Behavior of particles in a liquid‐solids fluidized bed

Abstract

The mechanics of particle motion in a fluidized bed were studied by focusing on the microscopic behavior of the particles. The local displacements of nylon particles fluidized by liquid were measured by the microcapacitance method, and the resultant time series was analyzed by determining its auto-correlation function and the corresponding power spectrum. This has given rise to a stochastic or statistical model of particle displacements in the fluidized bed. This model visualizes the particle motion in a fluidized bed to consist of the random movement, generating irregular signals, and the linear movement, generating wave-like signals. Recently, Yutani and Ototake (1980) analyzed the motion of particles in a liquidsolids fluidized bed by a statistical method. To enhance the theoretical basis of their approach, additional microscopic measurements need to be made, and a mechanistic model for the particle motion needs to be developed. N. YUTANIIn this study, local displacements of nylon particles fluidized by a fluidizing medium were measured by the micro-capacitance method. The resultant time series were analyzed by determining their autocorrelation function and power spectrum. An autocorrelation function gives rise to the variance of particle displacements and the relaxation time of particle movement in the field; it can provide useful information for estimating the local particle diffusivity which is of practical importance in understanding mechanism and in determining the mass or heat transfer between the fluid and particles in a fluidized bed. The power spectrum yields information related to the local velocity distribution of particles. CONCLUSIONS AND SIGNIFICANCEA new technique, which utilizes a micro-capacitance probe, has been developed to measure local fluctuations of particle motion in a liquid-solids fluidized bed. The results indicate that the recorded signals are composed of a sine wave component and a stochastic component. A model has been proposed by taking these two components into account, and the auto-correlation function of the model has been fitted to experimental data by adjusting the frequency of the sine wave, fo, and the intensity of transition of particles, A. In addition, fo/A has been found to be independent of the void fraction of the fluidized bed, c, but dependent on the viscosity of the fluidizing medium, p. The power spectral density function derived from the model has been compared with that from the data. Although a liquid-solids fluidized bed is used in this study, there is no reason to suspect that the methodology developed here can not be applied to a gas-solids fluidized bed. In fact, it is easier to use the microcapacitance probe in the latter than in the former because the probe need not be insulated in the gas-solids bed. THEORETICAL Mechanism of Particle MotionExperimental observations (e.g., Houghton, 1966;Carlos and Richardson, 1968) of the behavior of particles in liquid-solids fluidized beds have revealed that flow of the fluidizing medium induces not only convective fl...

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

“…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).…”

“…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.…”

Stochastic analysis of a three‐phase fluidized bed: Fractal approach

“…The resultant autocorrelation and power spectral density functions were then used to determine the frequency of the fluctuations. Among the stochastic models, one of the most notable has been the model proposed by Yutani et al (1983). Both Yutani et al (1983) and more recently Neogi et al (1988) have considered that any of the pressure fluctuation signals from fluidized beds consists of two components, a periodic component, and a random component; the latter is modeled as a continuous-time Markov process.…”

“…Our exhaustive review of the available data and the results of our experiments have indicated that the time series of pressure fluctuation signals from a fluidized bed exhibits long-term correlation similar to that observed in many hydrological time series. So far the Markov processes, including the Brownian motion, have played dominant roles in modeling the pressure fluctuations in fluidized beds (see, e.g., Yutani et al, 1983;Neogi et a!., 1988). Nevertheless, they tend to underestimate long-term trends such as the range of "cumulative departure" from the mean as suggested by Hurst (1956).…”

Pressure fluctuations and particle dispersion in liquid fluidized beds

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The performance of a liquid-solid fluidized bed is substantially influenced by various mutually interacting factors, such as flow regime, motion of fluidized particles, and voidage distribution; this gives rise to highly complicated, nonlinear and/or stochastic behavior of the bed. While some attempts had been made to stochastically analyze and model such behavior, they were based mostly on the Markovian assumptions and notion of classical Brownian motion (Yutani et al, 1983;Yutani and Fan, 1985;Fan et al, 1995).Recent works on multiphase flow systems demonstrated that some of the phenomena taking place in liquid-solid fluidized beds are amenable to the analysis couched in the parlance of the fractional Brownian motion (Bm) characterized by the Hurst exponent H or equivalently the local fractal dimension d,, (Feder, 1988;Fan et al, 1990bFan et al, , 1993. The model based on this concept was proposed originally by Mandelbrot and van Ness (1968) to identify the long-term correlation in a self-affine time series.

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