Neutronic Analysis of SiC/SiC Sandwich Cladding Design in APR-1400 under Normal Operation Conditions

Abstract

Our aim is to study the neutronic behaviour of potential accident-tolerant fuel (ATF) claddings in a pressurised water reactor under normal operations. This work compares ATF silicon carbide composite (SiC/SiC) cladding to conventional ZIRLO^TM cladding in APR-1400. Additionally, a “sandwich” cladding design developed by the CEA is used for SiC/SiC. The design structure includes a liner in between two layers of the composite to ensure leak tightness. The two proposed liners are Niobium (Nb) and Tantalum (Ta). Serpent 2, a Monte Carlo reactor physics lattice code, is employed to model both cladding materials in APR-1400 at three different levels: pin cell, fuel assembly, and core. The criticality, neutron spectrum, actinide inventory, and power distribution as a function of burnup are investigated. The simulations show that SiC/SiC with the Nb liner displays a far superior performance than the Ta liner across all examined characteristics. Ta leads to a harder neutron spectrum and increased Pu-239 content throughout the cycle, while Nb presents negligible effects. In fact, SiC/SiC with the Nb liner performs very similarly to ZIRLO^TM at all model levels. The results indicate that, in terms of neutronics, the adoption of the SiC/SiC composite would entail little to no changes to current APR-1400 operations.

1. Introduction

The fuel-cladding system plays a critical role in nuclear power plants (NPPs) as the first level of defence against the release of radioactive substances. Uranium dioxide (UO₂) and zirconium (Zr) alloys have been employed as fuel and cladding materials, respectively, for over 60 years in light water reactors (LWRs). However, in 2011, the severe accident at the Fukushima Daiichi NPP revealed the inherent vulnerability of these materials. Particularly, in a loss-of-coolant accident scenario, the Zr cladding undergoes an exothermic oxidation with high-temperature steam. The oxidation heat, coupled with the inevitable decay heat, accelerate the rate of temperature increase in the core. The oxidation also produces large amounts of ignitable free hydrogen. Consequently, core meltdown and gas explosion could ensue, as witnessed at Fukushima. In response, the nuclear industry was driven to explore alternative fuel and cladding materials that would enhance the safety and reliability of NPPs. Thus, accident-tolerant fuels (ATFs) have been proposed [1,2].

One of the most promising long-term ATF cladding materials is ceramic-based silicon carbide (SiC) [3,4,5]. In comparison with Zr alloys, SiC is anticipated to deliver an overall improved performance in LWRs at both normal and accident conditions due to its higher resistance to oxidation, wear, and creep; higher melting and sublimation point; higher strength; lower neutron-induced activation; smaller thermal neutron absorption cross-section; chemical inertness with both the fuel and coolant; and longer lifetime expectancy at higher burnup. In general, irradiation poses minimum effects on SiC, with the exception of a measured reduction in its thermal conductivity and fracture toughness. Various ongoing research efforts are invested in exploring ways to overcome such limitations. More details can be found in the literature [6,7,8,9].

Much of the early research on monolithic ceramics is focused on the compensation of their brittle nature. One approach has been the production of composites that incorporate ceramic fibres reinforced in a ceramic matrix. The matrix provides load distribution across the composite structure to protect the fibres. Different fibre winding and braiding patterns have also been investigated to further improve the material strength. The description and evaluation of potential fibre techniques can be found in [9,10,11,12]. In the case of SiC, SiC fibres are embedded in the SiC matrix to give a rise to the SiC/SiC composite. This composite has gained considerable commercial traction over the past decade, especially in high-temperature hostile applications. For example, within the aeronautic industry, SiC/SiC composites have successfully replaced Nickle (Ni) alloy components in jet engines. With continual advancements in the engineering production of ceramic composites, SiC/SiC of a nuclear grade is now possible to manufacture [1].

A prevalent SiC/SiC composite used in ATF cladding concepts is the “sandwich” design, led and patented by the CEA. As shown in Figure 1, it consists of a thin metallic liner placed in between two layers of SiC/SiC composites. A typical fuel rod cladding has a thickness of ~0.6 mm. Hence, the inner and outer thicknesses are 0.2–0.5 mm and 0.3–1 mm, respectively, to ensure the rod is viable for the current fleet of LWRs. Based on this, the CEA found that an optimum liner thickness of 50–100 µm was sufficient to compensate for the hermicity of SiC without the risk of embrittlement by the excessive plastic deformation of the metal under reactor stresses. Furthermore, it was found that such thickness would not introduce large neutron penalties, which is a typical neutronic characteristic associated with refractory metals or alloys. Thus, it would not affect the overall absorption cross-section of the cladding. Lastly, it was found that this thickness would also not cause any obstacles for employing conventional end-plug joining techniques such as welding to seal the cladding, which is one of the main advantages promoted for this sandwich design [13,14].

