Keywords

1 Introduction

As one type of the much anticipated fourth generation reactors, Lead or Lead-bismuth cooled Fast Reactor (LFR) was developed rapidly, its excellent capabilities in miniaturization, modularization and waste transmutation made it has great prospects in district heating, electricity and accelerator driven sub-critical system (ADS). Numerous of research institutes have great enthusiasm for LFRs, and a lot of experimental and teaching LFRs were developed, such as ELSY [1], SSTAR [2], SNCLFR [3], CLEAR-I [4] and MYRRHA [5]. Owing to the large thermal expansion coefficient and stable physical properties of Lead-based materials, LFRs have well natural circulation capability. At the same time, natural circulation capacity also guaranteed forced circulation passive security. Therefore, it is important to study the natural circulation thermal-hydraulic characteristics. With the development of computer hardware and software, computational fluid dynamics (CFD) methods was recognized as an accurate and efficient way, and it had been utilized widely. Nowadays, numerous of thermal-hydraulic programs or codes were developed. On the one hand, 1-D system analysis codes, such as RELAP5 and ATHLET, had been applied extensively. These codes can simulate the entire reactor system rapidly and precisely. However, system analysis codes were not good at reflecting thermal-hydraulic phenomena elaborately in LFRs, such as thermal stratification and flow details. On the other hand, numerous of CFD programs were adopted, the popular ones are ANSYS FLUENT, STAR-CCM . Through the simulation by these programs costs higher than system analysis codes, they can show heat transfer and flow characteristic details. In recent years, CFD programs became more and more extensive in investigating the thermal-hydraulic characteristics of LFRs.

In the past decades, a great deal of 2-D and 3-D simulations were carried out. In 2012, Jin [6] built a quarter 3-D model of CLEAR-I, carried out 3-D simulations by using ANSYS FLUENT to investigate the natural circulation capacity and thermal-hydraulic characteristics of CLEAR-I under steady state and loss of heat sink (LOHS) accident condition. In2013, in order to study the thermal stratification phenomena in CLEAR-I, Zhao [7] established a 2-D axisymmetric model and carried out 2-D simulations by utilizing ANSYS FLUENT, in which different power density was given based on the neutronics analysis. From the result, apparent thermal stratification appeared in the regions of the hot pool below the inlet window of heat exchanger under reactor scram conditions, but it never stopped the natural circulation of the primary circuit. In 2015, a self-developed CFD code namely NTC-2D was utilized by Gu [8] to investigate CLEAR-I under steady state, unprotected loss of heat sink (ULOHS) and unprotected transient overpower (UTOP) conditions. NTC-2D is a 2-D CFD code coupled with neutron transport kinetics model. The results demonstrated that the nice natural circulation capabilities contributed to the accident mitigation process. In 2015, to investigate the natural circulation characteristics of a small modular natural circulation LBE (Lead-Bismuth Eutectic) cooled fast reactor, 3-D simulations was conducted by using ANSYS FLUENT [9], in which a 3-D quarter reactor model was established, and the core power distribution was realized by UDF tools according to the reactor core layout. In 2015, to study the thermal-hydraulic characteristics of SNCLFR under UTOP accident, Chen [10] performed a 2-D simulation by using FLUENT coupled with neutron kinetics and pin thermal transfer models. In 2016, 3-D FLUENT simulations which aimed to evaluate two types of cooling systems, RVACS (reactor vessel air cooling system) and PHXs (primary heat exchangers), was conducted by Wang [11]. The results showed that both two cooling systems have excellent heat exchange capability, while PHXs is stronger than the RVACS. In 2017, Martelli [12] developed a RELAP5-ANSYS FLUENT coupling code to investigate the thermal-hydraulic characteristics of NACIE experimental loop. Natural circulation condition, isothermal gas enhanced circulation and unprotected loss of flow (ULOF) accident were simulated, in which the fuel pin was simulated by FLUENT while other parts were simulated by RELAP5. In 2020, aimed to study the hydraulic phenomena in M2LFR-1000 reactor, Zou [13] performed the simulations of steady state and ULOF accident conditions by using coupling ATHLET with OpenFOAM, in which a 3-D 1/8 model of hot pool was adopted. In 2021, Achuthan [14] studied the natural circulation characteristics of SESAME facility in steady state and several transient conditions.

