Abstract：[Objective] The Yarlung Zangbo River contains numerous hydropower resources, with high head and large flow rates in the downstream region, which is conducive to power generation by Pelton turbines. Pelton turbines convert the kinetic energy generated from the water potential energy into mechanical energy for rotating a runner. The runner is the core component for the flow and work of the Pelton turbine, and the shape of its bucket is crucial for the runner's performance, which is uniformly arranged along the hub of the runner. As the surface shape of the bucket is complex, several parameters are required to determine its geometry model, undoubtedly posing a huge obstacle to work. In this paper, a design method is proposed to address the problem of designing and improving the bucket based on the Bézier curve. The design space is simplified as much as possible based on geometry, and the Bézier curves are utilized for designing the bucket shape. An orthogonal analysis is applied for the optimization of bucket parameters, while the computational fluid dynamics method is employed for analyzing the energy characteristics and three-dimensional flow field of the Pelton turbine. In the bucket design method, the three-dimensional geometry of the bucket can be divided into contour, flow profile, and guidelines, and several characteristic parameters can be determined for those lines. Each type of line includes several biquadratic Bézier curve connections. The number of characteristic line parameters is decreased by establishing a connection between five control points of the Bézier curves. Thus, a three-dimensional design method for the bucket of the Pelton turbine is proposed based on the five controlled characteristic parameters. The main optimization parameters are chosen by the geometry. Subsequently, bucket depth, width increment, outflow angle, splitter angle, and cutout diameter are chosen to conduct orthogonal optimization for the Pelton turbine bucket. For further analysis of the flow characteristics of the optimized bucket, the runner is modeled based on the optimum parameters. In the computational fluid dynamics method, grids are meshed by ICEM, and computational fluid dynamics is performed with ANSYS FLUENT. The results of the polar analysis and three-dimensional unsteady flow field revealed that width had the maximum influence on runner efficiency; outflow angle, cutout diameter, and bucket depth had a smaller influence; and splitting angle had the minimum influence. After optimization, the hydraulic efficiency of the Pelton turbine was increased by 6.71 %. The optimized bucket demonstrated a larger torque peak than the prototype bucket. The bucket always showed large torque when its torque decreased to zero and exhibited smoother curve transition and longer work time. Thus, the optimized bucket demonstrated greater total torque than the prototype bucket; furthermore, the former's high-pressure area was larger, making the energy conversion of water from the nozzle to the bucket more effective. This paper proposes a three-dimensional design method for the Pelton turbine bucket based on the controlled characteristic parameters. The energy performance of the Pelton turbine was enhanced by the orthogonal optimization and three-dimensional flow simulation.
孙启轩, 谭磊. 冲击式水轮机水斗设计方法及性能优化[J]. 清华大学学报（自然科学版）, 2024, 64(5): 852-859.
SUN Qixuan, TAN Lei. Bucket design method and performance optimization of a Pelton turbine. Journal of Tsinghua University(Science and Technology), 2024, 64(5): 852-859.
[1] 国家能源局. "十四五"现代能源体系规划[EB/OL].[2024-01-04]. http://zfxxgk.nea.gov.cn/2022-01/29/c_1310524241.htm. National Energy Administration. 14th Five-Year Plan for modern energy system[EB/OL].[2024-01-04]. http://zfxxgk.nea.gov.cn/2022-01/29/c_1310524241.htm. (in Chinese) [2] 国家能源局. "十四五"可再生能源发展规划[EB/OL].[2024-01-04]. http://zfxxgk.nea.gov.cn/2021-10/21/c_1310611148.htm. National Energy Administration. 14th Five-Year Plan for renewable energy development[EB/OL].[2024-01-04]. http://zfxxgk.nea.gov.cn/2021-10/21/c_1310611148.htm. (in Chinese) [3] 杨康. 冲击式水轮机及其内部不良流动的数值模拟研究[D]. 哈尔滨:哈尔滨工业大学, 2014. YANG K. Numerical simulation on some phenomena of the badbehaved flow in the Pelton turbine[D]. Harbin:Harbin Institute of Technology, 2014. (in Chinese) [4] ZENG C J, XIAO Y X, WANG Z W, et al. Numerical analysis of a Pelton bucket free surface sheet flow and dynamic performance affected by operating head[J]. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy, 2017, 231(3):182-196. [5] 蒋勇其. 冲击式水轮机流固耦合数值模拟研究[D]. 武汉:武汉大学, 2017. JIANG Y Q. Flow-induced vibration analysis of Pelton turbine[D]. Wuhan:Wuhan University, 2017. (in Chinese) [6] XIAO Y X, WANG Z W, ZHANG J, et al. Numerical and experimental analysis of the hydraulic performance of a prototype Pelton turbine[J]. Proceedings of the Institution of Mechanical Engineers, Part A:Journal of Power and Energy, 2014, 228(1):46-55. [7] KUMASHIRO T, FUKUHARA H, TANI K. Unsteady CFD simulation for bucket design optimization of Pelton turbine runner[J]. IOP Conference Series:Earth and Environmental Science, 2016, 49(2):022003. [8] 葛新峰, 孙洁, 蔡建国, 等. 磨蚀对水斗式水轮机的水斗型线及性能影响的研究[J]. 中国电机工程学报, 2021, 41(21):7391-7402. GE X F, SUN J, CAI J G, et al. Study of the erosion influence on bucket profile and performance of Pelton turbine[J]. Proceedings of the CSEE, 2021, 41(21):7391-7402. (in Chinese) [9] ANAGNOSTOPOULOS J S, PAPANTONIS D E. A fast Lagrangian simulation method for flow analysis and runner design in Pelton turbines[J]. Journal of Hydrodynamics, Ser. B, 2012, 24(6):930-941. [10] ŽIDONIS A. Optimisation and efficiency improvement of Pelton hydro turbine using computational fluid dynamics and experimental testing[D]. Lancaster:Lancaster University, 2015. [11] 葛新峰, 孙洁, 李阳, 等. 泥沙直径和浓度对水斗式水轮机转轮的磨损特性[J]. 中国电机工程学报, 2021, 41(14):5025-5033. GE X F, SUN J, LI Y, et al. Erosion characteristics of sediment diameter and concentration on the runner of Pelton turbines[J]. Proceedings of the CSEE, 2021, 41(14):5025-5033. (in Chinese) [12] SMIRNOV P E, MENTER F R. Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart-Shur correction term[J]. Journal of Turbomachinery, 2009, 131(4):041010. [13] 曾崇济. 冲击式水轮机内流特性及流动干扰现象研究[D]. 北京:清华大学, 2020. ZENG C J. Research on the internal flow characteristic and flow interference in the Pelton turbine[D]. Beijing:Tsinghua University, 2020. (in Chinese) [14] 刘明, 谭磊, 曹树良. 基于分段四次速度矩分布的叶片式气液混输泵导叶设计方法[J]. 机械工程学报, 2022, 58(10):280-288. LIU M, TAN L, CAO S L. Design method of diffuser in rotodynamic multiphase pump based on fourth-order distribution of velocity moment[J]. Journal of Mechanical Engineering, 2022, 58(10):280-288. (in Chinese)
2024, Vol. 64 
