Improved k–ω–γ model for hypersonic boundary layer transition prediction

Abstract

Two improvements of the k–ω–γ transition model have been developed in this paper. One is reformulating the γ transport equation to retain the physical information contained in the empirical correlations of Dhawan and Narasimha; the other is modifying the timescale of the second-mode to improve the prediction accuracy of nose bluntness effects. Test cases including a supersonic flat plate, a straight cone at different Reynolds numbers, and straight cones with different nose bluntness are employed to assess the performance of the improved k–ω–γ transition model. It is demonstrated that both the original and improved k–ω–γ transition models can predict the correct trends of transition onsets with respect to Reynolds number and nose bluntness effects for hypersonic flow. The reasons for this have also been investigated. Compared with the original k–ω–γ transition model, the improved k–ω–γ transition model with reformulated γ transport equation can provide more accurate transition onsets at different Reynolds numbers, but not quite accurate transition onsets for different nose bluntness; while the improved k–ω–γ transition model with modified second-mode timescale can provide more accurate transition onsets for different nose bluntness. However, both the original and improved k–ω–γ transition models fail to predict the overshoot in wall skin friction and heat transfer observed in DNS and experimental results.