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控制棒下落与流体流动的耦合状态方程及其保辛算法

赵珂 陈昌义 席炎炎 黄东威 吴锋 钟万勰

赵珂,陈昌义,席炎炎,黄东威,吴锋,钟万勰. 控制棒下落与流体流动的耦合状态方程及其保辛算法 [J]. 应用数学和力学,2022,43(9):935-943 doi: 10.21656/1000-0887.430001
引用本文: 赵珂,陈昌义,席炎炎,黄东威,吴锋,钟万勰. 控制棒下落与流体流动的耦合状态方程及其保辛算法 [J]. 应用数学和力学,2022,43(9):935-943 doi: 10.21656/1000-0887.430001
ZHAO Ke, CHEN Changyi, XI Yanyan, HUANG Dongwei, WU Feng, ZHONG Wanxie. The Coupling State Equations and the Symplectic Algorithm for Control Rod Drop and Fluid Flow[J]. Applied Mathematics and Mechanics, 2022, 43(9): 935-943. doi: 10.21656/1000-0887.430001
Citation: ZHAO Ke, CHEN Changyi, XI Yanyan, HUANG Dongwei, WU Feng, ZHONG Wanxie. The Coupling State Equations and the Symplectic Algorithm for Control Rod Drop and Fluid Flow[J]. Applied Mathematics and Mechanics, 2022, 43(9): 935-943. doi: 10.21656/1000-0887.430001

控制棒下落与流体流动的耦合状态方程及其保辛算法

doi: 10.21656/1000-0887.430001
基金项目: 国家自然科学基金(11472067;51609034);辽宁省自然科学基金(2021-MS-119);中央高校基本科研业务费(DUT20RC(5)009;DUT20GJ216)
详细信息
    作者简介:

    赵珂(1993—),男,博士生(E-mail:zhaoke_93@163.com

    吴锋(1985—),男,副教授(通讯作者. E-mail:vonwu@dlut.edu.com.cn

  • 中图分类号: O352; TP391.9

The Coupling State Equations and the Symplectic Algorithm for Control Rod Drop and Fluid Flow

  • 摘要:

    针对核反应堆内控制棒下落问题,提出了描述控制棒下落与流体流动的耦合非线性状态方程。该状态方程对于落棒过程内不同的流体状态,具有统一的表达形式,可以很方便地处理不同工况下的落棒问题。为高效分析落棒过程,准确捕捉落棒过程内流动状态的突变,并保证时程积分的数值稳定,提出了一种基于时间步长自适应的保辛算法。数值算例表明,提出的数值模型可以采用较大的时间步长精确计算控制棒在下落过程中的位移、速度、加速度、落棒时间等关键数据,计算结果与商业软件所得结果高度吻合。

  • 图  1  控制棒在导向管内的下落示意图

    Figure  1.  The falling diagram of the control rod in the guide tube

    图  2  小型反应堆下本文模型与商业软件关于位移、速度、加速度随时间的变化对比

    Figure  2.  The comparison of time-varying displacements, velocities and accelerations, between the proposed model and the commercial software for the case of a small reactor

    表  1  小堆的主要输入参数

    Table  1.   Main input parameters for a small reactor

    parametervalueunit
    reactor in-core temperature312.22
    reactor in-core pressure15.5MPa
    control rod length2.5756m
    control rod diameter0.009675m
    control rod mass11.407kg
    control rod absolute roughness3.0 × 10−8m
    guide tube average diameter0.01124m
    guide tube absolute roughness4.0 × 10−7m
    control rod initial insertion depth0.2874m
    spring preload1876.4N
    spring stiffness123200N/m
    下载: 导出CSV

    表  2  本文模型在不同时间步长下与商业软件关于T5T5 + T6的比较

    Table  2.   The comparison of T5 and T5 + T6 between the commercial software and the proposed model for different initial time steps

    commercial softwareinitial time steps of this paper $\Delta {t_0}/{\rm{s}}$
    0.0010.0050.010.015
    T5/s2.1402.140
    (0%)
    2.1506
    (0.50%)
    2.1469
    (0.32%)
    2.1488
    (0.41%)
    (T5 + T6)/s3.5603.5575
    (0.07%)
    3.5675
    (0.21%)
    3.5706
    (0.30%)
    3.5559
    (0.12%)
    下载: 导出CSV
  • [1] YOON K H, KIM J Y, LEE K H, et al. Control rod drop analysis by finite element method using fluid-structure interaction for a pressurized water reactor power plant[J]. Nuclear Engineering and Design, 2009, 239(10): 1857-1861. doi: 10.1016/j.nucengdes.2009.05.023
    [2] 肖聪, 罗英, 杜华, 等. 基于动网格技术的单根控制棒落棒行为仿真分析[J]. 核动力工程, 2017, 38(2): 103-107 doi: 10.13832/j.jnpe.2017.02.0103

    XIAO Cong, LUO Ying, DU Hua, et al. Simulation and analysis of single control rod dropping behavior based on dynamic grid technique[J]. Nuclear Power Engineering, 2017, 38(2): 103-107.(in Chinese) doi: 10.13832/j.jnpe.2017.02.0103
    [3] RAJAN BABU V, THANIGAIYARASU G, CHELLAPANDI P. Mathematical modelling of performance of safety rod and its drive mechanism in sodium cooled fast reactor during scram action[J]. Nuclear Engineering and Design, 2014, 278: 601-617. doi: 10.1016/j.nucengdes.2014.08.015
    [4] 刘新, 陈先龙, 张修, 等. 控制棒下落时间计算模型[J]. 核技术, 2014, 37(11): 68-74 doi: 10.11889/j.0253-3219.2014.hjs.37.110604

