Boundary layers with strong interaction: from asymptotic theory to calculations method

Abstract

A quasi-simultaneous method is described to calculate laminar, incompressible boundary layers interacting with an inviscid external flow. The essential feature of this method is an interactive boundary condition prescribing a linear combination of pressure and displacement thickness, which models the behaviour of the external flow. This way the method avoids difficulties incurred when either direct or inverse methods are used, resulting in fast convergence of the iterative procedure involved. The design of the method has been guided by the properties of the "triple-deck", which asymptotically - in the limit of vanishing viscosity - can describe interacting boundary layers. Of special importance is the lack of hierarchy between the viscous and inviscid parts of the triple-deck; a situation which is termed "strong interaction". This observation suggests the (quasi-) simultaneous treatment of the boundary layer and the external flow, which is the essential feature of the present method. The quasi-simultaneous method will be demonstrated by means of two types of strongly interacting boundary layers : i) separated boimdary layers, and ii) trailing edge flow. In the latter case a comparison with results from asymptotic theory can be made.