The SiC/SiC composite is applied to both the inner and outer surfaces because it offers higher flexural stress and strain resistance. This is important for claddings as they are long and thin walled, which makes them susceptible to buckling under a wide array of situations, e.g., fuel handling, shipping, or deformation by circumferential heterogeneities in temperature and neutron flux. The liner is included to ensure leak tightness, provide bonding between the fibre and matrix, as well as assist in the deflection of cracks. Several metallics have been studied because the material must be able to withstand extreme temperatures presented during the interphase fabrication and matrix densification stages. It must also be thermochemically compatible and stable with the SiC/SiC composite cladding and surrounding H₂O coolant. Based on the studies conducted by the CAE under normal and off-normal operation conditions, it was deduced that current favourable liner candidates are Niobium (Nb) and Tantalum (Ta) [14,15,16,17].

Figure 1. CAE SiC/SiC composite cladding design [11,16].

Figure 1. CAE SiC/SiC composite cladding design [11,16].

To ensure safe, reliable, and economical nuclear power generation with new fuel-cladding materials over a desired NPP lifetime, reactor engineers must be confident that the core conditions will not deviate or breach any imposed operational limits enforced by regulatory bodies. Some typical core design constraints include maintaining criticality, negative reactivity coefficient, and minimum power oscillations. The prediction of such information entails the execution of numerous full-core calculations with many depletion steps and different configurations per step [18]. The process is complex due to the coupled neutronics, thermal hydraulics, and structure mechanics that need to be addressed [16,19].

With regard to neutronics, calculations are performed at numerous state points in a lattice physics code to cover core operation conditions with respect to both space and energy using neutron transport theory. In these state points, various neutronic characteristics such as the multiplication factor are updated to account for feedback effects caused by temperature, density, boron concentration, and so on. These data are simultaneously gathered to generate macroscopic cross-section tables that can then be fed into nodal routines. As a result, changes in criticality overtime brought about by the fission reaction, fuel composition depletion, and isotope evolution can be examined [19,20].

A number of eminent papers have been published on the neutronic performance of various ATF concepts via different codes. One example is the work of Alam et al. [21] whereby the researchers used WIMS-10 to study a small modular reactor assembly with micro-heterogeneous duplex fuel. Another example is Naceur and Marleau [22] who used DRAGON5 to assess SS-310, FeCrAl/APTAM, and Zr coated with SiC in a CANDU reactor assembly. For similar materials, George et al. [23] used SCALE/TRITON from SCALE 6.1.2 to perform 2D pin cell calculations based on a Westinghouse 17 × 17 PWR fuel rod. A parallel investigation was conducted by Mustafa, but with a Monte Carlo N-particle extended (MCNPX) code. A general consensus is that SiC reveals superior performance in comparison to Zr alloy claddings. However, these studies used monolithic SiC cladding and not composite SiC/SiC. Additionally, the majority were restricted to pin cell level with only a few at assembly level.

For a better understanding of the neutronic behaviour presented by ATFs in a LWRs, the neutron transport theory must be extended to core level. Therefore, the aim of this work is to examine the neutronics performance of SiC/SiC ‘sandwich’ design cladding in a pressurised water reactor (PWR) under normal operation conditions at two-dimensional pin cell, assembly, and core levels. The lattice physics calculations are carried out through Monte Carlo methods embedded in a Serpent Version 2.31 (Serpent 2) physics lattice code. The main neutronics of interest investigated herein include criticality, power distribution, and burnup. To establish the extent of variation in neutronic behaviour due to SiC/SiC cladding, the results are compared against ZIRLO^TM cladding for the initial fuel cycle.

The content is organised as follows: Section 2 describes the plant geometry and fuel rod material compositions; Section 3 details the Serpent 2 code and the input parameters; Section 4 presents and discusses the simulation results at the pin cell, assembly, and core levels; finally, Section 5 concludes with a summary of the main outputs.

2. Model Description

2.1. Plant Geometry

The reference PWR core in this study is APR-1400. It is a four-loop combustion engineering reactor developed by the Korea Electric Power Corporation (KEPCO). The reactor core consists of a total of 241 fuel assemblies arranged in a manner that approximates a right circular cylinder with an equivalent diameter of 3647 mm and a length of 3810 mm. It is surrounded by a shroud and barrel, all contained within the reactor pressure vessel. The reflector in the core barrel of APR-1400 is made of water [24]. An overall cross-sectional view of the core is illustrated in Figure 2a. The fuel assembly locations are arranged as depicted in Figure 2b. The associated fuel assembly schemes and types are presented in Figure 3.

Each fuel assembly is a 16 × 16 array square lattice that contains 256 pin cell positions allocated for 236 fuel rods (or a combination of fuel-burnable poison rods), 4 guide tubes, and 1 instrument tube. These tubes are hollow with a diameter equivalent to that of 4 pin cell positions, as shown in Figure 3. Each tube is encased with a cladding on the outside surface. The fuel assemblies have different designs and locations to optimise power distribution uniformity in the APR-1400 core. The designs are structured with particular fuel enrichment levels, fuel zones, and burnable absorber distributions.

