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Citation for published version
Zhang, WB and Yang, BB and Qian, XC and Yan, Yong (2016) Charge Distribution Reconstruction
in a Bubbling Fluidized Bed Using a Wire-Mesh Electrostatic Sensor. In: IEEE International
Instrumentation and Measurement Technology Conference, 23-26 May 2016, Taipei, Taiwan.
DOI
https://doi.org/10.1109/I2MTC.2016.7520328
Link to record in KAR
http://kar.kent.ac.uk/55765/
Document Version
Author's Accepted Manuscript
Charge Distribution Reconstruction in a
Bubbling Fluidized Bed Using a
Wire-Mesh Electrostatic Sensor
Wenbiao Zhang, Binbin Yang
School of Control and Computer Engineering
North China Electric Power University
Beijing 102206, P.R. China
wbzhang@ncepu.edu.cn, ncepu_ybb@126.com
Yong Yan
School of Engineering and Digital Arts
University of Kent
Canterbury, Kent CT2 7NT, U.K.
y.yan@kent.ac.uk
Abstract—The presence of electrostatic charge in a bubbling
fluidized bed influences the operation of the bed. In order to
maintain an effective operation, the electrostatic charges in
different positions of the bed should be monitored. In this paper
a wire-mesh electrostatic sensor is introduced to reconstruct the
charge distribution in a bubbling fluidized bed. The wire-mesh
sensor is fabricated by two mutually perpendicular strands of
insulated wires. A Finite Element Model is built to analyze the
sensing characteristics of the sensor. The sensitivity distributions
of each wire electrode and the whole sensor are obtained from
the model, which proves that wire-mesh electrostatic sensor has a
higher and more uniform sensitivity distribution than single wire
sensors. Experiments were conducted in a gravity drop test rig to
validate the reconstruction method. Experimental results show
that the charge distribution can be reconstructed when sand
particles pass through the cross section of the sensor.
Keywords
—charge distribution; reconstruction; wire-mesh
electrostatic sensor; sensor characterization; sensitivity distribution
I. INTRODUCTION
Due to the contact and frictions between the particles and
between the particles and wall, electrification is inevitable in a
fluidized bed. The presence of electrostatic charges in the bed
affects the operation of the bed. The hydrodynamics in the bed,
such as bubble size and shape and solids mixing rate, changes
with the level of electrostatic change in the bed. If the charge
on the particles exceeds a critical value, the particles in the
bed may adhere to the wall and even cause discharges and
explosion [1]. In order to maintain an effective operation of
the fluidized bed, the electrostatic charges in the bed should
be continuously monitored. However, there are few sensors
that are available for reliable, accurate and low-cost charge
density measurement at present.
As an off-line measurement tool, Faraday cups were used
to directly measure the charge density in the bed [2, 3].
However, charge generation and dispassion during the
sampling process would influence the measurement result and
Faraday cups were susceptible to variations in environmental
factors. Apart from Faraday cups, electrostatic probes were
developed to measure the electrostatic charges in fluidized
beds. A theoretical model was developed by Chen et al. to
explain the electrical current signals due to the passage of
isolated gas bubbles in a fluidized bed [5, 6]. Based on this
model, a collision probe was built to measure the particle
charge-to-mass ratios in a 2D bubbling fluidized bed. An
induction probe, which was mounted flush with the outside
wall of the bed, was also developed by Chen et al.. They
applied a number of induction probes to measure the induced
charge signals due to the passage of bubbles and the charge
distribution around the bubbles was reconstructed with
different algorithms [7-9]. He et al. [10, 11] developed a
dual-tip electrostatic probe for the measurements of particle
charge density and bubble properties in a bubbling fluidized
bed. The estimated particle charge density and bubble rise
velocity were in reasonable agreement with those obtained
using a Faraday cup and video imaging. However,
electrostatic probes can only provide localized charge
distribution information near the electrode. In order to
maintain an effective operation of the fluidized bed, the
electrostatic charge distribution in the whole cross section of
the bed should be monitored.
