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Turbulent Transition Simulation and Particulate Capture Modeling with an Incompressible Lattice Boltzmann Method

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Turbulent Transition Simulation and Particulate Capture Modeling with an Incompressible Lattice Boltzmann Method Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports 2017 TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD John R. Murdock Michigan Technological University, [email protected] Copyright 2017 John R. Murdock Recommended Citation Murdock, John R., "TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD", Open Access Dissertation, Michigan Technological University, 2017. https://doi.org/10.37099/mtu.dc.etdr/525 Follow this and additional works at: https://digitalcommons.mtu.edu/etdr Part of the Applied Mechanics Commons, Computer-Aided Engineering and Design Commons, and the Heat Transfer, Combustion Commons TURBULENT TRANSITION SIMULATION AND PARTICULATE CAPTURE MODELING WITH AN INCOMPRESSIBLE LATTICE BOLTZMANN METHOD By John R. Murdock A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY In Mechanical Engineering-Engineering Mechanics MICHIGAN TECHNOLOGICAL UNIVERSITY 2017 © 2017 John R. Murdock This dissertation has been approved in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering-Engineering Mechanics. Department of Mechanical Engineering-Engineering Mechanics Dissertation Advisor: Dr. Song-Lin Yang Committee Member: Dr. Franz X. Tanner Committee Member: Dr. Kazuya Tajiri Committee Member: Dr. Youngchul Ra Department Chair: Dr. William W. Predebon Dedication To my wife who provided the utmost support for this endeavor from the outset - without which I would neither be who I am nor would this work be what it is today. Contents List of Figures ................................. xv List of Tables .................................. xxiii Preface ...................................... xxv Acknowledgments ............................... xxvii Nomenclature .................................. xxix Abstract ..................................... xxxv 1 Introduction ................................. 1 1.1 Transition . 3 1.2 Filtration . 4 1.3 Research Objectives and Structure . 8 1.3.1 Objectives . 8 1.3.2 Document Structure . 9 2 Literature Review ............................. 11 vii 2.1 Incompressible Lattice Boltzmann Method . 11 2.2 Turbulence Simulation . 13 2.3 Particulate Matter Transport . 15 2.3.1 LBE-Lagrange . 16 2.3.2 LBE-LGA . 16 2.3.3 LBE-Euler for Particle Concentration . 18 2.4 Dominant Mechanisms . 19 2.5 Heat Transfer . 19 2.5.1 DDF-LBE . 20 2.5.2 Conjugate Heat Transfer . 21 2.6 Porous and Disordered Media . 22 2.6.1 REV Scale . 23 2.6.2 Pore Scale . 24 2.7 Aftertreatment Synthesis . 25 2.8 Summary . 27 3 Methodology ................................ 29 3.1 The Lattice Boltzmann Method . 29 3.1.1 Origins . 30 3.1.2 The Lattice Boltzmann Equation . 32 3.1.3 Lattices . 35 3.1.4 Boundary Conditions . 36 viii 3.1.5 Multiple Relaxation Time Collision Operator . 40 3.1.6 Heat Transfer . 41 3.1.7 Particle Concentration Transport . 44 3.2 Turbulence and Transition Simulation . 46 3.2.1 Modeling and Simulation of Turbulence . 46 3.2.2 Direct Numerical Simulation and Large Eddy Simulation . 47 3.2.3 Evaluation Methodology . 49 3.3 Substrate Approximation . 50 3.4 Computational Language and Parallelization . 52 4 The Incompressible LBE ......................... 55 4.1 Introduction . 56 4.2 Derivation of the D2Q9 Incompressible LBE . 59 4.2.1 Standard LBE Form . 59 4.2.2 An Incompressible LBE Derivation . 60 4.2.3 Discussion and Comparison . 67 4.3 Numerical Results . 68 4.3.1 Developing Channel Flow . 69 4.3.2 Lid Driven Cavity . 70 4.3.3 Womersley Flow . 73 4.3.4 Backward Facing Step . 77 4.3.5 3D Lid Driven Cavity . 78 ix 4.4 Conclusions . 80 4.5 MRT-iLBE for the D2Q9 Form . 81 5 2D DNS and 3D LES with the iLBE ................. 85 5.1 Transition Flow with an Incompressible Lattice Boltzmann Equation (2D DNS) . 87 5.1.1 Introduction . 88 5.1.2 Incompressible Multiple Relaxation Time Lattice Boltzmann Equation . 