Numerical Simulation of the Effect of Molten Salt Channel Number on Temperature Distribution in the Molten Salt Core Reactor

A critical aspect in the design of a nuclear reactor that needs to be considered is thermal analysis. This parameter relates to molten salt circulation, which serves as a fuel, and coolant in Molten Salt Reactor (MSR) core reactors. This study simulates the temperature distribution performance of the MSR core by considering the effect of the number of molten salt channels with inlet temperature variations. Knowing the temperature distribution will predict the characteristics of heat transfer in the form of natural convection for the survival of the reactor. The reactor used a Molten Salt Breeder Reactor (MSBR) design developed by Oak Ridge National Laboratory (ORNL). The Ansys software was used to simulate a 3D model under steady-state conditions. The geometry was divided into two regions: solid (graphite material) and fluid (molten salt). The thickness of the moderator and radius of the molten salt channel were 0.0508 and 0.0208 m, respectively. The moderator height was 1.98 m. The number of molten salt channels varied up to four. The results showed a temperature difference of 9 to 15 K when the channel increased from one to four at 839 K inlet temperature.


Introduction
One type of reactor developed in the Generation IV (GENIV) forum is the molten salt reactor (MSR), a reactor with fuel and coolant in molten salt, generally in the form of fluoride salt [1,2].MSR is built with the potential for accidents minimized by its advantages [3,4].The reactor has a closed fuel cycle and good passive safety.In the MSR, molten salt flows through graphite channels to produce a thermal spectrum [5].The first MSR by Oak Ridge National Laboratory (ORNL), named the Molten Salt Reactor Experiment (MSRE), received a positive response after operating for approximately four years [6,7].The reactor used fluoride-fueled salt and graphite as moderators, which is considered a successful demonstration of the potential of MSR technology [8].In 1971, ORNL developed the MSRE into a molten salt breeder reactor (MSBR).The development of the molten salt reactor concept continues to be proposed, including FUJI-MSR [9], integral MSR (Canadian Company Terrestrial Energy) [10], and Molten Salt Actinide Recycler and Transmuter (MOSART) [11,12].Reactors with similar concepts to MSRE were also developed in China [4] and by ThorCon [13].
A small modular reactor (SMR) is designed to produce up to 300 MW of electrical power with advanced safety features.Knowing the relationship between a reactor's natural circulation system and the size of the reactor's geometry is essential because it affects the reactor's safety.An MSR-type reactor is designed with inherent safety advantages.Therefore, it is necessary to develop an MSR with a smallsized reactor design that can be used on a wide scale [14].One important aspect in the design of a reactor is thermal-hydraulic analysis, which includes heat transfer, pressure drop, and temperature distribution.Studies related to the hydraulic thermal behavior in molten salt channels have been simulated in 2D [15].The results show that the distribution of output temperatures is affected by the volume of molten salt in the channel.However, this influence needs to be considered for a more realistic 3D analysis.Research analyzing natural circulation systems in nuclear reactors with variations in diameter size has been conducted [16].The results show that the relationship between the pipe diameter in the natural circulation system and the velocity of the fluid is inversely proportional.Simulations related to neutronic analysis and the fuel cycle of MSR have been widely performed [17][18][19][20][21][22][23][24].Related simulations for the safety analysis of modified freeze plug melting on MSR have also been performed using the semiimplicit moving particle method [25].Simulations with 2D analysis of the phenomenon of heat transfer from the natural circulation system using the COMSOL Multiphysics method on the MSR were performed, and the results of the characteristics of temperature distribution on the core, pressure in the primary cooling system, and speed over a certain time were displayed.Simulations have shown that the inlet velocity of the system strongly influences the flow velocity in a circulation system and can affect temperature distribution [26].
The present authors researched the geometry of the MSR reactor core [27,28], and simulations were conducted for one channel for simplification.Therefore, this study shows the effect of molten salt channel number on the temperature distribution in the core using previously described parameters [15,29,30].This simulation uses Ansys Fluent with the computed fluid dynamic method.Neutronic behavior and chemical processes, such as material corrosion, are beyond the scope of this study.

Method
Ansys is a software used in analyzing, designing, and solving problems such as structure, thermal, and fluid [31].This software can combine various mathematical models of transfer phenomena, such as heat transfer and chemical reactions, in complex forms [32].The basic mathematical models used include mass conservation, momentum conservation, energy conservation, and turbulence flow models [33].The geometry data of the moderators and molten salt channels used in this study are the same as in previous studies [27,28], which is the geometric applied in MSBR proposed by ORNL.The system's geometry was performed using Ansys Fluent software with 3D models.The geometry is divided into two regions: solid with graphite material as a moderator and fluid containing molten salt consisting of 7 LiF (71.7 mol%), BeF2 (16 mol%), ThF4 (12 mol%), and 233 UF4 (0.3 mol%) [34].The moderator thickness, molten salt channel radius, and moderator height were 0.0508 m, 0.0208 m, and 1.98 m, respectively.The material properties included in this simulation are density, specific heat, thermal conductivity, and viscosity [27,28].For numerical simulation purposes, the number of moderators was varied by 1-4 channels (Figure 1) with input temperature variations of 839 K and 908 K The boundary conditions in the simulation are inlet, outlet, internal, and wall.The inlet section setting is a velocityinlet type with a value of 1.47 m/s and an input temperature of 839 K, which is the parameter applied in the MSBR reactor by ORNL.The outlet setting is pressure-outlet, and the graphite wall temperature is set to be 300 K because it is considered to be at room temperature before interaction with another system and also to study the behavior of the channel more clearly.In this calculation, we neglected the gravity force.The generated mesh is hexahedral with an element size of 8 x 10 -3 m.The meshing quality is checked by examining the skewness and orthogonal quality value.The number and quality of the present mesh design is shown in Table 1.The meshing quality is in the excellent meshing criteria, the value for orthogonal quality is in the range of 0.95-1.00,and skewness is 0-0.25.

