Power Consumption in Agitation

The energy consumption in agitation depends on the basic principles of fluid mechanics however, the flow patterns in a mixing vessel are much too complex for their rigorous application. Therefore, empirical relationships based on dimensionless groups are used. Here, because most fluid foods are non-Newtonian in nature, the 

Henry Rushton and coworkers developed the concept of the power number (Po) for smdying mixing of fluids that for Newtonian fluids is defined as  

In laminar mixing conditions of Newtonian fluids, Po is linearly related to agitator rotational Reynolds number. Real 

The value of the constant A depends on the type of agitator. Laminar mixing conditions are encountered as long as Rea is less than about 10. 

For a non-Newtonian food, the viscosity is not constant, but depends on the shear due to agitation. Therefore, for FCOJ and other non-Newtonian fluids we would like 

---

Bohme G, Stenger M. Consistent scale-up procedure for power consumption in agitated non-Newtonian fluids. Chem Eng Technol 1988 11 199-205. 

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. 

G.B. Tatterson, Scale-up procedures and power consumption in agitated... 

Armenante, P.M. Chang, G.-M. Power consumption in agitated vessels provided with multiple disk turbines. Ind. Eng. Chem. Res. 1998, 37, 284-291. 

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... 

CIRCULATION, VELOCITIES, AND POWER CONSUMPTION IN AGITATED VESSELS... 

Circulation, Velocities, and Power Consumption in Agitated Vessels... 

Power number, Pn P P power input to agitator drag force Power consumption in agitated vessels... 

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. 

Yoshida et al. (Y4) obtained data on power consumption in a 25-cm-diameter vessel. Four different types of vaned-disk impellers and one turbine were used, but for all impellers the ratio of impeller to tank diameter was maintained at 0.4. Their results, as would be expected, showed that the power dissipation increased rapidly with agitator speed and decreased with increasing gas rate for vaned-disk impellers. At certain agitator speeds, the amount of gas held below the vaned disk reaches a saturation value that apparently... 

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. 

Rieger, F. and Novak, V. Trans. Inst. Chem. Eng. 52 (1974) 285. Power consumption for agitating viscoelastic liquids in the viscous regime. 

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. 

An early study of power consumption in a homogeneous liquid in the absence of an air-liquid interface was reported by Laity and Treybal (1957). They examined agitation in unbaffled vessels as well as baffled vessels with four radial baffles, each 16.7% of the vessel diameter, and concluded that dynamic similarity is obtained in geometrically similar, unbaffled vessels by operating with no air-liquid interface and equal Reynolds numbers. For both unbaffled and baffled vessels, unique relations between Ne and Re can be obtained. Continuous flow of liquid through an unbaffled vessel has a small effect on the power characteristics of the impeller. For baffled vessels, the effect of continuous flow is negligible. For unbaffled vessels and 103 < Re < 105,... 

Rieger, F. Novak, V. Power consumption of agitators in highly viscous non-Newtonian liquids. Trans. Instn. Chem. Engrs. 1973, 51, 105-111. 

The efect of rheological complexities on power consumption in an aerated, agitated vessel, Chem. Eng. Commun. 19 (1983) 4-6, p. 273-293... 

Power consumption in aerated turbine-agitated vessels. 

A reaction in which the product forms a crystalline solid has been studied in a 1-ft-diameter pilot-plant reactor equipped with a 4-in. six-blade turbine with curved blades. At stirrer speeds less than 600 r/min, a solid deposit sometimes forms on the bottom, and this condition must be avoided in the commercial reactor. Density of the liquid is 701b/ft viscosity is 3cP. (a) What is the power consumption in the small reactor, and what is recommended for an 8000-gal reactor if geometrical similarity is preserved (h) How much might the required power be lowered by using a different type of agitator or different geometry ... 

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. 

Sivashanmugam, R, and Prabhakaran, S. (2008), Simulation of an effect of a baffle length on the power consumption in an agitated vessel, International Journal of Food Engineering, 4(2) Article 3. 

Rewatkar VB, Rao KSMS, Joshi JB. (1990) Power consumption in mechanically agitated contactors using pitched bladed turbine impellers. Chem. Eng. Commun., 88(1) ... 

Hirose, T, and Y. Murakami, Two-dimensional viscous flow model for power consumption in close-clearance agitators , J. Chem. Eng. Japan 19, 6, 568-574 (1986). 

EXAMPLE 3.4-1. Power Consumption in an Agitator A flat-blade turbine agitator with disk having six blades is installed in a tank similar to Fig. 3.4-3. The tank diameter D, is 1.83 m, the turbine diameter... 

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,... 

---