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Detecting the Resistivity Distribution of Carbon Fiber Reinforced Concrete by Electrical Resistance Tomography Method
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作者 徐东亮 李卓球 +1 位作者 宋显辉 吕泳 《Journal of Southwest Jiaotong University(English Edition)》 2006年第4期323-330,共8页
According to the principle of electrical resistance tomography ( ERT), the resistivity distribution of the carbon fiber reinforced concrete (CFRC) in the sensing field can be measured by injecting exciting current... According to the principle of electrical resistance tomography ( ERT), the resistivity distribution of the carbon fiber reinforced concrete (CFRC) in the sensing field can be measured by injecting exciting current and measuring the voltage on the sensor electrode arrays installed on the surface of the object. Therefore, measurement of the resistivity distribution of CFRC is divided into first measuring the boundary conditions and then inversely computing the resistivity distribution. To reach this goal, an ERT system was constructed, which is composed of a sensor array unit, a data acquisition unit and an image reconstruction unit. Simulations of static ERT was performed on set-ups with many objects spread in a homogeneous background, and a simulation of dynamic ERT was also done on a rectangular board, the resistivity of which was changed within a small domain of it. Then, the resistivity distribution of a CFRC sample with a circlar hole as the target was detected by the ERT system. Simulation and experimental results show that the reconstructed ERT image reflects the resistivity distribution or the resistivity change of CFRC structure well. Especially, a small change in resistivity can be identified from the reconstructed images in the simulation of dynamic ERT images. 展开更多
关键词 electrical resistance tomography Carbon fiber reinforced concrete Resistivity distribution detection
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Exploration on electrical resistance tomography in characterizing the slurry spatial distribution in cemented granular materials
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作者 Bohao WANG Wei WANG +3 位作者 Feng JIN Handong TAN Ning LIU Duruo HUANG 《Frontiers of Structural and Civil Engineering》 SCIE EI CSCD 2024年第3期365-379,共15页
This study investigated the application of electrical resistance tomography(ERT)in characterizing the slurry spatial distribution in cemented granular materials(CGMs).For CGM formed by self-flow grouting,the voids in ... This study investigated the application of electrical resistance tomography(ERT)in characterizing the slurry spatial distribution in cemented granular materials(CGMs).For CGM formed by self-flow grouting,the voids in the accumulation are only partially filled and the bond strength is often limited,which results in difficulty in obtaining in situ samples for quality evaluation.Therefore,it is usually infeasible to evaluate the grouting effect or monitor the slurry spatial distribution by a mechanical method.In this research,the process of grouting cement paste into high alumina ceramic beads(HACB)accumulation is reliably monitored with ERT.It shows that ERT results can be used to calculate the cement paste volume in the HACB accumulation,based on calibrating the saturation exponent n in Archie’s law.The results support the feasibility of ERT as an imaging tool in CGM characterization and may provide guidance for engineering applications in the future. 展开更多
关键词 electrical resistance tomography cemented granular material GROUTING spatial distribution Archie’s law
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Hydrate formation and distribution within unconsolidated sediment:Insights from laboratory electrical resistivity tomography
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作者 Yanlong Li Nengyou Wu +5 位作者 Changling Liu Qiang Chen Fulong Ning Shuoshi Wang Gaowei Hu Deli Gao 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2022年第9期127-136,共10页
Laboratory visual detection on the hydrate accumulation process provides an effective and low-cost method to uncover hydrate accumulation mechanisms in nature.However,the spatial hydrate distribution and its dynamic e... Laboratory visual detection on the hydrate accumulation process provides an effective and low-cost method to uncover hydrate accumulation mechanisms in nature.However,the spatial hydrate distribution and its dynamic evolutionary behaviors are still not fully understood due to the lack of methods and experimental systems.Toward this goal,we built a two-dimensional electrical resistivity tomography(ERT)apparatus capable of measuring spatial and temporal characteristics of hydrate-bearing porous media.Beach sand(0.05–0.85 mm)was used to form artificial methane hydrate-bearing sediment.The experiments were conducted at 1°C under excess water conditions and the ERT data were acquired and analyzed.This study demonstrates the utility of the ERT method for hydrate mapping in laboratory-scale.The results indicate that the average electrical conductivity decreases nonlinearly with the formation of the hydrate.At some special time-intervals,the average conductivity fluctuates within a certain scope.The plane conductivity fields evolve heterogeneously and the local preferential hydrate-forming positions alternate throughout the experimental duration.We speculate that the combination of hydrate formation itself and salt-removal effect plays a dominant role in the spatial and temporal hydrate distribution,as well as geophysical parameters changing behaviors during hydrate accumulation. 展开更多
