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Thermophysical and Mechanical Analyses of UO_{2}-36.4vol % BeO Fuel Pellets with Zircaloy, SiC, and FeCrAl Claddings

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## Abstract

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_{2}-36.4vol % BeO fuel pellets cladded with Zircaloy, SiC, and FeCrAl, and Zircaloy cladding materials coated with SiC and FeCrAl, are investigated based on simulation results obtained by the CAMPUS code. In addition, the effect of coating thickness (0.5, 1 and 1.5 mm) on fuel performance and mechanical interaction is discussed. The modeling results show that Zircaloy claddings are more effective in decreasing fuel centerline temperature and fission gas release than other kinds of cladding material because of the smaller gap between cladding and fuel at the same burnup. SiC claddings and SiC-coated Zircaloy claddings possess smaller plenum pressure than other kinds of cladding. SiC claddings contribute more to fuel radial displacement but less to fuel axial displacement. FeCrAl claddings exhibit very different radial and axial displacements in different axial positions. FeCrAl-coated Zircaloy claddings have a lower fuel centerline temperature than Zircaloy claddings at burnup below 850 MWh/kg U, but a higher fuel centerline temperature at higher burnup. The gap between FeCrAl-coated Zircaloy claddings and fuel pellets closes earlier than that of Zircaloy claddings. SiC-coated claddings increase fuel radial and axial displacements, and cladding axial displacements of inner and outer cladding surfaces.

## 1. Introduction

_{2}composite fuel. The low thermal conductivity of UO

_{2}fuel has become one of the major concerns limiting nuclear reactor performance and safety. Incorporation of UO

_{2}with high thermal conductivity particles such as BeO or SiC could improve fuel thermal conductivity, one of the key criteria in balancing thermal energy and reactor safety demands [1,2]. Another way to mitigate against severe accidents is to develop enhanced strength and ductility ATF cladding, as this would alleviate the severity of reactivity-initiated accidents, and oxidation-resistant ATF cladding in the case of a loss-of-coolant accident (LOCA) [3]. Zr alloys, which have low neutron absorption cross-sections and a good neutron irradiation resistance, are currently used in nuclear fuel cladding for commercial LWRs [4]. However, in accident scenarios, Zr alloys react with hot steam, generating massive oxidation heat and hydrogen in a very short period. Additionally, the mechanical strength of Zr alloys undergoes significant recession and degradation during accidents. Therefore, it is important to develop new accident-tolerant fuel cladding materials [4]. SiC possesses an extremely low hydrogen liberation rate, excellent high temperature mechanical properties, a high melting point, and little irradiation creep compared with Zr alloys [5]. FeCrAl alloys present slower oxidation rates in high-temperature steam, which may help to preempt further damage resulting from an accident [6]. Surface-coated Zr alloy cladding is also a candidate for ATF owing to its improved corrosion performance compared with Zr alloy cladding and its high neutron economy compared with FeCrAl alloys [7].

_{2}-36.4vol % BeO is chosen as optimal due to its promising application in commercial LWRs to achieve better fuel performance. Temperature-dependent material properties, such as thermal conductivity, density, specific heat capacity, and thermal expansion, are incorporated into the CAMPUS code, and the fuel centerline temperature, gap size evolution, fission gas release, plenum pressure, and fuel and cladding axial and radial displacements are calculated and discussed in detail.

## 2. Materials and Methods

#### 2.1. Thermal Conductivity

_{2}-BeO fuel during irradiation. The irradiated fuel thermal conductivity k is calculated as follows:

- ${f}_{d}$—Dissolved fission products correction;
- ${f}_{p}$—Precipitated fission products correction;
- ${f}_{por}$—Porosity correction;
- ${f}_{x}$—Deviation from stoichiometry;
- ${f}_{r}$—Radiation damage correction.$${f}_{d}=\left(\frac{1.09}{b{u}^{3.265}}+0.0643\xb7\sqrt{\frac{T}{bu}}\right)\xb7arctan\left(\frac{1.0}{\frac{1.09}{b{u}^{3.265}}+0.0643\xb7\sqrt{\frac{T}{bu}}}\right)$$$${f}_{p}=1.0+\left(\frac{0.019\xb7bu}{3.0-0.019\xb7bu}\right)\xb7\left(\frac{1.0}{1.0-\mathrm{exp}\left(\frac{-\left(T-1200\right)}{100}\right)}\right)$$$${f}_{por}=\left(\frac{1-p}{1.0+0.5\xb7p}\right)$$$${f}_{r}=1.0-\frac{0.2}{1.0+\mathrm{exp}\left(\frac{T-900}{80}\right)}$$

_{2}-BeO fuel is calculated from the Hasselman and Johnson model, as shown below [10]. Considering the fabrication process of UO

_{2}-BeO fuel, introduced by Ishimoto et al. [2] and Solomon et al. [11], UO

_{2}is treated as a particle corresponding to subscript p in the Hasselman and Johnson model, and BeO is treated as a matrix, which corresponds to subscript m in the Hasselman and Johnson model.

