The paper discusses a novel LES turbulent model, first presented in a linearized version in 2019. The model, named “ESS-LES” (for Entropy Smoothing at Sub-grid-scales LES), is based on the local minimization of the entropy generation rate in each single cell. We present here the theoretical background in some detail. First, the exact entropy generation equation is written in each cell in terms of the instantaneous velocities U,V,W. Then, a set of explicit differential equation for the subgrid scale velocities u,v,w is obtained from the Lagrangian minimization of the entropy generation rate, and a closed form solution is derived in the form of an infinite sinh*sin series. By solving them and truncating the series at the relevant Kolmogorov scales, a formal integration of the uu, vv, ww within each cell provides the subgrid stress tSGS terms that can be added into the resolved Stokes-Navier equations that are in turn solved iteratively. The physical correctness of the model is first analyzed by studying the effect of the model on a number of externally imposed wavelike velocity solutions, to verify the congruency of the resulting shapes of the subgrid stresses. Some preliminary results (not described here in detail) indicate that the model is in a good agreement with the DNS solution and appears to be competitive with other “classical” LES models. A fully-3D simulation is being developed to validate the model on realistic geometries against available LES and DNS results, to verify that it properly reproduces the energy dynamics of turbulence.
A filter-less LES model based on the local minimization of the entropy generation rate: model description
Zullo F.
2022-01-01
Abstract
The paper discusses a novel LES turbulent model, first presented in a linearized version in 2019. The model, named “ESS-LES” (for Entropy Smoothing at Sub-grid-scales LES), is based on the local minimization of the entropy generation rate in each single cell. We present here the theoretical background in some detail. First, the exact entropy generation equation is written in each cell in terms of the instantaneous velocities U,V,W. Then, a set of explicit differential equation for the subgrid scale velocities u,v,w is obtained from the Lagrangian minimization of the entropy generation rate, and a closed form solution is derived in the form of an infinite sinh*sin series. By solving them and truncating the series at the relevant Kolmogorov scales, a formal integration of the uu, vv, ww within each cell provides the subgrid stress tSGS terms that can be added into the resolved Stokes-Navier equations that are in turn solved iteratively. The physical correctness of the model is first analyzed by studying the effect of the model on a number of externally imposed wavelike velocity solutions, to verify the congruency of the resulting shapes of the subgrid stresses. Some preliminary results (not described here in detail) indicate that the model is in a good agreement with the DNS solution and appears to be competitive with other “classical” LES models. A fully-3D simulation is being developed to validate the model on realistic geometries against available LES and DNS results, to verify that it properly reproduces the energy dynamics of turbulence.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
