Impeller Froude number

The impeller Reynolds number is proportional to the standard Reynolds number and is arrived at by assuming that the velocity of the solvent flow through the chamber is proportional to the speed of the impeller and the area through which it acts. The impeller Froude number is arrived at in a similar manner. 

The transitions between the various regimes generated by a gassed disk turbine can be quantified using dimensionless numbers such as the gas flow number, FIq(=Qg/ND ), the impeller Froude number, Fr (=N D/g), and system geometry ratios, such as the impeller diameter to tank diameter ratio (D/T)P For 6-blade disk turbines the cavity regime as well as other regimes are best obtained from the flow... 

Impeller Froude number = N D/g Modified impeller Froude number at Ajs for solid-liquid suspensions [Pl/(Ps Pl)1 Nf D/g... 

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

For NRc S 10, the liquid motion moves with the impeller, and off from the impeller, the fluid is stagnant [34]. The Froude number accounts for the force of gravity when it has a part in determining the motion of the fluid. The Froude numbers must be equal in scale-up situations for the new design to have similar flow when gravity controls the motion [16]. 

The first dimensionless group on the right is the Reynolds number, the second represents the ratio of the gas velocity to the impeller tip speed, the third is the Weber number, and the fourth is the Froude number. 

The correlation of Norwood and Metzner shows to be a complex function of the Reynolds number, the Froude number, the ratio of tank-to-impeller diameter, and the ratio of tank diameter to liquid level. However, to a reasonable first approximation for geometrically similar vessels operating at high Reynolds numbers. 

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... 

L T ), and v is the kinematic viscosity ofthe hquid (L" T ). Ihe dimensionless groups include N/v) = Reynolds number (Re) d N /g) = Froude number (Fr) and (Q/N d = aeration number (Na), which is proportional to the ratio of the superficial gas velocity with respect to the tank cross section to the impeller tip speed. 

The dimensionless group in the left-hand side of Eq. (9.53) is known as power number NP, which is the ratio of drag force on impeller to inertial force. The first term of the right-hand side of Eq. (9.53) is the impeller Reynolds number NRe. which is the ratio of inertial force to viscous force, and the second term is the Froude number NFr which takes into account gravity forces. The gravity force affects the power consumption due to the formation of the vortex in an agitating vessel. The vortex formation can be prevented by installing baffles. 

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

The corresponding impeller speed is Wmax. For commonly used propeller (Fig. 21 h) and turbine (Fig. 2 lg) stirrers, the highest allowable rotation speed is given in terms of the Froude number, as... 

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 ... 

Another equipment parameter is the Froude number (Fr), a dimensionless number calculated as shown in Eq. (2), where v represents the impeller speed (rpms) and r is the radius of the granulator bowl. 

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