1 Introduction

Nuclear power plants (NPPs) have a significant role in contributing dependable, clean, and cost-effective energy supply. Most developed NPPs are light-water reactors with UO2 as the candidate fuel. The high rate of uranium consumption, the prohibitive cost of the uranium ores, and the reduction in uranium mining (11%) in recent years (2017–2019) make the limitation of UO2 fuel [1]. At the same time, the utilization of nuclear fuel generates nuclear waste containing heavy metals, short-lived and long-lived radioactive nuclides, and radiotoxic waste. Plutonium has already been recycled in the thermal reactors to increase the utilization of nuclear fuel [2]. It has already been suggested to use the MOX fuel of uranium and plutonium blending in thermal reactors [3]. However, there are other options such as (Th, U) O2, (Ux Am1-x)O2, (Th, Pu)O2, and (Th, Np)O2 oxides as the MOX fuel [4,5,6, 39].

Usually, the plutonium-based MOX fuel contains between 3 and 5% of the PuO2 blended with the depleted or natural UO2 in 95–97% [7]. The PuO2 replaced the enrichment fraction of 235U in the conventional UO2 fuel. The advantage of thorium- or plutonium-based fuel over the conventional UO2 fuel is high neutron yield per absorbed neutrons; less generation of neutron poison (xenon, samarium), reducing radiotoxicity of spent fuel, and nonproliferation. The thorium-based fuel has high thermal conductivity, lowers thermal expansion coefficient and enthalpy than the UO2, and has a higher melting point (3,643 °C) (Table 2). The fission gases released from the irradiated MOX fuel are lower than the UO2 [8]. The thorium–plutonium coolant void reactivity for 21% contents of plutonium remains negative, whereas the modulation occurs at 16% for MOX fuel. However, the (Th, Pu)O2 delivers the impression of some advantages over MOX fuel with regard to boron worth's, coolant void reactivity (CVR), control rod, and consumption of plutonium [9, 10]. These properties of thorium fuel tend to improve the neutronic and thermal hydraulics of the NPPs when uranium and thorium MOX fuel is compared to the current uranium oxide fuel [10].

To use thorium as a nuclear fuel, the characteristics of thorium fuel are necessary to be known. The burnup, DRC, and the effective multiplication factor (keff) are the essential parameters for reactor safety to evaluate the feedback. The thermal and epithermal integral resonance absorption and fission cross section consider the largeness of the cross section, particularly for the resonance region. The resonance integral of 232Th, 238U, and 235U in JENDL-4.0(u) is shown in Table 1 [11, 12]. The resonance integral of the capture cross section of 232Th is about one-third of 238U. Therefore, the literature shows that the DRC of ThO2 is negatively smaller than that of UO2 [13].

Table 1 Summary of the neutronic properties of 233U, 235U, 232Th, & 238U in the epithermal and thermal region (average over Maxwellian spectrum at 300 °C (0.05 eV) [11, 12]
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On the other hand, the literature predicts that the Doppler reactivity of thorium fuel is negatively larger than that of U-fuel [14]. Thorium has less radioactive waste and a higher natural abundance than uranium. The absorption cross section of 232Th (4.62 barns) is also higher than 238U (1.73 barns) in the thermal range, which enables the thorium as an intemperate fertile material. The physical properties of U, UO2, Th, ThO2 Pu, and PuO2 are compared in Table 2 [12].

Table 2 Physical properties of U, UO2, Th, ThO2 Pu, and PuO2 [12]
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The current development of small modular reactors (SMRs) has the pivotal point of deliberation because they have various applications and advantages. The benefits of SMRs embrace better safety, prolonged fuel cycle, and the highest power density. Another critical advantage of SMRs is that the SMRs usually have a shorter construction time and lower financing costs (absolute capital costs and interest payments on debt). Thus, the financial risk to a utility building an SMR before it becomes operational and starts earning revenue to pay off debts is lower. The typical applications of SMRs are electricity generation, medical application isotopes generations, water desalination, nuclear propulsion, and chemical element generation. The compact and modular design of SMRs makes it permissible to operate in unfledged countries in energy [15, 16]. Some of the SMRs are presented in Table 3 which are of the outmost interest.

