solid fluidization in fluidized beds with different

Accepted Manuscript Characterization of gas–solid fluidization in fluidized beds with different particle size distributions by analyzing pressure fluctuations in wind caps Huawei Jiang, Hongwei Chen, Jianqiang Gao, Junfu Lu, Yang Wang, Cuiping Wang PII: DOI: Reference:

S1385-8947(18)30985-9 https://doi.org/10.1016/j.cej.2018.05.165 CEJ 19181

To appear in:

Chemical Engineering Journal

Received Date: Revised Date: Accepted Date:

31 January 2018 23 May 2018 27 May 2018

Please cite this article as: H. Jiang, H. Chen, J. Gao, J. Lu, Y. Wang, C. Wang, Characterization of gas–solid fluidization in fluidized beds with different particle size distributions by analyzing pressure fluctuations in wind caps, Chemical Engineering Journal (2018), doi: https://doi.org/10.1016/j.cej.2018.05.165

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Characterization of gas–solid fluidization in fluidized beds with different particle size distributions by analyzing pressure fluctuations in wind caps Huawei Jianga,b,*, Hongwei Chenb, Jianqiang Gaob, Junfu Luc, Yang Wangd, Cuiping Wanga,* a

b

Institute of Energy Engineering, Qingdao University, Qingdao 266071, China

Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Baoding 071003, China

c

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China d

Xi’an Thermal Power Research Institute Co., Ltd., Xi’an 710054, China

* Corresponding authors at: Institute of Energy Engineering, Qingdao University, Qingdao 266071, China (Cuiping Wang). E-mail addresses: jianghwwh@ qdu.edu.cn (Huawei Jiang), [email protected] (Cuiping Wang).

Abstract: For the operation of a fluidized bed, solid particle size distribution is related to fluid dynamic behaviors, heat transfer efficiency, combustion efficiency, and desulfurization performance. Measurement of pressure fluctuations has a great advantage for detecting fluidization and combustion conditions, due to its flexible adaption to any operating conditions. In this study, the measurement and analysis of pressure fluctuations in the inlet of a wind cap of fluidized beds were carried out, to investigate the effects of particle size distribution on the gas–solid fluidization behaviors. Pressure fluctuations in the inlet of central wind cap were measured at different primary air velocities in cold circulating fluidized beds with different particle size distributions. In order to obtain the corresponding characteristic parameters, pressure fluctuations were

analyzed by the methods including standard deviation, power spectral density estimation, wavelet analysis, and homogeneous index. Based on these characteristic parameters, the effects of particle size distribution on the gas–solid fluidization behaviors in fluidized beds were systematically analyzed. Variations of characteristic parameters of pressure fluctuations were found to be related to the variations of the gas–solid fluidization behaviors, which were caused by changes in particle size distribution or particle sizes. The results of this study indicate that the proposed method is practical, and the research achievements can be used as a theoretical basis for the condition monitoring of particle size distribution or the detection of agglomeration in fluidized beds based on pressure fluctuations in wind caps. Keywords: gas–solid flow; fluidized bed; wind cap; particle size distribution; pressure fluctuation 1. Introduction Circulating fluidized bed (CFB) boiler technology, as a reliable, economical, high-efficiency and low-polluting clean combustion technology, has made significant progress in the past two decades. It has several advantages, such as flexible and extensive fuel adaptability, high combustion efficiency, and high-efficiency desulfurization. In the furnace of a CFB boiler, fuel particles account for only 1–3% of total particles by weight [1], while other particles including incombustible solids particles, desulfurizer particles, ash residue particles and sands, are in the majority. Among them, particle sizes of fuels and inert bed materials are usually less than 8 mm with average value in the range of 1–1.5 mm. Particle sizes of desulfurizer are less than 1 mm. Thus, particles have a wide range of size in fluidized beds, rather than homogeneously-sized pulverized particles which are used in pulverized coal-fired boilers. The exceptional fluid dynamic behaviors of a fluidized bed ensure the good gas–solid mixing characteristics and solid–solid mixing characteristics. After being added into the furnace of a fluidized bed, fuels are mixed with a large number of bed materials and heated up to a temperature higher than ignition temperature, without any significant drop in the temperature of the bed materials. As long as the calorific value of the added fuels is higher than the heat quantity required for heating up the fuel and air mixture to the ignition temperature, any sort of fuels can be burned in a fluidized bed boiler without auxiliary fuels [2]. Good gas–solid mixing characteristics also lead to high combustion efficiency for fluidized beds [3], in particular, for the combustion of the coarse particles. A majority of unburned fuel particles can be recycled back

to the furnace, thus ensuring their continuous burning. This advantage permits the use of a wide size range for fuel and bed material particles in fluidized beds. Furthermore, a fluidized bed boiler is operated in the temperature range suitable for optimal desulfurization, and the residence time of desulfurizers in furnace can be significantly prolonged. This feature provides an excellent in-furnace desulfurization technology for the high-efficiency desulfurization of fluidized beds [4–7]. The solids in fluidized beds thus include desulfurizer particles as well, which make the size distribution of solid particles more complex. In view of these, particle size distribution of solids is not only related to fluid dynamic behaviors, gas–solid mixing characteristics, and solid–solid mixing characteristics, but also to heat transfer characteristics, combustion characteristics, as well as desulfurization characteristics in fluidized beds. Fluidized beds can be characterized by changes in the relative magnitude of pressure fluctuations. Pressure fluctuations in fluidized beds are dynamic reflections of various interactional factors, for instance, particle motion conditions [8–10], bubble behavior [11–17], geometrical structures of beds [18–20], operating parameters [14,19–21], and so on. Compared to other measuring methods, method involving measurement of pressure exhibits a great advantage. This method is especially suitable for measuring the actual operation of a boiler, as it can be used for the measurement and analysis of fluidization and combustion behaviors under any conditions. For this reason, many researchers have carried out relevant studies about the effects of particle sizes on the fluid dynamic behaviors and combustion characteristics, by pressure fluctuation measurement and analysis technique, for fluidized beds. Their research is mainly related to the following three fields: measurement of particle sizes or the average diameter of particles based on pressure fluctuations in fluidized beds [21–23], detection of early agglomeration in biomass fired fluidized beds using characteristic parameters of pressure fluctuation signals [24–34], and analysis of the relationship between mixed-firing characteristics of mixtures and particle size distribution based on pressure fluctuations in fluidized beds [35]. However, in all the above mentioned previous studies [22–35], the in-bed and wall pressure fluctuations were investigated, which were measured through wall-mounted pressure taps at a few locations along the furnace height. Unfortunately, these in-bed and wall pressure measuring points are exposed to the gas–solid flow such that they get easily blocked and worn out. As a result, the monitoring parameters obtained through these

measurements may not be reliable. Moreover, these related studies mainly focus on the effects of the macroscopic change of particle sizes or the change of mean particle size. However, the studies related to the effects of the shape change of particle size distribution have not been reported yet. Herein, this new technique involving the influences of the shape change of particle size distribution based on the analysis of pressure fluctuations on the fluid dynamic behaviors, gas–solid mixing characteristics, and solid–solid mixing characteristics of fluidized beds was reported. Furthermore, related articles have also confirmed that the pressure fluctuations of the inlet airflow of a wind cap are closely related to the pressure fluctuations of the outlet gas–solid flow of the wind cap [36]. The relationship between the pressure pci of the inlet airflow of a wind cap and the pressure pco of the outlet gas–solid flow of the wind cap, can be expressed as:

pci = pco + ∆pc

(1)

