David Vanden Abeele

Thermodynamic and Transport Properties for Inductive Plasma Modeling

A review is given of models for the thermodynamic and transport properties of inductive plasmas under conditions of local thermodynamic equilibrium. The thermodynamic properties of individual species are computed using a statistical mechanics formulation based upon the rigid rotator and harmonic oscillator model. Complex cut-off criteria for the electronic levels and anharmonicity corrections are not needed for practical equilibrium calculations. An efficient iterative technique is proposed for the calculation of the equilibrium mixture thermodynamics properties. Through a Schur-complement approach the number of unknowns in the nonlinear system, which determines the equilibrium chemical composition, may be reduced to the number of basic elements. The method is demonstrated for equilibrium air computations. The plasma transport properties are computed with the method of Chapman and Enskog. Accurate formulas for the heavy particle and electron transport properties are discussed. Through a straightforward argument the result of Butler and Brokaw for the reactive thermal conductivity is shown to be valid for ionized equilibrium mixtures. Computed results for the thermodynamic and transport properties of air are compared with numerical and experimental results of other researchers.

Numerical simulation of inductively coupled plasma flows under chemical non‐equilibrium

This paper presents a detailed review of the numerical modeling of inductively coupled air plasmas under local thermodynamic equilibrium and under chemical non‐equilibrium. First, the physico‐chemical models are described, i.e. the thermodynamics, transport phenomena and chemical kinetics models. Particular attention is given to the correct modelling of ambipolar diffusion in multi‐component chemical non‐equilibrium plasmas. Then, the numerical aspects are discussed, i.e. the space discretization and iterative solution strategies. Finally, computed results are presented for the flow, temperature and chemical concentration fields in an air inductively coupled plasma torch. Calculations are performed assuming local thermodynamic equilibrium and under chemical non‐equilibrium, where two different finite‐rate chemistry models are used. Besides important non‐equilibrium effects, we observe significant demixing of oxygen and nitrogen nuclei, which occurs due to diffusion regardless of the degree of non‐equilibrium in the plasma.

THERMODYNAMIC AND TRANSPORT PROPERTIES FOR INDUCTION PLASMA MODELING

The development at the von Karman Institute of an inductively heated plasma wind tunnel has brought a need for theoretical and numerical investigation of high-temperat ure gases (plasmas) of different types. The thermodynamic properties of individual species are computed using statistical thermodynamics formulations based on the rigid rotator and harmonic oscillator model. A discussion is made about cut-off criteria for the electronic levels, low-temperature corrections to the partition function and anharmonicity considerations. It is shown that sufficient accuracy is obtained for practical applications of chemical equilibrium without complex cut-off criteria and anharmonicity corrections. The mixture thermodynamic properties are computed at chemical equilibrium using the equilibrium reactions approach. An efficient formulation has been obtained for mole fraction or mass fraction computation which allows the reduction of the system of unknowns to a size equal to the number of basic nuclei types. The method is illustrated by 3-species argon and 13-species air plasma computations. Finally, transport properties are computed from kinetic theory of gases. The underlying mixture rules and the collisional data used as input are discussed and results are shown for a 13-species air plasma. Be c e f

Direct numerical simulation of bubbly Taylor-Couette flow

Taylor-Couette flow is a typical research target for investigating the fluid mechanical phenomena in shear flows. It features the flow of an incompressible, viscous fluid contained in the gap between two concentric cylinders at low Reynolds numbers (see references [1] and [2]). The Couette apparatus has originally been developed for measuring the viscosity of a fluid at small imposed angular velocities of the cylinders. A simple sketch of the test case geometry is shown in figure 1.

Direct numerical simulation of Taylor-Couette flows in the fully turbulent regime

In the present paper, we perform a numerical analysis of the turbulent flow between co-axial cylinders. We consider that only the inner cylinder rotates (angular velocity ω) while the outer one is at rest.

Simulation of Supersonic Flows in Inductively Coupled Plasma Tunnels

A numerical model for all speed ICP flows has been presented and applied to the VKI pilot ICP facility equipped with a converging-diverging nozzle producing a Mach 2.5 plasma jet. The main features of the model are the following: thermodynamic properties computed using a statistical mechanics formulation, transport properties evaluated from a perturbative Chapman-Enskog analyis, and computed using modern linear algebra algorithms, multiblock cell-centered finite volume formulation, with preconditioned AUSM+ flux formula for the convective terms in the Navier-Stokes equations, implicit time stepping/damped quasi-Newton iterative solution strategy with loose coupling of the electromagnetic and flow problems.

Analysis of Diffusion Phenomena in Reacting Mixtures Under LTE with Application to CO2/N2 Stagnation Line Flows

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 diusive fluxes of elements are computed as a linear combination of the species diusive 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 coecients we arrive at a deep understanding of the mass and heat transfer for a CO 2/N2 mixture.