Advances in flow and heat transfer research of liquid metal flowing across tube bundles

doi:10.16085/j.issn.1000-6613.2023-1221

Abstract

Abstract:

The helical coiled tube heat exchanger based on liquid metal has the characteristics of compactness and strong heat exchange capacity. It is valuable in energy and chemical systems such as thermochemical hydrogen production, fourth-generation nuclear energy, high-temperature solar thermal power generation, and waste heat recovery. The convective heat transfer issues of liquid metal flowing across tube bundles are getting more and more attention. However, turbulent heat transfer flowing across tube bundles is complicated, and the experimental and numerical simulation is chanllenging. At present, there is no reliable and relevant literature review, hindering the design and technical development of this type of heat exchanger. This paper reviewed convective heat transfer researches on liquid metal flowing across tube bundles. Firstly, it was pointed out the similarities and differences between liquid metal and other fluids in convective heat transfer characteristics. Then, it was summarized and compared flow and heat transfer empirical relations of liquid metal. It was recommended empirical formulas for the design of this type of heat exchanger. Subsequently, by applying the recommended empirical relations, the flow and heat transfer performance of different working fluid was compared with flowing across tube bundles, and the liquid metal flowing through different flow channels was also compared. The turbulent heat transfer of liquid metal has the potential to strengthen. The flow resistance caused by tube bundles is considerable, so it is recommended to take measures to reduce the resistance. This paper provided a reference for the subsequent design of heat exchangers involving liquid metal flowing across tube bundles.

Key words: heat transfer, convection, tube bundles, liquid metal, turbulent flow

摘要：

基于液态金属的螺旋管式换热器具有紧凑、换热能力强的特点，在热化学制氢、第四代核能、太阳能高温热发电、余热回收等能源化工系统极具价值，液态金属绕流管束流动传热问题越来越受到重视。然而，绕流管束湍流传热较复杂，实验和数值模拟难度较大，目前尚未有相关可靠文献综述，阻碍了该类换热器设计与技术进步。本文回顾了液态金属绕流管束相关研究，首先指出了液态金属流动传热特性与其他流体的异同，然后简述并比较了液态金属流动传热经验关系式，推荐了该类型换热器设计的流动传热经验公式，紧接着应用经验关系式分别对比了不同工质绕流管束、液态金属流经不同流道的流动传热性能。指出液态金属湍流传热具有一定强化潜力，且绕流管束带来形阻较大，建议采取减阻措施。本文为后续涉及液态金属绕流管束的换热器设计提供了参考。

关键词: 传热, 对流, 管束, 液态金属, 湍流

CLC Number:

TK172

XIAO Hui, ZHANG Xianjun, LAN Zhike, WANG Suhao, WANG Sheng. Advances in flow and heat transfer research of liquid metal flowing across tube bundles[J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 10-20.

肖辉, 张显均, 兰治科, 王苏豪, 王盛. 液态金属绕流管束流动传热进展[J]. 化工进展, 2023, 42(S1): 10-20.