As a noninvasive tomography method, electrostatic
tomography (EST) was applied to visualize the flow pattern
and reconstruct the charge distribution in the pneumatic
conveying pipeline [12-15]. A 16-electrode system was
applied by Green et al. to reconstruct the concentration profile
in a gravity conveyer [12]. Machida et al. combined a back
projection algorithm with the least squares method to
reconstruct the electrostatic charges carried by particles [13].
Zhou et al. used the permittivity distribution acquired from an
electrical capacitance tomography (ECT) system to improve
the charge sensitivity field of an EST system and to reduce the
uncertainty relating to the charge distribution reconstruction
[14]. However, the sensitivity distribution of the sensor used
for the EST system is not uniform, which may result in
reconstruction errors, especially in the central area of the pipe.
For the first time, a wire-mesh electrostatic sensor is
introduced in this paper to reconstruct the electrostatic charge
distribution in a bubble fluidized bed. In comparison with
ring-shaped and arc-shaped electrodes, the wire-mesh
electrode has higher and more uniform spatial sensitivity
especially in a large diameter fluidized bed. The drawback of
the electrode is that the wire-mesh can obstruct the flow of
particles in the bed and hence suffer from wear problems.
However, the degree of obstruction depends on the diameter
of the wire and the spacing between them and a wear resistant
material can be used to prevent the abrasion of the wire. A
wire-mesh electrostatic sensor was applied to measure the
mean size of pneumatically conveyed particles [16].
This paper is organized as follows. The sensor design of
the wire-mesh electrostatic sensor is introduced at first. Then
the characteristics of the sensor are analyzed by establishing a
finite element model (FEM). Finally, the charge distribution
reconstruction of the sensor is verified by experiments
conducted using a gravity drop test rig.
II. SENSOR DESIGN AND CHARACTERIZATION
In the bubbling fluidized bed, with the movement of
bubbles, electrostatic charge is generated due to the
interactions between particles, the frictions between particles
and walls of the bed and the relative motion of the particles
with air. Based on the electrostatic induction, a wire-mesh
electrostatic sensor is built to measure the charge distribution
in different parts of the bed. The wire-mesh electrostatic
sensor and its installation on a bubbling fluidized bed are
shown in Fig. 1.
The electrode of wire mesh electrostatic
sensor is made up from two mutually perpendicular strands of
insulated wires with a diameter of 1.5 mm. In each strand,
there are 8 wires with an even spacing of 20 mm. The wires in
the sensor are made from steel with a diameter of 1 mm.
Shrinkable plastic tubes, with thickness of 0.25 mm, are fitted
outside the wires to prevent the direct charge transfer between
the charged particles and the wires. When the charged
particles pass through the mesh, charges are induced on
different wires of the sensor. By measuring the induced
charges from the wires of the sensor, the charge distribution in
the cross section of the bed can be reconstructed. In the
present sensor design, approximately 14% of the bed is
blocked by the wires. With relatively less number of wires and
larger spacing between them, the effect of the blockage by the
wires can be reduced. Due to the intrusiveness of the
wire-mesh sensor, direct impact of particles with the electrode
introduces spike in the electrostatic signal. However, this
effect is minimized in signal conditioning electronics of the
measurement system.
Wire-mesh
electrostatic sensor
Fluidized bed
Air bubble
Fig. 1 Wire-mesh electrostatic sensor on a bubbling fluidized bed
In order to improve the performance of the wire-mesh
electrostatic sensor, the sensing characteristics of the sensor
should be analyzed. The electrostatic field due to the charged
particles in the bed is governed by the following equation:
2
0 r
ρ
ϕ
εε
∇=−
(1)
where is the electrical potential,
0
is the permittivity of free
space,
r
is the relative permittivity of the material and is
charge density in the bed. After solving the electrical potential,
the surface charge density can be found from the relation:
00rr
E
σ εε εε ϕ
= =−∇
(2)
The quantity of induced charge q
i
on the surface of the wire is
calculated from:
i
s
q ds
σ
=
∫
(3)
In view of the wire-mesh structure of the electrostatic
sensor (Fig. 1), it is impractical to find an analytical solution
to the above equations. However, it is possible to build a FEM
model to analyze the characteristics of the sensor. An FEM
model of the wire-mesh electrostatic sensor is built using
COMSOL, as shown in Fig. 2. A cylinder with the same
diameter of the bed (180 mm) is set to be the model domain.
