Figure 7 . Void fraction
measurement in water and different aqueous solutions of glycerin (G1 and
G3).
A parameter space was identified via careful inspection of the
experimental setup to formulate a correlation to predict the void
fraction using dimensional analysis. It was concluded that the parameter
space should be comprised of liquid properties (i.e. surface tension,
viscosity, and density), external body force (i.e. gravity), bubble size
(d32 ), and the gas flow rate (i.e. gas superficial velocity). The
effect of gas superficial velocity, gravity, and liquid properties were
accounted for using Froude number (Equation 5), Archimedes number
(Equation 9), and Eötvös number (Equation 10) for scaling the void
fraction. Equation (11) shows the resulting correlation for scaling the
void fraction, where G ( ) is an unknown function. Following Akita
and Yoshida,24 Mouza et al.,39Kazakis et al.,40 and Anastasiou et
al.,50 a power law functional form was considered for
the unknown function G . Figure 8 validates the correlation for
predicting the void fraction (ε ) in homogeneous regime against
experimental data showing that Equation (12) successfully predicts the
void fraction within ±5% accuracy of the current measurements.