4 Identification of micro flow structures and regime transition in gas-solid
4.4 Results and discussion 77
4.4.4 Micro flow structure analyses 89
The differences between BFB, TFB, CTFB, HDCFB and CFB regimes can be further studied by the natures of probability density function (PDF) of the solids holdups and moment features, such as skewness and kurtosis, as shown in Figs. 4.10-4.12. The results demonstrate that the fluidization regimes can be classified into two groups: flow dominated by high solids holdup peak and flow dominated by the dilute phase peak (Fig. 4.10), corresponding to the low-velocity and high-velocity fluidization regime groups discussed earlier. In the first group, BFB, TFB and CTFB have a clear peak in their PDF graphs around the dense phase solids holdup, and a more scattered dilute phase distribution. The dense phase peak also increases from the centre toward the wall, while the magnitude of the dilute phase reduces from the centre to the wall, implying more dense phase dominating toward the wall. In the second group, HDCFB and CFB only display a dilute phase peak on the left side in their PDF graphs, implying dilute phase dominating. From the centre to the wall, the dilute phase peak widens and shifts right, responding to the weakened dilute phase structure. The lack of high density peak for HDCFB and CFB regimes echoes the low density fraction as shown in Fig. 4.8.
The differences between the fluidization regimes displayed by PDF can be exhibited through the skewness and kurtosis features of the solids holdups, as shown in Figs. 4.11 and 4.12. Typically, skewness is a measure of the lack of symmetry in the probability density function (PDF) of the solids holdup signals around the mean value and reflects the predominance between the dense and dilute phases in the gas-solid phase flow, negative skewness reflecting dense phase dominating flow and positive skewness
reflecting dilute phase dominating flow. The negative skewness in BFB and most of TFB and CTFB confirms the dense phase dominated flow, while the high skewness in HDCFB and CFB confirms the dilute phase dominated flow. For CTFB and to a lesser extent also for TFB, the skewness is close to zero in the centre, suggesting a beginning of the transition of the flow from dense phase dominating to dilute phase dominating. On the other hand, kurtosis is a measure of the peakedness of the PDF and quantifies the magnitude of the variation of solids holdup distribution of the dispersive phase (bubbles in BFB and clusters in CFB). Therefore, the long and sharp tails in the PDF in Fig. 4.10 lead to higher kurtosis values, corresponding to the solids distribution in the core region of HDCFB and CFB and in the wall region of BFB, TFB and CTFB. On the other hand, a narrow phase distribution on the PDF in Fig. 4.10 corresponds to lower kurtosis values, representing the solids holdup distributions in the core region of BFB, TFB and CTFB and in the wall region of HDCFB and CFB.
0 0.6 0 20 s (-) P D F (-) 0 0.3 0 10 0 0.3 0 0.3 0 0.3 0 0.3 0 10 0 10 0 10 r/R=0.00 r/R=0.50 r/R=0.74 r/R=0.92 CFB HDCFB CTFB TFB BFB Figure 4.10 PDF profiles of BFB (ug= 0.53m/s), TFB (ug= 1.6 m/s), CTFB (ug = 2.57m/s, Gs = 234kg/m2s), HDCFB (ug = 8m/s, Gs = 550kg/m2s) and CFB (ug =
8m/s, Gs = 100kg/m2s), corresponding to the data at h/H = 0.60 in Fig. 4.11 and
0 1 0 6 r/R (-) S (-) 0 0.5 -6 0 0 0.5 0 0.5 0 0.5 0 0.5 -6 0 -6 0 h/H=0.85 h/H=0.60 h/H=0.40 CFB HDCFB CTFB TFB BFB
Figure 4.11 Radial skewness profiles for BFB (ug= 0.53m/s), TFB (ug= 1.6 m/s),
CTFB (ug = 2.57m/s, Gs = 234kg/m2s), HDCFB (ug = 8m/s, Gs = 550kg/m2s) and
CFB (ug = 8m/s, Gs = 100kg/m2s), (data for HDCFB and CFB from Yan and Zhu,
0 1 0 20 r/R (-) K (-) 0 0.5 0 10 0 0.5 0 0.5 0 0.5 0 0.5 0 10 0 10 h/H=0.85 h/H=0.60 h/H=0.40 CFB HDCFB CTFB TFB BFB
Figure 4.12 Profiles of dense phase fraction of BFB (ug= 0.53m/s), TFB (ug= 1.6
m/s), CTFB (ug = 2.57m/s, Gs = 234kg/m2s), HDCFB (ug = 8m/s, Gs =
550kg/m2s) and CFB (ug = 8m/s, Gs = 100kg/m2s), (data for HDCFB and CFB
from Yan and Zhu, 2004)
Conclusion
Experiments with FCC particles were carried out in two fluidized beds under five different fluidization regimes, bubbling (BFB), turbulent (TFB), circulating turbulent (CTFB), high density circulating (HDCFB) and circulating fluidized beds (CFB). Solids holdup signals were obtained with optical fibre probes at eleven radial positions at four elevations. The moments (mean, standard deviation, skewness and kurtosis) from the experimentally measured solids holdup signals were compared with those of equivalent ideal two phase flow systems and a Moment Consistency Data Processing Method
(MCDPM) was proposed to estimate the solids holdups and volume fractions of the dense and dilute phases at each measured location. These key parameters and their radial and axial distributions were used to study the detailed flow structures inside the various fluidized beds and the regime transitions among them. The results showed great similarities between the turbulent (TFB) and circulating turbulent (CTFB) fluidized beds but less similarities between the high-density circulating fluidized bed (HDCBF) and the circulating fluidized bed (CFB), with a more significant regime transition from TFB/CTFB to HDCFB. In the low-velocity regimes of BFB, TFB and CTFB, increasing gas velocity leads only to the decreasing of dense phase fraction but not the average dilute and dense phase holdups, while in the high-velocity regimes from HDCFB to CFB, it is the solids holdups of the dense phase that undergoes the most change. From the low- velocity to the high-velocity regimes, both the solids holdup and the fraction of the dense phase experience a drastic decrease, suggesting that this transition has a more profound change in the flow structure and further suggesting that CTFB is in reality still a turbulent fluidized bed although external solids recirculation has been imposed. Across the bed, the regime transition starts from the centre of the bed and then propagates towards the wall.
Acknowledgement
The authors are grateful to the Natural Sciences and Engineering Research Council of Canada for supporting this work.
Notation
D = bed diameter, m
Ek = relative kurtosis error
Es = relative skewness error
fd = volume fraction of dense phase
Gs = circulation rates, kg/m2s
K = kurtosis of local solids holdup fluctuations
Kth = theoretical kurtosis value
N = sampling population
r = radial position, m
R = radius of the column, m
S = skewness of local solids holdup fluctuations Sth = theoretical skewness value
ug = superficial air velocity, m/s
vp = instantaneous particle velocity, m/s
Vp = particle velocity, m/s
Z = elevation from the air distributor, m
Greek letters
= Instantaneous solids holdup
s
= local time-averaged solids holdup
εsd = local time-averaged solids holdup of dense phase p = particle density, kg/m3
= standard deviation of local solids holdup fluctuations
Subscripts c = phase b = Dilute phase g = gas P = particle s = solids
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