A flow instability model analysis method for multi-loop natural circulation systems

Abstract

The present invention discloses a method for analyzing flow instability models in multi-loop natural circulation systems, relating to the field of nuclear reactor safety technology. The key technical aspects of the method include: establishing a multi-loop natural circulation flow system model; utilizing a self-programming program to perform natural circulation calculations to obtain a bifurcation characteristic curve for a two-phase multi-loop natural circulation flow system; establishing a multi-loop pressure drop-flow equation set with strong flow-heat transfer coupling to obtain a parameter response curve for the two-phase multi-loop natural circulation flow system; and analyzing the influencing characteristics of system parameters using the bifurcation characteristic curve and the parameter response curve. Based on the extraction of a three-loop coupled natural circulation flow system from marine nuclear power source design, the present invention utilizes a self-programming program to perform natural circulation calculations for a two-phase multi-loop system. By screening factors influencing the natural circulation flow of each loop and the heat transfer between loops, the method is used to accurately analyze the influencing characteristics of parameters within a nonlinear multi-loop natural circulation system.

Description

Technical Field

[0001] The present invention relates to the field of nuclear reactor safety technology, and more particularly to a flow instability model analysis method for a multi-loop natural circulation system. Background Art

[0002] Advanced nuclear power plant passive waste heat removal systems utilize single-loop and dual-loop natural circulation methods, with forced circulation driven condenser water systems or large-capacity water tanks used to remove residual heat from the core. Because nuclear power sources in marine environments are isolated from the external power grid and remain unattended for extended periods, a complete power outage would render the three-loop condenser water system inoperable, rendering the natural circulation method for removing residual heat from the core ineffective. Consequently, compared to land-based nuclear power plants, marine nuclear power sources place even higher demands on inherent safety.

[0003] If the two-loop natural circulation is expanded to a three-loop natural circulation, and the first loop, the waste heat removal system and the condenser circulating water system are regarded as a whole to form an integrated multi-loop coupled natural circulation system, the requirements can be met; however, due to the strong multi-loop coupling characteristics within the three-loop coupled natural circulation system itself, coupled with the influence of flow instability that may be caused by phase change in the waste heat removal system, the characteristics of the system will become more complicated.

[0004] In recent years, Yu Jiyang et al. proposed a passive waste heat removal system using three coupled natural circulation loops, with a water storage tank as the final heat sink. This system was calculated and analyzed using the RETRAN02 program. The results show that, with appropriate system parameters, this passive system can effectively remove waste heat from the reactor core. Li Xiaowei et al., through theoretical analysis and numerical calculations, investigated the decoupling problem in multi-coupled natural circulation systems and proposed a method for numerically simulating the thermal-hydraulic characteristics of multi-coupled systems. However, marine nuclear power systems are complex, difficult to construct and maintain, and face significant uncertainty in both cost and cycle time. Current multi-loop natural circulation systems are calculated using theoretical numerical methods, and no method exists specifically for modeling and analyzing multi-loop natural circulation systems.

[0005] Therefore, the present invention aims to provide a flow instability model analysis method for a multi-loop natural circulation system to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to provide a flow instability model analysis method for a multi-loop natural circulation system. The present invention extracts a three-loop coupled natural circulation flow system from the design of a marine nuclear power source, uses a self-programming program to realize the natural circulation calculation of a two-phase multi-loop system, and screens the factors affecting the natural circulation flow of each loop and the heat transfer between loops to establish a multi-loop pressure drop-flow equation group with strong flow-heat transfer coupling, which can accurately analyze the influence characteristics of the parameters in the nonlinear multi-loop natural circulation system.

