Introduction
Since the 1990s, small modular reactors (SMRs) have received widespread attention owing to their inherent safety, low investment, and flexibility [1]. Many SMR concepts have been proposed, such as gas-cooled small reactors, liquid-metal-cooled small reactors, and small pressurized water reactors (SPWRs) [2-4]. PWRs have been researched for many years owing to their mature technology and low implementation difficulty. Furthermore, the SPWR has become the mainstream design [5-12].
A floating nuclear power station, MH-1A [13], was the first SPWR concept. It was built on a converted liberty ship and was part of a series of reactors in the US Army Nuclear Power Program, which developed small nuclear reactors to generate electrical and space-heating energy primarily at remote, relatively inaccessible sites. Westinghouse and the Massachusetts Institute of Technology also proposed the floating nuclear power station concepts [14]. Recently, a 50 MWe small modular reactor Nuscale was certified by the US Nuclear Regulatory Commission [15]. The first floating nuclear power station, Akademik Lomonosov, powered by two KLT-40S reactors, was constructed in Russia [16]. KLT-40S produces 150 MW of thermal power (approximately 52 MWe at 35% efficiency) and uses low-enriched uranium fuel enriched below 20%, averaging at 14.1% enrichment. The thermal hydraulics, breeding ratio, and depletion of KLT-40S were studied between 2011 and 2020. Furthermore, new floating nuclear power stations were developed in Russia based on new SPWR concepts such as ABV, SVBR, RITM 200, and VBER [17-19]. Argentina resumed the development of CAREM, an SPWR with an electric-power output ranging from 150 MW to 300 MW [20]. Japan proposed a 350 MWth integrated SPWR design [21]. South Korea has developed SMART, a 100 MW SPWR that can provide power and desalinate seawater [8]. China proposed the SPWR concept of ACP100S in 2010 and a floating nuclear power plant ACPR50S with a thermal power of 310 MW in 2015 [10, 22]. Uranium dioxide fuel and zirconium alloy claddings are widely used in current PWR designs. Despite its significant potential, the high fuel central temperature and zirconium-water chemical reaction limit its application in advanced SPWRs. The Fukushima nuclear power plant accident was partly caused by the major shortcomings of the traditional uranium-zirconium fuel system [23]. Some studies on the chemical interaction between uranium-oxide fuel pellets and zirconium-alloy cladding, control-rod ejection accident simulation, and sensitivity analysis in PWRs have also been performed [24, 25]. Hydrogen generated by the zirconium-water chemical reaction can accumulate at dangerous levels and cause explosions. Therefore, the research and development of new fuels and cladding materials to replace current uranium-zirconium fuel systems is urgently required. Accident-tolerant fuels (ATFs) have been developed globally to improve the safety of nuclear power plants during accidents [26]. Generally, ATFs focus on accident-tolerant fuel pellets by improving their thermal conductivity to decrease the fuel temperature and accident-tolerant cladding materials by reducing the rate of the chemical reaction between water and the cladding. Compared with traditional fuel systems, ATFs can resist serious accidents for a long time. The material characteristics of ATFs can slow down the accident process, allowing more time to take emergency measures and greatly reducing the risk of radioactive-product leakage. ATF research contains three roadmaps [23]: 1) improving the zirconium alloy by changing the ratio of trace elements to improve oxidation resistance, 2) using new cladding materials such as FeCrAl, SiC, and molybdenum (Mo) alloys, 3) using new fuels with high thermal conductivity and a strong ability to contain fission products, such as nitride fuels, silicide fuel, and fully ceramic microencapsulated fuel.
