer edge
over the range of test conditions. ♦, T u = 1.3%; , T u = 3.1%; ◦, T u =
4.2%; , T u = 6%; +, T u = 7%. ——, Trend line fit to experimental data
P D ∝ (ωRex )−0.47 . - - -, P D ∝ (ωRex )−0.133 by Jacobs and Durbin (1998). 104
5.17 Variation of penetration depth (PD) measured from the boundary layer edge
over the range of test conditions. ♦, T u = 1.3%; , T u = 3.1%; ◦, T u =
4.2%; , T u = 6%; +, T u = 7%. ——, Trend line fit to experimental data
P D ∝ (ωRex τw )−0.32 . - - -, P D ∝ (ωRex τ )−0.33 by Jacobs and Durbin
(1998), where τ was replaced with the current experimentally measured τw
values to allow for comparison. . . . . . . . . . . . . . . . . . . . . . . . . 105
5.18 Variation of penetration depth (PD) measured from the boundary layer edge
over the range of test conditions. ♦, T u = 1.3%; , T u = 3.1%; ◦, T u =
4.2%; , T u = 6%; +, T u = 7%. ——, Trend line fit to experimental data
√
P D ∝ (ωρUe Rex )−0.31 . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
2
5.19 Variation in penetration depth (PD) as a function of y/δ (non-dimensional
representation of PD), %T u and Rex . ——, trend line fit to data points,
0.378
y/δ = 164.3/%T uRex . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.20 Variation in penetration depth (PD) as a function of y/δ (non-dimensional
representation of PD), %T u and Reθ . ——, trend line fit to data points,
y/δ = 95/%T uRe0.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
θ
xv
16. 5.21 Variation in penetration depth (PD) as a function of y/δ (non-dimensional
representation of PD), %T u and Rex at transition onset. ——, trend line
fit to data points, y/δ = 200/%T uRe0.4 . Note that when these results are
x
plotted in terms of Reθ the correlation becomes y/δ = 128/%T uRe0.73 . . . 109
θ
6.1 Maximum positive and negative fluctuation velocities presented in terms
of a local disturbance intensity (%T uL ) at T u = 1.3%. (a) Reθ = 352.
(b) Reθ = 392. (c) Reθ = 577 (transition onset) with high-frequency
events removed. (d) Reθ = 577 without high-frequency events removed.
, maximum negative value; ♦, maximum positive value; ×, RMS value. . 111
6.2 Statistical distribution of the 5th and 95th , 1st , 99th , 0.1st and 99.9th , and
the 0.01st and 99.99th levels for T u = 1.3% and Reθ = 352. , 0.01th ; ♦,
99.99th ; ——, 0.1st ; - - -, 99.9th ; ——, 1st ; - - -, 99th ; ——, 5th ; - - -, 95th . . 113
6.3 Maximum positive and negative fluctuation velocities presented in terms of
a local disturbance intensity (%T uL ) at T u = 3.1%. (a) Reθ = 106. (b)
Reθ = 176. (c) Reθ = 186 (transition onset). , maximum negative value;
♦, maximum positive value; ×, RMS value. . . . . . . . . . . . . . . . . . 114
6.4 Maximum positive and negative fluctuation velocities presented in terms
of a local disturbance intensity (%T uL ) at T u = 4.2%. (a) Reθ = 76. (b)
Reθ = 107. (c) Reθ = 115. (d) Reθ = 181 (transition onset). , maximum
negative value; ♦, maximum positive value; ×, RMS value. . . . . . . . . . 115
6.5 Maximum positive and negative fluctuation velocities presented in terms
of a local disturbance intensity (%T uL ) at T u = 6%. (a) Reθ = 83. (b)
Reθ = 107. (c) Reθ = 131 (transition onset). , maximum negative value;
♦, maximum positive value; ×, RMS value. . . . . . . . . . . . . . . . . . 115
6.6 Maximum positive and negative fluctuation velocities presented in terms
of a local disturbance intensity (%T uL ) at T u = 7%. (a) Reθ = 66. (b)
Reθ = 93. (c) Reθ = 123 (transition onset). , maximum negative value;
♦, maximum positive value; ×, RMS value. . . . . . . . . . . . . . . . . . 116
xvi
17. 6.7 Wall-normal disturbance profiles of the low- and high-speed streaks corre-
sponding to the same results presented in figures 6.1, 6.3 and 6.5 where
the same symbols apply. (a) T u = 1.3%. (b) T u = 3.1%. (c) T u = 6%. . . 117
6.8 Variation in wall-normal location of the peak minimum of the streamwise
fluctuation velocities. (a) Results of Brandt et al. (2004) where the different
line styles represent difference freestream integral length scales at constant
T u = 4.7%. (b) Current results presented as a comparison to DNS. ,
T u = 1.3% where the Reynolds numbers have been reduced by a factor
of 10 to allow for a clear comparison; , T u = 3.1%; •, T u = 4.2%; ,
T u = 6%; +, T u = 7%, where where δ1 is the displacement thickness . . . 118
6.9 Maximum positive and negative fluctuation velocities presented in terms
of a disturbance intensity about the mean (% u/Umean ) at T u = 1.3%.
(a) Reθ = 352. (b) Reθ = 392. (c) Reθ = 577 with high-frequency
events removed. (d) Reθ = 577 without high-frequency events removed.
