A. Buoyancy problems

The force analysis of the CLEAR FA (without ballast) is shown in Fig. 1. The direction of total force of the FA in water is the same as gravity, whereas the direction of total force of the FA in LBE is the same as buoyancy, hence the need of a specific design to solve the problem of floating FA in the coolant.

Fig. 1.Full-screen View

(Color online) Force analysis of the FA (without ballast).

B. Fixation methods of typical reactors

In the European project of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED), the core consists of wrapped hexagonal FAs with pins, arranged in a triangular lattice. The 171 FAs are subdivided into two radial zones with different plutonium enrichment to ensure an effective power flattening, and surrounded by two rows of dummy elements serving as reflector. The ALFRED design uses upper tungsten ballast to guarantee the correct position of each FA in refueling operations. The high density of lead alloy causes a great buoyancy force and leads to the FA floatation. In normal operation, FAs are connected to the upper diagrid plate by preloaded springs; while in refueling operation, the upper diagrid plate is removed in order to reach the upper head of each FA. Thus, the FAs cannot change their position because of the upper ballast counterbalanced the buoyancy force.

In the Russian project of experimental accelerator driven system (XADS), the core includes 120 FAs, 162 dummy assemblies and 12 absorber assemblies. Each FA, consisting of hexagonal wrapper tube, operation head and position spike, is anchored to the lower diagrid through a locking device. The operation head can be connected to the transfer machine gripper, which has been improved referring to the sodium reactor technology and possesses the additional possibility to push the FA inside the LBE and keep its vertical trim. The transfer machine gripper locks/unlocks the FA to/from the lower diagrid, and unlocks/locks the FA from/to itself.

In the Belgian project of Multipurpose Hybrid Research Reactor for High-tech Applications (MYRRHA), the fresh core contains 68 FAs, which are kept to the core support plate by inserting them in holes of the core support plate from underneath. Each FA includes 91 pins and retains at their location by the buoyancy force. The sub-critical core is surrounded by the core barrel to prevent the FAs from moving away from each other. The refueling machine can move up and down for about 2 m, to extract the FAs from the core. The fuel handling system is performed underneath the core.

After weighing advantages and disadvantages of the three core designs (Table 1), an integrated system of ballast and fuel element guaranteed the correct FA-positioning in normal and refueling operations. In this paper, structural design of the FA, especially the fixation methods, will be described.

A. The FA structure

In view of reducing technical risk and R&D cost of FA, UO₂ was chosen as the reactor fuel due to its adequate chemical compatibility with the coolant lead-alloy. Based on the premise of the nuclear nonproliferation treaty and present situation in China, the enrichment of UO₂ was designed as 19.75%. The maximum temperature limit of fuel pellet was 2300 ℃, and the temperature gradient limit was 4×10⁴ ℃/m. Each FA includes 61 fuel pins, featuring a stainless steel cladding and holding UO₂ pellets [10, 11]. Considering service conditions and design load cases in CLEAR, the preliminary structure design parameters of FA are listed in Table 2.

B. The fixation method

Ballast was chosen as the fixation method for CLEAR FA. An integrated system of ballast and fuel element ensures correct positioning of FAs in normal and refueling operations. The design of ballast was analyzed with a detailed assessment of the service condition and accident risk.

2. Force analysis of the ballast

The force analysis of FA without and with ballast added in coolant LBE is shown in Fig. 2.

Fig. 2.Full-screen View

(Color online) Force analysis of FA without and with ballast in coolant LBE.

From Fig. 2(a), the total force of FA without ballast in coolant LBE is

$F_{\text{total}}=|F_{\text{b}}+F_{\text{sf}}-G|\mathrm{,}$ (1)

where, F_b = ρ_LBE·g·V_FA is the buoyancy, ρ_LBE=11 g/cm^-3 is the density of LBE, g is the acceleration of gravity, V_FA is the volume of FA; F_sf is the coolant scouring force estimated by thermal hydraulics calculations; and G is the gravity of FA.

With the ballast of a DU cylinder in radius of r_ba = 5.45 cm, height of h_ba, and gravity of F_ba, we have (Fig. 2(b))

$h_{\text{ba}}=F_{\text{ba}}/(S_{\text{ba}}\cdot {\rho }_{\text{DU}}\cdot g)=(F_{\text{b}}\text{'}+F_{\text{sf}}\text{'}-G)/(\pi r_{\text{ba}}^2\cdot {\rho }_{\text{DU}}\cdot g)\mathrm{,}$ (2)

where, S_ba is the section of ballast; $F_{\text{b}}\text{'}$ is the buoyancy of FA; $F_{\text{sf}}\text{'}$ is the scouring force estimated by thermal hydraulics calculations; and ρ_DU=19.1 g/cm^-3 is the density of DU. The thermal hydraulic calculation was performed, and the ballast height was estimate at h_ba=510 cm (F_total =0).

