Data-Driven Turbulence Modeling Approach for Cold-Wall Hypersonic Boundary Layers

Wall-cooling effect in hypersonic boundary layers can significantly alter the near-wall turbulence behavior, which is not accurately modeled by traditional Reynolds-averaged Navier–Stokes turbulence models. To address this shortcoming, this paper presents a turbulence modeling approach for hypersonic flows with cold-wall conditions using an iterative ensemble Kalman method. Specifically, a neural-network-based turbulence model is used to provide closure mapping from mean flow quantities to Reynolds stress as well as a variable turbulent Prandtl number. Sparse observation data of velocity and temperature are used to train the turbulence model. This approach is analyzed using a direct numerical simulation database for zero-pressure gradient boundary-layer flows over a flat plate with a Mach number between 6 and 14 and wall-to-recovery temperature ratios ranging from 0.18 to 0.76. Two training cases are conducted: 1) a single training case with observation data from one flow case, and 2) a joint training case where data from two flow cases are simultaneously used for training. Trained models are also tested for generalizability on the remaining flow cases in each of the training cases. The results are also analyzed for insights to inform the future work toward enhancing the generalizability of the learned turbulence model.