Keywords

1 Introduction

FuSTAR, the integral inherently safe Fluoride-Salt-cooled high-Temperature Advanced Reactor, is a kind of molten salt reactor using the solid fuel, which belongs to Gen-IV reactor concepts. It is jointly designed by Xi'an Jiaotong University and Shanghai Nuclear Engineering Research and Design Institute, aiming to effectively meet the multi-purpose energy needs of industrial facilities in remote western China.

FuSTAR has a core power of 125 MW and uses TRISO pellet fuel in the core. In this fuel, the granular nuclear fuel is wrapped in graphite. The very high melting point of the graphite layer enhances the failure temperature of the fuel to a high level, which is considered inherent safe to the reactor. During the operation of the reactor, the first loop molten salt coolant (FLiBe) flushes the core with a certain flow rate to take away the heat generated by fission in the core. After flowing out from the upper chamber of the core, the coolant passes through three heat exchangers between the first loop and the second loop to transfer heat to the molten salt (FLiNaK) in the second loop. Next, after being pressurized by three main pumps installed inside the core, most of the FLiBe flows back into the core again, and a small part passes through the passive residual heat removal system and then joins with the main flow of molten salt flowing out of the core, thus a closed cycle of the primary circuit is completed [1].

FLiNaK flows from the heat exchangers with obtained heat into the high-temperature molten salt pool to give heat to the energy conversion system, which converts the energy from heat to other forms of energy through the supercritical carbon dioxide cycle (Fig. 1).

Fig. 1.
figure 1

The FuSTAR system (1- Reactor (the first loop); 2- The second loop; 3- Molten salt pool; 4- Passive residual heat removal system; 5- Energy conversion system).

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2 Method and Modelling

The main purpose of this paper is to study the response characteristics of the first loop of FuSTAR. Therefore, the parts other than the primary loop system are simplified.

The energy conversion system and passive residual heat removal system are ignored. The flow of molten salt in the second loop is assumed to be constant, and it is assumed to flow into a node with constant pressure from a node with a constant temperature.

In the calculation of the core, using the point kinetics model, which is of 6 groups of delayed neutrons precursors (DNP) are as follows [2] (Table 1):

Table 1. Kinetics Data of DNPs.
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The equations involved are as follows:

$$\frac{dn\left(t\right)}{dt}=\frac{\rho \left(t\right)-\beta }{\Lambda }n\left(t\right)+\sum_{i=1}{\lambda }_{i}{C}_{i}\left(t\right)$$
(1)
$$\frac{d{C}_{i}\left(t\right)}{dt}=\frac{{\beta }_{i}}{\Lambda }n\left(t\right)-{\lambda }_{i}{C}_{i}\left(t\right)\cdot \cdot \cdot \cdot \cdot \cdot i=\mathrm{1,2},\cdot \cdot \cdot ,6$$
(2)

The above does not consider as the reflector, the radial distribution of core power, etc.

Modelica programming language is developed by Linköping University and it is a modern, strongly typed, declarative, and object-oriented language [5]. Modelica language is characterized by component-oriented and multi-disciplinary, making it able to simulate complex and dynamic systems. OpenModelica [6] is a free and open-source environment for Modelica language, and it provides facilities including debugging, optimization, visualization and plotting for Modelica program. In this paper, the DynamicPipe component in the Fluid library in OpenModelica is used to simulate each molten salt flow channel in the first loop of FuSTAR (among which, the Pipe component of the core part of FuSTAR is divided into ten nodes according to the axial direction); the valve component is used to integrate the local pressure loss in each flow channel of FuSTAR so that the simulation results of OpenModelica can be as close to the design parameters of FuSTAR as possible; the tank component is to simulate the pressurizer in FuSTAR; the pump component is to simulate the main pump; and in order to make the model more in line with the actual needs, the point kinetics model components and the axial distribution of the core power, the temperature feedback part, and the heat exchanger part of each Pipe component are added [3]. Finally, a schematic diagram of the model is shown in Fig. 2.

The physical property parameters are obtained by using OpenModelica.Media. Incompressible. Table Based to generate interpolation functions. The temperature coefficient of reactivity and the physical parameters of the related materials are shown in Table 2 and Table 3.

