In the context of hypersonic flows, shock-wave/turbulent boundary-layer interactions (SWTBLIs) can lead to substantial aerodynamic heating. The commonly used Reynolds-averaged Navier–Stokes (RANS) method in engineering applications faces challenges in accurately predicting heat transfer in these conditions, as the assumptions made by Morkovin’s assumption in the RANS method are not applicable in hypersonic SWTBLI flows. This article addresses these challenges by introducing a variable turbulent Prandtl number () model for non-adiabatic walls, established through field inversion and symbolic regression (SR) techniques. The methodology begins with field inversion for an oblique SWTBLI case at Mach 5. The corrected field, denoted as , obtained from this inversion, is integrated with selected local flow characteristics to derive a corrected expression using SR. Following the necessary adjustments, this expression is incorporated into the RANS solver. Various cases with different wall cooling ratios, Mach numbers, and Reynolds numbers are chosen to assess the generalization ability of the variable model. The outcomes demonstrate a substantial improvement in the model’s ability to predict heat transfer in hypersonic SWTBLI flows without compromising the baseline model’s performance in predicting the undisturbed boundary layer. The correction effect remains notably enhanced even in complex three-dimensional cases.

中文翻译：

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通过符号回归增强 SST 湍流模型以预测高超音速流中的热通量


在高超音速流中，冲击波/湍流边界层相互作用（SWTBLI）可能导致大量的气动加热。工程应用中常用的雷诺平均纳维-斯托克斯 (RANS) 方法在准确预测这些条件下的传热方面面临着挑战，因为 Morkovin 在 RANS 方法中的假设所做的假设不适用于高超声速 SWTBLI 流。本文通过引入非绝热壁的可变湍流普朗特数 () 模型来解决这些挑战，该模型是通过场反演和符号回归 (SR) 技术建立的。该方法首先对马赫数为 5 的倾斜 SWTBLI 情况进行场反演。从该反演获得的校正场（表示为 ）与选定的局部流动特性相结合，以使用 SR 导出校正表达式。经过必要的调整后，该表达式被合并到 RANS 求解器中。选择具有不同壁面冷却比、马赫数和雷诺数的各种情况来评估变量模型的泛化能力。结果表明，该模型预测高超音速 SWTBLI 流中传热的能力得到了显着提高，同时又不影响基线模型预测未受扰动边界层的性能。即使在复杂的三维情况下，校正效果仍然显着增强。