1.1 TRISO and Fuel pebble

The fuel design is related to the HTR-10 structure with TRISO coated particles [18], as shown in Fig. 1a. Taking into account the higher volumetric heat capacity of molten salt coolant, as well as the realistic method for obtaining fuel, the uranium loading of a single fuel pebble in this study is increased to 7 g, which relates to the fuel design of HTR-PM [19].

Fig. 1Full-screen View

(Color online) Schematic diagram of TRISO and fuel pebble. (a) TRISO, (b) simple cubic lattice model, (c) fuel pebble model

The fuel pebble diameter is 6 cm, including an external graphite shell with a thickness of 0.5 cm and the internal fuel filling zone with a diameter of 5 cm. There are 11669 TRISO particles filled in the fuel filling zone with 7.03% packing fraction. A simple cubic lattice equivalent model is used in this study, as shown in Fig. 1b. Meanwhile, other TRISO particle models, including the equivalently filled regular model, the disturbed regular model, the randomly filled regular model, and the fully random model, have been performed in a series of other studies [20]. The fuel element characteristic parameters are shown in Table 1.

1.2 Fuel pebble arrangement

In the active area, 2-cm-deep grooves are processed in line with surface curvature of the fuel pebbles in the bottom surface of a graphite reflector. These grooves are arranged in a square geography. If pebbles in the first layer fall into the grooves, the center of each series of four pebbles can form a new depression for the second layer, and accumulating layers form a pyramid. In order to keep this stable geometrical condition of the pebble bed, the inner surface of top graphite reflector is also processed with the same method. Besides, the side reflector constitutes an eight edges prism cavity, and the inner surface of the side reflector must be exactly tangent with the surface of the pebbles. In this ordered packed bed, the pebbles can support each other. The structure has strong stability against various changes, such as pressure changes and size or shape changes due to high temperature and strong irradiation. Fig. 2 shows the arrangement of fuel pebbles. This geometric selection maintains strong structural stability. If the centers of adjacent spheres are separated by 1.167 times their diameter (7.0 cm), the core can still maintain a relatively regular arrangement with sufficient constant packing fraction (PF) when the active surface area changes by less than 5% [17]. Under such condition, the vertical distance between the centers of two adjacent spheres is 0.5652 times the diameter of the ball (3.3912 cm), and the corresponding theoretical packing fraction is 68%.

Fig. 2Full-screen View

(Color online) Ordered packing schematic diagram. (a) Pebble packing model, (b) horizontal direction array, (c) vertical direction array

1.3 Core layout and fuel loading

The core model is demonstrated in Fig. 3. From the inside out, the core of the OPB-FHER mainly consists of the activity area, a graphite reflector, and the core barrel. The active area is approximately an octagonal prism with 185.0 cm height and two groups of edge distance of 111.0 cm and 114.9 cm, respectively, which forms a boundary that keeps the forces regular accumulation as mentioned above. The core is filled with 11043 fuel pebbles and 432 graphite pebbles. The reflector periphery size is 300 cm in height and 260 cm in diameter. With a 2-cm-thick metal barrel, the overall core size is 304 cm in height and 264 cm in diameter.

Fig. 3Full-screen View

(Color online) Core of the OPB-FHER. (a) Core cross section, (b) core longitudinal section, (c) fuel pebble array-layer I, (d) fuel pebble array-layer II, (e) graphite pebble array, and (f) top and bottom structure.

The packing fraction (PF) of pebbles in the active area due to accumulation can reach 68% and 65.8% for theoretical mode and the actual value, respectively. This fine distinction of PF is produced in the boundary effect. In this packing, some stable natural channels for the flow of molten salt can be formed among the pebbles from the bottom up. Graphite pebbles with 6.0 cm diameter at the top and bottom can form a transition zone between the fuel pebbles and graphite reflector, which can prevent overheating damage for fuel pebbles at the top and bottom due to a lack of coolant. There are 20 channels distributed in the graphite reflector, including 16 for control rods and 4 for experiments. 201 coolant flow channels each with 4 cm diameter are arranged in the top and bottom reflector.

For fuel management, whole loading and unloading are adopted in one cycle. Each cycle has one batch of fuel consisting of 11043 fuel pebbles and 432 graphite pebbles. The basic physical parameters for the core of one cycle are listed in Table 2.

