Dissertations / Theses: 'Rarefied gas dynamics'

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Parsons, Timothy Langdon. "Object-reuse-oriented design of direct simulation Monte-Carlo software for rarefied gas dynamics." Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314287.

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Mori, Hideo, Tomohide Niimi, Madoka Hirako, and Hiroyuki Uenishi. "Pressure Sensitive Paint Suitable to High Knudsen Number Regime." IOP, 2006. http://hdl.handle.net/2237/6960.

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Cave, Hadley Mervyn. "Development of Modelling Techniques for Pulsed Pressure Chemical Vapour Deposition (PP-CVD)." Thesis, University of Canterbury. Mechanical Engineering, 2008. http://hdl.handle.net/10092/1572.

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In this thesis, a numerical and theoretical investigation of the Pulsed Pressure Chemical Vapour Deposition (PP-CVD) progress is presented. This process is a novel method for the deposition of thin films of materials from either liquid or gaseous precursors. PP-CVD operates in an unsteady manner whereby timed pulsed of the precursor are injected into a continuously evacuated reactor volume. A non-dimensional parameter indicating the extent of continuum breakdown under strong temporal gradients is developed. Experimental measurements, supplemented by basic continuum simulations, reveal that spatio-temporal breakdown of the continuum condition occurs within the reactor volume. This means that the use of continuum equation based solvers for modelling the flow field is inappropriate. In this thesis, appropriate methods are developed for modelling unsteady non-continuum flows, centred on the particle-based Direct Simulation Monte Carlo (DSMC) method. As a first step, a basic particle tracking method and single processor DSMC code are used to investigate the physical mechanisms for the high precursor conversion efficiency and deposition uniformity observed in experimental reactors. This investigation reveals that at soon after the completion of the PP-CVD injection phase, the precursor particles have an approximately uniform distribution within the reactor volume. The particles then simply diffuse to the substrate during the pump-down phase, during which the rate of diffusion greatly exceeds the rate at which particles can be removed from the reactor. Higher precursor conversion efficiency was found to correlate with smaller size carrier gas molecules and moderate reactor peak pressure. An unsteady sampling routine for a general parallel DSMC method called PDSC, allowing the simulation of time-dependent flow problems in the near continuum range, is then developed in detail. Nearest neighbour collision routines are also implemented and verified for this code. A post-processing procedure called DSMC Rapid Ensemble Averaging Method (DREAM) is developed to improve the statistical scatter in the results while minimising both memory and simulation time. This method builds an ensemble average of repeated runs over small number of sampling intervals prior to the sampling point of interest by restarting the flow using either xi a Maxwellian distribution based on macroscopic properties for near equilibrium flows (DREAM-I) or output instantaneous particle data obtained by the original unsteady sampling of PDSC for strongly non-equilibrium flows (DREAM-II). The method is validated by simulating shock tube flow and the development of simple Couette flow. Unsteady PDSC is found to accurately predict the flow field in both cases with significantly reduced run-times over single processor code and DREAM greatly reduces the statistical scatter in the results while maintaining accurate particle velocity distributions. Verification simulations are conducted involving the interaction of shocks over wedges and a benchmark study against other DSMC code is conducted. The unsteady PDSC routines are then used to simulate the PP-CVD injection phase. These simulations reveal the complex flow phenomena present during this stage. The initial expansion is highly unsteady; however a quasi-steady jet structure forms within the reactor after this initial stage. The simulations give additional evidence that the collapse of the jet at the end of the injection phase results in an approximately uniform distribution of precursor throughout the reactor volume. Advanced modelling methods and the future work required for development of the PP-CVD method are then proposed. These methods will allow all configurations of reactor to be modelled while reducing the computational expense of the simulations.

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Leimkuehler, Thomas O. "Investigation of low-pressure laser induced fluorescence for measuring temperature profiles in a rarefied gas /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9999301.

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Gu, Yuxing. "Measurements of temperature and density profiles of iodine vapor between parallel plates in the transition regime using laser induced fluorescence /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9974999.

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Morris, Aaron Benjamin. "Investigation of a discrete velocity Monte Carlo Boltzmann equation." Thesis, [Austin, Tex. : University of Texas, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-127.

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Wishart, Stuart Jackson. "A Parallel Solution Adaptive Implementation of the Direct Simulation Monte Carlo Method." University of Sydney. School of Aerospace, Mechanical and Mechatronic Engineering, 2005. http://hdl.handle.net/2123/619.

