Further consideration of the shape-factor relationship for turbulent boundary layers

The lag-entrainment predictive scheme developed by Green et al. has been modified to include the pressure-gradient parameter Π1. In the original model suggested by Green et al. the mass-flow shape factor H1 is related to the common shape factor H, H1 = f(H). In the present model H1 is related to H, Reynolds number based on the local momentum thickness θ, and Π1; thus H1 = f(H, Reθ, Π1). The modified formula for H1, is introduced into the original lag-entrainment integral model. Calculations are made to examine the present model for the predictions of the development of boundary layers approaching separation studied experimentally by the authors. Slightly improved predictions are obtained using the model developed by El Telbany et al. However, the present model proved to give an improved representation of the development of wall shear stress in cases the two-equation turbulence model proved to be unsuccessful.