An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications

Abstract

An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundamental realizability inequality for the theoretical subgrid dissipation. Results are shown for a transitional and turbulent mixing layer at high Reynolds number and a turbulent channel flow. In both cases the present model is found to be more accurate than the Smagorinsky model and as good as the standard dynamic model. Unlike the Smagorinsky model, the present model is able to adequately handle not only turbulent but also transitional flow.

Validation of the LES approach in Kiva‐3V on a square duct geometry

“…The contributions to the shear stress indicate the reason for the stronger turbulent kinetic energy: the Vreman model dissipates a larger part of the resolved turbulence, compared to the WALE model. This deficit can be reduced by decreasing the model constant C v , as indicated by Vreman [9]. Moreover, as in this study the numerical scheme masks some of the effects of the SGS models, an additional study where the numerical contribution to the turbulent dissipation can be neglected is required to compare these two SGS models in detail.…”

“…Another version of this approach for a SGS model is proposed by Vreman [9]. Just like the WALE model this model needs only local filter information and first-order velocity derivatives.…”

Large Eddy Simulation of stratified flows over structures

“…The eddy viscosity is computed using the Vreman subgrid model [6]. We use a constant value of the Prandtl number to compute the eddy diffusivity, i.e.…”

Variational Multiscale LES and Hybrid RANS/LES Parallel Simulation of Complex Unsteady Flows

“…For the purpose of this study, three SGS eddy-viscosity models are considered: the classical model of Smagorinsky [25], and two recent and promising models, namely the WALE model [21] and the one of Vreman [31]. More details on this VMS-LES approach can be found in [13].…”