_{2}is from Fink [8]. The thermal conductivity of cladding materials of Zir [13], SiC, and FeCrAl [14] are calculated as follows:

#### 2.2. Thermal Expansion

_{2}and BeO.

_{2}and BeO are calculated as suggested by [16,17], respectively.

_{2}-BeO fuel, Zircaloy cladding (in r, phi, and z directions), SiC cladding, and FeCrAl cladding are plotted in Figure 2.

_{2}-BeO fuel, and Zr, SiC, and FeCrAl claddings.

#### 2.3. Model Implementation

#### 2.3.1. Heat Transfer

#### 2.3.2. Deformation Mechanics

## 3. Results and Discussions

_{2}-BeO fuel with SiC cladding possesses the highest fuel centerline temperature, leading to the largest fuel radial and axial displacements, while UO

_{2}-BeO fuel with Zircaloy cladding possesses the lowest fuel centerline temperature, which leads to the smallest radial and axial displacements.

## 4. Conclusions

_{2}-36.4vol % BeO fuel with Zircaloy, SiC, FeCrAl, and surface-coated Zircaloy cladding materials are investigated based on simulation results obtained using the CAMPUS code. The modeling results show that Zircaloy cladding is more effective in decreasing fuel centerline temperatures and fission gas release rates because of its smaller gap size compared with other cladding materials at the same burnup rates. SiC and SiC-coated Zircaloy claddings possess smaller plenum pressures than other claddings but have larger fuel radial displacements and smaller contributions to fuel axial displacement. FeCrAl cladding exhibits very different radial and axial displacements depending on the axial position. SiC-coated Zircaloy claddings still show higher fuel centerline temperatures and more fission gas release, due to their larger gap size compared with pure Zircaloy at the same burnup rate. FeCrAl-coated claddings have lower fuel centerline temperatures than Zircaloy cladding until the burnup exceeds 850 MWh/kg U, after which point they become higher. The gaps of FeCrAl-coated claddings are closed earlier than those of Zircaloy cladding. SiC-coated claddings increase the fuel radial, fuel axial, and cladding axial displacements. For cladding inner and outer surfaces, FeCrAl-coated claddings have wide variation, depending on the axial position.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

_{2}is given by [20] and the heat capacity of BeO is derived from [21].

_{1}= 296.7 J/kg K; K

_{2}= 0.0243 J/kg K

^{2}; K

_{3}= 8.75 × ${10}^{7}$ J/kg; R = 8.315 J/mole K; $\theta $ = 535.285 K; and E

_{D}= 1.577 × ${10}^{5}$ J/mole.

_{2}-BeO composite fuel is calculated based on

_{2}[8]:

_{2}were obtained from the formulas suggested by Martin [16].

