Ensuring the possibility of using Thorium as a fuel in a Pressurized Water Reactor (PWR)

Ensuring the possibility of using Thorium as a fuel in a Pressurized Water Reactor (PWR) 1 first-author 1 2 corresp *Agalahom@yahoo.com, Galhom_20102000@yahoo.com. *Agalahom@yahoo.com, Galhom_20102000@yahoo.com. Agalahom@yahoo.com https://orcid.org/0000-0002-1280-9363 Nuclear Engineering Department, Military Technical College, Kobry Elkobbah, Cairo, Egypt Nuclear Engineering Department, Military Technical College, Kobry Elkobbah, Cairo, Egypt Higher Technological Institute, 10th of Ramadan City, Egypt. Higher Technological Institute, 10th of Ramadan City, Egypt. The possibility of utilizing thorium as a fuel in a pressurized water reactor (PWR) has been proven from the neutronic perspective in our previously published work without assessing the thermal-hydraulic (TH) and solid structure performances. Therefore, the TH and solid structure performances must be studied to confirm these results and ensure the possibility of using a thorium-based fuel as an excellent accident-tolerant fuel. The TH and solid structure performances of thorium-based fuels were investigated and compared with those of UO 2 . The radial and axial power peaking factors (PPFs) for UO 2 , ( 232 Th, 235 U) O 2 , and ( 232 Th, 233 U) O 2 were examined with a PWR assembly to determine the total PPF of each one. Both Gd 2 O 3 and Er 2 O 3 were tested as burnable absorbers (BAs) to manage the excess reactivity at the beginning of the fuel cycle (BOC) and reduce the total PPF. Er 2 O 3 resulted in a more significant reduction to the total PPF and, therefore, a greater reduction to the temperature distribution compared to Gd 2 O 3 . Given these results, we analyzed the effects of adding Er 2 O 3 to thorium-based fuels on their TH and solid structure performances. Thermal hydraulic (TH) Solid structure Thorium-based fuel Gd 2 O 3 Er 2 O 3 . Introduction 1 Since the nuclear accident of Fukushima Daiichi, many efforts have been made to find an accident-tolerant fuel (ATF) that can safely operate under harsh conditions inside the reactor. This type of fuel would prevent the reactor core from melting down and causing a disaster [ 1 1 , 2 2 ]. ATFs must have better properties than traditional fuels to perform essential tasks during accident conditions, for example, decreasing oxidation kinetics and hydrogen generation rates. Thorium-based fuels have advantages that invite researchers to investigate the possibility of using them as AFTs, such as their high resistance to nuclear proliferation and the low quantity of long-lived minor actinides (MAs) and non-actinides in the discharged fuel from the reactor [ 3 3 – 8 8 3–8 ]. Various forms of thorium-based fuels have been certified, such as oxides, metals, nitrides, carbides, and molten salts. These fuels have also been nominated as nuclear fuels for different types of reactors, including heavy water reactors, light water reactors, accelerator-driven systems, and high-temperature gas-cooled reactors. The breeding capability of Th-U fuel material in accelerator-driven subcritical molten salt reactors has already been studied, where researchers determined the conversion ratio and net production of 233 U and the inventories of the various MAs [ 9 9 ]. Thorium dioxide carries significant research interest as an alternative to the traditional fuel material of uranium dioxide in Generation-IV reactors due to many reasons, including its high abundance in the earth's crust, its effectiveness in power flattening for nuclear reactors, its usefulness as a breeder blanket to generate 233 U, and its capability to suppress neutron leakage from the reactor core [ 5 5 , 10 10 , 11 11 ]. This interest also comes from its physical advantages, such as its high melting point, high corrosion resistivity, low thermal expansion coefficients, and high thermal conductivity compared to traditional fuel materials [ 4 4 , 12 12 , 13 13 ]. Moreover, the fission gas release is lower than in uranium dioxide, which keeps the fuel pellet away from any defects that could have side effects on the TH and solid structure performances. These advantages provide the fuel material with greater stability during severe operational conditions from the neutronic, TH, and solid structure viewpoints. Spark plasma sintering (SPS) is an example of the technologies used to produce high-density ( 232 Th, U)O 2 pellets, in which electric current flows through the sample and a conductive die provides rapid sintering and low temperatures ‎[ 2 2 ]. Thorium dioxide has a melting point of 3651 K and is used as a ceramic