关键词 natural gas hydrate electrical resistivity electrical resistivity tomography accumulation mechanism electrical conductivity
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Mapping Subsurface Seepage Flow Patterns in Proximity to a Coal Combustion Residual Landfill Using Electrical Resistivity Tomography
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作者 Ruobai Zhao Neil Anderson +2 位作者 David Rogers Evgeniy Torgashov Jing Sun 《Journal of Geoscience and Environment Protection》 2021年第2期144-157,共14页
Electrical resistivity tomography data were acquired in proximity to the coal combustion residual landfill in an effort to image and analyze seepage pathways through the shallow residual soil and underlying karsted li... Electrical resistivity tomography data were acquired in proximity to the coal combustion residual landfill in an effort to image and analyze seepage pathways through the shallow residual soil and underlying karsted limestone bedrock. The water table is at a depth of more than 45 m. The most prominent subsurface seepage pathways identified on the acquired electrical resistivity tomography data are located immediately adjacent to the toe of the landfill and are attributed to stormwater run-off. The moisture content of the limestone appears to decrease gradually with increasing distance from the toe of the landfill, suggesting there is also a horizontal component of moisture flow in the subsurface. Shallow limestone with higher moisture content generally underlies or is in close proximity to anthropogenic features such as drainage ditches and clay berms that are designed to channel run-off. At one location, electrical resistivity tomography data were acquired along essentially the same traverse at different times of the year, and the resistivity of shallow limestone overall was lower on the data acquired after heavy rains. 展开更多
关键词 Coal Ash electrical Resistivity tomography (ERT) SEEPAGE Solid Waste Landfill Geophysical Methods Coal Combustion Residual (CCR)
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Application of 3D Electrical Resistivity Tomography for Diagnosing Leakage in Earth Rock-Fill Dam
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作者 Xin Zhang Mingjie Zhao +2 位作者 Kui Wang Pan Liu Huan Liu 《Engineering(科研)》 2016年第5期269-275,共7页
The leakage occurs during operation of the dam in Liuhuanggou reservoir. It’s a threat to the safety of the people’s lives and property in downstream. In order to eliminate the hidden danger of reservoir, ensure the... The leakage occurs during operation of the dam in Liuhuanggou reservoir. It’s a threat to the safety of the people’s lives and property in downstream. In order to eliminate the hidden danger of reservoir, ensure the safety of the dam, play better the function of flood control and water storage of the reservoir etc., we apply the 3D electrical resistivity tomography detecting technology and volume rendering image processing technology, make the measurement in field, process the data and combine the field survey to find out the leakage channels inside the dam. The results show that the 3D resistivity images appear the low resistivity zone corresponding with the leakage channels. There are two main leakage channels that come from different location inside the dam. It is feasible to diagnose the leakage in earth rock-fill dam by applying 3D electrical resistivity tomography. 展开更多
关键词 Earth Rock-Fill Dam LEAKAGE 3D electrical Resistivity tomography Volume Rendering
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Numerical Simulation Study on the Detection of Weak Structural Plane of Rock Slope by Using 3D Electrical Resistivity Tomography
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作者 Xin Zhang 《Engineering(科研)》 2016年第7期438-444,共8页
The weak structure plane is an important factor affecting the stability of rock slope, and detecting the spatial structure of the weak structural plane is beneficial to analyze the stability of the slope and estimate ... The weak structure plane is an important factor affecting the stability of rock slope, and detecting the spatial structure of the weak structural plane is beneficial to analyze the stability of the slope and estimate the quantity of the landslide. Based on 3D electrical resistivity tomography, a model of rock slope with weak structure plane is established, and the characteristics of three-dimensional resistivity imaging of weak structure plane under different ground water conditions are simulated. The results show that the weak structural plane has a better reflection in 3D electrical resistivity tomography;the distribution of weak structural plane of 3D resistivity imaging can be roughly determined under different ground water conditions;the three-dimensional electrical resistivity tomography is feasible in the detection of weak structural plane of rock slope. 展开更多