Each pin cell in the fuel assemblies shown in Figure 3 is divided into two regions, one for the rod and one for the coolant surrounding the rod. The rods have a square cylinder surface parallel to the z-axis. The geometry of the ATF fuel rod modelled in this work is identical to the conventional fuel rod used to maintain forward and backward compatibility in current LWRs, apart from the modified internal cladding structure, as per the “sandwich” design. Thus, the pellet diameter, gas gap, and cladding thickness were correspondingly kept at constants of 0.8192, 0.0165, and 0.05715 cm. Additionally, to maintain power transfer, pitch-to-rod distance was kept at a constant of 1.2852 cm. Likewise, to maintain the thermal conductivity of the gap, the space between the pellet-cladding was kept at a constant of 0.01651 cm.

Furthermore, a sensitivity analysis was conducted to observe the influence of the sandwich design cladding constituents on the neutronics performance. The variables of interest were: (a) type of interphase metallic liner; (b) the degradation of thermal conductivity of irradiated SiC/SiC composite; and (c) thickness ratios of cladding layers. In total, 10 hypothetical pin cell models were developed. They are defined in

Table 1. Sensitivity input parameters for SiC/SiC pin cell models.

Pin Cell Model	Metallic Liner	Temperature (K) (Fuel:Cladding:Coolant)	Thickness Ratios (Cladding:Liner:Cladding)
1	Ta	900:600:600	0.3:0.1:0.6
2	Nb	900:600:600	0.3:0.1:0.6
3	Ta	1100:900:900	0.3:0.1:0.6
4	Nb	1100:900: 900	0.3:0.1:0.6
5	Ta	900:600:600	0.45:0.1:0.45
6	Nb	900:600:600	0.45:0.1:0.45
7	Ta	900:600:600	0.6:0.1:0.3
8	Nb	900:600:600	0.6:0.1:0.3
9	Ta	900:600:600	0.4:0.2:0.4
10	Nb	900:600:600	0.4:0.2:0.4

.

2.2. Material Compositions

In APR-1400, the conventional materials of the fuel rod components are UO₂ pellet, Helium (He) gap, and ZIRLO^TM cladding. For the fuel-burnable poisons rod, Gadolinia-Urania (Gd₂O₃-UO₂) pellets are used. In this study, only the material of the cladding was changed to SiC/SiC with Nb-13 or Ta-73 liner. The compositions and densities of all materials are listed in

Table 2. Cladding material composition of ZIRLO^TM [25] and SiC/SiC [9].

Composition (wt.%)
ZIRLOTM	Nat. Sn	Nb-13	Nat. Fe	O-16	Nat. Zr
	1.150	1.005	0.135	0.125	97.585
SiC/SiC	Nat. Si	Nat. C
	70.080	29.920

and

Table 3. Fuel rod material temperatures and densities [24,25].

Material	Temperature (K)	Density (g/cm3)
UO2	900	10.44 (95% of theoretical density)
Gd2O3-UO2	900	10.54
He	600	0.001625
ZIRLOTM	600	6.57

, respectively. The coolant around the rods is boronised H₂O with a boric acid concentration of 817 ppm [24].

3. Lattice Physics Code

3.1. Serpent 2

The APR-1400 models (see Figure 4 for examples) were developed in Serpent 2. This utilizes a multi-purpose Monte Carlo particle transport code developed by the VTT Technical Research Centre of Finland. Monte Carlo is a computational mathematical algorithm that employs the statistical nature of repeated randomness to yield a probability distribution of outcomes. Its use in neutronics numerical methods has become increasingly popular because of its independency of the problem in question. This is particularly attractive when the investigation lies beyond the capabilities of conventional deterministic lattice physics codes. For instance, in the case of new fuel cladding concepts such as ATFs, Monte Carlo has the ability to produce reliable radial distributions without the need for correction formula nor the implementation of approximations to account for fuel self-shielding. In another instance, the geometry approach in Monte Carlo is based on universes, cells, and surfaces, which allows the modelling of practically any two- or three-dimensional reactor configuration [26,27,28,29].

Furthermore, Monte Carlo has the capacity to predict various neutronic characteristics throughout temporal progression. The algorithm traces every neutron individually from the instant it is produced until it is removed from the system by capture or leakage. How far the neutron travels prior to interaction with matter, type of interaction, and the outcome of the interaction are all randomised based on known distributions. These distributions vary based on the target nuclide and neutron energy. The distributions have been widely researched around the world and collected into what are known as nuclear data libraries. These libraries offer a consistent set of data of the best available information on the distributions of reaction probabilities. Examples of predominant libraries include the Evaluated Nuclear Data File (ENDF) developed by the U.S. Cross-section Evaluation Working Group, the Joint Evaluated Fission and Fusion File (JEFF) developed by an international collaboration of OECD NEA databank countries, and the Japanese Evaluated Nuclear Data Library (JENDL) developed by Japan Atomic Energy Agency. Thermal collision libraries to account for moderation regions also exist [26].

Serpent 2 uses these nuclear data libraries to compute homogenised multi-group constants from continuous-energy neutron cross-sections for lattice physics calculations. Examples include criticality, burnup, fuel cycle, and fixed source calculations at the pin, assembly, and core levels. The routine scheme implemented to track neutrons involves surface-to-surface raytracing with Woodcock delta tracing. The combination of the two methods has been found efficient and well-suited for reactor core design. Hence, a range of neutronic characteristics can be obtained, such as infinite multiplication factor, flux distribution, fuel depletion, fission product evolution, scattering matrices, assembly discontinuity factors, and point kinetic parameters, to name a few of the standard outputs. It can also be combined with other disciplines such as thermal hydraulics, computational fluid dynamics, and fuel performance codes to execute coupled calculations [26].

