111Equation Chapter 1 Section 1Investigation of gas-solids flow in a circulating fluidized bed using 3D Electrical Capacitance Tomography

Mingxu Mao1,2, Jiamin Ye*1, Haigang Wang1 and Wuqiang Yang3

1. Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China2. University of Chinese Academy of Sciences, Beijing 100049, China3. School of Electrical and Electronic Engineering, The University of Manchester, Manchester,

M13 9PL, UK

E-mail: yejiamin@iet.cn

Abstract. The hydrodynamics of gas-solids flow in the bottom of a circulating fluidized bed (CFB) is complicated. Three-dimensional (3D) electrical capacitance tomography (ECT) has been used to investigate the hydrodynamics in risers of different shape. Four different ECT sensors with 12 electrodes each are designed according to the dimension of risers, including two circular ECT sensors, a square ECT sensor and a rectangular ECT sensor. The electrodes are evenly arranged in three planes to obtain capacitance in different heights and to reconstruct the 3D images by Linear Back Projection (LBP) algorithm. Experiments were carried out on the four risers using sands as the solids material. The capacitance and differential pressure are measured under the gas superficial velocity from 0.6 m/s to 3.0 m/s with a step of 0.2 m/s. The flow regime is investigated according to the solids concentration and differential pressure. The dynamic property of bubbling flows is analyzed theoretically and the performance of the 3D ECT sensors evaluated. The experimental results show that 3D ECT can be used in the CFB with different risers to predict the hydrodynamics of gas-solids bubbling flows.

Keywords: Circulating fluidized bed, electrical capacitance tomography, solids concentration, bubble characteristic

1. Introduction

In a gas-solids circulating fluidized bed (CFB), the bed is supplemented by separating particles from the outgoing fluid by a separator and returning the entrained particles back to the bed [1]. The ‘fluid-like’ solid partilces enable the CFB achieve well mixing of gas and solids and a high efficiency of heat transfer. For a gas-solids CFB, the particle distribtuion in the bottom of a riser in a CFB varies with time and space rapidaly and has great influence on the performance of a CFB. Furthermore, the hydronamics of the gas-solids flow in the CFB changes with the change in the shape and dimension of the riser [2].

To mointor the distribution of a gas-solids flow, a number of techniques have been applied, e.g. pressure measurement, ?? probes, ?? visualisation and tomgoraphy [3, 4]. In the past decade, the tomographic techqunic has been widly used for measuring gas-solids flows in CFBs owing to the

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abundant information compared with the sigle point measurement. Barthel et al. obtained the disperse phase velocity using a two-plane X-ray tomography sensor by cross-correlation and a new method, which can give a unique Lagrangian particle-related velocity information [5]. Compared with X-ray tomography, electrical capacitance tomography (ECT) has gained more attention due to the advantages of no radiation, simple structure, low cost, and fast imaging speed [6]. Based on the capacitance between different electrode pairs, an ECT sensor can give the permittivity distribution of the sensing domain with a suitable image reconstruction algorithm. Wang et al. carried out dynamic tests in a CFB with an external heat exchanger under different operating conditions using two circular ECT sensors with 8 electrodes and concluded that the gas-solids flow can be controlled based on the information obtained by ECT and pressure drop measurements [4]. Sun et al. studied the volumetric concentration and angular concentration of solids using ECT and by cross-correlating the capacitance fluctuations respectively [7]. Wang et al. measured the cross-sectional distribution of a dilute gas-solids flow in a large square CFB [8]. Azzopardi et al. employed a twin-plane ECT sensor to monitor the distribution and fluctuation of pulverized coal in dense-phase pneumatic conveying [9]. Qiu et al. characterized the flow regime of gas-solids flow in a CFB with three circular risers using a two-plane ECT sensor and a differential pressure transducer [10]. Weber et al. applied 3D ECT in a bubbling fluidized bed to study the hydrodynamics of fluidization processes, and bubbling frequency and bubble diameter were also computed using the data measured by ECT [11].

For process optimization, it is necessary to explore the flow behavior in CFB. However, literature review shows that few papers studied the hydrodynamics of gas-solids flow in a CFB with the risers of different shape. Furthermore, most of the studies were carried out using two-dimensional (2D) ECT sensors. This paper reports a lab-scale CFB with four different risers, which is equipped with 3D ECT sensors and differential pressure transducers. Based on theoretical analysis and experimental results, the flow behavior in the bottom of the risers and the performance of 3D ECT are compared.

