The Turbulent Wall Jet in an Arbitrary Pressure Gradient

Abstract

Summary A method for calculating the growth of a turbulent wall jet in streaming flow has been developed. The flow is assumed to be two-dimensional, incompressible and over a plane, smooth wall. Downstream variations of pressure are permitted and separation in an adverse pressure gradient may be predicted. The method incorporates procedures for matching the flow to that at the blowing slot, although it is postulated that the upstream boundary layer there is thin enough that the wall jet develops without an unmixed wake (i.e. there is not a minimum in the mean-velocity profile). The method incorporates four integral momentum equations taken from the wall to various points in the flow. The calculation of the outer shearing stress, although empirical, is based on the large-eddy equilibrium hypothesis and therefore has some foundation. The remaining empiricism in the method is based on measurements in self-preserving wall jets. The method has been used to predict the jet-momentum coefficient required to suppress separation over a trailing-edge flap attached to a thin aerofoil. Plausible curves have been obtained Using assumed values of upstream boundary layer at the slot. Of some practical interest is the indication that large savings in power are possible if the upstream boundary layer is removed. This indicates that blowing combined with upstream suction, or multiple-slot blowing, may give useful savings in the application of blowing to prevent separation.