Power consumption of agitators

Rieger, F. and Novak, V. 1973. Power consumption of agitators in highly viscous non-Newtonian Uquids. Trans. Inst. Chemi. Eng. 51 105-111. 

The prediction of power consumption for agitation of a given non-Newtonian fluid in a particular mixer, at a desired impeller speed, may be evaluated by the following procedure. 

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)].

Power consumption by agitation is a function of physical properties, operating condition, and vessel and impeller geometry. Dimensional analysis provides the following relationship ... 

S. Watano, K. Terashita, K. Miyanami, Frequency analysis of power consumption in agitation granulation of powder materials with sparingly soluble acetaminophen, Chem. Pharm. Bull. 40 (1992) 269-271. 

Power or energy dissipated in the aerated suspension has to be large enough (a) to suspend all solid particles and (b) to disperse the gas phase into small enough bubbles. It is essential to determine the power consumption of the stirrer in agitated slurry reactors, as this quantity is required in the prediction of parameters such as gas holdup, gas-liquid interfacial area, and mass- and heat-transfer coefficients. In the absence of gas bubbling, the power number Po, is defined as... 

Loiseau et al. (1977) found that their data for nonfoaming systems agreed well with Eq. (3.3). Calderbank (1958), Hassan and Robinson (1977), and Luong and Volesky (1979) have also proposed correlations for power consumption in gas-liquid systems. Nagata (1975) suggested that power consumption for agitated slurries can be reasonably predicted from these correlations by the correction factor psi/pL, where psl is the density of the slurry. Power consumption for a gas-liquid-solid system has also been studied by Wiedmann et al. (1980). They examined the influence of gas velocity, solid loading, type of stirrer, and position of the stirrer blades on power consumption plots of power numbers vs. Reynolds numbers for propeller and turbine type impellers proposed by them are shown in Fig. 13. 

Bertrand J., Couderc J.P., Evaluation of the power consumption in agitation of viscous Newtonian or pseudoplastic liquids by two-bladed, anchor or gate agitators, Chem. Eng. Res. Dev. 63 (1985) 7, p. 259-263... 

Savinsky J., Deak A., Havas G., Power consumption of screw agitators in Newtonian liquids of high liiscosity, Chem. Eng. Sci. 34 (1979), p. 1160-1162... 

Power consumption is an important mixing design parameter, dependent upon impeller diameter ( >), rotational speed (N), and fluid properties including viscosity (/ra) and density (p), and power consumption of impellers is usually provided as correlations of power number, Np, to Reynolds number, Nt. For fluids exhibiting time-independent power law viscosity functions, r = Kyn, the generalized Reynolds number in agitation can be expressed as ... 

The effect of fluid rheology on the power consumption of helical ribbon agitators has also been evaluated [54] and power consumption as a function of generalized Reynolds number for shear thinning but inelastic fluids defined. When shear thinning effects are small, and elasticity is negligible, deviations from the Newtonian... 

The power consumption of an impeller in a perfectly agitated tank of a Newtonian-type liquid can be calculated with the power number, P [11], This dimensionless number is conceived as a... 

Power consumption for agitation is another important design parameter. It increases with increased agitation speed and tank diameter. Power consumption decreases with increased gas velocity. Correlations have been summarized by Baldi [12]. The presence of solid catalyst particles influences power consumption only slightly [6]. 

The available literature contains very few references to studies of the power consumption for agitation and the volumetric oxygen transfer coefficients of multi-stage impeller fermenters. Takeda and Hoshino (1968) showed experimentally that closely spaced impellers caused serious interference between the flow streams from adjacent impellers and an overall reduction in power consumption. On the other hand, Oldshue (1966) has indicated that within fairly large ranges of geometric variables, a similar oxygen transfer coefficient is obtained if the power per unit volume is maintained at similar values under a constant aeration rate. 

The power consumption of the stirrer, expressed as kW/m or FlP/1000 gal, and the superficial velocity of the gas are the main adjustable parameters that determine the mass transfer coefficient. The agitator power can be estimated from the power number Np and the standard equation for liquids modified by a factor Pg/P to allow for the effect of aeration ... 

The power density Py is the characteristic quantity of turbulent flow. It determines the size of the smallest eddies and the intensity of microturbulence. In addition, it is a measure of the shear intensity in laminar flows or the intensity of cavitation in ultrasonic fields (see above). The power input P in the dispersion zone can be derived from the pressure drop (e.g. in pipes and nozzles) or can be measured caloricafly (e.g. for rotor-stator systems and ultrasonication Pohl 2005 Kuntzsch 2004). Additionally, P can be roughly approximated by the electric power consumption of the dispersion machine (e.g. for ultrasonication Mandzy et al. 2005 Sauter et al. 2008), even though the real values may be lower by a factor of 2 to 5. A further source of uncertainty is the volume of the dispersion zone (Vdisp). since the stress intensities are not uniformly distributed in dispersion apparatuses. In particular, this applies to agitated vessels, where the highest dissipation rates are obtained in the vicinity of the stirring instmment (Henzler and Biedermann 1996),... 

Wang, K., and S. Yu (1989). Heat transfer and power consumption of non-Newtonian fluids in agitated vessels, Chem. Eng. Sci., 44, 33-40. 

Pitched-blade turbines (Fig, 18-3) are used on top-entering agitator shafts instead of propellers when a high axial circulation rate is desired and the power consumption is more than 2,2 kW (3 hp), A pitched-blade turbine near the upper surface of liquid in a essel is effecth e for rapid submergence of floating particulate solids,... 

Interlock agitator power consumption to cutoff feed of reactants or catalyst or activate emergency cooling... 

Based on the practical history of scale-up, most fermentation processes for alcohol and organic acid production have followed the concepts of geometric similarity and constant power per unit volume. From the above concept, and as a strong basis for translation of process criteria, only physical properties of the process were considered in the scale-up calculation. For power consumption in an agitated vessel, there is a fixed relation between impeller speed, N, and impeller diameter, l)t. The constant power per unit volume, for a mechanical agitated vessel is given by ... 

The power per unit volume is constant. From power consumptions in a bench-scale bioreactor, the necessary agitation rate is calculated for the scale up ratio, using Equation (13.2.1). The choice of criterion is dependent on what type of fermentation process has been studied. The following equation expresses relations for the impeller size and agitation rate in small and large bioreactors. 

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