where ∆pc represents the pressure drop through a wind cap. Therefore, if the pressure taps are mounted at the inlets of wind caps, the problem caused by the blockages and wear of measuring points, can be easily solved. To address this issue in the present study, pressure fluctuations in the central wind cap, the inlet airflow and outlet gas–solid flow of which were less affected by the sidewall friction, were measured at different primary air velocities in a cold CFB with different particle size distributions. After eliminating trend components, pressure signals were analyzed or calculated by several methods such as standard deviation, power spectral density, the energy of typical low-frequency sub-signals and high-frequency sub-signals under a defined decomposition level, homogeneous index, and so on. Based on the characteristic parameters of pressure fluctuations, the effects of particle size distribution on the gas–solid fluidization characteristics in fluidized beds were analyzed. This study provides a new perspective to the understanding of gas–solid fluidization in CFBs with different particle size distributions by analysis of pressure fluctuations in wind caps. 2. Experimental section 2.1. Experimental apparatus This research was conducted using a cold CFB set-up consisting of a riser, a wind box, a distribution plate, bell-type wind caps located on the distribution plate with five rows and five columns, a cyclone and a bag filter

to separate the fines, a standpipe, a loop seal, two centrifugal fans, several flowmeters, several differential pressure sensor, and a data acquisition module. Fig. 1 shows the schematic representation of the CFB system used in this study. Detailed characteristics of equipment are listed in Table 1. Air at controlled flow rates was supplied to the riser with the cross-sectional dimensions of 0.288 m length, 0.288 m width, and 4 m height, from two series-wound centrifugal fans through a wind cap distribution plate having 5.1% open area. A small amount of air from the air bypass line was also sent to the loop seal to maintain it under minimum fluidizing condition. The riser, standpipe, and loop seal were made of transparent plexiglass, which makes it convenient for the visual observation of gas–solid flow regime in the bed. Solids used in this study were quartz sands with particle density of 2600 kg·m−3. Moreover, they were wide size range particles or narrow size range particles, with different particle size distributions. A uniform velocity tube flow meter with measuring range of 0–2000 m3·h−1 and flow uncertainty of ±2.00% was used to measure the primary air volume, and it was mounted at the primary air piping. For the measurement of pressure fluctuations in the wind cap, a pressure tap was mounted at the inlet tube wall of central wind cap below the distribution plate. However, for the wall-sampled measurements, pressure taps were mounted at different heights of backside wall of riser. Data acquisition system consisted of differential pressure sensors of type CGYL-300b, a data acquisition module of type USB7360, and a computer system. The differential pressure sensors were 0–15 kPa in measuring range, ±0.5% in degree of accuracy, and less than or equal to 1 ms in response time.

(1) centrifugal fan; (2) control valve; (3) uniform velocity tube flow meter; (4) rotameter; (5) wind box; (6) distribution plate; (7) wind cap; (8) wind cap pressure tap; (9) riser-wall pressure tap; (10) feed inlet; (11) secondary air inlet; (12) differential pressure sensor; (13) data acquisition module; (14) computer; (15) riser; (16) cyclone; (17) bag filter; (18) butterfly valve; (19) standpipe; (20) loop seal; (21) digital camera. Fig. 1. Schematic illustration of the experimental apparatus Table 1. Equipment characteristics Riser

Loop seal

Cyclone

Standpipe

Length = 0.288 m

Length = 0.225 m

Diameter = 0.348 m

Diameter = 0.09 m

Width = 0.288 m

Width = 0.112 m

Height = 1.44 m

Height = 1.648 m

Height = 4.0 m

Height = 0.25 m

Fig. 2 displays the distribution of wind caps on the distribution plate and the pressure measuring point fixed on the inlet wall of central wind cap. Structural diagram of wind caps and characteristic curve of the pressure drop through a wind cap are, respectively, shown in Figs. 3 and 4. Pressure drops between the inlet of middle wind cap in back row (shown on Fig. 2) and back-wall pressure tap at 0.1m height above the distribution plate, were measured at different gas velocities u without bed materials, which indicate the characteristics of pressure drop through a wind cap. The pressure drop through a wind cap exhibits a relationship with superficial gas velocity of primary air or gas velocity through an orifice of wind cap, which are quantified in formula (2). Gas velocity through an orifice of wind cap and perforated rate of wind caps can be, respectively, calculated by using formulas (3) and (4) as follows:

∆pc = ξ

ρg uor2

uor =

ηh =

2

ρg u 2 =ξ 2η h2

(2)

Q ∑ Aor

(3)

∑A

or

(4)

Ab

where ξ is the resistance coefficient of wind caps located on the distribution plate, ρ g denotes the gas density, uor represents the gas velocity through an orifice of wind cap calculated according to the total area of orifices, u is the superficial gas velocity through the cross section of the bed, ηh denotes the perforated rate of wind caps, Q is the gas volume flow,

∑A

or

represents the total area of orifices

of wind caps, and Ab denotes the effective area of distribution plate. According to the above mentioned formulas, the characteristic curve corresponding to the pressure drop through a wind cap was fitted from pressure drop data of the wind cap at different superficial gas velocities. The value of ξ used in the experiment was 1.144 with the standard error of 0.007.

Fig. 2. Distribution of wind caps on the distribution plate

Fig. 3. Structural diagram of wind caps

Fig. 4. Characteristic curve of the pressure drop through a wind cap 2.2. Experimental methods As shown in Fig. 1, during the experiment, the primary air volume is regulated using a control valve 2 mounted at the primary air piping, while the air volume of loop seal 20 is regulated using the two control valves, respectively, mounted at the two air bypass lines. The value of primary air volume is displayed through the intelligent flow integrating instrument of the uniform velocity tube flow meter 3, and then converted to primary air velocity. The solids in the dense bottom bed of the riser 15 are fluidized by the primary air, entrained, and transported up to the freeboard. In the freeboard, some fine particles are elutriated from the bed to the cyclone 16. As a result of the separation effect, most coarse particles in the cyclone are centrifuged, which then fall into the standpipe 19. Further, they are sent back to the riser by the loop seal, thus leading to the circulation of solids. A butterfly valve 18 is used to measure the solid circulation rate for the reasons of simplicity in operation and no loss in the solids that are circulated back into the riser. As the butterfly valve is just closed, a stopwatch is used to measure the time of solids accumulating on the butterfly valve up to a certain height. Based on the time for accumulation and bulk density of circulating solids, the solid circulation rate of the system is converted, then repeatedly measured, and finally converted to determine a mean value. On the one hand, in order to prevent the fan surge impacting the stability of air flow in the system, which would be caused by a too small airflow volume during the series operation of fans 1, a single fan is operated in case of lower primary air velocity. On the other hand, in case of higher primary air velocity, the series operation of two fans is used. In this study, a vertical dotted line is used, as shown in Fig. 10 and Figs. 14–16, to mark a

distinction between the operating condition of single fan and the series operation condition of two fans, wherein primary air velocity is the variable of the horizontal axis. On the left side of the vertical dotted line, the data correspond to different primary air velocities controlled in the operation of single fan. On the right side, the data correspond to different primary air velocities controlled in the series operation of two fans. The comparison of different data is made only under the same operating condition of fan. During the operation of the system, the pressure fluctuations of the central wind cap were measured at different primary air velocities u, and then converted to analog current signals in the range of 4–20 mA using a differential pressure sensor 12. The analog signals were then converted into digital signals by the data acquisition module 13 and finally stored in the computer 14. Pressure time series were recorded at a sampling frequency of 100 Hz, and the total test duration was 163.84 s. 3. Particle size distributions of bed materials In general, fuels and bed materials inside a CFB boiler are wide size range particles, during the combustion, with more complex fluid dynamic behaviors than narrow size range particles. Consequently, exploration of the pressure fluctuation characteristics in wind caps and the gas–solid fluidization characteristics for wide size range particles is of significant importance. In this study, seven groups of quartz sands with wide or narrow size range particles were used in a fluidized bed. The physical properties of seven groups of quartz sand bed materials are listed in Table 2. In the experiment, one of wide size range particles or narrow size range particles, physical properties of which are listed in Table 2, was used as bed materials. The particle size distribution of bed materials B is close to an equal distribution between Geldart B particles and Geldart D particles, while bed materials C correspond to a light skew distribution sloped to smaller size. Bed materials D is a heavy skew distribution sloped to larger size and bed materials E is a heavy skew distribution sloped to smaller size. Bed materials F have the particle size distribution similar to that of bed materials C, but only have a half solids inventory. Bed materials A is narrow size distribution of fine particles, and bed materials G is narrow size distribution of coarse particles. Sieving data and corresponding fitting curves of particle size distributions of the above mentioned wide size range particles are plotted in Fig. 5 for ease of visualization. The Rosin–Rammler distribution function has been used to fit the

sieving data on a particle-size distribution. It is usually given in the cumulative mass form, assuming that all particles have equal shape and density:

  dp m  Rd = exp  −      d e  

(5)

where dp represents the particle diameter, Rd is the mass fraction of bed materials occurring in particles of diameter greater than dp, and de and m are size parameter and distribution width parameter, respectively. Frequency of particle size distribution can be calculated by Eq. (6), which is the differential form of the Rosin–Rammler distribution function.

