Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows

TL;DR

This paper develops a simplified algebraic model for subgrid-scale turbulent kinetic energy in channel flows, maintaining accuracy in coarse grid simulations by leveraging local equilibrium assumptions and a new damping function.

Contribution

It introduces a zero-equation SGS energy model that replaces the transport equation, simplifying simulations while preserving accuracy in wall-bounded turbulence.

Findings

The algebraic model predicts total turbulent kinetic energy accurately.

The zero-equation model performs comparably to the transport-based SMM.

Near-wall behavior is effectively captured by the new damping function.

Abstract

To develop a more convenient subgrid-scale (SGS) model that performs well even in coarse grid cases, we investigate the transport and modeling of SGS turbulent kinetic energy (hereafter SGS energy) in turbulent channel flows based on the stabilized mixed model (SMM). In this paper, we try to increase the convenience of the SMM by replacing the modeled transport equation for the SGS energy with an algebraic model. The SMM quantitatively adequately predicts the total turbulent kinetic energy of the direct numerical simulation (DNS) even in coarse grid cases. For both the filtered DNS (fDNS) and large-eddy simulation (LES), the statistically averaged production term balances with the dissipation in the region away from the wall in the SGS energy transport equation. In contrast, we reveal that the correlation coefficient between the production and dissipation terms is high for the modeled transport equation in LES, whereas that for the fDNS is low. Based on the high correlation or local equilibrium between the production and dissipation observed in the LES, we demonstrate the reduction of the SMM into a zero-equation SMM (ZE-SMM). We construct a new damping function based on the grid-scale Kolmogorov length to reproduce the near-wall behavior of the algebraic model for the SGS energy. The ZE-SMM provides quantitatively the same performance as the original SMM that employs the SGS energy transport model. This result suggests that the local equilibrium model for the SGS energy provides the equivalent performance as the transport model in wall-bounded turbulent flows even in coarse grid cases.