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Flow regime identification in a novel circulating-turbulent fluidized bed
Chemical Engineering Journal 244 (2014) 493–504
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Flow regime identification in a novel circulating-turbulent fluidized bed Qiang Geng a, Xiaolin Zhu a, Jie Yang a, Xinghua You b, Yibin Liu a, Chunyi Li a,⇑ a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum (East China), Qingdao 266580, China Petrochemical Factory of the Yumen Oil-Field Company, PetroChina, Yumen 735200, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Flow behavior in C-TFB was a novel
The gas–solids flow dynamics especially flow regime in a circulating-turbulent fluidized bed (C-TFB) compared with other traditional flow regime were studied. Traditional original signal processing and novel wavelet analysis method were utilized to identify different flow regimes. Fuzzy system recognition method combined with wavelet analysis results were employed to judge whether flow regime in the C-TFB was a novel flow regime.
regime on the micro-level. Wavelet analysis was utilized to analyze the flow dynamics. Wavelet energy was obtained as unique features of flow regimes. Flow regimes were recognized by fuzzy system identification method. The C-TFB optimizes flow dynamics and gas–solid contact efficiency.
a r t i c l e
i n f o
Article history: Received 9 June 2013 Received in revised form 7 January 2014 Accepted 31 January 2014 Available online 8 February 2014 Keywords: Multiphase flow Wavelet analysis Fuzzy system identification analysis Circulating-turbulent fluidized bed Flow regime identification
a b s t r a c t Whether flow dynamics in a novel circulating-turbulent fluidized bed (C-TFB) belongs to a new flow regime or just a transition state is controversial. In order to resolve this confusion, transient fluctuation signal processing and wavelet analysis have been used to identify the flow regimes in five specially designed flow systems, which have been proven to be effective tools to extract detailed information of flow features in different flow regimes. Furthermore, the fuzzy system identification method, which was used to process wavelet energy data of various scales obtained by wavelet analysis, was employed to make a quantitative distinction among the flow regimes. The results showed that the flow regime in the C-TFB is a novel flow regime, which is different from traditional flow regimes such as bubbling, turbulent, fast fluidization (FF) and dense suspension up-flow (DSU) regimes. The new regime has some unique characteristics including intensive gas–solids interaction, high gas–solids contact efficiency, two peaks of probability density distribution (PDD) curves in the center of the fluidized bed, broader spectrum of solids holdup for PDD curves, a decreasing extent of gas–solids separation extent and unique radial detail wavelet energy percentage profiles. Quantitative analysis by the fuzzy system identification method further confirmed that the flow behavior in the C-TFB can be described as a novel flow regime. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction ⇑ Corresponding author. Tel.: +86 532 86981862; fax: +86 532 86981718. E-mail address: [email protected] (C. Li). http://dx.doi.org/10.1016/j.cej.2014.01.102 1385-8947/Ó 2014 Elsevier B.V. All rights reserved.
Circulating fluidized beds have not been restricted to traditional application areas such as coal combustion, FCC and gasification of
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Nomenclature a ai b di/Di Di dp E f Gs j J
dilation factor outline coefficient of discrete wavelet transform translation factor detail coefficient of discrete wavelet transform detail decomposition scale diameter of particle, lm wavelet energy sampling frequency, Hz solids flux, kg/m2s multi-resolution level the maximum level of transform
biomass [1,2]. The derived diameter-expanding riser has been adopted for industrial processes: Maximizing Iso-Paraffins process [3] and Two-Stage Riser Catalytic Cracking for Maximizing Propylene process [4]. The concept of circulating-turbulent fluidized bed (C-TFB) or multi-regime riser was proposed based on this diameter-expanding riser [5–7]. Several aspects of this diameter-expanding riser have been discussed in detail, including solids holdup, particle velocity, possibility density, local solids flux profiles [5,8], instantaneous solids holdup and intermittency index analysis [9]. The results showed that its flow behavior combines the flow characteristics of high density circulating fluidized bed and turbulent fluidized bed [10]. However, further systematical experimental and theoretical analyses of the flow regime in the C-TFB are lacking. Furthermore, different researchers have distinctive understanding about the flow regime in this diameter-expanding riser, which has been summarized in Table 1 [5–12]. Its flow dynamics was identified as dense suspension upflow (DSU) regime, expressed by operating conditions (Gs and Ug) [11] The macro-analysis including operating conditions’ relationship, solids holdup and tracer profiles, which is commonly used in flow regime diagram [11,13], cannot identify this novel flow regime from that in the bottom part of a traditional riser and a high density circulating fluidized bed [14,15]. Thus, it may be a good way to gain in-depth knowledge of a flow regime by micro-signal analysis including transient fluctuation signal processing and wavelet analysis as well as micromechanics of different particle–fluid flow regimes [16–19]. However, only a few reports covered original signal processing in C-TFB. There is lack of systematic in-depth extension at signal analysis [5,8–12], which leads to different conclusions about the flow regime in the C-TFB. This is because a fluidized bed is a complex system exhibiting multi-scale behavior, which leads to multiple components in the original time series [20,21]. The heterogeneous flow dynamics in a fluidization system, especially in this novel C-TFB, is far from being understood. Wavelet analysis, which is found to clarify the complicated structure of particle fluidization, offers an appropriate method to extract the features of such multi-scale flow behavior [19,22]. It has attracted wide attention in the field of engineering applications combined with mathematics [23–25]. The wavelet multiresolution analysis enables the signal data to be decomposed and recomposed quantitatively due to the orthonormal transform. According to wavelet transform, the original signals can be resolved into multi-resolution signals with different frequency bands. Corresponding quantitative information, including peak frequency and wavelet energy can be obtained. According to these characteristics, the wavelet transform method has been applied to investigate multi-scale flow behavior in different flow regimes. Detail wavelet signals were directly related to bubble phenomena, reflecting the information of bubbling frequency size [22,25]. Turbulent kinetic
k P T Ug
time shift detail wavelet energy percentage time, s superficial velocity, m/s
Greek letters es solids holdup at a radial position esmf solids holdup at minimum fluidization conditions es average solids holdup in one cross section qp particle density, kg/m3 W(x) wavelet basis function
energy in a turbulent boundary layer of a gas–liquid flow system was analyzed [26]. A criterion was set up to separate the original signal into the dense phase and the dilute phase by identifying the transition points between the two phases [27]. A large number of factors affect the flow regime, which results in no definite boundary in the process of flow regime transition. It means that flow regime identification is a fuzzy recognition division process. The fuzzy system identification method is a good way to identify the flow regime. It was initiated by Zadeh [28] to provide a scheme for handling a variety of problems, especially applying it to an indefinite one that arises more from a sort of intrinsic ambiguity than from a statistical variation. The fuzzy system identification method, which has been employed to predict and control different systems [29,30], was proved effective to solve the flow pattern identification problem when aided by other tools such as electrical capacitance tomography [31], impedance-based tomography [32]. However, its application to fluidization systems was rarely reported. From the above discussion, it is clear that systematic work on micro-signal analysis should be conducted and that a kind of unified method needs to be constructed to identify the flow regime quantitatively. This paper adopts signal processing, including probability density distribution (PDD) curves, amplitude spectra and peak points count to depict flow regime identification. We use wavelet transform analysis combined with the fuzzy system identification method to form a unified way to identify the bubbling, turbulent, dense suspension upflow, fast fluidization flow regimes and the flow regime in C-TFB. In this way we can judge whether the flow behavior in C-TFB is novel in comparison to the four known flow regimes. 2. Experimental The experiments were conducted in a specially designed system, consisting of multi-purpose units, schematically shown in Fig. 1. The system consisted of a hopper tank, a measuring tank, a riser, air distributors, and a disengager. The riser made out of plexiglass had a diameter of 0.1–0.2 m and a height of 10.06 m. The whole riser could be divided into three different parts: (1) the pre-lifting section (0.0–0.8 m) with a bottom multi-hole air distributor; (2) the multi-purpose section (0.8–2.6 m); (3) the conveying section (2.6–10.06 m). The plexiglass tube in the multi-purpose section could be easily exchanged depending on experimental purposes to achieve different types of fluidized beds. Fig. 1(a)–(c) represents a circulating fluidized bed, a bubble/turbulent fluidized bed and a circulating-turbulent fluidized bed respectively. Information about the fast fluidization (FF) regime and the dense suspension upflow (DSU) regime are indicated in Fig. 1(a) under different operating conditions. By controlling the gas velocity as indicated in Fig. 1(b) we could model bubbling flow regime and turbulent flow
495
Negative particle velocity near the wall; solids back-mixing near the wall Turbulent fluidization; dense suspension up-flow
Not given [6,7]; turbulent regime [16]; dense suspension up-flow [11] To be confirmed [10]; circulating-turbulent fluidization regime [5,8,9]
Other flow regimes as reference Flow regime
Micro-flow behaviors
Top diameter-expanding structure [5,8–10] 1–3 50–500 0.2–0.3 Uniform axial and radial solid holdup profiles; mainly dominated by dense phase Periodic motion at 1–3 Hz; intense particle–particle and particle–gas interaction Particles mostly upward near the wall; nearly no solids back-mixing Turbulent fluidization; dense suspension up-flow; fast fluidization Structure of riser Ug (m/s) Gs (kg/m2s) Overall solid holdup Macro-flow behaviors
Table 1 Key features of diameter-expanding riser with different research groups.
