基于非结构化同位网格的油浸式换流变压器流场数值计算方法研究

doi:10.19595/j.cnki.1000-6753.tces.242119

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Abstract Non-physical oscillations may arise from the upwind finite element method when solving the two-dimensional steady-state incompressible Navier-Stokes equations, and mesh generation in complex geometries can cause large computational errors. In addition, the structured staggered-grid finite volume method has limitations for complex geometries and boundary conditions. Thus, this paper proposes a finite volume method based on unstructured collocated grids. The proposed method utilizes an unstructured mesh constructed from irregular triangles, which offers flexibility and adaptability in handling complex flow geometries. A collocated grid arrangement for velocity and pressure is adopted to avoid additional interpolation operations when velocity and pressure are stored on different grids in a staggered grid configuration. The Rhie-Chow interpolation method is employed to eliminate spurious pressure oscillations. Furthermore, delayed correction high-order schemes and second-order central difference schemes are used to discretize the convection and diffusion terms, respectively. The SIMPLE algorithm is employed to optimize the solution process, thereby reducing memory and computational costs. In terms of sparse matrix storage, the COO format is used. It does not require additional calculations to recover the original matrix, which is easier to implement than CSR and CSC formats, thus saving storage space. The PARDISO solver, based on super node technology, is employed to improve computational efficiency and avoid convergence issues with iterative methods. This solver requires less memory and supports single-node decomposition, outperforming MUMPS and WSMP solvers. Finally, under-relaxation techniques are incorporated to optimize convergence performance and ensure the stability of the numerical solution. Accordingly, a flow field calculation program was developed for triangular and quadrilateral meshes, and the computational time for both types of meshes with a similar number of nodes was compared. By optimizing the under-relaxation factor combination, numerical simulations were performed for the classical driven cavity flow problem, and the results were compared with those obtained from COMSOL finite element simulation software and Ghia's vorticity-stream function method. The results show that the proposed method agrees with Ghia's computation for the horizontal velocity distribution along the vertical centerline and the vertical velocity distribution along the horizontal centerline at Reynolds numbers Re=100 and Re=3 200. The proposed method provides higher computational accuracy than the finite element method. When handling complex geometries and boundary conditions, the proposed method demonstrates greater flexibility and applicability than the structured staggered grid finite volume method. Finally, the method is applied to the oil flow analysis in oil-immersed converter transformers, verifying its accuracy and practicality for real engineering applications.

Key words： Unstructured collocated grid finite volume method incompressible Navier-Stokes equations SIMPLE algorithm oil-immersed power transformer

Received: 25 November 2024

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TM411

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	Xin Jiwei
	Li Lin
	Liu Gang

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Xin Jiwei,Li Lin,Liu Gang. Research on the Numerical Calculation Method for the Flow Field of Oil-Immersed Converter Transformers Based on Unstructured Collocated Grids[J]. Transactions of China Electrotechnical Society, 2025, 40(24): 7832-7845.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.242119 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I24/7832