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This thesis deals with the direct simulation Monte Carlo (DSMC) method of analysing gas flows. The DSMC method was initially proposed as a method for predicting rarefied flows where the Navier-Stokes equations are inaccurate. It has now been extended to near continuum flows. The method models gas flows using simulation molecules which represent a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation. Molecules are moved through a simulation of physical space in a realistic manner that is directly coupled to physical time such that unsteady flow characteristics are modelled. Intermolecular collisions and moleculesurface collisions are calculated using probabilistic, phenomenological models. The fundamental assumption of the DSMC method is that the molecular movement and collision phases can be decoupled over time periods that are smaller than the mean collision time. Two obstacles to the wide spread use of the DSMC method as an engineering tool are in the areas of simulation configuration, which is the configuration of the simulation parameters to provide a valid solution, and the time required to obtain a solution. For complex problems, the simulation will need to be run multiple times, with the simulation configuration being modified between runs to provide an accurate solution for the previous run�s results, until the solution converges. This task is time consuming and requires the user to have a good understanding of the DSMC method. Furthermore, the computational resources required by a DSMC simulation increase rapidly as the simulation approaches the continuum regime. Similarly, the computational requirements of three-dimensional problems are generally two orders of magnitude more than two-dimensional problems. These large computational requirements significantly limit the range of problems that can be practically solved on an engineering workstation or desktop computer. The first major contribution of this thesis is in the development of a DSMC implementation that automatically adapts the simulation. Rather than modifying the simulation configuration between solution runs, this thesis presents the formulation of algorithms that allow the simulation configuration to be automatically adapted during a single run. These adaption algorithms adjust the three main parameters that effect the accuracy of a DSMC simulation, namely the solution grid, the time step and the simulation molecule number density. The second major contribution extends the parallelisation of the DSMC method. The implementation developed in this thesis combines the capability to use a cluster of computers to increase the maximum size of problem that can be solved while simultaneously allowing excess computational resources to decrease the total solution time. Results are presented to verify the accuracy of the underlying DSMC implementation, the utility of the solution adaption algorithms and the efficiency of the parallelisation implementation.

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Wishart, Stuart Jackson. "A Parallel Solution Adaptive Implementation of the Direct Simulation Monte Carlo Method." Thesis, The University of Sydney, 2004. http://hdl.handle.net/2123/619.

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This thesis deals with the direct simulation Monte Carlo (DSMC) method of analysing gas flows. The DSMC method was initially proposed as a method for predicting rarefied flows where the Navier-Stokes equations are inaccurate. It has now been extended to near continuum flows. The method models gas flows using simulation molecules which represent a large number of real molecules in a probabilistic simulation to solve the Boltzmann equation. Molecules are moved through a simulation of physical space in a realistic manner that is directly coupled to physical time such that unsteady flow characteristics are modelled. Intermolecular collisions and moleculesurface collisions are calculated using probabilistic, phenomenological models. The fundamental assumption of the DSMC method is that the molecular movement and collision phases can be decoupled over time periods that are smaller than the mean collision time. Two obstacles to the wide spread use of the DSMC method as an engineering tool are in the areas of simulation configuration, which is the configuration of the simulation parameters to provide a valid solution, and the time required to obtain a solution. For complex problems, the simulation will need to be run multiple times, with the simulation configuration being modified between runs to provide an accurate solution for the previous run's results, until the solution converges. This task is time consuming and requires the user to have a good understanding of the DSMC method. Furthermore, the computational resources required by a DSMC simulation increase rapidly as the simulation approaches the continuum regime. Similarly, the computational requirements of three-dimensional problems are generally two orders of magnitude more than two-dimensional problems. These large computational requirements significantly limit the range of problems that can be practically solved on an engineering workstation or desktop computer. The first major contribution of this thesis is in the development of a DSMC implementation that automatically adapts the simulation. Rather than modifying the simulation configuration between solution runs, this thesis presents the formulation of algorithms that allow the simulation configuration to be automatically adapted during a single run. These adaption algorithms adjust the three main parameters that effect the accuracy of a DSMC simulation, namely the solution grid, the time step and the simulation molecule number density. The second major contribution extends the parallelisation of the DSMC method. The implementation developed in this thesis combines the capability to use a cluster of computers to increase the maximum size of problem that can be solved while simultaneously allowing excess computational resources to decrease the total solution time. Results are presented to verify the accuracy of the underlying DSMC implementation, the utility of the solution adaption algorithms and the efficiency of the parallelisation implementation.

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Masters, Nathan Daniel. "Efficient Numerical Techniques for Multiscale Modeling of Thermally Driven Gas Flows with Application to Thermal Sensing Atomic Force Microscopy." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/11574.

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The modeling of Micro- and NanoElectroMechanical Systems (MEMS and NEMS) requires new computational techniques that can deal efficiently with geometric complexity and scale dependent effects that may arise. Reduced feature sizes increase the coupling of physical phenomena and noncontinuum behavior, often requiring models based on molecular descriptions and/or first principles. Furthermore, noncontinuum effects are often localized to small regions of (relatively) large systemsprecluding the global application of microscale models due to computational expense. Multiscale modeling couples efficient continuum solvers with detailed microscale models to providing accurate and efficient models of complete systems. This thesis presents the development of multiscale modeling techniques for nonequilibrium microscale gas phase phenomena, especially thermally driven microflows. Much of this focuses on improving the ability of the Information Preserving DSMC (IP-DSMC) to model thermally driven flows. The IP-DSMC is a recent technique that seeks to accelerate the solution of direct simulation Monte Carlo (DSMC) simulations by preserving and transporting certain macroscopic quantities within each simulation molecules. The primary contribution of this work is the development of the Octant Splitting IP-DSMC (OSIP-DSMC) which recovers previously unavailable information from the preserved quantities and the microscopic velocities. The OSIP-DSMC can efficiently simulate flow fields induced by nonequilibrium systems, including phenomena such as thermal transpiration. The OSIP-DSMC provides an efficient method to explore rarefied gas transport phenomena which may lead to a greater understanding of these phenomena and new concepts for how these may be utilized in practical engineering systems. Multiscale modeling is demonstrated utilizing the OSIP-DSMC and a 2D BEM solver for the continuum (heat transfer) model coupled with a modified Alternating Schwarz coupling scheme. An interesting application for this modeling technique is Thermal Sensing Atomic Force Microscopy (TSAFM). TSAFM relies on gas phase heat transfer between heated cantilever probes and the scanned surface to determine the scan height, and thus the surface topography. Accurate models of the heat transfer phenomena are required to correctly interpret scan data. This thesis presents results demonstrating the effect of subcontinuum heat transfer on TSAFM operation and explores the mechanical effects of the Knudsen Force on the heated cantilevers.

