Abstract：In multi-electrode electromagnetic flowmeters, electromagnetic velocity tomography is a crucial technology for measuring the instantaneous velocity parameters of conductive-phase fluids, particularly under complex multiphase flow conditions. This technology provides a reliable and safe approach for characterizing transient, nonlinear, and intricate conductive-phase flow processes, which are common in dynamic industrial environments. It is essential for understanding the transient characteristics of flow velocity, assisting in the development of transient flow models, and plays an important role in system monitoring, production distribution, optimization of lifetime, and the safety of fluid distribution systems. This paper aims to optimize Helmholtz coils parameters to enhance the homogeneous magnetic field of electromagnetic velocity tomography, in order to overcome the challenge of accurately measuring the velocity distribution of non-axisymmetric complex conductive fluids. Firstly, multi-physics simulations and analysis are employed to elucidate the relationship between Helmholtz coils parameters and field characteristics in terms of magnetic field strength and homogeneity. Through multiple regression analysis, the optimal design expressions or best value ranges for the parameters of Helmholtz coils are established. Additionally, several general principles are summarized: (1) Increasing the winding current in both circular and rectangular Helmholtz coils linearly enhances the magnetic flux density without affecting field homogeneity; (2) The optimal shape for rectangular Helmholtz coils is square; (3) The optimal axial gap between windings for both coil types is 0 mm; (4) For fixed coil spacing, the radial equivalent total length of the coils should remain constant; (5) Under identical parameters, circular Helmholtz coils demonstrate superior magnetic field homogeneity compared to rectangular ones. Based on these findings, the optimal parameters for Helmholtz coils are determined for a pipeline with a diameter of 100 mm, coil spacing of 190 mm, and wire diameter of 0.8 mm. These adjustments result in a remarkable 4.42-fold increase in magnetic flux density and a 7.59% enhancement in homogeneity, leading to this configuration being designated as “optimal Helmholtz coils.” In parallel, based on previously established best practices, the designed configuration is “original Helmholtz coils.” The electromagnetic velocity tomography algorithm utilizes induced potential signals from electrode sensors to reconstruct velocity profiles. To ensure precise velocity measurements, equal amplitude forward and reverse currents are applied to both original and optimal Helmholtz coils, generating a homogeneous magnetic field as well as a reversed Helmholtz field. A comparison of induced signals reveals that the optimal Helmholtz coils enhance the signal amplitude by 4.48 times compared to the original coils. This increase significantly boosts the signal-to-noise ratio, reducing the need for signal amplification and minimizing distortion or overload. Larger signal amplitudes improve the ability to capture dynamic flow changes, such as velocity fluctuations. Velocity profiles are reconstructed from the induced signals using a high-order power-law imaging algorithm. The original and optimal coils show excellent agreement between the reconstructed and set velocity profiles. After optimizing the coils, the electromagnetic velocity tomography reduces the average velocity percentage deviation by 0.21% for the first velocity profile and 0.15% for the second profile, compared to the original coils. The phenomenon, where optimizing the coils does not significantly reduce the average percentage deviation of local velocity, is related to the physical implications of the weighting function. It fails to consider how flow patterns and velocity distributions affect attenuation of induced electromotive force.
毕欣雨, 姚泽, 朱劲源, 马璐. 基于优化匀强磁场的电磁流速层析成像技术[J]. 电工技术学报, 2025, 40(21): 6945-6955.
Bi Xinyu, Yao Ze, Zhu Jingyuan, Ma Lu. Optimization of Enhanced Homogeneous Magnetic Field of Electromagnetic Velocity Tomography. Transactions of China Electrotechnical Society, 2025, 40(21): 6945-6955.
