Dynamic subgrid-scale LES model for turbulent non-Newtonian flows: A priori and a posteriori analyses of Burgers turbulence

TL;DR

This paper develops a dynamic LES model for turbulent non-Newtonian flows, specifically shear-thinning fluids, using Burgers turbulence as a test case, and demonstrates its effectiveness through a priori and a posteriori analyses.

Contribution

It introduces a dynamic closure for NNSGS in LES of non-Newtonian flows, removing the need for calibration and validated through canonical Burgers turbulence simulations.

Findings

Shear-thinning increases small-scale motions and energy at high wave-numbers.

NNSGS modeling is crucial for accurate LES predictions.

Dynamic Smagorinsky closure performs well in high shear-thinning regimes.

Abstract

Large Eddy Simulation (LES) of turbulent non-Newtonian flows involves two additional closures, namely the Non-Newtonian SubGrid-Scale (NNSGS) stress tensor and filtered viscosity. Here, dynamic closures are proposed for NNSGS, eliminating the need for model calibration. In addition, for the primary evaluation of LES closures, two canonical case studies are designed by the extension of Newtonian forced Burgers turbulence to include power-law viscosity rheology. The characteristics of the proposed non-Newtonian turbulence are studied carefully using direct numerical simulation. For instance, it is revealed that the shear-thinning effect intensifies the small-scale motions and elevates the energy spectrum function at high wave-numbers. The subsequent a priori and a posteriori studies manifest that the NNSGS modeling is important for the present test cases. The omission of this term results in the under-prediction of kinetic energy due to the substantial backscatter effect of NNSGS. The proposed dynamic Smagorinsky based closure is recommended, based on the correlation coefficient measure in the a priori tests and the energy spectrum function in the a posteriori tests, for LES of turbulence at high shear-thinning rheology.