Figures/Tables 9

References 52

1	张群力, 黄昊天, 张琳, 等. 喷淋式烟气源热泵冷凝余热回收系统性能分析[J]. 化工进展, 2023, 42(2): 650-657.
	ZHANG Qunli, HUANG Haotian, ZHANG Lin, et al. Analysis of condensation waste heat recovery system of spray flue gas source heat pump[J]. Chemical Industry and Engineering Progress, 2023, 42(2): 650-657.
2	龙会松. 蒸汽发生器水室封头与管束组件环缝制造工艺分析[J]. 发电设备, 2022, 36(5): 355-357.
	LONG Huisong. Manufacturing process analysis of circumferential seam between water chamber head and tube bundle assembly of steam generators[J]. Power Equipment, 2022, 36(5): 355-357.
3	刘世杰, 莫逊, 涂爱民, 等. 新型纵流油冷却器壳程强化传热[J]. 化工进展, 2022, 41(7): 3475-3482.
	LIU Shijie, MO Xun, TU Aimin, et al. Shell-side heat transfer enhancement of a novel longitudinal flow oil cooler[J]. Chemical Industry and Engineering Progress, 2022, 41(7): 3475-3482.
4	LI Haiyan, LIU Jing. Revolutionizing heat transport enhancement with liquid metals: Proposal of a new industry of water-free heat exchangers[J]. Frontiers in Energy, 2011, 5(1): 20-42.
5	DENG Yueguang, JIANG Yi, LIU Jing. Low-melting-point liquid metal convective heat transfer: A review[J]. Applied Thermal Engineering, 2021, 193: 117021.
6	JI Yulong, WU Mengke, FENG Yanmin, et al. Experimental study on the effects of sodium and potassium proportions on the heat transfer performance of liquid metal high-temperature oscillating heat pipes[J]. International Journal of Heat and Mass Transfer, 2022, 194: 123116.
7	Nuclear-Energy-Agency. Handbook on lead-bismuth eutectic alloy and lead properties, materials compatibility, thermalhydraulics and technologies[M]. Paris: OECD Publishing, 2015.
8	REED Samuel, SUGO Heber, KISI Erich, et al. Extended thermal cycling of miscibility gap alloy high temperature thermal storage materials[J]. Solar Energy, 2019, 185: 333-340.
9	LIU Wei, XIAO Hui. Theoretical study on enhancing convective heat transfer based on strengthening synergy and reducing dissipation[J]. Scientia Sinica Technologica, 2021, 51(10): 1166-1177.
10	WANG Xinting, LIANG Yunmin, SUN Yue, et al. Experimental and numerical investigation on shell-side performance of a double shell-pass rod baffle heat exchanger[J]. International Journal of Heat and Mass Transfer, 2019, 132: 631-642.
11	邓靜. 螺旋缠绕管换热器流动传热性能研究[D]. 郑州: 郑州大学, 2016.
	DENG Jing. The heat transfer and flow characteristics analysis of helically coiled tube heat exchanger[D]. Zhengzhou: Zhengzhou University, 2016.
12	EL-GENK Mohamed S, SCHRIENER Timothy M. A review of experimental data and heat transfer correlations for parallel flow of alkali liquid metals and lead-bismuth eutectic in bundles[J]. Nuclear Engineering and Design, 2017, 317: 199-219.
13	JAEGER Wadim. Heat transfer to liquid metals with empirical models for turbulent forced convection in various geometries[J]. Nuclear Engineering and Design, 2017, 319: 12-27.
14	HOLMAN J P. Heat transfer [M]. 10th ed. Boston: McGraw-Hill, 2010.
15	JAKOB Max. Discussion: “Heat transfer and flow resistance in cross flow of gases over tube banks” (PIERSON O L, HUGE E C, GRIMISON E D, 1937, trans. ASME, 59, pp. 563-594)[J]. Journal of Fluids Engineering, 1938, 60(4): 384-386.
16	ŽKAUSKAS A. Heat transfer from tubes in crossflow[M]//Advances in Heat Transfer. Amsterdam: Elsevier, 1987: 87-159.
17	IDELCHIK I E. Handbook of hydraulic resistance, 4th Edition Revised and augmented[M]. 4th ed. New York: Begell House Inc., 2008.
18	JAMESON S L. Discussion: “A general correlation of friction factors for various types of surfaces in crossflow” (GUNTER A Y, SHAW W A, 1945, trans. ASME, 67, pp. 643-656)[J]. Journal of Fluids Engineering, 1945, 67(8): 658-659.
