熱晶格波茲曼法在不可壓縮極限之黏性熱消散模型

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研究生：	麥顥覺
論文名稱：	熱晶格波茲曼法在不可壓縮極限之黏性熱消散模型 A thermal lattice Boltzmann model for flows with viscous heat dissipation in the incompressible limit
指導教授：	林昭安
口試委員:
學位類別：	碩士 Master
系所名稱：	工學院 - 動力機械工程學系 Department of Power Mechanical Engineering
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	49
中文關鍵詞：	晶格波茲曼法、黏性熱消散
相關次數：	點閱：2 下載：0
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The thermal lattice Boltzmann model for ﬂows with viscous heat dissipation is proposed. In this model, the thermal equilibrium distribution function is similar to the density equilibrium distribution function in the thermal lattice BGK model, except that the leading quantities are density and scalar, respectively. The heat viscous heating dissipation term in this model can be expressed in macroscopic form which includes the strain rate tensor. The viscous heating dissipation term in this model is convenient to implement. The proposed thermal lattice Boltzmann model is applied to two-dimensional thermal Poiseuille ﬂow, thermal Couette ﬂow, thermal Couette ﬂow with wall injection, natural convection in a square cavity, and three-dimensional thermal Poiseuille ﬂow in a square duct. Numerical simulations indicate that each formulation is second order accurate.

Introduction 1
1 Lattice Boltzmann method . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Thermal lattice Boltzmann models . . . . . . . . . . . . . . . 2
2.2 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Thermal boundary conditions . . . . . . . . . . . . . . . . . . 4
3 Objective and motivation . . . . . . . . . . . . . . . . . . . . . . . . . 5
Governing equations 7
1 The Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 The BGK and the low-Mach-number approximation . . . . . . . . . . 9
2.1 The BGK approximation . . . . . . . . . . . . . . . . . . . . . 9
2.2 The low-Mach-number approximation . . . . . . . . . . . . . . 11
3 Discretization of the BGK equation . . . . . . . . . . . . . . . . . . . 12
3.1 Discretization of phase space . . . . . . . . . . . . . . . . . . . 12
3.2 Discretization of time . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Discretization of the external force term . . . . . . . . . . . . 15
4 The thermal lattice BGK equation with a viscous heat dissipation term 16
5 The Chapman-Enskog expansion . . . . . . . . . . . . . . . . . . . . 17
Numerical algorithm 19
1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Velocity boundary conditions . . . . . . . . . . . . . . . . . . . . . . 20
3 Thermal boundary conditions . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Dirichlet thermal boundary conditions . . . . . . . . . . . . . 22
3.2 Neumann thermal boundary conditions . . . . . . . . . . . . . 24
3.3 Corner thermal boundary conditions . . . . . . . . . . . . . . 24
Numerical results 27
1 2-D thermal Poiseuille flow . . . . . . . . . . . . . . . . . . . . . . . . 27
2 2-D thermal Couette flow . . . . . . . . . . . . . . . . . . . . . . . . 29
3 2-D thermal Couette flow with wall injection . . . . . . . . . . . . . . 31
4 3-D thermal Poiseuille flow in a square duct . . . . . . . . . . . . . . 33
5 2-D natural convection in a square cavity . . . . . . . . . . . . . . . . 35
Conclusions 33

                                

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