  dp m  dRd − m m −1 fd = − = md e d p exp  −    dd p   d e  

(6)

Solids E, C, B, and D were four groups of wide size range particles arranged in ascending order of mean particle size. Before being fluidized, the original stacking states of these wide size range particles corresponded to finer particles on the top and coarser particles underneath. Related articles on the mixing and segregation behavior of particle mixtures confirm that, for layered granular bed, as soon as the gas velocity exceeds the minimum fluidizing velocity, the segregation of particles gradually disappears and local mixing begins to occur at the upper layer with increasing gas velocity [37]. Further increase of gas velocity causes more intense bubbling and global mixing of the bed. Further, continuous increase in the gas velocity leads to the lifting of lightweight particles into the freeboard, due to their drag force being greater than gravity force. Thus, the segregation overtakes the mixing, leading to the occurrence of re-segregation. Table 2. Physical properties of quartz sand bed materials used for CFB Particle size distribution shape

Particle size distribution

Mean particle size

Solids inventory

(μm)

dpm (μm)

Iv (kg)

A

narrow size range

250–380 = 100%

315

20

1630

0.373

B

equal distribution between

676

40

1767

0.320

Serial number

250–380 = 16.65% 380–560 = 25.5%

Bulk density ρb (kg·m−3)

Bulk voidage εb

Geldart B particles and Geldart D particles C

light skew distribution sloped to smaller size

560–850 = 29.15% 850–991 = 16.4% 991–1400 = 12.3% 250–380 = 29.0%

562

40

1692

0.349

906

40

1646

0.367

434

40

1602

0.384

562

20

1814

0.302

1196

20

1304

0.499

380–560 = 30.4% 560–850 = 26.6% 850–991 = 10.0% 991–1400 = 4.0%

D

heavy skew distribution sloped to larger size

250–380 = 9.5% 380–560 = 12.5% 560–850 = 15.0% 850–991 = 15.25% 991–1400 = 47.75%

E

heavy skew distribution sloped to smaller size

250–380 = 60.75% 380–560 = 21.25% 560–850 = 13.0% 850–991 = 3.0% 991–1400 = 2.0%

F

light skew distribution sloped to smaller size

250–380 = 29.0% 380–560 = 30.4% 560–850 = 26.6% 850–991 = 10.0% 991–1400 = 4.0%

G

narrow size range

991–1400 = 100%

(a) Mass fraction of bed materials occurring in particles of diameter greater than dp

(b) Frequency distribution of particle size obtained from the fitting of Rosin–Rammler equation to sieving data Fig. 5. Particle size distributions of different wide size range particles used for CFB 4. Data processing techniques 4.1. Signal pretreatment

In order to investigate the characteristics of pressure fluctuation signals, pretreatments were carried out to remove the trend terms of the original signals before the signals were analyzed. Then the signals were processed and analyzed by the methods including standard deviation, power spectral density estimation, wavelet analysis, and homogeneous index. 4.2. Statistical standard deviation The standard deviation of the measured pressure fluctuation signals pi, is described in terms of Eq. (7) as follows:

σ=

1 n 2 ∑ ( pi − p ) n − 1 i =1

(7)

1 n ∑ pi n i =1

(8)

with the average pressure, p=

4.3. Power spectral density Power spectral density estimation is usually used to study the characteristics of signals in frequency domain. In order to improve the resolution and reduce the estimate variance, a modified Welch spectrum estimation method was adopted to calculate the power spectral density. The basic principle is that N numbers of data are firstly divided into L numbers of segments, and each segment can be partially overlapped. Then each segment of data are smoothed with an appropriate window function to determine the periodogram spectrum of each segment. Finally, the average periodogram spectrum of these segments is used to estimate the power spectral density of a signal. The periodogram spectrum I Mi (ω ) of each segment is defined as: I Mi (ω ) =

1 M ′U

N −1

2

∑ xi (n)w(n)e− jωn

(9)

n= 0

with the normalized factor,

U=

1 N −1 2 ∑ w ( n) M ′ n =0

(10)

where M ′ represents the number of data for each segment, x i ( n) is the n-th data in the i-th segment,

w( n) is window function, and ω is the angular frequency, with ω = 2π f , where f is the frequency. In

this study, for the estimation of power spectral density, pressure time series were equally divided into eight segments, the overlap rate was 50%, and Hamming window was chosen as the window function. 4.4. Wavelet analysis With the development of signal processing techniques, wavelet analysis has become a good method of choice for analyzing the fluid dynamic behaviors of gas–solid fluidized beds [38,39]. Wavelet analysis uses a series of functions to approximate one signal. The wavelet transform of a time series signal x(t) is expressed as follows: Wf ( a , b ) =

1

+∞

∫ x(t )ϕa,b ( | a | −∞ ∗

t −b )dt a

(11)

∗ (t ) represents a wavelet basis function, and a and b are dilation where Wf (a,b) is the wavelet coefficient, ϕa,b

factor and translation factor, respectively, and their values range from −∞ to ∞ with a ≠ 0. Wavelet functions are formed from the dilations and translations of a wavelet basis function to be a set of high frequency and small duration series. They are described as follows: φa,b (t ) =

1 |a|

ϕ(

t −b ) a

(12)

Successive approximations of a signal with different resolutions can be achieved by using formulas (11) and (12). Thus, wavelet analysis has the advantages of time-frequency localization and multi-resolution. Through using the method of wavelet analysis, an original signal is decomposed into its approximation and detail parts with different frequency ranges. The decomposition is carried out repeatedly until the desired decomposition level J is reached. The orthogonal wavelet series approximately expresses a sequence signal x(ti) as follows: x(ti) ≈ Aj(ti) + Dj(ti) + Dj−1(ti) + ⋅⋅⋅ + D1(ti)

(13)

where D1(ti), D2(ti),⋅⋅⋅, Dj(ti) represent detail signals at different resolution 2j and Aj(ti) represent the approximation signal at resolution 2j. The decomposition chart of wavelet multi-resolution analysis is shown in Fig. 6.

x A1 A2 A3 A4

A7

D2 D3

D4

A5 A6

D1

D5 D6

D7

Fig. 6. Decomposition chart of wavelet multi-resolution analysis Related studies have shown that the Daubechies wavelet of the second order (db2) is the optimal wavelet for the wavelet analysis of pressure fluctuation signals in fluidized beds due to its minimum decomposition error [40]. Thus, in this study, db2 was used to calculate the pressure fluctuation signals measured from the inlet of the wind cap until the seventh decomposition level was reached to obtain subsignals at appropriate resolution. According to Nyquist sampling theorem, sampling frequency being 100 Hz, signals in the range of 0 to 50 Hz can be measured. Based on the wavelet theory, the frequency band range that reconstruction signal D1 corresponded to was 25 to 50 Hz, D2 was 12.5 to 25 Hz, D3 was 6.25 to 12.5 Hz, D4 was 3.125 to 6.25 Hz, D5 was 1.563 to 3.125 Hz, D6 was 0.781 to 1.563 Hz, and D7 was 0.391 to 0.781 Hz. The squared sum of amplitude as the energy of a signal is represented as follows: n

