超临界流体在螺旋管内的对流换热研究进展
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摘要
超临界流体在螺旋管内的传热技术在化工领域被广泛应用。由于其传热与流动机理的复杂性,使得目前这方面的研究相较于直管内的还很匮乏。综述了近几年来国内外学者关于超临界流体在螺旋管内对流换热的研究进展,包括以CO_2和H_2O等常见工质为主的数值模拟研究与试验研究。对数值模型及传热机理进行了分析比较,提出该研究的未来发展方向;总结了现有研究中的浮升力影响准则,并分析了质量流量、压力、热流量以及螺旋管结构参数对传热特性的影响机理。此外,对目前螺旋管内超临界流体的换热关联式进行了归纳总结。期望能对超临界流体在螺旋管内的特殊换热机理有更深入的理解,为今后的具体研究工作奠定理论基础。
The heat transfer technology of supercritical fluids in helically coiled tubes is widely used in the chemical industry.However,due to the complexity of its flow and heat transfer mechanism,the current researches in this area are still scarce compared with that in straight tubes. In this paper,the progress in recent studies( including numerical simulations and experimental researches of common working media like CO_2 and H_2O) on the convective heat transfer of fluids( mainly carbon dioxide and water) at supercritical pressures in helically coiled tubes was reviewed. The numerical model and heat transfer mechanism were compared and analyzed,then the future development direction of this research was proposed; The influence criterions of buoyancy force in present research were summarized,and the influence mechanisms of mass flux,pressure,heat flux as well as tube geometric parameters on heat transfer performance were also analyzed. In addition,the current heat transfer correlations of supercritical fluids in the helically coiled tube were summarized,in the hope to obtain a deeper understanding of this unique heat transfer characteristics in helically coiled tubes,which aims at laying the theoretical foundation for the future specific research work.
The heat transfer technology of supercritical fluids in helically coiled tubes is widely used in the chemical industry.However,due to the complexity of its flow and heat transfer mechanism,the current researches in this area are still scarce compared with that in straight tubes. In this paper,the progress in recent studies( including numerical simulations and experimental researches of common working media like CO_2 and H_2O) on the convective heat transfer of fluids( mainly carbon dioxide and water) at supercritical pressures in helically coiled tubes was reviewed. The numerical model and heat transfer mechanism were compared and analyzed,then the future development direction of this research was proposed; The influence criterions of buoyancy force in present research were summarized,and the influence mechanisms of mass flux,pressure,heat flux as well as tube geometric parameters on heat transfer performance were also analyzed. In addition,the current heat transfer correlations of supercritical fluids in the helically coiled tube were summarized,in the hope to obtain a deeper understanding of this unique heat transfer characteristics in helically coiled tubes,which aims at laying the theoretical foundation for the future specific research work.
引文
[1]Jackson J D.Fluid flow and convective heat transfer to fluids at supercritical pressure[J].Nuclear Engineering and Design,2013,264:24-40.
[2]Song J H,Kim H Y,Kim H,et al.Heat transfer characteristics of a supercritical fluid flow in a vertical pipe[J].The Journal of Supercritical Fluids,2008,44(2):164-171.
[3]王英杰.超临界流体传热特性研究综述[J].科技导报,2012,30(33):74-79.
[4]Yamagata K,Nishikawa K,Hasegawa S,et al.Forced convective heat transfer to supercritical water flowing in tubes[J].International Journal of Heat and Mass Transfer,1972,15(12):2575-2593.
[5]Popov V N,Petrov N E.Calculation of heat-transfer and flow resistance in the turbulent pipe-flow of cooled carbon-dioxide in the supercritical region[J].Teplofizika Vysokikh Temp,1985,23(2):309-316.
[6]Cheng X,Schulenberg T.Heat Transfer at Supercritical Pressures:Literature Review and Application to an HPLWR[M].Karlsruhe:FZKA,2001:5-7.
[7]Pioro I L,Khartabil H F,Duffey R B.Heat transfer to supercritical fluids flowing in channels-empirical correlations(survey)[J].Nuclear Engineering and Design,2004,230(1-3):69-91.
[8]Joong H B,Jung Y Y.Direct numerical simulation of turbulent supercritical flows with heat transfer[J].Physics of Fluids,2005,17:105104.
[9]Jiang P X,Shi R F,Xu Y J,et al.Experimental investigation of flow resistance and convection heat transfer of CO2at supercritical pressures in a vertical porous tube[J].The Journal of Supercritical Fluids,2006,38(3):339-346.
