Modelling of an Inductively Coupled Plasma Torch: first step Andr

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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 dAlembert, University
  of Paris 6 , France
• 4. LM, Clermont University, , France

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Composition in molar fraction

• Mars

Titan
97 CO2 3 N2
97N2 2 CH4 1 Ar
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ICP Torch atmospheric pressure Low flow of
gaz Assumptions Thermal equlibrium Chemical
equilibrium Optical Thin plasma
Simple Case!
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Composition
Thermodynamic Properties
Spectral lines, Spectroscopy measurements
Interaction Potentials
Radiative loss term
Transport Coefficients
Modelling
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Composition
Thermodynamic Properties
Spectral lines, Spectroscopy measurements
Interaction Potentials
Radiative loss term
Transport Coefficients
Modelling
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• 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

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Mars
Titan
To calculate in gas phase, we consider the
temperature range 3000 15000
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Titan
Mars
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Composition
Thermodynamic Properties
Spectral lines, Spectroscopy measurements
Interaction Potentials
Radiative loss term
Transport Coefficients
Modelling
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• Intensities calculation (Boltzmann distribution)

Line CI 2582.9 10-10 m
Mars
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Composition
Thermodynamic Properties
Spectral lines, Spectroscopy measurements
Interaction Potentials
Radiative loss term
Transport Coefficients
Modelling
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Thermodynamic properties

• Massic density ? Internal energy e

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

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• Transport coefficients Chapman-Enskog method
• Electrical conductivity s 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.

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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
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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.

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• 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