Multiresolution analysis on identification and dynamics of clusters in a circulating fluidized bed

Abstract

). An appropriate level of approximation subsignal was systematically specified as a threshold for cluster identification, based on multiresolution analysis (MRA) of wavelet transformation. By the established threshold, the dynamic properties of clusters including the appearance time fraction of clusters F cl , average cluster duration time s cl , cluster frequency f cl , and local average solids holdup in clusters e sc , at different radial and axial positions were determined under the turbulent, transition and fast fluidization flow regimes. The results also describe the dynamic properties of clusters and flow patterns in the splash zone along with the dense bottom region of the circulating fluidized beds.

Development, Verification, and Validation of Multiphase Models for Polydisperse Flows

“…Pertaining to the impact of material properties on cluster duration (Figure 169), small glass consistently exhibits the highest duration towards the wall (r/R = 1), which agrees with previous work (Horio, Morishita et al 1988;Soong, Tuzla et al 1995; Wei, Yang et al 1995;Sharma, Tuzla et al 2000;Manyele, Parssinen et al 2002;Yang and Leu 2009); however, for the larger materials (large glass and large HDPE), the radial trend of increasing duration towards the wall is observed only at h/H ≤ 0.27. Moreover, interestingly, under low G s conditions (Figure 169a and c), large glass and large HDPE have very similar radial profiles, suggesting that particle size plays an influential role under such riser conditions.…”

“…Notably, similar to cluster duration (Figure 169), the trends for low G s (Figure 170a and c) conditions are similar, while the trends for high G s (Figure 170b and d) are similar. Regarding impact of operating condition, cluster frequency is greatest for the highest m (Figure 170b) for small glass (especially at the riser center), which agrees with previous work (Sharma, Tuzla et al 2000;Manyele, Parssinen et al 2002;Yang and Leu 2009). On the contrary, frequency is greatest for the lowest m condition (Figure 170c) for the larger materials (large glass and large HDPE), indicating again that the effects of operating condition and material property are coupled.…”

“…However, it is noted in Figure 169 that duration remains approximately constant at the center (r/R = 0) with height. Note that since the area at the center represents a smaller area relative to the annular area at the wall, the contributions from the riser center are drowned out when integrated radially, hence the results in this work do not necessarily contradict previous work.As for the effect of operating conditions, similar profiles are observed at the same G s conditions for h/H ≥ 0.27 (i.e., Figure 169a Figure 169, different trends are indeed seen depending on riser position, operating conditions, and particle material.Pertaining to the impact of material properties on cluster duration (Figure 169), small glass consistently exhibits the highest duration towards the wall (r/R = 1), which agrees with previous work (Horio, Morishita et al 1988;Soong, Tuzla et al 1995; Wei, Yang et al 1995;Sharma, Tuzla et al 2000;Manyele, Parssinen et al 2002;Yang and Leu 2009); however, for the larger materials (large glass and large HDPE), the radial trend of increasing duration towards the wall is observed only at h/H ≤ 0.27. Moreover, interestingly, under low G s conditions (Figure 169a and c), large glass and large HDPE have very similar radial profiles, suggesting that particle size plays an influential role under such riser conditions.…”

“…To use the fiber-optic measurements to distinguish between dense and dilute conditions, a method known as wavelet decomposition (Mallat 1998;Ren and Li 1998;Yang and Leu 2009) is implemented here via the wavelet toolbox in Matlab (Misiti, Misiti et al 2002). More specifically, wavelet decomposition provides a means of representing different frequencies of the raw voltage signal by repeatedly breaking down the signal into higherfrequency details (D) and lower-frequency approximations (A), as illustrated in Figure 133.…”

“…Therefore, a critical drawback of a Fourier transform of such signals is that the time (dynamic) component is lost during analysis, and hence deficient when signal properties continuously change with time as in a fluidized bed system(Ren and Li 1998; Ellis, Bi et al 2004). In the past decade, wavelet decomposition(Mallat 1989; Mallat 1998) has been acknowledged to be useful in its ability to extract different frequency ranges while retaining the timestamp of signals, thereby enabling classification of fluidized-bed measurement data into noise (micro-scale), flow structures like clusters or bubbles (meso-scale), and equipment (macro-scale) (Ren and Li 1998;Ellis, Briens et al 2003;Zhao and Yang 2003;Yang and Leu 2009).More specifically, wavelet decomposition(Mallat 1989; Mallat 1998) provides a means of extracting different frequency ranges of data signals by repeatedly breaking down the signal into higher-frequency details (D) and lower-frequency approximations (A), as illustrated in Figure 133. At the first scale of decomposition (Scale 1), the signal of N Hz is divided into the first scale of approximation (A 1 ) and the first scale of detail (D 1 ), whereby A 1 contains the lower half of the frequency range and D 1 contains the higher half.…”