[1] 谢裕清, 李琳, 宋雅吾, 等. 油浸式电力变压器绕组温升的多物理场耦合计算方法[J]. 中国电机工程学报, 2016, 36(21): 5957-5965, 6040.
Xie Yuqing, Li Lin, Song Yawu, et al.Multi-physical field coupled method for temperature rise of winding in oil-immersed power transformer[J]. Proceedings of the CSEE, 2016, 36(21): 5957-5965, 6040.
[2] 王永强, 马伦, 律方成, 等. 基于有限差分和有限体积法相结合的油浸式变压器三维温度场计算[J]. 高电压技术, 2014, 40(10): 3179-3185.
Wang Yongqiang, Ma Lun, Lü Fangcheng, et al.Calculation of 3D temperature field of oil immersed transformer by the combination of the finite element and finite volume method[J]. High Voltage Engin- eering, 2014, 40(10): 3179-3185.
[3] 刘刚, 胡万君, 郝世缘, 等. 油浸式变压器绕组瞬态温升降阶快速计算方法[J]. 电工技术学报, 2024, 39(3): 643-657.
Liu Gang, Hu Wanjun, Hao Shiyuan, et al.Reduced order calculation method of steady temperature rise of oil immersed power transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 643-657.
[4] 刘刚, 胡万君, 刘云鹏, 等. 降阶技术与监测点数据融合驱动的油浸式变压器绕组瞬态温升快速计算方法[J]. 电工技术学报, 2024, 39(19): 6162-6174.
Liu Gang, Hu Wanjun, Liu Yunpeng, et al.A fast calculation method for transient temperature rise of oil immersed transformer windings driven by fusion of order reduction technology and monitoring point data[J]. Transactions of China Electrotechnical Society, 2024, 39(19): 6162-6174.
[5] 唐智健, 邱志斌, 廖才波, 等. 外置式散热模块对配电变压器热点温升的影响[J]. 高压电器, 2024, 60(3): 135-143.
Tang Zhijian, Qiu Zhibin, Liao Caibo, et al.Influence of external cooling modules on hot-spot temperature rise of distribution transformer[J]. High Voltage Apparatus, 2024, 60(3): 135-143.
[6] Komen E M J, Hopman J A, Frederix E M A, et al. A symmetry-preserving second-order time-accurate PISO- based method[J]. Computers & Fluids, 2021, 225: 104979.
[7] Patankar S.Numerical Heat Transfer and Fluid Flow[M]. Boca Ration: CRC press, 2018.
[8] 刘刚, 靳艳娇, 马永强, 等. 基于非平均热源的油浸式变压器2维温度场分析[J]. 高电压技术, 2017, 43(10): 3361-3370.
Liu Gang, Jin Yanjiao, Ma Yongqiang, et al.Two- dimensional temperature field analysis of oil- immersed transformer based on non-uniformly heat source[J]. High Voltage Engineering, 2017, 43(10): 3361-3370.
[9] Gao Wei, Duan Yali, Liu Ruxun.The finite volume projection method with hybrid unstructured triangular collocated grids for incompressible flows[J]. Journal of Hydrodynamics, Ser B, 2009, 21(2): 201-211.
[10] 明平剑, 张文平. 计算多物理场: 有限体积方法应用[M]. 北京: 北京航空航天大学出版社, 2015.
[11] Rhie C M, Chow W L.Numerical study of the turbulent flow past an airfoil with trailing edge separation[J]. AIAA Journal, 1983, 21(11): 1525-1532.
[12] Sirianni G, Re B, Abgrall R, et al.Momentum Weighted Interpolation for unsteady weakly com- pressible two-phase flows on unstructured meshes[J]. Journal of Computational and Applied Mathematics, 2023, 428: 115209.
[13] Zhang Wei, Uh Zapata M, Bai Xin, et al.An unstructured finite volume method based on the projection method combined momentum interpolation with a central scheme for three-dimensional non- hydrostatic turbulent flows[J]. European Journal of Mechanics - B/Fluids, 2020, 84: 164-185.
[14] Chen Yujie, Ling Kong, Zhang Xiaoyu, et al.Appli- cation of IDEAL algorithm based on the collocated unstructured grid for incompressible flows[J]. Com- putational Geosciences, 2024, 28(5): 907-923.
[15] Patankar S V, Spalding D B.A calculation procedure for heat, mass and momentum transfer in three- dimensional parabolic flows[J]. International Journal of Heat and Mass Transfer, 1972, 15(10): 1787-1806.
[16] Liu X L, Tao W Q, He Y L.A simple method for improving the SIMPLER algorithm for numerical simulations of incompressible fluid flow and heat transfer problems[J]. Engineering computations, 2005, 22(8): 921-939.
[17] Issa R I.Solution of the implicitly discretised fluid flow equations by operator-splitting[J]. Journal of Computational Physics, 1986, 62(1): 40-65.
[18] Latimer B R, Pollard A.Comparison of pressure- velocity coupling solution algorithms[J]. Numerical Heat Transfer, Part B: Fundamentals, 1985, 8(6): 635-652.
[19] Chorin A J.Numerical solution of the Navier-Stokes equations[J]. Mathematics of Computation, 1968, 22(104): 745-762.
[20] 尹孟嘉, 许先斌, 何水兵, 等. GPU稀疏矩阵向量乘的性能模型构造[J]. 计算机科学, 2017, 44(4): 182-206.
