In many natural and laboratory conditions, plasmas are often in the non-equilibrium state due to presence of stationary flows, when one particle species (or a special group, such as group of high energy particles, i.e., beam) is moving with respect to the other plasma components. Such situations are common for a number of different plasma applications such as diagnostics with emissive plasma probes, plasma electronics devices and electric propulsion devices. The presence of plasmas flows often leads to the instabilities in such systems and subsequent development of large amplitude perturbations. The goal of this work is to develop physical insights and numerical tools for studies of ion sound instabilities driven by the ion flow in a system of a finite length. The ion sound waves are modified by the presence of ion beam resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasi-neutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instability is studied analytically and the results are compared with direct initial value numerical simulations. The numerical tools to simulate these systems are developed based on Godunov and multiple shooting methods. The initial value simulations show the time dependent evolution from which the growth rates were determined for different parameters of the system. The results of the simulations were benchmarked against the analytical results in some limiting cases. In the pursuit of simulation efficiency, the parallelization of the code was investigated for two basic types of parallel systems: shared and distributed memory. The OpenMP and MPI library were used correspondingly.

This thesis presents the derivation of the theory leading to the determination of the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental (de)mixing. As a result, new transport coefficients appear in the equations allowing a quantitative predictions and helping to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium. These transport coefficients have been computed for both air and carbon dioxide mixtures allowing the application of this theory to both Earth and Mars entry problems in the framework of the methodology for the determination of the catalytic activity of Thermal Protections Systems (TPS) materials. Firstly, we analyze the influence of elemental fraction variations on the computation of thermochemical equilibrium flows for both air and carbon dioxide mixtures. To this end, the equilibrium computations are compared with several chemical regimes to better analyze the influence of chemistry on wall heat flux and to observe the elemental fractions behavior along a stagnation line. The results of several computations are presented to highlight the effects of elemental demixing on the stagnation point heat flux and chemical equilibrium composition for air and carbon dioxide mixtures. Moreover, in the chemical nonequilibrium computations, the characteristic time of chemistry is artificially decreased and in the limit the chemical equilibrium regime, with variable elemental fractions, is achieved. Then, we apply the closed form of the equations governing the behavior of local thermodynamic equilibrium flows, accounting for the variation in local elemental concentrations in a rigorous manner, to simulate heat and mass transfer in CO2/N2 mixtures. This allows for the analysis of the boundary layer near the stagnation point of a hypersonic vehicle entering the true Martian atmosphere. The results obtained using this formulation are compared with those obtained using a previous form of the equations where the diffusive fluxes of elements are computed as a linear combination of the species diffusive fluxes. This not only validates the new formulation but also highlights its advantages with respect to the previous one : by using and analyzing the full set of equilibrium transport coefficients we arrive at a deep understanding of the mass and heat transfer for a CO2/N2 mixture. Secondly, we present and analyze detailed numerical simulations of high-pressure inductively coupled air plasma flows both in the torch and in the test chamber using two different mathematical formulations: an extended chemical non-equilibrium formalism including finite rate chemistry and a form of the equations valid in the limit of local thermodynamic equilibrium and accounting for the demixing of chemical elements. Simulations at various operating pressures indicate that significant demixing of oxygen and nitrogen occurs, regardless of the degree of nonequilibrium in the plasma. As the operating pressure is increased, chemistry becomes increasingly fast and the nonequilibrium results correctly approach the results obtained assuming local thermodynamic equilibrium, supporting the validity of the proposed local equilibrium formulation. A similar analysis is conducted for CO2 plasma flows, showing the importance of elemental diffusion on the plasma behavior in the VKI plasmatron torch. Thirdly, the extension of numerical tools developed at the von Karman Institute, required within the methodology for the determination of catalycity properties for thermal protection system materials, has been completed for CO2 flows. Non equilibrium stagnation line computations have been performed for several outer edge conditions in order to analyze the influence of the chemical models for bulk reactions. Moreover, wall surface reactions have been examined, and the importance of several recombination processes has been discussed. This analysis has revealed the limits of the model currently used, leading to the proposal of an alternative approach for the description of the flow-surface interaction. Finally the effects of outer edge elemental fractions on the heat flux map is analyzed, showing the need to add them to the list of parameters of the methodology currently used to determine catalycity properties of thermal protection materials.

This thesis presents the derivation of the theory leading to the determination of the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental (de)mixing. As a result, new transport coefficients appear in the equations allowing a quantitative predictions and helping to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium. These transport coefficients have been computed for both air and carbon dioxide mixtures allowing the application of this theory to both Earth and Mars entry problems in the framework of the methodology for the determination of the catalytic activity of Thermal Protections Systems (TPS) materials.<p>Firstly, we analyze the influence of elemental fraction variations on the computation of thermochemical equilibrium flows for both air and carbon dioxide mixtures. To this end, the equilibrium computations are compared with several chemical regimes to better analyze the influence of chemistry on wall heat flux and to observe the elemental fractions behavior along a stagnation line. The results of several computations are presented to highlight the effects of elemental demixing on the stagnation point heat flux and chemical equilibrium composition for air and carbon dioxide mixtures. Moreover, in the chemical nonequilibrium computations, the characteristic time of chemistry is artificially decreased and in the limit the chemical equilibrium regime, with variable elemental fractions, is achieved. Then, we apply the closed form of the equations governing the behavior of local thermodynamic equilibrium flows, accounting for the variation in local elemental concentrations in a rigorous manner, to simulate heat and mass transfer in CO2/N2 mixtures. This allows for the analysis of the boundary layer near the stagnation point of a hypersonic vehicle entering the true Martian atmosphere. The results obtained using this formulation are compared with those obtained using a previous form of the equations where the diffusive fluxes of elements are computed as a linear combination of the species diffusive fluxes. This not only validates the new formulation but also highlights its advantages with respect to the previous one :by using and analyzing the full set of equilibrium transport coefficients we arrive at a deep understanding of the mass and heat transfer for a CO2/N2 mixture.<p>Secondly, we present and analyze detailed numerical simulations of high-pressure inductively coupled air plasma flows both in the torch and in the test chamber using two different mathematical formulations: an extended chemical non-equilibrium formalism including finite rate chemistry and a form of the equations valid in the limit of local thermodynamic equilibrium and accounting for the demixing of chemical elements. Simulations at various operating pressures indicate that significant demixing of oxygen and nitrogen occurs, regardless of the degree of nonequilibrium in the plasma. As the operating pressure is increased, chemistry becomes increasingly fast and the nonequilibrium results correctly approach the results obtained assuming local thermodynamic equilibrium, supporting the validity of the proposed local equilibrium formulation. A similar analysis is conducted for CO2 plasma flows, showing the importance of elemental diffusion on the plasma behavior in the VKI plasmatron torch.<p>Thirdly, the extension of numerical tools developed at the von Karman Institute, required within the methodology for the determination of catalycity properties for thermal protection system materials, has been completed for CO2 flows. Non equilibrium stagnation line computations have been performed for several outer edge conditions in order to analyze the influence of the chemical models for bulk reactions. Moreover, wall surface reactions have been examined, and the importance of several recombination processes has been discussed. This analysis has revealed the limits of the model currently used, leading to the proposal of an alternative approach for the description of the flow-surface interaction. Finally the effects of outer edge elemental fractions on the heat flux map is analyzed, showing the need to add them to the list of parameters of the methodology currently used to determine catalycity properties of thermal protection materials. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

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