At present, on the one hand, most researches on thermal-hydraulic characteristics of LFRs in the whole reactor scale did not consider the core power distribution. One the other hand, simulations with considerations of core power distribution were restricted to 2-D or symmetrical 3-D scales. Comparing with the above scales, the whole 3-D simulations can reveal the thermal-hydraulic characteristics more elaborately and precisely. In this paper, a 3-D CFD model of a pool type LFR primary cooling system was established, and the mesh was structured by using block-structed strategy. The steady state simulation which considered power distribution in the core was performed, and the evaluation and discussion of velocity and temperature distribution were also conducted.

2 Calculation Model

2.1 Geometry Model

The geometry model was established based on a typical 10 MWth pool type experimental reactor. To guarantee the simulation efficiency and enhance the visuality of the simulation, some subordinate parts and unnecessary details were removed or simplified. After abundant rational consideration, the concrete components of interior structure in heat exchangers and subassemblies in reactor core was simplified. The CFD simulation geometry includes hot pool, cold pool, core, above core structure (simplified based on control rod driven system) and HXs. The hot pool and the cold pool were separated by a heat barrier. Four inlets and four outlets of each HX were located in the side of them. The geometry model was showed in Fig. 1.

Fig. 1.
figure 1

The calculated geometry model of the primary cooling system

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2.2 Mesh Construction and Sensitivity Analysis

To guarantee the accuracy of results and reduce simulation cost, the mesh was established by utilizing block-structed strategy. Specifically, mesh at the hot pool and core were more dense than other parts. To make the simulation results independent with the mesh quantity, the mesh sensitivity analysis was also carried out. Three mesh sizes, including 1.5 million, 5 million and 8 million were selected. Three cases distinguished by different mesh quantity were simulated, and the corresponding temperatures of core outlet were interpolated linearly and plotted in Fig. 2. Obviously, it can be found from this figure that the 1.5 million mesh agreed bad with the two others, while the result of 5 million mesh had tiny difference with the 8 million mesh ones. Therefore, 5 million mesh was selected for the subsequent simulations.

Fig. 2.
figure 2

The temperatures of core outlet for three cases

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2.3 Construction of Reactor Core Model

Limited to the simulation cost and complexity, the reactor core was divided into eleven annular sections instead of simulating all the sub-assemblies, which was illustrated in Table 1. Each section contained certain number of sub-assemblies which had similar characteristics, such as power density. Considering the existence of sub-assembly walls, the internal boundary conditions were used to prevent above sections from heat and mass transfer. For each section, the porous medium model was employed in ANSYS FLUENT to simulate the reactor core configuration, in which the volume fraction for structures was set to be 0.7, and the volume fraction of fluid was set to be 0.3. As the detail configuration for sub-assembly was not considered, the viscous resistance in the x and y direction was set to be extremely large to ignore the cross flow of fluid. Moreover, the power density distributions in each annular section was considered by using the UDF techniques of Fluent [15].

Table 1. Radial distribution of the reactor core
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2.4 The HXs Model

The HX is one of the significant components of LFR to establish the natural circulation, it determined the temperature level of primary cooling system. In HXs, the porous medium model was also used to simulate the primary coolant and heat transfer tube and prevent the coolant from flowing along the horizontal direction. As there are Eight HXs installed in the primary cooling system, meaning that each HXs needs to remove 1.25 MW. Fluid Inlets and outlets of HX were located at the side of two HXs ends. Average coolant temperature at HXs outlet was 573K. Just as demonstrated below, therefore, a volumetric heat source term model was used in each HX [11].

$$ Q = \frac{1.25\,{\rm{MW}}}{{0.73}} \times \frac{{T_{LBE} - 573}}{119} $$
(1)

2.5 Physical Properties

Density difference provided the driving force of natural circulation. The temperature dependent lead properties equations referred to the lead or lead-alloy properties handbook edited by OECD/NEA (2007) was used here. The equation of LBE density was given as Eq. (2). And other 2 key physical properties, conductivity and viscosity were also given. UDF tools were utilized to realize these items.

$$ \rho_{LBE} = 11065 - 1.293 * T \, $$
(2)
$$ C_{pLBE} = 164.8 - 0.0394*T + 0.0000125*T^{2} - 4.56 $$
(3)
$$ \mu_{LBE} = 0.000494*e^{{\frac{754.1}{T}}} $$
(4)

3 Results and Discussion

Aiming to obtain the velocity field and temperature distribution under full power conditions, the steady state analysis was implemented. For evaluating and discussing the simulation results, a plane y = 0 m, which crossed hot pool, cold pool, two HXs, above core structure and core was established, as shown in Fig. 3.