关键词 Rock Slope Soft Structure Plane 3D electrical Resistivity tomography Numerical Simulation
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Electrical geophysical evaluation of susceptibility to flooding in University of Nigeria, Nsukka main campus and its environs, Southeastern Nigeria
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作者 Daniel Nnaemeka Obiora Johnson Cletus Ibuot 《Journal of Groundwater Science and Engineering》 2023年第4期422-434,共13页
Flooding occurs when rainfall exceeds the absorption capacity of soil and causes significant environmental consequences.In this study,electrical resistivity techniques were employed to assess the flood susceptibility ... Flooding occurs when rainfall exceeds the absorption capacity of soil and causes significant environmental consequences.In this study,electrical resistivity techniques were employed to assess the flood susceptibility of the study area by examining variations in electrical properties.Prior to flooding,Vertical Electrical Sounding(VES)and Electrical Resistivity Tomography(ERT)profiles were conducted to determine the variations in resistivity within subsurface lithologies exposed to the injected current.The injected current penetrated the subsurface units characterised by resistivity ranging from 190.5Ω·m to 6,775.7Ω·m,42.3Ω·m to 7,297.4Ω·m,and 320.2Ω·m to 24,433.3Ω·m in the first,second and third layers,respectively.These layers were identified as lateritic topsoil,medium-coarse brownish grained sand,and coarse pebbly blackish sand,respectively.The calculated reflection coefficients between layers 1,2,and 3 reveal alternation in layers with values ranging from−0.04 to 0.66 and 0.36 to 0.95 for and,respectively.The transverse resistivity,longitudinal resistivity and anisotropy ranged from 243.59Ω·m to 24,115.42Ω·m,199.61Ω·m to 14,950.76Ω·m,and 1.02 to 2.14.Models derived from the ERT profiles reveal variations in resistivity,pinpointing areas of low resistivity which correspond to waterlogged and impermeable layers.The result of this study underscores the importance of integrated resistivity techniques in the study of floods,as it provides valuable insights into flood behaviour,and subsurface dynamics. 展开更多
关键词 ANISOTROPY Vertical electrical sounding electrical resistivity tomography Geoelectric layer Permeability
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Integrated Geoelectrical Resistivity Method for Environmental Assessment of Landfill Leachate Pollution and Aquifer Vulnerability Studies
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作者 Stanley U. Eze Omafume M. Orji +2 位作者 Abriku E. Onoriode Saleh A. Saleh Macpaul O. Abolarin 《Journal of Geoscience and Environment Protection》 2022年第9期1-26,共26页
Leachate plumes from landfills are a major source of pollution in Nigeria, especially in urban areas. Assessing leachate contamination in the subsoil is considered a complex process that needs detailed field measureme... Leachate plumes from landfills are a major source of pollution in Nigeria, especially in urban areas. Assessing leachate contamination in the subsoil is considered a complex process that needs detailed field measurement to accurately define the extent of contamination. To ascertain the extent of pollution of the subsoil and groundwater sources which were reportedly contaminated by leachate plumes from an old dumpsite located in Osubi town, an integrated geo-electrical method involving 1-D vertical electrical sounding (VES) and 2-D, 3-D ERT techniques were employed. Orthogonal set of 2-D apparent resistivity data was collected in a 100 × 50 m<sup>2</sup> rectangular grid around the dumpsite, using the Wenner array. Two years later, three (3) 2-D resistivity imaging profiles were also recorded in time-lapse mode at the dumpsite to monitor the possible effects of attenuation on the leachate over time. Ten (10) VES data were also acquired and used along with the 2-D imaging data. 2-D apparent resistivity data were inverted with Dipprowin software program. The orthogonal set of 2-D lines of apparent resistivity was merged into 3-D data and inverted with RES3DINV program to create a 3-D subsurface resistivity model. Geological models observed from 2-D and 3-D resistivity inversion revealed low resistivity values in the order ρ Ω·m which is indicative of leachate plumes in the saturation zone (pore water). The 2-D resistivity-depth sections imaged low resistivity leachate plumes at the near surface (<5 m) to a depth of 25.0 m, while 3-D inversion depth slices imaged leachate contaminant within the first, second and third layers at depth ranging from 0.00 - 2.50 m, 2.50 - 5.38 m and 5.38 - 8.68 m respectively. Thus, leachate contamination clearly increased with depth beyond the depth of first and second aquifers in the area which implies that available groundwater for domestic use is already contaminated with leachate from the dumpsite. Leachate contaminant-depth map estimated for the second geoelectric layers for VES 2, 3, 4, 7, 8, 9, and 10 shows that the second layer has been invaded completely by leachate contamination up to 6.5 m depth. 