Assessment of Large Eddy Simulation (LES) Sub-grid Scale Models Accounting for Compressible Homogeneous Isotropic Turbulence

TL;DR

This study evaluates four SGS models in LES for compressible homogeneous isotropic turbulence, comparing their ability to replicate physical decay and spectra, highlighting the need for improved models in complex compressible flows.

Contribution

It provides a systematic comparison of four SGS models in compressible turbulence, assessing their accuracy and limitations in capturing turbulence decay and spectra.

Findings

All models capture overall physical trends

Models need improvement for turbulence dynamics in compressible flows

LES can replicate key physical quantities reasonably well

Abstract

Most sub-grid scale (SGS) models employed in LES (large eddy simulation) formulations were originally developed for incompressible, single phase, inert flows and assume transfer of energy based on the classical energy cascade mechanism. Although they have been extended to numerically study compressible and reactive flows involving deflagrations and detonations, their accuracy in such sensitive and challenging flows is an open question. Therefore, there is a need for both assessing these existing SGS models and identifying the opportunities for proposing new ones, which properly characterize reacting flows in complex engine configurations such as those characterizing rotating detonation engines (RDEs). Accordingly, accounting for the decay of free homogeneous isotropic turbulence (HIT), this work provides a comparison of four different SGS models when compressibility effects are present, (i) the classical Smagorinsky model, (ii) the dynamic Smagorinsky model, (iii) the wall-adapting local eddy-viscosity (WALE) model, and (iv) the Vreman model. More specifically, SGS models are firstly implemented in the open-source computational tool PeleC, which is a high-fidelity finite-volume solver for compressible flows, and then numerical simulations are carried out using them. In terms of results, turbulent spectra, and the decay of physical quantities such as kinetic energy, enstrophy, temperature, and dilatation are computed for each SGS LES model and compared with direct numerical simulations (DNS) results available in literature. The LES numerical results obtained here highlight that the studied SGS models are capable of capturing the overall trends of all physical quantities accounted for. However, they also emphasize the need of improved SGS models capable of adequately describing turbulence dynamics in compressible flows.