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PDF MODELING of TURBULENT FLOWS on UNSTRUCTURED GRIDS J´Ozsef Bakosi, Phd George Mason University, 2008 Dissertation Director: Dr

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PDF MODELING of TURBULENT FLOWS on UNSTRUCTURED GRIDS J´Ozsef Bakosi, Phd George Mason University, 2008 Dissertation Director: Dr PDF modeling of turbulent flows on unstructured grids A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at George Mason University By J´ozsef Bakosi Master of Science University of Miskolc, 1999 Director: Dr. Zafer Boybeyi, Professor Department of Computational and Data Sciences Spring Semester 2008 George Mason University Fairfax, VA Copyright c 2008 by J´ozsef Bakosi All Rights Reserved ii Dedication This work is dedicated to my family: my parents, my sister and my grandmother iii Acknowledgments I would like to thank my advisor Dr. Zafer Boybeyi, who provided me the opportunity to embark upon this journey. Without his continuous moral and scientific support at every level, this work would not have been possible. Taking on the rather risky move of giving me 100% freedom in research from the beginning certainly deserves my greatest acknowl- edgments. I am also thoroughly indebted to Dr. Pasquale Franzese for his guidance of this research, for the many lengthy – sometimes philosophical – discussions on turbulence and other topics, for being always available and for his painstaking drive with me through the dungeons of research, scientific publishing and aesthetics. My gratitude extends to Dr. Rainald L¨ohner from whom I had the opportunity to take classes in CFD and to learn how not to get lost in the details. I found his weekly seminars to be one of the best opportunities to learn critical and down-to-earth thinking. I am also indebted to Dr. Nash’at Ahmad for showing me the example that with a careful balance of school, hard work and family nothing is impossible. I thank Dr. Thomas Dreeben for the many helpful and insightful discussions on the velocity model and elliptic relaxation. I am also grateful to the reviewers of our journal papers for their valuable comments and suggestions on our initial manuscripts. I will always remember my professors at home at the Departments of Mathematics, Mechanics, Physics, and Fluid and Heat Engineering at the University of Miskolc, who taught me the foundations of engineering and science: Drs. Bert´oti Edg´ar, K´alovics Ferenc, Koz´ak Imre, M´esz´aros J´ozsef, P´aczelt Istv´an, Ront´o Mikl´os, Szab´oSzil´ard, Szeidl Gy¨orgy, Tak´acs Csaba and Vince Endre. I further extend my thanks to Prof. T´oth L´aszl´o, who first gave me the opportunity to study abroad and introduced me to research. My admiration towards all of them turned into a passion for science. I am also thankful to Dr. Sergei Ivanov, my mentor at Fraunhofer in Boston, who encouraged me to do a Ph.D. I would also like to thank for the continous support of all my friends throughout the years. My friend from college, Feh´er Zolt´an, for keeping me sane with our long, challeng- ing and fruitful discussions every weekend. Sunil Kumar Appanaboyina for the countless philosophical discussions on culture, life, religion, food and women. Jarek Pietrzykowski who has always been a partner in crime. Fernando Mut for the many discussions on cod- ing, performance and for suggesting the algorithm for the particle search. My housemates Houmam Ali, Andrew Krapf and Chris Lafontaine who made me feel at home right back in college. The wonderful people here at the Laboratory for Atmospheric Hazard Modeling iv who have always been helpful and created an atmosphere so that I never felt alone: Dr. Guido Cervone, Laura Clemente, Yasemin Ezber, John Lindeman, Jacek Radzikowski and Priyanka Roy. Special thanks to my international student advisor, shuttle and jazz buddy, Amy Moffitt. But my greatest thank you goes to my family and friends at home, who never ceased to believe in me, even at times when I myself almost did. v Table of Contents Page ListofTables....................................... viii ListofFigures ...................................... ix ListofSymbols...................................... xi Abstract........................................... xx 1 Introduction...................................... 1 2 Governingequations ................................ 9 3 Numericalimplementation . .... 23 3.1 Introduction.................................... 23 3.2 Timesteppingprocedure . 24 3.3 Solution of the Eulerian equations . ..... 24 3.4 Estimation of Eulerian statistics . ...... 27 3.5 Derivatives of Eulerian statistics . ....... 30 3.6 Estimation of the velocity-conditioned scalar mean . ........... 31 3.7 Particletracking ................................ 33 3.8 Particle-number control . 36 3.9 No-slip wall-boundary conditions . ...... 41 3.10 Parallel random number generation . ...... 44 3.11 Solution procedure and execution profile . ........ 