Transition front prediction for the HyTRV model based on multi-dimensional stability theories
Ligeng Zhang, Xi Chen, Shuyi Liu, Qian Wang, Siwei Dong, Maochang Duan, Jianqiang Chen
Abstract
Abstract The prediction of three-dimensional boundary layer transition has long been an important issue in aircraft design. The eN method based on one-dimensional stability theories (LST-eN) is widely used in transition prediction, yet fails to capture transition features of large-scale vortical structures commonly present on the vehicle surface. The vortical structures cause substantial spanwise variations of the base flow and thereby render the one-dimensional stability theories invalid. We in the present study modulate the eN method by exploiting multi-dimensional stability theories, especially the plane-marching parabolized stability equations (PSE3D), to predict the windward transition front of a lifting body under a high-speed flight condition (FLT) and a wind-tunnel condition with two angles of attack (WT1 with 2-degree angle of attack and WT2 with 4-degree angle of attack). The modal instability characteristics for the centerline vortex region in these three cases are similar, featuring the upstream Mack-mode instability and the downstream vortex instabilities. The transition N -factor front qualitatively aligns well with direct numerical simulation (DNS) results for the flight case and the experimental measurements for the wind-tunnel cases. The transition N -factor is correlated to be around 2 for the flight case (based on the DNS data), around 4 for the wind-tunnel case WT1 and around 2 for the wind-tunnel case WT2. Intriguingly, the WT2 case experiences an earlier transition than the WT1 case although the former turns out to be more stable as predicted by the modal stability analysis. Preliminary non-modal analysis shows that non-modal growth is stronger in the WT2 case than in the WT1 case, implying that non-modal disturbances may play a role in the transition process. The cross-flow instability is also addressed for the flight case, focusing on the comparison of results from the one- and multi-dimensional stability analyses.