Turbulence Modeling of 3D High-speed Flows with Upstream-Informed Corrections

Abstract

Turbulence modeling has the potential to revolutionize high-speed vehicle design by serving as a co-equal partner to costly and challenging ground and flight testing. However, the fundamental assumptions that make turbulence modeling such an appealing alternative to its scale-resolved counterparts also degrade its accuracy for practical high-speed configurations, especially when fully 3D flows are considered. The current investigation develops a methodology to improve the performance of turbulence modeling for a complex Mach 8.3, 3D shock boundary layer interaction (SBLI) in a double fin geometry. A representative two-equation model, with low-Reynolds number terms, is used as a test-bed. Deficiencies in the baseline model are first elucidated using benchmark test cases involving a Mach~11.1 zero pressure gradient boundary layer and a Mach~6.17 flow over an axisymmetric compression corner. From among different possibilities, two coefficients are introduced to inhibit the non-physical over-amplification of (i) turbulence production and (ii) turbulence length-scale downstream of a shock wave. The coefficients rely on terms already present in the original model, which simplifies implementation and maintains computational costs. The values of the coefficients are predicated on the distribution of turbulence quantities upstream of the shock; this ensures that the modifications do not degrade the model predictions in simpler situations such as attached boundary layers, where they are unnecessary. The effects of the modifications are shown to result in significant improvements in surface pressure and wall heat flux for the 3D SBLI test case, which contains numerous features not observed in 2D situations, such as 3D separation, skewed boundary layers and centerline vortices. Considerations on the inflow values of turbulence variables and mesh resolution are provided.