Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2001 A study of the heat transfer and fluid mechanics of the turbulent separating and reattaching flow past a backward facing step using large eddy simulation Ravikanth V. R. Avancha Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Avancha, Ravikanth V. R., "A study of the heat transfer and fluid mechanics of the turbulent separating and reattaching flow past a backward facing step using large eddy simulation " (2001). Retrospective Theses and Dissertations. 625. https://lib.dr.iastate.edu/rtd/625 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 A study of the heat transfer and fluid mechanics of the turbulent separating and reattaching flow past a backward facing step using large eddy simulation by Ravikanth V. R. Avancha A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Mechanical Engineering Program of Study Committee: Richard H. Fletcher, Major Professor Gerald M. Colver Ganesh R. Rajagopalan Eugene S. Takle John C. Tannehill Iowa State University Ames, Iowa 2001 Copyright © Ravikanth V. R. Avancha, 2001. All rights reserved. UMI Number: 3034169 UMI* UMI Microform 3034169 Copyright 2002 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ii Graduate College Iowa State University This is to certify that the doctoral dissertation of Ravikanth V. R. Avancha has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Committee Member Signature was redacted for privacy. ittee Member Signature was redacted for privacy. mmittee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Major Professor Signature was redacted for privacy. or the Major Pro am iii TABLE OF CONTENTS NOMENCLATURE xiii ABSTRACT xx CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 Survey of Literature 3 1.2.1 Review of large eddy simulations 3 1.2.2 Review of RANS simulations 7 1.2.3 Review of experimental studies 10 1.2.4 Summary 14 1.3 Survey of Relevant Previous Work by Members of the ME CFD Research Group at Iowa State University 15 1.4 Objectives 17 1.5 Dissertation Organization 17 CHAPTER 2 MATHEMATICAL FORMULATION 19 2.1 Conservation Principles and Governing Equations 19 2.1.1 Conservation of mass 20 2.1.2 Conservation of momentum 20 2.1.3 Conservation of energy 22 2.1.4 Closure 23 2.1.5 Generic conservation equation 26 iv 2.2 Form of Governing Equations Used in this Study 27 2.2.1 Non-dimensionalization 28 2.3 Filtering Procedure 29 2.3.1 Types of filters 33 2.3.2 Favre filtering 34 2.4 Favre Filtered Compressible Governing Equations 34 2.5 Sub-grid Scale Models 37 2.5.1 Smagorinsky sub-grid scale model 37 2.5.2 Dynamic sub-grid scale models 39 CHAPTER 3 NUMERICAL FORMULATION 44 3.1 The Finite Volume Approach 44 3.2 The Cell Centered Algorithm 47 3.3 The Colocated Grid Approach 48 3.4 Cartesian Grid Limitation 51 3.5 Spatial Discretization 51 3.6 Evaluation of In viscid Fluxes 53 3.6.1 Second and fourth-order central differences 53 3.7 Viscous Flux Calculation 55 3.8 Unsteady Terms and Preconditioning 56 3.9 Primitive Variables and Linearization 58 3.10 Coupled Strongly Implicit Procedure 61 3.11 Convergence Criteria 62 3.12 Boundary Conditions 63 3.13 Navier-Stokes Characteristic Boundary Conditions (NSCBC) 63 3.13.1 Steps to provide NSCBC conditions 66 3.14 Boundary Conditions for the Flow Past a Backward-Facing Step 72 V 3.14.1 Stream wise boundary conditions 73 3.14.2 Wall-normal boundary conditions 75 3.14.3 Spanwise boundary conditions 77 CHAPTER 4 LES OF ISOTHERMAL TURBULENT FLOW 78 4.1 Introduction 78 4.2 Problem Description 78 4.3 Large Eddy Simulation of Turbulent Flow in a Channel 80 4.3.1 Problem description, simulation details, and results 82 4.4 Simulation Details: Flow Past a