Neutronic analysis of silicon carbide cladding accident-tolerant fuel assemblies in pressurized water reactors

Neutronic analysis of silicon carbide cladding accident-tolerant fuel assemblies in pressurized water reactors 1 first-author 1 corresp Corresponding author: epjjcai@scut.edu.cn Corresponding author: epjjcai@scut.edu.cn epjjcai@scut.edu.cn School of Electric Power, South China University of Technology, Guangdong 510640, China School of Electric Power, South China University of Technology, Guangdong 510640, China In resonance with the Fukushima Daiichi Nuclear Power Plant accident lesson, novel fuel design to enhance safety regarding severe accident scenarios has become increasingly appreciated in the nuclear power industry. This research focuses on analysis of the neutronic properties of a silicon carbide (SiC) cladding fuel assembly, which provides a greater safety margin as a type of accident-tolerant fuel for pressurized water reactors. The general physical performance of SiC cladding is explored to ascertain its neutronic performance. The neutron spectrum, accumulation of 239 Pu, physical characteristics, temperature reactivity coefficient, and power distribution are analyzed. Furthermore, the influences of a burnable poison rod and enrichment are explored. SiC cladding assemblies show a softer neutron spectrum and flatter power distribution then conventional Zr alloy cladding fuel assemblies. Lower-enrichment fuel is required when SiC cladding is adopted. However, the positive reactivity coefficient associated with the SiC material remains to be offset. The results reveal that SiC cladding assemblies show broad agreement with the neutronic performance of conventional Zr alloy cladding fuel. In the meantime, its unique physical characteristics can lead to improved safety and economy. Accident-tolerant fuels Silicon carbide cladding Neutronic characteristics Pressurized water reactor 1. Introduction 1 When beyond design basis accident (BDBA) scenarios occur, such as the Fukushima Daiichi Nuclear Power Plant accident, with loss of active cooling, conventional Zr alloy cladding fuel in pressurized water reactors (PWRs) is expected to provide a safety margin. Many institutions have made efforts to design accident-tolerance fuel (ATF) to satisfy these high safety demands [ 1 1 , 2 2 ] . Many concepts, which have primarily focused on improving fuel pellet characteristics, applying external coating, and replacing the conventional cladding with alternative materials, have been evaluated with respect to ATF. Neutronic evaluation is crucial for assessing the safety and economy of ATF. Represented by Oak Ridge National Laboratory, analysis of fully ceramic microencapsulated (FCM) fuel at the lattice-level and nodal full reactor simulation was carried out from the aspect of cycle length, temperature coefficient, and transient response, etc [ 3 3 , 4 4 ] . The neutronic feasibility of using a novel uranium mono nitride (UN) fuel in a light water reactor (LWR) has been verified [ 5 5 ] . Substitutive cladding and external coating material under normal operation conditions have also been evaluated. FeCrAl cladding design shows preferable characteristics, including a flattened axial temperature profile and delayed gap closure 6] . Neutronic parametric assessment has proceeded for alternative cladding material, such as austenitic type 310 (310SS), 304 stainless steels, silicon carbide (SiC), and advanced molybdenum alloy (TZM) [ 7 7 , 8 8 ] . Thermal and cold spray techniques have been adopted to coat a MAX phase (like Ti 3 AlC 2 ) on zirconium alloys cladding [ 9 9 ] and a TiAlN coating on ZIRLO fuel cladding [ 10 10 ] . Simulation of transient accidents has been carried out to investigate the behavior of an ATF-loaded reactor [ 11 11 , 12 12 ] . SiC cladding is included in the list of ATF concepts because of its extraordinary oxidation resistance capacity, chemical inertia, and other relevant strengths [ 13 13 , 14 14 ] . Related research has been carried out at the Massachusetts Institute of Technology [ 15 15 , 16 16 ] . Critical nuclear reactivity experiments for SiC material have been implemented as a foundation for numerical simulation [ 17 17 ] . We also completed neutronic analyses of ATF assemblies with SiC cladding in pressurized water reactors and pressurized water reactor core loading with SiC cladding fuels. In this paper, we will provide a detailed summary of the results of our research on the characteristics of SiC cladding ATF assemblies in PWRs from the viewpoint of neutronics. The remaining paper is organized as follows. Section 2 gives a description of the material compositions of the ATF assembly and some primary parameters for the neutron physical model. The results of the neutronic performance of the assemblies are addressed in Sect. 3. The conclusion is provided in Sect. 4. 