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Heat Transfer and Resistance Characteristics of Conical Spiral Tube Bundle Based on Field Synergy Principle 被引量:9
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作者 YAN Ke GE Peiqi +1 位作者 HU Ruirong MENG Haitao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2012年第2期370-376,共7页
Conical spiral tube bundle are universally used in heat transfer enhancement in heat exchangers.The heat transfer and resistance of the tube bundle are affected greatly by the conical structure,so the analysis of it i... Conical spiral tube bundle are universally used in heat transfer enhancement in heat exchangers.The heat transfer and resistance of the tube bundle are affected greatly by the conical structure,so the analysis of it is necessary.In order to a further evaluation,the heat transfer and resistance characteristics of conical spiral tube bundle are investigated with regression analysis based on numerical simulation data.The correlations of heat transfer and pressure drop of conical spiral tube bundle are proposed both in laminar and turbulent fluid flow.On the based of the field synergy principle,the synergy of four vectors,the velocity,the velocity gradient,the temperature gradient and the pressure gradient,are calculated and discussed via the user defined function(UDF) program.The synergy angles β and θ,which respectively denote the performance of heat transfer enhancement and pressure drop of the conical spiral tube bundle,are analyzed.Finally,the comprehensive performance of the conical spiral tube is evaluated by the synergy angle γ and all of the three synergy angles of conical spiral tube bundle are compared to both bare tube and thin cylinder-interpolated tube.The analysis of the synergy angles shows that the heat transfer enhancement and pressure drop of conical spiral tube bundle are smaller than that of the thin cylinder-interpolated tube,while the comprehensive performance of conical spiral tube bundle is greater.The analysis of the heat transfer and pressure drop of conical spiral tube is valuable and instructional on the design and optimum of conical spiral tube bundle heat exchangers. 展开更多
关键词 conical spiral tube bundle field synergy principle regression analysis
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Heat Transfer Enhancement with Mixing Vane Spacers Using the Field Synergy Principle 被引量:3
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作者 YANG Lixin ZHOU Mengjun TIAN Zihao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2017年第1期127-134,共8页
The single-phase heat transfer characteristics in a PWR fuel assembly are important. Many investigations attempt to obtain the heat transfer characteristics by studying the flow features in a 5 x 5 rod bundle with a s... The single-phase heat transfer characteristics in a PWR fuel assembly are important. Many investigations attempt to obtain the heat transfer characteristics by studying the flow features in a 5 x 5 rod bundle with a spacer grid. The field synergy principle is used to discuss the mechanism of heat transfer enhancement using mixing vanes according to computational fluid dynamics results, including a spacer grid without mixing vanes, one with a split mixing vane, and one with a separate mixing vane. The results show that the field synergy principle is feasible to explain the mechanism of heat transfer enhancement in a fuel assembly. The enhancement in subchannels is more effective than on the rod's surface. If the pressure loss is ignored, the performance of the split mixing vane is superior to the separate mixing vane based on the enhanced heat transfer. Increasing the blending angle of the split mixing vane improves heat transfer enhancement, the maximum of which is 7.1%. Increasing the blending angle of the separate mixing vane did not significantly enhance heat transfer in the rod btmdle, and even prevented heat transfer at a blending angle of 50%. This fmding testifies to the feasibility of predicting heat transfer in a rod bundle with a spacer grid by field synergy, and upon comparison with analyzed flow features only, the field synergy method may provide more accurate guidance for optimizing the use of mixing vanes. 展开更多
关键词 rod bundle mixing vane heat transfer enhancement field synergy
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Field synergy analysis of pollutant dispersion in street canyons and its optimization by adding wind catchers 被引量:2
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作者 Tingzhen Ming Huina Han +4 位作者 Zhen Zhao Renaud de Richter Yongjia Wu Wei Li Nyuk Hien Wong 《Building Simulation》 SCIE EI CSCD 2021年第2期391-405,共15页
