Large-eddy simulation of hypersonic flows. Selective procedure to activate the sub-grid model only where small scale turbulence is present

TL;DR

This paper introduces a selective LES method for hypersonic flows that activates sub-grid models only in regions with significant small-scale turbulence, improving accuracy over standard LES.

Contribution

A novel localization technique based on a scalar probe function to selectively activate sub-grid models in hypersonic flow simulations.

Findings

Selective LES reduces flow modification compared to classical LES.

Improved predictions of enstrophy, velocity, and density distributions.

Enhanced energy and density spectra accuracy.

Abstract

A new method for the localization of the regions where small scale turbulent fluctuations are present in hypersonic flows is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function $f$ which represents the magnitude of the stretching-tilting term of the vorticity equation normalized with the enstrophy (Tordella et al. 2007). For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that $f$ is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field of $f$ in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching-tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain, and with those of a standard Euler simulation with the same resolution. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy, mean velocity and density distributions and of the energy and density spectra are substantially improved.