Multi-resolution analysis of wavelet transform on pressure fluctuations in an L-valve

(1)

Multi-resolution analysis of wavelet transform on pressure

ﬂuctuations in an L-valve

T.-Y. Yang, L.-P. Leu

*

Department of Chemical Engineering, National Taiwan University, 1, Roosevelt Road, Sec. 4, Taipei 10617, Taiwan Received 1 August 2007; received in revised form 19 November 2007

Abstract

A novel diagnostic method to characterize the flow patterns in an 80 mm-i.d. L-valve had been developed by using multi-resolution analysis (MRA) of wavelet transformation on the pressure fluctuation signals which were acquired from the standpipe and the horizontal part of L-valve. Parameters including the aeration rate, aeration positions, riser gas velocity and composition of binary particle mixture (194-lm and 937-lm sand particles) were used to investigate the relationship of performance of L-valve and its pressure fluctuations. By means of MRA, the original pressure fluctuations were divided into multi-scale signals. They were macro-scale, meso-scale and micro-scale successfully described the structures of gas–solid flow in the L-valve, such as the gas bubbles/slugs, dune-ripple flow, suspension particle flow, etc.

Keywords: L-valve; Pressure ﬂuctuations; Wavelet transform; Multi-resolution analysis

1. Introduction

L-valve is one of the most effective and frequently used non-mechanical valve for conveying solid flow in the fluid-ized bed systems. It mainly consists of a long vertical pipe (standpipe) and a horizontal pipe. The solid flow through the L-valve is controlled by injecting small amount of aer-ation gas near the bottom of the standpipe. Although its performance, flow dynamic and design procedures had been investigated and reported by some previous studies (Knowlton and Hirsan, 1978; Geldart and Jones, 1991; Ozawa et al., 1991; Loung and Bhattacharya, 1993; Smol-ders and Baeyens, 1995; Arena et al., 1998), the study of the pressure fluctuations in L-valve for different flow patterns is sparse and the relationship between the standpipe and the L-valve is seldom discussed.Ozawa et al. (1991) mea-sured the fluctuations of static pressure at the lower part

of the standpipe. They qualitatively discussed the relation-ship between the pressure fluctuations and the correspond-ing flow patterns (packed-bed, coexistence, oscillation and pseudo-bridge patterns) in the standpipe. However, no fur-ther discussion of the pressure fluctuations in the horizon-tal part of L-valve was proposed in their study. To understand the more detail characteristics of different flow patterns in an L-valve, it is necessary to integrate the study of the pressure fluctuations in the standpipe and the hori-zontal part of L-valve.

In recent years, a powerful signal processing tool, wave-let transform, has been applied to analyze various kinds of signal in scientific and engineering fields. It is especially adequate to deal with a signal which contains multi-scale features and unsteady characteristics, such as the pressure fluctuations in the gas–solid flow systems. So far, it has been shown to provide much significant information from the pressure signals measured in literatures. Lu and Li (1999) proposed that wavelet function analyzes the pres-sure fluctuation signals and indicated the scale 4 detail sig-nal reflects the bubble behaviors in a fluidized bed.Ren and

*

Corresponding author. Tel.: +886 02 2365 7200; fax: +886 02 2362 3040.

E-mail address:[email protected](L.-P. Leu).

www.elsevier.com/locate/ijmulﬂow International Journal of Multiphase Flow 34 (2008) 567–579

(2)

Li (1998)used wavelet transform to decompose the original pressure fluctuations into three scales corresponding to macro-, meso- and micro-scales. The first one characterizes the effect of the processing unit on the system behavior, the second one describes the interaction of clusters or bubbles and the third one mainly characterizes particle motion in clusters or dilute phase. They verified that a fluidized bed exhibits multi-scale behaviors causing multi-resolution components in original time series of pressure fluctuations.

Park and Kim (2001)used wavelet and Fourier transforms to analyze the pressure fluctuations in a three-phase fluid-ized bed. They characterfluid-ized two different flow regimes in the bed by the dominant scale of wavelet coefficients and the highest wavelet energy.Li (2000, 2002)employed wave-let multi-resolution analysis and statistic methods (root mean square, skewness factor and probability density func-tion) to the pressure fluctuations of gas–solid flow in a hor-izontal pipe.

