interaction of free-stream turbulence with a …
TRANSCRIPT
D:/PhD_Thesis_June2020/final_PG section/final
thesis_Sep2020_submitted/thesis_latex_miktex_June2020/thesis_chandrahas_June2020.dviBOUNDARY
LAYER
© Indian Institute of Technology Delhi (IITD), New Delhi, 2020
INTERACTION OF FREE-STREAM TURBULENCE WITH A TURBULENT
BOUNDARY LAYER
Submitted
in fulfilment of the requirements of the degree of Doctor of Philosophy
to the
SEPTEMBER 2020
Certificate
This is to certify that the thesis entitled “Interaction of Free-stream Turbulence
with a Turbulent Boundary Layer” being submitted by Mr. Chandrahas S. Shet
to the Indian Institute of Technology Delhi for the award of the degree of Doctor of
Philosophy in Applied Mechanics department is a bonafide record of original research
work carried out by him under our supervision in conformity with rules and regulations
of the institute. The results contained in this thesis have not been submitted, in part or
in full, to any other University or Institute for the award of any Degree or Diploma.
Dr. S. V. Veeravalli Dr. Murali R. Cholemari
Professor Associate Professor
Indian Institute of Technology Delhi Indian Institute of Technology Delhi
New Delhi - 110 016 New Delhi - 110 016
India India
i
Acknowledgements
First and foremost, I consider it an honor to work with Prof. S. V. Veeravalli and Dr.
Murali R. Cholemari. I wish to express my deepest sense of gratitude to my research
supervisors Prof. S. V. Veeravalli and Dr. Murali R. Cholemari for their invaluable
guidance, support and encouragement, throughout the course of this work.
I am also grateful to members of student research committee (SRC) and department
research committee (DRC), namely Prof. V. Seshadri, Prof. S. N. Singh, Prof. Sawan
S. Sinha, Prof. Balaji Srinivasan, Prof. B. Premachandran, Prof. B. P. Patel and Prof.
Anupam Dewan for their valuable suggestions throughout the research work.
My special thanks go towards Prof. R. C. Malhotra, Prof. Puneet Mahajan, Prof.
Sanjeev Sanghi, Prof. Sriram Hegde, Prof. P. K. Sen, Prof. Suhail Ahmad, Late Prof.
Y. Nath, Prof. Y. Patel, Dr. Arghya Samanta and other faculty members of Applied
Mechanics department for their support and help during the research work.
I feel great pleasure to record my deep sense of gratitude and indebtedness to Prof. R.
D. Tarey, Prof. Ashish Ganguli and Prof. Arun Agarwala for their meticulous guidance,
patient discussions and personal involvement during my research work. Special thanks
to Mr. Josekutty A. J. for the continuous support and help during the research work.
I would like to express my deep gratitude to my external examiners Prof. Sanjay
Mittal (IIT Kanpur) and Prof. Laurent B. Mydlarski (McGill University, Quebec) for
their valuable comments and very detailed corrections. The thesis is vastly improved as
a result.
At this moment, I would also like to take this opportunity to thank Prof. Peter
Bradshaw, Prof. Zellman Warhaft and Prof. Charles Meneveau for all that I learnt from
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them, through their books and lectures, research articles, and through notes, on various
theoretical and experimental aspects of turbulence.
The help of Mr. Harbhajan Singh and Mr. Sunil Bhogal in modifying the wind tunnel
and fabricating the active grid is also gratefully acknowledged. My sincere thanks to Mr.
R. P. Bhogal and the other staff of the Gas Dynamics laboratory, namely Mr. Jugti
Ram, Mr. Rameshwar Dayal, Mr. Nand Lal, Mr. Suresh Sharma, Mr. Kunj Behari,
Mr. Rama Nand, Mr. Sunil Dayal & Mr. Anil for their continuous support during the
research work. The cooperation of Mr. Diwan Singh, Mr. Yogesh & Mr. Manohar from
Fluid Mechanics laboratory, Mr. D. C. Sharma & Mr. Madan Gopal from departmental
Workshop and Mr. Anil Kumar from MTS laboratory is greatly acknowledged. The
help of supporting staffs (Mr. Gregory Toppo, Mr. Manoj & many more) is also greatly
acknowledged.
I also express my gratitude towards administrative staffs from Applied mechanics
department, namely Mrs. Harkanwal Kaur, Mrs. Tajinder Kaur, Mrs. Amarjeet Kaur,
Ms. Harpreet Kaur, Mr. Vikram Singh, Mr. Rakesh Kr Garg, Mr. M. L. Sehgal, Mr.
Madan Lal, Mrs. Seema Saxena, Mr. Pawan Kumar, Mr. Jitender, Mr. Ram Singh,
Mr. Dharmender & Mr. Pramod Kumar and from other units of the institute (Accounts
section, Store purchase section, Audit section, IRD, PG section, Maintenance unit, etc)
who directly or indirectly contributed towards the research work.
I am also immensely grateful to IIT Delhi and Department of Science and Technol-
ogy, Government of India for funding the expenses that incurred during my research
work (Grant Nos.: SR/S3/MERC/16/2005 and SR/FST/ET1-212/2007). I express my
heartfelt thanks to Dr. D. R. Prasad Raju, Shri. S. S. Kohli, Dr. Mukhopadhyay and
Dr. Pratishtha Pandey of DST for their constant support.
I express my sincere appreciation to deans & wardens of Nilgiri hostel, namely Prof.
Aravind Nema, Prof. P M V Subbarao, Dr. Dinesh Kalyanasundaram, Prof. Apurba
Das, Prof. Abhijit Majumdar, Prof. Shashi Mathur, Prof. Anurag Sharma, Prof. S.
K. Gupta & Prof. Rajesh Khanna and care-takers (Mr. Shalikram Sharma, Mr. Gopal
Singh & Mr. Nitish Kumar) for their kind support and help during my fourteen years
iv
of stay at Nilgiri hostel.
I wish to thank my friends Dr. Ganapati N. Joshi, Dr. Praveen Pinnoji, Dr. Pawan
Kumar Yoganarasimha, Dr. S. Nasiruddin, Dr. Sunil Chandel, Dr. Rajesh Singh, Dr.
Jitendra, Mr. Rishav Rajora, Dr. Lakhvinder Singh, Dr. Shish Shukla, Dr. Paramanand
N and Dr. Manoj who stood with me in difficult times.
Last but not the least, I want to thank everyone else who played an essential role in
completing this work and also express an apology if I have forgotten to thank someone
personally.
IIT Delhi, New Delhi - 110 016
Chandrahas
Stamp
Abstract
We present measurements of a zero external pressure gradient two-dimensional (2D)
turbulent boundary layer (TBL) on a flat plate in the presence of grid-generated (passive
or active grid) isotropic free-stream turbulence (FST), as well as in the absence of any
grid. Free-stream intensities were approximately 0.3%, 4.8% and 9.3% for the no grid,
passive grid and active grid cases respectively, at the start of the boundary-layer. The
free-stream Taylor’s microscale based Reynolds number is about 490 and 120 for the
active grid and passive grid cases respectively. The measurements were made using
hot-wire anemometry (HWA) and two-dimensional particle image velocimetry (PIV).
We present an optimized procedure for generating isotropic, homogeneous, high inten-
sity turbulent flow behind an active grid. Isotropy in FST is first rigorously established
in the present set-up before conducting the boundary layer (BL) measurements. Exper-
imental investigation to check the validity of the Taylor’s ‘frozen’ turbulence hypothesis
for high intensity turbulence is also discussed.