The microenvironment,which involves pollutant dispersion of the urban street canyon,is critical to the health of pedestrians and residents.The objectives of this work are twofold:(i)to effectively assess the pollutant... The microenvironment,which involves pollutant dispersion of the urban street canyon,is critical to the health of pedestrians and residents.The objectives of this work are twofold:(i)to effectively assess the pollutant dispersion process based on a theory and(ii)to adopt an appropriate stratigy,i.e.,wind catcher,to alleviate the pollution in the street canyons.Pollutant dispersion in street canyons is essentially a convective mass transfer process.Because the convective heat transfer process and the mass transfer process are physically similar and the applicability of field synergy theory to turbulence has been verified in the literature,we apply the field synergy theory to the study of pollutant dispersion in street canyons.In this paper,a computational fluid dynamics(CFD)simulation is conducted to investigate the effects of wind catcher,wind speed and the geometry of the street canyons on pollutant dispersion.According to the field synergy theory,Sherwood number and field synergy number are used to quantitatively evaluate the wind catcher and wind speed on the diffusion of pollutants in asymmetric street canyons.The results show that adding wind catchers can significantly improve the air quality of the step-down street canyon and reduce the average pollutant concentrations in the street canyon by 75%.Higher wind speed enhances diffusion of pollutants differently in different geometric street canyons. 展开更多
关键词 street canyon field synergy theory CFD simulation pollutant dispersion wind catcher
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Experimental Study on Performance of Supercritical CO_2 Heat Exchanger with Four Different Inner Tubes
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作者 吕静 曹科 +2 位作者 石冬冬 吕锋 马逸平 《Journal of Donghua University(English Edition)》 EI CAS 2016年第1期138-143,共6页
The experiment was conducted to investigate the heat transfer performance of supercritical CO_2 in a casing heat exchanger by comparing their heat transfer,entropy production unit number,non-dimensional entropy produc... The experiment was conducted to investigate the heat transfer performance of supercritical CO_2 in a casing heat exchanger by comparing their heat transfer,entropy production unit number,non-dimensional entropy production rate and field synergy factor.The results show that both heat transfer and entropy production unit number in four tubes decrease with water temperature increasing.Heat transfer and entropy production unit number in multiple tubes( i. e.,triple straight tube and double helix tube) is higher than their single counterparts; the non-dimensional entropy production rate increases with water temperature. Non-dimensional entropy production rate of triple straight tube and double helix tube is far below the single tube. Field synergy factor of double helix tube is much higher than that of the triple straight tube under the same condition. Further experiment was carried out in double helix tube,under various CO_2 pressure and inlet water temperature,the results are analyzed and reported in this paper. 展开更多
关键词 supercritical CO2 casing tube heat exchanger entropy production unit number non-dimensional entropy production rate field synergy factor
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Numerical Investigation on Flow and Heat Transfer Performance of Supercritical Carbon Dioxide Based on Variable Turbulent Prandtlnumber Model
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作者 Xiaokai LIU Haiyan ZHANG +3 位作者 Keyong CHENG Xiulan HUAI Haiyan LIAO Zhongmei ZHANG 《Mechanical Engineering Science》 2021年第2期1-8,共8页
Flow and heat transfer characteristic of supercritical carbon dioxide(SCO_(2))are numerically investigated in the horizontal and vertical tubes.TWL turbulent Prandtl number model could well describe the behavior of SC... Flow and heat transfer characteristic of supercritical carbon dioxide(SCO_(2))are numerically investigated in the horizontal and vertical tubes.TWL turbulent Prandtl number model could well describe the behavior of SCO_(2) affected by the buoyancy.Under the cooling condition,the heat transfer performance of SCO_(2) along the upward direction is best and that along the downward direction is worst when bulk fluid temperatures are below the pseudocritical temperature.Reducing the ratio of heat flux to mass flux could decrease the difference of convective heat transfer coefficient in three flow directions.Under the heating condition,heat transfer deterioration only occurs in vertical upward and horizontal flow directions.Heat transfer deterioration of SCO_(2) could be delayed by increasing the mass flux and the deterioration degree is weakened in the second half of tube along the vertical upward flow direction.Compared with the straight tube,the corrugated tube shows better comprehensive thermal performance. 展开更多
关键词 Supercritical carbon dioxide Turbulent Prandtl number Flow and heat transfer field synergy principle Numerical investigation
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Heat Transfer and Friction Characteristics of Printed Circuit Heat Exchangers with Different Channel Structures for S-CO_(2) Power System