fuel pellet in nuclear reactors. Its melting point is the highest known melting point for an oxide. Thorium dioxide also has an identical fluorite structure to cerium, plutonium, and uranium dioxide. However, thorium dioxide has a higher oxidation state than uranium and plutonium dioxides, making it exceptionally stable in the presence of oxygen or water and boosting its corrosion resistance [ 14 14 ]. The existence of uranium in thorium dioxide can occur in two ways: either, through the doping process, in which, uranium is added to the thoria in a mixed oxide fuel (MOX); or, through the transmutation of the 232 Th isotope into the fissile 233 U isotope by bombarding it with a neutron, resulting in, two successive beta emissions [ 13 13 ]. This study has three primary sections. In the first section, we investigate and compare the TH and solid structure performances of the suggested thorium-based fuel types with those of traditional fuels; then, in the second section, we determine which of the two different burnable absorbers (BAs) (Gd 2 O 3 and Er 2 O 3 ) added to the standard fuel was most suitable; and lastly, in the third section, we investigate the optimum BA for thorium-based fuel. Methodology 1 Version 2.7 of the Monte Carlo N-Particle transport code system (MCNPX) was used with a cross-section library called ENDF/B-VII to design a three-dimensional model of the PWR fuel assembly (FA). The MCNPX code, based on the Monte Carlo method, is a multi-purpose code that can simulate almost all particles in the PWR environment. It was used to investigate the radial power distribution and specify the hot channel where the TH and solid structure analyses would be performed. [ 16 16 , 17 17 ]. Figure 1 Figure 1 illustrates the horizontal cross-section assembly model of the PWR, as generated by MCNPX. 70 000 histories per cycle, 20 ineffective cycles, and 100 effective cycles were used in the neutronic computations. The boundary surfaces of the fuel assembly are reflection surfaces that reflect the neutrons inside the fuel assembly. The calculations were carried out under hot full-power conditions (HFP). The COMSOL-Multiphysics computer software, which is dependent on the computational fluid dynamics (CFD) technique, was applied to investigate the TH and solid structure performances. The rod-centered subchannel model was utilized and solved numerically in the TH study. The temperature distribution for the fuel, cladding, and coolant materials, the coolant pressure drop, and the departure from nucleate boiling ratio (DNBR) was investigated using the rod-centered subchannel model. The most prominent advantage of the CFD approach is the coupling of various types of physics, which makes the solution more realistic than the analytical approach. The coupling of heat transfer and turbulence (K- <math id="M1"><mi>ϵ</mi></math> ) physics mimics the effects of coolant velocity fluctuation in the axial and radial directions, and therefore, the variation of the coolant heat transfer convection coefficient, on the temperature distribution of the fuel and cladding materials. For these reasons, we used this coupling to perform our TH analysis. The coupling of solid structure and heat transfer physics helps to investigate the effects of the thermal expansion of solid materials (fuel and cladding) on von Mises stress and total displacement. To simulate the effect of the coolant pressure on the solid materials, the turbulence and solid structure physics coupling was considered. We used the 2D axisymmetric space dimension, rather than the 3D space dimension, to simulate the TH and solid structure for the hot channel in each FA to simplify the simulation and reduce the calculation time and cost. To calculate the distribution of the DNBR, the EPRI-1 correlation for PWR was used [ 19 19 ]; this process has been illustrated in detail in our previously published article [ 18 18 ]. Table 1 Table 1 lists the properties of the examined fuel types. In this work, the TH and solid structure performances of UO 2 were investigated and compared with the thorium-based fuel types. Table 2 Table 2 shows‎ the main design features and input data used for simulating the TH and solid structure performances using COMSO‎L-Multiphysics. Table 3 Table 3 presents the correlations that describe the thermophysical and solid structure properties of the applied materials. 1 1 Fuel type 1 1 Enrichment (wt.