Fig. 3.
figure 3

The schematic diagram of the plane

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3.1 Discussion of Velocity Field

The velocity field was given in Fig. 4, it can be seen that a stable natural circulation was established in the primary cooling system. In hot pool, hot coolant raised perpendicularly until arrived at the bottom of above core structure, then it dispersed around, flow upward and entered HXs inlets at last. The larger velocity along wall of above core structure and swirl at the upper part of hot pool promoted coolant mixing. The maximum velocity in the core was 0.127 m/s presented at ring 4 (fuel zone). Figure 5 showed the velocity field approaching a HX. Obvious swirl can be seen near the right HX inlet, and velocities near inlets and outlets of HXs were significantly larger, the maximum velocity in primary cooling system was 0.44060713 m/s, located in a HX. However, velocities at two ends of HXs were slightly small, that may lead poor heat transfer capability in these areas. In cold pool, velocity in upper part of cold pool was relatively small, and occurred swirl that promoted coolant mixing. While at the lower part, owing to the reduction of flowing area at lower part of cold pool, the velocity increased obviously. In addition, it can be seen that velocity vectors above and below the core were extremely intensive, this was due to the slender shape of mesh blocks and big nodes number.

Fig. 4.
figure 4

Velocity field of the reactor system

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Fig. 5.
figure 5

Velocity field at HXs

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3.2 Discussion of Temperature Distribution

Temperature distributions under steady state at y = 0 m was illustrated in Fig. 6. In hot pool, the temperature of coolant reached maximum value of 710.51K at ring 8 (fuel zone). Owing to the heat exchange in reactor core, it can be seen apparent thermal stratification in vertical direction. In radial direction, the figure indicated that temperature at fuel rings was significantly higher than other parts. However, the temperature at lower parts of fuel zones was relatively small, the reason can be concluded combing with Fig. 7. The figure indicated that velocity at fuel zones was much higher than other parts, means that the temperature and density changed most drastically, and caused the mass flow rate at these zones was larger than other parts. In the upper part of hot pool, owing to the reasonable arrangement of subassemblies and hot pool structure, no obvious thermal stratifications can be observed. In cold pool, the temperature distribution was more homogeneous than in hot pool ones, and the maximum temperature was 578.323K occurred at an outlet of HX. However, the symmetry of temperature distribution was imperfect. In the preliminary analysis, this was due to the mesh was not symmetrical entirely.

Fig. 6.
figure 6

The temperature distribution of the reactor system

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4 Conclusion

In this paper, a 3-D global CFD simulation which aims to study the thermal-hydraulic characteristics of LFR under steady state was implemented. In the core, power distribution in both vertical and radial direction were realized by utilizing UDF tools. Basing on velocity field and temperature distribution, discussion and evaluation of natural circulation.

Fig. 7.
figure 7

The velocity vector at inlet of core (right side)

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were carried out. From the simulation results and discussion, the following results had been obtained:

  1. (1)

    Lead-bismuth fast reactors have good thermal-hydraulic characteristics under natural circulation conditions. Under steady state conditions, decay heat generated by the core can be removed welly by HXs to establish an ideal steady state. At the same time, maximum temperatures of the reactor, temperature in the center of reactor core were also lower than the safety limits, which also shows that the lead-bismuth reactor has good natural circulation capability.

  2. (2)

    Based on the analysis of the velocity field, it can be concluded that the coolant generated some swirls, and clear thermal stratification phenomena was occurred in many parts of the primary cooling system. It is recommended that structural design optimization or material reinforcement be carried out, such as decrease cavity volume between end face and inlets or outlets of HXs.

  3. (3)

    Referred to other relevant literature, the simulation results in this paper were accurate generally. However, under the condition that the mesh quality was acceptable, the mesh symmetry and mesh shape may still lead obvious difference of simulation results.

In our future work, a more detailed model will be established, a more regular and symmetrical mesh partition strategy will be utilized. Furthermore, point kinetic model in core will be considered.