The aim of this paper is to investigate the pressure fluctuations in the standpipe and the horizontal part of the L-valve under different operation conditions by using the multi-resolution analysis (MRA) of wavelet transfor-mation. According to this analytic method, the flow mechanism of the gas–solid flow in the L-valve was charac-terized by the energy distribution of the multi-scale signals. 2. Experimental setup and procedure

Experiments were conducted in a Plexiglas. L-valve which had an 80-mm-i.d. 380-mm-long horizontal sec-tion and its vertical secsec-tion was connected with an 80-mm-i.d. 1760-mm high Plexiglas standpipe. The 52-mm-i.d. riser was used for recirculation of solid particles from L-valve to the storage tank equipped at the top of the standpipe. Three aeration taps (labeled as A1, A2 and A3) were located at 0.17 m, 0.27 m and 0.37 m above the centerline of the horizontal section of the L-valve respectively. Fig. 1shows the scheme of the experimental setup. Ambient air was supplied by Roots blower to lift the solid particles in the riser. The aeration gas injected into the L-valve was supplied by a compressor and the aeration rate was measured by a rotameter. Two different sizes of sand particles were employed as bed materials and their properties are listed inTable 1. The solid flow rate of the sand particles was obtained by timing the solid particle velocity at the standpipe wall between two marks (0.1 m apart) at steady-state operation and calibrated by the solid flow rate determined by collecting the solids in a container over a measured time interval as proposed by Knowlton and Hirsan (1978).

Several pressure taps were installed in 0.1-m interval apart along the horizontal and vertical sections of the L-valve. To avoid the blockage by fine particles, the tip of each pressure probe was covered with screen of 400 mesh, and was flushed with the inside wall of the L-valve. In each run of experiments, the pressure fluctuation signals were recorded by an AD/DA card at a rate of 100 Hz with

81.92 s of sampling duration. The multi-resolution analysis of wavelet transformation was carried out oﬀ-line by using the wavelet toolkit of S-PLUS software.

3. Signal processing of experimental data 3.1. Wavelet transformation

Wavelet transform is a relatively novel mathematical tool for signal processing. Similar to a windowed Fourier transform, a wavelet transform can measure the time–fre-quency variations of spectral components, but it provides

Fig. 1. Experimental setup.

Table 1

Properties of solid particles

Geldart’s classiﬁcation B D dp(lm) 194 937 qs(kg/m 3 ) 2635 2635 Umf(m/s) a 0.0382 0.582 Ums(m/s)b 0.096 0.64

a _{Estimated from}_{Wen and Yu (1966)}_. b_{Estimated from}_{Stewart and Davidson (1967)}_.

(3)

more ﬂexible time–frequency resolutions. The transform on a discrete signal can be carried out by discrete wavelet transform (DWT). The essence of DWT is to expand a pressure signal, x(t) (t = 1, . . ., N), as a sum of base func-tions /j,k(t) and wj,k(t). They are produced by dilations and translations of the orthogonal father wavelet function /and the mother wavelet function w as follows:

/j;kðtÞ ¼ 2 j=2 / t 2 j_k 2j j; k2 I ð1Þ wj;kðtÞ ¼ 2 j=2 w t 2 j_k 2j j; k2 I ð2Þ

here the time shift k=1, 2, . . ., N/2j and the level j = 1,2, . . ., J. J is the maximum level of wavelet transform and is dependent on /, w and N. Thus, the wavelet trans-form of x(t) can be obtained by Eqs.(3) and (4),

sJ ;k¼ Z xðtÞ/J ;kðtÞdt ð3Þ dj;k¼ Z xðtÞwj;kðtÞdt ð4Þ

where sJ,k and dj,k are called the approximation/smooth and detail coefficients respectively. Roughly speaking, sJ,k mainly represents the smooth behavior of x(t) at the coar-ser scale and dj,krepresents the detail part at the finer scale. The latter also provides the deviation between two succes-sive scales of smooth coefficients sj,k and sj1,k.

