On the Scale Similarity in Large Eddy Simulation.A proposal of a new model

摘要

Among the most common LES models present in literature there are the Eddy Viscosity-type models. In these models the subgrid scale(SGS)stress tensor is related to the resolved strain rate tensor through a scalar eddy viscosity coefficient.These models are affected by three fundamental drawbacks:they are purely dissipative,i.e.they cannot account for back scatter;they assume that the principal axes of the resolved strain rate tensor and SGS stress tensor are aligned;and that a local balance exists between the SGS turbulent kinetic energy production and its dissipation. Scale similarity models(SSM)were created to overcome the drawbacks of eddy viscosity-type models.The SSM models,such as that of Bardina et al.and that of Liu et al.,assume that scales adjacent in wave number space present similar hydrodynamic features. This similarity makes it possible to effectively relate the unresolved scales,represented by the modified Cross tensor and the modified Reynolds tensor,to the smallest resolved scales represented by the modified Leonard tensor[1]or by a term obtained through multiple filtering operations at different scales [2]. The models of Bardina et al.and Liu et al.are affected,however,by a fundamental drawback:they are not dissipative enough,i.e they are not able to ensure a sufficient energy drain from the resolved scales of motion to the unresolved ones. In this paper it is shown that such a drawback is due to the fact that such models do not take into account the smallest unresolved scales where the most dissipation of turbulent SGS energy takes place. A new scale similarity LES model that is able to grant an adequate drain of energy from the resolved scales to the unresolved ones is presented.The SGS stress tensor is aligned with the modified Leonard tensor. The coefficient of proportionality is expressed in terms of the trace of the modified Leonard tensor and in terms of the SGS kinetic energy(computed by solving its balance equation). The validity of the proposed model was tested through channel flow simulation with friction- velocity-based Reynolds numbers ranging from 180 to 2340.