Table 3 Summary of the integral pressurized water cooled small modular reactors (SMRs) [17]
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Among the integrated SMRs, the SMART reactor is a unique type of reactor that has both forced and natural circulation. The SMART reactor supports natural circulation when operated at less than 45 MWe [18]. Various neutronic [19, 20, 22, 27], and thermal hydraulics [16, 20, 21, 26] have been conducted on the SMART reactor. However, the interesting study has been performed by Akbari-Jeyhouni et al. [24] to convert the SMART reactor core from conventional UO2 fuel to the (U-Th)O2 fuel without altering the basic design of the core and by Kamalpour et al. [25] to convert SMRT core with the FCM fuel. Recently, Al-Zahrani et al. [28] have investigated the feasibility of SMART reactor core for different types of FCM fuel. Therefore, this work focused on the SMART reactor's core assessment for the hybrid fuel configuration. The SMART reactor core is modeled for homogenous and heterogeneous configurations of the (U-Th)O2 fuels with the minimum alteration from the reference core design. The SMART reactor core has also been loaded with MOX fuel (PuO2 with 3.0 wt% and UO2 with 97.0 wt%). The calculation has been carried out using OpenMC, an open-source Monte Carlo code. The calculation has been performed without soluble boron and IFBA rods.

2 Material and Methods

2.1 Reference SMR

The system-integrated modular advanced reactor (SMART) is chosen as the reference SMR. The SMART reactor is an integrated and multipurpose reactor with a rated thermal power of 330 MWt (100 MWe) and 7,338 gallons per minute (GPM) of productions of desalinated water [29] developed by the Korean Atomic Energy Research Institute (KAERI). The SMART design incorporates both passive and active safety features by eliminating major piping systems and assembling major components inside the reactor pressure vessel (RPV), i.e., flow mixing heaters, coolant pumps, a pressurizer, and steam generators. The SMART reactor does not have an extensive piping system. Thus, fundamentally the possibility of a large break LOCA is eliminated. The SMART reactor design is depicted in Fig. 1 [23]. The SMART is the multipurpose reactor designed to generate 100 MWe of electricity, desalination, and process heat for the industries and small isolated grids [30, 31]. The primary design parameters of the SMART reactor are presented in Table 4.

Fig. 1
figure 1

The system-integrated advance and modular reactor (SMART) reactor [23]

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Table 4 Design parameter of SMART rector [28, 34, 35]
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The SMART reactor core design is based on the commercial PWR assemblies. There are 57 fuel assemblies of 17 × 17 array of KOFA technology [32] (Fig. 2) of six different types (Fig. 3). The reference core of the SMART reactor is depicted in Fig. 2, whereas the types of assemblies are shown in Fig. 3 [22]. Each assembly consists of 264 fuel rods and IFBA rods, 24 control rods guided tubes of Ag-In-Cd material, and one instrumentation thimble at the center of each assembly [33]. Notably, each fuel assembly is a square array of 289 rods. The fuel enrichment is less than 5.0% which delivers adequate fissile material for 36 months of continuous full power operation. Solid (U, Gd)O2 IFBA rods are provided in the core to reduce the boron concentration [34]. The SMART reactor core configuration, including numbers of IFBA, assembly type, and Gd2O3/UO2 weight percentage, is presented in Table 5.

Fig. 2
figure 2

Cross-sectional view of the core configuration of the SMART reactor [22]

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Fig. 3
figure 3

Fuel assemblies of SMART reactors [22, 28]

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Table 5 Fuel assembly's configuration of the SMART reactor [22, 28]
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2.2 MOX fuel Assembly Configuration

The use of MOX fuel in light-water reactors (LWRs) changes the neutronic of the core in numerous ways. The deviation in the cross section of plutonium isotopes with the energy is more convoluted than uranium isotopes [36]. In the thermal energy range, the absorption cross section of plutonium is much higher than the uranium, characterized by vast absorption resonances in the energy range and by overlapping resonances, as depicted in Table 1. In the first step, the identical core configuration of the reference core of the SMART reactor was used. In the next step, the MOX fuel in selected fuel assemblies was introduced. The same IFBA and control rod configuration in each assembly of the SMART reactor core has been employed in the MOX fuel configuration. The MOX fuel assemblies were introduced instead of the fuel assembly of type B (4.88 w/o% U-235) and fuel assembly of type C (2.82 w/o% U-235) with the same number of IFBA and control rods. In the MOX fuel rods, each fuel pellet contain 3.0 wt% of PuO2 and 97.0 wt % of UO2. The PuO2 enrichment is 2.35 wt% of Pu-241, and the UO2 enrichment is 2.82 wt% is U-235. The MOX fuel assemblies were introduced in the SMART reactor to enhance the capability of fission product retention and thermal conductivity. The MOX fuel configuration of the SMART reactor is depicted in Fig. 4, whereas the configuration of the MOX fuel pellet is expressed in Table 6. The SMART reactor core was for effective multiplication factor (keff), burnup, MTC, and DRC using the OpenMC Monte Carlo code.

Fig. 4
figure 4

Hybrid layout of SMART reactor core with MOX fuel assemblies and conventional fuel assemblies

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Table 6 MOX fuel pellet configuration
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2.3 (U-Th)O2 SMART Core Configuration

For the (U-Th)O2 hybrid fuel configuration, the exact geometry of the SMART reactor core (IFBA and control rods configuration) was used as that of the reference core, but the two different homogenous and heterogeneous configurations of fuel rods in the fuel assemblies have been employed. The homogenous and heterogeneous configurations can be seen in Fig. 5. It can be seen from Fig. 5 that the heterogeneous configuration has been arranged according to the seed and blanket concept. In a homogenous configuration, all the fuel rods have the same concentration of U-Th mix fuel. The U-Th fuel assemblies are enriched with 2.5% and 16.5% of 235U and 232Th, respectively, in the homogenous configuration with 25 control rods and 264 fuel rods. However, the central 11 × 11 fuel rods contain uranium dioxide with the same enrichment as the reference core in the heterogeneous fuel assembly configuration. The outer blanket of fuel assembly has (U-Th)O2 mixed fuel with a concentration identical to the homogeneous configuration. As a constraint, the enrichment of 235U is limited to the utmost to be the same as the reference core. Thus, the uranium enrichment for the (U-Th)O2 remains less than the 5.0 wt% U-235/(U-Th) in proposed configurations (homogenous and heterogeneous). The SMART reactor core with proposed homogeneous and heterogeneous configurations was analyzed for effective multiplication factor (keff), burnup, MTC, and DRC using OpenMC Monte Carlo code.

Fig. 5
figure 5

Homogeneous and heterogeneous fuel rod assembly configurations

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3 Methodology

3.1 Effective Multiplication Factor (k eff)

The effective multiplication factor (keff) is the dominant parameter for the neutron transport problem. The effective multiplication factor (keff) measurement is essential for the reactor's criticality. The keff is defined as the ratio of the generation of the thermal neutrons to the abrogation and leakage in the preceding generation via fission. The effective multiplication factor (keff) calculation f-energy cross sections from ENDF/B-VII.0 neutron data for all materials. The effective multiplication factor (keff) has been evaluated for UO2, MOX fuel, and (U-Th)O2 fuel in homogeneous and heterogeneous configurations. The variation in keff with temperature, burnup, and operation days has been assessed for UO2, MOX fuel, and (U-Th)O2 and compared.

3.2 Doppler Reactivity Coefficient

When the reactor operates, the temperature of the fuel increases, which results in a change in the effective multiplication factor (keff). The DRC is an efficacious parameter for the safety of the thermal reactors and improves reactor stability. DRC is defined as the reactivity alteration due to variation in fuel temperature. The probability of interaction of neutron dramatically depends on the fuel temperature. The resonance escape probability is affected by the change in fuel temperature via the thermal Doppler broadening of resonance capture cross section of fertile material, e.g., 235U, 240Pu, and 232Th. Thus, the Doppler effect arises from the dependence of the neutron interaction probability of the relative velocity or energy of the neutrons. The alteration in resonance escape probability affects the effective multiplication factor (keff), resulting in a change in reactivity. The DRC can be defined as follows and is measured in the unit of pcm K−1.