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Valougeorgis, Dimitris V. "The Fn method in kinetic theory." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/49949.

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A complete formulation of the recently developed. FN 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 FN 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 FN 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 FN 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

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Walus, Wlodzimierz Ignacy. "Stationary solutions of abstract kinetic equations." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/53613.

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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.

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Kobert, Maria [Verfasser], and Axel [Akademischer Betreuer] Klar. "Application of the Finite Pointset Method to moving boundary problems for the BGK model of rarefied gas dynamics / Maria Kobert. Betreuer: Axel Klar." Kaiserslautern : Technische Universität Kaiserslautern, 2015. http://d-nb.info/1077007167/34.

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Kamphorst, Carmo Henrique. "Fluxo de gases rarefeitos em dutos cilíndricos : uma abordagem via equações integrais." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2009. http://hdl.handle.net/10183/17880.

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Neste trabalho, é estudada a descrição do fluxo de um gás rarefeito em um duto cilíndrico de comprimento infinito. A formulação matemática do problema está baseada na forma integral de equações cinéticas derivadas da Equação de Boltzmann. Particularmente são estudados os modelos cinéticos conhecidos como BGK e S. Métodos espectrais são propostos para obtenção de soluções, em forma fechada, para quantidades de interesse como o perfil de velocidade do gás, bem como taxas de fluxo. As formulações espectrais são baseadas em duas abordagens: expansão clássica em termos de Polinômios de Legendre e expansão em termos de splines cúbicas de Hermite, neste caso, associada a um esquema de colocação. A implementação das propostas produz resultados computacionais satisfatórios do ponto de vista prático. Para obtenção de resultados com maior precisão, técnicas de tratamento da singularidade do núcleo da equação integral foram introduzidas, resultando em ganho computacional significativo. Finalmente, a proposta de solução espectral para problemas em geometria cilíndrica se mostrou adequada para problemas em que se admite reflexão especular na superfície do cilindro, situação onde outras abordagens clássicas disponíveis na literatura não podem ser utilizadas. In this work, rarefied gas flows in cylindrical ducts are studied. The mathematical formulation of the problems are based on the integral form of kinetic equations derived from the Boltzmann equation. Particularly, the BGK and S models are studied. Spectral methods are proposed to obtain closed form solutions for quantities of interest as velocity profile of the gas as well as flow rates. The spectral formulations are based on two approaches: classical expansions in terms of Legendre Polynomials and Hermite cubic splines expansions. In this case, associated with a collocation scheme. The approaches provide good computational results, from the practical point of view. On the other hand, for obtaining higher accuracy, some techniques were introduced to deal with the inherent singularity of the integral kernel. In this context, a significant computational gain is achieved. Finally, this spectral approach has shown to be adequate to solve problems where specular reflection is assumed at the surface, in which cases, classical approaches available in the literature can not be used.

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Scherer, Caio Sarmento. "Efeitos de evaporação em gases rarefeitos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2009. http://hdl.handle.net/10183/17889.

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Neste trabalho, o fenômeno de evaporação em gases rarefeitos e analisado, para o caso de uma espécie de gás bem como de misturas binárias. Evaporação fraca e forte são consideradas para escoamentos de gases em canal e semi-espaco. Também e investigado o fenômeno conhecido como reverso de temperatura, típico de gases em estado de rarefação. O método ADO, uma versão analítica do método de ordenadas discretas, é utilizado para construção de soluções em forma fechada para os diversos problemas e quantidades de interesse, como perfis de temperatura e fluxos de calor. Para o caso de um gás, uma solução unificada e desenvolvida para problemas formulados a partir dos modelos cinéticos, derivados da equação de Boltzmann, BGK, S, Gross- Jackson e MRS. No caso de mistura binária de gases, a formulação matemática e baseada no modelo McCormack. Particularmente, quando a evaporação forte e abordada, e aspectos não lineares devem ser incluídos, a versão não linear do modelo BGK e utilizada. Neste caso, a solução ADO do modelo linear e utilizada em um processo chamado de pós-processamento para inclusão dos termos não lineares do problema e reavaliação das quantidades de interesse, evidenciando melhoria dos resultados obtidos pela formulação linear. Uma serie de resultados numéricos são listados e é observada, de forma geral, excelente exatidão e eficiência computacional. In this work, evaporation phenomena in rarefied gas flow, for one gas case and binary mixtures, are analyzed. Weak and strong evaporation are considered in channel and half-space problems. The reverse of temperature problem, typical in rarefied gas dynamics, is also investigated. The ADO method, an analytical version of the discrete ordinates method, is used to develop closed form solutions, to several problems and quantities of interest, as temperature profiles and heat flows. For the one gas case, an unified solution is developed for the BGK, S, Gross-Jackson and MRS models, derived from the Boltzmann equation. For binary mixtures, the mathematical formulation is based on the McCormack model. Particularly, when strong evaporation is investigated, and nonlinear aspects have to be included, the nonlinear BGK model is used. In this case, the ADO solution, provided by the linear model, is considered in a post-processing procedure which takes into account the nonlinear terms to evaluate the quantities of interest, and improved results are obtained, in comparison with the linear version. A series of numerical results are listed and, in general, an excellent accuracy and good computational efficiency are observed.

