Shape factor impeller

The parameter S is called the proportionality constant or shape factor, and depends on the impeller and vessel geometry (Armenante and Nagamine, 1998) ... 

Let us derive this power dissipation by dimensional analysis. Recall that in dimensional analysis pi groups are to be found that are dimensionless. The power given to the fluid should be dependent on the various geometric measurements of the vessel. These measurements can be conveniently normalized against the diameter of the impeller D to make them into dimensionless ratios. Thus, as far as the geometric measurements are concerned, they have now been rendered dimensionless. These dimensionless ratios are called shape factors. 

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. 

Decreasing Si, the ratio of impeller diameter to tank diameter, increases Np when the baffles are few and narrow and decreases Np when the baffles are many and wide. Thus shape factors Sj and S5 are interrelated. With four baffles and S5 equal to as is common in industrial practice, changing Si has almost no effect on Np. 

It is common practice to use geometric similarity in the scaleup of stirred tanks (but not tubular reactors). This means that the production-scale reactor will have the same shape as the pilot-scale reactor. All linear dimensions such as reactor diameter, impeller diameter, and liquid height will change by the same factor, Surface areas will scale as Now, what happens to tmix upon scaleup ... 

It is common practice to use geometric similarity in the scaleup of stirred tanks (butnot tubular reactors). Geometric similarity means that the production-scale reactor will have the same shape as the pilot-scale reactor. All linear dimensions such as reactor diameter, impeller diameter, and liquid height will change by the same factor, 5. Surface areas will scale as. Now, what happens to tmx upon scaleup A classic correlation by Norwood and Metzner (1960) for turbine impellers in baffled vessels can be used to estimate tm. The full correlation shows fmix to be a complex function of the Reynolds number, the Froude number, the ratio of tank to impeller diameter, and the ratio of tank diameter to liquid level. However, to a reasonable first approximation for geometrically similar vessels operating at high Reynolds numbers. 

We want to know the variability of the responses as well as the shapes of their response surfaces. Variability is very difficult to measure experimentally. In order to estimate it by replicate measurements a very large number of experiments would be required. Here it was thought that variability might be due to small differences in the speed of the impeller blade of the mixer granulator. The blade speed was thus allowed to vary by a small amount about its normal value of 1100 rpm. This is therefore a noise factor. The two levels for the speed, 1000 and 1200 rpm, are believed to cover the range of random variation of the speed. 

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