The unsteady structure of two-dimensional steady laminar separation

Abstract

The two-dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time-step method, were used to investigate separation due to the application of an adverse pressure gradient to a low-Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauley et al. [J. Fluid Mech. 220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution, Cp. The computational results were time averaged over several shedding cycles and the results were compared with Gaster. The numerical study accurately reproduced the major characteristics of the separation found in Gaster’s study such as the separation point, the pressure plateau within the upstream portion of the separation bubble, and the reattachment point. The similarity between the experimental results and the time-averaged two-dimensional computational results indicates that the low-frequency velocity fluctuations detected by Gaster are primarily due to the motion of large vortex structures. This suggests that large-scale two-dimensional structures control bubble reattachment and small-scale turbulence contributes a secondary role.