A vortex method for wall bounded turbulent flows

Department of Mechanical Engineering University of Maryland College Park, MD 20742, USA

Abstract

Turbulent flow in a channel is simulated using a vortex method. Smoothed vortex sheets cover the near wall region while the vorticity in the remainder of the flow is contained in convecting and stretching vortex filaments. The sheet elements are convected and regridded at each time step thus enabling evaluation of their wall-normal viscous diffusion and vortex stretching using finite differences. New filaments are created during significant ejection events initiated by parent vortices. Chorin's hairpin removal algorithm is used as a physically based subgrid model to limit the range of resolved scales. Calculations on the order of 2000 time steps have been completed thus far. From a perturbed state, the numerical solution develops toward a self-sustained turbulent flow. An initial explosive growth in the number of new vortex structures occurs as the flow compensates for the absence of sufficient spanwise vorticity in the initial conditions. Vortex production is self-limiting, however, and the flow subsequently relaxes toward a quasi-equilibrium in which new vortex filament creation occurs at only a small number of spatially intermittent locations. Preliminary statistics taken from the ongoing simulations suggest that the computational field is approaching the correct physical state.