# Analysis of non-equilibrium phenomena in inductively coupled plasma generators

## Abstract

This article addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of themore »

- Authors:

- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Von Karman Inst. for Fluid Dynamics, Rhode-Saint-Genese (Belgium)

- Publication Date:

- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); Research Foundation-Flanders (FWO)

- OSTI Identifier:
- 1467840

- Alternate Identifier(s):
- OSTI ID: 1263713

- Grant/Contract Number:
- NA0002374; FWO G.0729.11N

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 7; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING; phase equilibria; Boltzmann equations; Maxwell equations; thermal models; chemically reactive flows; inductively coupled plasma; Navier Stokes equations; dissociation energies; reaction kinetics modeling

### Citation Formats

```
Zhang, W., Lani, A., and Panesi, M.
```*Analysis of non-equilibrium phenomena in inductively coupled plasma generators*. United States: N. p., 2016.
Web. doi:10.1063/1.4958326.

```
Zhang, W., Lani, A., & Panesi, M.
```*Analysis of non-equilibrium phenomena in inductively coupled plasma generators*. United States. doi:10.1063/1.4958326.

```
Zhang, W., Lani, A., and Panesi, M. Mon .
"Analysis of non-equilibrium phenomena in inductively coupled plasma generators". United States.
doi:10.1063/1.4958326. https://www.osti.gov/servlets/purl/1467840.
```

```
@article{osti_1467840,
```

title = {Analysis of non-equilibrium phenomena in inductively coupled plasma generators},

author = {Zhang, W. and Lani, A. and Panesi, M.},

abstractNote = {This article addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.},

doi = {10.1063/1.4958326},

journal = {Physics of Plasmas},

number = 7,

volume = 23,

place = {United States},

year = {Mon Jul 18 00:00:00 EDT 2016},

month = {Mon Jul 18 00:00:00 EDT 2016}

}

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