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

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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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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