Fractal analysis of fluidized particle behavior in liquid‐solid fluidized beds

Abstract

Liquid-solid fluidized beds have been adopted widely for catalytic liquid-phase reactions, separation and recovery of materials with ion exchange resin, adsorption, sedimentation, and wastewater treatment. Their unique features are the effective liquid-solid contact and the high rates of heat and mass transfer (Morooka et al., 1980;Muroyama et al., 1986;Kang and Kim, 1987). Nevertheless, the performance of a liquidsolid fluidized bed as a contactor or reactor is influenced appreciably by various factors, such as the flow regime (Volpicelli et al., 1966;Kang and Kim, 1988), the motion of fluidized particles (Handley et al., 1966;Kmiec, 1978;Yutani et al., 1983), and voidage distribution (Fan et al., 1985); this gives rise to highly complicated, nonlinear and stochastic behavior of the bed. While some attempts had been made to stochastically analyze and model such behavior, they were mostly based on the Markovian assumptions and notion of classical Brownian motion (Yutani et al., 1982(Yutani et al., , 1983Yutani and Fan, 1985;Fan et al., 1990a;Kang et al., 1990).Our recent works on multiphase flow systems (Fan et al., 1989(Fan et al., , 1990b have indicated that the concept of fractional Brownian motion (fBm), which can be characterized by the Hunt exponent, H , may be applicable to the analysis of liquidsolid fluidized beds. The model based on this concept has been proposed by Mandelbrot and van Ness (1968) to identify the long-term correlation in a time series, which is self-affine. It has been postulated that the rescaled range (R/S) analysis can be a means of estimating H for a given time series (Mandelbrot and Wallis, 1969a,b;Feder, 1988).In this work, pressure fluctuations in a liquid-solid fluidized bed have been examined by resorting to the R/S analysis; the effects of fluidized particle size, axial position, and liquid flow rate on the Hurst exponent, H, or the local fractal dimension, dpL, have been examined. The results have revealed that the pressure fluctuations in the bed, exhibiting long-term corre- Pressure taps were installed on the wall of the column at six different heights from the distributor. Each pressure tap was connected to one of the two input channels of a differential pressure transducer (Enterprise Model CJ3D), which produced an output voltage proportional to the pressure difference between the two channels. The remaining channel was exposed to the atmosphere.Signals were processed by an oscilloscope, a personal computer (Zenith 386), and a mainframe computer (IBM 3084). The voltage-time signal, corresponding to the pressure-time signal, from the transducer was fed to the recorder at the selected sampling rate of 0.005 s. A typical sample comprised 4,000 points. This combination of the sampling rate and sample length ensured that the full spectrum of hydrodynamic signals were captured from the liquid-solid fluidized bed; the signals were processed off-line. Results and DiscussionThe experimental results indicated that, in general, the amplitude of pressure fluctuations in the liquid-s...

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].…”

Application of Chaos Analysis for the Investigation of Turbulence in Heterogeneous Bubble Columns

“…All of these studies demonstrated that the methodology of time-series analysis based on chaos theory can provide us with important insights into the complex hydrodynamics of gas-liquid BCs. In addition, different methods such as statistical analysis [24][25][26], power spectrum analysis [27], fractal analysis [28] and wavelet analysis [29,30] have been proposed to successfully describe the dynamic behavior of two-phase flow. None of these previous studies has been focused on the application of the nonlinear chaos analysis to local gas holdup fluctuations for the identification of zones of increased turbulence in the BC.…”

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid-Liquid-Solid Fluidized Beds

“…That is, the lower value of K means the higher probability to anticipate the stable heat transport phenomena. If the temperature fluctuation signals were to be composed of two components, periodic and stochastic components, the periodic component would be more predictable than the stochastic one at the condition of relative low value of K [7,14]. Thus, it is reasonable that the heat transfer phenomena in liquid-liquid-solid fluidized beds are more stable, regular and periodic at the intermediate continuous liquid velocity, where K and Dh i attain their minima.…”

“…In other words, the flow regime of solid particles changes from circulation to turbulent random motion at this intermediate U c or bed porosity condition. It has already been reported that the particle flow behavior is most regular and periodic at intermediate U c or bed porosity in liquid-solid and gas-liquid-solid fluidized beds [3,7,16,17].…”