When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?

摘要

Large eddy simulation (LES) seeks to predict the dynamics of spatially filtered turbulent flows. The very essence is that the LES-solution contains only scales of size > A, where A denotes some user-chosen length scale. This property enables us to perform a LES when it is not feasible to compute the full, turbulent solution of the Navier-Stokes equations. Therefore, in case the large eddy simulation is based on an eddy viscosity model we determine the eddy viscosity such that any scales of size < A are dynamically insignificant. In this paper, we address the following two questions: how much eddy diffusion is needed to (a) balance the production of scales of size smaller than A; and (b) damp any disturbances having a scale of size smaller than A initially. From this we deduce that the eddy viscosity v-e has to depend on the invariants q =1/2tr(5-2) and r — 1/3tr(S-3) of the (filtered) strain rate tensor S. The simplest model is then given by v-e =3/2|(Δ/7r)~2|r|/q .This model is successfully tested for a turbulent channel flow (ReT =590).