3.2. Input Parameters

For the pin cell and assembly models, reflective boundary conditions were integrated to ensure that the neutrons were not stranded in the coolant and instead were scattered isotopically when they reached the boundary. As a result, most neutrons passed through the fuel rods once again. This makes the models infinite and neglects spectrum interaction between adjacent cells. The heterogeneous structures across the pins and fuel assemblies were taken to be homogeneous since they were much smaller in size in comparison to the overall core. To account for any homogenisation errors due to termination in the scalar flux occurring at the assembly interfaces, such as surfaces or corners, assembly discontinuity factors were activated in the core. As for the fuel-burnable poison rod, the radial cross-section was divided into 10 equal concentric rings because it possessed a high thermal neutron absorption cross-section, and hence short free mean path at the BOC. As neutrons are captured upon burnup, the absorption cross-section weakens in the form of layers that originate at the periphery and propagate to the centre. This onion-like impact is replicated through the annular rings. The rings also permit the study of the self-shielding effect intrinsic to burnable materials. Finally, the assemblies and core geometries possessed symmetry lines which were exploited to reduce the computational costs. The former had diagonal and reflection lines, and hence ⅛ was coded, whilst the latter had only reflection symmetry lines, and hence ¼ was coded. Within these geometries, the control rods and instruments were assumed to be fully retracted. Therefore, the guide and instrument tubes were programmed to be filled with coolant flowing in an axial direction.

The temperatures of fuel, cladding, and coolant materials were set to 900 K, 600 K, and 600 K, respectively. For Case B sensitivity analysis, these temperatures were increased to 1100 K, 900 K, and 900 K to consider the decrease in thermal conductivity of SiC. The code used these temperatures to obtain the corresponding neutron microscopic cross-sections from the nuclear data libraries. The library chosen for this investigation was ENDF/B-VII. It provides the necessary probability distributions needed for the simulation of particle interactions via random Monte Carlo particle number sampling. Additionally, the ENDF/B-VII radioactive decay and fission product yield libraries were included for the burnup calculations. These data are neutron-induced, and thus spontaneous. Lastly, the ENDF/B-VII thermal microscopic scattering cross-section library was also used to define the low-energy elastic-scattering microscopic cross-sections of H₂O [30].

The changes in material composition as a function of time caused by neutron-induced reactions and radioactive decay are calculated via the Bateman equation. The general mathematical formulation of the equation is given as:

$$N_n\left(t\right)=\frac{N_1\left(0\right)}{{\lambda }_n}{\displaystyle \sum }_{i=1}^n{\lambda }_i{a}_i{e}^{-{\lambda }_{i}t}$$

(1)

$$a_i={\displaystyle \prod }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^n\frac{{\lambda }_j}{\left({\lambda }_j-{\lambda }_i\right)}$$

(2)

where N_n is the nth nuclide after time t as a result of the ith nuclide production per time unit from the jth nuclide destruction at a transmutation rate λ. Serpent 2 uses inbuilt burnup algorithms to resolve the Bateman equation that depicts these changes. For this analysis, the selected algorithm was the Chebyshev Rational Approximation Method (CRAM). This is an advanced matrix exponential approach, which handles a system of nuclides and incorporates short-lived isotopes without the need to approximate the step length [26]. A predictor–corrector option was activated to produce a more accurate estimation of isotopic changes during each burnup step. Additionally, with burnup, the effectivity of fuel, burnable absorbers, and boron chemical shim in coolant reduce overtime as they become used up. The Bateman equation for depletion is a non-linear partial differential equation. Thereby, to linearise it, either the power or flux is assumed to be steady [26]. Here, the former was selected to be constant. The average power density was set to 40 kW/kgU with depletion steps divided over 1000 days.

The source distribution of each active cycle generation was calculated from the fission reaction distribution of its previous cycle. Since Monte Carlo is a pure statistical approach based on randomness, the fission source might fluctuate. If the calculations are to take place prematurely, then follow-up active cycle generation would begin from a non-stationary value. As a result, the simulated outcomes would be biased. To overcome this drawback, a number of inactive cycle generation are skipped to account for fission source convergence before the results are collected and stored. The accompanying statical accuracy depends on the neutron history run, which is affected by the number of iterations of active cycle generations. This means the statistical noise is influenced by the number of neutrons in each generation [26]. Based on these considerations, the running parameters were set to 1,000,000 neutrons, 500 iterations, and 50 skip cycles.

4. Pin Cell Model Analysis

On a pin level, the effect of (A) metallic liner, (B) the thermal conductivity of irradiated SiC, and (C) the thickness ratios of cladding constituents on the multiplication factor, neutron spectrum, and Pu-239 production were examined for a fuel enriched at 3.14 w/o.

