Burnable Poison Design for Supercritical Water Cooled Reactor With Annular Fuel

Supercritical water-cooled reactor (SCWR) is the only water-cooled reactor in six Gen-IV reactor systems [1]. SCWRs have high thermal efficiency, simplified system, and economics advantages over conventional pressurized water reactors (PWRs). In most published SCWR designs, the inlet and outlet water temperatures are 280 °C and 500 °C, respectively. The outlet water density is only one seventh of the inlet water density. Besides, the flow rate of SCWRs is only one tenth of PWR's flow rate. The neutron is under-moderated in SCWRs. Annular fuels have been used by Massachusetts Institute of Technology to improve power density of PWRs [2,3]. The water hole inside the annular fuel will improve the neutron moderator for SCWRs. In 2014, annular fuel was applied to SCWR, and the pre-conceptual design is proposed in Xi'an Jiaotong University [4]. In the annular fuel SCWR, the initial excess reactivity is rather larger. Burnable poisons are required to reduce the initial excess reactivity and the number of necessary control rods.

In this article, the burnable poison design of SCWRs with annular fuel is analyzed. First, the material and the position of burnable poison rods are analyzed, and the assembly safety is estimated from the viewpoint of neutronics after using burnable poison. Second, fuel assembly with burnable poison is applied in the core, and the effects of burnable poison on core neutronic performance is studied. Finally, an optimized core scheme is proposed, and the neutronic performance is calculated.

Due to dramatic changes of water density in SCWRs, neutronics and thermal-hydraulics coupling calculation is necessary during SCWR designs. In this article, a three-dimensional N/TH coupling code, FENNEL, is developed. FENNEL has two main modules: neutronics calculation model FENNEL-N and single-channel calculation model for thermal-hydraulics. Like conventional PWR designs tools, the “two-step” method is used in FENNEL-N. First, the assembly calculation is carried out using HELIOS [5] which can handle complex geometry; after the assembly calculation, assembly homogenized cross sections are fitted into polynomial by Lilac [6]. With these polynomials, the core calculation is performed using home-made diffusion code. The solver is based on the three-dimensional nodal code, SIXTUS [7]. Thermal hydraulics calculation is based on single-channel model, in which each fuel assembly is treated as one single channel. Neutronics and thermal-hydraulics codes are integrated into one program. Data are exchanged inside the program using arrays. The coupling flow chart is shown in Fig. 1.

The equilibrium core is required in the core performance analysis. The equilibrium core is defined as follows: after the coupling calculation of one cycle, the burnup distribution at the beginning of next cycle can be obtained according to the fuel loading pattern. If the average burnup distribution relative error of two adjacent cycles satisfies the criteria, an equilibrium core is achieved.

The hexagonal fuel assembly is shown in Fig. 2. The fuel assembly consists of 19 annular fuel rods [4]. The tight fuel rod arrangement is taken. There are six layers in annular fuel rod. They are, from inside to outside, inner cladding, thermal isolation, inner gas, fuel, outer gas, outer cladding, respectively. Stainless Steel 316L is used as cladding material. In SCWRs, the closed fuel assembly is applied for the purpose of adjusting flow rate of each fuel assemblies [8]. The thickness of fuel assembly box is 1.0 mm, taking reference of the HPLWR design. The box material is the same as fuel cladding. Dimensions of fuel rods and the fuel assembly are shown in Table. 1.

There are several principles for selecting burnable poison: First, it is used as neutron poison; thus a relatively large neutron absorption cross section is expected. Second, it should be burnable; thus the absorption cross section of its product after absorbing neutron should be as small as possible. Third, at the end of cycle, the concentration of the burnable poison should be so low as not to affect the core cycle length. According to these principles, four burnable poisons are studied, and the composition is shown in Table 2; the bold isotopes are ones with larger thermal neutron absorption cross section.

Five cases are calculated. In one case, there is no burnable poison in the fuel assembly. In other four cases, each burnable poison in Table 2 is added into all fuel rods of the fuel assembly. The volume fraction of burnable poison in the fuel rods is adjusted so that the initial k_inf of the fuel assembly will be about 1.10. The fuel enrichment is 5.5% in all cases. The results are shown in Fig. 3.