[0007] The above technical objectives of the present invention are achieved through the following technical solutions: A method for analyzing flow instability models of a multi-loop natural circulation system, comprising the following steps:

[0008] S1. Extract and establish a multi-loop natural circulation flow system model based on marine nuclear power design;

[0009] S2. Based on the multi-loop natural circulation flow system model, a self-programming program is used to perform natural circulation calculations to obtain a bifurcation characteristic curve of a two-phase multi-loop natural circulation flow system;

[0010] S3. Screen the factors affecting the natural circulation flow and heat transfer between each loop in the multi-loop natural circulation flow system model, establish a multi-loop pressure drop-flow equation system with strong flow-heat transfer coupling, and obtain the parameter response curve of the two-phase multi-loop natural circulation flow system;

[0011] S4. Analyze the influence characteristics of system parameters through bifurcation characteristic curves and parameter response curves.

[0012] The present invention is further configured as follows: the self-programming program in step S2 is compiled based on the C++ language to complete the calculation program, and the natural circulation calculation is performed by selecting a suitable thermal hydraulic model and a numerical calculation algorithm.

[0013] The present invention is further configured as follows: the thermal hydraulic model includes a natural circulation model, a flow resistance model, a heat exchange model and a net steam generation point model.

[0014] The present invention is further configured as follows: in the natural circulation model, the system model is divided into several sections according to the different heating conditions of the fluid in the system model, various pressure drops in several sections are calculated respectively, and then the various pressure drops in several sections of the same circuit are added together to obtain the total pressure drop of the same circuit.

[0015] The present invention is further configured as follows: the flow resistance model uses an artificial assumption to determine each local pressure loss, by pre-setting a constant, and then performing an impact analysis on the change of the local resistance coefficient to offset the influence of the local resistance caused by the local structure of the pipeline on the flow of the fluid.

[0016] The present invention is further configured such that the heat exchange model includes calculations of convection heat exchange between the one-way liquid and the tube wall, steam condensation heat exchange, and liquid boiling heat exchange.

[0017] The present invention is further configured such that the liquid in the secondary circuit in the net steam generation point model is heated to a gas-liquid two-phase flow, and the dividing point between the single-phase water and the gas-liquid two-phase flow in the heat exchanger is determined by calculation using the Saha-Juber relationship.

[0018] In summary, the present invention has the following beneficial effects:

[0019] This invention extracts a three-loop coupled natural circulation flow system from the new concept marine nuclear power source design, and uses a self-programming program based on the C++ language to realize the natural circulation calculation of the two-phase multi-loop system. Through preliminary screening of the natural circulation flow of each loop and the factors affecting the heat transfer between loops, a multi-loop pressure drop-flow equation group with strong flow-heat transfer coupling is established, which can accurately analyze the influence characteristics of the parameters in the nonlinear multi-loop natural circulation system. The research results show that increasing the temperature of the three-loop cold source, reducing the three-loop pressure, increasing the second loop pressure, and reducing the second loop local resistance coefficient can be beneficial to system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 1 is a flow chart of a method for analyzing a flow instability model of a multi-loop natural circulation system according to an embodiment of the present invention;

[0021] Figure 2 is a simplified diagram of a three-loop coupling system in an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram of the numerical algorithm flow structure in an embodiment of the present invention;

[0023] Figure 4 1 is a bifurcation characteristic curve diagram of a two-phase single-loop natural circulation system in an embodiment of the present invention;

[0024] Figure 5 1 is a graph showing the bifurcation characteristics of a natural circulation system of a two-phase multi-circuit system according to an embodiment of the present invention;

[0025] Figure 6 This is a diagram showing the relationship between pressure drop and mass flow rate at various heating powers in the secondary circuit of the embodiment of the present invention;

[0026] Figure 7 is the bifurcation characteristic curve of different three-circuit cold source temperatures in the embodiment of the present invention;

[0027] Figure 8 1 is a bifurcation characteristic curve diagram of different three-circuit pressures in an embodiment of the present invention;

[0028] Figure 9 1 is a bifurcation characteristic curve diagram of different secondary circuit inlet resistance coefficients in an embodiment of the present invention;

