A free-streamline theory for bluff bodies attached to a plane wall

Abstract

A free-streamline theory is presented for the separated flow past two-dimensional bluff bodies attached to a long plane wall on which a turbulent boundary layer has developed. The non-uniform velocity profile in the turbulent boundary layer which would be measured if the bluff bodies were absent has been replaced by a hypothetical inviscid parallel shear flow which has a constant vorticity. This model admits analytical solutions and automatically yields closed streamlines in front of the bluff bodies such as the normal plate and the semicircular projection, which are geometrically very similar to observed front separation bubbles. The present theory involves three or four parameters which must be determined on the basis of experimental information, the number of parameters depending upon the shape of bluff bodies. Two typical examples of bluff bodies, i.e. the normal plate and the semicircular projection, are worked out. Pressure distributions around these bodies predicted by the present theory are found to give a good agreement with experimental measurements.