Abstract
To alleviate the wear of a thrust bearing in a reactor coolant pump (RCP) while ensuring the hydraulic performance of the pump, an adjoint-based optimization method is proposed in this study. This method reduces the axial force of the RCP impeller and synchronously improves the impeller’s hydraulic efficiency. By combining the adjoint solution with the radial basis function (RBF)-based mesh deformation, the optimization proceeds along the gradient direction, which greatly reduces the time and cost of the calculation. In the adjoint method, the adjoint equations in the rotating coordinate system are established, a joint objective function of the head constraint, hydraulic efficiency, and axial force is expressed, and then the blade surface sensitivity to the joint objective function is determined. In the RBF mesh deformation, the control points on the blade strand are evenly spaced, which ensures the smoothness of the deformed 3D twisted blade. Using the proposed optimization method, the hydraulic axial force of the impeller is reduced by approximately 3.8%, while the hydraulic efficiency of a scaled RCP impeller is increased by approximately 3.2%, and the head remains at an almost constant value. The obtained results validate the feasibility of the adjoint method for optimizing the design of centrifugal pumps.
概要
目的:核主泵轴向力过大容易造成水润滑轴承磨损,因 此在保证扬程和效率性能的同时需要降低核主 泵轴向力。本文旨在建立目标性能与叶轮几何形 状的函数关系,探究基于伴随求解的扭曲叶轮的 变形方案,在保证扬程不变的条件下同步优化叶 轮的轴向力和效率,并找到影响该综合性能的叶 轮关键区域。
创新点:1. 提出一种同步改进多个目标性能的叶轮形状优 化方法;2. 将伴随求解和径向基函数网格变形相 结合以实现核主泵叶轮三维曲面优化。
方法:1. 通过理论分析,建立基于径向基函数网格变形 的伴随优化方法,并在开源平台编写迭代程序; 2. 通过公式推导,构建扬程、效率和轴向力对应 的目标函数(公式(19)~(21)),并运用正交 实验确定各个目标函数的参数因子;3. 通过迭代 计算,在保证扬程不变的条件下实现轴向力和效 率的同步优化,确定影响该综合性能的关键区域 (图8),并获得叶轮的改进设计方案;4. 通过流 场分析,对比改进前后流场内部的压力和流速分 布情况(图9 和10),并验证改进方案的可行性 和有效性。
结论:1. 与传统的随机算法相比,该优化方法直接沿梯 度方向进行迭代优化,可以避免使用大量样本数 据来寻找优化路径;2. 该优化方法将伴随求解和 径向基函数网格变形相结合,实现了流场计算和 结构变形的自动化,可以保证流场网格光滑高效 地更迭;3. 叶轮靠近出口边的下半部分是同步优 化核主泵轴向力和效率的关键区域。
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Jia-ming WANG, Peng-fei WANG, Xu ZHANG, Xiao-dong RUAN, and Xin FU declare that they have no conflict of interest.
Project supported by the National Basic Research Program (973 Program) of China (No. 2015CB057301), the Zhejiang Provincial Natural Science Foundation of China (No. LQ18E060002), and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (No. 51821093)
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Wang, Jm., Wang, Pf., Zhang, X. et al. An adjoint-based optimization method for reducing the axial force of a reactor coolant pump. J. Zhejiang Univ. Sci. A 20, 852–863 (2019). https://doi.org/10.1631/jzus.A1900156
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DOI: https://doi.org/10.1631/jzus.A1900156