Validation of OpenMC Reactor Physics Simulations ...

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Reactor Physics: General—I

1301

Validation of OpenMC Reactor Physics Simulations with the B&W 1810 Series Benchmarks Jonathan A. Walsh, Benoit Forget, and Kord S. Smith Massachusetts Institute of Technology Department of Nuclear Science and Engineering 77 Massachusetts Avenue, Cambridge, MA 02139-4307 Email: [email protected], [email protected], [email protected]

INTRODUCTION In this work, we present the results of simulations which provide further validation of the OpenMC particle WUDQVSRUW FRGH¶V UHDFWRU SK\VLFV PRGHOLQJ FDSDELOLWLHV The results come from both simplified two-dimensional and detailed three-dimensional models of the B&W 1810 series of critical benchmark experiments. This set of experiments has been analyzed extensively by the reactor physics code development community and provides reference data from a range of core configurations for code validation. The results of OpenMC k-eigenvalue calculations are shown to be in good agreement with the experimental results. Comparisons of two-dimensional and three-dimensional results are also made. OPENMC PARTICLE TRANSPORT CODE The open-source OpenMC particle transport code [1] has been in development at the Massachusetts Institute of Technology for the past three years. Its main intended area of application is in performing reactor physics simulations on massively-parallel, high-performance computing architectures. To this end, OpenMC has previously shown excellent accuracy and scalability in criticality benchmark and full core k-eigenvalue calculations. OpenMC has been validated against several of the International Criticality Safety Benchmark Evaluation Project (ICSBEP) [2] and Doppler-Defect Benchmark [3] models. Validation has also been carried out with the full core Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS) [4] and Monte Carlo Performance Benchmark [5] models. Results of these simulations have been compared to, and shown to agree well with, results obtained with MCNP5 [6]. The OpenMC and MCNP5 inputs for these benchmark models are online [7]. The code has also been designed to handle the extremely large number of tallies that is required for practical, full core, Monte Carlo reactor physics simulations. Utilizing constructive solid geometry, OpenMC allows users to model arbitrarily complex features. This capability can be especially useful in detailed full core simulations. Through so-FDOOHG³ODWWLFH´ DQG ³XQLYHUVH´ JHRPHWU\ FRQVWUXFWV 2SHQ0& DIIRUGV users the opportunity to efficiently define repeated

structures. This is another feature particularly suited to modeling large reactor physics problems. Other generally useful features of OpenMC include its use of ACE-formatted continuous-energy nuclear cross section data. This allows for a highly faithful representation of neutron interaction processes. Additionally, 2SHQ0&¶V;0/LQSXWILOHIRUPDWSrovides a straightforward way for users to define their model. B&W 1810 SERIES MODELS Models of the Babcock and Wilcox (B&W) 1810 Series of critical benchmark experiments [8] are created in OpenMC. These critical experiments are often used for cross section data and reactor physics code validations [9][10][11][12]. The majority of past code validation work is aimed at benchmarking deterministic lattice physics codes. The series of critical benchmarks ± each referred to DV D ³FRUH´ ± covers a range of physical configurations relevant to pressurized-water reactor (PWR) analysis. The core configurations are described briefly in Table 1.

Core

Table 1. Core Configuration Descriptions Assembly Size Control Rods Gd Pins Critical Boron (ppm)

1

15x15

-

-

1337.9

2

15x15

16

-

1250.0

3

15x15

-

20

1239.3

4

15x15

16

20

1171.7

5

15x15

-

28

1208.0

6

15x15

16

28

1155.8

7

15x15

-

28

1208.8

8

15x15

-

36

1170.7

9

15x15

16

36

1130.5

10

15x15

-

36

1177.1

12

15x15

-

-

1899.3

13

15x15

16

-

1635.4

14

15x15

-

28

1653.8

15

15x15

16

28

1479.7

16

15x15

-

36

1579.4

17

15x15

16

36

1432.1

18

16x16

-

-

1776.8

19

16x16

-

16

1628.3

20

16x16

-

32

1499.0

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

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Reactor Physics: General—I

All of the experiments in the series consist of a central 3x3 array of standard fuel assemblies surrounded by a radial zone of driver rods. All rods are contained in a large aluminum tank filled with unpressurized water at 298 K. Cores 18, 19 and 20 are composed of 16x16 fuel rod lattice assemblies representative of Combustion Engineering PWR designs. All other cores contain 15x15 fuel rod assemblies representative of B&W PWR designs. Fuel rods enriched to 2.46 wt. %, 4.02 wt. %, and 1.944 wt. % are arranged in multiple loading patterns. The 2.46 wt. % rods are solid UO2 fuel pellets clad and capped with aluminum. The 4.02 wt. % rods consist of powdered UO2 fuel swaged in stainless steel cladding. The swaging process (i.e. compression of the fuel rod in order to increase fuel density) produces rods that have no fuel-cladding gap. These fuel rods are modeled with aluminum plug caps, though an uncertain number of these rods are actually capped with stainless steel in the experiments. The 1.944 wt. % rods are solid uraniagadolinia UO2-Gd2O3 fuel, with approximately 4 wt. % gadolinia burnable absorber. They are clad and capped with aluminum. There are also some annular uraniagadolinia fuel rods that are identical to the solid rods except for the presence of their inner void. Some assemblies contain Ag-In-Cd (AIC) control rods, while others have B4C rods. All control rods are clad in aluminum. Void aluminum tubes are also present in some assemblies. In the experiments, the level of soluble boron in the water is adjusted until a slightly supercritical multiplication factor of 1.00070 is achieved and this boron concentration is then recorded. A more detailed description of the B&W 1810 Series can be found in the original technical report [8]. For each core configuration, a k-eigenvalue calculation is performed in OpenMC with both a twodimensional and a three-dimensional model. The twodimensional models are axially homogeneous, as seen in Fig. 1, with vacuum boundary conditions on all boundaries. The region outside of the radial driver rod zone is bounded by a square and filled with water. The core tank is neglected. This is done so that the OpenMC geometry models are consistent with those of previous two-dimensional analyses of the benchmarks [9]. The lower and upper axial planes are chosen to correspond to the water level of 145 cm in the actual experimental setup. In making this selection, we have neglected the small segments of the fuel rods that extend out of the water. An axial cross section of the two-dimensional core geometry can be seen in Fig. 2. Three-dimensional models are also constructed in order to determine the effects of axial heterogeneities not typically modeled. Among these commonly neglected features, seen in Fig. 3, are the aluminum core tank, grid plates, and base plate, and the previously-mentioned fuel rod segments, complete with end caps, that extend above

