A method for integrating the boundary-layer equations through a region of reverse flow.

Abstract

Development of a procedure for numerically integrating the boundary-layer equations through a region of reverse flow which takes downstream influence into account. This method is applied to the problem of uniform flow past a parallel flat plate of finite length whose surface has a constant velocity directed opposite to that of the main stream. Although singularities occur at both the point of detachment (x sub s) and reattachment (x sub r) of the psi = 0 streamline, this integration technique provides a solution which ceases to apply only in the close proximity of these singular points. From this solution it is evident that, throughout a large portion of the separated region, the flow is strongly affected by conditions near x sub r, thereby demonstrating the importance of allowing information to be transmitted upstream in a region of backflow. Near x sub s, however, it is found that, in spite of the presence of reverse flow, the solution has a self-similar form in this particular example.