3.2. Multi-resolution analysis (MRA)

Multi-resolution analysis, ﬁrst developed by Mallat (1989), can be applied to decompose the signal x(t) into various scales of orthogonal signal component. They are the approximation subsignal SJ(t) and the detail subsignal Dj(t), which represent the components of x(t) at diﬀerent resolutions, calculated as follows:

SJðtÞ ¼ X k sJ ;k/J ;kðtÞ J ; k2 I ð5Þ DjðtÞ ¼ X k dj;kwj;kðtÞ j; k 2 I ð6Þ

The Dj(t) contents an approximate frequency band of [fs/ 2j+1–fs/2j] Hz and the SJ(t) contents an approximate fre-quency band of [0–fs/2J+1] Hz, here fsis the sampling fre-quency. Thus, the ﬁner scales of Dj(t) mainly capture the detail/high frequency feature of x(t), while the larger scales of Dj(t) and Sj(t) mainly reveal the whole-view/low-fre-quency feature of x(t). After that, the original signal x(t) can be recovered in terms of these subsignals with diﬀerent scales:

xðtÞ SJðtÞ þ DJðtÞ þ DJ1ðtÞ þ þ D1ðtÞ ð7Þ

The energy of SJ(t) and Dj(t) are deﬁned as follows: ES_J ¼X N t¼1 jSJðtÞj 2 ð8Þ ED j ¼ XN t¼1 jDjðtÞj 2 ð9Þ So, the energy distribution of x(t) can be calculated by Eqs.

(8) and (9)under various levels.

Based on the orthogonality and the energy conservation of wavelet transform, the total energy of x(t), E, can be cal-culated by the sum of ED

jðj ¼ 1; . . . ; J Þ and E S J as follows: E¼X t jxðtÞj2¼ ES J þ XJ j¼1 ED_j ð10Þ

In this study, the third-order Daubechies’ wavelet (Dau-blet3) was used as wavelet function to carryout MRA on the pressure ﬂuctuation signals. The normalized energy of the individual approximation eS

J and detail subsignals eDj can be calculated as follows:

eS_J ¼E S J E ð11Þ eD_j ¼E D j E ð12Þ

4. Results and discussion

4.1. Observation of the ﬂow patterns and pressure ﬂuctuations

In this study, the pressure fluctuation signals were measured simultaneously at the center of standpipe (z = 0.67 m) and the horizontal portion of L-valve. As shown in Table 2, the pressure fluctuations appeared to change obviously as increasing the aeration rate Qain the L-valve. Meanwhile, under different Qas, three kinds of flow patterns were observed respectively in the standpipe and the horizontal part of L-valve. They were the packed-bed flow (PBF), fluidized-bed flow (FBF) and slugging-bed flow (SBF) patterns for the standpipe; and the fast-moving stream flow (FMSF), ripple flow (DRF), and dune-slug flow (DSF) patterns for the horizontal portion of the L-valve. Some similar phenomena had also been observed by the others (Leung and Jones, 1978; Geldart and Jones, 1991; Ozawa et al., 1991; Knowlton, 1997).

4.1.1. PBF and FMSF patterns

At the low aeration rate Q_a< Q_a< Q_mf, where Q_a was the threshold aeration and Qmfwas the aeration rate based on minimum fluidization velocity Umf, the solid particles flowed smoothly downward with no bubbles in the stand-pipe. This kind of flow was commonly referred to as the packed-bed/moving-bed flow (PBF) (Knowlton and Hir-san, 1978). The corresponding pressure fluctuations had a small amplitude and high frequency component. It

(4)

repre-Table 2

Flow patterns and the pressure ﬂuctuations in the standpipe and the L-valve Device Aeration

rate, Qa

Relative velocity, Ur

Flow pattern Pressure ﬂuctuations

Standpipe Low <Qmf <Umf Packed-bed/moving-bed ﬂow (PBF): No bubbles are detected Solids ﬂow very

slowly downward

Leung and Jones (1978), Knowlton and Hirsan (1978), Jones and Leung (1985), and Ozawa et al. (1991)

Medium >Qmf

>Umf Fluidized-bed ﬂow (FBF):

Bubbles are formed Bubbles move upward

and bubble size grow with increasing Ur

Leung and Jones (1978)

High >Qms

>Ums Slugging-bed ﬂow (SBF):

Large slug/cavity are formed near the aeration tap Solid ﬂow is hindered

and relatively instable Pseudo-bridge pattern

is observed

Jones and Leung (1985)

L-valve Low <Qmf

<Umf Fast-moving stream ﬂow

(FMSF):

Most of solid particles are stagnant, only a suspension particle stream moves fast at the top of horizontal part

Geldart and Jones (1991)

