Compressible Falkner–Skan–Cooke boundary layer on a flat plate

Abstract

The incompressible Falkner–Skan–Cooke (FSC) boundary layer is extended to the compressible regime on a flat plate, aiming at establishing a generalized model to facilitate the crossflow-related investigations. The compressible FSC flow is also compatible with the two-dimensional compressible Blasius boundary layer characterized by a self-similarity solution. A family of boundary layer with local self-similarity is obtained from an ordinary differential equation system. Pressure-gradient parameter and local swept angle are introduced to parameterize the crossflow, which can vary in both direction and magnitude. The results reveal that the crossflow is oriented toward the curvature center of the inviscid streamline, regardless of the direction of pressure gradient. The existence of crossflow results in moderate directional deviation of skin friction, while tiny difference is observed for the magnitude. In comparison, much less effect is observed on the thermal properties of boundary layer. Crossflow also leads to the distortion of vorticity inside boundary layer, accompanied by the production of helicity. In addition, it is revealed that cross-flow strength varies monotonously with the pressure-gradient parameter, while it varies non-monotonously with the local swept angle. The effects of Mach number and wall temperature on crossflow are investigated as well.