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Carcaud, Pierre. "Étude de quelques modèles cinétiques décrivant le phénomène d'évaporation en gravitation." Phd thesis, Université Rennes 1, 2014. http://tel.archives-ouvertes.fr/tel-01018326.

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L'étude de l'évolution de galaxies, et tout particulièrement du phénomène d'évaporation, a été pour la première fois menée à l'aide de modèles physiques, par Chandrasekhar notamment, dans les années 40. Depuis, de nouveaux modèles plus sophistiqués ont été introduits par les physiciens. Ces modèles d'évolution des galaxies sont des modèles cinétiques; bien connus et bien étudiés par les mathématiciens. Cependant, l'aspect évaporation (le fait que des étoiles sortent du système étudié) n'avait pas encore été étudié mathématiquement, à ma connaissance. La galaxie est vue comme un gaz constitué d'étoiles et le modèle consiste en une équation de Vlasov-Poisson, l'interaction étant la gravitation universelle, couplée avec au second membre un terme de collision de type Landau. On rajoute à ce modèle une condition d'évaporation qui consiste à dire que les étoiles dont l'énergie cinétique est suffisamment élevée pour quitter le système sont exclues. Ce modèle étant trop compliqué à étudier tel quel, je propose dans cette thèse plusieurs modèles simplifiés qui sont des premières étapes nécessaires à l'étude du modèle général et qui permettent de mieux comprendre les difficultés à surmonter. Dans une première partie, je m'intéresse au cas homogène en espace, pour lequel le terme de Vlasov-Poisson est remplacé par une simple dérivée en temps. Je fais une étude précise du cas à symétrie radiale en vitesse avec un potentiel Maxwellien, le terme de Landau étant alors remplacé par un terme de type Fokker-Planck, et je montre dans ce cas l'existence et l'unicité d'une solution régulière et l'existence d'un profil asymptotique des solutions. Dans le cas homogène général, je montre l'existence et l'unicité d'une solution régulière tout pendant que la masse ne s'est pas totalement évaporée. J'illustre ces résultats théoriques par des simulations numériques réalisés à l'aide de schéma numériques conservateurs. Dans une seconde partie, je m'intéresse au cas non homogène en espace en dérivant un modèle hydrodynamique pour un modèle de type Vlasov-BGK (plus simple que le modèle Vlasov-Poisson-Landau) avec évaporation.

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Cromianski, Solange Regina. "SOLUÇÃO DE PROBLEMAS EM SEMIESPAÇO NA DINÂMICA DE GASES RAREFEITOS BASEADA EM MODELOS CINÉTICOS." Universidade Federal de Santa Maria, 2012. http://repositorio.ufsm.br/handle/1/9976.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior The method discrete ordinates is used to solve problems involving rarefied gas dynamics. In this work, a version of the analytical method discrete ordinates (ADO) is used to solve problems in a semi-infinite. The complete analytical development, in cartesian coordinates, the solution of the Thermal-Slip and Viscous-Slip problems is presented, for four kinetic models: BGK model, S model, Gross Jackson model and MRS model in a unified approach. In addition, to describe the interaction between gas and surface, we use the Cercignani-Lampis boundary condition defined in terms of the coefficients of accommodation of tangential momentum and energy accommodation coefficient kinetic corresponding the velocity normal. Numerical results are presented, where we obtain quantities of interest, such as: velocity profile and heat flow profile, which were implemented computationally through the FORTRAN program. O método de ordenadas discretas é utilizado na solução de alguns problemas envolvendo a dinâmica de gases rarefeitos. Neste trabalho, uma versão analítica do método de ordenadas discretas (ADO) é usada para resolver problemas em meio semiinfinito. O desenvolvimento analítico completo, em coordenadas cartesianas, da solução dos problemas Deslizamento Térmico e Deslizamento Viscoso é apresentada, para quatro modelos cinéticos: modelo BGK, modelo S, modelo Gross Jackson e modelo MRS em uma abordagem unificada. Além disso, para descrever o processo de interação entre o gás e a parede utiliza-se o núcleo de Cercignani-Lampis definido em termos do coeficiente de acomodação do momento tangencial e do coeficiente de acomodação da energia cinética correspondendo a velocidade normal. Resultados numéricos são apresentados, onde obtém-se grandezas de interesse, tais como: perfil de velocidade e perfil de fluxo de calor, os quais foram implementados computacionalmente através do programa FORTRAN.

