Comparison of Four Eddy-viscosity Sgs Models in Large-eddy Simulation of Flows over Rough Walls

Large Eddy Simulation (LES) has become an increasingly attractive option for turbulence modeling due to the rise in computing power and the improvement in sub-grid scale (SGS) parameterizations. This study tests the improvements in simulations of wall-bounded flows over heterogeneous surfaces attained by the implementation of three improvements in the eddy-viscosity SGS closure: the dynamic model by Germano et al. [1], the Lagrangian model by Meneveau et al. [2], and the scale-dependent approach by Porté-Agel et al. [3]. The dynamic model consists of using the resolved scales to ‘measure’ the model coefficient during the simulation; therefore, no a-priori knowledge of the coefficient or the flow physics is needed. The traditional dynamic approach averages the coefficient over statistically homogeneous directions to numerically stabilize the simulations. The Lagrangian model relaxes the need for homogeneous directions by averaging the coefficient over pathlines, hence allowing local determination of the coefficient and facilitating applications to complex-geometry flows. The scale-dependent approach uses the dynamic formulation but does not assume that the SGS coefficients are scale-invariant, as is the case in traditional dynamic formulations. The deficiencies of the traditional Smagorinsky model are confirmed. Implementation of a dynamic model treats some of these deficiencies but is found to be under-dissipative close to the wall in high Reynolds number LES that does not resolve the viscous layer. The sensitivity of the model coefficient to the wall roughness is demonstrated thus confirming the need for a local SGS model such as the Lagrangian model used here. Finally, when the Lagrangian-dynamic model is implemented with the scale-dependent formulation, the results improve significantly. INTRODUCTION The Large-Eddy Simulation (LES) approach originated in meteorological modeling [4-6] but its scope has broadened and it is currently a very appealing technique for a wide range of engineering applications as well. The filtering of the Navier-Stokes equations that yields the LES equations gives rise to a subgrid-scale (SGS) stress term that represents the effect of the small unresolved scales of motion on the resolved scales. Modeling of this term is needed to close the system of equations and solve it numerically. The sensitivity of LES results to the specific SGS closure used was appreciated only gradually and continues to be a current research topic. Early studies [5-6] attempted to optimize the coefficients of the eddy-viscosity model proposed by Smagorinsky [4] and to adapt this model to geophysical and engineering flows. However, as the shortcomings of the classic Smagorinsky parameterization became apparent (as detailed later in this paper), the need for new models became obvious. In the last 15 years, several new SGS formulations appeared; the understanding of SGS physics improved due to numerical and experimental studies; verification, validation, and comparison of SGS models expanded; and the relation between filtering and SGS closure became clearer [7-9]. Eddy-viscosity models continue to be widely used and good results can be obtained with such models for a great variety of flows. This paper will focus on the effect of some SGS modeling improvements on eddy-viscosity SGS models. Simulations over homogeneous and heterogeneous surfaces will be performed using: the simple Smagorinsky or Smagorinsky-Lilly model with a wall damping function