Liquid lead and lead bismuth eutectic (LBE) are emerging as promising coolants for next-generation advanced nuclear energy systems, primarily due to their superior thermal-hydraulic properties, increased inertness, and optimal neutron characteristics (Abram and Ion, 2008). Both the China Initiative Accelerator Driven Subcritical System (CiADS) (Gu and Su, 2021) and the Multi-purpose Hybrid Research Reactor for High-tech Applications (MYRRHA) (Abderrahim et al., 2012) have identified liquid LBE as the preferred coolant in their subcritical reactors. The CiADS project, however, faced technical and engineering challenges. This led to the formulation of two distinct fuel assembly designs: wire-type spacers and grid-type spacers. The aim was to thoroughly assess and integrate these designs into the CiADS framework. Initial research was directed toward the design and thermal-hydraulic engineering of LBE-cooled fuel assemblies using wire-type spacers (Peng et al., 2017). Recent developments in the structural design of the CiADS triangular fuel assembly with wire-type spacers were highlighted by Yu et al. (2021). Furthermore, Fan et al. (2020) embarked on flow experiments with wire-wrapped 19-rod bundles tailored for CiADS. Using the Reynolds analogy and visualization methods, they derived the flow pressure drop and cross-sectional pressure drop profiles for the wire-type spacer’s fuel assembly. On the computational side, Liu et al. (2022) fine-tuned a sub-channel analysis code for simulating thermo-hydraulics of wire-type spacer fuel assemblies cooled by liquid LBE. Leveraging this code, they analyzed the thermo-hydraulic characteristics of a comprehensive 61-rod wire-type spacers fuel assembly.

Wire-type spacers play a pivotal role in preserving the ideal spacing of fuel rods, curtailing mechanical vibrations, bolstering turbulent mixing among sub-channels, and avoiding temperature peaks. However, these spacers increase flow resistance. Conversely, grid-type spacers, with their compact volume, permit a more substantial core allocation for fuel, thereby amplifying the breeding ratio and diminishing the doubling time. Furthermore, the built-in flow channels in the fuel assembly are straightforward, reducing flow resistance and the risk of obstructions from LBE corrosion impurities. Preliminary research at CiADS has addressed the structural design and the hydrostatic and dynamic attributes of the triangular fuel assembly with grid-type spacers (Sheng, 2022). It is imperative now to delve deeper into the thermal hydraulics of liquid LBE within this structure, ensuring alignment with CiADS thermal design norms. The sub-channel analysis method strikes a balance between the detailed three-dimensional computational fluid dynamics approach and the simplified one-dimensional system safety assessment, offering an efficient, cost-effective, and swift assessment of LBE’s thermal hydraulics in the fuel assembly. Several renowned codes cater to the thermal hydraulic evaluation of liquid metal-cooled fast reactors: 1) COBRA-WC (George et al., 1980), which can simulate multiple fuel assemblies at the same time as well as several operating conditions including forced and natural cycles. 2) MATRA-LMR (Kim et al., 2002), which uses the distributed resistance model and improves the sodium properties, heat transfer relations and pressure drop relations. 3) ATHAS-LMR (Chen, 2012), which deduces a three-dimensional drag model instead of the lumped parameter method by theory, and finally calculates the experimental results of the flow blockage accident in the liquid metal fast neutron breeder reactor. The results show that the calculated results are in good agreement with the experimental results. 4) SACOS-PB (Wang et al., 2013a), which is concluded that the hexagonal fuel assembly is the best choice for the LBE fast reactor by analyzing the temperature distribution of the fuel assembly and diverse component types. Wu et al. (2021) improved SACOS-PB, and Wang et al. (2021) utilized it for flow blockage incident analysis. 5) ANTEO+ (Lodi et al., 2016a), which can be used to calculate liquid metal cooled fast reactors, including sodium, lead, LBE, and is suitable for a variety of geometric structures such as bare-rod, grid-type spacers, and wire-type spacers. 6) KMC-sub (Li et al., 2017), which adds the relation applicable to liquid LBE and is used to calculate the steady-state condition of SNCLFR-100. (7)

