Prediction Method of Cross-Flow Instabilities-Induced Transition Based on Spalart-Allmaras-γ-${\overline {Re} _{\theta {\rm{t}}}}$ Transition Model

The prediction of cross-flow instabilities transition phenomenon is difficult to be combined with modern CFD parallel computation using traditional stability theory. To solve this problem, on the basis of SA-γ-${\overline {Re} _{\theta {\rm{t}}}}$ transition model, a new transition model was presented in this paper, which solved cross-flow displacement thickness Reynolds number locally using three-dimentional boundary layer similar solution and also set cross-flow instabilities transition criterion referring to C1-criterion. Thereby, it can solve the cross-flow instabilities transition prediction method locally and parallelly. Then, the streamwsie transition of NLF(1)-0416 airfoil was predicted to prove the validity of present SA-γ-${\overline {Re} _{\theta {\rm{t}}}}$ -CF transition model. Adopting this model, numerical simulations of cross-flow instabilities transition were conducted for both infinite swept NLF(2)-0415 wing and standard 6:1 prolate spheroid. Computing results show that calculating transition locations are in good agreement with experimental data, which demonstrates the rationality of the model presented.