E = ∑ | x(ti ) | 2

(14)

i =1

Simultaneously, EDj and EAJ as level energy are defined, respectively, which are the cumulative energy of detail signals at different level j and approximation signal at level J. n

EDj = ∑ | D j (ti ) | 2

(15)

i =1

n

EAJ = ∑ | AJ (ti ) | 2 i =1

4.5. Homogeneous index

(16)

In this study, the pressure fluctuation signals were analyzed by the wavelet multiresolution analysis as introduced in formulas (11)–(13), until the seventh decomposition level was reached. As a result, eight subsignals, namely D1, D2, D3, D4, D5, D6, D7, and A7 were obtained, and the corresponding frequency bands were from high frequency to low frequency. The subsignals were classified into the following three specific scales: the microscale corresponding to higher frequency and small fluctuations (SSF), mesoscale corresponding to intermediate frequency and large fluctuations (SLF), and macroscale corresponding to lower frequency (SDC). q

SSF = ∑ D j ( t ), 1 ≤ q < J

(17)

j =1

where the subsignal SSF represents a composite signal of detail signals below level q and has an approximate frequency band [ fs / 2 q +1 , fs / 2 ] Hz, where fs is the sampling frequency. It mainly captures the behavior of particle movement, small and rapid bubbles, or voids. The definition of mesoscale subsignal SLF is given as follows: J

S LF =

∑

D j ( t ), 1 ≤ q < J

(18)

j = q +1

In the present study, the maximum decomposition level J was set as seven. The subsignal SLF with approximate frequency band [ fs / 2 J +1 , fs / 2 q +1 ] Hz captures the fluctuations contribution from large bubbles or voids. Macroscale subsignal SDC that is AJ(t), with frequency band [0, fs / 2 J +1 ] Hz, shows the intensity of moving average in the original signal, which is a calculation to analyze data points by creating series of averages of different subsets of the full data set. With the change in the fluidization regime and gas–solid flow condition, a competition was observed between the energy of SSF and SLF. Therefore, a variable called homogeneous index (H) was defined, which was determined by the ratio of the energy of SSF to the energy of SLF [39], to characterize the transition of fluidization regimes and gas–solid flow conditions. The definition of H is given as follows:

∑ j =1 D 2j (t ) J ∑ j =q +1 D 2j (t ) q

E H = SF = E LF

where ESF is the energy of microscale SSF subsignal and E LF denotes the energy of mesoscale SLF subsignal. Apparently, the energy ratio of the SSF to SLF increases due to the acceleration of particle movements or the

(19)

splitting of big bubbles into small bubbles or voids, indicating that the gas–solid flow and particle mixing in fluidized beds tend to be uniform. In this study, variable q representing the dividing level between SSF and SLF subsignals, was set as three in the calculation of H. 5. Experimental results and discussion 5.1. Distribution plate to bed pressure drop ratio Under the fluidization of a certain mass of bed materials, bed pressure drop varies with particle size distribution. Thus, the distribution plate to bed pressure drop ratio needs to be estimated to find out whether it can satisfy the stable and successful operation of fluidized bed. There should be a critical value of pressure drop ratio, which is the lowest distribution plate to bed pressure drop ratio, in order to maintain the uniformity of gas distribution and stable operation of fluidized bed. Qureshi and Creasy [41] proposed a correlation for estimating the critical pressure drop ratio Rsc, considering the influence of the aspect ratio of a bed as follows:

Rsc =

  0.5 Db   (∆pdir )sc = 0.01 + 0.2 1 − exp  −  ∆ pb H b   

(20)

where ∆pdir is pressure drop through the distribution plate, ∆pb is bed pressure drop, Db denotes the bed diameter, and Hb is the bed height. When pressure drop through the distribution plate exceeds its critical pressure drop, the bed gets fluidized stably. In developing a design, the following correlation needs to be met:

R > Rsc where R is the distribution plate to bed pressure drop ratio, R =

(21)

∆pdir . ∆pb

Qureshi and Creasy [41] also collected a few published data about the distribution plate to bed pressure drop ratio R for stable operation of gas fluidized bed combustion furnace, which are listed in Table 3. For wind cap distribution plate or perforated plate, Karri and Knowlton [42] proposed that the distribution plate to bed pressure drop ratio for stable operation of fluidized bed can be estimated by using the following representation:

R=K

(22)

where K is a constant, and its value is considered as 0.3 for gas flowing upward or breadthwise from the open pore of distribution plate.

Values of R for bed materials of 40 kg weight with different wide particle size distributions, were respectively, calculated and compared to the value of Rsc calculated by using the formula (20) as well as with the values of R for stable operation of fluidized bed given by formula (22) and listed in Table 3, which are shown in Fig. 7. Values of R for four groups of bed materials of different wide particle size distributions were all larger than the value of Rsc. The value of R for bed materials of light skew distribution sloped to smaller size was the maximum among four groups of wide size range particles, while that of equal distribution between Geldart B particles and Geldart D particles was the second largest. This might be attributed to the fact that particles of smaller size were elutriated into the freeboard circulating in the circulation loop, which resulted in reduction in the pressure drop in the riser. Moreover, the voidage of dense bed formed by larger-size particles was larger, which also resulted in the reduction of the pressure drop through the dense bed. However, excess particles of smaller size exceeded saturated carrying capacity of gas in the freeboard, and the voidage of dense bed formed by smaller-size particles was smaller as well, which led to the increase in the pressure drop through the dense bed. This resulted in minimum value of R for bed materials of heavy skew distribution sloped to smaller size. When particles of larger size were in excess, dense bed formed by larger-size particles was higher, and very small amount of particles were elutriated into the freeboard circulating in the circulation loop, thus resulting in a second smallest value of R corresponding to particles of heavy skew distribution sloped to larger size. Table 3. ∆pdir/∆pb of a fluidized bed reactor under the stable operation [41] Process of a stable operation

Type of distribution plate

Bed diameter Db

coke combustion

perforated plate

6.5

2.5

80

0.43

incinerator

wind cap distribution plate

1.2

0.66

90

0.40

coal combustion

wind cap distribution plate

0.7

1.1

5

0.13

2.2

5

0.25

∆pdir Db/Hb

R = ∆pdir/∆pb (cm H2O)

(m)

Fig. 7. ∆pdir/∆pb of bed materials with different wide particle size distributions 5.2. Bed pressure drop curves Bed pressure drop data of different wide particle size distributions or narrow particle size distributions under different primary air velocities were plotted as presented in Fig. 8, which were measured within the height ranged from 0.1 to 0.7 m from the distribution plate. Based on the variety trend, bed pressure drop data of fixed bed and bubbling fluidization were, respectively, analyzed by the linear curve fitting methods with the intercept of zero and slope of zero. However, data of turbulent fluidization and fast fluidization were, respectively, analyzed by using non-linear curve fitting (cubic) and linear curve fitting methods. The figure clearly indicates that bed pressure drop increases linearly with the increase in the gas velocity in a fixed bed. When gas velocity exceeds minimum fluidization velocity, bed pressure drop does not exhibit significant change with increasing gas velocity in bubbling fluidization. Once onset velocity to turbulent fluidization is achieved, bed pressure drop increases again with increasing gas velocity. This is attributed to the fact that in turbulent fluidization, the gas velocity is high enough to result in bubbles being limited in size by the bottom bed height, and there is a large through-flow of gas through the bed during fluidization [43]. With the further increase in gas velocity, as soon as transition velocity between turbulent and fast fluidization is achieved, bed pressure drop decreases with increasing gas velocity, due to the elutriation of a large number of fine particles into freeboard circulating in the outside circulation loop.

