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Fluidised bed dynamics diagnosis from measurements of low-frequency out-bed passive acoustic emissions
Powder Technology 162 (2006) 145 – 156 www.elsevier.com/locate/powtec
Fluidised bed dynamics diagnosis from measurements of low-frequency out-bed passive acoustic emissions Javier Villa Briongos, Jose´ M. Arago´n *, Marı´a C. Palancar University Complutense of Madrid, Department of Chemical Engineering, Faculty of Chemistry, Av. Complutense s/n, 28040 Madrid, Spain Received 24 January 2005; received in revised form 28 September 2005 Available online 3 February 2006
Abstract The purpose of this research is to show that measurements of low frequency out-bed passive acoustic emissions are useful for monitoring gas – solid fluidised bed hydrodynamics. A methodology is proposed to develop portable measurement systems (PMS) feasible for both laboratory scale optimisations and, later, for process diagnosis within industrial facilities. The methodology includes a multirate technique where the first sampling frequency used was about 11 kHz that was successfully later reduced to 500 Hz, which is far from the most common used for sampling ultrasonic ranges. The acoustic frequency range of interest (0 – 200 Hz) allows the use of a commercial jukebox and two low cost condenser microphones to record the out-bed acoustic emissions. The underlying bed dynamic process was studied by monitoring both acoustic and pressure fluctuation signals and by applying time, frequency and state space analysis over the measured time series. The crude acoustic signals exhibit marked random behaviour due to a high content of background noise. This is detected by the mutual information function. The power spectral density of the acoustic time series shows high complexity and claims for reducing the acoustic frequency range to be evaluated (initially 0 – 5.5 kHz). To decide an optimal frequency range and, consequently, a better sampling frequency, the acoustic pressure was estimated from a numerical simulation based on the well-known particle array model. From the results of the simulations, and in agreement to the literature, it is concluded that the bed dynamic acoustic information mainly lies within the range 0 – 200 Hz. According to that, the signals were subsequently re-sampled at a sampling frequency of 500 Hz. Finally, by comparing the pressure time series monitoring to the analysis of the mesoscale bed acoustic region (mainly due to bubbles, 0 – 20 Hz), it is concluded that from out-bed acoustic time series monitoring, only the state space analysis is able to fully characterize the slugging dynamics by means of a correlation dimension in the range 2.5 – 3.5 for the experimental conditions covered. D 2005 Elsevier B.V. All rights reserved. Keywords: Fluidised bed hydrodynamics; Passive acoustic emission; Monitoring; Dynamic diagnosis; Non-linear dynamics; Noisy time series analysis
1. Introduction Fluidised bed monitoring for resolving dynamical features is an issue of major importance in fluidisation engineering and several measurement techniques based on pressure fluctuations and acoustic emissions in fluidised beds have been proposed. Although the commercial and research applications are diverse, it is required new non-intrusive monitoring systems suitable for characterizing the bed dynamics in processes performed, for example, under severe, corrosive and high pressure/temperature conditions.
* Corresponding author. Tel./fax: +34 913944173. E-mail address: [email protected] (J.M. Arago´n). 0032-5910/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2005.12.009
The measurement of the passive acoustic emission that is created by the fluidising process itself has become a promising monitoring tool, thanks to the development of modern digital instrumentation and cheaper but more and more powerful computers. Diverse techniques based on the acoustic emission have been successfully applied for dynamics diagnosis [1] as well as for monitoring the performance of several operations and processes in gas – solid fluidised beds [2,3]. These techniques do not require direct contact between the bed and the measurement probes. Therefore, they have the clear advantage of providing a non-intrusive source of information about the phenomenon being monitored. In order to characterize the bed dynamics the hypothesis of Finney et al. has been assumed [1], i.e. that the bed acoustic signal contains information from two types of collisions,
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particle –particle and particle – wall, as well as of the motion of the bubbles and the global fluidised bed. According to Boyd and Marley [2], the sound generated from the microscale and macroscale bed phenomena will take place up to 200 Hz. This fact disagrees with most previous literature on this subject, in which the measurement is focused to higher frequencies, within the ultrasonic range ( f > 20 kHz) and up to several hundreds of kHz [4 –6] in order to avoid noise from the background and secondary mechanical vibrations. It is the aim of this research to improve the current techniques to reduce the sampling frequency that is necessary to have a reliable bed dynamics monitoring in order to develop a portable on-line measurement system (PMS) that can be used for both laboratory-scale process optimisation and later process diagnosis within industrial facilities. Working at lower sampling frequencies avoids digital processing of large time series and spans the number of data processing techniques that can be applied over the signal. Within the research project this paper focuses on the establishment of the out-bed passive acoustic monitoring methodology from noisy time series. With this purpose, both passive acoustic emissions and pressure bed fluctuation measurements are used to understand how the recorded signals are related to the overall bed dynamics and, therefore, to show the extent the out-bed passive acoustic measurement collected within a moderate noisy environment of 73 db, with local maxima up to 79 db, can be used to monitor fluidised bed dynamics. Time, frequency and state space analysis have been applied over the measured acoustic and pressure time series in order to find useful information from the crude experimental data and to characterize the bed dynamics.
2. Experimental Acoustic and pressure time series were recorded from a fluidised bed confined in a 5 cm ID glass vessel with a perforated plate distributor (Fig. 1). The distributor/bed pressure drop ratio, DP d/DP b, was around 0.6 at minimum fluidisation velocity to provide [7] a uniform gas distribution throughout the bed. However, it was not enough to damp the fast downward travelling pressure fluctuation waves through the perforated plate [8,9]. Therefore, the possible resonance between pressure bed and plenum fluctuations must be taken into account before extending the results obtained with pressure sensors to other fluidised systems. The fluidised bed is of Ballotini glass beads, 320 < d p < 500 Am (Group 1) and 800 < d p < 1400 Am (Group 2) (Geldart B and D type, respectively). The bed height/diameter ratio is H/D = 2. The bed was fluidised with air at ambient conditions and relative superficial velocities, U r = U 0/U mf, ranging from 1.4 to 4.1 (Group 1) and from 1.1 to 1.9 (Group 2). Under these fluidisation conditions a slugging behaviour was promoted within the bed. 2.1. Acoustic measurement system The acoustic time series were collected by means of two out-bed unidirectional condenser microphones AUDIO TECHNICA PRO 42 with XLRM-type connectors. Each acoustic sensor (microphone) is fitted to a circular mounted surface that is inclined 60- above the horizontal axis to obtain the best recording quality performance. Those sensors have a frequency response up to 14 kHz, which suffices for the purpose of the
Fig. 1. Experimental set-up.
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research, and were located externally to the system, one just above the distributor and the other one 10 cm above, near the bed surface (Fig. 1). The outlet signal resulting from the microphones is amplified through a mixing console EURORACK\ MXB1002 and sent to a CREATIVE\ NOMAD JUKEBOX 3 where the data are finally digitised as ‘‘wav’’ files. To reduce the low-frequency influence of background noise and mechanical vibration, the microphones are placed within a silencer rectangular box, where the face in contact to the vessel is open to facilitate the out-bed passive acoustic measurement. During the runs, it was observed that, due to the small size of the vessel and the low bed mass (m b = 0.33 kg), the signals collected in both position were identical, so for those conditions the measurement system acts as non-intrusive global technique. Consequently, only the results from the acoustic time series measured at the top bed surface (h = 0.1 m) are presented through the rest of the paper. 2.2. Pressure fluctuation measurement Pressure fluctuations were measured by means of two AP32 KEYENCE pressure gauges. The signal was digitised through a PCI 6023E I/O board (NATIONAL INSTRUMENT Co.). As depicted in Fig. 1, the bed pressure fluctuations were recorded at two different positions: position 1 (above the distributor) and position 2 (10 cm from the distributor plate, bed surface). Some complementary runs were carried out by measuring simultaneously the fluctuations in position 2 and within the plenum to evaluate the degree of coherence between the bed and plenum pressure fluctuations. 2.3. Data acquisition protocol A multirate technique was applied where the passive acoustic emissions were collected initially with a sampling frequency, f s, of 11 025 Hz. A low-pass filter having a cut-off frequency of f c = f s/2 was applied over the signals to avoid further possible aliasing problems. The time series recorded were 3 min long (about 2 000 000 points); longer time series lead to many computer problems during the digital processing of the signal. The state space analysis was made with signals re-sampled at 500 Hz and low-pass filtered with a cut-off frequency of 20 Hz in order to study the mesoscale bed dynamic region, mainly due to bubbles. The pressure fluctuation signals were sampled at 200 Hz. The samples were taken for over 4 min. Thus, each resulting time series was 48 000 points long. In order to keep the overall bed dynamics information, the time series were filtered using a digital low pass filter Chebyshev type 1 with a cut-off frequency of f c = 20 Hz. Brown and Brue [10] have reported that the use of sampling times from 20 to 60 min is recommended to distinguish spectral features from pressure fluctuation signals. Nevertheless, it is worth to mention here that within this paper the spectral analysis is a complementary tool for signal analysis
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and that there are neither modelling nor scaling purposes. Therefore, the sampling time used here, much less than the values reported by these authors, suffices for a reliable estimation of the spectral features of the bed dynamics. 3. Result and discussion In order to asses the reliability of passive acoustic measurement to bed dynamic characterization within a working environment, the fluidisation conditions were carefully chosen to promote slugging regime. The slugging behaviour was monitored by measuring the pressure bed fluctuations. The pressure time series served to make dynamic diagnosis that was compared further to those obtained from the acoustic monitoring. 3.1. Modelling the bed acoustics Since measuring passive acoustic emission at a sampling frequency of 11 025 kHz by means of out-bed microphones is affected by many acoustic sources that take place within the range of bed dynamics frequencies, in order to extract the dynamic information stored within the acoustic signals, it seems that reducing the frequency range to be studied becomes critical. So, following the hypothesis of Finney et al. [1], it is assumed that the acoustic signal measured from a fluidised bed is originated by the particle – particle and particle – wall collisions as well as by the bubbles and global bed motion. According to that, the particle array model [11] has been used to estimate the acoustic pressure, P a, from the particle – particle and particle –wall collisions. The model has been solved according to the expressions given in [12]. The results from the model served to elucidate the frequency range within which the dynamic information is contained, as well as provide data of particle acoustic dynamics within the 0– 20 Hz region. The acoustic pressure was estimated, according to Patitsas [13] by the following expressions: Pa ¼ b
b¼
yn ua yt Dt `b ` bua ; yy yy Dy
q2 U2 qp dp2 02 : 3 DS
ð1Þ
It was assumed that the particle velocity defined in [13], u a = yn/yt, can be computed directly from the particle array model [11] since the small amplitude to which the particle oscillates in a compressible fluid will lead to acoustic waves [14]. Moreover, particle oscillations have already been related to sound waves in fluidised beds [15]. The three main variables in Eq. (1), Dt, Dy, and DS, are also computed from the particle array model. The values of U 0, d p and q p are known parameters. Finally, q 2 is a parameter that serves to compute the bulk modulus, b. It has been set, according to [13], at a value q 2 = 1 for the simulations made here. The PSD of a simulated time series is shown in Fig. 2. It can be
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and 80. Moreover, the bubble information carried on the lowest frequency range, see detail in Fig. 3, will be blurred through the time series by the higher frequency components of the signal that have larger energy content. So, the time series was again filtered, now with a digital Chebyshev type 1 low-pass filter with a cut-off frequency f c = 20 Hz, in order to study better the acoustic signal within the region of frequencies in the range 0– 20 Hz. 3.2. Influence of background noise Fig. 2. Power spectral density estimation from a simulated time series, U r = 1.3, d p = 1020 Am.