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作者 JIANG Tao LI Mingjia 《Journal of Thermal Science》 SCIE EI CAS CSCD 2024年第3期1132-1147,共16页
Printed circuit heat exchanger(PCHE)has been widely used in supercritical carbon dioxide(S-CO_(2))power systems because of its high heat transfer efficiency and good compactness.However,due to the large variety of PCH... Printed circuit heat exchanger(PCHE)has been widely used in supercritical carbon dioxide(S-CO_(2))power systems because of its high heat transfer efficiency and good compactness.However,due to the large variety of PCHE configurations,channel selection in practical applications lacks a basis.Therefore,this paper discussed the heat transfer and friction characteristics and the synergy of three fields in the channel under the guidance of the field synergy principle for four typical PCHE channels.Additionally,the comprehensive performance of four channels was compared.Finally,the heat transfer and friction factor correlations for S-CO_(2)in four channels were established.The findings demonstrate that the synergy of velocity and pressure fields of the straight channel PCHE is better(β≈180°),so its resistance loss is relatively small.The zigzag and sinusoidal wavy channels and the airfoil fins can reduce the angle a between the temperature gradient and velocity,thus enhancing the heat transfer.The sinusoidal wavy channel can reduce flow resistance compared to the zigzag channel due to the rounded corners.The streamlined airfoil structure can guide the flow and reduce backflow,thus reducing resistance losses.In the range of Re studied in this paper,the maximum error of the proposed heat transfer and friction factor correlations of PCHE is 7.0%,which shows good fitting accuracy.The research in this paper can provide a reference for the selection and design of PCHE with different channel configurations. 展开更多
关键词 printed circuit heat exchanger supercritical carbon dioxide typical channel structure field synergy analysis
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Enhancement of laminar flow heat transfer with single/doubleinclined ribs for unilaterally-heated channel 被引量:3
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作者 WANG XiangYu XU XiangHua LIANG XinGang 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2023年第7期2108-2118,共11页
To deal with the aerodynamic heating on the aircraft surface,a potential solution is to utilize liquid cooling via the channels in part of the fuselage.This is a typical problem of flow and heat transfer in channels w... To deal with the aerodynamic heating on the aircraft surface,a potential solution is to utilize liquid cooling via the channels in part of the fuselage.This is a typical problem of flow and heat transfer in channels with unilaterally-heated surfaces.The enhancement of heat transfer in the channel is significant due to the high heating flux.The optimal velocity and temperature fields are obtained first based on the field synergy optimization method.Four rib configurations are proposed to produce the longitudinal vortices suggested by the optimal velocity field.The flow and heat transfer characteristics of different rib configurations are obtained by numerical simulation.The numerical simulations show that the heat transfer enhancement of the rib configurations are quite different,but the pressure drop increases similarly in the laminar flow range of Re = 500–1500.The mechanism of heat transfer enhancement with the single/double-inclined ribs for the unilaterally-heated channel is analysed.The best enhancement of geometric parameter among the investigated parameters such as the angle,length,radius and the spacing of the ribs is obtained. 展开更多
关键词 heat transfer enhancement field synergy optimization inclined ribs unilaterally-heated channel
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Constructal design progress for eight types of heat sinks 被引量:31
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作者 CHEN LinGen YANG AiBo +2 位作者 FENG HuiJun GE YanLin XIA ShaoJun 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2020年第6期879-911,共33页
This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the met... This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the methods of theoretical analysis and numerical calculation.The eight types of heat sinks are uniform height rectangular fin heat sink,non-uniform height rectangular fin heat sink,inline cylindrical pin-fin heat sink(ICPHS),plate single-row pin fin heat sink(PSRPHS),plate inline pin fin heat sink(PIPHS),plate staggered pin fin heat sink(PSPHS),single-layered microchannel heat sink(SLMCHS)with rectangular cross sections and double-layered microchannel heat sink(DLMCHS)with rectangular cross sections,respectively.And the ten performance indexes are heat transfer rate maximization,maximum thermal resistance minimization,minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization,entropy generation rate minimization,operation cost minimization,thermo-economic function value minimization,pressure drop minimization,enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization,respectively.The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other.The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition.The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed.The results obtained herein have some important theoretical significances and application values,and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications. 展开更多