2. Models and technical parameters 1 The open-source lattice calculation code "DRAGON" was employed for neutronic physics calculation. As a fully functional lattice cell code, it includes various integral transport equation solutions [ 18 18 ] . It is a full-scale lattice cell code made at the Institute of Nuclear Engineering of Polytechnique Montréal, Canada, with different algorithms to solve transport-diffusion equivalence, homogenizing group constants, and isotopic depletion calculations. We have used the code to successfully analyze the neutronics characteristics of SCWRs and PWRs [ 19 19 - 21 21 19-21 ] . Also, the DRAGON code has been used to analyze the neutronic properties of the CANDU-6 reactor [ 22 22 ] . In this paper, a collision probability algorithm was chosen for solving the neutron transport equation, and the generalized Stamm’ler method was used to consider the resonance self-shielding. 2.1 Rationale for using SiC 2 SiC has potential material characteristics advantages over zirconium alloy, among which are sufficient resistance to oxidation and creep, irradiation stability, attractive thermal endurance, and low thermal neutron capture cross-sections. SiC has excellent compatibility with UO 2 , moderators, and coolant under operation conditions. Even in accident scenarios, it would avoid hydrogen explosion. On the occasion of volumetric swelling saturation caused by irradiation, SiC remains highly resistant to a high fast flux [ 22 22 ] . Neutronic irradiation has a minimum effect on SiC, except for the thermal conductivity. Compared with Zr alloy, SiC has been shown to have a superior antioxidant ability [ 24 24 , 25 25 ] . 2.2 Physical design of assemblies 2 Figure 1 Figure 1 shows the typical 17×17 assembly layout without a burnable poison rod. The blue dots represent fuel cells, while the white ones correspond to guide tubes with flow coolant. The center white cell is deemed to be a guide tube for the process of calculation, even if it should be an instrumentation thimble in an actual reactor assembly. Considering the diagonal symmetry and reflection symmetry, one-eighth of the assembly is selected for simulation calculation. Table 1 Table 1 and Table 2 Table 2 summarize the steady-state parameters for the PWR design. 1 1 Assembly Parameter 1 1 SiC Clad Fuel 1 1 Zr alloy Clad Fuel 1 1 Fuel assembly rod array 1 1 17×17 1 1 17×17 1 1 Number of guide thimbles 1 1 24 1 1 24 1 1 Number of instrumentation thimbles 1 1 1 1 1 1 1 1 Pin-to-pin pitch (mm) 1 1 12.6 1 1 12.6 1 1 Number of fuel rods per assembly 1 1 264 1 1 264 1 1 Specific power (Kw/Kg) 1 1 39.98 1 1 39.98 1 1 Gap conductance (W/m 2. K) 1 1 7500 1 1 Gap thickness (cm) 1 1 0.0103 1 1 Cladding thickness (cm) 1 1 0.057 1 1 Coolant velocity (m/s) 1 1 5.5 2.3 Cladding models 2 Typical zirconium (Zr alloy) cladding is regarded as a reference case, and two types of SiC cladding assemblies are proposed for contrast. Simply, case one consists of SiC cladding with UO 2 fuel; case two is SiC cladding with UO 2 /BeO fuel. Because of the low thermal conductivity of irradiated SiC material (one-third the thermal conductivity of irradiated zirconium alloy), case two explores the performance of a mixture of UO 2 /BeO fuel. As a high-thermal conductivity material, BeO is used to keep SiC cladding fuel at a similar thermal conductivity as Zr alloy cladding fuel. Tables 3 Tables 3 , 4 4 , 5 5 show the data in detail. The enrichment setting in Table 3 Table 3 is used to maintain a uniform 235 U load. Equations for enrichment calculation are shown as follows. 