Bottom diameter-expanding structure [6,7,11,12] 1–2 200–400 0.2–0.4 Uniform axial and radial solid holdup profiles; mainly dominated by dense phase; optimizing the oil–catalyst contact Periodic motion at 1–3 Hz; intense particle–particle and particle–gas interaction
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regime when the circulating system was blocked by a shut-off butterfly valve. Finally a circulating-turbulent fluidized bed was achieved by changing the diameter of the riser from 0.1 m to 0.2 m in the multi-purpose section. In order to simulate gas–solid flow behavior of the stratified injection, consistent with industrial application, upper and lower feed units were used with heights of 0.8 m and 3.6 m above the bottom of the riser respectively. The lower feed unit contained a ring-feeder internal to improve the gas–solid interaction. The ring-feeder internal was designed with 12 nozzles at an angle of 90° to the internal underneath. Moreover, 4 nozzles were fixed symmetrically for the upper feed part. The operational processes have been described in detail in a previous paper [11]. Particles used in the experiments were FCC catalysts with a mean diameter dp of 80 lm and particle density qp of 1780 kg/m3. The size distribution of the FCC particles measured by a BT-9300ST laser particle size analyzer was normal (Fig. 2). The solids flow rate (Gs) was determined based on a specially designed measuring tank system, by measuring the height difference after a sudden close of a butterfly valve within certain time intervals to calculate the Gs value. The solids holdup information was obtained in our experiments by PV-56 D optical fiber probes developed by the Institute of Processing Engineering, Chinese Academy of Sciences. The probe, whose diameter was 4 mm, consisted of two sub-probes each with an effective tip area of 1 1 mm. Each of the two sub-probes included a bunch of quartz fibers arranged in square shape. The gap between the two sub-probes was 1.67 mm, and each probe was composed of light-emitting and receiving quartz fibers (25 lm in diameter) arranged in alternating array. 0.2 mm glass film covers were placed over the two sub-probe’s tips to prevent solids from occupying the probe’s blind zone. When sampling, the probe would emit light to the particles, and receive light reflected by the particles at the same time. The optical signals were converted into voltage signals by a photo-multiplier and fed to a PC. Before use, the fiber probes were calibrated to convert the voltage signals to the solids holdup fluctuations before used. The conversation from voltage signal to solids concentration signal is shown in Fig. 3. In each experimental run, the solids holdup fluctuations signal was sampled at a rate of 1000 Hz for 16 s, thereby yielding 16,000 data points. 3. Discrete wavelet transform principle Wavelet transform is a novel mathematical tool for analyzing multiphase systems including fluidized beds by signal processing [22,25,27]. Discrete wavelet transforms are utilized to transform a one-dimensional time series into a two-dimensional region displaying wavelet coefficients amplitudes as a function of both time and frequency. This approach makes it possible to analyze frequency while remaining time and space information [33]. In this paper the Daubechies wavelet was used as the basic wavelets to make sure of the precise signal analysis with higher order of polynomials utilized for approximation for its highest number of vanishing moments for a given support width [34]. The basic wavelet function can be set as W(x) with dilation factor a and translation factor b. Integer wavelet transform (IWT) for function f(x) e L2(R) was defined by the following equation:
1 WT x ða; bÞ ¼ pffiffiffi a
Z
1
1
f ðxÞW
xb dx a
ð1Þ
The corresponding algorithm of the discrete dyadic wavelet transform is given below:
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Fig. 1. Schematic diagram of experimental apparatus, including three different flow systems (a–c).
Fig. 2. Powders’ particle size distribution.
j
WT x ðj; kÞ ¼ 22
Z
1
f ðxÞWð2j x kÞ dx j; k 2 z
ð2Þ
1
where the time shift k ranged from 1 to N/2j and the level j changed from 1 to J. J was the maximum level of transformation, which was determined by W(x) and N. For computer sampling of the digital signal, the discrete dyadic wavelet transform (DWT) can be obtained by the Mallat algorithm [21].
f ðxÞ ¼ AJ1 f ðxÞ ¼
J2 X X C J1 ;k /J1; k ðxÞ ¼ A2 f ðxÞ þ Dj f ðxÞ k2Z
AJ2 f ðxÞ ¼
X C J2 ;k /J2 ;k ðxÞ
ð3Þ
j¼J 1 þ1
ð4Þ
k2Z
Dj f ðxÞ ¼
X Dj;k Wj;k ðxÞ
ð5Þ
k2Z
C jþ1;k ¼ ðHC j Þk ¼
X hl2k C j;k l2Z
ð6Þ Fig. 3. The relationship between solids holdup signal and voltage signal.
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Djþ1;k
X ¼ ðGC j Þk ¼ g l2k C j;k
ð7Þ
l2Z
C jþ1;k ¼ HC j ;
Djþ1;k ¼ GC j
ðj ¼ J 1 KJ 2 1Þ
ð8Þ
After multi-resolution analysis by the Mallat algorithm, the original signal was decomposed into various scales of orthogonal signal components, which were combined with approximation subsignal A2f(x) (4) with low frequency band (
Fig. 4. Plots of multi-resolution decomposition of the solids holdup fluctuations signals.
A thorough investigation of the micro-phase structures would be helpful to better understand the hydrodynamics of different flow regimes. The typical solids holdup fluctuations reflecting the flow features of the bubbling flow regime (Ug = 0.2 m/s), the transition flow regime (Ug = 0.4 m/s), the turbulent flow regime (Ug = 0.8 m/s), the fast fluidization regime (Ug = 12 m/s, Gs = 173 kg/m2s), the dense suspension upflow regime (Ug = 12 m/s, Gs = 400 kg/m2s) and the flow regime in C-TFB (Ug = 12 m/s,
Fig. 5. Comparisons of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m).
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Gs = 400 kg/m2s) were shown in Fig. 5. Generally, the solids holdup fluctuations showed the coexistence of voids and dense emulsion covering bubbling regime, transition flow regime, turbulent flow regime and flow regime in the C-TFB with solids holdup at minimum fluidization, esmf = 0.52. The magnitudes of the solids holdup fluctuations in the FF and DSU regimes are much lower, which indicated that the flow regimes are dominated by the gas phase. At a lower gas velocity of 0.2 m/s in the bubbling regime, solids holdup fluctuations remain 0 and 0.52 alternatively. Dense emulsion appears at the maximum magnitude, while fluctuations sharply drop near to zero representing the appearance of bubbles. The magnitude of the fluctuations reflects the effect of interactions between bubbles and solids. With a further increase of the superficial gas velocity from 0.4 to 0.8 m/s, well within the transition and turbulent flow regime, the magnitudes of the fluctuations decrease slightly and a higher fluctuations frequency is observed, which indicates that a series of bubbles coalesce and break quickly. It is consistent with the phenomenon depicted by Du et al. [35] and the mechanism explained by Cai et al. [36]. Comparisons between the FF and DSU regimes have been done systematically to identify some unique characteristics in the DSU regime such as upflow of particles at the wall, higher solids holdup, more uniform axial and radial solids holdup profiles [14]. The time series of instantaneous solids holdup in the FF and DSU regimes are somewhat similar that both of them are lack of voids or bubbles. Due to the specific operating conditions of higher solids fluxes and superficial velocities in the DSU regime, the mean solids holdup es is much higher than that in the FF regime. From a fluctuations analysis point of view, solids holdup fluctuations in the C-TFB share dual characteristics of violent particle– particle interactions consistent with TFB and fluctuations signal outline similar to DSU regime in spite of higher solids holdup in C-TFB, which has been confirmed and reflected by other researchers. Flow dynamics in the C-TFB was identified as dense suspension upflow (DSU) regime at a macro-level expressed by operating conditions (Gs and Ug) [11]. Qi et al. defined it as a novel circulatingturbulent fluidization regime at a micro-level [9] with uniform flow structure (axial and radial solids holdup profiles), upflow of particles profiles similar to the DSU regime and higher solids holdup, higher gas–solid contact efficiency similar to the TF regime. Gas–solid separation, contact and mixing are different in each flow regime. The probability density distribution (PDD) was obtained by MATLAB processing to get more information about the phase structures, which reflected the interaction between phases and properties of fluctuations in the frequent domain as shown in Fig. 6, for two typical radial positions (r/R = 0, r/R = 0.8). In general, two peaks are found in the PDD curves, one represents bubble/dilute phase with solids holdup between 0 and 0.08 and the other at a higher solids holdup of 0.4–0.55 for the dense phase. It is obvious that the gas phase tends to pass through the center and that the particles are likely to aggregate near the wall. This core-annulus structure aroused by the wall effect resulted in a significant difference of the PDD at radial positions. With radial position moving towards the wall, the peak shifts from the bubble/ dilute phase to the dense phase with a broader density distribution. Due to separation of the gas phase from the solids phase, the gas–solid interaction is worse for the FF and DSU regime in CFB, as indicated by Lin et al. [17] and Zhu and Zhu [8]. This narrow range of solids concentration distribution in the center and near the wall of the riser represented that the dilute gas–solids suspension is mainly composed of gas phase whereas the dense solids suspension is mainly composed of solids phase [12]. This flow structure is not good for mass/heat transfer due to low gas–solid contact efficiency. In contrast to the FF and DSU regimes, the broad and continuous spectra of solids holdup are found in the bubbling
Fig. 6. Comparisons of probability density distributions of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m) under different operating conditions.
