Wide band energy analysis of fluidized bed pressure fluctuation signals using a frequency division method

Abstract

Abstract:A statistical method based on approximation of the cumulative energy distribution by Student's t-distribution is proposed for the unbiased frequency domain division. The proposed method fixes the number of samples needed to estimate the power spectrum and its corresponding cumulative energy distribution using the Kolmogorov-Smirnov test. The reliability of the method to divide the frequency domain was shown for different fluidization velocities by changing the bed aspect ratio and using different pressure probes. Water-induced defluidization tests were conducted to illustrate the use of wide band energy as a monitoring tool. The Student's t-distribution results are compared with an analysis performed using the traditional visual inspection method. The energy of the power spectrum contained within the frequency regions obtained by the visual method is not able to detect changes in the bed aspect ratio or the start of the rotating distributor. No meaningful differences could be observed in the frequency regions using different quality pressure sensors because the approach using Student's t-distribution focuses on the sharp energy increase produced by the primary frequencies of the power spectrum. The sensitivity exhibited by the proposed frequency division approach for the range of fluidization conditions tested improves the use of the energy contained in these regions as a diagnostic tool in fluidized bed processes.

Characterization of pressure fluctuations from a gas–solid fluidized bed by structure density function analysis

“…Small-scale structures, represented by Region II on the amplitude division and corresponding to the domain frequency region on power spectra (Johnsson, et al, 2000), represented over half of the total cumulative energy. This observation is consistent with results reported derived from frequency division (Gómez-Hernandez et al, 2014).…”

“…Typically, the energy contained by macro-structures related to dynamics of "bubble flow" contain about 70-85% of the total energy of pressure signals for gas-solid fluidized beds (Johnsson, et al, 2000;Gómez-Hernandez et al, 2014), while that contributed by Region I is generally less than 25% of the total energy (Gómez-Hernandez et al, 2014). In our case, disturbances related to large bubbles and small bubbles/particle clusters contained about 74% -85% of energy of all disturbances in pressure fluctuations, as shown in Fig.…”

“…Since pressure signals from pressure transducers are usually complex and unsteady, they need to be characterized. Methodologies to describe the structure of fluctuations quantitatively or qualitatively have been proposed to study the hydrodynamics of fluidized beds (Zhao et al, 2003;Gómez-Hernandez et al, 2014). Here, we present a method, denoted "structure density function," to characterize the dynamics of multi-scale structures in the flow.…”

Flow pattern map and multi-scale entropy analysis in 3 × 3 rod bundle channel

“…Among they (Chen et al, 2014;Gómez-Hernández et al, 2014;Guilizzoni, 2013;Li et al, 2014;Shaban and Tavoularis, 2014;Zhang et al, 2014). Lee et al (2008) adopted chaotic characteristics of two-phase flow to identify flow pattern and developed a method to identify flow pattern by applying simple classification rules to the density map.…”

Application of Scaling-Law and CFD Modeling to Hydrodynamics of Circulating Biomass Fluidized Bed Gasifier

“…According to Di Felice et al [11], dimensionless pressure properties (signal amplitude and frequency) can be used as a powerful means to compare behavior of different fluidized systems. That is, two systems hydrodynamics are equivalent if the statistical properties of their counterpart pressure signals are similar; such properties as mean, standard deviation, probability density function and power spectral density (PSD) function [19][20][21]. Although the mean and variance of pressure-time series are simpler to be evaluated and compared, additional methods are to be implemented to confirm these mean-based conclusions.…”