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Research Papers: Conduction

Deterministic Phonon Transport Predictions of Thermal Conductivity in Uranium Dioxide With Xenon Impurities

[+] Author and Article Information
Jackson R. Harter

Radiation Transport and Reactor Physics,
Nuclear Science and Engineering,
Oregon State University,
Corvallis, OR 97330
e-mail: harterj@oregonstate.edu

Laura de Sousa Oliveira

Department of Mechanical Engineering,
University of California,
Riverside, CA 92521
e-mail: laura.rita.oliveira@gmail.com

Agnieszka Truszkowska

School of Mechanical, Industrial,
and Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97330
e-mail: truszkoa@oregonstate.edu

Todd S. Palmer

Professor
Nuclear Science and Engineering,
Oregon State University,
Corvallis, OR 97330
e-mail: palmerts@engr.orst.edu

P. Alex Greaney

Materials Science and Engineering Program,
Department of Mechanical Engineering,
University of California,
Riverside, CA 92521
e-mail: agreaney@engr.ucr.edu

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 19, 2016; final manuscript received October 18, 2017; published online January 30, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 140(5), 051301 (Jan 30, 2018) (11 pages) Paper No: HT-16-1523; doi: 10.1115/1.4038554 History: Received August 19, 2016; Revised October 18, 2017

We present a method for solving the Boltzmann transport equation (BTE) for phonons by modifying the neutron transport code Rattlesnake which provides a numerically efficient method for solving the BTE in its self-adjoint angular flux (SAAF) form. Using this approach, we have computed the reduction in thermal conductivity of uranium dioxide (UO2) due to the presence of a nanoscale xenon bubble across a range of temperatures. For these simulations, the values of group velocity and phonon mean free path in the UO2 were determined from a combination of experimental heat conduction data and first principles calculations. The same properties for the Xe under the high pressure conditions in the nanoscale bubble were computed using classical molecular dynamics (MD). We compare our approach to the other modern phonon transport calculations, and discuss the benefits of this multiscale approach for thermal conductivity in nuclear fuels under irradiation.

