Inflow turbulence generation for compressible turbulent boundary layers

Abstract

It is still challenging to generate high-quality inflow turbulence for the direct numerical and large-eddy simulations of compressible turbulent boundary layers (CTBL). Recently, Wang et al. [“Inflow turbulence generation using an equivalent boundary layer model,” Phys. Fluids 35, 075110 (2023)] proposed a new inflow turbulence generation method based on an equivalent boundary layer model for incompressible turbulent boundary layers. In the present study, the compressible equivalent boundary layer (CEBL) model is proposed and applied to the direct numerical simulation of supersonic turbulent boundary layers. The streamwise equilibrious CEBL approximates the streamwise developing CTBL by adding source terms to the governing equations to recover the mean mass, momentum, and energy balances at a given Reynolds number. Direct numerical simulation is performed to CEBL at free-stream Mach number 5.86 and friction Reynolds number 380. Comparison with the CTBL statistics at the same parameters validates the fidelity and reliability of the CEBL model. Turbulence generated by CEBL as well as the digital filtering and recycling-rescaling methods is used, respectively, to construct the inflow conditions for the direct numerical simulation of supersonic turbulent boundary layers. Results show that the CEBL method has great superiority in reducing the adjustment length compared with the other two methods. In addition, a correction method designed for the high inflow Reynolds number is also introduced.