  Wall-cooling effect in hypersonic boundary layers can significantly alter the
near-wall turbulence behavior, which is not accurately modeled by traditional
RANS 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 direct numerical simulation database for
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, 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 towards
enhancing the generalizability of the learned turbulence model.
