A hypersonic shock wave/turbulent boundary layer interaction (STBLI) is investigated using direct numerical simulation (DNS). The geometry is an $8^{\circ }$ compression ramp, and the flow conditions upstream of the interaction are Mach $7.2$ and $R{e}_{\theta }=3500$. Consistent with experiments at similar conditions, the flow is found to be attached in the mean, although the DNS shows that the probability of observing reversed flow on an instantaneous basis is significant. Due to the high Mach number of the flow combined with a low deflection angle, the shock angle is shallow and the shock is immersed in the boundary layer for a streamwise distance equal to several incoming boundary layer thicknesses downstream of the compression corner. The instantaneous flow structure observed in the DNS is in good agreement with filtered Rayleigh scattering images obtained experimentally that are available in the literature. The behavior of the turbulence is described based on the evolution of the Reynolds stresses, the anisotropy tensor, the wall pressure spectra, and the TKE budget through the interaction. The various Reynolds stress components are found to be amplified by factors of 1.8 to 2.5 with the wall-normal and spanwise components more amplified than the streamwise component. While the flow is attached in the mean, the effect of the adverse pressure gradient is apparent: the mean velocity profiles in the interaction have an inflection point, the turbulence is amplified and becomes more isotropic, and the probability of reversed flow is significant at up to $31\%$. The heat transfer through the interaction is also investigated, as well as the relationship between the velocity and temperature fields. The Reynolds Analogy is found to break down in the interaction, where a heat transfer-pressure scaling more closely describes the behavior observed in the DNS. In the present attached STBLI, the strong Reynolds analogy (SRA), including the assumption of a constant turbulent Prandtl number around unity, is satisfied reasonably well in the interaction, although there are significant departures in the near-wall region.

中文翻译：

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高超声速压缩斜流中的湍流

使用直接数值模拟（DNS）研究了高超声速冲击波/湍流边界层相互作用（STBLI）。几何是$8^{\circ }$ 压缩斜率，并且相互作用上游的流动条件为马赫 $7.2$ 和 $\mathrm{[R}{Ë}_{\theta }=3500$。与在类似条件下进行的实验一致，尽管DNS显示在瞬时基础上观察到反向流量的可能性很大，但发现流量平均存在关联。由于流动的马赫数高且偏转角小，因此冲击角很浅，冲击以一定的流向距离浸没在边界层中，该距离等于压缩角下游几个进入边界层的厚度。在DNS中观察到的瞬时流结构与通过实验获得的滤波瑞利散射图像非常吻合，该图像可从文献中获得。基于雷诺应力的演化，各向异性张量，壁压力谱和通过相互作用的TKE预算，描述了湍流的行为。发现各种雷诺应力分量被放大1.8到2.5倍，壁法向分量和翼展方向分量比流态分量更大。当流量以均值形式附着时，逆向压力梯度的影响是显而易见的：相互作用中的平均速度分布具有拐点，湍流被放大并变得更加各向同性，并且反向流动的概率在上升时显着。至$31％$。还研究了通过相互作用的热传递，以及速度和温度场之间的关系。雷诺模拟被发现在相互作用中破裂，传热压力缩放更紧密地描述了在DNS中观察到的行为。在当前所附的STBLI中，尽管在近壁区域有明显的偏离，但在相互作用中可以很好地满足强雷诺类比（SRA），包括假设统一周围存在恒定的湍流普朗特数。