Modelling of an Inductively Coupled Plasma Torch: first step André P. 1, Clain S. 4, Dudeck M. 3, Izrar B. 2, Rochette D 1, Touzani R 3, Vacher D LAEPT, Clermont University, France 2. ICARE, Orléans University, France 3. Institut Jean Le Rond d’Alembert, University of Paris 6, France 4. LM, Clermont University,, France

Composition in molar fraction Mars 97% CO 2 ; 3% N 2 Titan 97%N 2 ; 2% CH 4 ; 1% Ar

ICP Torch: atmospheric pressure Low flow of gaz Assumptions Thermal equlibrium Chemical equilibrium Optical Thin plasma Simple Case!

Composition Spectral lines, Spectroscopy measurements Transport Coefficients Modelling Thermodynamic Properties Radiative loss term Interaction Potentials

Composition Spectral lines, Spectroscopy measurements Transport Coefficients Modelling Thermodynamic Properties Radiative loss term Interaction Potentials

Chemical and Thermal equilibrium: Gibbs Free Energy minimisation Dalton Law Electrical Neutrality Chemical species: Mars Monatomic species (11): C, C-, C+, C++, N, N+, N++, O, O-, O+, O++ Diatomic species (18): C 2, C 2 -, C 2 +, CN, CN -, CN +, CO, CO -, CO +, N 2, N 2 -, N 2 +, NO, NO -, NO +, O 2, O 2 -, O 2 + Poly_atomic species (23): C 2 N, C 2 N 2, C 2 O, C 3, C 3 O 2, C 4, C 4 N 2, C 5, CNN, CNO, CO 2, CO 2 -, N 2 O, N 2 O 3, N 2 O 4, N 2 O 5, N 2 O +, N 3, NCN, NO 2, NO 2 -, NO 3, O 3 e-, solid phase: graphite Titan: Monatomic species (13): Ar, Ar+, Ar++, C, C-, C+, C++, H, H+, H-, N, N+, N++, Diatomic Species (18) : C 2, C 2 -, C 2 +, CN, CN -, CN +, CO, CO -, CO +, N 2, N 2 -, N 2 +, NO, NO -, NO +, O 2, O 2 -, O 2 + Poly_atomic species (26 ): C 2 H, C 2 H 2, C 2 H 4, C 2 N, C 2 N 2, C 3, C 4, C 4 N 2, C 5, CH 2, CH 3, CH 4, CHN, CNN, H 2 N, H 2 N 2, H 3 N, H 4 N 2, N 3, NCN, H 3 +, NH 4 +, C 2 H 3, C 2 H 5, C 2 H 6, HCCN e-, solid phase: graphite

To calculate in gas phase, we consider the temperature range [3000; 15000] MarsTitan

Mars Titan

Composition Spectral lines, Spectroscopy measurements Transport Coefficients Modelling Thermodynamic Properties Radiative loss term Interaction Potentials

*Intensities calculation (Boltzmann distribution) Mars Line CI m

Composition Spectral lines, Spectroscopy measurements Transport Coefficients Modelling Thermodynamic Properties Radiative loss term Interaction Potentials

Thermodynamic properties Massic density: ρ Internal energy: e

Composition Spectral lines, Spectroscopy measurements Transport Coefficients Modelling Thermodynamic Properties Radiative loss term Interaction Potentials

Potential interactions Charged-Charged: Shielded with Debye length Coulombian potential Neutral-Neutral: Lennard Jones Potential (evalaute and combining rules) Charged-Neutral: Dipole and charge transfer Electrons-neutral: Bibliography and estimations

Transport coefficients : Chapman-Enskog method Electrical conductivity σ: third order Viscosity coefficient μ: fourth order Total thermal conductivity k : summation of four terms translational thermal conductivity due to the electrons, translational thermal conductivity due to the heavy species particles, internal thermal conductivity, chemical reaction thermal conductivity.

Axisymmetry LTE model for inductive plasma torches LTE flow field equations U: conservative variable vector F r (U), F z (U): convective fluxes G r (U), G z (U): diffusive fluxes S(U): source term Equation of state of the plasma considered: with  : internal energy defined by: Viscous terms Conductive heat fluxes Lorentz force Joule heating Radiative loss term P Rad Physical model: assumptions - Classical torch geometry  axisymmetric geometry - Local Thermodynamic Equilibrium (LTE) conditions for the plasma - Unsteady state, laminar, swirling plasma flow (tangential component) - Optically thin plasma - Negligible viscous work and displacement current

MHD induction equations B: magnetic induction H: magnetic field E: electric field J and J 0 : current density and source current density  : magnetic permeability  : electric conductivity Equations formulated in terms of electric field E Numerical method Hydrodynamics (three steps) To obtain an approximation of the solution U on each cell, we use a fractional step technique coupling the finite volume method and the finite element method:  First step: To compute the convective fluxes, we use a finite volume scheme with multislope MUSCL reconstruction where the fluxes are calculated using a HLLC scheme.  Second step: We use a Runge Kutta method to integrate the source terms.  Third step: We use a finite element method to evaluate the diffusive contribution. Electromagnetic To solve the partial differential equation, we use a standard finite element method with a standard triangulation of the domain and the use of a piecewise linear approximation. Using the cylindrical coordinates (r, ,z) and assuming  -invariance we obtain:

Basic data composition Intensity calculation Thermodynamic properties First estimation of interaction potentials First estimation of transport coefficients Future Upgrade the interaction potentials Estimate the accuracy need to calculate the transport coefficients Radiative loss Understand the energy transfer from the inductive coils Modify the ICP torch