A simplified approach to laminar separation bubbles

A simple method is developed for modeling the flow and heat transfer in steady two-dimensional laminar boundary layer flows containing thin separation bubbles. The boundary layer in the local interactive region is divided into two1 layers: a viscous region near the wall and a quasi-inviscid rotational layer. The streamline which divides these two regions is somewhat arbitrary at the outset; but numerous calculations and comparisons with interacting boundary layer and triple-deck results show that, within a certain range based on the length scale of the problem, the results are insensitive to its choice. The viscous layer establishes a simple relationship between the pressure distribution and either the wall shear stress or streamline variation. Investigions of solutions to these equations show that certain constraints must be satisfied by a pressure distribution at and between separation and reattachment, thus demonstrating why difficulties are encountered in calculating through separation with a fixed pressure distribution. Furthermore, the general features of the solutions which can be obtained through an inverse method of solution be qualitatively typical of separated flows. When this model is applied to several basic geometries, solution of the nonlinear ordinary differential equation for the pressure and that for the outer elliptic flow which includes the displacement effect of the boundary layer requires only several seconds of computation time yet yields results for the boundary layer quantities of interest that agree well with results of detailed numerical investigations.