    LIU Xin, CHEN Xianlong, ZHANG Xiu, et al. Calculation model of controlling rod drop time[J]. Nuclear Technology, 2014, 37(11): 68-74.(in Chinese) doi: 10.11889/j.0253-3219.2014.hjs.37.110604
    [5] 刘言午, 黄炳臣, 冉小兵, 等. 反应堆控制棒落棒时间计算方法分析[J]. 核动力工程, 2014, 35(6): 106-110 doi: 10.13832/j.jnpe.2014.06.0106

    LIU Yanwu, HUANG Bingchen, RAN Xiaobing, et al. Analysis of calculation method of reactor control rod drop time[J]. Nuclear Power Engineering, 2014, 35(6): 106-110.(in Chinese) doi: 10.13832/j.jnpe.2014.06.0106
    [6] 王栋. 算子分裂法及其在解抛物型方程中的应用[D]. 硕士学位论文. 长春: 吉林大学, 2009.

    WANG Dong. Operator-splitting method and its application for solving parabolic equations[D]. Master Thesis. Changchun: Jilin University, 2009. (in Chinese)
    [7] 孔珑. 工程流体力学[M]. 北京: 中国电力出版社, 2001.

    KONG Long. Engineering Fluid Mechanics[M]. Beijing: China Electric Power Press, 2001. (in Chinese)
    [8] WU F, GAO Q, ZHONG W X. Fast precise integration method for hyperbolic heat conduction problems[J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(7): 791-800. doi: 10.1007/s10483-013-1707-6
    [9] 邢誉峰, 杨蓉. 动力学平衡方程的Euler中点辛差分求解格式[J]. 力学学报, 2007, 39(1): 100-105 doi: 10.3321/j.issn:0459-1879.2007.01.013

    XING Yufeng, YANG Rong. Application of Euler midpoint symplectic integation method for the solution of dynamic equilibrium equations[J]. Acta mechanica Sinica, 2007, 39(1): 100-105.(in Chinese) doi: 10.3321/j.issn:0459-1879.2007.01.013
    [10] 吴锋, 姚征, 孙雁, 等. 位移浅水内孤立波[J]. 计算力学学报, 2016, 36(3): 297-303.

    WU Feng, YAO Zheng, SUN Yan, et al. Displacement shallow water internal solitary wave[J]. Chinese Journal of Computational Mechanics, 2016, 36(3): 297-303. (in Chinese)
    [11] 钟万勰. 离散动力学数值积分应该保辛近似[J]. 北京工业大学学报, 2016, 42(12): 12-14.

    ZHONG Wanxie. Symplectic conservative approximation for discrete dynamics integration[J]. Journal of Beijing University of Technology, 2016, 42(12): 12-14. (in Chinese)
    [12] 钟万勰. 离散动力学只能说保辛[J]. 应用数学和力学, 2016, 37(8): 775-777

    ZHONG Wanxie. Only symplectic conservation is characteristic of discrete dynamics[J]. Applied Mathematics and Mechanics, 2016, 37(8): 775-777.(in Chinese)
    [13] 高强, 彭海军, 吴志刚, 等. 非线性动力学系统最优控制问题的保辛求解方法[J]. 动力学与控制学报, 2010, 8(1): 1-7.

    GAO Qiang, PENG Haijun, WU Zhigang, et al. Symplectic method for solving optimal control problem of nonlinear dynamical systems[J]. Journal of Dynamics and Control, 2010, 8(1): 1-7. (in Chinese)
    [14] 王昕炜, 彭海军, 钟万勰. 具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略[J]. 应用数学和力学, 2019, 40(7): 701-712

    WANG Xinwei, PENG Haijun, ZHONG Wanxie. Optimal vaccination strategies of time-varying SEIR epidemic model with latent delay[J]. Applied Mathematics and Mechanics, 2019, 40(7): 701-712.(in Chinese)
    [15] 钟万勰, 吴锋, 孙雁, 等. 保辛水波动力学[J]. 应用数学和力学, 2018, 39(8): 855-874

    ZHONG Wanxie, WU Feng, SUN Yan, et al. Symplectic water wave dynamics[J]. Applied Mathematics and Mechanics, 2018, 39(8): 855-874.(in Chinese)
    [16] 吴锋, 钟万勰. 浅水问题的约束Hamilton变分原理及祖冲之类保辛算法[J]. 应用数学和力学, 2016, 37(1): 1-13 doi: 10.3879/j.issn.1000-0887.2016.01.001

    WU Feng, ZHONG Wanxie. The constrained Hamilton variational principle for shallow water problems and the Zu-type symplectic algorithm[J]. Applied Mathematics and Mechanics, 2016, 37(1): 1-13.(in Chinese) doi: 10.3879/j.issn.1000-0887.2016.01.001
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出版历程
  • 收稿日期:  2022-01-04
  • 修回日期:  2022-01-19
  • 网络出版日期:  2022-09-05
  • 刊出日期:  2022-09-30

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