Extensive research on the use of ATFs in PWRs has been conducted both locally and globally. In 2013, neutronics, thermal hydraulics, and thermodynamics were analyzed for a traditional PWR with fully ceramic microencapsulated (FCM) pellet fuel [27]. In 2014, Chun et al. studied the cladding peak temperature during small- and large-break loss-of-coolant accidents [28]. In 2016, the neutronic characteristics of AP1000 were studied for different ATFs including the cladding material of SiC, FeCrAl alloy, and Mo alloy [29]. In 2017, the University of Wisconsin-Madison confirmed the good performance of FeCrAl alloy claddings in reducing hydrogen production and delaying accident processes [30]. Sadiel et al. studied the neutronic performance of the NuScale core by using ATFs (U3Si2) with different coating materials (Cr and FeCrAl) [31]. Kyung Hee University applied FCM fuel to a SPWR, SMART, and analyzed its thermal-hydraulic characteristics. In 2021, Mohsen et al. analyzed the comparative neutronic and thermal-hydraulic characteristics of nitride fuels (UN), carbide fuel (UC), and UO2 fuels based on the VVER 1000 fuel assembly [32]. In 2020, the Nuclear Regulatory Commission reviewed ATF and cladding designs to identify the fuel/cladding behavior, degradation, and radiological release [33], including silicide fuels (U2Si3), UN, and UC for fuel design, and Cr, FeCrAl, and SiC for cladding design. Research on ATFs has also been conducted in China. In 2014, Harbin Engineering University studied the feasibility of applying ATF FCM pellets to an SPWR and the neutronic characteristics of silicon carbide cladding-ATF combinations in small modular reactors [34-37]. Xi’an Jiaotong University analyzed the transient response of CPR1000 PWR with FCM-SiC in large break losses of coolant accidents and the variation in cladding temperature for different ATF systems based on RELAP5 code [38]. In 2020, the South China University of Technology conducted a safety analysis for a Nuscale reactor employing U3Si2, U3Si5, FeCrAl, and SiC [39]. Sun Yat-sen University studied the neutronics of UO2-BeO fuel with various claddings, including SiC and FeCrAl [40].
As mentioned above, some studies on ATFs in PWRs have been conducted domestically and internationally with a focus on ATF characteristics during accidents especially for UO2-BeO fuel, U2Si3, FeCrAl claddings, and SiC claddings. ACPR50S is a modular marine-pressurized water reactor with a thermal power of 300 MW; it was designed by China General Nuclear Power to develop a floating nuclear power plant. In this study, the neutronic and thermal-hydraulic characteristics of a SPWR, ACPR50S, with different ATFs were studied using the PWR fuel-management code Bamboo-C, which was developed by the Nuclear Engineering Computational Physics Laboratory at Xi’an Jiaotong University (NECP lab) [41]. Four types of ATFs including BeO+UO2-SiC, BeO+UO2-FeCrAl, U3Si2-SiC, and U3Si2-FeCrAl were employed. Various steady-state analyses were performed, including burnup calculations and the calculation of reactivity coefficients, power and temperature distributions, and control-rod reactivity worth. The transients of the control-rod ejection accident for the two control rods with the maximum and minimum reactivity worth were analyzed. The remainder of this paper is organized as follows. In Sect. 2, the ACPR50S reactor core and calculation method are introduced. Steady-state and transient analyses are presented in Sect. 3 and 4, respectively. Finally, the conclusions are summarized in Sect. 5.
Reactor configurations and calculation method
The goal of ATF is to develop safer fuel types to replace traditional UO2 fuel and Zr-4 alloy claddings. This study applied ATF to ACPR50S to improve safety and decrease nuclear power-generation costs. Furthermore, steady-state and transient neutronics/thermal-hydraulic characteristics were analyzed using Bamboo-C code, which is based on the “two-step" procedure, coupled neutronic-diffusion calculation, and parallel multi-channel thermal-hydraulic calculation.
Accident-tolerant fuel
The primary focus of research on advanced fuel technologies is the selection of appropriate fuels and cladding materials. The main method of improving the thermal conductivity of ATF pellets is to incorporate materials with high thermal conductivity into the matrix. including doped high-thermal-conductivity UO2 pellets (UO2+BeO / SiC / Mo), uranium silicon compound pellets (U3Si2), FCM pellets, UN, and inert matrix dispersion pellets.
Materials such as BeO, SiC, carbon nanomaterials, and metals are suitable for doping UO2, owing to their high thermal conductivities. BeO is chemically stable, thermally conductive, compatible with cladding materials, and has a low neutron-absorption cross-section. Compared with UO2, the uranium-nitride-based composite fuel has a higher fuel density and better thermal conductivity. However, the high amount of U-238 in UN and the added cost of N-15 enrichment make its economic benefits less noticeable. Moreover, it can easily chemically react with water at high temperatures. Uranium-silicon compounds, U3Si and U3Si2, exhibit excellent thermodynamic properties, making them ideal candidates. When subjected to high temperatures and irradiation, U3Si2 exhibits enhanced stability and improved resistance to swelling. With the aim of small-scale improvement of existing SPWRs, ATF is used to improve the thermal conductivity of the fuel. In this study, a uranium dioxide-based ATF, UO2+BeO, and U3Si2, which has good swelling resistance, were selected.