1 1   1 1 Zr alloy cladding 1 1 SiC cladding 1 1 SiC cladding with BeO 1 1 Cladding thickness (cm) 1 1 0.057 1 1 0.057 1 1 0.089 1 1 Enrichment (%) 1 1 3.393 1 1 3.393 1 1 3.749 1 1 Gap Thickness (cm) 1 1 0.0103 1 1 0.0103 1 1 0.0103 1 1 Cladding Density (g/cm 3 ) 1 1 6.55 1 1 2.58 1 1 2.58 1 1 Microscopic thermal neutron absorption cross-section (barns) 1 1 0.20 1 1 0.086 1 1 0.086 2 1 Material 1 1 Fe 1 1 Cr 1 1 Zr alloy 1 1 Sn 1 1 Si 1 1 C 2 1 wt% 1 1 1 1 Zircaloy 1 1 0.15 1 1 0.1 1 1 98.26 1 1 1.49 1 1   1 1   1 1 1 1 SiC 1 1   1 1   1 1   1 1   1 1 70.08 1 1 29.92 2 1 at% 1 1 1 1 Zircaloy 1 1 0.24 1 1 0.17 1 1 98.43 1 1 1.15 1 1 1 1 SiC 1 1   1 1   1 1   1 1   1 1 50 1 1 50 1 1 BeO at% 1 1 9.51% 1 1 Density of BeO (g/cm 3 ) 1 1 2.85 1 1 Thermal conductivity for 100% UO 2 1 1 257.99×T -0.627 1 1 Thermal conductivity for 90%UO 2 +10%BeO 1 1 497.6×T -0.679 1 1 Thermal conductivity for 91%UO 2 +9%BeO 1 1 443.32×T -0.67 <math display="block" id="M1"><mrow><msub><mi>c</mi><mn>5</mn></msub><mo>=</mo><msup><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>0.9874</mn><mo>×</mo><mo stretchy="false">(</mo><mfrac><mn>1</mn><mi>ε</mi></mfrac><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> <math display="block" id="M2"><mrow><msub><mi>M</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub><mo>=</mo><msub><mi>M</mi><mrow><msub><mtext>U</mtext><mrow><mtext>235</mtext></mrow></msub></mrow></msub><mo>×</mo><msub><mi>c</mi><mn>5</mn></msub><mo>+</mo><msub><mi>M</mi><mrow><msub><mtext>U</mtext><mrow><mtext>238</mtext></mrow></msub></mrow></msub><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>c</mi><mn>5</mn></msub><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mo>×</mo><msub><mi>M</mi><mtext>O</mtext></msub></mrow></math> <math display="block" id="M3"><mrow><msub><mi>ρ</mi><mtext>m</mtext></msub><mo>=</mo><mi>v</mi><msub><mi>%</mi><mrow><mtext>BeO</mtext></mrow></msub><mo>×</mo><msub><mi>ρ</mi><mrow><mtext>BeO</mtext></mrow></msub><mo>+</mo><mi>v</mi><msub><mi>%</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub><mo>×</mo><msub><mi>ρ</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub></mrow></math> <math display="block" id="M4"><mrow><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><msub><mi>%</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub><mo>=</mo><mfrac><mrow><mi>v</mi><msub><mi>%</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub><mo>×</mo><msub><mi>ρ</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub></mrow><mrow><msub><mi>ρ</mi><mtext>m</mtext></msub></mrow></mfrac></mrow></math> <math display="block" id="M5"><mrow><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><msub><mi>%</mi><mtext>U</mtext></msub><mo>=</mo><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><msub><mi>%</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub><mo>×</mo><mfrac><mrow><msub><mi>M</mi><mtext>U</mtext></msub></mrow><mrow><msub><mi>M</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub></mrow></mfrac></mrow></math> <math display="block" id="M6"><mrow><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><msub><mi>%</mi><mrow><mtext>U</mtext><mrow><mtext>235</mtext></mrow></mrow></msub><mo>=</mo><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><msub><mi>%</mi><mtext>U</mtext></msub><mo>×</mo><mi>ε</mi></mrow></math> where <math id="M7"><mrow><msub><mi>c</mi><mn>5</mn></msub></mrow></math> is the number of <math id="M8"><mrow><msup><mrow/><mrow><mtext>235</mtext></mrow></msup><mtext>U</mtext></mrow></math> nuclides divided by the sum of <math id="M9"><mrow><msup><mrow/><mrow><mtext>235</mtext></mrow></msup><mtext>U</mtext></mrow></math> and <math id="M10"><mrow><msup><mrow/><mrow><mtext>238</mtext></mrow></msup><mtext>U</mtext></mrow></math> nuclides; <math id="M11"><mi>ε</mi></math> denotes enrichment of a fuel pellet; <math id="M12"><mrow><mi>w</mi><msub><mi>t</mi><mtext>T</mtext></msub><mi>%</mi></mrow></math> is set as the volume ratio; and <math id="M13"><mrow><msub><mi>ρ</mi><mrow><msub><mrow><mtext>UO</mtext></mrow><mtext>2</mtext></msub></mrow></msub></mrow></math> is 10.42 g/cm 3 . The setting of 0.089 cm for the thickness of UO 2 /BeO cladding results from manufacturing technique used for SiC material in practical industrial production. Six groups of temperature perturbations are adopted for moderator and fuel temperature coefficient calculation. Table 6 Table 6 lists these temperature perturbations. 