Medium >Qmf

>Umf Dune-ripple ﬂow (DRF):

Dunes and ripples move continuously and periodically along the top of horizontal part Fluctuations of solid

discharge rate and pressure measured just above the aeration position is observed

Geldart and Jones (1991)

High >Qms

>Ums Dune-slug ﬂow (DSF):

Highly instable, solid ﬂow is hindered seriously Large dunes and

cavities coexist and ﬂow out irregularly

(5)

sented that the flow pattern in the standpipe was mainly predominated by stable solid particles flow. Simulta-neously, a fast-moving stream flow (FMSF) is observed at the narrow top of horizontal portion of L-valve (Geldart and Jones, 1991). It produces small and regular pressure fluctuations caused by the small ripples periodically entrained with the solid particles stream.

4.1.2. FBF and DRF patterns

At the medium aeration rate Qmf< Qa< Qms, where Qms was the aeration rate based on incipient slugging velocity Ums, a part of the aeration gas formed small bub-bles with frequency about 0.5–1.5 Hz and flowed upward in the standpipe that somewhat hindered the solid flow and produced larger fluctuations. Because the solid particles were fluidized in the standpipe, so the flow pattern was regarded as the fluidized-bed flow (FBF). On the other hand, the else part of aeration gas was entrained downward by solid flow into the horizontal section of the L-valve. It formed lager ripples and dunes at the inner corner of the bend that produced the pressure fluctuations of higher amplitude. This kind of flow pattern consequently was regarded as the dune-ripple flow (DRF).

4.1.3. SBF and DSF patterns

At the high aeration rate Qa> Qms, the large slugs/cavi-ties began to develop at the upper section of the standpipe and its size enlarged gradually as moving downward with

the solid flow. Once it reached the inner corner of the bend, it was pushed by the large dunes rapidly through the L-valve. Because the clear slugs/cavities were observed in the standpipe, thus the flow pattern was regarded as the slugging-bed flow (SBF). It was very similar with the ‘‘pseudo-bridge” pattern observed by Jones and Leung (1985)who demonstrated that this flow pattern may form as the position of aeration at the standpipe is too high. In the horizontal portion of the L-valve, the corresponding flow pattern was regarded as the dune-slug flow (DSF). The solid flow was highly instable due to the hindrance of the large slugs/cavities. That occasionally caused huge fluc-tuations of pressure signals both measured at the standpipe and L-valve. The rest part of pressure fluctuations was anal-ogous to that of the DRF pattern with higher amplitude.

4.2. Multi-resolution analysis (MRA) of pressure ﬂuctuations

To further understand the characteristics of pressure fluctuations in the L-valve, the MRA of wavelet transform was applied under various flow patterns introduced in the last section. The decomposition level of MRA was set as eight, thus each pressure fluctuation signal was decom-posed into nine subsignals. In this case, eight detail subsig-nals (D1–D8) and one approximation subsignal (S8) were obtained from each pressure fluctuation signal under the six flow patterns in the standpipe and the horizontal part

Fig. 2. Multi-resolution analysis of pressure ﬂuctuations in the standpipe at (a) Qa= 1.69 104m 3 /s, (b) Qa= 3.42 104m 3 /s, and (c) Qa= 5.18 104m 3 /s.

(6)

of L-valve, as shown inFigs. 2a–c and3a–c, respectively. For the purpose of comparison, each subsignal was plotted as the same scale of coordinates as the original pressure fluctuations. These figures simultaneously provided the information of the fluctuating data in frequency and time domains. Furthermore, the multi-scale behavior of original pressure fluctuations was characterized by recombination of these subsignals. The micro-scale behavior of pressure fluctuations was mainly presented by the finer scales of MRA, e.g. D1and D2, which had the frequency bandwidth of [fs/8–fs/2] = [12.5–50] Hz as discussed before. These scales were relatively significant in the PBF pattern. The meso-scale behavior corresponding to the small bubbles and dunes/ripples in the standpipe and L-valve respectively was mainly captured by the detail subsignals D3, D4, D5 and D6 with the frequency bandwidth of [0.78–12.5] Hz. The macro-scale behavior corresponding to the large slugs/cavities and instable pressure oscillation was described by D7, D8and S8with extremely low-frequency range of [0–0.78] Hz. The amplitude of these subsignals would be expected to increase remarkably in SBF and DSF patterns.Fig. 4shows the result of multi-scale analy-sis on the pressure fluctuations in the standpipe and the horizontal part of L-valve.