%) 1 1 Density (g/cm 3 ) 1 1 UO 2 1 1 3.5 1 1 10.32 1 1 ( 232 Th, 235 U) O 2 1 1   1 1 9.64 1 1 ( 232 Th, 233 U) O 2 1 1   1 1 9.5 1 1 Parameters 1 1 Value 1 1 Inlet coolant pressure (MPa) 1 1 15.41 1 1 Inlet coolant temperature (K) 1 1 562.15 1 1 Coolant mass flow rate (kg/sec) 1 1 16720 1 1 Core thermal power (MW th ) 1 1 3358 1 1 Critic‎al flux 1 1 EPRI-1 Correlation [ 15 15 ] 1 1 Wall condition 1 1 No-slip 1 1 Turbulence model 1 1 K - <math id="M2"><mi>ε</mi></math>   1 1 Thermophysical property 1 1 Applied correlation 1 1 UO 2 1 1 K 0.95 ［ <math id="M3"><mrow><mfrac><mi>W</mi><mrow><mrow><mo>(</mo><mrow><mtext>cm</mtext><mo>⋅</mo><mtext>K</mtext></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ］ 1 1 <math id="M4"><mrow><mfrac><mn>1</mn><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mi>T</mi></mrow></mfrac><mo>+</mo><mfrac><mi>E</mi><mrow><msup><mi>T</mi><mn>2</mn></msup></mrow></mfrac><msup><mi>e</mi><mrow><mfrac><mrow><mo>−</mo><mi>F</mi></mrow><mi>T</mi></mfrac></mrow></msup></mrow></math> [ 17 17 ] 1 1 <math id="M5"><mrow><mi>C</mi><mi>p</mi><mrow><mo>[</mo><mrow><mfrac><mi>J</mi><mrow><mtext>mole</mtext><mo>⋅</mo><mtext>K</mtext></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></math>   1 1 <math id="M6"><mrow><msub><mi>c</mi><mn>2</mn></msub><mo>+</mo><mn>2</mn><msub><mi>c</mi><mn>3</mn></msub><mi>t</mi><mo>+</mo><mn>3</mn><msub><mi>c</mi><mn>4</mn></msub><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msub><mi>c</mi><mn>5</mn></msub><msup><mi>t</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msub><mi>c</mi><mn>6</mn></msub><msup><mi>t</mi><mn>4</mn></msup><mo>−</mo><msub><mi>c</mi><mn>7</mn></msub><msup><mi>t</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math> [ 17 17 ] 1 1 <math id="M7"><mi>ρ</mi></math> ［ <math id="M8"><mrow><mfrac><mrow><mtext>Kg</mtext></mrow><mrow><msup><mtext>m</mtext><mn>3</mn></msup></mrow></mfrac></mrow></math> ］ 1 1 ρ ( T )= ρ ° ×( K i )[ 19 19 ] 1 1   1 1 K i =0.9967+1.179×10 -5 × T -2.429×10 -9 × T 2 +1.2190×10 -12 × T 3 1 1 E (GPa) 1 1 ρ ° (273)=10.961 g/cm 3 (217.24±4.01)(1-1.92× P )[ 20 20 ] P is the porosity 1 1 <math id="M9"><mi>ν</mi></math>   1 1 <math id="M10"><mrow><mrow><mo>(</mo><mrow><mn>1.323</mn><mo>×</mo><mrow><mo>[</mo><mrow><mfrac><mrow><mn>1</mn><mo>−</mo><mn>1.92</mn><mo>×</mo><mi>P</mi></mrow><mrow><mn>1</mn><mo>−</mo><mn>1.66</mn><mo>×</mo><mi>P</mi></mrow></mfrac><mo>−</mo><mn>1</mn></mrow><mo>]</mo></mrow></mrow><mo>)</mo></mrow></mrow></math> [ 20 20 ] P is the porosity 1 1 <math id="M11"><mi>α</mi></math> ［ <math id="M12"><mrow><mfrac><mn>1</mn><mtext>K</mtext></mfrac></mrow></math> ］ 1 1 <math id="M13"><mrow><mfrac><mrow><mi>α</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi><mrow><mo>(</mo><mrow><mn>273</mn></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mn>0.9973</mn><mo>+</mo><mn>9.802</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mi>T</mi><mo>−</mo><mn>2.705</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>10</mn></mrow></msup><msup><mi>T</mi><mn>2</mn></msup><mo>+</mo><mn>4.219</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>13</mn></mrow></msup><msup><mi>T</mi><mn>3</mn></msup></mrow></math> 1 1   1 1 For 323 < T < 923 K 1 1   1 1 <math id="M14"><mrow><mfrac><mrow><mi>α</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow><mrow><mi>α</mi><mrow><mo>(</mo><mrow><mn>273</mn></mrow><mo>)</mo></mrow></mrow></mfrac><mo>=</mo><mn>0.9967</mn><mo>+</mo><mn>1.179</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mi>T</mi><mo>−</mo><mn>2.429</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><msup><mi>T</mi><mn>2</mn></msup><mo>+</mo><mn>1.219</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>12</mn></mrow></msup><msup><mi>T</mi><mn>3</mn></msup></mrow></math> 1 1   1 1 For 923 < T < 3120 K <math id="M15"><mrow><mi>α</mi><mrow><mo>(</mo><mrow><mn>273</mn></mrow><mo>)</mo></mrow></mrow></math> equal to <math id="M16"><mrow><mo> </mo><mo> </mo><mn>9.75</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> [ 19 19 ] 1 1 (Zicalloy-4) 1 1 K ［ <math id="M17"><mrow><mfrac><mtext>W</mtext><mrow><mrow><mo>(</mo><mrow><mtext>m</mtext><mo>.</mo><mtext>K</mtext></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ］ 1 1 23.5-0.0192× T +1.86×10 -5 × T 2 [ 19 19 ] 1 1 Cp ［ <math id="M18"><mrow><mfrac><mtext>J</mtext><mrow><mrow><mo>(</mo><mrow><mtext>Kg</mtext><mo>⋅</mo><mtext>K</mtext></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ］ 1 1 238+0.159 T [ 19 19 ] 1 1 <math id="M19"><mi>ρ</mi></math> ［ <math id="M20"><mrow><mfrac><mrow><mtext>Kg</mtext></mrow><mrow><msup><mtext>m</mtext><mn>3</mn></msup></mrow></mfrac></mrow></math> ］ 1 1 6650-0.286 T [ 19 19 ] 1 1 E (Pa) 1 1 9.21×10 10 -4.05×10 7 × T [ 21 21 ] 1 1 <math id="M21"><mi>ν</mi></math>   1 1 0.37 1 1 <math id="M22"><mi>α</mi></math> ［ <math id="M23"><mrow><mfrac><mn>1</mn><mtext>K</mtext></mfrac></mrow></math> ］ 1 1 (5.22+1.82×10 -3 T )×10 -6 [ 19 19 ] 1 1 (U, Th) O 2 1 1 K ［ <math id="M24"><mrow><mfrac><mtext>W</mtext><mrow><mrow><mo>(</mo><mrow><mtext>m</mtext><mo>⋅</mo><mtext>K</mtext></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ］ 1 1 14.242-0.022 T +1.764×10 -5 T 2 -6.380×10 -9 T 3 +8.038×10 -13 T 4 [ 6 6 ] 1 1 Cp ［ <math id="M25"><mrow><mfrac><mtext>J</mtext><mrow><mrow><mo>(</mo><mrow><mtext>mole</mtext><mo>.