<div> Large thermal gradients can cause very nonintuitive effects in the flowfield, as flow motion and even a force (often referred to as a Knudsen thermal force) can be induced even with a freestream velocity of zero. These flows can be exploited on the microscale, where temperature gradients of 10E6K/m are achievable. These flows have been studied experimentally many times, and it has been shown that Knudsen forces have a bimodal relationship with pressure, where the peak is in the transitional flow regime. It has also been shown that these thermal gradients cause thermal diffusion, or species separation in a mixture.</div><div> </div><div> A MEMS based device called the Microscale In-Plane Knudsen Radiometric Actuator (MIKRA) was developed to use Knudsen forces to calculate pressure and gas composition. The direct simulation Monte Carlo (DSMC) method was used to analyze the device to calculate the device forces and calculate the flowfield. DSMC proved to be a reliable method of simulating these types of flows, as the force results agreed well with experiments, and the DSMC results matched the results of other numerical methods.</div><div> </div><div> N2 and H2O mixtures were also simulated, and it was shown that the force is sensitive to the composition. At the same pressure, the force is larger for mixtures dominated by N2. Heat flux is also larger for N2 dominated flows.</div>

The focus of this work is to present in detail the implementation of a three dimensional direct simulation Monte Carlo methodology on unstructured Delaunay meshes (U-DSMC). The validation and verification of the implementation are shown using a series of fundamental flow cases. The numerical error associated with the implementation is also studied using a fundamental flow configuration. Gas expansion from microtubes is studied using the U-DSMC code for tube diameters ranging from 100Æ’ÃÂ�m down to 100nm. Simulations are carried out for a range of inlet Knudsen numbers and the effect of aspect ratio and inlet Reynolds number on the plume structure is investigated. The effect of scaling the geometry is also examined. Gas expansion from a conical nozzle is studied using the U-DSMC code for throat diameters ranging from 250 Æ’ÃÂ�m down to 250 nm. Simulations are carried out for a range of inlet Knudsen numbers and the effect of inlet speed ratio and inlet Reynolds number on the plume structure is investigated. The effect of scaling the geometry is examined. Results of a numerical study using the U-DSMC code are employed to guide the design of a micropitot probe intended for use in analyzing rarefied gaseous microjet flow. The flow conditions considered correspond to anticipated experimental test cases for a probe that is currently under development. The expansion of nitrogen from an orifice with a diameter of 100Æ’ÃÂ�m is modeled using U-DSMC. From these results, local ¡¥free stream¡¦ conditions are obtained for use in U-DSMC simulations of the flow in the vicinity of the micropitot probe. Predictions of the pressure within the probe are made for a number of locations in the orifice plume. The predictions from the U-DSMC simulations are used for evaluating the geometrical design of the probe as well as aiding in pressure sensor selection. The effect of scale on the statistical fluctuation of the U-DSMC data is studied using Poiseuille flow. The error in the predicted velocity profile is calculated with respect to both first and second-order slip formulations. Simulations are carried out for a range of channel heights and the error between the U-DSMC predictions and theory are calculated for each case. From this error, a functional dependence is shown between the scale-induced statistical fluctuations and the decreasing channel height.

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.