2 1 Coolant temperature perturbation (K) 2 1 Fuel temperature perturbation (K) 1 1 Case 1 1 1 Reference and Case 2 1 1 Case 1 1 1 Reference and Case 2 1 1 560 1 1 560 1 1 1235 1 1 1187 1 1 570 1 1 570 1 1 1285 1 1 1237 1 1 580 1 1 580 1 1 1335 1 1 1287 1 1 590 1 1 590 1 1 1385 1 1 1337 1 1 600 1 1 600 1 1 1435 1 1 1387 1 1 610 1 1 610 1 1 1485 1 1 1437 3. Results and Analysis 1 Neutronic parameters were analyzed for SiC cladding with the purpose of evaluating the assembly characteristics. What follows in this section includes the thermal neutron spectrum, characteristic factors (coefficient), influence of burnable poison rod power, and flux and power distributions. 3.1 Neutron spectrum and 239 Pu analysis 2 Figures 2 Figures 2 - 3 3 represent the neutron spectrum curves corresponding to the three cases. The computational domain for the neutron flux was the perpendicular plane in the axial direction of the fuel rod. Figure 2 Figure 2 shows the neutron spectrum in the range of 0-4 eV at the beginning of cycle (BOC). Zooming in on part of Fig. 2 Fig. 2 (in the range of 0.1 eV-0.62 eV), Fig. 2 Fig. 2 clearly shows that Zr alloy case has a harder thermal neutron spectrum than the SiC case and SiC/BeO case. Similar to Fig. 2 Fig. 2 , Fig. 3 Fig. 3 presents the neutron spectrum at the end of cycle (EOC). Compared with Fig. 2 Fig. 2 , there is little flux disparity (in the range of 0.1 eV) observed in Fig. 3 Fig. 3 . In the meantime, the thermal neutron flux decreases at 0.1 eV. This is due to the depletion of the 235 U and accumulation of absorbent fission products. This effect becomes more prominent in the SiC case and SiC/BeO case because of their high thermal neutron peak at BOC. Lower neutron capture cross-sections for the SiC material contribute to better thermal neutron spectrum performance, and a softer thermal neutron spectrum provides an economic advantage for a thermal-neutron reactor. In addition to the neutron spectrum study, the amount of 239 Pu is displayed in Fig. 4 Fig. 4 . The hardening thermal neutron spectrum in the Zr alloy case results in higher accumulation of 239 Pu. 239 Pu has a significant influence on the reactivity. Therefore, it may contribute a slight reactive increase at EOC. 3.2 Characteristic factor results 2 Enrichment analysis was carried out by comparing infinite multiplication factors. Two kinds of fuel assemblies were involved for implementing enrichment analysis. Enrichment in the SiC case and initial Zr alloy case were 3.393%. Increasing enrichment stepwise by 0.5% in six other Zr alloy case groups, there are 7 groups of Zr alloy cases in total. Other parameters remain unchanged, in accordance with Table 3 Table 3 . Fig. 5 Fig. 5 shows that all curves have a similar tendency as a function of burnup. Detailed drawings are inserted in Fig. 5 Fig. 5 . In the beginning, the SiC case is quite close to that of Zr alloy (3.643%). The fluctuate part of the curve in this stage results from xenon poisoning. Because of the rapid drop for the SiC curve, its Kinf is close to that of Zr alloy (3.443%) in the end. Depending on the burnup level, the reduction value of enrichment is approximately 0.05% -0.25%. In the case where no power control is applied, a softer thermal neutron spectrum leads to more speedy consumption of 235 U in the SiC assembly. Furthermore, by inserting an amount of burnable poison rods in the assemblies, the impact of burnable poison control was analyzed, as discussed in the subsequent paragraph. Fig. 6 Fig. 6 shows the plot of Kinf when various numbers of burnable poison rods are inserted in assemblies. The results obviously demonstrate that as more burnable poison rods were inserted in the SiC cladding assembly, the Kinf value that appears at the early stage decreased. A quite similar trend is observed regarding the SiC case and Zr alloy case. This result demonstrates that conventional burnable poison rods maintain a favorable regulating effect on SiC cladding assemblies. Fig. 7 Fig. 7 shows the power peak factor (Ppf) for various assemblies. The SiC/BeO case has the highest power peak factor. Zr alloy cladding has a Ppf that is slightly higher than that of SiC cladding. All of the curves increase in the early stage. Because of the negative feedback associated with the fuel rod power, the value of Ppf decreases slowly at later stages. The curve for the SiC case is consistent with that for the Zr alloy case. This result means that the SiC case would cause few operational changes from