The experimental investigations on FST-TBL interactions confirm that, at a funda-
mental level, the presence of the FST increases the growth rate of the TBL and the
wall shear stress. The effect of FST extends deep into the TBL, affecting the wall re-
gion as well as the small scale statistics throughout the boundary layer; the greater
the free stream turbulence intensity, the deeper is the extent where it influences the
TBL. A comprehensive set of statistics like velocity spectra, velocity correlation maps,
and velocity PDFs of various kinds, as well as velocity profiles, both from HWA and
PIV measurements, are presented to support and quantify this view. Changes in the
structural organization of the TBL because of the FST are discussed.
v
vi
We educe the interacting structures of the FST and TBL using kinetic energy (KE)
maps and proper orthogonal decomposition (POD). The data is used to propose a mech-
anism of growth enhancement observed in the TBL in the presence of FST. Very large
scale structures, of sizes 2δ or more, spanning regions across the boundary layer inter-
face nearly up to the wall are seen to drive the interaction. We propose and evaluate an
engulfment and diffusion model of the BL-FST interaction and model the growth of the
boundary layer.
- (2D) (TBL)
- (/ ) (FST) ,
- 0.3%,
4.8% 9.3% , -
490 120
- (HWA) - (PIV)
, ,
, -
(BL)
‘
FST-TBL , -
- ,
,
, (PDFs), HWA PIV
vii
viii
-
(KE) (POD)
- -
, 2δ ,
: BL-FST ( )
Contents
1 Introduction 1 1.1 Outline of the following chapters . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature Review and Objectives 7 2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 High intensity FST Generation . . . . . . . . . . . . . . . . . . . 7 2.1.2 Interaction of FST with a Turbulent Boundary Layer . . . . . . . 22 2.1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Experimental Set-up and Instrumentation 26 3.1 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Plenum chamber and contraction sections . . . . . . . . . . . . . 27 3.1.2 Test section and diffuser . . . . . . . . . . . . . . . . . . . . . . . 30 3.1.3 Axial fan, drive and controller . . . . . . . . . . . . . . . . . . . . 31
3.2 Design and fabrication of traverse mechanism . . . . . . . . . . . . . . . 31 3.3 Passive grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Active grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.1 Design and fabrication of active grid . . . . . . . . . . . . . . . . 34 3.4.2 Active grid control system . . . . . . . . . . . . . . . . . . . . . . 39 3.4.3 Active grid control protocol . . . . . . . . . . . . . . . . . . . . . 42
3.5 Configuration of boundary layer plate and trip wire selection . . . . . . . 43
ix
Admin
CONTENTS x
3.6 Mean velocity measurement . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.6.1 Pitot and Pitot-Static tubes . . . . . . . . . . . . . . . . . . . . . 47 3.6.2 Flat Pitot tube or boundary layer Pitot probe . . . . . . . . . . . 48
3.7 Fluctuating velocity measurement . . . . . . . . . . . . . . . . . . . . . . 48 3.7.1 Hot Wire Anemometer (HWA) . . . . . . . . . . . . . . . . . . . 48 3.7.2 Particle Image Velocimetry (PIV) . . . . . . . . . . . . . . . . . . 51
3.8 Shear stress measurement using Preston tube or Clauser fit . . . . . . . . 54 3.9 Pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.9.1 16-channel pressure scanner . . . . . . . . . . . . . . . . . . . . . 55 3.9.2 Floating scale manometer . . . . . . . . . . . . . . . . . . . . . . 56
3.10 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.11 Data acquisition (DAQ) system . . . . . . . . . . . . . . . . . . . . . . . 57 3.12 Power supply for the instruments . . . . . . . . . . . . . . . . . . . . . . 57
4 Flow Qualification 59 4.1 Uniformity of the flow at the exit of the double contraction . . . . . . . . 61 4.2 Homogeneity of the flow in the test section . . . . . . . . . . . . . . . . . 61 4.3 Variation of the static pressure across the boundary layer plate and Zero-
pressure gradient condition . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4 Decay laws and Free-stream length scale (Lu
∞/δ995) . . . . . . . . . . . . 69 4.5 Two-dimensionality of the boundary layer . . . . . . . . . . . . . . . . . 72 4.6 Internal consistency of the velocity measurement techniques . . . . . . . 72
4.6.1 Mean and r.m.s. boundary layer velocity profiles . . . . . . . . . . 72 4.6.2 Compassion of transverse correlation (C11(0, r, 0)) measured using
a single wire with a cross wire probe . . . . . . . . . . . . . . . . 75 4.6.3 Comparison of the correlations obtained from two-point HWA and
PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.7 Optimizing the performance of an active grid to generate high intensity
isotropic free-stream turbulence . . . . . . . . . . . . . . . . . . . . . . . 77 4.7.1 Velocity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.7.2 Longitudinal F11(k1) and transverse F22(k1) spectra . . . . . . . . 80 4.7.3 Flow parameters relevant to the different configurations reported
in the present work . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.7.4 Isotropy and Correlation Functions . . . . . . . . . . . . . . . . . 84 4.7.5 Correlation Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.7.6 Conclusions to the chapter . . . . . . . . . . . . . . . . . . . . . . 97
5 Assessment of Taylor’s Hypothesis for the Active Grid Turbulence 100 5.1 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Eulerian spatial & temporal integral scales and Comparison of the spatial
correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.3 Conclusions to the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 115
CONTENTS xi
6 Results and Discussions 116 6.1 Effect of large-scale isotropy of FST on the turbulent boundary layer . . 116 6.2 The parameter ‘β’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Boundary layer mean velocity profiles . . . . . . . . . . . . . . . . . . . . 122 6.4 Mean velocity deficit profiles . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.5 Turbulence intensity profiles . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.6 Reynolds stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.7 Shear-stress correlation coefficient profiles . . . . . . . . . . . . . . . . . 130 6.8 Effect of FST on the anisotropy, u2 / v2 of the boundary layer . . . . 133 6.9 Kurtosis and Skewness profiles . . . . . . . . . . . . . . . . . . . . . . . . 134 6.10 Fluctuating velocity and fluctuating vorticity for the BL . . . . . . . . . 136 6.11 Velocity probability density functions (PDFs) . . . . . . . . . . . . . . . 137 6.12 Spatial longitudinal spectra using PIV data . . . . . . . . . . . . . . . . 138 6.13 Spatial longitudinal spectra using HWA data . . . . . . . . . . . . . . . . 141 6.14 Normalized correlation maps for (1) wall parallel and (2) wall normal
velocity fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.14.1 Normalized correlation maps for wall parallel velocity fluctuations 147 6.14.2 Normalized correlation maps for wall normal velocity fluctuations 150
6.15 Conditional PDFs of velocity differences (P (u)|v<0) . . . . . . . . . . . 154 6.16 Variation of integral length scales . . . . . . . . . . . . . . . . . . . . . . 156 6.17 Kinetic energy maps and structures educed using Proper Orthogonal De-
composition (POD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.18 Engulfment and diffusion model of growth . . . . . . . . . . . . . . . . . 165 6.19 Joint Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.19.1 Joint probability density functions (JPDFs) . . . . . . . . . . . . 168
7 Conclusions 172 7.1 Recommendations for further work . . . . . . . . . . . . . . . . . . . . . 174
Appendix A Coordinates for the wind tunnel primary contraction section176
Appendix B Coordinates for the wind tunnel secondary contraction sec- tion 179
Appendix C Calculation of torque required by the stepper motors used in the active grid 182
Appendix D Coordinates for the ogive-shaped nose for leading edge of the BL plate 185
Bibliography 188
Biodata 203
List of Figures
2.1 Schematic of the active turbulence generator developed by Makita, 1991. 8 2.2 Schematic sketch of the active grid developed by Mydlarski & Warhaft
(1996). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Active grid of Poorte & Biesheuvel (2002). . . . . . . . . . . . . . . . . . 11 2.4 Active grid from Larssen & Devenport (2011). . . . . . . . . . . . . . . . 13 2.5 Active grid of Hearst & Lavoie (2015). . . . . . . . . . . . . . . . . . . . 14 2.6 Active grid from Bewley et al. (2013) or Bodenschatz et al. (2014). . . . 15
3.1 Schematic sketch of the wind tunnel used in the present study. . . . . . . 29 3.2 Photograph of the wind tunnel used for present boundary layer study. . . 30 3.3 Schematic of the two-axes traverse mechanism (1.0 m x 0.5 m) for the 0.61