[10]He S,Kim W S,Jackson J D.A computational study of convective heat transfer to carbon dioxide at a pressure just above the critical value[J].Applied Thermal Engineering,2008,28(13):1662-1675.
[11]Bae Y Y,Kim H Y.Convective heat transfer to CO2at a supercritical pressure flowing vertically upward in tubes and an annular channel[J].Experimental Thermal and Fluid Science,2009,33(2):329-339.
[12]Kim D E,Kim M H.Experimental study of the effects of flow acceleration and buoyancy on heat transfer in a supercritical fluid flow in a circular tube[J].Nuclear Engineering and Design,2010,240(10):3336-3349.
[13]Zhang P,Huang Y,Shen B,et al.Flow and heat transfer characteristics of supercritical nitrogen in a vertical mini-tube[J].International Journal of Thermal Sciences,2011,50(3):287-295.
[14]Sharabi M,Ambrosini W,He S,et al.Prediction of turbulent convective heat transfer to a fluid at supercritical pressure in square and triangular channels[J].Annals of Nuclear Energy,2008,35(6):993-1005.
[15]Li Z H,Wu Y X,Tang G L,et al.Comparison between heat transfer to supercritical water in a smooth tube and in an internally ribbed tube[J].International Journal of Heat and Mass Transfer,2015,84:529-541.
[16]杨俊兰,马一太,李敏霞.超临界CO2流体及其换热特性分析[J].流体机械,2013,41(5):66-71.
[17]Mahdi M,Majid B.The effect of the low Reynolds number k-e turbulence models on simulation of the enhanced and deteriorated convective heat transfer to the supercritical fluid flows[J].Heat and Mass Transfer,2011,47(5):609-619.
[18]Jiang P X,Zhang Y,Zhao C R,et al.Convection heat transfer of CO2at supercritical pressures in a vertical mini tube at relatively low reynolds numbers[J].Experimental Thermal and Fluid Science,2008,32(8):1628-1637.
[19]Ma T,Chu W X,Xu X Y,et al.An experimental study on heat transfer between supercritical carbon dioxide and water near the pseudo-critical temperature in a double pipe heat exchanger[J].International Journal of Heat and Mass Transfer,2016,93:379-387.
[20]Huang D,Wu Z,Sunden B,et al.A brief review on convection heat transfer of fluids at supercritical pressures in tubes and the recent progress[J].Applied Energy,2016,162:494-505.
[21]Wen Q L,Gu H Y.Numerical simulation of heat transfer deterioration phenomenon in supercritical water through vertical tube[J].Annals of Nuclear Energy,2010,37(10):1272-1280.
[22]Negoescu C C,Li Y L,Al-Duri B,et al.Heat transfer behaviour of supercritical nitrogen in the large specific heat region flowing in a vertical tube[J].Energy,2017,134:1096-1106.
[23]刘丹,张忠国,赵可卉,等.螺旋管式二次流混合器的混合性能[J].化工学报,2011,62(10):2707-2712.
[24]朱辉,王汉青,刘志强.螺旋管内迪恩涡强化传热的试验研究[J].热能动力工程,2014,29(6):645-757.
[25]Naphon P,Wongwises S.A review of flow and heat transfer characteristics in curved tubes[J].Renewable and Sustainable Energy Reviews,2006,10(5):463-490.
[26]陈永东.大型LNG汽化器的选材和结构研究[J].压力容器,2007,24(11):40-47.
[27]Jayakumar J S,Mahajani S M,Mandal J C,et al.Experimental and CFD estimation of heat transfer in helically coiled heat exchangers[J].Chemical Engineering Research and Design,2008,86(3):221-232.
[28]Pioro I L,Duffey R B.Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Power-engineering Applications[M].New York:ASME Press,2007:45-46.
[29]Rao N T,Oumer A N,Jamaludin U K.State-of-the-art on flow and heat transfer characteristics of supercritical CO2in various channels[J].The Journal of Supercritical Fluids,2016,116:132-147.
[30]Zappoli B,Beysens D,Garrabos Y.Heat Transfers and Related Effects in Supercritical Fluids[M].Dordrecht:Springer,2015:1-4.
[31]Jung Y Y.The turbulent flows of supercritical fluids with heat transfer[J].Annual Review of Fluid Mechanics,2013,45:495-525.
