A Coherent vorticity preserving eddy viscosity correction for Large-Eddy Simulation (1707.01556v2)

Abstract: This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by large-scale and/or laminar vortical motion. The proposed Coherent vorticity preserving (CvP) LES methodology is based on the evaluation of the ratio of the test-filtered to resolved (or grid-filtered) enstrophy $\sigma$. Values of $\sigma$ close to 1 indicate low sub-test-filter turbulent activity, justifying local deactivation of the SGS dissipation. The intensity of the SGS dissipation is progressively increased for $\sigma < 1$ which corresponds to a small-scale spectral broadening. The SGS dissipation is then fully activated in developed turbulence characterized by $\sigma \le \sigma_{eq}$, where the value $\sigma_{eq}$ is derived assuming a Kolmogorov spectrum. The proposed approach can be applied to any eddy-viscosity model, is algorithmically simple and computationally inexpensive. LES of Taylor-Green vortex breakdown demonstrates that the CvP methodology improves the performance of traditional, non-dynamic dissipative SGS models, capturing the peak of total turbulent kinetic energy dissipation during transition. Similar accuracy is obtained by adopting Germano's dynamic procedure albeit at more than twice the computational overhead. A CvP-LES of a pair of unstable periodic helical vortices is shown to predict accurately the experimentally observed growth rate using coarse resolutions. The ability of the CvP methodology to dynamically sort the coherent, large-scale motion from the smaller, broadband scales during transition is demonstrated via flow visualizations. LES of compressible channel are carried out and show a good match with a reference DNS.