2. Experimental setup

2.1 CFB

As shown in Figure 1, the CFB consists of a plenum chamber, a riser, a cyclone, a down-comer and a loop seal. The cyclone is made of steel and the rest of the CFB is made of Plexiglas. To investigate the hydrodynamics of gas-solids flows in the risers with different shape and dimension, four risers are built. As listed in Table 1, the shape of cross-section of the risers is circular (R1), circular (R2), square (R3) and rectangular (R4), respectively. The areas of cross-section in the bottom of R2, R3 and R4 risers are similar to each other. The area of R1 riser is larger than R2. An air distributor and a fine mesh are placed above the plenum chamber to hold solids and to provide a uniform air distribution. The number of holes of the air distributors is given in Table 1. The height of the risers is 2.2 m. During experiment, the riser and plenum chamber can be replaced as a whole. A pressure transducer (Keller PD23) is used to acquire the pressure drop in the dense-phase zone, as shown in Figure 1.

Table 1 Parameters of risers

Riser Shape Size (inner diameter)in the bottom (cm)

Area of cross-sectionin the bottom（cm2） Hole number

of air distributor

R1 Circular 14.0 154 308R2 Circular 13.0 133 234R3 Square 11.5×11.5 132 256R4 Rectangular 6.7×20.1 135 288

2

2.2

m Riser

ECT

Cyclone

Downcomer

7.0 cm14.5 cm

Inner diameter13 cm

Inner diameter14 cm

Pressuresignal

Air distributor

Plenum chamber

Filter

Air compressor

Roots blower

Loop seal

h

Figure 1 Circulating fluidized bed with R1 riser

2.2 3D ECT Sensor and Image Reconstruction

Figure 2 shows 3D ECT sensors for the risers. Each of the ECT sensors consists of 12 electrodes evenly arranged in three planes. The width of the electrodes is 3.5 cm. The length of the electrodes for the 4 risers is different to cope with different dimension of the risers. The detailed parameters of the 3D ECT sensors are given in Table 2. One of the ECT sensors is installed in the bottom of the riser, with 14.5 cm in height and 7.0 cm from the air distributor, as shown in Figure 1. An AC-ECT system is used to acquire the measurement data. Linear back projection (LBP) algorithm with a threshold [12] is used to reconstruct images. For reconstruction, the imaging space is divided into some small voxels to calculate and display the permittivity distribution. The dividing method and the number of voxels in the imaging space are given in Table 3. Note that the number of pixels in one plane is only about 300 although the voxels in the whole sensing domain are around 5000. Before measurement, sand and air are used to calibrate the ECT system.

(a) R1 (b) R2 (c) R3 (d) R4Figure 2 3D ECT sensors

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Table 2 Electrode parameters of ECT sensors (cm)

Riser Length Width Gap in radial direction Gap in axial direction

R1 11.6 3.5 0.5 1.0

R2 10.8 3.5 0.5 1.0

R3 11.5 3.5 0.5 1.0

R4 14.4 3.5 0.5 1.0

Table 3 Voxels in sensing domain

RiserGrid partition

(length×width×height)

Number of voxels in sensing domain Number of pixels in one plane

R1 20×20×16 5056 316

R2 20×20×17 5372 316

R3 17×17×16 4624 289

R4 11×30×16 5280 330

2.3 Experimental Condition

Sand is used in the experiment with bulk density of 2597 kg/m3 and a packing factor of 0.65. The size distribution of sand is shown in Figure 3 (a). The median size of the particle diameter is 288 and most particles concentrate in a range of 100 and 600 , which are in Group B according to Geldart classification [13]. The relation of pressure drop and superficial gas velocity for sand is shown in Figure 3 (b). It can be seen that the critical fluidization velocity of sand is 0.28 m/s. The height of sand in the risers is all set to 25 cm and the quality of sand is 6.49 kg, 5.60 kg, 5.58 kg and 5.68 kg, respectively. During experiment, the superficial gas velocity is changed from 0.6 m/s to 3.0 m/s with a step of 0.2 m/s. The data acquisition rate of the ECT system is 130 frames per second and 1000 sets of capacitance data are collected for each case. The data acquisition rate of pressure transducer is 1000 samples per second and the data acquisition time is 10 s.

(a) Particle size distribution (b) Critical fluidization velocity

Figure 3 Properties of sands

3. Results and Discussion

3.1 Solids concentration

To investigate the hydrodynamics of the gas-solids flow, the standard deviation of solids concentration calculated using the ECT data and the pressure drop for all cases is shown in Figure 4. The

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area-averaged solids concentration is defined as [10]

22\*MERGEFORMAT()

where is the area-averaged solids volume fraction, is the close-packing volume fraction of particles, is the normalized permittivity obtained from the image reconstructed by LBP, is the

effective pixel area in the sensing domain, and is the number of the effective pixels.

