  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.
