Surface vortex Froude number

Equal surface motion is related most often to vortex formation. The depth of the vortex is related by geometric similarity and equal Froude number = DN fg... 

The Froude number is associated with the formation of a vortex on the liquid free surface around the impeller shaft. At low impeller speeds... 

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 ... 

The second group, the ratio of inertial to gravity forces, important when the liqui surface is wavy or curved, as with a vortex, is the Froude number. With u and L defined as before, it becomes Fr = dfN /g. 

For two-phase dispersions, other groups such as the iVeber number We = pu dp/ag, the ratio of inertial to surface forces, may be significant. Sherwood and Schmidt numbers are of course important in mass transfer. For dynamic similarity in two sizes of vessels operated with a vortex, the Reynolds and Froude numbers must be the same for both vessels. Since the impellers would be geometrically similar but unequally sized, it becomes impossible to specify the impeller speeds in the two vessels containing the same liquid to accomplish this. Thus, equal Reynolds numbers require... 

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... 

Later Mayle, 1970 [400] continued their research by performing measurements of velocity and pressure within the fire whirl. He found that the behavior of the plume was governed by dimensionless plume Froude, Rossby, second Damkohler Mixing Coefficient and Reaction Rate numbers. For plumes with a Rossby number less than one the plume is found to have a rapid rate of plume expansion with height. This phenomenon is sometimes called vortex breakdown , and it is a hydraulic jump like phenomena caused by the movement of surface waves up the surface of the fire plume that are greater than the speed of the fluid velocity. Unfortunately, even improved entrainment rate type models do not predict these phenomena very well. 

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