A multiscale subgrid model for both free vortex flows and wall-bounded flows

Abstract

A new subgrid-scale (SGS) model which has an adequate behavior in both vortical flows and wall-bounded flows is proposed. In wall-bounded flows with “wall-resolved” large eddy simulation (LES), the theory predicts that the SGS dissipation should vanish as y+3 near the wall. In free vortex flows, one needs to have models which do not dissipate energy in the strongly vortical and essentially laminar part of the flow, e.g., in the vortex core regions. The wall adapting local eddy (WALE) viscosity model of Nicoud and Ducros [Flow, Turbul. Combust. 62, 183 (1999)] has the correct near-wall behavior. It is, however, demonstrated here that it produces values of effective eddy viscosity which are too high in vortical flows: this constitutes a major drawback for LES of vortex flows. On the other hand, the regularized variational multiscale models are suitable to simulate vortical flows as demonstrated by Cocle et al. [Complex Effects in LES (Springer, New York, 2007), p. 56], but they do not have a correct behavior in wall-bounded flows as shown by Jeanmart and Winckelmans [Phys. Fluids 19, 055110 (2007)]. The model presented here aims at combining the strengths of the two models: it is a multiscale model, thus acting on the high pass filtered LES field, and for which the SGS viscosity is evaluated using the WALE model, itself also computed using the high pass filtered field. Hence, this model is only active when there is locally a significant high wavenumber content in the flow and it has a natural near-wall damping behavior. The ability of this model to simulate vortex and wall-bounded flows is demonstrated on three test cases. The first case is the turbulent channel flow at Reτ=395 and Reτ=590. The second test concerns a counter-rotating four-vortex system at ReΓ=20 000. The third case concerns a two-vortex system in ground effect at ReΓ=20 000. It is shown that the model allows to perform successfully the LES of these flows with the proper dissipative behavior in both the near-wall and the vortical regions.