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研究生：	高柏浩 Kao, Po-Hao
論文名稱：	晶格波茲曼方法應用於工程與科學計算 Lattice Boltzmann Method in Scientific and Engineering Applications
指導教授：	楊瑞珍 Yang, Ruey-Jen
學位類別：	博士 Doctor
系所名稱：	工學院 - 工程科學系 Department of Engineering Science
論文出版年：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	170
中文關鍵詞：	移動邊界、自然對流、多孔性介質、晶格波茲曼方法
外文關鍵詞：	natural convection, moving boundary, lattice Boltzmann method, porous medium
相關次數：	點閱：121 下載：9
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This dissertation employs the lattice Boltzmann method (LBM) to study the fundamental problems in simulating flow through porous medium problems with heat transfer and chemical reaction in a microreactor, the oscillatory flow of Rayleigh-Bénard convection, the natural convection flows within closed rectangular cavities at the macroscopic and mesoscopic scales, and applying an interpolation-free concept to treat curved and moving boundary problems in LBM for engineering and scientific applications.
In Chapter 1, the general background for the subjects in this dissertation and the fundamental theory of the lattice Boltzmann method are introduced. The fluid flow LB model, thermal LB model, and their corresponding boundary treatments are formulated in Section 1.2.3, 1.2.4, and 1.3, respectively. Finally, some remarks on numerical characteristics in LBM are also discussed and provided in Section 1.4.
The fixed-bed microreactor is an important component in many biochip, microsensor, and microfluidic devices. Meanwhile, the LBM provides a powerful technique for investigating such microfluidic systems. Accordingly, in Chapter 2 of this dissertation, an investigation commences by performing LBM-based simulations for fluid flows through a fixed-bed microreactor comprising a micro-array of porous solids. During operation, the fluid and porous solid species are heated to prompt the chemical reaction necessary to generate the required products. Using the LB model, the flow fields and temperature fields in the microreactor are simulated for different Reynolds numbers, heat source locations, the reacting block aspect ratios, and porosity. A simple model is proposed to evaluate the chemical reactive efficiency of the microreactor based on the steady-state temperature field. The results of this model enable the optimal configuration and operating parameters to be established for the microreactor.
The study in Chapter 3 utilizes a simple LB thermal model with the Boussinesq approximation to investigate the 2D Rayleigh-Bénard problem from the threshold of the primary instability with a theoretical value of critical Rayleigh number 1707.76 to the regime near the flow bifurcation to the secondary instability. Since the fluid of LBM is compressible, an appropriate velocity scale for natural convection is carefully chosen at each value of the Prandtl number to ensure that the simulations satisfy the incompressible condition. The simulation results show that periodic unsteady flows take place at certain Prandtl numbers with an appropriate Rayleigh number. Furthermore, the Nusselt number is found to be relatively insensitive to the Prandtl number in the current simulation ranges. The relationship between the Nusselt number and the Rayleigh number is also investigated.
In Chapter 4, the same simple thermal LB model is then employed to simulate the natural convection flows within closed rectangular cavities. In order to overcome the difficulty for determining an appropriated value of the buoyant velocity (i.e. V), a characteristic velocity model is formulated based on the principles of kinetic theory. This model provides a useful criterion for choosing the V value applied to the natural convection problems at both macroscopic and mesoscopic scales. The simulations are then performed at a constant Prandtl number of Pr=0.71 and the reference Rayleigh numbers of Ra*<2E4 at both the macroscopic scale and the mesoscopic scale. The simulations are designed to identify the flow and cavity geometry conditions under which the initial diffusive-dominated thermal conduction flow transits to convective-dominated stationary, time-independent steady flow (i.e. the primary instability condition). The formation of secondary instability with an oscillatory flow structure is investigated using a spectrum analysis based on the fast-Fourier transform (FFT) technique. The relationship between the Nusselt number and the reference Rayleigh number is also systematically examined. In general, the simulation results show that unstable flow is generated at particular values of the Rayleigh number, Knudsen number, and cavity aspect ratio. Meanwhile, the Knudsen number and the aspect ratio play key roles in determining the evolution of oscillatory flows beyond the threshold of secondary instability.
Curved and moving boundary treatments provide a means of improving the computational accuracy of the conventional stair-shaped approximation used in LB simulations. Therefore, the study in Chapter 5 commences by investigating three conventional interpolation-based treatments for curved boundaries in LBM. However, according to the results by previous investigations, these interpolation-based curved boundary models would break the mass conservation at the boundary surfaces, hence, a concept of interpolation-free treatment for modeling the curved and moving boundary conditions is then proposed and studied to overcome the drawback of these interpolation-based models. Overall, the numerical results in the present study show that the proposed interpolation-free models significantly improve the accuracy of the mass flux computation near the solid surface, and thus enhance the accuracy of the momentum interaction at the moving boundaries.
Finally, Chapter 6 briefly summarizes concluding remarks for all investigation problems in this dissertation, and provides some indications of the intended direction for further research.