Claddings under accident conditions are among the most fragile structures of a reactor, and new cladding materials with accident tolerance must be considered. After evaluation, the cladding materials that could replace the Zr-4 alloy mainly included metal and ceramic materials [31-33]. Metallic materials include FeCrAl, Mo, and other refractory metals and their alloys, while ceramic materials include SiC and its composite materials. Mo has a high melting point and thermal conductivity, as well as large neutron-absorption cross-sections, which can result in large reactivity penalties. The loss of the neutron economy can be compensated by reducing the thickness of the cladding; however, this will increase the technical difficulty and research and development costs. FeCrAl alloys have been widely used owing to their good mechanical properties and high-temperature oxidation resistance. High-temperature steam oxidizes their surfaces, and dense oxides are generated to prevent further oxidation. Similarly, they have the disadvantage of a large reactivity penalty due to neutron absorption. In 2017, the China Nuclear Power Research and Design Institute developed a full-scale FeCrAl alloy-cladding tube for the first time and conducted irradiation tests. Given these disadvantages, FeCrAl alloy can be set as a short-term development target for ATF claddings. The SiC composite material not only has high strength but can also maintain its good mechanical properties and radiation resistance under the high-temperature and -pressure conditions of the reactor. Simultaneously, it maintains good compatibility with UO2 fuel pellets.
As mentioned above, UO2+BeO and U3Si2 and FeCrAl and SiC were chosen for the fuel and cladding as ACPR50S’s candidate materials, respectively. Thus, the neutronic and thermal-hydraulic characteristics of four new fuel-cladding systems, BeO+UO2-SiC, BeO+UO2-FeCrAl, U3Si2-SiC, and U3Si2-FeCrAl, were analyzed based on the PWR fuel-management code, Bamboo-C, developed by NECP.
ACPR50S core description
The core arrangement of the SPWR, ACPR50S, is shown in Fig. 1, which contained 21 burnable poison assemblies and 16 control assemblies, with light water acting as the surrounding reflector. The thermal power was 300 MW and the design parameters of the core are listed in Table 1.
| Parameters | Value |
|---|---|
| Thermal power (MWt) | 300 |
| Number of assembly | 37 |
| Height of active core (m) | 2.5 |
| Assembly pitch (cm) | 21.41728 |
| Average power density (MWt/m3) | 49.03 |
| FeCrAl: Fe/Cr/Al=75/20/5 | |
| Cladding (wt%) | SiC: Si/C=70.08/29.92 |
| BeO-UO2: U/Be/O= 85.806/0.954/13.230 | |
| Fuel (wt%) | U3Si2: U/Si= 92.7237/7.2763 |
| Enrichment of BeO-UO2 (%) | 4.8 |
| BeO volume fraction in BeO-UO2 (%) | 10 |
| UO2/BeO density (g/cm3) | 10.47/2.85 |
| U3Si2 density (g/cm3) | 11.57 |
| Zr-4 density (g/cm3) | 6.56 |
| FeCrAl density (g/cm3) | 7.1 |
| SiC density (g/cm3) | 2.58 |
| Radius of fuel pellet (mm) | 4.24575 |
| Gap thickness (μm) | 82.55 |
| Cladding thickness (μm) | 571.5 |
Control rods and burnable poisons were employed in ACPR50S to control the reactivity during operation. The control rod is a silver-indium-cadmium alloy (Ag-In-Cd) composed of 80% silver, 15% indium, and 5% cadmium, and the burnable poison adopts wet annular burnable absorbers (WABA) developed by Westinghouse Electric Company. A WABA rodlet comprises annular pellets of an alumina-boron carbide (Al2O3/B4C) burnable absorber material contained within two concentric Zircaloy-4 tubes. Each WABA rodlet contained an annular plenum that accommodated the helium gas released from the reaction between boron and neutrons. As shown in Fig. 2, the assembly was configured using a 17×17 array of fuel, control, and WABA rods. The pitch size of the assembly was 21.41728 cm. The WABA assembly contained 21 WABA rods, and the control assembly contained 33 control-rod guide tubes.
Bamboo-C code
Bamboo-C code was developed in-house by the Nuclear Engineering Computational Physics Laboratory (NECP) at Xi’an Jiaotong University based on “two-step" PWR fuel management [41, 42]. The calculation flowchart for Bamboo-C is shown in Fig. 3, which includes the lattice code LOCUST, core calculation code SPARK, and the lattice-core link code LtoS.
LOCUST adopts a multi-group library based on the ENDF/B-VII.0 evaluated library, a global-local method to calculate an effective self-shielding cross-section, and a modular MOC method to efficiently solve the neutron-transport equation. The point burnup Bateman equation was solved using the high-efficiency CRAM method. The few-group homogenization cross section was calculated using the equivalent homogenization method.