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Zheng, Yingsong. "Analysis of kinetic models and macroscopic continuum equations for rarefied gas dynamics." 2004. http://hdl.handle.net/1828/662.

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The Boltzmann equation is the basic equation to describe rarefied gas flows. Some kinetic models with simple expressions for the collision term have been proposed to reduce the mathematical complexity of the Boltzmann equation. All macroscopic continuum equations can be derived from the Boltzmann equation or kinetic models through the Chapman-Enskog method, Grad's moment method, etc. This thesis is divided into three parts. In the first part, existing kinetic models (BGK model, ES-BGK model, v(C) -BGK model, S model, and Liu model), and two newly proposed v(C)-ES-BGK type kinetic models are described and compared, based on properties that need to be satisfied for a kinetic model. In the new models a meaningful expression for the collision frequency is used, while the important properties for a kinetic model are retained at the same time. In the second part of this work, the kinetic models (BGK, ES-BGK, v(C) -BGK, and two new kinetic models) are tested numerically for one-dimensional shock waves and one-dimensional Couette flow. The numerical scheme used here is based on Mieussens's discrete velocity model (DVM). Computational results from the kinetic models are compared to results obtained from the Direct Simulation Monte Carlo method (DSMC). It is found that for hard sphere molecules the results obtained from the two new kinetic models are very similar, and located in between the results from the ES-BGK and the v(C)-BGK models, while for Maxwell molecules the two new kinetic models are identical to the ES-BGK model. For one-dimensional shock waves, results from the new kinetic model II fit best with results from DSMC; while for one-dimensional Couette flow, the ES-BGK model is suggested. Also in the second part of the work, a modified numerical scheme is developed from Mieussens's original DVM. The basic idea is to use a linearized expression of the reference distribution function, instead of its exact expression, in the numerical scheme. Results from the modified scheme are very similar to the results from the original scheme for almost all done tests, while 20-40 percent of the computational time can be saved. In the third part, several sets of macroscopic continuum equations are examined for one-dimensional steady state Couette flow. For not too large Knudsen numbers (Knc=O.l) in the transition regime, it is found that the original and slightly linearized regularized 13 moment equations give better results than Grad's original 13 moment equations, which, however, give better results than the Burnett equations, while the Navier-Stokes-Fourier equations give the worst results, which is in agreement with the expectation. For large Knudsen number situations (Kn>O.l), it turns out that all macroscopic continuum equations tested fail in the accurate description of flows, while the Grad's 13 moment equations can still give better results than the Burnett equations.

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Tharkabhushanam, Sri Harsha 1979. "A conservative deterministic spectral method for rarefied gas flows." 2008. http://hdl.handle.net/2152/17913.

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The mathematical analysis of the Boltzmann equation for a wide range of important models is well developed. It describes physical phenomena which are often of great engineering importance (in aerospace industry, semiconductor design, etc.). For that reason, analytical and computational methods of solving the Boltzmann equation are studied extensively. The idea of describing processes on a scale of the order of the relaxation scales of time and space has been realized. The nonlinear Boltzmann equation possesses the important essence of a physically realistic equation, so it is possible not only to consider the flows of simple media but to formulate new problems due to the ability of this equation to describe nonequilibrium states. In this dissertation, a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation for variable hard potential (VHP) collision kernels with conservative or non-conservative binary interactions is proposed. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in the collision integral computation is reduced to a separate integral over the unit sphere S2. In addition, the conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or to elastic model of slowing down processes. We prove the accuracy, consistency and conservation properties of the proposed conservative spectral method. Existing spectral methods have consistency proofs which are only for elastic collisions, and also such methods do not conserve all the necessary moments of the collision integral. In this dissertation, error estimates for the conservation routine are provided. Such conservation correction is implemented as an extended isoperimetric problem with the moment conservation properties as the constraints. We use and extend an existing bound estimate of Gamba, Panferov and Villani for the inelastic/elastic space homogeneous Boltzmann collision operator. The result is an original extension to the work of Gustaffson. Using these estimates along with projection error estimates and conservation correction estimates, we prove that the conservation correction is bounded by the spectral accuracy. Simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation for both elastic and inelastic VHP interactions. Benchmarking of the self-similar simulations involves the selection of a time rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard-spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods. Recognizing the importance of the Boltzmann equation in the analysis of shock structures and nonequilibrium states, such a study is done for 1D(x) × 3D(v). The classic Riemann problem is numerically analyzed for Knudsen numbers close to continuum. The shock tube problem of Sone and Aoki, where the wall temperature is suddenly changed, is also studied. We consider the problem of heat transfer between two parallel plates with diffusive boundary conditions for a range of Knudsen numbers from close to continuum to a highly rarefied state. Finally, the classical infinite shock tube problem that generates a non-moving shock wave is studied. The point worth noting is that the flow in the final case turns from a supersonic flow to a subsonic flow across the shock. text

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Rahimi, Behnam. "A macroscopic approach to model rarefied polyatomic gas behavior." Thesis, 2016. http://hdl.handle.net/1828/7258.