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References

Duderstadt, J. , and Hamilton, L. , 1976, Nuclear Reactor Analysis, Wiley, New York.
Todreas, N. , and Kazimi, M. , 2012, Nuclear Systems, Vol. 1, CRC Press, Boca Raton, FL.
Tennery, V. , 1959, “Review of Thermal Conductivity and Heat Transfer in Uranium Dioxide,” Oak Ridge National Laboratory, Oak Ridge, TN, Report No. ORNL-2656.
Popov, S. , Carbajo, J. , Ivanov, V. , and Yoder, G. , 2000, “Thermophysical Properties of MOX and UO2 Fuels Including the Effects of Irradiation,” Oak Ridge National Laboratory, Oak Ridge, TN, Report No. ORNL/TM-2000/351. https://rsicc.ornl.gov/fmdp/tm2000-351.pdf
Meyer, M. K., Gan, J., Jue, J. F., Keiser, D. D., Perez, E., Robinson, A., Wachs, D. M., Woolstenhulme, N., Hofman, G. L., and Kim, Y. S., 2014, “Irradiation Performance of U-Mo Monolithic Fuel,” Nucl. Eng. Technol., 46(2), pp. 169–182. [CrossRef]
Szpunar, B. , and Szpunar, J. , 2014, “Thermal Conductivity of Uranium Nitride and Carbide,” Int. J. Nucl. Energy, 2014, p. 178360.
Du, S. , Gofryk, K., Andersson, D. A., Liu, X. Y., and Stanek, C. R., 2011, “A Molecular Dynamics Study of Anisotropy and the Effect of Xe on UO2 Thermal Conductivity,” Los Alamos National Laboratory, Los Alamos, NM, Report No. M3MS-13LA0602045. http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-13-20713
Morel, J. E. , and McGhee, J. M. , 1999, “A Self-Adjoint Angular Flux Equation,” Nucl. Sci. Eng., 132(3), pp. 312–325.
Wang, Y. , 2013, “Nonlinear Diffusion Acceleration for the Multigroup Transport Equation Discretized With S N and Continuous FEM with Rattlesnake,” International Conference on Mathematics, Computational Methods Applied to Nuclear Science & Engineering (M&C), Sun Valley, ID, May 5–9. https://pdfs.semanticscholar.org/273b/d7abff75d6eabba5c114aecfb01ca467b70c.pdf
Gaston, D. , Newman, C., Hansen, G., and Lebrun-Grandié, D., 2009, “MOOSE: A Parallel Computational Framework for Coupled Systems of Nonlinear Equation,” Nucl. Eng. Des., 239(10), pp. 1768–1778. [CrossRef]
Harter, J. , Greaney, P. A. , and Palmer, T. S. , 2015, “Characterization of Thermal Conductivity Using Deterministic Phonon Transport in Rattlesnake,” Trans. Am. Nucl. Soc., 112, pp. 829–832. http://alexgreaney.com/media/publications/Harter_2015_ANS_PhononBTE.pdf
Ziman, J. , 2001, Electrons and Phonons: The Theory of Transport Phenomena in Solids, Oxford University Press, London. [CrossRef]
Majumdar, A. , 1993, “Microscale Heat Conduction in Dielectric Thin Films,” ASME J. Heat Transfer, 115(1), pp. 7–16. [CrossRef]
Knoll, D. , and Keyes, D. , 2004, “Jacobian-Free Newton–Kryloc Methods: A Survey of Approaches and Applications,” J. Comput. Phys., 193(2), pp. 357–397. [CrossRef]
Wang, Y. , Zhang, H. , and Martineau, R. , 2014, “Diffusion Acceleration Schemes for Self-Adjoint Angular Flux Formulation With a Void Treatment,” Nucl. Sci. Eng., 176(2), pp. 201–225.
Allu, P. , and Mazumder, S. , 2016, “Hybrid Ballistic-Diffusive Solution to the Frequency Dependent Phonon Boltzmann Transport Equation,” Int. J. Heat Mass Transfer, 100, pp. 165–177. [CrossRef]
Li, W. , Carrete, J., Katcho, N. A., and Mingo, N., 2014, “ShengBTE: A Solver of the Boltzmann Transport Equation for Phonons,” Comput. Phys. Commun., 185(6), pp. 1747–1758.
de Sousa Oliveira, L. , 2015, “Thermal Resistance From Irradiation Defects in Graphite,” Comput. Mater. Sci., 103, pp. 68–76.
Chernatynskiy, A. , and Phillpot, S. R. , 2015, “Phonon Transport Simulator (PhonTS),” Comput. Phys. Commun., 192, pp. 196–204. [CrossRef]
Yilbas, B. , and Bin Mansoor, S. , 2012, “Phonon Transport in Two-Dimensional Silicon Thin Film: Influence of Film Width and Boundary Conditions on Temperature Distribution,” Eur. Phys. J. B, 85, p. 243. [CrossRef]
Bergman, T. L., Lavine, A. S., Incropera, F. P., and Dewitt, D. P., 2007, Introduction to Heat Transfer, 5th ed., Wiley, Hoboken, NJ.
Morris, R. , 2015, “CUBIT 14.1 User Documentation,” Sandia National Laboratory, Albuquerque, NM, Report No. SAND2017-6895 W. https://cubit.sandia.gov/public/14.1/help_manual/WebHelp/cubithelp.htm
Saad, Y. , and Schultz, M. , 1986, “GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,” SIAM J. Sci. Comput., 7(3), pp. 856–869.
Saad, Y. , 2003, Iterative Methods for Sparse Linear Systems, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, PA. [CrossRef]
Xiao-Feng, T. , Chong-Sheng, L. , Zheng-He, Z. , and Tao, G. , 2010, “Molecular Dynamics Simulation of Collective Behaviour of Xe in UO2,” Chin. Phys. B, 19(5), p. 057102.
Colbert, M. , Tréglia, G. , and Ribeiro, F. , 2014, “Theoretical Study of Xenon Adsorption in UO2 Nanoporous Matrices,” J. Phys.: Condens. Matter, 26(48), p. 485015.
Sasaki, S. , Wada, N. , and Kume, H. T. , 2008, “High-Pressure Brillouin Study of the Elastic Properties of Rare-Gas Solid Xenon at Pressures Up to 45 GPa,” J. Raman Spectrosc., 40(2), pp. 121–127.
Bates, J. , 1970, “High-Temperature Thermal Conductivity of round ‘Robin Uranium’ Dioxide,” Office of Scientific and Technical Information, Oak Ridge, TN, Report No. BNWL-1431. https://www.osti.gov/scitech/servlets/purl/4084378/
Lewis, E. , and Miller, W. , 1993, Computational Methods of Neutron Transport, American Nuclear Society, La Grange Park, IL.
Togo, A. , Oba, F. , and Tanaka, I. , 2008, “First-Principles Calculations of the Ferroelastic Transition Between Rutile-Type and Cacl 2-Type Sio 2 at High Pressures,” Phys. Rev. B, 78(13), p. 134106. [CrossRef]
Kresse, G. , and Hafner, J. , 1994, “Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal–Amorphous-Semiconductor Transition in Germanium,” Phys. Rev. B, 49(20), p. 14251. [CrossRef]
Kresse, G. , and Furthmüller, J. , 1996, “Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set,” Comput. Mater. Sci., 6(1), pp. 15–50. [CrossRef]
Kresse, G. , and Furthmüller, J. , 1996, “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set,” Phys. Rev. B, 54(16), p. 11169. [CrossRef]
Perdew, J. P. , and Zunger, A. , 1981, “Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems,” Phys. Rev. B, 23(10), p. 5048. [CrossRef]
Wang, B.-T. , Zhang, P. , Lizárraga, R. , Di Marco, I. , and Eriksson, O. , 2013, “Phonon Spectrum, Thermodynamic Properties, and Pressure-Temperature Phase Diagram of Uranium Dioxide,” Phys. Rev. B, 88(10), p. 104107. [CrossRef]
Plimpton, S. , 1995, “Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J. Comput. Phys., 117(1), pp. 1–19.
Kubo, R. , Yokota, M. , and Nakajima, S. , 1957, “Statistical-Mechanical Theory of Irreversible Processes—II: Response to Thermal Disturbance,” J. Phys. Soc. Jpn., 12(11), pp. 1203–1211. [CrossRef]
Acree, W. E., Jr., and Chickos, J. S., 2017, Thermochemical Data in NIST ChemistryWebBook, NIST Standard Reference Database Number 69, P. J. Linstrom and W. G. Mallard, eds., National Institute of Standards and Technology, Gaithersburg, MD.
Mansoor, S. B. , and Yilbas, B. , 2012, “Phonon Radiative Transport in Silicon-Aliuminum Thin Films: Frequency Dependent Case,” Int. J. Therm. Sci., 57, pp. 54–62.
Mansoor, S. B. , and Yilbas, B. , 2011, “Phonon Transport in Silicon-Silicon and Silicon-Diamond Thin Films: Consideration of Thermal Boundary Resistance at Interface,” Phys. B, 406(11), pp. 1307–1330.
Singh, D. , Guo, X. , Alexeenko, A. , Murthy, J. Y. , and Fisher, T. S. , 2009, “Modeling of Subcontinuum Thermal Transport Across Semiconductor-Gas Interfaces,” J. Appl. Phys., 106, p. 024314.
Landry, E. , and McGaughey, A. , 2009, “Thermal Boundary Resistance Predictions From Molecular Dynamics Simulations and Theoretical Calculations,” Phys. Rev. B, 80(16), p. 165304.
Yang, R. , and Chen, G. , 2004, “Thermal Conductivity Modeling of Periodic Two-Dimensional Nanocomposites,” Phys. Rev. B, 69(19), p. 195316.
Swartz, E. , and Pohl, R. , 1989, “Thermal Boundary Resistance,” Rev. Mod. Phys., 61(3), pp. 605–667.
Thomas, I. , and Srivastava, G. , 2014, “Theory of Interface and Anharmonic Phonon Interactions in Nanocomposite Materials,” IOP Conf. Ser.: Mater. Sci. Eng., 68, p. 012007.
Cooper, M. , Stanek, C. , and Andersson, D. , 2017, “Simulations of Thermal Conductivity Reduction Due to Extended Xe-Vacancy Clusters and Defining Requirements for Modeling Spin-Phonon Scattering,” Los Alamos National Laboratory, Los Alamos, NM, Report No. M3MS-17LA0201033.

