Evaluation of wall modeled large eddy simulation of cold wall hypersonic boundary layer

Large eddy simulation (LES) of wall bounded high Reynolds number flows is challenging due to strict cell size and time-step requirements necessary to resolve the inner layer. This restriction motivated the development of wall models which approximate the near wall behavior using a simplified set of equations, allowing for larger near wall cells and larger time-steps. In this work, we apply wall modeled LES (WMLES) to three turbulent boundary layer test cases to assess the performance of WMLES under cold-wall hypersonic conditions through comparison with direct numerical simulation (DNS) data. We compare velocity and temperature profiles as well as surface statistics including skin friction coefficient and wall heat transfer rate with DNS data. We find that the velocity profile is well captured using WMLES for adiabatic wall conditions, but is slightly under-predicted by WMLES in cases with wall cooling. All cases considered exhibit some error in the predicted temperature profile normal to the wall, particularly around the point where data is exchanged between the LES simulation and the wall model. The skin friction coefficient predicted at the wall is in good agreement with the DNS data, with less than 6% error across the range of conditions studied. We also investigate the effect of moving the wall exchange point for the wall model and find that selecting the first point off the wall yields significant errors as observed by previous researchers.