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.