observed that most of the signal energy content is comprised in the frequency range 0 –200 Hz; this fact is in agreement to the literature [2]. Therefore, it was decided to study the acoustic signal within the region 0 – 250 Hz. Thus, the acoustic time series were re-sampled at f s = 500 Hz and lowpass filtered ( f c = f s/2 = 250 Hz). An example of the data analysis is shown in Fig. 3. It can be observed that, even with the filtering of the sampled data, the PSD of the acoustic time series is still difficult to interpret because it exhibits a great complexity with the clear presence of harmonics mainly due to a near gas compressor and the background noise from several sources. Through the paper, the well known Welch’s averaged periodogram method was used [16] to compute the PSD. It should be noted that the energy of the spectrum is dimensionless, since the time series were previously normalized to time series having a mean of zero and a standard deviation, r, of unity. This fact makes the ordinate of the power spectrum to be P xx/r 2, allowing reliable comparison to be made [17]. According to Brown and Brue [10], no less than 15 periodograms have been averaged to compute the PSD. Depending on the time series, the number of averaged periodograms, N, ranges between 40
The influence that background noises and mechanical vibrations have on characteristic frequencies can be fairly well monitored by the time-dependent Fourier transform. An example of how the 0 –250 Hz region is highly sensitive to the presence of background noise is shown in Fig. 4. As a result, both the subsequent time series and the corresponding data analysis will be influenced. The region of interest, 0 –20 Hz, is less influenced by those extra frequency components due to harmonics and background noises. Nevertheless, the possible influence of these components over the final results should be taken into account when interpreting the results. The mutual information function, I, is used to account for the influence of the background noise on the deterministic chaotic features exhibited by the acoustic signal (Fig. 5). As it is well known, the mutual information function is based on the uncertainty concept developed by Shanon and Weaver [18]. According to this theory, the uncertainty associated with any measure depends on the probability of all possible outcomes. The mutual information function is usually measured in bits to give quantitative information about time series predictability. In contrast to the Kolmogorov entropy, I does not take into account the time correlation existing in dynamics. Besides, it does not assume any functional relationship between the data to be analysed and, consequently, it is suitable to detect persistence within non-linear time series
Fig. 3. Power spectral density of an acoustic time series re-sampled at f s = 500 Hz with a low-pass filter of f c = 250 Hz. Detail of the low frequency region (0 – 20 Hz).
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Fig. 4. Time dependent Fourier transform for a run with group 1 particles, U r = 2.8; (a) influence over the acoustic signal of harmonics introduced by a near gas compressor existing in the facility, (b) effect of several noises generated from different sources, which can take place randomly within the working environment, on the measured acoustic signal.
[19]. By all these reasons, the mutual information function was used here to identify the dynamics under evaluation. When the mutual information function is computed from a signal sampled at 500 Hz without low-pass filtering at 20 Hz, it can be observed that the presence of harmonics, as those detected in Fig. 4a, introduces a strong artificial persistence within the signal. In contrast, once the signal is low-pass filtered at 20 Hz, it presents the chaotic features that are characteristic in fluidised beds (Fig. 5, curves b and c). Finally, the presence of a high content of background noise in the signal, even when this noise introduces a large number of harmonics (Fig. 4a,b), slightly reduces the value of I (Fig. 5, curves b and c). The persistence introduced by the harmonics (Fig. 5c) is so small that, as it will be shown later, the chaotic features exhibited by the fluidised bed will remain almost unaltered.
3.3. Visual description of the flow regimes As a result of the qualitative visual observation of the bed, five different slugging modes have been identified (Fig. 6). (1) Pseudo Slug-flow, PS-F: At this regime, several small slugs that rise through the bed and burst at the bed surface were observed. This Fsingle bubbling_ makes that the bubbles rise, erupt at the surface and project solids well dispersed into the freeboard. (2) Axial Slug-flow, AS-F: Axial stable slugs cross the bed leading to a plug-flow like global bed motion. At this slugging mode, the solid thrown away the bed, as a consequence of the bubble eruption, is not well dispersed into the freeboard.
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existing from previous bubble bursting provides a turbulent appearance to the bed surface. 4. Pressure fluctuations and passive acoustics emission diagnosis 4.1. Time domain analysis
Fig. 5. Mutual information function for: (a) non-filtered (raw) acoustic time series; (b) acoustic time series re-sampled at f s = 500 Hz with a low-pass filter of f c = 20 Hz without the presence of harmonics; (c) acoustic time series resampled at f s = 500 Hz with a low-pass filter of f c = 20 Hz with the presence of harmonics.
(3) Wall Slug-flow, WS-F: The observed rising slugs tend to adhere to the wall and slide-up the wall, the eruption of such bubbles give rise to a vigorous particle dispersion within the freeboard region near the bed surface. (4) Flat Slug-flow (square-nosed slugs), FS-F: The features of this regime are fairly well described in the literature [7,20]. So, the slugs grow up to block the bed section and, as a consequence, the bed is separated in slices. Under this regime, a plug-flow like global bed motion, similar as for the Axial Slug-Flow regime, was observed. (5) Churn-Turbulent Flow, T-F: Since this regime was only reached at its incipiently stage for both solid groups, it will be little referenced when interpreting the pressure and passive acoustic time series. This regime is characterised by a violent bursting promoted by large slugs, which lead to a strong agitation of the bed surface and to the throwing of larger quantities of solids that are well dispersed into the freeboard region. The mixing of those fresh solids from erupting slugs with the solid
Fig. 6. Pictures showing the five different slug-flow regimes observed during the runs.
4.1.1. Pressure time series The bed slugging dynamics can be characterized by estimating the cross correlation coefficient between the pressure signals collected from the two sensors placed at positions 1 and 2, respectively. The cross correlation coefficient has been used, as reported in [21], to distinguish between Axial and Pseudo Slug-Flow for the group 1 particle system. Thus, as it is shown in Fig. 7a, r for AS-F exhibits a significant peak, r å 0.4, that is due to the stable slugs that block effectively the bed section as they rise. In contrast (Fig. 7b), the slugs in the PS-F regime block the bed only momentarily and, hence, the correlation existing between the two signals from positions 1 and 2 is lower, r å 0.2, than for fully developed slugging regime. Therefore, it can be concluded from the correlation
Fig. 7. Cross-correlation analysis of pressure time series of group 1 particles. (a) Cross-correlation coefficient for axial-slug flow, U r = 2.8. (b) Cross-correlation coefficient for pseudo slug-flow, U r = 1.4.
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analysis that the B particles bed will operate at Axial and Pseudo Slug-Flow regimes within the fluidisation conditions covered. According to that analysis, the D particles bed will operate at fully developed slugging regime, r å 0.6, through the fluidisation conditions covered. The average absolute deviation, r d, has been used, instead the most common standard deviation of the signal, as a measure of the signal amplitude. According to [21], the measure of the absolute deviation is a better magnitude to express the ‘‘intensity’’ of the pressure fluctuation. As depicted in Fig. 8, r d increases for both B and D particle systems with gas velocity. However, it is not very sensitive to the different slugging modes that are taking place and, as it is described below, the state space analysis is preferred for the diagnosis of the bed dynamics.
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acoustic monitoring is because it gives a measure of the magnitude of a set of numbers as the root mean square does when applied for acoustic monitoring. The trend followed by r d is difficult to interpret in terms of physical phenomena and must be addressed taking into account the relative influence of each different acoustic source (e.g. particle –particle, particle – wall, bubbles and global bed motion) on the currently measured acoustic signal. These influences will be discussed below through the frequency domain analysis section. Finally, as the correlation analysis is highly influenced by the presence of harmonics and high frequency components in the measured signals, the useful bubble information that can be drawn by those tools is poor when they are applied over out-bed passive acoustic time series. 4.2. Frequency domain analysis
4.1.2. Passive acoustic time series Referring again to Fig. 8a,b, it can be observed that, as a difference to the pressure fluctuations time series, the average absolute deviation, r d, computed from passive acoustic emissions is apparently able to discern either between Pseudo and Axial slug-flow (group 1) or between Wall and Flat SlugFlow (group2). The reason why r d seems to be so useful for
Fig. 8. Average absolute deviation estimated from pressure and acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.
The spectral analysis of experimental time series has been widely applied to gas –solid fluidised bed time series [16,23] providing information about bed dynamics with several purposes such as monitoring [24] and dynamic scaling-up [25]. The frequency domain representation of the signal can be described by the estimation of its power spectral density, PSD, whose computation has been described previously. The joint spectral properties of signals measured simultaneously at different locations in the bed can be evaluated from 2 the coherence function, c xy ( f), which is calculated from the cross power spectral density. As it is well known, the coherence 2 function ranges from 0 to 1, where a value of c xy = 1 indicates that the PSD of the two compared time series are fully 2 correlated at that frequency. However, since c xy ( f) is a linear spectral tool, it cannot reveal non-linear correlation between two signals. 4.2.1. Pressure time series The estimation of the PSD provides a reliable representation of the characteristic bed dynamic frequencies. It is shown in the detail of Fig. 3 how, within the fluidisation condition covered, the slugging regime will be characterized by a main peak, f M, ranging between 2.3 and 3.1 Hz. Moreover, it was found that the energy peaks belonging to the group 2 particle system were larger than for the particle group 1, as a result of the different magnitude of the pressure fluctuation showed by those two particle groups used, which was found larger for group 2 (Fig. 8). The slugging frequency has been estimated from the autocorrelation function [26]. Although it slightly depends on the gas velocity, it takes a mean value f s = 2.7 Hz. This value matches fairly well the observed f M as shown in Fig. 3. The average cycle frequency has been used to monitor the f s trend as a function of the relative gas velocity. As expected (Fig. 9) f av decreases with the gas flow rate, since the coalescence effects reduce the number of bubbles bursting at the bed surface. However, the spurious crossing induced by high content of background noise due to the pressure sensor characteristics leads to an over-estimation of f s. Furthermore, the average cycle frequency estimated from pressure bed fluctuations has been later used as a measure of the Facoustic
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corresponding to bubbles dynamics can be drawn from the pressure time series (Fig. 9) the values of f av are near to 12 Hz when particle – particle and particle –wall collisions govern the acoustic dynamics (Pseudo, Wall and Fast Slug-Flows). Moreover, when the bed of B particles performs in Axial Slug-Flow, the values of f av from pressure and from acoustic time series match. Therefore, it is concluded that the acoustic signal is mainly due to the acoustic pressure generated by the bursting bubbles. In the D particles bed it seems that during the Flat Slug-Flow regime there is a compromise between the acoustic pressure generated by the particle – particle and particle – wall interactions and the bursting bubbles that give decrease of f av (Fig. 9b). Furthermore, the value of f av around 6 Hz is still far from the bubble frequency computed from the pressure time series, which is about 3 Hz. 4.3. State space analysis Methods of state space analysis deal with the reconstruction of attractors in an embedded phase space and the study of attractor properties, such as Kolmogorov entropy and correlation dimension. Several authors have studied and exploited the fluidised beds chaotic features [27 – 32] and have successfully applied the state space analysis to several fields of fluidisation engineering such as modelling [33], control [34] and scaling-up [35]. Fig. 9. Average cycle frequency estimated from pressure and acoustic time series for both particles groups vs. U r. The f av from the model has been computed after applied a low-pas filter of f c = 20 Hz over the simulated time series. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.; mod: Simulated passive acoustic time series.