Conducting heat transfer experiments using LBE is challenging due to its corrosive and opaque nature (Schroer et al., 2012). For the purpose of generating experimental data and validating sub-channel analysis codes specifically designed for LBE-cooled fuel assemblies with spacer grids, several notable experiments have been undertaken: 1) Pacio et al. (2014) constructed the THEADES loop at the Karlsruher Liquid Metals Laboratory (KALLA) with reference to the geometry of MYRRHA. They used 19 rods with grid-type spacers and conducted heat transfer experiments under steady-state and forced convection conditions. 2) Di Piazza et al. (2016) also carried out a heat transfer experiment with 19 rods using wire-type spacers in the NACIE-UP circuit for the MYRRHA reactor. Unlike the experiments by Pacio et al., the NACIE-UP loop experiments adopted steady-state, adiabatic, and natural cycles, and placed more focus on the heat transfer phenomenon of liquid LBE at a low flow rate (Re = 1000–10000). 3) Lyu et al. (2016) carried out heat transfer experiments of 61 rods bundle wire-wrapped fuel assemblies on the KYLIN-II lead reactor comprehensive experimental circuit, in which the experimental sections included a 350 mm inlet flow section, a 800 mm heating section and a 132 mm outlet flow section, in order to eliminate the effect of inlet flow instability and outlet effect on the heating section. In these experiments, Pacio et al. carried out a detailed study on the heat transfer process of high-temperature liquid LBE in 19 rods bundle with grid-type spacers, and obtained multiple groups of coolant temperatures and heating rod temperatures, which were widely applied to the validation of sub-channel analysis code for LBE cooling.

Since most of the sub-channel analysis code are closed-source, for the sake of studying the thermal hydraulic characteristics of CiADS LBE cooling fuel assemblies with grid-type spacers, this study is based on the optimization of the sub-channel analysis code for LBE cooling winding fuel assemblies with grid-type spacers by Liu et al. (2022). By incorporating flow pressure drop, convective heat transfer, and turbulent mixing models suitable for the fuel assembly with grid-type spacers cooled by lead and bismuth, the code’s development aims to analyze the thermal hydraulics of the CiADS lead and bismuth-cooled fuel assembly with grid-type spacers. The validity and reliability of the sub-channel analysis code developed in this study were verified by using the available information of 19 rods with grid-type spacers heat transfer experiments cooled by lead and bismuth. Then, based on the current version of the sub-channel analysis code, the thermal hydraulic behavior of coolant temperature, cladding temperature and fuel rod temperature distribution for a single CiADS full-size fuel assembly with grid-type spacers was investigated. Previously, the latest structural design and thermal hydraulic of the current CiADS LBE cooled fuel assemblies with grid-type spacers were reviewed. Finally, the influence of different rod numbers on the internal temperature distribution characteristics of the fuel assembly is analyzed. By incorporating the flow pressure drop model, convective heat transfer model, and turbulent mixing model suitable for the fuel assembly with grid-type spacers cooled by lead and bismuth, the code’s development aims to analyze the thermal hydraulics of the CiADS lead and bismuth cooled fuel assembly with grid-type spacers. The validity and reliability of the sub-channel analysis code developed in this study were verified using the available data from heat transfer experiments involving 19 rods with grid-type spacers cooled by lead and bismuth. Subsequently, based on the current version of the sub-channel analysis code, the thermal hydraulic behavior of coolant temperature, cladding temperature, and fuel rod temperature distribution for a single full-size CiADS fuel assembly with grid-type spacers was investigated. Furthermore, the latest structural design and thermal hydraulics of the current CiADS LBE-cooled fuel assemblies with grid-type spacers were reviewed. Finally, the influence of different rod numbers on the internal temperature distribution characteristics of the fuel assembly is analyzed.