the water line. An axial cross section of the threedimensional core geometry can be seen in Fig. 4.

Fig. 1. 2-D model x-z cross section, color by material

Fig. 2. 2-D model x-y cross section, color by material RESULTS Each simulation consists of 50 inactive cycles, 250 active cycles, and 3 million particles per cycle. These parameters are sufficient to converge keff to a one sigma standard deviation of 5 pcm for all cores. The simulations are performed in parallel on 64 processors.

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

Reactor Physics: General—I As Table 2 shows, switching from a simplified twodimensional model to a detailed three-dimensional model results in increases in reactivity of ~100 pcm. The lower reactivity of the two-dimensional models is due, at least in part, to the neglected upper fuel rod segments that are included in the three-dimensional models. The inclusion of the base plate in the three-dimensional models likely

1303 also makes a small contribution to the increases in reactivity due to its reflection of neutrons that would otherwise OHDNRXWRIWKHV\VWHP¶VYDFXXPERXQGDU\LQ the two-dimensional models. The keff values calculated from the three-dimensional models agree well ± to within ~20 pcm, on average ± with the value of 1.00070 for which the experimentally-obtained critical boron concentrations are valid. The keff eigenvalues for cores 12 through 20 appear to show some reduction in reactivity relative to the other cores. Cores 12 through 20 contain the 4.02 wt. % swaged fuel rods. This swaging leads to the uncertainties in the fuel diameter and the clad thickness that are documented in the original report [8]. Some of the bias is also likely due to the uncertainty in the composition of the stainless steel cladding. There are no other readily discernible patterns in the reactivity differences between the OpenMC results and those obtained by experiment. Thus, the OpenMC code, using ENDF/B-VII data [13], is able to accurately model a variety of fuel enrichments, boron concentrations, control rod and burnable absorber rod positions, and loading patterns without producing biased results.

Core

Fig. 3. 3-D model x-z cross section, color by material

Table 2. Calculated keff and Standard Error Values 2-D 3-D keff

keff

ǻNeff (2D-to-3D)

1

0.99979

0.00005

1.00123

0.00005

0.00144

2

0.99920

0.00004

1.00081

0.00004

0.00161

3

0.99954

0.00004

1.00097

0.00004

0.00143

4

1.00028

0.00005

1.00166

0.00004

0.00138

5

0.99938

0.00005

1.00079

0.00005

0.00141

6

0.99955

0.00005

1.00096

0.00005

0.00141

7

0.99940

0.00004

1.00063

0.00004

0.00123

8

0.99958

0.00005

1.00093

0.00005

0.00135

9

0.99946

0.00004

1.00077

0.00004

0.00131

10

0.99936

0.00005

1.00063

0.00005

0.00127

12

0.99914

0.00005

0.99977

0.00005

0.00063

13

0.99932

0.00005

1.00027

0.00004

0.00095

14

0.99906

0.00004

0.99984

0.00005

0.00078

15

0.99941

0.00005

1.00037

0.00005

0.00096

16

0.99913

0.00005

0.99997

0.00005

0.00084

17

0.99918

0.00005

1.00021

0.00005

0.00103

18

0.99888

0.00005

0.99978

0.00005

0.00090

19

0.99890

0.00004

0.99977

0.00005

0.00087

20

0.99913

0.00005

1.00000

0.00005

Mean

0.99935

1.00049

0.00114

Std. Dev.

0.00033

0.00055

0.00023

0.00087

CONCLUSIONS Fig. 4. 3-D model x-y cross section, color by material

Three-dimensional features of the B&W 1810 Series of critical benchmarks have a small, but significant, effect on core reactivity. Not surprisingly, the keff values

Transactions of the American Nuclear Society, Vol. 109, Washington, D.C., November 10–14, 2013

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Reactor Physics: General—I

obtained using the three-dimensional models agree more closely with experimental results than do those values obtained with two-dimensional models. The OpenMC particle transport code is shown to accurately calculate keigenvalues for a set of well-established reactor physics benchmarks that covers a wide range of relevant PWR physical configurations. REFERENCES   3 . 5RPDQR DQG % )RUJHW ³7KH 2SHQ0& 0RQWH &DUOR 3DUWLFOH 7UDQVSRUW &RGH´ Ann. Nucl. Energy, 51, 274 (2013). 2. NEA Nuclear Science Committee, 2009³International Handbook of Evaluated Criticality Safety Benchmark Experiments´ NEA/NSC/DOC(95)03, OECD Nuclear Energy Agency (2009). 5'0RVWHOOHU³7KH'RSSOHU-Defect Benchmark: 2YHUYLHZDQG6XPPDU\RI5HVXOWV´Proc. Joint International Topical Meeting on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007), Monterey, CA, April 15-19, 2007.

Fuel Management IV (ANFM 2009), Hilton Head Island, SC, April 12-15, 2009. 10$