4.1. Case A: Metallic Liners

Metallic liners are included in the “sandwich” design to provide leak tightness. The current favourable candidates are niobium (Nb) and tantalum (Ta) [8,9]. Figure 5 presents the influence of Ta liner on Model 1 and Nb liner on Model 2 on the multiplication factor with respect to burnup. The behaviours exhibited by the proposed liners were very different from each other. Compared to the ZIRLO^TM cladding, Model 2 showed negligible disparity whilst Model 1 showed a drastic disparity. At the BOC, Model 1 yielded to a multiplication factor of 1.09, which was 20% lower than Model 2 and the datum. At this stage of the cycle, the reactor condition was clean (no neutron poison) and cold (room temperature).

Additionally, from Figure 6a, the neutron spectra at BOC shows that all models had approximately the same number of thermal neutrons initially. Then, one possible reason for the contrast in the multiplication factor profiles displayed could largely be attributed to the microscopic absorption cross-sections of the different materials employed. Evident from Figure 7, Ta possesses higher absorption cross-sections across the entire defined energy range. For instance, the cross-section of Ta is ~100 barns and Nb is ~3 barns at 0.01 eV, a notable difference of two orders of magnitude. As a result, a Ta liner would absorb more thermalised neutrons than its competitor Nb liner, as seen in Figure 6b. This, in turn, gives arise to the smaller multiplication factor witnessed by the former liner.

Furthermore, a closer look at Figure 5 reveals that the absolute difference in the multiplication factor between Model 1 and the other two models decreased over time. At the BOC the variation was ~20%, whereas at the EOC the variation was ~15%. In other words, the rate reduction in the multiplication factor in the former declines with burnup. Such a trend can be explained by the greater hardening of the neutron spectrum demonstrated by Model 1 overtime. First, with respect to thermal neutrons, the density remained almost the same for Model 1 but increased for both Model 2 and the datum with burnup. On the other hand, whilst the density of fast neutrons amplified for all models, Model 1 presented the largest increase. For example, the number of neutrons with an energy of 2.5 MeV increased from 5.8 × 10¹² cm⁻²s⁻¹ at BOC to 8.8 × 10¹² cm⁻²s⁻¹ at EOC for Ta liner, and from 4.5 × 10¹² cm⁻²s⁻¹ at BOC to 7.3 × 10¹² cm⁻²s⁻¹ at EOC for Model 2 and the datum. With a higher number of fast neutrons, a higher probability of U-238 nuclides transmute to Pu-239 nuclides. Consequently, a higher percentage of Pu-239 can be observed by the former model in Figure 8. Since Pu-239 is a fissile isotope, it will contribute to the production of more neutrons for the subsequent fission reactions and offset the multiplication factor overtime. Thus, the evolution of the multiplication factor revealed in Figure 5 is quite parallel for all three cladding materials. This was also expected, as they all share the same fuel geometry and operation conditions.

4.2. Case B: Thermal Conductivity of Irradiated SiC

The thermal conductivity of irradiated SiC was accounted through the modification of the fuel rod temperatures. Based on literature suggestions, the temperatures of the pellet, cladding, and coolant were correspondingly increased to 1100 K, 900 K, and 900 K [9]. Overall, it was found that the neutronic performance as a function of burnup did not substantially degrade in any aspect. For instance, the multiplication factor for Models 3 and 4 were 1.08 and 1.33 at BOC, respectively, which is a trivial difference when compared to Models 1 and 2 in Case A. A similar pattern is also noted for the neutron spectra and Pu-239 production. The negligible variation witnessed mainly stems from the fact that the thermal conductivity of irradiated SiC has been found in experiments to reach a saturation of 80 W/mK at 650 K. Beyond this point, the thermal conductivity exhibits a plateau as a function of dpa [14].

4.3. Case C: Thickness Ratios of Cladding Constituents

In Cases A and B, the dimensions used for the inner SiC/SiC layer, metallic liner, and outer SiC/SiC layer were of the ratios of 0.3:0.1:0.6, as per the CEA patent “sandwich” model [15]. To further investigate the impact of these ratios over the burnup cycle, the relative proportion of the cladding constituents was altered in accordance with Table 1.

The simulations revealed that a change in the dimensions of the SiC/SiC cladding constituents can degrade the neutronics performance. When the sizes of the inner and outer SiC/SiC layers were the same (i.e., ratio 0.45:0.1:0.45), the multiplication factors of Models 5 and 6 deteriorated to 1.07 and 1.32. Likewise, but to a lesser degree, when the sizes of the inner and outer SiC/SiC layers were switched (i.e., ratio 0.6:0.1:0.3), the multiplication factors of Models 7 and 8 were reduced to 1.08 and 1.34. However, when the thickness of the metallic layer was increased (i.e., ratio 0.4:0.2:0.4), the multiplication factors of Models 9 and 10 substantially decreased to 0.93 and 1.30. For example, the extent of degradation demonstrated by Model 9 in comparison with Model 1 was ~20%. Again, this would largely be attributed to its higher thermal neutron absorption cross-section. Thus, a thicker Ta liner would cause more thermal neutrons to be lost in the intermediate layer and less to reach to the fuel pellet. Then, a lower number of U-235 fission reactions take place. The same patterns are observed in the neutron spectra and Pu-239 production.