[32]Incropera F P,Dewitt D P,Bergman T L,et al.Fundamentals of Heat and Mass Transfer[M].6THEdition.Notre Dame,Indiana,USA:University of Notre Dame,2007:324-325.
[33]康奥峰,张鹏.螺旋管内超临界氮的对流换热研究[J].低温与超导,2012,40(3):1-8.
[34]王淑香,张伟,牛志愿,等.超临界压力下CO2在螺旋管内的混合对流换热[J].化工学报,2013,64(11):3917-3926.
[35]Xu X X,Liu C,Dang C B,et al.Experimental investigation on heat transfer characteristics of supercritical CO2cooled in horizontal helically coiled tube[J].International Journal of Refrigeration,2016,67:190-201.
[36]Wang K Z,Xu X X,Liu C,et al.Experimental and numerical investigation on heat transfer characteristics of supercritical CO2in the cooled helically coiled tube[J].International Journal of Heat and Mass Transfer,2017,108:1645-1655.
[37]Lazova M,Huisseune H,Kaya A,et al.Performance evaluation of a helical coil heat exchanger working under supercritical conditions in a solar organic rankine cycle installation[J].Energies,2016,9(6):432-451.
[38]Li L J,Lin C X,Ebadian M A.Turbulent heat transfer to near-critical water in a heated curved pipe under the conditions of mixed convection[J].International Journal of Heat and Mass Transfer,1999,42(16):3147-3158.
[39]Zhao H J,Li X W,Wu X X.Numerical investigation of supercritical water turbulent flow and heat transfer characteristics in vertical helical tubes[J].The Journal of Supercritical Fluids,2017,127:48-61.
[40]Xu J L,Yang C Y,Zhang W,et al.Turbulent convective heat transfer of CO2in a helical tube at near-critical pressure[J].International Journal of Heat and Mass Transfer,2015,80:748-758.
[41]Wang K Z,Xu X X,Wu Y Y,et al.Numerical investigation on heat transfer of supercritical CO2in heated helically coiled tubes[J].The Journal of Supercritical Fluids,2015,99:112-120.
[42]Liu X X,Xu X X,Liu C,et al.Numerical study of the effect of buoyancy force and centrifugal force on heat transfer characteristics of supercritical CO2in helically coiled tube at various inclination angles[J].Applied Thermal Engineering,2017,116:500-515.
[43]Yang M.Numerical study of the characteristic influence of the helically coiled tube on the heat transfer of carbon dioxide[J].Applied Thermal Engineering,2016,102:882-896.
[44]Yang M.Numerical study of the heat transfer to carbon dioxide in horizontal helically coiled tubes under supercritical pressure[J].Applied Thermal Engineering,2016,109:685-696.
[45]Li Z H,Zhai Y L,Li K Z,et al.A quantitative study on the interaction between curvature and buoyancy effects in helically coiled heat exchangers of supercritical CO2rankine cycles[J].Energy,2016,116:661-676.
[46]Zhao Z X,Che D F,Zhang Y,et al.Numerical investigation on conjugate heat transfer to supercritical CO2in membrane helical coiled tube heat exchangers[J].Numerical Heat Transfer,Part A,2016,69(9):977-995.
[47]王成刚,孙宝坤,晏芙蓉,等.超临界LNG汽化器热流耦合传热研究[J].低温与超导,2016,44(11):1-6.
[48]Kawai S.Direct numerical simulation of transcritical turbulent boundary layers at supercritical pressures with strong real fluid effects[C]//AIAA Sci Tech.54th AIAA Aerospace Sciences Meeting.San Diego,California,USA:2016:1-21.
[49]Tian R,Dai X Y,Wang D B,et al.Study of variable turbulent prandtl number model for heat transfer to supercritical fluids in vertical tubes[J].Journal of Thermal Science,2018,27(3):213-222.
[50]Hanjalic K.One-point closure models for buoyancydriven turbulent flows[J].Annual Review of Fluid Mechanics,2002,34:321-347.
[51]Peeters J W R,Pecnik R,Rohde M,et al.Characteristics of turbulent heat transfer in an annulus at supercritical pressure[J].Physical Review Fluids,2017,2(2):024602.
[52]Sandeep P,Xu C,Eckart L.Investigation of in-tube cooling of carbon dioxide at supercritical pressure by means of direct numerical simulation[J].International Journal of Heat and Mass Transfer,2017,114:944-957.