4.3. Energy distribution of multi-scale signals

The energy distribution helped us to realize which sub-signal was dominant in the corresponding ﬂow pattern.

Fig. 5 shows the energy distribution of MRA calculated from Eqs.(8) and (9) in various flow patterns. It was evi-dent that whether in the standpipe or the horizontal part of L-valve, S8 often had a largest energy. That was con-tributed to the global pressure drop oscillations or the instable solid mass flow in the entire system. Jones and Leung (1985) also introduced that a jerky flow mode, so-called the slip-stick flow, is observed in the standpipe. It oscillates between flow and no-flow at a frequency in the range of approximately 0.1–1 Hz which is well consis-tent with the frequency bandwidth of S8subsignal in this study. In PBF pattern, D1usually had higher energy than any of other detail subsignals, however, it was relative small in the other flow patterns. It was because that D1 subsignal with highest frequency content was mainly con-tributed from the background noise and the fluctuations of interstitial gas flow in the packed-bed. When Qa was increased, D1would be covered by the other detail subsig-nals of larger scale which was produced by bubbles or big voids. Furthermore, in the horizontal part of L-valve, the energy of meso-scale subsignals (D3–D6) played an impor-tant role due to the dunes and ripples flow patterns pre-dominated here.

To quantitatively investigate the eﬀect of operation parameters on the pressure ﬂuctuations, the energy of micro-, meso- and macro-scale signals were calculated directly by the sum of corresponding energy of the subsig-nals (D1–D8and S8) based on energy conservation. There-fore, from Eq.(10)we had,

Fig. 3. Multi-resolution analysis of pressure ﬂuctuations in the horizontal part of L-valve (a) Qa= 1.69 104m 3

/s, (b) Qa= 3.42 104m 3

/s, and (c) Qa= 5.18 104m3/s.

(7)

E¼X t jxðtÞj2¼X 8 j¼1 ED_j þ ES

8¼ Emicroþ Emesoþ Emacro

Emicro¼ ED1 þ E D 2 Emeso¼ ED3 þ E D 4 þ E D 5 þ E D 6 Emacro¼ ED7 þ E D 8 þ E S 8 ð13Þ In addition, the normalized energy Eiof each scale of signal was obtained as follows:

Ei¼ Ei=E; i¼ micro; meso; macro ð14Þ

4.4. Eﬀect of the aeration rates Qa

Fig. 6shows the normalized energy of micro-, meso- and macro-scale signals (Emicro, Emesoand Emacro), deduced from

MRA, as a function of Qain different flow patterns. It was evident that the multi-scale signals strongly depended on Qa. In the standpipe (Fig. 6a), the most of energy was con-centrated in the macro-scale signal with relatively larger amplitude. The micro-scale signal had higher energy con-tent than the meso-scale signal in the PBF pattern where almost no bubbles were observed in the standpipe. In the FBF pattern Emicro decreased apparently with the increase of Qa, on the contrary, Emeso first increased slightly with the increase of Qa, and then dramatically increased as Qa approached Qms. It provided that the bubbles flowed upwards and grew in the standpipe at the relatively higher Qa. In the horizontal part of L-valve (Fig. 6b), Emeso appeared to be higher than that in the standpipe. It repre-sented that the small dunes and ripples dominated at low aeration (FMSF pattern), however it was rapidly surpassed by Emacro due to the increase of solid flow oscillations Fig. 4. Multi-scale of pressure fluctuations in the (a) standpipe and (b) horizontal part of L-valve at Ug= 7.22 m/s, Qa= 4.00 104m3/s.

(8)

caused by the formation of large bubbles/cavities. At the medium Qa(DRF pattern), Emeso increased smoothly with increasing Qa then decreased as the large and instable slugs/cavities formed at the higher Qa (DSF pattern). Emicrowas almost independent of Qaand was of little signif-icance in the horizontal part of L-valve where the dunes and ripples of larger scale predominated.

