1 Introduction

As one of the six highest potential reactor types proposed by the Generation IV International Forum, molten salt-cooled fast reactor has drawn much attention due to its strong inherent safety and favorable neutronic economy. Molten chloride salt is a preferred coolant in nuclear reactor systems, which displays superiority in its higher thermodynamic efficiency, higher volumetric heat capacity, high boiling point, harder neutron spectrum, and excellent natural circulation performance [1, 2]. The potential benefits of small modular reactors without on-site refuelling include lower construction costs, lower investment costs and risks, possibly greater or easier non-proliferation, and enhanced safety [3]. With these, a 120 MWt small modular molten chloride-cooled fast reactor (MCCFR) with 30-year life without on-site refuelling is proposed.

The application of liquid salt on the reactor technology is derived from the 2.5 MW aircraft reactor experiment (ARE) and Molten Salt Reactor (MSR) project developed at Oak Ridge National Laboratory (ORNL) [4]. The liquid salt-cooled reactor attracted researchers again until the 2000s, when several kinds of liquid salt fuel and liquid salt-cooled reactors were investigated, such as 2-MW and 373-MW molten salt reactors [5, 6], advanced high-temperature reactor (AHTR) [7], small modular advanced high-temperature reactor (SmAHTR) [8], and ordered-pebble-bed fluoride-salt-cooled high-temperature experimental reactor [9]. A flexible conversion ratio for a fast reactor using molten chloride salt as coolant was proposed due to its low moderating capacity at the Massachusetts Institute of Technology (MIT) [10]. Later, a compact liquid chloride salt-cooled fast reactor (SPARK-LS) was also suggested in Xi’an Jiaotong University [11]. Compared to liquid fluoride salt, chloride salts are preferable in realizing a high conversion ratio and achieving a long core lifetime for small modular reactors.

MCCFR is designed for local small grids operating for a long period without refuelling. To achieve its design goals, there are several design requirements proposed for the MCCFR core design:

1) For the safety operation of the reactor, small reactivity swing and negative overall reactivity feedback coefficients are required during the core lifetime.

2) One of the important life-limiting factors of a reactor is the state of its structural materials. Structural materials, such as the reactor pressure vessel (RPV) and fuel cladding, are continuously damaged and irradiated by neutrons particularly fast neutrons, gamma ray, and other particles from fission reactions. The integrated measure of their damage is represented by the displacement per atom (DPA), which is the number of times each atom is displaced from its lattice site. DPA could be applied for the characterization of varying mechanical properties and corrosion resistance, which guides the material endurance. The safe operation of MCCFR should ensure the integrity of RPV and fuel cladding over the core lifetime [12].

3) Molten salt-cooled reactors have higher operating temperatures than traditional pressurized water reactors. Hence, for the purpose of meeting certain economic and safety considerations, a set of design limits should be implemented in the thermal-hydraulics design of the MCCFR core. These design limits are focused on the coolant, cladding, and fuel temperatures.

This paper focuses on the conceptual design, neutronic characteristics analysis, radiation damage, fuel swelling analysis, and preliminary thermal-hydraulic performance evaluation of the MCCFR core. The main goal of this paper is to perform a feasibility study of an innovative MCCFR. Firstly, MCCFR, which can approach long cycle and high burnup, is described. Secondly, its steady-state neutronics and depletion behavior are analyzed. Thirdly, the maximum accumulated DPA of RPV and fuel cladding materials are assessed by their design criteria, followed by performing a fuel swelling analysis. Finally, its main thermal-hydraulic parameters are calculated and evaluated using a sub-channel analysis code. The results achieved in this paper will provide reliable evidence for the ultra-long life of the MCCFR core.

2 MCCFR core description

2.2 Parameters of the MCCFR core

MCCFR is designed to operate at a 120-MW thermal power without refuelling for 30 years [18]. The schematic of its primary cooling system is depicted in Fig. 1a. The primary coolant of molten chloride salt is driven by natural circulation during a nominal steady-state operation and after shutdown. Molten chloride salt has large thermal expansion coefficient, which makes natural circulation highly possible. The heat generated in the reactor core is transported to the heat exchanger by the circulating molten salt. The cooled molten salt leaving the heat exchanger flows down through the downcomer to the lower plenum before reentering the core.

