An interactive boundary layer model compared to the triple deck theory

Abstract

The aim of this article is to give a new insight leading to a better understanding of two-dimensional steady laminar incompressible separated flows on an indented flat plate. The asymptotic structure of the strong viscous interaction has been widely studied with the so-called “triple deck theory”. This theory will be recalled firstly. For this, we will use the method of matched asymptotic expansions with a matching principle called “Modified Van Dyke principle” which removes all known counter-examples to the classical matching of Van Dyke. Then, using a new method called the “successive complementary expansions method”, we are able to obtain the interactive boundary layer equations (IBL). The IBL theory relies upon generalized boundary layer equations which are strongly coupled to inviscid flow equations. Here, the IBL theory is established on a rational basis thanks to the use of generalized asymptotic expansions. It is then demonstrated that the triple deck is obtained as regular expansions of the IBL formulation. Finally, numerical results for a standard indentation on the flat plate are given. IBL theory, contrary to triple deck, is non-local. Moreover, it is shown that the triple deck hypothesis of zero pressure gradient normal to the wall is not always appropriate.