A small-eddy-dissipation mechanism for turbulence modeling and application to wall-bounded flows

Abstract

A small-eddy-dissipation (SED) mechanism is proposed in the present study for the development of turbulence models. According to the SED mechanism, a turbulence model introduces artificial dissipation to filter out small eddies so that a lower resolution mesh can be used in the simulation. In addition, the artificial dissipation should be applied outside the energy-containing range so that the large-scale motions are not affected. A small-eddy-dissipation mixing length (SED-ML) model is developed based on the SED mechanism to calculate wall-bounded flows. A local Reynolds number ys+=|det(∇u)|1/3/s is introduced in the SED-ML model to distinguish laminar flows from turbulent flows. Therefore, in addition to fully turbulent flows, the SED-ML model can also be used to calculate weakly turbulent or laminar flows. To demonstrate the performance of the SED-ML model, turbulent channel flows with the Reynolds numbers Reτ up to 4200 are simulated. The numerical results are extensively compared with the large eddy simulation (LES) results using the classical subgrid-scale models. The numerical results show that the SED-ML model predicts the statistical results with a good accuracy, while requiring a lower mesh resolution than the classical LES models. The accuracy of the calculated statistical results can be further improved by the parameter extension. The friction coefficient f for channel flows can be extended directly from the reference solution according to the relation ∂f/∂ϕ/f=−9, where ϕ is a dissipative strength coefficient. The energy and dissipation spectra confirm that the SED-ML model introduces significant dissipation at high wavenumbers. This feature is beneficial in maintaining the high accuracy of the simulation results and reducing the computational cost. The numerical study also shows that a sharp filtering of the turbulent kinetic energy in the wavenumber space is essential for the development of the turbulence model with high performance.