, maximum negative value; ♦, maximum positive value. . . . . . . . . . . 121
6.10 Maximum positive and negative fluctuation velocities presented in terms
of a disturbance intensity about the mean (% u/Umean ) at T u = 3.1%. (a)
Reθ = 106. (b) Reθ = 176. (c) Reθ = 186 (transition onset). , maximum
negative value; ♦, maximum positive value. . . . . . . . . . . . . . . . . . 121
6.11 Maximum positive and negative fluctuation velocities presented in terms
of a disturbance intensity about the mean (% u/Umean ) at T u = 4.2%. (a)
Reθ = 76. (b) Reθ = 107. (c) Reθ = 181 (transition onset). , maximum
negative value; ♦, maximum positive value. . . . . . . . . . . . . . . . . . 122
6.12 Maximum positive and negative fluctuation velocities presented in terms
of a disturbance intensity about the mean (% u/Umean ) at T u = 6%. (a)
Reθ = 83. (b) Reθ = 107. (c) Reθ = 131 (transition onset). , maximum
negative value; ♦, maximum positive value. . . . . . . . . . . . . . . . . . 122
xvii
18. 6.13 Maximum positive and negative fluctuation velocities presented in terms
of a disturbance intensity about the mean (% u/Umean ) at T u = 7%. (a)
Reθ = 66. (b) Reθ = 93. (c) Reθ = 123 (transition onset). , maximum
negative value; ♦, maximum positive value. . . . . . . . . . . . . . . . . . 123
6.14 Evolution of the maximum negative and positive of the streamwise fluctua-
tion velocities over the range of FST levels investigated. (a) Maximum neg-
ative values. (b) Maximum positive values. , T u = 1.3%; , T u = 3.1%;
•, T u = 4.2%; , T u = 6%; +, T u = 7%. . . . . . . . . . . . . . . . . . . 126
6.15 Trendline fit to maximum negative fluctuation values when scaled with
0.5
%T u and Rex . , T u = 1.3%; , T u = 3.1%; •, T u = 4.2%; , Tu =
6%; +, T u = 7%. ——, Trend line fit to experimental data, %T uL(max,neg) /%T u =
0.066(Rex )0.44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.16 Trendline fit to maximum positive fluctuation values when scaled with
0.5
%T u and Rex . , T u = 1.3%; , T u = 3.1%; •, T u = 4.2%; , Tu =
6%; +, T u = 7%. ——, Trend line fit to experimental data, %T uL(max,pos) /%T u =
0.082(Rex )0.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.17 Comparison between the transition onset prediction correlations of Mayle
(1991), Fransson et al. (2005) and the current results. ——, Correlation
presented in the current investigation Reθ = (370/%T u)1.17 ; · · ·, Fransson
et al. (2005) correlation Reθ = 745/%T u; - - - , Mayle (1991) correlation
Reθ = 400%T u−5/8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.18 Non-dimensionalised skewness distribution at transition onset. Reθ = 410
and T u = 1.3%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.19 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 1.26.
The hotwire probe is labelled ”wire” and the location of the film probes
are given by their distance downstream of the plate leading edge. ——,
xle = 221mm; ——, xle = 241.3mm; ——, W ire xle = 250mm; ——,
xle = 261.6mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
xviii
19. 6.20 Zoomed in view for fluctuating voltage trace of all four simultaneously
sampled probes at Reθ = 410 and T u = 1.3%. The SN probe is at y/δ =
1.26. (a) Fluctuating voltage. (b) Corresponding (du/dt)2 . Same legend as
figure 6.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.21 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 1.07. Same
legend as figure 6.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.22 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 1.07. (a)
fluctuating voltage. (b) corresponding (du/dt)2 . Same legend as figure 6.19. 133
6.23 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 1.07. (a)
fluctuating voltage. (b) corresponding (du/dt)2 . (c) fluctuating voltage.
(d) corresponding (du/dt)2 . Same legend as figure 6.19. . . . . . . . . . . 133
6.24 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 0.9 (close
to peak skewness). Same legend as figure 6.19. . . . . . . . . . . . . . . . 134
6.25 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 0.9. (a)
Fluctuating voltage. (b) Corresponding (du/dt)2 . (c) Fluctuating voltage.
(d) Corresponding (du/dt)2 . Same legend as figure 6.19. . . . . . . . . . . 135
6.26 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 410 and T u = 1.3%. The hotwire probe is at y/δ = 0.9. (a)
Fluctuating voltage. (b) Corresponding (du/dt)2 . Same legend as figure 6.19.136
6.27 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 450 and T u = 1.3%. The hotwire probe is at y/δ = 0.9 (close
to peak skewness). ——, xle = 221mm; ——, xle = 241.3mm; ——,
W ire xle = 247.7mm; ——, xle = 261.6mm. . . . . . . . . . . . . . . . . 137
xix
20. 6.28 Fluctuating voltage traces for all four simultaneously sampled probes at
Reθ = 450 and T u = 1.3%. The hotwire probe is at y/δ = 0.9. Same
legend as figure 6.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.29 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 450 and T u = 1.3%. The hotwire probe is at y/δ = 0.6. Same
legend as figure 6.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.30 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 450 and T u = 1.3%. The hotwire probe is at y/δ = 0.41. Same
legend as figure 6.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.31 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 158 and T u = 4.2%. The hotwire probe is at y/δ = 0.8. ——,
xle = 231.2mm; ——, xle = 246.4mm; ——, W ire xle = 259.1mm;
——, xle = 272mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.32 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 158 and T u = 4.2%. The hotwire probe is at y/δ = 0.8. (a)
Fluctuating voltage. (b) Corresponding (du/dt)2 without wire. (c) Fluctu-
ating voltage. (d) Corresponding (du/dt)2 without wire. Same legend as
figure 6.31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.33 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 123 and T u = 7%. The hotwire probe is at y/δ = 0.58. ——,
xle = 231.2mm; ——, xle = 241.3mm; ——, W ire xle = 254mm; ——,
xle = 264.2mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6.34 Fluctuating voltage trace for all four simultaneously sampled probes at
Reθ = 123 and T u = 7%. The hotwire probe is at y/δ = 0.58. (a)
Fluctuating voltage. (b) Corresponding (du/dt)2 . (c) Fluctuating voltage.