The few-group homogenization parameters under discrete operation states generated by the LOCUST code and are functionalized by LtoS code using the least-squares fitting or linear interpolation methods. The few-group homogenization parameters at the target state position can be expressed as the sum of the base state and disturbance terms, as shown in Eq. (1). The functionalization coefficients obtained by fitting or the linear interpolation method are saved in files and used in the following reactor core calculation:
For the disturbance term δ∑, LtoS code can optionally use polynomial fitting or a multidimensional Lagrangian interpolation method. In addition, only the multidimensional Lagrangian interpolation method was used for the burnup parameter Bu, as shown in Eq. (2) and Eq. (3):
The SPARK code employs a nodal expansion method based on nonlinear iterations to solve the three-dimensional (3D) neutron-diffusion equation. In the transient calculations, the time-derivative term in the diffusion equation is treated using the theta method. Thermal-hydraulic feedback utilizes parallel multichannel models for steady-state and transient calculations. Compared to time-consuming computational fluid dynamics (CFD) or subchannel models, multichannel models ignore the cross-flow between fuel rods, which can have a large impact on heat transfer. However, this impact can be corrected using the equivalent convection heat-transfer coefficient. In the parallel multichannel thermal-hydraulic calculation, each assembly consisted of four meshes in the radial direction, and each mesh was treated as an independent channel. The flow distributions in these channels were determined using equal pressure drops. The macro/micro burnup method was adopted to calculate the reactor core burnup distribution, evolution of heavy-metal nuclides, and changes in the fission product density. More detailed information can be obtained in reference [41, 42].
Homogenization and functionalization of few-group parameters
The few-group parameters of three types of assembly, including control, WABA, and reflector assemblies, were generated using the LOCUST code. Two energy groups with demarcation energies of 0.625 eV were used. When homogenizing the fuel assemblies at LOCUST, geometrically fine modeling of the fuel assembly was performed, and reflective boundary conditions were applied. The fuel rod was divided into nine flat source regions with radii ranging from 0.1 cm to 0.42 cm. The gap and cladding were divided into one flat source region. The water region outside the cladding was divided into five flat-source regions with radii of 0.495, 0.50, 0.53, 0.56, and 0.60 cm. For the WABA rod, the absorber region was divided into four flat-source regions, whereas the other water and cladding regions were divided into one flat-source region.
The leakage spectrum in the surrounding water reflector plays an important role in the accuracy of few-group parameters. According to the type of adjacent assembly, the few-group homogenized parameters of the four types of water reflectors were generated using three homogenization models, as shown in Fig. 4. The right boundary condition of the water reflector was a vacuum in all the models, and the other boundary conditions were reflective. The arrangements of the four types of homogenized water reflectors in the 1/4 reactor core are shown in Fig. 4. Notably, the assembly discontinuity factor was adopted in the calculation.
The thermal-hydraulic feedback must be considered in the following calculations. The few-group parameters for the discrete-state parameters were calculated using LOCUST and functionalized by LtoS code. Based on the characteristics of ACPR50S, the control-rod fraction (CR), coolant density (DC), fuel temperature (TF), and coolant temperature (TC) were employed for functionalization. CR has only two states in 2D lattice calculation: fully withdrawn and fully inserted. Ten points were used for the DC: 0.8158 g/cm3, 0.8015 g/cm3, 0.7861 g/cm3, 0.7697 g/cm3, 0.7521 g/cm3, 0.7329 g/cm3, 0.6883 g/cm3, 0.6612 g/cm3, 0.6283 g/cm3. Six state points were used for TF: 800 K, 900 K, 1000 K, 1100 K, 1200 K, and 1300 K. TC contained 10 state points: 520 K, 530 K, 540 K, 550 K, 560 K, 570 K, 580 K, 590 K, 600 K, and 610 K. In the LOCUST calculation, the reference states of TF, TC, and DC are 1000 K, 570 K, and 0.7329 g/cm3, respectively. The burnup state points consisted of four segments from 0 to 30 GWd/tU. Each segment has an equal burnup step: 4.8 MWt/tU for 0–120 MWd/tU, 120 MWd/tU for 120–2520 MWd/tU, and 600 MWd/tU for 2520–30000 MWd/tU.
Reactor-core calculation
In the reactor core neutronic calculation, each homogenized assembly region was radially divided into four meshes. The active core with a height of 250 cm was divided into 25 layers with thicknesses of 10 cm. The upper and lower reflectors, each 10 cm in thickness, were equally divided into two layers. The boundary conditions were set to a vacuum. The mesh used in the thermal-hydraulic calculation was the same as that used in the neutronic calculation. The total thermal power of the core was 300 MW with an average power of 8.1081 MW per fuel assembly, and the coolant inlet temperature was 286 ℃ with a mass flow rate of 82.12102 kg/s for each assembly.