Overall, the sensitivity analysis showed that the general neutronics performance of the Nb liner was much more positive when compared to the Ta liner. For this reason, only the SiC/SiC sandwich cladding with the Nb liner was modelled in the proceeding assembly and core levels. The temperatures were increased to the suggested values to consider irradiation effects on the thermal conductivity, and the dimensions of the cladding constituents were set to the ratios established by the CEA.

5. Assembly Model Analysis

The fuel assemblies were designed and organised in a particular manner to optimise the neutronics performance with respect to both space and energy. The calculations were performed at various state points that covered operation conditions to initially ensure criticality through, for example, the multiplication factor and flux distribution. In these state points, the fuel composition, irradiated material, temperature, boron concentration, and so on, changed. Thereby, any changes had to be updated in the calculations to cover the feedback effects. Furthermore, in this study, on an assembly level, burnup calculations were integrated to measure the changes due to fission, decay, and the production of new isotopes over the reactor lifetime. Additionally, to examine the impact of different fuel enrichments and the inclusion of burnable absorbers, the C0 and B2 assembly designs were used as examples. Group constant generation, depletion, spectral, and radial analysis are presented and discussed for SiC/SiC cladding with the Nb liner in comparison to ZIRLO^TM cladding.

5.1. Group Constants

The continuous-energy neutron cross-section was used in the computation of the neutron transport equation. The change in the rate of neutron density was defined as the production rate minus the leakage and absorption rates. Each rate was determined by its relevant macroscopic cross-section, which varied with energy. To resolve such information is too computationally expensive for a full core. Thus, initially, various reaction rates for individual fuel assemblies were computed. In these simulations, homogenisation and two-group approximation were applied. Hence, the cross-sections were averaged over the depletion steps and a single value was given per energy group. The diffusion parameters and delayed neutrons were also obtained.

The neutron reaction cross-sections were ultimately used to derive the thermal power output. The various grouped constants for the macroscopic reaction cross-sections are shown in

Table 4. Reaction cross-sections for fuel assembly C0 design.

Reaction Type	ZIRLOTM		SiC/SiC with Nb Liner
	Thermal Cross-Section (cm−1)	Fast Cross-Section (cm−1)	Thermal Cross-Section (cm−1)	Fast Cross-Section (cm−1)
Total	1.4355	0.5579	1.4359	0.5527
Scattering	1.3360	0.5478	1.3363	0.5425
Absorption	0.0994	0.0101	0.0996	0.0102
Capture	0.0455	0.0077	0.0457	0.0077
Fission	0.0540	0.0024	0.0540	0.0024
Energy per fission (MeV)	203.6858	204.3466	203.7065	204.3780
No. of emitted fission neutrons	2.5416	2.603	2.5416	2.6042

and

Table 5. Reaction cross-sections for fuel assembly B2 design.

Reaction Type	ZIRLOTM		SiC/SiC with Nb Liner
	Thermal Cross-Section (cm−1)	Fast Cross-Section (cm−1)	Thermal Cross-Section (cm−1)	Fast Cross-Section (cm−1)
Total	1.4362	0.5583	1.4194	0.5465
Scattering	1.3376	0.5483	1.3331	0.5371
Absorption	0.0987	0.0099	0.0863	0.0094
Capture	0.0428	0.0078	0.0427	0.0074
Fission	0.0459	0.0021	0.0435	0.0021
Energy per fission (MeV)	203.9681	204.6392	203.9431	204.6821
No. of emitted fission neutrons	2.5634	2.6263	2.5585	2.6266

for fuel assemblies C0 and B2, respectively. It is evident that the simulated macroscopic cross-sections are consistent for both cladding materials. Similar patterns were found for the diffusion coefficient and transport cross-section, as well as the delayed neutron groups. This was anticipated, as the models utilise the same fuel and coolant materials. All group constants generated by Serpent 2 for both the conventional and ATF models were equivalent to those documented in the literature for PWRs and APR-1400 [24].

5.2. Multiplication Factor and Neutron Spectrum

At the BOC, the multiplication factors of the fuel assemblies C0 and B2 were 1.243 and 1.048 for both cladding materials, respectively. The difference in these initial values arises because the former holds higher enrichment fuel rods and the latter contains burnable absorber rods made from Gd₂O3-UO₂. The predominant elements in the burnable absorber are Gd-155 and Gd-157, with absorption cross-sections of 61,000 and 255,000 barns, respectively [30]. With time, the trends associated with the multiplication factors of the assemblies begin to differ from each other. For C0 assembly, the value decreases sharply and continues to do so to the end of the depletion steps. Table 4 and Table 5 reveal that, for every neutron consumed by the fissile isotopes in the fuel, namely, U-235 and the subsequently produced Pu-239 from U-238, approximately 2.6 neutrons are emitted. This means that the number of the neutrons produced by the fission available in generation ‘i’ should be more than the neutrons lost through absorption in the preceding, which in turn should increase the multiplication factor. However, that was not the case due to the presence of poison fission products as well as boron in the moderator, which capture the newly born fission neutrons. The concentration of boron was tuned with burnup and decreased to accommodate for the declining multiplication factor with time.