Abstract..................................................I
Acknowledgements.........................................IV
Contents.................................................VI
List of Tables............................................X
List of Figures..........................................XI
Nomenclature.............................................XV

Chapter 1 Introduction....................................1
1 General Background....................................1
2 Overview of Lattice Boltzmann Method..................4
2.1 Introduction to Boltzmann Equation..................4
2.2 From Lattice Gas Automata to Lattice Boltzmann Method....................................................6
2.3 Lattice Boltzmann Method for Fluid Flow.............9
2.4 Lattice Boltzmann Method for Species and Thermal Transport................................................13
3 Boundary Conditions..................................14
3.1 Periodic Boundary Conditions.......................15
3.2 No-Slip Boundary Conditions........................16
3.3 Sliding Wall Boundary Conditions...................18
3.4 Perturbative Acceleration Model for Fluid Flows within Closed Channel....................................19
3.5 Open Boundaries in Incompressible Flow using Porous Plug Model...............................................21
4 Numerical Characteristics of Lattice Boltzmann Method...................................................24

Chapter 2 An Investigation into Fixed-Bed Microreactors..27
1 Introduction.........................................27
2 Numerical Method.....................................29
2.1 Lattice Boltzmann Model............................29
2.2 Analysis of Chemical Reactive Efficiency within Porous Block.............................................32
3 Validation...........................................33
4 Results and Discussion...............................41
4.1 Flow Field and Temperature Distributions...........42
4.2 Estimated Efficiency of Chemical Reaction..........48
5 Conclusions..........................................52

Chapter 3 Simulating Oscillatory Flows in Rayleigh-Bénard Convection...............................................55
1 Introduction.........................................55
2 Numerical Method.....................................57
2.1 Lattice Boltzmann Model............................57
2.2 Symmetry...........................................60
2.3 Dimensionless Frequency............................61
3 Validations of LB Model using 2D Square Cavity.......61
4 Simulations of Rayleigh-Bénard Convection............64
4.1 A Correction Procedure for Threshold of Primary Instability..............................................66
4.2 Results obtained at Pr=0.71........................69
4.3 Results obtained at Pr=6...........................71
4.4 Results obtained at Pr=25..........................74
4.5 Results obtained at Pr=70..........................76
4.6 Relationship between Nusselt number and Rayleigh number...................................................78
5 Conclusions..........................................80

Chapter 4 Simulations of Natural Convection Flows within Rectangular Cavities.....................................83
1 Introduction.........................................83
2 Numerical Method.....................................86
2.1 Lattice Boltzmann Model............................86
2.2 Dimensionless Frequency............................87
2.3 Model for determining the appropriate value of buoyant characteristic velocity in LBM simulations for natural convection problems..............................88
3 Validation of Characteristic Velocity Model..........89
4 Simulations of Natural Convection within Closed Rectangular Cavities.....................................91
4.1 Natural Convection within Cavities at Macroscopic Scale....................................................93
4.2 Natural Convection within Cavities at Mesoscopic Scale....................................................98
4.3 Comparison of Results at Macroscopic and Mesoscopic Scales..................................................108
5 Conclusions.........................................109

Chapter 5 An Interpolation-Free Concept to treat Curved and Moving Boundaries...................................113
1 Introduction........................................113
2 Boundary Treatments at Solid Curved Surfaces........115
2.1 Filippova and Hänel (FH) model for curved boundary treatment...............................................117
2.2 Bouzidi and Yu interpolation-based models for curved boundary treatment......................................118
2.3 An interpolation-free model for curved boundary treatment...............................................121
2.4 Application of curved boundary treatment to moving boundary problems.......................................126
3 Simulations.........................................127
3.1 Verification of curved boundary models using stationary square block.................................128
3.2 Application of curved boundary treatment models to moving boundary problems................................135
4 Conclusions.........................................139

Chapter 6 Conclusion....................................143

References..............................................151
Appendix-A: From Dynamic Theory to Fluid Dynamics.......161
Curriculum Vitae........................................169
                                    

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