Turbulent Shear Layer Re-Attachment with Special Emphasis on the Base Pressure Problem

Abstract

SummaryAn analysis is presented which enables the boundary-layer thickness parameters of a re-attaching shear layer to be determined when the free-stream flow upstream of the base is supersonic, the base pressure is known, and die initial boundary layer is turbulent. The application of this analysis to some experimental results, on the flow behind blunt-trailing-edge wings and over a back-step where both the base pressure and the initial boundary layer are known, would appear to indicate that the re-attached profile could be specified by one parameter, namely the transformed shape parameter, the transformation used being a turbulent analogue of the well-known Stewartson-Illingworth transformation of the laminar boundary layer and where the shape parameter is defined as the ratio of boundary-layer displacement to momentum thickness. By adopting a value of the shape parameter in advance, it is possible to use the analysis to determine the base pressure by an iterative process and so, on this basis, it is suggested that this analysis is used to replace the existing recompression criterion of the Chapman-Korst model of separated flow which aims to predict base pressures and is known to be capable of improvement.As part of this investigation, an improvement had to be made to the existing compressible turbulent shear layer velocity profiles of Korst and others and this was achieved by means of the compressibility transformation.