Agitated vessels power consumption

In thin and tall vessels H/T > 1), multistage impeller systems are commonly used. The resulting shaft power is highly influenced by the clearance Ah between the impeller stages. In fully baffled systems and for Ah > 1.2, the power for the single stages can be summed up. When multiphase systems are agitated, the power consumption can extremely differ from the one-phase system (see Section 13.6). 

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 ... 

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... 

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 ... 

The energy of dissipation per unit mass of liquid in a liquid-solid agitated vessel is related to the power consumption per unit volume of liquid (Ps) as follows (Kato et al., 2001) ... 

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

The dimensionless group in the left-hand side of Eq. (9.53) is known as power number NP, which is the ratio of drag force on impeller to inertial force. The first term of the right-hand side of Eq. (9.53) is the impeller Reynolds number NRe. which is the ratio of inertial force to viscous force, and the second term is the Froude number NFr which takes into account gravity forces. The gravity force affects the power consumption due to the formation of the vortex in an agitating vessel. The vortex formation can be prevented by installing baffles. 

The power consumption by an agitator in an unbaffled vessel can be expressed as... 

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,... 

Another important design parameter for miscible liquids is the power consumption, which can be obtained from Fig. 24. For viscous liquids, flow is in most part laminar. When the agitated vessels contain baffles, turbulence is achieved at a lower Reynolds number. Once the flow becomes turbulent, the power number attains a constant value. 

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 ... 

Oyama and Endoh (012) studied the solution of sugar in water in 6.7- and 10.8-in. baffled vessels using paddles and flat-blade turbines. They report a mass-transfer coefficient which was proportional to the cube root of the particle diameter and to the cube root of the impeller power consumption per unit mass of agitated liquid. 

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 vessel is effective for rapid submergence of floating particulate solids. 

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

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

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

POWER CONSUMPTION. An important consideration in the design of an agitated vessel is the power required to drive the impeller. When the flow in the tank is turbulent, the power requirement can be estimated from the product of the flow q produced by the impeller and the kinetic energy (. per unit volume of the fluid. These are... 

Power consumption in aerated turbine-agitated vessels. 

HEAT-TRANSFER COEFFICIENTS. In an agitated vessel, as shown in Chap. 9, the dimensionless group D np/fi is a Reynolds number useful in correlating data on power consumption. This same group has been found to be satisfactory as a correlating variable for heat transfer to jackets or coils in an agitated tank. The following equations are typical of those that have been offered for this purpose. 

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

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