RANS Calculations of the Evolution of Vortices on Unstructured Grids

The evolution of laminar vortices was calculated using the Reynolds-averaged Navier-Stokes solver ANSYS CFX. Vortices of different strengths were modelled on unstructured grids using different element types and different node densities, then compared to an approximate solution of the Navier-Stokes equation. Grids using hexahedral or prismatic elements aligned with the vortex yielded significantly more accurate solutions than tetrahedral grids, especially when the circulating velocity was much smaller than the convection velocity. Over-diffusion of the circumferential velocity is the major source of error in these solutions. ANSYS CFX was also used to determine the effect of grid density on a turbulent vortex, though in this case there is no analytic solution to compare with. As with the laminar vortex, grids using hexahedral or prismatic elements aligned with the vortex converge much more rapidly with cell size than tetrahedral grids, suggesting that they are more accurate. In these solutions the over-diffusion of turbulent viscosity by artificial viscosity is an important source of error. The solutions are used to make recommendations for the density of unstructured grids required for accurate predictions of the pressure in the core as the vortex evolves over hundreds of core diameters.