x 0.61 m2 wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Schematic of the passive grid (M = 5.8 cm). . . . . . . . . . . . . . . . . 35 3.5 Schematic arrangement of the active grid used in the present study. . . . 38 3.6 Schematic of the active grid: a) side view b) top view. . . . . . . . . . . . 40 3.7 Schematic of the active grid rod with winglets. . . . . . . . . . . . . . . . 40 3.8 Photograph of active grid of mesh size 6.9 cm. . . . . . . . . . . . . . . . 41 3.9 Schematic layout of the stepper motor control system. . . . . . . . . . . . 41 3.10 Stepper motor controller and variable power supply to control active grid. 41 3.11 Configuration of the boundary layer plate (a) and schematic of the PIV
measurement set-up (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.12 Mean velocity profiles in inner variables at x ≈ 107.0 cm for the no grid
case with different trip wire sizes, compared with measurements in literature. 46 3.13 Schematic of the cross-wire probe calibration set-up. . . . . . . . . . . . . 51 3.14 Dimension of the laser sheet across the boundary layer plate. . . . . . . . 54 3.15 Schematic of the data acquisition set-up for the hot wire measurements. . 57
4.1 Schematic of the set-up used to measure the flow uniformity and measure- ment locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Variation of mean velocity, the r.m.s. of turbulent fluctuations and cross- correlation coefficient across the tunnel . . . . . . . . . . . . . . . . . . . 65
4.3 Schematic of the location of static pressure taps across the boundary layer plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
xii
LIST OF FIGURES xiii
4.4 Pressure gradient across the boundary layer plate measured using a 16- channel pressure scanner after adjusting the height of the tunnel top wall. 68
4.5 Mean velocity measurement along the length of the tunnel with the bound- ary layer plate for the cases: (a) no grid, (b) passive grid and (c) active grid respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6 (a) Decay of longitudinal velocity variance, u2 / U2 for the passive and active grids. (b) Values of FST length scale (Lu
∞) along X for the passive grid and active grid cases. . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.7 Comparison of mean velocity profiles measured at two different z locations of the boundary layer plate in the presence of passive grid generated FST. 73
4.8 (a) Comparison of BL mean velocity profiles for the no grid case with results of Purtell et al. (1981). (b) Comparison of boundary layer data measured using a flat Pitot tube with HWA and PIV data for the active grid case D16b. (c) Comparison of BL r.m.s. velocity profile for the active grid case (D08) measured using HWA with PIV. . . . . . . . . . . . . . . 74
4.9 Comparison of transverse correlation measured using single-wire with cross- wire probe for the active grid case: D08. . . . . . . . . . . . . . . . . . . 75
4.10 Comparison of spatial correlation functions obtained using PIV and two- point HWA measurements for the active grid case: D08. . . . . . . . . . 76
4.11 Longitudinal and transverse power spectra F11(k1) and F22(k1) for the active grid case D08. Case (a) t > 60 ms and case (b) t ≈ 40 ms. . . 80
4.12 Longitudinal F11(k1) and transverse F22(k1) velocity spectra (at X/M ≈ 42) for the active grid cases: (a) D16b (b) D08. . . . . . . . . . . . . . . 81
4.13 Longitudinal and transverse correlations obtained from single-point mea- surements (D08, X/M ≈ 42). . . . . . . . . . . . . . . . . . . . . . . . . 85
4.14 Isotropy test based on single-point measurements for different values of α (a) D02, (b) D04 and (c) D08. . . . . . . . . . . . . . . . . . . . . . . . . 88
4.15 Isotropy test based on two-point measurements for different values of α (a) D02, (b) D04, (c) D08 and (d) D16b. . . . . . . . . . . . . . . . . . . 89
4.16 Comparison of the transverse correlation C11(0, r, 0) for the four different values of α. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.17 Comparison of the longitudinal and transverse correlation functions ob- tained from single-point and two-point measurements. (a) active grid (D08), (b) passive grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.18 Longitudinal and transverse correlations (across-stream separation) at dif- ferent mean velocities and therefore different grid-bar rotation rates, but with the same α (= 0.08) i.e. cases D08 and D08b. . . . . . . . . . . . . 91
4.19 Schematic for the calculation of longitudinal and transverse correlations along any direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.20 Longitudinal (a) and transverse (b) correlation maps for the passive grid. 94 4.21 Longitudinal (a) and transverse (b) correlation maps for the active grid
(expt. D015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
LIST OF FIGURES xiv
4.22 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D04). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.23 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D08). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.24 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D16b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.25 Schematic for the calculation of longitudinal and transverse correlation functions along 0o and 90o directions. . . . . . . . . . . . . . . . . . . . . 97
4.26 Ratio of correlation functions CS urur
(0o)/ CS urur
(0o)/ CS utut
(90o)) for the cases: D015, D04, D08, D16b and passive grid. . . . . . . . . . . . 98
5.1 The temporal correlation CT uu with the separation ‘τ ’ scaled with T0.4. . . 108
5.2 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with L′ 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with LM 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with L′′ 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Comparison of the spatial correlation CS uu(r) computed by various means
for the active-grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.6 Comparison of the spatial correlation CS
uu(r) computed by various means, for low intensity turbulence with passive grid. . . . . . . . . . . . . . . . 114
6.1 Comparison of normalized (a) mean velocity profiles and (b) variance of u measured using two different type of grids. . . . . . . . . . . . . . . . . 117
6.2 Plot of δ995/x versus Rex. . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Values of (urms/ U)∞ and Lu
∞/δ995 for the TBL measurements. . . . . . 121 6.4 Correlation of fractional change in skin friction coefficient as a function of
FST intensity and length scale. . . . . . . . . . . . . . . . . . . . . . . . 121 6.5 Mean velocity profiles normalized by inner variable, uτ for the cases: (a)
no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . . . 124 6.6 Effect of Reθ in the outer region of the BL for the same FST intensities
(a) and Effect of FST intensities on the wake strength in the outer region of the BL (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.7 Variation of skin-friction coefficient, Cf with Reθ. . . . . . . . . . . . . . 128 6.8 Effect of FST on the mean velocity deficit profiles. . . . . . . . . . . . . . 129 6.9 Turbulence intensity profiles. . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.10 Reynolds stress profiles normalized by u2τ for the boundary layer. . . . . . 131 6.11 Cross-correlation coefficients profiles. . . . . . . . . . . . . . . . . . . . . 132 6.12 Effect of FST on the anisotropy, u2 / v2, of the boundary layer. . . . . 133 6.13 Kurtosis and Skewness profiles of velocity fluctuations. . . . . . . . . . . 135 6.14 Fluctuating velocity and fluctuating vorticity for the BL measured using
PIV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
LIST OF FIGURES xv
6.15 The distribution of the density functions (PDFs) of wall parallel velocity fluctuations at various positions across the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . 139
6.16 The distribution of the probability density functions (PDFs) of wall nor- mal velocity fluctuations at various positions across the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . 140
6.17 Comparison of spatial longitudinal spectra F11(k1) for the no grid, passive grid and active grid cases respectively measured using PIV. . . . . . . . . 142
6.18 Comparison of spatial longitudinal spectra F11(k1) plotted at same y+ for the no grid, passive grid and active grid cases respectively measured using PIV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.19 Comparison of longitudinal spectra F11(k1) for the no grid, passive grid and active grid cases respectively measured using HWA. . . . . . . . . . 144
6.20 Three-dimensional plots of normalized pre-multiplied energy spectra over the height of the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.21 Normalized correlation maps for the wall parallel velocity fluctuations for the cases no grid, passive grid and active grid respectively. . . . . . . . . 149
6.22 Schematic of the deformation of correlated structures by the mean shear. 150 6.23 Angle of tilt (θ(y)) with the flow direction, in the structures in the corre-
lation maps in figure 6.21. . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.24 Ratio of the measured angle to the calculated angle, in figure 6.23. . . . . 152 6.25 Normalized correlation maps for the wall normal velocity fluctuations for