As shown in Fig. 1, the reactor had four control-rod banks: A, B, C, and D. When fully inserted, the bottom of the control rod remained at the bottom of the active core. Each control rod moving step was 1 cm; thus, step 0 corresponded to full insertion, and step 260 corresponded to full withdrawal. In burnup calculations, the control rods must be adjusted to keep the reactor core critical. Thus, the bottom of the control rod may remain inside a node, and strong neutron absorption causes a distorted flux distribution at this node. Traditional volume-weighting methods cannot ensure the conservation of reaction rates before and after the homogenization of this node when the control rod is partly inserted, resulting in a large error, that is, the control-rod cusping effect.
In the SPARK code, a 1D transverse integration equation was solved using the fine-mesh finite-difference method for an axially adjacent three-node model, as shown in Fig. 5. Subsequently, a fine-mesh neutron flux was used to correct the control-rod cusping effect. The axial boundary condition of the neutron current was determined using the 3D nodal method, and the radial boundary was represented by the transverse leakage. Therefore, the fine-mesh fluxes in the three local nodes were calculated, and the homogenized few-group parameters of a node with a partially inserted control rod can be obtained by flux-volume weighting.
Steady-state Analysis
Similar to the homogenization method, reactor-core configuration, and core-calculation methods mentioned above, a steady-state analysis of ACPR50S, including burnup calculations, reactivity coefficients, power/temperature distributions, and control-rod worth, is performed for different ATFs: BeO+UO2-SiC, BeO+UO2-FeCrAl, U3Si2-SiC, and U3Si2-FeCrAl.
Burnup calculation
Four different B-10 enrichments of 0%, 5%, 10%, and 20% were used in ACPR50S. The keff variation with operation time is shown in Fig. 6. The figure shows that different ATF cases exhibit similar trends. B-10 enrichments of both 20% and 10% have a large reactivity penalty at the end of life (EOL), and 5% B-10 enrichment can effectively reduce the initial residual reactivity without significantly decreasing the operational lifetime. A comparison of different ATF cases at 5% B-10 enrichment is shown in Fig. 7. The residual reactivity of BeO+UO2 was higher than that of U3Si2 for the same cladding material and B4C. This is because the moderating ability of BeO-UO2 is better than that of U3Si2. The core with BeO+UO2 has a shorter operation lifetime of approximately 50 days compared with the core with U3Si2. In addition, FeCrAl cladding has a larger neutron absorption than SiC, and using SiC can increase the operation time by 200 days for the same fuel. As depicted in Fig. 7, the cladding type had a greater impact on the lifetime than the fuel type. The burnup comparison shows that the BeO+UO2 fuel and SiC cladding are superior to the other types.
Reactivity coefficient
The reactivity coefficient is a key safety parameter. In addition to depletion and fission-product accumulation, the fuel temperature, moderator temperature, and void fraction also affect the reactivity. In this section, the fuel temperature, coolant temperature, void reactivity, and power coefficients are calculated.
During normal operation, the fuel temperature generally remains in the range of 900–1200 K. In the fuel-temperature coefficient calculation, fuel-temperature points were set at intervals of 100 K, and the coolant temperature was maintained at 600 K. The fuel-temperature coefficients of cores with different ATFs are listed in Table 2. The table shows that the fuel-temperature coefficients are -2.74 pcm/K, -2.54 pcm/K, -2.348 pcm/K, and -2.161 pcm/K for the four ATFs, which are all negative. The fuel-temperature coefficient of BeO+UO2-SiC is more negative than those of the others, whereas U3Si2-FeCrAl has the smallest negative coefficient. As mentioned above, BeO+UO2 has a stronger moderation ability than the other fuel types. More fast neutrons entered the resonance-energy region, and the fuel Doppler effect was more pronounced, resulting in a more negative fuel-temperature coefficient. Fe nuclides in FeCrAl cladding can absorb a few resonant neutrons, thereby weakening the Doppler effect. From the viewpoint of the fuel-temperature coefficient, ACPR50S fueled with BeO+UO2-SiC performed better than the other cases.
