Wavelet transform analysis of pressure fluctuation signals in a three-phase fluidized bed
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Wavelet Transform Analysis of Pressure Fluctuation Signals in a Three-Phase Fluidized Bed Soung Hee Park * and Sang Done Kim* Department of Chemical Engineering, Woosuk Univ., Chonbuk 565-701, Korea *Department of Chemical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea (Received I0 April 200I 9 accepted 23 July 200I)
Abstract-The wavelet traitsfonn based Oll localized wavelet functions is applicable to analysis of pressure fluctuation
sigllalS from different flow regimes of a tlu-ee-pliase fluidized beck wkich usually is nonlinear or nonstationary. The pressure fluctuation has been analyzed by resorting to the discrete wavelet transform such as wavelet coefficients, wavelet energy, mKl trine-scale plane. The dominant scale of wavelet coefficients mKl the highest wavelet energy in the bubble-disintegrating regime are finer than ones in the bubble-coalescence regime. The cells COlresponding to fine scale of time-scale plane in bubble-disintegrating regime are more shaded and energetic, while the cells corresponding to coarse scale in bubble-coalescence regime are more energetic. Therefore, the wavelet transform enables us to obtain the frequency content of objects in a ttu-ee-pliase fluidized bed locally in time. Key words: Wavelet Transferal, Fourier Traltsfom~ Tlu-ee-Pliase Fluidized Beck t~-essure Fluctuation, Flow Regime
INTRODUCTION Three-phase fluidized beds have been adopted widely for various chemical, pharmaceutical and biochemical systems as reactors, contactors and separation units since they exhibit high heat and mass Wansfer rates due to efficient contact between the phases during contmuous operation [Fan, 1989; Kang et al., 1999]. Since the heat and mass Wansfer as well as hydredynamic properties such as phase holdup and bed porosity, bubble prcrperties, and mixing characteristics show very different characterisScs as the flow regime changes, many archers have studied the flow regime transition in three-phase fluidized beds. The identification of flow regime is a fundamental basis of fluid dynamic analysis for reactor m(xleling. However, the lack of more complete knowledge of the three-phase fluidized bed fluid dynamic behavior muses several operational difficulties and design uncertainties. Therefore, several investigators [Hart 1990; Han and Kim, 1993; Kwon et al., 1994] have examined the bubble properties and its flow behavior by analysis of pressure fluctuations obtained from the three-phase fluidized bed. The characteristics of the pressure fluctuations have been studied by several analysis meth(x,ls such as statistical analysis, Fourier Wansfoml and deterministic chaos analysis based on fractional Brownian motion [tNrk, 1989; Kwon et al., 1994; Kim and Han, 1999; Lee et al., 2(x)l]. The Fourier transform and its inverse establish a one-to-one relation between the time domain and the frequency domain, which is a classical analysis tool widely used This transform uses sine and cosine as its bases to map a time domain function into frequency domain. Thus, t
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