the cases no grid, passive grid and active grid respectively. . . . . . . . . 153 6.26 Schematic of the PDF of the velocity differences calculated between two
points separated by distance . . . . . . . . . . . . . . . . . . . . . . . . 154 6.27 Schematic of coherence of toward wall moving fluid for the condition
P (u)|v<0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.28 Conditional PDFs of velocity differences P (u)|v<0 for the cases: no grid,
passive grid and active grid respectively. . . . . . . . . . . . . . . . . . . 157 6.28 Conditional PDFs of velocity differences P (u)|v<0 for the cases: no grid,
passive grid and active grid respectively. . . . . . . . . . . . . . . . . . . 158 6.29 Variation of transverse and longitudinal integral scales as function of wall
normal (y) distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 6.30 Kinetic energy maps and reconstructed kinetic energy map for the active
grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.31 Sample kinetic energy maps and corresponding POD reconstructions for
the no grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.32 Sample kinetic energy maps and corresponding POD reconstructions for
the passive grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.33 Sample kinetic energy maps and corresponding POD reconstructions for
the active grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6.34 Variation of the BL thickness, δ(x) against x. . . . . . . . . . . . . . . . 167
LIST OF FIGURES xvi
6.35 Joint probability density functions (JPDFs), P (u, v) of u and v fluctua- tions for the cases no grid, passive grid and active grid respectively. . . . 170
6.35 Joint probability density functions (JPDFs), P (u, v) of u and v fluctua- tions for the cases no grid, passive grid and active grid respectively. . . . 171
A.1 Schematic of wind tunnel primary contraction section. . . . . . . . . . . . 176 A.2 Wind tunnel primary contraction section profile. . . . . . . . . . . . . . . 178
B.1 Schematic of wind tunnel secondary contraction section. . . . . . . . . . 179 B.2 Wind tunnel secondary contraction section profile. . . . . . . . . . . . . . 181
C.1 Agitator wing for active grid. . . . . . . . . . . . . . . . . . . . . . . . . 182
D.1 Schematic of ogive-shaped nose for leading edge of the boundary layer plate.185 D.2 Ogive shaped nose profile for leading edge of the boundary layer plate. . 187
List of Tables
2.1 Comparison of various active grid parameters from the present work with those of previous studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1 Comparison of various active grid parameters from the present work with those of previous studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Parameters for the forcing protocol used in the various runs considered in the present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 PIV data processing parameters for BL measurements. . . . . . . . . . . 54
4.1 Percentage deviation of the local velocity from the mean across the tunnel test section (with passive grid). . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Parameters used in previous investigations of isotropy of active grid tur- bulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Free-stream flow parameters for passive grid and active grid employed for the present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Coefficients used in the Exponential fit in figures 4.13 to 4.15. . . . . . . 86
5.1 Experimental conditions of three different HWA runs. . . . . . . . . . . . 104 5.2 Values of the various length scales obtained in the three HWA runs and
in the PIV run for the active and passive grid cases, respectively. . . . . . 105 5.3 Values of r.m.s. deviation calculated between spatial correlation func-
tion scaled with L0.4 with the spatial correlation obtained using Taylor’s hypothesis scaled with different length scales (L′
0.4, L M 0.4 and L′′
0.4). . . . . 111
LIST OF TABLES xviii
5.4 Values of r.m.s. deviation calculated between spatial correlation function scaled with L0.4 with the spatial correlation obtained using Taylor’s hy- pothesis, and instantaneous Taylor’s hypothesis and the application of the model, scaled with different length scales (LM
0.4 and L′′ 0.4). . . . . . . . . . 113
6.1 Boundary layer parameters for the different cases discussed. . . . . . . . 127 6.2 The wall normal distance at which the conditional PDFs of velocity dif-
ferences first becomes symmetric for the shortest separation of 2. . . . . 156 6.3 Ratio of the BL thickness measured to the calculated. . . . . . . . . . . . 167
C.1 Dynamic torque required by the stepper motor for different size wind tunnel.184
Nomenclature
β (≡ ( (u21/2/U)∞
Cf (≡ Cf − Cfo) Fractional change in the skin friction coefficient
t Time delay between successive calls to the random number generator
t ′
δ∗ Displacement thickness
δ995 ≡ δ Boundary layer thickness defined by the position at which U/ U =
0.995
η (≡ (ν 3
νT δ Average turbulent diffusivity at a location x
U Mean velocity in x or X direction
uv Reynolds shear stress
ν (≡ µ/ρ) Kinematic viscosity
Π Coles parameter
ρo Mass density of the manometer liquid
ρuv cross-correlation coefficient
τ ′
under dynamic conditions
C Constant in logarithmic law of BL velocity profile
C Winglet chord length
C11(0, r, 0) Transverse correlation based on two-point measurements
C22(0, r, 0) Longitudinal correlation based on two-point measurements
Cfo Value of skin friction coefficient for the no grid case
Cf (≡ 2τw ρa<U>2
∞
CS uu(r) Spatial correlation function
CT uu(τ) Temporal correlation function
D Outer diameter
d Inner diameter
f(r) Autocorrelation coefficient
g(r) cross-correlation coefficient
k Von Karman constant
K,Ku,Kv Kurtosis factor ( u4
L Eulerian integral length scale
L Length of the contraction section
l Integral length scale
l ′
l11 Longitudinal length scale calculated using longitudinal autocorrelation
function
tion
n Exponent in decay law
p2 Absolute pressure at the end of the tubing
r Spatial separation
Rλ (≡ urmsλ ν
Rl (≡ urmsl/ν) Turbulence Reynolds number
Ro (≡ <U> M
Reθ (≡ <U>θ ν
Nomenclature xxii
ReM (≡ <U>M ν
) Mesh Reynold’s number
Rex (≡ <U>∞x ν
(u2)3/2 , v3
T Torque required by the stepper motors
t Time
Tux FST intensity at the measurement location ‘x′
U Local streamwise mean velocity
u Fluctuating velocity in X direction
U∞ Free-stream mean velocity
uSd oru T d Decorrelation velocity
Uk Velocity one diameter away from the wall, in the absence of the BL
trip wire
vrms or v ′
Vtip Speed of the active grid winglet at its tip
X Downstream coordinate
x Distance downstream from the boundary layer plate leading edge
XLE Distance of leading edge from the grid
y or Y Wall normal coordinate
z or Z Transverse coordinate
Nomenclature xxiii
Acronym
AC Alternating current A/D Analog to digital A or AG Active grid BL Boundary layer BNC Bayonet Neill-Concelman CTA Constant temperature anemometer DAQ Data acquisition DC Direct current DR or D double-random FR Fully random FS Free-stream FS Full scale FST Free-stream turbulence HEPA High efficiency particulate absolute HWA Hot wire anemometry HW Hot wire anemometry IC Integrated circuit ID Internal diameter I/O Input/Output KE Kinetic energy LC Least count LDA Laser Doppler anemometry LES Large eddy simulation LSB Low-swirl burner NUSS NetScanner Unified Startup Software OD Outer diameter OFI Oil-film interferometry OHR Overheat ratio for hot wire PCI Peripheral Component Interconnect (hardware bus) PDF Probability density function P or PG Passive grid PIV Particle image velocimetry PLIF Planar laser-induced fluorescence
Nomenclature xxiv
POD Proper orthogonal decomposition PVC Polyvinyl chloride RAM Random-access memory r.p.s. Revolutions per second SHC Shielded cable SLS Selective laser sintering SLS Selective laser sintering SR or S Single-random SS Stainless steel SSH Simultaneous sampling and hold TBL Turbulent boundary layer TKE Turbulent kinetic energy TH Taylor’s ‘frozen’ turbulence hypothesis THI Instantaneous Taylor’s hypothesis UPS Uninterrupted power supply WC Water column ZPG Zero-pressure gradient
Subscripts
Superscripts
+ Quantity normalized by the frictional velocity S Spatial correlation T Temporal correlation
CHANDRAHAS S. SHET.pdf
© Indian Institute of Technology Delhi (IITD), New Delhi, 2020
INTERACTION OF FREE-STREAM TURBULENCE WITH A TURBULENT
BOUNDARY LAYER
Submitted
in fulfilment of the requirements of the degree of Doctor of Philosophy
to the
SEPTEMBER 2020
Certificate
This is to certify that the thesis entitled “Interaction of Free-stream Turbulence
with a Turbulent Boundary Layer” being submitted by Mr. Chandrahas S. Shet
to the Indian Institute of Technology Delhi for the award of the degree of Doctor of
Philosophy in Applied Mechanics department is a bonafide record of original research
work carried out by him under our supervision in conformity with rules and regulations
of the institute. The results contained in this thesis have not been submitted, in part or
in full, to any other University or Institute for the award of any Degree or Diploma.