Yin Mengjia, Xu Xianbin, He Shuibing, et al.Performance model of sparse matrix vector multip- lication on GPU[J]. Computer Science, 2017, 44(4): 182-206.
[21] ZhangMin, Li Linpeng, Wang Hai, et al. Optimized compression for implementing convolutional neural networks on FPGA[J]. Electronics, 2019, 8(3): 295.
[22] Puzyrev V, Koric S, Wilkin S.Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems[J]. Computers & Geosciences, 2016, 89: 79-87.
[23] 苏朝阳, 沈金松, 罗辉. 基于PARDISO直接求解器的三维自然电位正反演[J]. 物探与化探, 2024, 48(2): 451-460.
Su Chaoyang, Shen Jinsong, Luo Hui.3D forward and inverse modeling of self-potential data based on the PARDISO direct solver[J]. Geophysical and Geoche- mical Exploration, 2024, 48(2): 451-460.
[24] 柏威, 鄂学全. 基于非结构化同位网格的SIMPLE算法[J]. 计算力学学报, 2003, 20(6): 702-710.
Bai Wei, E Xuequan. Implement of SIMPLE algo- rithm based on unstructured colocated meshes[J]. Chinese Journal of Computational Mechanics, 2003, 20(6): 702-710.
[25] 刘刚, 高成龙, 胡万君, 等. 基于鲸鱼优化算法超参数优化的径向基函数响应面模型的油浸式变压器绕组挡板结构优化[J]. 电工技术学报, 2024, 39(17): 5331-5343.
Liu Gang, Gao Chenglong, Hu Wanjun,et al.Optimi- zation of winding block washer structure for oil immersed transformers based on radial basis function response surface model with whale optimization algorithm hyper-parameters optimization[J]. Transa- ctions of China Electrotechnical Society, 2024, 39(17): 5331-5343.
[26] Anderson J D.Governing Equations of Fluid Dyna- mics[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992.
[27] Moukalled F, Mangani L, Darwish M.The Finite Volume Method in Computational Fluid Dynamics[M]. Cham: Springer International Publishing, 2016.
[28] Khosla P K, Rubin S G.A diagonally dominant second-order accurate implicit scheme[J]. Computers & Fluids, 1974, 2(2): 207-209.
[29] 彭丽丹. 电力变压器温度场数值计算研究[D]. 北京: 华北电力大学, 2016.
[30] 王立, 喻高明, 傅宣豪, 等. 基于反距离加权插值法的产量劈分新方法[J]. 断块油气田, 2018, 25(5): 617-621.
Wang Li, Yu Gaoming, Fu Xuanhao, et al.New method for production cleavage by inverse distance weighted interpolation[J]. Fault-Block Oil & Gas Field, 2018, 25(5): 617-621.
[31] Ghia U, Ghia K N, Shin C T.High-Re solutions for incompressible flow using the Navier-Stokes equ- ations and a multigrid method[J]. Journal of Com- putational Physics, 1982, 48(3): 387-411.
[32] 王衍, 葛云路, 黄国庆, 等. 干气密封旋转流场的宏观特性与介观速度场的逻辑关系研究[J]. 摩擦学学报, 2020, 40(3): 364-377.
Wang Yan, Ge Yunlu, Huang Guoqing, et al.The logic relationship between macroscopic characteristics and mesoscopic velocity field of high-speed rotating flow field of dry gas seal[J]. Tribology, 2020, 40(3): 364-377.
[33] Wu Hongbin, Zhang Qizhao, Wang Yifan, et al.Influence factors of converter transformer tempera- ture field with finite element method[C]//2021 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), Chengdu, China, 2021: 1004-1010.
[34] 谭又博, 余小玲, 臧英, 等. 谐波电流对换流变压器绕组损耗及温度分布特性的影响[J]. 电工技术学报, 2023, 38(2): 542-553.
Tan Youbo, Yu Xiaoling, Zang Ying, et al.The influence of harmonic current on the loss and temperature distribution characteristics of a converter transformer winding[J]. Transactions of China Elec- trotechnical Society,2023, 38(2): 542-553.
[35] 宋浩永, 黄青丹, 陈于晴, 等. 110 kV环保型天然酯绝缘油变压器绕组的温度场分析[J]. 高压电器, 2024, 60(5): 117-123.
Song Haoyong, Huang Qingdan, Chen Yuqing, et al.Temperature field analysis of windings of natural ester insulating oil-immersed transformer 110 kV environment friendly[J]. High Voltage Apparatus, 2024, 60(5): 117-123.
[36] 刘刚, 郝世缘, 胡万君, 等. 基于子循环自适应串行交错时间匹配算法的油浸式变压器绕组瞬态温升计算[J]. 电工技术学报, 2024, 39(4): 1185-1197.
Liu Gang, Hao Shiyuan, Hu Wanjun, et al.Transient temperature rise calculation of oil immersed trans- former winding based on sub cyclic adaptive staggered time matching algorithm[J]. Transactions of China Electrotechnical Society, 2024, 39(4): 1185-1197.
[37] Garelli L, Ríos Rodriguez G A, Kubiczek K, et al. Thermo-magnetic-fluid dynamics analysis of an ONAN distribution transformer cooled with mineral oil and biodegradable esters[J]. Thermal Science and Engineering Progress, 2021, 23: 100861.
[38] Zhang Xiang, Wang Zhongdong, Liu Qiang.Predi- ction of pressure drop and flow distribution in disc- type transformer windings in an OD cooling mode[J]. IEEE Transactions on Power Delivery, 2017, 32(4): 1655-1664.