Modeling of Supersonic Radiative Marshak Waves Using Simple Models and Advanced Simulations. Issue 4 (19th September 2018) - Cohen, Avner P.; Heizler, Shay I.
Abstract: 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 SiO2 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.