Analysis and Modeling of Pressure Recovery for Separated Reattaching Flows

Analyses have been carried out on the mean pressure data for separated reattaching flows downstream of a variety of 2-D bluff-bodies to reveal some similarity features. The step height has been identified as an important parameter in relationships such as the correlation between the reattachment length $xr$ and the initial shear-layer angle. The separation velocity (deduced from separation pressure $cps)$ in the direction perpendicular to the upstream flow increases linearly with the reattachment length at fixed step heights. The streamwise location of the vortex center $xv$ (deduced from mean streamline plots) correlates with the location of minimum pressure $xm$ and each varies linearly with the reattachment length. Pressure force, moment and center of pressure induced by the standing vortex also increase with the reattachment length. An inviscid flow model of a rectilinear stationary vortex above a flat wall leads to a general form of the pressure recovery $cp−cp min/cp max−cp min)=8/9x^2x^2+1/x^2+1/32xm<,<xr$ where $0⩽x^1=Xm/Xr$ and $cp max$ and $cp min$ are respectively the maximum and minimum pressure coefficients. It is demonstrated that the present analyses allow the pressure distributions downstream of various fore-bodies to be realistically predicted.