[53]徐峰,郭烈锦.超临界压力下水在螺旋管内的混合对流换热[J].西安交通大学学报,2005,39(9):978-981.
[54]Jackson J D,Hall W B.Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions[J].Turbulent Forced Convection in Channels and Bundles,1979,2:613-640.
[55]Ciofalo M,Arini A,Liberto M D.On the influence of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved pipes and coils[J].International Journal of Heat and Mass Transfer,2015,82:123-134.
[56]Jackson J D,Hall W B,Fewster J,et al.Heat Transfer to Supercritical Pressure Fluids[R].UK:United Kingdom Atomic Energy Authority,1975.
[57]刘新新,叶建,徐肖肖,等.超临界CO2在水平螺旋管内的冷却换热特性[J].化工学报,2016,67(增刊2):120-127.
[58]王淑香,牛志愿,张伟,等.超临界压力下CO2在螺旋管中沿程传热的实验研究[J].核动力工程,2014,35(1):28-31.
[59]贾金才.几何参数对绕管式换热器传热特性影响的数值研究[J].流体机械,2011,39(8):33-37.
[60]Zeng M,Zhang G P,Li Y,et al.Geometrical parametric analysis of flow and heat transfer in the shell side of a spiral-wound heat exchanger[J].Heat Transfer Engineering,2015,36:790-805.
[61]Ferng Y M,Lin W C,Chieng C C.Numerically investigated effects of different dean number and pitch size on flow and heat transfer characteristics in a helically coiltube heat exchanger[J].Applied Thermal Engineering,2012,36:378-385.
[62]夏春杰,陈永东,王严冬,等.超临界氮在螺旋管内的流动与传热研究[J].压力容器,2017,34(10):27-31.
[63]黄志刚,曾小康,李永亮,等.超临界传热关联式的整理与评估[J].核动力工程,2012,33(1):28-31.
[2]Song J H,Kim H Y,Kim H,et al.Heat transfer characteristics of a supercritical fluid flow in a vertical pipe[J].The Journal of Supercritical Fluids,2008,44(2):164-171.
[3]王英杰.超临界流体传热特性研究综述[J].科技导报,2012,30(33):74-79.
[4]Yamagata K,Nishikawa K,Hasegawa S,et al.Forced convective heat transfer to supercritical water flowing in tubes[J].International Journal of Heat and Mass Transfer,1972,15(12):2575-2593.
[5]Popov V N,Petrov N E.Calculation of heat-transfer and flow resistance in the turbulent pipe-flow of cooled carbon-dioxide in the supercritical region[J].Teplofizika Vysokikh Temp,1985,23(2):309-316.
[6]Cheng X,Schulenberg T.Heat Transfer at Supercritical Pressures:Literature Review and Application to an HPLWR[M].Karlsruhe:FZKA,2001:5-7.
[7]Pioro I L,Khartabil H F,Duffey R B.Heat transfer to supercritical fluids flowing in channels-empirical correlations(survey)[J].Nuclear Engineering and Design,2004,230(1-3):69-91.
[8]Joong H B,Jung Y Y.Direct numerical simulation of turbulent supercritical flows with heat transfer[J].Physics of Fluids,2005,17:105104.
[9]Jiang P X,Shi R F,Xu Y J,et al.Experimental investigation of flow resistance and convection heat transfer of CO2at supercritical pressures in a vertical porous tube[J].The Journal of Supercritical Fluids,2006,38(3):339-346.
[10]He S,Kim W S,Jackson J D.A computational study of convective heat transfer to carbon dioxide at a pressure just above the critical value[J].Applied Thermal Engineering,2008,28(13):1662-1675.
[11]Bae Y Y,Kim H Y.Convective heat transfer to CO2at a supercritical pressure flowing vertically upward in tubes and an annular channel[J].Experimental Thermal and Fluid Science,2009,33(2):329-339.
[12]Kim D E,Kim M H.Experimental study of the effects of flow acceleration and buoyancy on heat transfer in a supercritical fluid flow in a circular tube[J].Nuclear Engineering and Design,2010,240(10):3336-3349.
[13]Zhang P,Huang Y,Shen B,et al.Flow and heat transfer characteristics of supercritical nitrogen in a vertical mini-tube[J].International Journal of Thermal Sciences,2011,50(3):287-295.