(d) Corresponding (du/dt)2 . Same legend as figure 6.33. . . . . . . . . . . 142
xx
21. 6.35 (a) Simple illustration for the argument put forward against the concept that
a turbulent spot may develop at the wall, where xU∞ is the unknown veloc-
ity that the upper portion of the spot must travel in order for the near-wall
breakdown hypothesis to be correct. (b) Boundary layer edge breakdown
scenario. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
xxi
22. Nomenclature
A Hotwire calibration constant [-]
a Overheat ratio [-]
B Hotwire calibration constant [-]
b Wavelet constant [-]
Cd Dissipation coefficient [-]
Cf Skin friction coefficient [-]
c Wavelet conversion from scale to frequency [-]
d Grid bar diameter [m]
d1 Energy converted to heat by viscous dissipation [Wm2 k−1 ]
E Disturbance energy [-]
E Energy spectral density [m2 s−1 ]
E Expectation operator [-]
Ec Temperature corrected voltage [volts]
Es Temperature corrected measured voltage [volts]
E0 Zero voltage [volts]
f Frequency [Hz]
fc Frequency cut-off [Hz]
G Disturbance energy growth [-]
g(t) Time series [-]
h Maximum height of frequency response curve [-]
k(y) Wall-normal wavenumber [m−1 ]
M Turbulence grid mesh length [m]
n Power law exponent in hotwire calibration [-]
R(T ) Autocorrelation function [-]
Rw Wire resistance [ohms]
R20 Wire resistance at room temperature [ohms]
Red Reynolds number based on hotwire diameter [-]
xxii
23. Rex Reynolds number based on streamwise distance [-]
Reθ Reynolds number based on momentum thickness [-]
T Temperature [K]
T Time delay [s]
Tu Turbulence intensity [-]
T uL Local turbulence intensity [-]
Tr Reference temperature [K]
Ts Sensor temperature [K]
Tw Temperature of wire [K]
T20 Ambient temperature [K]
U Local, instantaneous streamwise velocity [m/s]
U Mean streamwise velocity (Umean ) [m/s]
Uτ Skin friction velocity [m/s]
U+ Non-dimensional streamwise velocity [-]
u Fluctuating streamwise velocity [m/s]
V Mean tranverse velocity [m/s]
Vs Measured mean voltage [volts]
vs Measured fluctuating voltage [volts]
w(t) Wavelet function [-]
w(f, t) Wavelet coefficient [-]
x Streamwise distance [m]
Y+ Non-dimensional wall-normal velocity [-]
y Wall-normal distance [m]
Greek Symbols
α20 Thermal coefficient of resistance at ambient [K−1 ]
β Spanwise wavenumber [m−1 ]
γ Intermittency [-]
∆L Distance between turbulence grid and leading edge [m]
∆t Time difference [s]
xxiii
24. δ Boundary layer thickness [m]
δ1 Boundary layer displacement thickness [m]
Local rate of energy dissipation [m2 s−3 ]
Rate of energy dissipation per unit area [ms−3 ]
η Blasius parameter [-]
θ Momentum thickness [m]
Λ Integral length scale [m]
λ Dissipation length scale [m]
µ Dynamic viscosity [Nsm−2 ]
µ3 Third central moment about the mean [-]
ν Kinematic viscosity [m2 s−1 ]
ρ Density [kg.m−3 ]
Σ Summation sign [-]
σ Standard deviation [-]
τ Shear stress [Nm−2 ]
τ Time constant [s]
τw Wall shear stress [Nm−2 ]
Φ Incompressible viscous dissipation function [Jm−3 s−1 ]
ω Frequency of the largest freestream eddies [Hz]
Subscripts
le Leading edge conditions
max Maximum quantity
mean Time-averaged quantity
min Minimum quantity
neg Negative quantity
pos Positive quantity
RM S Root mean square
∞ Freestream parameter
xxiv
25. Chapter 1
Introduction
1.1 Research Motivation
The transition from a laminar to a turbulent state is one of the most ubiquitous features
of fluid flow. Traditionally, the term laminar flow suggested that the flow is comprised of
laminae or layers of fluid which glide over one another with relative ease and little mixing.
At some stage in the laminar boundary layer development the flow becomes unstable and
transitions to a turbulent state. Given long enough all flow types will transition and this fact
gave rise to the statement by Moin and Kim (1997) that in nature ”turbulence is the rule
rather than the exception”.
There are generally three main types of boundary layer transition scenario depending
on the level of ambient disturbance; one is known as the orderly route to transition where
Tollmien-Schlichting (TS) instabilities develop and the flow eventually breaks down into
patches of turbulence called turbulent spots. This mode of transition is well understood
(Tollmien, 1929; Schlichting, 1933) and occurs when the level of freestream disturbance is
very low. In the second mode of transition the TS instabilities are bypassed, hence the term
bypass transition is used to describe this process (Morkovin, 1969), and turbulent spots
develop almost spontaneously. The third type of transition scenario occurs in regions of
highly adverse pressure gradient such as in a gas turbine cascade (Van Treuren et al., 2002)
where the flow breaks down into turbulent motion at or just downstream of the separation
zone.
This investigation deals with the bypass mode of transition induced by elevated levels
1
26. of FST downstream of turbulence generating grids. Bypass transition occurs above some
level of freestream turbulence (FST), usually above 1% of the freestream velocity. The
bypass transition process is studied extensively due its industrial applications by virtue of
the fact that it occurs in regions where elevated levels of FST are present such as in the
downstream wake passage of a gas turbine blade.
Although the transition process has been studied for some time (the most relevant early
example is Reynolds (1883)), until recently the mechanisms involved in the bypass route to
transition remained elusive both experimentally and numerically. Recently, the full Navier-
Stokes equations have been solved using direct numerical simulations (DNS) thereby giv-
ing much sought after insight into the complete transition process. However, experimental
support of such complex results is necessary and challenging.
The complexity of the transition process can be highlighted by considering the various
factors that affect the destabilisation of laminar flow to a turbulent state in real life flow
processes, such as: pressure gradient, surface curvature, surface roughness, heat transfer
effects, disturbances in the freestream and the spectrum of the freestream flow. The impor-
tance of these parameters is recognised in this investigation; however, the objective of this
study is to focus on the fundamental fluid dynamics leading to the generation of turbulent
spots in zero pressure gradient (ZPG) flow subject to varying levels of FST. The study of
each individual factor named above is outside the scope of the current investigation. A
noteworthy point is that the results herein are fundamental and have the potential to be
extended to include these factors in future work.
It is not only necessary to study the transition process due to its ubiquitous nature, it
is also necessary to understand it due to its many and varied industrial applications. It
is well known that laminar to turbulent transition can have adverse effects on wall shear
stresses and heat transfer rates in fluid flow processes, with the gas turbine engine being
the most widely quoted. Wang and Zhou (1998) and Brandt (2003) state that as much as
50-80% of the surface of a typical turbine blade can be covered by transitional flow and this
will have severe consequences on the overall losses and thereby increasing the operating
cost of the engine drastically. Walsh and Davies (2005) measured the transition region in
realistic Mach number conditions over a turbine blade profile and showed that the transition
2
27. region occupied over 20% of the total suction surface length. According to Bowles (2000)
it has been estimated that 20% savings could be attained if the majority of flow on a gas
turbine blade was kept laminar. Bowles (2000) also comments on the reduced life span of
the turbine blades due to the increased heat transfer properties involved in the transition
process. The breakdown process on a gas turbine is significantly more complicated than
that on a flat plate. One major source of this complexity is due to the fact that the highly
turbulent wake (T u = 20% according to Mayle (1991)) from upstream rows impinges
on the leading edge of the blade and causes the transition process to be unsteady. This
type of FST is more complicated than grid generated turbulence which can be considered
statistically steady under controlled conditions (Lewalle et al., 1997). Furthermore, in a gas
turbine engine the flow also has to contend with pressure gradients, streamwise curvature,
surface roughness and very large heat transfer rates with temperatures high enough to melt
the blades.