1.4 SCALE codes and data

The SCALE code system [21] developed at Oak Ridge National Laboratory has been used for many years for various light water reactor applications. In recent years, features have been added that allow handling of problems specific to high-temperature gas-cooled reactors. Such specific features include the treatment of the double heterogeneity of fuel that is characteristic of HTGRs, for both the prismatic and pebble bed designs. Furthermore, it does account for the double heterogeneity of the fuel through the way the cross-section self-shielding is carried out by using the DOUBLEHET cell data option for cross-section processing [22]. All neutronics physics calculations and simulations described in this paper were performed with KENOVI in SCALE6.1 and used nuclear cross sections based on ENDF/B-VII.0 data that were further processed by the CSAS6 sequence of SCALE in energy libraries for 238 groups. The TRITON control module, couple KENOVI, and ORIGENS were used for burnup analysis in SCALE.

2.1 Reactivity control

Two independent reactivity control systems with two radial positions are set in the graphite reflector, as shown in Fig. 2a. The first system consists of 10 rods in the inner circle and 2 rods in the outer circle surrounding the active area. These rods provide power regulation, burnup compensation, temperature control, and shut down at all kinds of operating conditions. The second reactivity control system is composed of 4 rods in the inner circle (marked in blue) that force shutdown when the first shutdown system fails to perform properly. The absorber material is B₄C (19.9 at% ¹⁰B) under Hastelloy-N alloy cladding. The inner and outer diameters of the control rod are 55 mm and 110 mm, respectively. The specific structural parameters and material composition of the control rod are shown in Fig.4 and Table 3.

Fig. 4Full-screen View

Control rod geometry

Three main temperature states are analyzed in the core design, namely, 615 ºC, 590 ºC, and 459 ºC, representing the power operation status, normal cold status, and accident cold status, respectively. Table 4 shows the reactivity compensation and reactor safety requirements. It can be seen that the first shutdown system can provide 15120–15820 pcm worth with 12 rods at different lifetime stages. Thus, it has sufficient margin at various working conditions, including the extreme accident state, the FLibe’s melting point 459 ºC, and single-rod failure accident (seen as the -8310 to -4620 pcm shutdown depth of 11 rods). The second shutdown system also has sufficient margin of about -4320 to -3420 pcm, even at 590 ºC. All the control rods are worth about 18000–20000 pcm. If the accident is out of control for the second system of rods, the molten salt drain system will be in the working condition, which can provide a maximum of -6980 pcm reactivity and guarantee safe reactor shutdown.

2.2 Neutron spectrum

The neutron spectrum is dependent on fuel composition, moderator type, and the structural materials of reactor core, and it determines the basic physical properties of the core. Therefore, it is important to analyze the neutron spectrum in the reactor design. Fig. 5 shows the normalized neutron spectrum for different single fuel cells in 3 typical reactors. The HTR and OPB-FHER used the same lattice model geometry shown in Fig. 2a. The difference between the two models is the use of different coolants.

Fig. 5Full-screen View

(Color online)Neutron spectrum for different reactor elements

The square unit cell model of a standard Westinghouse 17x17-lattice assembly is adopted as a reference for pressurized water reactor (PWR). In the PWR pin cell model, the value of the fuel pellet radius, fuel pellet to cladding gap, cladding inner radius, cladding outer radius, and pin pitch were 0.4096 cm, 0.0082 cm, 0.4178 cm, 0.4750 cm, 1.26 cm, respectively. In addition, the three cell models used the same level of ²³⁵U enrichment (17.08%) but different coolant, followed by helium, molten salt, and water. Further, the white reflection boundary condition is used in the calculation with SCALE.

It can be seen that, no matter what core material is used, the neutron energy spectrum has two peaks consisting of the fission energy spectrum in the fast area and the Maxwell spectrum in the thermal area. As high-enrichment fuel was used in the calculation, the energy spectrum of this PWR occupies the high-energy region compared to that in PWR, and the peak in thermal area is not obvious. The shape of the neutron energy spectrum is different in a high-temperature gas-cooled reactor. It has a higher peak in thermal area and a lower peak in fast area, in contrast to the spectrum in PWR. This distinction arises because the proportion of coated particle fuel is much lower than in PWR. Thus, the macro-absorption cross section of the thermal neutron in the core region of the OPB-FHER is much smaller than that in PWR, resulting in a high proportion of thermal neutrons. The neutron spectrum in a molten salt pebble-bed reactor is similar to that in a high temperature gas cooled reactor for the same fuel pebble. But due to the moderation and neutron absorption effect in BeF₂-2LiF, the OPB-FHER spectrum occupies a slightly lower energy region.