[14]Sharabi M,Ambrosini W,He S,et al.Prediction of turbulent convective heat transfer to a fluid at supercritical pressure in square and triangular channels[J].Annals of Nuclear Energy,2008,35(6):993-1005.
[15]Li Z H,Wu Y X,Tang G L,et al.Comparison between heat transfer to supercritical water in a smooth tube and in an internally ribbed tube[J].International Journal of Heat and Mass Transfer,2015,84:529-541.
[16]杨俊兰,马一太,李敏霞.超临界CO2流体及其换热特性分析[J].流体机械,2013,41(5):66-71.
[17]Mahdi M,Majid B.The effect of the low Reynolds number k-e turbulence models on simulation of the enhanced and deteriorated convective heat transfer to the supercritical fluid flows[J].Heat and Mass Transfer,2011,47(5):609-619.
[18]Jiang P X,Zhang Y,Zhao C R,et al.Convection heat transfer of CO2at supercritical pressures in a vertical mini tube at relatively low reynolds numbers[J].Experimental Thermal and Fluid Science,2008,32(8):1628-1637.
[19]Ma T,Chu W X,Xu X Y,et al.An experimental study on heat transfer between supercritical carbon dioxide and water near the pseudo-critical temperature in a double pipe heat exchanger[J].International Journal of Heat and Mass Transfer,2016,93:379-387.
[20]Huang D,Wu Z,Sunden B,et al.A brief review on convection heat transfer of fluids at supercritical pressures in tubes and the recent progress[J].Applied Energy,2016,162:494-505.
[21]Wen Q L,Gu H Y.Numerical simulation of heat transfer deterioration phenomenon in supercritical water through vertical tube[J].Annals of Nuclear Energy,2010,37(10):1272-1280.
[22]Negoescu C C,Li Y L,Al-Duri B,et al.Heat transfer behaviour of supercritical nitrogen in the large specific heat region flowing in a vertical tube[J].Energy,2017,134:1096-1106.
[23]刘丹,张忠国,赵可卉,等.螺旋管式二次流混合器的混合性能[J].化工学报,2011,62(10):2707-2712.
[24]朱辉,王汉青,刘志强.螺旋管内迪恩涡强化传热的试验研究[J].热能动力工程,2014,29(6):645-757.
[25]Naphon P,Wongwises S.A review of flow and heat transfer characteristics in curved tubes[J].Renewable and Sustainable Energy Reviews,2006,10(5):463-490.
[26]陈永东.大型LNG汽化器的选材和结构研究[J].压力容器,2007,24(11):40-47.
[27]Jayakumar J S,Mahajani S M,Mandal J C,et al.Experimental and CFD estimation of heat transfer in helically coiled heat exchangers[J].Chemical Engineering Research and Design,2008,86(3):221-232.
[28]Pioro I L,Duffey R B.Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Power-engineering Applications[M].New York:ASME Press,2007:45-46.
[29]Rao N T,Oumer A N,Jamaludin U K.State-of-the-art on flow and heat transfer characteristics of supercritical CO2in various channels[J].The Journal of Supercritical Fluids,2016,116:132-147.
[30]Zappoli B,Beysens D,Garrabos Y.Heat Transfers and Related Effects in Supercritical Fluids[M].Dordrecht:Springer,2015:1-4.
[31]Jung Y Y.The turbulent flows of supercritical fluids with heat transfer[J].Annual Review of Fluid Mechanics,2013,45:495-525.
[32]Incropera F P,Dewitt D P,Bergman T L,et al.Fundamentals of Heat and Mass Transfer[M].6THEdition.Notre Dame,Indiana,USA:University of Notre Dame,2007:324-325.
[33]康奥峰,张鹏.螺旋管内超临界氮的对流换热研究[J].低温与超导,2012,40(3):1-8.
[34]王淑香,张伟,牛志愿,等.超临界压力下CO2在螺旋管内的混合对流换热[J].化工学报,2013,64(11):3917-3926.
[35]Xu X X,Liu C,Dang C B,et al.Experimental investigation on heat transfer characteristics of supercritical CO2cooled in horizontal helically coiled tube[J].International Journal of Refrigeration,2016,67:190-201.
[36]Wang K Z,Xu X X,Liu C,et al.Experimental and numerical investigation on heat transfer characteristics of supercritical CO2in the cooled helically coiled tube[J].International Journal of Heat and Mass Transfer,2017,108:1645-1655.
