The two-layer modeling approach has become one of the most promising and successful methodology for simulating turbulent boundary layers in the past ten years. In the present study, a mixed wall model for large-eddy simulations (LES) of high-speed flows is proposed which combine two approaches; the thin-Boundary Layer Equations (TBLE) model of Kawai and Larsson (1994) and the analytical wall-layer model of Duprat et al. (2011) for streamwise pressure gradients. The new hybrid model has been efficiently implemented into a three-dimensional compressible LES solver and validated against DNS of a spatially-evolving supersonic boundary layer (BL) under moderate and strong pressure gradients, before being employed for the prediction of nozzle flow separations at different flow conditions, ranging from weakly to highly over-expanded regimes. A good agreement is obtained in terms of mean and fluctuating quantities compared to the DNS results. Particularly, the current wall-modeled LES results are found to perfectly match the DNS data of supersonic BL with/out pressure gradient. It is also shown that the model can account for the effect of the large-scale turbulent motions of the outer layer, indicating a good interaction between the inner and the outer part of the wall layer. In terms of simulations costs and improvements of computing power, the obtained results highlight the capability of the current wall-modeling LES strategy in saving a considerable amount of computational time compared to the wall-resolved LES counterpart, allowing to push further the simulations limits. Furthermore, the application of these computationally low-costly LES simulations to nozzle flow separation allows to clearly identify the origin of the shock unsteadiness, and the existence of broadband and energetically-significant low-frequency oscillations (LFO) in the vicinity of the separation region.

在过去的十年中，两层建模方法已成为模拟湍流边界层的最有希望和成功的方法之一。在本研究中，提出了一种结合了两种方法的高速流动大涡模拟（LES）的混合壁模型。Kawai和Larsson（1994）的薄边界层方程（TBLE）模型以及Duprat等人的分析性壁层模型。（2011年）的流向压力梯度。新的混合模型已被有效地实现为三维可压缩的LES解算器，并在中等和强压力梯度下针对空间演化的超声边界层（BL）的DNS进行了验证，然后用于预测不同位置的喷嘴流分离流量条件，范围从微弱到高度过度扩展。与DNS结果相比，在均值和波动量方面都获得了很好的协议。特别是，发现当前的壁模型LES结果与带/不带压力梯度的超音速BL的DNS数据完全匹配。还显示出该模型可以解释外层的大规模湍流运动的影响，表明壁层的内部和外部之间有良好的相互作用。在仿真成本和计算能力的提高方面，所获得的结果凸显了当前的墙建模LES策略与墙解析的LES相比节省大量计算时间的能力，从而进一步推动了仿真极限。此外，