Obviously, among the four groups of bed materials of wide particle size distributions, particles of heavy skew distribution sloped to smaller size were the easiest to be fluidized and not found a fixed bed existing in the range of gas velocities from 1.0 to 1.5 m·s−1. Minimum fluidization velocity increases in the order of heavy skew distribution sloped to larger size, light skew distribution sloped to smaller size, and equal distribution between Geldart B particles and Geldart D particles. Similarly, onset velocity to turbulent fluidization increases in the order of heavy skew distribution sloped to smaller size, heavy skew distribution sloped to larger size, light skew distribution sloped to smaller size, and equal distribution between Geldart B particles and Geldart D particles. These conclusions are consistent with the fluidization regimes shown in Figs. 9(a)–(d). Compared to the particles with wide size distributions, particles of narrow size distributions are easier to be fluidized from a fixed bed. Onset velocity to turbulent fluidization of bed materials of wide particle size distributions is larger than narrow size distribution of fine particles; however, smaller than narrow size distribution of coarse particles. Fine particles with narrow size distribution are the easiest to be fluidized in fast fluidization. These conclusions are consistent with the fluidization regimes shown in Figs. 9(e)–9(g).

Fig. 8. Bed pressure drops between 0.1 m height and 0.7 m height from the distribution plate under different particle size distributions

(a) Particles B of equal distribution between Geldart B particles and Geldart D particles, 0.290 m static bed height

(b) Particles C of light skew distribution sloped to smaller size, 0.302 m static bed height

(c) Particles D of heavy skew distribution sloped to larger size, 0.310 m static bed height

(d) Particles E of heavy skew distribution sloped to smaller size, 0.318 m static bed height

(e) Particles F of light skew distribution sloped to smaller size, 0.150 m static bed height

(f) Narrow size distribution of fine particles A, 0.165 m static bed height

(g) Narrow size distribution of coarse particles G, 0.202 m static bed height Fig. 9. Fluidization regimes under the stable operations of fluidized beds with different particle size distributions from u = 1.4 to 1.9 m⋅⋅ s−1 5.3. Standard deviations of pressure fluctuations in a wind cap Fig. 10 shows the effects of particle size distribution on the standard deviations σc of pressure fluctuations in the central wind cap at different primary air velocities u. It reflects the effects of particle size distribution on the global pressure fluctuations in fluidized beds. Fig. 10(a) shows that the values of σc of pressure fluctuations in the bed using different wide size range particles increase with the increase in the primary air velocity at lower air velocities. However, they do not show obvious variation trends at higher air velocities, with increasing primary air velocity. This is due to the bubbling fluidization accompanied with the particle mixing of different particle sizes at lower gas velocities, in a fluidized bed using wide size range particles. With the increase in the gas velocity, solids in the bed were mixed more and more intensely, bubbles were promoted to coalesce to a larger size, causing the increment in the amplitudes of pressure fluctuations. With the further increase in gas velocity, fine solids were lifted into the upper region of the bed, due to the drag force being greater than the gravity force, and then they were fluidized in turbulent fluidization. At the same time, coarser solids in the lower region of the bed were still in bubbling fluidization. The decreasing effect caused by the turbulent fluidization in conjunction with the increasing effect caused by the bubbling fluidization, brought about only a little variation

trend for the amplitudes of pressure fluctuations. Under this condition, with the further increase in the gas velocity, solids fluidized in turbulent fluidization and even in dilute phase pneumatic conveying, became more numerous; however, bubbles in the lower region became larger. They together brought about only a little variation trend for the values of σc of pressure fluctuations in a certain range of gas velocities, with increasing gas velocity.

(a) Comparison between different wide size range particles

(b) Comparison between wide size range particles and narrow size range particles Fig. 10. Standard deviations of pressure fluctuations in a wind cap at different particle size distributions Fig. 10(a) shows that the values of σc of pressure fluctuations in the bed using bed materials B, with equal distribution between Geldart B particles and Geldart D particles, are the least in contrast with other three wide size range particles at lower gas velocities. The gas velocity corresponding to the maximum value of σc for bed

materials B was the largest one, in contrast with other three wide size range particles. This is attributed to the relatively homogeneous particle size distribution of bed materials B. When bed materials B were used, solids of different particle sizes exhibited difficulty in mixing with each other in bubbling fluidization, and finer solids were not readily lifted into the upper region with further increase in the gas velocity. Thus, the range of gas velocities corresponding to the mixing and separation processes of solids was wider. Poor behavior of mixing and separation of bed materials B led to a poor bubbling fluidization behavior, which could be justified by Fig. 9(a). This resulted in the smallest bubble sizes and amplitudes of pressure fluctuations in contrast with other three bed materials at lower gas velocities. Fig. 10(a) also shows that the values of σc of pressure fluctuations in the bed using bed materials E, with a heavy skew distribution sloped to smaller size, are the largest in contrast with other three wide size range particles, when the gas velocity was lower than 1.9 m⋅⋅ s−1. Moreover, the gas velocity corresponding to the maximum value of σc for solids E was the smallest one, in contrast with other three bed materials. This is ascribed to the extremely inhomogeneous particle size distribution of bed materials E. Bed materials E were made of majority of finer solids. Thus, in this case solids were easily mixed with each other in bubbling fluidization, and finer solids were more easily lifted into the upper region with further increase in the gas velocity. Thus, the range of gas velocities corresponding to the mixing and separation processes of solids was narrower. Good mixing and separation behavior of bed materials E led to a good bubbling fluidization behavior, which could be justified by Fig. 9(d), coupled with a large number of finer solids, further bringing the biggest bubble sizes and amplitudes of pressure fluctuations, in contrast with the three other bed materials at lower gas velocities. Besides, Fig. 10(a) also exhibits that σc of pressure fluctuations in the bed using bed materials C, with a light skew distribution sloped to smaller size, or using bed materials D, with a heavy skew distribution sloped to larger size, are intermediate between the values of σc of bed materials B and bed materials E, when the gas velocity was lower than 1.9 m⋅⋅ s−1. Furthermore, the gas velocity u corresponding to the maximum value of σc, when using one group of these two bed materials, was also intermediate between those of bed materials B and bed materials E. This is attributed to the fact that the mixing and separation behaviors of light skew distribution

particles sloped to smaller size or heavy skew distribution particles sloped to larger size, were intermediate between those of equal distribution particles between Geldart B particles and Geldart D particles and heavy skew distribution particles sloped to smaller size. At gas velocities lower than 2.4 m⋅⋅ s−1, when using heavy skew distribution particles D sloped to larger size, σc values of pressure fluctuations were larger than σc values when using light skew distribution particles C sloped to smaller size; nonetheless, the gas velocity u corresponding to the maximum value of σc was less. Interestingly, these results clearly reveal that the effects of the shape change of particle size distribution on the fluidization behaviors are more obvious than the effects of mean particle size, when wide size range particles are fluidized in bubbling fluidization. Moreover, Fig. 10(a) also demonstrates that the maximum value of σc of pressure fluctuations, when using particles with equal distribution between Geldart B particles and Geldart D particles, was larger than the maximum value of σc when using particles with skew distribution. Fig. 10(b) shows the comparison between pressure fluctuations in the beds when using wide size range particles and narrow size range particles. The second vertical dotted line from left to right dividing data symbols of bed materials G was used to distinguish between the data measured in the operation including a bag filter and the data measured in the operation without the bag filter. Data on the right side corresponded to the data measured in the operation without the bag filter. Fig. 10(b) shows that with the increase in primary air velocity, σc values of pressure fluctuations in the bed, by either using narrow size distribution of fine particles A or using narrow size distribution of coarse particles G, both reach a maximum value and then drop down. However, σc value of pressure fluctuations in the bed using wide size range particles F, exhibits no obvious variation trends with increasing gas velocity after it reaches a maximum value, which provides the same conclusion as presented in Fig. 10(a). This is attributed to the turbulent fluidization occurring in the entire bed when using narrow size range particles, after the amplitude of pressure fluctuations reach a maximum with increasing gas velocity. Thus, use of narrow size range particles did not lead to the fluidization stratification phenomena as observed in the beds using wide size range particles. Moreover, narrow size distribution of coarse particles G belonging to Geldart D particles [44], were more difficult to be fluidized than narrow size distribution of fine particles A belonging to Geldart B particles [44], which could be justified by Figs. 9(f) and (g). This could also be confirmed

