Mixers power number

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

P0 = Np = Power number, dimensionless, Equation 5-19 Ppew = Plate coil width, one plate, ft Ap = Pressure drop, psi AP0 = Pressure drop for open pipe, psi AP, = Static mixer pressure drop in turbulent flow, psi Q = Flow rate or pumping capacity from impeller, cu l t/sec, or Ls/1... 

Figure 7,6. Power number re, a function of ReynoUJs number for a propeUer mixer...

Figure 7.7. Power number as a function of Reynolds number for a turbine mixer...

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.

Mixers. See also Agitation blend time, 290 dimensionless groups, 290 gas dispersion, 296-301 in line type, 300,301 liquids, power and speed need, 293,295 powders and pastes, 301,303,304 power number, 290-292 quality characterization, 290-292 suspension of solids, 295-299 tank desien. 287.288 Moisture c tent, critical, 237 Molecular distillation, 425-427 equipment sketches, 427 Hickman still, 427 operating conditions, rate of evaporation. 

Newton (power) number, which relates the drag force acting on a unit area of the impeller and the inertial stress, represents a measure of power requirement to overcome friction in fluid flow in a sfirred reacfor. In mixer-granulation applications, this number can be calculated from the power consumption of the impeller or estimated from the power consumption of the motor. 

As we have indicated before, for any desired endpoint, the power consumption will be proportional to the Newton power number, at a constant mixer speed. 

For accuracy, in power number Np calculations, the power of the load on the impeller rather than the mixer motor should be used. Before attempting to use dimensional analysis, one has to measure/estimate power losses for empty bowl or dry stage mixing. Unlike power consumption of the impeller (based on torque measurements), the baseline for motor power consumption does not stay constant and changes significantly with load on the impeller, mixer condition, or motor efficiency. This may present inherent difficulties in using power meters instead of torque. Torque, of course, is directly proportional to power drawn by the impeller (the power number can be determined... 

Fig. 12 Case study II. Regression lines of the Newton power number on the product of Reynolds number, Froude Number, and the length ratio for three different Fielder mixers. (Reprinted from Ref., copyright 1996, with permission from Elsevier.)...

Once the desired end-point is determined, it can be reproduced by stopping the batch at the same level of net power consumption AP (for the same mixer, formulation, speed, batch size, and amount/rate of granulating liquid). To account for changes in any of these variables, you have to compute the Newton power number Np for the desired end-point ... 

In other words, if you have established an end-point in terms of some net impeller or motor power AP and would like to reproduce this end-point on the same mixer at a different speed or wet mass density, calculate Newton power number Np from the given Net Impeller power AP, impeller speed n, blade radius d, and wet mass density p (assuming the same batch size). 

Unfortunately, the power number only provides a relationship between impeller size, rotational speed, and fluid properties. The power number does not tell whether a mixer will work for an application. Successful operating characteristics for an anchor mixer usually depend on experience with a similar process or experimentation in a pilot plant. Scale-up of pilot-plant experience is most often done for a geometrically similar impeller and equal tip (peripheral) speed. 

This section describes mixer geometry impellers (types listed in Figure 9.3), the number required, their characteristics, importance of location, vessel shape, and effects of baffles. An example is given to show a basic calculation of mixer power and flow. 

The power consumption of a mixer is characterised by the power number Np defined as ... 

The remarkably small effect of Reynolds number indicated by Eq. (198) is well borne out experimentally. The torque on rotating bodies has been extensively studied in connection with power requirements for mixers, agitators, and similar devices. In the so-called laminar regime, logarithmic plots of the dimensionless Power number... 

Here N - mixer power spent on liquid mixing, n - number of mixer revolutions, dM - mixer s diameter, G2 - gas volume throughput, w - volume of gas-liquid mixture in apparatus. 

Scale-up also assumes that the same entering feed and solvent concentrations and the same solvent-to-feed ratio, S/F, are used in the miniplant and the large unit, hi addition, we need geometric similarity of the two mixers by keeping the ratios d/dtank> H/d ajj, and (baffle width)/dtank constant. Finally, the residence time V/(Qd + Qc) must be equal in the two units. Based on equal power numbers and geometric similarily for the two units. 

Plots for power number against Reynolds number on log-log coordinates, the so-called power curves, are available in the literature for particular mixer configurations. Power curves are independent of vessel size and are particularly useful in the scale-up of liquid mixers from pilot plant studies. It must be considered, however, that a given curve is only applicable to the geometric configuration for which it was developed. 

TABLE 7-7 Typical Power Number for Mixers in Turbulent Flows... 

S-2.3.2 Power and Power Number. The power consumed by a mixer can be obtained by multiplying pumping, Q, and head, H, and is given by... 

The power number for helical ribbon mixers depends on Reynolds number blade/wall clearance, e height, h pitch of the helix, p (height of one turn around the helix) blade width, w and number of helical flights, n. The relationship is... 

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