4.2 Gravity-Driven Flow Regime Characterization
167
0.012 m/s at the outlet orifice and 0.0018 m/s inside the bed for R d = 600 particles/min.
This discharging flow rate can be achieved by the experimental test facility built at
the INET of Tsinghua University. For the comparative study, a fast flow rate of R d =
6000 particles/min is used, which is one order of magnitude higher than the lowest
one and can be viewed as a relatively rapid dense flow.
For probing into the different flow regimes, the essential characteristics of intermittency concerning particle flows can be correlated through some specific forms of
the flow properties. In particular, the numerical data of the contact force and velocity
are employed to analyze the flow properties.
4.2.1.2 Evolution of Mean Force and Mean Velocity
The mean contact force and mean velocity of all the particles in the bed can be
formulated as
F =
1
N p
i
j
|F ji |,
(4.11)
V =
1
N p
i
|V i |,
(4.12)
where F ji is the contact force vector from particle “j” to particle “i”, which is nondimensionalized by the gravity force magnitude. The operator “| · |” means the norm
of a vector, and “··” mean the ensemble averaging procedure.
In Fig. 4.3a, the time variation of mean contact force demonstrates that
• The mean force gradually decreases when the discharging process begins, since the
contact force in the bed under the discharging condition is always smaller than the
stationary packing bed. The decrease rate mainly depends on the discharging rate,
i.e., the mean force under the higher discharging rate (R d = 6000 particles/min)
drops faster than the lower discharging rate (R d = 600 particles/min);
• A temporally stationary level of the variation of mean contact force is eventually
reached, and the stationary levels are the same in different flow rates. This means
that the discharging of particles inside the bed has attained a fully developed
condition;
• More importantly, a sudden increase of mean force, e.g., a pulsing increases of
mean force at t 1 and t 2 , takes place intermittently for all discharging flow rates.
The increase of the mean force is always followed by a relatively slowly falling
process until a steady local level is reached or interruption of another impulse
occurs.
The time variation of mean velocity for all discharging flow rates is depicted
in Fig. 4.3b. It can be observed that the mean velocities are fluctuating with time.
For the high discharging rate (R d = 6000 particles/min), the fluctuation frequency
167
0.012 m/s at the outlet orifice and 0.0018 m/s inside the bed for R d = 600 particles/min.
This discharging flow rate can be achieved by the experimental test facility built at
the INET of Tsinghua University. For the comparative study, a fast flow rate of R d =
6000 particles/min is used, which is one order of magnitude higher than the lowest
one and can be viewed as a relatively rapid dense flow.
For probing into the different flow regimes, the essential characteristics of intermittency concerning particle flows can be correlated through some specific forms of
the flow properties. In particular, the numerical data of the contact force and velocity
are employed to analyze the flow properties.
4.2.1.2 Evolution of Mean Force and Mean Velocity
The mean contact force and mean velocity of all the particles in the bed can be
formulated as
F =
1
N p
i
j
|F ji |,
(4.11)
V =
1
N p
i
|V i |,
(4.12)
where F ji is the contact force vector from particle “j” to particle “i”, which is nondimensionalized by the gravity force magnitude. The operator “| · |” means the norm
of a vector, and “··” mean the ensemble averaging procedure.
In Fig. 4.3a, the time variation of mean contact force demonstrates that
• The mean force gradually decreases when the discharging process begins, since the
contact force in the bed under the discharging condition is always smaller than the
stationary packing bed. The decrease rate mainly depends on the discharging rate,
i.e., the mean force under the higher discharging rate (R d = 6000 particles/min)
drops faster than the lower discharging rate (R d = 600 particles/min);
• A temporally stationary level of the variation of mean contact force is eventually
reached, and the stationary levels are the same in different flow rates. This means
that the discharging of particles inside the bed has attained a fully developed
condition;
• More importantly, a sudden increase of mean force, e.g., a pulsing increases of
mean force at t 1 and t 2 , takes place intermittently for all discharging flow rates.
The increase of the mean force is always followed by a relatively slowly falling
process until a steady local level is reached or interruption of another impulse
occurs.
The time variation of mean velocity for all discharging flow rates is depicted
in Fig. 4.3b. It can be observed that the mean velocities are fluctuating with time.
For the high discharging rate (R d = 6000 particles/min), the fluctuation frequency