Dynamic LES of Colliding Vortex Rings Using a 3D Vortex Method

Abstract

A Lagrangian particle method is used to simulate the collision of coaxial vortex rings in three dimensions. The scheme combines a 3D, adaptive, viscous, vortex element method with a dynamic eddy viscosity model of the subfilter scale stresses. The vortex method is based on discretization of the vorticity field into Lagrangian vortex elements and transport of the elements along particle trajectories. The computations incorporate a mesh redistribution algorithm which creates new elements in regions of high strain and locally redistributes the vorticity field into a smaller number of elements when particles tend to cluster. The subfilter scale vorticity model consists of approximating the effect of unresolved vorticity stresses using a gradient–diffusion eddy viscosity model, following the development in Part I (J. R. Mansfield, O. M. Knio, and C. Meneveau, J. Comput. Phys.145, 693 (1998)). Dynamic implementation of the model relies on determining model coefficients through test-filtering the Lagrangian particle representation of the filtered vorticity field. Computations of ring collisions show that, combined, the mesh redistribution scheme and subfilter scale model result in a robust scheme that can be extended into the late stages of evolution of the flow. In addition, it is shown that the Lagrangian LES scheme captures several experimentally observed features of the ring collisions, including turbulent breakdown into small-scale structures and the generation of small-scale radially propagating vortex rings.