The main goal of this investigation is to gain further insight into the physical attributes
of pre-transitional flow with the prospect of this increased understanding improving the
modelling of the flow. Specifically, this thesis examines the laminar region up to the point of
breakdown to turbulent motion. The breakdown from a laminar to a turbulent state contains
three main stages: 1) the receptivity phase, i.e., how disturbances from the freestream enter
into the boundary layer, 2) the disturbance amplification phase, i.e., the development of the
disturbances in the boundary layer up to the point of breakdown to turbulent motion and 3)
the breakdown of these disturbances into turbulent motion.
Recently the similarity between ZPG transition and pressure gradient transition phe-
nomena has been demonstrated (Maslowe and Spiteri, 2001; Zaki and Durbin, 2006) thereby
further illustrating the importance of completely understanding the transition process in
ZPG flow. However, the transition process on a flat plate is still not fully understood and the
latest analytical and numerical results are still lacking experimental support. An overview
of the literature describing the current understanding of the stages of laminar to turbulent
breakdown in a ZPG flow follows. This section is separated into experimental, theoreti-
cal and numerical investigations. Following this, Section 1.3 will give an overview of the
thesis and finally Section 1.4 will outline the main objectives of the work.
3
28. 1.2 Laminar to Turbulent Transition: The Bypass Route
1.2.1 Experimental Investigations
The first experimental work into the transition process on a flat plate was by Dryden (1937).
The main observation from this work was that the streamwise fluctuations in the boundary
layer were of low frequency and were several times larger in amplitude than the fluctuations
found in the freestream. Following from this, experimental work into the bypass transition
process has demonstrated that under the influence of elevated FST the laminar boundary
layer develops high- and low-speed fluctuations relative to the mean streamwise velocity
that are extended in the streamwise direction and are termed streaky structures (Matsubara
and Alfredsson, 2001). Experiments have shown that the maximum of the root mean square
(RMS) streamwise disturbance is located approximately in the middle of the boundary
layer and at transition onset the maximum streamwise disturbance is approximately 10%
of the freestream velocity (Roach and Brierley, 2000; Matsubara and Alfredsson, 2001).
As stated by Matsubara and Alfredsson (2001), as a matter of comparison, a TS wave has
its amplitude maximum located in the near-wall region and breaks down at amplitudes of
approximately 1% of the freestream velocity.
An illustration of the streaky structures in a laminar boundary layer is shown in fig-
ure 1.1(a) where the low-speed streaks (regions of smoke) and the high-speed streaks (re-
gions without smoke) are clearly visible. These streaky structures were first discovered by
Klebanoff (1971) where he referred to them as ”breathing modes” due to the fact that their
occurrence seemed to correspond to a thickening and thinning of the boundary layer. The
time-averaged representations of the streaky structures are termed Klebanoff modes, due to
Kendall (1985). Kendall (1985) demonstrated that the low-frequency fluctuations associ-
ated with the streaky structures in the flow grow proportionally with the laminar boundary
layer thickness (δ).
After this linear growth secondary instabilities on the streaks develop leading to ex-
ponential growth signifying the breakdown to turbulence. Under certain conditions the
streaky structures have been shown to develop a streamwise waviness which eventually
breaks down into a turbulent spot, as shown in the flow visualizations of Matsubara and
4
29. Figure 1.1: Smoke flow visualisation of streamwise streaks, streamwise wiggles and turbu-
lent spots (Matsubara and Alfredsson, 2001).
Alfredsson (2001) (figure 1.1). The upper parts of figure 1.1(a) and (c) show the stream-
wise waviness that Matsubara and Alfredsson (2001) refer to as streamwise ”wiggles”. The
wiggles signify the exponential growth on the streak and eventually the flow breaks down
into a turbulent spot as illustrated in figure 1.1(b) and (d). The flow process here is that
the streak disturbance magnitude reaches a sufficiently high level for secondary instabil-
ities on the streaks to develop (the wiggle referred to previously) which will provoke the
breakdown to turbulence.
It will be demonstrated in this investigation that the negative component of the fluc-
tuating velocity is critical in the transition process. A number of experimental studies
have demonstrated the evolution of structures with associated negative fluctuation veloc-
ity from the near-wall region towards the boundary layer edge (see e.g., Wygnanski et al.,
1976; Kuan and Wang, 1990; Blair, 1992; Kendall, 1998; Westin et al., 1998; Chong and
Zhong, 2005). Well upstream of transition onset Blair (1992) observed large scale struc-
tures with associated negative fluctuation velocities near the boundary layer edge region;
Blair termed these structures negative spikes. Approaching the point of transition onset
the negative spikes developed high-frequency components and Blair commented that the
demarcation between multiple negative spikes and a turbulent structure became ‘blurred’.
Artificially generated turbulent spots have been investigated extensively (Wygnanski et al.,
5
30. 1976; Westin et al., 1998; Chong and Zhong, 2005). The major advantage of artificially
generating the turbulent structures is that it allows for an ensemble-averaged representation
of the spots as the same disturbance is generated every time. Chong and Zhong (2005)
showed that high-frequency negative fluctuations develop near the boundary layer edge be-
fore any near-wall positive fluctuations were observed; however, they did not discuss the
connection between their results and DNS and the question still remains as to the similarity
between artificially and naturally occurring turbulent spots.
The importance of elevated freestream turbulence intensity at the leading edge (T u)
in the bypass transition process has been further demonstrated in the work of Fransson
et al. (2002). They demonstrated that the initial disturbance energy in the boundary layer is
proportional to T u2 and the transition Reynolds number is inversely proportional to T u2 .
Recent investigations such as Roach and Brierley (2000), Jonas et al. (2000) and Frans-
son et al. (2005) have discussed the importance of accurate determination of the FST length
scales and energy spectra in the laminar boundary layer receptivity process. By virtue of
the fact that the length scales have an effect on the receptivity process it can be expected
that they too will affect the transition process, a fact demonstrated by Jonas et al. (2000).
Through some of the above referenced investigations into the bypass transition process
came the observation that under the influence of increased FST a laminar velocity profile
deviates substantially from the theoretical velocity profiles of Blasius and Pohlhausen. This
characteristic has been observed by many experimental investigators such as Fasihfar and
Johnson (1992), Roach and Brierley (2000), Matsubara and Alfredsson (2001) and Hernon
and Walsh (2007).
Although this deviation in velocity gradient has been noted previously, the associated
increase in energy dissipation (where the energy dissipation rate is equivalent to the entropy
generation rate) due to enhanced viscous shear rates has not been quantified. This departure
in velocity profile compared to the well established theories of Blasius and Pohlhausen
has a two fold effect on the velocity gradients of the flow; 1) a reduction in the velocity
gradient in the outer layer region occurs, increasing the boundary layer thickness compared
to theory; 2) an increase in the velocity gradient in the near-wall region develops causing an
increase in the wall shear stress with an attendant increase in the rate of energy dissipation.