Figures

Grahic Jump Location
Fig. 1

Comparison to Ref. [20] for silicon test problem. Coarse and fine meshes give nearly identical solutions.

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Fig. 2

A 25 nm cell of UO2 with xenon bubble; 100,379 tetragonal mesh elements

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Fig. 3

Total and partial (for the orbitals listed in the legend) electronic density of states for UO2 with U correction

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Fig. 4

Phonon dispersion relations for UO2

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Fig. 5

Xenon properties from MD simulations. Clockwise from top left: density, thermal conductivity, mean free path, phonon speed. Xenon experiences a phase change with increasing temperatures.

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Fig. 6

Upwind and downwind phonon radiance at a physical interface between two materials

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Fig. 7

Transmission coefficients TUO2→Xe and TXe→UO2 as functions of material properties U, vg for 300–1500 K

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Fig. 8

Upper plot: κ computed with ΛBates; triangle―κ with xenon bubble; square―κ from unirradiated UO2 [28]. Lower plot: κ computed with ΛDu; diamond―κ with xenon bubble; triangle―κ with no xenon; star―κ with no xenon [7]; circle―κ with xenon bubble [7]

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Fig. 9

Dimensionless temperature Θ for all simulation temperatures. The presence of the xenon bubble is clear, as the gradient in the center region becomes steeper. This simulation was conducted using ΛBates.

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Fig. 10

Heat flux along z-axis normalized to the 300 K value, which shows the presence of the xenon bubble and its effect on the local heat flux. Heat flux steadily decreases with increasing temperature as phonon transport becomes gradually more diffuse. This simulation was conducted using ΛBates.

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Fig. 11

Phonon radiance (temperature) of the Xe bubble and streamlines of the heat flux in the UO2 region at 300 K. Higher temperature phonons are incident on the right side of the bubble; the resistance encountered increases phonon scattering, which decreases heat flux at the interface. The opposite effect occurs on the left side of the Xe bubble, where heat flux is greater as colder phonons have decreased scattering and flow away from the bubble.

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