Physics of vortical flows

Abstract

Separation in three-dimensional flows leads to the formation of vortical structures resulting from rolling up of the viscous flow sheet, initially contained in a thin boundary layer, which springs up from the surface into the outer perfect fluid flow. A clear physical understanding of this phenomenon must be based on a rational analysis of the flowfield structure using the critical-point theory. With the help of this theory, it is possible to interpret correctly the surface flow patterns that constitute the imprints of the outer flow and to give a rational and coherent description of the vortical system generated by separation. This kind of analysis is applied to separated flows forming on typical obstacles, the field of which has been thoroughly studied by means of visualizations and probings using multihole pressure probes and laser velocimetry. Thus, the skin friction line patterns of a transonic channel flow and of a multibody launcher are interpreted. Then, the vortical systems of a delta wing and an afterbody at an incidence are considered. The last two configurations are a missile fuselage-type body and an oblate ellipsoid. I. Introduction F LIGHT at high-incidenc e of combat aircraft or hypersonic vehicles during re-entry, as well as that of tactical missiles, raises practical interest on the study of three-dimensional separated flows. Applications also concern internal flows, in particular air intakes and turbomachines in which the often complex geometry of the channel and the existence of shock waves almost inevitably lead to boundary-laye r separation. In three-dimensional flows, separation entails the formation of vortical structures—frequently, but improperly, called vortices to simplify—form ed by rolling up of the viscous flow sheet, previously confined in a thin layer attached to the wall, which suddenly springs into the outer nondissipative flow. Although it has been known for a long time, this phenomenon is still incompletely understood from a physical point of view and it is delicate to model due to the flowfield complexity, all the components of which are difficult to capture properly. Many predictive methods are based on perfect fluid models, the first of which use the vortex sheet concept. Such a sheet is defined as a surface of tangential discontinuity for the velocity field. The computational method can use different schemes: doublets, vortex filaments, vortex particles, and so forth. Publications in this domain are too numerous to be cited here. A greater accuracy in flow prediction can be obtained in the solution of the complete Euler equations, which allows, in theory, automatic capture of sheet-like disconti