$$ {\text{DRC}} = \frac{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 k}}\right.\kern-0pt} \!\lower0.7ex\hbox{$k$}} - {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {k^{^{\prime}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k^{^{\prime}} }$}}}}{{{\text{d}}T}} = \frac{{{\raise0.7ex\hbox{${{\text{d}}k}$} \!\mathord{\left/ {\vphantom {{{\text{d}}k} {kk^{^{\prime}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${kk^{^{\prime}} }$}}}}{{{\text{d}}T}} $$
(1)

where dT is the change in temperature, k, and k' are the neutron multiplication factors before and after the temperature change. The value of DRC depends upon the fuel temperature, burnup, and enrichment. The DRC always remains negative in the thermal reactors with low enrichment of 3.0%–5.0%. The sensitivity of the DRC has defined the ratio of relative change in multiplication factor to the relative change in cross section. Thus, the sensitivity coefficient of DRC can be defined as follow.

$$ S_{i,R,g}^{k} = \frac{{{\raise0.7ex\hbox{${{\text{d}}k}$} \!\mathord{\left/ {\vphantom {{{\text{d}}k} k}}\right.\kern-0pt} \!\lower0.7ex\hbox{$k$}}}}{{\left( {{\raise0.7ex\hbox{${{\text{d}}\sigma }$} \!\mathord{\left/ {\vphantom {{{\text{d}}\sigma } \sigma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\sigma $}}} \right)_{i,R,g} }} $$
(2)

where \(S_{i,R,g}^{k}\) is the sensitivity coefficient of the DRC, which depends upon the change in the multiplication factor. The σ is the cross section, and the suffix i, R, and g are the nuclides, reaction type, and energy group, respectively. For reactivity feedback, the impact on the reactor core, the DRC must be determined, and it is one of the vital parameters in stabilizing the thermal reactors. At the beginning of the fuel cycle, the Doppler effect of 238U and 232Th ensures the negative reactivity feedback. However, it decreases with the accumulation of fission gases and 239Pu at the end of the fuel cycle. The DRC of the SMART reactor has been analyzed for the core configurations, which are described in Figs. 4 and 5.

3.3 Moderator Temperature Coefficients of Reactivity

When the reactor operates, the temperature of the coolant increases. This change in moderator temperature alters the multiplication factor. The MTC of reactivity is defined as the change in reactivity for a unit change in temperature and is represented by αM. Thus, the MTC of reactivity can be expressed as [38].

$$ \alpha_{M} = { }\frac{{{\text{d}}\rho }}{{{\text{d}}T}} $$
(3)

where T is the fuel temperature and \(\rho \) is reactivity is, which is a function of the criticality of the system and can be expressed as:

$$ \rho = \frac{{k_{{{\text{eff}}}} - 1}}{{k_{{{\text{eff}}}} }} $$
(4)

Thus, the MTC of reactivity can be expressed as

$$ \alpha_{M} = { }\frac{{{\text{d}}\rho }}{{{\text{d}}T}} = \frac{{\text{d}}}{{{\text{d}}T}}\left( {\frac{{k_{{{\text{eff}}}} - 1}}{{k_{{{\text{eff}}}} }}} \right) = \frac{1}{{k_{{{\text{eff}}}}^{2} }}\frac{{{\text{d}}k_{{{\text{eff}}}} }}{dT} \approx \frac{1}{{k_{{{\text{eff}}}} }}\frac{{{\text{d}}k_{{{\text{eff}}}} }}{{{\text{d}}T}} $$
(5)

where keff is the effective multiplication factor. The MTC and DRC are usually expressed in units of pcm °C−1 or pcm K−1. The DRC is supposed to be more critical than the MTC of reactivity. Especially in all reactivity initiation accident (RIA), the DRC is the first and most significant feedback that compensate for the positive reactivity feedback. The computational model has been developed and implemented in OpenMC. The Doppler effect is dominantly responsible for the change in reactivity. The Doppler effect, DRC, and MTC have been evaluated for the SMART reactor core for the proposed models of fuel assembly using OpenMC and benchmarked with the reference core.