关键词 constructal theory entropy generation minimization principle field synergy principle extremum principle of entransy dissipation generalized thermodynamic optimization multi-objective optimization of heat sinks
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NUMERICAL SIMULATION OF FLOW AND HEAT TRANSFER CHARA-CTERISTICS OUTSIDE A PERIODICALLY VIBRATING TUBE 被引量:14
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作者 JIANG Bo TIAN Mao-cheng LENG Xue-li TANG Yu-feng PAN Ji-hong 《Journal of Hydrodynamics》 SCIE EI CSCD 2008年第5期629-636,共8页
Fluid flow and heat transfer characteristics outside a vibrating tube were numerically simulated by the dynamic mesh method. The mechanism of heat transfer enhancement via periodic vibration of the tube was explored b... Fluid flow and heat transfer characteristics outside a vibrating tube were numerically simulated by the dynamic mesh method. The mechanism of heat transfer enhancement via periodic vibration of the tube was explored by using the field synergy principle. It is found that the field synergy angle between fluid velocity vector and temperature gradient vector for a periodically vibrating tube is significantly smaller than that for a stationary tube, and it changes approximately according to the sinusoidal law in a vibration period. The effect of time phase of the vibration on the field synergy angle and convective heat transfer coefficient were also discussed. Results indicate that the vibration can enhance heat transfer and this effect is more remarkable when time phase angle ranges between 50° and 1400 in a half period. Especially when the time phase angle is 90°, the average field synergy angle outside the tube reaches the minimum, which leads to the best heat transfer performance. 展开更多
关键词 heat transfer enhancement dynamic mesh vibration field synergy Computational Fluid Dynamics (CFD)
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Flow characteristics of tangential leakage in a scroll compressor for automobile heat pump with CO_(2) 被引量:5
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作者 ZHENG SiYu WEI MingShan +2 位作者 HU ChenXing SONG PanPan TIAN Ran 《Science China(Technological Sciences)》 SCIE EI CAS CSCD 2021年第5期971-983,共13页
Tangential leakage loss reduction has great significance on improving the performance of scroll compressors.In this study,the flow field of a scroll compressor working with CO_(2) was numerically investigated.The deve... Tangential leakage loss reduction has great significance on improving the performance of scroll compressors.In this study,the flow field of a scroll compressor working with CO_(2) was numerically investigated.The development characteristics of the tangential leakage flow in different working chambers were carried out,which was obtained by analyzing the field quantities distributions.The impacts of the radial clearances and sidewall roughness on the tangential leakage were also taken into consideration,in order to explore the feasible method of the flow control for the tangential leakage in scroll compressors.Results showed that the tangential leakage flow had various characteristics in the suction and compression chambers due to the different interactions between the tangential leakage flow and mainstream.Owing to little reverse pressure gradient,the tangential leakage flow maintained the typical jet form in the suction chambers.By contrast,the mixing of the tangential leakage flow and mainstream induced the passage vortex and secondary flows in the compression chamber.The secondary flow was the primary factor that results in the occurrence of localized high temperature region rather than the tangential leakage.With the increase of the radial clearance,the volumetric efficiency declined and the discharge temperature increased rapidly.In terms of flow control of the tangential leakage,the increase of sidewall roughness by 2μm could achieve the same effect as the decrease of the radial clearance by 4μm,while the volumetric efficiency increased by almost 5%and average discharge temperature decreased by 5K. 展开更多
关键词 carbon dioxide scroll compressor field synergy principle tangential leakage sidewall roughness
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Enhanced Heat Transfer of Carbon Nanotube Nanofluid Microchannels Applied on Cooling Gallium Arsenide Cell 被引量:5
