116
5 The Role of Solid Mechanics in Stabilising Structured Flows
control over designing structured fluidised granular flows represents a major leap in
the operation of fluidised beds, and opens new avenues for advance intensification
strategies in many processes where interphase heat and mass transfer are essential
e.g. particle drying, coating and solid-catalysed gas-phase reactions [1].
Gas fluidised beds of granular particles are increasingly modelled using a multiscale approach, with different models aiming to represent the dominant physics at
different scales [11, 15, 26]. Both two-fluid models (denoted as TFM) (Euler-Euler)
and discrete element methods (denoted as DEM) coupled with computational fluid
dynamic tools (denoted as CFD) (Euler-Lagrange) are widely employed. Inelastic
collisions between solids are directly resolved in a discrete description [25], whereas
they are modelled via an effective viscosity derived from the kinetic theory of granular
flow (KTGF) in a continuum framework [12]. Over the last two decades, the Eulerian formulation modelling of gas-solid multiphase flows has achieved significant
improvement. These models succeed in providing a general picture of the hydrodynamics of fluidised bubbling beds [4, 14] but rely on constitutive relations of a limited
range of application [21]. The transition of the granular rheology through inertial
dilute and dense regimes to transitional and quasi-static state is a major challenge for
continuum frameworks. Chapter 4 shows that a classic continuum model can predict
typical bubbling properties in pulsed beds but fails to capture how bubbles rearrange in reality. This fact reflects missing of key physics at the very origin of bubble
nucleation, hence it should not be considered as a trivial handicap of a continuum
framework, which remains the only viable alternative at relevant scales.
On the other hand, Eulerian-Lagrangian models are increasingly used to describe
dense granular flows in recent years. Despite entailing a higher computational cost,
discrete models are naturally implemented to track the dissipation of pseudo thermal
energy caused by persistent contacts and anisotropy in the distribution of particle
contacts that naturally occurs in sheared dense flows. Without applying coarsegraining or hybrid technique [18, 23], so far, only lab-scale systems are practical
to be modelled directly. Regarding the study of regular bubble patterns in pulsed
fluidised beds, a few attempts have been conducted in the past [3, 17, 27]. In particular, the work in Chap. 4 demonstrated that the appearance of the structured flows
is correctly reproduced using a Eulerian-Lagrangian model. The study of simulated
gas and solid dynamics points out the essential role of solid friction in reproducing
the alternation of bubble nucleation sites and stabilising the structure of bubbles.
To progress further, this chapter discusses the behaviour of structured, quasi-2D,
pulsed fluidised beds at different pulse frequencies and compares quantitatively the
observed experimental flow pattern with numerical patterns predicted in classical
implementations of discrete and continuum models. The work also investigates the
role of interparticle friction in creating and stabilising structured flows by imposing
particles of different levels of friction in numerical models. As interparticle friction
increases, the structure of bubbles becomes increasingly stable. When solid friction becomes sufficiently large, the bed suppresses long-range solid circulation and
develops dense regions, which crucially determines the nucleation of bubbles. In
5 The Role of Solid Mechanics in Stabilising Structured Flows
control over designing structured fluidised granular flows represents a major leap in
the operation of fluidised beds, and opens new avenues for advance intensification
strategies in many processes where interphase heat and mass transfer are essential
e.g. particle drying, coating and solid-catalysed gas-phase reactions [1].
Gas fluidised beds of granular particles are increasingly modelled using a multiscale approach, with different models aiming to represent the dominant physics at
different scales [11, 15, 26]. Both two-fluid models (denoted as TFM) (Euler-Euler)
and discrete element methods (denoted as DEM) coupled with computational fluid
dynamic tools (denoted as CFD) (Euler-Lagrange) are widely employed. Inelastic
collisions between solids are directly resolved in a discrete description [25], whereas
they are modelled via an effective viscosity derived from the kinetic theory of granular
flow (KTGF) in a continuum framework [12]. Over the last two decades, the Eulerian formulation modelling of gas-solid multiphase flows has achieved significant
improvement. These models succeed in providing a general picture of the hydrodynamics of fluidised bubbling beds [4, 14] but rely on constitutive relations of a limited
range of application [21]. The transition of the granular rheology through inertial
dilute and dense regimes to transitional and quasi-static state is a major challenge for
continuum frameworks. Chapter 4 shows that a classic continuum model can predict
typical bubbling properties in pulsed beds but fails to capture how bubbles rearrange in reality. This fact reflects missing of key physics at the very origin of bubble
nucleation, hence it should not be considered as a trivial handicap of a continuum
framework, which remains the only viable alternative at relevant scales.
On the other hand, Eulerian-Lagrangian models are increasingly used to describe
dense granular flows in recent years. Despite entailing a higher computational cost,
discrete models are naturally implemented to track the dissipation of pseudo thermal
energy caused by persistent contacts and anisotropy in the distribution of particle
contacts that naturally occurs in sheared dense flows. Without applying coarsegraining or hybrid technique [18, 23], so far, only lab-scale systems are practical
to be modelled directly. Regarding the study of regular bubble patterns in pulsed
fluidised beds, a few attempts have been conducted in the past [3, 17, 27]. In particular, the work in Chap. 4 demonstrated that the appearance of the structured flows
is correctly reproduced using a Eulerian-Lagrangian model. The study of simulated
gas and solid dynamics points out the essential role of solid friction in reproducing
the alternation of bubble nucleation sites and stabilising the structure of bubbles.
To progress further, this chapter discusses the behaviour of structured, quasi-2D,
pulsed fluidised beds at different pulse frequencies and compares quantitatively the
observed experimental flow pattern with numerical patterns predicted in classical
implementations of discrete and continuum models. The work also investigates the
role of interparticle friction in creating and stabilising structured flows by imposing
particles of different levels of friction in numerical models. As interparticle friction
increases, the structure of bubbles becomes increasingly stable. When solid friction becomes sufficiently large, the bed suppresses long-range solid circulation and
develops dense regions, which crucially determines the nucleation of bubbles. In