Modelling of an Inductively Coupled Plasma Torch: first step André P. 1 , Clain S. 4 , Dudeck M. 3 , Izrar B. 2 , Roc

1. Modelling of an Inductively Coupled Plasma Torch: first stepAndré P.1, Clain S. 4, Dudeck M. 3, Izrar B.2, Rochette D1, Touzani R3, Vacher D.1 1. LAEPT, Clermont University, France 2. ICARE, Orléans University, France 3. Institut Jean Le Rond d’Alembert, Universityof Paris 6, France 4. LM, Clermont University, , France

2. Composition in molar fraction Titan Mars 97% CO2; 3% N2 97%N2; 2% CH4; 1% Ar

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

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

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

6. 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): C2, C2-, C2+, CN, CN-, CN+, CO, CO-, CO+, N2, N2-, N2+, NO, NO-, NO+, O2, O2-, O2+ • Poly_atomic species (23): • C2N, C2N2, C2O, C3, C3O2, C4, C4N2, C5, CNN, CNO, CO2, CO2-, N2O, N2O3, N2O4, N2O5, N2O+, N3, NCN, NO2, NO2-, NO3, O3 • e-, solid phase: graphite • Titan: • Monatomic species (13): Ar, Ar+, Ar++, C, C-, C+, C++, H, H+, H-, N, N+, N++, • Diatomic Species (18) : C2, C2-, C2+, CN, CN-, CN+, CO, CO-, CO+, N2, N2-, N2+, NO, NO-, NO+, O2, O2-, O2+ • Poly_atomic species (26 ): C2H, C2H2, C2H4, C2N, C2N2, C3, C4, C4N2, C5, CH2, CH3, CH4, CHN, CNN, H2N, H2N2, H3N, H4N2, N3, NCN, H3+, NH4+, C2H3, C2H5, C2H6, HCCN • e-, solid phase: graphite

7. Mars Titan To calculate in gas phase, we consider the temperature range [3000; 15000]

8. Titan Mars

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

10. *Intensities calculation (Boltzmann distribution) Line CI 2582.9 10-10 m Mars

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

12. Thermodynamic properties Massic density: ρ Internal energy: e

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

14. 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

15. 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.

17. Axisymmetry LTE model for inductive plasma torches 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 LTE flow field equations Lorentz force Viscous terms • U: conservative variable vector • Fr(U), Fz(U): convective fluxes • Gr(U), Gz(U): diffusive fluxes • S(U): source term Joule heating Radiative loss term PRad Conductive heat fluxes Equation of state of the plasma considered: with : internal energy defined by:

18. MHD induction equations • B: magnetic induction • H: magnetic field • E: electric field • J and J0: current density and source current density • : magnetic permeability • : electric conductivity Equations formulated in terms of electric field E Using the cylindrical coordinates (r,,z) and assuming -invariance we obtain: 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.

19. 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