Industrial-scale simulations of fluidized bed reactors are currently performed using a Two-Fluid modeling approach, where both the gas and the particles are treated as inter-penetrating continua. Yet, the size of the mesh used is usually larger than the size of the mesoscale structures that appear in such gas-solids flows, namely clusters of particles.

Previous studies showed that neglecting the influence of these sub-grid scale (SGS) structures results in poor predictions of macroscopic bed properties. In this talk, two challenges regarding the SGS modeling of such flows will be discussed.

First, the SGS gas-particle drag term is shown to be the dominant contribution in the coarse-grid momentum conservation equation. The modeling of this term is based on the so-called drift velocity which arises from the correlation between the solid volume fraction and the gas velocity at the sub-grid scale. Until now, only functional models have been proposed, without much physical grounding. In this study, a novel modeling approach is proposed. We first derive a transport equation for the drift velocity itself. Fine-grid simulations of a tri-periodic fluidized bed reactor are then performed to obtain mesh-independent results and the data are spatially filtered to perform a priori analyses of the coarse-grid equations. A new explicit model is finally proposed where the drift velocity is expressed as a function of the resolved slip velocity and an algebraic function of a few moments of the solid volume fraction.

Second, we address the SGS modeling of granular temperature production. The correct estimation of the granular temperature on coarse grids is crucial for wall boundary conditions in the Two-Fluid framework, as well as for the simulation of polydisperse flows. In this regard, preliminary results based on an analogy with dissipation models used in single-phase Large Eddy Simulations will be discussed.

Speaker : Dr. Baptiste Hardy - postdoc at IMFT Toulouse