The main purpose of the sub-channel analysis code is to accurately calculate and analyze the thermal hydraulic behavior of coolant and fuel rods in fuel assemblies. Due to the significantly higher boiling point of liquid lead compared to the operating temperature within the reactor, the coolant can be treated as a single-phase flow without boiling. The code utilizes discrete mass, axial momentum, transverse momentum, and energy conservation equations to calculate the mass flow rate and temperature distribution of coolant in different sub-channels. The conservation equations for incompressible fluids are solved using the finite difference method, which ensures the conservation of the total mass entering and leaving a control volume. The thermal hydraulic parameters are then calculated using the conservation equations for mass, energy, and momentum (Liu et al., 2022).

Mass Conservation Equation: A ∂ ρ ∂ t + ∂ m ∂ z + ∑ k ∈ i e i k w = 0 (1) where A is the axial flow area; ρ is the coolant density; t is the time; m is the axial mass flow; Δ z is the axial control body height; e i k is the symbolic function; w is the unit length transverse mass flow. Each term of the equation is the change of mass with time, the change of axial mass flow with space, and the total transverse mass flow in and out of the gap.

Energy Conservation Equation: A ∂ ρ h ∂ t + ∂ m h ∂ z + ∑ k ∈ i e i k w h * = ∑ k ∈ i P W ϕ i r q + ∑ k ∈ i C Q ϕ i n q ′ − ∑ k ∈ i w ′ Δ h − ∑ k ∈ i C k s Δ T (2) where h is the enthalpy of the fluid; P W is the heating perimeter of the fuel rod r facing the subchannel i; ϕ i r is the share of fuel rod r facing channel i ; q is the linear power density of the fuel rod; C Q is the heat production share of the coolant; ϕ i n is the contact share between the fuel rod and the channel; q ′ is the line power density of fuel rod incoming the coolant; Δ h is the enthalpy difference between adjacent channels; C k is the transverse heat transfer coefficient and Δ T is the temperature difference between adjacent channels.

Axial Momentum Conservation Equation: ∂ m ∂ t + ∂ m U ∂ z + ∑ k ∈ i e i k w U = − A ∂ p ∂ z − ρ g A ⁡ cos ⁡ θ − 1 2 ρ U 2 A f D + K Δ z − f T ∑ k ∈ i e i k w ′ U (3) where U is the axial flow rate; P is the pressure; g is the acceleration of gravity; θ is the angle between the coolant channel and the vertical direction; f is the friction coefficient; D is the diameter of fuel rod; K is the form resistance coefficient; f T is the turbulent momentum exchange coefficient and w ′ is the turbulent mixing flow per unit length.

Transverse Momentum Conservation Equation: ∂ w ∂ t + ∂ w U ∂ z = s l Δ p − K G s l w w 2 ρ s 2 (4) where l is the centroid distance between sub-channel i and sub-channel k . K G is the lateral resistance coefficient. The items on Eq. 4 left side are the variation of transverse flow rate with time and the variation of transverse flow flux with space. The items on Eq. 4 right side are the transverse pressure difference term and clearance resistance term.

This chapter introduces the friction pressure drop model, convective heat transfer model, and turbulent mixing model that have been integrated into the code. Furthermore, the correlations for physical properties and fundamental numerical analysis models continue to rely on the sub-channel code COBRA-LFR developed by Liu et al. (2022).

To investigate the thermal hydraulics of LBE eutectic in a reactor, a heat transfer experiment was conducted in 2016 at the KALLA Laboratory in Germany. The experiment involved a 19-rod fuel rod bundle equipped with grid-type spacers and used LBE as the coolant (Pacio et al., 2014). Over 80 different operating conditions were simulated, resulting in the collection of hundreds of experimental data points. These abundant experimental data offer valuable references for reactor design. In this study, the heat transfer experimental data from the 19-rod bundle with grid-type spacers, as conducted by Pacio, were selected as the validation benchmark. The computed data from the sub-channel analysis were compared with the experimental results to verify the accuracy of the calculations. The specific geometric parameters of the individual rods are detailed in Table 3, while the experimental conditions are outlined in Table 4. Temperature measurements were taken at distances of 532 and 855 mm from the inlet of the heated section. This is illustrated in Figure 1, which provides a visualization of the sub-channel division.

