Two-Dimensional Flow With Standing Vortexes in Ducts and Diffusers

Abstract

The conditions for the equilibrium of two vortexes in a two-dimensional flow through a duct or diffuser are derived. Potential-flow considerations and a few basic results from viscous-flow theory are used for the discussion of the role of cusps as separation control and trapping devices for standing vortexes. The investigations are applied to cusp diffusers especially with regard to the wind tunnel of the James Forrestal Research Center of Princeton University.

Discussion: “Remarks on Snow Cornice Theory and Related Experiments With Sink Flows” (Heskestad, Gunnar, 1966, ASME J. Basic Eng., 88, pp. 539–547)

“…Three points particularly seem to need comment: (i) the explanation for lack of stability of Ringleb geometries based on arguments about vorticity, (ii) the description of the separated regions with suction as "sink flows," and (iii) the question of three-dimensionality and end conditions. All these comments stem from Heskestad's omission of the continuity condition used by Chapman, et al [13], 3 Korst, et al [14], and the present discusser [15] for various purposes in connection with separated flows of various configurations. Consequently this concept is briefly restated next.…”

“…The crux here is the need for an escape path for the stagnation pressure deficient fluid. 3 Numbers in braekets designate References at end of discussion.…”