Effect of Variation in the Number of Molten Salt Channels
Figure 2 shows the temperature contour in the variation of channel number.The inlet temperature of the molten salt is 839 K at an inlet velocity of 1.47 m/s.Heat transfer in the molten salt channel includes convection, conduction, and radiation.Convection heat transfer occurs between molten salt molecules, and conduction heat transfer happens in graphite.The temperature difference between the molten salt and graphite as a moderator is caused by the material's thermal conductivity.Figure 3 shows the temperature distribution in the inlet, middle, and outlet sections (xy plane direction).Data was generated in the middle line of the molten salt and graphite moderator area.Based on Figure 3, it can be seen that in the middle region, graphite temperature increases caused by molten salt flowing in the channel.This is due to the heat transfer from the molten salt to the surrounding graphite.The temperature slightly decreases at the molten salt channel outlet compared to the middle area.The heat transfers to the surrounding channel walls (Twall = 300 K).The temperature difference between the inlet and the outlet for each number of channels (z-direction) is shown in  Based on Figure 4, it can be seen that the system with one channel (▬ CH1) has a temperature difference of 14 K, whereas two channels (▬ CH2) have a temperature difference of 15 K.The system with three channels (▬ CH3) showed a temperature difference of 11-12 K, and the system with four channels (▬ CH4) showed a temperature difference of 9 K.This shows that the increase in the channels number causes the outlet temperature closer to the input temperature.However, the system with two channels has a different behavior.The temperature outlet for two channels is lower than the system with one channel.This phenomenon happens because the heat from the molten salt channel is distributed along both sides of moderators at room temperature.Therefore, the heat loss is much higher than the other channel.In addition, the variation of channel number also changes the temperature in the graphite section along the molten salt channel (plot in the middle area of the z-direction).Graphite with four channels (▬ CH4-mid) has a higher temperature than other channels.Graphite as a moderator with two/three/four channels receives a heat contribution from two/three/four numbers of high-temperature molten salt.This condition shows that an increase in the number of channels increases the outlet temperature of the molten salt channel.

Effect of input temperature variation
The numerical simulation for input temperature variations in the molten salt with channels 1 to 4 is shown in Figure 5.The spectrum shows the difference in temperature values, where dark blue contours indicate the lowest temperature and red contours indicate the highest temperature.Based on the figure, it can be seen that the higher the input temperature of molten salt, the higher the temperature along the molten salt channel.The effect of these two input temperatures on the flow in the channel is shown in Figure 6.The temperature difference between the outlet from the inlet with input temperatures of (▬) 839 K and (▬) 908 K for 1 to 4 channels is 14 K and 16 K for one channel (CH1), 15 K and 17 K for two channels (CH2), 11 K-12 K and 12 K-14 K for three channels (CH3), and 9 K and 11 K for four channels (CH4).Based on the numerical simulation, it can be seen that adding a temperature of 69 K will increase the outlet temperature difference by ~1-2 K.The temperature drops relatively higher in high temperature (908 K) to low temperature (839 K).  Figure 7 shows the temperature in the graphite section for 1 to 4 molten salt channels.The figure shows that the graphite also undergoes temperature changes.The graphite temperature increases with the increase of input temperature.The higher the molten salt inlet temperature entering through the channel, the higher the temperature transferred to the graphite.Based on the numerical simulation, it was found that adding a temperature of 69 K will increase the graphite moderator temperature by ~57 K (in the middle area).In the reactor core, high operating temperatures will result in a high-temperature rise.However, high temperatures can have a negative impact on the instrumentation system device and reactor core components.

Conclusion
A numerical simulation of the temperature distribution was successfully performed on the MSR reactor core with differences in the number of molten salt channels.Based on the numerical simulations of the variation in the number of channels, it was obtained that increases the number of molten salt channels at a constant input temperature, the difference in output temperature was obtained by 2-4 K.The difference in inlet and outlet temperatures at an input temperature of 839 K from one channel to four channels was 14 K, 15 K, 11-12 K, and 9 K, respectively.The difference in inlet and outlet temperatures at an input temperature of 908 K from one channel to four channels is 16 K, 17 K, 12-14 K, and 11 K, respectively.Based on the simulation results, it was found that adding a temperature of 69 K will increase the output temperature by ~57 K in the middle area of the graphite moderator and around 1-2 K for molten salt outlet temperature in the z-direction, respectively.However, the temperature drop is relatively higher for high-temperature flow.Knowing the behavior that occurs in the reactor core, especially regarding the number and geometry of molten salt channels, can provide a reference for designing a reactor with a small size.

Figure 1 .
Figure 1.Boundary conditions of the system and meshing geometry for 1 to 4 channels.

Figure 2 .
Figure 2. The temperature distribution in the middle position of the xy-plane with the inlet temperature of 839 K: (a) one channel, (b) two channels, (c) three channels, and (d) four channels.

Figure 3 .
Figure 3. Temperature distribution at the inlet (▬ IN), middle (▬ MID), and outlet (▬ OUT) for one to four channels for xy-plane direction.The gray area in the graph represents the molten salt channel region.

Figure 4 .
The dashed line indicates the second channel in the same geometry.

Figure 4 .
Figure 4.The temperature distribution in the z-direction.

Figure 7 .
Figure 7.The temperature distribution (z-direction) in the graphite section for 1 to 4 molten salt channels.The dashed line described the second graphite moderator in the same geometry (blue line plot).

Table 1
Number and quality meshing