Large eddy simulation of flow in porous media: Analysis of the commutation error of the double-averaged equations

TL;DR

This paper applies double-averaging and large eddy simulation techniques to analyze flow in porous media, focusing on commutation errors at interfaces and their impact on simulation accuracy.

Contribution

It introduces a space-time filtering approach to evaluate commutation errors in double-averaged Navier-Stokes equations for porous media flows.

Findings

Commutation errors are significant at the porous-fluid interface.

Neglecting commutation errors has less impact than inaccuracies in drag models.

The developed solver accurately simulates flow in porous media geometries.

Abstract

The continuum approach employing porous media models is a robust and efficient solution method in the area of the simulation of fixed-bed reactors. This paper applies the double-averaging methodology to refine the continuum approach, opening a way to alleviate its main limitations: space-invariant averaging volume and inaccurate treatment of the porous/fluid interface. The averaging operator is recast as a general space-time filter allowing for the analysis of commutation errors in a classic large eddy simulation (LES) formalism. An explicit filtering framework has been implemented to carry out an a posteriori evaluation of the unclosed terms appearing in the double-averaged Navier-Stokes (DANS) equations, also considering a space-varying filter width. Two resolved simulations have been performed. First, the flow around a single, stationary particle has been used to validate derived equations and the filtering procedure. Second, an LES of the turbulent flow in a channel partly occupied with a porous medium has been realized and filtered. The commutation error at the porous-fluid interface has been evaluated and compared to the prediction of two models. The significance of the commutation error terms is also discussed and assessed. Finally, the solver for DANS equations has been developed and used to simulate both of the studied geometries. The magnitude of the error associated with neglecting the commutation errors has been investigated, and an LES simulation combined with a porous drag model was performed. Very encouraging results have been obtained indicating that the inaccuracy of the drag closure overshadows the error related to the commutation of operators.