45 4 Channel flow simulations: results and discussion . ........... 51 4.1 Introduction.................................... 51 4.2 Modelingspecificsofchannelflow. .... 52 4.2.1 Modelingthefluiddynamics . 53 4.2.2 Modelingthepassivescalar . 55 4.3 Results....................................... 58 4.3.1 Fluiddynamics.............................. 58 4.3.2 Comparison of the IEM and IECM micromixing models . 59 4.3.3 Scalar statistics with the IECM model . 65 4.3.4 Conditional statistics . 70 4.4 The effect of numerical parameters on the results . ....... 78 vi 4.5 Computationalcost............................... 92 4.6 Discussion..................................... 96 5 Street canyon simulations: results and discussion . ............ 99 5.1 Introduction.................................... 99 5.2 Modeling specifics of the street canyon . ...... 103 5.3 Results....................................... 105 5.4 Discussion..................................... 113 6 Cylinder flow simulations: results and discussion . ........... 117 6.1 Introduction.................................... 117 6.1.1 A short review of cylinder flow regimes . 119 6.1.2 Past experimental and numerical studies . ..... 121 6.2 Results....................................... 124 6.2.1 Transient and cylinder surface statistics . ....... 126 6.2.2 Near wake statistics . 131 6.3 Discussion..................................... 142 7 Summaryanddiscussion .............................. 146 A Derivation of the Eulerian PDF transport equation . .......... 152 B Computation of the velocity-conditioned scalar mean . ............ 158 C Basic particle redistribution algorithm . .......... 160 D A more efficient particle redistribution algorithm . ........... 162 Bibliography ....................................... 167 vii List of Tables Table Page 3.1 Profile and relative execution times for a timestep . ......... 46 3.2 Two designs of a loop to update particles . ..... 47 3.3 Comparison of serial and parallel loop performances . .......... 49 4.1 Constants to model the joint PDF of velocity and frequency......... 54 4.2 Model constants for the micromixing timescale . ........ 62 4.3 Number of particles required for convergent statistics ............. 91 5.1 Model constants for the full joint PDF . ..... 105 5.2 Concentration sampling locations along the street canyon walls . 106 6.1 Cylinder surface and recirculation bubble region statistics .......... 129 A.1 SamplespaceoftheEulerianjointPDF . .... 154 D.1 Particle redistribution benchmarks . ....... 165 viii List of Figures Figure Page 3.1 Estimation of Eulerian statistics . ...... 29 3.2 Particle tracking with triangular elements; FEM mapping .......... 35 3.3 Particle tracking at concave boundaries . ....... 36 3.4 Domain for a testcase to investigate the error of particle redistribution . 38 3.5 The number of particles moved by particle redistribution........... 40 3.6 Results of a simplified testcase with particle redistribution.......... 41 3.7 Evolution of total relative numerical error with particle redistribution . 42 3.8 Comparison of cache misses for different loops . ....... 48 3.9 Overall speedups on different types of shared memory machines....... 50 4.1 Eulerian domain for fully developed turbulent channel flow ......... 56 4.2 Cross-stream profiles of velocity statistics in turbulent channel flow . 59 4.3 Comparison of the IEM and IECM models, scalar mean and PDFs ..... 63 4.4 Cross-stream profiles of the first four moments of scalar concentration . 66 4.5 Downstream evolutions of scalar mean peak, mean width and r.m.s. width . 68 4.6 PDFs of scalar concentration fluctuations . ....... 69 4.7 Velocity fluctuation conditioned on the scalar concentration . 73 4.8 Mean scalar dissipation conditioned on the concentration .......... 76 4.9 Mean scalar diffusion conditioned on the concentration . .......... 77 4.10 Re-dependence of cross-stream velocity statistics in channelflow ...... 79 4.11 The effect of the anisotropic length-scale constant on the Reynolds stresses 81 4.12 The effect of the number of conditioning bins using Fox’s projection . 83 4.13 The effect of the number of conditioning bins with the proposed method . 85 4.14 The effect of the number of particles using Fox’s projectionmethod. 87 4.15 The effect of the number of particles with the proposed method....... 89 4.16 Comparison of computational cost vs. Re ................... 93 5.1 Eulerian grid to compute a street canyon with full resolution . 106 5.2 Eulerian grid to compute a street canyon with wall-functions ........ 107 5.3 Velocty statistics in a street canyon . ....... 108 ix 5.4 Turbulent intensities in a street canyon . ........ 110 5.5 Mean concentrations along the wall of a street canyon . ......... 111 5.6 Scalar concentration statistics in a street canyon . ........... 112 5.7 PDFs of concentration fluctuations in a street canyon . ......... 114 6.1 Eulerianmeshforflowaroundcylinder
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