4.2 Model Implementation
97
expressed by:
F
i
f = −V i ∇ P +
V i β
1 − ε
(U g − U s,i )
(4.24)
where V i is the volume of the particle, β is the drag force coefficient per unit volume
of suspension, and U g and U s,i are the centroid gas and particle velocity, respectively.
For a monodisperse solid phase, the gas-solid phase momentum transfer term M
in Eq. (4.11) is estimated based on all particles located in the cell:
M =
1
V c
N
i=1
ξ i V i β
1 − ε
(U g − U s,i )
(4.25)
where V c is the cell volume, N is the number of particles in the present cell, and ζ i
is an interpolation factor correcting for the contribution of each particle based on its
distance from the cell centroid.
4.2.4 Experimental Implementation
The experimental rigs described in Sect. 2.2.1 are used to conduct the validation test.
Quasi-monodisperse, spherical soda-lime glass beads, with an average diameter of
238 μm (G2 particles described in Sect. 2.2.4), are fluidised at ambient conditions
under a periodically oscillating gas flow U 0 :
U 0
U mf = A + B[1 + sin(2π f t)]
(4.26)
where A and B are the normalised offset and amplitude, respectively. The static bed
depth is set to 4.5 cm to reduce computational load, and it is observed sufficiently
deep to accommodate at least one array of bubbles.
4.2.5 Computational Setup and Numerical Implementation
Correct granular mechanical properties are essential to contact models and constitutive relations. The range of particle properties used stems from the literature and
sensitivity analysis of the effects on the flow conditions leading to structured flows.
In the present work, the particle-particle friction coefficient μ f is set 0.35 according
to the measurement of the angle of repose θ r of particle piles on a horizontal surface;
particle-wall friction μ w is reduced to 0.1. The coefficient of restitution e, and Poisson
ratio set according to the commonly reported values [17]. Following the standard
practice describing slowly bubbling fluidised beds [17, 37], an artificially small
97
expressed by:
F
i
f = −V i ∇ P +
V i β
1 − ε
(U g − U s,i )
(4.24)
where V i is the volume of the particle, β is the drag force coefficient per unit volume
of suspension, and U g and U s,i are the centroid gas and particle velocity, respectively.
For a monodisperse solid phase, the gas-solid phase momentum transfer term M
in Eq. (4.11) is estimated based on all particles located in the cell:
M =
1
V c
N
i=1
ξ i V i β
1 − ε
(U g − U s,i )
(4.25)
where V c is the cell volume, N is the number of particles in the present cell, and ζ i
is an interpolation factor correcting for the contribution of each particle based on its
distance from the cell centroid.
4.2.4 Experimental Implementation
The experimental rigs described in Sect. 2.2.1 are used to conduct the validation test.
Quasi-monodisperse, spherical soda-lime glass beads, with an average diameter of
238 μm (G2 particles described in Sect. 2.2.4), are fluidised at ambient conditions
under a periodically oscillating gas flow U 0 :
U 0
U mf = A + B[1 + sin(2π f t)]
(4.26)
where A and B are the normalised offset and amplitude, respectively. The static bed
depth is set to 4.5 cm to reduce computational load, and it is observed sufficiently
deep to accommodate at least one array of bubbles.
4.2.5 Computational Setup and Numerical Implementation
Correct granular mechanical properties are essential to contact models and constitutive relations. The range of particle properties used stems from the literature and
sensitivity analysis of the effects on the flow conditions leading to structured flows.
In the present work, the particle-particle friction coefficient μ f is set 0.35 according
to the measurement of the angle of repose θ r of particle piles on a horizontal surface;
particle-wall friction μ w is reduced to 0.1. The coefficient of restitution e, and Poisson
ratio set according to the commonly reported values [17]. Following the standard
practice describing slowly bubbling fluidised beds [17, 37], an artificially small