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Large Eddy Simulation of Dispersed Multiphase Flow Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Dissertations, Master's Theses and Master's Reports - Open Reports 2012 Large Eddy Simulation of dispersed multiphase flow Yejun Gong Michigan Technological University Follow this and additional works at: https://digitalcommons.mtu.edu/etds Part of the Applied Mathematics Commons, and the Mechanical Engineering Commons Copyright 2012 Yejun Gong Recommended Citation Gong, Yejun, "Large Eddy Simulation of dispersed multiphase flow", Dissertation, Michigan Technological University, 2012. https://doi.org/10.37099/mtu.dc.etds/729 Follow this and additional works at: https://digitalcommons.mtu.edu/etds Part of the Applied Mathematics Commons, and the Mechanical Engineering Commons LARGE EDDY SIMULATION OF DISPERSED MULTIPHASE FLOW By Gong, Yejun A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY (Computational Science & Engineering) MICHIGAN TECHNOLOGICAL UNIVERSITY 2012 c 2012 Gong, Yejun This dissertation, "Large Eddy Simulation of Dispersed Multiphase Flow," is hereby ap- proved in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOS- OPHY IN COMPUTATIONAL SCIENCE & ENGINEERING. Department of Mathematical Science Signatures: Dissertation Advisor Dr. Tanner, Franz X Committee Member Dr. Feigl, Kathleen A Committee Member Dr. Yang, Song Lin Committee Member Dr. Kolkka, Robert W Department Chair Dr. Gockenbach, Mark S Date Dedication "Large Eddy Simulation of Dispersed Multiphase Flow" Ph.D. thesis by Yejun Gong, Dedicated to My parents and teachers and friends and in loving memory of my grandparents! . Contents List of Figures ..................................... xi List of Tables ...................................... xv Acknowledgments ...................................xvii ABBREVIATIONS ..................................xviii Abstract .........................................xxiii 1 Introduction .................................... 1 1.1 Motivation ................................... 1 1.2 Research Objectives .............................. 3 2 Background ..................................... 4 2.1 Governing equations ............................. 4 2.1.1 Mass Balance Equation ........................ 4 2.1.2 Momentum Balance Equation .................... 5 2.1.3 Energy Balance Equation ....................... 7 2.2 Introduction to turbulence ........................... 7 2.2.1 The physical nature of turbulence .................. 10 2.2.2 Overview of turbulence solution approaches ............. 11 2.2.2.1 Direct numerical simulation ................ 11 2.2.2.2 Reynolds-averaged Navier-Stokes method ......... 13 2.2.2.3 Large eddy simulation ................... 14 2.3 Reynolds-averaged Navier-Stokes method .................. 15 2.3.1 Time averaging ............................ 15 2.3.1.1 Reynolds time averaging .................. 15 2.3.1.2 Favre time averaging .................... 16 2.3.2 Time-averaged Navier-Stokes equations ............... 17 2.3.3 RANS closure problem ........................ 18 2.3.3.1 Standard k − ε model .................... 18 2.3.3.2 RNG k − ε model ..................... 20 2.4 Large eddy simulation ............................. 20 2.4.1 Spatial filtering ............................ 21 vii 2.4.2 Spatial-filtered Navier-Stokes equations ............... 24 2.4.3 Subgrid-scale closure models .................... 24 2.4.3.1 Smagorinsky model .................... 25 2.4.3.2 LES one-equation model .................. 26 2.5 Computational Aspects ............................ 27 2.5.1 Computation code ........................... 28 2.5.2 Discretization ............................. 29 2.5.3 Pressure-velocity coupling ...................... 32 2.5.3.1 SIMPLE .......................... 33 2.5.3.2 PISO ............................ 37 3 Simulation of flows over a backward-facing step ................ 40 3.1 Introduction .................................. 40 3.2 Flow configuration and initial conditions ................... 42 3.3 LES/RANS results and discussion ...................... 44 3.4 Conclusion .................................. 47 4 Simulation of fuel sprays ............................. 50 4.1 Liquid phase modeling ............................ 51 4.1.1 Droplet injection ........................... 53 4.1.2 Droplet breakup ............................ 54 4.1.3 Droplet drag .............................. 56 4.1.4 Droplet evaporation .......................... 58 4.1.5 Droplet dispersion .......................... 60 4.1.6 Droplet collision ........................... 61 4.2 Gaseous phase modeling ........................... 62 4.3 Test conditions ................................ 65 4.4 LES/RANS results and discussion ...................... 