pressure_ due to bubbles when interpreting the results drawn from acoustic time series. 4.2.2. Passive acoustics time series As for the pressure time series, the average cycle frequency has been computed from several passive acoustic time series (Fig. 9). Here, as for the average absolute deviation, the trend followed by this quantity is difficult to interpret. It can be concluded from the data in Fig. 9 that it is possible to use f av for monitoring purposes. The average cycle frequency takes values ranging from 6 to 8 Hz for fully developed slugging regime and for both particle groups. It shows a local maximum at the transitions between Wall and Flat Slug-Flow for the particle group 2 (Fig. 9b) and between Pseudo and Axial Slug-Flow for the particle group 1. Nevertheless, as it will be seen later, the state space analysis is preferred for dynamics diagnosis. To explain the behaviour of f av for acoustic time series, the results from the modified particle array model have been plotted on Fig. 9b. According to that, the average cycle frequency related to the acoustic pressure generated from the particle –particle and particle – wall collisions within the frequency region from 0 to 20 Hz, takes values ranging from 13.3 to 15.5 Hz. Therefore, assuming that the frequency
4.4. Correlation dimension This attractor property is obtained from the spatial correlation between random points on the reconstructed attractor. Several methods have been described for computing the correlation integral [36,37]. Nevertheless, these methods are all based on the algorithm of Grassberger and Procaccia [38]. Here the use of that algorithm is followed by application of an embedding dimension equal to 10, chosen by a previous false neighbour analysis [39]. A time delay of 1 was used during the reconstruction of the attractor and the interpoint distances were computed by using the maximum norm [40]. 4.5. Kolmogorov entropy The Kolmogorov entropy, K, is a direct measure of the chaos level and provides qualitative and quantitative information on the underlying dynamics of a system by measuring the average ‘‘surprise’’ one experiences by making a new measurement in spite of available knowledge of the system past history [41]. Moreover, the Kolmogorov entropy takes into account the time correlation in the dynamics and considers the effects that several past measurements have on the current measure. Kolmogorov entropy is usually expressed in units of bits/s, reflecting the rate of information loss by the system (unpredictability). Thus, when dealing with periodic, fully deterministic data, the Kolmogorov entropy equals zero, whereas for random time series the entropy is infinite. Finally, deterministic chaotic processes occurring between both these situations have positive Kolmogorov entropy.
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Fig. 10. Correlation dimension, D 2, estimated from pressure and acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.
There are several methods for estimating the Kolmogorov entropy from experimental time series [41,42]. The algorithm used here is based on the maximum likelihood method [43] and, it uses the averaged absolute deviation as cut-off length and maximum norm to compute interpoint distances. Moreover, as for the correlation dimension, an embedding dimension of 10 and a time delay of 1 have been used during the reconstruction of the attractor for computing K. 4.5.1. Pressure time series The correlation dimension (Fig. 10) has been used for monitoring the fluidised bed hydrodynamics. It has been found during the data processing that the pressure sensor placed at the bottom (position 1) is more sensitive to bubble dynamics, since it is less influenced by the bed surface and the global bed motion. It can be seen in Fig. 10 how the first maximum of the sensor located near to the distributor plate indicates the transition either from Pseudo to Axial Slug-Flow regime for particle group 1 and, from Wall to Flat Slug-Flow for group 2. In contrast, the correlation dimension estimated from the sensor placed at 10 cm over the distributor plate (position 2) is not sensitive to the change of the slugging condition from Pseudo
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to Axial Slug-Flow for the group 1 and shows a delay detecting the transition from Wall to Flat Slug-Flow when monitoring particle group 2. Additionally, it is plotted in the same figure the correlation dimension computed from acoustic time series monitoring, which is rather preferable to monitor the existing slugging flow regime as well as the different transitions that are taking place, as it will be discussed later. To conclude with the correlation dimension analysis, D 2 takes values mostly ranging between 3.5 and 4. According to the literature [22], this would indicate a hydrodynamic regime near to bubbling. However, due to the used particle size, vessel and bed aspect ratio, a value next to 3 or less, corresponding to slugging regime, was expected instead. The deviation from the expected value of 3 is mainly attributed either to the background noise or to the fact that the distributor to bed pressure drop ratio was relatively low, therefore resonance between the plenum and bed pressure fluctuations [8] could take place. Consequently, the measured signal will be influenced by resonance and, under these circumstances, it is not suitable to extend the quantitative results obtained from pressure fluctuations measurements to others systems. The coherence function (Fig. 11) serves to quantify the relation between bed and plenum pressure fluctuations. It can be observed how the bed and plenum pressure fluctuations are highly correlated as expected from the low DP d/DP b ratio. The Kolmogorov entropy is used as a complementary tool for bed dynamics diagnosis (Fig. 12). As for the correlation dimension, the magnitude computed from the signal recorded at the bottom is the most sensitive to bubble dynamics. In this case, the transition between regimes is indicated by a local maximum. Thus, for the particle group 1, the entropy computed from position 1 decreases as the bed performance gets the fully slugging regime, so the axial slugs dominate bubble dynamics and the entropy decreases as increases the slug size (the signal becomes more Fperiodic_). In contrast, the entropy computed from the signal collected near to the surface is more influenced by the global bed motion (plug-flow like), it does not show any local maximum and smoothly decreases up to a limit indicating that the bed has reached the fully slugging regime condition. The particle group 2 (Fig. 12b) behaves different due to the different fluidisation quality promoted by D particles. This fact is fairly well detected by the Kolmogorov entropy, as for the
Fig. 11. Coherence function between a pressure probe placed within the plenum and the probe located at position 2 for group 2 particles, U r = 1.6.
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Fig. 12. Kolmogorov entropy, K [bits/s], estimated from pressure time series and K c [bits/cycle] computed from acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. K PCh1: Pressure fluctuations in position 1; K PCh2: Pressure fluctuations in position 2; K p A: Passive acoustic monitoring.
case of group 1, the sensor place at position 1 is more sensitive to bubble dynamics. It is shown in Fig. 12b how the transition from both Wall to Flat and from Flat to Fast Slug-Flow are detected by a local maximum of the Kolmogorov entropy. Finally it must be pointed out that for comparison between Fig. 12a and b, it can be observed how the Kolmogorov entropy computed from group 1 is larger than for group 2 according to the expected effect that particle size has on signal persistence [32]. 4.5.2. Passive acoustics time series Neither frequency nor time domain analysis have been able to fully characterize the bed dynamics from acoustic time series collected by means of out-bed microphones. Concretely, the slugging characteristics of the flow have not been yet detected by any of those analyses. The noise included in the signal makes traditional tools like cross and autocorrelation analysis unable to characterize the bubble dynamics. However, as Fig. 5b shows, in contrast to the original acoustic signal (Fig. 5a), after filtering at 20 Hz, the time series now exhibit chaotic features. This fact can be used to characterize the time series through state space analysis. The estimation of the correlation dimension can be used to identify the slugging regime existing within the bed for full dynamic diagnosis purposes. A plot of D 2 of the acoustic time
series versus the relative gas velocity, U r = U 0/U mf, is shown in Fig. 10. It can be observed how the correlation dimension takes values raging within 2.5 < D 2 < 3.5 for both solid groups. According to [22] those values are characteristics of slugging regime. Therefore, now the hydrodynamic regime has been fully identified from acoustic time series analysis. Moreover, the transition between the different slugging modes, identified previously by means of pressure time series monitoring, is fairly well indicated by the correlation dimension. Thus, the transition between different slugging states is preceded by a minimum of D 2. Since the out-bed acoustic monitoring acts like a global measurement technique for the fluidised bed systems under study, the observed behaviour of D 2 is in agreement to the results shown by Villa-Briongos and Guardiola [32]. Those authors, working with a non-intrusive global technique to measure the bed surface fluctuations [23], have found that the correlation dimension takes a minimum before taking place the transition between different bubbling regimes. Accordingly, it is assumed that the presence of large bubbles before taking place the transition explains the minimum of D 2. Ending with the correlation dimension analysis, it must be pointed out that when working at the worst noise conditions, the effects on D 2 are less than 5% of the final value of D 2. It is important to mention too that using IIR filters over the time series affects the estimation of invariant measures such as D 2 [44]. In fact, the Chebyshev type 1 IIR filter used here to treat the data processing affects less than 3% to D 2 when comparing to the value of D 2 estimated when filtering with a FIR filter. Therefore, since IIR filters provide better spectral features to the time series, they have been preferred here to filter the actual data. As for the pressure time series analysis, the Kolmogorov entropy is used to complementarily monitor the dynamics. Although the presence of noise is the main factor affecting the length scales below the cut-off length, it has been found that, in contrast to D 2, the Kolmogorov entropy value is affected up to 15% at the worst noise conditions, when it is expressed in bits/s, but it is affected less than 10% when it is expressed in bits/cycle. Moreover, Vander Stappen et al. [22,45] showed the usefulness of entropy per cycle for monitoring bed dynamics when the system operates at different conditions within a similar hydrodynamic regime. Therefore, the use of Kolmogorov entropy in bits/cycle has been preferred to dynamic diagnosis from the passive acoustic time series under evaluation. Furthermore, the values of K c obtained (Fig. 12) are easily compared to those reported in the literature. So, for both particle groups, the entropy per average cycle is ranging between 2.8 to 4 bits/cycle for fully developed slugging regime, where the acoustic dynamics is ruled by bursting bubbles (Axial and some region of Wall and Flat slug-flows). This is in agreement to the reported value of 3.5 bits/cycle appeared in [22]. As expected when particle – particle and particle – wall dominate the acoustic signal (Pseudo, Wall and Fast slug-flows), the information lost per cycle is clearly higher, as a consequence of the observed turbulence of vigorous solid mixing, promoted by the erupting bubbles as
