Reconstruction of electrical capacitance tomography images based on fast linearized alternating direction method of multipliers for two-phase flow system

Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.

Damage Detection for CFRP Based on Planar Electrical Capacitance Tomography

Due to the widespread use of carbon fiber reinforced polymer/plastic(CFRP),the nondestructive structural health monitoring for CFRP is playing an increasingly essential role.As a nonrad iative,noninvasive and nondestructive detection technique,planar electrical capacitance tomography(PECT)electrodes array is employed in this paper to reconstruct the damage image according to the calculated dielectric constant changes.The shape and duty ratio of PECT electro-des are optimized according to the relations between sensitivity distribution and the dielectric constant of different anisotropic degrees.The sensitivity matrix of optimized PECT sensor is more uniform as the result shows,because the sensitiv-ity of insensitivity area can be increased by adding rotation of optimized electro-des.The reconstructed image qualities due to different PECT arrays and different damage locations are investigated at last.The simulation results indicate that:PECT can be used to detect the surface damage of CFRP;the sensitivity matrix of PECT for CFRP is highly relevant with the degree of anisotropic dielectric con-stant;the rotatable PECT sensor with rotation has better performance in unifor-mity of sensitivity;for different damage locations,the rotatable sensor with rotation has better image quality in most cases.

Visualization Detection of Solid-Liquid Two-Phase Flow in Filling Pipeline by Electrical Capacitance Tomography Technology

During mine filling,the caking in the pipeline and the waste rock in the filling slurry may cause serious safety accidents such as pipe blocking or explosion.Therefore,the visualization of the innermine filling of the solid-liquid two-phase flow in the pipeline is important.This paper proposes a method based on capacitance tomography for the visualization of the solid-liquid distribution on the section of a filling pipe.A feedback network is used for electrical capacitance tomography reconstruction.This reconstruction method uses radial basis function neural network fitting to determine the relationship between the capacitance vector and medium distribution error.In the reconstruction process,the error in the linear back projection is removed;thus,the reconstruction problem becomes an accurate linear problem.The simulation results showthat the reconstruction accuracy of this algorithm is better than that of many traditional algorithms;furthermore,the reconstructed image artifacts are fewer,and the phase distribution boundary is clearer.This method can help determine the location and size of the caking and waste rock in the cross section of the pipeline more accurately and has great application prospects in the visualization of filling pipelines in mines.

A Multiresolution Reconstructive Algorithm Based on Network Theory for Electrical Capacitance Tomography

Electrical capacitance tomography technique reconstructs dielectric constant distribution in an object by measuring the capacitances between the eletrode pairs which are mounted around this object. Because of the limitation of measurement condition, the measured data are imcomplet. This paper describes a multiresolution reconstructive algorithm which is based on network theory for electrical capacitance tomography technique. The dielectric constant distribution of flow of two components in a pipeline is reconstructed. The algorithm is as follows: Firstly, construct a rough, first level system model, and assume the dielectric constant distribution of the region to be reconstructed. After iteration, the dielectic constant of each unit can be reconstructed. Secondly, construct a finer, second level the system model and determine the initial dielectric constant of each unit in the region to be reconstructed according to related information between two levels. After iteration, the image of the pipeline's cross section can be reconstructed. The results of simulated experiments about different kinds of medium distributions show that this algorithm is effective and can converge.

Modeling and Implementation of AC Electrical Capacitance Tomography

Electrical Capacitance Tomography (ECT) determines the dielectric permittivity of the interior object depending on the measurements of exterior capacitance. Generally, the electrodes are placed outside the PVC cylinder where the medium to be imaged is present;but in ECT using inter-electrode capacitance measurements can be achieved by placing inside of the dielectric medium. In the proposed ECT system, the ECT sensor is modeled using ANSYS software and the model is implemented in real ECT system. For each step of measurement, a stable AC signal is applied to a pair of electrodes that form a capacitor. The novel system is to measure the capacitance range variation in picofarad and the corresponding voltage ranges from 1 volt to 4 volts. The switching speed of all combinational electrodes is implemented using embedded system to achieve higher speed performance of AC ECT system which eliminates the drift and stray capacitance error. This is yielding the original image of unknown multiphase medium inside the electrodes using Lab VIEW. This paper investigates several advantages such as improved overall system performance;simple structure, avoids stray capacitance effect, reduces the drift problem and achieves high signal to noise ratio.