2-D apparent resistivity data acquired two years after show lower resistivity anomalies of the leachate plume caused by time-lapse attenuation effect on the observed resistivity of the leachate. This indicates that the leachate plume has become more conductive and toxic to the environment. The Longitudinal conductance map of the area shows that the aquifer protective capacity of this area is weak (0.1 - 0.19 Mho) thus, aquifers in the area are prone to pollution from the dumpsite. The three techniques used in this study (2-D, 3-D ERT and 1-D VES) fitly provided crucial information on the degree of contamination caused by the landfill leachate plume. Therefore, it is advisable to implement an environmental remediation and leachate management program. 展开更多
关键词 Leachate Contamination Groundwater Pollution 2D and 3D electrical Resistivity tomography (ERT) Aquifer Vulnerability Environmental Assessment
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Determination of rock mass integrity coefficient using a non-invasive geophysical approach 被引量:1
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作者 Muhammad Hasan Yanjun Shang +2 位作者 Xuetao Yi Peng Shao Meng He 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第6期1426-1440,共15页
Determination of rock mechanical parameters is the most important step in rock mass quality evaluation and has significant impacts on geotechnical engineering practice.Rock mass integrity coefficient(KV)is one of the ... Determination of rock mechanical parameters is the most important step in rock mass quality evaluation and has significant impacts on geotechnical engineering practice.Rock mass integrity coefficient(KV)is one of the most efficient parameters,which is conventionally determined from boreholes.Such approaches,however,are time-consuming and expensive,offer low data coverage of point measurements,require heavy equipment,and are hardly conducted in steep topographic sites.Hence,borehole approaches cannot assess the subsurface thoroughly for rock mass quality evaluation.Alternatively,use of geophysical methods is non-invasive,rapid and economical.The proposed geophysical approach makes useful empirical correlation between geophysical and geotechnical parameters.We evaluated the rock mass quality via integration between KV measured from the limited boreholes and inverted resistivity obtained from electrical resistivity tomography(ERT).The borehole-ERT correlation provided KV along various geophysical profiles for more detailed 2D/3D(two-/three-dimensional)mapping of rock mass quality.The subsurface was thoroughly evaluated for rock masses with different engineering qualities,including highly weathered rock,semi-weathered rock,and fresh rock.Furthermore,ERT was integrated with induced polarization(IP)to resolve the uncertainty caused by water/clay content.Our results show that the proposed method,compared with the conventional approaches,can reduce the ambiguities caused by inadequate data,and give more accurate insights into the subsurface for rock mass quality evaluation. 展开更多
关键词 Geotechnical engineering Rock mass integrity coefficient Rock mechanical parameters Geophysical parameters electrical resistivity tomography(ERT) Induced polarization(IP)
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MEASUREMENT OF SOLID SLURRY FLOW VIA CORRELATION OF ELECTROMAGNETIC FLOW METER,ELECTRICAL RESISTANCE TOMOGRAPHY AND MECHANISTIC MODELLING 被引量:3
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作者 XU Jing-yu WU Ying-xiang +5 位作者 ZHENG Zhi-chu WANG M. MUNIR B. OLUWADAREY H. I. SCHLABERG H. I. WILLIAMS R. A. 《Journal of Hydrodynamics》 SCIE EI CSCD 2009年第4期557-563,共7页
The study presented here was carried out to obtain the actual solids flow rate by the combination of electrical resistance tomography and electromagnetic flow meter. A new in-situ measurement method based on measureme... The study presented here was carried out to obtain the actual solids flow rate by the combination of electrical resistance tomography and electromagnetic flow meter. A new in-situ measurement method based on measurements of the Electromagnetic Flow Meters (EFM) and Electrical Resistance Tomography (ERT) to study the flow rates of individual phases in a vertical flow was proposed. The study was based on laboratory experiments that were carded out with a 50 mm vertical flow rig for a number of sand concentrations and different mixture velocities. A