Equation of state driven radiative models for simulation of lightning strikes

TL;DR

This paper develops and compares radiative heat loss models for lightning strike simulations, highlighting the importance of spectral absorption and proposing a computationally efficient net emission coefficient method validated against experiments.

Contribution

It introduces a range of RTE approximation models and demonstrates that the net emission coefficient offers a good balance of accuracy and efficiency for multi-dimensional plasma arc simulations.

Findings

Spectral absorption inclusion is essential for consistent results.

Geometry-dependent models are computationally intensive for multi-dimensional cases.

Net emission coefficient method matches experimental measurements effectively.

Abstract

This work is concerned with the numerical simulation of plasma arc interaction with aerospace substrates under conditions akin to lightning strike and in particular with the accurate calculation of radiative heat losses. These are important because they have a direct effect on the calculation of thermal and pressure loads on the substrates, which can lead to material damage under certain conditions. Direct numerical solution of the radiation transport equation (RTE) in mesoscale simulations is not viable due to its computational cost, so for practical applications reduced models are usually employed. To this end, four approximations for solving the RTE are considered in this work, ranging from a simple local thermodynamical behaviour consideration, to a more complex spectral absorption dependent on the arc geometry. Their performance is initially tested on a one-dimensional cylindrical arc, before implementing them in a multi-dimensional magnetohydrodynamics code. Results indicate that inclusion of spectral absorption is necessary in order to obtain consistent results. However, the approaches accounting for the arc geometry require repeated solution of the computationally intensive Helmholtz equations, making them prohibitive for multi-dimensional simulations. As an alternative, a method using the net emission coefficient is employed, which provides a balance between computational efficiency and accuracy, as shown by comparisons against experimental measurements for a plasma arc attaching to an aluminium substrate.