Fig. 14 Variations with (a) gas phase kinetic factor and (b) liquid
spray density of the rotational flow ratio for the gas-liquid phase in
spray distribution.
Fig. 14a, b shows the variations of the gas-liquid phase rotational flow
ratio with the liquid spray density and gas-phase kinetic factor,
respectively. In Fig. 14a, the trend of the gas-phase rotational flow
ratio with an increasing gas-phase kinetic energy factor is similar to
that under the overflow distribution, which increases slightly and then
decreases significantly. The ratio is also greater than 0.6, and the
action mechanism is similar to that under the overflow distribution. The
transition point of the FJF and JMF is F s = 1.6
(m/s*(kg/m3)0.5), indicating that
the transition of the two flow patterns is only affected by the gas
phase. However, the liquid rotational flow ratio shows a linear downward
trend without a transition because, under the spray distribution, the
liquid spray density is large. The liquid phase pushed by the airflow
will be supplemented immediately; therefore, the transition of the
rotational flow ratio in the two flow patterns is buffered, and the
declining trend of the rotational flow ratio for the liquid phase is
more stable.
As shown in Fig. 14b, the rotational flow ratio for the gas phase
remains unchanged, above 0.6, with the increasing spray density for the
liquid phase. The liquid rotational flow ratio shows a slight increase
and remains below 0.4 under the spray distribution. Because of the large
liquid phase volume, the gas-liquid phase load at the sieve holes are
saturated. The liquid phase cannot produce more perforated flow with the
increasing liquid spray density. Only rotational flow is shown,
resulting in a gradual increase in the rotational flow ratio of the
liquid phase. However, the gas-phase rotational flow ratio is dominated
by the gas phase, and the liquid phase has minimal influence. The change
is relatively stable.
3.4.3. Prediction model for the rotational flow
ratio
A prediction model for the rotational flow ratio is required for the
selection and regulation of suitable conditions in future engineering
applications. Therefore, the mathematical modeling of the rotational
flow ratio of the gas-liquid phase under overflow and spray distribution
is carried out in this section.
3.4.3.1. Prediction model in overflow
distribution
As previously discussed, the change of the rotational flow ratio is
mainly affected by the operating conditions of the gas-liquid phase. To
facilitate mathematical modeling, the gas and liquid Reynolds number and
Weber number are applied to analyze the changes.
The flow of the liquid phase on the guide plate is falling film flow
under the overflow distribution for the liquid phase32,33. In addition,
the Reynolds number for the liquid
phase can be expressed as:
, (5)
where the liquid phase density isρ l; the liquid film thickness is δ ; the
average velocity for the liquid phase is u m, and
the liquid phase dynamic viscosity is μ l.
In the vertical direction, one side of the liquid film is in contact
with the guide plate, and the other side is in contact with the
atmosphere. The boundary conditions can be expressed as follows.
Guide plate side: (6)
Atmosphere side: (7)
Here, τ is the shear stress
in the flow direction, and y is the distance between the calculated
point and guide plate.
According to the characteristics of falling film flow and Newton’s law
of momentum conservation and shear stress, the velocity distribution
equation of the liquid film can be
obtained:
, (8)
where is the angle between the
inclined plate and vertical direction in the liquid falling film flow.
In this experiment, , and the average velocity of the liquid film can be
obtained from the velocity distribution equation.