Backward-Facing Step 84 4.5 Results and Discussion 87 4.5.1 Mean velocity distributions 87 4.5.2 Reattachment length 88 4.5.3 Spanwise averaged coefficients of friction and pressure 90 4.5.4 Velocity fluctuations and turbulent kinetic energy 91 4.5.5 Reynolds shear stresses 93 4.5.6 Triple velocity correlations 93 4.5.7 Effect of subgrid scale model 93 4.6 Significance of the Study 100 CHAPTER 5 LES OF TURBULENT FLOW WITH HEAT TRANSFER AND PROPERTY VARIATIONS 103 5.1 Introduction 103 5.2 Problem Description and Simulation Details 103 5.3 Results and Discussion 105 5.3.1 Mean velocity and mean temperature distributions 105 5.3.2 Velocity and temperature fluctuations 123 5.3.3 Cross-correlations of the velocity and temperature fluctuations .... 128 VI 5.3.4 Density fluctuations 130 5.4 Summary 131 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 134 6.1 Summary and Contributions 134 6.2 Recommendations for Future Work 137 APPENDIX A JACOBIAN MATRICES FOR FAVRE FILTERED SYSTEM OF EQUATIONS 139 APPENDIX B AN ESTIMATE OF FLUID BULK TEMPERATURE 142 APPENDIX C AN ESTIMATE OF BUOYANCY EFFECTS 144 APPENDIX D COMPARISON OF TURBULENT TRANSPORT TERMS BASED ON REYNOLDS- AND FAVRE AVERAGED FLUCTUATIONS . 145 APPENDIX E PARALLELIZATION AND OPTIMIZATION OF A LARGE EDDY SIMULATION CODE USING OpenMP FOR SGI 0rigin2000 PER­ FORMANCE 153 BIBLIOGRAPHY 169 ACKNOWLEDGEMENTS 182 vii LIST OF FIGURES Figure 3.1 Geometry of flow variables 48 Figure 3.2 Arrangement of unknowns for the colocated grid approach 49 Figure 3.3 Arrangement of unknowns for the staggered grid approach 49 Figure 3.4 Nomenclature for discretization 52 Figure 3.5 Waves entering and leaving the backward-facing step domain .... 67 Figure 4.1 Backward-facing step geometry 79 Figure 4.2 Law of the wall plot 84 Figure 4.3 Streamwise RMS velocity profile 85 Figure 4.4 Wall-normal RMS velocity profile 85 Figure 4.5 Spanwise RMS velocity profile 85 Figure 4.6 Streamline of mean velocity 88 Figure 4.7 Streamwise mean velocity profiles 89 Figure 4.8 Wall-normal mean velocity profiles 89 Figure 4.9 Spanwise mean velocity profiles 89 Figure 4.10 Temporal variation of the spanwise average reattachment locations . 90 Figure 4.11 Coefficient of pressure 92 Figure 4.12 Coefficient of friction 92 Figure 4.13 Streamwise RMS velocity profiles 94 Figure 4.14 Wall-normal RMS velocity profiles 94 Figure 4.15 Spanwise RMS velocity profiles 94 viii Figure 4.16 Contour lines of turbulent kinetic energy 95 Figure 4.17 Reynolds shear stress: — <uV>t. 96 Figure 4.18 Reynolds shear stress: — <u'w'>tz 96 Figure 4.19 Reynolds shear stress: — < v'w' >tz 96 Figure 4.20 Skewness profiles: < u'u'u' >tz 97 Figure 4.21 Skewness profiles: < u'u'v' >tz 97 Figure 4.22 Skewness profiles: < u'u'w' >t= 97 Figure 4.23 Skewness profiles: < u'v'v' >tz 98 Figure 4.24 Skewness profiles: < u'v'w' >tz 98 Figure 4.25 Skewness profiles: < u'w'w' >tz 98 Figure 4.26 Skewness profiles: < v'v'v' >tz 99 Figure 4.27 Skewness profiles: < v'v'w' >tz 99 Figure 4.28 Skewness profiles: < u'w'w' >tz 99 Figure 4.29 Skewness profiles: < w'w'w' >tz 100 Figure 4.30 Plot of e(x) 101 Figure 4.31 Plot of l(x) 101 Figure 4.32 Streamwise profiles of the dynamic model coefficient 101 Figure 5.1 Backward-facing step geometry 104 Figure 5.2 Mean streamwise velocity 107 Figure 5.3 Mean wall-normal velocity 107 Figure 5.4 Mean spanwise velocity 107 Figure 5.5 Mean temperature 108 Figure 5.6 Mean temperature 108 Figure 5.7 Mean temperature 108 Figure 5.8 Bulk temperature 110 Figure 5.9 Wall temperature 110 ix Figure 5.10 Nusselt number 110 Figure 5.11 Mean streamwise velocity in wall coordinates 113 Figure 5.12 Mean streamwise velocity in wall coordinates 114 Figure 5.13