the perspective of controlling power distribution. Additionally, Zr alloy case has a higher Ppf than SiC cladding as the burnup progresses. The performance of the SiC case reveals its ability to flatten the power distribution within the assemblies. The relatively poor performance in the SiC/BeO case may be caused by its thicker cladding and the addition of BeO. The relative power distribution at BOC in the SiC case assembly is presented in Fig. 8 Fig. 8 . All values have been normalized. Fig. 8 Fig. 8 clearly describes the relative power distribution in the assembly. It is easy to see that regions close to the water rod possess low power. Additionally, Fig. 9 Fig. 9 describes the relative power transformation between BOC and EOC. In contrast with the BOC power, the green parts in Fig. 9 Fig. 9 stand for areas where power decreases, and the orange parts correspond to areas where the power increases. In the process of burnup, the power in the exterior zone would increase while the power in the interior area decreases. This phenomenon is due to the faster depletion of 235 U inside the assembly than in the exterior assembly. 3.3 Radial profile analysis 2 Differences in the neutron absorption ability of cladding material would lead to radial differentiations in fuel pellets [ 26 26 , 27 27 ] . The radial flux distribution is explored in four areas by segmenting the inner UO 2 pellet into four equal concentric annulus. The innermost concentric annulus is called Part 1, and the others are called Parts 2, 3, and 4 in turn. Regions in Fig. 8 Fig. 8 that are surrounded by black bold squares with marked numbers are chosen for analysis (specific to the SiC assembly). Figure 10 Figure 10 describes the normalization flux in the four regions in the SiC cladding assembly fuel pellet. The four regions have a similar tendency overall. Nearby water rod regions have highest flux in Part 1. Others have the highest flux in Part 4. Part 2 in the marginal area (Region 1) has less flux value compared with the interior area (Region 4). This result shows that the layout of the water rod and boundary interference can affect the radial flux distribution in fuel pellets. Figures 11 Figures 11 - 12 12 show the relative fission power distribution in fuel pellets. From Figs. 11 Figs. 11 - 12 12 , similar trends among these three cases can be observed. Because of the spatial self-shielding that may prevent thermal neutrons from penetrating to the inner fuel pellet, the outer part of the fuel pellet possess higher fission power. Also, as burnup proceeds, spatial self-shielding leads to an increase in the plutonium produced in the outer fuel pellet. Accumulation of extra fission material makes the slope of the curves in Fig. 12 Fig. 12 steeper than those in Fig. 11 Fig. 11 . The Zr alloy case has smallest fission power at BOC and the largest at EOC. This is due to the higher thermal neutron capture cross-section in Zr alloy material, which is more likely to block thermal neutrons and slow down the outside moderator at BOC. Nevertheless, the harder neutron spectrum in the Zr alloy case results in the production of more plutonium in the outer fuel pellet. The additional fission material would increase the relative fission power at later stages. Unavoidably, compared with the Monte Carlo method, the accuracy of DRAGON may for radial power calculation may be lower, although a revised resonance self-shielding calculation modular and fine neutron energy groups in DRAGON may partially compensate for this. There has been some excellent research in this field using Monte Carlo methods [ 28 28 , 29 29 ] . 3.4 Moderator temperature coefficient analysis 2 Respectively, Fig. 13 Fig. 13 and Fig. 14 Fig. 14 describe the moderator and fuel temperature coefficients as a function of burnup. The moderator and fuel temperature coefficients appear in the following equation: <math display="block" id="M14"><mrow><mo>∂</mo><mtext>=</mtext><mfrac><mrow><mi>Δ</mi><mi>ρ</mi></mrow><mrow><mi>Δ</mi><mi>T</mi></mrow></mfrac></mrow></math> where <math id="M15"><mo>∂</mo></math> is the temperature coefficient, <math id="M16"><mrow><mi>Δ</mi><mi>ρ</mi></mrow></math> is the reactivity difference, and <math id="M17"><mrow><mi>Δ</mi><mi>T</mi></mrow></math> stands for temperature difference. As shown in Table 6 Table 6 , <math