Reynolds Number Effects on an Adverse Pressure Gradient Turbulent Boundary Layer

208 Pages·2005·10.69 MB·English

Reynolds Number Effects on an Adverse Pressure
Gradient Turbulent Boundary Layer
a dissertation
submitted to the department of mechanical engineering
and the committee on graduate studies
of stanford university
in partial fulfillment of the requirements
for the degree of
doctor of philosophy
Carolyn D. Aubertine
June 2005
(cid:176)c Copyright by Carolyn D. Aubertine 2005
All Rights Reserved
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I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
John K. Eaton
(Principal Adviser)
I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
James P. Johnston
I certify that I have read this dissertation and that in my
opinion it is fully adequate, in scope and in quality, as a
dissertation for the degree of Doctor of Philosophy.
Juan G. Santiago
Approved for the University Committee
on Graduate Studies.
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Abstract
While much recent work has focused on equilibrium turbulent boundary layers, those which
are out of equilibrium have been examined much less frequently. Typically they have been
examined far from equilibrium, making it difficult to draw general conclusions regarding
the changes in the turbulence and mean velocity profiles. When the turbulence is out of
equilibriumwiththemeanflowthestandardinnerandouterlayervelocityandlengthscales
are no longer the only relevant scales in the flow and additional scales become necessary to
characterize the flow.
This thesis examines an adverse pressure gradient boundary layer developing along a
4◦ ramp. A moderate range of Reynolds numbers, factor of 7, is achieved using a wind
tunnel located inside a pressure vessel by varying the freestream velocity and the ambient
pressure, and thus the air density. A custom made high resolution 2-component laser
Doppler anemometer with a 40 µm by 80 µm measurement volume allows for measurement
of the mean and turbulence over the range of Reynolds numbers examined.
Experimentally the mean velocity profiles are observed to be weak functions of Reyn-
olds number, while the turbulence quantities are more affected by the changing Reynolds
number. The mean velocity profiles are only moderately affected by the adverse pressure
gradient, with no measurable inflection point developing in the flow along the ramp. The
turbulence quantities are observed to change greatly along the adverse pressure gradient
ramp when scaled in traditional flat plate coordinates. The overall turbulence structure as
indicated by the single-point structure parameters is not strongly affected by this adverse
pressure gradient. The mean velocity profiles are observed to collapse in standard inner
layer coordinates over the Reynolds number range. In addition, the mean flow at various
locations along the ramp also collapses using previously developed empirical scalings. The
traditional flat plate normal stress scalings do not collapse the adverse pressure gradient
profiles over this Reynolds number range onto the flat plate profiles; therefore, new empir-
ical scalings were determined for this flow. These empirical scalings for the normal stresses
collapse the flat plate stress profiles along with the adverse pressure gradient profiles for
this range of Reynolds numbers. These scalings are mostly based on flat plate reference
profile parameters, implying that the normal stresses are determined almost entirely by the
upstream flow. The small angle that the flow must turn and the resulting pressure gradient
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only weakly affect the normal stresses. The streamwise normal stress collapses in the inner
layer using local values implying that for the inner layer the pressure gradient does play a
role in this region of the streamwise stress profile unlike in the outer layer.
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Acknowledgements
First, I would like to thank my advisor, John Eaton, for all his support throughout this
experience. He allowed me the freedom and flexibility necessary to finish this project. I
know that without his support I would not have made it to the end of this journey.
IwouldliketothankmyreadingcommitteeJamesJohnstonandJuanSantiagofortheir
valuable insight, comments and discussions. In addition, I would like to thank them for
their support and encouragement at the end of this experience. I would also like to thank
Juan Alonso for serving as the chair of my defense committee and providing additional
insight into the computational aspects of this work.
I am indebted to Dr. Simon Song for his help in teaching me how to operate this facility
at the start of my time at Stanford. I am also indebted to Lakhbir Johal for his technical
assistance in fabricating many of the necessary components for this experiment.
The members of the Eaton group both past and present have provided an invaluable set
of resources both inside and outside the lab. I am particularly grateful to Chuck Booten,
Paul Kodzwa and Claude Matalanis for their support and assistance over the last year of
thisprojectbothinandoutofthelab. Myfriends,bothatStanfordandafar,haveprovided
me with an incredible amount of encouragement during this time and I thank them for this
and more importantly for their friendship.
I want to thank my family for their love and support throughout my entire educational
experience and for their reminders that I could do it. Finally, I want to thank my husband,
Dan, who has supported me through this entire ordeal. I could not have done it without
your support and love.
