Non-equilibrium plasma including EEDF computation (two-term approximation)

[qumale]

---

name: Non-equilibrium plasma including EEDF computation (two-term approximation)
about: Computation of an EEDF providing a set of electron collision cross sections and a reduced electric field E/N
title: Non-equilibrium plasma including EEDF
labels: feature-request
assignees: '@QuentinMale, @NicolasBarleon'

---

Abstract

We aim to solve
$\frac{\partial}{\partial \varepsilon}\left(\tilde{W} F_0-\tilde{D} \frac{\partial F_0}{\partial \varepsilon}\right)=\tilde{S}+\tilde{R}$
using numerical methods described in Ref. [1] to obtain rate coefficients for the plasma reactions
$k_k = \gamma \int_0^\infty \varepsilon \sigma_k F_0 d \varepsilon$ .

Motivation

Describe the need for the proposed change:

• What problem is it trying to solve?
  Solving EEDF to define reaction rate for electron collision reactions.
  Reproducing the work of Ref. [2] for a complete non-equilibrium plasma modeling.
• Who is affected by the change?
  Users of the plasma WIP feature.
• Why is this a good solution?
  We need to solve the EEDF to be able to compute the plasma reaction rates. The approach is robust and has been used and validated in Refs [1,2].

Possible Solutions

Implementation of the numerical methods of Ref. [1] as already done in the open-source code BOLOS (https://github.com/aluque/bolos). Use of the work of @BangShiuh for the cross section reading and usage.

Implementation of new reaction types may be needed to take into account feeding of vibrational energy during collisional processes and fast gas heating (see Section 3.2 Ref. [2]).

Work in progress branch(es)
https://github.com/QuentinMale/canteraBS/tree/collision-reaction
https://github.com/QuentinMale/canteraBS/tree/canteraPlasma

References

[1] Hagelaar, G. J. M., & Pitchford, L. C. (2005). Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Science and Technology, 14(4), 722–733. https://doi.org/10.1088/0963-0252/14/4/011
[2] Cheng, L., Barleon, N., Cuenot, B., Vermorel, O., & Bourdon, A. (2022). Plasma assisted combustion of methane-air mixtures: Validation and reduction. Combustion and Flame, 240, 111990. https://doi.org/10.1016/j.combustflame.2022.111990

[BangShiuh]

The plasma reaction rates (electron collision reactions) is determined by EEDF which is a phase property like temperature. Two-term approximation needs E/N (electric field strength divided by gas number density) to calculate EEDF. Electric field is an external force but not a phase property. I would suggest making a class PlasmaReactor with a member variable electricFieldStrength. We will put PlasmaPhase object into PlasmaReactor, and the EEDF can be calculated in the reactor and set for PlasmaPhase.

[QuentinMale]

We have a working prototype here: https://github.com/QuentinMale/canteraBS/tree/collision-reaction

See commits and samples/python/thermo/plasmatest.py

This is a first prototype for demonstration of feasibility. Will require clean-up, and development for proper interface between PlasmaPhase and the EEDF solver in EEDFTwoTermApproximation. Before continuing the work, I suggest we have a chat so that everyone agrees on the design.

[BangShiuh]

Cantera/cantera#1262 (comment) could be considered.

[qumale]

We have recently made a number of new developments, including the creation of a "PlasmaReactor" reactor class containing additional equations to take account of vibrational energy, and the modification of the RHS term in the temperature equation to take account of discharge heating.

https://github.com/QuentinMale/canteraBS/tree/canteraPlasma

[BangShiuh]

Hi All, https://github.com/BangShiuh/cantera/tree/collision-new This is the branch I just wrote to make PlasmaPhase using Kinetics and ElectronCollisionPlasmaRate. This implementation uses weak_ptr, registerChangeCallback, and store ElectronCollisionPlasmaRate as m_collisionRates. I hope this implementation satisfies the requirements and can be useful for future development. I will take some time to finish addressing the issues for the PR Cantera/cantera#1731 this month. Best, Bang

…

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