Effect of Leading-Edge Curvature on Receptivity of Stationary Cross-Flow Modes in Swept-Plate Boundary Layers (Advances in Applied Mathematics and Mechanics, 2020)
The prediction and control of the laminar-turbulent transition in three-dimensional boundary layers are crucial for the designs of vehicles, aircrafts, etc. Receptivity, the initial stage of transition, is the key to implement the prediction and control of the transition process. Former experimental results showed that, under a relatively low-level turbulence, the three-dimensional boundary-layer transition is mainly induced by the stationary cross-flow modes rather than the travelling ones. Near the leading edge, stationary cross-flow modes can be excited by three-dimensional localized roughness. And the receptive process is affected by both the size of roughness and the shape of leading edge which distorts the mean flow over the plate. Therefore, we perform direct numerical simulation to investigate the excitation of stationary cross-flow modes by three-dimensional localized wall roughness in swept-plate boundary layers with various elliptic leading edges. The effect of the leading-edge curvature on the induced stationary cross-flow modes is revealed. And the relations of the leading-edge curvatures with the amplitudes and dispersion relations of the stationary cross-flow modes are determined. Furthermore, the correlations between the receptivity coefficients and the geometries, locations and numbers of the roughness respectively are analyzed in different leading-edge curvatures. This research aims to complement the study of receptivity in the cross-flow boundary layer.