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previously described by those slugging modes. The local maximum of K c observed in Fig. 12b indicates the transition from Wall to Flat Slug-Flow. The instability that often characterizes the transition between different dynamic states makes the system normally to exhibit a local maximum of entropy to indicate the transition [32]. 5. Conclusions It has been shown how for noisy time series, passive acoustic emissions measurements by means of out-bed monitoring can take place at very low sampling frequency by studying the frequency region from 0 to 20 Hz [1], instead of the ultrasound region, which is the most commonly studied. This procedure does not make necessary the digital processing of large time series and improves substantially the time of data processing for state and time domain analysis. It has been proved that the dynamic information contained in the measured noisy acoustic signals from 0 to 20 Hz can be used for fluidised bed diagnosis. Moreover, in contrast to pressure time series, acoustics monitoring is not influenced by resonance between bed and plenum pressure fluctuation and, consequently, there is not overestimation on the resulting chaotic properties such as the correlation dimension. The estimation of the acoustic pressure from the particle array model has become very useful to decide the frequency range suitable to dynamic diagnosis, as well as to estimate the theoretical value of the average cycle frequency of acoustic pressure due to particle –particle and particle –wall collisions. Neither time nor frequency domain analysis seem able to fully characterize the bed dynamics from the information provided by passive acoustic emission signals. Only the state space analysis by means of the correlation dimension analysis, which ranges within the interval 2.5 < D 2 < 3.5, identifies the slugging regime existing through the several runs and, therefore, fully characterizes the dynamics under evaluation. The research has been carried out by using small beds (m b å 0.33 kg) and within a moderate noisy environment. The measurement system was exposed to extra mechanical noises like gas compressors and screw feeders existing within the facilities. These environmental conditions introduce a high number of harmonic components into the signal, plus other background noises from other very common industrial facilities sources like workers shouting, valves, air distribution system, etc. The proposed measurement system will hopefully work even better for monitoring larger beds, since those systems will provide passive acoustic emission of larger magnitude. Notation D Column diameter, m D2 Correlation dimension, (– ) E Power spectrum energy, (– ) dp Mean particle size, m f Frequency, Hz fc Cut-off frequency, Hz
fM fn fs H h I K Kc Ma mb Pa P xx q2 r t t stp t stp ua U0 U mf Ur
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Frequency corresponding to the main peak of the PSD, Hz Natural frequency, Hz Slugging frequency, Hz Settle bed height, m Vertical position, m Mutual information function, bits Kolmogorov entropy, bits/s Kolmogorov entropy, bits/cycle Magnitude of acoustic fluctuation, (– ) Bed mass, kg Acoustic pressure, N/m2 Power spectrum energy, (– ) Parameter to compute b, (– ) Cross-correlation coefficient, (– ) Time, s Time step used during the computation of I, s Time index to compute the mutual information function, (– ) Particle velocity, m/s Superficial gas velocity, m/s Experimental minimum fluidisation velocity, m/s Relative gas velocity, U 0/U mf
Greek letters b Bulk modulus of the fluidised bed, N/m2 DS Average distance between particles, m Dt Simulation time step, s Dy Particle displacement, m yn/yt Particle velocity due to acoustic wave motion, m/s c2 Coherence function, (– ) qp Particle density, kg/m3 rd Average absolute deviation, (– ) Acknowledgments The authors would like to thank the students, now Chemical Engineers, Jorge Ruiz and Gema Are´valo for their skills during the experimental work. Moreover, the financial support from the Spanish Ministry of Research project PPQ2003-05256 is kindly acknowledged. References [1] C.E.A. Finney, C.S. Daw, J.S. Halow, Measuring slugging bed dynamics with acoustic sensors, in: KONA: Powder and Particle, 16, 1998, pp. 125 – 135. [2] J.W.R. Boyd, J. Varley, The uses of passive measurement of acoustic emissions from chemical engineering processes, Chem. Eng. Sci. 56 (2001) 1749 – 1767. [3] W. Zukowsky, An acoustic method of studying sequential explosions during gas combustion in bubbling fluidized beds, Combust. Flame 125 (2001) 1075 – 1082. [4] A.H.G. Cents, D.W.F. Brilman, G.F. Versteeg, P.J. Wijnstra, P.P.L. Regtien, Measuring bubble, drop, and particle sizes in multiphase systems with ultrasound, AIChE J. 50 (2004) 2750 – 2762. [5] M.A. Morton, S.V. Shepherd, Detecting bulk solid flow with acoustic monitoring technology, InTech 51 (8) (2004) 26 – 28.
156
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[6] H. Tsujjimoto, T. Yokoyama, C.C. Huang, S. Isao, Monitoring particle fluidization in a fluidized bed granulator with an acoustic emission sensor, Powder Technol. 113 (2000) 88 – 96. [7] D. Kunii, O. Levenspiel, Fluidization Engineering, Butterworth-Heinemann, Boston, 1991. [8] A. Svensson, F. Jhonsson, B. Leckner, Fluidization regimes in nonslugging fluidized beds: the influence on pressure drop across the air distributor, Powder Technol. 86 (1996) 299 – 312. [9] J. Vander Schaaf, J.C. Schouten, F. Johnsson, C.M. Van den Bleek, Nonintrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series, Int. J. Multiph. Flow 28 (2002) 865 – 880. [10] R.C. Brown, E. Brue, Resolving dynamical features of fluidized beds from pressure fluctuations, Powder Technol. 119 (2001) 68 – 80. [11] T.E. Broadhurst, Particle oscillation in fluidized beds, in: N.P. Cheremisinoff (Ed.), Encyclopedia of Fluid Mechanics, vol. 4, Gulf publishing company, Houston, 1986, Chapter 25. [12] C.M. Van den Bleek, J.C. Schouten, Can deterministic chaos create order in a fluidized-bed scale-up, Chem. Eng. Sci. 48 (1993) 2367 – 2373. [13] A.J. Patitsas, Booming and singing acoustic emissions from fluidized granular beds, J. Fluids Struct. 17 (2003) 287 – 315. [14] C.A. Herrera, E.K. Levy, J. Ochs, Characteristics of acoustic standing waves in fluidized beds, AIChE J. 48 (2002) 503 – 513. [15] R. Roy, J.F. Davidson, V.G. Tuponogov, The velocity of sound in fluidised beds, Chem. Eng. Sci. 45 (1990) 3233 – 3245. [16] F. Johnsson, R.C. Zjierveld, J.C. Schouten, C.M. Van den Bleek, B. Leckner, Characterization of fluidization regimes by time-series analysis of pressure fluctuations, Int. J. Multiph. Flow 26 (2000) 663 – 715. [17] V.D. Shrikant, G.E. Klizing, Pressure fluctuation analysis for fluidized bed, AIChE Sym. Ser. 89 (1993) 170 – 183. [18] C.E. Shanon, W. Weaver, The Mathematical Theory of Communication, The University of Illinois press, Urbana, 1949. [19] A.I. Karamavrue, N.N. Clarck, Local differential pressure analysis in a slugging bed using deterministic chaos theory, Chem. Eng. Sci. 52 (1997) 357 – 370. [20] J.F. Davidson, R. Clift, D. Harrison, Fluidization, Academic Press Inc., London, 1985. [21] J. Drahos, J. Cermak, Diagnostics of gas – liquid flow patterns in chemical engineering systems, Chem. Eng. Process. 26 (1989) 147 – 164. [22] M.L.M. Vander Sttapen, J.C. Schouten, C.M. Van den Bleek, Deterministic chaos analysis of the dynamical behaviour of slugging and bubbling fluidized beds, in: Proc. 12th Int. Conf. on Fluidized Bed Combustion, vol. 1, ASME, 1993, pp. 129 – 140. [23] J. Villa Briongos, J. Guardiola, Free top fluidized bed surface fluctuations as a source of hydrodynamic data, Powder Technol. 134 (2003) 133 – 144. [24] O. Trnka, V. Vesely, M. Hartman, Z. Beran, Identification of the state of a fluidized bed by pressure fluctuations, AIChE J. 46 (2000) 509 – 514. [25] W.K. Lord, G. McAndrews, M. Skagami, J.A. Valenzuela, L.R. Glicksman, measurement of bubble properties in fluidized beds, Proc. of 7th Int. Conf. on Fluidized Bed Combustion, 1982, pp. 76 – 88.
[26] B.H. Nelson, C.L. Briens, M.A. Bergougnou, Pressure fluctuations at individual grid holes of a gas-solid fluidized bed, Powder Technol. 77 (1993) 95 – 112. [27] C.S. Daw, F.L William, J.D. Darryl, N.E. Clapp Jr., Chaotic characteristics of a complex gas – solids flow, Phys. Rev., A 41 (1990) 1179 – 1181. [28] J.M. Hay, B.H. Nelson, C.L. Briens, M.A. Bergougnou, The calculation of the characteristics of a chaotic attractor in a gas – solid fluidized bed, Chem. Eng. Sci. 50 (1995) 373 – 380. [29] L. Huilin, D. Gidaspow, J.X. Bouillard, Dimension measurements of hydrodynamic attractors in circulating fluidized beds, AIChE Sym. Ser. 91 (1995) 103 – 110. [30] C.M. Van den Bleek, M.-O. Coppens, J.C. Schouten, Application of chaos analysis to multiphase reactors, Chem. Eng. Sci. 57 (2002) 4763 – 4778. [31] M.-O. Coppens, J.R. van Ommen, Structuring chaotic fluidized beds, Chem. Eng. J. 96 (2003) 117 – 124. [32] J. Villa Briongos, J. Guardiola, Using free bed surface fluctuations in a 3D fluidized bed for dynamic characterization, AIChE J. 50 (2004) 3060 – 3067. [33] B.G.M. Van Wachem, J.C. Schouten, R. Krihsna, C.M Van den Bleek, Validation of the eulerian model simulated dynamic behaviour of gas – solid fluidized beds, Chem. Eng. Sci. 54 (1999) 2141 – 2149. [34] J.R. Van Ommen, M.-O. Coppens, C.M. Van den Bleek, J.C. Schouten, Early warning of agglomeration in fluidized beds by attractor comparison, AIChE J. 46 (2000) 2183 – 2197. [35] J.C Schouten, M.L.M. Vander Stappen, C.M. Van den Bleek, Scale-up of chaotic fluidized bed hydrodynamics, Chem. Eng. Sci. 51 (1996) 1991 – 2000. [36] J.C Schouten, F. Takens, C.M. Van den Bleek, Estimation of the dimension of a noisy attractor, Phys. Rev., E 50 (1994) 1851 – 1861. [37] S. Ellner, Estimating attractor dimensions from limited data: a new method, with error estimates, Phys. Rev. Lett. A 133 (1988) 128 – 133. [38] P. Grassberger, I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983) 346 – 349. [39] H.D.Y. Abarbanel, Analysis of Observed Chaotic Data, Springer Verlag New York, Inc., 1996. [40] J.P. Eckman, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617 – 656. [41] C.S. Daw, J.S. Hallow, Evaluation and control of fluidization quality through chaotic time series analysis of pressure drop measurements, AIChE Symp. Ser. 89 (296) (1993) 103 – 122. [42] P. Grassberger, I. Procaccia, Estimation of Kolmogorov entropy from a chaotic signal, Phys. Rev., A 28 (1983) 2591 – 2593. [43] J.C. Schouten, F. Takens, C.M. van den Bleek, Maximun likelihood estimation of the entropy of an attractor, Phys. Rev., E 49 (1994) 126 – 129. [44] M.E. Davies, Reconstructing attractors from filtered time series, Physica, D 101 (1997) 195 – 206. [45] M.L.M. Vander Sttapen, J.C. Schouten, C.M. Van den Bleek, Application of deterministic chaos theory in understanding the fluid dynamics behaviour of gas – solids fluidization, AIChE Sym. Ser. 89 (1993) 91 – 102.
