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Integrated Radiation Transport and Thermo-Mechanics Simulation of a PWR Assembly*

K. T. Clarno, S. P. Hamilton, B. Philip, R. Sampath, S. Allu, M. A. Berrill, P. Barai, and J. E. Banfield

Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (clarnokt@ornl.gov)

INTRODUCTION

The Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) [1] is focused on predicting the temperature and strain within a nuclear fuel assembly to evaluate the performance and safety of existing and advanced nuclear fuel bundles within existing and advanced nuclear reactors. AMPFuel was extended to include an integrated nuclear fuel assembly capability for (one-way) coupled radiation transport (Denovo [2]) and nuclear fuel assembly thermo-mechanics. This capability is the initial step towards incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source terms, such as the neutron flux distribution, coolant conditions, and assembly mechanical stresses, of traditional (single-pin) nuclear fuel performance simulation.

AMPFuel was used to model an entire 17×17 Pressurized Water Reactor (PWR) fuel assembly with many of the features resolved in three dimensions (for thermo-mechanics and/or neutronics), including the fuel, gap, and cladding of each of the 264 fuel pins, the 25 guide tubes, top and bottom structural regions, and the upper and lower (neutron) reflector regions. The final full-assembly calculation was executed on Jaguar (Cray XT5) at the Oak Ridge Leadership Computing Facility [3] using 40,000 cores in under 10 hours to model over 162 billion degrees of freedom for 10 loading steps. DENOVO RADIATION TRANSPORT

Denovo [2] is a framework for solving the Boltzmann radiation transport equation. It has the capability to solve the 2D and 3D deterministic multigroup discrete-ordinates equations. The deterministic component of Denovo makes use of the Koch-Baker-Alcouffe (KBA) parallel spatial decomposition on non-uniform Cartesian grids using MPI-based communication. Volume-weighted subcell mixing of materials is utilized to offset geometric difficulties associated with the use of Cartesian meshes. The accuracy of Denovo has been verified for nuclear reactor simulation through the use of standard numerical benchmarks for radiation

transport. Additional parallelism in the form of an energy decomposition is also available, extending the parallel scalability to hundreds of thousands of processors. Numerous spatial discretizations are available, as well as a variety of angular quadrature sets and boundary condition options. Advanced Krylov subspace solvers from several Trilinos packages can be used to solve both the fixed-source and k-eigenvalue formulations of the transport equation with optional preconditioning in the form of Diffusion Synthetic Acceleration (DSA) and a novel multi-level energy preconditioner. AMPFUEL THERMO-MECHANICS

AMPFuel computes the temperature and strain within the fuel and cladding to provide an estimate of critical temperatures and the deformation of the cladding to predict the performance of nuclear fuel during normal operation.

The quasi-static conjugate heat transfer is modeled using nonlinear thermal conduction within each volume (fuel region and clad of each pin) and a Robin boundary condition to account for the transfer of heat between volumes (fuel-to-fuel and fuel-to-clad) and from the cladding to the coolant. The coolant, like the gap, is not modeled as an explicit volume. The thermal conduction component of AMPFuel uses a standard continuous finite-element discretization of each volume. Specific power, rather than power density, is used as an input in AMPFuel; thus, the power can easily be mapped from the Denovo solution to the thermo-mechanics mesh (even when the mesh is moving) because it is based on the initial geometry.

The mechanics component within AMPFuel uses standard finite-element methodology to model the static mechanical equilibrium of each body and compute the displacement of each node in the mesh. Each fuel region (four fuel pellets smeared together) and each cladding tube are modeled as independent and (where applicable) interacting bodies. Elastic and plastic deformations are modeled, as well as the densification and swelling, but these are negligible because the problem is based on fresh fuel.

17×17 WESTINGHOUSE PWR ASSEMBLY

A standard Westinghouse 17×17 nuclear fuel assembly, with 264 fuel pins (UO2 fuel; Zircaloy-4 cladding) and 25 guide tubes, with a 1.26 cm pin pitch in a square array was modeled as the demonstration problem. Each fuel pin (396.24 × 0.475; height × radius in cm) is surrounded by water coolant at 555 Kelvin. The fuel is composed of 5% enriched UO2 at 10.4 g/cc; the clad, plug, guide tube, and top/bottom plate are composed of Zircaloy-4 at 6.55 g/cc; the gap is filled with pure helium at 0.0002 g/cc; and the coolant is H2O with 1000 ppm natural boron. Each fuel pin is composed of 360 cylindrical fuel pellets (1.016 × 0.4095) with an initial gap of 0.085 cm and a plenum height of 28.448 cm. In the radiation transport simulation, the regions beyond the fuel pins (upper and lower plenum, smeared end plate, and coolant regions) were modeled explicitly; in the thermo-mechanics they were neglected. The 44 energy-group cross sections for radiation transport were computed with SCALE [4] using an assumed axial coolant density distribution. The entire problem was meshed with for both radiation transport (10 million structured Cartesian elements) and thermo-mechanics (3.3 billion unstructured, hexagonal elements), and the radiation transport utilized a Quadruple-Range (QR) angular quadrature set with 128 total directions. The specific power was mapped from the coarse radiation transport mesh to the fine thermo-mechanics mesh using a previous documented smoothing scheme [5].

