Propeller power number correlations

Figure 7.8 Correlation between Reynolds number (Re) and Power number (Np). Curve (a) six-flat blade turbine, four baffles, W, = 0.1 D (Figure 7.7) curve (b) two-flat blade paddle, four baffles, = 0.1 D and curve (c) three-blade marine propeller, four baffles, = 0.1 D.

Loiseau et al. (1977) found that their data for nonfoaming systems agreed well with Eq. (3.3). Calderbank (1958), Hassan and Robinson (1977), and Luong and Volesky (1979) have also proposed correlations for power consumption in gas-liquid systems. Nagata (1975) suggested that power consumption for agitated slurries can be reasonably predicted from these correlations by the correction factor psi/pL, where psl is the density of the slurry. Power consumption for a gas-liquid-solid system has also been studied by Wiedmann et al. (1980). They examined the influence of gas velocity, solid loading, type of stirrer, and position of the stirrer blades on power consumption plots of power numbers vs. Reynolds numbers for propeller and turbine type impellers proposed by them are shown in Fig. 13. 

Fig. 3. Power number—Reynolds number correlation for a 12-in. propeller in a tank without baffles. Tank diameter = 54 in. Liquid depth = 54 in. Data of Rushton et al. (R13).

Figure 4-5 gives the power number versus Reynolds number correlation for different types of agitators. The pitch referred to is the axial distance that a free propeller would move in a nonyielding liquid in one revolution. 

Conventional stirred-tank polymeric reactors normally use turbine, propeller, blade, or anchor stirrers. Power consumption for a power-law fluid in such reactors can be expressed in a dimensionless form, Ne = Reynolds number based on the consistency coefficient for the power-law fluid. Various forms for the function f(m) in terms of the power-law index have been proposed. Unlike that for Newtonian fluid, the shear rate in the case of power-law fluid depends on the ratio dT/dt and the stirrer speed N. For anchor stirrers, the functionality g developed by Beckner and Smith (1962) is recommended. For aerated non-Newtonian fluids, the study of Hocker and Langer (1962) for turbine stirrers is recommended. For viscoelastic fluids, the works of Reher (1969) and Schummer (1970) should be useful. The mixing time for power-law fluids can also be correlated by the dimensionless relation NO = /(Reeff = Ndfpjpti ) (Tebel et aL 1986). 

POWER CORRELATIONS FOR SPECIFIC IMPELLERS. The various shape factors in Eq. (9.16) depend on the type and arrangement of the equipment. The necessary measurements for a typical turbine-agitated vessel are shown in Fig. 9.7 the corresponding shape factors for this mixer are Sj = DalD S2 = EID S = L/D , S4 == W /Od. S5 = J/D, and Sg = HfD,. In addition, the number of baffles and the number of impeller blades must be specified. If a propeller is used, the pitch and number of blades are important. 

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