Fluidised bed dynamics diagnosis from measurements of low-frequency out-bed passive acoustic emissions Javier Villa Briongos, Jose´ M. Arago´n *, Marı´a C. Palancar University Complutense of Madrid, Department of Chemical Engineering, Faculty of Chemistry, Av. Complutense s/n, 28040 Madrid, Spain Received 24 January 2005; received in revised form 28 September 2005 Available online 3 February 2006
Abstract The purpose of this research is to show that measurements of low frequency out-bed passive acoustic emissions are useful for monitoring gas – solid fluidised bed hydrodynamics. A methodology is proposed to develop portable measurement systems (PMS) feasible for both laboratory scale optimisations and, later, for process diagnosis within industrial facilities. The methodology includes a multirate technique where the first sampling frequency used was about 11 kHz that was successfully later reduced to 500 Hz, which is far from the most common used for sampling ultrasonic ranges. The acoustic frequency range of interest (0 – 200 Hz) allows the use of a commercial jukebox and two low cost condenser microphones to record the out-bed acoustic emissions. The underlying bed dynamic process was studied by monitoring both acoustic and pressure fluctuation signals and by applying time, frequency and state space analysis over the measured time series. The crude acoustic signals exhibit marked random behaviour due to a high content of background noise. This is detected by the mutual information function. The power spectral density of the acoustic time series shows high complexity and claims for reducing the acoustic frequency range to be evaluated (initially 0 – 5.5 kHz). To decide an optimal frequency range and, consequently, a better sampling frequency, the acoustic pressure was estimated from a numerical simulation based on the well-known particle array model. From the results of the simulations, and in agreement to the literature, it is concluded that the bed dynamic acoustic information mainly lies within the range 0 – 200 Hz. According to that, the signals were subsequently re-sampled at a sampling frequency of 500 Hz. Finally, by comparing the pressure time series monitoring to the analysis of the mesoscale bed acoustic region (mainly due to bubbles, 0 – 20 Hz), it is concluded that from out-bed acoustic time series monitoring, only the state space analysis is able to fully characterize the slugging dynamics by means of a correlation dimension in the range 2.5 – 3.5 for the experimental conditions covered. D 2005 Elsevier B.V. All rights reserved. Keywords: Fluidised bed hydrodynamics; Passive acoustic emission; Monitoring; Dynamic diagnosis; Non-linear dynamics; Noisy time series analysis
1. Introduction Fluidised bed monitoring for resolving dynamical features is an issue of major importance in fluidisation engineering and several measurement techniques based on pressure fluctuations and acoustic emissions in fluidised beds have been proposed. Although the commercial and research applications are diverse, it is required new non-intrusive monitoring systems suitable for characterizing the bed dynamics in processes performed, for example, under severe, corrosive and high pressure/temperature conditions.
* Corresponding author. Tel./fax: +34 913944173. E-mail address: [email protected] (J.M. Arago´n). 0032-5910/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2005.12.009
The measurement of the passive acoustic emission that is created by the fluidising process itself has become a promising monitoring tool, thanks to the development of modern digital instrumentation and cheaper but more and more powerful computers. Diverse techniques based on the acoustic emission have been successfully applied for dynamics diagnosis [1] as well as for monitoring the performance of several operations and processes in gas – solid fluidised beds [2,3]. These techniques do not require direct contact between the bed and the measurement probes. Therefore, they have the clear advantage of providing a non-intrusive source of information about the phenomenon being monitored. In order to characterize the bed dynamics the hypothesis of Finney et al. has been assumed [1], i.e. that the bed acoustic signal contains information from two types of collisions,
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particle –particle and particle – wall, as well as of the motion of the bubbles and the global fluidised bed. According to Boyd and Marley [2], the sound generated from the microscale and macroscale bed phenomena will take place up to 200 Hz. This fact disagrees with most previous literature on this subject, in which the measurement is focused to higher frequencies, within the ultrasonic range ( f > 20 kHz) and up to several hundreds of kHz [4 –6] in order to avoid noise from the background and secondary mechanical vibrations. It is the aim of this research to improve the current techniques to reduce the sampling frequency that is necessary to have a reliable bed dynamics monitoring in order to develop a portable on-line measurement system (PMS) that can be used for both laboratory-scale process optimisation and later process diagnosis within industrial facilities. Working at lower sampling frequencies avoids digital processing of large time series and spans the number of data processing techniques that can be applied over the signal. Within the research project this paper focuses on the establishment of the out-bed passive acoustic monitoring methodology from noisy time series. With this purpose, both passive acoustic emissions and pressure bed fluctuation measurements are used to understand how the recorded signals are related to the overall bed dynamics and, therefore, to show the extent the out-bed passive acoustic measurement collected within a moderate noisy environment of 73 db, with local maxima up to 79 db, can be used to monitor fluidised bed dynamics. Time, frequency and state space analysis have been applied over the measured acoustic and pressure time series in order to find useful information from the crude experimental data and to characterize the bed dynamics.
2. Experimental Acoustic and pressure time series were recorded from a fluidised bed confined in a 5 cm ID glass vessel with a perforated plate distributor (Fig. 1). The distributor/bed pressure drop ratio, DP d/DP b, was around 0.6 at minimum fluidisation velocity to provide [7] a uniform gas distribution throughout the bed. However, it was not enough to damp the fast downward travelling pressure fluctuation waves through the perforated plate [8,9]. Therefore, the possible resonance between pressure bed and plenum fluctuations must be taken into account before extending the results obtained with pressure sensors to other fluidised systems. The fluidised bed is of Ballotini glass beads, 320 < d p < 500 Am (Group 1) and 800 < d p < 1400 Am (Group 2) (Geldart B and D type, respectively). The bed height/diameter ratio is H/D = 2. The bed was fluidised with air at ambient conditions and relative superficial velocities, U r = U 0/U mf, ranging from 1.4 to 4.1 (Group 1) and from 1.1 to 1.9 (Group 2). Under these fluidisation conditions a slugging behaviour was promoted within the bed. 2.1. Acoustic measurement system The acoustic time series were collected by means of two out-bed unidirectional condenser microphones AUDIO TECHNICA PRO 42 with XLRM-type connectors. Each acoustic sensor (microphone) is fitted to a circular mounted surface that is inclined 60- above the horizontal axis to obtain the best recording quality performance. Those sensors have a frequency response up to 14 kHz, which suffices for the purpose of the
Fig. 1. Experimental set-up.
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research, and were located externally to the system, one just above the distributor and the other one 10 cm above, near the bed surface (Fig. 1). The outlet signal resulting from the microphones is amplified through a mixing console EURORACK\ MXB1002 and sent to a CREATIVE\ NOMAD JUKEBOX 3 where the data are finally digitised as ‘‘wav’’ files. To reduce the low-frequency influence of background noise and mechanical vibration, the microphones are placed within a silencer rectangular box, where the face in contact to the vessel is open to facilitate the out-bed passive acoustic measurement. During the runs, it was observed that, due to the small size of the vessel and the low bed mass (m b = 0.33 kg), the signals collected in both position were identical, so for those conditions the measurement system acts as non-intrusive global technique. Consequently, only the results from the acoustic time series measured at the top bed surface (h = 0.1 m) are presented through the rest of the paper. 2.2. Pressure fluctuation measurement Pressure fluctuations were measured by means of two AP32 KEYENCE pressure gauges. The signal was digitised through a PCI 6023E I/O board (NATIONAL INSTRUMENT Co.). As depicted in Fig. 1, the bed pressure fluctuations were recorded at two different positions: position 1 (above the distributor) and position 2 (10 cm from the distributor plate, bed surface). Some complementary runs were carried out by measuring simultaneously the fluctuations in position 2 and within the plenum to evaluate the degree of coherence between the bed and plenum pressure fluctuations. 2.3. Data acquisition protocol A multirate technique was applied where the passive acoustic emissions were collected initially with a sampling frequency, f s, of 11 025 Hz. A low-pass filter having a cut-off frequency of f c = f s/2 was applied over the signals to avoid further possible aliasing problems. The time series recorded were 3 min long (about 2 000 000 points); longer time series lead to many computer problems during the digital processing of the signal. The state space analysis was made with signals re-sampled at 500 Hz and low-pass filtered with a cut-off frequency of 20 Hz in order to study the mesoscale bed dynamic region, mainly due to bubbles. The pressure fluctuation signals were sampled at 200 Hz. The samples were taken for over 4 min. Thus, each resulting time series was 48 000 points long. In order to keep the overall bed dynamics information, the time series were filtered using a digital low pass filter Chebyshev type 1 with a cut-off frequency of f c = 20 Hz. Brown and Brue [10] have reported that the use of sampling times from 20 to 60 min is recommended to distinguish spectral features from pressure fluctuation signals. Nevertheless, it is worth to mention here that within this paper the spectral analysis is a complementary tool for signal analysis
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and that there are neither modelling nor scaling purposes. Therefore, the sampling time used here, much less than the values reported by these authors, suffices for a reliable estimation of the spectral features of the bed dynamics. 3. Result and discussion In order to asses the reliability of passive acoustic measurement to bed dynamic characterization within a working environment, the fluidisation conditions were carefully chosen to promote slugging regime. The slugging behaviour was monitored by measuring the pressure bed fluctuations. The pressure time series served to make dynamic diagnosis that was compared further to those obtained from the acoustic monitoring. 3.1. Modelling the bed acoustics Since measuring passive acoustic emission at a sampling frequency of 11 025 kHz by means of out-bed microphones is affected by many acoustic sources that take place within the range of bed dynamics frequencies, in order to extract the dynamic information stored within the acoustic signals, it seems that reducing the frequency range to be studied becomes critical. So, following the hypothesis of Finney et al. [1], it is assumed that the acoustic signal measured from a fluidised bed is originated by the particle – particle and particle – wall collisions as well as by the bubbles and global bed motion. According to that, the particle array model [11] has been used to estimate the acoustic pressure, P a, from the particle – particle and particle –wall collisions. The model has been solved according to the expressions given in [12]. The results from the model served to elucidate the frequency range within which the dynamic information is contained, as well as provide data of particle acoustic dynamics within the 0– 20 Hz region. The acoustic pressure was estimated, according to Patitsas [13] by the following expressions: Pa ¼ b
b¼
yn ua yt Dt `b ` bua ; yy yy Dy
q2 U2 qp dp2 02 : 3 DS
ð1Þ
It was assumed that the particle velocity defined in [13], u a = yn/yt, can be computed directly from the particle array model [11] since the small amplitude to which the particle oscillates in a compressible fluid will lead to acoustic waves [14]. Moreover, particle oscillations have already been related to sound waves in fluidised beds [15]. The three main variables in Eq. (1), Dt, Dy, and DS, are also computed from the particle array model. The values of U 0, d p and q p are known parameters. Finally, q 2 is a parameter that serves to compute the bulk modulus, b. It has been set, according to [13], at a value q 2 = 1 for the simulations made here. The PSD of a simulated time series is shown in Fig. 2. It can be
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and 80. Moreover, the bubble information carried on the lowest frequency range, see detail in Fig. 3, will be blurred through the time series by the higher frequency components of the signal that have larger energy content. So, the time series was again filtered, now with a digital Chebyshev type 1 low-pass filter with a cut-off frequency f c = 20 Hz, in order to study better the acoustic signal within the region of frequencies in the range 0– 20 Hz. 3.2. Influence of background noise Fig. 2. Power spectral density estimation from a simulated time series, U r = 1.3, d p = 1020 Am.
