Turbulence Modeling in Hypersonic Turbulent Boundary Layers Subject to Convex Wall Curvature

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 Re-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'v') 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).