91 5.1.3 Simulation Parameters . 95 5.1.3.1 Post Processing . 97 5.1.4 Results . 100 5.1.4.1 Verifying MRT-iLBM with steady LDC Flow . 100 5.1.4.2 The First Hopf Bifurcation and Transition to Chaos 102 5.1.4.3 Post-Transition Statistics . 105 5.1.5 Conclusions . 112 5.2 3D LES of a Driven Cavity . 114 5.2.1 Simulation Parameters . 115 5.2.2 Vreman Sub-grid Scale Model . 119 5.2.3 Statistical Processing and Post Processing . 121 5.2.4 Numerical Results . 122 5.2.4.1 Verifying D3Q15 MRT-iLBE with Steady Flow . 122 x 5.2.4.2 The Hopf Bifurcation . 125 5.2.5 Conclusions . 129 6 Substrate Generation and Verification ................ 131 6.1 Introduction . 132 6.2 Substrate Generation and Measurement Algorithm and Pseudocode 134 6.3 The Lattice Boltzmann Method . 137 6.3.1 The Incompressible Lattice Boltzmann Equation . 137 6.3.2 The Lattice . 141 6.3.3 Boundary Conditions . 142 6.3.4 Multiphysics Capability . 143 6.4 Verification Methodology . 144 6.4.1 Darcy's Law . 144 6.4.2 Ergun Equation . 145 6.4.3 Koponen Model . 147 6.4.4 A New Semi-Empirical Model . 148 6.4.4.1 The Conduit-Model: Gebart Model . 149 6.4.4.2 Flow Past a Submerged Body Model and the Cell Model . 150 6.4.4.3 Tortuosity Factor . 151 6.4.4.4 Blending functions/Basis-functions . 152 6.4.4.5 The Model Equations . 153 xi 6.5 Results . 155 6.5.1 Verification by Darcy's Law . 157 6.5.2 Verification by Ergun Equation . 158 6.5.3 Verification by Porosity-Permeability Correlations . 159 6.5.3.1 Verification by Koponen Model . 160 6.5.3.2 Verification by Gebart-Brinkmann (GB) Model . 161 6.5.3.3 Verification by Gebart-Kubawara (GK) Model . 161 6.5.4 Experimental Verification . 163 6.6 Conclusions . 164 7 Multiphysics and PM Filtration .................... 167 7.1 Heat Transfer . 168 7.1.1 Recovery of the Advection-Diffusion Equation . 168 7.1.2 Numerical Results . 168 7.1.2.1 Thermal Lid Driven Cavity . 169 7.1.2.2 Conjugate Heat Transfer-Channel Flow . 170 7.2 Particle Transport and Deposition . 173 7.2.1 Diffusion, Advection, and Deposition Bases . 173 7.2.2 Implementation on a Lattice . 174 7.2.3 Numerical Results . 176 7.2.3.1 Backward Facing Step . 176 7.2.3.2 Cylinder in Flow . 179 xii 7.3 Full Coupling in a Filtration Model . 186 7.3.1 Low Porosity and High Sticking Probability . 188 7.3.2 High Porosity and Moderate Sticking Probability . 196 7.3.3 Low Porosity and Low Sticking Probability . 201 8 Conclusions ................................. 211 8.1 Contributions to the Incompressible Lattice Boltzmann Method and its Applications . 211 8.2 Summary of Findings . 212 8.2.1 Incompressible Lattice Boltzmann Equation . 212 8.2.2 Turbulent Transition . 214 8.2.3 Multiphysics Filtration . 215 8.3 Future Work . 219 Bibliography .................................. 225 A iLBE Derivations .............................. 237 A.1 Chapman-Enskog Expansion for the iLBE . 237 A.2 MRT-iLBE . 243 A.2.1 D2Q9 . 243 A.2.2 D3Q15 . 249 B Thermal D2Q4 LBE Derivations .................... 253 B.1 Equilibrium Distribution Form: Ansatz Method . 253 xiii B.2 Chapman-Enskog Expansion for the Thermal D2Q4 LBE . 255 C Units ..................................... 259 D Filter Pseudocode ............................. 265 E Copyright Agreements and Permissions ............... 271 xiv List of Figures 1.1 Schematic of DPF flow. 5 3.1 PDF of He-4 particle velocities at different temperatures. 32 3.2 Some valid lattices of the LBM. 36 3.3 Bounce-back schematics over a single time step. 39 3.4 Speedup of LDC OpenMP code on Superior. 54 4.1 D2Q9 lattice velocities, a. ....................... 61 4.2 Developing channel flow convergence of umax error with node count. 71 4.3 Developing channel flow residual history of standard and incompress- ible LBEs. 72 4.4 Comparison of x and y-velocities along the centerlines in the lid driven cavity flow for Re 1000 with Marchi et al.. 74 4.5 Lid driven cavity flow streamlines at Re 1000. 75 4.6 Womersley flow centerline velocity as a function of time and y. 76 4.7 Backward facing step streamlines for Re 800. 77 4.8 D3Q19 Lattice. ..
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