3.4 Power Peaking Factor

The local power density (LPD) should be measured accurately to ensure that several safety limits imposed on the fuel pellets and cladding are not violated during the normal operation of the reactor. Since the LDP at the hottest point of the core is the primary concern from the safety point of view, the LPD at the hot part of the reactor core provides more vital information than any other position of the core. The LPD of the heated fuel rod, which is presented as the power peaking factor (PPF), is more important than the LPD. Especially the LPD monitoring in operating nuclear reactor is essential to prevent the fuel melting. The LPD at the hottest part of the heated fuel rods, which can be expressed by the power peaking factor (PPF), is more important than LDP at any other point of the reactor core [40]. It is defined as the ratio of LPD to the average power density of the core. Thus, the integrity of the fuel rods needs to be ensured during the normal operation of the reactor by monitoring the PPF. Therefore, three-dimensional core power distribution is required to be monitored. Thus, in this study, the three-dimensional thermal neutron flux has been evaluated for the (U-Th)O2 mixed fuel of homogeneous and heterogeneous configurations and MOX fuel configuration of the SMART enactor core and compared with the reference core. The two-dimensional PPF of the (U-Th)O2 mixed fuel of homogeneous and heterogeneous configurations and MOX fuel configuration has also been evaluated using OpenMC for the Proposed configuration of the homogeneous and heterogeneous (U-Th)O2 mixed fuel and for the MOX fuel configuration of the SMART reactor core as described in Figs. 4 and 5.

3.5 Calculation Procedure

The prime objective of this study is to analyze the SMART reactor core for MOX, mixed (U-Th) O2 fuel with the minimum change in the design of the SMART reactor core. The described models have been modeled in OpenMC [37] Monte Carlo-based code and core parameters (e.g., burnup, Doppler reactivity coefficient (DRC), effective multiplication factor (keff), thermal neutron flux, power peaking factor (PPF), and moderator temperature coefficient (MTC)) have been evaluated. A set of criteria has been attributed to the calculation which includes:

  1. 1.

    The whole core geometry, including fuel rods, control rods, IFBA rods, burnable absorbers, and instrumentation rod diameter and pitch, must be kept the same.

  2. 2.

    235U enrichment remains lower or the same as the enrichment of the reference core.

  3. 3.

    Keep the kinetics parameter of the SMART reactor core in all types of fuel configuration (MOX and (U-Th)O2) near the reference core value.

  4. 4.

    The fuel cycle is kept near 36 months.

The following steps have been embarked upon to meet the requirements.

  1. a.

    SMART reactor core configuration has been chosen to compare the different configurations of MOX, (U-Th)O2 fuel with the reference core. In this study, the calculation for MOX core, (U-Th)O2 core (Homogeneous and Heterogeneous) has been performed without the burnup poison and IFBA rods.

  2. b.

    A set of assumptions has been considered for MOX, (U-Th)O2 core (homogeneous and heterogeneous) configuration which according to that proposed configuration, i.e., a minimum change in the geometry and operation conditions.

  3. c.

    Proposing (U-Th)O2 core configurations (homogeneous and heterogeneous) for the SMART reactor core. For this purpose, two possible fuel assembly arrangements have been considered: homogenous mixed U-Th fuel assemblies and heterogeneous seed-blanket concept with uranium fuel at the center of each assembly and mixed U-Th at the outer region (blank) of fuel assembly (Fig. 5).

  4. d.

    Comparison between the configuration and fuel types and choose the best configuration that meets the criteria.

4 Results and Discussion

In this work, the feasibility study of MOX fuel (U-Th) fuel has been evaluated for the SMART reactor. The SMART reactor core has been selected as the reference core. The MOX (2.35% w/o of Pu-241 and 2.82% w/o of U-235) fuel and (U-Th)O2 has been investigated in homogeneous and heterogeneous configuration for SMART reactor core with the minimum changes from the reference core. The basic design like fuel, control rod diameter, lattice pitch, IFBA, and burnable absorbers concentration (Gd2O3) remains the same for all fuel configurations. The DRC has been calculated for the proposed fuel configurations of the SMART reactor and compared with the reference core ensuring the minimum changes in the design specifications of the SMART reactor. The DRC has been evaluated at the temperature range of 300 K–1000 K. The DRC for MOX fuel, (U-Th)O2 fuel in homogeneous and heterogeneous configuration is shown in Fig. 6. It can be seen from Fig. 6 that the DRC remains negative for all core configurations. However, it rapidly decreased with the increase in temperature from 300 to 600 K and then started increasing after 650 K. It has also been observed from Fig. 6 that the DRC most negative value of DRC for UO2, MOX, homogeneous (Th-U)O2, and heterogeneous (Th-U)O2 fuels has been found as − 4.741 pcm K−1, 3.496 pcm K−1, 4.896 pcm K−1, and 4.826 pcm K−1. The uranium fuel has less negative reactivity than thorium. This difference has been dominated at the temperature of 600 K and 1,000 K, The DRC of the MOX fuel configuration of the SMART reactor core showed a strange behavior. The DRC of MOX fuel starts decreasing from 300 to 700 K, then increases about linearly with a small trivial sloop, and again drops monotonically after 900 K.

