2.1 Rationale for using SiC

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 UO₂, 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]. 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 ^[24,25].

2.2 Physical design of assemblies

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 and Table 2 summarize the steady-state parameters for the PWR design.

Fig.1Full-screen View

(Color online) Structural arrangement of assemblies

2.3 Cladding models

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 UO₂ fuel; case two is SiC cladding with UO₂/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 UO₂/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, 4, 5 show the data in detail. The enrichment setting in Table 3 is used to maintain a uniform ²³⁵U load. Equations for enrichment calculation are shown as follows.

where $c_5$ is the number of ${}^{\text{235}}\text{U}$ nuclides divided by the sum of ${}^{\text{235}}\text{U}$ and ${}^{\text{238}}\text{U}$ nuclides; $\epsilon$ denotes enrichment of a fuel pellet; $w{t}_{\text{T}}\%$ is set as the volume ratio; and ${\rho }_{{\text{UO}}_{\text{2}}}$ is 10.42 g/cm³.

The setting of 0.089 cm for the thickness of UO₂/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 lists these temperature perturbations.

3.1 Neutron spectrum and ²³⁹Pu analysis

Figures 2-3 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.

Fig.2Full-screen View

Thermal neutron spectrum at beginning of cycle

Fig.3Full-screen View

Thermal neutron spectrum at end of cycle

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 (in the range of 0.1 eV-0.62 eV), 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. 3 presents the neutron spectrum at the end of cycle (EOC). Compared with Fig. 2, there is little flux disparity (in the range of 0.1 eV) observed in Fig. 3. In the meantime, the thermal neutron flux decreases at 0.1 eV. This is due to the depletion of the ²³⁵U 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 ²³⁹Pu is displayed in Fig. 4. The hardening thermal neutron spectrum in the Zr alloy case results in higher accumulation of ²³⁹Pu. ²³⁹Pu has a significant influence on the reactivity. Therefore, it may contribute a slight reactive increase at EOC.

Fig.4Full-screen View

²³⁹Pu content

3.2 Characteristic factor results

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.

Fig. 5 shows that all curves have a similar tendency as a function of burnup. Detailed drawings are inserted in 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 ²³⁵U in the SiC assembly.

Fig.5Full-screen View

Trend of Kinf in assemblies with various enrichments

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 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.6Full-screen View

Kinf in various assemblies with burnable poison rod

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.

Fig.7Full-screen View

Ppf for various assemblies

The relative power distribution at BOC in the SiC case assembly is presented in Fig. 8. All values have been normalized. 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 describes the relative power transformation between BOC and EOC. In contrast with the BOC power, the green parts in 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 ²³⁵U inside the assembly than in the exterior assembly.

Fig.8Full-screen View

(Color online) Distribution of relative power in SiC cladding assembly at beginning of cycle

Fig.9Full-screen View

(Color online) Power variation in SiC cladding assembly at end of cycle

3.3 Radial profile analysis

Differences in the neutron absorption ability of cladding material would lead to radial differentiations in fuel pellets ^[26,27]. The radial flux distribution is explored in four areas by segmenting the inner UO₂ 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 that are surrounded by black bold squares with marked numbers are chosen for analysis (specific to the SiC assembly).

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.

Fig.10Full-screen View

Normalization flux in four parts. (a) flux in region one (b) flux in region two (c) flux in region three (d) flux in region four

Figures 11-12 show the relative fission power distribution in fuel pellets. From Figs. 11-12, 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 steeper than those in 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 ^[28,29].

Fig.11Full-screen View

Relative radial power distribution at beginning of cycle

Fig.12Full-screen View

Relative radial power distribution at end of cycle

3.4 Moderator temperature coefficient analysis

Respectively, Fig. 13 and 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:

Fig.13Full-screen View

Moderator temperature coefficient

Fig.14Full-screen View

Fuel temperature coefficient

where $\partial$ is the temperature coefficient, $\Delta \rho$ is the reactivity difference, and $\Delta T$ stands for temperature difference. As shown in Table 6, $\Delta T$ is equal to 10K for the moderator temperature coefficient (MTC) calculation, while it is 50K for the fuel temperature coefficient (FTC) calculation.

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 ²³⁵U, which relatively enhances the ²³⁸U 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 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 ²³⁹Pu and ²⁴¹Pu 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 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.

Fig.15Full-screen View

Total temperature coefficient