Fig. 1.Full-screen View

(Color online) Schematic of MCCFR: of primary cooling system (a), core configuration (b), and fuel rod (c)

The configuration of the MCCFR core is shown in the Fig. 1b and its design and operating parameters are listed in Table 2. The active core length and diameter are designed as 125 cm and 134 cm, respectively. Fig. 1b and 1c show the fuel rod configuration: 2.62 cm in diameter, 0.02 cm gas gap, 0.2 cm thickness cladding, and 3.10 cm fuel rod pitch, thereby resulting in a pitch-to-diameter ratio of 1.18. The core contains five zones with different fuel enrichment. Two central low enrichment zones corresponding to 1.2 and 2.6 Pu/HM% enrichment and three enrichment zones corresponding to 12.8, 14.1, and 15.4 Pu/HM% enrichment are designed to lower the power peak and the burnup reactivity swing. The core consists of a single cassette/assembly composed of 1566 rods clustered in groups. From the innermost to outermost area from zone 1 to 5, the number of rods are 84, 144, 402, 360, and 566, respectively. Two sets of control rods are provided to control the reactivity and to shut down the reactor. The inlet temperature of the coolant and inlet mass flow are set to 500 °C and 4180.5 kg/s, respectively.

Table 2Full-screen View

Parameters of the MCCFR core.

Parameters	Value
Geometric parameters:
Power (MWt)	120
Fuel	(Pu-U)N fuel
Coolant	NaCl-KCl-MgCl2 (30-20-50%) mol%
Cladding	SiC/SiCf
Structure material	Hastelloy-N
Reflector material	Titanium
Number of fuel rod from inner to outer core	84/144/402/360/566
Number of control rods	Two sets control system (25/30)
Enrichment (Pu/HM%)	1.2/2.6/12.8/14.1/15.4
Discharge Burnup (MWd/kg HM)	131
Fuel/Gap/Cladding Outer Diameter (cm)	2.18/2.22/2.62
Fuel Pin/Control Rod Diameter (cm)	2.62
Pitch-to-Diameter ratio	1.18
Wire diameter (cm)	0.34
Wire axial pitch (cm)	25
Active core Height/Diameter (cm)	125/134
Inlet operating characteristics:
Inlet temperature (°C)	500
Inlet coolant flow rate (kg/s)	4180.5
Inlet coolant velocity (m/s)	4.38
Average heat flux(W/cm2)	74.9

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In the design of the MCCFR core, (Pu-U)N fuel is selected due to its high density, high thermal conductivity, high melting temperature, low swelling, thermal stability, and low fission gas release [19]. The isotopic vectors of plutonium listed in Table 3 are obtained from the spent fuel discharged from LWRs with 50 MWd/kgHM burnup and 5-year cooling [20]. This plutonium is then blended with natural uranium (0.7 wt%²³⁵U) then enriched in N¹⁵ to form (Pu-U)N fuel. The compositions of (Pu-U)N fuel in five fuel regions are shown in Table 4.

Table 3Full-screen View

Isotopic vectors of plutonium

Isotope	wt.%
238PU	1.6
239PU	58.2
240PU	23.5
241PU	11.2
242PU	5.5

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Table 4Full-screen View

Compositions of (Pu-U)N fuel

Isotope	1st fuel region	2nd fuel region	3rd fuel region	4th fuel region	5th fuel region
238Pu (wt.%)	0.0203	0.0418	0.2052	0.2267	0.2470
239Pu (wt.%)	0.7376	1.5187	7.4634	8.2444	8.9821
240Pu (wt.%)	0.2978	0.6132	3.0135	3.3290	3.6268
241Pu (wt.%)	0.1420	0.2923	1.4362	1.5865	1.7285
242Pu (wt.%)	0.0697	0.1435	0.7053	0.7791	0.8488
15N (wt.%)	5.9000	5.9000	5.9000	5.9000	5.9000
235U (wt.%)	0.7113	0.7016	0.6280	0.6184	0.6092
238U (wt.%)	92.1213	90.7889	80.6483	79.3160	78.0577
Density (g/cm3)	14.3000	14.3000	14.3100	14.3100	14.3100

