Quasi-3D CFD algorithm for the flow and heat transfer process in steam condensers
WU Jiahao1, DAI Shoubao2, ZHANG Guihua1, WANG Xiongshi1, ZHAO Yanwei1, WU Yuxin1
1. Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China; 2. No. 703 Research Institute of China State Shipbuilding Co., Ltd., Harbin 150078, China
Abstract：[Objective] Shell-and-tube steam condensers are widely used in power stations and ships; their performance, which requires an in-depth understanding of the internal flow and heat transfer process, ensures device efficiency and safety. The distribution of tube-side cooling water in its flow (z -direction) and transverse (x-y plane) directions influences the distributions of various physical quantities inside a condenser and its design optimization, which cannot be calculated by purely two-dimensional (2D) computational fluid dynamics (CFD) simulation. Moreover, the complexity of the two-phase flow, turbulence, phase change, and heat transfer mechanisms inside the condenser makes full 3D CFD simulations computationally expensive. Herein, a quasi-3D algorithm considering the transverse distribution of cooling water was proposed and applied to simulate the condensation process in a shell-and-tube steam condenser. The tube bundle region was simplified through porous media assumption, introducing extra resistance source terms to momentum transport equations. The condensation source term in the continuity equation was computed based on equivalent thermal resistance, referring to the summation of cooling-water convection, tube wall, condensate water, and noncondensable gas (air) thermal resistance. Considering the temperature rise along the z -direction, the quasi-3D algorithm split the condenser into several sections along the z -direction, performed 2D simulation in the midplane of each section, and used the secant iteration method to balance the steam pressure drop. The simulation was conducted based on ConDesign-2D, a self-developed 2D CFD code for the condensation process of shell-and-tube condensers, which adopted unstructured meshes and the collocated-grid-based SIMPLE algorithm. The temperature rise of cooling water along the flow direction directly reduced the heat transfer temperature difference by 10 % and affected the distribution of important physical quantities such as the condensation rate. Compared with the reference condensation rates of different sections, the calculated values considering the transverse distribution of cooling water are more accurate than those that do not. Additionally, the transverse distribution of the cooling water led to a more uniform condensation rate distribution due to the negative feedback between cooling-water temperature and condensation rate. However, this variable had less influence on the distribution of noncondensable gas (air). The comparison with 2D results revealed that 2D and quasi-3D simulations gave similar results on the midplane of the condenser, which illustrates the linearity of field distributions in the z -direction. According to the computation complexity analysis, the complexity of the full 3D simulation can be 2-3 orders of magnitude higher than that of 2D simulation, whereas quasi-3D simulation can be only 1 order of magnitude higher. Compared with 2D simulation, the proposed quasi-3D algorithm can compute the 3D distribution information of the flow field in the cooling-water flow direction and avoid the high computational cost brought by full 3D simulation. Therefore, for the rapid and accurate prediction of 3D flow and the heat transfer process inside a practical shell-and-tube condenser, the proposed quasi-3D algorithm is preferred over 2D and full 3D simulations.
吴家豪, 代守宝, 张归华, 王雄师, 赵艳伟, 吴玉新. 蒸汽冷凝器流动传热过程的准三维CFD模拟算法[J]. 清华大学学报（自然科学版）, 2024, 64(5): 860-868.
WU Jiahao, DAI Shoubao, ZHANG Guihua, WANG Xiongshi, ZHAO Yanwei, WU Yuxin. Quasi-3D CFD algorithm for the flow and heat transfer process in steam condensers. Journal of Tsinghua University(Science and Technology), 2024, 64(5): 860-868.
[1] PATANKAR S V, SPALDING D B. A calculation procedure for the transient and steady-state behaviour of shell-and-tube heat exchangers[M]. London:Imperial College of Science and Technology, Department of Mechanical Engineering, 1972. [2]BECKETT G, DAVIDSON B J, FERRISON J A. The use of computer programs to improve condenser performance[C]//Condensers:Theory and Practice. Symposium. Oxford, UK:Pergamon Press, 1983:97-110. [3]俞茂铮, 姚秀平, 汪国山, 等. 大功率汽轮机凝汽器汽相流动与传热特性的数值分析[J]. 动力工程, 1995, 15(6):42-49. YU M Z, YAO X P, WANG G S, et al. Numerical analysis of the steam flow behavior and heat transfer performance of condensers of large steam turbines[J]. Power Engineering, 1995, 15(6):42-49. (in Chinese) [4]RHODES D B, CARLUCCI L N. Predicted and measured velocity distributions in a model heat exchanger[C]//Proceedings of the International Conference on Numerical Methods in Nuclear Engineering. Montreal, Quebec:American Nuclear Society/Canadian Nuclear Society, 1983:935-948. [5]NUMRICH R, BERKEMEIER D, RENNHACK R. Heat and mass-transfer on condensation of water-vapor in the presence of air at pressure up to 21-bar[J]. Chemie Ingenieur Technik, 1989, 61(8):666-667. [6]ZHANG C, SOUSA A C M, VENART J E S. The numerical and experimental study of a power plant condenser[J]. Journal of Heat Transfer, 1993, 115(2):435-445. [7]姚秀平, 李红梅, 朱光宇, 等. 电站凝汽器汽相流动与传热特性的准三维数值分析[J]. 西安交通大学学报, 1998, 32(12):29-33. YAO X P, LI H M, ZHU G Y, et al. Quasi-three-dimensional analysis of steam flow and heat transfer of a large power plant condenser[J]. Journal of Xi'an Jiaotong University, 1998, 32(12):29-33. (in Chinese) [8]ZHANG C, ZHANG Y. A quasi-three-dimensional approach to predict the performance of steam surface condensers[J]. Journal of Energy Resources Technology, 1993, 115(3):213-220. [9]邢朱苗. 大型电站凝汽器三维数值研究[D]. 保定:华北电力大学(保定), 2009. XING Z M. Three-dimensional numerical value research on the large power station condenser[D]. Baoding:North China Electric Power University (Baoding), 2009. (in Chinese) [10]PETUKHOV B S. Heat transfer and friction in turbulent pipe flow with variable physical properties[J]. Advances in Heat Transfer, 1970, 6:503-564. [11]HU H G, ZHANG C. A new inundation correlation for the prediction of heat transfer in steam condensers[J]. Numerical Heat Transfer, Part A:Applications, 2008, 54(1):34-46. [12]GHIAASIAAN S M. Two-phase flow, boiling and condensation:In conventional and miniature systems[M]. New York:Cambridge University Press, 2008. [13]ZHANG C, BOKIL A. A quasi-three-dimensional approach to simulate the two-phase fluid flow and heat transfer in condensers[J]. International Journal of Heat and Mass Transfer, 1997, 40(15):3537-3546. [14]MOUKALLED F, MANGANI L, DARWISH M. The finite volume method in computational fluid dynamics:An advanced introduction with OpenFOAM® and Matlab®[M]. Cham:Springer, 2016.
2024, Vol. 64 