</mo><mtext>K</mtext></mrow><mo>)</mo></mrow></mrow></mfrac></mrow></math> ］ 1 1 239.9+8.512×10 -5 T -5.754×10 -8 T 2 +1.528×10 -11 T 3 [ 22 22 ] 1 1 <math id="M26"><mi>ρ</mi></math> ［ <math id="M27"><mrow><mfrac><mrow><mtext>Kg</mtext></mrow><mrow><msup><mtext>m</mtext><mn>3</mn></msup></mrow></mfrac></mrow></math> ］ 1 1 9326-0.0004 T +2.54×10 -7 T 2 -7.897×10 -11 T 3 [ 22 22 ] 1 1 E ［Pa］ 1 1 259.87×10 9 ×(1- P 2 )[ 6 6 ] P is the porosity 1 1 <math id="M28"><mi>ν</mi></math>   1 1 0.36 1 1 <math id="M29"><mi>α</mi></math> ［ <math id="M30"><mrow><mfrac><mn>1</mn><mtext>K</mtext></mfrac></mrow></math> ］ 1 1 <math id="M31"><mrow><mn>5.416</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>+</mo><mn>3.747</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><mi>T</mi><mo>+</mo><mn>3.0107</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup><msup><mi>T</mi><mn>2</mn></msup><mo>−</mo><mn>1.2212</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>15</mn></mrow></msup><msup><mi>T</mi><mn>3</mn></msup><mo>+</mo><mo>+</mo><mn>4.181</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup><msup><mi>T</mi><mn>4</mn></msup></mrow></math> [ 14 14 ] 2 1 Water (compressed liquid) and Helium (gas) 2 1 Their thermophysical properties exist in the material library of COMSOL-Multiphysics Results and discussion 1 The TH and solid structure performances were investigated to provide an integrated study on the effectiveness of using ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 as nuclear fuels in the PWR. Performances in TH and solid structures have been investigated at the HFP near the BOC. This state is characterized by a higher PPF relative to the PPF value during the rest of the fuel cycle. This is true because the PPF decreases as the fuel burn-up increases. The TH and solid structure performances of ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 , without burnable absorbers, will be discussed and compared with UO 2 in the following section. Comparing thorium-based fuel with UO 2 without a burnable absorber. 2 The TH and solid structure performances of ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 were investigated and compared with those of UO 2 . To study the TH and solid structure of the proposed fuel types, it is important to analyze the radial and axial power distributions through the FA. The power distribution was determined using the MCNPX code. Figure 2 Figure 2 presents the radial and axial PPF distributions of the investigated fuel types, with the hot channels where the power is peaking marked by orange cells. The total PPF is calculated from the axial and radial PPFs using Eq.(1). <math display="block" id="M32"><mrow><mtext>Total PPF = Radial PPF</mtext><mo>×</mo><mtext>Axial PPF</mtext><mo>×</mo><mtext>channel factor</mtext></mrow></math> [23]. Table 4 Table 4 lists the radial, axial, and total PPF for the investigated fuel types. It is observed that the total PPF in the case of ( 232 Th, 233 U) O 2 is smaller than that of the other fuel materials studied. This is because the infinite multiplication factor ( K inf ) at the HFP and the beginning of the fuel cycle length for ( 232 Th, 233 U) O 2 is greater than that of the other investigated fuel assemblies [ 3 3 ]. The normalization factor used in the multiplier card in the tallies (FM) is inversely proportional to the K inf for the same thermal power. Therefore, to produce almost the same thermal power from the three investigated fuel assemblies, the normalization factor for both the flux and power for ( 232 Th, 233 U) O 2 is smaller than that of the other fuel materials studied. 