Dr. S. V. Veeravalli Dr. Murali R. Cholemari
Professor Associate Professor
Indian Institute of Technology Delhi Indian Institute of Technology Delhi
New Delhi - 110 016 New Delhi - 110 016
India India
i
Acknowledgements
First and foremost, I consider it an honor to work with Prof. S. V. Veeravalli and Dr.
Murali R. Cholemari. I wish to express my deepest sense of gratitude to my research
supervisors Prof. S. V. Veeravalli and Dr. Murali R. Cholemari for their invaluable
guidance, support and encouragement, throughout the course of this work.
I am also grateful to members of student research committee (SRC) and department
research committee (DRC), namely Prof. V. Seshadri, Prof. S. N. Singh, Prof. Sawan
S. Sinha, Prof. Balaji Srinivasan, Prof. B. Premachandran, Prof. B. P. Patel and Prof.
Anupam Dewan for their valuable suggestions throughout the research work.
My special thanks go towards Prof. R. C. Malhotra, Prof. Puneet Mahajan, Prof.
Sanjeev Sanghi, Prof. Sriram Hegde, Prof. P. K. Sen, Prof. Suhail Ahmad, Late Prof.
Y. Nath, Prof. Y. Patel, Dr. Arghya Samanta and other faculty members of Applied
Mechanics department for their support and help during the research work.
I feel great pleasure to record my deep sense of gratitude and indebtedness to Prof. R.
D. Tarey, Prof. Ashish Ganguli and Prof. Arun Agarwala for their meticulous guidance,
patient discussions and personal involvement during my research work. Special thanks
to Mr. Josekutty A. J. for the continuous support and help during the research work.
I would like to express my deep gratitude to my external examiners Prof. Sanjay
Mittal (IIT Kanpur) and Prof. Laurent B. Mydlarski (McGill University, Quebec) for
their valuable comments and very detailed corrections. The thesis is vastly improved as
a result.
At this moment, I would also like to take this opportunity to thank Prof. Peter
Bradshaw, Prof. Zellman Warhaft and Prof. Charles Meneveau for all that I learnt from
ii
iii
them, through their books and lectures, research articles, and through notes, on various
theoretical and experimental aspects of turbulence.
The help of Mr. Harbhajan Singh and Mr. Sunil Bhogal in modifying the wind tunnel
and fabricating the active grid is also gratefully acknowledged. My sincere thanks to Mr.
R. P. Bhogal and the other staff of the Gas Dynamics laboratory, namely Mr. Jugti
Ram, Mr. Rameshwar Dayal, Mr. Nand Lal, Mr. Suresh Sharma, Mr. Kunj Behari,
Mr. Rama Nand, Mr. Sunil Dayal & Mr. Anil for their continuous support during the
research work. The cooperation of Mr. Diwan Singh, Mr. Yogesh & Mr. Manohar from
Fluid Mechanics laboratory, Mr. D. C. Sharma & Mr. Madan Gopal from departmental
Workshop and Mr. Anil Kumar from MTS laboratory is greatly acknowledged. The
help of supporting staffs (Mr. Gregory Toppo, Mr. Manoj & many more) is also greatly
acknowledged.
I also express my gratitude towards administrative staffs from Applied mechanics
department, namely Mrs. Harkanwal Kaur, Mrs. Tajinder Kaur, Mrs. Amarjeet Kaur,
Ms. Harpreet Kaur, Mr. Vikram Singh, Mr. Rakesh Kr Garg, Mr. M. L. Sehgal, Mr.
Madan Lal, Mrs. Seema Saxena, Mr. Pawan Kumar, Mr. Jitender, Mr. Ram Singh,
Mr. Dharmender & Mr. Pramod Kumar and from other units of the institute (Accounts
section, Store purchase section, Audit section, IRD, PG section, Maintenance unit, etc)
who directly or indirectly contributed towards the research work.
I am also immensely grateful to IIT Delhi and Department of Science and Technol-
ogy, Government of India for funding the expenses that incurred during my research
work (Grant Nos.: SR/S3/MERC/16/2005 and SR/FST/ET1-212/2007). I express my
heartfelt thanks to Dr. D. R. Prasad Raju, Shri. S. S. Kohli, Dr. Mukhopadhyay and
Dr. Pratishtha Pandey of DST for their constant support.
I express my sincere appreciation to deans & wardens of Nilgiri hostel, namely Prof.
Aravind Nema, Prof. P M V Subbarao, Dr. Dinesh Kalyanasundaram, Prof. Apurba
Das, Prof. Abhijit Majumdar, Prof. Shashi Mathur, Prof. Anurag Sharma, Prof. S.
K. Gupta & Prof. Rajesh Khanna and care-takers (Mr. Shalikram Sharma, Mr. Gopal
Singh & Mr. Nitish Kumar) for their kind support and help during my fourteen years
iv
of stay at Nilgiri hostel.
I wish to thank my friends Dr. Ganapati N. Joshi, Dr. Praveen Pinnoji, Dr. Pawan
Kumar Yoganarasimha, Dr. S. Nasiruddin, Dr. Sunil Chandel, Dr. Rajesh Singh, Dr.
Jitendra, Mr. Rishav Rajora, Dr. Lakhvinder Singh, Dr. Shish Shukla, Dr. Paramanand
N and Dr. Manoj who stood with me in difficult times.
Last but not the least, I want to thank everyone else who played an essential role in
completing this work and also express an apology if I have forgotten to thank someone
personally.
IIT Delhi, New Delhi - 110 016
Chandrahas
Stamp
Abstract
We present measurements of a zero external pressure gradient two-dimensional (2D)
turbulent boundary layer (TBL) on a flat plate in the presence of grid-generated (passive
or active grid) isotropic free-stream turbulence (FST), as well as in the absence of any
grid. Free-stream intensities were approximately 0.3%, 4.8% and 9.3% for the no grid,
passive grid and active grid cases respectively, at the start of the boundary-layer. The
free-stream Taylor’s microscale based Reynolds number is about 490 and 120 for the
active grid and passive grid cases respectively. The measurements were made using
hot-wire anemometry (HWA) and two-dimensional particle image velocimetry (PIV).
We present an optimized procedure for generating isotropic, homogeneous, high inten-
sity turbulent flow behind an active grid. Isotropy in FST is first rigorously established
in the present set-up before conducting the boundary layer (BL) measurements. Exper-
imental investigation to check the validity of the Taylor’s ‘frozen’ turbulence hypothesis
for high intensity turbulence is also discussed.
The experimental investigations on FST-TBL interactions confirm that, at a funda-
mental level, the presence of the FST increases the growth rate of the TBL and the
wall shear stress. The effect of FST extends deep into the TBL, affecting the wall re-
gion as well as the small scale statistics throughout the boundary layer; the greater
the free stream turbulence intensity, the deeper is the extent where it influences the
TBL. A comprehensive set of statistics like velocity spectra, velocity correlation maps,
and velocity PDFs of various kinds, as well as velocity profiles, both from HWA and
PIV measurements, are presented to support and quantify this view. Changes in the
structural organization of the TBL because of the FST are discussed.
v
vi
We educe the interacting structures of the FST and TBL using kinetic energy (KE)
maps and proper orthogonal decomposition (POD). The data is used to propose a mech-
anism of growth enhancement observed in the TBL in the presence of FST. Very large
scale structures, of sizes 2δ or more, spanning regions across the boundary layer inter-
face nearly up to the wall are seen to drive the interaction. We propose and evaluate an
engulfment and diffusion model of the BL-FST interaction and model the growth of the
boundary layer.
