The effect of different fuels and clads on neutronic calculations in a boiling water reactor using the Monte Carlo method

In this study, a Boiling Water Reactor (BWR) modeling was done for the reactor core divided into square lattice 8 × 8 type using the Monte Carlo Method. Each of the square lattices in the reactor core was divided into small square lattices 7 × 7 type in groups of four. In the BWR designed in this study, modeling was made on fuel assemblies at pin-by-pin level by using neptunium mixed fuels as fuel rod, Zr-2 and SiC as fuel cladding, H2O as coolant. In fuel rods were used NpO2 and NpF4 fuels at the rate of 0.2%-1% as neptunium mixed fuels. In this study, the effect on the neutronic calculations as keff, neutron flux, fission energy, heating of NpO2 and NpF4 fuels in 0.2%-1% rates, and Zr-2 and SiC clads were investigated in the designed BWR system. The three-dimensional (3-D) modelling of the reactor core and fuel assembly into the designed BWR system was performed by using MCNPX-2.7.0 Monte Carlo method and the ENDF/B-VII.0 nuclear data library.


Scientific Reports
| (2020) 10:22114 | https://doi.org/10.1038/s41598-020-79236-8 www.nature.com/scientificreports/ Method Core geometry and fuel assembly geometry. In this study, Peach Bottom-2 nuclear power plant 18 was used for the selection of design parameters values of BWR in our model. BWR design parameters values of this study are shown in Table 1. The core design of the cylindrical BWR that we modeled in MCNPX is shown in Fig. 1. Moreover, as shown in Fig. 1, the reactor core is divided into the square lattice 8 × 8 type. The constant pitch of the square lattice 8 × 8 type is 30.48 cm. The core was surrounded by a graphite reflector. The outboard side of the reflector was surrounded by SS316LN ferritic steel. The core surrounded with approximately 40 reflector assemblies. As shown in Fig. 2, the fuel rods were put into square lattices and every square lattice was divided into four small square regions. Every small square region was divided into 7 × 7 type the small square lattices. The constant pitch of the small square lattice 7 × 7 type is 1.94084 cm.
Cylindrical fuel pins were placed in the small square lattices. The fuel pins were created from the fuel rod, gap and clad. The pin cell geometry in the small square lattice of the designed BWR system is shown in Fig. 3 19 . 49 fuel rods inside every small square lattice and 196 fuel rods inside every square lattice were placed in the designed BWR system. 0.2-1% NpO 2 and NpF 4 were filled into the fuel rods and Zircaloy-2 and SiC were used as clad in this study.
As seen in Fig. 2, the control rods used to ensure reactivity control were placed in cruciform between four small square lattices. The blade radius of the control rod is 0.39624 cm and the blade half length is 11.98626 cm. The control rods were filled by B 4 C in the designed BWR system. The absorber pins were made in cylinder shape into the cruciform. In the every cruciform were used total 84 absorber pins (21 per wing). Thus, it was used total 15,540 absorber pins in the designed BWR system. Type-304 stainless steel was used as structural material in the cruciform. H 2 O was used as coolant in the designed BWR system.  26,27 .
The Monte Carlo method is generally used because of the complex three-dimensional configuration of the materials, reactor physics modeling and simulation, and the many physics problems of deterministic methods. MCNPX (MCNP eXtended) 28 , which the combination of MCNP and LAHET 29 codes is a Monte Carlo radiation transport code that tracks all particles at almost any energies. The MCNPX transport code uses the continuous energy cross-sections 30 to transport low-energy particles (< 20 meV), while it uses cross section libraries for low energy particles (< 150 meV) and nuclear models for high energy particles (> 150 meV) 31 . The MCNPX uses standard cross-section libraries compiled from ENDF/B for neutron, proton and photonuclear interactions. Different intranuclear, preequilibrium and evaporation-fission models have been implemented into MCNPX-2.7.0 version, which offers seven different options based on four physics packages: Bertini 32,33 and ISABEL 34,35 , , the CEM2k 39 package and two evaporation-fission models Dresner 40 , ABLA 41 . Bertini, ISABEL, and INCL4 are INC models, which can be coupled with ABLA and Dresner evaporation-fission codes. CEM2k is a cascade-preequilibrium-evaporation model 4243 . The three-dimensional (3-D) modelling of the reactor core and fuel assembly into the designed BWR system was performed by using MCNPX-2.7.0 Monte Carlo method and the ENDF/B-VII.0 nuclear data library.