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The ternary NaCl-KCl-MgCl₂ (30–20–50%) salt is selected as the most suitable coolant salt for high power density fast reactor applications. The salt was also applied to design a flexible conversion ratio for the fast reactor of Petroski [21] in MIT. Hastelloy-N (INOR-8) is recommended as the structural material in MCCFR design. In order to reduce the coolant void reactivity, titanium was used as the reflector material on account of its low density, good corrosion resistance, and large strength-to-density ratio. In fission nuclear reactors, the fuel cladding is an extremely crucial security barrier. In recent years, Silicon has been widely used in reactors [22] with SiC/SiC_f cladding considered as the priority candidate materials for Gen-IV reactors. In the current design, SiC/SiC_f is used as the cladding material of the MCCFR. The cladding liner is used to prevent possible incompatibility with nitride fuel [17].

3 Analysis tools and methodology

In the neutronics analysis of the core design, SCALE6.1/CSAS6 was used to evaluate k-effective (k_eff) and SCALE6.1/TRITON was applied for burnup calculation. Criticality Safety Analysis Sequence with KENO-VI (CSAS6) was developed to provide cross-section processing followed by the calculation of the neutron multiplication factor for systems modeled using KENO-VI [23]. TRITON computer code is a multipurpose SCALE control module for transport, depletion, uncertainty, and sensitivity analysis [24].

In order to achieve self-sustaining and stable operation for 30 years, the reactivity control code coupling CASA6 and TRITON modules in SCALE6.1 code package was built to manage the excess reactivity during burnup. The flowchart of the code is illustrated in Fig. 2. At the beginning, the code will guess a reasonable position of the control rods and evaluate k_eff through CASA6. Linear interpolation method was applied to obtain the position of control rods until k_eff achieves the critical condition. Subsequently, depletion calculations are executed to note the control rods depletion and fuel density change, which should be taken into consideration in the code. The next cycle will read the standard composition specifications as part of the input to provide the fuel state at the beginning of the next operational cycle. This cycle will repeat the aforementioned processes until the cycle is stopped.

Fig. 2.Full-screen View

Flow chart of reactivity control code

Radiation damage is usually quantified by DPA. In order to perform the calculations, a fine discretization in energy was implemented in the DPA cross-section and the rate of DPA was calculated from the following formula [12]:

where E_G is the maximum energy of the incident particle, E_g is the minimum energy of the incident particle, δ_dis(Ei) is the energy-dependent displacement cross-section, and Φ(Ei) is the energy-dependent particle flux per unit energy. φ_i and ${\delta }_{dis}^i$ are the microscopic cross-section and flux in the i group, respectively. The accumulated DPA is then computed by

For the thermal-hydraulic analysis of the MCCFR design, the core consists of only a single cassette/assembly composed of 1566 rods clustered in groups; so, sub-channel analysis method should be employed in the core. In recent years, a series of codes [25, 26] was developed by the Shanghai Institute of Applied Physics for molten salt reactor. The sub-channel analysis code (TSUB) is developed and validated for thermal-hydraulic analysis of MCCFR [18]. In TSUB, a single-phase model is used due to the high boiling point (~1400 °C) of molten chloride salt, which is considered as an incompressible liquid. TSUB code is applied for evaluating the thermal-hydraulic design parameters of MCCFR in terms of the coolant, cladding and fuel temperature distributions in its core.

