Effects of nose-bluntness on linear optimal disturbance of high-speed blunt wedge boundary layers

The leading-edge bluntness of high-speed vehicles is a key parameter affecting their boundary-layer transition characteristics. To investigate the transition mechanism of large blunt-nose models under conditions in which traditional linear stability theory (LST) fails, this paper studied the influence of nose bluntness on linear optimal disturbances (i.e., non-modal instability) in the boundary layer for eight blunt wedge models with different bluntness levels under Mach 5.96 conditions. The research employed a combined approach of numerical simulation and theoretical analysis: first, the fifth-order WENO scheme was used to solve the Navier-Stokes equations to obtain high-precision two-dimensional base flows; subsequently, based on the optimal growth disturbance theory using linear parabolized stability equations (LPSE), the optimal disturbance energy gain at zero frequency and its spatial evolution characteristics for different bluntness levels were calculated and analyzed. The results indicate that significant transient growth characteristics exist within the boundary layer of the blunt wedges. As bluntness increases, the optimal inlet starting position of the optimal disturbance moves downstream, and both the optimal energy gain and its corresponding N-factor gradually decrease. This suggests that increased bluntness suppresses the growth of optimal disturbances, which is qualitatively consistent with the experimentally observed phenomenon of the transition location moving downstream with increasing bluntness. Although the linear optimal disturbance growth theory adopted in this study cannot explain the "transition reversal" phenomenon observed when bluntness exceeds a certain threshold, it can explain the phenomenon of transition delay for relatively small bluntness.