Linear-stability-theory-based [Formula: see text] method plays an important role in boundary-layer transition prediction of aeronautical flows. Based on the simplification of linear stability theory (Drela and Giles, AIAA J, 1987), the amplification factor transport (AFT) equation for Tollmien–Schlichting waves using local variables was first proposed in 2013 (Coder and Maughmer, AIAA J, 2014). However, in transonic high-Reynolds-number flows, the AFT model seriously overestimates the value of [Formula: see text]. To fix this problem, we have conducted many linear stability analyses to rebuild the formulations of AFT model. Compressibility effect, which has a significant impact on the prediction of [Formula: see text] value, has been considered in the improved version. Coupled with the [Formula: see text] model for crossflow instabilities (Xu et al., CJA, 2020), the improved AFT model is established for transonic boundary layers. Several classic test cases are successfully employed to validate present AFT model, including a flat plate, an airfoil, an infinite swept wing, a sickled-shape wing, a 6:1 inclined prolate spheroid, the NASA Common Research Model, and ARA Transonic Swept Wing. Our prediction results show that both Tollmien–Schlichting instabilities and stationary crossflow instabilities can be captured and predicted well by the improved [Formula: see text] model in subsonic and transonic boundary layers.

The forebody/inlet shape of the scramjet engine is significant to airplane performance. A multi-object optimization of hypersonic body-intake configuration is reported in the present work. The optimization system consists of geometry parameterization, mesh deformation, aerodynamic performance evaluation via computational fluid dynamics (CFD) and the top level driving optimization algorithm. In the present work, geometry parameterization is accomplished through B-Spline based free form deformation (FFD) method, volume mesh deformation is computed via inverse distance weight (IDW) method. Aerodynamic performance is evaluated with shear stress transportation model closed Reynolds averaged Navier-Stokes equations. At the top level, optimization is driven by the non-dominated sorting genetic algorithm II (NSGA-II) algorithm. Finally, the present optimization system is applied to a two dimensional hypersonic combined forebody-intake configuration. Numerical result shows that optimization gained improvement of 5% thrust, 9% pressure rise ratio and 7% total mass flow rate, which approved the effectiveness of the present optimization methodology.

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