Numerical study on evolution of stationary vortices in a hypersonic delta wing boundary layer

Taking a hypersonic delta wing as the research object, this study first applied Linear Stability Theory (LST) to analyze the growth characteristics of stationary vortices with different spanwise wavenumbers, revealing that significantly higher growth rates occur near the leading edge due to strong crossflow effects, which diminish along with the vortex growth rates as the distance from the leading edge increases. Then, the excitation and evolution process of stationary crossflow vortices in the boundary layer under steady blowing and suction at the leading edge of the wing was studied by direct numerical simulation (DNS). The reliability of e^N method for predicting the linear evolution of stationary vortices in the three-dimensional boundary layer was tested. The results show that the downstream evolution path of stationary vortices in the boundary layer is closely related to its spanwise wavenumber. The larger the spanwise wavenumber is, the greater the deviation between the evolution path and the integral path usually used by e^N method in three-dimensional boundary layers —— inviscid streamline, resulting in the deviation on the amplitude of disturbance evolution. Therefore, a method to modify the integral path based on inviscid streamline was proposed. Comparative assessments against DNS data for specific wavenumbers (β = 7.5 and 10) demonstrated a significant improvement in prediction accuracy. The maximum amplitude prediction deviation was reduced from 12% to 1% for β = 7.5 and from 6% to 1% for β = 10, confirming the effectiveness of the path modification and the validity of LST for amplitude prediction when using the corrected integration path. The results show that the e^N method can predict the amplitude evolution of stationary vortices in the delta wing boundary layer more accurately by integrating along this path. This work provides a practical improvement to transition prediction for high-speed delta-wing configurations, where crossflow instability plays a dominant role.