Enhancing the SST turbulence model for predicting heat flux in hypersonic flows through symbolic regression

• Published in: Acta astronautica 2024-09, Vol.222, p.244-271
• Main Authors: Tang, Denggao, Zeng, Fanzhi, Yi, Chen, Zhang, Tianxin, Yan, Chao
• Format: Article
• Language: English
• Subjects: Data-driven; Heat transfer; SWTBLI; Turbulence model; Turbulent Prandtl number
• ISSN: 0094-5765; 1879-2030
• DOI: 10.1016/j.actaastro.2024.06.018

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 (Prt) 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 β(x), 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 Prt 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. •Corrected heat flux and skin friction by adjusting Reynolds stress and turbulent Prandtl number.•Developed a variable Prandtl number model using symbolic regression.•Analyzed physical mechanisms of the modified SST model for separated flow. analyzed.•Nine hypersonic SWTBLI flows showed significant improvements in calculations.