The fission gas release (FGR) was calculated using the modified Forsberg–Massih model in FRAPCON-4.0 (Forsberg and Massih, 1985). Fission gas is released with a fraction F if the calculated surface gas area density N (atoms/m²) is larger than the saturation concentration N_s.

Equation 1 Forsberg–Massih fission gas release model N S = [ 4 r F ( θ ) V c 3 K B T sin 2 ( θ ) ] ( 2 γ r + P e x t ) , F = N − N s N N _s = saturation concentration (atoms/m²)θ = dihedral half-angle = 50°K _B = Boltzmann constant.γ = surface tension = 0.6 (J/m²)V _c = critical area coverage fraction = 0.25r = bubble radius = 0.5 (µm)F(θ) = 1–1.5 cos (θ) + 0.5 cos³ (θ)P _ext = external pressure on bubbles = gas pressure (Pa)

In the case of the Forsberg–Massih model, when the temperature of the nuclear fuel is sufficiently high to allow interconnection among intergranular bubbles, it simulates the release when the opening pathway to release is created. Thus, this is a general thermal release process that assumes that fission gas is released from a high-temperature fuel. However, at a low temperature, athermal fission gas release which is owing to the recoil and knock-out of fission gas atoms is the dominant mechanism, and the Forsberg–Massih model predicts a release of less than 1–2%, whereas 4–5% FGR values have been measured at burn-ups of 60 GWd/MTU (Killeen, Turnbull and Sartori, 2007). Therefore, an empirical athermal release model was suggested that can predict fission gas release at relatively low temperatures (as stated in Equation 2) (Turnbull, 1996). If the temperature of the nuclear fuel is sufficiently low, the higher F_LT value from the low-temperature model will be calculated than F from Forsberg–Massih model. In this case, the code was set to use the F_LT value instead of the F.

Equation 2 Low-temperature fission gas release model F L T = 7 × 10 − 5   B U + C F _LT = fission gas release fraction by low temperature model.BU = local burnup (GWd/tU)C = 0; for BU ≤ 40 GWd/tU.= 0.01(BU - 40)/10; (BU > 40 GWd/tU and F ≤ 0.05)

The amount of plutonium produced by breeding is larger than that produced by the LWR owing to the characteristic of the fast reactor fuel. The major fissile isotope is Pu-239. Furthermore, in the case of MicroURANUS, the production of approximately 465 kg during 30 EFPY was calculated in the core design process (as shown in Figure 1A) (Nguyen et al., 2021). Variations in the thermal conductivity, heat capacity, and thermal expansion of the fuel caused by plutonium generation were considered as variations during operation through the weight fraction and composition of Pu-239, Pu-240, and Pu-241. The properties that vary during operation owing to Pu generation include density, heat capacity, thermal expansion, enthalpy, modulus, and thermal conductivity.

In addition to the fuel material properties, the influence of the variations in fuel irradiation behavior caused by plutonium generation was investigated. It is reported that a fission gas release enhancement effect occurs in the case of a MOX with 20 wt% plutonium (which is operated in a fast reactor) it is reported that there is a fission gas release enhancement effect owing to inhomogeneity caused by the segregation of PuO₂ (Walker, Goll, and Matsumura, 1996). However, in the case of nuclear fuel operating at low power and temperature, the fission gas release enhancement effects owing to plutonium segregation are negligible, and the plutonium composition at the end of life of the current nuclear fuel is approximately 3 wt% (as shown in Figure 1B) (White et al., 2001). This is significantly low to be considered in the MicroURANUS case.

Plutonium generation also affects the radial flux inside the pellet because of the generation of the local fissile element Pu-239. In the LWR, owing to the self-shielding effect by resonance capture of the thermal neutron, it has a higher burnup and neutron flux at the edge part of the pellet. However, radial flux depression can be disregarded in fast reactors because of the low-resonance capture of neutrons (Guerin, 2012; Medvedev et al., 2018). A few studies were conducted to develop a new burn-up module for fast-reactor MOX fuel that considers the generation of minor actinide elements (MA) and helium from the decay of MA (Cechet et al., 2021). The plutonium generation is considerably marginal in the present design (a maximum of 3 wt%). Furthermore, the initial fuel form is UO₂ rather than MOX. Therefore, a flat power profile was applied to the present code.

The most important life-limiting factor of cladding in the case of the fast reactor is irradiation-induced void swelling. Meanwhile, ferritic/martensitic stainless steel has been used widely in SFR because of the superior resistance to irradiation void swelling. However, when it is irradiated at a relatively low temperature (below approximately 400°C), it considerably affects the decrease in fracture resistance owing to irradiation embrittlement (Chen, 2013; Cabet et al., 2019). In addition, the ductile-to-brittle transition temperature (DBTT) of ferritic/martensitic stainless steel increases with irradiation at a low irradiation temperature. This could induce brittle fracture of cladding. Therefore, austenitic stainless steel cladding is used in the case of the present MicroURANUS core design because the inlet/outlet temperature is 250°C/350°C. This temperature is lower than the irradiation temperature of the existing fast reactor (approximately 500°C).