## References

- Yeo, S.; McKenna, E.; Baney, R.; Subhash, G.; Tulenko, J. Enhanced thermal conductivity of uranium dioxide–silicon carbide composite fuel pellets prepared by Spark Plasma Sintering (SPS). J. Nucl. Mater.
**2013**, 433, 66–73. [Google Scholar] [CrossRef] - Ishimoto, S.; Hirai, M.; Ito, K.; Korei, Y. Thermal conductivity of UO
_{2}-BeO pellet. J. Nucl. Sci. Technol.**1996**, 33, 134–140. [Google Scholar] [CrossRef] - Zinkle, S.J.; Terrani, K.A.; Gehin, J.C.; Ott, L.J.; Snead, L.L. Accident tolerant fuels for LWRs: A perspective. J. Nucl. Mater.
**2014**, 448, 374–379. [Google Scholar] [CrossRef] - Markham, G.; Hall, R.; Feinroth, H. Recession of silicon carbide in steam under nuclear plant loca conditions up to 1400 °C. In Ceramic Materials for Energy Applications II; Fox, K.M., Katoh, Y., Lin, H.-T., Belharouak, I., Eds.; John Wiley & Sons: Hoboken, NJ, USA, 2012; pp. 111–120. [Google Scholar]
- Kim, D.; Lee, H.-G.; Park, J.Y.; Kim, W.-J. Fabrication and measurement of hoop strength of sic triplex tube for nuclear fuel cladding applications. J. Nucl. Mater.
**2015**, 458, 29–36. [Google Scholar] [CrossRef] - Terrani, K.A.; Zinkle, S.J.; Snead, L.L. Advanced oxidation-resistant iron-based alloys for LWR fuel cladding. J. Nucl. Mater.
**2014**, 448, 420–435. [Google Scholar] [CrossRef] - Kim, H.-G.; Kim, I.-H.; Jung, Y.-I.; Park, D.-J.; Park, J.-Y.; Koo, Y.-H. Adhesion property and high-temperature oxidation behavior of Cr-coated Zircaloy-4 cladding tube prepared by 3D laser coating. J. Nucl. Mater.
**2015**, 465, 531–539. [Google Scholar] [CrossRef] - Fink, J.K. Thermophysical properties of uranium dioxide. J. Nucl. Mater.
**2000**, 279, 1–18. [Google Scholar] [CrossRef] - Lucuta, P.G.; Matzke, H.; Hastings, I.J. A pragmatic approach to modelling thermal conductivity of irradiated UO
_{2}fuel: Review and recommendations. J. Nucl. Mater.**1996**, 232, 166–180. [Google Scholar] [CrossRef] - Hasselman, D.P.H.; Johnson, L.F. Effective thermal conductivity of composites with interfacial thermal barrier resistance. J. Compos. Mater.
**1987**, 21, 508–515. [Google Scholar] [CrossRef] - Solomon, A.A.; Revankar, S.; McCoy, J.K. Enhanced Thermal Conductivity Oxide Fuels, Final Report; PU 2002-180-1.2, NERI Contract OER-32; School of Nuclear Engineering, Purdue University: West Lafayette, IN, USA, 2005. [Google Scholar]
- Touloukian, Y.S. Thermophysical Properties of Matter: The Tprc Data Series; A Comprehensive Compilation of Data; Ifi/Plenum: Wilmington, NC, USA, 1970; Volume 1. [Google Scholar]
- International Atomic Energy Agency. Thermophysical Properties Database of Materials for Light Water Reactors and Heavy Water Reactors; IAEA-TECDOC-1496; International Atomic Energy Agency: Vienna, Austria, 2006. [Google Scholar]
- Wu, X.; Kozlowski, T.; Hales, J.D. Neutronics and fuel performance evaluation of accident tolerant fecral cladding under normal operation conditions. Ann. Nucl. Energy
**2015**, 85, 763–775. [Google Scholar] [CrossRef] - Latta, R.; Revankar, S.T.; Solomon, A.A. Modeling and measurement of thermal properties of ceramic composite fuel for light water reactors. Heat Transf. Eng.
**2008**, 29, 357–365. [Google Scholar] [CrossRef] - Martin, D.G. The thermal expansion of solid UO
_{2}and (U, Pu) mixed oxides—A review and recommendations. J. Nucl. Mater.**1988**, 152, 94–101. [Google Scholar] [CrossRef] - Gomes, D.S.; Abe, A.Y.; Muniz, R.O.R.; Giovedi, C. Analysis of UO
_{2}-BeO fuel under transient using fuel performance code. In Proceedings of the 2017 International Nuclear Atlantic Conference—INAC 2017, Belo Horizente, MG, Brazil, 22–27 October 2017. [Google Scholar] - MacDonald, P.E.; Thompson, L.B. Matpro: Version 09. A Handbook of Materials Properties for Use in the Analysis of Light Water Reactor Fuel Rod Behavior; TREE-NUREG-1005; SEE CODE-9502158 Aerojet Nuclear Co.: Idaho Falls, ID, USA; Idaho National Engineering Lab.: Idaho Falls, ID, USA, 1976. [Google Scholar]
- Liu, R.; Prudil, A.; Zhou, W.; Chan, P.K. Multiphysics coupled modeling of light water reactor fuel performance. Prog. Nucl. Energy
**2016**, 91, 38–48. [Google Scholar] [CrossRef] - Carbajo, J.J.; Yoder, G.L.; Popov, S.G.; Ivanov, V.K. A review of the thermophysical properties of mox and UO
_{2}fuels. J. Nucl. Mater.**2001**, 299, 181–198. [Google Scholar] [CrossRef] - Chandramouli, D.; Revankar, S.T. Development of thermal models and analysis of UO
_{2}-BeO fuel during a loss of coolant accident. Int. J. Nucl. Energy**2014**, 2014, 751070. [Google Scholar] [CrossRef] - Lucuta, P.G.; Matzke, H.; Verrall, R.A. Thermal conductivity of hyperstoichiometric simfuel. J. Nucl. Mater.
**1995**, 223, 51–60. [Google Scholar] [CrossRef] - Liu, R.; Zhou, W.; Shen, P.; Prudil, A.; Chan, P.K. Fully coupled multiphysics modeling of enhanced thermal conductivity UO
_{2}-BeO fuel performance in a light water reactor. Nucl. Eng. Des.**2015**, 295, 511–523. [Google Scholar] [CrossRef] - Soga, N. Elastic constants of polycrystalline BeO as a function of pressure and temperature. J. Am. Ceram. Soc.
**1969**, 52, 246–249. [Google Scholar] [CrossRef]