2.3 Neutron flux density and power density distribution

In this section, four control rods were inserted into the core in order to reach criticality during analysis. The neutron flux density distributions in the core active area at the beginning of life with xenon equilibrium are shown in Fig. 6. The coordinate origin is the center of the active region. The total flux density is about 0.5–1.45·10¹⁴ n/cm²/s. The maximum radial neutron flux density is in the center of the active area. However, the maximum axial neutron flux density appears at about 20 cm below the center plane, and this downward shift of the maximum flux density is due to the insertion of the control rods.

Fig. 6Full-screen View

(Color online)Neutron flux density in the active area at beginning of life with xenon equilibrium. (a) Axial neutron flux density, (b) radial neutron flux density

For the calculation of power density distribution (Fig. 7), the active area is divided into 27 meshes with 6.7824 cm size in the axial direction. The maximum axial power density is 11.40 W/cm³, located 20 cm below the center of the active area. The axial average power density is 9.10 W/cm³. The axial power peak factor is 1.25.

Fig. 7Full-screen View

(Color online) Power density distribution in the active area at beginning of life with xenon equilibrium. (a) Axial power density distribution, (b) radial power density distribution (W/cm³)

The radial mesh size is 7 cm×7 cm. The radial maximum and mean power density are 9.10 W/cm³ and 7.56 W/cm³, respectively. The radial power factor is 1.20. Therefore, the total power peak factor is 1.25×1.20=1.50 for the core active area.

Using a thermal hydraulic calculation, the maximum average temperature of the fuel pebble in the core is found to be 682 ºC and appears 20 cm below the center.

2.4 Temperature coefficients of reactivity

Reactivity temperature coefficients are the key parameters for assessing reactor safety, which primarily includes the contribution of fuel, coolant, moderator, and reflector. In this study, the KENO module in SCALE6.1 code is used to calculate K_eff for these coefficients. Statistical uncertainty is inherent in the Monte Carlo method, and K_eff was calculated at multiple temperature points. The 1/K quadratic curve fitting method or linear fitting [22] was used to process the data. All results at different burning lifetime for one cycle are shown in Table 5.

The fuel reactivity temperature coefficient exists due to the Doppler Effect. In the OPB-FHER, the fuel reactivity temperature coefficient is -2.71 to -2.35 pcm/K, which agrees well with LWR. The coolant reactivity temperature coefficient, also called the void coefficient, is slightly negative due to thermal expansion of the coolant. The moderator reactivity temperature coefficient is -3.98 to -3.11 pcm/K. The total reactivity temperature coefficient is negative throughout the reactor lifetime, illustrating the safety of the reactor to some extent.

2.5 Burnup, ⁶Li depletion, and tritium production

The burnup time of one cycle for the core is analyzed as shown in Fig. 8. If K_eff = 1 was selected as the lifetime truncation, equivalent full power operation will exceed 120 days.

Fig. 8Full-screen View

K_eff change over equivalent full power running time

In addition to the initial ⁶Li stock in the FLiBe coolant, ⁶Li is a strong neutron absorber in molten salt and is primarily produced through the ⁹Be (n, nt) →⁶Li nuclear reaction and removed through the ⁶Li (n, t) →⁴He reaction [23]. The consumption and production rates for ⁶Li in molten salt are related to the core power, and they eventually reach a balance after a very long runtime ^[9]. Fig. 9 shows the concentration change of ⁶Li along with the burnup time. It is seen that the concentration of ⁶Li declines gradually in a short-to-medium term, just like burnable poison. However, if the reactor was operated in a very long time, the ⁶Li quantity will reach a steady state. Therefore, the reactivity will be released at last, which needs to be considered and analyzed for long runtimes.

Fig. 9Full-screen View

Concentration variation of ⁶Li and ³H

Tritium is a very lively nuclide that is easy to spread and causes a hydrogen embrittlement effect in structural materials. In addition, it has strong radioactivity both in the working environment of the nuclear power plant and the natural environment outside the plant [24]. Therefore, tritium production is an important source term and should be considered in the design of radiation protection, including its behavior in the reaction channel and its accumulation, dissolution, and diffusion in the reactor components. In a 10 MW OPB – FHER reactor, ⁶Li in FLiBe coolant is the main production source of Tritium by the nuclear reaction ⁶Li+n→³H+⁴He+4.79 MeV [25]. Moreover, some ⁷Li can also generate Tritium through the nuclear reaction ⁷Li+n→³H+⁴He+n. Fig. 9 shows the tritium concentration in the 10 MW OPB-FHER over short-to-medium timescales.