As shown in Fig. 3, the Gd₂O₃ is rapidly consumed. The annular fuel pellet is thin, besides there are neutron influxes from both sides of fuel pellet. Thus the space self-shielding effects is weak. It causes much faster consumption of burnable poison in annular fuels than that in regular solid fuels. In this calculation, Gd₂O₃ is consumed faster than other burnable poisons. This is because that Gd₂O₃ has higher neutron absorption cross section than other burnable poisons. As illustrated in Fig. 4, ¹⁵⁵Gd and ¹⁵⁷Gd have higher thermal neutron absorption cross section than other burnable poison isotopes. In Fig. 3, the k_inf of cases with Dy₂O₃ and HfO₂ are much lower than that of no-burnable poison (BP) case. It means that there is residual Dy₂O₃ and HfO₂ at the end of cycle. Dy₂O₃ and HfO₂ are not proper candidates. In the case with Er₂O₃, the k_inf changes mildly. The release of reactivity is maintained at a proper level to flatten power distribution. It also satisfies the needs of control initial excess reactivity. The reactivity penalty of Er₂O₃ is acceptable comparing to that of Dy₂O₃ and HfO₂. In this article, it is chosen as the burnable poison. The volume fraction of BPs, for fuels with enrichment of 5.5%, is 1.0%.

In above calculations, all fuel rods in the assembly are mixed with burnable poison. The burnable poison volume content is 1% in each fuel rod. This scheme is referred as uniform pattern. Two other different burnable poison patterns are proposed, as shown in Fig. 5, to evaluate the influence of burnable poison distributions on assembly performance. In pattern 1, the center rod No. 1 and the outer rods No. 4–6 contain burnable poison. There are 13 burnable poison fuel rods in the assembly. In pattern 2, the center rod No. 1 and the inner rods No. 2–3 contain burnable poison. There are seven burnable poison fuel rods in the assembly. Total burnable poison content is the same. Volume content in pattern 1 is 1.5%, and 2.7% in pattern 2.

The changing of k_inf along with burnup steps at different burnable poison loading patterns is shown in Fig. 6. As we can see, with same burnable poison content, the consumption of burnable poison is slower in pattern 2 than that in pattern 1 and uniform pattern. This is because higher volume content in each fuel rod strengthens the spatial self-shielding effect.

It shows the changing of assembly radial power peaking factors along with burnup steps at different burnable poison loading patterns in Fig. 7. With uniform loading pattern, the burnable poison has little effect on pin power distribution, and the peaking power factor is about 1.005. With pattern 1 and pattern 2, burnable poison causes a peak in pin power distribution at the beginning of burnup. The peaking factor decreases as burnup increases.

According to the above results, loading pattern 1 is chosen for it has mildest influence on power distribution in the fuel assembly.

In order to keep the fuel assembly and core safe, negative void reactivity effects and negative fuel temperature coefficient of the fuel assembly is required from the view point of neutronics. If burnable poison is mixed with fuel, the reactivity coefficients will be affected. According to BP loading pattern 1, three different volume contents, 1.0%, 1.5%, and 2.0%, are applied to calculate the coolant void reactivity effects and fuel temperature coefficient.

The changing curve of void effect with void fraction using different BP volume contents for fresh fuel is shown in Fig. 8. It can be seen that the absolute value of coolant void effect increases with increase of burnable poison volume content. It means that the reactivity changes of fuel assembly with higher burnable poison volume content are more sensitive to water density variability.

The changing curve of fuel temperature coefficient with burn-up using different BP volume content is shown in Fig. 9. The absolute value of fuel temperature reactivity coefficient increases with the increase of burnable poison volume content. When the burnup is low, the coefficient differences between different cases are much larger than the difference under higher burnup.

It also can be seen in both Figs. 8 and 9 that the coolant void effect and fuel temperature reactivity coefficient keep negative and become more negative with higher burnable poison volume content. The safety criteria will be satisfied from the view point of neutronics.

In this article, the previous preconceptual SCWR design [4] which contains no BP is taken as reference case. The coolant flow scheme and core fuel loading pattern are taken from that design. The fuel rod is divided into three partitions axially, and the heights are 126, 168, and 126 cm, respectively. The fuel enrichment for three partitions is 5.0%, 5.5%, and 5.8%, respectively. The average fuel enrichment is 5.44%. The three-dimensional N/TH coupling code FENNEL is used for equilibrium core calculation. After the calculation converges, the results show that the core radial power peaking factor is 1.632 at the beginning of cycle (BOC), and the maximum cladding surface temperature (MCST) is 645 °C. The axial power distribution at BOC, middle of cycle (MOC), and end of cycle (EOC) is shown in Fig. 10. At BOC, the power peak is at the top of the core. It is because the inlet coolant density is relatively large at the top, and the neutron is well moderated.

