Impeller power number, table

Power Number, Np The power number, Np, sometimes referred to as Po, is a measure of the relative drag of the impeller. Streamline curved blades, like hydrofoils and retreat-curve impellers, have less drag than flat blades consequently, their power numbers are lower than those for flat-blade impellers. Power numbers of some of the more popular impellers are given in Table 9.1. The calculation of power from impeller diameter, speed, and liquid density is given by Equation (9.1). 

The correlation for Cd (Uke the friction factor and the impeller power number, Np) covers several hydrodynamic regimes. The corresponding ranges for Rep and the correlating expression for Cd are shown in Table 10-1 for three hydrodynamic regimes. 

Table I shows the three areas of consideration in mixer design. The first area is process design, which will be covered in detail in succeeding pages. Process design entails determining the power and diameter of the impeller to achieve a satisfactory result. The speed is then calculated by referring to the Reynolds number-power number curve, shown in Fig. 12. Such a curve allows trial-and-error calculations of the speed once the fluid properties, P, D, and the impeller design are known.

The distinguishing characteristic of each reported study is, usually, the physical design of the apparatus involved. In Table I, a brief outline of the published information on power requirements in one-liquid-phase systems is presented. This table gives the significant mechanical characteristics of the systems studied the range of liquid viscosities and the range of values for the impeller Reynolds number, which will be discussed below. In most of these studies the general objective was to relate the power consumption to tank diameter, impeller type and diameter, rotational speed, and liquid properties. Other variables studied are also indicated in the table. The major features of this work will now be reviewed. 

There is a different power number for each impeller, reflecting its uniqne shape and drag-producing characteristics. The power number values given in Table 9.1 are only applicable for tnrbulent flow. Mannfactnrers offer a variety of impellers, the characteristics of which are given in Table 9.1. 

The Rushton impeller is still the most commonly used radial mixing device for standard applications. New, more efficient impeller types were developed in the 1980s and 1990s (see Table 1.6). These developments improved mixing at significantly smaller power numbers. They are also favorable in the context of prevention of stirrer flooding. 

The power numbers of several other commonly used impellers under turbulent conditions are given in Table 6-4. 

Table 6-4 Power Numbers of Various Impellers under Turbulent Conditions with Four Standard Baffles...

Multiple impellers are recommended if H/T 1.2 or if Ap > 150 kg/m. Assuming a less dense dispersed phase, the second or top impeller often is a hydrofoil placed midway between the RDT and the surface of the liquid. This impeller produces high flow at low power, provides excellent circulation, and complements the flow pattern produced by the RDT. The diameter of the second impeller is usually greater than the RDT, typically D/T > 0.45. A good practice is to distribute the total power to f 20% for the hydrofoil and f 80% for the RDT. Since the power number, Np, is known for each turbine, setting the power distribution enables the diameter of the hydrofoil to be determined. The vertical position of the upper turbine must ensure that fluid reaches the lower impeller, but must avoid gas entrainment that could occur if placement is too close to the hquid surface. Flow from a PBT does not complement that from a RDT and is therefore not recommended. Power requirements are discussed in Section 12-7.3. Table 12-6 lists equipment options for different drop sizing objectives (desired result). If ds2 must be less than 30 tim, the use of a stirred tank is not recommended, so other devices are also included in the table. 

Table 5-2 presents the effects of expected performance on various parameters or relationships for mixing. To actually calculate a numerical result of comparing impeller performances, the dimensionless numbers for flow power and force are needed. Note that in Table 5-2 the constant basis is across the horizontal top of the chart and the function to be examined or compared is along the vertical left side. The functions in the body of the table are used as ratios for condition (1) and condition (2), holding the basis constant. 

The last of these methods has been applied particularly to chemical reaction vessels. It is covered in detail in Chapter 17. In most cases, however, the RTDs have not been correlated with impeller characteristics or other mixing parameters. Largely this also is true of most mixing investigations, but Figure 10.3 is an uncommon example of correlation of blend time in terms of Reynolds number for the popular pitched blade turbine impeller. As expected, the blend time levels off beyond a certain mixing intensity, in this case beyond Reynolds numbers of 30,000 or so. The acid-base indicator technique was used. Other details of the test work and the scatter of the data are not revealed in the published information. Another practical solution of the problem is typified by Table 10.1 which relates blend time to power input to... 

For liquid-liquid mixtures, the calculations of mixing time and power (or Newton) number outlined above are valid for unbaffled vessels only as long as the vortex created by the stirrer does not reach the stirrer head. Otherwise, gas entrainment occurs and the physical properties of the system change. The depth of the liquid-gas interface at the vessel axis with respect to static liquid surface level, HL, can be related to the Froude and Galileo numbers. Some of the reported relationships are summarized in Table XIV. The value of H, at which the vortex reaches the upper impeller blades level can be expressed as... 

In Eq. (6) Kq/u (=Pg/Pxj) is the gassing factor or relative power demand (RPD) between (otherwise identical) gassed and ungassed systems, g/u depends on the impeller type, Qq, N, and D, and generally decreases with increasing gas flow number, Flo- A summary of typical g/u values for popular impellers at high gas flow rates (Mg = 0.1) is given in Table 3. 

With a straight-blade open turbine the effect of changing S4, the ratio of blade width to impeller diameter, depends on the number of blades. For a six-blade turbine Np increases directly with S4 for a four-bladed turbine Np increases with With pitched-blade turbines the effect of blade width on power consumption is much smaller than with straight-blade turbines (see Table 9.2). 

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