[37]Lazova M,Huisseune H,Kaya A,et al.Performance evaluation of a helical coil heat exchanger working under supercritical conditions in a solar organic rankine cycle installation[J].Energies,2016,9(6):432-451.
[38]Li L J,Lin C X,Ebadian M A.Turbulent heat transfer to near-critical water in a heated curved pipe under the conditions of mixed convection[J].International Journal of Heat and Mass Transfer,1999,42(16):3147-3158.
[39]Zhao H J,Li X W,Wu X X.Numerical investigation of supercritical water turbulent flow and heat transfer characteristics in vertical helical tubes[J].The Journal of Supercritical Fluids,2017,127:48-61.
[40]Xu J L,Yang C Y,Zhang W,et al.Turbulent convective heat transfer of CO2in a helical tube at near-critical pressure[J].International Journal of Heat and Mass Transfer,2015,80:748-758.
[41]Wang K Z,Xu X X,Wu Y Y,et al.Numerical investigation on heat transfer of supercritical CO2in heated helically coiled tubes[J].The Journal of Supercritical Fluids,2015,99:112-120.
[42]Liu X X,Xu X X,Liu C,et al.Numerical study of the effect of buoyancy force and centrifugal force on heat transfer characteristics of supercritical CO2in helically coiled tube at various inclination angles[J].Applied Thermal Engineering,2017,116:500-515.
[43]Yang M.Numerical study of the characteristic influence of the helically coiled tube on the heat transfer of carbon dioxide[J].Applied Thermal Engineering,2016,102:882-896.
[44]Yang M.Numerical study of the heat transfer to carbon dioxide in horizontal helically coiled tubes under supercritical pressure[J].Applied Thermal Engineering,2016,109:685-696.
[45]Li Z H,Zhai Y L,Li K Z,et al.A quantitative study on the interaction between curvature and buoyancy effects in helically coiled heat exchangers of supercritical CO2rankine cycles[J].Energy,2016,116:661-676.
[46]Zhao Z X,Che D F,Zhang Y,et al.Numerical investigation on conjugate heat transfer to supercritical CO2in membrane helical coiled tube heat exchangers[J].Numerical Heat Transfer,Part A,2016,69(9):977-995.
[47]王成刚,孙宝坤,晏芙蓉,等.超临界LNG汽化器热流耦合传热研究[J].低温与超导,2016,44(11):1-6.
[48]Kawai S.Direct numerical simulation of transcritical turbulent boundary layers at supercritical pressures with strong real fluid effects[C]//AIAA Sci Tech.54th AIAA Aerospace Sciences Meeting.San Diego,California,USA:2016:1-21.
[49]Tian R,Dai X Y,Wang D B,et al.Study of variable turbulent prandtl number model for heat transfer to supercritical fluids in vertical tubes[J].Journal of Thermal Science,2018,27(3):213-222.
[50]Hanjalic K.One-point closure models for buoyancydriven turbulent flows[J].Annual Review of Fluid Mechanics,2002,34:321-347.
[51]Peeters J W R,Pecnik R,Rohde M,et al.Characteristics of turbulent heat transfer in an annulus at supercritical pressure[J].Physical Review Fluids,2017,2(2):024602.
[52]Sandeep P,Xu C,Eckart L.Investigation of in-tube cooling of carbon dioxide at supercritical pressure by means of direct numerical simulation[J].International Journal of Heat and Mass Transfer,2017,114:944-957.
[53]徐峰,郭烈锦.超临界压力下水在螺旋管内的混合对流换热[J].西安交通大学学报,2005,39(9):978-981.
[54]Jackson J D,Hall W B.Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions[J].Turbulent Forced Convection in Channels and Bundles,1979,2:613-640.
[55]Ciofalo M,Arini A,Liberto M D.On the influence of gravitational and centrifugal buoyancy on laminar flow and heat transfer in curved pipes and coils[J].International Journal of Heat and Mass Transfer,2015,82:123-134.
[56]Jackson J D,Hall W B,Fewster J,et al.Heat Transfer to Supercritical Pressure Fluids[R].UK:United Kingdom Atomic Energy Authority,1975.
[57]刘新新,叶建,徐肖肖,等.超临界CO2在水平螺旋管内的冷却换热特性[J].化工学报,2016,67(增刊2):120-127.
[58]王淑香,牛志愿,张伟,等.超临界压力下CO2在螺旋管中沿程传热的实验研究[J].核动力工程,2014,35(1):28-31.
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