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研究生:周維紀
研究生(外文):Chou, Wei-Chi
論文名稱:Numerical simulations of microflow by lattice Boltzmann method with different lattice models and wall functions
論文名稱(外文):以晶格波玆曼法應用不同晶格模型配合壁面修正函數模擬微流道流體
指導教授:林昭安
指導教授(外文):Lin, Chao-An
口試委員:何正榮牛仰堯
口試日期:2011-7-14
學位類別:碩士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:69
中文關鍵詞:晶格波茲曼微流道
外文關鍵詞:lattice Boltzmannmicroflow
相關次數:
  • 被引用被引用:0
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  • 下載下載:5
  • 收藏至我的研究室書目清單書目收藏:0
Microchannel flows study has been focused due to MEMS applications recently. In this thesis, we employ kinetic Lattice Boltzmann method(LBM) to simulate microchannel flows. In our simulation, considering a long microchannel with pressure boundary conditions at both inlet and outlet, using three different models, D2Q9, D2Q13, and D2Q21 to simulate Poiseuille flow, respectively. In order to predict
the accurate slip velocity at the wall and pressure distribution along streamwise direction, it is essential to apply modification to these models. There are two key
points, one is correction of wall function, the other is boundary condition. Firstly, we use three different wall functions to test, which are Lockerby’s wall function(LWF),
Stop’s wall function(SWF), and Guo’s wall function(GWF). LWF,SWF,and GWF not only lower the slip velocity but also predict a nonlinear behavior in nearwall region. Here, wall function is applied to the modification of relaxation time.
Secondly, boundary condition is discussed. The traditional boundary conditions were implemented for walls, such as bounceback scheme, but it can not generate enough slip velocity on walls. However, kinetic boundary condition like diffuse scattering boundary conditions(DSBC) [18], may over predict the slip velocity on wall. For capturing the slip velocity correctly, we introduce β-weighted diffusive-bounceback boundary condition, which combines the bounceback and diffuse-scattering boundary condition. β is a function of Knudsen number and it ’s obtained by fitting the linearized Boltzmann solutions at wall. In addition, we utilize two different schemes to calculate the unknown distribution function at inlet and outlet after streaming
step. All present results are compared with Direct Simulation Monte Carlo (DSMC).
1 Introduction
1.1 Introduction to Lattice Boltzmann method and microflow Lattice Boltzmann method
1.1.1 Lattice Boltzmann method
1.1.2 Micro-flows
1.2 Literature survey
1.2.1 Lattice boltzmann microflow model
1.2.2 Kundsen layer correction
1.2.3 Poiseuille microflow by using pressure boundary condition
1.2.4 Boundary condition in lattice boltzmann method
1.3 Objective and motivation

2 Theory and governing equations
2.1 The Boltzmann equation
2.2 The BGK approximation
2.3 The low-Mach-number approximation
2.4 Higher-order expansion of equilibrium distribution for gas flow in the micro-channel
2.5 Discretization of the Lattice Boltzmann equation for phase space
2.6 Discretization of the Lattice Boltzmann equation for time
2.7 Modifications for simulating isothermal gas flow in microflow by using lattice Boltzmann equation
2.7.1 Relaxation time
2.7.2 Wall functions for bounded system

3 Numerical algorithm
3.1 Simulation procedure
3.2 Pressure boundary condition
3.3 Boundary conditions in LBE simulations for microflow
3.3.1 Bounceback boundary condition
3.3.2 Diffuse-scattering boundary condition
3.3.3 Diffusive-bounceback boundary condition
3.4 Periodic boundary condition

4 Numerical results
4.1 2-D Poiseuille microflow driven by pressure
4.1.1 LWF/SWF/GWF wall function with D2Q9 model by using
extrapolation scheme
4.1.2 LWF/SWF/GWF wall function with D2Q9 model by using
equilibrium distribution function scheme
4.1.3 LWF/SWF/GWF wall function with D2Q13 model by using
extrapolation scheme
4.1.4 LWF/SWF/GWF wall function with D2Q13 model by using
equilibrium distribution function scheme
4.1.5 LWF/SWF/GWF wall function with D2Q21 model by using
extrapolation scheme
4.1.6 LWF/SWF/GWF wall function with D2Q21 model by using
equilibrium distribution function scheme

5 Conclusions

6 Figures

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