Results and discussion
Effective neutron multiplication factor. The effective neutron multiplication factor (k eff ) plays an extremely important role in determining nuclear reactor behavior. The criticality factor k eff is effective in determining the contribution of nuclear reactions to neutron multiplication. k eff is defined as the net increase in the number of neutrons from one generation to the next (Eq. 1). k eff = 1 is the desired critical operating mode of a reactor. If k eff < 1, the number of neutrons will decrease exponentially. If k eff > 1, the number of neutrons will increase exponentially, which will be dangerous to operate the reactor 44,45 .  www.nature.com/scientificreports/ In this study, k eff was examined for Zr-2 and SiC as clad and NpO 2 and NpF 4 fuels as Neptunium Mixed Fuels. Figure 4 shows the k eff value for the Zr-2 and SiC clad at 0.2-1% relative to the NpO 2 and NpF 4 fuel compositions. The effective multiplication constant must k eff ≤ 1 in the designed BWR system to avoid the critical accident. As shown in Fig. 4, the k eff value increases as the NpO 2 and NpF 4 fuel contents ratios increase from 0.2% to 1%. Figure 4 shows that the lower and upper k eff limit values of 0.6-0.8% NpO 2 are 0.98033-1.08004 for Zr-2, and those of 0.6-0.8% NpO 2 are 0.98517-1.08856 for SiC clads, respectively. Table 2 shows the calculated k eff values for three different fuel ratios of NpO 2 and NpF 4 between 0.6-0.8% in Zr-2 and SiC clads. As shown in Fig. 4 and Table 2, the k eff values for Zr-2 and SiC clads of NpO 2 fuel, and k eff values for Zr-2 and SiC clads of NpF 4 fuel are similar because of the similar thermal neutron absorption cross sections of Zr-2 (σ = 0.18 b) and SiC (σ = 0.12 b) clads values. Moreover, for the fuel ratios used, the k eff values obtained from SiC are higher than those of Zr-2. As a conclusion, the calculated k eff value for 0.6-0.8% NpO 2 fuel and SiC clad provided the desired (k eff ≤ 1) critical value. Therefore, considering the fuel ratios (0.6-0.8%) for which the k eff critical value was obtained, the lower limit of the fuel ratio was determined as 0.2% for below 0.6%, and the upper limit as 1% for above 0.8%.

