Numerical modeling of viscous separated flow in the near wake

Abstract

The present paper studies laminar flow in the near wake behind a short blunt body. We have obtained the dependence on the Mach number and Reynolds number of the incident stream of a number of geometrical characteristics of the wake, the relative base pressure, and its contribution to the total body drag. Examples are given of the influence of body shape and its surface thermal regime on the base pressure. It has been observed that for some incident stream parameters fine-scale vortices form near the separation point (an analogous phenomenon has been mentioned earlier in individual experimental studies), and a local supersonic zone can occur on the axis of symmetry in the reverse flow. i. Formulation of the Problem and Method of Solution. We consider flow about an axisymmetric body with a vertical base truncation. A uniform supersonic stream of viscous compressible heat-conducting gas flows over the body at zero angle of attack. In accordance with theoretical ideas and on the basis of the available test data (see, e.g., [i, 3]) we can give the following scheme for the separated flow in the near wake. Under the influence of inertia forces, which predominate over the viscous forces, the boundary layer leaving the body separates from the body corner at the point G (Fig. i), located somewhat below the corner point F. The separated viscous layer entrains part of the gas occupying the wake region, thereby lowering the pressure there, and together with the external stream it is deviated toward the axis, where at some distance from the base rim it merges with the symmetric viscous layer, forming the wake throat. In the merge zone the base pressure increases, the flow is turned again (almost parallel to the axis), and a tail shock forms. The internal part of the viscous layer, close to the axis, losing speed due to interaction with the gas from the separated region, cannot overcome the increased pressure in the wake throat, and turns back toward the base of the body, and in the established near wake there forms a closed region of recirculating flow, separated from the rest of the flow by the dividing streamline GH. In the external inviscid flow there is flow expansion in the vicinity of the corner point F; immediately beyond the fan of expansion waves there is a stern shock wave, due to re-expansion of the wall viscous layer at the corner point. (Figure 1 also shows stream lines and pressure profiles obtained in one of the computations, and in these one can see the location of the tail shock.)