A study of turbulent boundary-layer separation and reattachment

Abstract

An experimental and theoretical study is made of a suddenly separating and reattaching two-dimensional turbulent boundary layer on a flat surface. A separation bubble is formed on the floor of a wide parallel-sided wind-tunnel duct with the pressure field causing the bubble formation produced by fixing the shape of the flexible roof of the duct. Boundary layers on the roof are controlled and remain attached. It is found that a very satisfactory model for the flow is an inviscid one.The boundary layer on the floor of the duct is represented by a region of constant vorticity with slip at the boundary, and it is assumed that the separation process is dominated by the interaction between this ‘vortical’ region and the irrotational field between the vortical region and the roof (of prescribed shape). The interface between the rotational and irrotational regions is a free boundary and may be located when all necessary boundary conditions are given. These conditions include two characteristic parameters for the adverse-pressure-gradient turbulent boundary layer which is developing upstream of the region of interest.The problem is solved by an electrical analog method. The theoretical size and shape of the bubble and positions of separation and reattachment are in agreement with observations. The advantage of the model over most previous attempts to predict separation is that the governing equations are elliptic rather than parabolic or hyperbolic and therefore the interaction between the boundary-layer flow and the irrotational free stream is included in the calculations.