4 Neutronics analysis

MCCFR reactor with 120-MW thermal power can operate for 30 effective full power years (EFPY) without refuelling. Fig. 3(a) shows the normalized neutron spectra of the MCCFR core. Fig. 3(b) shows the variations of k_eff over time. The initial k_eff is 1.0525 and the burnup reactivity swing is 4988.1 pcm. k_eff declined rapidly at BOL. After around 10 years, there are more ²³⁸U, which would be converted to ²³⁹Pu, thereby causing the slow decrease of the reactivity until it reached zero. The key core k_eff, reactivity coefficients, and kinetic parameters of MCCFR at BOL and end of core life (EOL) are shown in Table 5. The reactor has negative overall reactivity feedback coefficients including the fuel, coolant, core radial, and axial expansions reactivity coefficients, and coolant void reactivity during the lifetime. The fuel Doppler coefficient further decreased at EOL due to the slightly softened neutron spectrum caused by the accumulation of fission products. The coolant void reactivity in the full core is negative during the core lifetime. The radial power factors at BOL and EOL are shown in Fig. 4. The peak radial power factor is 1.328 and 1.325 at BOL and EOL, respectively. At BOL, the power densities of the inner two fuel zones are significantly small and the outer three fuel zones had more contributions to the core power. At EOL, the maximum power zone moved toward the core center owing to the fuel loading pattern strategy. At a higher burnup, the outer fuel zones is depleted and the Pu quality deteriorated while the inner fuel zones accumulated enough fissile material, resulting in larger radial power factors of the inner fuel zones than those in the outer ones.

Fig. 3.Full-screen View

Normalized neutron spectra of MCCFR core (a) and k_eff variations during its lifetime (b)

Fig. 4.Full-screen View

Radial power distribution at BOL (a) and EOL (b)

As shown in Fig. 1b, two groups of control rods, each composed of 25 control rods, are provided for the independence and redundancy of the scram. Group 1 is applied for both normal control of the reactor (start-up, reactivity control during core lifetime, and power regulation) and shutdown. Group 2 is applied for emergency shutdown. The control rods are made of B₄C with a B-10 concentration of 94%. When both control rods groups are completely inserted, k_eff is 0.90945 (hot condition) and 0.91447 (cold condition). Therefore, these two control systems could meet the shutdown margin (1000 pcm) in the MCCFR core. This will ensure the safety of the reactor during accidents. Table 6 shows the control rod worth of group 1 and 2 rods under different operating conditions. At EOL, The control rod worth of group 1 was significantly reduced at EOL. When group 1 control rods are inserted in the reactor, the Boron concentration decreased due to neutron irradiation during the core lifetime. This would significantly reduce the control rod worth of group 1. Although group 2 control rods are not inserted into the core, its control rod value is also reduced due to the neutron flux change at EOL. In the reactor, group 1 control rods are withdrawn from the core to compensate excess reactivity. Fig. 5(a) shows the position of the group 1 control rods every burnup cycle during operation. All control rods are then extracted after 30 years. Fig. 5(b) shows good results of the k_eff swing between 0.9995 and 1.0005, which could ensure safe operation of the reactor during its lifetime. The burnup cycle is 50 days in BOL and 100 days after 40 cycles. Hence, the line is compact in the first 6 years. At EOL, the fluctuation range of the reactivity is significantly reduced. This effective reactivity control strategy could achieve self-sustaining and stable operation for 30 years without on-site refuelling.

Fig. 5.Full-screen View

The inserted depth of control rods (a) and the variation of k_eff with control rods moving during core lifetime (b)

The fuel compositions in the core at BOL and EOL are shown in Table 7. After 30 EFPY of depletion, 4710.6 and 137020.0 g of ²³⁵U and ²³⁸U were consumed, respectively, and ²³⁹Pu was bred from ²³⁸U with a net product of 6943.6 g. The mass of ²³⁹Pu increased in the 1^st, 2^nd, and 3^rd fuel regions while that of the 4^th and 5^th fuel region decreased. Moreover, the mass of ²³⁸Pu and ²⁴⁰Pu increased while that of ²⁴¹Pu and ²⁴²Pu decreased. The reason for the significant decrease of the fissionable isotope ²⁴¹Pu is its lower half-life than other plutonium isotopes. The mass of ²⁴²Pu converted by ²⁴¹Pu is less than its consumption, causing the decline of its own mass. The mass of minor actinides such as ²³⁷Np and ²⁴¹Am all significantly increased due to the relatively higher plutonium enrichment in MCCFR.

