Impellers unbaffled

David and Colvin [Am. Inst. Chem. Eng. J., 7, 72 (1961)]. Continuous heat transfer between kerosine and water unbaffled vessel. Open impellers (paddles and propellers) are better than closed (centrifugal and disk impellers) at the same tip speed. 

Fluid Velocities in Mixing Equipment Fluid velocities have been measured for various turbines in baffled and unbaffled vessels. Typical data are summarized in Uhl and Gray, op. cit., vol. I, chap. 4. Velocity data have been used for calculating impeller discharge and circulation rates but are not employed directly in the design of mixing equipment. 

Vortex Depth In an unbaffled vessel with an impeller rotating in the center, centrifugal force acting on the fluid raises the fluid level at the wall and lowers the level at the shaft. The depth and shape of such a vortex (Rieger, Ditl, and Novak, Chem. Eng. ScL, 34, 397 (1978)] depend on impeller and vessel dimensions as well as rotational speed. 

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... 

Additional power data for other impeller types such as anchors, cui ved-blade turbines, and paddles in baffled and unbaffled vessels are available in the following references Holland and Chapman, op. 

Impeller and Flow Characteristics— Viscous, Baffled or Unbaffled Systems Simple Ratio Relationships... 

Axial flow7 impellers in an unbaffled tank will produce vortex swirling about the vertical shaft. This will be discussed later in more detail. 

Derksen (2006a) continued along this line of approach and—by means of a clever strategy—mimicked the long-time behavior of solids suspension in an unbaffled tall stirred tank equipped with four hydrofoil impellers (Lightnin A310). The time span covered by his LES amounted to some 20,000 impeller revolutions (some 20 min). Running a LES for a Reynolds number of 1.6 x 10 over the entire time span is not an option, and for that reason a particular flow... 

The same value holds for the angular off-center position of the impeller in an unbaffled vessel. The number in parenthesis conesponds to the curves in Figure 3.24. 

The Reynolds number NBe accounts for viscous forces, and the Froude number NFr for the force of gravity when this is important. For a typical impeller-tank arrangement, curves of the sort shown in Fig. 1 result, based on Eq. (2). Briefly, at low values of NRe (viscous flow, A to 5 in the figure) for both baffled and unbaffled tanks, no vortex is produced and the Froude number is unimportant n = 0). In turbulent flow the... 

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,... 

For liquid-liquid mixtures, the calculations of mixing time and power (or Newton) number outlined above are valid for unbaffled vessels only as long as the vortex created by the stirrer does not reach the stirrer head. Otherwise, gas entrainment occurs and the physical properties of the system change. The depth of the liquid-gas interface at the vessel axis with respect to static liquid surface level, HL, can be related to the Froude and Galileo numbers. Some of the reported relationships are summarized in Table XIV. The value of H, at which the vortex reaches the upper impeller blades level can be expressed as... 

Laity and Treybal (1957) showed that with the above definitions of pd and /id for two-phase mixtures, the correlations for Ne for two-phase and singlephase liquids can be identical. Laity and Treybal (1957) also showed that the impeller height in relation to the liquid-liquid interface of two-phase systems has little effect between one and two impeller diameters from the bottom of an unbaffled vessel. Impeller height in baffled vessels is important in the agitation of two-phase liquids. For more effective agitation, the vessel should be operated, if possible, with the impeller in the low-viscosity phase. 

In these runs, the presence of the Geiger-Mueller counter may affect the flow pattern significantly. Further, examination of the results presented shows that the radial velocities do not satisfy material balance requirements. Nevertheless, several of Aiba s conclusions are of interest. With baffles, the vertical circulation is large compared with the unbaffled case, but considerable tangential flow remains. In neither the baffled nor unbaffled case do the mean flow velocities approach the tip velocity of the impeller the ratio of fluid velocity to impeller-tip velocity is essentially independent of impeller rotation speed, varies... 

Two situations were encountered which did not give the typical correlation curve. First, in unbaffled vessels with a liquid height 50% or 75% of the vessel diameter, a speed is reached at which the vortex formed in the liquid becomes deep enough to reach the impeller, and the power consumption drops very quickly with any further increase in speed. The onset of this deep vortexing was not correlated with the other system variables in limited tests, even one baffle was found suf-... 

Power requirement data for three-bladed marine propellers were published by Stoops and Lovell (S8), who worked with axially-mounted propellers in an unbaffled tank. They found no effect of variations in liquid depth or impeller height, and did not report the extent of vortexing, which must have been present. They correlated their data in a dimensionless form similar to that discussed above, i.e.,... 

Fick et al. (FI) found that Eq. (31) applied over a range of 0.13-0.65 in impeller width-to-diameter ratio. In addition, measurements without baffles showed that for other conditions constant the interfacial area in the unbaffled system was about 0.6 of the area in the baffled vessel. 

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 ... 

Pavlushenko et al. (P2) studied the suspension of screened fractions of sand and iron ore in a variety of liquids, with a 1-ft. diameter unbaffled vessel filled to a depth of one foot. Square-pitch three-blade propellers of 3-, 4-, and 5-in. diameter were used, and most of the observations were made with a 1 to 4 weight ratio of solids to liquid. Thief samples were taken at various levels in the vessel. In some cases, the contents did not become uniform at any impeller speed in other cases the contents became uniform at some impeller speed and remained so at higher speeds in a third type of behavior, the upper part of the vessel reached the over-all vessel average and then exceeded it as impeller speed was increased. Using the observations from the second and third types of behavior, a critical speed was defined as the lowest impeller speed at which the solids concentration at each level, or in the upper layers of the liquid, was equal to the over-all average solids concentration. This critical speed Nc in revolutions per second had the following relation to the operating variables ... 

FIG. 18-12 Typical flow pattern for either axial- or radial-flow impellers in an unbaffled tank. 

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