A set of 16 cylinders with a diameter of 1.5 mm is used to
model the wire-mesh. Because the thickness of the insulated
material is only 0.25 mm, it will have less effect on the
sensing characteristics. As a result, the effect of the insulated
material is not considered in the FEM modeling. A sphere
with a radius of 1 mm is applied to model the charged particle.
The materials of the wires and the model domain are set to
steel and air respectively. The relative permittivity of the
particle is set to 2.5 and the charge on the particle is set to 1
µC. The boundary condition is set to ground for the electrodes
and zero charge for the outer surface of the model domain.
Tetrahedral quadratic Lagrange elements are used in the mesh
mode of the FEM model. The wire electrodes are meshed
much finer than other subdomains so as to reflect the charge
distribution in the electrode explicitly. In order to obtain the
sensitivity distribution of the sensor, the cross section of the
bed is divided into a 9 × 9 grid. During the simulation, the
charged particle is placed in the center of different grids of the
cross section and the induced charges on each electrode of the
sensor are calculated according to equations (1)-(3).
X1
X2
X3
X4
X5
X6
X7
X8
Y1
Y2Y3Y4
Y5
Y6
Y7
Y8
Y
X
(a) (b)
Fig. 2 FEM model of the wire-mesh electrostatic sensor (a) and the cross
section of the model (b)
The sensitivity S
i
(x, y) of the ith electrode of the
wire-mesh sensor when the charged particle is placed in the
position (x, y) of the cross section is calculated by
(, ) /
i is
S xy q q=
(4)
where q
i
is the induced charge on the ith electrode and q
s
is
the charge on the particle. By placing the charged particle in
different positions of the cross section, the sensitivity profile
of each electrode of the sensor can be obtained. The
sensitivity distribution of the wire-mesh sensor is shown in
Fig. 3. It can be concluded from the sensitivity profiles of
wires X1 and X4 that each electrode is more sensitive to the
charged particle near the wire. The sensitivity distribution of
the whole sensor is obtained by summing up the sensitivity
profiles of all the electrodes, as shown in Fig. 3(c). The
average sensitivity of the sensor is 0.985. The relative
deviation of the sensitivity at each point from the average
value is shown in Fig. 3 (d). It is evident that the wire-mesh
sensor has a higher and more uniform sensitivity distribution
than other forms of electrostatic sensor[12].
(a)
(b)
(c)
(d)
Fig. 3 Sensitivity distribution of the wire-mesh electrostatic sensor: (a)
sensitivity distribution of wire X1, (b) sensitivity distribution of wire X4, (c)
sensitivity distribution of the whole sensor, (d) relative deviation from the
mean sensitivity
III. CHARGE DISTRIBUTION RECONSTRUCTION
Given the sensitivity distribution of the wire-mesh sensor,
if the charge distribution in the bed is known, the induced
charge on each electrode of the sensor is calculated. Inversely,
if the induced charge on each electrode of the sensor is
available, the charge distribution in the bed can be
reconstructed. The charge distribution reconstruction method
is explained by the following equation:
16
1
1
(, ) / (, )
16
rec i i
i
q xy q S xy
=
=
∑
(5)
where q
rec
(x, y) is the reconstructed charge in the position (x,
y), q
i
is the induced charge on the ith electrode of the sensor
and S
i
(x, y) is the sensitivity of the ith electrode in the
position (x, y). According to equation (4), the charge on
particle q
s
in the position (x, y) can be obtained by dividing
the induced charge q
i
on the ith electrode with the sensitivity
S
i
(x, y) of the ith electrode. The reconstructed charge in the
position (x, y) is the average of the contribution from all the
electrodes of the sensor. By calculating the reconstructed
charge in different positions of the cross section of the bed, a
9 × 9 matrix of the charge distribution is obtained. Finally, the
reconstructed charge distribution is calculated by the
triangle-based linear interpolation from the 9 × 9 matrix.
