110
4 Modelling Dynamically Structured Fluidisation
4.3.4 Discussion
The simulations demonstrated that a classic Eulerian-Lagrangian approach is able to
successfully reproduce the physics underlying structured flows in quasi-2D, pulsed,
gas-solid fluidized beds. Spatiotemporal structures emerge and associate with the
oscillation of granules around the minimum fluidisation state which induces a
dynamic transition between solid-like and fluid-like collectively behaviour. Frictional stress stems from such oscillations, and changes drastically in each cycle. The
solid stress in the area adjacent to the distributor exhibits a sharp increase during the
half-cycle of increasing gas velocity. Nevertheless, when the system is fully fluidised,
solids, circulated by the rising bubbles, concentrate in the wake of the bubbles, maintaining in a packed form of transitioning to the plastic regime. Spatiotemporal transitions give rise to a set of growing stress, which therefore alternate the nucleation sites
of bubbles. The data presented show that solid mechanics are necessary to capture
sustained, structured bubble patterns.
The deficiency of a continuous, Eulerian-Eulerian approach in describing dense
frictional flow leads to particular challenges when simulating structured flows. For a
Eulerian description of solids, modelling granular rheology requires complex numerical treatments and constitutive closures to reconcile the stress-strain relationships,
which vary dramatically from a rapid, dilute flow to a creeping, dense flow. In
contrast, a Lagrangian framework for the particulate phase resolves particle contacts,
and, therefore, directly tracks the evolution of relevant stress and strain across the
domain. The data have shown that the commonly used continuum models equipped
with the most used correlations of solid frictional stress are incapable of reproducing
the experimentally witnessed bubble pattern, and, in particular, the characteristics
of alternating bubble nucleation sites [61]. Thus, it is believed that a more accurate
description of the rheology across a full range of packing must be crucial in predicting
the correct physics underpinning the phenomenon. Similarly, Eulerian modelling of
sand piles, an hourglass and U-tubes confront similar challenges where enduring,
correlated, multi-particle contacts dominate [8, 38]. Besides, frictional stress is also
known to affect simulated fluidisation behaviour for slow bubbling columns [16,
49]. Classic expressions derived from the critical state theory of soil mechanics are
empirical or semi-empirical. Different models predict frictional stress varying over
many orders of magnitude [39, 55]. Over the last few years, tremendous efforts have
been devoted to improving the account of friction in modelling dense granular flows
[25, 62]. Advanced frictional stress models, based on rheological principles, offer
new opportunities for simulating dense granular flow by bridging the viscous and
the plastic regime [8, 26]. Although these approaches are still in an early stage,
they already demonstrated promising improvement in reproducing more accurate
properties of dense granular flows.
On the other hand, the results also highlight the ability of the structured flow to be
used as an excellent benchmark for validating implementations of multiphase flow
models for computer simulations of fluidization phenomena. Its unique appearance
4 Modelling Dynamically Structured Fluidisation
4.3.4 Discussion
The simulations demonstrated that a classic Eulerian-Lagrangian approach is able to
successfully reproduce the physics underlying structured flows in quasi-2D, pulsed,
gas-solid fluidized beds. Spatiotemporal structures emerge and associate with the
oscillation of granules around the minimum fluidisation state which induces a
dynamic transition between solid-like and fluid-like collectively behaviour. Frictional stress stems from such oscillations, and changes drastically in each cycle. The
solid stress in the area adjacent to the distributor exhibits a sharp increase during the
half-cycle of increasing gas velocity. Nevertheless, when the system is fully fluidised,
solids, circulated by the rising bubbles, concentrate in the wake of the bubbles, maintaining in a packed form of transitioning to the plastic regime. Spatiotemporal transitions give rise to a set of growing stress, which therefore alternate the nucleation sites
of bubbles. The data presented show that solid mechanics are necessary to capture
sustained, structured bubble patterns.
The deficiency of a continuous, Eulerian-Eulerian approach in describing dense
frictional flow leads to particular challenges when simulating structured flows. For a
Eulerian description of solids, modelling granular rheology requires complex numerical treatments and constitutive closures to reconcile the stress-strain relationships,
which vary dramatically from a rapid, dilute flow to a creeping, dense flow. In
contrast, a Lagrangian framework for the particulate phase resolves particle contacts,
and, therefore, directly tracks the evolution of relevant stress and strain across the
domain. The data have shown that the commonly used continuum models equipped
with the most used correlations of solid frictional stress are incapable of reproducing
the experimentally witnessed bubble pattern, and, in particular, the characteristics
of alternating bubble nucleation sites [61]. Thus, it is believed that a more accurate
description of the rheology across a full range of packing must be crucial in predicting
the correct physics underpinning the phenomenon. Similarly, Eulerian modelling of
sand piles, an hourglass and U-tubes confront similar challenges where enduring,
correlated, multi-particle contacts dominate [8, 38]. Besides, frictional stress is also
known to affect simulated fluidisation behaviour for slow bubbling columns [16,
49]. Classic expressions derived from the critical state theory of soil mechanics are
empirical or semi-empirical. Different models predict frictional stress varying over
many orders of magnitude [39, 55]. Over the last few years, tremendous efforts have
been devoted to improving the account of friction in modelling dense granular flows
[25, 62]. Advanced frictional stress models, based on rheological principles, offer
new opportunities for simulating dense granular flow by bridging the viscous and
the plastic regime [8, 26]. Although these approaches are still in an early stage,
they already demonstrated promising improvement in reproducing more accurate
properties of dense granular flows.
On the other hand, the results also highlight the ability of the structured flow to be
used as an excellent benchmark for validating implementations of multiphase flow
models for computer simulations of fluidization phenomena. Its unique appearance