4.5. Eﬀect of the aeration positions (A1, A2, and A3)

Fig. 7shows the dependency of Gson Qawith the aera-tion posiaera-tions (A1, A2, and A3) as a parameter. It was found that with increasing the aeration gas the difference of Gs among A1, A2, and A3 was not obvious for the low and medium Qa. However, as Qawas increased near Qms (4.83 104m3/s for 194-lm sand particles in this study), the difference appeared to be noticeable. Beyond Qms, the deviations between A1, A2 and A3 gradually increased with increasing Qa. In addition Gs for A3 did not increase with increasing Qa, but decreased instead. The similar results were also found byKnowlton and Hir-san (1978), who attributed the decreasing of Gs at higher aeration position to the decreasing of effective downcom-er/standpipe length.Ozawa et al. (1991)observed the for-mation of bubbles and cavity in the standpipe when the aeration tap was relative high. Their static pressure data in the standpipe exhibit high amplitude with low-frequency fluctuations and Gsis much smaller than that of the lower aeration tap.

Fig. 8shows the normalized energy of subsignals D1–D8 and S8, obtained from Eqs.(11) and (12), for diﬀerent aer-ation positions. In PBF and FBF pattern (Figs. 8a and b),

the energy distributions of A1, A2, and A3 were quite sim-ilar. While in the SBF pattern (Fig. 8c), the energy of D4, D5, and D6at higher aeration positions (A2 and A3) was much larger than that for A1. It revealed that considerable amount of bubbles appeared in the standpipe at the higher aeration positions and hindered the solid flow. In the hor-izontal part of L-valve, there was no significant effect of the aeration positions on the energy distribution of MRA sig-nals (Figs. 8d–f).

Fig. 9 shows Emicro, Emeso and Emacro as the functions of the aeration positions in the same operational conditions inFig. 8. In each of flow pattern, Emicro was almost inde-pendent of the aeration positions. Emeso at the PBF and FBF patterns in the standpipe had relative small values and showed almost no difference among the three aeration positions (Figs. 9a and b). The effect of aeration positions on these flow patterns was not significant in the standpipe. However, when Qa was increased to 5.18 104m3/s, at which the SBF pattern was presented, Emeso appeared to increase with heightening the aeration position (Fig. 9c). It indicated that the interference from bubbles flowing upwards in the stand-pipe became more significant at the higher aeration posi-tion. In the horizontal part of the L-valve, the effect on Emicro also was insignificant. Emeso, at the FMSF and DRF patterns, increased slightly with heightening the aer-ation position (Figs. 9d and e). As Qa was increased beyond Qms, Emeso attenuated to a lower value (<0.2) and also slightly decreased with heightening the aeration position (Fig. 9f). In summary, the aeration positions showed significant effect on Emeso, Emacro and Gs only at relatively higher Qa in the standpipe.

(9)

4.6. Eﬀect of the riser gas velocities Ug

Fig. 10shows the solid mass ﬂux Gsversus the riser gas velocities Ugwith the aeration rates as the parameter. For lower aeration rate (Qa1and Qa2), Gsdid not change obvi-ously with increasing Ug. However, for higher aeration

rates (Qa3–Qa5) Gs increased remarkably with increasing Ug. This phenomenon was in agreement with a previous study by Loung and Bhattacharya (1993). Besides, if Qa was too high (5.79 104_m3

/s in this study), the solid ﬂow in the L-valve was obviously hindered for the lower Ug. As at Ug= 6.23 m/s inFig. 10, Gsof Qa5curve was even lower than that of Qa3and Qa4. It was found that increasing Ug would be contributive to eliminate the hindrance to the solid ﬂow.

The comparison of energy distribution at the diﬀerent Ugis shown inFig. 11. For relatively higher aeration rate, as decreasing the riser velocity Ug, the energy distribution both in the standpipe and the horizontal part of L-valve gradually shifted from the medium level (D4, D5, D6) to the higher level (D8 and S8) of subsignals. It indicated the L-valve was primarily occupied by low-frequency slugs and cavities with large amplitude at the lower Ug. On the other hand, increasing the Ugwas helpful to elim-inate large slugs/cavities and enlarged the operation range of the L-valve. Fig. 12shows that Emacro decreased appar-ently as expected with increasing Ug in the riser bed. It Fig. 6. Normalized energy of micro-, meso- and macro-scale signals in the (a) standpipe and (b) horizontal part of L-valve at Ug= 7.22 m/s.