[0029] Figure 10 1 is a bifurcation characteristic curve diagram of different secondary circuit outlet resistance coefficients in an embodiment of the present invention;

[0030] Figure 11 is a driving force-resistance relationship diagram for different inlet resistance coefficients in an embodiment of the present invention;

[0031] Figure 12 is a driving force-resistance relationship diagram for different outlet resistance coefficients in an embodiment of the present invention;

[0032] Figure 13 is a bifurcation characteristic curve diagram of different secondary circuit pressures in an embodiment of the present invention;

[0033] Figure 14 1 is a flow instability boundary diagram for different three-circuit cold source temperatures in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] The following is combined with Figure 1-14 The present invention is described in further detail.

[0035] Example: A method for analyzing a flow instability model of a multi-loop natural circulation system includes the following steps:

[0036] S1. Extract and establish a multi-loop natural circulation flow system model based on the design of marine nuclear power, such as Figure 2 As shown in the figure, the system model is a simple three-circuit coupled system, in which one circuit consists of an electric heater, a pressure stabilizer, a shell and tube heat exchanger, a ball valve, a canned motor pump and a pipeline. The fluid is heated by the electric heater (or heat exchanger) in the three circuits and then flows into the heat exchanger (or cold source) through the ascending section, transferring the heat to the next circuit (or cold source). After being cooled, it returns to the electric heater (or heat exchanger) through the descending section, forming a cycle; when the initial cycle established by the canned motor pump is established, the canned motor pump is turned off and the fluid will be driven by natural circulation.

[0037] The inlet and outlet fluids of the first circuit are all single-phase water, the inlet fluids of the second and third circuits are single-phase water, and the outlet fluids are gas-liquid two-phase flows. For the convenience of calculation, the situation where the outlet fluid of the second circuit is single-phase water and superheated steam is not considered in this embodiment. The heat removed by the cooling water in the condenser of the third circuit is equal to the heat input by the electric heater, and its temperature is set to be constant to simulate the temperature of seawater. The system pressure of the three circuits is controlled by the regulator of each circuit and is always stable at the set pressure. At the same time, for the convenience of calculation, the electric heater, shell and tube heat exchanger, and condenser used in this embodiment are all ideal components. The system is an adiabatic system and has no heat exchange with the outside world other than the system components. The center height difference between the heat source and the cold source is 6m for the first circuit, 2m for the second circuit, and 4m for the third circuit.

[0038] S2. Based on the multi-loop natural circulation flow system model, a self-programming program is used to perform natural circulation calculations to obtain the bifurcation characteristic curve of the two-phase multi-loop natural circulation flow system; the self-programming program is compiled based on the C++ language to complete the calculation program, and the natural circulation calculation is performed by selecting a suitable thermal-hydraulic model and a numerical calculation algorithm, and the thermal-hydraulic model includes a natural circulation model, a flow resistance model, a heat exchange model and a net steam generation point model.

[0039] The numerical calculation algorithm flow of the system in this embodiment is as follows: Figure 3 As shown, since the temperature of the cold sources of the three circuits is set to be constant and known in this embodiment, this embodiment adopts the method of calculating from the three circuits to the first circuit in sequence, that is, the flow of the three circuits is calculated first (when calculating the third circuit, there is no need to run the operation of calculating the inlet temperature and outlet temperature), and then based on the flow of the three circuits, the inlet temperature and outlet temperature of the second circuit are calculated through the heat exchange correlation formula, and then the flow of the second circuit is calculated, and finally the flow of the first circuit is calculated.

[0040] In the natural circulation model, the system can be divided into several sections according to the different heating conditions of the fluid in the system (adiabatic, heating, cooling). The various pressure drops in each section are calculated separately. Then, the various pressure drops of each section in the same circuit are added together to obtain the total pressure drop of the circuit. If one section is taken out, the mathematical expression of its total pressure drop is:

[0041] ΔP=ΔP el +ΔP a +ΔP f +ΔP c (1)

[0042] where ΔP el Indicates the boost pressure drop, ΔP a Indicates the accelerating pressure drop, ΔP f represents the friction pressure drop, ΔP c Indicates the form resistance voltage drop.

