Examining OpenFOAM-based LES analysis in terms of inviscid energy conservation and viscous turbulence decay

The present study examines an OpenFOAM-based LES analysis from the viewpoints of inviscid energy conservation and viscous turbulence decay. The Smagorinsky model is employed as the sub-grid scale (SGS) model, and a two-dimensional periodic analytical solution and a three-dimensional periodic Taylor-Green vortex (TGV) are employed to represent inviscid flows. The analytical relationship for the kinetic energy K, dK/dt = 0, with t as the dimensionless time, is utilized to validate the OpenFOAM results. For the viscous flow case, the TGV flow in a three-dimensional periodic cubic domain is adopted, and its turbulence kinetic energy distribution is compared with that obtained by a spectral method to examine the analysis. The OpenFOAM-based analysis exhibits energy conservation error in flows that should ideally conserve energy. For the two-dimensional flow, this error decreases with increasing grid resolution N. However, in the three-dimensional flow, the error does not improve even with higher N. In the three-dimensional TGV flow, the turbulence kinetic energy predicted by OpenFOAM exhibits a strong agreement with that from the spectral method when a standard constant value of the Smagorinsky model is employed and the mesh is sufficiently refined. Conversely, for a condition of relatively coarse mesh, the decay characteristics of turbulent kinetic energy deviate from those of the spectral method, and a higher constant value of the Smagorinsky model than the default value becomes necessary to reproduce comparable results. These results suggests that even in LES simulations where highly accurate conservation laws are not satisfied, adjusting the model constants so that the predicted values match experimental or numerical reference data can improve the apparent reliability of the turbulent kinetic energy in the decaying turbulence.