Roughness-induced laminar-turbulent transition prediction over complex geometries

In natural laminar flow design, aircraft manufacturers aim to delay laminar-to-turbulent transition by modifying the geometric features of the aircraft. The presence surface inhomogeneities greatly affects the transitional properties of the flow and need to be considered for transitional predictions. Historically, linear stability theory (LST) and parabolized stability equations (PSE) have been used to study transition over simple geometries with roughness elements in the incompressible regime. In realistic high-speed aeronautical flows with complex geometries, compressibility, pressure gradients, and roughness effects are no longer negligible. Here, we present a novel numerical framework to investigate roughness-induced transition in compressible flows over complex geometries. The model is formulated in dimensionless variables and uses curvilinear coordinates to account for the curvature of the boundary. The base flow is computed using a general laminar compressible Navier-Stokes solver and interpolated onto the curvilinear coordinate system. The equations for the fluctuating flow are based on the LST/PSE theory and solved using a multi-domain spectral collocation method.