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Elemental Demixing in Inductively Coupled Air Plasma Torches at High Pressures

We present and analyze detailed numerical simulations of high-pressure inductively coupled air plasma flows 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. Ideally, this effect should therefore be taken into account when the results of tests of thermal protection materials for (re-)entry spacecraft in inductively coupled plasma wind tunnels are processed. 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.

Elemental Demixing in Air and Carbon Dioxide Stagnation Line Flows

The influence of elemental fraction variations on the computation of thermochemical equilibrium flows is analyzed for both air and carbon dioxide mixtures. First the thermochemical equilibrium stagnation line equations for a mixture of perfect gases are presented for both the cases of constant and variable elemental fractions. Then, 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. 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.

Numerical Simulation of Nonequilibrium Stagnation-Line CO2 Flows with Catalyzed Surface Reactions

A methodology developed at the Institute for Problems in Mechanics of Moscow is used for the analysis of the catalytic properties of thermal protection materials in a CO 2 environment. The method relies on a combination of 1) heat-transfer and pitot-pressure measurements in a subsonic plasma jet and 2) numerical flow simulations. The simulated environments are typical of Mars entry conditions. In particular, this work is focused on the finite-rate chemistry part of the flow description. 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 CO 2 flows. Nonequilibrium 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

State-to-State Simulation of Nonequilibrium Nitrogen Stagnation-Line Flows: Fluid Dynamics and Vibrational Kinetics

An advanced model of fluid dynamics and nonequilibrium vibrational-chemical kinetics in high-temperature viscous flows along the stagnation line is proposed. The present model takes into account detailed state-to-state kinetics and state-dependent transport properties. Fluid dynamics equations are self-consistently coupled to vibrational kinetics, and state-dependent transport terms are properly incorporated in the governing equations. As an example, vibrational kinetics, macroscopic flow parameters, and heat transfer in a N 2 /N mixture are calculated for different flow conditions. A comparison with thermal equilibrium and vibrational frozen flows is presented, showing the important role of detailed kinetics coupled to fluid dynamics. Several models of chemical and vibrational kinetics are assessed and a strong dependence of the flow parameters and surface heat flux on the chemical model is demonstrated.

Analysis of chemical nonequilibrium and elemental demixing in plasmatron facility

A detailed numerical analysis is performed in the torch and in the test chamber of an inductively coupled plasma facility. The main purpose is the analysis of the plasma jet in the test chamber and the assessment of its degree of nonequilibrium together with the level of elemental demixing. To this end three different mathematical formulations have been used: an extended chemical nonequilibrium formalism including finite-rate chemistry and two forms of equation valid in the limit of local thermochemical equilibrium, i.e. the equilibrium formulation with variable elemental fractions, which takes into account the demixing of chemical elements and the classical formulation, where the molar fraction of elements is supposed to be constant. To assess the influence of the finite-rate chemistry model on the results, two models have been used. Simulations at various operating pressures indicate that the model dependency is strongly reduced at sufficiently high pressures (above 10 kPa) while relevant at lower pressure. As the operating pressure is increased, chemistry becomes increasingly fast and the nonequilibrium results correctly approach those obtained assuming local thermochemical equilibrium, provided that elemental fraction variations are correctly taken into account.

Sensitivity Analysis of the Local Heat Transfer Simulation for the Application to Thermal Protection Systems

A methodology that determines chemical surface properties is presented. It has been developed by Russian scientists in order to test Thermal Protection Systems for re-entering vehicles. It is based on experimental measurements and numerical simulations. Its reliability has been investigated and it was found that the source of the largest uncertainty is the heat flux measurement compared with the error that comes from the other measurements and modeling constraints.

Analysis of diffusion phenomena in CO2/N2 mixtures under thermochemical equilibrium

In this paper we apply a recently published formulation 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 the boundary layer near the stagnation point of a hypersonic vehicle entering the 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 used in this contribution 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 CO 2 /N 2 mixture.

Analysis of chemical non-equilibrium and elemental demixing in the VKI Plasmatron

A detailed numerical analysis is performed in the torch and in the test chamber of an inductively coupled plasma facility. The main purpose is the analysis of the plasma jet in the test chamber and the assessment of its degree of non equilibrium together with the level of elemental demixing. To this end three dierent mathematical formulations have been used: an extended chemical non-equilibrium formalism including finite-rate chemistry and two forms of equation valid in the limit of local thermo-chemical equilibrium: the LTE-VEF formulation, that takes into account the demixing of chemical elements and the LTE-CEF formulation, where the molar fraction of elements is supposed to be constant. In order to assess the influence of the finite rate chemistry model on the results, two models have been used. Simulations at various operating pressures indicate that the model dependency is strongly reduced at suciently high pressures while relevant at lower pressure. As the operating pressure is increased, chemistry becomes increasingly fast and the non-equilibrium results correctly approach both in the torch and in the test chamber those obtained assuming local thermo-chemical equilibrium, provided that elemental fraction variations are correctly taken into account. Nomenclature kf = Forward reaction rate Mi = Molar mass of species i Nel = Number of elements Nsp = Number of species p = Mixture pressure T = Mixture temperature = Mixture density u = Mixture velocity xs = Mole fraction of species s Xc = Volumetric fraction of element c

Detailed Vibrational‐Chemical Kinetics and Transport Properties in a Non‐Equilibrium Stagnation Line Flow

A self‐consistent model of fluid dynamics and non‐equilibrium vibrational‐chemical kinetics in a high temperature viscous N2/N mixture flow along the stagnation line is proposed. The model takes into account detailed state‐to‐state kinetics and state dependent transport phenomena; the state‐to‐state kinetic and transport terms are properly coupled to fluid dynamics equations. The sensitivity of the macroscopic flow parameters and heat transfer to the accuracy of fluid dynamics equations, to the scheme of chemical reactions and vibrational transitions, and to the rates of non‐equilibrium processes is evaluated.

Elemental Diffusion and Heat Transfer Coefficients for Mixtures of Weakly Ionized Gases

The phenomena of elemental diffusion is described in detail expressing the elemental fluxes as an explicit function, at constant pressure, of temperature and elemental composition gradients. This study is inspired by the definition of Murphy for elemental combined and thermal diffusion coefficients for mixtures of homonuclear molecules and it is extended to more general mixtures containing hetero-nuclear species. As a direct consequence, the formulation of Butler and Brokaw, for the diffusive transport of species enthalpy, has been generalized introducing both a correction term to the thermal reactive conductivity and the new concept of elemental heat transfer coefficients. These new transport properties are presented both for air and carbon dioxide mixtures of partially ionized gases suited for Earth and Mars entry applications.