Froude number range

Reference 2 gives a case history for a 30-in. line at I3,000gpm, and the author has observed a plant example for a 6-in. line at I45gpm. Both had Froude numbers in the troublesome range and both caused big problems. 

The power input in stirred tanks can be calculated using the equation P = Ne pnM if the Newton number Ne, which at present still has to be determined by empirical means, is known. For stirred vessels with full reinforcement (bafQes, coils, see e.g. [20]), the only bioreactors of interest, this is a constant in the turbulent flow range Re = nd /v> 5000-10000, and in the non-aerated condition depends only on geometry (see e.g. [20]). In the aerated condition the Newton number is also influenced by the Froude number Fr = n d/g and the gas throughput number Q = q/nd (see e.g. [21-23]). 

Hughmark (Hll) has extended this approach to obtain an empirical correlation covering wide ranges of data for the air-water systems in vertical flow. Basically the correlation consists of using Eq. (70) with a variable value of the coefficient K. This coefficient was expressed by Hughmark as a function of the mixture Reynolds number, Froude number, and liquid volume-fraction. Hughmark s approach gives... 

Curves of power group as a function of Reynolds number (and Froude number in the case of unbaffled systems) are given in Fig. 6 for several different agitation systems which were studied. These systems and the ranges over which they were studied are described in Table III. Certain generalizations may be made from these results ... 

Fig. 9 The range of Froude numbers for Collette Gral high-shear mixers.

The range of Froude numbers for Fielder PMA series mixers is shown on Fig. 10. The 10-L laboratory scale mixer at its lowest speed settings can reach the Froude numbers of all other mixers, except one. These considerations can be useful for planning a scale-up or technology transfer operation. 

Froude number DrP-/g should remain constant. Bhrany showed (Table 9) that this is approximately true for a considerable range of actual balling disc operations. 

Zlokarnik [619] found no effect of a and S in measurements with a turbine stirrer of conventional design in pure liquids and in glycerine-water mixtures (coalescing material systems ). Surprisingly, the Froude number also had no effect on Ne in the industrially interesting range of Fr 0.65, so that for Re S 10 the power characteristic could just be described by Ne(Q) (Fig, 2.5). The process equation is ... 

This, as the components themselves, is a fimction of the Froude number. Fig. 4.33 shows the course of this function. It shows, that there are two operating ranges ... 

Below the above-mentioned Re range, however, significant differences were found also in the turbulent range between both bubble movements. The Re values, above which the horizontal and vertical bubble streams were held in equilibrium, could be predicted with a turbulent Froude number. 

The velocities VG and VL are superficial velocities based on the total pipe cross section. These Froude numbers exhibit several features in the range 0 < (Np,) and (Np ) < 2. 

The effect of inertia has been investigated by Edvinsson and Irandoust (1996) by using finite element analysis of Taylor flow in a cylindrical capillary. The effects of Ca, Re, and Fr numbers over a wide range were studied, and the simulations revealed that the film thickness was also dependent on Re and Fr numbers. By increasing the Re number the film thickness and the velocity difference between the two phases also increased, while the effect of Fr number (Froude number) was more obvious at higher Ca numbers, with results depending on the flow orientation (downward or upward flow). 

Figure 3.27. Typical plot of data of surface aerator efficiencies expressed as modified oxygen transfer number versus Froude number iVpr. The shaded area includes the range of different tested types. (Adapted from Zlokamik, 1979.)...

Dimensionless numbers such as Froude number can also be used to design and select high-shear granulators of different scales. It is therefore necessary to characterize and compare high-shear granulators of different types and sizes by the range of... 

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