Neutron flux
The neutron flux distribution in a nuclear reactor core is important for neutronic calculations of all neutroninduced nuclear reactions such as fission energy, heating, fissile fuel production. Neutron flux is the total length travelled by all neutrons per unit time and volume 46 . The process of neutron transport should be investigated to determine the neutron flux distribution in the reactor. For this purpose, Boltzmann equation also called the neutron transport equation 46,47 is commonly used to calculate neutron flux in a reactor. (1) k eff = (numberofneutronsgeneratedinthenextgeneration) (numberofneutronsgeneratedinageneration) 1 v Contribution of neutrons on neutron flux due to scattering, = s(r, E, �, t)Contribution of neutron source independent on the neutron flux.
In this study, neutron flux distribution was calculated using MCNPX-2.7.0 code and ENDF/B-VII.0 to solve Boltzmann Eqs. (2) 46,47 and (4) 46,47 . F4 tally was used to calculate the neutron flux distribution by track-length estimates of the total cell flux. Since neutron flux distribution is an important parameter in evaluating the neutronic performance of a reactor, neutron flux distribution for different clad and fuels was calculated in this study. Figure 5 shows that the neutron flux value for Zr-2 and SiC clads increases as the NpO 2 and NpF 4 fuel content ratios increase from 0.2% to 1%. As seen in Fig. 5 (for SiC captures less thermal neutrons than Zr-2), the highest neutron flux (1.696.10 13 n/cm 2 .s) result from 1% NpO 2 fuel for SiC clad and the lowest neutron flux (1.107.10 13 n/ cm 2 .s) result from 0.2% NpF 4 fuel for Zr-2 clad.
Fission energy. Almost all fast neutrons in a nuclear reactor are obtained by fission reactions. Fission energy is produced by fission reactions. The fission energy released consists of various energy modes, such as kinetic energy from fission products and fission neutrons, fast gamma rays and energy from subsequent neutron capture 43,48 . Fission energy was calculated using F7 tally. Fission energy is an important parameter for neutronic calculations of a nuclear reactor. Figure 6 shows the calculated fission energy values for Zr-2 and SiC clads, and NpO 2 and NpF 4 fuel content ratios (0.2-1%) in the designed BWR system. The fission energy values increased as the NpO 2 and NpF 4 fuel content ratios increase from 0.2% to 1%, for both Zr-2 and SiC clads. Since the thermal neutron cross section of Zr-2 is larger than SiC, fewer thermal neutrons in the Zr-2 cladding will contribute to fission energy generation. Hence, as seen in Fig. 6, the highest fission energy value (83.28 meV/n) was obtained from 1% NpO 2 fuel for SiC clad and the lowest fission energy value (16.64 meV/n) was obtained from 0.2% NpF 4 fuel for Zr-2 clad.
Heating. Neutron flux distribution and neutron multiplicity per incident neutron determine the performance of the nuclear reactor system. Therefore, the contribution of neutron spectrum and neutron multiplicity to heat energy production should be determined in the nuclear system. Moreover, heating expressed as heat energy production is produced through neutron flux, fission and other reactions. Most of the fission energy of the nuclear reactor, especially in the fuel zone, is converted into heating. A small heat release will occur through neutron and γ-ray radiation in the coolant around the fuel rods 49,50 . F6 tally was used to calculate the heating by track-length heating of the total cell heating. Figure 7 shows the heating values calculated in the relevant regions of the designed BWR system for both Zr-2 and SiC clads, and NpO 2 and NpF 4 fuel contents (0.2-1% rates). In this study, neutron flux in fuel region is more intense than other regions, since fission reaction occurs in Np additive fuel rods in the fuel region of the designed reactor. For this reason, as seen in Fig. 7, the heating value increases as the NpO 2 and NpF 4 fuel content increase from 0.2% to 1% in the fuel region where the neutron flux is intense (for Zr-2, SiC clads). When Fig. 7 is examined for the fuel region, it is seen that the highest contribution to heating comes from 1% NpO 2 with values of 11.85911 W/gr for Zr-2 and 11.93478 W/gr for SiC, while the lowest contribution to heating comes from 0.2% NpF 4 with values of 2.40284 W/gr for Zr-2 and 2.40285 W/gr for SiC. As a result, the heating value in the fuel region for 1% NpO 2 fuel content and SiC clad is higher than other fuel content ratios and clads. The heating values of the water region (coolant) shown in Fig. 7 are presented in detail in Table 3. The heating value generated in the water region around the fuel rods through neutron and γ-ray radiation with fission products is smaller than in the fuel region. As shown in Table 3, the heating value in the water region increased slightly   Figure 7 shows that the heating values in the clad and cruciform region decreases as the NpO 2 and NpF 4 fuel content ratios increase from 0.2% to 1%, for Zr-2 and SiC clads. For the clad and fuel content ratios, the contributions of the regions to heating from higher to lower value are fuel, water, cruciform and clad, respectively. Table 4 shows the integrated heating for NpO 2 and NpF 4 fuel content ratios (0.2-1%), and Zr-2 and SiC clads, in our BWR system. It is seen that the integrated heating value increased due to the increase in the fission reaction resulting from the increase of NpO 2 and NpF 4 fuel content from 0.2% to 1%, for Zr-2 and SiC clads. Integrated heating values for Zr-2 and SiC clads of NpO 2 fuel, and integrated heating values for Zr-2 and SiC clads of NpF 4 fuel are similar because of the similar thermal neutron absorption cross sections of Zr-2 and SiC clads values. Moreover, when Zr-2 and SiC clads are compared with NpO 2 and NpF 4 fuel content, it is seen that the integrated heating value found when using SiC is greater than those of Zr-2. As the highest integrated heating value was obtained from 1% NpO 2 fuel for SiC clad with 24.51 W/gr, the lowest integrated heating value was obtained from 0.2% NpF 4 fuel for Zr clad with 5.51 W/gr.

Conclusions
In this study, a BWR system with 8 × 8 type square lattice is designed. Each square lattice was divided into small square lattices of 7 × 7 type, which consist of Zr-2 and SiC clads, 0.2-1% NpO 2 , NpF 4 fuel rods, water and cruciform. In the study; k eff , neutron flux, fission energy, heating were calculated for 0.2-1% NpO 2 , NpF 4 fuels and Zr-2, SiC clads. In the designed BWR system, these neutronic calculations were made using the MCNPX-2.7.0 Monte Carlo method and ENDF/B-VII.0 nuclear data library.
In the study, it was observed that k eff , neutron flux, fission energy, heating values increased with the increasing rates of NpO 2 and NpF 4 fuels in both Zr-2 and SiC clads.
It was found that neutronic results calculated with NpO 2 fuel and SiC clad were higher than NpF 4 fuel and Zr-2 clad. As a conclusion, considering the neutronic results obtained from k eff , neutron flux, fission energy and heating values, it is recommended to use NpO 2 fuel and SiC clad in BWR reactor models.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.