Io, the innermost Galilean satellite of Jupiter, exhibits a wide variety of complex phenomena such as interaction with Jupiter’s magnetosphere, volcanic activity, and a rarefied multi-species sublimating and condensing atmosphere with an ionosphere. Io’s orbital resonance with Jupiter and the other Galilean satellites produces intense tidal heating. This makes Io the most volcanically active body in the solar system with plumes that rise hundreds of kilometers above the surface. In the present work, the interaction of Io’s atmosphere with the Jovian plasma torus is simulated via the Direct Simulation Monte Carlo (DSMC) method and the aurora produced via electron-neutral excitation collisions is examined using electron transport Monte Carlo simulation. The electron-transport Monte Carlo simulation models the electron collisions with the neutral atmosphere and their transport along field lines as they sweep past Io, using a pre-computed steady atmosphere and magnetic field. As input to the Monte Carlo simulation, the neutral atmosphere was first modeled using prior 2D sunlit continuum simulations of Io’s atmosphere produced by others. In order to justify the use of a sunlit atmosphere for eclipse, 1D two-species (SO2 and a non-condensable) DSMC simulations of Io’s atmospheric dynamics during and immediately after eclipse were performed. It was found that the inclusion of a non-condensable species (SO or O2) leads to the formation of a diffusion layer which prevents rapid collapse. The degree to which the diffusion layer slowed the atmospheric collapse was found to be extremely sensitive to both the initial non-condensable mole fraction and the reaction (or sticking) probability on the surface of the “non-condensable”. Furthermore, upon egress, vertical stratification of the atmosphere occurred with the non-condensable species being lifted to higher altitudes by the rapid sublimation of SO2 as the surface warms. Simulated aurorae (specifically the [OI] 6300 Å and the S2, SO, and SO2 molecular band emission in the middle ultraviolet) show good agreement with observations of Io in eclipse and an attempt was made to use the simulations to constrain the upstream torus electron temperature and Io’s atmospheric composition, structure, and volcanic activity. It is found that the position of the bright [OI] 6300 Å wake spot relative to Io’s equator depends on the position of Io relative to the plasma torus’ equator and the asymmetric electron number flux that results. Using HST/STIS UV-Vis spectra, the upstream electron temperature is weakly constrained to be between 3 eV and 8 eV depending on the flux of a low energy (35 eV), non-thermal component of the plasma (more non-thermal flux requires lower thermal plasma temperatures to fit the spectrum). Furthermore, an upper limit of 5% of the thermal torus density (or 180 cm−3 based on the Galileo J0 plasma density at Io) is obtained for the low energy non-thermal component of the plasma. These limits are consistent with Galileo observations of the upstream torus temperature and estimates for the the non-thermal component. Finally, plume activity and S2 content during eclipse observations with HST/STIS were constrained by examining the emission intensity along the spatial axis of the aperture. During the August 1999 UV-Vis observations, the auroral simulations indicate that the large volcanoes Pele and Surt were inactive whereas Tvashtar was active and that Dazhbog and possibly Loki were also actively venting gas. The S2 content inferred for the large Pele-type plumes was between 5% (Tvashtar) and 30% (Loki, if active), consistent with prior observations (Spencer et al., 2000; Jessup et al., 2007). A 3D DSMC simulation of Io’s sublimation and sputtered atmosphere including photo- and plasma-chemistry was developed. In future work these atmospheric simulations will replace the continuum target atmosphere in the auroral model and thus enable a better match to the observed high altitude auroral emission. In the present work, the plasma interaction is modeled by a flux of ions and electrons which flow around and through Io’s atmosphere along pre-computed fields and interact with the neutral gas. A 3D DSMC simulation of Io’s atmosphere assuming a simple thermal model for the surface just prior to ingress into eclipse and uniform frost coverage has been performed in order to understand how Io’s general atmospheric dynamics are affected by the new plasma model with chemistry and sputtering. Sputtering was found to supply most of the nightside atmosphere (producing an SO2 column of ~5×1013 cm−2); however, the dense dayside sublimation atmosphere was found to block sputtering of the surface. The influence of the dynamic plasma pressure on the day-to-night circumplanetary flow was found to be quite substantial causing the day-to-night wind across the dawn terminator to flow slightly towards the equator. This results in a region of high density near the equator that extends far (~2000 km for the condensable species) onto the nightside across the dawn terminator. Thus, even without thermal lag due to rotation or variable surface frost, highly asymmetric equatorial column densities relative to the subsolar point are obtained. The non-condensable O2, which is a trace species on the dayside, is the dominant species on the nightside despite increased SO2 sputtering because the loss rate of O2 is slow. Finally, a very intriguing O2 flow feature was observed near the dusk terminator where the flow from the leading hemisphere (pushed by the plasma) meets the flow from the dayside trailing hemisphere. Since the O2 does not condense on the surface, it slowly convects towards the poles and then back onto the nightside, eventually to be dissociated or stripped away by the plasma. / 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.