Conventional 304 and 316 grades were mainly used for austenitic stainless steel cladding, which is mainly used in SFR in the early stage of development. In addition, 304LN and 316 L(N) grades were applied gradually (these are low-carbon and nitrogen-controlled austenitic stainless steels) (Dai, Zheng, and Ding, 2021). This could suppress the decrease in corrosion resistance owing to grain boundary carbon precipitation and improve the mechanical strength owing to the high nitrogen content (Mathew, 2010; Ravi et al., 2012). In addition, swelling of cladding is the most crucial life-limiting factor in high burn-up and high neutron energy environments. Ti-stabilized austenitic stainless steels such as 316Ti and 15-15Ti have been developed to solve this problem (Maillard et al., 1994). These are swelling-resistant alloys. 15-15Ti shows a remarkable void swelling resistance of up to 130 dpa (Courcelle et al., 2016). Therefore, 15-15Ti steel was adopted as the cladding material because the peak cladding radiation damage attained approximately 120 dpa under the present reactor operating conditions. Luzzi et al. developed a “generalized 15-15Ti” model to fit the swelling data of several 15-15Ti steel groups in a conservative manner, and this model was used in this work (Luzzi et al., 2014). The irradiation swelling data of 15–25% cold worked 15–15Ti steels were used to establish the model (Hübner, 2000; Bergmann et al., 2003; Cheon et al., 2009; Dubuisson, 2013). The cladding correlations show the swelling correlation of 15-15Ti applied to this code (see Table 1). It has a peak value at 450°C. Furthermore, it increases exponentially with the increase in temperature and increases by a factor of 2.75 for fast fluence on cladding.

The corrosion of cladding in an LBE flow environment is also one of the highly important degradation mechanisms. The approximate coolant limit temperature is acknowledged to be 550°C (Li et al., 2017). In general, austenitic steels in lead-bismuth eutectic systems between 450 and 500°C oxidize with the formation of dual-layer porous magnetite (Fe₃O₄)/compact inner spinel layer for short-term operation (Müller, Schumacher and Zimmermann, 2000). However, it was verified that a uniform and protective Fe-Cr spinel single layer is formed in austenitic steel SS316L and 15–15Ti during long-term operation at a temperature below 450°C (Tsisar et al., 2016; Lee et al., 2021) Therefore, the single layer oxidation parabolic law of 15-15Ti was applied, and the parabolic rate constant and activation energy were calculated by fitting the literature data on long-term oxidation at 400°C, 450°C, and 550°C in flowing LBE (2 m/s) with 10^–7 mass% of dissolved oxygen. (Tsisar et al., 2016). In addition, the existing ZrO₂ thermal conductivity model was modified to the thermal conductivity of Fe–Cr spinel obtained from first-principle calculations (Liu et al., 2016).

Equation 3 Parabolic law and constants for 15-15Ti x = 2 k p t   ,   k p = Z ∙ exp ⁡ ⁡ ( − Q R T ) x : c o r r o s i o n   t h c i n e s s , k p : c o r r o s i o n   c o n s t a n t ,   a n d t : c o r r o s i o n   t i m e Q : a c t i v a t i o n   e n e r g y ,   R : g a s   c o n t a n t ,   a n d   T : T e m p e r a t u r e ( K ) Q = 176.07   ±   22.98   k J / m o l ,   R l n Z = 1.7417 ± 31.84

The operating conditions of MicroURANUS are summarized in Table 4. The linear power of the rod of the MicroURANUS core was calculated based on a reactor physics study (Nguyen et al., 2021). The performance of the peak power rod was evaluated to consider the safety margin of this core from the operation limit, through thermal and mechanical calculations of the nuclear fuel rod. Figure 2 shows the average and peak linear heat rates of the peak power rod and the average burn-up of the rod. These were calculated using the LFR fuel performance code. The MCS calculation in the reactor physics study revealed that the local peak linear heat rates of the hottest assembly were 9.91, 11.24, and 12.50 at 0, 15, and 30 EFPY, respectively. In the actual core design, the top and bottom 25 cm of the fuel rod have different enrichment designs, called onion zoning. However, simple cosine-shaped axial zoning is considered for the present calculations to evaluate nuclear fuel performance. An average-to-peak power ratio of 1.2 was applied. The rod average linear heat rate was calculated to be approximately 8.26, 9.37, and 10.42 at 0, 15, and 30 EFPY, respectively. The rod average discharged burn-up was approximately 46 GWd/tU when operated for 30 EFPY. Figure 3 shows the linear heat rate as a function of the axial elevation location of the fuel rod during operation.

The flow velocity variation between assembly channels should be treated carefully for the hot channel analysis. However, in the case of the current reactor system called MicroURANUS, it is a conceptual design stage, and the reactor physics study was based on constant fluid velocity obtained from a one-dimensional thermal hydraulics code (Nguyen et al., 2021). Therefore, the preliminary fuel performance analysis was performed on the unit cell without considering detailed assembly and grid structure to consider the coolant assembly velocity variation. For this reason, the core averaged mass flow rate is used in the current stage which is the same value as the current study (see Table 4). In addition, the axial temperature distribution data was calculated based on an average bundle mass flow rate.