Based on the reference case, the fuel assembly with BP which is optimized in sec. 2 is used as fresh fuel in the core loading pattern. The BP volume content is 1.0% and axially uniform. The equilibrium core is obtained using FENNEL in current case. The radial power peaking factor is 1.407 at BOC which is smaller than that of the reference case. The MCST is 757 °C, over 100 °C higher than that of the reference case. The axial power distribution is shown in Fig. 11. Comparing with the reference case, the axial power peaking factor is much larger, and the power peak moves toward the top of the core. This is why the MCST is much higher.

In order to find out the reason that axial power peaking factor increases and the power peak moves toward the top after using BP, one single fuel assembly is analyzed. The fuel assembly at the center of the core is selected. The coolant and moderator densities from the reference case are marked as distribution 1 (D1). By increasing moderator density at the lower plenum while keeping the coolant density the same, distribution 2 (D2) is obtained. Two distributions are shown in Fig. 12. Using these two distributions and two fuel loading patterns shown in Table 3, axial power distributions of four cases are calculated. The BP volume content is 1.0% in all cases.

The axial power distributions are shown in Fig. 13. It can be seen that axial power peak moves toward the top after using BP and increasing moderator density at the lower plenum will mitigate this effect. In thermal reactors, the power is proportion to the number of thermal neutron. More thermal neutron means softer spectrum. The spectrum shape can be affected by water density and BP.

The fuel assembly calculation is carried out to get the spectrum. Cases in Table 4 are calculated. The water density is taken from 145 cm (bottom) and 355 cm (top) in two water density distributions. The average fuel enrichment, 5.44%, is used.

The spectrum of water density distribution 1 is shown in Fig. 14. When no BP is in the fuel, the spectrum of the top is 38% softer than that of the bottom due to higher water density. Once the BP is used, the spectrum difference increases to 43%. Larger top–bottom spectrum difference causes larger axial peaking factor. At the bottom, spectrum of case with BP is 1% harder than that of case without BP. At the top, the difference decreases to 0.3%. The spectrum is harder with BP because BP will absorb thermal neutron. But higher moderator density at the top will mitigate BP's influence by introducing more thermal neutron.

The spectrum of water density distribution 2 is shown in Fig. 15. With water density at the lower plenum increases, the top–bottom spectrum difference for case without BP decreases to 16% and to 19% for case with BP. It shows that increasing water density at the lower plenum makes axial power distribution flatter.

According to the above analysis, two ways of axial power distribution optimization are: first, increase moderator density at the lower plenum; second, optimize axial fuel enrichment partition.

The core design is optimized based on the above strategy. First, the moderator flow rate of each fuel assembly is optimized based on the fuel assembly power. It will help decreasing the moderator density at the lower plenum. Second, the axial fuel enrichment is adjusted to 5.4%, 6.0%, and 6.4%. The average fuel enrichment is 5.94%.

The equilibrium core is calculated with optimized designs, and the core axial power distribution is shown in Fig. 16. The axial power peaking factor at BOC decreases to 1.4. The radial power peaking factor at BOC is 1.484. The MCST is 685 °C. This MCST is 72 °C lower than the previous design due to lower axial power peaking factor.

Three-dimensional N/TH coupling calculation code FENNEL is developed. The influence of BP on annular fuel assembly and SCWR core performance is studied using FENNEL. The following conclusions can be made:

1. (1)

   The spatial self-shielding effect is weak because of the geometry properties of annular fuel. Comparing to solid fuel, BPs are burned faster in the annular fuel. Er₂O₃ is chosen as BP in annular fuel.

2. (2)

   With BP loading pattern 1, the fuel assembly radial power peaking factor is small, and the reactivity is well controlled.

3. (3)

   With BP, the coolant void reactivity effect and fuel temperature reactivity coefficient keep negative. The fuel assembly is safe from the view point of neutronics.

4. (4)

   The core axial power peaking factor increases, and the power peak moves toward the top after using BP. The axial power peaking factor can be decreased by increasing water density at the lower plenum and axial fuel enrichment partition optimization.

This study was supported by the “Strategic Priority Research Program” of the Chinese Academy of Sciences, Grant No. XDA0205050.

• Chinese Academy of Sciences (XDA0205050)

k_inf =

infinite multiplication factor

N/TH =

neutronics and thermal hydraulics

$σa$ =

microscope absorption cross section