6
31. The increase in wall shear stress can be attributed to the enhanced mixing caused by the
FST that has been shown experimentally by Volino and Simon (2000) and numerically by
Jacobs and Durbin (2001) to penetrate into the boundary layer. The effect of increasing the
near-wall velocity gradient has significantly more influence on the energy dissipation rate
as the majority of energy dissipation takes place in the near-wall region.
Wavelet techniques have been used to great advantage in fluid dynamic processes, espe-
cially in the phenomenon of transition to turbulence which is a complicated and stochastic
process. The advantage of wavelet over fast Fourier transform (FFT) analysis is that the
wavelet provides both sequential and spectral information on the flow. Wavelets allow for
a more in depth view of the time-dependent scales found in the complex process that is
laminar to turbulent transition under the influence of elevated FST. Lewalle et al. (1997)
used a number of different wavelet techniques as a means of gaining more information
on the various time scales present in the transition process through ensemble and condi-
tional statistics. They found that there was a lack of energy-dominant time scales inside
the turbulent spots. They identified transport dominant scales within the spots which were
responsible for the largest part of the Reynolds stress. Kaspersen and Krogstad (2001) used
continuous wavelet techniques to detect turbulent spots and burst phenomena and Volino
(2002) used wavelet analysis to define the variation in turbulent scales throughout the tran-
sition process.
1.2.2 Theoretical Investigations
Theoretical studies into the transition process have been beneficial in elucidated some of
the transition mechanisms and a brief review of the most important work relating to the
experimental results presented in this investigation are given here.
According to Andersson et al. (2001) the classical starting point for a theoretical de-
scription of the transition process involves linear stability theory. Using this method expo-
nentially growing solutions to the linearised Navier-Stokes equations are sought to signify
the breakdown to turbulence. If these solutions are not found then the flow is considered
to be stable. These authors state that many flow types may undergo transition for Reynolds
numbers well below the critical value predicted by linear stability theory. Therefore, the
7
32. theory failed to capture all of the physics involved in the transition process when com-
pared to experiment. This led to the development of further theories that could predict the
algebraic/transient growth on the streaks before the evolution of the exponential behavior.
According to Berlin and Henningson (1999) a re-examination into the Orr-Sommerfeld
and Squire operators showed that the eigenfunctions are nonorthogonal. This implies that
disturbances other than exponentially growing instabilities can grow in the boundary layer
and this theory is referred to as nonmodal, transient or algebraic growth. The theories on
transient growth have been developed to accurately predict the features of the streaks before
they breakdown to turbulent motion. These theories show that the growth on the streaks is
linear along the length of the plate and scales with the boundary layer thickness upstream of
the exponential growth that signifies the breakdown to turbulence. According to Andersson
et al. (2001), Wundrow and Goldstein (2001) and Zaki and Durbin (2005) the secondary
instability on the streak can be caused by the presence of inflection type instabilities in the
laminar flow velocity profile.
It has been demonstrated theoretically that the streaks are caused by streamwise vor-
tices at the leading edge of the plate (Landahl, 1975, 1980; Andersson et al., 1999, 2001;
Luchini, 2000). One of the first sound theoretical attempts at explaining the streak growth
phenomenon was proposed by Landahl (1975, 1980) and termed the linear lift-up effect.
According to Andersson et al. (2001) this theory argued that vortices aligned in the stream-
wise direction advect the mean velocity gradient towards and away from the wall, generat-
ing spanwise inhomogeneities, i.e, the streaks. In this theory a wall-normal displacement
of fluid (due to the freestream vortices) will initially retain its horizontal momentum and
therefore generate the low- and high-speed regions within the flow.
Andersson et al. (1999) and Luchini (2000) have since predicted that the energy growth
of the optimal disturbances in the freestream is proportional to the distance from the lead-
ing edge. These theories on optimal disturbances also accurately predict the wall-normal
shape of the time-averaged streamwise fluctuations and show that streamwise-orientated
disturbances in the freestream are the cause of maximum growth of the high- and low-
speed streaky structures in the boundary layer. It was stated by Andersson et al. (2001) that
”the streamwise vortices leave an almost permanent scar in the boundary layer in the form
8
33. of long-lived, elongated streaks of alternating high and low streamwise speed”.
Wundrow and Goldstein (2001) commented on the significance of looking at maximum
disturbance magnitudes compared to RMS values when considering what disturbances are
critical in causing the transition to turbulence. Their investigation also illustrated the de-
velopment of negative spike structures and the evolution of an inflectional velocity profile
near the boundary layer edge as the point of transition onset approached. Furthermore, in
the majority of studies on the transition process the disturbances that amplify to generate
turbulent spots are presented in time-averaged form (e.g., the so-called Klebanoff mode)
where the most prominent disturbances that lead to transition remain recondite due to the
averaging process.
In order to more fully understand the bypass transition process it is necessary to under-
stand how freestream disturbances (such as freestream vortices, freestream acoustic waves
and most importantly freestream turbulence in the context of this investigation) penetrate
and interact with the underlying boundary layer. This phase in the flow’s development is
referred to as the receptivity phase. According to Reshotko (1994), receptivity describes
the signature in the boundary layer of some externally imposed disturbance. More recently
the study of receptivity has been examined in a new light mainly due to the recent devel-
opments in the theory of shear sheltering (see e.g., Jacobs and Durbin, 1998; Hunt and
Durbin, 1999; Maslowe and Spiteri, 2001; Zaki and Durbin, 2005, 2006).
Jacobs and Durbin (1998) solved the model problem of a two-dimensional Orr-
Sommerfeld disturbance for a Blasius boundary layer profile and determined that the pene-
tration depth (PD) of disturbances (defined as the point where the disturbance eigenfunction
(φ) dropped and remained below 0.01 which was defined by the location in the boundary
layer where the freestream function lost its oscillatory nature) from the freestream into the
boundary layer is given by P D ∝ (1/ωR)−0.133 , where ω and R are the frequency of the
largest freestream disturbances and the Reynolds number of the flow. This dependence was
also demonstrated in Maslowe and Spiteri (2001) for varying pressure gradients. Zaki and
Durbin (2005) stated that the measure of PD by Jacobs and Durbin (1998) was rather sub-
jective as they restricted attention to a single wall-normal wavenumber. Zaki and Durbin
(2005) further enhanced the concept of PD by introducing a coupling coefficient which
9
34. better represented the interaction between the freestream disturbances and the underlying
boundary layer.
