Agitation Reynolds number

Figure 8-5 Curves of Power Law Agitation Reynolds Number (Rep ) versus Power Number (Po) for Several Agitators, Adapted From Skelland (1967). Curve A—single turbine with 6 flat blades, B— two turbines with 6 flat blades, C—a fan turbine with 6 blades at 45°C, D and E— square-pitch marine propeller with 3 blades with shaft vertical and shaft 10°C from vertical, respectively, F and G— square-pitch marine propeller with shaft vertical and with 3 blades and 4 blades, respectively, and H— anchor agitator.

Substituting the expression for apparent viscosity in the rotational Reynolds number for Newtonian fluids, Rea = D N pIt], the power law agitation Reynolds number is ... 

Flow number, q(nDl Nq, at gas redispersion point Re Agitator Reynolds number, nDlp/p for non-newtonian fluid,... 

The film coefficient h is for the inner wall Dj is the inside diameter of the mixing vessel. The term L N p/ is the Reynolds number for mixing in which L is the diameter and Nr the speed of the agitator. Recommended values of the constants a, b, andm are given in Table 18-2. 

Impeller Reynolds number and equations for mixing power for particle suspensions are in Sec. 5. Dispersion of gasses into liquids is in Sec. 14. Usually, an increase in mechanical agitation is more effective than is an increase in aeration rate for improving mass transfer. 

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. 

Figure 7-15 shows plots of Pumping number Nq and Power number Np as functions of Reynolds number Np for a pitched-blade turbine and high-efficiency impeller. Hicks et al. [8] further introduced the scale of agitation, S, as a measure for determining agitation intensity in pitched-blade impellers. The scale of agitation is based on a characteristic velocity, v, defined by... 

Figure 7-15. Power number and Pumping number as functions of Reynolds number for a pitched-blade turbine and high-efficiency impeller. (Source Bakker, A., and Gates L. , Properly Choose Mechanical Agitators for Viscous Liquids," Chem. Eng. Prog., pp. 25-34, 1995.)...

Agitator type Baffled Reynolds number (Np ) Nusselt number Remarks... 

A reaction is to be carried out in an agitated vessel. Pilot scale tests have been carried out under fully turbulent conditions in a tank 0.6 m in diameter, fitted with baffles and provided with a flat-bladed turbine, and it has been found that satisfactory mixing is obtained at a rotor speed of 4 Hz when the power consumption is 0.15 kW and the Reynolds number 160,000. What should be the rotor speed in order to achieve the same degree of mixing if the linear scale of the equipment if increased by a factor of 6 and what will be the Reynolds number and the power consumption ... 

A Reynolds number for the bubble flow which represents the term for agitation may be defined as ... 

In discussing equations 9.207 and 9.208 Fletcher 96 has summarised correlations obtained for a wide range of impeller and agitator designs in terms of the constant before the Reynolds number and the index on the Reynolds number as shown in Table 9.11. 

An agitated tank with a standard Rushton impeller is required to disperse gas in a solution of properties similar to those of water. The tank will be 3 m diameter (1 m diameter impeller), A power level of 0.8 kW/m3 is chosen. Assuming fully turbnlent conditions and feat the presence of fee gas does not significantly affect the relation between fee Power and Reynolds numbers ... 

Heat transfer can, of course, be increased by increasing the agitator speed. An increase in speed by 10 will increase the relative heat transfer by 10. The relative power input, however, will increase by 10In viscous systems, therefore, one rapidly reaches the speed of maximum net heat removal beyond which the power input into the batch increases faster than the rate of heat removal out of the batch. In polymerization systems, the practical optimum will be significantly below this speed. The relative decrease in heat transfer coefficient for anchor and turbine agitated systems is shown in Fig. 9 as a function of conversion in polystyrene this was calculated from the previous viscosity relationships. Note that the relative heat transfer coefficient falls off less rapidly with the anchor than with the turbine. The relative heat transfer coefficient falls off very little for the anchor at low Reynolds numbers however, this means a relatively small decrease in ah already low heat transfer coefficient in the laminar region. In the regions where a turbine is effective,... 

BTU/hr. sq.ft. over a wide range of viscosities and rotational speeds. This is equivalent to the thermal resistance of a fluid film equal to about 1/2 the clearance between the helical agitator and the vessel wall. This represents Reynolds numbers in the range of 10 to 10. This is the region of creeping flow where, with no inertial effects, there is little displacement of the fluid adjacent to the wall. 

Figure 11. Flow patterns with an anchor agitator as in Figure 10 but at higher Reynolds numbers (above 10-20) where inertial effects become significant. Streamline schematic (12) shows stable trailing vortex.

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