On the choice of closure complexity in anisotropic drag closures for filtered Two Fluid Models

Filtered Two Fluid Models (fTFMs) aim to enable accurate industrial-scale simulations of fluidized beds by means of closures accounting for the effects of bubbles and clusters. The present study aims to improve anisotropic closures for the drift velocity, which is the primary sub-grid effect altering the filtered drag force, by deriving increasingly complex closures by considering additional independent variables (markers). Three different anisotropic closures, as well as an isotropic closure, are evaluated. A priori tests revealed a significant increase in the predictive capability of the closures as the complexity, in terms of the number of markers considered, increases. However, this improvement is relatively small when compared to the effect of considering anisotropy. Next, a posteriori tests were completed by comparing coarse-grid simulations of bubbling, turbulent and core-annular fluidization against benchmark resolved TFM simulations. This analysis shows good performance of all anisotropic closures, with negligible to minor effects of increasing the drag closure’s complexity by considering additional markers. On the other hand, the isotropic closure lacks generality and shows poor grid independence behaviour. It is therefore concluded that it is essential to include important physical effects, such as anisotropy, in fTFM closures, while complexity in terms of the number of markers considered is of lesser importance.