It has also been demonstrated that streamwise streaks can be generated by the interac-
tion of oblique waves in the freestream which combine to form streamwise vortices which
in turn force the generation of streaks in the boundary layer (Schmid and Henningson,
1992; Berlin and Henningson, 1999; Brandt et al., 2002, 2004). This transition scenario
is initiated with the introduction of two oblique waves with small amplitude. The two
oblique waves can be characterised by (ω ± β), where ω is their angular frequency and ±β
is their spanwise wavenumbers. This type of investigation has opened up a new type of
study where different mechanisms for triggering or delaying transition are being developed
(Fransson et al., 2002).
There are generally two different receptivity mechanisms proposed in the literature
(Brandt et al., 2004): 1) a linear mechanism for streak generation which is due to the dif-
fusion and/or propagation of freestream streamwise vortices into the boundary layer. If the
linear process is present it has been shown that the growth of the streaks is caused directly
√
by the freestream vortices at the leading edge and is proportional to Rex . 2) a nonlinear
mechanism involving oblique modes in the freestream was proposed by Berlin and Hen-
ningson (1999) and Brandt et al. (2002). As stated in Brandt et al. (2004) this nonlinear
mechanism is a two step process. Firstly, the nonlinear generation of streamwise vorticity
occurs due to the interaction between the oblique modes which penetrate the underlying
boundary layer. Secondly, the streaks are then formed due to the lift-up effect. This non-
linear mechanism acts along the length of the plate above the boundary layer and causes
the continuous forcing from the freestream on the underlying boundary layer.
1.2.3 Numerical Investigations
DNS studies have been a major influence in elucidating the routes to bypass transition (see
e.g., Wu et al., 1999; Jacobs and Durbin, 2001; Brandt et al., 2004; Zaki and Durbin, 2005,
2006). These studies have also illustrated that the low-speed components of the flow lift
away from the wall towards the boundary layer edge due to the upward motion of the vor-
tical structures found in the freestream region. The breakdown process put forward by
10
35. DNS is illustrated in figure 1.2 where the low-speed streaks lift up towards the boundary
layer edge (denoted by δ). In DNS the low-speed regions are termed negative or backward
jets due to the fact that their associated instantaneous velocity (U) is significantly less than
the local mean value (U ), therefore such structures have negative fluctuation velocity (u).
The low-speed streaks (negative jet structures) can be lifted up to the height of the mean
boundary layer thickness. When the low-speed streaks reach the outer region of the bound-
ary layer they are subject to inflection point instability and a form of Kelvin-Helmholtz
type instability develops (Zaki and Durbin, 2005) which is signified by rolling of the shear
layer. At this stage the flow is locally unstable to the high-frequency disturbances con-
tained in the freestream and the disturbance at the boundary layer edge region intensifies
until eventually the lifted low-speed streak (negative jet) breaks down into a turbulent spot
in the outer region of the boundary layer. As stated previously, Zaki and Durbin (2005)
developed a coupling coefficient which gave a measure of the propensity of a certain mode
(where mode refers to the frequency content and hence the size of freestream disturbance)
to penetrate and continue oscillating within the boundary layer. In that paper, using DNS,
Zaki and Durbin (2005) demonstrated that with two weakly penetrating modes at the inlet
the boundary layer was weakly perturbed; with two strongly penetrating modes at the in-
let, Klebanoff modes were produced in the boundary layer; with one strongly penetrating
low-frequency mode and one weakly penetrating high-frequency mode the complete tran-
sition process was simulated. This work further illustrates the necessity for the interaction
between low- and high-frequency modes in order to initiate the transition process.
This route to bypass transition differs significantly from those presented before the
application of DNS where it was believed that turbulent structures were generated, almost
spontaneously, in the near-wall region. One postulate put forward (Johnson and Dris, 2000)
was that transition occurs due to a local near-wall flow separation which develops when
the instantaneous velocity drops below 50% of the mean value. Furthermore, before the
development of DNS, such was the contention that the flow broke down in the near-wall
region that some experiments only examined the flow in this region (Lewalle et al., 1997;
Johnson and Dris, 2000).
Andersson et al. (2001) used DNS to follow the nonlinear evolution of boundary layer
11
36. δ
Inflectional-
FST type wave
U
Lifted streaks Turbulent spot
Laminar Transitional Turbulent
Figure 1.2: Sketch of the bypass transition process adapted from Zaki and Durbin (2006).
streaks. They showed that the streak critical amplitude via the sinuous mode is approxi-
mately 26% of the freestream velocity. This is the critical amplitude for the onset of sec-
ondary instability but not necessarily for the breakdown of the flow which develops when
an inflectional profile is present. The critical amplitude of the streaks when undergoing
the varicose mode of breakdown was shown be approximately 37% of the freestream ve-
locity; therefore, the sinuous mode is far less stable than the varicose mode. Brandt et al.
(2004) demonstrated that either sinuous or varicose secondary instabilities on the streaks
may be the precursors to turbulent spot formation and they also investigated the receptivity
of the boundary layer to changes in the freestream integral length scale (Λ). They demon-
strated that, by varying the energy spectrum of the freestream disturbances, the transition
location moved to lower Reynolds numbers when the integral length scale of the FST was
increased. It is a demanding experimental task to vary T u while keeping the same scales
of turbulence, or vice versa, and it is in this regard that DNS becomes a sensible option.
In that study they also found two distinct receptivity mechanisms depending on the energy
content of the external disturbance: 1) if low-frequency modes diffuse into the boundary
layer at the leading edge the streaks are generated in the normal way due to streamwise
vorticity through the linear lift-up effect and 2) if the freestream disturbances are mainly
located above the boundary layer a non-linear process is needed to generate the streaks
within the boundary layer. The DNS of Brandt et al. (2004) also illustrated the evolution
12
37. of the peak locations of the maximum positive and negative fluctuation velocities in the
streamwise direction. They demonstrated that the peak of the negative value shifted to-
wards the boundary layer edge and the peak of the positive value shifted towards the wall
as the point of transition onset approached. Their study further demonstrates the impor-
tance of examining maximum disturbance levels associated with the low- and high-speed
streaks when compared to time-averaged results. Their study also demonstrated that it is
on the low-speed components of the flow that are located away from the wall where the
flow first breaks down.