It can be seen from Figure 4 that the standard deviation of solids concentration increases with the increase in superficial gas velocity and then decreased. The first peak of standard deviation of solids concentration for the four risers appears at 1.2 m/s, 1.2 m/s, 1.0 m/s and 0.8 m/s, respectively. The standard deviation of pressure drop has a similar variation tendency to solids concentration while the position of peaks has a slightly difference. The peak of pressure drop for the four risers appears at 1.2 m/s, 1.2 m/s, 1.2 m/s and 1.0 m/s, respectively. The difference in position of the first peak is mainly due to the fact that the pressure probe measures a point near the wall while the ECT measures the average in the whole imaging space. On the other hand, the standard deviation of pressure drop for R1 has the largest value compared with other risers. One possible reason is that the area of cross-section of R1 is the largest, thus the quality of the particle materials is different at a same height. This might exert a significant influence on the gas-solids flow. The peak of standard deviation of solids concentration or pressure drop means that the fluctuation is the largest under this velocity and corresponds to a transition of flow regime. With the increase in superficial gas velocity, the flow regime changes from bubbling flow to slugging flow and then to turbulent flow. To further investigate the hydrodynamic of gas-solids flow quantitatively, only the bubbling flow below 1.2 m/s in superficial gas velocity is considered in the following sections.

(a) Solids concentration (b) Pressure drop

Figure 4 Standard deviation

3.2 Bubble image

A gas bubble is defined as a region that the solids volume fraction is lower than a certain value [14]. In this paper, the regions of a solids concentration lower than 20% of the close-packing volume fraction is regarded as gas bubble [15]. Figure 5 shows 3D images of a moving bubble at 0.6 m/s in four risers. These images are a series of continuous signals. For R1, a single bubble exists in the sensing space and keeps moving upwards. As the bubble moves out of the space gradually, a new bubble enters the sensing domain, demonstrating that a 3D ECT sensor can reflect the path of a moving bubble. Compared with R1, the shape and size of bubbles in other risers has a slightly different on account of the change in flow condition and the shape of the cross-section of risers.

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frame 1 frame 4 frame 6 frame 10 frame 15 frame 17(a) R1

frame 1 frame 4 frame 6 frame 10 frame 15 frame17

(b) R2

frame 1 frame 4 frame 6 frame 10 frame 15 frame 17

(c) R3

frame 1 frame 4 frame 6 frame 10 frame 15 frame 17

(d) R4

Figure 5 3D images of moving bubbles at 0.6 m/s

3.3 Bubble diameter

To quantify the bubble size under different operating conditions, a semi-empirical formula [14] is used to describe the bubble growth.

33\*MERGEFORMAT()

where is the bubble diameter, is the superficial gas velocity, is the height of the bubble above

air distributor as shown in Figure 1, is the area of cross-section, is the hole number of air

distributor, and is the gravitational acceleration.

Equation 3 indicates that the bubble diameter increases with the increase in the axial position of bubbles. Table 4 gives the height of each electrode plane for comparing the bubble diameter. Using the experimental data, the bubble diameter is defined as the equivalent diameter of the gas bubble region.

Table 4 Axial position used in calculating bubble diameter

Planes P1 P2 P3

(cm) 10.25 14.25 18.25

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Figure 6 shows the bubble diameter calculated and the solids concentration from the ECT sensors by equation 3, where “T” means theoretical results and “E” means experimental results. It can be seen that the theoretical bubble diameter increases with the increase in superficial gas velocity and axial height. The bubble diameter calculated using the experimental data has a similar variation tendency except for some data points. For R1, the experimental results are much closer to the theoretical results, indicating that the solids concentration with 3D ECT can be used to estimate the bubble growth process. For the other risers, the increase in bubble diameter with the axial height is not obvious. Therefore, the estimated bubble diameter on the second and third planes has larger divergence compared with the theoretical results. A possible reason is the bubble diameter is the equivalent size to the regions with a solids concentration lower than 20%. The estimated bubble diameters are similar to each other if the equivalent bubble has no obvious difference at the three heights. Note that the bubble diameter on P3 under superficial velocities of 1.2 m/s and 1.0 m/s has a dramatic decrease for R3 and R4, respectively. A possible reason is the effect of flow regime transition according to the analysis on the standard deviation of solids concentration in Figure 4.

(a) R1 (b) R2

(c) R3 (d) R4

Figure 6 Experimental results of bubble diameter

3.4 Bubble velocity

The capacitance signal can represent the moving process of bubbles. To investigate the bubble velocity using capacitance data from the 3D ECT sensors, the distribution of raw capacitance measurements is analyzed. Figure 7 shows the relative frequency of capacitance data for R1 based on histogram. It can be seen that the distribution of capacitance data for the three planes under the same superficial gas velocity is similar to each other. Most of the capacitance data are concentrated near a certain value. With the increase in superficial gas velocity, the peaks are gradually moving to smaller capacitance. Figure 8 shows the time series of capacitance for R1 under 0.6 m/s superficial gas velocity. The capacitance signal in the downward plane has a shift compared with the upward plane. The higher similarity and the obvious shift of capacitance signals on the three planes make it possible to calculate the bubble velocity using the capacitance data by cross-correlation.

