Mass Flux
Using the extraction probe, both the upward and downward local mass flux at each radial position was measured over 20 to 30 s. The overall mass flux at each axial position was calculated as the net mass flux integrated across the riser cross-section 15,21:
\(G_{s}=\sum_{r=1}^{\text{total\ radial\ positions}}\left[\left(G_{r,upward}-G_{r,downward}\right)\times A_{r}\right]\)(3)
where \(G_{r}\) is the measured local mass flux at radial positionr , and \(A_{r}\) is the annular area corresponding to eachr . The local mass flux was normalized with respect to the overall mass flux for a fairer comparison in view of experimental variations of\(\pm 10\%\) in \(G_{s}\) 15,21:
\(G_{r,net,norm}=\frac{G_{r,upward}-G_{r,downward}}{G_{s}}\) (4)
Figure 6 presents the boxplots of the overall and local mass flux data, specifically 1320 datasets from the fast fluidized bed15 and 255 datasets from the turbulent one21. Clearly, the overall flux (Gs ) in the fast fluidized bed was a few orders of magnitude greater than that in the turbulent fluidized bed. It should be noted that the overall flux in the fast fluidized bed was controlled to meet targeted values by a slide valve that controls the amount of particles entering the riser, whereas that in the turbulent fluidized bed depended on the targeted superficial gas velocity (Ug ). As for the normalized local flux (\(G_{r,net,norm}\)), using the two-sample t-test, the null hypothesis was rejected, indicating the data from the fast and turbulent fluidized beds had different means at the 95% confidence level. Although the median values were of the same order of magnitude for both beds, the spread of values was a lot greater for the turbulent bed relative to the fast bed, suggesting greater radial and axial variations of local flux in the former.