A Morphing Continuum Analysis of Energy Transfer in Compressible Turbulence

TL;DR

This paper introduces a new computational approach using Morphing Continuum Theory (MCT) to analyze energy transfer in compressible turbulence, demonstrating its efficiency and ability to capture multiscale energy dynamics.

Contribution

The paper presents a shock-preserving finite volume solver for MCT, validating it against experiments and showing it requires larger mesh cells and less computational resources than classical methods.

Findings

MCT accurately models supersonic turbulent flow at Mach 2.93.

MCT requires nearly an order larger mesh cells than DNS.

MCT reveals multiscale energy transfer and coupling in turbulence.

Abstract

A shock-preserving finite volume solver with the generalized Lax-Friedrichs splitting flux for Morphing Continuum Theory (MCT) is presented and verified. The numerical MCT solver is showcased in a supersonic turbulent flow with Mach 2.93 over an $8^{\circ}$ compression ramp. The simulation results validated MCT with experiments as an alternative for modeling compressible turbulence. The required size of the smallest mesh cell for the MCT simulation is shown to be almost an order larger than that in a similar DNS study. The comparison shows MCT is a much more computationally friendly theory than the classical NS equations. The dynamics of energy cascade at the length-scale of individual eddies is illuminated through the subscale rotation introduced by MCT. In this regard, MCT provides a statistical averaging procedure for capturing energy transfer in compressible turbulence, not found in classical fluid theories. Analysis of the MCT results show the existence of a statistical coupling of the internal and translational kinetic energy fluctuations with the corresponding eddy rotational energy fluctuations, indicating a multiscale transfer of energy. In conclusion, MCT gives a new characterization of the energy cascade within compressible turbulence without the use of excessive computational resources.