DU ballast in two versions was added into the FA to improve comprehensive density and to balance the upward force. Version A ballast was outside the FA, while Version B ballast was inside FA on every fuel element.

3. Comparison of the two ballast versions

Force analysis of the two versions were presented in Table 3.

TABLE 3.Full-screen View

Parameters of force analysis

Designs	V (cm3)	G (N)	Fba (N)	Fb (N)	Fsf_max (N)
No ballast	10292.5	846.83	0	1109.4	26.25
Ballast A	15657.7	1851.1	1004.3	1687.8	26.25
Ballast B	14512.3	1482.3	635.5	1422.2	26.25

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The Version A ballast (Fig. 3(a)) was made of several DU plates, connected with FA on the entrance of coolant. The pressure at entrance of coolant, P_EC, can be calculated by

Fig. 3.Full-screen View

(Color online) Schematics of the fuel assembly with Version A (a) and Version B (b) ballast.

$P_{\text{EC}}=F_{\text{cw}}/S_{\text{E}}\mathrm{,}$ (3)

where, F_cw = F_b + F_sf – G = 600 N and S_E = 2.34 cm² is the sectional area of entrance of coolant. So, P_EC = 2.56 MPa. The refueling cycle was designed at ten years. Corrosion at corner will occur due to the small section area at the entrance of coolant. In the ten years, performance of stainless steel will decrease significantly, and deformation of coolant entrance was possible in normal and refueling operations. In addition, the crack grew much frequently owing to holes at the entrance of coolant.

Figure 3(b) shows the FA structure with the Version B ballast, which is divided to every fuel element. Design specifications of the fuel element are given in Table 4.

TABLE 4.Full-screen View

Design specifications (in mm) of CLEAR fuel element

Items	Values
Pin length	1675
Pin diameter	12
Pellet diameter	10.9
Active zone length	800
Ballast length	510
Cladding material	Stainless steel

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The pressure of one cladding tube, P_CT, can be calculated by

$P_{\text{CT}}=f_{\text{cw}}/S_{\text{CT}}\mathrm{,}$ (4)

where f_cw=10.4 N is the gravity of ballast in one fuel element, and S_CT=0.1457 cm²> is the sectional area of one cladding tube. Thus, P_CT=0.714 MPa, being much smaller than P_EC. Therefore, under the same service environment, the safety margin of Version B is much larger than that of Version A. After weighting the pros and cons (Table 5), Version B was proposed as the most potential design for CLEAR FA, with fewer technological risks.

TABLE 5.Full-screen View

The pros and cons of two versions

Features	Version A	Version B
Force analysis	–, Deformation of coolant entrance occurs.	+, Smaller deformation
Inherent safety	–, FA may float in reactor accidents.	+, FA always sinks under coolant.
Safety margin	–, Crack grows much easier.	+, Service life is longer.

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In normal operations, sufficient safety margin of ballast design should be given for service environment [14]. Therefore, safety analysis of the ballast should be carried out.

A. Model of ballast

As cross section of the ballast is central symmetry, 1/6 of the structure was chosen to establish the calculation model [15, 16] (Fig. 4). The DU pellet has a 15-15Ti cladding, with a helium layer between the pellet and cladding. Properties of the materials are given in Table 6.

Fig. 4.Full-screen View

(Color online) The cross section of the ballast.

B. Boundary conditions

The heat of ballast is transferred from DU pellet to cladding by helium, and the heat of cladding is transferred by the LBE coolant [17, 18]. When the reactor is in normal operation, the electromagnetic load is too small to be considered. Service parameters of the ballast in the lead alloy-cooled reactor are given in Table 7. Temperatures of the cladding and DU were obtained using empirical formulas. To ensure a sufficient safety, they were calculated conservatively.

C. The simulation results of steady-state operation

The finite element code ANSYS was used to simulate the ballast calculation model. The temperature field is shown in Fig. 5(a), on the basis of steady-state operation. Figure 5(b) shows the radial temperature of ballast pellet. After an amount of theoretical and experimental verification, the operation temperature limit of 15-15Ti was set to 550 ℃ [19, 20]. The simulation results show that the ballast temperature did not increase dramatically when the reactor was in steady-state operation. Thus, DU does not introduce damage to the cladding and other structural materials. In summary, the ballast design meets the requirements of design criteria.

Fig. 5.Full-screen View

(Color online) Temperature field of ballast (a) and radial temperature variation of ballast pellet (b).