observed that most of the signal energy content is comprised in the frequency range 0 –200 Hz; this fact is in agreement to the literature [2]. Therefore, it was decided to study the acoustic signal within the region 0 – 250 Hz. Thus, the acoustic time series were re-sampled at f s = 500 Hz and lowpass filtered ( f c = f s/2 = 250 Hz). An example of the data analysis is shown in Fig. 3. It can be observed that, even with the filtering of the sampled data, the PSD of the acoustic time series is still difficult to interpret because it exhibits a great complexity with the clear presence of harmonics mainly due to a near gas compressor and the background noise from several sources. Through the paper, the well known Welch’s averaged periodogram method was used [16] to compute the PSD. It should be noted that the energy of the spectrum is dimensionless, since the time series were previously normalized to time series having a mean of zero and a standard deviation, r, of unity. This fact makes the ordinate of the power spectrum to be P xx/r 2, allowing reliable comparison to be made [17]. According to Brown and Brue [10], no less than 15 periodograms have been averaged to compute the PSD. Depending on the time series, the number of averaged periodograms, N, ranges between 40
The influence that background noises and mechanical vibrations have on characteristic frequencies can be fairly well monitored by the time-dependent Fourier transform. An example of how the 0 –250 Hz region is highly sensitive to the presence of background noise is shown in Fig. 4. As a result, both the subsequent time series and the corresponding data analysis will be influenced. The region of interest, 0 –20 Hz, is less influenced by those extra frequency components due to harmonics and background noises. Nevertheless, the possible influence of these components over the final results should be taken into account when interpreting the results. The mutual information function, I, is used to account for the influence of the background noise on the deterministic chaotic features exhibited by the acoustic signal (Fig. 5). As it is well known, the mutual information function is based on the uncertainty concept developed by Shanon and Weaver [18]. According to this theory, the uncertainty associated with any measure depends on the probability of all possible outcomes. The mutual information function is usually measured in bits to give quantitative information about time series predictability. In contrast to the Kolmogorov entropy, I does not take into account the time correlation existing in dynamics. Besides, it does not assume any functional relationship between the data to be analysed and, consequently, it is suitable to detect persistence within non-linear time series
Fig. 3. Power spectral density of an acoustic time series re-sampled at f s = 500 Hz with a low-pass filter of f c = 250 Hz. Detail of the low frequency region (0 – 20 Hz).
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Fig. 4. Time dependent Fourier transform for a run with group 1 particles, U r = 2.8; (a) influence over the acoustic signal of harmonics introduced by a near gas compressor existing in the facility, (b) effect of several noises generated from different sources, which can take place randomly within the working environment, on the measured acoustic signal.
[19]. By all these reasons, the mutual information function was used here to identify the dynamics under evaluation. When the mutual information function is computed from a signal sampled at 500 Hz without low-pass filtering at 20 Hz, it can be observed that the presence of harmonics, as those detected in Fig. 4a, introduces a strong artificial persistence within the signal. In contrast, once the signal is low-pass filtered at 20 Hz, it presents the chaotic features that are characteristic in fluidised beds (Fig. 5, curves b and c). Finally, the presence of a high content of background noise in the signal, even when this noise introduces a large number of harmonics (Fig. 4a,b), slightly reduces the value of I (Fig. 5, curves b and c). The persistence introduced by the harmonics (Fig. 5c) is so small that, as it will be shown later, the chaotic features exhibited by the fluidised bed will remain almost unaltered.
3.3. Visual description of the flow regimes As a result of the qualitative visual observation of the bed, five different slugging modes have been identified (Fig. 6). (1) Pseudo Slug-flow, PS-F: At this regime, several small slugs that rise through the bed and burst at the bed surface were observed. This Fsingle bubbling_ makes that the bubbles rise, erupt at the surface and project solids well dispersed into the freeboard. (2) Axial Slug-flow, AS-F: Axial stable slugs cross the bed leading to a plug-flow like global bed motion. At this slugging mode, the solid thrown away the bed, as a consequence of the bubble eruption, is not well dispersed into the freeboard.
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existing from previous bubble bursting provides a turbulent appearance to the bed surface. 4. Pressure fluctuations and passive acoustics emission diagnosis 4.1. Time domain analysis
Fig. 5. Mutual information function for: (a) non-filtered (raw) acoustic time series; (b) acoustic time series re-sampled at f s = 500 Hz with a low-pass filter of f c = 20 Hz without the presence of harmonics; (c) acoustic time series resampled at f s = 500 Hz with a low-pass filter of f c = 20 Hz with the presence of harmonics.
(3) Wall Slug-flow, WS-F: The observed rising slugs tend to adhere to the wall and slide-up the wall, the eruption of such bubbles give rise to a vigorous particle dispersion within the freeboard region near the bed surface. (4) Flat Slug-flow (square-nosed slugs), FS-F: The features of this regime are fairly well described in the literature [7,20]. So, the slugs grow up to block the bed section and, as a consequence, the bed is separated in slices. Under this regime, a plug-flow like global bed motion, similar as for the Axial Slug-Flow regime, was observed. (5) Churn-Turbulent Flow, T-F: Since this regime was only reached at its incipiently stage for both solid groups, it will be little referenced when interpreting the pressure and passive acoustic time series. This regime is characterised by a violent bursting promoted by large slugs, which lead to a strong agitation of the bed surface and to the throwing of larger quantities of solids that are well dispersed into the freeboard region. The mixing of those fresh solids from erupting slugs with the solid
Fig. 6. Pictures showing the five different slug-flow regimes observed during the runs.
4.1.1. Pressure time series The bed slugging dynamics can be characterized by estimating the cross correlation coefficient between the pressure signals collected from the two sensors placed at positions 1 and 2, respectively. The cross correlation coefficient has been used, as reported in [21], to distinguish between Axial and Pseudo Slug-Flow for the group 1 particle system. Thus, as it is shown in Fig. 7a, r for AS-F exhibits a significant peak, r å 0.4, that is due to the stable slugs that block effectively the bed section as they rise. In contrast (Fig. 7b), the slugs in the PS-F regime block the bed only momentarily and, hence, the correlation existing between the two signals from positions 1 and 2 is lower, r å 0.2, than for fully developed slugging regime. Therefore, it can be concluded from the correlation
Fig. 7. Cross-correlation analysis of pressure time series of group 1 particles. (a) Cross-correlation coefficient for axial-slug flow, U r = 2.8. (b) Cross-correlation coefficient for pseudo slug-flow, U r = 1.4.
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analysis that the B particles bed will operate at Axial and Pseudo Slug-Flow regimes within the fluidisation conditions covered. According to that analysis, the D particles bed will operate at fully developed slugging regime, r å 0.6, through the fluidisation conditions covered. The average absolute deviation, r d, has been used, instead the most common standard deviation of the signal, as a measure of the signal amplitude. According to [21], the measure of the absolute deviation is a better magnitude to express the ‘‘intensity’’ of the pressure fluctuation. As depicted in Fig. 8, r d increases for both B and D particle systems with gas velocity. However, it is not very sensitive to the different slugging modes that are taking place and, as it is described below, the state space analysis is preferred for the diagnosis of the bed dynamics.
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acoustic monitoring is because it gives a measure of the magnitude of a set of numbers as the root mean square does when applied for acoustic monitoring. The trend followed by r d is difficult to interpret in terms of physical phenomena and must be addressed taking into account the relative influence of each different acoustic source (e.g. particle –particle, particle – wall, bubbles and global bed motion) on the currently measured acoustic signal. These influences will be discussed below through the frequency domain analysis section. Finally, as the correlation analysis is highly influenced by the presence of harmonics and high frequency components in the measured signals, the useful bubble information that can be drawn by those tools is poor when they are applied over out-bed passive acoustic time series. 4.2. Frequency domain analysis
4.1.2. Passive acoustic time series Referring again to Fig. 8a,b, it can be observed that, as a difference to the pressure fluctuations time series, the average absolute deviation, r d, computed from passive acoustic emissions is apparently able to discern either between Pseudo and Axial slug-flow (group 1) or between Wall and Flat SlugFlow (group2). The reason why r d seems to be so useful for
Fig. 8. Average absolute deviation estimated from pressure and acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.
The spectral analysis of experimental time series has been widely applied to gas –solid fluidised bed time series [16,23] providing information about bed dynamics with several purposes such as monitoring [24] and dynamic scaling-up [25]. The frequency domain representation of the signal can be described by the estimation of its power spectral density, PSD, whose computation has been described previously. The joint spectral properties of signals measured simultaneously at different locations in the bed can be evaluated from 2 the coherence function, c xy ( f), which is calculated from the cross power spectral density. As it is well known, the coherence 2 function ranges from 0 to 1, where a value of c xy = 1 indicates that the PSD of the two compared time series are fully 2 correlated at that frequency. However, since c xy ( f) is a linear spectral tool, it cannot reveal non-linear correlation between two signals. 4.2.1. Pressure time series The estimation of the PSD provides a reliable representation of the characteristic bed dynamic frequencies. It is shown in the detail of Fig. 3 how, within the fluidisation condition covered, the slugging regime will be characterized by a main peak, f M, ranging between 2.3 and 3.1 Hz. Moreover, it was found that the energy peaks belonging to the group 2 particle system were larger than for the particle group 1, as a result of the different magnitude of the pressure fluctuation showed by those two particle groups used, which was found larger for group 2 (Fig. 8). The slugging frequency has been estimated from the autocorrelation function [26]. Although it slightly depends on the gas velocity, it takes a mean value f s = 2.7 Hz. This value matches fairly well the observed f M as shown in Fig. 3. The average cycle frequency has been used to monitor the f s trend as a function of the relative gas velocity. As expected (Fig. 9) f av decreases with the gas flow rate, since the coalescence effects reduce the number of bubbles bursting at the bed surface. However, the spurious crossing induced by high content of background noise due to the pressure sensor characteristics leads to an over-estimation of f s. Furthermore, the average cycle frequency estimated from pressure bed fluctuations has been later used as a measure of the Facoustic
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corresponding to bubbles dynamics can be drawn from the pressure time series (Fig. 9) the values of f av are near to 12 Hz when particle – particle and particle –wall collisions govern the acoustic dynamics (Pseudo, Wall and Fast Slug-Flows). Moreover, when the bed of B particles performs in Axial Slug-Flow, the values of f av from pressure and from acoustic time series match. Therefore, it is concluded that the acoustic signal is mainly due to the acoustic pressure generated by the bursting bubbles. In the D particles bed it seems that during the Flat Slug-Flow regime there is a compromise between the acoustic pressure generated by the particle – particle and particle – wall interactions and the bursting bubbles that give decrease of f av (Fig. 9b). Furthermore, the value of f av around 6 Hz is still far from the bubble frequency computed from the pressure time series, which is about 3 Hz. 4.3. State space analysis Methods of state space analysis deal with the reconstruction of attractors in an embedded phase space and the study of attractor properties, such as Kolmogorov entropy and correlation dimension. Several authors have studied and exploited the fluidised beds chaotic features [27 – 32] and have successfully applied the state space analysis to several fields of fluidisation engineering such as modelling [33], control [34] and scaling-up [35]. Fig. 9. Average cycle frequency estimated from pressure and acoustic time series for both particles groups vs. U r. The f av from the model has been computed after applied a low-pas filter of f c = 20 Hz over the simulated time series. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.; mod: Simulated passive acoustic time series.
