On the three-dimensional wake flow behind a normal flat plate

Abstract

Two-dimensional (2D) and three-dimensional (3D) numerical simulations are carried out for uniform flow past a normal flat plate with two semicircular ends to investigate the three-dimensional effects of the wake flow behind the plate. The Reynolds numbers under investigation based on the inflow velocity and the width of the plate (H) are R e = 125, 200, 250, 500, and 1000. The instantaneous vortical structures show that the three-dimensionality characterized by streamwise vortical ribs becomes obvious at R e = 200. Their spatial densities increase with the increasing R e. The time-averaged drag coefficient remains almost the same from R e = 500 to 1000. The relative difference of the predicted drag coefficients between 2D and 3D simulations can be up to 77%. The amplitude of the lift force obtained using 2D simulations can be up to 30 times that obtained using 3D simulations. A drag force element decomposition analysis is conducted for the results obtained using 2D and 3D simulations. It is found that although the time-averaged wake flows obtained using the 2D and 3D simulations are different, the relative difference of their contributions to the time-averaged drag coefficient is only 10% while the difference comes mainly from the contribution of the Reynolds shear stress. The three-dimensionality of the wake flow is further investigated using quadrant and the Lumley triangle analysis of the Reynolds stress. The spanwise spatial scales of the streamwise vortices are quantified using Hilbert transform along the spanwise direction. The width of the streamwise vortices is approximately 0.5 - 1 H in the near wake region. The dependence of the spatial scales on R e is discussed.