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.
Highlights
Ionization is an endothermic process in which a sufficient amount of energy exceeding the ionization energy of an atom or molecule is supplied to it, leading to the liberation of an electron
This section is divided into three main parts; the first and second parts are devoted to presenting the equations governing the thermo-fluid and electric field variables of the plasma, with proposed algorithms to solve for the electric fields
We shed light on important factors that affect the electric conductivity of the plasma, through applying the electric submodel described in the previous section
Summary
Ionization is an endothermic process in which a sufficient amount of energy exceeding the ionization energy of an atom or molecule is supplied to it, leading to the liberation of an electron. Recent interest in MHD generation has aroused due to different factors, including stronger magnets which boost the output power from MHD channels, enhanced combustor designs that help lengthening the electrode life, and the advance in computational fluid dynamics (CFD) enabling more reliable prediction of the performance of MHD units [17] It is the aim of this work to provide a complete mathematical model that describes the temporal and spatial evolution of plasma-gas fields and electric fields within the channel, such that computational researchers can pursue further and use this model in numerical simulations (e.g., based on finite volume discretization) to predict the performance of arbitrary MHD channel designs. Three different computational approaches are discussed to resolve the electric fields, coping with poor numerical behavior at plasma conditions characterized by a large Hall parameter
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