Image Reconstruction Using a Genetic Algorithm for Electrical Capacitance Tomography

Electrical capacitance tomography （ECT） has been used for more than a decade for imaging dielectric processes. However, because of its ill-posedness and non-linearity, ECT image reconstruction has always been a challenge. A new genetic algorithm （GA） developed for ECT image reconstruction uses initial results from a linear back-projection, which is widely used for ECT image reconstruction to optimize the threshold and the maximum and minimum gray values for the image. The procedure avoids optimizing the gray values pixel by pixel and significantly reduces the search space dimension. Both simulations and static experimental results show that the method is efficient and capable of reconstructing high quality images. Evaluation criteria show that the GA-based method has smaller image error and greater correlation coefficients. In addition, the GA-based method converges quickly with a small number of iterations.

Investigation of gas-solids flow hydrodynamics in a cold model of a dual fluidised bed gasifier using electrical capacitance tomography sensors

The flow characteristics of a dual fluidised bed gasifier(DFBG)are more complex than those of a single fluidised bed gasifier.For stable operation and appropriate control,a cold DFBG test facility with both an upper and a lower U-valve was built,and electrical capacitance tomography(ECT)sensors were installed with pressure transducers to investigate the effects of operating conditions on gas-solids flow hydrodynamics.The operating parameters included gas velocities in the riser and in the bubbling fluidised bed,aeration velocity in the lower U-valve,bed material inventory,and particle size.This is the first time that ECT was applied in different flow zones of a dual fluidised bed gasifier system.The experimental results indicated that ECT in the recycle chamber could monitor the performance of the lower U-valve under different operating conditions for early detection of gas shortcut from the riser to the bubbling bed.Three main flow regimes in the riser and the differences between the reactors were identified by two sets of ECT sensors with pressure transducers.Finally,the effects of the operating conditions on the pressure drop in different parts of the DFBG was investigated.

An Advanced Algorithm of Electrical Capacitance Tomography

We describe a new two phase flow electrical capacitance tomography algorithm of image reconstruction which is based on 12 electrode capacitance transducers. According to the result of computer simulation, this algorithm is able to greatly increase the imaging fidelity without decreasing the imaging velocity.

Structure-guided Capacitance Relationships in Oxidized Graphene Porous Materials Based Supercapacitors

Supercapacitors formed from porous carbon and graphene-oxide(GO)materials are usually dominated by either electric double-layer capacitance,pseudo-capacitance,or both.Due to these combined features,reduced GO materials have been shown to offer superior capacitance over typical nanoporous carbon materials;however,there is a significant variation in reported values,ranging between 25 and 350 F g^(−1).This undermines the structure(e.g.,oxygen functionality and/or surface area)-performance relationships for optimization of cost and scalable factors.This work demonstrates important structure-controlled charge storage relationships.For this,a series of exfoliated graphene(EG)derivatives are produced via thermal-shock exfoliation of GO precursors and following controlled graphitization of EG(GEG)generates materials with varied amounts of porosity,redox-active oxygen groups and graphitic components.Experimental results show significantly varied capacitance values between 30 and 250 F g^(−1)at 1.0 A g^(−1)in GEG structures;this suggests that for a given specific surface area the redox-active and hydrophilic oxygen content can boost the capacitance to 250–300%higher compared to typical mesoporous carbon materials.GEGs with identical oxygen functionality show a surface area governed capacitance.This allows to establish direct structure-performance relationships between 1)redox-active oxygen functional concentration and capacitance and 2)surface area and capacitance.

Image Reconstruction for ECT under Compressed Sensing Framework Based on an Overcomplete Dictionary

Electrical capacitance tomography(ECT)has great application potential inmultiphase processmonitoring,and its visualization results are of great significance for studying the changes in two-phase flow in closed environments.In this paper,compressed sensing(CS)theory based on dictionary learning is introduced to the inverse problem of ECT,and the K-SVD algorithm is used to learn the overcomplete dictionary to establish a nonlinear mapping between observed capacitance and sparse space.Because the trained overcomplete dictionary has the property to match few features of interest in the reconstructed image of ECT,it is not necessary to rely on the sparsity of coefficient vector to solve the nonlinear mapping as most algorithms based on CS theory.Two-phase flow distribution in a cylindrical pipe was modeled and simulated,and three variations without sparse constraint based on Landweber,Tikhonov,and Newton-Raphson algorithms were used to rapidly reconstruct a 2-D image.

