（11）
Then, equations (11) and (9) are substituted into equation (5) to
obtain.
The gas Reynolds number and Weber
number can be calculated from equations (12) and (13), respectively.
（12）
Weber number :
（13）
Here, is the superficial velocity
of the column; is the hydraulic
diameter of the gas phase inlet, which can be calculated according to
equations (14) and (15), respectively;
is the gas phase density,
and σ is the surface
tension coefficient between the two phases.
（14）
（15）
Here, G is the gas volume;C is the perimeter of the
gas infiltration edge;d e is the
hydraulic diameter of the gas-phase inlet, andσ is the surface tension
coefficient between the water and air phase.
Taking into account the above parameters, the rotational flow ratio for
the gas phase under the condition of overflow distribution can be
expressed as follows.
（16）
The prediction model of the swirling ratio of the gas phase under the
overflow distribution is obtained.
R2=0.975 （17）
Similarly, the prediction model of the liquid-phase rotational flow can
be obtained as follows.
R2=0.987 （18）
3.4.3.2. Prediction model in spray
distribution
The contact mode between the liquid phase and blade unit changes under
the spray distribution for the liquid phase. Thus, the Reynolds number
for the liquid phase is calculated according to the following formula:
, （19）
where is the hydraulic diameter of
the distributor for the liquid phase, which can be calculated as
follows.
（20）
Here, s 0 is
the area of the spray hole, andc 0 is the
perimeter of the spray hole. Substituting equation (20) into equation
(19), the liquid Reynolds number under the spray distribution can be
obtained as follows.
（21）
Because the gas-phase flow pattern under spray distribution remains the
same, the Reynolds number for the gas phase and Weber number are
consistent with that under the overflow distribution, and the gas-phase
rotational flow ratio can be expressed as follows.
（22）
The prediction model of the rotational flow ratio for the gas phase
under the spray distribution is obtained.
R2=0.948 （23）
Similarly, the prediction model for the liquid-phase rotational flow
ratio is as follows.
R2=0.985 （24）
Fig. 15 shows the calculated and experimental values. The error is
controlled within 10%. In contrast, the error of the rotational flow
ratio is smaller, within 5%, which shows that the mathematical model
can predict the rotational flow ratio accurately. In addition, the
suitable conditions for the prediction model are 2134 <Re l-o ≤ 8536 ，2565 <Re l-s ≤ 5131 ，2870 <Re g ≤ 14353，and 0.521 < We ≤
13.021.