Computation of the Starting Vortex Flow Past a Flat Plate

Abstract

This paper compares two numerical methods applied to compute the starting vortex flow past a flat plate. The plate is inclined relative to a constant background flow at angle α, with α = 90°, 60°, 30°. The numerical methods considered are (1) direct numerical simulation of the viscous flow (DNS), and (2) an inviscid vortex sheet model. The viscous DNS solves the Navier- Stokes equations by an operator splitting finite-difference method, for Reynolds numbers Re = 250, 500, 1000, 2000. The inviscid flow is computed by a regularized vortex sheet method, with the unsteady Kutta condition imposed at the edges of the plate, for regularization parameters δ = 0.2, 0.1, 0.05. We present viscous vorticity contours, and compare streaklines and shed circulation obtained with both methods. Good agreement is found in the large-scale features of the separated spiral streaklines and the shed circulation as Re increases and δ decreases. For small inclination angle α, secondary separation on the downwind side of the plate introduces small-scale features in the viscous flow that are absent in the inviscid model. The vortex sheet model is much less costly than the viscous DNS, but it is limited by the omission of the boundary layers present in the viscous flow.