19	VASSALLO Peter, SYMOLON Paul. Friction factor measurements in an equally spaced triangular array of circular tubes[J]. Journal of Fluids Engineering, 2008, 130(4): 1.
20	GILLI P V. Heat transfer and pressure drop for cross flow through banks of multistart helical tubes with uniform inclinations and uniform longitudinal pitches[J]. Nuclear Science and Engineering, 1965, 22(3): 298-314.
21	吕科锋. 液态铅铋合金在带绕丝棒束组件内热工水力行为研究[D]. 合肥: 中国科学技术大学, 2016.
	Kefeng LYU. Study on thermohydraulic behavior of liquid Pb-Bi alloy in wire-wound rod bundle assembly[D].Hefei: University of Science and Technology of China, 2016.
22	SHAMS A, DE SANTIS A, KOLOSZAR L K, et al. Status and perspectives of turbulent heat transfer modelling in low-Prandtl number fluids[J]. Nuclear Engineering and Design, 2019, 353: 110220.
23	CHENG Xu, Nam-il TAK. Investigation on turbulent heat transfer to lead-bismuth eutectic flows in circular tubes for nuclear applications[J]. Nuclear Engineering and Design, 2006, 236(4): 385-393.
24	XIE Xiaoyang, ZHAO Houjian, LI Xiaowei, et al. Numerical investigation on heat transfer characteristics of liquid metal cross flow over tube bundles[J]. Annals of Nuclear Energy, 2023, 180: 109465.
25	MASTERSON Robert. Nuclear reactor thermal hydraulics: An introduction to nuclear heat transfer and fluid flow[M] CRC Press, 2020..
26	KIM Namhyeong, KIM Hyungmo, Jaehyuk EOH, et al. One-dimensional design approach to integrated steam generator with helical-coil tube bundles for a sodium-cooled fast reactor[J]. Nuclear Engineering and Design, 2020, 361: 110554.
27	GILLI P V. Heat transfer characteristics of helical tube bundles as used in steam generators of gas-cooled reactors [Z]. ICPUAEUN. Geneva. 1964
28	尹清辽, 孙玉良, 居怀明, 等. 模块式高温气冷堆超临界蒸汽发生器设计[J]. 原子能科学技术, 2006, 40(6): 707-713.
	YIN Qingliao, SUN Yuliang, JU Huaiming, et al. Supercritical steam generator design of modular high-temperature gas-cooled reactor[J]. Atomic Energy Science and Technology, 2006, 40(6): 707-713.
29	杨自强. 小型模块化反应堆螺旋管式直流蒸汽发生器热工水力研究[D]. 重庆: 重庆大学, 2018.
	YANG Ziqiang. Study on thermal hydraulics of helical tube steam generator for small modular reactor[D]. Chongqing: Chongqing University, 2018.
30	范弘毅, 李晓伟, 吴莘馨, 等. 高温气冷堆螺旋管式超临界蒸汽发生器热工水力程序开发及分析[J]. 原子能科学技术, 2022, 56(11): 2343-2353.
	FAN Hongyi, LI Xiaowei, WU Xinxin, et al. Thermal-hydraulic code development and analysis of HTGR helical tube supercritical steam generator[J]. Atomic Energy Science and Technology, 2022, 56(11): 2343-2353.
31	李晓伟, 吴莘馨, 张作义. 高温气冷堆螺旋管式直流蒸汽发生器热工水力学[J]. 原子能科学技术, 2019, 53(10): 1906-1917.
	LI Xiaowei, WU Xinxin, ZHANG Zuoyi. Thermal hydraulics of HTGR helical tube once through steam generator[J]. Atomic Energy Science and Technology, 2019, 53(10): 1906-1917.
32	NEERAAS Bengt O, FREDHEIM Arne O, AUNAN Bjørn. Experimental shell-side heat transfer and pressure drop in gas flow for spiral-wound LNG heat exchanger[J]. International Journal of Heat and Mass Transfer, 2004, 47(2): 353-361.
33	MOSTAFAZADE ABOLMAALI Ali, AFSHIN Hossein. Development of Nusselt number and friction factor correlations for the shell side of spiral-wound heat exchangers[J]. International Journal of Thermal Sciences, 2019, 139: 105-117.
34	SHEN Cong, LIU Limin, XU Ziyi, et al. Influence of helix angle on flow and heat transfer characteristics of lead-bismuth flow in helical-coiled tube bundles[J]. Annals of Nuclear Energy, 2023, 180: 109483.
35	刘尚华. 螺旋管内核态沸腾流动与换热特性数值模拟分析[D]. 哈尔滨: 哈尔滨工程大学, 2017.