(10)

Fig. 9. Normalized energy of micro-, meso- and macro-scale signals in the standpipe and the horizontal part of L-valve for diﬀerent aeration positions. Fig. 8. Normalized energy distribution of MRA subsignals for diﬀerent aeration positions.

(11)

meant that the large slugs/cavities split into smaller bub-bles/gas void and Emeso consequently increased with increasing Ug.

4.7. Effect of the compositions of binary particle mixture In order to understand the effect of the compositions of binary particle mixture on the performance of L-valve, 194-lm and 937-194-lm sand particles were mixed up in four spe-cific compositions. Some of their properties are listed in

Table 3.

In Fig. 13, Gs for each binary particle mixture pair increased linearly with increasing the aeration number U/ Umf, here U was the superﬁcial gas velocity based on the cross-sectional area of the standpipe/L-valve. In addition, the workability range (i.e. the diﬀerence between the

Fig. 11. Normalized energy distribution of MRA subsignals at diﬀerent riser velocities.

Fig. 10. Solid mass ﬂux versus riser velocities with diﬀerent aeration rates.

Fig. 12. Dependency of normalized energy of micro-, meso- and macro-scale signals on the Ug for (a) Qa= 4.60 104m

3 /s and (b) Qa= 5.79 104m 3 /s. Table 3

Properties of binary particle mixture

Composition of mixtures (xB:xD) 8:2 7:3 6:4 5:5 dp(lm) 231 254 284 321 qs(kg/m3) 2635 2635 2635 2635 Umf(m/s)a 0.0426 0.0488 0.0591 0.0755 Ums(m/s)b 0.105 0.111 0.121 0.138 a _{Estimated from}_{Cheung et al. (1974)}_.

(12)

maximum and the minimum of U/Umf) increased as the fraction of the 194-lm sand particles (xB) was increased. Furthermore, at constant Ugand U/Umf, Gsof binary par-ticle mixture reached a maximum value at xB= 0.7, as shown in Fig. 14. The normalized energy of multi-scale pressure signals also showed signiﬁcant dependency on the composition of binary particle mixture. As shown in

Fig. 15b, Emeso in the horizontal part of L-valve revealed a similar dependency as Gs of the binary particle mixture on xB. It was explained that, for the xB-rich binary particle mixture (xB= 0.7, 0.8 and 1.0), decreasing xBor increasing xDwas helpful to reduce the shear stress between the pipe wall and the solid particles as the contact surface area was reduced. Hence, the solid particles were entrained through the L-valve more easily and the dune-ripple ﬂow was enhanced in the horizontal part that caused Gs and Emeso to increase. However, on the other hand, decreasing xBalso reduced the contact surface area between the gas and solid phases that would cause the abatement of drag forces on

the solid particles. Therefore Gsand Emeso decreased when xBwas below 0.7. The variance of Emeso inFig. 15a could also elucidate the effect of the compositions on the perfor-mance of the standpipe. At approximately constant U/Umf, Emeso gradually increased with decreasing xB. It indicated that increasing the amount of the larger sand particles would increase the amount of gas flowing upwards along the standpipe. Further decreasing xB, the big bubbles/slugs even formed in the standpipe since the superficial gas veloc-ity in the standpipe was higher than the incipient slugging velocity of the binary particle mixtures of xB= 0.5 and 0.6. This result also agreed withKnowlton’s (1997) obser-vation. He described that if large particles are employed as bed material or when the solid flow rate in the standpipe is low, the aeration gas will flow upwards along the standpipe rather than be entrained by the solid particles flowing downwards. Consequently, the big bubbles/slugs are usu-ally observed in the standpipe at these situations.

5. Conclusions

In this study, the flow dynamics of the six flow patterns was investigated by the pressure fluctuation signals mea-sured at the standpipe and the horizontal part of the L-valve. The multi-scale concept of MRA was applied to

Fig. 13. Solid mass ﬂux of diﬀerent compositions of binary particle mixture.

Fig. 14. Gsversus xBfor diﬀerent U/Umf.

Fig. 15. Dependency of the normalized energy of micro-, meso- and macro-scale signals on the compositions of binary particle mixture.

(13)

decompose the pressure fluctuations into micro-, meso- and macro-scale signals. The energy of these multi-scale signals had been reported to characterize the effects of operational parameters on the performance and pressure fluctuations of the L-valve. Several results had been concluded as follows,

The energy of meso-scale signal Emeso at the standpipe increased apparently with heightening the aeration posi-tion. It represented bubbles formed in the standpipe and hindered the solid particles ﬂowing through the L-valve especially at higher aeration rate.

