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Power consumption is a basic integral quantity in a mixing operation that, in part, determines other process quantities. Blend time, holdup, and mass transfer coefficients such as k,a in gas-liquid contacting, drop size in liquid-liquid processing, reaction times for fast chemical reactions, and heat transfer coefficients are all related to power consumption. The effect of shear and elongation on biological systems in a mixing tank depends as well on power consumption. Utility costs in mixing are also important in plant operations from the viewpoint of operating costs.The distribution of the power usage in mixing operations is of interest, and power actually delivered to the mixing is very important in judging the mixing performance being received from the agitator. Ironically, power consumption in industrial mixing operations is most often left unverified.A mixing unit consumes power in its three basic subunits: the motor, the gearbox, and the tank in which the mixing takes place, Of these, power usage in mixing in the tank has the reputation of being very difficult to measure. Typically, specialized equipment is usually necessary to perform such measurements, and calibration of the measuring equipment is difficult. Such measurements are not performed on-site in a chemical plant and the end result is that power input to mixing is not documented in actual plant operations. The accepted power consumption in mixing for actual plant operation is that obtained from correlations used in design of the unit.Differences occur between the power input calculated from design correlations and the actual power consumed in the mixing operation. Internal geometries in industrial tanks are not typically those used in the development of the power number correlations. Design changes frequently occur after the unit is in place. Furthermore, certain power data reported in the accepted engineering design literature are not accurate. Nagata and Yokoyama (1955), Bates et al. (1963), andNovak et al. (1982) have discussed the known inaccuracies for turbulent mixing. In laminar mixing, power measurements and correlations are still developing due to the complexities of the impeller/tank geometries, nowNewtonian flow behavior, and viscosity characterization. Chavan and Ulbrecht (1973a, b, 1974), Kappel (1979), and Chavan (1983) discuss inaccuracies in laminar power correlations. As a result of these factors, there is uncertainty concern-R. L. King, R. A. Hiller, G. B. TattersonTexas A & M University College Station, TX 77843 ing power consumed in actual mixing and the distribution of power usage in plant mixing operations generally.In this study, a power meter is used to measure power usage in a 2 hp agitator unit. Power consumption data are obtained for the motor, gearbox, and in mixing. Power-number curves are generated for a pitched-blade turbine and a flat-blade open impeller from the power meter data and are compared with standard correlations and published data. Power-number data are also obtained for the gearbox. This work shows how ...

The determination of power consumption of rotating impellers in an agitated tank has primarily relied on traditional dimensional analysis concepts and correlations. Another traditional approach based on form and skin drag is also possible in determining the power consumption occurring in mixing. This approach, however, appears to have been neglected in the literature on mixing.Traditionally, power number correlations for turbulent flow usually appear as = K pN3D5 where the constant, K, is dependent on the type of impeller. Power can also be written as a drag force times a velocity:where the velocity, U , is related to impeller tip speed or ND. The drag force is usually expressed as function of a drag coefficient, the projected area (which is proportional to D2), fluid density, and velocity asThe total drag force is a sum of skin and form drag forces. The force arising from skin drag is simply 1 2where T , is the wall (or blade) shear stress. The force arising from form drag can be expressed as trailing vortex systems have a low pressure core that coalesces sparged gas to form gas cavities behind the impeller blades. These low-pressure vortex regions may contribute substantially to the form drag contribution of the power. The second objective of this paper is to investigate the possible interrelationship between vortex systems and power consumption for the pitched-blade turbine. This investigation includes a study of the effects of the addition of winglets and fins (added to the impeller blades in the vicinity of the vortex systems) on power consumption.The impeller used in this study was a 45" pitched-blade turbine with four blades. The flows, which may be of importance, are shown in Figure 1 and exist as boundary layers on both the front and back sides of the impeller blades, a wake behind the blade, and a vortex system on the impeller blade tip. However, visual observation studies (Yuan et al., 1980) using neutrally buoyant tracer particles of the flow through the impeller indicate that the wake region behind the blade is not significant, the flow resembling a boundary layer.For the calculation of the skin drag in this work, the boundary layers shown in Figure 1 were assumed to be turbulent on both sides of the impeller blade. It was further assumed that the boundary layers were turbulent, since the impeller Reynolds numbers indicated turbulent conditions in the tank. This, however, was not a critical assumption for the outcome of this study, and a standard correlation was used to calculate skin drag. The calculation of the form drag portion of the power required experimental determination of the pressure drop occurring across the blade. having a projected area A . The drag coefficient in Eq. incorpotaps, 2.4 mm in dia,, on the front and back sides of the blade, as shown in rates both skin and form drag contributions to the drag force. The objective of this paper, in part, is to investigate the contributions of skin and form drag to the power that is transferred from a in mixing has demonstrated the importance ...

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