Figure 10 . Scaled bubble
size versus scaled specific input power using results from the
literature in addition to the current study.
In the rest of this section void fraction measurements and scaling in
heterogeneous regime are discussed. The same parameter space for
producing Equation (11) was employed for scaling the void fraction and
finding the function form of G() . Here, it was assumed that the
bubbles are traveling at terminal velocity (see Figure 11); therefore,
the drag force (FD \(\propto\)ρLd322Ub2 )
was balanced with buoyancy force (FB =
ρLgd323 ). This
assumption establishes a relationship between bubble size and bubble
velocity (Ub2 ~
gd323 ). It is known that the void
fraction is the ratio of gas superficial velocity to the bubble velocity
(ε = USG/Ub ); therefore, the void
fraction is proportional to bubble Froude number (Fr =
USG/[gd32]0.5 ).
Assuming that void fraction scales as a power law function of Froude
number (Equation 5), Archimedes number (Equation 9), and Eötvös number
(Equation 10), then Equation (17) gives the general form of G() .
The exponents in Equation (17) (i.e. Χ , Ψ , and Ω )
were calculated from Equation (18) (Χ= 1.117, Ψ= 0.1, andΩ= -0.032). Figure 12 shows that the proposed coordinates (see
Equation 19) were able to successfully scale the void fraction within
the heterogeneous regime. Equation (19) successfully predicts the void
fraction within ±25% accuracy for the current data.