Empirical Correlations

Fournol et al., (1973) describes the TDH (F) - as inversely proportional to the Froude number. Despite this proposition, the authors note that this height is significantly higher than predicted by Zenz and Weil (1958):

Hamdullahpur et al., (1986) proposed an equation that characterizes the TDH(C) as dependent on the bubble diameter:

Baron et al., (1988) suggested a new correlation to estimate the TDH(F), in which the maximum height reached by the large clusters is directly proportional to the velocity square of the particle (KUb) ejection, which in turn would be the gas velocity:

Sciazko et al., (1988) have shown though, that the ratio between both the splash-zone height and the bed height is strongly influenced by the excess gas velocity (U-Umf). This volumetric fraction would be the critical value of the bubbles fraction, which is related to the difference in the velocities mentioned above:

Sciazko et al., (1991) determined a new correlation for the TDH(C) depending on the diameter of the bubble on the bed surface:

Pinto et al., (1999) proposed a correlation for the TDH(C) depending on the physical characteristics of both the particles (particle diameter), and the gas (density and viscosity) and the operating conditions (solid mass and gas velocity):

Cipolato et al., (2004 stablished a new correlation for the TDH(C) depending on the solid mass through the statistical analysis, for a first order model with two interactions: