On the Behavior of Turbulent Boundary Layers near Separation

Abstract

Theme O NE of the most important problems in aerodynamics is the phenomenon of separation that defines the initiation of the wake. The location of separation can be determined analytically by virtue of the boundary-layer theory, even though this theory is not valid in the immediate neighborhood of separation. In most practical applications the boundary layers are turbulent along the largest portion of the solid boundaries and most often, in the vicinity of separation. A large number of methods have been developed to solve the turbulent boundary-layer equations with an appropriate closure assumption, but a straightforward numerical integration in their differential form was attempted only in the late sixties. A number of such investigations is referenced in the accompanying engineering report of this paper.{ For steady laminar and turbulent boundary-layer flow the location of separation is signaled by the vanishing of the wall shear. This criterion has been extensively used in laminar flows for both experimental and analytical investigations.2 However, for turbulent flow the use of simplified theoretical models has forced investigators to develop heuristic criteria based on approximate expressions that approach certain values in the neighborhood of separation. The present report reconsiders the problem of turbulent separation. The classical closure assumptions are restated and their applicability in the neighborhood of separation is discussed. Some typical features of the flow are checked against available experimental data and previous theoretical predictions. Further, the location of separation is calculated and the response of the boundary-layer equations in the neighborhood of separation is carefully investigated. The present effort is intended to be a step towards the generalization of the method to unsteady flow.