1 1 FA 1 1 FA with UO 2 1 1 FA with ( 232 Th, 235 U)O 2 1 1 FA with ( 232 Th, 233 U)O 2 1 1 Radial PPF 1 1 1.140 1 1 1.159 1 1 1.113 1 1 Axial PPF 1 1 1.650 1 1 1.625 1 1 1.550 1 1 Total PPF 1 1 1.692 1 1 1.695 1 1 1.552 Thermal-hydraulic performance 3 The subchannel model based on the CFD technique was used to solve the equations of the coupled system (partial differential heat generation equation for heat transfer and Navier-Stokes equation for fluid dynamics). The rod-centered subchannel model is discussed in detail in our previously published work [ 18 18 ]. The primary goal of the TH analysis was to obtain the DNBR distribution and the temperature distribution of the coolant, clad, and fuel. Figure 3 Figure 3 presents the temperature distribution of the coolant, cladding, and fuel materials, where the maximum fuel temperatures for the examined FAs of UO 2 , ( 232 Th, 235 U)O 2 , and ( 232 Th, 233 U)O 2 are 1565.21 K, 1497.56 K, and 1403.49 K, respectively. The safety limits for the fuel temperatures are less than 2873 K for UO 2 and 3500 K for (U, Th) O 2 , which ensures safe operation and the impossibility of fuel meltdown at the BOC. For the maximum clad inner surface temperature, the UO 2 FA had a maximum temperature of 611.859 K, while for the thorium-based fuels, the maximum temperatures were 610.29 K for ( 232 Th, 235 U)O 2 and 606.18 K for ( 232 Th, 233 U)O 2 . Additionally, the maximum clad temperatures indicate that the clad material meltdown is impossible because the maximum clad temperatures are less than 2123 K, the melting point of zircalloy-4. Furthermore, these temperatures ensure the impossibility of the pellet cladding chemical interactions (PCCI) because they are less than 1135 K. The EPRI-1 correlation was utilized to determine the critical heat flux (CHF), which was divided by the actual heat flux to calculate the DNBR. The DNBR was then studied to explain how far the coolant is from the nucleate boiling hazards by comparing the minimum DNBR with the PWR's safety margin of 1.75. The minimum DNBR values were 1.767, 1.765, and 1.8615 for UO 2 , ( 232 Th, 235 U)O 2 , and ( 232 Th, 233 U)O 2 , respectively, which emphasizes that the formulation of nucleate boiling is impossible. It can be noticed that the temperature distributions of the investigated fuel materials are similar. This is primarily because the values of thermal conductivity for the UO 2 and the two suggested thorium-based fuels are almost equal, as shown in Table 3 Table 3 . However, the thorium-based fuels show a safe performance relative to that of UO 2 because of their higher melting points compared to those of the traditional fuel. There are various types of temperature changes with radius within the radial temperature distribution, where it is parabolic (1/ r 2 ) across the fuel materials. Furthermore, in both the He-gap and clad materials, the temperature changes exponentially (ln(1/ r )). Finally, in the coolant material, the temperature changes with 1/ r . Figure 4 Figure 4 presents the distributions of the temperature along the channels that have the maximum PPF inside the fuel types under examination. Solid structure performance 3 In this section, the primary solid structure parameters (von Mises stress and the displacement of the outer fuel surface) were simulated. The von Mises stress is the total stress that affects the materials and is caused by either thermal or pressure loads. The thermal loads are due to the fission energy that is transferred to the coolant through the fuel and clad materials, which causes thermal expansion. The pressure loads were caused by the coolant pressure. If the von Mises stress is larger than the yield stress, the fuel material transfers from the elastic zone to the plastic or ductile zone. Therefore, for safe operation, the von Mises stress should not exceed the yield stress. The possibility of PCCI can be determined from the displacement of the fuel outer surface. The main causes of PCCI are the temperature of the clad materials reaching 1135, and the surfaces of both fuel and clad materials coming into contact. Under these conditions, the uranium atoms interact chemically with the zirconium atoms to form PCCI. Another type of interaction between the fuel and clad materials is called pellet clad mechanical interaction (PCMI). This type of interaction occurs when the outer surface of the fuel pellets expands thermally to reach the surface of the clad materials, resulting in excessive compression stress on the clad material, or where the clad exerts excess compression stress on the fuel material owing to its thermal expansion. Figure 5 Figure 5 shows that the highest von Mises pressures occurring on the investigated FAs of UO 2 , ( 232 Th, 235 U)O 2 , and ( 232 Th, 233 U)O 2 were 144.42, 111.06, and 103.08 MPa, respectively. The displacements of the fuel’s outer surface for the examined FAs of UO 2 , ( 232 Th, 235 U)O 2 , and ( 232 Th, 233 U)O 2 were 0.145, 0.098, and 0.089 mm, respectively. Although the displacements of the fuel’s outer surface for the examined fuel materials were greater than the thickness of the He-gap, the occurrence