by the larger gas velocity for particles G corresponding to the maximum value of σc, representing a larger minimum transition velocity from bubbling to turbulent fluidization. Minimum transition velocity from bubbling to turbulent fluidization of wide size range particles was found to be intermediate between narrow size distribution of fine particles and narrow size distribution of coarse particles. 5.4. Power spectral density of pressure fluctuations in a wind cap Fig. 11 shows the original signals x and power spectral density Pxx of pressure fluctuations in the central wind cap at different particle size distributions under u = 1.6 m⋅s−1, which is a gas velocity for seven groups of bed materials all being fluidized in bubbling fluidization. Fig. 11 (a) illustrates the time domain features of pressure fluctuations. In Fig. 11 (b), the unit of Pxx was kPa2/Hz. It was found that the power of low-frequency pressure fluctuations, which related to the bubble behaviors, mainly concentrated in the frequency range of 0–4 Hz, and the dominant frequency for seven groups of bed materials varied in the range of 1–2 Hz.

(a) Original signals of pressure fluctuations having removed the average pressures

(b) Power spectral density of pressure fluctuations Fig. 11. Original signals and power spectral density of pressure fluctuations in a wind cap at different particle size distributions under u = 1.6 m⋅s−1 Fig. 12 shows the power spectral density Pxx of pressure fluctuations in the central wind cap at different particle size distributions under u = 2.8 m⋅s−1, 3.3 m⋅s−1, and 3.9 m⋅s−1. The power of low-frequency pressure fluctuations, mainly concentrated in the frequency range of 0–4 Hz, and the dominant frequency for seven groups of bed materials varied in the range of 1–2.5 Hz. Low-frequency fluctuations tended to concentrate in frequency domain, for particles C, particles D, particles E, and particles F, when gas velocity u increased from 1.6 m⋅s−1 to 2.8 m⋅s−1, due to the transition from bubbling to turbulent fluidization in the upper region of a bed. This phenomenon was also found for Particles B, when gas velocity u increased from 2.8 m⋅s−1 to 3.3 m⋅s−1. Particles

A were fluidized in fast fluidization under u = 2.8 m⋅s−1 and 3.3 m⋅s−1, thus had a large high-frequency distributional energy. Although particles C, particles F, and particles G were still in turbulent fluidization under u = 3.9 m⋅s−1, large high-frequency distributional energy could also be clearly observed.

(a) Power spectral density of pressure fluctuations under u = 2.8 m⋅s−1

(b) Power spectral density of pressure fluctuations under u = 3.3 m⋅s−1

(c) Power spectral density of pressure fluctuations under u = 3.9 m⋅s−1 Fig. 12. Power spectral density of pressure fluctuations in a wind cap at different particle size distributions under u = 2.8 m⋅s−1, 3.3 m⋅s−1, and 3.9 m⋅s−1 Fig. 13 shows the power spectral density of differential pressure fluctuations measured from different heights at different particle size distributions, under u = 2.8 m⋅s−1. The power of low-frequency pressure fluctuations, mainly concentrated in the frequency range of 0–4 Hz. Fig. 13(a) demonstrates that the dominant frequency of differential pressure fluctuations varied in the range of 0.9–2.3 Hz, for seven groups of bed materials, which were measured between 0.1 m height and 0.3 m height from the distribution plate. However, Fig. 13(b) shows that when the differential pressure fluctuations were measured between 0.5 m height and 0.7 m height from the distribution plate, the dominant frequency varied in the range of 0.3–1.8 Hz. These illustrates that the frequencies of low-frequency pressure fluctuations were lower at a higher height, due to the larger bubbles or voids. It was also found that high-frequency distributional energy was larger, for the differential pressure fluctuations between 0.5 m height and 0.7 m height, due to the measuring position was adjacent to the bed

surface through which bubbles emerge and burst. High-frequency distributional energy was even close to low-frequency distributional energy, for particles G and particles F, which was attributed to the fact that the measuring height range contained the bed surface.

(a) Power spectral density of differential pressure fluctuations between 0.1 m height and 0.3 m height from the distribution plate under u = 2.8 m⋅s−1

(b) Power spectral density of differential pressure fluctuations between 0.5 m height and 0.7 m height from the distribution plate under u = 2.8 m⋅s−1 Fig. 13. Power spectral density of differential pressure fluctuations measured from different heights at different particle size distributions Based on the analysis to Figs. 11–13, in this study, reconstruction signal D6 was used to characterize the low-frequency pressure fluctuations in the wavelet analysis, which corresponded to a main low-frequency fluctuation range of 0.781 to 1.563 Hz. Reconstruction signal D1 was used to characterize the high-frequency pressure fluctuations, which corresponded to a high-frequency fluctuation range of 25 to 50 Hz. In view of the large distance between signal D1 and main low-frequency energy range of 0–4 Hz in frequency domain, signal D1 may be generated from inter-particle collisions, but not by small scales of bubbles. Variable q was set as three in

the calculation of H, SSF thus corresponded to the frequency range of 6.25 to 50 Hz, having not included the low-frequency fluctuation range of 0–4 Hz. 5.5. Wavelet energy of pressure fluctuations in a wind cap Fig. 14 shows the effects of particle size distribution on the low-frequency wavelet energy ED6 of pressure fluctuations in the wind cap at different primary air velocities u. It reflects the effects of particle size distribution on the low-frequency pressure fluctuations in fluidized beds. Fig. 14(a) demonstrates that the ED6 of pressure fluctuations in the beds using wide size range particles B, C, and E, increases at lower gas velocities and then drops down, with increasing primary air velocity. Thus, the ED6 is able to identify the transition from bubbling to turbulent fluidization in the upper region of the bed, during the fluidization of wide size range particles. The ED6 of pressure fluctuations did not exhibit obvious decreasing trends with increasing gas velocity, when using heavy skew distribution particles D sloped to larger size. This may be attributed to the fact that the main frequencies of bubble fluctuations were not within the frequency band range corresponding to subsignal D6. The comparative analysis of wavelet energy ED6 of pressure fluctuations using four different wide size range particles at lower gas velocities, similarly shows that the more serious the skew degree of particle size distribution, the better mixing and separation behavior of particles, the better bubbling fluidization behavior, and the larger bubble sizes.