Fig. 6
figure 6

Doppler reactivity coefficient (DRC) as a function of temperature for UO2 and MOX HomG (Th/U) O2 and HetG (Th/U)O2 fuels configurations

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In contrast, the DRC of the heterogeneous configuration linearly increases after 700 K (Elapsing temperature). However, the change in reactivity with the temperature gradient of 100 K for MOX, (U-Th)O2 in homogeneous and heterogeneous configurations is presented in Table 7. The effective multiplication factor (keff) has been calculated without boron absorbers and IFBA rods using OpenMC at temperatures (i.e., 300.0 K, 400.0 K, 500.0 K, 600.0 K, 700.0 K, 800.0 K, 900.0 K, and 1000.0 K). The effective multiplication factor (keff) for reference core, MOX, and homogeneous and heterogeneous configurations of (U-Th)O2 fuel is compared in Table 8 and depicted in Fig. 7. It can be seen from Fig. 7 that the MOX fuel has the least keff value since 239Pu and 241Pu have high absorption cross-sections in contrast to 232Th and 235U. The effective multiplication factor (keff) decreased with the increase in temperature (Fig. 7). It has also been noticed that the keff slightly decreases between 500 and 700 K for all the fuel configurations and linearized after 700 K except MOX fuel. The effective multiplication factor (keff) of MOX fuel again decreases after 900 K. The decrease in the effective multiplication factor (keff) is due to the increase in absorption cross section of U, Th, and Pu due to the temperature rise.

Table 7 Calculation of DRC for UO2 and MOX HomG (Th/U) O2 and HetG (Th/U)O2 fuels
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Table 8 Comparison of effective multiplication factor (keff) as a function of temperature for UO2, MOX. (U-Th)O2 homogenous and heterogeneous configurations
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Fig. 7
figure 7

Effective multiplication factor (keff) as a function of temperature for UO2, MOX, (U-Th)O2 configurations

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The UO2 fuel has prominent keff because of the significant concentration of 238U and 235U. A monotonic decrease in keff has been observed between fuel temperatures of 500 K to 700 K. The MOX fuel configuration has the least keff value compared to other (U-Th) fuel configurations due to the high absorption cross section of plutonium 239Pu (1,045 barns) and 241Pu (1121 barns). On the other hand, the 238U and 235U thermal microscopic cross sections are 1.73 barns and 405 barns, respectively. The change in keff with fuel temperature for the U-Th hybrid configuration is quite identical to the reference core. The effective multiplication factor (keff) for one complete fuel cycle at full power of operation is depicted in Fig. 8. The effective multiplication factor (keff) has also been analyzed versus the burnup for the UO2, MOX, (U-Th)O2 homogeneous and heterogeneous fuel configuration. It can be seen from Fig. 9 that the MOX fuel configuration has the least keff value with the burnup when compared over the fuel cycle. At lower burnup (20.27 GWd/tHM to 20.67 GWd/tHM), the MOX fuel has a significantly large effective multiplication factor (keff).

Fig. 8
figure 8

Effective multiplication factor (keff) for one complete fuel cycle for core, MOX, (U-Th)O2 homogenous and heterogeneous configurations

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Fig. 9
figure 9

Effective multiplication factor (keff) of reference core, MOX, (U-Th)O2 homogenous and heterogeneous configurations vs. burnup for one complete fuel cycle for the core

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Moreover, the MOX fuel has the least burn up as well. The lowest multiplication and burnup of MOX fuel is due to its lower value of absorption to fission ratio. The absorption to fission ratio of 241Pu is 0.75, while the absorption to fission ratio of 235U is 0.85. It can be seen from Fig. 9 that the UO2, MOX, (U-Th)O2 in homogeneous and heterogeneous configurations has the maximum value of keff 1.26, 1.14, 1.22 and 1.23 at the burnup 21.13 GWd/tHM, 20.67 GWd/tHM, 21.02 GWd/tHM, 20.94 GWd/tHM and 21.021 GWd/tHM, respectively. The keff values decrease almost linearly with the decrease in the burnup.