pressure_ due to bubbles when interpreting the results drawn from acoustic time series. 4.2.2. Passive acoustics time series As for the pressure time series, the average cycle frequency has been computed from several passive acoustic time series (Fig. 9). Here, as for the average absolute deviation, the trend followed by this quantity is difficult to interpret. It can be concluded from the data in Fig. 9 that it is possible to use f av for monitoring purposes. The average cycle frequency takes values ranging from 6 to 8 Hz for fully developed slugging regime and for both particle groups. It shows a local maximum at the transitions between Wall and Flat Slug-Flow for the particle group 2 (Fig. 9b) and between Pseudo and Axial Slug-Flow for the particle group 1. Nevertheless, as it will be seen later, the state space analysis is preferred for dynamics diagnosis. To explain the behaviour of f av for acoustic time series, the results from the modified particle array model have been plotted on Fig. 9b. According to that, the average cycle frequency related to the acoustic pressure generated from the particle –particle and particle – wall collisions within the frequency region from 0 to 20 Hz, takes values ranging from 13.3 to 15.5 Hz. Therefore, assuming that the frequency
4.4. Correlation dimension This attractor property is obtained from the spatial correlation between random points on the reconstructed attractor. Several methods have been described for computing the correlation integral [36,37]. Nevertheless, these methods are all based on the algorithm of Grassberger and Procaccia [38]. Here the use of that algorithm is followed by application of an embedding dimension equal to 10, chosen by a previous false neighbour analysis [39]. A time delay of 1 was used during the reconstruction of the attractor and the interpoint distances were computed by using the maximum norm [40]. 4.5. Kolmogorov entropy The Kolmogorov entropy, K, is a direct measure of the chaos level and provides qualitative and quantitative information on the underlying dynamics of a system by measuring the average ‘‘surprise’’ one experiences by making a new measurement in spite of available knowledge of the system past history [41]. Moreover, the Kolmogorov entropy takes into account the time correlation in the dynamics and considers the effects that several past measurements have on the current measure. Kolmogorov entropy is usually expressed in units of bits/s, reflecting the rate of information loss by the system (unpredictability). Thus, when dealing with periodic, fully deterministic data, the Kolmogorov entropy equals zero, whereas for random time series the entropy is infinite. Finally, deterministic chaotic processes occurring between both these situations have positive Kolmogorov entropy.
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Fig. 10. Correlation dimension, D 2, estimated from pressure and acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. A: Passive acoustic monitoring; PCh1: Pressure fluctuations in position 1; PCh2: Pressure fluctuations in position 2.
There are several methods for estimating the Kolmogorov entropy from experimental time series [41,42]. The algorithm used here is based on the maximum likelihood method [43] and, it uses the averaged absolute deviation as cut-off length and maximum norm to compute interpoint distances. Moreover, as for the correlation dimension, an embedding dimension of 10 and a time delay of 1 have been used during the reconstruction of the attractor for computing K. 4.5.1. Pressure time series The correlation dimension (Fig. 10) has been used for monitoring the fluidised bed hydrodynamics. It has been found during the data processing that the pressure sensor placed at the bottom (position 1) is more sensitive to bubble dynamics, since it is less influenced by the bed surface and the global bed motion. It can be seen in Fig. 10 how the first maximum of the sensor located near to the distributor plate indicates the transition either from Pseudo to Axial Slug-Flow regime for particle group 1 and, from Wall to Flat Slug-Flow for group 2. In contrast, the correlation dimension estimated from the sensor placed at 10 cm over the distributor plate (position 2) is not sensitive to the change of the slugging condition from Pseudo
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to Axial Slug-Flow for the group 1 and shows a delay detecting the transition from Wall to Flat Slug-Flow when monitoring particle group 2. Additionally, it is plotted in the same figure the correlation dimension computed from acoustic time series monitoring, which is rather preferable to monitor the existing slugging flow regime as well as the different transitions that are taking place, as it will be discussed later. To conclude with the correlation dimension analysis, D 2 takes values mostly ranging between 3.5 and 4. According to the literature [22], this would indicate a hydrodynamic regime near to bubbling. However, due to the used particle size, vessel and bed aspect ratio, a value next to 3 or less, corresponding to slugging regime, was expected instead. The deviation from the expected value of 3 is mainly attributed either to the background noise or to the fact that the distributor to bed pressure drop ratio was relatively low, therefore resonance between the plenum and bed pressure fluctuations [8] could take place. Consequently, the measured signal will be influenced by resonance and, under these circumstances, it is not suitable to extend the quantitative results obtained from pressure fluctuations measurements to others systems. The coherence function (Fig. 11) serves to quantify the relation between bed and plenum pressure fluctuations. It can be observed how the bed and plenum pressure fluctuations are highly correlated as expected from the low DP d/DP b ratio. The Kolmogorov entropy is used as a complementary tool for bed dynamics diagnosis (Fig. 12). As for the correlation dimension, the magnitude computed from the signal recorded at the bottom is the most sensitive to bubble dynamics. In this case, the transition between regimes is indicated by a local maximum. Thus, for the particle group 1, the entropy computed from position 1 decreases as the bed performance gets the fully slugging regime, so the axial slugs dominate bubble dynamics and the entropy decreases as increases the slug size (the signal becomes more Fperiodic_). In contrast, the entropy computed from the signal collected near to the surface is more influenced by the global bed motion (plug-flow like), it does not show any local maximum and smoothly decreases up to a limit indicating that the bed has reached the fully slugging regime condition. The particle group 2 (Fig. 12b) behaves different due to the different fluidisation quality promoted by D particles. This fact is fairly well detected by the Kolmogorov entropy, as for the
Fig. 11. Coherence function between a pressure probe placed within the plenum and the probe located at position 2 for group 2 particles, U r = 1.6.
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Fig. 12. Kolmogorov entropy, K [bits/s], estimated from pressure time series and K c [bits/cycle] computed from acoustic time series for both particles groups vs. U r. The transition regions between the different slugging modes are indicated by dotted lines. K PCh1: Pressure fluctuations in position 1; K PCh2: Pressure fluctuations in position 2; K p A: Passive acoustic monitoring.
case of group 1, the sensor place at position 1 is more sensitive to bubble dynamics. It is shown in Fig. 12b how the transition from both Wall to Flat and from Flat to Fast Slug-Flow are detected by a local maximum of the Kolmogorov entropy. Finally it must be pointed out that for comparison between Fig. 12a and b, it can be observed how the Kolmogorov entropy computed from group 1 is larger than for group 2 according to the expected effect that particle size has on signal persistence [32]. 4.5.2. Passive acoustics time series Neither frequency nor time domain analysis have been able to fully characterize the bed dynamics from acoustic time series collected by means of out-bed microphones. Concretely, the slugging characteristics of the flow have not been yet detected by any of those analyses. The noise included in the signal makes traditional tools like cross and autocorrelation analysis unable to characterize the bubble dynamics. However, as Fig. 5b shows, in contrast to the original acoustic signal (Fig. 5a), after filtering at 20 Hz, the time series now exhibit chaotic features. This fact can be used to characterize the time series through state space analysis. The estimation of the correlation dimension can be used to identify the slugging regime existing within the bed for full dynamic diagnosis purposes. A plot of D 2 of the acoustic time
series versus the relative gas velocity, U r = U 0/U mf, is shown in Fig. 10. It can be observed how the correlation dimension takes values raging within 2.5 < D 2 < 3.5 for both solid groups. According to [22] those values are characteristics of slugging regime. Therefore, now the hydrodynamic regime has been fully identified from acoustic time series analysis. Moreover, the transition between the different slugging modes, identified previously by means of pressure time series monitoring, is fairly well indicated by the correlation dimension. Thus, the transition between different slugging states is preceded by a minimum of D 2. Since the out-bed acoustic monitoring acts like a global measurement technique for the fluidised bed systems under study, the observed behaviour of D 2 is in agreement to the results shown by Villa-Briongos and Guardiola [32]. Those authors, working with a non-intrusive global technique to measure the bed surface fluctuations [23], have found that the correlation dimension takes a minimum before taking place the transition between different bubbling regimes. Accordingly, it is assumed that the presence of large bubbles before taking place the transition explains the minimum of D 2. Ending with the correlation dimension analysis, it must be pointed out that when working at the worst noise conditions, the effects on D 2 are less than 5% of the final value of D 2. It is important to mention too that using IIR filters over the time series affects the estimation of invariant measures such as D 2 [44]. In fact, the Chebyshev type 1 IIR filter used here to treat the data processing affects less than 3% to D 2 when comparing to the value of D 2 estimated when filtering with a FIR filter. Therefore, since IIR filters provide better spectral features to the time series, they have been preferred here to filter the actual data. As for the pressure time series analysis, the Kolmogorov entropy is used to complementarily monitor the dynamics. Although the presence of noise is the main factor affecting the length scales below the cut-off length, it has been found that, in contrast to D 2, the Kolmogorov entropy value is affected up to 15% at the worst noise conditions, when it is expressed in bits/s, but it is affected less than 10% when it is expressed in bits/cycle. Moreover, Vander Stappen et al. [22,45] showed the usefulness of entropy per cycle for monitoring bed dynamics when the system operates at different conditions within a similar hydrodynamic regime. Therefore, the use of Kolmogorov entropy in bits/cycle has been preferred to dynamic diagnosis from the passive acoustic time series under evaluation. Furthermore, the values of K c obtained (Fig. 12) are easily compared to those reported in the literature. So, for both particle groups, the entropy per average cycle is ranging between 2.8 to 4 bits/cycle for fully developed slugging regime, where the acoustic dynamics is ruled by bursting bubbles (Axial and some region of Wall and Flat slug-flows). This is in agreement to the reported value of 3.5 bits/cycle appeared in [22]. As expected when particle – particle and particle – wall dominate the acoustic signal (Pseudo, Wall and Fast slug-flows), the information lost per cycle is clearly higher, as a consequence of the observed turbulence of vigorous solid mixing, promoted by the erupting bubbles as