of the PCCI is impossible because the maximum clad temperatures in the aforementioned fuel materials were less than 1135 K. The obtained solid structure results show a remarkable superiority of the two thorium-based fuel over the traditional UO 2 fuel material: the thermal expansion coefficient for the thorium-based fuel is lower than that for the traditional fuel material UO 2 , which reduces the thermal stress occurring on the fuel materials and decreases the displacement of the fuel’s outer surface. Because of the excess reactivity at the BOC that occurred in the investigated FAs of UO 2 , ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 , it is important to use BAs to reduce this excess reactivity. Therefore, two BAs are investigated in the following section to distinguish which is more suitable from the TH and solid structure viewpoints. Determination of the most suitable IFBA 2 The main goal of utilizing the BA is to suppress the excess reactivity at the BOC. This section aims to determine the most suitable integral fuel burnable absorber (IFBA) material to be applied to the investigated fuel types in an attempt to enhance their performance in both TH and solid structures, in addition to achieving suitable reactivity management. Both Er 2 O 3 and Gd 2 O 3 at a concentration of 2% were mixed with UO 2 . The IFBA rods are marked in this work by the green cells in the FA. As shown in Fig. 6 Fig. 6 , the IFBAs were distributed near the guide tubes (coolant channels), where they occupied positions near the regions with the highest probability of neutron moderation, the highest probability of fission reactions, and hence the highest excess reactivity. The main goal of this distribution is to reduce the excess reactivity in this region and achieve fine-tuning of the power distribution across the FA. This is what happened after the use of (UO 2 +Er 2 O 3 ), where the total PPF decreased from 1.692 for UO 2 (without BAs) to 1.571 and the power distribution became flatter. In contrast, after the use of (UO 2 +Gd 2 O 3 ), the total PPF increased from 1.692 to 2.116. This is due to the large thermal neutron absorption cross-section (49000 barn) [ 24 24 ]. The three examined FAs were designed to produce nearly the same average thermal power. Therefore, the significant decrease in the power values of the IFBA rods in the case of (UO 2 +Er 2 O 3 ) was compensated by increasing the power values at the periphery of the FA. Table 5 Table 5 presents the maximum PPF in both the axial and radial directions and the total PPF for UO 2 with and without IFBAs. The total PPF in the case of UO 2 without IFBAs was 1.692. This value increases to 2.116 when Gd 2 O 3 is used. The opposite occurred after applying Er 2 O 3 , where the total PPF was reduced to 1.571. Therefore, the use of Er 2 O 3 not only reduces excess reactivity at the BOC, as proved in the first annex of this paper [ 3 3 ], but also decreases the total PPF and fine-tunes the power density distribution, which enhances the TH and solid structure performance. 1 1 Assembly 1 1 FA with (UO 2 +Gd 2 O 3 ) 1 1 FA with (UO 2 +Er 2 O 3 ) 1 1 Max radial PPF 1 1 1.238 1 1 1.125 1 1 Max axial PPF 1 1 1.900 1 1 1.552 1 1 Total PPF 1 1 2.116 1 1 1.571 Thermal-hydraulic performance 3 Figure 7 Figure 7 presents the results of the main TH parameters, where the maximum fuel temperatures for assemblies fueled with UO 2 , (UO 2 +Er 2 O 3 ), and (UO 2 +Gd 2 O 3 ) were 1646.67 K, 1585.64 K, and 1760.87 K, respectively. The maximum clad temperatures for the three investigated FAs of UO 2 , (UO 2 +Er 2 O 3 ), and (UO 2 +Gd 2 O 3 ) were 629.46 K, 623.77 K, and 643.25 K, respectively. The MDNBR values for the FAs of UO 2 , (UO 2 +Er 2 O 3 ), and (UO 2 +Gd 2 O 3 ) were 1.767, 1.847, and 1.530, respectively. In the case of using Gd 2 O 3 , the MDNBR value is lower than 1.75, which is the safety limit for the MDNBR according to the EPRI-1 correlation. Figure 8 Figure 8 displays the temperature distributions in 3D, where the temperature is maximum at the center of the fuel rod and decreases in the direction of the coolant. The results of the TH parameters indicate that the use of Er 2 O 3 decreases the total PPF, which reduces the maximum fuel and clad temperatures and increases the DNBR safety margin. Therefore, the use of Er 2 O 3 led to a more significant improvement in the thermal hydraulic performance than using Gd 2 O 3 . Solid structure performance 3 Figure 9 Figure 9 illustrates the variation in the main solid structure parameters (the von Mises stress operating on the fuel material and the displacement of the fuel outer