flow regime, turbulent flow regime and flow regime in C-TFB, indicating the decrease of radial solids holdup gradient and the improvement of solids holdup distribution uniformity. It was noted that the peak of PDD curves in dilute phase is near 0 and that in the dense phase is 0.54, which is near the solids holdup at minimum fluidization esmf in the bubbling flow regime. It indicates that gas and solid phases have bad contact efficiency. Interaction between the gas–solids phases in the flow regime of C-TFB is similar to the turbulent flow regime observed from PDD curves. Two peaks exist in the PDD curves when the sampling position was in the center of the fluidized bed, which is different from other flow regimes except for the turbulent fluidization, indicating the coexistence of dilute and dense phases at the center radial positions. Continuous variation in solids holdup revealed that gas–solid separation weakens, more gas enters the dense phase and more particles are contained between gas phases. Gas–solid contact efficiency is improved due to intensive gas–solid interaction, which is consistent with the previous result that the contact efficiency is better in C-TFB than that in HDCFB (high density circulating fluidized bed) at macro-level [11]. Although radial profiles of time-mean particle velocity in the C-TFB have proved that no solids back-mixing and particles flowing mostly upward are characterized as unique features, which are different from those in TFB [8,9,12], there is a lack of method or criterion to identify the flow regime by fluctuating signals at the micro-level, except for the slightly broader spectrum of solids holdup for PDD curves in the C-TFB. To get in-depth knowledge about the flow regime characteristics in C-TFB distinct from others, amplitude spectra by means of fast Fourier transform was obtained to demonstrate the periodicity of the signal fluctuations, and comparative results were plotted in Fig. 7. It is noteworthy that different flow regimes are characterized by a certain dominant frequency, which could be utilized as one method to identify the flow regime. With an increase in the
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Fig. 7. Comparisons of power spectral density distributions of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m) under different operating conditions.
gas velocity from 0.2 to 0.8 m/s representing bubbling flow regime and turbulent flow regime respectively, the dominant frequency decreased from 3 to 1 Hz, while the spectral energy further increased [16,25,36,37]. The dominant frequency is very low and the spectral energies are distributed over a broad frequency range, and no clear dominant frequency is observed in the center of the low/high density circulating fluidized bed riser for both FF and DSU regimes [38], suggesting a lower degree of periodic particle motion. The dominant frequency occurs at 1 Hz for flow regime in C-TFB, indicating that its characteristics may be similar to those in the turbulent flow regime. From the above discussions, it can be concluded that original signal analysis is restricted to identify flow regimes, especially for the distinction between the turbulent flow regime and the flow regime in C-TFB. This is because a fluidized bed is a complex system and, by only analyzing signals obtained with optical fibers, one can get more detailed information. Therefore, wavelet transforms are introduced to extract the features of such multi-scale behavior by resolving the original signals into multi-resolution signals with different frequency bands. 4.2. Wavelet transform analysis As stated about the discrete wavelet transform principle in Section 3, the wavelet transform separates the signal into 9 scales, where D1 and D2 represent detail components that reflect the fine scale features and the coarse scale components D8 and D9 correspond to lower frequency oscillations or outline information. Fig. 8 shows the plots of the multi-resolution decomposition of
the solids holdup fluctuation signals in five flow regimes, typical D5–D8 scale components revealing the transition from detail to outline information. The dominant scale over the sampling time is the D8 scale, which could reflect the interaction between bubble/dilute phase and dense phase. It is noteworthy that although detail decomposition signals for the flow regime in the C-TFB are similar to those in the turbulent flow regime, as shown in Fig. 8(a), some differences were also found. The amplitude slightly decreased in the C-TFB, which indicated that the bed has a smaller bubble corresponding to higher gas–solid interaction and contact efficiency. On the other hand, the amplitude was dramatically enhanced compared to the flow regimes in traditional circulating fluidized bed according to the plots of Fig. 8(b). This could be attributed to higher solids holdup and lower local particle velocity in the C-TFB. In order to make clear which factor dominated flow dynamics in the C-TFB CFB from the perspective of interaction between dilute phase and dense phase, dominant detail wavelet signal peaks were processed by a unique method. As shown in Fig. 9, the peak points of dominant scale D8 found by origin software were divided into three sections, a bubble peak points (BPP) zone, a turbulent peak points (TPP) zone and a dilute peak points (DPP) zone according to the amplitudes (the absolute boundary condition is 0.24 and 0.12). The width, height, and minimum height of a pick-peaks toolbar were 0.50, 9.00 and 5.00 respectively. The number of bubbling peak points, turbulent peak points and dilute phase peak points were obtained by summing for consecutive 16 s in different flow regimes. At the same time, the average peak frequency was
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Fig. 8. Plots of multi-resolution decomposition for signal in C-TFB compared with that in other flow regimes.
Fig. 9. Category of multi-resolution decomposition peaks for scale 8 detail wavelet signal.
obtained by summing the number of peak points and dividing this sum by the sampling time. Since all signals were sampled within the same time, peak points count was applied to interrupt gas–solid interaction. Peak points count profiles in different flow regimes presented in Fig. 10 shows that the regulation of peak points count profiles in CTFB is between that in turbulent fluidized bed and DSU bed. The bubble size is much smaller in the C-TFB than that in the turbulent fluidized bed, which indicates that the bubble coalescence and breakup frequency are improving and the interaction between gas and solids phases is intensive. Vigorous gas radial exchange between the dilute and dense phases due to breakdown of slugs into smaller voids improves the gas–solids contact efficiency [39]. On the other hand, the dilute phase peak points count is much smaller than that in the DSU fluidized bed, which reflects that the extent of gas–solids separation between gas and solids phases decreases. This means that the coexistence of dilute phase and dense phase in the C-TFB is an important feature rather than the traditional core-annulus flow structure in the DSU fluidized bed.
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different flow dynamics. Further work has been done to identify the flow regime quantitatively by one unified method based on the above recognition results, by combining the fuzzy system recognition method and the wavelet analysis in the analysis of the flow regime identification problem. Finally, the flow regime membership degree was calculated to judge whether the C-TFB belongs to a novel flow regime or not. A series of calculations have been done including a large range of operating conditions, Ug = 0.15–1.2 m/s without circulating system and Ug = 6–14 m/s, Gs = 100–400 kg/m2s with circulating system and different sampling positions to find some unique characteristics reflecting different flow regimes in detail. Because the wavelet spectrum function is the energy distribution, the 9 scales wavelet energies are obtained from the coefficients of the discrete wavelet transform, which is defined as:
E¼
X
D2j;k þ
j;k
Ej ¼
X 2 Dj;k
X 2 C J2 ;k
J1 1 6 j 6 J2
ð9Þ
k
J1 1 6 j 6 J2
ð10Þ
k2Z
Fig. 10. Peak points count versus three different peak types.
Lu and Li [22] indicated that the bubbling frequency was directly proportional to (Ug Umf)0.2 and that the average peak value of the dominant scale detail signal was proportional to (Ug Umf)0.4 as well for the bubbling flow regime. The bubbling peak points were extracted from bubbling and turbulent flow regimes within superficial velocity from 0.15 to 1.2 m/s. Indeed, it was obvious that peak point count is directly proportional to (Ug Umf)0.2, however, bubbling peak points for flow regime in the C-TFB were under the line as shown in Fig. 11. This phenomenon also proved that larger bubbles in this novel flow regime decrease significantly, to put it another way, smaller bubbles are dominant in the C-TFB. Based on the above analysis, it could be deduced that the characteristics in the C-TFB could be defined as a novel flow regime whose flow dynamics are much better than that in turbulent and DSU flow regimes. 4.3. Flow regime fuzzy system recognition According to the experimental observations summarized above, the typical signal processing results and multi-resolution decomposition scale signal information reflected certain features of
Fig. 11. Peak points count versus (UgUmf)0.2.
where E is the total energy of the sampling signal and Ej is the energy of detail signal in different decomposition scales. In order to represent the system features based on different scales energy characteristic, energy percentage of detail signal, P is also defined here to reflect system energy information.
