A combined criteria-based method for hypersonic three-dimensional boundary layer transition prediction

In this paper, a new method for predicting hypersonic three-dimensional (3D) boundary layer transition is developed. It is based on the Re_θ/M_e criterion for streamwise instability and on the Re_cf,new criterion for crossflow instability. An intermittency function is also formulated and applied to combine laminar and turbulent flows. Additionally, a computational grid pretreating method, compatible with modern computational fluid dynamics (CFD) techniques based on parallel execution is adopted in order to obtain the boundary layer parameters. Four criteria are compared to define the boundary layer edge. A HIFiRE-5 elliptic cone at different Reynolds numbers is adopted to validate the performance of the criteria-based transition model and the effectiveness of the four criteria for boundary layer edge definition. The results show that the boundary layer edge of complex hypersonic 3D flows could be obtained properly with the computational grid pretreating method and the combination of h₀/h_0,∞=0.995 and (du/dH)/(du/dH)_w=0.1 criteria. Moreover, the computed Re_θ/M_e and Re_cf,new distributions in the region between the leading edge and the centerline are similar to the N-factor for streamwise and crossflow instabilities from linear parabolized stability equation (PSE) methods. The shape and trend of the transition onsets predicted by the criteria-based transition model between the centerline and leading edge of HIFiRE-5 agree well with the experiment. However, as for the transition on the centerline, which is dominated by the inflection point in streamwise velocity profiles, using the criteria-based transition model related to boundary layer thickness would predict the transition onset prematurely.