带相变瞬态温度场问题的扩展有限元解析

doi:10.7522/j.issn.1000-0240.2016.0121

冰川冻土 ›› 2016, Vol. 38 ›› Issue (4): 1044-1051.doi: 10.7522/j.issn.1000-0240.2016.0121

• 特殊土的力学特性与工程问题 • 上一篇下一篇

带相变瞬态温度场问题的扩展有限元解析

何敏^{1 2}, 李宁¹, 高焕焕², 刘乃飞¹

1. 西安理工大学岩土工程研究所, 陕西西安 710048;
2. 西北勘测设计研究院有限公司, 陕西西安 710065

收稿日期:2016-05-28 修回日期:2016-07-11 出版日期:2016-08-25 发布日期:2016-09-19
作者简介:何敏(1981-),男,湖北随州人,高级工程师,2013年在西安理工大学获博士学位,现从事水电站设计及寒区岩土工程三场耦合方面的研究.E-mail:hem81@163.com
基金资助:
国家自然科学基金项目（11572246；5117913）；西安理工大学博士学位论文创新基金项目（207-002J1306）资助

Extended finite element method analysis for the transient temperature field with phase change

HE Min^{1 2}, LI Ning¹, GAO Huanhuan², LIU Naifei¹

1. Institute of Geotechnical Engineering, Xi'an University of Technology, Xi'an 710048, China;
2. Xibei Engineering Corporation Limited of the Power Construction Corporation of China, Xi'an 710065, China

Received:2016-05-28 Revised:2016-07-11 Online:2016-08-25 Published:2016-09-19

摘要/Abstract

摘要： 带相变瞬态传热问题是寒区工程多场耦合问题求解的关键.在剖析常规有限元法在求解带相变瞬态温度场问题的不足的基础上，结合冻土冻融温度变化的特点，提出采用扩展有限元法求解冻土工程带相变瞬态传热问题的新方法，以四边形单元为例推导了冻土工程温度场的求解格式，详细剖析了瞬态传热过程中移动界面水平集函数的构造、单元刚度矩阵的形成及高斯积分的求解.据此编写了相应的扩展有限元程序，通过经典Stefan问题全面验证了程序的正确性与合理性.

关键词: 水热力耦合, 相变, 瞬态温度场, 扩展有限元

Abstract: Transient heat transfer with phase change is the key to the solving of the multi-field coupling problems in cold regions. The freezing process of frozen soil can be divided into four stages based on the measured freezing curves in Changchun. Analyzing the shortage of the traditional finite element method in solving the phase change problem and the characteristic of frozen soil's freezing process, the extended finite element method (XFEM) was proposed for solving the transient heat transfer problem with phase change for permafrost engineering. The XFEM interpolating function and solving format of temperature field with phase change was derived that taking quadrilateral element as an example. Based on the study of the constructing and solving of the level set function, building of the stiffness matrix and subdividing of the elements, a XFEM program for the transient heat transfer problem with phase change was proposed in this paper which has been verified by classical Stefan problem.

Key words: THM coupling, ice-water phase change, transient temperature field, extended finite element method

中图分类号:

P642.14

何敏, 李宁, 高焕焕, 刘乃飞. 带相变瞬态温度场问题的扩展有限元解析[J]. 冰川冻土, 2016, 38(4): 1044-1051.

HE Min, LI Ning, GAO Huanhuan, LIU Naifei. Extended finite element method analysis for the transient temperature field with phase change[J]. JOURNAL OF GLACIOLOGY AND GEOCRYOLOGY, 2016, 38(4): 1044-1051.