Pj ¼
Ej E
ð11Þ
Wavelet energy profiles with different decomposition scales are plotted in Fig. 12. With the change of radial sampling position from the center of the bed to the wall, the scale of wavelet energy percentage peak is transformed from fine scale to coarse scale, indicating that more clusters are inclined to aggregate near the wall. At the same time, the wavelet energy percentage decreases for turbulent, DSU flow regimes due to dense-phase dominant near the wall. The peak point occurs at the 4th scale position for the FF regime rather than at the large scale for DSU flow regime, which showed that relatively higher velocity and lower solids holdup is not conductive to larger bubbles formation. The wavelet energy percentage profiles remain nearly constant from center to the wall for flow regime in the C-TFB, which indicates that fully gas–solids interaction results in uniform solids holdup profiles at radial positions. Different flow regimes have their own curve characteristics, theoretically, if a specific signal is chosen to decompose, any scale could be used to detect the difference of flow regimes. However, some problems would be aroused in practice because if too many scales are chosen, recognition of the flow regime would be complex; in contrast, few scales may result in less exact and precise information. Through analysis of Fig. 12, detail energy percentage of D3, 4, 5, 6, 7, 8, 9 and total energy results obtained in the center of the fluidized bed were chosen as criteria to identify the different flow regimes, since the features of detail energy percentage profiles are distinct for each flow regime in the center of the reactors. While the characteristic of signal fluctuations near the wall is likely to be not obvious due to the solids aggregation, higher solids holdup. The pipe wall electrostatic effect may influence the accuracy of signal values obtained near the wall, which is not beneficial to the fuzzy identification. Detail energy percentage profiles in different decomposition scales would be overlapping, which reflected that flow regime transition is a fuzzy and gradual process. The identification processes are summarized as following several steps with the fuzzy system identification method [31]. The bubbling, turbulent, fast fluidization, DSU, C-TFB flow regimes can be replaced by symbols u1, u2, u3, u4, u5 respectively forming the universe of discourse U = {u1, u2, u3, u4, u5}. In this flow
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Fig. 12. Wavelet energy percentage profiles with different decomposition scales.
Table 2 Typical wavelet energy profiles of different flow regimes. Flow regime
u1
u2
u3
u4
u5
f1 f2 f3 f4 f5 f6 f7 f8
(1–9) 104 (1–5) 103 (1–8) 103 0.01–0.03 0.04–0.05 0.04–0.08 0.01–0.04 5000–7000
(1–7)103 0.01–0.03 0.01–0.05 0.03–0.06 0.04–0.08 0.04–0.08 0.05–0.10 2000–3000
0.04–0.05 0.06–0.13 0.06–0.12 0.03–0.05 0.04–0.05 0.02–0.06 0.01–0.05 20–80
0.02–0.03 0.03–0.06 0.03–0.07 0.03–0.07 0.06–0.09 0.06–0.11 0.11–0.21 50–100
(1–7)103 0.01–0.03 0.01–0.05 0.03–0.05 0.03–0.06 0.04–0.08 0.04–0.11 1000–2000
(P3, (P4, (P5, (P6, (P7, (P8, (P9, (E)
%) %) %) %) %) %) %)
regime identification system, the recognition process, according to wavelet analysis results, includes detail energy percentage of D3, 4, 5, 6, 7, 8, 9 and total energy data in different flow regimes, which are represented symbolically by f1, f2, f3, f4, f5, f6, f7, f8, and can be recognized to reflect characteristics of typical flow regimes in different operating conditions. This information is defined as a mathematical object, which is given by F = {f1, f2, f3, f4, f5, f6, f7, f8} in which each element stand for energy scope since every flow regime can be achieved within different operating conditions as shown in Table 2. Then the membership function Bðfj Þ should be defined to ex press the degree of membership, which indicates the degree of possibility. It is supposed to meet the boundary conditions and be expressed as the following form, where is a special operative symbol, which applied to transform x to another form m 10n in which the value of m ranged from 0.1 to 1 (not including 1) and is extracted as new value of x in order to form a reasonable distincTable 3 The membership function Bðfj Þðui Þ and membership degree Aðui Þ lists.
Bðfi Þð0Þ;
Bðfi Þð1Þ ¼ 0
ð12Þ
BðxÞ ¼ 1; min 6 x 6 max
ij
8 x > > =10n > min > < ij Bðfi Þ ¼ 1 > > > 1x > : 1max=10n
ij
0 < x < min=10n ij
min 6 x 6 max ij
n
ð13Þ
ij
max=10 < x < 1 ij
ij
The triangular norm is employed to depict the degree of membership for all elements in a specific fluidized system. The eightdimensional triangular norm T8 could be expressed as follows:
u2
u3
u4
u5
f1 f2 f3 f4 f5 f6 f7 f8 Aðui Þ
0.45 0.36 0.63 0.65 0.86 0.89 0.38 0.35 6.75 103
0.96 0.92 0.94 0.90 0.75 0.96 0.88 0.85 0.40
0.13 0.28 0.55 0.95 0.86 0.73 0.75 0.32 2.86 103
0.19 0.37 0.74 0.92 0.84 0.90 0.44 0.25 3.98 103
0.99 0.99 0.98 0.96 1 0.95 0.96 1 0.84
8 Y j¼1
u1
(
T 8 ðBðf1 Þðui Þ; Bðf2 Þðui Þ; . . . ; Bðf7 Þðui Þ; Bðf8 Þðui ÞÞ ¼
Bðfj Þðui Þ
tion degree. Solids holdup fluctuations signal obtained in the C-TFB was randomly selected to get the mean values of membership function shown in Table 3.
Bðfj Þðui Þ
ð14Þ
Aðui Þ Bð1Þð1ðui ÞÞ
¼ T 8 ðBðf1 Þðui Þ; Bðf2 Þðui Þ; . . . ; Bðf7 Þðui Þ; Bðf8 Þðui ÞÞ
ð15Þ
where the degree of membership for all elements Aðui Þ was calcu lated to identify whether the flow regime in the C-TFB is distinct from other regimes, including the bubbling, turbulent, fast fluidization and DSU flow regimes according to the principle of the degree of maximum membership.
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The results of Aðui Þ according to the signal information of C-TFB are presented in Table 3. It is obvious that the percentage of membership degree remains at a low level for the former four flow regimes, which indicates that flow regime in C-TFB is supposed to belong to a novel flow regime independently separated from other known flow regimes. It is worth noting that C-TFB fluidization is mostly similar to turbulent flow regime, which is consistent with the results discussed above. Another important information was found that the flow regime in the C-TFB is near turbulent flow regime on lower decomposition levels and similar to that in circulating fluidized bed on higher decomposition levels, which indicated that flow dynamics are consistent with turbulent state in terms of micro-flow mechanism and represent features of circulating fluidized bed from the aspect of outline information to some extent. At the same time, it illustrated that why different researchers made distinctive conclusions about this flow regime on the micro or macro level. Combined the results of this paper and other research groups, the flow dynamics in this diameter-expanding riser can be illustrated clearly: when solids leave from the bottom region of riser forming dense suspension upflow regime [12,15], it has a trend to form turbulent fluidization since the diameter-expanding structure leading to low superficial velocity (1–3 m/s) [9,12]. However, gas in circulating fluidized bed system provide adequate power to drive the solids continuously go upward into the fast fluidization in the top of the riser, combined with high density conditions in the diameter-expanding part, resulting in particles mostly upward (slightly downward near the wall) which is different from turbulent fluidization with severe solids back-mixing (particle velocity remaining 3 to 3 m/s) [40,41]. 5. Conclusion Given the restriction of traditional flow regime analysis including operating conditions’ relationship and solids holdup and tracer profiles in the reactor, the original solids holdup fluctuating signals have been analyzed by the PDD curves, amplitude spectra through Fourier transform and wavelet transform analysis. Fluctuations’ characteristics including violent particle–particle interactions and fluctuations signal outline in C-TFB are consistent with TFB and DSU regimes respectively. From the PDD curves analysis point of view, the existence of two peaks is different from other flow regimes except for the turbulent fluidization, indicating that the coexistence of voids and dense emulsion. The wavelet transform separates the signal into 9 scales and the dominant scale of multi-resolution decomposition is 8th. Peak points count profiles of the dominant scale indicates that the bubble coalescence and breakup frequency (gas–solids contact efficiency) are improving and the interaction between gas and solids phases is intensive. It means this novel flow regime has features distinct from other regimes, such as intensive gas–solids interaction, high contact efficiency, and a decreasing extent of separation between gas and solids phases. The flow regime identification was performed by combining the fuzzy recognition membership method with wavelet analysis results (energy percentage profiles with unique characteristics). It allowed concluding that the flow regime in C-TFB is different from other known flow regimes and that flow dynamics in the C-TFB belong to a novel flow regime. Acknowledgements The authors gratefully appreciate the financial support of the National Program on Key Basic Research Project (973 Program) of China (No. 2012CB215000).