The energy of macro-scale signal Emacro at both the standpipe and the horizontal part of L-valve decreased with increasing the riser gas velocity. It implied that large slugs/cavities were gradually eliminated and the solid ﬂow became smoother in the entire system. The dependency of Emeso on the composition of binary

particle mixture xB showed a similar trend as the solid mass flux Gs at the horizontal part of L-valve. Both Emeso and Gsreached a maximum value at xB= 0.7. Though the pressure fluctuation measurement indeed presented a convenient way for understanding the dynamic behavior of gas-solid flow in the L-valve, different kind of analytical tools including gamma or X-ray scan, CCD micro-camera, laser-sheet techniques, etc. should be used to re-confirm or check the flow regimes in the L-valve. References

Arena, U., Langeli, C.B., Cammarota, A., 1998. L-valve behaviour with solids of diﬀerent size and density. Powder Technol. 98, 231–240. Cheung, L., Nienow, A.W., Rowe, P.N., 1974. Minimum ﬂuidisation

velocity of a mixture of diﬀerent sized particles. Chem. Eng. Sci. 29, 1301–1303.

Geldart, D., Jones, P., 1991. The behavior of L-valve with granular powders. Powder Technol. 67, 163–174.

Jones, P.J., Leung, L.-S., 1985. Downﬂow of solids through pipes and valves. In: Davidson, J.F., Clift, R., Harrison, D. (Eds.), Fluidization. Academic Press, London, pp. 293–329.

Knowlton, T.M., Hirsan, I., 1978. L-valves characterized for solids ﬂow. Hydrocarbon Proc. 57, 149–156.

Knowlton, T.M., 1997. Standpipes and return systems. In: Grace, J., Avidan, A.A., Knowlton, T.M. (Eds.), Circulating Fluidized Beds. Blackie Academic and Professional, New York, pp. 214–260. Leung, L.S., Jones, P.J., 1978. Flow of gas–solid mixtures in standpipes. A

review. Powder Technol. 20, 145–160.

Li, H., 2000. Multiresolution analysis of pressure ﬂuctuation in horizontal swirling ﬂow pneumatic conveying using wavelets. Adv. Powder Technol. 11, 423–438.

Li, H., 2002. Application of wavelet multi-resolution analysis to pressure ﬂuctuations of gas–solid two-phase ﬂow in a horizontal pipe. Powder Technol. 125, 61–73.

Loung, P.H., Bhattacharya, S.C., 1993. A study of solid circulation rate in a circulating ﬂuidized bed. Int. J. Energy Res. 17, 479–490.

Lu, X., Li, H., 1999. Wavelet analysis of pressure ﬂuctuation signals in a bubbling ﬂuidized bed. Chem. Eng. J. 75, 113–119.

Mallat, S., 1989. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693.

Ozawa, M., Tobita, S., Mii, T., Tomoyasu, T.Y., Takebayashi, T., Suzuki, K., 1991. Flow pattern and ﬂow behavior of solid particles in L-valve. In: Basu, P., Horio, M., Hasatani, M. (Eds.), Circulating Fluidized Bed Technology III. Pergamon Press, Oxford, pp. 615–620.

Park, S.H., Kim, S.D., 2001. Wavelet transform analysis of pressure ﬂuctuation signals in a three-phase ﬂuidized bed. Korea J. Chem. Eng. 18, 1015–1019.

Ren, J., Li, J., 1998. Wavelet analysis of dynamic behavior in ﬂuidized beds. In: Fan, L.-S., Knowlton, T.M. (Eds.), Proceedings of the Ninth Engineering Foundation Conference on Fluidization, Durango, Col-orado, pp. 629–636.

Smolders, K., Baeyens, J., 1995. The operation of L-valves to control standpipe ﬂow. Adv. Powder Technol. 6, 163–176.

Stewart, P.S.B., Davidson, J.F., 1967. Slug ﬂow in ﬂuidised beds. Powder Technol. 1, 61–80.

Wen, C.H., Yu, Y.H., 1966. A generalized method for predicting the minimum ﬂuidization velocity. AIChE J. 12, 610–612.