京都大学 / 新制・課程博士 / 博士(工学) / 甲第24611号 / 工博第5117号 / 新制||工||1978(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 大和田 拓, 教授 髙田 滋, 講師 杉元 宏 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

A new discrete velocity scheme for solving the Boltzmann equation has been implemented for homogeneous relaxation and one-dimensional problems. Directly solving the Boltzmann equation is computationally expensive because in addition to working in physical space, the nonlinear collision integral must also be evaluated in a velocity space. To best solve the collision integral, collisions between each point in velocity space with all other points in velocity space must be considered, but this is very expensive. Motivated by the Direct Simulation Monte Carlo (DSMC) method, the computational costs in the present method are reduced by randomly sampling a set of collision partners for each point in velocity space. A collision partner selection algorithm was implemented to favor collision partners that contribute more to the collision integral. The new scheme has a built in flexibility, where the resolution in approximating the collision integral can be adjusted by changing how many collision partners are sampled. The computational cost associated with evaluation of the collision integral is compared to the corresponding statistical error. Having a fixed set of velocities can artificially limit the collision outcomes by restricting post collision velocities to those that satisfy the conservation equations and lie precisely on the grid. A new velocity interpolation algorithm enables us to map velocities that do not lie on the grid to nearby grid points while preserving mass, momentum, and energy. This allows for arbitrary post-collision velocities that lie between grid points or completely outside of the velocity space to be projected back onto the nearby grid points. The present scheme is applied to homogeneous relaxation of the non-equilibrium Bobylev Krook-Wu distribution, and the numerical results agree well with the analytic solution. After verifying the proposed method for spatially homogeneous relaxation problems, the scheme was then used to solve a 1D traveling shock. The jump conditions across the shock match the Rankine-Hugoniot jump conditions. The internal shock wave structure was then compared to DSMC solutions, and good agreement was found for Mach numbers ranging from 1.2 to 6. Since a coarse velocity discretization is required for efficient calculation, the effects of different velocity grid resolutions are examined. Although using a relatively coarse approximation for the collision integral is computationally efficient, statistical noise pollutes the solution. The effects of using coarse and fine approximations for the collision integral are examined and it is found that by coarsely evaluating the collision integral, the computational time can be reduced by nearly two orders of magnitude while retaining relatively smooth macroscopic properties. / text

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Yoshiaki Kuwano. / M.S.

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.

The macroscopic chemistry method for modelling non-equilibrium reacting gas flows with the direct simulation Monte Carlo (DSMC) method is developed and tested. In the macroscopic method, the calculation of chemical reactions is decoupled from the DSMC collision routine. The number of reaction events that must be performed in a cell is calculated with macroscopic rate expressions. These expressions use local macroscopic information such as kinetic temperatures and density. The macroscopic method is applied to a symmetrical diatomic gas. For each dissociation event, a single diatom is selected with a probability based on internal energy and is dissociated into two atoms. For each recombination event, two atoms are selected at random and replaced by a single diatom. To account for the dissociation energy, the thermal energies of all particles in the cell are adjusted. The macroscopic method differs from conventional collision-based DSMC chemistry procedures, where reactions are performed as an integral part of the collision routine. The most important advantage offered by the macroscopic method is that it can utilise reaction rates that are any function of the macroscopic flow conditions. It therefore allows DSMC chemistry calculations to be performed using rate expressions for which no conventional chemistry model may exist. Given the accuracy and flexibility of the macroscopic method, it has significant potential for modelling reacting non-equilibrium gas flows. The macroscopic method is tested by performing DSMC calculations and comparing the results to those obtained using conventional DSMC chemistry models and experimental data. The macroscopic method gives density profiles in good agreement with experimental data in the chemical relaxation region downstream of a strong shock. Within the shock where strongly non-equilibrium conditions prevail, the macroscopic method provides good agreement with a conventional chemistry model. For the flow over a blunt axisymmetric cylinder, which also exhibits strongly non-equilibrium conditions, the macroscopic method also gives reasonable agreement with conventional chemistry models. The ability of the macroscopic method to utilise any rate expression is demonstrated by using a two-temperature rate model that accounts for dissociation-vibration coupling effects that are important in non-equilibrium reacting flows. Relative to the case without dissociation-vibration coupling, the macroscopic method with the two-temperature model gives reduced dissociation rates in vibrationally cold flows, as expected. Also, for the blunt cylinder flow, the two-temperature model gives reduced surface heat fluxes, as expected. The macroscopic method is also tested with a number density dependent form of the equilibrium constant. For zero-dimensional chemical relaxation, the resulting relaxation histories are in good agreement with those provided by an exact Runge-Kutta solution of the relaxation behaviour. Reviews of basic DSMC procedures and conventional DSMC chemistry models are also given. A method for obtaining the variable hard sphere parameters for collisions between particles of different species is given. Borgnakke-Larsen schemes for modelling internal energy exchange are examined in detail. Both continuous rotational and quantised vibrational energy modes are considered. Detailed derivations of viscosity and collision rate expressions for the generalised hard sphere model of Hassan and Hash [Phys. Fluids 5, 738 (1993)] and the modified version of Macrossan and Lilley [J. Thermophys. Heat Transfer 17, 289 (2003)] are also given.

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.

