Figure 7. Random Forest out-of-bag
permuted predictor importance estimates for local (left column) and
overall (right column) mass flux. For local flux, the fast fluidized bed
had 1320 datasets 15, while the turbulent fluidized
bed had 255 datasets 21. For overall flux, the fast
fluidized bed had 1320 datasets 15, while the
turbulent fluidized bed had 378 datasets 21.
Entrainment correlations typically incorporate dimensionless numbers
such as Reynolds (Re), Archimedes (Ar) and Froude (Fr), and also
particle properties in terms of minimum fluidization velocity
(Umf ) and terminal velocity
(Ut ) 30. The equations to
calculate these parameters (namely, particle Re (Rep),
relative Re (Rei), terminal Re (Ret),Ut , Ar, Umf , and Fr) are
presented in the Appendix.
Figure 8 shows the relative influence of the variables on the overall
flux in the fast and turbulent fluidized beds. Comparing the two
regimes, the relative influence of the variables were different. An
earlier study has indicated that the pressure at the bottom of the riser
(Pbot ) was the most influential on overall flux
in the fast fluidization regime, while other variables comparatively had
a negligible influence 27. ThePbot data was unfortunately not available for the
turbulent dataset, so cannot be shown for comparison between the
regimes. Nonetheless, it can be inferred from the approximately two-fold
larger magnitudes of the estimates for the turbulent bed the relatively
greater importance of particle properties, which implies thatPbot was not as dominant an influence.
In addition, Figure 9 shows the SOM weight planes, which are useful for
ascertaining the dominance of the influence 27, of the
two most dominant influencers, the least dominant influencer and also
the overall flux for each regime. Specifically, the shades reflect the
weights, with lighter and darker representing larger and smaller
weights, respectively. The more similar the color gradients are, the
stronger the correlation of the variables is. Clearly, (i) the color
distributions for overall flux of the fast fluidized bed are rather
dissimilar even with the top two influences (top row) shown in Figure 8,
indicating a less significant effect of particle-related properties on
overall flux, since Pbot was an overly dominant
influence 27; and (ii) the color distributions for
overall flux of the turbulent fluidized bed are much more similar to the
top two influences (top row), indicating a more significant influence of
these particle properties related parameters. The SOM weight planes of
the least influence (bottom row) in each fluidization regime are also
shown in Figure 9. For the fast regime, the patterns are dissimilar. For
the turbulent regime, some similarity in patterns with the overall flux
is evident, but lesser compared to the top influences. Thus, the SOM
analysis further affirms the more significant influence of particle
properties or its related parameters on the turbulent bed relative to
the fast one. Interestingly, although the driver for the overall flux in
the turbulent bed was Ug , it had the least
influence as a standalone variable, which again emphasizes the
importance of particle properties in affecting overall flux in the
turbulent regime.