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Contents lists available at ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Flow regime identification in a novel circulating-turbulent fluidized bed Qiang Geng a, Xiaolin Zhu a, Jie Yang a, Xinghua You b, Yibin Liu a, Chunyi Li a,⇑ a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum (East China), Qingdao 266580, China Petrochemical Factory of the Yumen Oil-Field Company, PetroChina, Yumen 735200, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Flow behavior in C-TFB was a novel
The gas–solids flow dynamics especially flow regime in a circulating-turbulent fluidized bed (C-TFB) compared with other traditional flow regime were studied. Traditional original signal processing and novel wavelet analysis method were utilized to identify different flow regimes. Fuzzy system recognition method combined with wavelet analysis results were employed to judge whether flow regime in the C-TFB was a novel flow regime.
regime on the micro-level. Wavelet analysis was utilized to analyze the flow dynamics. Wavelet energy was obtained as unique features of flow regimes. Flow regimes were recognized by fuzzy system identification method. The C-TFB optimizes flow dynamics and gas–solid contact efficiency.
a r t i c l e
i n f o
Article history: Received 9 June 2013 Received in revised form 7 January 2014 Accepted 31 January 2014 Available online 8 February 2014 Keywords: Multiphase flow Wavelet analysis Fuzzy system identification analysis Circulating-turbulent fluidized bed Flow regime identification
a b s t r a c t Whether flow dynamics in a novel circulating-turbulent fluidized bed (C-TFB) belongs to a new flow regime or just a transition state is controversial. In order to resolve this confusion, transient fluctuation signal processing and wavelet analysis have been used to identify the flow regimes in five specially designed flow systems, which have been proven to be effective tools to extract detailed information of flow features in different flow regimes. Furthermore, the fuzzy system identification method, which was used to process wavelet energy data of various scales obtained by wavelet analysis, was employed to make a quantitative distinction among the flow regimes. The results showed that the flow regime in the C-TFB is a novel flow regime, which is different from traditional flow regimes such as bubbling, turbulent, fast fluidization (FF) and dense suspension up-flow (DSU) regimes. The new regime has some unique characteristics including intensive gas–solids interaction, high gas–solids contact efficiency, two peaks of probability density distribution (PDD) curves in the center of the fluidized bed, broader spectrum of solids holdup for PDD curves, a decreasing extent of gas–solids separation extent and unique radial detail wavelet energy percentage profiles. Quantitative analysis by the fuzzy system identification method further confirmed that the flow behavior in the C-TFB can be described as a novel flow regime. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction ⇑ Corresponding author. Tel.: +86 532 86981862; fax: +86 532 86981718. E-mail address: [email protected] (C. Li). http://dx.doi.org/10.1016/j.cej.2014.01.102 1385-8947/Ó 2014 Elsevier B.V. All rights reserved.
Circulating fluidized beds have not been restricted to traditional application areas such as coal combustion, FCC and gasification of
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Nomenclature a ai b di/Di Di dp E f Gs j J
dilation factor outline coefficient of discrete wavelet transform translation factor detail coefficient of discrete wavelet transform detail decomposition scale diameter of particle, lm wavelet energy sampling frequency, Hz solids flux, kg/m2s multi-resolution level the maximum level of transform
biomass [1,2]. The derived diameter-expanding riser has been adopted for industrial processes: Maximizing Iso-Paraffins process [3] and Two-Stage Riser Catalytic Cracking for Maximizing Propylene process [4]. The concept of circulating-turbulent fluidized bed (C-TFB) or multi-regime riser was proposed based on this diameter-expanding riser [5–7]. Several aspects of this diameter-expanding riser have been discussed in detail, including solids holdup, particle velocity, possibility density, local solids flux profiles [5,8], instantaneous solids holdup and intermittency index analysis [9]. The results showed that its flow behavior combines the flow characteristics of high density circulating fluidized bed and turbulent fluidized bed [10]. However, further systematical experimental and theoretical analyses of the flow regime in the C-TFB are lacking. Furthermore, different researchers have distinctive understanding about the flow regime in this diameter-expanding riser, which has been summarized in Table 1 [5–12]. Its flow dynamics was identified as dense suspension upflow (DSU) regime, expressed by operating conditions (Gs and Ug) [11] The macro-analysis including operating conditions’ relationship, solids holdup and tracer profiles, which is commonly used in flow regime diagram [11,13], cannot identify this novel flow regime from that in the bottom part of a traditional riser and a high density circulating fluidized bed [14,15]. Thus, it may be a good way to gain in-depth knowledge of a flow regime by micro-signal analysis including transient fluctuation signal processing and wavelet analysis as well as micromechanics of different particle–fluid flow regimes [16–19]. However, only a few reports covered original signal processing in C-TFB. There is lack of systematic in-depth extension at signal analysis [5,8–12], which leads to different conclusions about the flow regime in the C-TFB. This is because a fluidized bed is a complex system exhibiting multi-scale behavior, which leads to multiple components in the original time series [20,21]. The heterogeneous flow dynamics in a fluidization system, especially in this novel C-TFB, is far from being understood. Wavelet analysis, which is found to clarify the complicated structure of particle fluidization, offers an appropriate method to extract the features of such multi-scale flow behavior [19,22]. It has attracted wide attention in the field of engineering applications combined with mathematics [23–25]. The wavelet multiresolution analysis enables the signal data to be decomposed and recomposed quantitatively due to the orthonormal transform. According to wavelet transform, the original signals can be resolved into multi-resolution signals with different frequency bands. Corresponding quantitative information, including peak frequency and wavelet energy can be obtained. According to these characteristics, the wavelet transform method has been applied to investigate multi-scale flow behavior in different flow regimes. Detail wavelet signals were directly related to bubble phenomena, reflecting the information of bubbling frequency size [22,25]. Turbulent kinetic
k P T Ug
time shift detail wavelet energy percentage time, s superficial velocity, m/s
Greek letters es solids holdup at a radial position esmf solids holdup at minimum fluidization conditions es average solids holdup in one cross section qp particle density, kg/m3 W(x) wavelet basis function
energy in a turbulent boundary layer of a gas–liquid flow system was analyzed [26]. A criterion was set up to separate the original signal into the dense phase and the dilute phase by identifying the transition points between the two phases [27]. A large number of factors affect the flow regime, which results in no definite boundary in the process of flow regime transition. It means that flow regime identification is a fuzzy recognition division process. The fuzzy system identification method is a good way to identify the flow regime. It was initiated by Zadeh [28] to provide a scheme for handling a variety of problems, especially applying it to an indefinite one that arises more from a sort of intrinsic ambiguity than from a statistical variation. The fuzzy system identification method, which has been employed to predict and control different systems [29,30], was proved effective to solve the flow pattern identification problem when aided by other tools such as electrical capacitance tomography [31], impedance-based tomography [32]. However, its application to fluidization systems was rarely reported. From the above discussion, it is clear that systematic work on micro-signal analysis should be conducted and that a kind of unified method needs to be constructed to identify the flow regime quantitatively. This paper adopts signal processing, including probability density distribution (PDD) curves, amplitude spectra and peak points count to depict flow regime identification. We use wavelet transform analysis combined with the fuzzy system identification method to form a unified way to identify the bubbling, turbulent, dense suspension upflow, fast fluidization flow regimes and the flow regime in C-TFB. In this way we can judge whether the flow behavior in C-TFB is novel in comparison to the four known flow regimes. 2. Experimental The experiments were conducted in a specially designed system, consisting of multi-purpose units, schematically shown in Fig. 1. The system consisted of a hopper tank, a measuring tank, a riser, air distributors, and a disengager. The riser made out of plexiglass had a diameter of 0.1–0.2 m and a height of 10.06 m. The whole riser could be divided into three different parts: (1) the pre-lifting section (0.0–0.8 m) with a bottom multi-hole air distributor; (2) the multi-purpose section (0.8–2.6 m); (3) the conveying section (2.6–10.06 m). The plexiglass tube in the multi-purpose section could be easily exchanged depending on experimental purposes to achieve different types of fluidized beds. Fig. 1(a)–(c) represents a circulating fluidized bed, a bubble/turbulent fluidized bed and a circulating-turbulent fluidized bed respectively. Information about the fast fluidization (FF) regime and the dense suspension upflow (DSU) regime are indicated in Fig. 1(a) under different operating conditions. By controlling the gas velocity as indicated in Fig. 1(b) we could model bubbling flow regime and turbulent flow
495
Negative particle velocity near the wall; solids back-mixing near the wall Turbulent fluidization; dense suspension up-flow
Not given [6,7]; turbulent regime [16]; dense suspension up-flow [11] To be confirmed [10]; circulating-turbulent fluidization regime [5,8,9]
Other flow regimes as reference Flow regime
Micro-flow behaviors
Top diameter-expanding structure [5,8–10] 1–3 50–500 0.2–0.3 Uniform axial and radial solid holdup profiles; mainly dominated by dense phase Periodic motion at 1–3 Hz; intense particle–particle and particle–gas interaction Particles mostly upward near the wall; nearly no solids back-mixing Turbulent fluidization; dense suspension up-flow; fast fluidization Structure of riser Ug (m/s) Gs (kg/m2s) Overall solid holdup Macro-flow behaviors
Table 1 Key features of diameter-expanding riser with different research groups.
