Dynamic viscoplastic granular flows: A persistent challenge in gas-solid fluidization

Abstract

Fluidization is a prime example of complex granular flows driven by fluid-solid interactions. The interplay of gravity, particle-particle and fluid-particle forces leads to a rich spectrum of hydrodynamic behavior. A number of complex mathematical formulations exist to describe granular flows. At a macroscopic scale, Eulerian models based on the Kinetic Theory of Granular Flow (KTGF) have been successfully employed to simulate dilute and moderately dense systems, such as circulating fluidized bed reactors. However, their applications to dense flows are challenging, because sustained particle contacts are important. As solid fraction rises, the behavior of granular media responds dramatically to particle properties and changes in concentration. Lacking a coherent transition between formulations of dilute, dense and quasistatic flow behavior, kinetic models are incapable of describing how microstructure emerges and affects the rheology. The behavior of transitional granular flows, such as pulsed fluidized beds, for which the particulate phase transitions between the viscous and plastic regimes, are good reminders of this limitation. In recent years, tremendous effort has been devoted to finding new ways to describe the effects of sustained solids friction and dense flow rheology. This article provides a perspective on this matter from the viewpoint of gas-solid fluidization and discusses advances in describing the dilute-to-dense transition in a continuum framework. Four innovative approaches prevail to extend or supersede the existing kinetic theory: (i) including effective restitution coefficients, (ii) coupling local granular rheological correlations, 2 (iii) introducing rotational granular energy, and (iv) combining non-local laws. While their reliability is still far from that of a Eulerian-Lagrangian approach, they lay a promising foundation for developing a rigorous description of granular media that merges the classical frameworks of continuous fluid and soil mechanics. The progress of continuum formulations does not compete with multi-scale modeling platforms with an applied focus. Ultimately, combining both is a prerequisite to developing new solid stress models that will improve not only the performance of macroscopic models, but also our understanding of granular physics.

Dynamically structured fluidization: Oscillating the gas flow and other opportunities to intensify gas-solid fluidized bed operation

“…Due to the persistent oscillation of the gas flow, it is constantly pushed out of equilibrium, creating simultaneous fluidlike like and solid-like zones at all times -thus, even if the velocity temporarily drops below 𝑢 )$ , many particles remain in motion. Computational work [51,198] and PTV (particle tracking velocimetry) analysis of ultrahigh speed videos [199] have associated the bubble self-organisation to the creation of intermittent locally dense areas in the bed that restrict the solid circulation. These areas form between each pair of bubbles where the solid flow converges, creating a jammed solid-like obstruction that prevents the lateral mixing.…”

“…In quasi-2D beds, such as the ones described here, solid flow patterns can be studied with digital image analysis and well known PTV and PIV algorithms [199]. Figure 20 provides an example.…”

“…As already indicated by Wu et al [51], frictional properties and energy dissipation will undoubtedly play an important role in the self-organization of bubbles in fluidized beds. For that reason, continuum models based on the KTGF have not yet been able to replicate the same behavior convincingly [199]. Even integrating frictional stress models underpinned by the critical-state theory of soil mechanics seem to lack a sufficiently accurate description of the physics to reproduce complex gas-driven patterns.…”

“…These works extend the existing KTGF in the Eulerian framework to account for the impact of interparticle friction in the dense, quasi-static regime, by including effective restitution coefficients [234][235][236], through "mesoscience" by addressing also interactions at the mesoscale in variational approaches [237,238], introducing rotational granular energy and an associated effective viscosity [239,240], and constructing granular flow localrheology [226,[241][242][243] and non-local rheology laws [244][245][246] that govern the correlation between stress and strain rate. These promising methods provide a theoretical basis for future development and have been discussed in more detail in a recent work [199].…”

From Quasi-static to Intermediate Regimes in Shear Cell Devices: Theory and Characterisation

“…There have been different ways to incorporate the frictional contribution of a dense flow into the KTFG (Wu et al, 2020). For example, Chialvo et al (2012) carried out homogeneous shear DEM simulations of frictional and frictionless particles in the quasi-static and inertial regimes, and proposed corrections to the model of Garzó and Dufty (1999) to bridge these regimes using the μ(I) rheology model.…”