On the other hand, after a small decline in the multiplication factor in the first step of the calculation for B2 assembly, the value did not drop anymore between approximately 5 and 15 MWd/kgU. On the contrary, it began to increase. This is because the Gd-155 and Gd-157 isotopes in the burnable absorber consume neutrons in generation ‘i-1′ and transmute them into Gd-156 and Gd-158 isotopes, respectively. The absorption cross-sections of these subsequent isotopes were ~2 barns, meaning they were less effective by a factor of 30,000–100,000 than their predecessors. Moreover, when the burnable absorbers began to deplete at ~15 MWd/kgU, the multiplication factor did not increase any more. Instead, it began to fall in a similar manner to C0 assembly, owing to the poison fission products and boron in the moderator. Overall, the drop in the multiplication factor is a critical aspect of safe reactor design because it guarantees that the system has a negative reactivity feedback in operating conditions. Thus, the changes which follow the increase in reactor power, e.g., the increase in fuel and coolant/moderator temperature, result in the decrease in multiplication factor. If it were to increase, then the reactor would be in a supercritical condition, making it uncontrollable.

The averages of the multiplication factors for the two assemblies C0 and B2 were, 1.025 and 0.9628, respectively, for both cladding materials. This implies that assemblies with no burnable absorbers (such as A0, B0, and C0) will be in a slight supercritical state, whilst those with burnable absorbers will be in a slight subcritical state initially. As mentioned before, referring back to Figure 2, the non-uniform property approach in the reactor leads to flat power density. Together, the different multiplication factors of the fuel assemblies would counter each other to achieve criticality.

The averaged neutron flux spectra for the C0 and B2 assemblies of both cladding materials are visualised in Figure 9. Overall, the simulated spectra in each assembly design are fairly similar across time. The higher thermal neutron density witnessed in C0 is attributed to the absence of neutron poisons. Thus, more neutrons are available to fission with U-235 nuclides, whereas in B2, the presence of burnable absorbers means that neutrons are captured and less are available for fission with U-235 nuclides. These are further supported by the exhibited corresponding multiplication factors. Additionally, inherent to fission reactions is the increase in the fraction of born fast neutrons in the system. As a result, C0 possesses a higher fast neutron density.

5.3. Isotopic Evolution

The mass/atomic densities of various isotopes in a fuel assembly are continuously changing due to fission, neutron capture, and radioactive decay. The key products are presented in Figure 10. Monitoring the inventory of these products is important because some of them are neutron poisons, which could inhibit subsequent nuclear reactions. Therefore, the accumulation of fission product poisons is a vital factor in determining the maximum duration a given fuel element can be kept within the reactor. There are two main fission products addressed in reactor design: Xe-135 and Sm-149. These two isotopes have a very high absorption cross-section to the degree of causing reactor shutdown. In addition, their build-up may interfere with the normal control of the reaction during restart or the restoration of full power, potentially causing or contributing to an accident scenario. No notable disparity between the model with conventional cladding and the one with ATF cladding was seen. Once again, this mainly stems from the fact that the same fuel, fuel enrichment, and fuel positions were used in the assembly models.

5.4. Pin Power and Flux Distribution

The pin power distribution is an important output in neutronic safety analysis because it deduces the power peaking factor and highlights the restricting fuel rod, i.e., the fuel rod with the highest fuel centreline temperature or highest heat flux at the cladding surface. It is also important to see if the distribution varies with time. Figure 11 was calculated and plotted using radial reaction rate density distributions based on the detector output. The linear power of each pin is indicated by colour and text. For both fuel assemblies at the BOC, the maximum linear powers displayed in dark red range between 190 and 220 W/cm. These values correspond to the pins at the lattice positions located mainly at the borders of the instrument and guide tubes. For B2 assembly, they also appear at the inner periphery of the outer boundary. This could be explained using mesh plots.

In Figure 12, the mesh plot’s colour scheme consists of “hot” shades of red and yellow, representing relative fission power, and “cold” shades of blue, representing relative thermal flux (i.e., below 0.625 eV). Darker colours indicate lower values and lighter colours indicate higher values. Therefore, one reason for such pin power distribution is that both the highest fission and thermal flux are in the proximity of tubes, as shown in Figure 10. The average linear powers for C0 and B2 were 186.68 and 185.93 W/cm, respectively. In contrast, it can easily be seen that the pins located at the outer boundaries possessed the lowest power. This is because a larger surface area of outer cladding was in contact with a larger volume of coolant. On the other hand, the linear power of the burnable absorber rods in B2, as expected, were the lowest with a value of approximately 40 W/cm. Additionally, the fuel rods nearest to the inner-located burnable absorbers had lower linear powers than the remaining fuels. Based on the mesh plot in Figure 12b, it can be observed that the fission power was much lower in the burnable absorber rods than in the fuel rods. Moreover, a depression in the thermal flux distribution can be seen in the immediate surroundings of the burnable absorbers. This is caused due to their poison nature, stemming from their large absorption cross-section that kills neutrons.