Table 2. Temperature coefficient of reactivity.
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Table 3. Physical property parameters.
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Fig. 2.
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Model diagrams in OpenModelica (1- Pressurizer; 2- Upper chamber; 3- Heat exchanger; 4- The point reactor model; 5- Pump; 6- Downpipe; 7- The lower chamber).

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3 Results and Discussion

3.1 Steady-State Calculation

The steady-state model is simulated under the core power of 125 MW, and the calculated results are compared with the design parameters in Table 4. It shows that the steady-state results are in good agreement with the design parameters, and the transient calculation can be carried out based on this model and dataset.

Table 4. Comparison between calculated results and design parameters.
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3.2 Step Reactivity Insertion Transient Analysis

In the case that the steady-state results are verified, this paper gets the results under inserting 10 pcm, 50 pcm, and 100 pcm [4] of step reactivity into the core at t = 650 s. The temperature change in the molten salt coolant at the core exit, the change in the average temperature of the fuel, and the change in the core power after the insertion of the step reactivity are shown in Figs. 3, 4 and 5. Figure 6 is an image of changes in Core Power and Heat removed from the second loop under the insertion of 100 pcm step reactivity, and Fig. 7 is the temperature of the molten salt of the second loop at the outlet of the heat exchanger. Figure 8 shows the temperature change in the fuel center at the node with the highest power in the core (the hottest spot).

Fig. 3.
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Transient change in relative power.

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Fig. 4.
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Transient change in the average temperature of the fuel.

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Fig. 5.
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Coolant salt temperature change at the core outlet.

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Fig. 6.
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Changes in core power and Heat removed from the second loop at 100 pcm insertion.

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Fig. 7.
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The temperature change in the molten salt of the second loop at the outlet of the heat exchanger.

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Fig. 8.
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Transient change in the hottest spot.

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As can be seen in Fig. 3, after the step reactivity is inserted, the change in the core power can be divided into three stages: In the first stage, the power increases rapidly and then decreases rapidly; in the second stage, there is an increasing process for a short period; in the third stage, the system reaches a steady state again. For other images, there are three such processes. For example, the temperature change of the molten salt coolant at the core exit shown in Fig. 5, it can be seen that the coolant temperature first increased rapidly, then decreased with a very small amplitude, and finally increased slowly to reach the final steady state.

For such a changing image, it is necessary to analyze the characteristics of the system and how the step input influence on the system. The following analysis is performed in the order of the three stages of parameter change.

In the first stage, the core power is increased sharply due to the insertion of a step reactivity to the reactor. At the same time, the molten salt coolant and fuel temperature will also increase. The increase in both adds negative reactivity to the reactor through the temperature feedback, so the power peaks quickly and starts to drop. During this process, the temperature rise of the molten salt in the core also increases rapidly in response to the power change.

In the second stage, due to the temperature feedback, the core power rapidly drops from peak, and the molten salt cannot maintain the temperature rise at high power. Therefore, both the molten salt and the fuel will have a temperature drop at this time, and these changes are reflected in Fig. 4 and Fig. 5. It adds positive reactivity to the core through the temperature feedback, which leads to a second increase in core power between 670 s and 700 s.

In the third stage, such a temperature drop will not last too long, and the core power will return to the increasing trend immediately due to the temperature feedback, thus, the system has entered the third stage of change. It can be seen in Fig. 6 that the heat removed by the second loop does not keep up with the rapidly change in core power, it is a slowly increasing process that eventually equals the heat generated by the core, allowing the system to achieve a new steady state. Therefore, during the whole process, the temperature of the molten salt in the second loop is always increasing, and this change can be seen in Fig. 7. For a long period, the second loop cannot remove all the heat generated by the primary loop, which leads to a slow increase in the temperature of the molten salt in the third stage. Eventually, the system will reach a new steady state around 850 s.

From the point of view of safety analysis, it can be seen that even if 100 pcm of reactivity is inserted, the molten salt temperature is still lower than 986 K, and the peak temperature of the hottest spot of nuclear fuel will be lower than 1240 K. The design safety limit of FuSTAR is: the hottest spot temperature needs to be lower than 1873 K, and the temperature of the fluorine salt coolant needs to be lower than 1089 K, both temperatures are well below the limit with the insertion of 100 pcm of reactivity. Without adding any safety facilities, the FuSTAR system is still safe under the insertion of 100 pcm reactivity only by the temperature feedback.

