Chaotic behavior of fluidized beds based on pressure and voidage fluctuations

Abstract

Absolute and differential fluctuations and local voidage fluctuations are commonly used in characterizing gas-fluidized beds. Pressure fluctuations can result from several different causes including bubble formation and eruption, selfexcited oscillations of fluidized particles, pressure oscillations in the plenum chamber due to piston-like motion of the bed, bubble coalescence, and bubble splitting (Bi et al., 1995). Pressure waves from these sources can be propagated through the emulsion phase, although the amplitudes of the signals are attenuated during their propagation (Bi et al., 1995). Therefore, an absolute pressure probe records phenomena on a macroscopic scale from other locations in addition to local variations. Differential pressure measurements can, to a limited extent, filter out pressure waves originating outside the interval between the two ports connected to the differential pressure transducer, that is, measurements are on a meso-scale. Voidage probes reflect local (that is, microscale) voidage variations caused by bubble passage and the particle movement of the emulsion phase. The amplitude of local voidage fluctuations is independent of bubble size, unlike pressure fluctuations whose amplitude increases with bubble size. Previous studies (Bi et al., 1995;Bi and Grace, 1995) have shown that statistical characteristics (such as standard deviation, skewness, dominant frequency, probability distribution) calculated from these three types of signals differ significantly from one another.In recent years, the application of deterministic chaos theory to fluidized beds has been pioneered by several research groups (such as Daw and Halow, 1991;van den Bleek and Schouten, 1993;Skrzycke et al., 1993;Halow and Daw, 1994;van der Stappen et al., 1995). Analysis of pressure fluctuation signals (such as the phase-space portrait, Lyapunov exponent, correlation dimension, and Kolmogorov entropy) has provided evidence that gas-solids fluidized beds are deterministic chaotic systems. The correlation dimension of the time series has been calculated based on time series from absolute (van der Stappen et al., 1993) ExperimentsThe experiments were carried out in a 102-mm-dia. column described previously (Bi and Grace, 1995). Both FCC particles of zp = 60 pm, pp = 1,580 kg/m3 and sand particles of Lip = 214 pm, pp = 2,640 kg/m3 were used in the tests with the static bed height maintained at 0.6 m for all tests. (ap is the mean particle diameter and pp is the particle density.) Three gas velocities were used, corresponding to different flow regimes. Pressure fluctuations were measured from ports on the wall of the column using Omega PX162 pressure transducers. A low-pass filter eliminates signals with frequencies above 20 Hz. Absolute pressure fluctuations and local voidages were measured 0.28 m above the distributor, while differential pressure fluctuations were measured across an interval from 0.20 to 0.41 m above the distributor. The optical probe (see Zhou et al., 1994 for details) was located with its 1.5 mm tip ...

Two-Phase Bubble Columns: A Comprehensive Review

“…These methods are based on the analysis of ε G data. Other flow regime identification methods are the fractal [319], wavelet [320,321], Hurst's [322,323], spectral and nonlinear chaos [93,320,[324][325][326][327][328][329][330][331][332][333] and Kolmogorov entropy [332][333][334] approaches. Some authors have used methods based on the Shannon entropy, which measures the degree of indeterminacy in a system [335,336].…”

A critical review of the complex pressure fluctuation phenomenon in gas–solids fluidized beds

“…Advanced statistical analysis tools such as chaotic and wavelet analyses have also been applied to the pressure fluctuation signals to improve the understanding of their complexity. It was shown (Bai et al, 1997;Zhao and Yang, 2003) that two correlation dimensions could be identified in both absolute and differential pressure signals, with the higher dimension being speculated as originating from the small-scale signals associated with particle movement and the lower dimension from large-scale signals associated with bubble motion. The existence of pressure waves and bed oscillations will definitely further complicate the interpretation of those correlation dimensions.…”

Evaluation of flow regimes in a semi‐cylindrical spouted bed through statistical, mutual information, spectral and Hurst's analysis

“…Different analytical methods, including statistical or correlation methods, powerspectral density, deterministic chaos, and the Wigner distribution have been used (e.g. Fan et al, 1990;Kage et al, 1991;Bai et al, 1997;He et al, 1997;Briens et al, 1997a,b;Ohara et al, 1999;Briens and Briens, 2002;Chaplin et al, 2004Chaplin et al, , 2005. However, the application of these methods in spouted beds is scarce, with only a few attempts reported in the literature (Wang et al, 2001;Freitas et al, 2004;Xu et al, 2004a,b,c;Piskova and Morl, 2007).…”