[0043] For a closed natural circulation loop, the accelerating pressure drop ΔP in the system a is 0, the total pressure drop ΔP is 0, and formula (1) can be transformed into:

[0044] -ΔP el =ΔP f +ΔP c (2)

[0045] If ΔP d is the driving pressure head, then ΔP d =-ΔP el , if we record ΔP r is the flow resistance, then ΔP r =ΔP f +ΔP c , so formula (2) can be rewritten as:

[0046] ΔP d =ΔP r (3)

[0047] When the driving pressure head generated by the increased pressure drop in the system is consistent with the system's flow resistance, the natural circulation system reaches a stable state. When the system flow rate is constant, if the driving pressure head and the flow resistance are different, the system flow rate will be adjusted until the system reaches a steady state. Based on this principle, this embodiment compiled a C++ language system program for a multi-loop coupled natural circulation system to study the steady-state characteristics of the system.

[0048] In the flow resistance model, the flow of fluid in a pipeline is affected by two types of resistance: one is the longitudinal resistance caused by friction, and the other is the local resistance caused by the local structure of the pipeline (such as variable cross-section, change in flow direction, etc.). For pipe flow, the flow resistance expression is:

[0049]

[0050] Where k is the sum of the loss coefficients caused by friction, local loss, turning loss, expansion loss, and contraction loss, and V is the fluid velocity.

[0051] When a fluid flows through a straight pipe, friction will generate resistance along the way, which in turn generates friction pressure drop. For the resistance along the way, k can be expressed as:

[0052]

[0053] Where f is the friction factor, L is the channel length, and D e Indicates equivalent diameter.

[0054] For round tubes, D e Take the cross-sectional diameter. When the cross-sectional area is not circular, De Taking the hydraulic diameter, the expression is:

[0055]

[0056] Where A f Indicates the channel cross-sectional area, P W Indicates wet periphery.

[0057] The friction factor f of the single-phase friction pressure drop is usually calculated by an empirical formula. It is a single-valued function of the Reynolds number Re. The calculation expressions of Re and f are shown in Equations (7) and (8), respectively:

[0058]

[0059] Where μ represents the dynamic viscosity of the fluid.

[0060]

[0061] The two-phase friction pressure drop adopts the homogeneous flow model, which can be expressed as:

[0062] ΔP tp =Φ 2 tp ΔP tf (9)

[0063] Where, Φ 2 tp represents the two-phase friction factor, which can be determined by formula (10), and ΔP tf It is determined by the above single-phase formula.

[0064]

[0065] Where v represents the specific volume, subscript g represents saturated steam, and subscript f represents saturated water.

[0066] Among them, when the fluid flows through a boundary with a sharp change, pressure loss will occur, and then a form resistance pressure drop will be generated. The key to solving its specific value is to determine the local pressure loss coefficient k. However, since this coefficient often cannot be derived from a certain mathematical calculation formula and needs to be determined by experimental measurement, this brings certain difficulties to theoretical calculations. Therefore, in this embodiment, the local pressure losses are temporarily determined by artificial assumptions. By pre-setting constants, the impact analysis of the changes in the local resistance coefficient is then performed.

[0067] The heat transfer model includes calculations for convective heat transfer between the one-way liquid and the tube wall, steam condensation heat transfer, and liquid boiling heat transfer. For convective heat transfer between the single-phase liquid and the tube wall, this paper uses the precise Gnielinski formula, as shown in Equation 11:

[0068]

[0069] It is applicable to the case where Re=2300×106 and Pr=0.6×105; wherein Nu represents the Nusselt number, Pr represents the Prandtl number, and f represents the drag coefficient. In this embodiment, the Konakov formula is used:

[0070] f=(1.8lgRe-1.5) -2 (12)

[0071] In steam condensation heat exchange, when the fluid in the vertical heat exchanger is saturated steam under a certain pressure, it condenses into single-phase water in the pipe. The convective heat transfer coefficient correlation formula used in this embodiment is as follows.

