Mixing power number

The power number depends on impeller type and mixing Reynolds number. Figure 5 shows this relationship for six commonly used impellers. Similar plots for other impellers can be found in the Hterature. The functionality between and Re can be described as cc Re in laminar regime and depends on p. N in turbulent regime is constant and independent of ]1. 

At high Reynolds, at which most mixing operations are performed, the Power number is constant, that is, Np P/pN D = constant. 

Using curve 6 in Figure 7-14, the Power number is Np = 5.0. The theoretical power for mixing is... 

Sano, Y. and Usui, H., Interrelations among mixing time, power number and discharge flow rate number in baffled mixing vessels, J. Chem. Eng., Japan, 18 47-52, 1985. 

Flow and power numbers each decrease as the Reynolds number increases. In unbaffled tanks, a vortex forms that takes over the flow regime and does not allow the usual relationship to describe the performance of the mixing operation. It is proper and good practice to provide baffles in all vessels (see later description for the physical configurations). 

The shape, size, and baffling of a specific mixing vessel significantly influences the Reynolds number, flow, and power numbers. 

The power number becomes independent on mixing at turbulent conditions, which are achieved at Reynolds numbers greater than 20,000. Typical power numbers at high Reynolds number for some common stirrer types are shown in Table 5.4.22. 

It can be shown by dimensional analysis [Holland and Chapman] that the power number Po can be related to the Reynolds number for mixing ReM, and the Froude number for mixing FrM, by the equation... 

A power curve is a plot of the power function 4> or the power number Po against the Reynolds number for mixing ReM on log-log coordinates. Each geometrical configuration has its own power curve and since the plot involves dimensionless groups it is independent of tank size. Thus a power curve used to correlate power data in a 1 m3 tank system is also valid for a 1000 m3 tank system provided that both tank systems have the same geometrical configuration. 

If a power curve is available for a particular system geometry, it can be used to calculate the power consumed by an agitator at various rotational speeds, liquid viscosities and densities. The procedure is as follows calculate the Reynolds number for mixing ReM , read the power number Po or the power function from the appropriate power curve and calculate the power PA from either equation 5.13 rewritten in the form... 

In the case of highly elastic liquids mixed by a Rushton turbine, flow reversal may occur in the low Reynolds number region, ReM< 30, leading to values of the power number as much as 60 per cent higher than for inelastic liquids. In the intermediate region, 50 1000, the power... 

Figure 1 Various dimensionless parameters [dimensionless velocity, v = v/ND pumping number, Nq = Q/ND power number, Np=[Pgc/pN D ) and dimensionless mixing time, f = as a function of the Reynolds number for the analysis of turbine-agitator systems. Source Adapted from Ref. 22.

Figure 20. Correlations for mixing power number vs. Reynolds number.

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