A near-wall eddy viscosity for compressible turbulent flows based on velocity transformation with application to wall models

A near-wall eddy viscosity is derived for zero-pressure gradient compressible turbulent flows based on a velocity transformation kernel. This is only valid in the inner layer of the flow with application to wall models. A priori analysis is performed using high-speed Direct Numerical Simulation (DNS) databases of turbulent boundary layers and channels over a range of Mach numbers and thermal conditions using the new formulation to assess its accuracy, and compare it with existing eddy viscosity models. Preliminary results are encouraging, and indicate that the errors in the wall model prediction is directly correlated with the error in the velocity transformation. More specifically, the eddy viscosity obtained with the proposed methodology and using the recent compressible velocity transformation of Volpiani et al. (2019) yields accurate results for supersonic and hypersonic turbulent boundary layers.