(a) ED6 of different wide size range particles

(b) ED6 of different wide size range particles and narrow size range particles Fig. 14. Wavelet energy ED6 of pressure fluctuations in a wind cap at different particle size distributions Fig. 14(b) shows that the ED6 of pressure fluctuations reaches a maximum value and then drops down with increasing gas velocity, when using one of the three groups of bed materials, among wide size range particles F, narrow size distribution of fine particles A, and narrow size distribution of coarse particles G. The results prove that the use of low-frequency wavelet energy can not only help to identify the transition from bubbling to turbulent fluidization, as narrow size range particles are fluidized, but also the transition from bubbling to turbulent fluidization in the upper region of a bed, when wide size range particles are fluidized. The maximum value of ED6 when using narrow size distribution of coarse particles G, was found to be less than that by using narrow size distribution of fine particles A, indicating that the maximum stable bubble diameter for a fluidized bed of Geldart D particles is less than that for a fluidized bed of Geldart B particles. Moreover, Fig. 14(b) also illustrates that the transition gas velocity from bubbling to turbulent fluidization of wide size range particles, is intermediate between narrow size distribution of fine particles and narrow size distribution of coarse particles. Furthermore, maximum stable bubble diameter for a fluidized bed of wide size range particles is less than that for a fluidized bed of narrow size range particles. Fig. 15 shows the effects of particle size distribution on the high-frequency wavelet energy ED1 of pressure fluctuations in the wind cap at different primary air velocities u. It reflects the effects of particle size distribution on the high-frequency pressure fluctuations in fluidized beds. Fig. 15(a) shows that the ED1 of pressure fluctuations when using different wide size range particles as bed materials, increases with the increase in the

gas velocity at lower gas velocities; however, no obvious variation trends are observed after they reach a maximum value. This is owing to the fact that, in bubbling fluidization, particle concentration of the bed was higher, and vertical and horizontal movements of large quantities of particles occurred due to the movements of large quantities of bubbles, resulting in frequent collisions among the particles in the bed. With the increase in the gas velocity u, inter-particle collisions became more and more frequent, resulting in an increasing trend for the ED1. Further increase in the gas velocity led to the lifting up of finer solids into the upper region of the bed to be fluidized in turbulent fluidization. Thus, high-frequency collisions in the upper region of the bed reduced. However, at the same time, coarser solids in the lower region were still fluidized in bubbling fluidization, and high-frequency collisions in this region continued heightening with increasing gas velocity. This difference between the upper and the lower regions, made ED1 without any obvious variation trends in the entire bed with increasing gas velocity. The comparative analysis of wavelet energy ED1 of pressure fluctuations using four different wide size range particles, at lower gas velocities, similarly shows that the more serious skew degree of particle size distribution, the better bubbling fluidization behavior, the more frequent collisions of particles due to movements of bubbles, and the larger value of ED1.

(a) ED1 of different wide size range particles

(b) ED1 of different wide size range particles and narrow size range particles Fig. 15. Wavelet energy ED1 of pressure fluctuations in a wind cap at different particle size distributions Fig. 15(b) exhibits that the ED1 of pressure fluctuations in the bed using wide size range particles F, reaches a maximum value and then shows a small increasing trend, with increasing gas velocity. In contrast, it reaches a maximum value and then drops down, when using narrow size distribution of fine particles A or narrow size distribution of coarse particles G. It can be interpreted that in a fluidized bed of wide size range particles, with the increase in the gas velocity u, finer solids in the upper region of the bed, appeared to undergo transition from bubbling to turbulent fluidization, leading to reduction in high-frequency collisions of particles in this region. However, coarser solids in the lower region were still fluidized in bubbling fluidization, leading to enhancement in high-frequency collisions of particles in this region, thus the effects of lower region played the leading role. However, in a fluidized bed of narrow size range particles, fluidization stratification phenomena were not observed. With the increase in the gas velocity u, narrow size range particles appeared to undergo transition from bubbling to turbulent fluidization in the entire bed, leading to reduction in high-frequency collisions of particles. Thus, in a fluidized bed with narrow size range particles, the value of ED1 dropped down after reaching a maximum value. Besides, the maximum value of ED1 using narrow size distribution of coarse particles G was larger than that using narrow size distribution of fine particles A, due to their lower bed expansion height in fluidization, bringing about a higher particle concentration of the bed and more frequent inter-particle collisions.

5.6. Homogeneous index of pressure fluctuations in a wind cap Fig. 16 shows the effects of particle size distribution on homogeneous index H of pressure fluctuations in the central wind cap at different primary air velocities u. Fig. 16(a) demonstrates that homogeneous index H of pressure fluctuations in the bed of particles B with equal distribution between Geldart B particles and Geldart D particles, decreases rapidly at gas velocities lower than 1.8 m⋅⋅ s−1 and then remains almost unchanged within a considerable range of gas velocities, with increasing gas velocity. This result is markedly different from the experimental results using other skew size distribution particles. This might be ascribed to the relatively wide and homogeneous particle size distribution of bed materials B. When bed materials B were used, solids of different particle sizes encountered difficulty in mixing with each other or separating from each other in bubbling fluidization. Thus, more collisions were caused by overcoming the resistances of mixing and separation. These ensured that the contribution of high-frequency pressure fluctuation energy caused by inter-particle collisions was approximately equal to the contribution of low-frequency pressure fluctuation energy caused by the movements of bubbles or voids, with increasing gas velocity in a certain range of gas velocities. H values of pressure fluctuations in the bed using skew size distribution particles C, D, and E, decreased at first and then exhibited an increasing trend, with increasing gas velocity. This was attributed to the movements of bubbles or voids playing a key role in the effects on pressure fluctuations, in bubbling and turbulent fluidization, when skew size distribution particles were used. At lower gas velocities, with the increase in the gas velocity, diameters of bubbles increased gradually, the energy of low-frequency pressure fluctuations increased, and the fluidization became more inhomogeneous. With the further increase in the gas velocity, fine particles were lifted into the upper region of the bed and fluidized in turbulent fluidization. The restriction and splitting effects of turbulent fluidization on the large-diameter bubbles in the upper region, in conjunction with the effects of high-frequency collisions of particles, exceeded the effects of bubble movements in bubbling fluidization of the lower region. These led to a more homogeneous fluidization in the bed and an increasing trend of H with increasing gas velocity.

(a) Comparison between different wide size range particles

(b) Comparison between wide size range particles and narrow size range particles Fig. 16. Homogeneous indexes of pressure fluctuations in a wind cap at different particle size distributions Fig. 16(b) shows that H values of pressure fluctuations, when using wide size range particles F or narrow size distribution of coarse particles G, both exhibit a decreasing trend at lower velocities, with increasing gas velocity. This can be explained as follows: two groups of bed materials were still fluidized in bubbling fluidization in the range of gas velocities shown in the figure. With the increase in the gas velocity, bubbles in the bed became larger, and the fluidization became more inhomogeneous, leading to a larger ratio of low-frequency energy to high-frequency energy and a decreasing H value. However, narrow size distribution of fine particles A underwent a transition from bubbling fluidization to turbulent fluidization in the range of gas velocities from 1.4

to 1.6 m⋅⋅ s−1, resulting in a relatively constant H value. With increasing gas velocity, the reduction in H value occurred earlier for wide size range particles F than for narrow size distribution of coarse particles G, indicating easier fluidization of the wide size range particles F than of the narrow size distribution of coarse particles G. With the further increase in the gas velocity, an increasing trend was found for H values of all the three groups of bed materials because all three groups of bed materials were fluidized in turbulent fluidization at these gas velocities, leading to a restriction of bubble coalescences and an intensification of bubble splitting. With increasing gas velocity, sizes of bubbles or voids in the bed became smaller, fluidizations tended to more homogeneous regimes, and ratios of high-frequency energy to low-frequency energy increased. Fig. 16(b) also shows that when the gas velocity is increased, the sequential order of three bed materials according to the appearance of an increasing trend for H value, is A, F, and G. The sequential order of three bed materials according to their H values at the same gas velocities from the largest one to the smallest one, after the appearances of increasing trends for their H values, is also A, F, and G. These features illustrate that fine particles with narrow size distribution are most easily fluidized into turbulent fluidization and exhibit the most homogeneous fluidization. Wide size range particles take second place, if their mean particle size is far smaller than narrow size distribution of coarse particles. Coarse particles with narrow size distribution, which belong to Geldart D particles, are the most difficult to be fluidized into turbulent fluidization and show the most inhomogeneous fluidization. 5.7. Solid circulation rates Fig. 17 shows solid circulation rates measured from the standpipe at different particle size distributions. It confirms the analysis results presented in Figs. 10–15. The effect of particle size distribution on solid circulation rate for wide size range particles is apparent in Fig. 17(a). With an increase in the gas velocity, particles E with heavy skew distribution sloped to the smaller size were the earliest to be fluidized to maintain the solid circulation. Heavy skew distribution particles D sloped to larger size were second to be found having solid circulation. Light skew distribution particles C sloped to smaller size were the last to be fluidized to solid circulation condition. Particles B with equal distribution between Geldart B particles and Geldart D particles were not even found to exhibit solid circulation at gas velocities lower than 4.1 m⋅⋅ s−1. These findings clearly

