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.

In the design of the nacelle outer cover profile, it is crucial to maintain the boundary layer's laminar state to minimize wall friction and enhance payload capacity. Understanding the boundary-layer transition mechanisms and accurately predicting the transition front is fundamental to effectively evaluate different designs of the nacelle. In this work, we focus on the stability characteristics of boundary layers over nacelle with three different outer covers under cruise conditions. Considering transition mechanisms correlated with the T-S waves and the shock wave-induced separation bubbles, the transition fronts are predicted. The results indicate that as the unfavorable pressure gradient increases, T-S waves become more unstable, leading to earlier boundary-layer separation. Therefore, maintaining a relatively large range of favourable pressure gradient as well as reducing unfavorable pressure gradient will delay the boundary-layer transition. In addition, for a scaled nacelle model, the predicted transition front and that obtained in wind tunnel tests are morphologically similar, confirming the validity of the prediction method.

As transition occurs in the boundary layer, the flow changes from a laminar state to a turbulent state, resulting in a significant increase of the skin friction. For a nacelle, an accurate prediction of its boundary layer transition is necessary for the accurate calculation of the nacelle surface friction as well as the effective evaluation of the drag on the whole airplane induced by the nacelle outline. So far, the most reliable approach of transition prediction in practice is the linear stability theory based e^N method. In this work, a nacelle under the wing of a wide-body aircraft was studied, with the focus on the boundary layer stability characteristics and the transition location prediction. Firstly, the base flow was obtained by a computational fluid dynamic (CFD) solver using the multiple-block grid and parallel computation technique, and the stability characteristics of the boundary layer over the nacelle were analyzed under typical conditions using the linear stability theory. Secondly, the e^N method was used to provide the transition front distributions. Effects of the angle of attack and the flight Mach number on the boundary layer stability charateristics and the transition location were quantified. The results show that the boundary layer transition over the nacelle is mainly induced by the instability of T-S waves, while the cross-flow instability is weak due to the fact that the cross-flow velocity is less than 3% of the velocity at the outer edge of the boundary layer. As the angle of attack increases, the transition location moves forward in the leeward section as well as in most of the lateral zones, while it moves backward in the windward section. With the increase of the flight Mach number, the frequency range of the T-S wave tends to shrink and its growth rate decreases, the boundary layer becomes more stable, and the transition location appears further downstream.