Computation of Unsteady Turbulent Boundary Layers with Flow Reversal, and Evaluation of Two Separate Turbulence Models

In this paper we extend the unsteady laminar boundary-layer method of Cebeci to turbulent boundary layers with flow reversal. Using the algebraic eddy-viscosity formulation of Cebeci and Smith, we consider several test cases to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Since the accuracy of turbulent flow calculations also depends on the closure assumption for the Reynolds shear-stress term, we also perform calculations by using the turbulence model of Bradshaw, Ferriss and Atwell; we solve the governing equations for both models by using the same numerical scheme and compare their predictions, restricting the comparisons to cases in which wall shear is positive. The study reveals that, as in laminar flows, the unsteady turbulent boundary layers seem to be free from singularities but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. The study also reveals that the predictions of both turbulence models are the same for all practical purposes.