range of sand slurries with median particle size from 212 μm to 355 μm was tested. The solid concentration by volume covered was 5% and 15%, and the corresponding density of 5% was 1078 kg/m^3 and of 15% was 1238 kg/m^3. The flow velocity was between 1.5 m/s and 3.0 m/s. A total of 6 experimental tests were conducted. The equivalent liquid model was adopted to validate in-situ volumetric solids fraction and calculate the slip velocity. The results show that the ERT technique can be used in conjunction with an electromagnetic flow meter as a way of measurement of slurry flow rate in a vertical pipe flow. However it should be emphasized that the EFM results must be treated with reservation when the flow pattern at the EFM mounting position is a non-homogenous flow. The flow rate obtained by the EFM should be corrected considering the slip velocity and the flow pattern. 展开更多
关键词 slurry measurement electrical resistance tomography (ERT) Electromagnetic Flow Meters (EFM) in-situ mean volumetric fraction slip velocity
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Distribution characteristics of holdups in a multi-stage bubble column using electrical resistance tomography 被引量:1
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作者 Haibo Jin Yicheng Lian +2 位作者 Yujian Qin Suohe Yang Guangxiang He 《Particuology》 SCIE EI CAS CSCD 2013年第2期225-231,共7页
Based on the principle of chemical reaction engineering, the addition of perforated plates can improve the performance of conventional bubble column and decrease the backmixing behaviors. The distribution characterist... Based on the principle of chemical reaction engineering, the addition of perforated plates can improve the performance of conventional bubble column and decrease the backmixing behaviors. The distribution characteristics of gas holdup in a multi-stage bubble column embedded with five types of sieve plates and three types of tongue plates were studied using electrical resistance tomography (ERT). The effects of superficial gas velocity and the geometric design of perforated plates on the gas holdup and its radial distribution above and below the plates of the bubble column were discussed. Experimental results show ERT is suitable as an online monitoring tool to provide useful information on the hydrodynamic param-eters of multi-stage bubble columns. With increasing superficial gas velocity, local gas holdup increases, and gas holdup below the plate increases with decrease of free area (%FA), hole diameters or angle of tongue plates. ERT technique facilitates noninvasive and nonintrusive visualization of cross-sectional distribution of gas holdup in a bubble column. 展开更多
关键词 Bubble column electrical resistance tomography Differential pressure method Sieve plates Tongue plate
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Field Sensing Characteristic Research of Carbon Fiber Smart Material 被引量:1
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作者 张小玉 吕泳 +1 位作者 CHEN Jianzhong LI Zhuoqiu 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2015年第5期914-917,共4页
In order to research the field sensing characteristic of the carbon fiber smart material, the Tikhonov regularization principle and the modified Newton-Raphson(MNR) algorithm were adopted to solve the inverse problem ... In order to research the field sensing characteristic of the carbon fiber smart material, the Tikhonov regularization principle and the modified Newton-Raphson(MNR) algorithm were adopted to solve the inverse problem of the electrical resistance tomography(ERT). An ERT system of carbon fiber smart material was developed. Field sensing characteristic was researched with the experiment. The experimental results show that the specific resistance distribution of carbon fiber smart material is highly consistent with the distribution of structural strain. High resistance zone responds to high strain area, and the specific resistance distribution of carbon fiber smart material reflects the distribution of sample strain in covering area. Monitoring by carbon fiber smart material on complicated strain status in sample field domain is realized through theoretical and experimental study. 展开更多
关键词 carbon fiber smart material field sensing characteristic PIEZORESISTIVITY image reconstruction electrical resistance tomography
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Engineering Geological and Geotechnical Studies of Taprang Landslide, West-central Nepal: An Approach for Slope Stability Analysis
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作者 Ashok Sigdel Radha Krishna Adhikari 《Journal of Geological Research》 2020年第4期22-35,共14页