id="M18"><mrow><mi>Δ</mi><mi>T</mi></mrow></math> is equal to 10K for the moderator temperature coefficient (MTC) calculation, while it is 50K for the fuel temperature coefficient (FTC) calculation. Figure 13 Figure 13 reveals that three kinds of assemblies show negative MTC during the overall burnup period. There is no obvious difference in the early stage. In the intermediate stage, the SiC/BeO case has a more strongly negative coefficient than the other cases. Conversely, the SiC case has the weakest negative coefficient. The feedback coefficient in the SiC/BeO case becomes weaker at later stages. The Zr alloy case has a strongly negative coefficient. Because of the depletion of 235 U, which relatively enhances the 238 U resonance absorption, the MTC becomes more sensitive to changes in the moderator temperature and density. Nevertheless, accumulation of fission products at the later period leads to a less negative MTC value. Fig. 14 Fig. 14 shows the trend for the FTC. For the SiC case, there is a strongly negative feedback coefficient throughout the burnup progress. The Zr alloy case has the weakest value. The lower absolute value of FTC is a result of the influence of 239 Pu and 241 Pu and the contribution of the reduced resonance absorption. The fuel and moderator temperature coefficients are the two most important elements of the reactor feedback coefficient. Fig. 15 Fig. 15 combines these two temperature coefficients into one total feedback coefficient. For a short time in the early stage, the SiC case has the most strongly negative coefficient. The SiC/BeO case has strong feedback in middle of cycle (MOC). As burnup increases, the SiC and SiC/BeO cases have weaker negative feedback coefficients than the Zr alloy case. To briefly summarize the temperature feedback coefficient results, in a reasonable range, the SiC case has the weakest negative MTC and most strongly negative FTC. SiC and SiC/BeO cases have more strongly negative feedback coefficient in the early burnup stage. At later stages of burnup, the most strongly negative coefficient is observed in the Zr alloy case. The positive reactivity coefficient brought about by SiC cladding should be given more attention. 4. Conclusion 1 Neutron analysis with respect to SiC cladding fuel assemblies was implemented. Characteristic parameters, with the exception of power distribution at beginning of cycle and inner UO 2 pellet flux and fission power distribution, were compared with a Zr alloy cladding assembly. In addition, fuel enrichment and normalization power transformation in the assembly were discussed. SiC cladding fuel and SiC cladding with UO 2 /BeO fuel have quite similar neutronic performances. Neutron spectral analysis reveals that the SiC cladding fuel assembly has a softer thermal neutron spectrum than the Zr alloy cladding fuel assembly, which results in less 239 Pu accumulation in the SiC cladding assembly. The analytic results for the neutronic parameters demonstrate that the SiC cladding assemblies have the advantage of reducing the necessary fuel enrichment and a favorable, flattened distribution. The low neutron capture ability of SiC cladding assemblies is conducive to extending discharge burnup. A softer thermal neutron spectrum allows a larger fuel pin lattice space without an apparent reactivity penalty. The flux trend in four parts of the SiC cladding assembly reveals that the water rod and boundary interference would have an effect on the radial flux distribution. The influence of different kinds of cladding material on the fission power distribution in fuel pellets is limited. 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Science and Technology and Nuclear Installations , 2016 ,( 2016-2-17 ). 2016 , 1 - 8 (2016) . The, A Simple Formula for Local Burnup and Isotope Distributions Based on Approximately Constant Relative Reaction Rate 10.1007/s41365-019-0575-5 This work was supported by the National Natural Science Foundation of China (No. 11675057) and the Fundamental Research Funds for the Central Universities (No. 2017ZD100). 2018-03-03 2018-07-25 2018-09-13 2019-02-14 2019-03-01 2021-04-10 © 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. 2019 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/s41365-019-0575-5 http://dx.doi.org/10.1007/s41365-019-0575-5 . 2019 Nuclear Science and Techniques 03 30