Possibility of a Novel Warm-Up Strategy Using Capacitive and Resistive Electric Transfer: A Pilot Study

[Purpose] Capacitive and resistive electric transfer (CRET) is becoming prevalent in sports settings. CRET is effective for improving pain and healing injured tissue;however, its influence on muscle function and morphology is still unclear. This study confirmed the immediate effects of CRET on the duration of muscular stiffness and range of motion (ROM). [Method] This study describes the protocol for a single-arm trial with the non-blinding of participants and researchers. Twenty-four healthy men participated in the study. They received CRET therapy for their low back areas. The muscular stiffness of the multifidus muscle (superficial and deep) and the ROM using the active straight leg raise (ASLR) test were measured pre-intervention, post-intervention (immediately), and 15 and 30 min post-intervention. We compared these parameters using a one-way analysis of variance and Dunnett’s test (multiple comparison tests for subtests). [Results] The muscular stiffness of the superficial and deep multifidus muscles was significantly decreased, and the ASLR test showed a significant increase compared with the test performed pre-intervention. In addition, these effects persisted for 30 min. [Conclusion] Warm-up is vital for improving muscular stiffness and increasing the ROM. CRET is a useful device for achieving these aims, particularly as a passive warm-up method in sports settings.

Twin-array capacitance sensor for multi-parameter measurements of multiphase flow

We propose a twin-array capacitance （TAC） sensor for the measurement of concentration, velocity, and flowrate of gas-solid two-phase flow. Using the sensitivity non-uniformity of a neighboring electrode, the regional concentration of the cross-section was reconstructed directly. Additionally, the finite element method was used to analyze the capacitance of the sensors composed of a different number of electrodes. TAC sensors with 4, 6, and 8 electrodes were found to be the best for regional concentration measurements. Based on this, the 8-electrode twin-plane electrical capacitance tomography （ECT） sensor, the 4-electrode TAC sensor, and the 6-electrode TAC sensor were used to measure the concentration, velocity, and fiowrate of granules in granular flow. The flowrates measured by ECT and TAC were compared with the flowrate obtained by a gravity sensor to verify the measurement accuracy. Experiments on vertical and inclined pipelines with granular flow were carried out. We found that the flowrate accuracy of the 4-electrode TAC is distinctly better than that of the 6-electrode TAC in the vertical pipeline while the flowrate accuracy of the 4-electrode TAC and the 6-electrode TAC were similar for the inclined pipeline.

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds.Accurate prediction of bubbling behavior in deep fluidized beds,however,has been a challenge due to the higher degree of bubble coalescence and break up,high probability of the slugging regime,partial fluidization,and chaotic behavior in the bubbling regime.In this work,the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography(ECT)system.Solid volume fraction,average bubble velocity,average bubble diameter,and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios(H/D=3.5 and H/D=3.78).This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed.The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights,with larger values observed in the deeper bed compared to the shallower one.Predicted values for bubble diameter,bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work.Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16%and 15%for the bed height of 49 cm and 13%and 8%for the bed height of 53 cm,respectively.

Transportation characteristics of gas-solid two-phase flow in a long-distance pipeline

In this study, experiments on fly ash conveying were carried out with a home-made long-distance positive-pressure pneumatic conveying system equipped with a high performance electrical capacitance tomography system to observe the transient characteristics of gas-solid two-phase flow. The experimen- tal results indicated that solids throughput increased with increasing solids-gas ratio when the conveying pipeline was not plugged. Moreover, the optimum operating state was determined for the 1000 m long conveying pipeline with a throttle plate of 26 orifices. At this state the solids throughput was about 12.97 t/h. Additionally, the transportation pattern of fly ash gradually changed from sparse-dense flow to partial and plug flows with increasing conveying distance because of the conveying pressure loss, These experimental results provide important reference data for the development of pneumatic conveying technology.

Online monitoring of gas-solid two-phase flow using projected CG method in ECT image reconstruction

Electrical capacitance tomography （ECT） is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient （CG） method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Kryiov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas-solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas-solid two-phase flow measurement,

FLOW DYNAMICS OF GAS-SOLID FLUIDIZED BEDS WITH EVAPORATIVE LIQUID INJECTION

The electrical capacitance tomography （ECT） with neural network multi-criteria image reconstruction technique （NN-MOIRT） is developed for real time imaging of a gas-solid fluidized bed using FCC particles with evaporative liquid injection. Some aspects of the fundamental characteristics of the gas-solid flow with evaporative liquid injection including real time and time averaged cross-sectional solids concentration distributions, the cross-sectional solids concentration fluctuations and the quasi-3D flow structures are studied. A two-region model and a direct image calculation are proposed to describe the dynamic behavior in both the bubble/void phase and the emulsion phase based on the tomographic images. Comparisons are made between the fundamental behaviors of the gas-solid flows with and without evaporative liquid injection for various gas velocities ranging from bubbling to turbulent fluidization regimes. Significant differences are observed in the behavior of the gas-solid flow with the evaporative liquid injection compared to the fluidized bed without liquid injection.