Funding for this work was provided by the Office of Naval Research under contract
N00014-00-10078. Inaddition,IgratefullyacknowledgethefinancialsupportoftheStanford
Graduate Fellowship Program and the National Science Foundation Graduate Fellowship
Program,whichprovidedmewithfundingforthefirstthreeyearsofmygraduateeducation.
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Contents
Abstract iv
Acknowledgements vi
List of Tables x
List of Figures xi
Nomenclature xviii
1 Introduction and Objectives 1
1.1 Introduction and Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Experimentally studied adverse pressure gradient boundary layers . . . . . 4
1.2.1 Equilibrium boundary layers . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Flows near separation . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.3 Complex and practical geometry flows . . . . . . . . . . . . . . . . . 19
1.2.4 Turbulence structure in adverse pressure gradient flows . . . . . . . 23
1.2.5 Summary of experimental observations in adverse pressure gradient
flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3 Computational work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.1 Integral/Algebraic Techniques . . . . . . . . . . . . . . . . . . . . . . 29
1.3.2 Two Equation Models . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.3.3 Reynolds Stress Transport Models . . . . . . . . . . . . . . . . . . . 32
1.3.4 LES and DES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.5 Comparisons of various types of models . . . . . . . . . . . . . . . . 34
1.3.6 The Attached Eddy Model . . . . . . . . . . . . . . . . . . . . . . . 35
1.4 Scaling of Mean Velocity and Turbulence . . . . . . . . . . . . . . . . . . . 37
1.4.1 Mean Flow Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.4.2 Turbulent Stress Scaling . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
1.6 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
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2 Experimental Setup and Techniques 53
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 High Reynolds Number Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . 53
2.2.1 Pressure vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2.2 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2.3 Tunnel Condition Monitoring . . . . . . . . . . . . . . . . . . . . . . 57
2.3 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 High Resolution LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.4.1 Optical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.2 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.4.3 Vibration Isolation System . . . . . . . . . . . . . . . . . . . . . . . 63
2.4.4 Seeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.4.5 LDA Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.5 Wall Static Pressure Measurements . . . . . . . . . . . . . . . . . . . . . . . 69
2.5.1 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.6 Skin Friction Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.6.1 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3 Development of Adverse Pressure Gradient Boundary Layer 78
3.1 Wall Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2 Mean Flow Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.3 Reynolds Stress Development . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.4 Turbulent kinetic energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.5 Structural Parameter Development . . . . . . . . . . . . . . . . . . . . . . . 96
3.6 Quadrant Analysis of Adverse Pressure Gradient Flow . . . . . . . . . . . . 101
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4 Reynolds Number Effects on the Mean Flow and Turbulence 106
4.1 Overall Reynolds number effects on the flow development . . . . . . . . . . 107
4.2 Wall Static Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 Mean Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.1 Law of the wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.2 Velocity Deficit Scaling . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.4 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
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4.4.1 Flat Plate Reference Location . . . . . . . . . . . . . . . . . . . . . . 118
4.4.2 Adverse Pressure Gradient Ramp . . . . . . . . . . . . . . . . . . . . 118
4.5 Structural and Quadrant Analysis . . . . . . . . . . . . . . . . . . . . . . . 135
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5 Conclusions and Future Work 140
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
A Vibration Isolator Redesign 143
B Flat Plate Boundary Layer Produced in Two Different Ways 148
C Computational Modeling of Adverse Pressure Gradient Flow 151
C.1 Model Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
C.2 Comparison of Experimental Data and Fluent Results at Re = 3300 . . . . 152
θ
C.3 Fluent Trends with Reynolds Number . . . . . . . . . . . . . . . . . . . . . 157
C.4 Reynolds Number Scaling for Outer Layer for Fluent Data . . . . . . . . . . 161
C.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
D LDA Data Archive 167
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List of Tables
2.1 Uncertainty in LDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1 Flow parameters at Re = 3300 . . . . . . . . . . . . . . . . . . . . . . . . . 79
θ
4.1 Wind tunnel conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2 Flow parameters at Re = 3300 . . . . . . . . . . . . . . . . . . . . . . . . . 110
θ
4.3 Flow parameters at Re = 14,100 . . . . . . . . . . . . . . . . . . . . . . . . 110
θ
4.4 Flow parameters at Re = 20,600 . . . . . . . . . . . . . . . . . . . . . . . . 111
θ
D.1 Data for Re = 3300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
θ
D.2 Data for Re = 14,100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
θ
D.3 Data for Re = 20,600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
θ
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