[0072] When Re < 1800, the liquid film is in a laminar state, and McAdams recommends using the correlation formula:

[0073]

[0074] Where r represents the latent heat of vaporization, λ represents the thermal conductivity, and t s represents the saturation temperature, t w represents the wall temperature.

[0075] When Re>1800, the liquid film is in a turbulent state. This embodiment adopts the Kirkbride formula, as shown in formula (14):

[0076]

[0077] After the liquid is heated to a saturated state in the pipe, it undergoes saturated boiling heat exchange with the wall. In this embodiment, the convective heat transfer coefficient of this heat exchange process is calculated using the Jens-Lottes equation:

[0078]

[0079] Where Δθ J represents the film temperature difference, is the heat flux, Q is the heating power, L s Represents the length of the heating section, and Δθ is calculated by formula (15) J Then, by substituting it into formula (16), the convective heat transfer coefficient h can be obtained:

[0080]

[0081] In the net steam generation point model, the liquid in the secondary circuit may be heated to form a gas-liquid two-phase flow. Therefore, it is necessary to determine the dividing point between single-phase water and gas-liquid two-phase flow in the heat exchanger, that is, the net steam generation point. The result is calculated in this paper using the Saha-Juber relationship.

[0082] When Pe < 70000,

[0083]

[0084] When Pe > 70000,

[0085]

[0086] In the formula denotes the Peclet number, M denotes the mass flow rate, denotes the mass velocity, denotes the cross - sectional area of the pipe, denotes the heating power per unit area, Q denotes the heating power, t in denotes the inlet temperature.

[0087] In the two - phase natural circulation system under given structural conditions and heating power, the mass flow rate of the system is jointly determined by the driving head and the flow resistance. However, at the same time, there is a strong mutual influence between the two and the system flow rate. When and only when there is a flow rate such that the driving head is equal to the flow resistance, the three reach equilibrium. At this time, the flow rate is the mass flow rate under the steady - state condition of the system.

[0088] Figure 4 The bifurcation characteristic curve of the two - phase single - loop natural circulation system is given. When the heating power Q < Q1, the system is in single - phase natural circulation, that is, the outlet fluid is still single - phase water; when Q > Q1, the system is in two - phase natural circulation, that is, the outlet fluid is gas - liquid two - phase flow.

[0089] From Figure 4 it can be seen that when Q < Q2 or Q > Q3, there is only one equilibrium solution for the mass flow rate, and there is a one - to - one correspondence between the heating power and the mass flow rate. However, when Q2 < Q < Q3, there are three different solutions for the mass flow rate under the same heating power, that is, the system can operate at three operating points at this time. Which operating point it operates on is determined by the historical conditions of the system and the disturbance situation. Therefore, when Q2 < Q < Q3, the system undergoes a bifurcation phenomenon.

[0090] Figure 5 The bifurcation characteristic curve of the two - phase multi - loop natural circulation system is given. It can be found that the two - phase system is similar to the single - phase system and both will undergo bifurcation phenomena. Figure 6 shows that at a heating power of 30 kW, there is only one intersection point between the driving force and the resistance, corresponding to Figure 6 the situation of the driving force and the resistance in the region with only one operating point on the left. The 34 - KW system corresponds to the situation with only one operating point on the right. Both are stable operating conditions consistent with the two - phase single - loop system. The 32 - KW system corresponds to Figure 6There are three operating points in the region of driving force and resistance. This region can be stable or unstable, just like the two-phase single-loop system, which is determined by the system conditions.

