Improvement of Baldwin–Lomax turbulence model for supersonic complex flows

Entropy represents the dissipation rate of energy. Through direct numerical simulation (DNS) of supersonic compression ramp flow, we find the value of entropy is monotonously decreasing along the wall-normal direction no matter in the attached or the separated region. Based on this feature, a new version of Baldwin–Lomax turbulence model (BL-entropy) is proposed in this paper. The supersonic compression ramp and cavity-ramp flows in which the original Baldwin–Lomax model fails to get convergent solutions are chosen to evaluate the performance of this model. Results from one-equation Spalart–Allmaras model (SA) and two-equation Wilcox k–ω model are also included to compare with available experimental and DNS data. It is shown that BL-entropy could conquer the essential deficiency of the original version by providing a more physically meaningful length scale in the complex flows. Moreover, this method is simple, computationally efficient and general, making it applicable to other models related with the supersonic boundary layer.