Figure 4 compares the temperature calculation results with the preliminary thermal-hydraulics analysis results obtained by MARS-LBE (Shin et al., 2017). Thermo-mechanical feedback of the material was not considered in the case of the RELAP5/MOD3 code and COBRA-TF used in the MARS code. The initial gap at cold zero power (CZP) was set to 150 μm in the MARS-LBE and LFR fuel performance codes in this study. However, in the case of the LFR fuel performance code, the thermo-mechanical response in both fuel and cladding owing to thermal expansion from CZP to hot zero power (HZP) was considered. The fuel surface and cladding inner radius displacements at the HZP were calculated to be approximately 60 and 110 μm, respectively. Consequently, the increase in the initial gap was approximately 200 μm at the beginning of life condition in the LFR fuel performance code. This is 50 μm larger than the initial inputted cold gap of 150 μm. Thereby, the LFR fuel performance code fuel rod temperature calculation result differed from the fuel centerline temperature (see Figure 4A). The fuel temperature was determined to be about 150 K higher in the case of the LFR fuel performance code. In the case of cladding and coolant temperatures, the MARS-LBE temperature was higher than the LFR fuel performance code results in Figures 4B,C. The differences among these codes exist mainly because of the 1) heat transfer coefficient models and the 2) calculation methods. 1) In MARS-LBE, convective heat transfer is obtained by calculating the convective heat transfer coefficient from Nu which is given by the function of Re and Pr. Seban-Shimazaki correlation is applied to obtain Nu in the MARS-LBE system (Seban and Shimazaki, 1949). Therefore, the heat transfer coefficient value is calculated and updated simultaneously according to the fuel rod axial position and temperature of the coolant using the Seban-Shimazaki correlation. Also, the MARS-LBE code considers mass, momentum, and flow condition change due to pressure loss by friction on the fluid flow model. However, in this work, the LFR fuel performance code was developed to verify that the reactor can be operated safely during steady-state operation from a nuclear fuel perspective through multiphysics modeling of fuel and cladding. Therefore, the characteristics of the fluid, which were considered in detail in the thermal-hydraulics code (MARS-LBE), were simplified in this work. In this work, the core-averaged constant heat transfer coefficient obtained by MARS-LBE was applied as stated in Table 4. In addition, the coolant temperature is calculated as an energy balance through a one-dimensional convection heat transfer coefficient without considering momentum change or friction. 2) In the MARS-LBE code, the temperature calculation proceeds from the initial geometry without considering the thermomechanical deformation of the fuel rod. On the other hand, in this work, heat flux emitted out of the rod due to the He gap size increase caused by the thermal expansion of the cladding. As mentioned, there is a slight difference in the temperature calculation results due to the heat exchange capability of coolant and the effect of the geometry difference caused by the difference in detailed calculation methods among these two codes. Therefore, although the inlet temperature was set to have the same value of 523 K, the coolant temperature was calculated to be relatively low to be a maximum of about 20 K in the LFR fuel performance code. Furthermore, a low coolant temperature causes the cladding temperature to be calculated low and the maximum difference was calculated to be about 40 K in the outlet region. If we consider the different characteristics between the two codes, the temperature results were slightly different. However, thermomechanical iterations and a series of interactions can provide a more realistic simulation to analyze fuel rod multiphysics behavior with acceptable coolant temperature difference with thermal-hydraulics code. In the case of fuel temperature, the maximum temperature of the fuel at a point slightly higher than the mid-region was identical in both code cases. In addition, it was confirmed that the cladding and coolant temperatures were well increased according to the axial elevation.

Table 5 summarizes the comparison results of the thermomechanical behavior of the peak power fuel rod of the MicroURANUS system and the design limit factors. First, the maximum fuel temperature was evaluated as 1200 K. A sufficiently low fuel temperature provided a large safety margin for fuel melting and low pressure build-up fission gas release. The cumulative damage fraction (CDF) was calculated to predict the probability of creep rupture failure using the Larson–Miller parameter (LMP) for 15-15Ti steel (Filacchioni et al., 1990). Because the cladding hoop stress showed an equal value at all the axial nodes, the CDF of the hottest part of the cladding (which is aixial region 9) was calculated as 9.08 × 10^–13 using Equation 5. This result reveals a negligibly low failure probability when a limit of approximately 0.2 is considered to account for the safety margin for the mechanical integrity of cladding (International Atomic Energy Agency, 2012).

Equation 5 Larson–Miller Parameter for 15-15Ti L M P = T [ 16.0 + log 10 ( t R ) ] = ( 2060 − σ H ) / 0.095 t R = rupture time (h), σ H = hoop stress (MPa), and T = cladding temperature C D F = ∫ 0 t d t t R