Improved Amplification Factor Transport Transition Model for Transonic Boundary Layers

Linear-stability-theory-based e^N 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 N_TS. 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 N_TS value, has been considered in the improved version. Coupled with the N_CF 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 N_TS - N_CF model in subsonic and transonic boundary layers.