Although it may be said that DNS has been the most influential technique used to inves-
tigate the breakdown to turbulence since the invention of the hotwire probe, the disadvan-
tage of DNS is that it is computationally very expensive. For example, the study by Zaki
and Durbin (2006) used 26 million grid points and took several months to solve. Currently,
DNS studies neglect the leading edge region due to the increased numerical cost; however,
it is well known that the leading edge region is critical in the receptivity process and there-
fore also in the transition process (Hammerton and Kerschen, 1996; Westin et al., 1998;
Kendall, 1998; Saric et al., 2002; Fransson, 2004, discuss the importance of the leading
edge in the receptivity process). Therefore, experimental techniques are still a necessary
approach to solving many of the complex flow problems, especially one as complex as the
transition process.
1.3 Thesis Overview
The main aim of this work is to provide new insights into the bypass transition process over
a range of turbulence intensities for ZPG flow. In order to do this the subsonic wind tunnel
at the University of Limerick is utilised and a range of experimental and data analysis
techniques are implemented to gain further insight into the flows development.
Chapter 2 details the experimental techniques, facility and freestream turbulence char-
acteristics. The experimental techniques section describes the operation of the constant
temperature probes and the hotwire system as well as the other measurement techniques
used throughout the investigation. The section on the experimental facility includes the
13
38. design and characterisation of the new flat plate and turbulence grids used in the investi-
gation of bypass transition. It is demonstrated that the flow characteristics on the flat plate
and downstream of the turbulence generating grids all compare favourably to those in the
literature giving confidence in the design of the test facility and also in the various data
analysis techniques used.
Chapter 3 presents the advanced data analysis techniques used throughout the current
investigation. The data analysis techniques are explained fully and this will allow for a
better understanding of the interpretation of the measurements throughout the main body
of the thesis. This section will include details on the hotwire calibration, the intermittency
detector function, the estimation of the energy dissipation in the flow, the determination of
the signal level probability and the techniques used to gain further insight into the spectral
content of the flow through the fast Fourier transforms and wavelet analysis. The determi-
nation of the maximum positive and negative of the streamwise fluctuation velocities are
also presented. This chapter will be concluded with an account of the various uncertainties
involved in the measurements and data analysis.
Chapter 4 presents some important characteristics of pre-transitional flow up to the
emergence of turbulent spots near the wall. This chapter discusses the velocity profiles, the
Klebanoff mode disturbance profiles and the shear-sheltering phenomena is also illustrated
through the velocity traces and energy spectra. Results are presented on the scaling of the
peak disturbance associated with the Klebanoff mode over a range of turbulence intensities
and Reynolds numbers. The question of whether the receptivity mechanism is linear or
non-linear in grid generated turbulence experiments is addressed and comparisons to recent
numerical simulations are made. Another important aspect of the flow is the change in
structure of the high-frequency turbulent spots as the flow is traversed from the wall to the
freestream. This chapter provides an important introduction to some of the flow features
and associated terminology that will form the basis of discussion in the results chapters
that follow. Chapter 4 also quantifies and provides a new correlation that accounts for the
increased energy dissipation rates in a laminar boundary layer when under the influence of
elevated FST. The correlation presented has the advantage that it needs only information on
the FST level at the leading edge of the plate and also the momentum thickness Reynolds
14
39. number in order to accurately predict the increased energy dissipation rates to within 10%
of those measured.
Chapter 5 describes the change in receptivity of pre-transitional flow when under the in-
fluence of elevated FST by analysing the skewness function. The location of peak negative
skewness is shown to penetrate further into the boundary layer with increased FST level.
It was decided to use the location of peak negative skewness as a measure of the change
in receptivity of the boundary layer due to the response in the peak skewness level to the
change in forcing from the freestream. Once the location of peak skewness was shown to
demonstrate the correct parameter dependence an equation is presented that predicts the
wall-normal location of the most probable point of the breakdown to turbulent motion. The
term most probable is used as this predicts the location where the most negative spike ac-
tivity is observed. These results represent novel experimental findings that account for the
change in receptivity of a laminar boundary layer when under the influence of elevated FST
under naturally occurring disturbance conditions.
The importance of the Klebanoff mode disturbance was discussed in Chapter 1 and in
more detail in Chapter 4; however, due to the time averaging of the streaky structures in
the flow, the Klebanoff mode gives little information in the way of describing which flow
structures may propagate and grow to the point of breakdown. For this reason it was de-
cided to analyse the time traces with respect to the maximum positive and negative of the
streamwise fluctuating velocities and present these in terms of a local disturbance magni-
tude when normalised with the freestream velocity. Chapter 6 presents such distributions
over a range of Reynolds numbers and FST levels. The results give experimental support
to the recent DNS results which demonstrated that the flow breaks down into turbulent
motion near the boundary layer edge region on the low-speed streaks. Relationships are
presented that accurately predict the maximum disturbances on the low- and high-speed
streaks and these relationships also provide a new means of predicting the location of tran-
sition onset based on local parameters. These results are further supported by simultaneous
measurements between a hotwire probe that is traversed from the wall to the freestream
and a hotfilm array at the wall. The results demonstrate that the high-frequency turbulent
structures are produced near the boundary layer edge before any near-wall turbulent events
15
40. are observed and these results indicate the wall-normal size of the leading edge overhang.
1.4 Objectives
The main objectives of the current investigation are to:
1) Design and characterise a new flat plate and turbulence grid facility which will allow
for comparison against the wealth of experiments in the literature on ZPG flow when under
the influence of elevated freestream turbulence.
2) The importance of elevated FST throughout the transition process was highlighted in the
introduction. The elevated levels of FST impressed upon the underlying laminar boundary
layer must have some measurable effect on the energy dissipation rates in the flow; how-
ever, little information exists in the literature to account for this. To this end, the increased
energy dissipation rates over a range of turbulence intensities need to be quantified and a
correlation developed that accurately predicts this increase with minimum a priori knowl-
edge thus allowing for simple implementation into numerical codes.
3) Finally, a major goal of this work is to provide experimental insights into the bypass
transition to turbulence and give experimental support to the recent direct numerical simu-
lations and theoretical investigations that have enlightened the flow’s development towards
the breakdown to turbulence. Experimental support of such advanced theories and simula-
tions has been achieved slowly due to the inherent difficulties in measuring such a stochas-
tic process as the breakdown to turbulence. This objective contains two main aspects.
Firstly, it is hoped to gain insight into the receptivity phase in which disturbances from
the freestream penetrate into the laminar boundary layer and secondly, it is hoped to gain
insight into the way streamwise disturbances evolve to the point of breakdown. Following
these novel measurements it will be possible to provide new relationships that accurately
predict the change in flow structure when under the influence of elevated FST.