[1] 谭超, 董峰. 多相流过程参数检测技术综述[J]. 自动化学报, 2013, 39(11): 1923-1932. Tan Chao, Dong Feng.Parameters measurement for multiphase flow process[J]. Acta Automatica Sinica, 2013, 39(11): 1923-1932. [2] Hari S, Krishna S, Patel M, et al.Influence of wellhead pressure and water cut in the optimization of oil production from gas lifted wells[J]. Petroleum Research, 2022, 7(2): 253-262. [3] 李亭, 张金发, 管英柱, 等. 水平井分段压裂各段产能评价技术研究进展[J]. 科学技术与工程, 2023, 23(21): 8916-8927. Li Ting, Zhang Jinfa, Guan Yingzhu, et al.Progress on each section productivity evaluation technology of horizontal well staged fracturing[J]. Science Technology and Engineering, 2023, 23(21): 8916-8927. [4] Mitchell B, Zhou Yiwen, Hayes M P, et al.Non- invasive groundwater velocity measurements using a novel electromagnetic flowmeter[J]. IEEE Transactions on Instrumentation Measurement, 2022, 71: 3147322. [5] 陈定, 罗刚, 赵春峰, 等. 电磁流量计在疏浚管道流速测量中的误差及修正[J]. 电力系统及其自动化学报, 2022, 34(4): 71-76. Chen Ding, Luo Gang, Zhao Chunfeng, et al.Flow rate measurement error using electromagnetic flowmeter in pipeline dredging and the corresponding adjustment[J]. Proceedings of the CSU-EPSA, 2022, 34(4): 71-76. [6] 唐杨成. 油田专用智能高压由壬型电磁流量计的开发和应用[J]. 流体测量与控制, 2023, 4(4): 70-73. Tang Yangcheng.The development and application of intelligent high-pressure electromagnetic flowmeter for oil field[J]. Fluid Measurement & Control, 2023, 4(4): 70-73. [7] 马云峰, 付雪莹. 电磁流量计在线校准方法的探讨[J]. 自动化与仪表, 2024, 39(9): 118-119, 137. Ma Yunfeng, Fu Xueying.Discussion on on-line calibration method of electromagnetic flowmeter[J]. Automation & Instrumentation, 2024, 39(9): 118-119, 137. [8] 罗来军, 韩建, 马庆华, 等. 基于四电极电磁流量计的水平井油水两相流实验研究[J]. 石油管材与仪器, 2024, 10(4): 92-96. Luo Laijun, Han Jian, Ma Qinghua, et al.Experimental study of four-electrode electromagnetic flowmeter in oil-water two-phase flow in horizontal well[J]. Petroleum Tubular Goods & Instruments, 2024, 10(4): 92-96. [9] Zhou Feng, Yang Qifan, Lin Kun.Evaluation index and performance structure optimization of magnetic field uniformity of complex multiphase flow electro- magnetic flowmeter[J]. Measurement and Control, 2022, 55(1/2): 62-71. [10] 葛亮, 袁一萍, 白洋, 等. 气泡影响下的电磁流量测量优化技术研究[J]. 仪器仪表学报, 2023, 44(1): 242-252. Ge Liang, Yuan Yiping, Bai Yang, et al.Research on optimization technology of electromagnetic flow measurement under the influence of air bubbles[J]. Chinese Journal of Scientific Instrument, 2023, 44(1): 242-252. [11] Salustiano Martim A L S, Dalfré Filho J G, de Faria Lemos De Lucca Y, et al. Electromagnetic flowmeter evaluation in real facilities: velocity profiles and error analysis[J]. Flow Measurement and Instrumenta- tion, 2019, 66: 44-49. [12] Gao Kai, Cui Ziqiang, Xia Zihan, et al.Hardware implementation and evaluation of electromagnetic flow tomography system for water-continuous flows[J]. IEEE Transactions on Instrumentation Measurement, 2022, 71: 3134722. [13] Arif M Z, Seppänen A, Vauhkonen M.State estimation approach to dual-modal imaging of two- phase flow based on electromagnetic flow tomography and electrical tomography[J]. Inverse Problems, 2023, 39(8): 084003. [14] 万裁, 何为, 沈晟, 等. 超低场磁共振膝关节正交接收线圈设计[J]. 