Transport equation for the drift velocity in predicting the filtered Eulerian drag force: a theoretical development

TL;DR

This paper derives a transport equation for the drift velocity from the two-fluid model to improve the prediction of the filtered Eulerian drag force in gas-solid flows.

Contribution

It provides a novel theoretical derivation of the drift velocity transport equation directly from the two-fluid model equations, without extra assumptions.

Findings

The derived equation offers potential for more accurate sub-grid drift velocity estimation.

It aims to enhance the prediction of the filtered drag force in gas-solid fluidization.

The approach introduces new unresolved terms requiring additional closures.

Abstract

The drift velocity has been proven to have significant relevance to the filtered Eulerian drag force by numerous correlative analyses of fully resolved simulations. It is a sub-grid quantity defined as the difference between the filtered gas velocity seen by the particle phase and the resolved filtered gas velocity. In literature, it is shown that various algebraic models for the drift velocity fail to give entirely satisfactory prediction of the filtered drag force. Unlike previous works, we theoretically derived the transport equation for the drift velocity from the standard two-fluid model (TFM) equations without any additional assumptions. The new approach, though requires additional closures for the new unresolved terms, is believed to have the potential to improve the precision of the estimation of this sub-grid quantity and hence give better prediction of the filtered drag force for gas-solid fluidization problems.