surface) along the axial direction. The greatest von Mises stresses operating on the fuel materials of UO 2 , (UO 2 +Er 2 O 3 ), and (UO 2 +Gd 2 O 3 ) are 144.42, 135.70, and 158.76 MPa, respectively. Additionally, the maximum displacement of the fuel’s outer surface for the FAs of UO 2 , (UO 2 +Er 2 O 3 ), and (UO 2 +Gd 2 O 3 ) was 0.145, 0.130, and 0.172 mm. The solid structure results indicate the safe operation of the three investigated FAs because the maximum von Mises stress acting on the fuel materials was less than the yield stress of UO 2 . Furthermore, although the displacement of the fuel outer surface is greater than the thickness of the He-gap, PCCI will not occur because the maximum clad temperature in the three investigated FAs is smaller than the safety limit of 1135 K. Er 2 O 3 provided the best solid structure performance compared to UO 2 and the suggested FA (UO 2 +Gd 2 O 3 ). The results of the TH and solid structure parameters confirmed our findings from neutronic calculations, in which Er 2 O 3 gave the best performance and now provided the best and safest TH and solid structure performances relative to Gd 2 O 3 in the case of UO 2 . Therefore, Er 2 O 3 is applied to the investigated thorium-based fuel types in the following section. Effect of Er 2 O 3 on thorium-based fuel types 2 After investigating the TH and solid structure performances of the traditional FA with Er 2 O 3 and Gd 2 O 3 , the former proved to be the best IFBA for application to thorium-based fuels. Figure 10 Figure 10 presents the distribution of the radial and axial PPFs for the examined FAs (UO 2 +Er 2 O 3 , ( 232 Th, 235 U) O 2 + Er 2 O 3 , and ( 232 Th, 233 U) O 2 +Er 2 O 3 ). As shown in Table 6 Table 6 , the use of Er 2 O 3 reduces the total PPF for ( 232 Th, 235 U) O 2 from 1.695 to 1.663 and reduces the total PPF for ( 232 Th, 233 U) O 2 from 1.552 to 1.469. This reduction in the total PPF reflects the effective role of Er 2 O 3 in enhancing the neutronic performance, as discussed in the first annex of this work, and the performance of the TH and solid structure. The main objective of this section is to reduce the maximum fuel and cladding temperatures and increase the value of MDNBR by applying Er 2 O 3 to the two thorium-based fuel types and the standard fuel material. 1 1 Assembly 1 1 FA with ( 232 Th, 235 U) O 2 +Er 2 O 3 1 1 FA with ( 232 Th, 233 U) O 2 +Er 2 O 3 1 1 Max radial PPF 1 1 1.155 1 1 1.096 1 1 Max axial PPF 1 1 1.600 1 1 1.490 1 1 Total PPF 1 1 1.663 1 1 1.469 Thermal-hydraulic performance 3 In this section, the gain in TH performance after applying Er 2 O 3 to the investigated thorium-based FAs of UO 2 , ( 232 Th, 235 U)O 2 +Er 2 O 3 , and ( 232 Th, 233 U)O 2 +Er 2 O 3 is illustrated. As shown in Fig. 11 Fig. 11 , for UO 2 , the maximum fuel temperature decreased from 1565.21 K to 1481.99 K, the maximum clad temperature decreased from 622.07 K to 615.95 K, and the MDNBR increased from 1.767 to 1.847. For ( 232 Th, 235 U) O 2 , the maximum fuel, clad temperatures, and the MDNBR are 1497.56 K, 620.20 K, and 1.765 respectively. These values are reduced to 1474.70 K, 619.01 K, and 1.787, respectively, after applying Er 2 O 3 . For ( 232 Th, 233 U)O 2 , the maximum fuel temperature decreased from 1403.49 K to 1352.20 K, the maximum clad temperature decreased from 615.26 K to 612.51 K, and the MDNBR increased from 1.8615 to 1.919. Figure 12 Figure 12 presents the 3D temperature distributions for the three examined FAs (UO 2 , ( 232 Th, 235 U) O 2 +Er 2 O 3 , and ( 232 Th, 233 U)O 2 +Er 2 O 3 ). Solid structure performance 3 The gain in solid structure performance after applying Er 2 O 3 to the investigated FAs (UO 2 +Er 2 O 3 , ( 232 Th, 235 U)O 2 +Er 2 O 3 , and ( 232 Th, 233 U)O 2 +Er 2 O 3 ) is illustrated in Fig. 13 Fig. 13 . For UO 2 , the von Mises stress and the displacement of the fuel’s outer surface decreased after applying Er 2 O 3 from 144.42 MPa and 0.145 mm to 135.70 MPa and 0.130 mm respectively. For ( 232 Th, 235 U)O 2 , the von Mises stress operating on the fuel material decreased from 111.06 to 109.12 MPa and the fuel outer surface displacement decreased from 0.098 to 0.095 mm. Finally, the greatest von Mises stress, acting on the ( 232 Th, 233 U)O 2 , decreased from 103.08 to 98.74 MPa and the displacement of its fuel’s outer surface decreased from 0.089 to 0.084 mm after applying Er 2 O 3 . Table 7 Table 7 presents a summary of the results obtained from neutronic, TH, and solid structure analyses. This illustrates the effectiveness of each type of fuel and proves that the thorium-based fuels are a very good alternative to UO 2 . There are several reasons for the difference between the results of the TH and solid structure parameters of the investigated FAs, firstly, the difference in the values of the various thermophysical properties that are used in the solution of the heat generation partial differential equation such as (thermal conductivity ( K ), heat capacity at constant pressure ( Cp ), density ( <math id="M33"><mi>ρ</mi></math> ), and heat source (total PPF)), as illustrated in Table 3 Table 3 . Additionally, the difference in the solid structure properties of the investigated FAs is based on the variation in Young's modulus ( E ), Poisson’s ratio ( <math id="M34"><mi>ν</mi></math> ), and thermal expansion coefficient ( <math id="M35"><mi>α</mi></math> ). The dominant factors that strongly affect the TH and solid structure results are the heat source value (total PPF) and the thermal expansion coefficient, assuming that the remaining factors are almost the same for all the investigated fuel materials. The main turbulence properties are assumed to be the same for all investigated fuel assemblies, such as the coolant mass flow rate of 16720 kg/s, coolant inlet pressure of 15.41 MPa, turbulence model ( K - <math id="M36"><mi>ε</mi></math> ), and wall condition (no-slip). 1 1 Physics 1 1 Parameters 1 1 UO 2 + Er 2 O 3 ‎ 1 1 ( 232 Th, 235 U) O 2 + 2% Er 2 O 3 ) ‎ 1 1 ( 232 Th, 235 U) O 2 + 2% Er 2 O 3 ) ‎ 1 1 Safety limits 1 1 Neutronic 1 1 Max radial PPF 1 1 1.125 1 1 1.155 1 1 1.096 1 1 - 1 1   1 1 Max axial PPF 1 1 1.552 1 1 1.600 1 1 1.490 1 1 - 1 1   1 1 Total PPF 1 1 1.571 1 1 1.663 1 1 1.469 1 1   1 1 Actinide inventory 1 1 Top 1 1 Medium 1 1 Least 1 1 - 1 1   1 1 Non-actinide inventory 1 1 Top 1 1 Medium 1 1 Least 1 1 - 1 1 TH 1 1 Max fuel temperature (K) 1 1 1481.99 1 1 1474.70 1 1 1352.20 1 1 For UO 2 , it mustn`t be greater than solidus point 2873 K <math id="M37"><mrow><mo> </mo><mtext>in LWRs </mtext></mrow></math> [ 13 13 ] 1 1   1 1   1 1   1 1   1 1   1 1 For (U, Th) O 2 , it mustn`t be greater than the melting point of 3500 K 1 1   1 1 Max clad temperature (K) 1 1 615.95 1 1 619.01 1 1 612.51 1 1 It should be less than melting point 2123 <math id="M38"><mrow><mi>K</mi><mo> </mo></mrow></math> [ 13 13 ] 1 1   1 1 MDNBR 1 1 1.847 1 1 1.787 1 1 1.919 1 1 It should be greater than 1.75 [ 13 13 ] 1 1 Solid structure 1 1 Max von-Mises stress (MPa) 1 1 135.70 1 1 109.12 1 1 98.74 1 1 For UO 2 , it must be less than 170 MPa [ 20 20 ] 1 1   1 1   1 1   1 1   1 1   1 1 For ThO 2 , it must be less than 175 MPa [ 25 25 , 26 26 ] 1 1   1 1 Max displacement of the fuel outer surface (mm) 1 1 0.130 1 1 0.095 1 1 0.084 1 1 It should not be greater than the thickness of the He-gap of 0.08 mm [ 17 17 ] Conclusion 1 From the neutronic perspective, the results show that the use of ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 reduced the actinides and non-actinides nuclide inventory, which decreased the radioactivity of the spent fuel during the storage step. From the TH perspective, the high melting point of the thorium ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 is one of its essential thermophysical properties. Additionally, the maximum fuel and cladding temperatures for the (Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 are lower than those for the standard fuel ‎(UO 2 ), while the MDNBR values of ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 were greater than those of UO 2 . From the solid structure perspective, owing to the superiority of the solid structure properties of ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 over that of UO 2 , the maximum von Mises stress operating on ‎the fuel and cladding materials and the displacement of the fuel’s outer surface are less than that of UO 2 . Thus, it can be concluded from the neutronic, TH, and solid structure perspectives that ( 232 Th, 235 U)O 2 and ( 232 Th, 233 U)O 2 are good alternatives for the traditional fuel material UO 2 . References L.G. G. Fonseca , M. Hedberg , L. 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Material preparation, data collection and analysis were performed by Mohamed Y.M. Mohsen, Mohamed A.E. Abdel-Rahman and A. Abdelghafar Galahom. The first draft of the manuscript was written by Mohamed Y.M. Mohsen and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. 10.1007/s41365-021-00981-0 2021-09-28 2021-11-02 2021-11-06 2021-12-10 2022-01-14 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2021 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-021-00981-0 http://dx.doi.org/10.1007/s41365-021-00981-0 . 2021 Nuclear Science and Techniques 12 32