| ATF type | Fuel temperature coefficient (pcm/K) | Coolant-temperature coefficient (pcm/K) | Void coefficient (pcm/%) | Power coefficient (pcm/%FP) |
|---|---|---|---|---|
| BeO+UO2-SiC | -2.74 | -71.4 | -479.4 | -8.76 |
| BeO+UO2-FeCrAl | -2.54 | -62.9 | -433.9 | -7.78 |
| U3Si2-SiC | -2.34 | -72.7 | -483.0 | -8.25 |
| U3Si2-FeCrAl | -2.16 | -64.2 | -440.3 | -7.57 |
Water in ACPR50S acts as both a coolant and moderator. The change in the water temperature influences its density, which in turn, affects its moderation ability and neutron absorption. During normal operation, the water temperature changes in the range of 520–610 K. An interval of 10 K was employed for the coolant temperature-reactivity calculation, and the density and temperature changed synchronously. Figure 8 shows the change in keff with the coolant temperature. The reactivity decreases with an increase in coolant temperature, which means that the coolant-temperature coefficient is negative. Table 2 lists the reactivity variation when the coolant temperature changes between 520 and 610 K and the coolant-temperature coefficient. Notably, ACPR50S does not contain soluble boron; thus, the negative value of the coolant-temperature coefficient is relatively large because soluble boron has a positive effect on the coolant-temperature coefficient. Fuels with the same cladding had similar reactivity coefficients, and the SiC-case is more negative than the FeCrAl-case. FeCrAl cladding has stronger thermal neutron absorption than SiC, which has a positive effect on the coolant-temperature coefficient.
The change in the void fraction in the coolant plays an important role in reactivity, especially in loss-of-coolant accidents. An increase in the void fraction in the coolant reduces the moderation ability. Therefore, the neutron spectrum hardens, resulting in an increased neutron leakage and decreased reactivity. The void-reactivity coefficient was calculated by setting the void fractions to 0% and 100%. The fuel and coolant temperatures were 900 K and 600 K, respectively. The results are listed in Table 2. The table shows that the void-reactivity coefficients are all negative for ACPR50S in the four ATF cases. Similarly, the absence of soluble boron in the coolant led to a significantly negative void-reactivity coefficient. Compared to SiC cladding, FeCrAl had stronger neutron absorption, and the void coefficient of SiC-based ATFs was more negative. The power coefficient was also calculated for these four ATFs, which was a comprehensive quantity that included the fuel temperature, coolant temperature, and void effects. The results are listed in Table 2. The table shows that the four cases have negative power coefficients, which meet the core-design safety criteria. Due to the combined influence of the strong moderation ability of BeO+UO2 and small neutron absorption of SiC, the power coefficient -8.76 pcm/%FP of BeO+UO2-SiC was more negative compared with the other three cases.
In summary, the reactivity coefficients ACPR50S of the four ATFs were all negative. ATFs with the same cladding had similar coolant-temperature, void-reactivity, and power coefficients because the neutron absorption of the cladding played a major role. For the temperature coefficient, the strong moderating ability of BeO+UO2 had a negative effect; however, the neutron absorption of FeCrAl cladding caused a positive effect. Thus, the fuel-temperature coefficient of BeO+UO2-SiC fuel was 2.74 pcm/K more negative than the other three cases. Because of the absence of soluble boron in the coolant, the coolant temperature and void reactivity coefficients were significantly more negative than those of general PWRs.
Power and temperature distribution
The assembly normalized power, fuel-temperature, and coolant-temperature distributions of ACPR50S for the four ATFs were calculated, as shown in Fig. 9, where A, B, C, and D represent the BeO+UO2-SiC, BeO+UO2-FeCrAl, U3Si2-SiC, and U3Si2-FeCrAl cases, respectively. In the calculation, the nominal power of the 300 MWth and coupling thermal-hydraulic calculations were performed, and all control rods remained outside the reactor core.
As shown in Fig. 9, the power peak factors of BeO+UO2-SiC and BeO+UO2-FeCrAl were 1.63 and 1.65, respectively, which were marginally larger than those of the other two cases. This is because BeO+UO2 had a strong moderating ability and SiC-based ATF had a low fuel temperature owing to the high thermal conductivity of SiC[43]. The fuel-temperature distributions of the four cases were similar, and the gradient of the cases fueled by BeO+UO2 was larger than that of U3Si2. The maximum fuel temperature of the core fueled by BeO+UO2 was approximately 604 ℃. However, the maximum fuel temperature of the core fueled by U3Si2 was approximately 595 ℃. The coolant-temperature distributions of the four ATF cases were nearly identical because all heat generated by the fission reaction was transferred to the coolant at the steady state. The maximum coolant temperature was approximately 327 ℃, and the difference between the maximum and minimum values of the entire core did not exceed 20 ℃.