indicate that, the more serious the skew degree of the particle size distribution, the narrower the gas velocity range of bubbling fluidization and turbulent fluidization. Furthermore, fine particles inside beds were more easily lifted into the freeboard and elutriated from the bed, leading to solid circulation. Fig. 17(b) shows that, at higher gas velocities, fine particles A with narrow size distribution were fluidized with large solid circulation rates, while wide size range particles F were fluidized with very small solid circulation rates at the same gas velocities. Coarse particles G with narrow size distribution did not exhibit solid circulation at gas velocities lower than 3.9 m⋅⋅ s−1. This may be attributed to the fact that as the fine particles with narrow size distribution are fluidized, mixing and separation of different size particles do not exist. Their fluidization behaviors are better than that of wide size range particles. Owing to their small particle sizes, they are fluidized rapidly, bringing about large solid circulation rates. However, for wide size range particles, the range of gas velocities in bubbling fluidization was wide, and at higher gas velocities, fine particles in the upper bed were only fluidized in dilute phase pneumatic conveying, bringing about only small solid circulation rates. For coarse particles G with narrow size distribution, which belonged to Geldart D particles, owing to their large particle sizes, they were still in turbulent fluidization at higher gas velocities, leading to an absence of the solid circulation.

(a) Comparison between different wide size range particles

(b) Comparison between wide size range particles and narrow size range particles Fig. 17. Solid circulation rates at different particle size distributions 6. Conclusions In this study, the effects of particle size distribution on the gas–solid fluidization characteristics in fluidized beds were researched. The study was carried out based on the relationship between primary air velocity and characteristic parameters of pressure fluctuations in the wind cap of a circulating fluidized bed (CFB) with different particle size distributions. Both the values of the standard deviations and the high-frequency wavelet energy of pressure fluctuations in the beds using different wide size range particles increased with increasing primary air velocity at lower gas velocities; however, did not exhibit obvious trends with increasing gas velocity at higher gas velocities. This feature was found to be significantly different from that of narrow size range particles. Nonetheless, low-frequency wavelet energy increased at lower gas velocities and then dropped down with increasing primary air velocity, thus enabling easy identification of the transition from bubbling to turbulent fluidization in the upper region of the bed, during the fluidization of wide size range particles. When wide size range particles were utilized, during bubbling fluidization, the more serious the skew degree of particle size distribution, the better the mixing and separation behaviors of particles, and the larger the bubble sizes and amplitudes of pressure fluctuations.

The maximum amplitude of pressure fluctuations and transition gas velocity between bubbling and turbulent fluidization, using narrow size distribution of coarse particles, were larger than that by using narrow size distribution of fine particles. The value of transition gas velocity between bubbling and turbulent fluidization, using wide size range particles, was between that of fine particles and coarse particles with narrow size distribution. However, the maximum amplitude of pressure fluctuations for wide size range particles was less than that of narrow size range particles. When having a more serious skew degree of particle size distribution or a smaller mean particle size, wide size range particles were more easily fluidized to turbulent fluidization, exhibiting an increasing trend in H value at a lower gas velocity. Fine particles with narrow size distribution were most easily fluidized to turbulent fluidization and fluidized most evenly. When using these particles as bed materials, the gas velocity of beginning to appear an increasing trend for H value with the increase in the gas velocity, was the lowest, compared to other size distribution particles; however, their H values at higher gas velocities were the largest, at the same gas velocities. Coarse particles with narrow size distribution were fluidized with the most difficulty to turbulent fluidization and fluidized most unevenly. When having a smaller mean particle size than coarse particles with narrow size distribution, wide size range particles took second place for difficulty of fluidization, compared to coarse particles and fine particles with narrow size distribution. Acknowledgement The authors greatly acknowledge the financial support from the National Natural Science Foundation of China (51676102), the Natural Science Foundation of Shandong Province (ZR2015EM004), and the Foundation of State Key Laboratory of Coal Clean Utilization and Ecological Chemical Engineering (Grant No. 2016-07). The National Natural Science Foundation of China (U1710251) is sincerely acknowledged. Nomenclature a

dilation parameter

effective area of distribution plate, (m2)

Ab

approximation signal of multiresolution decomposition at resolution 2j, (Pa)

Aj(ti)

∑A

total area of orifices of wind caps, (m2)

b

translation parameter

Db

bed diameter, (m)

de

size parameter, (m)

or

Dj(ti)

detail signals of multiresolution decomposition at different resolution 2j, (Pa)

dp

particle diameter, (m)

dpm

mean particle size, (m)

E

the energy of a signal, (Pa2)

EAJ

the decomposed cumulative energy of level J approximation signal, (Pa2)

EDj

the decomposed cumulative energy of different level j detail signals, (Pa2)

ELF

energy of mesoscale LF subsignal, (Pa2)

ESF

energy of microscale SF subsignal, (Pa2)

f

frequency, (Hz)

fd

frequency of particle size distribution, (m−1)

fs

sampling frequency, (Hz)

H

homogeneous index

Hb

bed height, (m)

I Mi (ω )

the periodogram spectrum of each segment for the modified Welch spectrum estimation

Iv

solids inventory, (kg)

J

the desired decomposition level of multiresolution decomposition

m

distribution width parameter

M′

number of data for each segment

n

number of samplings

p

average pressure, (Pa)

pi

measured pressure, (Pa)

∆pb

bed pressure drop, (Pa)

∆pc

pressure drop through a wind cap, (Pa)

pci

the pressure of the inlet airflow of a wind cap, (Pa)

pco

the pressure of the outlet gas–solid flow of a wind cap, (Pa)

∆pdir

pressure drop through the distribution plate, (Pa)

(∆pdir )sc critical pressure drop through the distribution plate, (Pa)

Pxx q Q

power spectral density, (Pa2/Hz)

decomposition level of the boundary between microscale subsignals and mesoscale subsignals gas volume flow, (m3·s−1)

R

distribution plate to bed pressure drop ratio

Rd

mass fraction of bed materials occurring in particles of diameter greater than dp, (%)

RSC

critical pressure drop ratio

SDC

macro-scale subsignal, (Pa)

SLF

mesoscale subsignal, (Pa)

SSF

microscale subsignal, (Pa)

t

time, (s)

u

superficial gas velocity of the primary air, (m·s−1)

U

normalized factor

uor

gas velocity through an orifice of wind cap, (m·s−1)

w(n)

window function

Wf (a,b)

wavelet coefficient

x(t)

time sequence function, (Pa)

x i ( n)

the n-th data in the i-th segment

Greek symbols εb

bulk voidage

ηh

perforated rate of wind caps

ξ

resistance coefficient of wind caps

ρb

bulk density, (kg·m−3)

ρg

gas density, (kg·m−3)

σ

standard deviation, (Pa)

σc1

standard deviations of pressure fluctuations in the central wind cap, (Pa)

∗ (t ) ϕa,b

basic wavelet function

ω

angular frequency, (rad/s)

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Highlights •

Pressure fluctuations are related to particle size distribution in a fluidized bed.

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Bottom bed fluidization can be characterized by pressure fluctuations in wind caps.

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Wavelet energy can identify fluidization transition of wide size range particles.

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In bubbling fluidization, particle size distribution affects bubble sizes.

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For wide size range particles, maximum amplitude of pressure fluctuations was small.