The laminar separation of an incompressible fluid streaming past a smooth surface

Abstract

Abstract Sychev’s (1972) proposal, that in general the laminar separation and breakaway of an incompressible fluid streaming past a smooth surface (e. g. on a bluff body) takes place through a triple-deck structure around the separation point, is examined numerically in this paper. The proposed pattern for large Reynolds number (Re) flows is based on a modification of the classical Kirchhoff (1869) free streamline theory, in which a slight adverse pressure gradient is provoked in the inviscid motion immediately ahead of the breakaway. This pressure gradient is just enough to generate a triple-deck development closer to the separation point. The major task then is to decide whether or not a solution of the basic triple-deck problem exists, and is regular at separation, and if it is unique. The numerical in-vestigation, an iterative calculation of the relevant boundary layer problem, together with the potential flow relation between the unknown pressure and displacement, points fairly firmly to both the existence and uniqueness of a solution. Thus, for the bluff body problem when Re ≫1, the triple-deck determines exactly how far the separation point lies from the position implied by inviscid (Kirchhoff) theory. Comparisons with separating incompressible fluid motions determined numerically from the Navier-Stokes equations and measured experimentally give some support overall to the triple-deck description. For the flow past a circular cylinder the agreement in the variation of pressure and skin friction near separation is in general very encouraging, for Reynolds numbers as low as 30.