- (2D) (TBL)
- (/ ) (FST) ,
- 0.3%,
4.8% 9.3% , -
490 120
- (HWA) - (PIV)
, ,
, -
(BL)
‘
FST-TBL , -
- ,
,
, (PDFs), HWA PIV
vii
viii
-
(KE) (POD)
- -
, 2δ ,
: BL-FST ( )
Contents
1 Introduction 1 1.1 Outline of the following chapters . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature Review and Objectives 7 2.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 High intensity FST Generation . . . . . . . . . . . . . . . . . . . 7 2.1.2 Interaction of FST with a Turbulent Boundary Layer . . . . . . . 22 2.1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Experimental Set-up and Instrumentation 26 3.1 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 Plenum chamber and contraction sections . . . . . . . . . . . . . 27 3.1.2 Test section and diffuser . . . . . . . . . . . . . . . . . . . . . . . 30 3.1.3 Axial fan, drive and controller . . . . . . . . . . . . . . . . . . . . 31
3.2 Design and fabrication of traverse mechanism . . . . . . . . . . . . . . . 31 3.3 Passive grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Active grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.1 Design and fabrication of active grid . . . . . . . . . . . . . . . . 34 3.4.2 Active grid control system . . . . . . . . . . . . . . . . . . . . . . 39 3.4.3 Active grid control protocol . . . . . . . . . . . . . . . . . . . . . 42
3.5 Configuration of boundary layer plate and trip wire selection . . . . . . . 43
ix
Admin
CONTENTS x
3.6 Mean velocity measurement . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.6.1 Pitot and Pitot-Static tubes . . . . . . . . . . . . . . . . . . . . . 47 3.6.2 Flat Pitot tube or boundary layer Pitot probe . . . . . . . . . . . 48
3.7 Fluctuating velocity measurement . . . . . . . . . . . . . . . . . . . . . . 48 3.7.1 Hot Wire Anemometer (HWA) . . . . . . . . . . . . . . . . . . . 48 3.7.2 Particle Image Velocimetry (PIV) . . . . . . . . . . . . . . . . . . 51
3.8 Shear stress measurement using Preston tube or Clauser fit . . . . . . . . 54 3.9 Pressure measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.9.1 16-channel pressure scanner . . . . . . . . . . . . . . . . . . . . . 55 3.9.2 Floating scale manometer . . . . . . . . . . . . . . . . . . . . . . 56
3.10 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.11 Data acquisition (DAQ) system . . . . . . . . . . . . . . . . . . . . . . . 57 3.12 Power supply for the instruments . . . . . . . . . . . . . . . . . . . . . . 57
4 Flow Qualification 59 4.1 Uniformity of the flow at the exit of the double contraction . . . . . . . . 61 4.2 Homogeneity of the flow in the test section . . . . . . . . . . . . . . . . . 61 4.3 Variation of the static pressure across the boundary layer plate and Zero-
pressure gradient condition . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4 Decay laws and Free-stream length scale (Lu
∞/δ995) . . . . . . . . . . . . 69 4.5 Two-dimensionality of the boundary layer . . . . . . . . . . . . . . . . . 72 4.6 Internal consistency of the velocity measurement techniques . . . . . . . 72
4.6.1 Mean and r.m.s. boundary layer velocity profiles . . . . . . . . . . 72 4.6.2 Compassion of transverse correlation (C11(0, r, 0)) measured using
a single wire with a cross wire probe . . . . . . . . . . . . . . . . 75 4.6.3 Comparison of the correlations obtained from two-point HWA and
PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.7 Optimizing the performance of an active grid to generate high intensity
isotropic free-stream turbulence . . . . . . . . . . . . . . . . . . . . . . . 77 4.7.1 Velocity Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.7.2 Longitudinal F11(k1) and transverse F22(k1) spectra . . . . . . . . 80 4.7.3 Flow parameters relevant to the different configurations reported
in the present work . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.7.4 Isotropy and Correlation Functions . . . . . . . . . . . . . . . . . 84 4.7.5 Correlation Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.7.6 Conclusions to the chapter . . . . . . . . . . . . . . . . . . . . . . 97
5 Assessment of Taylor’s Hypothesis for the Active Grid Turbulence 100 5.1 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2 Eulerian spatial & temporal integral scales and Comparison of the spatial
correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.3 Conclusions to the chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 115
CONTENTS xi
6 Results and Discussions 116 6.1 Effect of large-scale isotropy of FST on the turbulent boundary layer . . 116 6.2 The parameter ‘β’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Boundary layer mean velocity profiles . . . . . . . . . . . . . . . . . . . . 122 6.4 Mean velocity deficit profiles . . . . . . . . . . . . . . . . . . . . . . . . . 128 6.5 Turbulence intensity profiles . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.6 Reynolds stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.7 Shear-stress correlation coefficient profiles . . . . . . . . . . . . . . . . . 130 6.8 Effect of FST on the anisotropy, u2 / v2 of the boundary layer . . . . 133 6.9 Kurtosis and Skewness profiles . . . . . . . . . . . . . . . . . . . . . . . . 134 6.10 Fluctuating velocity and fluctuating vorticity for the BL . . . . . . . . . 136 6.11 Velocity probability density functions (PDFs) . . . . . . . . . . . . . . . 137 6.12 Spatial longitudinal spectra using PIV data . . . . . . . . . . . . . . . . 138 6.13 Spatial longitudinal spectra using HWA data . . . . . . . . . . . . . . . . 141 6.14 Normalized correlation maps for (1) wall parallel and (2) wall normal
velocity fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 6.14.1 Normalized correlation maps for wall parallel velocity fluctuations 147 6.14.2 Normalized correlation maps for wall normal velocity fluctuations 150
6.15 Conditional PDFs of velocity differences (P (u)|v<0) . . . . . . . . . . . 154 6.16 Variation of integral length scales . . . . . . . . . . . . . . . . . . . . . . 156 6.17 Kinetic energy maps and structures educed using Proper Orthogonal De-
composition (POD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.18 Engulfment and diffusion model of growth . . . . . . . . . . . . . . . . . 165 6.19 Joint Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.19.1 Joint probability density functions (JPDFs) . . . . . . . . . . . . 168
7 Conclusions 172 7.1 Recommendations for further work . . . . . . . . . . . . . . . . . . . . . 174
Appendix A Coordinates for the wind tunnel primary contraction section176
Appendix B Coordinates for the wind tunnel secondary contraction sec- tion 179
Appendix C Calculation of torque required by the stepper motors used in the active grid 182
Appendix D Coordinates for the ogive-shaped nose for leading edge of the BL plate 185
Bibliography 188
Biodata 203
List of Figures
2.1 Schematic of the active turbulence generator developed by Makita, 1991. 8 2.2 Schematic sketch of the active grid developed by Mydlarski & Warhaft
(1996). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Active grid of Poorte & Biesheuvel (2002). . . . . . . . . . . . . . . . . . 11 2.4 Active grid from Larssen & Devenport (2011). . . . . . . . . . . . . . . . 13 2.5 Active grid of Hearst & Lavoie (2015). . . . . . . . . . . . . . . . . . . . 14 2.6 Active grid from Bewley et al. (2013) or Bodenschatz et al. (2014). . . . 15
3.1 Schematic sketch of the wind tunnel used in the present study. . . . . . . 29 3.2 Photograph of the wind tunnel used for present boundary layer study. . . 30 3.3 Schematic of the two-axes traverse mechanism (1.0 m x 0.5 m) for the 0.61
x 0.61 m2 wind tunnel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Schematic of the passive grid (M = 5.8 cm). . . . . . . . . . . . . . . . . 35 3.5 Schematic arrangement of the active grid used in the present study. . . . 38 3.6 Schematic of the active grid: a) side view b) top view. . . . . . . . . . . . 40 3.7 Schematic of the active grid rod with winglets. . . . . . . . . . . . . . . . 40 3.8 Photograph of active grid of mesh size 6.9 cm. . . . . . . . . . . . . . . . 41 3.9 Schematic layout of the stepper motor control system. . . . . . . . . . . . 41 3.10 Stepper motor controller and variable power supply to control active grid. 41 3.11 Configuration of the boundary layer plate (a) and schematic of the PIV
measurement set-up (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.12 Mean velocity profiles in inner variables at x ≈ 107.0 cm for the no grid
