(478f) Identification of Various Transition Velocities in An Air-Polyethylene Fluidized Bed Based On Chaos Analysis of Computed Tomographic Scans
Fluidization is an efficient means of contacting gas and solids. The nonlinear dynamics of gas-solid fluidized beds has attracted much attention for understanding complex gas-solid flow behavior for the purpose of reliable modeling and design as well as optimum control of fluidized beds. Analysis of pressure fluctuation signals has provided evidence that gas-solids fluidized beds are deterministic chaotic systems (van den Bleek and Schouten, 1993). The successful flow regime identification in gas-solid fluidized beds is very important for improving their mixing, mass and heat transfers. The performance of fluidized beds is affected strongly by the prevailing flow regime. In this work the main three transition velocities were successfully identified on the basis of chaos analysis of Computed Tomography (CT) scans. The Kolmogorov entropies (KEs) were extracted from the raw photon counts measured by nine scintillation detectors and it was shown that the results are somewhat different and they are dependent on the position of the detector with respect to the center line on which the gamma-ray source (Cs-137) is located. The investigated fluidized bed was made of a Plexiglas column of outside diameter 0.46 m (ID 0.44 m) and of 1.77 m height. The gas distributor was made of porous polyethylene sheet with a pore size of 15-40 microns. The plenum was located at the bottom which consisted of a sparger tube. The CT scanner consisted of one radioactive source (Cs-137) on one side of the column and an array of scintillation detectors on the opposite side. The detectors were 0.051×0.051 m in diameter and length and were made of sodium iodide (NaI) crystals. The source and the detectors were located at a height of 0.37 m above the distributor. The bed aspect ratio was set equal to 2. Compressed air was used as a gas phase and low-density (755 kg/m3) polyethylene particles was the solid phase. Eleven different superficial gas velocities Ug were examined. They covered the range from 0.06 to 0.28 m/s, respectively. The CT scans were run at both ambient temperature and pressure. The KE values were estimated by applying the maximum-likelihood algorithm developed by Schouten et al. (1994). Each state vector consisted of 50 elements, the delay time was set equal to unity and a cut-off length equal to three times the average absolute deviation was used. The photon counts were recorded with a time step of 0.1 s. It was found that the KE results from the sixth detector (central one) were the most reliable since it was located practically opposite to the gamma-ray source. Three clear KE peaks were distinguished that correspond to three points of instability. Every local KE maximum indicates that a significant difference in the dynamic behavior of the gas-solid system takes place. The three KE peaks occur at Ug=0.086, 0.155 and 0.206 m/s, respectively. The first transition velocity corresponds to the minimum fluidization velocity. The second transition velocity delineates the boundary between two subregimes of bubbling fluidization: fast bubble subregime and slow bubble subregime (Trnka et al., 2000). Beyond Ug=0.206 m/s the turbulent fluidization is established. Exactly the same three transitional velocities were identified based on the KE peaks extracted from the readings of the eighth detector. The KE results from the fourth detector confirm also the existence of three points of instability (at Ug=0.086, 0.12 and 0.19 m/s). It is worth noting that the first point of instability coincides with the one identified from both the sixth and eighth detectors. The KE results based on the photon counts from the other scintillation detectors cannot detect all three peaks. In most cases only 2 peaks are clearly identifiable corresponding to the second and third transition velocities. Since the first three detectors are peripheral with respect to the position of the radioactive source, their KE results are not as reliable as the ones from the sixth detector which was centrally located. It was also found that the KE values monotonously decrease in the turbulent fluidization regime. The above-mentioned results were confirmed by the information entropies derived from the CT scans of all detectors. The profiles of average number of photon counts, average absolute deviation and average cycle time were also used for verification of the transition velocities. In summary, by means of the KE algorithm applied to CT scans performed by several centrally located detectors three different transitional velocities were identified successfully which determine the boundaries of the main fluidization regimes. A chaos analysis of such radioactive data has not been performed in the field of gas-solids fluidized beds yet.
Schouten, J. C., F. Takens, C. M. Van den Bleek, Physical Review E 1994, 49, 126.
Trnka, O., V. Vesely, M. Hartman, Z. Beran, AIChE J. 2000, 46, 509.
Van den Bleek, C. M., J. C. Schouten, Chem. Eng. J. 1993, 53, 75.
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