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Modeling of Supersonic Radiative Marshak Waves Using Simple Models and Advanced Simulations
Journal of Computational and Theoretical Transport ( IF 0.7 ) Pub Date : 2019-01-27 , DOI: 10.1080/23324309.2018.1489846
Avner P. Cohen 1 , Shay I. Heizler 1
Affiliation  

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 P1 approximation, which is a combination of the asymptotic P1 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 P1 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.



中文翻译:

使用简单模型和高级仿真对超音速辐射Marshak波建模

我们使用先进的近似方法研究辐射热(Marshak)波的问题。传播到材料中的超音速辐射Marshak波以辐射为主(即,流体动力运动可忽略不计),可以用玻耳兹曼方程描述。然而,确切的热辐射传递问题是不平凡的,并且仍然需要简单解决的近似方法。在以前的工作中,通过理论基准测试了不连续渐近P 1逼近,它是渐近P 1和不连续渐近扩散逼近的组合。在这里,我们分析了超音速Marshak波在低密度SiO 2中传播的基本和典型实验泡沫缸,嵌入金墙。首先,我们提供了一个简单的分析模型,该模型掌握了控制物理系统的主要影响。基于对问题所涉及的不同辐射温度的仔细观察,我们发现控制该系统的物理学受简单的一维效应支配。该模型具有主要的二维效应,该效应是由金壁能量损失引起的。其次,我们将不连续渐近P 1逼近的有效性与精确度较高的精确仿真进行比较。具体而言,与精确的玻尔兹曼解相比,热前位置作为时间的函数得到了完美的再现。

更新日期:2019-01-27
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