Multi-Physics Mathematical Model for Weakly-Ionized Plasma Flows

TL;DR

This paper develops a comprehensive mathematical model for weakly-ionized plasma flows, incorporating fluid, thermal, and electric fields, and proposes numerical methods to solve for electric fields under challenging conditions.

Contribution

It introduces a versatile, coupled multi-physics model for partially-ionized plasmas, including novel numerical approaches and detailed submodels for electric properties and collision cross-sections.

Findings

Demonstrates the effect of fuel composition and ionizing species on plasma conductivity.

Provides three numerical methods with varying stability for high Hall parameters.

Develops an analytical collision cross-section for argon gas.

Abstract

This work presents a multidisciplinary mathematical model, as a set of coupled governing equations and auxiliary relations describing the fluid-flow, thermal, and electric fields of partially-ionized plasma with low magnetic Reynolds numbers. The model is generic enough to handle three-dimensionality, Hall effect, compressibility, and variability of fluid, thermal, and electric properties of the plasma. The model can be of interest to computational modelers aiming to build a solver that quantitatively assesses direct extraction of electric energy from a plasma flow. Three different approaches are proposed to solve numerically for the electric fields with different levels of tolerance toward possible numerical instability encountered at a large Hall parameter, where the effective conductivity tensor loses diagonal dominance and becomes close to singular. A submodel for calculating the local electric properties of the plasma is presented in detail and is applied to demonstrate the effect of different factors on the electric conductivity, including the fuel's carbon/hydrogen ratio and the alkaline seed element that acts as the ionizing species. An analytical expression for the collision cross-section for argon is developed, such that this noble gas can be included as one of the gaseous species comprising the plasma.