Bottom diameter-expanding structure [6,7,11,12] 1–2 200–400 0.2–0.4 Uniform axial and radial solid holdup profiles; mainly dominated by dense phase; optimizing the oil–catalyst contact Periodic motion at 1–3 Hz; intense particle–particle and particle–gas interaction
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regime when the circulating system was blocked by a shut-off butterfly valve. Finally a circulating-turbulent fluidized bed was achieved by changing the diameter of the riser from 0.1 m to 0.2 m in the multi-purpose section. In order to simulate gas–solid flow behavior of the stratified injection, consistent with industrial application, upper and lower feed units were used with heights of 0.8 m and 3.6 m above the bottom of the riser respectively. The lower feed unit contained a ring-feeder internal to improve the gas–solid interaction. The ring-feeder internal was designed with 12 nozzles at an angle of 90° to the internal underneath. Moreover, 4 nozzles were fixed symmetrically for the upper feed part. The operational processes have been described in detail in a previous paper [11]. Particles used in the experiments were FCC catalysts with a mean diameter dp of 80 lm and particle density qp of 1780 kg/m3. The size distribution of the FCC particles measured by a BT-9300ST laser particle size analyzer was normal (Fig. 2). The solids flow rate (Gs) was determined based on a specially designed measuring tank system, by measuring the height difference after a sudden close of a butterfly valve within certain time intervals to calculate the Gs value. The solids holdup information was obtained in our experiments by PV-56 D optical fiber probes developed by the Institute of Processing Engineering, Chinese Academy of Sciences. The probe, whose diameter was 4 mm, consisted of two sub-probes each with an effective tip area of 1 1 mm. Each of the two sub-probes included a bunch of quartz fibers arranged in square shape. The gap between the two sub-probes was 1.67 mm, and each probe was composed of light-emitting and receiving quartz fibers (25 lm in diameter) arranged in alternating array. 0.2 mm glass film covers were placed over the two sub-probe’s tips to prevent solids from occupying the probe’s blind zone. When sampling, the probe would emit light to the particles, and receive light reflected by the particles at the same time. The optical signals were converted into voltage signals by a photo-multiplier and fed to a PC. Before use, the fiber probes were calibrated to convert the voltage signals to the solids holdup fluctuations before used. The conversation from voltage signal to solids concentration signal is shown in Fig. 3. In each experimental run, the solids holdup fluctuations signal was sampled at a rate of 1000 Hz for 16 s, thereby yielding 16,000 data points. 3. Discrete wavelet transform principle Wavelet transform is a novel mathematical tool for analyzing multiphase systems including fluidized beds by signal processing [22,25,27]. Discrete wavelet transforms are utilized to transform a one-dimensional time series into a two-dimensional region displaying wavelet coefficients amplitudes as a function of both time and frequency. This approach makes it possible to analyze frequency while remaining time and space information [33]. In this paper the Daubechies wavelet was used as the basic wavelets to make sure of the precise signal analysis with higher order of polynomials utilized for approximation for its highest number of vanishing moments for a given support width [34]. The basic wavelet function can be set as W(x) with dilation factor a and translation factor b. Integer wavelet transform (IWT) for function f(x) e L2(R) was defined by the following equation:
1 WT x ða; bÞ ¼ pffiffiffi a
Z
1
1
f ðxÞW
xb dx a
ð1Þ
The corresponding algorithm of the discrete dyadic wavelet transform is given below:
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Fig. 1. Schematic diagram of experimental apparatus, including three different flow systems (a–c).
Fig. 2. Powders’ particle size distribution.
j
WT x ðj; kÞ ¼ 22
Z
1
f ðxÞWð2j x kÞ dx j; k 2 z
ð2Þ
1
where the time shift k ranged from 1 to N/2j and the level j changed from 1 to J. J was the maximum level of transformation, which was determined by W(x) and N. For computer sampling of the digital signal, the discrete dyadic wavelet transform (DWT) can be obtained by the Mallat algorithm [21].
f ðxÞ ¼ AJ1 f ðxÞ ¼
J2 X X C J1 ;k /J1; k ðxÞ ¼ A2 f ðxÞ þ Dj f ðxÞ k2Z
AJ2 f ðxÞ ¼
X C J2 ;k /J2 ;k ðxÞ
ð3Þ
j¼J 1 þ1
ð4Þ
k2Z
Dj f ðxÞ ¼
X Dj;k Wj;k ðxÞ
ð5Þ
k2Z
C jþ1;k ¼ ðHC j Þk ¼
X hl2k C j;k l2Z
ð6Þ Fig. 3. The relationship between solids holdup signal and voltage signal.
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Djþ1;k
X ¼ ðGC j Þk ¼ g l2k C j;k
ð7Þ
l2Z
C jþ1;k ¼ HC j ;
Djþ1;k ¼ GC j
ðj ¼ J 1 KJ 2 1Þ
ð8Þ
After multi-resolution analysis by the Mallat algorithm, the original signal was decomposed into various scales of orthogonal signal components, which were combined with approximation subsignal A2f(x) (4) with low frequency band (
Fig. 4. Plots of multi-resolution decomposition of the solids holdup fluctuations signals.
A thorough investigation of the micro-phase structures would be helpful to better understand the hydrodynamics of different flow regimes. The typical solids holdup fluctuations reflecting the flow features of the bubbling flow regime (Ug = 0.2 m/s), the transition flow regime (Ug = 0.4 m/s), the turbulent flow regime (Ug = 0.8 m/s), the fast fluidization regime (Ug = 12 m/s, Gs = 173 kg/m2s), the dense suspension upflow regime (Ug = 12 m/s, Gs = 400 kg/m2s) and the flow regime in C-TFB (Ug = 12 m/s,
Fig. 5. Comparisons of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m).
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Gs = 400 kg/m2s) were shown in Fig. 5. Generally, the solids holdup fluctuations showed the coexistence of voids and dense emulsion covering bubbling regime, transition flow regime, turbulent flow regime and flow regime in the C-TFB with solids holdup at minimum fluidization, esmf = 0.52. The magnitudes of the solids holdup fluctuations in the FF and DSU regimes are much lower, which indicated that the flow regimes are dominated by the gas phase. At a lower gas velocity of 0.2 m/s in the bubbling regime, solids holdup fluctuations remain 0 and 0.52 alternatively. Dense emulsion appears at the maximum magnitude, while fluctuations sharply drop near to zero representing the appearance of bubbles. The magnitude of the fluctuations reflects the effect of interactions between bubbles and solids. With a further increase of the superficial gas velocity from 0.4 to 0.8 m/s, well within the transition and turbulent flow regime, the magnitudes of the fluctuations decrease slightly and a higher fluctuations frequency is observed, which indicates that a series of bubbles coalesce and break quickly. It is consistent with the phenomenon depicted by Du et al. [35] and the mechanism explained by Cai et al. [36]. Comparisons between the FF and DSU regimes have been done systematically to identify some unique characteristics in the DSU regime such as upflow of particles at the wall, higher solids holdup, more uniform axial and radial solids holdup profiles [14]. The time series of instantaneous solids holdup in the FF and DSU regimes are somewhat similar that both of them are lack of voids or bubbles. Due to the specific operating conditions of higher solids fluxes and superficial velocities in the DSU regime, the mean solids holdup es is much higher than that in the FF regime. From a fluctuations analysis point of view, solids holdup fluctuations in the C-TFB share dual characteristics of violent particle– particle interactions consistent with TFB and fluctuations signal outline similar to DSU regime in spite of higher solids holdup in C-TFB, which has been confirmed and reflected by other researchers. Flow dynamics in the C-TFB was identified as dense suspension upflow (DSU) regime at a macro-level expressed by operating conditions (Gs and Ug) [11]. Qi et al. defined it as a novel circulatingturbulent fluidization regime at a micro-level [9] with uniform flow structure (axial and radial solids holdup profiles), upflow of particles profiles similar to the DSU regime and higher solids holdup, higher gas–solid contact efficiency similar to the TF regime. Gas–solid separation, contact and mixing are different in each flow regime. The probability density distribution (PDD) was obtained by MATLAB processing to get more information about the phase structures, which reflected the interaction between phases and properties of fluctuations in the frequent domain as shown in Fig. 6, for two typical radial positions (r/R = 0, r/R = 0.8). In general, two peaks are found in the PDD curves, one represents bubble/dilute phase with solids holdup between 0 and 0.08 and the other at a higher solids holdup of 0.4–0.55 for the dense phase. It is obvious that the gas phase tends to pass through the center and that the particles are likely to aggregate near the wall. This core-annulus structure aroused by the wall effect resulted in a significant difference of the PDD at radial positions. With radial position moving towards the wall, the peak shifts from the bubble/ dilute phase to the dense phase with a broader density distribution. Due to separation of the gas phase from the solids phase, the gas–solid interaction is worse for the FF and DSU regime in CFB, as indicated by Lin et al. [17] and Zhu and Zhu [8]. This narrow range of solids concentration distribution in the center and near the wall of the riser represented that the dilute gas–solids suspension is mainly composed of gas phase whereas the dense solids suspension is mainly composed of solids phase [12]. This flow structure is not good for mass/heat transfer due to low gas–solid contact efficiency. In contrast to the FF and DSU regimes, the broad and continuous spectra of solids holdup are found in the bubbling
Fig. 6. Comparisons of probability density distributions of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m) under different operating conditions.