67 4.4.1 Non-evaporating sprays ........................ 67 4.4.1.1 Spray tip penetration of Cases 1–3 ............. 69 4.4.1.2 Comparison between RANS and LES ........... 70 4.4.2 Evaporating sprays .......................... 78 4.5 Conclusion .................................. 84 5 Hydrotreated vegetable oil (HVO) sprays .................... 86 5.1 Introduction .................................. 87 5.1.1 ReFuel project ............................ 87 5.1.2 Fuel spray properties ......................... 88 5.2 Computation details .............................. 92 5.3 LES/RANS results and discussions ...................... 93 5.3.1 Non-evaporating sprays ........................ 93 5.3.2 Evaporating spray ........................... 99 5.4 Conclusion ..................................109 viii 6 Future work ....................................110 References .......................................111 A Computation Tool: OpenFOAM .........................123 A.1 New dieselSpray Submodels .........................123 A.1.1 IDSD: power law ...........................123 A.1.2 Atomization Model: Levich .....................124 A.1.3 Breakup Model: CAB .........................126 A.2 dieselLES: diesel spray LES solver ......................127 A.3 New Fuel Realization .............................129 A.4 Compile the user-defined libraries ......................132 A.4.1 Move an existed library to user’s directory ..............132 A.4.2 Add a new library or library components ...............133 B Spray source term .................................135 B.1 Introduction ..................................135 B.2 Simulations and Results ............................137 B.3 Discussion ...................................140 B.4 OpenFOAM Realization ...........................140 B.4.1 Add a subfield sks to dieselSpray class ...............141 B.4.2 Add a member function updateSpraySource to class RASModel . 144 B.4.3 Add the spray source term sks_ to k − ε equations ..........146 B.4.4 Update the spray source term in solvers ...............147 ix x List of Figures 2.1 Turbulence models ordered according to their decreasing level of complex- ity. Abbreviations: RST = Reynolds-Stress Transport models; ARS = Al- gebraic Reynolds-Stress models. ....................... 13 3.1 Backward-facing step geometry,1 S = 4.9mm,h = 5.2mm,H = 10.1mm,W = 5mm,L = 300mm. ............................... 42 3.2 2D Nonuniform Mesh, 8 × 22 before step and 312 × 40 after step. ........ 43 3.3 Experimental and computed velocity profiles for Re = 389 at different x/S−locations ................................. 43 3.4 Velocity near the lower wall for Re = 389. Experimental reattachment point, •; LES: Laminar, ◦−; Smagorinsky, −; OneEq, ·−; RANS: Lami- nar, ◦−−; k − ε, −−; RNG k − ε, ·−− .................. 44 3.5 Experimental and computed velocity profiles for Re = 1000 at different x/S−locations ................................. 47 3.6 Velocity near the lower wall for Re=1000. Experimental reattachment point, •; LES: Laminar, ◦−; Smagorinsky, −; OneEq, ·−; RANS: Lami- nar, ◦−−; k − ε, −−; RNG k − ε, ·−− .................. 48 3.7 Velocity color plot of ux for Re=1000 ..................... 48 3.8 Velocity near the top wall for Re=1000. Experimental detachment point, •; LES: Laminar, ◦−; Smagorinsky, −; OneEq, ·−; RANS: Laminar, ◦−−; k − ε, −−; RNG k − ε, ·−− ........................ 48 4.1 Computation domain. ............................. 66 4.2 Temporal change in spray tip penetration with different grid size for RANS simu- lation. ..................................... 68 4.3 Temporal change in spray tip penetration with different grid size for LES simula- tion. ...................................... 68 4.4 Temporal change in spray tip penetration for RANS and LES using DF2. 70 4.5 Gas phase velocity vector at cross section for RANS Case 1 at time 0.0024 s. ... 71 4.6 Gas phase velocity vector at cross section for LES Case 1 at time 0.0024 s. .... 71 4.7 Cross-sectional plot for RANS Case 1 colored by magnitude of vorticity at time 0.0024 s. .................................... 72 4.8 Cross-sectional plot for LES Case 1 colored by magnitude of vorticity at time 0.0024 s. .................................... 72 xi 4.9 Cross-sectional plot for RANS Case 1 colored by turbulent kinetic energy at time 0.0024 s. .................................... 73 4.10 Cross-sectional plot for LES Case 1 colored by turbulent kinetic energy at time 0.0024 s. .................................... 73 4.11 Turbulent kinetic energy k versus nozzle distance along centerline of Case 1. 73 4.12 Cross-sectional plot for RANS Case 1 colored by the magnitude of the fluid veloc- ity at time 0.0024 s. .............................. 75 4.13 Cross-sectional plot for
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