Impeller disk turbines

Joshi (1980) proposed a relation on the basis of liquid circulation generated by an impeller (disk turbine) as... 

Radial flow Flat-blade impeller, disk turbine (Rushton), hollow-blade turbine (Smith)... 

Power Consumption of Impellers Power consumption is related to fluid density, fluid viscosity, rotational speed, and impeller diameter by plots of power number (g P/pN Df) versus Reynolds number (DfNp/ l). Typical correlation lines for frequently used impellers operating in newtonian hquids contained in baffled cylindri-calvessels are presented in Fig. 18-17. These cui ves may be used also for operation of the respective impellers in unbaffled tanks when the Reynolds number is 300 or less. When Nr L greater than 300, however, the power consumption is lower in an unbaffled vessel than indicated in Fig. 18-17. For example, for a six-blade disk turbine with Df/D = 3 and D IWj = 5, = 1.2 when Nr = 10. This is only about... 

Mechanical agitation is needed to break up the gas bubbles but must avoid rupturing the cells. The disk turbine with radial action is most suitable. It can tolerate a superficial gas velocity up to 120 m/h. (394 ft/h) without flooding, whereas the propeller is limited to about 20 i7i/h (66 ft/h). When flooding occurs, the impeller is working in a gas phase and cannot assist the transfer of gas to the liquid phase. Power input by agitation and air sparger is 1 to 4 W/L (97 to 387 Btu/[fF-h]) of liquid. 

Paddle A paddle is similar to a turbine impeller but typically has only two large blades and operates at lower speeds than a turbine. They are primarily used in high viscosity mixing operations. In European and Japanese literature the term "paddle" also is used to describe the flat blade and pitched blade turbines discussed above. The term "turbine" generally is reserved for disk turbines. 

Double-impeller combinations Bouaifi et al. (2001) derived the following correlations for stirred gas-liquid reactors with various combinations of double impellers. The impellers used were the lightning axial flow impeller (A-310), the four 45° pitched blade turbine pumping down (PBTD) and the Rushton disk turbine (RDT). Furthermore, the tank was a dish-bottom cylindrical tank equipped with four baffles, while the gas was introduced by a ring sprager. The gas-flow rate ranged from 0.54 to 2.62 L/s, whereas the rotational speed was from 1.66 to 11.67 s. The gas holdup is... 

Figure 10.11. Power consumption, (a) Ratio of power consumptions of aerated and unaerated liquids. Q is the volumetric rate of the gas (O) glycol ( X ) ethanol ( ) water. [After Calderbank, Trans. Inst. Chem. Eng. 36, 443 (1958)]. (b) Ratio of power consumptions of aerated and unaerated liquids at low values otQ/Nd3. Six-bladed disk turbine ( ) water ( ) methanol (10%) (A) ethylene glycol (8%) (A) glycerol (40%) Pg = gassed power input P = ungassed power input Q = gas flow rate IV = agitator speed d = agitator-impeller diameter. [Luong and Volesky, AIChE J. 25, 893 (1979)].

Calderbank (1958) also correlated the Sauter-mean diameter for the gas-liquid dispersion agitated by a flat-blade disk turbine impeller as follows ... 

The power required by an impeller in a gas sparged system Pm is usually less than the power required by the impeller operating at the same speed in a gas-free liquids Pmo. The Pm for the flat-blade disk turbine can be calculated from Pmo (Nagata, 1975), as follows ... 

A cylindrical tank (1.22 m diameter) is filled with water to an operating level equal to the tank diameter. The tank is equipped with four equally spaced baffles, the width of which is one tenth of the tank diameter. The tank is agitated with a 0.36 m diameter, flat-blade disk turbine. The impeller rotational speed is 4.43 rps. The air enters through an open-ended tube situated below the impeller and its volumetric flow rate is 0.0217 m3/s at 1.08 atm and 25°C. Calculate ... 

Flow patterns in a mechanically agitated reactor with disk turbine, pitched-blade turbine, and propeller types of agitator are schematically illustrated by Joshi et al. (1982). The flow pattern in the presence of gas is described later in the section on slurry reactors. In each of these cases, the dimensionless velocity profile with respect to the impeller tip velocity has been found to be independent of the impeller speed and has shown slight dependence on the impeller diameter. 