参考文献

[1] Li Ning, Cheng Guodong, Xie Dingyi. Geomechanics development in civil construction in western China[J]. Chinese Journal of Rock Mechanics and Engineering, 2001, 23(3): 268-272. [李宁, 程国栋, 谢定义. 西部大开发中的岩土力学问题[J]. 岩土工程学报, 2001, 23(3): 268-272.]
[2] Zhang Qinglong, Li Ning, Ma Wei, et al. Analyses of the thawing consolidation of fill embankments in warm permafrost regions[J]. Journal of Glaciology and Geocryology, 2014, 36(3): 614-621. [张青龙, 李宁, 马巍, 等. 高温冻土区填土路基融化固结变形分析[J]. 冰川冻土, 2014, 36(3): 614-621.]
[3] Cao Yuanbing, Sheng Yu, Wu Jichun, et al. Influence of upper boundary conditions on simulated ground temperature field in permafrost regions[J]. Journal of Glaciology and Geocryology, 2014, 36(4): 802-810. [曹元兵, 盛煜, 吴吉春, 等. 上边界条件对多年冻土地温场数值模拟结果的影响分析[J]. 冰川冻土, 2014, 36(4): 802-810.]
[4] Zhu Hehua, Yang Baohong, Cai Yongchang, et al. Application of meshless natural element method to elastoplastic analysis[J]. Rock and Soil Mechanics, 2004, 25(4): 671-674. [朱合华, 杨宝红, 蔡永昌, 等. 无网格自然单元法在弹塑性分析中的应用[J]. 岩土力学, 2004, 25(4): 671-674.]
[5] Cai Yongchang, Zhu Hehua. Meshless method for numerical calculation of geotechnical engineering and its uauto-arrangement of discrete nodes[J]. Rock and Soil Mechanics, 2003, 24(1): 21-24. [蔡永昌, 朱合华.岩土工程数值计算中的无网格方法及其全自动布点技术[J]. 岩土力学, 2003, 24(1): 21-24.]
[6] Gao Zhihua, Zhang Mingyi, Liu Zhiqiang, et al. A meshless method for nonlinear transient field with phase change[J]. Chinese Journal of Computational Physics, 2006, 23(5): 545-550. [高志华, 张明义, 刘志强, 等. 相变温度场中无网格伽辽金法的应用[J]. 计算物理, 2006, 23(5): 545-550.]
[7] Ma Wentao, Shi Junping, Li Ning. Coupling of level set and meshless method application to crack propagation and[J]. Rock and Soil Mechanics, 2012, 33(11): 3447-3453. [马文涛, 师俊平, 李宁. 水平集和无网格耦合法在裂纹扩展中的应用[J]. 岩土力学, 2012, 33(11): 3447-3453.]
[8] Liu Xinghong, Zhou Chuangbing, Chang Xiaolin, et al. Simulation of mass concrete temperature cracking propagation process[J]. Rock and Soil Mechanics, 2010, 31(8): 2666-2670. [刘杏红, 周创兵, 常晓林, 等. 大体积混凝土温度裂缝扩展过程模拟[J]. 岩土力学, 2010, 31(8): 2666-2670.]
[9] Zhang Xiaodong, Ding Yong, Ren Xuchun. Simulation of the concrete crack propagation process with the extended finite element method[J]. Engineering Mechanics, 2013, 30(7): 14-21. [张晓东, 丁勇, 任旭春. 混凝土裂纹扩展过程模拟的扩展有限元法研究[J]. 工程力学, 2013, 30(7): 14-21.]
[10] Liu Yongjie, Ling Feng. A heat balance integral method for the Stefan problem with time-dependent boundary conditions[J]. Journal of Inner Mongolia University: Natural Science Edition, 2010, 41(6): 625-631. [刘永杰, 令锋. 边界条件随时间变化Stefan问题的一种热平衡积分解法[J]. 内蒙古大学学报: 自然科学版, 2010, 41(6): 625-631.]
[11] Zhang Dongsheng, Wang Qiuwang, Tao Wenshuan. Numerical investigation of laminar convective heat transfer in parallel channel with one moving boundary[J]. Journal of Xi'an Jiaotong University, 2002, 36(5): 473-476. [张东升, 王秋旺, 陶文铨. 具有移动边界平行平板通道内的层流对流换热[J]. 西安交通大学学报, 2002, 36(5): 473-476.]
