New insights from inviscid modelling of starting flow separation with roll-up

Abstract

Abstract

A theoretical model for the separated flow around an accelerating flat plate using time-dependent self similarity

“…As mentioned in Ref. [17], the higher-order terms in (1) introduce additional topological features. In the case of (2), the regular flow opposes the singular flow on one wedge face and contributes to it on the other face, and so a hyperbolic stagnation point z s appears on the surface of opposing flows at a radial distance from the apex of…”

“…In the particular case of flow around a sharp wedge of interior angle βπ (0 ≤ β < 1) with apex located at z = 0 (see figure 1 for geometry), the complex potential of the attached flow can be written as [17]…”

“…3,11). In DeVoria & Mohseni [17] we significantly augmented the solution space by considering an entrainment boundary condition (in place of no through-flow) that allows a complex coefficient A 1 ∈ C and the shedding of a vortex-entrainment sheet [19].…”

“…We refer the reader to Refs. [18] and [17] for more details on the self-similar problem setup. It can be shown that the velocity induced by one vortex sheet on the other at the opposing edge is of the same order as terms that we eventually will ignore and is therefore neglected now.…”

“…In particular, when η α = J o = 0, (13) reduces to the equation numerically solved by Pullin [18] and thus inclusion of non-zero values of these parameters requires only minor amendment. We use the numerical scheme described in DeVoria & Mohseni [17], which studied cases of non-zero entrainment in the starting-flow separation over sharp wedges.…”