The comparison of the axial thermal neutron flux profiles is depicted in Fig. 10. For the core safety and power distribution, it is essential to monitor the neutron flux distribution of the core. Figure 10 presents the three-dimensional plots of thermal neutron fluxes of UO2 core, (U-Th)O2 homogenous and heterogeneous core, and MOX fuel configuration core. The plots showed the simulated model at full power operation without control rods and burnable absorbers within the total length and width of 192.8 cm and 192.8 cm with the diminutive mesh of 0.48 cm on the x-axis and y-axis. It has been seen that there is an insignificant difference in the reference core and (U-Th)O2 homogenous, heterogeneous, and MOX fuel configuration. This is because the enrichment of the (U-Th)O2 fuel configuration remains under the IAEA described limits (< 5.0) wt%) with the concentration of 2.5% and 16.5% of 235U and 232Th, respectively, in the homogenous configuration. However, in the heterogeneous configuration, assembly C is replaced with the U-Th fuel assembly. However, in the heterogeneous configuration, only the 11 × 11 inner matrix of the fuel assembly contains UO2 with the same enrichment as that of the reference core, and the outer blanket has the (U-Th)O2 fuel identical to the homogeneous configuration. Therefore, the thermal neutron flux is not significantly altered in homogeneous and heterogeneous configurations of (U-Th)O2 core.

Fig. 10
figure 10

Comparison of thermal neutron flux distribution of a reference core, b homogeneous, c heterogeneous, and d MOX fuel

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Contrary to that, it has been noticed that the MOX fuel has slightly less neutron flux compared to the reference core. This is because only assembly C has been replaced with the MOX fuel assembly. Thus, the difference in neutron flux is only due to the replacement of Assembly C with the MOX assembly in MOX fuel assembly. The overall enrichment of MOX (UO2, PuO2) (≈2.82wt% of 235-U and 2.35 wt% 241-Pu) is less than the enrichment of Type C fuel Assembly (2.82 wt%). Thus, less enrichment also results in a lower multiplication factor of MOX fuel configuration (Figs. 7, 8, and 9). Notably, it is validated the MOX fuel has the lowest multiplication factor throughout the fuel cycle (Figs. 8 and 9). The reference core (UO2) has the highest multiplication factor. However, (U-Th)O2 homogeneous and heterogeneous fuel configuration has a relative multiplication factor at the full power operation of the complete fuel cycle. The burnup of all the fuel configurations decreases drastically (Fig. 8) at the end of the fuel cycle due to fissile isotopes' depletion. This results in a decrease in the effective multiplication factor (keff) (Fig. 9).

The power peaking factor (PPF) is also an essential parameter of reactor safety. It ensures fuel safety under normal operations. The LPD is predicted to prevent nuclear fuel from melting. Practically, LDP at the hottest position of the nuclear reactor core is more important to prevent the fuel from melting at that position and is related to the PPF. Thus, the PPF is one of the most important parameters that need to be monitored continuously from the point of safety aspects. The PPF of the reference core, homogeneous and heterogeneous configurations of (U-Th)O2 core and MOX fuel configuration are depicted in Fig. 11. The PPF values per fuel assembly for the quarter of the core are depicted in Fig. 12 at the beginning of the fuel cycle. The maximum value of PPF at the hottest location of the core has been measured as 1.998, 1.958, 1.827, and 1.846 for UO2, homogeneous configuration of (U-Th)O2, the heterogeneous configuration of (U-Th)O2, and MOX fuel, respectively (Fig. 12). Thus, from the PPF point of view, it can be said that all the fuel configurations can be operated under safe limits under normal operation.