**Figure 1.**Thermal conductivity of UO

_{2}-36.4vol % BeO with measured and modeled results, and Zr, SiC, and FeCrAl cladding materials.

**Figure 2.**Thermal expansion of UO

_{2}-36.4vol % BeO, Zr (in r, phi, and z directions), SiC, and FeCrAl.

**Figure 3.**(

**a**) Comparison of fuel centerline temperature vs. burnup, with various cladding materials; (

**b**) Gap size evolutions with Zircaloy, SiC, and FeCrAl claddings.

**Figure 4.**Fuel displacement evolution against the axial positions of Zircaloy, SiC, and FeCrAl claddings, at a burnup of 1200 MWh/kg U. (

**a**) Fuel radial displacement and (

**b**) fuel axial displacement.

**Figure 5.**Cladding displacement of inner and outer surfaces of Zircaloy, SiC, and FeCrAl claddings at a burnup of 1200 MWh/kg U. (

**a**) Cladding radial displacement and (

**b**) cladding axial displacement.

**Figure 6.**Fuel centerline temperature of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings.

**Figure 7.**Gap size evolutions of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings.

**Figure 8.**Fuel radial displacement evolutions of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings, at a burnup of 1200 MWh/kg U.

**Figure 9.**Fuel axial displacement evolutions of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings, at a burnup of 1200 MWh/kg U.

**Figure 10.**Cladding radial displacements of inner and outer surfaces of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings, at a burnup of 1200 MWh/kg U.

**Figure 11.**Cladding radial displacements of inner and outer surfaces of (

**a**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm SiC claddings; (

**b**) Zircaloy, Zircaloy coated with 0.5, 1 and 1.5 mm FeCrAl claddings, at a burnup of 1200 MWh/kg U.

T (K) | 301.4 | 319.4 | 325.8 | 332.9 | 359 | 367.6 | 397 | 426.2 | 475.2 | 514.7 | 524.6 |

k(BeO) | 219 | 204 | 194 | 187.9 | 167.4 | 164.7 | 145.4 | 131.6 | 113.1 | 99.5 | 94.2 |

T (K) | 560.5 | 652.7 | 712.4 | 850 | 905 | 1080 | 1182 | 1270 | 1360 | 1405 | 1490 |

k(BeO) | 87.2 | 70.4 | 61.4 | 58.3 | 57.1 | 39.1 | 34.3 | 26.1 | 22.3 | 21.2 | 20.5 |

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**MDPI and ACS Style**

Zhou, W.; Zhou, W.
Thermophysical and Mechanical Analyses of UO_{2}-36.4vol % BeO Fuel Pellets with Zircaloy, SiC, and FeCrAl Claddings. *Metals* **2018**, *8*, 65.
https://doi.org/10.3390/met8010065

**AMA Style**

Zhou W, Zhou W.
Thermophysical and Mechanical Analyses of UO_{2}-36.4vol % BeO Fuel Pellets with Zircaloy, SiC, and FeCrAl Claddings. *Metals*. 2018; 8(1):65.
https://doi.org/10.3390/met8010065

**Chicago/Turabian Style**

Zhou, Wei, and Wenzhong Zhou.
2018. "Thermophysical and Mechanical Analyses of UO_{2}-36.4vol % BeO Fuel Pellets with Zircaloy, SiC, and FeCrAl Claddings" *Metals* 8, no. 1: 65.
https://doi.org/10.3390/met8010065