Representing the Small Scales of Turbulence by Periodic Box Homogeneous Isotropic Turbulence Simulations

Abstract

Large Eddy Simulations (LESs) use Sub-Grid Scale (SGS) models to account for the effects of the unresolved scales of turbulence. The complex processes that occur in the small scales make the development of SGS models challenging. This complexity is even compounded in the presence of multiphase physics due to the mutual interactions between the small-scale hydrodynamics and the dispersed phase distribution and behaviour. In this study, we propose to avoid using an SGS model and demonstrate a novel technique to use a Periodic Box (PB) Direct Numerical Simulation (DNS) solver to find and represent the local SGS turbulence for supplementing a LES. This technique involves matching the local characteristic strain rate in the LES with the large-scale characteristic strain rate in the PB DNS. For simplicity, we assume Homogeneous Isotropic Turbulence (HIT) to be a good representation of SGS turbulence. For a test case, viz. HIT, we compare the averaged turbulence spectra from the LES and the PB DNS with the exact solution from a full DNS simulation. The results show an almost seamless coupling between the large and small scales. As such, this model is more accurate than the common Smagorinsky model in describing the properties of small scales while working within the same assumptions. Further, the effective Smagorinsky constant predicted by our model and the DNS simulation agree. Finally, a two-way coupling is introduced where an effective viscosity is computed in the PB DNS and supplied back to the LES. The results show a definitive improvement in the LES while maintaining stability. The findings showcase the capability of a PB DNS to support a LES with a near-exact simulation of the SGS turbulence.