Modeling of Supersonic Radiative Marshak Waves Using Simple Models and Advanced Simulations

• Published in: Journal of computational and theoretical transport Vol. 47; no. 4-6; pp. 378 - 399
• Main Authors: Cohen, Avner P., Heizler, Shay I.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 19.09.2018; Taylor & Francis Ltd
• Subjects: Approximation; asymptotic diffusion; Asymptotic properties; Boltzmann transport equation; Computer simulation; Cylinders; Gold; Marshak wave; Mathematical models; Radiative transfer; Silicon dioxide; Two dimensional models; Wave propagation
• ISSN: 2332-4309; 2332-4325
• DOI: 10.1080/23324309.2018.1489846

We study the problem of radiative heat (Marshak) waves using advanced approximate approaches. Supersonic radiative Marshak waves that are propagating into a material are radiation dominated (i.e., hydrodynamic motion is negligible), and can be described by the Boltzmann equation. However, the exact thermal radiative transfer problem is a non-trivial one, and there still exists a need for approximations that are simple to solve. The discontinuous asymptotic P 1 approximation, which is a combination of the asymptotic P 1 and the discontinuous asymptotic diffusion approximations, was tested in previous work via theoretical benchmarks. Here, we analyze a fundamental and typical experiment of a supersonic Marshak wave propagation in a low-density SiO 2 foam cylinder, embedded in gold walls. First, we offer a simple analytic model that grasps the main effects dominating the physical system. We find the physics governing the system to be dominated by a simple, one-dimensional effect, based on the careful observation of the different radiation temperatures that are involved in the problem. The model is completed with the main two-dimensional effect which is caused by the loss of energy to the gold walls. Second, we examine the validity of the discontinuous asymptotic P 1 approximation, comparing to exact simulations with good accuracy. Specifically, the heat front position, as a function of the time, is reproduced perfectly in comparison to exact Boltzmann solutions.