Unbaffled tanks

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... 

A Mierosoft Exeel spreadsheet (Example7-2.xls) was developed for an unbaffled tank. 

Flow and power numbers each decrease as the Reynolds number increases. In unbaffled tanks, a vortex forms that takes over the flow regime and does not allow the usual relationship to describe the performance of the mixing operation. It is proper and good practice to provide baffles in all vessels (see later description for the physical configurations). 

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

If turbine or marine propeller agitators are used to mix relatively low viscosity liquids in unbaffled tanks, vortexing develops. In this case the liquid level falls in the immediate vicinity of the agitator shaft. Vortexing increases with rotational speed N until eventually the vortex passes through the agitator. As the liquid viscosity increases, the need for baffles to reduce vortexing decreases. 

Figure 3.19 Typical flow pattern in an unbaffled tank.

The values of VP are approximate. At low Reynolds numbers, about 300, the power number curves for baffled and unbaffled tanks are identical (McCabe et al., 1993). For higher NAV, the power number for unbaffled tanks is lower than the values for baffled tanks. 

The coefficients in unbaffled tanks increased with only the 0.3 power of the stirrer speed. At the speed needed for complete suspension in a baffled tank, the coefficients are about the same with or without baffles. At higher speeds, the more uniform dispersion of the particles and the greater velocity fluctuations make the coefficients larger with baffles present. 

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... 

Unbaffled tanks have a tendency to produce a vortex and swirl in the liquid. Such conditions may be wanted. Frequently, however, a good top-to-bottom turnover and the elimination of vortexing is needed. Therefore, baffles... 

Figure 7-16. Mixing times in agitated vessels. Dashed lines represent unbaffled tanks solid lines represents a baffled tank. (Source McCabe, W. L, et at., Unit Operations of Chemical Engineering, 4th ed., McGraw-Hill Book Company, New York, 1985.)...

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.,... 

Fig. 4. Use of Froude group in correlation of power data in unbaffled tanks. From Rushton et al. (R13).

Van de Vusse also made some limited investigations of other factors. For an unbaffled tank, van de Vusse s data indicate a possible variation of 40% in mixing time with propeller location. Limited data (from an unbaffled vessel) on the influence of turbine design indicate that the mixing time decreases as the proportion of radial to axial or tangential flow is increased. 

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

UnbafflecTTanks If a low-viscosity liquid is stirred in an unbaffled tank by an axially mounted agitator, there is a tendency for a swirling... 

How does axial circulation, a precondition for large-space mixing, take place in an unbaffled tank A purely rotational motion would be useless. Answer A boundary layer is formed at the wall due to the van der Waals and the viscosity forces, which is kept there by the shear stress. The tank contents therefore rotates more slowly than the stirrer, and the centrifugal forces of the stirrer convey the liquid radially outwards. (It has been found that axial rotation immediately almost completely fails, when a friction-reducing tenside is added [572].) The deceleration of the tank contents is much more effective with baffles (stream crossways to the baffle surfaces) than by hydrodynamic boundary layers (stream parallel past the wall surface). 

For turbulent flow, the local velocity components, which are approximately equal to the axial flow velocities are a constant proportion of the tip speed of the stirrer u v /u = constant (see also [497]). This fact is, however, not confirmed in unbaffled tanks. In this case these velocity components decrease with the diameter of the tank. 

A three dimensional turbulent flow field in unbaffled tank with turbine stirrer or 6-paddle stirrer was numerically simulated by the method of finite volume elements [80], whereas in the case of free surface the vortex profile was also determined using iterative techniques. The prediction of the velocity and turbulence fields in the whole tank and the stirrer power was compared with literature data and their own results. Of the two simulation techniques used, turbulent eddy-viscosity/zc-e turbulence model and the DS model (differential 2. order shear stress), only the latter produced satisfactory results. In particular it proved that fluctuating Coriolis forces have to be taken into account by source terms in the transport equation for the Reynolds shear stress. 

Stirring in unbaffled tanks produced liquid rotation and the formation of a liquid vortex. Experimental results showed that the acceleration due to gravity g and hence the Froude number Fr = n d/g had no influence under such conditions. This was confirmed by the points on the lower Ne(Re) curve, where the same Re value was set for liquids with different viscosities. This could only be done by a proportional change in stirrer speed. Thus for Re = idem Fr idem, but this had no influence upon Ne g was therefore irrelevant ... 

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