A dynamic Lagrangian large eddy simulation scheme for the vorticity transport equation

J. Mansfield
PhD Thesis, Johns Hopkins University
June 1997, Baltimore MD

ABSTRACT: A Lagrangian large eddy simulation (LES) scheme is developed for simulating turbulent flows with concentrated large-scale vorticity. The scheme combines an adaptive, viscous, three-dimensional vortex element scheme with a dynamic eddy viscosity model. The eddy viscosity model is used to represent effects of sub-filter scales in the filtered vorticity transport equation. Its dynamic implementation relies on determining model coefficients through test-filtering of Lagrangian particle representation of the filtered vorticity field. The vortex element scheme incorporates particle splitting and recombination algorithms, which enable the simulations to efficiently accommodate large strain fields. The vorticity-based dynamic model is examined using a priori tests based on direct numerical simulations of forced homogeneous, isotropic turbulence. These tests show a fair correlation of the turbulence model with the sub-filter scale convection of vorticity. Moreover, the computed value of the dynamic model coefficient is in agreement with predictions based on enstrophy balances. The Lagrangian LES scheme is then applied to the simulation of the evolution of a single vortex ring in free space, and of the co-axial collision of two vortex rings. The simulations show that the Lagrangian scheme is capable of reproducing intricate details of the vorticity field, including small-scale generation and vortex reconnection. In particular, the computations show that the evolution of vortex structure during the collision depends on the initial alignment between the perturbations growing on each of the vortex rings. When the initial perturbations are in phase the rings break down into small-scale structures following the collisions. When the initial perturbations are out of phase, the colliding rings reconnect to form several smaller rings. The dynamic model coefficient is low in magnitude at the initial (laminar) stages of the flow, and only rises once small-scale spatial vorticity fluctuations develop.

Thesis (ps.gz - over 13 Mbytes) (@ J. Mansfield, 1997)