Velocity distributions in the separated flow behind a wedge-shaped model hill: technical report

Abstract

A portion of the velocity distributions in an incompressible turbulent separated flow behind a two-dimensional model hill is investigated experimentally. A 2" x 2" wedge is used as a model hill. The mixing region investigated lies between the crest of the hill where the flow separated, and the reattachment point where the separated flow reattaches itself to the floor. Gortler's half-jet mixing theory is used to analyze the separated flow which is curved by the action of the pressure gradient across the separated flow. The width of the mixing region was found to spread linearly with the distance as expressed by the half-jet theory. If a suitable similarity parameter is chosen, the theoretical velocity distribution of half-jet agrees satisfactorily with the experiments, except in the region near the floor and directly behind the hill. However, it was found that the similarity parameter is not a constant, but is proportional to the one-half power of the distance downstream from the hill. Corrections were applied to account for the effects of the initial boundary layer thickness and for the curvature. The corrections are based on Sawyer's first order theory and Kirk's approximation, but the results indicate that these effects should be investigated further.