IV. EXPERIMENTAL SETUP
In order to validate the charge distribution reconstruction
method of the wire-mesh electrostatic sensor, experiments
were conducted in a gravity drop test rig. The diagram of the
test rig is given in Fig. 4. Sand particles were dropped from a
funnel to the cross section of the sensor. The average diameter
of the sands used in the experiments was 175 µm. The
diameter of the outlet of the funnel was 12 mm and the
distance between the outlet of the funnel and the sensor’s
cross section is less than 10 mm. As a result, the sand particles
were concentrated to a small region of the cross section when
they passed through the wire-mesh sensor. A holder was used
to fix the funnel and the radial position of the funnel could be
adjusted. The picture of the wire-mesh electrostatic sensor is
shown in Fig. 5. With the fluctuation of electrostatic charges
on the particles and the movement of the particles, a minute
change in electric current is detected on the electrode. The
current signal is converted to a voltage signal through an
amplifier. The signal is then fed into a second-order low-pass
filter with a bandwidth of 2000 Hz. Finally the signal is
further amplified through a gain adjustable amplifier. The
amplified signals from the circuit are sampled using a NI USB
data acquisition card. The electrostatic signals from all
electrodes of the wire-mesh sensor were sampled
simultaneously with a sampling frequency of 5 kHz and a
sampling time of 30 seconds.
Wire-mesh
electrostatic sensor
Funnel
Holder
Sand
Fig. 4 Gravity drop test rig
Fig. 5 Picture of the wire-mesh electrostatic sensor
V. RESULTS AND DISCUSSION
According to equation (5), the induced charge on each
electrode of the sensor should be measured in order to
reconstruct the charge distribution. However, it is difficult to
directly measure the induced charge on each electrode of the
wire-mesh electrostatic sensor. The electrostatic signal is
generated due to the fluctuation of induced charge on the
electrode, which is related to the charges on the particles in
the sensitivity volume of the electrode. In this paper, Root
Mean Square (RMS) value of the electrostatic signal is
calculated to reflect the quantity of the induced charge on the
electrode. Based on the RMS value of the electrostatic signal,
equation (5) is reformulated as
16
1
1
(, ) ( )/ (,)
16
ii
rlc i
i
i
RMS RMSN
q xy S xy
RMSN
=
−
=
∑
(6)
where q
rlc
(x, y) represents the relative level of charge in the
position (x, y), S
i
(x, y) is the sensitivity of the ith electrode in
the position (x, y), RMS
i
is the RMS value of the ith electrode
when particles passed and RMSN
i
is the RMS value of the ith
electrode when no particles are present. By calculating the
relative difference of the RMS values when sand particles
pass the sensor and when no particle flow, the influence of the
noise on the reconstruction result is reduced. By calculating
the relative level of charge in the whole cross section of the
bed, the relative charge distribution is obtained. During the
experiments, the funnel was placed in the center and near the
wall of the bed, respectively. The charge distributions under
the two conditions are reconstructed, which are shown in Fig.
6. The valley of the distribution can reproduce the dropping
positions of sand particles. Since the induced charge on the
electrode has an opposite sign with the charge on the particle,
the distribution from the RMS value of the signal is opposite
to the real distribution, which can qualitatively represent the
charge distribution.
(a)
(b)
Fig. 6 Relative charge distributions when sand particles passed through the
wire-mesh sensor in the center (a) and near the wall (b)
VI. CONCLUSIONS
In this paper, a wire-mesh electrostatic sensor is
introduced to reconstruct the charge distribution in the
bubbling fluidized bed. A FEM model of the sensor is built to
investigate to sensing characteristics of the sensor. It is found
