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 ii 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. iii 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 iv 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. v 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. vi 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 vii 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 viii 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 ix 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 x