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作者 ZHANG Huiying YAN Suying +3 位作者 WANG Tao WU Yuting ZHAO Xiaoyan ZHAO Ning 《Journal of Thermal Science》 SCIE EI CAS CSCD 2020年第6期1475-1486,共12页
Carbon nanotube nanofluids have wide application prospects due to their unique structure and excellent properties.In this study,the thermal conductivity properties of carbon nanotube nanofluids and SiO2/water nanoflui... Carbon nanotube nanofluids have wide application prospects due to their unique structure and excellent properties.In this study,the thermal conductivity properties of carbon nanotube nanofluids and SiO2/water nanofluids were compared and analyzed experimentally using different preparation methods.The physical properties of nanofluids were tested using a Malvern Zetasizer Nano Instrument and a Hot Disk Thermal Constant Analyzer.Combined with field synergy theory analysis of the heat transfer performance of nanofluids,results show that the thermal conductivity of carbon nanotube nanofluids is higher than that of SiO2/water nanofluids,and the thermal conductivity of nanofluid rises with the increase of mass fraction and temperature.Moreover,the synergistic performance of carbon nanotube nanofluids is also superior to that of SiO2/water nanofluids.When the mass fraction of the carbon nanotube nanofluids is 10%and the SiO2/water nanofluids is 8%,their field synergy numbers and heat transfer enhancement factors both reach maximum.From the perspective of the preparation method,the thermal conductivity of nanofluids dispersed by high shear microfluidizer is higher than that by ultrasonic dispersion.This result provides some reference for the selection and use of working substance in a microchannel cooling concentrated photovoltaic and thermal(CPV/T)system. 展开更多
关键词 concentrated photovoltaic solar cell thermal conductivity carbon nanotube nanofluids field synergy principle heat transfer property
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Simulation, experimentation, and collaborative analysis of adjacent heat exchange modules in a vehicular cooling system 被引量:4
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作者 Yu-qi HUANG Rui HUANG +1 位作者 Xiao-li YU Feng LV 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2013年第6期417-426,共10页
A cooling system consisting of several heat exchange modules is a necessary part of an automobile, and its performance has a direct effect on a vehicle's energy consumption. Heat exchangers, such as a charged air ... A cooling system consisting of several heat exchange modules is a necessary part of an automobile, and its performance has a direct effect on a vehicle's energy consumption. Heat exchangers, such as a charged air cooler (CAC), radiator, oil cooler, or condenser have different structures and can be arranged in various orders, and each combination may produce different effects because of interactions among them. In this study, we aimed to explore the principles governing interactions among adjacent heat exchangers in a cooling system, using numerical simulation and experimental technology. 3D models with different combinations were developed, compared, and analyzed comprehensively. A wind tunnel test platform was constructed to validate the computational results. We found that the heat dissipation of the modules was affected slightly by their relative position (the rules basically comply with the field synergy principle), but was independent of the modules' spacing within a certain distance range. The heat dissipation of one module could be effectively improved by restructuring, but with a penalty of higher resistance. However, the negative effect on the downstream module was much less than expected. The results indicated that the intensity of heat transfer depends not only on the average temperature difference between cold and hot mediums, but also on the temperature distribution. 展开更多
关键词 Collaborative analysis Heat exchangers field synergy principle Computational fluid dynamics (CFD) Wind tunnel
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Heat Transfer and Flow Resistance Characteristics of Helical Baffle Heat Exchangers with Twisted Oval Tube 被引量:2
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作者 GU Xin ZHENG Zhiyang +3 位作者 XIONG Xiaochao JIANG Erhui WANG Tongtong ZHANG Dongwei 《Journal of Thermal Science》 SCIE EI CAS CSCD 2022年第2期370-378,共9页