In the process of burnup, the power in the interior zone would decrease while the power in the exterior area would increase. This stems from the faster depletion of U-235 inside the assembly compared to the exterior. Nonetheless, the average linear powers for both Zr and SiC models remained almost constant for both assembly designs. The distribution for C0 was nearly the same; for B2, the distribution became more evened out after the depletion of the burnable absorbers. Overall, the simulated data were very close to the 183.7 W/cm full-power core average stated in the APR-1400 design control document [24]. The influence of different kinds of cladding materials on fission power distribution in fuel pellets appears to be limited.

6. Core Model Analysis

The safety and reliability of a core is strongly linked to the neutronics characteristics that influence criticality. The main attributes examined throughout this study so far on all pin and assembly models have been the multiplication factor, fission product evolution, and flux and power distribution, with respect to both space and energy, to understand the feedback effects of variations in fuel composition, irradiated material, delayed neutrons, temperature, boron concentration, and so on. The same process applies on a core model to examine the overall neutronics performance of SiC/SiC cladding in comparison with the ZIRLO^TM cladding. The analysis would also highlight if any changes, e.g., in the core loading pattern, were required for the replacement of this ATF cladding.

Figure 13 demonstrates the behaviour of the multiplication factor over time for the APR-1400 core. A total replication can be seen in the core model that used ZIRLO^TM claddings and that which used SiC/SiC sandwich claddings over the entire burnup cycle. The multiplication factor for both core models was 1.016 at the BOC, which fell down to 0.785 at EOC. The simulation values for ZIRLO^TM are in good agreement with those listed in the design control document for APR-1400 [24].

The neutron spectra presented by both core models also matched the simulation throughout. The thermal peaks occurred at around 0.012 eV, whilst the fast peaks occurred at around 2.3 MeV. With burnup, the former peaks increased from 3.4 × 10¹⁸ to 3.9 × 10¹⁸ cm⁻²s⁻¹, whilst the latter peaks increased from 6.2 × 10¹⁸ to 8.7 × 10¹⁸ cm⁻²s⁻¹. This was expected as neutrons were born by fission reactions with high energies, hence adding to the fast peaks, and then moderated to lower energies, hence adding to the thermal peaks. Furthermore, the difference in thermal peaks overtime was smaller than that of the fast peaks. The disparity stemmed from the various neutron poisons present in the core—whether in the form of burnable absorbers, boric acid, or fission products—that kill thermal neutrons. This is supported by Figure 14, which shows the build-up of, e.g., Xe-135. It also stems from the transmutation of U-238 to Pu-239, which is fissile and therefore produces more fast neutrons as it undergoes fission. Again, from Figure 14, the accumulation of Pu-239 can be seen over time.

Power Distribution

As mentioned earlier, the fission products released during burnup must be monitored as some isotopes would initiate fission reactions whilst others would impede them. The record of isotopic evolution plays an integral part in setting the parameters of the control methods, such as boron concentration in the coolant overtime. These fission products also affect the power and flux distribution in the core. From Figure 14, it can be noticed that the power distribution for both core models are very alike. Figure 15a shows that, at the BOC, the two present the highest power at the core outer region and the lowest power at the core centre. This emanates from the highest and lowest enriched assemblies placed at those locations, respectively, as can be seen in Figure 2b. It should be noted that the core with SiC/SiC cladding displays less hotspots at BOC, which is attributed to its initial high thermal conductivity that causes heat to transfer more efficiently to the coolant. Nonetheless, with time, the power becomes more uniform across the core cross-sectional area for both due to the depletion of fuel isotopes, the accumulation of fission products, and the implementation of control methods in the reactor. Power continues to be produced, especially with the contribution of Pu-239. As opposed to the BOC, Figure 15b shows that the power at EOC concentrates in the inner region of the core. The higher enriched assemblies at the outer region that produced power initially, and at a higher rate due to their higher density of U-235, would have been consumed by the end. As a result, shades of blue are visualised at the periphery. Even so, the power distribution is mostly uniform, even at the EOC.

7. Conclusions

All in all, while SiC has been chosen as an ATF cladding candidate due to its enhanced thermo-physical and thermo-mechanical properties, the inclusion of a metallic liner to overcome the hermicity issue of the ceramic material can introduce some penalties on the neutronic performance overtime. When the two proposed liners were contrasted, it was observed that Nb resulted in a far superior profile to Ta for all neutronic characteristics examined. The increased Pu-239 content throughout the cycle in the presence of the harder neutron spectrum for the Ta liner translated to a significant reduction in operational cycle lengths. This is an undesirable objective for the achievement of longer core lifetime. Thus, from the pin cell models, it can be deduced that a fuel rod enclosed in a cladding composed of SiC/SiC with a Nb liner would not only deliver better neutronic performance than that with a Ta liner, but also deliver an equivalent neutronic performance to conventional Zr, with the potentiality of enhanced safety aspects. Subsequently, the assembly and core analysis verified that such positive performances were also witnessed in the higher-level models for SiC/SiC with a Nb liner. The similarity of this ATF cladding candidate with conventional cladding means that, in terms of neutronics, the replacement procedure would entail little to no changes to reactor operation. Recommended future work includes benchmarking the burnup results using spent fuel measurements, such as those described in [31], for ZIRLO^TM cladding versus SiC/SiC cladding to validate the burnup calculations from the Serpent code.