Dense-phase pneumatic conveying under pressure in horizontal pipeline

The gas/solid flow regime of dense-phase pneumatic conveying of pulverized coal under a pressure of 4.0 MPa in horizontal pipeline 10 mm in diameter, is monitored by electrical capacitance tomography （ECT） using 8 electrodes. To improve the accuracy of the capacitance measurement, an AC-based singlechannel capacitance measuring circuit was developed, and a modified iterative Landweber algorithm was used to reconstruct the image. A two-fluid model based on the kinetic theory of granular flow was used to study the three-dimensional steady-state flow behavior of dense-phase pneumatic conveying of pulverized coal.

A qualitative study on the pulsatile flow phenomenon in a dense fly ash pneumatic conveyor

Understanding of the dynamic particulate flow structures within a dense gas-fly ash pneumatic conveyor must be improved in order to better aid its design guidance.The complex pulsatile movement of the gas-fly ash mixture dominates the flow performance within the pipeline,and historically,non-invasive measurement devices such as the electrical capacitance tomography（ECT） were often used to sufficiently capture the flow dynamics.However,inadequate studies have been conducted on the pulsatile flow phenomenon,which directly relate to the gas-fly ash two-phase flow performance.This paper aims to investigate the pulsatile flows using an ECT device.Initially,pulsatile flow patterns under various experimental conditions were obtained through ECT.Pulses within a flow were then characterised into pulse growth and decay segments,which represent the superficial fluidisation and deaeration processes during conveying.Subsequently,structural and statistical analyses were performed on the pulse growth and decay segments.Results suggested that the increasing air mass flow rate led to the decrease of the superficial fluidisation/deaeration magnitude,however,the increase of the superficial fluidisation/deaeration durations.Also,the air mass flow rate was indicated as the dominant factor in determining the pulsing statistical parameters.This research provides fundamental insights for further modelling the dense fly ash pneumatic flows.

Effects of riser geometry on gas-solid flow characteristics in circulating fluidized beds

The performance of a circulating fluidized bed strongly depends on its parameter settings,including that of riser geometry.In this study,a laboratory-scale circulating fluidized bed with three different riser geometries(circular,square,and rectangular)that had the same cross-sectional area and height was operated under two static bed heights(20,and 35 cm).Electrical capacitance tomography was combined with differential pressure transducers and an optical-fiber probe to measure the solids'volume fraction,differential pressure fluctuations,and radial particle concentration variations.Computational particle fluid dynamics simulations were also performed.The results showed that single bubbles appeared in the bottom region of the circular and square risers and double bubbles in the bottom region of the rectangular riser.The autocorrelation of capacitance signals was periodic for the circular and square risers and non-periodic for the rectangular riser.The radial particle concentration profiles showed a single-core annulus structure in the circular and square risers,but a double-core annulus structure along the long side and single-core annulus structure along the short side in the rectangular riser.Shannon entropy analysis showed that fluidization was less disordered and most predictable for the rectangular riser.

Three-dimensional dynamic characterization of square-nosed slugging phenomena in a fluidized bed

Slugging represents one of the major regimes in fluidization,which occurs in small diameter beds with large bed height-to-diameter ratio or in large diameter beds with internals that resemble multiple small diameter fluidized beds.Slug types include round-nosed slug,wall slug and square nosed slug.Studies of the slugs have been mainly focused on round-nosed or wall slugs known as half slug.typically occurring in Geldart group A particle fuidization.The square-nosed slug typically occurring for Geldart group D particles appears to be regarded as simple in its structure.The Electrical Capacitance Volume Tomogra phy(ECVT)imaging of the square-nosed slugging phenomena conducted in this study reveals otherwise.That is the structure of the square nosed slug is,in fact,complex,particularly with respect to its dynamic variation in fluidization.More broadly.this study examines experimentally the hydrodynamic character-istics of the square-nosed fluidization regime.Specifically,simultaneous measurements from multiple ECVT sensors provide non-inv asive,continuous,3.dimensional imaging of the entire flow region of the slugging bed and hence enabling the dynamic characterization of the evolution of the slugs.The analysis of the 3D images reconstructed for real time gas-solid volume fraction profile of the slugging fluidized bed indicates that there are three different zones.namely.the bottom fluidization zone,the gas slug zone,and the solid slug zone,co-existing in the bed.The three zones present different hydrodynamic characteristics during the slug evolution.It is found that varying the gas velocity of the slugging bed mainly varies the maximum length of the gas slug zone,while it only has a minor effect on the lengths of the bottom fluidization zone and solid slug zone.It also has an insignificant efect on the solid volume fraction of the three zones.