La source d'ions des injecteurs de neutres d'ITER devra produire un fort courant d'ions négatifs de deutérium qui seront accélérés puis neutralisés afin d'obtenir un faisceau d'atomes qui chauffera le plasma thermonucléaire. Un plasma froid d'hydrogène à basse pression et forte puissance est généré par induction dans la source et les ions négatifs sont produits par des réactions en volume et en surface et extraits à travers une série de grilles électrostatiques. Cette thèse est consacrée à la modélisation de ce plasma, afin d'étudier des phénomènes peu abordés à ce jour : aspect hors équilibre des espèces neutres, déplétion et chauffage du gaz, génération et transport des atomes, et génération des ions négatifs sur les parois. Un code fluide bidimensionnel de simulation plasma a pour cela été modifié afin de simuler la cinétique des espèces neutres au moyen d'un module Direct Simulation Monte-Carlo et a été utilisé pour simuler le plasma de manière auto-cohérente. / The ion source of the ITER neutral beam injectors will have to deliver a high current of negative deuterium ions which will be accelerated and neutralized, and the resulting atom beam will heat the thermonuclear plasma. A low pressure and high power cold hydrogen plasma is inductively generated in the source and negative ions are produced by volume and surface reactions and are extracted through a set of electrostatic grids. This thesis aims at modelling this plasma, and focuses on topics that haven't been studied much before : out of equilibrium neutral kinetics, gas heating and depletion, atoms production and transport, and negative ions generation on the walls. To this end, a two-dimensional fluid plasma code has been modified to simulate the neutrals kinetics with a Direct Simulation Monte Carlo module and has been used to perform self-consistent simulations of the plasma.

Made available in DSpace on 2014-06-11T19:22:36Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-06-11Bitstream added on 2014-06-13T20:09:52Z : No. of bitstreams: 1 damazo_ga_me_ilha.pdf: 760851 bytes, checksum: d1a0f2a22e4917da6787ce545199a696 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O enfoque principal do trabalho foi dado ao Controle Discreto com Modos Deslizantes(CDMD) aplicado em sistemas que possuem atraso no processamento do sinal de controle e acesso somente à saída do sistema. A estratégia de controle tem por objetivo a utilização de técnicas de controle com modos deslizantes para a elaboração de uma lei de controle simples e robusta às incertezas da planta e ao atraso. O observador de estados apresentado possui características de modo deslizante, o qual realiza a estimação robusta do vetor de estados que na maioria dos casos práticos não é totalmente acessível. Os métodos de projetos propostos podem ser aplicados no controle de plantas estáveis ou instáveis com atraso no sinal de controle e acesso somente à saída da planta. Para comprovar a eficiência dos projetos apresentados neste trabalho, analisou-se o controlador atuando com acesso a todos estados e o controlador atuando juntamente com o observador robusto para a estimação dos estados. Os resultados foram obtidos através de simulações no Sistema Bola e Viga, Sistema Pêndulo Invertido Linear e Sistema Pêndulo Invertido Rotacional que são exemplos de plantas de natureza instável. / The main focus was placed on the Discrete Sliding Mode Control (DSMC) applied to systems that have a delay in the processing of the control signal and access to the system output only. The control strategy is intended to use control techniques of sliding modes to elaborate a simple and robust control law against the uncertainties of the plant and the delay. The states observer presented has the characteristics of a sliding mode, which performs the robust estimation of the states vector that, in most practical cases, is not fully accessible. The design methods proposed may be applied to the control of stable or unstable plants with delay on the control signal and access to the plant output only. In order to attest the efficiency of the design presented in this work, the controller was analyzed at work with access to all states and jointly with the robust observer to estimate the states. The results were obtained by means of simulations in the Ball and Beam System, Linear Inverted Pendulum System, and Rotational Inverted Pendulum System, which are examples of plants of unstable nature.