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Large Eddy Simulation of Turbulent Flow Over a Backward-Facing Step

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Large Eddy Simulation of Turbulent Flow Over a Backward-Facing Step IT 18 009 Examensarbete 45 hp Mars 2018 Large Eddy Simulation of Turbulent Flow over a Backward-Facing Step Edmond Shehadi Institutionen för informationsteknologi Department of Information Technology Abstract Large Eddy Simulation of Turbulent Flow over a Backward-Facing Step Edmond Shehadi Teknisk- naturvetenskaplig fakultet UTH-enheten This work studies the effect of grid resolution and subgrid scale modeling on the predictive accuracy of Large Eddy Simulation. In particular, the problems considered Besöksadress: are: turbulent flow over a backward-facing step and fully-developed turbulent channel Ångströmlaboratoriet Lägerhyddsvägen 1 flow. A SGS-free model and four subgrid scale models are used: Smagorsinky, Hus 4, Plan 0 k-equation, dynamic k-equation and WALE. Different combinations of streamwise and spanwise grid resolutions are considered along with different strategies for the Postadress: cell-size distribution in the wall-normal direction. Box 536 751 21 Uppsala First, a detailed study pertaining to fully-developed turbulent channel flow is Telefon: presented for target friction Reynolds numbers 180 and 300. A symmetric 018 – 471 30 03 three-layered wall-normal meshing strategy in conjunction with a SGS-free model is Telefax: shown to be the best compromise between computational efficiency and agreement 018 – 471 30 00 with benchmark data. Overall, the accuracy of the results was observed to be most sensitive to the spanwise resolution of the grid. Cell sizes in wall units ranging in Hemsida: between 25-28 and 12-20 in the streamwise and spanwise directions, respectively, http://www.teknat.uu.se/student yielded excellent agreement with reference data. Second, a detailed study of turbulent flow over a backward-facing step at a step-height Reynolds number of 5100 is conducted. This includes analysis of first- and second-order statistical moments of the velocity field for three different grid refinement levels and several SGS models. Additional quantities are computed on the finest grid, such as high-order statistics, one-dimensional spanwise power spectral density and spatial autocorrelation of the velocity, turbulent kinetic energy budget, as well as the first- and second-order statistics of the vorticity field. In line with the channel flow study, the WALE and SGS-free models produce the best results when compared with experimental and numerical benchmark data. All presented datasets are made available online for public use. Handledare: Saleh Rezaeiravesh Ämnesgranskare: Timofey Mukha Examinator: Jarmo Rantakokko IT 18 009 Tryckt av: Reprocentralen ITC “Out of clutter, find simplicity. From discord, find harmony. In the middle of difficulty lies opportunity.” – Albert Einstein iii THIS PAGE IS INTENTIONALLY LEFT BLANK Acknowledgments I would like to start off by expressing my gratitude to Uppsala University for all the resources I had access to. Also, I would like to thank all the members involved in the evaluation of my report, such as my supervisors, reviewer and examiner. I highly appreciate the time investment they put forth into helping me improve my thesis. More particularly, I would like to thank my two supervisors: Timofey Mukha and Saleh Rezaeiravesh. They both helped introduce me to turbulence modeling as well as bolstered my motivation for advanced CFD studies. Moreover, the exciting scientific discussions pertaining to CFD were fun and essential to this work’s fruition and my career development. Thank you for offering me this amazing opportunity to workon something I really enjoy. On a personal level, I would like to express my eternal gratitude to my wonderful parents: Antoine, George, Aida and Kenaan. They were/are always there for me, despite the distance. You perpetually advocate me to become a better person and consistently place very high emphasis on my education, while making sure I have everything I need to achieve it; you believed in my success, even when I, myself, did not. I cannot find words to express how indebted I am to your unceasing support. Additionally, I thank my dear uncle, Antoine, for all his support throughout the recent years of my academic life. Also, I cannot but mention my friends (especially Michel), both near and far, that helped me along my academic journey and made it a little more fun and much more bearable. Last, but definitely not least, I want to thank God. In my humble opinion, while I did my part and worked diligently, yet none of the outstanding opportunities could have ever been possible for me if it wasn’t – and still isn’t – for him. Also, I thank God for all the delightful people I have met, and still meet, along my journey. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Centre for High Performance Comput- ing (PDC-HPC). v THIS PAGE IS INTENTIONALLY LEFT BLANK Contents 1 Introduction1 2 Turbulence Modeling7 2.1 Navier-Stokes Equations.........................7 2.2 Direct Numerical Simulation.......................9 2.3 Reynolds Averaged Navier-Stokes.................... 11 2.4 Large Eddy Simulation.......................... 13 2.4.1 Smagorinsky Model........................ 16 2.4.2 SGS Turbulent Kinetic Energy Equation Model........ 18 2.4.3 Dynamic SGS TKE Equation Model.............. 19 2.4.4 Wall-Adapting Local Eddy-viscosity (WALE) Model...... 20 2.4.5 Subgrid-Scale (SGS)-Free Model................. 23 3 Numerical Implementation 25 3.1 The Finite Volume Method....................... 25 3.1.1 Spatial Discretization....................... 27 3.1.1.1 Convective Term.................... 27 3.1.1.2 Diffusive Term..................... 27 3.1.2 Temportal Discretization..................... 28 3.1.3 System of Algebraic Equation.................. 29 3.2 Pressure-velocity Coupling........................ 31 3.2.1 SIMPLE Algorithm........................ 31 3.2.2 PISO Algorithm.......................... 32 vii 3.2.3 PIMPLE.............................. 32 4 Wall-bounded Turbulence 35 4.1 Wall-bounded Flows........................... 36 4.1.1 Turbulent Boundary Layer Flow................. 36 4.1.2 Turbulent Channel Flow..................... 38 4.2 Near-wall Flow Characteristics...................... 40 4.2.1 Wall Regions........................... 40 4.2.2 Velocity Fluctuation Behavior.................. 42 5 Turbulent Channel Flow 45 5.1 Objective................................. 45 5.2 Literature Review............................. 46 5.3 Simulation Set-up............................. 48 5.3.1 Computational Domain...................... 49 5.3.2 Initial and Boundary Conditions................. 51 5.3.3 Physical and Flow Parameters.................. 52 5.4 Results and Discussion.......................... 52 5.4.1 Numerical Simulations for a Target Re휏 of 180 ......... 53 5.4.1.1 Mean Velocity Profiles................. 54 5.4.1.2 Reynolds Stress Components............. 56 5.4.1.3 Vorticity Fluctuations................. 58 5.4.1.4 Turbulent Kinetic Energy Budget........... 60 5.4.1.5 High-order Central Statistical Moments....... 62 5.4.2 SGS Study on the Same Wall-normal Grid Resolution..... 65 5.4.2.1 Mean Velocity Profiles................. 67 5.4.2.2 Reynolds Stress Components............. 67 5.4.3 SGS Study on Different Wall-normal Grid Resolutions.... 73 5.4.3.1 Mean Velocity Profiles................. 74 5.4.3.2 Reynolds Stress Components............. 75 5.4.3.3 Subgrid Scale Viscosity................ 78 viii 5.4.4 Spectral Analysis of SGS Models and Grid Resolutions.... 78 5.4.4.1 One-dimensional Streamwise Power Spectral Density 81 5.4.4.2 One-dimensional Spanwise Power Spectral Density. 92 5.4.4.3 Convergence of the Friction Velocity......... 102 5.5 Concluding Remarks........................... 103 6 Turbulent Flow over a BFS 107 6.1 Objective................................. 107 6.2 Literature Review............................. 108 6.3 Simulation Set-up............................. 110 6.3.1 Computational Domain...................... 112 6.3.2 Initial and Boundary Conditions................. 114 6.3.3 Physical and Flow Parameters.................. 115 6.4 Results and Discussion.......................... 116 6.4.1 Numerical Simulation: Coarse Mesh............... 117 6.4.1.1 Mean Streamwise Velocity............... 118 6.4.1.2 Reynolds Stress Components............. 119 6.4.1.3 Pressure and Skin-friction Coefficients........ 121 6.4.1.4 Friction Velocity and Friction Reynolds Number... 122 6.4.2 Numerical Simulation: Intermediate Mesh........... 123 6.4.2.1 Mean Streamwise Velocity............... 124 6.4.2.2 Reynolds Stress Components............. 126 6.4.2.3 Pressure and Skin-friction Coefficients........ 128 6.4.2.4 Friction Velocity and Friction Reynolds Number... 128 6.4.3 Numerical Simulation: Fine Mesh................ 129 6.4.3.1 Mean Streamwise Velocity............... 130 6.4.3.2 Reynolds Stress Components............. 131 6.4.3.3 Pressure and Skin-friction Coefficients........ 132 6.4.3.4 Friction Velocity and Friction Reynolds Number... 133 6.4.4 Comprehensive Numerical Simulation on a Fine Mesh..... 134 ix 6.4.4.1 Mean Pressure Profiles................. 134 6.4.4.2 Mean Velocity Profiles................. 134 6.4.4.3 Reynolds Stress Components............. 139 6.4.4.4 Vorticity......................... 142 6.4.4.5 High-order Statistical Moments............ 147 6.4.4.6 Turbulent Kinetic Energy Budget........... 160 6.4.4.7 One-dimensional Spanwise Spectra.......... 167 6.4.4.8 Auto-correlation Function in the Spanwise Direction 172 6.4.4.9 Probability of Backflow and Reattachment.....
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