A unified theory of the self-similar supersonic Marshak wave problem

We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power la...

Full description

Saved in:
Bibliographic Details
Published in:Physics of fluids (1994) 2024-05, Vol.36 (5)
Main Authors: Krief, Menahem, McClarren, Ryan G.
Format: Article
Language:English
Subjects:
Exact solutions
Exponents
Local thermodynamic equilibrium
Opacity
Perturbation theory
Power law
Radiative heat transfer
Radiative transfer
Self-similarity
Similarity solutions
Simulation
Temperature dependence
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We present a systematic study of the similarity solutions for the Marshak wave problem in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity, and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat and does possess its common sharp characteristic; this characteristic is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer–Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non-sharp fronts. The solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0208111