To overcome the defect of the significant increase in pressure drop when the heat transfer performance of helical baffle heat exchanger is improved,a novel helical baffle heat exchanger with twisted oval tube is propo... To overcome the defect of the significant increase in pressure drop when the heat transfer performance of helical baffle heat exchanger is improved,a novel helical baffle heat exchanger with twisted oval tube is proposed.Numerical simulation was done to exhibit the shell side heat transfer and flow characteristics with CFD software Fluent.The field synergy principle was used to evaluate the shell side performance.The results show that the flow velocity distribution on the shell side of the spiral baffle heat exchanger is more uniform and the velocity near the tube wall increases in the range of research parameters,as the circular tube is replaced by a twisted elliptical tube with the same perimeter length.Moreover,the helical baffle heat exchanger with twisted oval tube has better field synergy of velocity and temperature gradient,velocity and pressure gradient.The helical baffle heat exchanger with helix angle of 15°has better performance than that of circular tube,and its heat transfer coefficient is improved about 3.3%and pressure drop is reduced by 17.1%–19.1%.Hence,the comprehensive heat transfer performance is improved by 21.5%–22.5%.When the helix angle is 20°,the comprehensive heat transfer performance is increased by 16.1%–18.0%with heat transfer coefficient improvement of 3.6%and pressure drop reduction of 13.9%–16.5%. 展开更多
关键词 twisted oval tube helical baffle field synergy principle heat transfer enhancement
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A novel porous channel to optimize the cooling performance of PV modules
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作者 Yingbo Zhang Chao Shen +3 位作者 Chunxiao Zhang Jihong Pu Qianru Yang Cheng Sun 《Energy and Built Environment》 2022年第2期210-225,共16页
This paper dealt with a series of numerical investigations on a new porous cooling channel applied to PV/T systems in order to improve the insufficient heat transfer in the conventional channel.The proposed porous coo... This paper dealt with a series of numerical investigations on a new porous cooling channel applied to PV/T systems in order to improve the insufficient heat transfer in the conventional channel.The proposed porous cooling channel based on field synergy theory had a higher overall heat transfer coefficient,which enhanced the total efficiency of the PV/T system.The numerical model was validated with experimental data.The results showed that holes distributed non-uniformly near the outlet of the cooling water led to a better cooling effect,and a hole diameter of 0.005 m led to an optimal performance.The total efficiency of the PV module with the new cooling channel was 4.17%higher than the conventional one at a solar irradiance of 1000 W/m^(2)and an inlet mass flow rate of 0.006 kg/s.In addition,as the solar irradiance increased from 300 to 1200 W/m^(2),the total efficiency of the new PV/T system dropped by 5.07%,which included reductions in both the electrical and thermal efficiency.The total efficiency was improved by 18.04%as the inlet mass flow rate of cooling water increased from 0.002 to 0.02 kg/s. 展开更多
关键词 PV modules Heat regulation field synergy theory PV cell temperature
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Impact of gravitation on gaseous pollutant source identification 被引量:2
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作者 Pang Liping Zhang Yu +2 位作者 Qu Hongquan Hu Tao Zhao Jingquan 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2013年第2期261-268,共8页
It is necessary to identify a gaseous pollutant source rapidly so that prompt actions can be taken, but this is one of the difficulties in the inverse problem areas. In this paper, an approach to identifying a sudden ... It is necessary to identify a gaseous pollutant source rapidly so that prompt actions can be taken, but this is one of the difficulties in the inverse problem areas. In this paper, an approach to identifying a sudden continuous emission pollutant source based on single sensor information is developed to locate a source in an enclosed space with a steady velocity field. Because the gravity has a very important influence on the gaseous pollutant transport and the source identification, its influence is analyzed theoretically and a conclusion is drawn that the velocity of fluid is a key factor to effectively help weaken the gravitational influence. Further studies for a given 2-D case by using the computational fluid dynamics (CFD) method show that when the velocity of inlet is less than one certain value, the influence of gravity on the pollutant transport is very significant, which will change the velocity field obviously. In order to quantitatively judge the practical applicability of identification approach, a synergy degree of the velocity fields before and after a source appearing is proposed as a condition for considering the influence of gravity. An experimental device simulating pollutant transmission was set up and some experiments were conducted to verify the practical application of the above studies in the actual gravitational environment. The results show that the proposed approach can successfully locate the sudden constant source when the experimental situations meet the identified conditions. 展开更多
关键词 EXPERIMENT Gaseous pollutant source identification Gravitational field Location probability synergy degree of velocity fields Ventilated enclosed space
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