[0091] S3. Screen the factors affecting the natural circulation flow and heat transfer between each loop in the multi-loop natural circulation flow system model, establish a multi-loop pressure drop-flow equation system with strong flow-heat transfer coupling, and obtain the parameter response curve of the two-phase multi-loop natural circulation flow system;

[0092] Figure 7 、 Figure 8 They respectively represent the influence of the bifurcation characteristic curve of the two-phase multi-circuit natural circulation system when the three-circuit cold source temperature and the three-circuit pressure are different; Figure 7 It can be seen from the figure that when the temperature of the three-circuit cold source increases, the area where the bifurcation phenomenon occurs becomes smaller, which is more conducive to system stability. This is because when the temperature of the three-circuit cold source increases, the temperature at the second circuit inlet will also increase accordingly, that is, the underheating at the second circuit inlet will decrease. When other system conditions remain unchanged, the fluid only needs to absorb less heat to reach the two-phase state, resulting in a decrease in the power of flow drift, thereby increasing the stable area.

[0093] from Figure 8 It can also be seen that the change of the third-circuit pressure has little effect on the second-circuit bifurcation characteristic curve, but a certain trend can still be seen from the figure, that is, the reduction of the third-circuit pressure can slightly reduce the unstable area, thereby improving the stability of the system. This is because the increase of the third-circuit pressure will lead to an increase in the heat transfer coefficient of the third circuit, which will reduce the inlet temperature of the second circuit. From the above, it can be seen that the lower the inlet temperature of the second circuit, the more unstable the system.

[0094] Figure 9 、 Figure 10 The influence of the change of the secondary circuit inlet resistance coefficient and outlet resistance coefficient on the bifurcation characteristic curve of the secondary circuit system is shown; Figure 9 、 Figure 10 It can be seen that the increase of the resistance coefficient at the secondary circuit inlet is conducive to system stability, while the increase of the resistance coefficient at the secondary circuit outlet is not conducive to system stability.

[0095] The reason is that the fluid at the secondary circuit inlet is single-phase water. Increasing the secondary circuit inlet resistance coefficient is equivalent to increasing the single-phase resistance coefficient, which increases the resistance of the single-phase part, while the resistance of the two-phase part remains unchanged. In general, it reduces the influence of the two-phase area. Figure 11 The performance is that the second half of the resistance curve is "raised", while the first half remains unchanged, which makes the curvature of the resistance curve smaller, resulting in a decrease in the probability of the resistance curve and the driving force curve having three intersections, thereby improving the stability of the system.

[0096] Increasing the resistance coefficient at the secondary circuit outlet will increase the resistance of the two-phase region at the same flow rate, while the single-phase region remains almost unchanged, which will increase the influence of the two-phase region. Figure 12 The performance is that the resistance curve rises as a whole, but finally converges to the same point, which causes the curvature of the resistance curve to become larger. The resistance curve is more likely to have three intersections with the driving force curve, which increases the instability of the system.

[0097] Figure 13 This figure shows the effect of changes in the secondary circuit pressure on the bifurcation characteristic curve of a two-phase multi-circuit natural circulation system. As can be seen from the figure, higher secondary circuit pressure reduces the unstable region and improves system stability. This is because as the system pressure increases, the difference in the gas-liquid density of steam and water decreases, reducing the influence of the two-phase region on the resistance curve in the driving force-relationship diagram, thereby increasing system stability.

[0098] S4. Analyze the influence characteristics of system parameters through bifurcation characteristic curves and parameter response curves.

[0099] By changing the temperature of the cold source of the three circuits and calculating the phase change of the second circuit and supercooling number Derive N sub and N pch is the flow instability boundary diagram of the horizontal and vertical axes, such as Figure 14 As shown. The square data is approximated from left to right Figure 6 The data obtained from the unstable region in Figure 6 The point f in the figure is obtained from right to left. Figure 6 Point c in .