flow regime, turbulent flow regime and flow regime in C-TFB, indicating the decrease of radial solids holdup gradient and the improvement of solids holdup distribution uniformity. It was noted that the peak of PDD curves in dilute phase is near 0 and that in the dense phase is 0.54, which is near the solids holdup at minimum fluidization esmf in the bubbling flow regime. It indicates that gas and solid phases have bad contact efficiency. Interaction between the gas–solids phases in the flow regime of C-TFB is similar to the turbulent flow regime observed from PDD curves. Two peaks exist in the PDD curves when the sampling position was in the center of the fluidized bed, which is different from other flow regimes except for the turbulent fluidization, indicating the coexistence of dilute and dense phases at the center radial positions. Continuous variation in solids holdup revealed that gas–solid separation weakens, more gas enters the dense phase and more particles are contained between gas phases. Gas–solid contact efficiency is improved due to intensive gas–solid interaction, which is consistent with the previous result that the contact efficiency is better in C-TFB than that in HDCFB (high density circulating fluidized bed) at macro-level [11]. Although radial profiles of time-mean particle velocity in the C-TFB have proved that no solids back-mixing and particles flowing mostly upward are characterized as unique features, which are different from those in TFB [8,9,12], there is a lack of method or criterion to identify the flow regime by fluctuating signals at the micro-level, except for the slightly broader spectrum of solids holdup for PDD curves in the C-TFB. To get in-depth knowledge about the flow regime characteristics in C-TFB distinct from others, amplitude spectra by means of fast Fourier transform was obtained to demonstrate the periodicity of the signal fluctuations, and comparative results were plotted in Fig. 7. It is noteworthy that different flow regimes are characterized by a certain dominant frequency, which could be utilized as one method to identify the flow regime. With an increase in the
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Fig. 7. Comparisons of power spectral density distributions of transient solids holdup fluctuations of different flow regimes at the same axial height (z = 1.74 m) under different operating conditions.
gas velocity from 0.2 to 0.8 m/s representing bubbling flow regime and turbulent flow regime respectively, the dominant frequency decreased from 3 to 1 Hz, while the spectral energy further increased [16,25,36,37]. The dominant frequency is very low and the spectral energies are distributed over a broad frequency range, and no clear dominant frequency is observed in the center of the low/high density circulating fluidized bed riser for both FF and DSU regimes [38], suggesting a lower degree of periodic particle motion. The dominant frequency occurs at 1 Hz for flow regime in C-TFB, indicating that its characteristics may be similar to those in the turbulent flow regime. From the above discussions, it can be concluded that original signal analysis is restricted to identify flow regimes, especially for the distinction between the turbulent flow regime and the flow regime in C-TFB. This is because a fluidized bed is a complex system and, by only analyzing signals obtained with optical fibers, one can get more detailed information. Therefore, wavelet transforms are introduced to extract the features of such multi-scale behavior by resolving the original signals into multi-resolution signals with different frequency bands. 4.2. Wavelet transform analysis As stated about the discrete wavelet transform principle in Section 3, the wavelet transform separates the signal into 9 scales, where D1 and D2 represent detail components that reflect the fine scale features and the coarse scale components D8 and D9 correspond to lower frequency oscillations or outline information. Fig. 8 shows the plots of the multi-resolution decomposition of
the solids holdup fluctuation signals in five flow regimes, typical D5–D8 scale components revealing the transition from detail to outline information. The dominant scale over the sampling time is the D8 scale, which could reflect the interaction between bubble/dilute phase and dense phase. It is noteworthy that although detail decomposition signals for the flow regime in the C-TFB are similar to those in the turbulent flow regime, as shown in Fig. 8(a), some differences were also found. The amplitude slightly decreased in the C-TFB, which indicated that the bed has a smaller bubble corresponding to higher gas–solid interaction and contact efficiency. On the other hand, the amplitude was dramatically enhanced compared to the flow regimes in traditional circulating fluidized bed according to the plots of Fig. 8(b). This could be attributed to higher solids holdup and lower local particle velocity in the C-TFB. In order to make clear which factor dominated flow dynamics in the C-TFB CFB from the perspective of interaction between dilute phase and dense phase, dominant detail wavelet signal peaks were processed by a unique method. As shown in Fig. 9, the peak points of dominant scale D8 found by origin software were divided into three sections, a bubble peak points (BPP) zone, a turbulent peak points (TPP) zone and a dilute peak points (DPP) zone according to the amplitudes (the absolute boundary condition is 0.24 and 0.12). The width, height, and minimum height of a pick-peaks toolbar were 0.50, 9.00 and 5.00 respectively. The number of bubbling peak points, turbulent peak points and dilute phase peak points were obtained by summing for consecutive 16 s in different flow regimes. At the same time, the average peak frequency was
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Fig. 8. Plots of multi-resolution decomposition for signal in C-TFB compared with that in other flow regimes.
Fig. 9. Category of multi-resolution decomposition peaks for scale 8 detail wavelet signal.
obtained by summing the number of peak points and dividing this sum by the sampling time. Since all signals were sampled within the same time, peak points count was applied to interrupt gas–solid interaction. Peak points count profiles in different flow regimes presented in Fig. 10 shows that the regulation of peak points count profiles in CTFB is between that in turbulent fluidized bed and DSU bed. The bubble size is much smaller in the C-TFB than that in the turbulent fluidized bed, which indicates that the bubble coalescence and breakup frequency are improving and the interaction between gas and solids phases is intensive. Vigorous gas radial exchange between the dilute and dense phases due to breakdown of slugs into smaller voids improves the gas–solids contact efficiency [39]. On the other hand, the dilute phase peak points count is much smaller than that in the DSU fluidized bed, which reflects that the extent of gas–solids separation between gas and solids phases decreases. This means that the coexistence of dilute phase and dense phase in the C-TFB is an important feature rather than the traditional core-annulus flow structure in the DSU fluidized bed.
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different flow dynamics. Further work has been done to identify the flow regime quantitatively by one unified method based on the above recognition results, by combining the fuzzy system recognition method and the wavelet analysis in the analysis of the flow regime identification problem. Finally, the flow regime membership degree was calculated to judge whether the C-TFB belongs to a novel flow regime or not. A series of calculations have been done including a large range of operating conditions, Ug = 0.15–1.2 m/s without circulating system and Ug = 6–14 m/s, Gs = 100–400 kg/m2s with circulating system and different sampling positions to find some unique characteristics reflecting different flow regimes in detail. Because the wavelet spectrum function is the energy distribution, the 9 scales wavelet energies are obtained from the coefficients of the discrete wavelet transform, which is defined as:
E¼
X
D2j;k þ
j;k
Ej ¼
X 2 Dj;k
X 2 C J2 ;k
J1 1 6 j 6 J2
ð9Þ
k
J1 1 6 j 6 J2
ð10Þ
k2Z
Fig. 10. Peak points count versus three different peak types.
Lu and Li [22] indicated that the bubbling frequency was directly proportional to (Ug Umf)0.2 and that the average peak value of the dominant scale detail signal was proportional to (Ug Umf)0.4 as well for the bubbling flow regime. The bubbling peak points were extracted from bubbling and turbulent flow regimes within superficial velocity from 0.15 to 1.2 m/s. Indeed, it was obvious that peak point count is directly proportional to (Ug Umf)0.2, however, bubbling peak points for flow regime in the C-TFB were under the line as shown in Fig. 11. This phenomenon also proved that larger bubbles in this novel flow regime decrease significantly, to put it another way, smaller bubbles are dominant in the C-TFB. Based on the above analysis, it could be deduced that the characteristics in the C-TFB could be defined as a novel flow regime whose flow dynamics are much better than that in turbulent and DSU flow regimes. 4.3. Flow regime fuzzy system recognition According to the experimental observations summarized above, the typical signal processing results and multi-resolution decomposition scale signal information reflected certain features of
Fig. 11. Peak points count versus (UgUmf)0.2.
where E is the total energy of the sampling signal and Ej is the energy of detail signal in different decomposition scales. In order to represent the system features based on different scales energy characteristic, energy percentage of detail signal, P is also defined here to reflect system energy information.