5 RPV and fuel cladding radiation damage and fuel swelling analysis

5.1 Radiation damage of RPV and fuel cladding

The calculation formulas of the rate of DPA and accumulated DPA are shown in section 3. The neutron flux distribution of the MCCFR core is calculated and generated by SCALE6.1/CSAS6. A total of 86 energy groups of DPA cross-section for Hastelloy-N is shown in Fig. 6a [27]. Chang et al. [28] obtained the displacement damage cross section of SiC/SiC_f shown in Fig. 6b by applying Norgett Robinson-Torrens model.

Fig. 6.Full-screen View

DPA Cross Section of Hastelloy-N (a) and SiC/SiC_f (b)

In order to evaluate the DPA of the reactor pressure vessel (RPV), the calculation model can be simplified as Fig. 7 with respect to θ=30° plane according to symmetry of the core. Fig. 8a and 8b show the rate of DPA (R_DPA) on the inner surface of the RPV at BOL and EOL, respectively. The maximum R_DPA is 9.368e-09 and 9.491e-09 dpa/s at BOL and EOL, respectively. At EOL, the neutron flux in the core is higher than in BOL, causing a larger maximum R_DPA at BOL. The results indicate that the maximum irradiation dose at EOL for the RPV is about 8.92 dpa, which is far from the 200 dpa limit.

Fig. 7.Full-screen View

Simplified calculation model

Fig. 8.Full-screen View

(Color online) RDPA in term of Z and Theta on the inner surface of the RPV at BOL (a) and EOL (b)

Fig. 9 illustrates R_DPA distribution of the SiC/SiC_f cladding at BOL, middle of life (MOL), and EOL. The maximum R_PDA shifted inward towards the centerline due to the shift of the maximum neutron flux toward the core center during the lifetime. The maximum values of R_DPA are 2.209e-07, 2.162e-07, and 2.395e-07 dpa/s at BOL, MOL, and EOL, respectively. The maximum irradiation dose at EOL for SiC/SiC_f cladding in the MCCFR core is about 197.03 dpa, which is smaller than the 200 dpa limit.

Fig. 9.Full-screen View

(Color online) RDPA distribution of SiC/SiC_f cladding at BOL (a), MOL (b), and EOL (c)

6 Thermal hydraulics analysis

The power distribution of the MCCFR core used as the input data of the TSUB code calculated and generated by SCALE6.1/CSAS6. Gnielinski, Cheng-Todreas, and Rogers-Rosehart correlations are utilized for heat transfer, pressure drop, and turbulent mixing models, respectively [18]. For the thermal-hydraulic design and analysis of the MCCFR core using TSUB code, it is necessary to first define the numbering of the rods and sub-channels. Due to symmetry of the core, 1/12 symmetrical cross section of the core is modeled and 18 axial nodes are adopted for the MCCFR. Fig. 10 indicates the numbering of the sub-channels starting from the center of the core. There are 262 sub-channels including 250 interiors and 12 edge sub-channels at 151 rods. In Fig. 10, the green sub-channels (sc3, sc20, sc77, sc102, and sc164) correspond to two lower enrichment zones (1^st and 2^nd) and three higher enrichment zones (3^rd, 4^th and 5^th). To compare within different enrichment zones, five sub-channels are selected for comparison in this study.

Fig. 10.Full-screen View

(Color online) Numbering scheme of 142 sub-channels.

Fig. 11 (Color online) shows the temperature distribution of molten chloride salt coolant, fuel interior, and fuel cladding in the 1/12 symmetrical core at BOL. The temperature ranges from 500 to 1400 °C in the core. The temperatures of the fuel rods are much higher than that of the coolant. The maximum temperature is obtained between the axial location of Z=60 cm and Z=70 cm.

Fig. 11.Full-screen View

(Color online) The temperature distribution in the 1/12 symmetrical core.