case with different trip wire sizes, compared with measurements in literature. 46 3.13 Schematic of the cross-wire probe calibration set-up. . . . . . . . . . . . . 51 3.14 Dimension of the laser sheet across the boundary layer plate. . . . . . . . 54 3.15 Schematic of the data acquisition set-up for the hot wire measurements. . 57
4.1 Schematic of the set-up used to measure the flow uniformity and measure- ment locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2 Variation of mean velocity, the r.m.s. of turbulent fluctuations and cross- correlation coefficient across the tunnel . . . . . . . . . . . . . . . . . . . 65
4.3 Schematic of the location of static pressure taps across the boundary layer plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
xii
LIST OF FIGURES xiii
4.4 Pressure gradient across the boundary layer plate measured using a 16- channel pressure scanner after adjusting the height of the tunnel top wall. 68
4.5 Mean velocity measurement along the length of the tunnel with the bound- ary layer plate for the cases: (a) no grid, (b) passive grid and (c) active grid respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6 (a) Decay of longitudinal velocity variance, u2 / U2 for the passive and active grids. (b) Values of FST length scale (Lu
∞) along X for the passive grid and active grid cases. . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.7 Comparison of mean velocity profiles measured at two different z locations of the boundary layer plate in the presence of passive grid generated FST. 73
4.8 (a) Comparison of BL mean velocity profiles for the no grid case with results of Purtell et al. (1981). (b) Comparison of boundary layer data measured using a flat Pitot tube with HWA and PIV data for the active grid case D16b. (c) Comparison of BL r.m.s. velocity profile for the active grid case (D08) measured using HWA with PIV. . . . . . . . . . . . . . . 74
4.9 Comparison of transverse correlation measured using single-wire with cross- wire probe for the active grid case: D08. . . . . . . . . . . . . . . . . . . 75
4.10 Comparison of spatial correlation functions obtained using PIV and two- point HWA measurements for the active grid case: D08. . . . . . . . . . 76
4.11 Longitudinal and transverse power spectra F11(k1) and F22(k1) for the active grid case D08. Case (a) t > 60 ms and case (b) t ≈ 40 ms. . . 80
4.12 Longitudinal F11(k1) and transverse F22(k1) velocity spectra (at X/M ≈ 42) for the active grid cases: (a) D16b (b) D08. . . . . . . . . . . . . . . 81
4.13 Longitudinal and transverse correlations obtained from single-point mea- surements (D08, X/M ≈ 42). . . . . . . . . . . . . . . . . . . . . . . . . 85
4.14 Isotropy test based on single-point measurements for different values of α (a) D02, (b) D04 and (c) D08. . . . . . . . . . . . . . . . . . . . . . . . . 88
4.15 Isotropy test based on two-point measurements for different values of α (a) D02, (b) D04, (c) D08 and (d) D16b. . . . . . . . . . . . . . . . . . . 89
4.16 Comparison of the transverse correlation C11(0, r, 0) for the four different values of α. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.17 Comparison of the longitudinal and transverse correlation functions ob- tained from single-point and two-point measurements. (a) active grid (D08), (b) passive grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.18 Longitudinal and transverse correlations (across-stream separation) at dif- ferent mean velocities and therefore different grid-bar rotation rates, but with the same α (= 0.08) i.e. cases D08 and D08b. . . . . . . . . . . . . 91
4.19 Schematic for the calculation of longitudinal and transverse correlations along any direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.20 Longitudinal (a) and transverse (b) correlation maps for the passive grid. 94 4.21 Longitudinal (a) and transverse (b) correlation maps for the active grid
(expt. D015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
LIST OF FIGURES xiv
4.22 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D04). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.23 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D08). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.24 Longitudinal (a) and transverse (b) correlation maps for the active grid (expt. D16b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.25 Schematic for the calculation of longitudinal and transverse correlation functions along 0o and 90o directions. . . . . . . . . . . . . . . . . . . . . 97
4.26 Ratio of correlation functions CS urur
(0o)/ CS urur
(0o)/ CS utut
(90o)) for the cases: D015, D04, D08, D16b and passive grid. . . . . . . . . . . . 98
5.1 The temporal correlation CT uu with the separation ‘τ ’ scaled with T0.4. . . 108
5.2 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with L′ 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with LM 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4 The spatial correlation CS uu obtained using Taylor’s hypothesis with the
separation ‘r’ scaled with L′′ 0.4. . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Comparison of the spatial correlation CS uu(r) computed by various means
for the active-grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.6 Comparison of the spatial correlation CS
uu(r) computed by various means, for low intensity turbulence with passive grid. . . . . . . . . . . . . . . . 114
6.1 Comparison of normalized (a) mean velocity profiles and (b) variance of u measured using two different type of grids. . . . . . . . . . . . . . . . . 117
6.2 Plot of δ995/x versus Rex. . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3 Values of (urms/ U)∞ and Lu
∞/δ995 for the TBL measurements. . . . . . 121 6.4 Correlation of fractional change in skin friction coefficient as a function of
FST intensity and length scale. . . . . . . . . . . . . . . . . . . . . . . . 121 6.5 Mean velocity profiles normalized by inner variable, uτ for the cases: (a)
no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . . . 124 6.6 Effect of Reθ in the outer region of the BL for the same FST intensities
(a) and Effect of FST intensities on the wake strength in the outer region of the BL (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.7 Variation of skin-friction coefficient, Cf with Reθ. . . . . . . . . . . . . . 128 6.8 Effect of FST on the mean velocity deficit profiles. . . . . . . . . . . . . . 129 6.9 Turbulence intensity profiles. . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.10 Reynolds stress profiles normalized by u2τ for the boundary layer. . . . . . 131 6.11 Cross-correlation coefficients profiles. . . . . . . . . . . . . . . . . . . . . 132 6.12 Effect of FST on the anisotropy, u2 / v2, of the boundary layer. . . . . 133 6.13 Kurtosis and Skewness profiles of velocity fluctuations. . . . . . . . . . . 135 6.14 Fluctuating velocity and fluctuating vorticity for the BL measured using
PIV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
LIST OF FIGURES xv
6.15 The distribution of the density functions (PDFs) of wall parallel velocity fluctuations at various positions across the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . 139
6.16 The distribution of the probability density functions (PDFs) of wall nor- mal velocity fluctuations at various positions across the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . 140
6.17 Comparison of spatial longitudinal spectra F11(k1) for the no grid, passive grid and active grid cases respectively measured using PIV. . . . . . . . . 142
6.18 Comparison of spatial longitudinal spectra F11(k1) plotted at same y+ for the no grid, passive grid and active grid cases respectively measured using PIV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.19 Comparison of longitudinal spectra F11(k1) for the no grid, passive grid and active grid cases respectively measured using HWA. . . . . . . . . . 144
6.20 Three-dimensional plots of normalized pre-multiplied energy spectra over the height of the boundary layer for the cases: (a) no grid, (b) passive grid and (c) active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.21 Normalized correlation maps for the wall parallel velocity fluctuations for the cases no grid, passive grid and active grid respectively. . . . . . . . . 149
6.22 Schematic of the deformation of correlated structures by the mean shear. 150 6.23 Angle of tilt (θ(y)) with the flow direction, in the structures in the corre-
