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5 The Role of Solid Mechanics in Stabilising Structured Flows
decreasing. In the following pulse, the solid pressure causes nucleation sites to shift to
the location of the lowest compressive yield, which locates in between the preceding
bubble wakes. Newly formed bubbles thus alternate their positions and the entire
process repeats itself in the next cycle.
This mechanism suggests the correlation between bubble size and wavelength.
Large bubbles are robust and lead to large pitches, as they circulate solids more effectively to form a lock region of a bigger area. An increased pulsation frequency dictates
a reduction in size associated with the excess flow injected every cycle. Smaller
rising bubbles are expected to generate compressive stress over a smaller section of
the following horizontal channel at the base, which then grows into closely spaced
bubbles of small size. However, smaller bubbles are more sensitive to imbalance, and
they tend to coalesce and do not lead to stable patterns. As a result, one would expect
a set of bubble size and wavelength that fit the system dynamics optimally. When
solids are largely static within the system, the resulting arrangement of bubbles is
dependent on how the preceding bubble array interacts with the channel-like structure behind. The discrete simulations show this is linked to the pressure gradients
observed in the two alternating bubbling regions. For the system with particles of
low friction, at maximum load, solid pressure gradients do not differ largely. Consequently, the created flow gives rise to the alternation of bubbles nucleation, but the
nucleation sites are largely unpredictable in time.
Contrary to the discrete models, the classic form of TFMs does not capture any
sign of rearrangement in the bubble nucleation sites. A regular pattern, when it
forms, is unstable and, more importantly, shows no variation in the position of the
nucleation sites: simulated bubbles continuously originate from the regions near
the walls and rise to the centre. The TFM simulations neither track the formation of
jammed regions due to sustained friction nor describe their impact thereafter because
it has no means to account for enduring contacts and anisotropic distribution of
force chains, both naturally occur in dense systems [8]. This is well known when
modelling sandy piles, an hourglass, and U-tubes where static interparticle friction is
essential [20]. The use of frictional models in granular flows means to address such
a handicap. Opposite to what is observed in the CFD-DEM results, the TFM cannot
track the sharp and localised changes in solid stress physics. In relation to modelling
practices, it has bubble flow in TFM drives solids to continuously travel throughout
the entire domain in a one order magnitude larger speed than those in CFD-DEM,
independent of fluidisation or defluidisation half-cycle. Due to underprediction of
energy dissipation, the convection inside the bed keeps the solids mobile at any point,
the fluid behaviour dominates over the role of solid mechanics. The bubbling process
is largely associated with flow kinematic properties. As a result, the formed bubbles
couple with solids and travel in a similar pathway to the surface.
Among other limitations of the current TFM implementation, a critical distinction
between the two simulated patterns can be attributed to the inaccurate description
of interparticle frictional stress as well as its level of energy dissipation in the dense
regime. KTGF applies well to describe rapid flows where the granular phase is
sufficiently dilute. Its inherent assumptions of frictionless particles and uncorrelated
5 The Role of Solid Mechanics in Stabilising Structured Flows
decreasing. In the following pulse, the solid pressure causes nucleation sites to shift to
the location of the lowest compressive yield, which locates in between the preceding
bubble wakes. Newly formed bubbles thus alternate their positions and the entire
process repeats itself in the next cycle.
This mechanism suggests the correlation between bubble size and wavelength.
Large bubbles are robust and lead to large pitches, as they circulate solids more effectively to form a lock region of a bigger area. An increased pulsation frequency dictates
a reduction in size associated with the excess flow injected every cycle. Smaller
rising bubbles are expected to generate compressive stress over a smaller section of
the following horizontal channel at the base, which then grows into closely spaced
bubbles of small size. However, smaller bubbles are more sensitive to imbalance, and
they tend to coalesce and do not lead to stable patterns. As a result, one would expect
a set of bubble size and wavelength that fit the system dynamics optimally. When
solids are largely static within the system, the resulting arrangement of bubbles is
dependent on how the preceding bubble array interacts with the channel-like structure behind. The discrete simulations show this is linked to the pressure gradients
observed in the two alternating bubbling regions. For the system with particles of
low friction, at maximum load, solid pressure gradients do not differ largely. Consequently, the created flow gives rise to the alternation of bubbles nucleation, but the
nucleation sites are largely unpredictable in time.
Contrary to the discrete models, the classic form of TFMs does not capture any
sign of rearrangement in the bubble nucleation sites. A regular pattern, when it
forms, is unstable and, more importantly, shows no variation in the position of the
nucleation sites: simulated bubbles continuously originate from the regions near
the walls and rise to the centre. The TFM simulations neither track the formation of
jammed regions due to sustained friction nor describe their impact thereafter because
it has no means to account for enduring contacts and anisotropic distribution of
force chains, both naturally occur in dense systems [8]. This is well known when
modelling sandy piles, an hourglass, and U-tubes where static interparticle friction is
essential [20]. The use of frictional models in granular flows means to address such
a handicap. Opposite to what is observed in the CFD-DEM results, the TFM cannot
track the sharp and localised changes in solid stress physics. In relation to modelling
practices, it has bubble flow in TFM drives solids to continuously travel throughout
the entire domain in a one order magnitude larger speed than those in CFD-DEM,
independent of fluidisation or defluidisation half-cycle. Due to underprediction of
energy dissipation, the convection inside the bed keeps the solids mobile at any point,
the fluid behaviour dominates over the role of solid mechanics. The bubbling process
is largely associated with flow kinematic properties. As a result, the formed bubbles
couple with solids and travel in a similar pathway to the surface.
Among other limitations of the current TFM implementation, a critical distinction
between the two simulated patterns can be attributed to the inaccurate description
of interparticle frictional stress as well as its level of energy dissipation in the dense
regime. KTGF applies well to describe rapid flows where the granular phase is
sufficiently dilute. Its inherent assumptions of frictionless particles and uncorrelated