3.3 Increasing the Outlet Pressure of the Pump

At t = 800 s, the outlet pressure of the three main pumps are simultaneously increased from 2.15 MPa to 2.16 MPa within 50 s. Figure 9 shows the change in the pump outlet pressure and the total flow of molten salt coolant under this condition. Figure 10, 11 and 12 show the change in the core power, the change in temperature of the molten salt coolant at the core outlet, and changes in the hottest temperature of nuclear fuel under the transient. And in this transient, the size of the temperature coefficient of reactivity is artificially changed. Multiply its value by 5 or divide it by 5, and the obtained parameter changes are also put into Figs. 10, 11 and 12.

Fig. 9.
figure 9

Changes in pump outlet pressure and molten salt mass flow.

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Fig. 10.
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Change in core power.

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Fig. 11.
figure 11

Coolant salt temperature change at the core outlet.

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Fig. 12.
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Change of the hottest temperature of the fuel.

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It can be seen from Fig. 9 that under the operation of the pump changing the outlet pressure value, the total mass flow value of molten salt in the circuit will increase with the increase of pressure, which is determined by the momentum conservation equation in the Pipe component. When the pressure of the fluid is increased, there must be a concomitant increase in its flow. When the pump outlet pressure increases by 0.01 Mpa, it can be seen that the flow value will increase by 90 kg/s.

Analyzing Figs. 9, 10, 11 and 12, it can be found that when the flow rate of molten salt increases, its temperature rises in the core becomes smaller, which increases the heat taken away by the coolant from the core at the same time. Therefore, the coolant temperature at the core exit will decrease and the fuel temperature will decrease accordingly. At the same time, due to the existence of the temperature feedback, the change in both will add a positive reactivity to the core. Then it can be seen from Fig. 10 that the total power of the reactor will be increased accordingly.

In the process of increasing power due to the existence of a negative feedback, the hottest temperature of nuclear fuel will change from decreasing to increasing at a certain time (Fig. 11, Fig. 12). However, the temperature of the molten salt coolant will always decrease due to the operation of increasing the flow rate for 50 s. After the pump pressurization process is over, the excessive power will cause the coolant that is no longer increasing its flow to start to heat up, which will add a positive reactivity to the core, and the power will also start to decrease at this time. Then the system re-establishes a new equilibrium, the temperature of the coolant will rise again, and the power of the reactor will reach a new steady state value with the presence of temperature feedback.

Figure 10, 11 and 12 do a sensitivity analysis on the temperature coefficient of reactivity. Figure 10 shows that a system with a larger temperature coefficient of reactivity will have a greater rate of power boost during this transient and a shorter time for the system to establish a new steady state. Because such system feedback is stronger. As can be seen in Fig. 11, the strong negative feedback will cause the change in molten salt coolant temperature to be smaller than in other systems. In systems with smaller temperature coefficients of reactivity, the results are reversed, with lower power peaks, larger changes in molten salt temperature, and a longer time to establish a new steady state.

4 Conclusion

In this paper, a model of the primary loop system of FuSTAR is established. After the steady state results are verified, two transients are considered: adding step reactivity and increasing pumps outlet pressure. Then, reasonable analysis of parameters changes images obtained under the transient is carried out. Finally, the following conclusions are drawn:

After the insertion of positive reactivity in the core, the fuel temperature and nuclear power of the core will quickly reach a peak value due to the existence of the temperature feedback after a brief increase, followed by a new steady state establishment process of the order of 200 s;

Under the transient state of inserting 10 pcm, 50 pcm, and 100 pcm of positive reactivity, FuSTAR can still operate under the safety limit without taking any action and only relying on temperature feedback;

During the transient of the pump pressurization, the flow of molten salt coolant is increased and pictures of the system response due to the temperature feedback are obtained;

A system with a larger temperature coefficient of reactivity (absolute value) will have a stronger power response and weaker changes in molten salt temperature during pump pressurization transients.