Dynamic fk Estimates for Partially-Averaged Navier-Stokes Around a Circular Cylinder

Partially-averaged Navier-Stokes equations represent a bridging model between fully resolved direct numerical simulations and Reynolds-averaged Navier-Stokes equations. The model can seamlessly switch between these by specifying the ratios of resolved-to-total turbulent quantities to obtain an intermediate flow resolution. In particular, the ratio of modeled-to-total turbulent kinetic energy represents the main parameter of this formulation, especially at high Reynolds numbers. Imposing a correct distribution of this quantity becomes crucial to obtain the desired accuracy in flow prediction. Many estimates of this parameter have been recently proposed, yet no consensus was found on the superiority of one estimate over the others, as different approaches performed better for different flows. In this paper, guidelines on the use of this approach are given for the flow around a circular cylinder at Reynolds number Re�� = 50000 , a flow with a self-induced instability culminating in large vortex shedding. Attention is paid to the performance of existing estimates in relation to spatial and temporal discretization and some new estimates are proposed.