The final full-assembly calculation was executed on Jaguar using 40,000 cores in under 10 hours to model over 162 billion degrees of freedom for 10 mechanical loading steps. [6] RESULTS

Note that all figures have the axial height (z-dimension) compressed by a factor of 10 to more clearly visualize the in-plane (x-y) variations. The pin-to-pin power distribution, shown in Fig. 1 on the thermo-mechanics mesh, displayed a significant pin-to-pin and within-pin axial, radial, and azimuthal power distribution, especially in pins adjacent to the guide tubes. The temperature distribution, shown in Fig. 2, appears quite axisymmetric, because of the significant temperature gradient across the pin, but the effects of that temperature gradient in a full-length fuel rod are significant on the mechanical deformation, shown in Fig. 3.

Several significant findings were discovered in this effort. The fuel pins cannot be modeled as single smeared regions because the azimuthal

variation in temperature, and thermal expansion, causes the fuel pins to artificially bow away from the guide tubes; when the fuel pins are modeled as many individual fuel regions, the spacing between regions (or pellets) reduces the total rod bowing. The computational burden of the radiation transport (44 energy groups and 128 discrete ordinates per element) was approximately 50% of the total CPU time per mechanical loading step, because a coarse-spatial mesh accurately represented the axial and radial variation in the power. If a fine mesh, comparable in resolution to the thermo-mechanical mesh, were used, the radiation transport would have required 98% of the CPU time. Accuracy in the radiation transport solution requires a fine resolution in energy and angle, which would render a coupling with thermo-mechanics unfeasible without efficient solution mapping to allow for the use of a significantly different resolution in the spatial mesh. CONCLUSIONS

The results of the full-assembly simulation clearly show the axial, radial, and azimuthal variation of the neutron flux, power, temperature, and deformation of the assembly, highlighting behavior that is neglected in traditional axisymmetric fuel performance codes that do not account for assembly features, such as guide tubes and control rods. This capability is the initial step towards incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source terms, such as the neutron flux distribution, coolant conditions, and assembly mechanical stresses, of traditional (single-pin) nuclear fuel performance simulation. Future work will include the use of this capability to model other assembly types, two-way coupling with neutronics, and coupling with fluid flow.

ACKNOWLEDGMENTS

The development of the AMP Nuclear Fuel Performance code was funded by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program of the U.S. Department of Energy Office of Nuclear Energy, Advanced Modeling and Simulation Office. This project acknowledges support for Mark Berrill from the Eugene P. Wigner Fellowship at Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy under Contract DE-AC05-00OR22725 and for James Banfield using funding received through a grant to the University of Tennessee-Knoxville from the DOE Office of Nuclear Energy’s Nuclear Energy

University Programs (NEUP). Computational resources were provided through a U.S. Department of Energy INCITE (Innovative and Novel Computational Impact on Theory and Experiment) Award: “Uncertainty Quantification for Three- Dimensional Reactor Assembly Simulations.” The AMP Nuclear Fuel Performance code is available, with limited distribution, through the Radiation Safety Information Computational Center (RSICC) at Oak Ridge National Laboratory as BCC-001. REFERENCES

1. J. TURNER, K. CLARNO, and G. HANSEN,

Roadmap to An Engineering-Scale Nuclear Fuel Performance and Safety Code, ORNL/TM-2009/233, Oak Ridge National Laboratory, Oak Ridge, TN, September 2009.

2. T. EVANS, A. STAFFORD, and K. CLARNO, Nuclear Technology 171(2), 171 (2010).

3. http://www.nccs.gov/computing-resources/jaguar/

4. SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, Oak Ridge, TN, June 2011. Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-785

5. S. P. HAMILTON and K. T. CLARNO, “Mathematical Framework for the Coupling of the AMP and Denovo Codes,” Trans. Am. Nucl. Soc. 105, 515-517 (2011).

6. K. T. CLARNO, S. P. HAMILTON, B. PHILIP, M. A. BERRILL, R. S. SAMPATH, S. ALLU, D. PUGMIRE, J. E. BANFIELD, and G. DILTS, Integrated Radiation Transport and Nuclear Fuel Performance for Assembly-Level Simulations, ORNL/TM-2012/33, Oak Ridge National Laboratory, Oak Ridge, TN, February 2012.

Fig. 1. Power distribution within the assembly, in gigawatts per metric tonne of UO2.

Fig. 2. Temperature distribution within the assembly, in Kelvin.

Fig. 3. Axial displacement within the assembly, in meters.