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previously described by those slugging modes. The local maximum of K c observed in Fig. 12b indicates the transition from Wall to Flat Slug-Flow. The instability that often characterizes the transition between different dynamic states makes the system normally to exhibit a local maximum of entropy to indicate the transition [32]. 5. Conclusions It has been shown how for noisy time series, passive acoustic emissions measurements by means of out-bed monitoring can take place at very low sampling frequency by studying the frequency region from 0 to 20 Hz [1], instead of the ultrasound region, which is the most commonly studied. This procedure does not make necessary the digital processing of large time series and improves substantially the time of data processing for state and time domain analysis. It has been proved that the dynamic information contained in the measured noisy acoustic signals from 0 to 20 Hz can be used for fluidised bed diagnosis. Moreover, in contrast to pressure time series, acoustics monitoring is not influenced by resonance between bed and plenum pressure fluctuation and, consequently, there is not overestimation on the resulting chaotic properties such as the correlation dimension. The estimation of the acoustic pressure from the particle array model has become very useful to decide the frequency range suitable to dynamic diagnosis, as well as to estimate the theoretical value of the average cycle frequency of acoustic pressure due to particle –particle and particle –wall collisions. Neither time nor frequency domain analysis seem able to fully characterize the bed dynamics from the information provided by passive acoustic emission signals. Only the state space analysis by means of the correlation dimension analysis, which ranges within the interval 2.5 < D 2 < 3.5, identifies the slugging regime existing through the several runs and, therefore, fully characterizes the dynamics under evaluation. The research has been carried out by using small beds (m b å 0.33 kg) and within a moderate noisy environment. The measurement system was exposed to extra mechanical noises like gas compressors and screw feeders existing within the facilities. These environmental conditions introduce a high number of harmonic components into the signal, plus other background noises from other very common industrial facilities sources like workers shouting, valves, air distribution system, etc. The proposed measurement system will hopefully work even better for monitoring larger beds, since those systems will provide passive acoustic emission of larger magnitude. Notation D Column diameter, m D2 Correlation dimension, (– ) E Power spectrum energy, (– ) dp Mean particle size, m f Frequency, Hz fc Cut-off frequency, Hz
fM fn fs H h I K Kc Ma mb Pa P xx q2 r t t stp t stp ua U0 U mf Ur
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Frequency corresponding to the main peak of the PSD, Hz Natural frequency, Hz Slugging frequency, Hz Settle bed height, m Vertical position, m Mutual information function, bits Kolmogorov entropy, bits/s Kolmogorov entropy, bits/cycle Magnitude of acoustic fluctuation, (– ) Bed mass, kg Acoustic pressure, N/m2 Power spectrum energy, (– ) Parameter to compute b, (– ) Cross-correlation coefficient, (– ) Time, s Time step used during the computation of I, s Time index to compute the mutual information function, (– ) Particle velocity, m/s Superficial gas velocity, m/s Experimental minimum fluidisation velocity, m/s Relative gas velocity, U 0/U mf
Greek letters b Bulk modulus of the fluidised bed, N/m2 DS Average distance between particles, m Dt Simulation time step, s Dy Particle displacement, m yn/yt Particle velocity due to acoustic wave motion, m/s c2 Coherence function, (– ) qp Particle density, kg/m3 rd Average absolute deviation, (– ) Acknowledgments The authors would like to thank the students, now Chemical Engineers, Jorge Ruiz and Gema Are´valo for their skills during the experimental work. Moreover, the financial support from the Spanish Ministry of Research project PPQ2003-05256 is kindly acknowledged. References [1] C.E.A. Finney, C.S. Daw, J.S. Halow, Measuring slugging bed dynamics with acoustic sensors, in: KONA: Powder and Particle, 16, 1998, pp. 125 – 135. [2] J.W.R. Boyd, J. Varley, The uses of passive measurement of acoustic emissions from chemical engineering processes, Chem. Eng. Sci. 56 (2001) 1749 – 1767. [3] W. Zukowsky, An acoustic method of studying sequential explosions during gas combustion in bubbling fluidized beds, Combust. Flame 125 (2001) 1075 – 1082. [4] A.H.G. Cents, D.W.F. Brilman, G.F. Versteeg, P.J. Wijnstra, P.P.L. Regtien, Measuring bubble, drop, and particle sizes in multiphase systems with ultrasound, AIChE J. 50 (2004) 2750 – 2762. [5] M.A. Morton, S.V. Shepherd, Detecting bulk solid flow with acoustic monitoring technology, InTech 51 (8) (2004) 26 – 28.
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[6] H. Tsujjimoto, T. Yokoyama, C.C. Huang, S. Isao, Monitoring particle fluidization in a fluidized bed granulator with an acoustic emission sensor, Powder Technol. 113 (2000) 88 – 96. [7] D. Kunii, O. Levenspiel, Fluidization Engineering, Butterworth-Heinemann, Boston, 1991. [8] A. Svensson, F. Jhonsson, B. Leckner, Fluidization regimes in nonslugging fluidized beds: the influence on pressure drop across the air distributor, Powder Technol. 86 (1996) 299 – 312. [9] J. Vander Schaaf, J.C. Schouten, F. Johnsson, C.M. Van den Bleek, Nonintrusive determination of bubble and slug length scales in fluidized beds by decomposition of the power spectral density of pressure time series, Int. J. Multiph. Flow 28 (2002) 865 – 880. [10] R.C. Brown, E. Brue, Resolving dynamical features of fluidized beds from pressure fluctuations, Powder Technol. 119 (2001) 68 – 80. [11] T.E. Broadhurst, Particle oscillation in fluidized beds, in: N.P. Cheremisinoff (Ed.), Encyclopedia of Fluid Mechanics, vol. 4, Gulf publishing company, Houston, 1986, Chapter 25. [12] C.M. Van den Bleek, J.C. Schouten, Can deterministic chaos create order in a fluidized-bed scale-up, Chem. Eng. Sci. 48 (1993) 2367 – 2373. [13] A.J. Patitsas, Booming and singing acoustic emissions from fluidized granular beds, J. Fluids Struct. 17 (2003) 287 – 315. [14] C.A. Herrera, E.K. Levy, J. Ochs, Characteristics of acoustic standing waves in fluidized beds, AIChE J. 48 (2002) 503 – 513. [15] R. Roy, J.F. Davidson, V.G. Tuponogov, The velocity of sound in fluidised beds, Chem. Eng. Sci. 45 (1990) 3233 – 3245. [16] F. Johnsson, R.C. Zjierveld, J.C. Schouten, C.M. Van den Bleek, B. Leckner, Characterization of fluidization regimes by time-series analysis of pressure fluctuations, Int. J. Multiph. Flow 26 (2000) 663 – 715. [17] V.D. Shrikant, G.E. Klizing, Pressure fluctuation analysis for fluidized bed, AIChE Sym. Ser. 89 (1993) 170 – 183. [18] C.E. Shanon, W. Weaver, The Mathematical Theory of Communication, The University of Illinois press, Urbana, 1949. [19] A.I. Karamavrue, N.N. Clarck, Local differential pressure analysis in a slugging bed using deterministic chaos theory, Chem. Eng. Sci. 52 (1997) 357 – 370. [20] J.F. Davidson, R. Clift, D. Harrison, Fluidization, Academic Press Inc., London, 1985. [21] J. Drahos, J. Cermak, Diagnostics of gas – liquid flow patterns in chemical engineering systems, Chem. Eng. Process. 26 (1989) 147 – 164. [22] M.L.M. Vander Sttapen, J.C. Schouten, C.M. Van den Bleek, Deterministic chaos analysis of the dynamical behaviour of slugging and bubbling fluidized beds, in: Proc. 12th Int. Conf. on Fluidized Bed Combustion, vol. 1, ASME, 1993, pp. 129 – 140. [23] J. Villa Briongos, J. Guardiola, Free top fluidized bed surface fluctuations as a source of hydrodynamic data, Powder Technol. 134 (2003) 133 – 144. [24] O. Trnka, V. Vesely, M. Hartman, Z. Beran, Identification of the state of a fluidized bed by pressure fluctuations, AIChE J. 46 (2000) 509 – 514. [25] W.K. Lord, G. McAndrews, M. Skagami, J.A. Valenzuela, L.R. Glicksman, measurement of bubble properties in fluidized beds, Proc. of 7th Int. Conf. on Fluidized Bed Combustion, 1982, pp. 76 – 88.
[26] B.H. Nelson, C.L. Briens, M.A. Bergougnou, Pressure fluctuations at individual grid holes of a gas-solid fluidized bed, Powder Technol. 77 (1993) 95 – 112. [27] C.S. Daw, F.L William, J.D. Darryl, N.E. Clapp Jr., Chaotic characteristics of a complex gas – solids flow, Phys. Rev., A 41 (1990) 1179 – 1181. [28] J.M. Hay, B.H. Nelson, C.L. Briens, M.A. Bergougnou, The calculation of the characteristics of a chaotic attractor in a gas – solid fluidized bed, Chem. Eng. Sci. 50 (1995) 373 – 380. [29] L. Huilin, D. Gidaspow, J.X. Bouillard, Dimension measurements of hydrodynamic attractors in circulating fluidized beds, AIChE Sym. Ser. 91 (1995) 103 – 110. [30] C.M. Van den Bleek, M.-O. Coppens, J.C. Schouten, Application of chaos analysis to multiphase reactors, Chem. Eng. Sci. 57 (2002) 4763 – 4778. [31] M.-O. Coppens, J.R. van Ommen, Structuring chaotic fluidized beds, Chem. Eng. J. 96 (2003) 117 – 124. [32] J. Villa Briongos, J. Guardiola, Using free bed surface fluctuations in a 3D fluidized bed for dynamic characterization, AIChE J. 50 (2004) 3060 – 3067. [33] B.G.M. Van Wachem, J.C. Schouten, R. Krihsna, C.M Van den Bleek, Validation of the eulerian model simulated dynamic behaviour of gas – solid fluidized beds, Chem. Eng. Sci. 54 (1999) 2141 – 2149. [34] J.R. Van Ommen, M.-O. Coppens, C.M. Van den Bleek, J.C. Schouten, Early warning of agglomeration in fluidized beds by attractor comparison, AIChE J. 46 (2000) 2183 – 2197. [35] J.C Schouten, M.L.M. Vander Stappen, C.M. Van den Bleek, Scale-up of chaotic fluidized bed hydrodynamics, Chem. Eng. Sci. 51 (1996) 1991 – 2000. [36] J.C Schouten, F. Takens, C.M. Van den Bleek, Estimation of the dimension of a noisy attractor, Phys. Rev., E 50 (1994) 1851 – 1861. [37] S. Ellner, Estimating attractor dimensions from limited data: a new method, with error estimates, Phys. Rev. Lett. A 133 (1988) 128 – 133. [38] P. Grassberger, I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983) 346 – 349. [39] H.D.Y. Abarbanel, Analysis of Observed Chaotic Data, Springer Verlag New York, Inc., 1996. [40] J.P. Eckman, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617 – 656. [41] C.S. Daw, J.S. Hallow, Evaluation and control of fluidization quality through chaotic time series analysis of pressure drop measurements, AIChE Symp. Ser. 89 (296) (1993) 103 – 122. [42] P. Grassberger, I. Procaccia, Estimation of Kolmogorov entropy from a chaotic signal, Phys. Rev., A 28 (1983) 2591 – 2593. [43] J.C. Schouten, F. Takens, C.M. van den Bleek, Maximun likelihood estimation of the entropy of an attractor, Phys. Rev., E 49 (1994) 126 – 129. [44] M.E. Davies, Reconstructing attractors from filtered time series, Physica, D 101 (1997) 195 – 206. [45] M.L.M. Vander Sttapen, J.C. Schouten, C.M. Van den Bleek, Application of deterministic chaos theory in understanding the fluid dynamics behaviour of gas – solids fluidization, AIChE Sym. Ser. 89 (1993) 91 – 102.