A Modified Entrainment Theory for the Prediction of Turbulent Boundary Layer Growth in Adverse Pressure Gradients

Abstract

An approach based on the “entrainment” theory is presented as a tool for the prediction of turbulent boundary layer growth in adverse pressure gradients. The rate of entrainment of free-stream fluid by the boundary layer is assumed to be a unique function of the shape factor. A two parameter velocity profile has been assumed, which reduces to the Spalding [24] profile for zero pressure gradient flows and to the half-power profile of Stratford [26] for separating flows. The integral equations of continuity and momentum are solved with the above empirical input to predict the growth of the boundary layer parameters, both in two-dimensional and axisymmetric flows. The predictions are compared with some of the available experimental data in both the cases. The technique is found to give improved predictions compared with those of previous methods. Results in the case of conical diffusers indicate that the theory predicts slightly higher shape factors than actual, especially in the far downstream portions of the diffuser and thus furnishes a slightly conservative method for design.