[0100] The area between the circular data and the square data in the figure is the unstable area of ​​the system. When the steady-state operating point of the system is in this area, the system is unstable and will change to other steady-state operating points after being disturbed.

[0101] Can be obtained from Figure 14 It can be seen from the figure that with the increase of the temperature of the cold source of the three circuits, the unstable area of ​​the system gradually decreases. When the temperature of the cold source increases to a certain level, the unstable area of ​​the system is completely eliminated.

[0102] Conclusion: The present invention aims at a two-phase multi-circuit natural circulation system under marine conditions. It calculates the steady-state flow rate under different heating powers through a self-programming program, gives the bifurcation characteristic curve of the two-phase natural circulation system, and analyzes its cause. It also draws the parameter response curve of the system by changing the system parameters, and analyzes whether the system parameters are conducive to system stability. Finally, the calculation results show that increasing the temperature of the three-circuit cold source, reducing the three-circuit pressure, increasing the two-circuit pressure, and reducing the two-circuit local resistance coefficient are beneficial to the stability of the two-phase multi-circuit natural circulation system.

[0103] This specific embodiment is merely an explanation of the present invention and is not intended to limit the present invention. After reading this specification, those skilled in the art may make non-creative modifications to this embodiment as needed. However, as long as such modifications are within the scope of the claims of the present invention, they are protected by patent law.

Claims

1. A method for analyzing flow instability models in a multi-loop natural circulation system, characterized by: The following steps are involved: S1. Extract and establish a multi-loop natural circulation flow system model based on marine nuclear power design; S2. Based on the multi-loop natural circulation flow system model, a self-programming program is used to perform natural circulation calculations to obtain a bifurcation characteristic curve of a two-phase multi-loop natural circulation flow system; S3. Screen the factors affecting the natural circulation flow and heat transfer between each loop in the multi-loop natural circulation flow system model, establish a multi-loop pressure drop-flow equation system with strong flow-heat transfer coupling, and obtain the parameter response curve of the two-phase multi-loop natural circulation flow system; S4. Analyze the influence characteristics of system parameters through bifurcation characteristic curves and parameter response curves; The self-programming program in step S2 is compiled based on the C++ language to complete the calculation program, and the natural circulation calculation is performed by selecting a suitable thermal hydraulic model and numerical calculation algorithm; The thermal hydraulic model includes a natural circulation model, a flow resistance model, a heat exchange model and a net steam generation point model; In the natural circulation model, the system model is divided into several sections according to the different heating conditions of the fluid in the system model, and the various pressure drops in the sections are calculated respectively. Then, the various pressure drops in the sections of the same circuit are added together to obtain the total pressure drop of the same circuit; The flow resistance model uses artificial assumptions to determine the local pressure loss. By presetting constants, the impact analysis of changes in local resistance coefficients is then performed to offset the impact of local resistance caused by the local structure of the pipeline on the flow of the fluid. The heat transfer model includes calculations of convective heat transfer between the one-way liquid and the tube wall, steam condensation heat transfer, and liquid boiling heat transfer; In the net steam generation point model, the liquid in the secondary circuit is heated to a gas-liquid two-phase flow, and the Saha-Juber relationship is used to determine the dividing point between single-phase water and gas-liquid two-phase flow in the heat exchanger. The system model is a simple three-circuit coupled system, in which one circuit consists of an electric heater, a voltage stabilizer, a shell-and-tube heat exchanger, a ball valve, a canned motor pump, and a pipeline. The fluid in the three circuits is heated by the electric heater and then flows into the heat exchanger through the ascending section, transferring the heat to the next circuit. After being cooled, it returns to the electric heater through the descending section to form a cycle. After the initial cycle established by the canned motor pump is established, the canned motor pump is turned off and the fluid will be driven by natural circulation. The inlet and outlet fluids of the first circuit are both single-phase water, the inlet fluids of the second and third circuits are single-phase water, and the outlet fluids are gas-liquid two-phase flows.

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