Impeller pumping number

The pumping number is a function of impeller type, the impeller/tank diameter ratio (D/T), and mixing Reynolds number Re = pND /p.. Figure 3 shows the relationship (2) for a 45° pitched blade turbine (PBT). The total flow in a mixing tank is the sum of the impeller flow and flow entrained by the hquid jet. The entrainment depends on the mixer geometry and impeller diameter. For large-size impellers, enhancement of total flow by entrainment is lower (Fig. 4) compared with small impellers. 

Impellers are sometimes viewed as pumping devices the total volumetric flow rate Q discharged by an impeller is made dimensionless in a pumping number ... 

Large tanks tend to develop a recirculation pattern from the impeller through the tank back to the impeller. This results in a behavior similar to that for a number of tanks in a series. The net result is that the mean circulation time is increased over what woiild be pre-dic ted from the impeller pumping capacity. This also increases the standard deviation of the circulation times around the mean. 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

The primary pumping capacity of an impeller is determined by the impeller diameter, the Pumping number, and the rotational speed. The Pumping number Nq is defined by [13]... 

The Pumping number is used to determine the pumping rate Qp of an impeller,... 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

Figure 7-15 shows plots of Pumping number Nq and Power number Np as functions of Reynolds number Np for a pitched-blade turbine and high-efficiency impeller. Hicks et al. [8] further introduced the scale of agitation, S, as a measure for determining agitation intensity in pitched-blade impellers. The scale of agitation is based on a characteristic velocity, v, defined by... 

Figure 7-15. Power number and Pumping number as functions of Reynolds number for a pitched-blade turbine and high-efficiency impeller. (Source Bakker, A., and Gates L. , Properly Choose Mechanical Agitators for Viscous Liquids," Chem. Eng. Prog., pp. 25-34, 1995.)...

Equation 13 is the empirical relationship obtained by the linear regression between D/T and terminal pumping numbers (4). It is important to note that a family of curves exists for each D/T ratio when Nq (pumping number) is plotted versus the impeller Reynolds number (5). In the turbulent range (iVRe > 2000), the Nq curves flatten out and thus are independent of the Reynolds number. 

Figure 1 Pumping number versus impeller Reynolds number for turbine and marine type propeller agitators.

A 137.5-in-diameter tank has a cross-sectional area of (jr/4)(137.5 in)2 = 14,849 in2 or 103 ft2, so the required impeller pumping capacity is bulk velocity times cross-sectional area (0.4 ft/s)(103 ft2) = 41.2 ft3/s or 2472 ft3/min (1.17 m3/s). Geometry of the actual tank will be taken into consideration by location and number of impellers after the horsepower and speed of the agitator are determined. 

Select impeller diameter and determine required agitator speed. The pumping capacity Q for a pitched-blade impeller with four blades (NP = 1.37) can be related to other mixing parameters by the correlation shown in Fig. 12.3. The correlation is between two dimensionless variables pumping number (Q/ND3) and Reynolds number (D2NpIp.). Since impeller diameter D and rotational speed N appear in both variables, an iterative solution may be required. A convenient approach to such a solution is as follows ... 

FIGURE 12.3 Pumping number as a function of impeller Reynolds number for pitched-blade impeller (Np = 1.37). (From Chemical Engineering, 1976.)... 

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