Modified Froude number

Froude number, modified, Fr Pg gas density inertial force Fluid behavior of gas-liquid systems... 

Figure 3.9 compares the separated-to-intermittent flow regime boundaries for both 8-in.- and 4-in.-pipe experiments. The conditions are presented in terms of nondimensional superficial velocities J = Jk[pk/(pL - pc)gZ)]1/2 (or the density-modified Froude numbers). For 4-in.-pipe experiments, data have been obtained only for 3 MPa, while for the 8-in.-pipe experiments, data have been obtained for pressures of 3.0, 5.0, and 7.3 MPa. Note the value of J at the flow regime transition increased with pressure for the 8-in.-pipe experiments. 

The good agreement obtained for all data using the modified Froude number signifies the physical significance of the parameter. In fact, the dependence of jet penetration on the two-phase Froude number can be derived theoretically from the buoyancy theory following that of Turner (1973). 

Modified Froude group Modified Reynolds number... 

NFr Froude number Npr Substitution given in the text NFr Modified Froude group NRe Reynolds number Nrc Substitution given in the text Nr, Modified Reynolds number NwlCr Critical Weber number of maximum bubble size capable of survival... 

The fu st term is a modified Archimedes number, while the second one is the Froude number based on particle size. Alternatively, the first term can be substituted by the Reynolds number. To attain complete similar behavior between a hot bed and a model at ambient conditions, the value of each nondimensional parameter must be the same for the two beds. When all the independent nondimensional parameters are set, the dependent parameters of the bed are fixed. The dependent parameters include the fluid and particle velocities throughout the bed, pressure distribution, voidage distribution of the bed, and the bubble size and distribution (Glicksman, 1984). In the region of low Reynolds number, where viscous forces dominate over inertial forces, the ratio of gas-to-solid density does not need to be matched, except for beds operating near the slugging regime. 

However, this is unsatisfactory because we must expect the hydrodynamics of a bubble column to be substantially governed by gAp. Consequently, the process number must contain gAp. We must therefore combine H2 and n3 in order to obtain the modified Froude number Fr, which is probably the true process number. 

When liquids discharge vertically downward from orifices into gas, gravity increases the discharge coefficient. Figure 6-19 shows this effect, giving the discharge coefficient in terms of a modified Froude number, Fr = pg p/D ... 

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

Unbafiled tanks. At low Reynolds numbers, below about 300, the power number curves for baffled and unbaffled tanks are identical. At higher Reynolds numbers the curves diverge, as shown by the dashed portions of curve D in Fig. 9.12 and curve B in Fig. 9.13. In this region of Reynolds numbers, generally avoided in practice in unbaffled tanks, a vortex forms and the Froude number has an effect. Equation (9.16) is then modified to... 

Stratified-Wavy. At high vapor velocities, the flow deviates from the idealized situation just described. First of all, heat transfer in the stratified liquid pool at the bottom of the tube may not be negligible. Secondly, axial interfacial vapor shear may influence the motion and heat transfer in the thin film region around the top part of the tube. Dobson [144] studied this more complex situation and reported that stratified-wavy flow exists when G < 500 kg/m2s and Frm < 20, where Frm is a modified Froude number given by ... 

Figure 5.10. Excess hydraulic gradient due to solids as function of modified Froude number. Comparison of results of different workers...

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.)...

White and de Villiers (1977) defined a modified Froude number. For N=N, ... 

FIGURE 9.6 Impeller performance index as a function of modified Froude number, Fr. (Reproduced from Zundelevich, 1979 with permission from John WUey and Sons. Copyright 1979 American Institute of Chemical Engineers.)... 

Equation 27 indicates that the normalized hydraulic gradient, (i - i,)/i, is a function of the modified Froude number, the single particle drag coefficient and the delivered solids volume fraction. 

D Mean particle size, mm F Bed frequency of oscillation, s Solids mass flow rate, kg/s Fr Froude number for slurry flow in the drum, V/[2 g R (Ss - 1) ] Fr, Modified Froude number for pipe... 

Fr Modified Froude number for open channel flow V /[g L (S - 1)] ... 

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