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A high-order macroscopic model for the accurate description of rarefied polyatomic gas flows is introduced based on a simplified kinetic equation. The different energy exchange processes are accounted for with a two term collision model. The order of magnitude method is applied to the primary moment equations to acquire the optimized moment definitions and the final scaled set of Grad's 36 moment equations for polyatomic gases. The proposed kinetic model, which is an extension of the S-model, predicts correct relaxation of higher moments and delivers the accurate Prandtl (Pr) number. Also, the model has a proven H-theorem. At the first order, a modification of the Navier-Stokes-Fourier (NSF) equations is obtained, which shows considerable extended range of validity in comparison to the classical NSF equations in modeling sound waves. At third order of accuracy, a set of 19 regularized PDEs (R19) is obtained. Furthermore, the terms associated with the internal degrees of freedom yield various intermediate orders of accuracy, a total of 13 different orders. Attenuation and speed of linear waves are studied as the first application of the many sets of equations. For frequencies were the internal degrees of freedom are effectively frozen, the equations reproduce the behavior of monatomic gases. Thereafter, boundary conditions for the proposed macroscopic model are introduced. The unsteady heat conduction of a gas at rest and steady Couette flow are studied numerically and analytically as examples of boundary value problems. The results for different gases are given and effects of Knudsen numbers, degrees of freedom, accommodation coefficients and temperature dependent properties are investigated. For some cases, the higher order effects are very dominant and the widely used first order set of the Navier Stokes Fourier equations fails to accurately capture the gas behavior and should be replaced by a higher order set of equations. Graduate 0346, 0791, 0548, 0759 behnamr@uvic.ca

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Zhang, Ju Goldstein David B. Varghese Philip L. "Simulation of gas dynamics, radiation and particulates in volcanic plumes on Io." 2004. http://repositories.lib.utexas.edu/bitstream/handle/2152/2103/zhangj042.pdf.

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Su, Cheng-Chin, and 蘇正勤. "Parallel Direct Simulation Monte Carlo (DSMC) Methods for Modeling Rarefied Gas Dynamics." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/76866430894334062848.

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博士 國立交通大學 機械工程系所 101 Rarefied gas dynamics has played an important role in various research disciplines, which include hypersonic fluid dynamics, vacuum pump technology, low-pressure semiconductor related materials processing, and micro- and nano-scale gas dynamics, to name a few. The Boltzmann equation that governs rarefied gas dynamics is generally very difficult to solve. The particle-based method, the direct simulation Monte Carlo (DSMC) method, has been considered as the most efficient and accurate numerical method for solving the Boltzmann equation statistically, as long as the number of simulation particle is large enough. However, its computational expense is generally very high, especially in the transitional and near-continuum flow regimes. Thus, parallel processing of the DSMC method to reduce the computational time is necessary for an efficient application of the method in general rarefied gas dynamics. In this thesis, two major categories of parallel processing for the DSMC method are presented. These include a new parallel 2D/3D DSMC code with an unstructured grid using message passing interface (MPI) and a parallel 2D DSMC code with a structured grid using hybrid MPI-CUDA (CUDA: Compute Unified Device Architecture), which are described briefly next. In the first part of the thesis, a new general-purpose parallel 2D/3D DSMC (named PDSC++, hereafter) based on the C++ language using a 2-D or 3-D hybrid unstructured grid was developed and validated. Several key features of the PDSC++ code are presented and discussed in the thesis, including a variable time-step (VTS) scheme, a transient adaptive sub-cell (TAS) method, and parallel processing of the DSMC method. For the VTS scheme, the simulation time step, which is proportional to the weight of simulation particles, varies in each cell based on local mean free path. This leads to an efficient particle tracing algorithm on an unstructured grid, which enforces conservation of mass, momentum and energy. This results in great reduction of total simulation particles as compared to the constant time-step scheme. For the TAS method, a dynamically adaptive number of sub-cells, based on the local mean free path or number of simulation particles, is imposed in each cell to ensure the average collision distance is less than the local mean free path. The results show that this TAS method coupled with the VTS scheme results in great reduction of computational time of DSMC while maintaining very high quality of collision between particles. For the parallel processing of DSMC method, a simple and efficient method which is termed as domain re-decomposition (DRD) method is presented to improve the parallel performance of parallel DSMC simulation without resorting to dynamic domain decomposition. The results indicate that up to 123-135 times of speedup can be reached using 192 processors for the large scale problems which is performed at the ALPS cluster of the National Center for High-Performance Computing (NCHC), Taiwan. In addition, we also have demonstrated the powerful capability of the PDSC++ code by simulating a three-dimensional problem with one billion simulation particles using 768 cores of ALPS. In the second part of the thesis, the development of the two-dimensional direct simulation Monte Carlo (DSMC) code using an MPI-CUDA parallelization paradigm on Graphics Processing Units (GPUs) clusters, named PDSC-MG, is presented. An all-device (i.e. GPU) computational approach is adopted where the entire computation is performed on the GPU device, leaving the CPU idle during all stages of the computation, including particle moving, indexing, particle collisions and state sampling. Communication between the GPU (device) and the CPU (host) is only performed to enable multiple-GPU computation by Message Passing Interface (MPI) protocol. In this method, the MPI protocol is used to distributed/gather data into/from memory of different MPI-processors and communication between all MPI-processors (CPU). GPU is used to accelerate the DSMC-related simulation components by the Compute Unified Device Architecture (CUDA) which is one of the General Purpose computing on Graphics Processing Units (GPGPU). Results show that the computational expense can be reduced by 16 and 185 times when using a single GPU and 16 GPUs (NVIDIA Tesla M2070), respectively when compared to a single core of CPU (Intel Xeon X5670). The demonstrated parallel efficiency is 75% when using 16 GPUs as compared to a single GPU for simulations using 30 million simulated particles. Finally, several very large-scale simulations in the near-continuum regime are employed to demonstrate the excellent capability of the current parallel DSMC method. Results show that approximately 21.81 hours are required for 120,000 simulation time steps with approximately 255 million particles and 6.4 million cells using 16 GPU devices (NVIDIA Tesla M2070). At the end of the thesis, major findings are summarized and directions of future work are outlined.