16
41. Chapter 2
Experimental Techniques, Facility and
Freestream Turbulence Characteristics
2.1 Introduction to Measurement Techniques
2.1.1 Hotfilm and Hotwire Anemometry
For almost 100 years hotwire anemometry has been the main research tool in the field of
fluid dynamics. One early example using hotwire anemometry which is cited extensively
in the literature is Dryden (1937). It is fair to say that the majority of experimental studies
into boundary layer phenomena owe their success to the hotwire or hotfilm probe (see fig-
ure 2.1). It was not until relatively recently that new techniques have been put to good use,
such as particle image velocimetry (PIV) and Laser Doppler Anemometry (LDA), however,
when compared to the advantages of hotwire anemometry these optical techniques suffer
greatly.
The main advantages of hotwire anemometry are (Bruun, 1995):
• A very broad range of velocities can be measured from 0.3m/s to supersonic speeds.
• Standard hotwire probes have very high temporal resolution. This implies that these
probes can measure fluctuations in the flow in the kHz range.
17
42. • The spatial resolution of the probes is reasonably good with the possibility of mea-
suring scales of the order 1mm.
• There are various probe types available, such as: single normal (SN), slant, x-wire,
triple wire and 4 wire probes which can measure all three components of velocity
and may also include temperature measurement. However, as the complexity of the
probe increases the size also increases which implies the advantage of good spatial
resolution is lost.
• The output from the probe can provide instantaneous measurements as well as allow
for the calculation of higher order moments which give insightful information into
the flow characteristics.
The two types of probe used in the current investigation are the SN hotwire probe and
the hotfilm probe shown in figure 2.1. The hotwire probe is shown in figure 2.1(a) and this
probe is usually mounted to some form of traverse system that allows the probe to move
in set increments from the wall to the freestream. The single hotfilm probe is shown in
figure 2.1(b) and this probe is typically attached to the wall. An array of hotfilms was also
used in the current investigation and is detailed in section 2.1.6.
(a)
Ceramic probe support
Stainless steel prongs
Electrical connections
for probe holder
5µm Tungsten wire
(b) 16
0.1mm dia. Cu-wire
Length 55mm
8 0.9 0.1
Figure 2.1: Sketches of constant temperature anemometer probes (DantecDynamics, 2006).
(a) Hotwire probe. (b) Hotfilm probe.
18
43. R1 R2 Servo amplifier
E
R3
Bridge
voltage
Probe
(Rw)
Figure 2.2: Simple schematic of Wheatstone bridge used to maintain probes in constant
temperature mode.
2.1.2 Principle of Operation
The basic principle behind the operation of a hotwire probe is that there is a cooling effect
of a flow on a heated body. A Constant Temperature Anemometer (CTA) system basically
consists of a probe, an electronic feedback circuit which drives the probe and produces an
output voltage that is proportional to the velocity, and a signal conditioning circuit which
provides noise reduction and signal amplification. Shown in figure 2.2 is a simple rep-
resentation of the Wheatstone bridge that is used to keep the hotwire probe in constant
temperature mode. The bridge should be almost balanced at room temperature. The wire
(represented by Rw in figure 2.2) is connected to one arm of the bridge and is heated by an
electric current. The servo amplifier holds the bridge in balance by continuously control-
ling the current to the sensor. This control of current keeps the sensor operating at constant
resistance and therefore also at constant temperature. Point E in figure 2.2 represents the
bridge voltage and is a measure of the heat transfer from the sensor which can be directly
related to a velocity through a calibration procedure.
Bruun (1995) states that the sensitivity of the hotfilm or wire probe to fluctuations in
the flow is dependent on the overheat ratio at which the hotwire is operated; however, the
probe can be destroyed if the overheat ratio is too high due to oxidation effects. The value
at which the variable resistor on the CTA bridge is set to give the desired sensor overheat
ratio may be evaluated using the following equation
19
44. Rw = R20 [1 + α20 (Tw − T20 )]. (2.1)
In the current investigation the overheat temperature of the hotwire and hotfilm probes was
250◦ C and 110◦ C, respectively.
2.1.3 Hotwire Calibration
Each hotwire probe needs careful calibration in order to be sure that the quantities measured
have the desired accuracy. This is especially the case when taking near-wall measurements
as the accuracy of the measurement decreases due to the reduction in velocity as the wall
is approached. In the current investigation a single normal hotwire is used extensively and
the following calibration procedure is outlined for this probe type.
Bruun (1995) states that a hotwire probe should be calibrated in situ, i.e., in the environ-
ment that the actual measurements will be taken. The flow in which the probe is calibrated
must also be of very low turbulence intensity and the probe must be placed perpendicular
to the flow. It was explained previously that the basic operation of a hotwire probe is that
the increase in power needed to maintain the bridge at constant temperature can be related
to the fluid velocity. Therefore, in order to relate the increased heat transfer from the sensor
to the velocity of the flow the probe must be calibrated in a known velocity field. This is
achieved by placing the hotwire probe in the wind tunnel test section in close proximity to
a Pitot-static probe, but not close enough that any interference effects are present. Initially
the voltage across the Wheatstone bridge is measured without any flow over the sensor.
This is referred to as the zero voltage (E0 ). At each power setting on the wind tunnel the
differential pressure from the Pitot-static probe, the temperature of the airflow in the tunnel
and the output voltage of the hotwire probe are measured for a range of flow velocities.
The calibration of the probe is carried out according to King’s law which provides for a
linear relationship between the Wheatstone bridge output voltage and the fluid velocity of
the flow and is given by
20
45. 16
y=7.07x − 0.83
R2 = 0.99
E2−E2 (Volts2)
12
0
8
c
4
0
0 0.5 1 1.5 2 2.5
Ren
d
Figure 2.3: Hotwire calibration using King’s law. , Measured data points. ——, Trend
line fit to data points. The equation of the trend line gives the coefficients in King’s law
with A = −0.83 and B = 7.075 and n = 0.45.
Es − E0 = A + BRen .
2 2
d (2.2)
Here, Es is the voltage sensed by the hotwire when there is a flow passing over the probe,
A, B, Red are the calibration constants and the Reynolds number of the flow based on the
diameter of the hotwire (d) and n is an exponent that is recommended to be in the range
0.4-0.5 (Bradshaw, 1971; Bruun, 1995). In the current investigation the hotwire calibration
was typically obtained between test velocities of 0.4m/s-20m/s.
Variation in fluid temperature above the temperature at which the probe was calibrated
was compensated for by using the technique of Kavence and Oka (1973) given by
0.5
TS − T∞
Ec = Es . (2.3)
TS − TR
Shown in figure 2.3 is a typical calibration graph obtained during the current set of
experiments. The calibration constants can be read directly from the graph by relating the
equation of the trend line fit to the measured data points to King’s law given by Eqn. 2.2,
21
