马伟超, 杨桀彬, 赵志高, 杨威嘉, 杨建东. 混流式水轮机特性曲线在多重边界条件下的分区方法[J]. 农业工程学报, 2021, 37(11): 31-39. DOI: 10.11975/j.issn.1002-6819.2021.11.004
    引用本文: 马伟超, 杨桀彬, 赵志高, 杨威嘉, 杨建东. 混流式水轮机特性曲线在多重边界条件下的分区方法[J]. 农业工程学报, 2021, 37(11): 31-39. DOI: 10.11975/j.issn.1002-6819.2021.11.004
    Ma Weichao, Yang Jiebin, Zhao Zhigao, Yang Weijia, Yang Jiandong. Domain partitioned of characteristic curve in a Francis turbine under multiple boundary conditions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(11): 31-39. DOI: 10.11975/j.issn.1002-6819.2021.11.004
    Citation: Ma Weichao, Yang Jiebin, Zhao Zhigao, Yang Weijia, Yang Jiandong. Domain partitioned of characteristic curve in a Francis turbine under multiple boundary conditions[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2021, 37(11): 31-39. DOI: 10.11975/j.issn.1002-6819.2021.11.004

    混流式水轮机特性曲线在多重边界条件下的分区方法

    Domain partitioned of characteristic curve in a Francis turbine under multiple boundary conditions

    • 摘要: 完整的水轮机特性曲线是水电站运行仿真和过渡过程计算的基础,然而厂家提供的水轮机模型综合特性曲线仅反映了水轮机高效率区域的特性,不能满足水轮机动态过程仿真需求。该研究提出了一种扩展方法:首先以零转速、零流量、飞逸曲线、零开度线、单位力矩交点为边界条件,作为划分特性曲线区域与约束各分区延拓范围的特征点,并依据内特性模型和外特性数据辨识水轮机结构参数,计算边界条件;然后针对不同区域的特点,提出不同拟合方法得到各区的特性曲线;最后对分区界线两侧拟合结果进行平滑连接,形成完整的可用于仿真分析的混流式水轮机特性曲线。对某水轮机进行实例分析,与典型外特性法和内特性法的对比表明,本文方法既保证了外特性试验数据处的拟合精度,又能反映水轮机的水力特性;与典型外特性法进行过渡过程实测反演对比可知,本文所提方法将最大蜗壳压力的相对误差从2.03%降至1.69%,小开度工况下区域平均蜗壳压力的相对误差从3.48%降至1.47%,动态过程时域响应更接近实测结果。本文特性曲线处理方法有利于提高过渡过程计算精度,也可为类似叶片式农业机械的设计及特性曲线处理提供参考。

       

      Abstract: A complete characteristic curve was fundamental to the simulation of the transition process in a Francis turbine. However, only a high-efficiency region is provided in the efficiency hill diagram and combined characteristic curve in the turbine. It is necessary to expand the characteristic curve of the Francis turbine, thereby improving the simulation precision of the hydraulic turbine model, or the dynamic test. The main expanding was the external and the internal characteristics at present. The external characteristics with over-reliance on experience were only used in the mathematical way to increase the experimental data of the turbine efficiency hill diagram, particularly combing the characteristic curve and runaway speed curve. The internal characteristics were adopted in a theoretical way to process according to the internal laws of the turbine, but suffered from the difficult calculation and inaccurate results at present. In this research, a novel domain partitioned expanding method was proposed for the characteristic curve in a Francis turbine under multiple boundary conditions. The specific procedure was that: feature points were first taken from the boundary conditions of zero speed, zero discharge, runaway speed curve, and zero GVO, as well as the intersection point of unit torque, in order to divide the characteristic curve region, while constraining the extension range of each partition. Then, the structure parameters of a turbine were identified to calculate the boundary conditions of characteristic curves, according to the simplified mathematical model of internal and external characteristic data. Various fitting methods were also proposed for the characteristic curves of each region, according to the features of different regions. Finally, the fitting data on both sides of the boundary were connected smoothly, in order to form a complete turbine characteristic curve for the simulation of the transition process. The method in this study (MIS) was applied in an example of a hydraulic turbine, compared with the typical external characteristic method (TECM) and typical internal characteristic method (TICM). The performances of MIS and TICM were compared using the velocity triangle. The results showed that the MIS was more consistent with the inner structure of the runner. The fitting accuracy of experimental data was improved significantly via effectively integrating TECM and TICM, particularly considering the boundary conditions. The hydraulic characteristics and evolution of the turbine were qualitatively represented in the low-speed area, where the unit discharge was relatively stable. The unit discharge of each guide vane opening (GVO) gradually approached, with the increase of the unit speed and then decreased sharply after the runaway operation. The sign of unit discharge was changed, after passing the zero-discharge boundary. The MIS in the transition was reduced with the relative error of the maximum volute pressure from 2.03% to 1.69%, and the relative error of volute pressure in the small GVO region from 3.48% to 1.47%. It infers that the time-domain response of the dynamic process was closer to the measured data. The absolute average error of MIS was 0.010 MPa, when simulating the volute pressure oscillation in the range of small GVO region. It was reduced by 0.013MPa, compared with the absolute average error of 0.023MPa of TECM, while the relative error was reduced from 3.48% to 1.47%. The simulation of transition showed the time-domain response of the dynamic process was closer to the measured data. Hence, the expanding characteristic curve contributed to the calculation accuracy of transition in the modeling of hydropower units. The finding can provide strong support to the design of similar vane-type agricultural machinery, the expanding of characteristic curves, and the promotion of digital hydropower construction.

       

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