[12] Deng Linyong, Zhou Dai, Zhao Yaojun. The improved spring analogy of mesh generation and update on the moving boundary of fluid-solid interface[J]. Journal of Shanghai Jiaotong University, 2009, 43(6): 994-998. [邓麟勇, 周岱, 赵尧军. 流固移动边界网格剖分和更新的改进弹簧近似法[J]. 上海交通大学学报, 2009, 43(6): 994-998.]
[13] Zeng Xin, Xin Mingdao. An enthalpy method of solving phase change problems by coupling the enthalpy and the moving boundary[J]. Journal of Chongqing University: Natural Science Edition, 1992, 15(3): 62-67. [曾欣, 辛明道. 耦合求解焓及移动边界位置的多维相变传热问题的数值焓法[J]. 重庆大学学报: 自然科学版, 1992, 15(3): 62-67.]
[14] Lu Wenqiang, Li Shufen. Boundary element method for analyzing transient temperature fields with phase-change moping interface in the heat pipe[J]. Journal of Engineering Thermophysics, 1995, 16(3): 349-353. [卢文强, 李淑芬. 热管中分析带相变运动界面瞬态温度场的边界元方法[J]. 工程热物理学报, 1995, 16(3): 349-353.]
[15] Li Nansheng, Wu Qingbai. Chebyshev pseudo-spectral method for the calculation of temperature in active layer of permafrost with phase-change[J]. Chinese Journal of Computational Mechanics, 2009, 26(5): 703-709. [李南生, 吴青柏. 冻土活动层相变温度场Chebyshev拟谱分析[J]. 计算力学学报, 2009, 26(5): 703-709.]
[16] Li Nansheng, Deng Shibin, Wu Qingbai. Asymptotic evaluation of temperature in the permafrost active layer with time dependent boundary conditions[J]. Journal of Glaciology and Geocryology, 2007, 29(1): 16-20. [李南生, 邓世斌, 吴青柏. 非定常边界多年冻土活动层温度的积分渐近计算[J]. 冰川冻土, 2007, 29(1): 16-20.]
[17] Yang Zhen, Wen Zhi, Ma Wei, et al. Numerical simulation on the dynamic evolution process of thermokarst lake based on the moving mesh technology[J]. Journal of Glaciology and Geocryology, 2015, 37(1): 183-191. [杨振, 温智, 马巍. 基于移动网格技术的热融湖动态演化过程数值模拟[J]. 冰川冻土, 2015, 37(1): 183-191.]
[18] Xu Xiaozu, Wang Jiacheng, Zhang Lixin. Physics of frozen soils[M]. Beijing: Science Press, 2001. [徐敩祖, 王家澄, 张立新. 冻土物理学[M]. 北京: 科学出版社, 2001.]
[19] Chessa J, Smolinski P, Belyschko T. The extended finite element method (XFEM) for solidification problem[J]. International Journal for Numerical Methods in Engineering, 2002, 53: 1959-1977.
[20] Merle R, Dolbow J. Solving thermal and phase change problems with the extended finite element method[J]. Computational Mechanics, 2002, 28: 339-350.
[21] Yu Tiantang, Wan Linlin. Extended finite element method for heat transfer problems in heterogeneous material[J]. Chinese Journal of Cmputational Mechanics, 2011, 38(6): 884-890. [余天堂, 万林林. 非均质材料热传导问题的扩展有限元法[J]. 计算力学学报, 2011, 28(6): 884-890.]
[22] Kong Xiangqian. The application of the finite element method in heat transfer[M]. 3rd ed. Beijing: Science and Technology Press, 1998. [孔祥谦. 有限单元法在传热学中的应用[M]. 3版. 北京: 科学技术出版社, 1998.]

带相变瞬态温度场问题的扩展有限元解析

Extended finite element method analysis for the transient temperature field with phase change

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