Pj ¼
Ej E
ð11Þ
Wavelet energy profiles with different decomposition scales are plotted in Fig. 12. With the change of radial sampling position from the center of the bed to the wall, the scale of wavelet energy percentage peak is transformed from fine scale to coarse scale, indicating that more clusters are inclined to aggregate near the wall. At the same time, the wavelet energy percentage decreases for turbulent, DSU flow regimes due to dense-phase dominant near the wall. The peak point occurs at the 4th scale position for the FF regime rather than at the large scale for DSU flow regime, which showed that relatively higher velocity and lower solids holdup is not conductive to larger bubbles formation. The wavelet energy percentage profiles remain nearly constant from center to the wall for flow regime in the C-TFB, which indicates that fully gas–solids interaction results in uniform solids holdup profiles at radial positions. Different flow regimes have their own curve characteristics, theoretically, if a specific signal is chosen to decompose, any scale could be used to detect the difference of flow regimes. However, some problems would be aroused in practice because if too many scales are chosen, recognition of the flow regime would be complex; in contrast, few scales may result in less exact and precise information. Through analysis of Fig. 12, detail energy percentage of D3, 4, 5, 6, 7, 8, 9 and total energy results obtained in the center of the fluidized bed were chosen as criteria to identify the different flow regimes, since the features of detail energy percentage profiles are distinct for each flow regime in the center of the reactors. While the characteristic of signal fluctuations near the wall is likely to be not obvious due to the solids aggregation, higher solids holdup. The pipe wall electrostatic effect may influence the accuracy of signal values obtained near the wall, which is not beneficial to the fuzzy identification. Detail energy percentage profiles in different decomposition scales would be overlapping, which reflected that flow regime transition is a fuzzy and gradual process. The identification processes are summarized as following several steps with the fuzzy system identification method [31]. The bubbling, turbulent, fast fluidization, DSU, C-TFB flow regimes can be replaced by symbols u1, u2, u3, u4, u5 respectively forming the universe of discourse U = {u1, u2, u3, u4, u5}. In this flow
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Fig. 12. Wavelet energy percentage profiles with different decomposition scales.
Table 2 Typical wavelet energy profiles of different flow regimes. Flow regime
u1
u2
u3
u4
u5
f1 f2 f3 f4 f5 f6 f7 f8
(1–9) 104 (1–5) 103 (1–8) 103 0.01–0.03 0.04–0.05 0.04–0.08 0.01–0.04 5000–7000
(1–7)103 0.01–0.03 0.01–0.05 0.03–0.06 0.04–0.08 0.04–0.08 0.05–0.10 2000–3000
0.04–0.05 0.06–0.13 0.06–0.12 0.03–0.05 0.04–0.05 0.02–0.06 0.01–0.05 20–80
0.02–0.03 0.03–0.06 0.03–0.07 0.03–0.07 0.06–0.09 0.06–0.11 0.11–0.21 50–100
(1–7)103 0.01–0.03 0.01–0.05 0.03–0.05 0.03–0.06 0.04–0.08 0.04–0.11 1000–2000
(P3, (P4, (P5, (P6, (P7, (P8, (P9, (E)
%) %) %) %) %) %) %)
regime identification system, the recognition process, according to wavelet analysis results, includes detail energy percentage of D3, 4, 5, 6, 7, 8, 9 and total energy data in different flow regimes, which are represented symbolically by f1, f2, f3, f4, f5, f6, f7, f8, and can be recognized to reflect characteristics of typical flow regimes in different operating conditions. This information is defined as a mathematical object, which is given by F = {f1, f2, f3, f4, f5, f6, f7, f8} in which each element stand for energy scope since every flow regime can be achieved within different operating conditions as shown in Table 2. Then the membership function Bðfj Þ should be defined to ex press the degree of membership, which indicates the degree of possibility. It is supposed to meet the boundary conditions and be expressed as the following form, where is a special operative symbol, which applied to transform x to another form m 10n in which the value of m ranged from 0.1 to 1 (not including 1) and is extracted as new value of x in order to form a reasonable distincTable 3 The membership function Bðfj Þðui Þ and membership degree Aðui Þ lists.
Bðfi Þð0Þ;
Bðfi Þð1Þ ¼ 0
ð12Þ
BðxÞ ¼ 1; min 6 x 6 max
ij
8 x > > =10n > min > < ij Bðfi Þ ¼ 1 > > > 1x > : 1max=10n
ij
0 < x < min=10n ij
min 6 x 6 max ij
n
ð13Þ
ij
max=10 < x < 1 ij
ij
The triangular norm is employed to depict the degree of membership for all elements in a specific fluidized system. The eightdimensional triangular norm T8 could be expressed as follows:
u2
u3
u4
u5
f1 f2 f3 f4 f5 f6 f7 f8 Aðui Þ
0.45 0.36 0.63 0.65 0.86 0.89 0.38 0.35 6.75 103
0.96 0.92 0.94 0.90 0.75 0.96 0.88 0.85 0.40
0.13 0.28 0.55 0.95 0.86 0.73 0.75 0.32 2.86 103
0.19 0.37 0.74 0.92 0.84 0.90 0.44 0.25 3.98 103
0.99 0.99 0.98 0.96 1 0.95 0.96 1 0.84
8 Y j¼1
u1
(
T 8 ðBðf1 Þðui Þ; Bðf2 Þðui Þ; . . . ; Bðf7 Þðui Þ; Bðf8 Þðui ÞÞ ¼
Bðfj Þðui Þ
tion degree. Solids holdup fluctuations signal obtained in the C-TFB was randomly selected to get the mean values of membership function shown in Table 3.
Bðfj Þðui Þ
ð14Þ
Aðui Þ Bð1Þð1ðui ÞÞ
¼ T 8 ðBðf1 Þðui Þ; Bðf2 Þðui Þ; . . . ; Bðf7 Þðui Þ; Bðf8 Þðui ÞÞ
ð15Þ
where the degree of membership for all elements Aðui Þ was calcu lated to identify whether the flow regime in the C-TFB is distinct from other regimes, including the bubbling, turbulent, fast fluidization and DSU flow regimes according to the principle of the degree of maximum membership.
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The results of Aðui Þ according to the signal information of C-TFB are presented in Table 3. It is obvious that the percentage of membership degree remains at a low level for the former four flow regimes, which indicates that flow regime in C-TFB is supposed to belong to a novel flow regime independently separated from other known flow regimes. It is worth noting that C-TFB fluidization is mostly similar to turbulent flow regime, which is consistent with the results discussed above. Another important information was found that the flow regime in the C-TFB is near turbulent flow regime on lower decomposition levels and similar to that in circulating fluidized bed on higher decomposition levels, which indicated that flow dynamics are consistent with turbulent state in terms of micro-flow mechanism and represent features of circulating fluidized bed from the aspect of outline information to some extent. At the same time, it illustrated that why different researchers made distinctive conclusions about this flow regime on the micro or macro level. Combined the results of this paper and other research groups, the flow dynamics in this diameter-expanding riser can be illustrated clearly: when solids leave from the bottom region of riser forming dense suspension upflow regime [12,15], it has a trend to form turbulent fluidization since the diameter-expanding structure leading to low superficial velocity (1–3 m/s) [9,12]. However, gas in circulating fluidized bed system provide adequate power to drive the solids continuously go upward into the fast fluidization in the top of the riser, combined with high density conditions in the diameter-expanding part, resulting in particles mostly upward (slightly downward near the wall) which is different from turbulent fluidization with severe solids back-mixing (particle velocity remaining 3 to 3 m/s) [40,41]. 5. Conclusion Given the restriction of traditional flow regime analysis including operating conditions’ relationship and solids holdup and tracer profiles in the reactor, the original solids holdup fluctuating signals have been analyzed by the PDD curves, amplitude spectra through Fourier transform and wavelet transform analysis. Fluctuations’ characteristics including violent particle–particle interactions and fluctuations signal outline in C-TFB are consistent with TFB and DSU regimes respectively. From the PDD curves analysis point of view, the existence of two peaks is different from other flow regimes except for the turbulent fluidization, indicating that the coexistence of voids and dense emulsion. The wavelet transform separates the signal into 9 scales and the dominant scale of multi-resolution decomposition is 8th. Peak points count profiles of the dominant scale indicates that the bubble coalescence and breakup frequency (gas–solids contact efficiency) are improving and the interaction between gas and solids phases is intensive. It means this novel flow regime has features distinct from other regimes, such as intensive gas–solids interaction, high contact efficiency, and a decreasing extent of separation between gas and solids phases. The flow regime identification was performed by combining the fuzzy recognition membership method with wavelet analysis results (energy percentage profiles with unique characteristics). It allowed concluding that the flow regime in C-TFB is different from other known flow regimes and that flow dynamics in the C-TFB belong to a novel flow regime. Acknowledgements The authors gratefully appreciate the financial support of the National Program on Key Basic Research Project (973 Program) of China (No. 2012CB215000).
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