Fig. 11
figure 11

Comparison of normalized PPF of the a reference core, b homogeneous, c heterogeneous, and d MOX fuel

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Fig. 12
figure 12

Power peaking factors PPF for the different fuel configurations at the beginning of the cycle (BOC)

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Figures 13 and 14 indicate the DRC and MTC for the complete fuel cycle. The gradient of temperature has been taken as the difference between the fuel temperature at the room temperature (startup) and the operating temperature of the fuel. In comparison, the gradient of coolant temperature has been taken as the difference between room temperature to the average coolant temperature during normal operation. When the coolant temperature increases, the density decreases due to the thermal expansion of the coolant. Thus, resonance escape probability decreases, which results in neutron spectrum hardening.

Fig. 13
figure 13

DRC for one complete fuel cycle with the constant 10B concentration

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Fig. 14
figure 14

MTC for one complete fuel cycle with the constant 10B concentration

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Furthermore, it is notable that the DRC and MTC decrease (Figs. 13 and 14) with the reduction in burnup. The DRC and MTC became more negative with the fuel cycle and reached the most negative value due to fission products and plutonium accumulation. The DRC remains in the range of − 0.681 pcm K−1 to − 4.446 pcm K−1 for all types of fuel configurations. At the same time, the MTC remains in the range of − 2.108 pcm K−1 to − 13.767 pcm K−1. Figures 13 and 14 show that the DRC and MTC of the reference core (UO2) remain less negative than MOX and (U-Th)O2 homogeneous and heterogeneous configuration.

In general, the behavior of thorium in the (U-Th)O2 configurations (homogeneous and heterogeneous) has been observed to be precisely identical to the UO2 core. The DRC of thorium remains nearly identical to the UO2 fuel but shows a slightly diverse performance at a high temperature (> 900 K). The MOX fuel configuration has the least DRC value compared to the other core configurations. Thus, this study signifies the use of MOX and (U-Th)O2 (homogeneous and heterogeneous) configuration in the SMART reactor.

5 Conclusion

In this work, the SMART reactor core has been analyzed for the MOX fuel (PuO2 with 3.0 wt% and UO2 with 97.0 wt%), homogenous and heterogeneous (U-Th)O2 configuration and compared with the reference fuel (UO2). The MOX fuel pellets are composed of 3.0 wt% of PuO2 and 97.0 wt % of UO2. The PuO2 enrichment is 2.35 wt% of 241-Pu, and UO2 enrichment is 2.82 wt% of 235-U, whereas in a (U-Th) homogenous configuration, all the fuel rods have the same concentration of U-Th mix fuel. The fuel assembly with 2.50% and 16.50% enrichment of 235U and 232Th, respectively, was presented in the homogenous configuration of (U-Th) with 25 control rods and 264 rods per assembly. The (U-Th) heterogeneous fuel assembly has been designed on the seed and blanket concept with the central 11 × 11 fuel rods containing uranium dioxide and the outer blanket fuel rods in fuel assembly containing (U-Th)O2 mixed fuel. The SMART reactor core for the candidate fuel configuration has been analyzed for DRC, burnup, multiplication factor, DRC, and MTC. The results show that the DRC for uranium is less negative than thorium. In comparison, the DRC of MOX fuel has been observed to be higher than any other fuel configuration. With the increase in fuel temperature, the reactivity for all core configurations has been observed to decrease. The MOX fuel configuration has the least neutron flux and neutron multiplication factor due to lower enrichment of MOX (UO2, PuO2) (≈2.5wt% of (235U and 241-Pu) than the enrichment of type C fuel Assembly (2.82 wt% 235-U). This also results in a lower PPF value of the MOX fuel configuration. The MOX fuel has significantly higher effective multiplication compared to other fuels. Thus, it can be concluded that the MOX fuel could be an appreciable choice for the SMART rector if it is needed to be operated at low burnup (20.27 GWd/tHM to 20.67 GWd/tHM). The DRC and MTC became more negative with the decrease in burnup and reached their most negative value due to the accumulation of plutonium fission gasses at the end of the cycle. The results show that the DRC and MTC of reference core (UO2) remain less negative compared to MOX and (U-Th)O2 fuel configurations (homogeneous and heterogeneous). However, the results signify MOX and (U-Th)O2 fuel in the SMART reactor.