电工技术学报, 2024, 39(7): 1923-1931. Wan Cai, He Wei, Shen Sheng, et al.Design of a quadrature receive coil for ultra-low-field knee magnetic resonance imaging[J]. Transactions of China Electrote- chnical Society, 2024, 39(7): 1923-1931. [15] 杨丹, 刘素羽, 张昊, 等. 基于永磁体和线圈复合结构的磁性粒子成像零磁场研究[J]. 电工技术学报, 2025, 40(2): 335-345. Yang Dan, Liu Suyu, Zhang Hao, et al.Research on magnetic particle imaging zero magnetic field based on permanent magnet and coil composite structure[J]. Transactions of China Electrotechnical Society, 2025, 40(2): 335-345. [16] Liu Renzhe, Rong Cancan, Lu Conghui, et al.Modified tri-axial square Helmholtz coil for omnidirec- tional wireless power transfer[J]. Electrical Engineering, 2022, 104(6): 4347-4356. [17] 汤云东, 丁宇彬, 金涛. 基于亥姆霍兹线圈装置的磁热疗优化方法[J]. 电工技术学报, 2023, 38(5): 1248-1260. Tang Yundong, Ding Yubin, Jin Tao.Research on optimization method of magnetic hyperthermia based on Helmholtz coil device[J]. Transactions of China Electrotechnical Society, 2023, 38(5): 1248-1260. [18] 汤云东, 丁宇彬, 金涛. 考虑磁场均匀性优化的开放式磁粒子成像检测装置改进方法[J]. 电工技术学报, 2025, 40(6): 1718-1728. Tang Yundong, Ding Yubin, Jin Tao.Research on the improved method of open detection device for magnetic particle imaging considering magnetic field uniformity optimization[J]. Transactions of China Electrotechnical Society, 2025, 40(6): 1718-1728. [19] Wang Sijin, Ge Liang, Tian Guiyun, et al.Research progress on optimization techniques for electro-magnetic flowmeters: a review[J]. IEEE Sensors Journal, 2025, 25(9): 14557-14574. [20] 石明. 电磁流量计在造纸行业中的应用[J]. 流体测量与控制, 2021, 2(5): 34-38. Shi Ming.Application of electromagnetic flowmeter in the paper industry[J]. Fluid Measurement & Control, 2021, 2(5): 34-38. [21] Li Bin, Hou Xueqing, Chen Jie, et al.Study on the match-filtering ability of the electromagnetic flowmeter signals based on the generalized dual-frequency Walsh transform[J]. Flow Measurement and Instrumentation, 2025, 102: 102767. [22] 刘铁军, 宫通胜. 一种时分双频励磁电磁流量计设计[J]. 传感技术学报, 2013, 26(8): 1064-1067. Liu Tiejun, Gong Tongsheng.Design of a time-division dual-frequency excited electromagnetic flowmeter[J]. Chinese Journal of Sensors and Actuators, 2013, 26(8): 1064-1067. [23] Kollár L E, Lucas G P, Zhang Zhichao.Proposed method for reconstructing velocity profiles using a multi-electrode electromagnetic flow meter[J]. Measure- ment Science and Technology, 2014, 25(7): 075301. [24] Kollár L E, Lucas G P, Meng Yiqing.Reconstruction of velocity profiles in axisymmetric and asymmetric flows using an electromagnetic flow meter[J]. Measure- ment Science and Technology, 2015, 26(5): 055301. [25] Sanchez H, Liu F, Trakic A, et al.Three-dimensional gradient coil structures for magnetic resonance imaging designed using fuzzy membership functions[J]. IEEE Transactions on Magnetics, 2007, 43(9): 3558-3566. [26] Yang Yong, Song Zhiquan, Jiang Li, et al.An improved two-coil configuration for low-frequency magnetic field immunity tests and its field inhomogeneity analysis[J]. IEEE Transactions on Industrial Electronics, 2018, 65(10): 8204-8214. [27] Agolom M O, Lucas G, Webilor R O.Measurement of velocity profiles in transient single and multiphase flows using inductive flow tomography[J]. Flow Measurement and Instrumentation, 2018, 62: 246-254.
2025, Vol. 40 