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

The macroscopic chemistry method for modelling non-equilibrium reacting gas flows with the direct simulation Monte Carlo (DSMC) method is developed and tested. In the macroscopic method, the calculation of chemical reactions is decoupled from the DSMC collision routine. The number of reaction events that must be performed in a cell is calculated with macroscopic rate expressions. These expressions use local macroscopic information such as kinetic temperatures and density. The macroscopic method is applied to a symmetrical diatomic gas. For each dissociation event, a single diatom is selected with a probability based on internal energy and is dissociated into two atoms. For each recombination event, two atoms are selected at random and replaced by a single diatom. To account for the dissociation energy, the thermal energies of all particles in the cell are adjusted. The macroscopic method differs from conventional collision-based DSMC chemistry procedures, where reactions are performed as an integral part of the collision routine. The most important advantage offered by the macroscopic method is that it can utilise reaction rates that are any function of the macroscopic flow conditions. It therefore allows DSMC chemistry calculations to be performed using rate expressions for which no conventional chemistry model may exist. Given the accuracy and flexibility of the macroscopic method, it has significant potential for modelling reacting non-equilibrium gas flows. The macroscopic method is tested by performing DSMC calculations and comparing the results to those obtained using conventional DSMC chemistry models and experimental data. The macroscopic method gives density profiles in good agreement with experimental data in the chemical relaxation region downstream of a strong shock. Within the shock where strongly non-equilibrium conditions prevail, the macroscopic method provides good agreement with a conventional chemistry model. For the flow over a blunt axisymmetric cylinder, which also exhibits strongly non-equilibrium conditions, the macroscopic method also gives reasonable agreement with conventional chemistry models. The ability of the macroscopic method to utilise any rate expression is demonstrated by using a two-temperature rate model that accounts for dissociation-vibration coupling effects that are important in non-equilibrium reacting flows. Relative to the case without dissociation-vibration coupling, the macroscopic method with the two-temperature model gives reduced dissociation rates in vibrationally cold flows, as expected. Also, for the blunt cylinder flow, the two-temperature model gives reduced surface heat fluxes, as expected. The macroscopic method is also tested with a number density dependent form of the equilibrium constant. For zero-dimensional chemical relaxation, the resulting relaxation histories are in good agreement with those provided by an exact Runge-Kutta solution of the relaxation behaviour. Reviews of basic DSMC procedures and conventional DSMC chemistry models are also given. A method for obtaining the variable hard sphere parameters for collisions between particles of different species is given. Borgnakke-Larsen schemes for modelling internal energy exchange are examined in detail. Both continuous rotational and quantised vibrational energy modes are considered. Detailed derivations of viscosity and collision rate expressions for the generalised hard sphere model of Hassan and Hash [Phys. Fluids 5, 738 (1993)] and the modified version of Macrossan and Lilley [J. Thermophys. Heat Transfer 17, 289 (2003)] are also given.

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.

The macroscopic chemistry method for modelling non-equilibrium reacting gas flows with the direct simulation Monte Carlo (DSMC) method is developed and tested. In the macroscopic method, the calculation of chemical reactions is decoupled from the DSMC collision routine. The number of reaction events that must be performed in a cell is calculated with macroscopic rate expressions. These expressions use local macroscopic information such as kinetic temperatures and density. The macroscopic method is applied to a symmetrical diatomic gas. For each dissociation event, a single diatom is selected with a probability based on internal energy and is dissociated into two atoms. For each recombination event, two atoms are selected at random and replaced by a single diatom. To account for the dissociation energy, the thermal energies of all particles in the cell are adjusted. The macroscopic method differs from conventional collision-based DSMC chemistry procedures, where reactions are performed as an integral part of the collision routine. The most important advantage offered by the macroscopic method is that it can utilise reaction rates that are any function of the macroscopic flow conditions. It therefore allows DSMC chemistry calculations to be performed using rate expressions for which no conventional chemistry model may exist. Given the accuracy and flexibility of the macroscopic method, it has significant potential for modelling reacting non-equilibrium gas flows. The macroscopic method is tested by performing DSMC calculations and comparing the results to those obtained using conventional DSMC chemistry models and experimental data. The macroscopic method gives density profiles in good agreement with experimental data in the chemical relaxation region downstream of a strong shock. Within the shock where strongly non-equilibrium conditions prevail, the macroscopic method provides good agreement with a conventional chemistry model. For the flow over a blunt axisymmetric cylinder, which also exhibits strongly non-equilibrium conditions, the macroscopic method also gives reasonable agreement with conventional chemistry models. The ability of the macroscopic method to utilise any rate expression is demonstrated by using a two-temperature rate model that accounts for dissociation-vibration coupling effects that are important in non-equilibrium reacting flows. Relative to the case without dissociation-vibration coupling, the macroscopic method with the two-temperature model gives reduced dissociation rates in vibrationally cold flows, as expected. Also, for the blunt cylinder flow, the two-temperature model gives reduced surface heat fluxes, as expected. The macroscopic method is also tested with a number density dependent form of the equilibrium constant. For zero-dimensional chemical relaxation, the resulting relaxation histories are in good agreement with those provided by an exact Runge-Kutta solution of the relaxation behaviour. Reviews of basic DSMC procedures and conventional DSMC chemistry models are also given. A method for obtaining the variable hard sphere parameters for collisions between particles of different species is given. Borgnakke-Larsen schemes for modelling internal energy exchange are examined in detail. Both continuous rotational and quantised vibrational energy modes are considered. Detailed derivations of viscosity and collision rate expressions for the generalised hard sphere model of Hassan and Hash [Phys. Fluids 5, 738 (1993)] and the modified version of Macrossan and Lilley [J. Thermophys. Heat Transfer 17, 289 (2003)] are also given.