lation maps in figure 6.21. . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.24 Ratio of the measured angle to the calculated angle, in figure 6.23. . . . . 152 6.25 Normalized correlation maps for the wall normal velocity fluctuations for
the cases no grid, passive grid and active grid respectively. . . . . . . . . 153 6.26 Schematic of the PDF of the velocity differences calculated between two
points separated by distance . . . . . . . . . . . . . . . . . . . . . . . . 154 6.27 Schematic of coherence of toward wall moving fluid for the condition
P (u)|v<0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.28 Conditional PDFs of velocity differences P (u)|v<0 for the cases: no grid,
passive grid and active grid respectively. . . . . . . . . . . . . . . . . . . 157 6.28 Conditional PDFs of velocity differences P (u)|v<0 for the cases: no grid,
passive grid and active grid respectively. . . . . . . . . . . . . . . . . . . 158 6.29 Variation of transverse and longitudinal integral scales as function of wall
normal (y) distance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 6.30 Kinetic energy maps and reconstructed kinetic energy map for the active
grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.31 Sample kinetic energy maps and corresponding POD reconstructions for
the no grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.32 Sample kinetic energy maps and corresponding POD reconstructions for
the passive grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 6.33 Sample kinetic energy maps and corresponding POD reconstructions for
the active grid case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 6.34 Variation of the BL thickness, δ(x) against x. . . . . . . . . . . . . . . . 167
LIST OF FIGURES xvi
6.35 Joint probability density functions (JPDFs), P (u, v) of u and v fluctua- tions for the cases no grid, passive grid and active grid respectively. . . . 170
6.35 Joint probability density functions (JPDFs), P (u, v) of u and v fluctua- tions for the cases no grid, passive grid and active grid respectively. . . . 171
A.1 Schematic of wind tunnel primary contraction section. . . . . . . . . . . . 176 A.2 Wind tunnel primary contraction section profile. . . . . . . . . . . . . . . 178
B.1 Schematic of wind tunnel secondary contraction section. . . . . . . . . . 179 B.2 Wind tunnel secondary contraction section profile. . . . . . . . . . . . . . 181
C.1 Agitator wing for active grid. . . . . . . . . . . . . . . . . . . . . . . . . 182
D.1 Schematic of ogive-shaped nose for leading edge of the boundary layer plate.185 D.2 Ogive shaped nose profile for leading edge of the boundary layer plate. . 187
List of Tables
2.1 Comparison of various active grid parameters from the present work with those of previous studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1 Comparison of various active grid parameters from the present work with those of previous studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Flow conditions and their relevant flow parameters from the previous work on active grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Parameters for the forcing protocol used in the various runs considered in the present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 PIV data processing parameters for BL measurements. . . . . . . . . . . 54
4.1 Percentage deviation of the local velocity from the mean across the tunnel test section (with passive grid). . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Parameters used in previous investigations of isotropy of active grid tur- bulence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3 Free-stream flow parameters for passive grid and active grid employed for the present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Coefficients used in the Exponential fit in figures 4.13 to 4.15. . . . . . . 86
5.1 Experimental conditions of three different HWA runs. . . . . . . . . . . . 104 5.2 Values of the various length scales obtained in the three HWA runs and
in the PIV run for the active and passive grid cases, respectively. . . . . . 105 5.3 Values of r.m.s. deviation calculated between spatial correlation func-
tion scaled with L0.4 with the spatial correlation obtained using Taylor’s hypothesis scaled with different length scales (L′
0.4, L M 0.4 and L′′
0.4). . . . . 111
LIST OF TABLES xviii
5.4 Values of r.m.s. deviation calculated between spatial correlation function scaled with L0.4 with the spatial correlation obtained using Taylor’s hy- pothesis, and instantaneous Taylor’s hypothesis and the application of the model, scaled with different length scales (LM
0.4 and L′′ 0.4). . . . . . . . . . 113
6.1 Boundary layer parameters for the different cases discussed. . . . . . . . 127 6.2 The wall normal distance at which the conditional PDFs of velocity dif-
ferences first becomes symmetric for the shortest separation of 2. . . . . 156 6.3 Ratio of the BL thickness measured to the calculated. . . . . . . . . . . . 167
C.1 Dynamic torque required by the stepper motor for different size wind tunnel.184
Nomenclature
β (≡ ( (u21/2/U)∞
Cf (≡ Cf − Cfo) Fractional change in the skin friction coefficient
t Time delay between successive calls to the random number generator
t ′
δ∗ Displacement thickness
δ995 ≡ δ Boundary layer thickness defined by the position at which U/ U =
0.995
η (≡ (ν 3
νT δ Average turbulent diffusivity at a location x
U Mean velocity in x or X direction
uv Reynolds shear stress
ν (≡ µ/ρ) Kinematic viscosity
Π Coles parameter
ρo Mass density of the manometer liquid
ρuv cross-correlation coefficient
τ ′
under dynamic conditions
C Constant in logarithmic law of BL velocity profile
C Winglet chord length
C11(0, r, 0) Transverse correlation based on two-point measurements
C22(0, r, 0) Longitudinal correlation based on two-point measurements
Cfo Value of skin friction coefficient for the no grid case
Cf (≡ 2τw ρa<U>2
∞
CS uu(r) Spatial correlation function
CT uu(τ) Temporal correlation function
D Outer diameter
d Inner diameter
f(r) Autocorrelation coefficient
g(r) cross-correlation coefficient
k Von Karman constant
K,Ku,Kv Kurtosis factor ( u4
L Eulerian integral length scale
L Length of the contraction section
l Integral length scale
l ′
l11 Longitudinal length scale calculated using longitudinal autocorrelation
function
tion
n Exponent in decay law
p2 Absolute pressure at the end of the tubing
r Spatial separation
Rλ (≡ urmsλ ν
Rl (≡ urmsl/ν) Turbulence Reynolds number
Ro (≡ <U> M
Reθ (≡ <U>θ ν
Nomenclature xxii
ReM (≡ <U>M ν
) Mesh Reynold’s number
Rex (≡ <U>∞x ν
(u2)3/2 , v3
T Torque required by the stepper motors
t Time
Tux FST intensity at the measurement location ‘x′
U Local streamwise mean velocity
u Fluctuating velocity in X direction
U∞ Free-stream mean velocity
uSd oru T d Decorrelation velocity
Uk Velocity one diameter away from the wall, in the absence of the BL
trip wire
vrms or v ′
Vtip Speed of the active grid winglet at its tip
X Downstream coordinate
x Distance downstream from the boundary layer plate leading edge
XLE Distance of leading edge from the grid
y or Y Wall normal coordinate
z or Z Transverse coordinate
Nomenclature xxiii
Acronym
AC Alternating current A/D Analog to digital A or AG Active grid BL Boundary layer BNC Bayonet Neill-Concelman CTA Constant temperature anemometer DAQ Data acquisition DC Direct current DR or D double-random FR Fully random FS Free-stream FS Full scale FST Free-stream turbulence HEPA High efficiency particulate absolute HWA Hot wire anemometry HW Hot wire anemometry IC Integrated circuit ID Internal diameter I/O Input/Output KE Kinetic energy LC Least count LDA Laser Doppler anemometry LES Large eddy simulation LSB Low-swirl burner NUSS NetScanner Unified Startup Software OD Outer diameter OFI Oil-film interferometry OHR Overheat ratio for hot wire PCI Peripheral Component Interconnect (hardware bus) PDF Probability density function P or PG Passive grid PIV Particle image velocimetry PLIF Planar laser-induced fluorescence
Nomenclature xxiv
POD Proper orthogonal decomposition PVC Polyvinyl chloride RAM Random-access memory r.p.s. Revolutions per second SHC Shielded cable SLS Selective laser sintering SLS Selective laser sintering SR or S Single-random SS Stainless steel SSH Simultaneous sampling and hold TBL Turbulent boundary layer TKE Turbulent kinetic energy TH Taylor’s ‘frozen’ turbulence hypothesis THI Instantaneous Taylor’s hypothesis UPS Uninterrupted power supply WC Water column ZPG Zero-pressure gradient
Subscripts
Superscripts
+ Quantity normalized by the frictional velocity S Spatial correlation T Temporal correlation
CHANDRAHAS S. SHET.pdf