Pacio et al. (2014) proposed a dimensionless temperature to describe the relative deviation between the temperature at the measurement location and the average temperature of the cross section. Equation 15 is used to describe this dimensionless temperature. θ = T − T a v e λ / q w d h (15)

Where T is measurement temperature K); T a v e is average temperature K); q w is surface heat flux of the rod ( W / m 2 ); d h is equivalent diameter m).

Figures 2A–D show the calculation results, which indicate good consistency between the sub-channel code calculations and experimental results. With increasing Pe, the turbulent mixing phenomenon becomes more apparent, and the difference between the wall temperature of R1 and the average temperature of the cross section gradually decreases, as does the difference between the temperature of sub-channel 33 and the average temperature of the cross section. The red and black lines represent the fitted results for the experimental and calculated data, respectively, offering a clearer visualization of their differences. The temperature distribution within each sub-channel also becomes more uniform. These observations are consistent with the anticipated outcomes, and the discrepancy between the non-dimensional cladding temperature and the non-dimensional coolant temperature, calculated using Eq. 15, remains within 0.03. As depicted in Eq. 15, changes in the dimensionless temperature are influenced by significant fluctuations in the measured or computed temperatures. With a temperature fluctuation of 10K, the impact on the dimensionless temperature reaches 0.05. This implies that there is a 10K error between the sub-channel code calculations and the experimental results, which could arise from uncertainties in the physical property relationships utilized in the code or inaccuracies in the experimental measurement equipment.

As mentioned earlier, the present sub-channel code possesses the capability to precisely compute coolant temperature and cladding outer surface temperature, enabling comprehensive thermal hydraulic analysis of fuel assemblies featuring grid-type spacers. This capacity facilitates in-depth investigations into the characteristics of CiADS fuel assemblies.

The main function of CiADS subcritical reactor core is coupling with accelerator and spallation target to generate strong fast neutron field and offer an experimental setting for nuclear waste transmutation. The CiADS LBE cooled reactor is designed to operate under subcritical conditions with power regulation by the accelerator beam. The core consists of 52 hexagonal fuel assemblies, a dummy assembly and associated test channels, with a circular hole in the middle for placing spallation target tubes. The core layout of CiADS LBE cooled reactor is shown in Figure 3, and the core design parameters are shown in Table 5.

Building upon the sub-channel code developed by Liu et al. for thermal hydraulic analysis of LBE wound wire fuel assemblies, this study conducted a secondary development. A thermal hydraulic analysis code was developed specifically for fuel assemblies of LBE cooled fast reactors with grid-type spacers. A comparison was made between the results of the 19-rod flow heat transfer experiment carried out by Pacio and the calculations of coolant temperature to verify the code’s accuracy. Furthermore, an analysis was performed on the CiADS 91-rod fuel assembly using the sub-channel analysis code, based on design parameters. The analysis investigated the impact of coolant temperature, fuel rod temperature, coolant mass flow rate, and rod bundle arrangement. The findings can be summarized as follows:

Different models were evaluated for their applicability, and the Rehme, Petrunik, and Mikityuk models were recommended for calculating friction pressure drop, turbulent mixing, and convective heat transfer in CiADS sub-channel analysis.

The results from the code calculations closely aligned with the experimental data. As the Péclet number (Pe) increased, the temperatures of various sub-channels tended to approach the average temperature.

The code’s calculations indicated that the maximum coolant temperature occurred in sub-channel 8, while the maximum fuel rod temperature was in rod 18. Under steady operating conditions, the maximum fuel center temperature reached 756.65 K, and the maximum cladding temperature was 666.92 K.

By analyzing different rod numbers, it was determined that 37 rods were recommended as the minimum rod bundle configuration for simulating the full-scale fuel assembly.