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

Chitrarth Prasad, Datta V. Gaitonde

Published 2022-05-30Version 1

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 high-fidelity counterparts also degrade its accuracy in practical high-speed configurations, especially when fully 3D flows are considered. The current investigation develops a methodology to improve the performance of two-equation turbulence models for a series of increasingly complicated benchmark problems that collectively encompass many of the major phenomena expected in the hypersonic regime. Emphasis is given to both axisymmetric and 3D configurations at Mach numbers in excess of 6. Using the $k-\epsilon$ model as a baseline, two user-defined coefficients are introduced to inhibit the non-physical amplification of (i) turbulence production and (ii) turbulence length-scale downstream of a shock wave. A crucial step is to select the values of these coefficients based on the distribution of turbulence quantities upstream of the shock; this ensures that these modifications do not degrade the model predictions in cases where they are not necessary. Another key feature of these modifications is the reliance on terms already present in the baseline model. Thus, these corrections are straightforward to implement in any existing code and do not increase computational costs. Significant improvements in surface pressure and wall heat flux are obtained for all test cases while retaining the exact computational cost as the baseline. Considerations on the inflow values of turbulence variables and mesh resolution are provided for each test case.