At a nominal power of 300 MWth, comparison analyses were performed for ACPR50S with the four ATFs, including the normalized power distribution, fuel-temperature distribution, and moderator-temperature distribution. The U3Si2 fuel core had a better power-flattening effect than BeO+UO2, and the overall fuel-temperature change was smaller. Moreover, the coolant-temperature distributions differed marginally among all ATF cases. Although the moderating abilities of UO2-BeO and U3Si2 and the neutron absorption of SiC and FeCrAl differed, these differences had a small impact on the power and temperature distributions.
Reactivity worth
ACPR50S adopts burnable poison and control rods to adjust the reactivity. Twenty-one burnable poison and 16 control assemblies were configured in the reactor core. Both the burnable poison and control-rod reactivity worth were calculated, as shown in Table 3 and Fig. 10. Burnable-poison reactivity worth is defined as the reactivity difference between loading pure fuel without burnable poison (0% B-10 enrichment) and loading burnable poison (5% B-10 enrichment). ACPR50S loaded with BeO+UO2-SiC had the largest burnable-poison reactivity, worth 8153 pcm, because BeO had a better moderating ability than U3Si2. For the same fuel type, FeCrAl cladding had a larger absorption cross-section than SiC, which resulted in a reactivity penalty of approximately 800 pcm.
| ATF type | Burnable poison worth (pcm) | Control rod total worth (pcm) |
|---|---|---|
| BeO+UO2-SiC | 8153.0 | 29638 |
| BeO+UO2-FeCrAl | 7240.7 | 26114 |
| U3Si2-SiC | 7873.7 | 28732 |
| U3Si2-FeCrAl | 7012.9 | 25430 |
ACPR50S employs four groups of control rods: A, B, C, and D. The differential and total reactivity worths of the four control-rod groups were calculated. In the calculations for a control-rod group, the other control-rod groups remained outside the reactor core, and a B-10 enrichment of 5% was employed. Furthermore, the correction method for the control-rod cusping effect was employed in the differential-worth calculation using the Bamboo-C code. BeO+UO2-SiC had the maximum total control-rod reactivity of 29638 pcm among all ATF cases, and U3Si2-FeCrAl had the minimum (25430 pcm). When all poisons were inserted into the reactor, a shutdown margin of 1300 pcm of the design criteria was reached. Fig. 10 shows that control-rod group B had the largest differential worth, and A had the smallest because control-rod A stays in the outer region of the reactor core, whereas B stays in the inner region. For all control-rod groups, the differential worth appeared similar between the different ATFs, and the maximum difference did not exceed 10 pcm/step.
ACPR50S did not contain soluble boron; thus, criticality is maintained by adjusting the control-rod position, and the order of adjustment was B-A-C-D. During the operation, the critical positions of the control rod were calculated for the four ATFs, as shown in Fig. 10, where the fully inserted and withdrawn control rods corresponded to steps 0 and 260, respectively. Because of the difference in the initial residual reactivity, the critical position of control-rod B in step 30 was reached for the BeO+UO2-SiC core, and the U3Si2-FeCrAl core had the highest critical position in step 67. The critical positions of the control rod were different for ACPR50S fueled by different ATFs. Comparing all cases, the control rods of the U3Si2-FeCrAl core were the first to be fully withdrawn, and those of BeO+UO2-SiC were the last. Control-rod groups B, A, C, and D of the U3Si2-FeCrAl core were fully withdrawn on days 166, 186, 516, and 806, respectively. However, those for the BeO+UO2-SiC core were observed on days 556, 606, 1046, and 1406.
Transient Analysis
Transient characteristic analysis is an important aspects of safety design. In this section, the transients of the control-rod ejection accident for two control rods with the maximum and minimum reactivity worth are analyzed. In the transient state, control-rod A was ejected from steps 0 to 100, control rod B was ejected from step 100 to fully withdrawn, and each step was 1 cm.
In the calculation, the control-rod ejection was completed in 0.1 s, a time step of 0.01 s was employed, and the entire simulation continued for 10 s. At the beginning of the transient, the reactor core maintained criticality by adjusting the nu-fission cross-section because the critical control-rod position was different for different ATFs, and the reactor core remained in a hot and full-power state. The reactivity changes caused by the control-rod ejection are illustrated in Fig. 11. At time 0 s, the positive reactivity increased quickly owing to the control-rod ejection. The reactor power and core temperature increased simultaneously. The negative reactivity feedback then restrained the increase in reactivity, and it reached a maximum value at approximately 0.4 s. Furthermore, the negative reactivity feedback started to dominate, and the reactivity decreased smoothly. For the different ATF types, the reactivity changed similarly, and the U3Si2-SiC core exhibited the largest reactivity insertion. The maximum difference in the reactivity insertion between the different ATF cases was approximately 0.09 $ for control-rod A and 0.02 $ for control-rod B.