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Mohammadzadeh, Alireza. "Moment method in rarefied gas dynamics: applications to heat transfer in solids and gas-surface interactions." Thesis, 2016. http://hdl.handle.net/1828/7626.

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It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier’s law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the It is well established that rarefied flows cannot be properly described by traditional hydrodynamics, namely the Navier-Stokes equations for gas flows, and the Fourier's law for heat transfer. Considering the significant advancement in miniaturization of electronic devices, where dimensions become comparable with the mean free path of the flow, the study of rarefied flows is extremely important. This dissertation includes two main parts. First, we look into the heat transport in solids when the mean free path for phonons are comparable with the length scale of the flow. A set of macroscopic moment equations for heat transport in solids are derived to extend the validity of Fourier's law beyond the hydrodynamics regime. These equations are derived such that they remain valid at room temperature, where the MEMS devices usually work. The system of moment equations for heat transport is then employed to model the thermal grating experiment, recently conducted on a silicon wafer. It turns out that at room temperature, where the experiment was conducted, phonons with high mean free path significantly contribute to the heat transport. These low frequency phonons are not considered in the classical theory, which leads to failure of the Fourier's law in describing the thermal grating experiment. In contrast, the system of moment equations successfully predict the deviation from the classical theory in the experiment, and suggest the importance of considering both low and high frequency phonons at room temperature to capture the experimental results. In the second part of this study, we look into the gas-surface interactions for conventional gas dynamics when the gas flow is rarefied. An extension to the well-known Maxwell boundary conditions for gas-surface interactions are obtained by considering velocity dependency in the reflection kernel from the surface. This extension improves the Maxwell boundary conditions by providing an extra free parameter that can be fitted to the experimental data for thermal transpiration effect in non-equilibrium flows. The velocity dependent Maxwell boundary conditions are derived for the Direct Simulation Monte Carlo (DSMC) method and the regularized 13-moment (R13) equations for conventional gas dynamics. Then, a thermal cavity is considered to test and study the effect of these boundary conditions on the flow formation in the slip and early transition regime. It turns out that using velocity dependent boundary conditions allows us to change the size and direction of the thermal transpiration force, which leads to marked changes in the balance of transpiration forces and thermal stresses in the flow. Graduate

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Lee, Wei-Lung, and 李威龍. "From Continuum Fluid to Rarefied Gas Dynamics Analysis of Blunt Bodies at Hypersonic Flights." Thesis, 1994. http://ndltd.ncl.edu.tw/handle/44199177276599216406.

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碩士 國立中央大學 機械工程研究所 82 Currently there is a renewed interest in the aerothermodynamics of external flows about vehicles at very high altitudes. The main factors are the development of the space transportation system and the orbital transfer vehicles. It is the purpose of this paper to conduct numerical experiments for the hypersonic flow around two diifferent shaped blunt bodies, rectangular shaped and rounded shaped blunt bodies. The general flowfield information, Mach number, pressure, density and tempature distributions were calculated by using the continuum flow approach and the molecular gas dynamics approach respectively. The MacCormack implicit method and DSMC method are used. The change of flow properties through shock and the effects of rare faction under different Knudsen number will also be investigated in the proposal.

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30

Zhang, Ju. "Simulation of gas dynamics, radiation and particulates in volcanic plumes on Io." Thesis, 2004. http://hdl.handle.net/2152/2103.

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Taheri, Bonab Peyman. "Macroscopic description of rarefied gas flows in the transition regime." Thesis, 2010. http://hdl.handle.net/1828/3018.