Detailed investigation of Taprang landslide was carried out in order tounderstand the surface, subsurface lithological information and physicalproperties of soil by using multi-disciplinary methods such as engineering... Detailed investigation of Taprang landslide was carried out in order tounderstand the surface, subsurface lithological information and physicalproperties of soil by using multi-disciplinary methods such as engineeringgeological, geophysical and geotechnical studies for the determinationof factor of safety for slope stability analysis. Geological study wascarried out by detail mapping of surface geology, soil condition, propertiesof bedrock and its discontinuities. The geophysical survey (ElectricalResistivity Tomography-ERT) were carried out to know the electricalresistivity of soil for identifying the groundwater table and slip surface ofthe landslide. Geotechnical analysis such as grain size analysis, liquid limitand direct shear test were carried out in order to evaluate soil classification,moisture content, cohesion and the angle of internal friction of soil forknowing the strength the soil. These soil parameters indicate the soil is verylow strength. The combination of these results were used for calculatingthe factor of safety (FoS) by Limit Equilibrium Method (LEM) proposedby Bishop and Janbu methods. The result of factor of safety in the Tapranglandslide demonstrates that the slope become stable in drained (dry)condition, remain ultimate stage in undrained (wet) condition and finallyfailure occurs if applied the seismic load in both drained and undrainedconditions. 展开更多
关键词 Taprang Landslide electrical Resistivity tomography(ERT) Groundwater Table Limit Equilibrium Method(LEM) Factor of Safety Kinematic Analysis Slope Stability
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Investigation of dense slurry suspensions with coaxial mixers:Influences of design variables through tomography and mathematical modelling
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作者 Prakash Mishra Farhad Ein-Mozaffari 《Particuology》 SCIE EI CAS CSCD 2022年第6期1-16,共16页
The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor.In this research work,the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system(comprised of a... The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor.In this research work,the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system(comprised of a close clearance anchor rotating with a low speed and an inner axial impeller rotating with a high speed)was analyzed employing ERT(electrical resistance tomography,a non-intrusive flow visualization technique),and computational fluid dynamics(CFD).The numerical models were validated by comparing the axial solid concentration profiles generated using the ERT data and the CFD simulation results.The influences of various important parameters such as the diameter of the inner axial impeller,the inner impeller type,and the inner impeller spacing on the hydrodynamic characteristics of the slurry suspensions in a coaxial mixing vessel were thoroughly analyzed.The radial and axial velocity profiles of solid particles were generated using the validated mathematical models.The assessment of energy loss due to the solid-solid collisions,the particle-fluid frictions,and the particle-vessel wall collisions was conducted.The evaluation of optimum inner impeller clearance and inner impeller diameter is essential to attain a high degree of solids suspension and dissemination in a coaxial slurry mixing system. 展开更多
关键词 Coaxial mixer Slurry suspension HOMOGENEITY Mixing index electrical resistance tomography(ERT) Computational fluid dynamics(CFD)
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Effect of impeller type on mixing of highly concentrated slurries of large particles
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作者 Argang Kazemzadeh Farhad Ein-Mozaffari Ali Lohi 《Particuology》 SCIE EI CAS CSCD 2020年第3期88-99,共12页
Many chemical engineering processes deal with dense suspensions of large solid particles in liquid.Behaviors of such systems are difficult to predict because the many solid particles strongly affect the hydrodynamics ... Many chemical engineering processes deal with dense suspensions of large solid particles in liquid.Behaviors of such systems are difficult to predict because the many solid particles strongly affect the hydrodynamics produced by the impeller.The main objective was to assess the performances of the PBT,A310,and PF3 impellers in agitating highly concentrated slurries of large particles.Electrical resistance tomography was used to determine the degree of homogeneity and solid particle distribution within the slurry reactor.To gain more insight into the complex behavior of the flow inside the dense suspensions,computational fluid dynamics simulations were conducted using a Eulerian-Eulerian multiphase model.Both qualitative and quantitative analyses were performed to obtain details on the dispersed solid phase distribution and its effect on the mixing quality.We found that the PBT impeller was the most efficient in terms of consuming power and generating velocity and turbulent kinetic energy within the mixing tank. 展开更多
关键词 SUSPENSION Highly concentrated slurry electrical resistance tomography Computational fluid dynamics HOMOGENEITY
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