Numerical modeling of thermoelasticity problems for constructions with inner heat source

  • Vasilyeva Maria V., vasilyevadotmdotv@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
  • Zakharov Petr E., zapetch@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
  • Sivtsev Petr V., sivkapetr@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
  • Spiridonov Denis A., d.stalnov@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: thermoelasticity problems, thermal expansion, heat transfer, linear elasticity problem, plasticity models, nonlinear problems, finite element method, mathematical modeling

Abstract

We consider the numerical simulation of the thermomechanical state of a structure consisting of a heat source, a gas gap and a shell. The mathematical model is described by a nonlinear system of equations for temperature and displacements. The heat is released in the subdomain of the heat source. The resulting displacements due to the temperature gradient are calculated in the heat source region and separately in the shell, and can be described by both linear elasticity models and nonlinear plasticity models. The numerical implementation is based on the finite element method. The results of numerical modeling of a nonlinear model problem in two- and three-dimensional domains are presented.

References

[1]Newman C., Hansen G., Gaston D., “Three dimensional coupled simulation of thermomechanics, heat, and oxygen diffusion in UO2 nuclear fuel rods”, J. Nuclear Materials, 392:1 (2009), 6–15  crossref  elib  scopus
[2]Williamson R. L., Hales J. D., Novascone S. R., Tonks M. R., Gaston D. R., Permann C. J., Andrs D., Martineau R. C., “Multidimensional multiphysics simulation of nuclear fuel behavior”, J. Nuclear Materials, 423:1 (2012), 149–163  crossref  scopus
[3]Kang C. H., Lee S. U., Yang D. Y., Kim H. C., Yang Y. S., “3D FE simulation of the nuclear fuel rod considering the gap conductance between the pellet and cladding”, Proc. KNS Fall Meeting (Kyungju, Rep. Korea, Oct. 23-25, 2013), KNS, Daejeon, Rep. Korea, 2013
[4]Kang C. H., Lee S. U., Yang D. Y., Kim H. C., Yang Y. S., “3D finite element analysis of a nuclear fuel rod with gap elements between the pellet and the cladding”, J. Nuclear Sci. Technology, 53:2 (2016), 232–239  crossref  scopus
[5]Philip B., Berrill M. A., Allu S., Hamilton S. P., Sampath R. S., Clarno K. T., Dilts G. A., “A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins”, J. Comput. Phys., 286 (2015), 143–171  crossref  mathscinet  zmath  scopus
[6]Ramirez J. C., Stan M., Cristea P., “Simulations of heat and oxygen diffusion in UO2 nuclear fuel rods”, J. Nuclear Materials, 359:3 (2006), 174–184  crossref  mathscinet  elib  scopus
[7]Mihaila B., Stan M., Ramirez J., Cristea P., “Simulations of coupled heat transport, oxygen diffusion, and thermal expansion in UO2 nuclear fuel elements”, J. Nuclear Materials, 394:2 (2009), 182–189  crossref  elib  scopus
[8]Brown D. L., Vasilyeva M. A., “A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling”, J. Comput. Appl. Math., 297 (2016), 132–146  crossref  mathscinet  zmath  elib  scopus
[9]Brown D. L., Vasilyeva M. A., “A generalized multiscale finite element method for poroelasticity problems I: Linear problems”, J. Comput. Appl. Math., 294 (2016), 372–388  crossref  mathscinet  zmath  elib  scopus
[10]Hales J. D. et al., BISON theory manual. The equations behind nuclear fuel analysis, Idaho Nat. Lab., 2013
[11]Rashid Y., Dunham R., Montgomery R., Fuel analysis and licensing code: FALCON MOD01., EPRI Rep. EPRI, 2004  mathscinet
[12]Veshchunov M. S. et al., “Code Package SVECHA: Modeling of core degradation phenomena at severe accidents”, Proc. 7th Int. Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH-7 (Saratoga Springs, NY, Sept. 10-15, 1995), 1995, 1914
[13]Berdyshev A. V., Boldyrev A. V., Palagin A., Shestak V., Veshchunov M. S., “SVECHA/QUENCH code for the modeling of reflooding phenomena in severe accidents conditions”, Proc. 9th Int. Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH-9 (San Francisco, CA), 1999
[14]Hagrman D. L., Reymann G. A., MATPRO-VERSION 11. Handbook of materials properties for use in the analysis of light water reactor fuel rod behavior, Idaho Nat. Eng. Lab., Idaho Falls (USA), 1979
[15]Hales J. D. et al., “Asymptotic expansion homogenization for multiscale nuclear fuel analysis”, Comput. Materials Sci., 99 (2015), 290–297  crossref  scopus
[16]Vabishchevich P. N., Vasilyeva M. V., and Kolesov A. E., “Splitting scheme for poroelasticity and thermoelasticity problems”, Comput. Math. Math. Phys., 54:8 (2014), 1305–1315  mathnet  crossref  crossref  mathscinet  zmath  elib  elib  scopus
[17]Geuzaine C. and Remacle J.-F., Software GMSH, http://geuz.org/gmsh
[18]Logg A., Mardal K. A., Wells G., Automated solution of differential equations by the finite element method: The FEniCS book, Springer Sci. & Business Media, New York, 2012  mathscinet  zmath
[19]Samarskij A. A. and Vabishhevich P. N., Vychislitel'naia Teploperedacha, Editorial URSS, Moscow, 2003
[20]Vasilyeva M. V. and Stal'nov D. A., “Mathematical modeling of the thermomechanical state of a heat-inducing element”, Vestn. SVFU, 2016, no. 1, 45–59
[21]Vabishhevich P. N. and Vasilyeva M. V., “Numerical modeling for thermoelasticity problems”, Vestn. SVFU, 10:3 (2013), 5–9
[22]Sivtsev P. V., Vabishchevich P. N., Vasilyeva M. V., “Numerical simulation of thermoelasticity problems on high performance computing systems”, Proc. Int. Conf. Finite Difference Methods, Springer, Berlin, 2014, 364–370  mathscinet
[23]Simo J. C., Hughes T. J. R., Computational inelasticity, Interdiscip. Appl. Math., 7, Springer, New York, 1998  mathscinet  zmath
[24]De Souza Neto E., Peric D., Owen D. R. J., Computational methods for plasticity: Theory and applications, John Wiley & Sons, New York, 2008
How to Cite
Vasilyeva, M., Zakharov, P., Sivtsev, P. and Spiridonov, D. ( ) “Numerical modeling of thermoelasticity problems for constructions with inner heat source”, Mathematical notes of NEFU, 24(3), pp. 52-64. doi: https://doi.org/10.25587/SVFU.2018.3.10889.
Section
Mathematical Modeling