The core-power response during the transient is shown in Fig. 11. Control-rod ejection introduced positive reactivity, causing a rapid increase in the reactor core power. However, the negative feedback of the fuel and coolant temperature reduced the core power, eventually stabilizing it at a new level. In the transient of the control-rod A ejection, the core power of the U3Si2-SiC core changed the most and reached the maximum relative power of 1.85 at time 0.11 s. However, the BeO+UO2-FeCrAl core with the slowest increase reached a maximum relative power of 1.60 at time 0.19 s. The power changes were similar for the control-rod B ejection case. The U3Si2-SiC core reached a maximum relative power of 2.5 at time 0.08 s, and the BeO+UO2-FeCrAl core reached a maximum relative power of 2.29 at time 0.08 s because control-rod B had a larger reactivity worth than control-rod A. The power response of the core fueled by BeO+UO2 changed more gradually than that of the other ATFs during the positive reactivity insertion transient owing to the more negative fuel and coolant-temperature coefficients.
The changes in the fuel and coolant temperatures during the transient were also calculated, as illustrated in Fig. 11. The fuel temperature increased quickly at the beginning of the transient, along with an increase in reactor power, and then became steady. Similar to the core-power response in the transient ejection of both control-rods A and B, the fuel temperature of the U3Si2-SiC core reached the highest values of 516 ℃ and 560 ℃, respectively, when reaching stability. Conversely, the BeO+UO2-FeCrAl core exhibited the lowest fuel temperatures of 511 ℃ and 552 ℃, respectively, after reaching stability. The coolant temperature and density changed similarly with the fuel temperature in the transient, and the maximum difference in the average coolant temperature between the cores fueled by different ATFs did not exceed 2 ℃. Overall, during the same control-rod ejection, the changes in the fuel and coolant temperatures and density appeared to be minimal, with only a maximum difference of 10 ℃ for the fuel temperature and 2 ℃ for the coolant temperature. The transient responses mainly depended on the neutronic and thermal-hydraulic characteristics of the ATFs. Although differences exist in the moderation ability of UO2-BeO and U3Si2 and neutron absorption of SiC and FeCrAl, these differences have a small impact on the change in reactivity insertion and relative core power during the transient state.
Conclusion
This study focused on the coupling neutronics and thermal-hydraulic analysis of a SPWR, ACPR50S, for different ATFs including BeO+UO2-SiC, BeO+UO2-FeCrAl, U3Si2-SiC, and U3Si2-FeCrAl, using the Bamboo-C deterministic code developed by the NECP laboratory.
A steady-state analysis, including burnup calculations, reactivity coefficients, power and temperature distributions, and control-rod reactivity worth, was performed. A 5% B-10 enrichment in the WABA assembly effectively reduced the initial reactivity and EOL reactivity penalty. The reactivity coefficients ACPR50S of the four ATFs were all negative. Owing to the good moderation ability of BeO+UO2 and the small neutron absorption of SiC, the BeO+UO2-SiC core has better burnup characteristics and a more negative fuel-temperature reactivity coefficient and power coefficient compared to other ATFs. The BeO+UO2-SiC and U3Si2-SiC cores had coolant-temperature and void-reactivity coefficients similar to those of the other cases because the neutron absorption of FeCrAl had a positive effect. The U3Si2 fuel core had a better power-flattening effect than BeO+UO2, and the fuel and coolant temperatures differed little among all ATF cases. The differential worth of each control-rod group appeared similar between the different ATFs, and the maximum difference did not exceed 10 pcm/step.
Two transient states were also calculated, including control-rod ejection accidents with the maximum and minimum reactivity worth. The maximum difference in the reactivity insertion between the different ATF cases was approximately 0.09 $ for control-rod A and 0.02 $ for control-rod B. The changes in the fuel temperature, coolant temperature, and coolant density in the transient of the same control-rod ejection were similar. The maximum difference did not exceed 10 ℃ for the fuel temperature and 2 ℃ for the coolant temperature. Although differences exist in the moderating ability of UO2-BeO and U3Si2 and the neutron absorption of SiC and FeCrAl, these differences had a small impact on the change in reactivity insertion and relative core power during the transient state.
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