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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

When a lander approaches a dusty surface, the plume from the descent engine impinges on the ground and entrains loose regolith into a high velocity spray. This problem exhibits a wide variety of complex phenomena such as highly under-expanded plume impingement, transition from continuum to free molecular flow, erosion, coupled gas-dust motions, and granular collisions for a polydisperse distribution of aerosolized particles. The focus of this work is to identify and model the important physical phenomena and to characterize the dust motion that would result during typical lunar landings. A hybrid continuum-kinetic solver is used, but most of the complex physics are simulated using the direct simulation Monte Carlo method. A descent engine of comparable size and thrust to the Lunar Module Descent Engine is simulated because it allows for direct comparison to Apollo observations. Steady axisymmetric impingement was first studied for different thrust engines and different hovering altitudes. The erosion profiles are obtained from empirically derived scaling relationships and calibrated to closely match the net erosion observed during the Apollo missions. Once entrained, the dust motion is strongly influenced by particle-particle collisions and the collision elasticity. The effects of two-way coupling between the dust and gas motions are also studied. Small particles less than 1 µm in diameter are accelerated to speeds that exceed 1000 m/s. The larger particles have more inertia and are accelerated to slower speeds, approximately 350 m/s for 11 µm grains, but all particle sizes tend obtain their maximum speed within approximately 40 m from the lander. The maximum particle speeds and erosion rates tend to increase as the lander approaches the lunar surface. The erosion rates scale linearly with engine thrust and the maximum particle speed increases for higher thrust engines. Dust particles are able to travel very far from the lander because there is no background atmosphere on the moon to inhibit their motion. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20 m to 3 m. Larger particles are accelerated to slower speeds and are deposited closer to the lander than smaller particles. Many of the gas molecules exceed lunar escape speed, but some gas molecules become trapped within the dust cloud and remain on the moon. The high velocity particulate sprays can be damaging to nearby structures, such as a lunar outpost. One way of mitigating this damage is to use a berm or fence to shield nearby structures from the dust spray. This work attempts to predict the effectiveness of such a fence. The effects of fence height, placement, and angle as well as the model sensitivity to the fence restitution coefficient are discussed. The expected forces exerted on fences placed at various locations are computed. The pressure forces were found to be relatively small at fences placed at practical distances from the landing site. The trajectories of particles that narrowly avoid the fence were not significantly altered by the fence, suggesting that the dust motion is weakly coupled to the gas in the near vicinity of the fence. Future landers may use multi-engine configurations that can form 3-dimensional gas and dust flows. There are multiple plume-plume and plume-surface interactions that affect the erosion rates and directionality of the dust sprays. A 4-engine configuration is simulated in this work for different hovering altitudes. The focusing of dust along certain trajectories depends on the lander hovering altitude, where at lower altitudes the dust particles focus along symmetry planes while at higher altitudes the sprays are more uniform. The surface erosion and trenching behavior for a 4-engine lander are also discussed. / text

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this paper, we present numerical results for macroscopic quantities of interest (velocity profile, the heat ow profile and shear stress) for the ow of a binary mixture of rarefied gases in microchannels of arbitrary planes, defined by two infinite parallel lates without symmetry condition. The ow of gas mixture is due to a constant pressure gradient (Poiseuille's Problem), a temperature gradient (Problem Thermal-Creep) and a density gradient (Fuzzy Problem) in the direction parallel to the surface surrounding gases. The kinetic theory for the ow of gas mixture is described by a linearized model of the Boltzmann equation, the McCormack model. To better describe the interaction between gas and wall is used by Maxwell kernel in the terms of a single accommodation coefficient and the Cercignani-Lampis kernel defined in terms of the coefficients of accommodation of tangential momentum accommodation coefficient and the kinetic energy corresponding to normal velocity, which according to literature is a more appropriate model than the usual model that involves specular and diffuse. In seeking solutions to the problem proposed, it uses a analytical version of the discrete ordinates method (ADO), based an arbitrary quadrature scheme, whereby it is determined a problem of eigenvalues and their constant separation. The numerical calculations are performed for three mixtures of noble gases: Neon-Argon, Helium-Argon and Helium-Xenon, and computationally implemented using the FORTRAN computer program. / Neste trabalho, apresenta-se resultados numéricos para grandezas macroscropicas de interesse (perfil de velocidade, perfil do fluxo de calor e tensão de cisalhamento) relativas ao fluxo de uma mistura binária de gases de rarefação arbitrária em microcanais planos, definidos por duas placas paralelas infinitas sem condição de simetria. O fluxo da mistura gasosa ocorre devido a um gradiente constante de pressão (Problema de Poiseuille), um gradiente de temperatura (Problema Creep-Térmico) e um gradiente de densidade (Problema Difuso), na direção paralela a superfície que cerca os gases. A teoria cinética para o fluxo da mistura gasosa é descrita por um modelo linearizado da equação de Boltzmann, o modelo de McCormack. Para melhor descrever o processo de interação entre o gás e a parede utiliza-se o núcleo de Maxwell em termos de um único coeficiente de acomodação e o núcleo de Cercignani-Lampis definido em termos dos coeficientes de acomodação do momento tangencial e o coeficiente de acomodação da energia cinética correspondendo a velocidade normal, que segundo a literatura é um modelo mais apropriado do que o usual modelo que envolve reflexão especular e difusa. Na busca de soluções do problema proposto, usa-se uma versão analítica do método de ordenadas discretas (ADO), baseada num esquema de quadratura arbitrário, segundo a qual determina-se um problema de autovalores e respectivas constantes de separação. Os cálculos numéricos são realizados para três misturas de gases nobres: Neônio-Argônio, Hélio-Argônio e Hélio-Xenônio, e implementados computacionalmente através do programa computacional FORTRAN.

In this work, an analytical version of the method of discrete ordinates (ADO) is used in developing solutions to problems of rarefied gases confined by two infinite parallel plates with different chemical constitutions, that is, without the symmetry condition. The modeling of problems (Poiseuille Flow and Thermal Creep) are performed using the kinetic models of BGK and S, derived from the linearized Boltzmann equation. In order to describe the interaction between gas and surface, we use the core of Maxwell presenting a single accommodation coefficient and the Cercignani-Lampis core defined in terms of the coefficients of accommodation of tangential momentum and energy accommodation coefficient kinetics. A series of results are presented in order to establish a comparison of surface effects to the problems presented. / Neste trabalho, uma vers ao anal´ıtica do m´etodo de ordenadas discretas (ADO) ´e utilizada no desenvolvimento de solu¸c oes para problemas de gases rarefeitos confinados por duas placas paralelas infinitas com constitui¸c oes qu´ımicas diferentes, isto ´e, sem a condi¸c ao de simetria. A modelagem dos problemas (Fluxo de Poiseuille e Creep T´ermico) s ao realizados a partir dos modelos cin´eticos BGK e S, derivados da equa¸c ao linearizada de Boltzmann. A fim de descrever o processo de intera¸c ao entre o g´as e a superf´ıcie, utiliza-se o n´ucleo de Maxwell que apresenta um ´unico coeficiente de acomoda¸c ao e o n´ucleo de Cercignani-Lampis definido em termos dos coeficientes de acomoda¸c ao do momento tangencial e o coeficiente de acomoda¸c ao da energia cin´etica. Uma s´erie de resultados s ao apresentados a fim de estabelecer uma compara¸c ao dos efeitos de superf´ıcie para os problemas apresentados.