Computing Blunt Body Flows on Coarse Grids Using Vorticity Confinement

Abstract

Over the last few years, a new flow computational methodology, vorticity confinement, has been shown to be very effective in treating concentrated vortical regions. These include thin vortex filaments which can be numerically convected over arbitrary distances on coarse Eulerian grids, while requiring only ∼2 grid cells across their cross section. They also include boundary layers on surfaces “immersed” in nonconforming uniform Cartesian grids, with no requirement for grid refinement or complex logic near the surface. In this paper we use vorticity confinement to treat flow over blunt bodies, including attached and separating boundary layers, and resulting turbulent wakes. In the wake it serves as a new, simple effective large-eddy simulation (LES). The same basic idea is applied to all of these features: At the smallest scales (∼2 cells) the vortical structures are captured and treated, effectively, as solitary waves that are solutions of nonlinear discrete equations on the grid. The method does not attempt to accurately discretize the Euler/Navier-Stokes partial differential equations (pde’s) for these small scales, but, rather, serves as an implicit, nonlinear model of the structures, directly on the grid. The method also allows the boundary layer to be effectively “captured.” In the turbulent wake, where there are many scales, small structures represent an effective small scale energy sink. However, they do not have the unphysical spreading due to numerical diffusion at these scales, which is present in conventional computational methods. The basic modeling idea is similar to that used in shock capturing, where intrinsically discrete equations are satisfied in thin, modeled regions. It is argued that, for realistic high Reynolds number flows, this direct, grid-based modeling approach is much more effective than first formulating model pde’s for the small scale, turbulent vortical regions and then discretizing them. Results are presented for three-dimensional flows over round and square cylinders and a realistic helicopter landing ship. Comparisons with experimental data are given. Finally, a new simpler formulation of vorticity confinement is given together with a related formulation for confinement of passive scalar fields.