	LIU Shanghua. Numerical simulation the flow and heat transfer characteristics of nucleate boiling in helically coiled tubes[D]. Harbin: Harbin Engineering University, 2017.
36	HOE R J, DROPKIN D, DWYER O E. Heat-transfer rates to crossflowing mercury in a staggered tube bank—Ⅰ[J]. Journal of Fluids Engineering, 1957, 79(4): 899-905.
37	RICKARD C L, DWYER O E, DROPKIN D. Heat-transfer rates to cross-flowing mercury in a staggered tube bank—Ⅱ[J]. Journal of Fluids Engineering, 1958, 80(3): 646-652.
38	赵后剑, 谢箫阳, 高伟凯, 等. 液态铅铋合金横掠管束对流换热数值计算[J]. 工程热物理学报, 2021, 42(7): 1837-1843.
	ZHAO Houjian, XIE Xiaoyang, GAO Weikai, et al. Numerical simulation of liquid lead-bismuth eutectic cross flow heat transfer over tube bundles[J]. Journal of Engineering Thermophysics, 2021, 42(7): 1837-1843.
39	DWYER O. Recent developments in liquid-metal heat transfer [J]. Atomic Energy Review, 1966, 4(BNL-9597).
40	BORISHANSKIY V, ANDREYEVSKIY A, ZHILKINA V, et al. Heat transfer of tube bundles in cross-flow of liquid metal [M]. Moscow: Gosatomizdat, 1963.
41	BEZNOSOV Alexandr Viktorovich, YARMONOV Mikhail Vladimirovich, ZUDIN Artyom Dmitrievich, et al. Experimental studies of heat transfer characteristics and properties of the cross-flow pipe flow melt lead[J]. Open Journal of Microphysics, 2014, 4(4): 54-65.
42	ABRAMOV Alexey G, LEVCHENYA Alexander M, SMIRNOV Evgueni M, et al. Numerical simulation of liquid metal turbulent heat transfer from an inline tube bundle in cross-flow[J]. St Petersburg Polytechnical University Journal: Physics and Mathematics, 2015, 1(4): 356-363.
43	KALISH Sheldon, DWYER Orrington E. Heat transfer to NaK flowing through unbaffled rod bundles[J]. International Journal of Heat and Mass Transfer, 1967, 10(11): 1533-1558.
44	Hsu CHIA-JUNG. Analytical study of heat transfer to liquid metals in cross-flow through rod bundles[J]. International Journal of Heat and Mass Transfer, 1964, 7(4): 431-446.
45	XU Rongshuan, ZHANG Dalin, TIAN Wenxi, et al. Thermal-hydraulic analysis code development for sodium heated once-through steam generator[J]. Annals of Nuclear Energy, 2019, 127: 385-394.
46	杨宇鹏, 王成龙, 张大林, 等. 液态金属螺旋管式直流蒸汽发生器数值模拟研究[J]. 原子能科学技术, 2021, 55(7): 1288-1295.
	YANG Yupeng, WANG Chenglong, ZHANG Dalin, et al. Numerical study of liquid metal helical coil once-through tube steam generator[J]. Atomic Energy Science and Technology, 2021, 55(7): 1288-1295.
47	YANG Yupeng, LI Yong, WANG Chenglong, et al. Parametric sensitivity analysis of liquid metal helical coil once-through tube steam generator[J]. Nuclear Engineering and Design, 2021, 383: 111427.
48	LI Xiaowei, WU Xinxin, HE Shuyan. Numerical investigation of the turbulent cross flow and heat transfer in a wall bounded tube bundle[J]. International Journal of Thermal Sciences, 2014, 75: 127-139.
49	KATINAS V, TUMOSA A. Heat transfer and flow past tube bundles in the wall region[J]. Heat Transfer Research, 1993, 25: 161-164.
50	ZHANG Yan, WANG Chenglong, CAI Rong, et al. Experimental investigation on flow and heat transfer characteristics of lead-bismuth eutectic in circular tubes[J]. Applied Thermal Engineering, 2020, 180: 115820.
51	MIKITYUK Konstantin. Heat transfer to liquid metal: Review of data and correlations for tube bundles[J]. Nuclear Engineering and Design, 2009, 239(4): 680-687.
52	RAZZAGHPANAH Zahra, SARUNAC Nenad. Natural convection heat transfer from a vertical column of finite number of heated circular cylinders immersed in molten solar salt[J]. International Journal of Heat and Mass Transfer, 2019, 134: 694-706.