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The fast-paced growth in microelectromechanical systems (MEMS), microfluidic fabrication, porous media applications, biomedical assemblies, space propulsion, and vacuum technology demands accurate and practical transport equations for rarefied gas flows. It is well-known that in rarefied situations, due to strong deviations from the continuum regime, traditional fluid models such as Navier-Stokes-Fourier (NSF) fail. The shortcoming of continuum models is rooted in nonequilibrium behavior of gas particles in miniaturized and/or low-pressure devices, where the Knudsen number (Kn) is sufficiently large. Since kinetic solutions are computationally very expensive, there has been a great desire to develop macroscopic transport equations for dilute gas flows, and as a result, several sets of extended equations are proposed for gas flow in nonequilibrium states. However, applications of many of these extended equations are limited due to their instabilities and/or the absence of suitable boundary conditions. In this work, we concentrate on regularized 13-moment (R13) equations, which are a set of macroscopic transport equations for flows in the transition regime, i.e., Kn≤1. The R13 system provides a stable set of equations in Super-Burnett order, with a great potential to be a powerful CFD tool for rarefied flow simulations at moderate Knudsen numbers. The goal of this research is to implement the R13 equations for problems of practical interest in arbitrary geometries. This is done by transformation of the R13 equations and boundary conditions into general curvilinear coordinate systems. Next steps include adaptation of the transformed equations in order to solve some of the popular test cases, i.e., shear-driven, force-driven, and temperature-driven flows in both planar and curved flow passages. It is shown that inexpensive analytical solutions of the R13 equations for the considered problems are comparable to expensive numerical solutions of the Boltzmann equation. The new results present a wide range of linear and nonlinear rarefaction effects which alter the classical flow patterns both in the bulk and near boundary regions. Among these, multiple Knudsen boundary layers (mechanocaloric heat flows) and their influence on mass and energy transfer must be highlighted. Furthermore, the phenomenon of temperature dip and Knudsen paradox in Poiseuille flow; Onsager's reciprocity relation, two-way flow pattern, and thermomolecular pressure difference in simultaneous Poiseuille and transpiration flows are described theoretically. Through comparisons it is shown that for Knudsen numbers up to 0.5 the compact R13 solutions exhibit a good agreement with expensive solutions of the Boltzmann equation.

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Beckmann, Alexander Felix. "Modeling evaporation in the rarefied gas regime by using macroscopic transport equations." Thesis, 2018. https://dspace.library.uvic.ca//handle/1828/9238.

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Due to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work. Graduate

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Das, Shankhadeep. "Fluid-structure interactions in microstructures." 2013. http://hdl.handle.net/2152/21611.

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Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches. These devices typically consist of a metallic membrane which is activated by a time-periodic electrostatic force and makes periodic contact with a contact pad. The increase in switch capacitance at contact causes the RF signal to be deflected and the switch thus closes. Membrane motion is damped by the surrounding gas, typically air or nitrogen. As the switch opens and closes, the flow transitions between the continuum and rarefied regimes. Furthermore, creep is a critical physical mechanism responsible for the failure in these devices, especially those operating at high RF power. Simultaneous and accurate modeling of all these different physics is required to understand the dynamical membrane response in these devices and to estimate device lifetime and to improve MEMS reliability. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this work, we develop a single unified finite volume method based numerical framework to study this multi-physics problem in RF MEMS. Our objective required us to develop structural solvers, fluid flow solvers, and electrostatic solvers using the finite volume method, and efficient mechanisms to couple these different solvers. A particular focus is the development of flow solvers which work efficiently across continuum and rarefied regimes. A number of novel contributions have been made in this process. Structural solvers based on a fully implicit finite volume method have been developed for the first time. Furthermore, strongly implicit fluid flow solvers have also been developed that are valid for both continuum and rarefied flow regimes and which show an order of magnitude speed-up over conventional algorithms on serial platforms. On parallel platforms, the solution techniques developed in this thesis are shown to be significantly more scalable than existing algorithms. The numerical methods developed are used to compute the static and dynamic response of MEMS. Our results indicate that our numerical framework can become a computationally efficient tool to model the dynamics of RF MEMS switches under electrostatic actuation and gas damping. text

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Benkreira, Hadj, and J. Bruce Ikin. "Slot Coating Minimum Film Thickness in Air and in Rarefied Helium." 2016. http://hdl.handle.net/10454/8260.

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Yes This study assesses experimentally the role of gas viscosity in controlling the minimum film thickness in slot coating in both the slot over roll and tensioned web modes. The minimum film thickness here is defined with respect to the onset of air entrainment rather than rivulets, the reason being that rivulets are an extreme form of instabilities occurring at much higher speeds. The gas viscosity effects are simulated experimentally by encasing the coaters in a sealed gas chamber in which various gases can be admitted. An appropriate choice of two gases was used to compare performances: air at atmospheric pressure and helium at sub-ambient pressure (25mbar), which we establish has a significantly lower “thin film” viscosity than atmospheric air. A capacitance sensor was used to continuously measure the film thickness on the web, which was ramped up in speed at a fixed acceleration whilst visualizations of the film stability were recorded through a viewing port in the chamber. The data collected show clearly that by coating in rarefied helium rather that atmospheric air we can reduce the minimum film thickness or air/gas entrainment low-flow limit. We attribute this widening of the stable coating window to the enhancement of dynamic wetting that results when the thin film gas viscosity is reduced. These results have evident practical significance for slot coating, the coating method of choice in many new technological applications, but it is their fundamental merit which is new and one that should be followed with further data and theoretical underpinning.

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Molda, Vojtěch. "Simulace proudění multiclonou pomocí Boltzmannovy kinetické rovnice." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313950.

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An attempt to numerically predict flow rate of experimental configuration of orifices in transition between molecular and viscous flow regime is described in detail. Discretization of Boltzmann kinetic equation known as lattice-Boltzmann method is derived and applied unfortunately with very little connection to the original experimental problem due to nearly supersonic nature of the experimental setup. Current quite unsatisfactory state of the art of compressible lattice-Boltzmann method is also presented.

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Dissertations / Theses on the topic 'Rarefied gas dynamics'

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