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(a) U = 0.6 m/s (b) U = 0.8 m/s

(c) U = 1.0 m/s (d) U = 1.2 m/sFigure 7 Capacitance distribution for R1

Figure 8 Time series of capacitance for R1 under 0.6 m/s in superficial gas velocity

Cross-correlation function can be expressed as

44\*MERGEFORMAT()

where is the signal of the upstream, is the signal of the downstream, is the sample number,

and is the number of samples that correspond to the delay time. The delay time is computed by

55\*MERGEFORMAT()

where is sampling interval of ECT system, which is 7.7 ms for the AC-ECT system. The bubble velocity can be calculated by

66\*MERGEFORMAT()

where is the bubble velocity, and is the distance between the upstream and the downstream.

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To calculate the velocity using capacitance data, three sets of correlated planes are considered as shown in Figure 9. For L1, P1 and P2 are used as the correlated planes. For L2 and L3, the correlated planes are P2-P3 and P1-P3. The length of L1, L2 and L3 is 4 cm, 4 cm and 8 cm, respectively. Figure 10 shows the correlation coefficient with L1 for the four risers under different superficial gas velocity. It can be seen that the peaks of the curve are clear.

Figure 9 Correlated planes

(a) R1 (b) R2

(c) R3 (d) R4Figure 10 Correlation coefficient for L1 under different operating conditions

Theoretical values of bubble velocity can be calculated using (6) proposed by Davidson and Harrison [16] for comparison with the experimental results.

77\*MERGEFORMAT()

Figure 11 shows the theoretical and experimental results of the bubble velocity under different operating conditions. It can be seen that the theoretical bubble velocity keeps growing with the superficial gas velocity linearly. The gap between different planes is minor and has a little effect on the bubble velocity. In comparison, the bubble velocity calculated using the capacitance data also increases with the increase in superficial gas velocity in most cases. Note that the bubble velocity for R4 decreases

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obviously when the superficial gas velocity increases from 1.0 m/ to 1.2 m/s due to the influence of slugging flow. However, the experimental results are smaller than the theoretical results regardless of the shape of cross-section. The velocity calculated by cross-correlation is the superficial velocity, not the real bubble velocity.

(a) R1 (b) R2

(c) R3 (d) R4Figure 11 Theoretical bubble velocity and bubble velocity calculated using capacitance data.

To further explain the divergence between the experimental results and theoretical results, the number of samples corresponding to the delay time is given in Table 5. It can be seen that the maximum value of the number of samples is 22. For L1 and L2, most of the number of samples is smaller than 10. A smaller sample number means a larger estimation error for the bubble velocity.

Table 5 Number of samples corresponding to delay time

Riser R1 R2 R3 R4U (m/s) 0.6 0.8 1.0 1.2 0.6 0.8 1.0 1.2 0.6 0.8 1.0 1.2 0.6 0.8 1.0 1.2L1 7 8 7 6 9 7 8 7 12 9 8 7 8 7 6 8L2 7 6 6 5 8 6 7 8 10 9 8 6 7 6 5 7L3 13 13 12 11 18 13 13 14 22 18 16 12 14 13 10 14

4. Conclusions

Four three-plane ECT sensors are designed and used to investigate the hydrodynamics of gas-solids flow in the bottom of a circulating fluidized bed with four risers of different shapes, including two circular risers, a square riser and a rectangular riser. Using the capacitance data, the solids concentration and bubble image are obtained to describe the dynamic behavior of gas-solids flows. Some conclusions are summarized as follows.

(1) The bubbling flow regime can be identified by the standard deviation of solids concentration and pressure drop for the four risers. The flow regime transition estimated using the two methods is

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slightly different due to different measuring regions. For R4 with a rectangular riser, the transition velocity is smaller than others.

(2) Using the three-plane ECT, the bubble moving process can be represented by 3D images. The shape of equivalent bubbles is associated with the shape of risers.

(3) The bubble diameter and velocity increases with the increase in gas velocity and axial height for the four risers. The experimental results have a similar variation tendency to the theoretical results. However, the flow regime transition from bubbling flow to slugging flow has a certain effect on the estimation of bubble property. Furthermore, an ECT system with a higher data acquisition rate is necessary to enhance calculation accuracy of bubble velocity by cross correlation.

Acknowledgement

The authors would like to thank the National Natural Science Foundation of China (No. 61374018) for supporting this work.

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