Most sub-grid scale (SGS) models employed in LES (large eddy simulation) formulations were originally developed for incompressible, single phase, inert flows and assume transfer of energy based on the classical energy cascade mechanism. Although they have been extended to numerically study compressible and reactive flows involving deflagrations and detonations, their accuracy in such sensitive and challenging flows is an open question. Therefore, there is a need for both assessing these existing SGS models and identifying the opportunities for proposing new ones, which properly characterize reacting flows in complex engine configurations such as those characterizing rotating detonation engines (RDEs). Accordingly, accounting for the decay of free homogeneous isotropic turbulence (HIT), this work provides a comparison of four different SGS models when compressibility effects are present, (i) the classical Smagorinsky model, (ii) the dynamic Smagorinsky model, (iii) the wall-adapting local eddy-viscosity (WALE) model, and (iv) the Vreman model. More specifically, SGS models are firstly implemented in the open-source computational tool PeleC, which is a high-fidelity finite-volume solver for compressible flows, and then numerical simulations are carried out using them. In terms of results, turbulent spectra, and the decay of physical quantities such as kinetic energy, enstrophy, temperature, and dilatation are computed for each SGS LES model and compared with direct numerical simulations (DNS) results available in literature. The LES numerical results obtained here highlight that the studied SGS models are capable of capturing the overall trends of all physical quantities accounted for. However, they also emphasize the need of improved SGS models capable of adequately describing turbulence dynamics in compressible flows.

翻译：大多数在大涡模拟（LES）公式中采用的亚网格尺度（SGS）模型最初是为不可压缩、单相、惰性流动开发的，并基于经典的能量级串机制假设能量传递。尽管这些模型已被扩展用于数值研究涉及爆燃和爆震的可压缩与反应流动，但它们在如此敏感且具有挑战性的流动中的准确性仍是一个悬而未决的问题。因此，既需要评估这些现有的SGS模型，也需要识别提出新模型的机会，以恰当表征复杂发动机结构（如旋转爆震发动机（RDEs））中的反应流动。据此，本研究考虑均匀各向同性湍流（HIT）的自由衰减，在存在可压缩性效应的情况下，对四种不同的SGS模型进行了比较：（i）经典的Smagorinsky模型，（ii）动态Smagorinsky模型，（iii）壁面自适应局部涡黏性（WALE）模型，以及（iv）Vreman模型。具体而言，首先在开源计算工具PeleC（一种用于可压缩流动的高保真有限体积求解器）中实现这些SGS模型，随后使用它们进行数值模拟。在结果方面，针对每种SGS LES模型计算了湍流谱以及动能、拟涡能、温度和膨胀率等物理量的衰减，并与文献中直接数值模拟（DNS）的结果进行了比较。本文得到的LES数值结果表明，所研究的SGS模型能够捕捉所有考虑中的物理量的总体趋势。然而，这些结果也凸显了需要改进的SGS模型，以充分描述可压缩流动中的湍流动力学。