Mechanically agitated reactors have been used for cultivation of plant cells (Kato et al., 1972 Tanaka, 1981). Ajar fermenter with a six fiat-blade turbine and a modified paddle has been used by Tanaka (1981) and a similar jar fermenter with two disk turbine impellers has been used by Kato et al. (1972) at about 50 rpm with no significant shear damage to plant cells. Paddle-type impellers were found to be more appropriate (less shear damage) than flat-blade turbine type impellers (Kato et al., 1972). The only production-scale reactor used for shikonin production in Japan is also an agitated vessel. 

The critical stirrer speed can also be predicted on the basis of the liquid flow generated by the impeller. For a six-bladed disk turbine, the average liquid circulation velocity in the bulk can be expressed as... 

The extent of gas entrainment depends on the turbulence at the liquid surface and the downward volumetric flow rate. Thus, the impeller design, diameter, and location are very important. Matsumura et al. (1977) proposed the following correlation for a 0.218 in. diameter vessel using a disk turbine ... 

A dished head tank of diameter DT = 1.22 m is filled with water to an operating level equal to the tank diameter. The tank is equipped with four equally spaced baffles whose width is one-tenth of the tank diameter. The tank is agitated with a 0.36-m-diameter, flat, six-blade disk turbine. The impeller rotational speed is 2.8 rev/s. The sparging air enters through an open-ended tube situated below the impeller, and its volumetric flow, Q, is 0.00416 m3/s at 25°C. Calculate the following the impeller power requirement, Pm gas holdup (the volume fraction of gas phase in the dispersion), H and Sauter mean diameter of the dispersed bubbles. The viscosity of the water, //, is 8.904 x 10 4 kg/(m-s), the density, p, is 997.08 kg/m3, and, therefore, the kinematic viscosity, v, is 8.93 x 10 7 m2/s. The interfacial tension for the air-water interface, a, is 0.07197 kg/s2. Assume that the air bubbles are in the range of 2-5 mm diameter. 

Laity and Treybal (LI) report on experiments with a variety of two-phase systems in a covered vessel which was always run full, so that there was no air-liquid interface at the surface of the agitated material. Under these circumstances no vortex was present, even in the case of operation without baffles. Mixing Equipment Company flat-blade disk-turbines were used in 12- and 18-in. diameter vessels whose heights were about 1.07 times their diameters. Impeller diameter was one-third of tank diameter in each case. For operation without baffles, using only one liquid phase, the usual form of power-number Reynolds-number correlation fit the data, giving a correlation curve similar to that given in Fig. 6 for disk-turbines in unbaffled vessels. In this case, however, the Froude number did not have to be used in the correlation because of the absence of a vortex. For two-phase mixtures, Laity and Treybal could correlate the power consumption results for unbaffled operation by means of the same power number-Reynolds number correlation as for one-phase systems provided the following equations were used to calculate the effective mean viscosity of the mixture For water more than 40% by volume ... 

Sykes and Gomezplata13 determined the liquid-solid mass-transfer coefficient for 0.32-cm-diameter spherical particles suspended in stirred aqueous iodine solutions. The particle density was within 5 percent of the liquid density. The effects of impeller speed (200 through 600 rev min- ), Schmidt number (770 through 11,300), and impeller type (fan-disk turbine, propeller, and 45° paddle and turbine) on the mass-transfer coefficient were examined. The data were correlated with an average deviation of 8 percent by the following expression ... 

Here, P0 is the impeller power, s0 is the impeller speed, d, is the impeller diameter, Pl and v l are the density and kinematic viscosity of the liquids, respectively. The term tf Myr adjusts the actual impeller speed to the speed at which a fan-disk turbine would rotate for the same power input per unit mass. Although no gas was used in this study, the correlation should be useful as a first estimate for Ks in various types of stirred three-phase slurry reactors. 

The gas flow pattern depends on the regime of gas-impeller interaction. For 6-blade disk turbines and similar impellers, three regimes of flow in the vessel can be defined, as shown in Fig. 4. 

---