(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.