Attempt to compensate for effects of energy conservation error on static pressure fluctuation using sub-grid scale components with the Reynolds number dependence of isotropic/anisotropic steady turbulence

Abstract

Abstract This study focuses on the kinetic energy conservation error and the compensation effect by adjusting a model constant. The kinetic energy conservation error is caused by the implicit time integration of the second-order Crank-Nicholson method, and we investigate how much this error affects the RMS of the static pressure fluctuation. Anisotropic and isotropic external force terms are used to generate a steady turbulent flow field, and the numerical analysis employs Large Eddy Simulation (LES) and the Smagorinsky model. Studies have shown that the influence of kinetic energy conservation errors on turbulent kinetic energy is limited, but large-scale turbulent structures are affected by errors in anisotropic turbulent fields with large Re numbers. Ta. Regarding the compensation of the RMS of the static pressure fluctuation, it was shown that the error could be reduced in both isotropic and anisotropic fields by adjusting the model constant, but there was a clear difference for the turbulent kinetic energy. This result shows that the compensation of kinetic energy conservation errors by a model constant is not perfect and that the errors can have different effects on the turbulence statistics.