Interaction of compressible turbulence and radiation of heat using large-eddy simulation

由于需要大量的计算工作，目前还不可能对受热辐射影响的湍流进行直接数值模拟（除非在高度简化的情况下）。然而，目前可用的高性能计算机足够强大，可以进行大涡模拟（LES）湍流-辐射相互作用（TRI）。到目前为止，除了极少数例外，TRI都是在统计水平上处理的，即光谱吸收系数和光谱辐射强度（这只是辐射传递方程中出现的一个特定项）的平均乘积是使用统计平均量建模的。当对辐射传递方程（RTE）进行低通滤波以执行LES时，会出现需要建模以关闭方程的未知项。然而，在这方面的初步尝试，在文献中发现，是不完整的。该项目的目的是为非散射介质的低通滤波RTE中的所有未闭合项制定建模策略，即为亚电网尺度对光谱发射和吸收的贡献。为此，建立并求解了包含温度和物质质量分数（或混合物分数）的过滤密度函数（PDF）的输运方程。PDF允许对所有未知的过滤项求值。该分析的先验试验将通过在最小通道中使用1200 K温度水平的水蒸气对超音速湍流（无辐射）进行DNS进行。壁面温度在1000 K左右时，由于动能耗散，堆芯流动至少达到1200 K。该流场包含温度和物质质量分数的波动，允许计算辐射特性和辐射强度，而无需计算辐射与湍流之间的完全耦合。将过滤后的DNS数据与辐射传输方程中的建模项进行比较（先验检验）将显示该方法的有效性，并允许TRI的LES。

Direct numerical simulations of turbulent flows that are affected by radiation of heat are not possible at the present time (except in strongly simplified settings) due to the enormous computational effort needed. Presently available high-performance computers are, however, powerful enough to allow for large-eddy simulations (LES) of turbulence-radiation interaction (TRI). With very few exceptions TRI has, up to now, been treated on a statistical level, i.e. the mean product of spectral absorption coefficient and spectral radiation intensity (which is just one specific term appearing in the radiative transfer equation) was modelled using statistically averaged quantities. When the radiative transfer equation (RTE) is low-pass filtered to perform an LES, unknown terms appear that need modelling to close the equation. First attempts in this direction, found in the literature, are however incomplete.It is the aim of this project to develop a modelling strategy for all unclosed terms in the lowpass filtered RTE for a non-scattering medium, i.e. for the subgrid-scale contributions to spectral emission and absorption. To this end a transport equation for the filtered density function (PDF) involving temperature and species mass fractions (or the mixture fraction) is modelled and solved. The PDF allows the evaluation of all unknown filtered terms. A priori tests of this ansatz will be made by performing a DNS of supersonic turbulent flow (without radiation) In a minimal channel using water vapour at a temperature level of 1200 K. When the wall temperatures are of the order of 1000 K the core flow will at least reach 1200 K as a result of kinetic energy dissipation. This flow field contains fluctuations of temperature and species mass fraction and allows the computation of radiation properties and radiation intensities without computing the full coupling between radiation and turbulence. A comparison of filtered DNS data and modelled terms in the radiative transfer equation (a priori test) will show the validity of the approach and allow for LES of TRI.