Hypersonic boundary layers are crucial in aerospace applications such as hypersonic glide vehicles, rockets, and other advanced space vehicles. Hypersonic flows present unique transport phenomena, including nonnegligible flow compression/dilation, extra strain rates, and large momentum/thermal gradients. In this paper, the performance of three widely used turbulence models is compared, namely, the standard $k-\omega$, the shear stress transport (SST) $k-\omega$, and the Spalart–Allmaras (SA). Based on our turbulence modeling assessment plus the analysis of turbulent transport equation budgets over the experimental geometry from a previous study at a Mach number of 4.9, a moderate supremacy of SA over two equation models was found. To back our conclusions, previous experiments and direct numerical simulations at Mach numbers around 5 have been employed. Overall, the three considered models exhibited a consistent ability to predict first-order statistics both inside and outside the boundary layer. The SST variants were capable of describing the amplification of the constant shear layer induced by the presence of an adverse pressure gradient (APG). Furthermore, the SST $k-\omega$ model also replicated the second peak of turbulence production induced by the concave wall. There was a more aggressive distortion of the boundary layer by APG than by favorable pressure gradient (FPG) as compared with a zero pressure gradient (ZPG) boundary layer. A reasonable performance by Walz’s equation in the FPG region is also shown, whereas a notable lack of agreement is seen in the APG. Overall, one could argue for the SA model’s best compromise between accurate predictions, numerical stability, and mesh resolution insensitivity in the FPG and ZPG regions, particularly, in outer or integral boundary-layer parameters such as $\delta$ or $R{e}_{\delta 2}$. That being said, the two-equation models are far superior in terms of predicting near-wall parameters (such as $u_{\tau }$ or $u^{\prime }{v}^{\prime }$) or their ability to accurately describe the physics of the hypersonic boundary layer for APG regions (for instance, outer-secondary peaks of turbulent kinetic energy production).

高超音速边界层在航空航天应用中至关重要，例如高超音速滑翔飞行器、火箭和其他先进的航天器。高超声速流动呈现出独特的传输现象，包括不可忽略的流动压缩/膨胀、额外的应变率和大的动量/热梯度。本文比较了三种广泛使用的湍流模型的性能，即标准$克-\omega$, 剪应力传递 (SST) $克-\omega$和斯帕拉特-阿尔马拉斯 (SA)。根据我们的湍流建模评估以及对先前研究中马赫数为 4.9 的实验几何结构的湍流输运方程预算的分析，发现 SA 相对于两个方程模型具有适度的优势。为了支持我们的结论，我们采用了之前的实验和马赫数为 5 左右的直接数值模拟。总体而言，三个考虑的模型表现出一致的能力来预测边界层内外的一阶统计数据。SST 变体能够描述由不利压力梯度 (APG) 的存在引起的恒定剪切层的放大。此外，SST$克-\omega$模型还复制了由凹壁引起的湍流产生的第二个峰值。与零压力梯度 (ZPG) 边界层相比，APG 对边界层的变形比有利压力梯度 (FPG) 产生的变形更大。还显示了 Walz 方程在 FPG 区域中的合理表现，而在 APG 中则明显缺乏一致性。总的来说，人们可以争论 SA 模型在 FPG 和 ZPG 区域中准确预测、数值稳定性和网格分辨率不敏感性之间的最佳折衷，特别是在外部或整体边界层参数中，例如$\delta$ 或者 $\mathrm{电阻}{\mathrm{电子}}_{\delta 2}$. 话虽如此，两方程模型在预测近壁参数（例如${你}_{\tau }$ 或者 ${你}^{\prime }{v}^{\prime }$) 或他们准确描述 APG 区域高超音速边界层物理的能力（例如，湍流动能产生的外次级峰值）。