No abstract

A computational study of laminar/turbulent and subsonic/supersonic horseshoe vortex systems generated by a cylindrical protuberance mounted on a flat plate is presented. Various vortex structures have been predicted and are discussed. For a low subsonic laminar flow, the number of computed vortex arrays increases with Reynolds number (with fixed incoming boundary-layer thickness), in agreement with experimental and previous numerical observations. The relationships among pressure extrema, vorticity, and the singular points in the flow structure on the plane of symmetry over the flat plate are studied. Mach number effects have also been investigated for laminar flow at one Reynolds number. The outermost singular point moves upstream when freestream Mach number increases. The size of the whole vortex structure increases dramatically due to shock-wave/boundary-layer interaction. The computed laminar horseshoe vortex systems start from a saddle point of attachment. In the case of a supersonic turbulent flow at a high Reynolds number, the computed results predict the same features as those indicated by the experimental results, such as the upstream shock-wave/ boundary-layer interaction and the classical horseshoe vortex system starting from a saddle point of separation. The calculations provide details of the downstream wake/shock-wave interaction and the near wake tornadolike vortex structure. The overall flow topology is discussed. Nomenclaturemeasured from the flat plate and cylinder E = extremum of p(x) H = height or semiheight of cylinder (clear from context) MOO = freestream Mach number N, N' = node and half-node, respectively p = pressure Re D = Reynolds number based on cylinder diameter S = saddle or separation (clear from context) S'-half-saddle u = velocity component in x direction x, y, z = Cartesian coordinates (origin is at center of cylinder) 6, = incoming boundary-layer thickness <5= cylinder-location boundary-layer thickness £, ry = vorticity components in x, y directions 9 = angle of separation or attachment IJL, IJL ( = molecular and turbulence eddy viscosity

Because of its reputed benign nature, the saddle point of attachment has not received critical attention to nearly the same extent as has the saddle point of separation. Recently, Visbal calculated low-speed flows around a cylinder mounted on a flat plate. Here, it was fully to be expected that the outermost critical point in the surface flow pattern ahead of the obstacle would be a saddle point of separation. The results indicated that the critical point was actually a saddle point of attachment, not separation. These results have brought to light a number of issues requiring additional study. In the present study, two numerical codes are used for a wide range of Mach numbers, Reynolds numbers, grid sizes, and numbers of grid points to confirm the existence of the saddle point of attachment in the flow before an obstacle. The computational results near the critical point are theoretically analyzed. The impact and significance of the saddle point of attachment to the interpretation of experimental surface flow patterns and the definitions of lines of separation and attachment are discussed. A line of oil accumulating from both sides can be either a line of separation or a line of attachment, depending on the characteristics of the saddle point.

No abstract