Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17512号 / 工博第3671号 / 新制||工||1558(附属図書館) / 30278 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 青木 一生, 教授 稲室 隆二, 教授 斧 髙一 / 学位規則第4条第1項該当

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

The content of Chapter 1 is an author produced version of a paper published in Physics of Fluids. The final publication is available at AIP via http://dx.doi.org/10.1063/1.3691262. The content of Chapters 2 and 4 is an author produced version of papers published in Journal of Statistical Physics. The final publications are available at Springer via http://dx.doi.org/10.1007/s10955-012-0512-z and http://dx.doi.org/10.1007/s10955-015-1364-0, respectively. / 京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19682号 / 工博第4137号 / 新制||工||1638(附属図書館) / 32718 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 青木 一生, 教授 髙田 滋, 教授 稲室 隆二 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19686号 / 工博第4141号 / 新制||工||1639(附属図書館) / 32722 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 稲室 隆二, 教授 青木 一生講師杉元 宏 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21757号 / 工博第4574号 / 新制||工||1713(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 髙田 滋, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The field of Computational Fluid Dynamics (CFD) primarily involves the approximation of the Navier-Stokes equations. However, these equations are only valid when the flow is considered continuous such that molecular interactions are abundant and predictable. The Knudsen number, $Kn$, which is defined as the ratio of the flow's mean free path, $\lambda$, to some characteristic length, $L$, quantifies the continuity of any flow, and when this parameter is large enough, alternative methods must be employed to simulate gases. The Direct Simulation Monte Carlo (DSMC) method is one which simulates rarefied gas flows by directly simulating the particles that compose the flow and using probabilistic methods to determine their collisions and properties. This thesis discusses the development of a new DSMC simulation code, named SINATRA, which was written in object-oriented C++ and validated on Cartesian grids. The code demonstrates the ability to perform standard simulation code tasks which include reading-in a user-made input file, performing the specified simulation, and generating visualization files compatible with Tecplot 360\texttrademark, a commercial post-processing software. SINATRA strategically uses an octree data structure as a storage scheme for computational grid data and uses this a backbone for particle interactions. The discussed validation cases include comparisons of initial particle properties to theoretical data, convergence studies for the sampling of macroscopic properties, and validation of transport properties through natural diffusion and Couette flow simulations. The results show successful implementation of simple DSMC procedures, and a path for future development of the code is thoroughly discussed.

The abstract kinetic equation Tψ’=-Aψ is studied with partial range boundary conditions in two geometries, in the half space x≥0 and on a finite interval [0, r]. T and A are abstract self-adjoint operators in a complex Hilbert space. In the case of the half space problem it is assumed that T is a (possibly) unbounded injection and A is a positive compact perturbation of the identity satisfying a regularity condition, while in the case of slab geometry T is a bounded injection and A is a bounded Fredholm operator with a finite dimensional negative part. Existence and uniqueness theory is developed for both models. Results are illustrated on relevant physical examples. / Ph. D.

A complete formulation of the recently developed. F_N method in kinetic theory is presented and the accuracy of this advanced semi-analytical-numerical technique is demonstrated by testing the method to several classical problems in rarefied gas dynamics. The method is based on the existing analysis for the vector transport equation arising from the decomposition of the linearized BGK equation. Using full-range orthogonality, a system of singular integral equations for the distribution functions at the boundaries is established. The unknown distribution functions are then approximated by a finite expansion in terms of a set of basis functions and the coefficients of the expansion are found by requiring the set of the reduced algebraic equations to be satisfied at certain collocation points. By studying the half-space heat transfer and weak evaporation problems and the problem of heat transfer between two parallel plates it is demonstrated that the F_N method is a viable solution technique yielding results of benchmark accuracy. Two different sets of basis functions are provided for half-space and finite media problems, respectively. In all cases, highly accurate numerical results are computed and compared to existing exact solutions. The obtained numerical results help in judging the accuracy to expect of the method and indicate that the F_N method may be applied with confidence to problems for which, more exact methods of analysis do not appear possible. Then, the cylindrical Poiseuille flow and thermal creep problems, which are not amenable to exact treatment, are solved. The F_N method is formulated and tested successfully for the first time in cylindrical geometry in kinetic theory. The complete solution of the two aforementioned problems is presented with the numerical results quoted as converged being of reference-quality good for benchmark accuracy. / Ph. D. / incomplete_metadata

The Direct Simulation Monte Carlo method is a computational tool for modelling rarefied flows. The Macroscopic Chemistry Method was developed to simplify the modelling of dissociation and recombination reactions in DSMC. The ability to understand and predict the behaviour of chemically reacting, rarefied flows is a critical aspect in the development of high altitude, high speed bodies such as re-entry craft, high altitude aircraft, space transport vehicles and missiles. Computational methods are an invaluable source of information when experimental techniques are difficult, costly or time-consuming. However, traditional methods of modelling chemical kinetics using DSMC suffer from a number of drawbacks. The Macroscopic Chemistry Method overcomes a number of these problems, but has previously only been applied to simulations of a single diatomic gas. The Macroscopic Chemistry Method (MCM) is extended to consider multiple species and multiple reaction sets, thermal non-equilibrium effects, trace species modelling, unsteady flows, vibrational state specific chemistry, electronic excitation, relaxation and ionization and coupled nonequilibrium radiation emission. The Macroscopic Method is described as a general DSMC modelling philosophy rather than as a single formulated method. That is, the flexibility and utility of the method are shown through examples of applying a macroscopic approach to a number of problems, and by highlighting instances where a macroscopic approach is useful or even necessary. The problems investigated include reservoir relaxation calculations, 1-D shock, expansion and shock-expansion calculations, two-dimensional flows over a vertical step and through a cavity, and axis-symmetric flow about a sphere. The studies demonstrate that although MCM may often present a simplified approach as compared to traditional 'non-macroscopic' methods, it does not necessarily lead to more approximate solutions. On the contrary, the ability of macroscopic methods to combine different models of physical processes with the most recent (verified) data means that they are particularly suited to simulate high altitude, rarefied flows. It is also shown that, like any model approach, the validity of the approximations employed must be justified for a particular problem. In general, macroscopic methods of varying complexity and accuracy may be implemented to model a specific physical process. Adoption of the Macroscopic Chemistry Method in DSMC has the potential to enhance the modelling of chemical kinetics, charged-particle effects and radiation in rarefied hypersonic flows. This capability may be attributed to the simplicity and flexibility which the macroscopic approach affords over methods which seek to avoid the use of collective information. Macroscopic methods have already been employed to model weakly ionized flows. Their further application to model chemical kinetics and other processes would be useful for modelling and understanding the behaviour of objects in rarefied hypersonic flow-fields.

No description available.