Assessment of turbulence modeling for massively-cooled turbulent boundary layer flows with transpiration cooling

Abstract

We assess Reynolds-averaged Navier–Stokes (RANS) turbulent closures for the prediction of a turbulent boundary layer with transpiration cooling via comparison with a high-fidelity direct numerical simulation database. This study considers the canonical zero-pressure gradient, flat-plate, turbulent boundary layer over a massively cooled wall, with transpiration cooling. The simulations are conducted at a low-subsonic Mach number and we study two transpiration cooling configurations with uniform and slit injection at various blowing ratios. The DNS and RANS simulation setups are nearly identical. The RANS-based turbulence models perform well in the qualitative estimation of the velocity and thermal boundary layer evolution at low-blowing ratios (F = 0.2 and 0.6%); more significant differences are noted at higher blowing ratios (F=2.0%). The RANS models, especially the Spalart–Allmaras model, over-predict turbulence production near the wall which results in faster growth in the boundary thickness; this error becomes more pronounced at higher blowing ratios. Despite the greater mixing of momentum, the thermal mixing is under-predicted compared to the DNS in the uniform blowing case but over-predicted for the slit case. These results suggest that modeling errors in the temperature distribution due to turbulent thermal flux modeling can be significant even if the velocity is correctly modeled.