Three dimensional laminar boundary layer with small cross-flow

Important problems involving three-dimensional boundary layer occur in almost all internal and external aerodynamic configurations. For many of these, the flow outside the boundary layer may be resolved into a large principal component and a small crosswise velocity. In this paper, three-dimensional laminar boundary-layer flows over flat and curved surfaces are treated under such a simplification. For flat surfaces, the solutions demonstrate the effect of the free stream turning on the velocity profiles in the crosswise and primary flow directions. When the surface curvature is large and varies so as to resemble a corner, the computed examples show the manner in which the asymmetric behavior of the boundary layer results from the cross-flow. The detailed examples are chosen to illustrate flows occurring on the casing and in the blade fillets of turbomachinery.