Considering the influence of temperature on the corrosion behavior of the cladding material, a detailed analysis of the local temperatures of each sub-channel and fuel rod is critical. The power density and neutron flux of the MCCFR core continuously changed during the core lifetime. With this, the following analyses are carried out at the BOL, MOL, and EOL.

Fig. 12 illustrates the distribution of the coolant temperatures of sc3, sc20, sc77, sc102, and sc164 in the five fuel zones over the active heights at BOL, MOL, and EOL. At BOL, due to lower enrichment in the two central zones (1^st and 2^nd) and large neutron leakage in the core boundary, sc102 corresponding to the 4^th fuel zone was recorded as the hottest channel. As the operation proceeds, ²³⁸U in the two central lower enrichment zones is converted to ²³⁹Pu during burnup. The peak power/burnup location gradually shifted towards the center, temporarily resulting in the highest temperatures of different pins. At MOL, sc77 became the hottest channel. At EOL, the increase of the channel temperature gradually shifted into the inner zone of the reactor. The maximum coolant temperatures are as high as 551.8 °C, 550.0 °C, and 557.3 °C at BOL, MOL, and EOL, respectively. The inlet temperature of 500 °C is the minimum coolant temperature, which is higher than the temperature limit of 450 °C. Moreover, the maximum coolant temperature of the core in different periods is significantly lower than the coolant boiling temperature design limit of 1400 °C.

Fig. 12.Full-screen View

(Color online) Distribution of coolant outlet temperature in 1/12 symmetrical core at BOL (a), MOL (b), and EOL (c).

Figs. 13 and 14 describe the temperature distributions at the hottest layer of the claddings and fuel rods at BOL, MOL, and EOL. The radial temperature distribution gradient is similar to that of the coolant temperature, where the hottest temperatures of the claddings and fuel rods shifted towards the centerline. Fig. 15a and 15b show the hottest cladding outer and fuel centerline temperatures, respectively, along the axial direction during BOL, MOL and EOL. The peak cladding outer temperature reached as high as 681.2 °C in rod66, 668.3 °C in rod53, and 674.5 °C in rod6 at BOL, MOL, and EOL, respectively. The peak fuel centerline temperature is as high as 1363.4 °C at BOL, 1298.8 °C at MOL, and 1318.5 °C at EOL. The peak cladding is far below the cladding temperature limit of 900 °C and the fuel centerline temperature is below the melting temperature of 3035 °C during different periods.

Fig. 13.Full-screen View

(Color online) Distribution of cladding outer temperature at the hottest layer at BOL (a), MOL (b), and EOL (c).

Fig. 14.Full-screen View

(Color online) Distribution of fuel temperature at the hottest layer at BOL (a), MOL (b), and EOL (c).

Fig. 15.Full-screen View

(Color online) Distribution of cladding temperature and fuel centerline temperature along the axial direction of the core in five representative sub-channels.

7 Conclusion

In this study, an innovative conceptual design of a small molten chloride-cooled fast reactor with 30-year life without on-site refuelling is proposed. To evaluate the feasibility of its core design, neutronics, thermal-hydraulics, radiation damage, and fuel swelling analysis were performed using analysis tools, including SCALE6.1, reactivity control, and TSUB codes. The results are as follow:

1) The initial k_eff is 1.0525 and burnup reactivity swing is 4988 pcm during 30 EFPY. The reactivity coefficients provided sufficient negative feedback. Two control systems were also implemented to provide sufficient shutdown margins. This ensured the safety of the reactor should accidents occur. The effective reactivity control strategy could achieve self-sustaining and stable operation for 30 years without on-site refuelling.

2) The maximum irradiation dose at EOL for the RPV and fuel cladding is 8.92 and 197.03 dpa respectively, which are both less than the design limit of 200 dpa. At EOL, the total fuel volume expanded by 8.64%.

3) The maximum coolant temperature, cladding temperature, and fuel centerline temperature at BOL, MOL and EOL were all lower than the design limits.

Therefore, these confirm the feasibility of the preliminary conceptual design of the MCCFR core. For future studies, safety analysis could be performed to ensure the inherent safety feature of MCCFR.