工质	ρ/kg·m^-3	μ/kg·m^-1·s^-1	λ/W·m^-1·K^-1	c_p /J·kg^-1·K^-1	Pr
高温熔盐	1687.8	2.17×10^-3	0.56	1551.9	6.01
22MPa高压水	568.1	6.53×10^-5	0.453	9448.7	1.36
液态金属LBE	10246.3	1.63×10^-3	12.60	143.7	0.019
7MPa氦气	5.249	3.356×10^-5	0.266	5189.1	0.655

工质	ρ/kg·m^-3	μ/kg·m^-1·s^-1	λ/W·m^-1·K^-1	c_p /J·kg^-1·K^-1	Pr
高温熔盐	1687.8	2.17×10^-3	0.56	1551.9	6.01
22MPa高压水	568.1	6.53×10^-5	0.453	9448.7	1.36
液态金属LBE	10246.3	1.63×10^-3	12.60	143.7	0.019
7MPa氦气	5.249	3.356×10^-5	0.266	5189.1	0.655

[1]	ZHAO Chen, MIAO Tianze, ZHANG Chaoyang, HONG Fangjun, WANG Dahai. Heat transfer characteristics of ethylene glycol aqueous solution in slit channel under negative pressure [J]. Chemical Industry and Engineering Progress, 2023, 42(S1): 148-157.
[2]	CHEN Lin, XU Peiyuan, ZHANG Xiaohui, CHEN Jie, XU Zhenjun, CHEN Jiaxiang, MI Xiaoguang, FENG Yongchang, MEI Deqing. Investigation on the LNG mixed refrigerant flow and heat transfer characteristics in coil-wounded heat exchanger (CWHE) system [J]. Chemical Industry and Engineering Progress, 2023, 42(9): 4496-4503.
[3]	ZHANG Fan, TAO Shaohui, CHEN Yushi, XIANG Shuguang. Initializing distillation column simulation based on the improved constant heat transport model [J]. Chemical Industry and Engineering Progress, 2023, 42(9): 4550-4558.
[4]	BU Zhicheng, JIAO Bo, LIN Haihua, SUN Hongyuan. Review on computational fluid dynamics (CFD) simulation and advances in pulsating heat pipes [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4167-4181.
[5]	WANG Jiansheng, ZHANG Huipeng, LIU Xueling, FU Yuguo, ZHU Jianxiao. Analysis of flow and heat transfer characteristics in porous media reservoir [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4212-4220.
[6]	WANG Yungang, JIAO Jian, DENG Shifeng, ZHAO Qinxin, SHAO Huaishuang. Experimental analysis of condensation heat transfer and synergistic desulfurization [J]. Chemical Industry and Engineering Progress, 2023, 42(8): 4230-4237.
[7]	LIU Houli, GU Zhonghao, YANG Kang, ZHANG Li. Effect of groove width on pool boiling heat transfer characteristics in 3D printing groove structure [J]. Chemical Industry and Engineering Progress, 2023, 42(5): 2282-2288.
[8]	ZHANG Chenyu, WANG Ning, XU Hongtao, LUO Zhuqing. Performance evaluation of the multiple layer latent heat thermal energy storage unit combined with nanoparticle for heat transfer enhancement [J]. Chemical Industry and Engineering Progress, 2023, 42(5): 2332-2342.
[9]	GUO Wenjie, ZHAI Yuling, CHEN Wenzhe, SHEN Xin, XING Ming. Analysis of convective heat transfer and thermo-economic performance of Al₂O₃-CuO/water hybrid nanofluids [J]. Chemical Industry and Engineering Progress, 2023, 42(5): 2315-2324.
[10]	MA Runmei, YANG Haichao, LI Zhengda, LI Shuangxi, ZHAO Xiang, ZHANG Guoqing. Influence analysis of coating on deformation and frictional wear of mechanical seal end for high-speed bearing cavity [J]. Chemical Industry and Engineering Progress, 2023, 42(4): 1688-1697.
[11]	SHANG Yu, XIAO Man, CUI Qiufang, TU Te, YAN Shuiping. Recovery characteristics of PVDF/BN-OH flat composite membrane for waste heat of hot stripped gas in CO₂ capture process [J]. Chemical Industry and Engineering Progress, 2023, 42(3): 1618-1628.
[12]	XIE Yingchun, MA Hongting, XU Chang, MA Shuo, CHEN Mo, LIU Jun, SUN Guoqiang. Analysis of heat transfer characteristics in vertical tube of seepage falling film evaporative condenser [J]. Chemical Industry and Engineering Progress, 2023, 42(3): 1187-1194.
[13]	ZOU Yincai, LI Qingguo, WU Hui, ZHONG Xiaobing, CHEN Xianzhi. Heat transfer simulation and optimization of missile borne phase change heat sink [J]. Chemical Industry and Engineering Progress, 2023, 42(3): 1248-1256.
[14]	GAO Tingting, JIANG Zhen, WU Xiaoyi, HAO Tingting, MA Xuehu, WEN Rongfu. Experimental investigation on lithium-ion battery heat dissipation performance of oscillating heat pipe with micro-nano emulsion [J]. Chemical Industry and Engineering Progress, 2023, 42(3): 1167-1177.
[15]	YANG Maofei, LI Jinwang, ZHOU Liuwei. Heat transfer performance of hydrophilic modified ultra-thin flat heat pipe [J]. Chemical Industry and Engineering Progress, 2023, 42(2): 692-698.