A high-precision numerical simulation method applied to lead-based reactor vessel closure head seal gasket (sgtr) accident analysis

Abstract

The application discloses a high-precision numerical simulation method applied to lead-based reactor SGTR accident analysis, utilizes the advantage that an integrated severe accident analysis program is accurate in simulating pipeline-related problems, models the pipeline part of the system, for the region where complex interactions occur during the accident, a core disassembly analysis program which can accurately analyze phase change and multi-fluid interaction problems is used for modeling, and the two programs are coupled through a coupling component, so that precise analysis capability for the lead-based reactor SGTR accident is realized. The application can fully utilize the respective advantages of the integrated severe accident analysis program and the core disassembly analysis program, can fully reflect the geometric characteristics of the modeling object, and can finely model the region, so that the precision of the lead-based reactor SGTR accident simulation is improved.

Description

Technical Field

[0001] This invention belongs to the field of nuclear reactor thermal-hydraulic technology, specifically relating to a high-precision numerical simulation method for SGTR accident analysis of lead-based reactors. Background Technology

[0002] A steam generator heat transfer tube rupture (SGTR) accident is a typical lead-based reactor accident. In the steam generator, because liquid lead and water are separated by only one wall, and there is a significant pressure and temperature difference between them, the large mechanical and thermal stresses can easily lead to vibration and corrosion effects during operation. Therefore, the heat transfer tubes in the primary loop of the steam generator are at risk of accidents. When an SGTR accident occurs in a lead-based reactor, high-pressure water from the secondary side is injected into the primary side, causing direct contact between the high-pressure water and the low-pressure, high-temperature heavy metal coolant. The water will evaporate rapidly, accompanied by the generation of pressure waves, which can potentially threaten reactor safety. Several phenomena in an SGTR accident can adversely affect the reactor: First, the interaction between coolants can cause steam to migrate to the core, leading to positive reactivity. Second, the generation of pressure waves can affect the structural integrity of the pressure vessel. Third, the mechanical collisions caused by the heavy metal liquid can cause sloshing of the liquid lead / lead-bismuth pool. Therefore, the analysis of SGTR accidents should be emphasized in the design and safety analysis of lead-based reactors. Accurately simulating the complex accident processes and phenomena of SGTR in lead-based reactors, and thus making a correct overall safety assessment, has always been a challenging research area. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a numerical simulation method for lead-based reactor SGTR accidents that comprehensively utilizes the advantages of an integrated severe accident analysis program and a core disintegration analysis program and couples them together for calculation. This method can fully utilize the advantages of the integrated severe accident analysis program and the core disintegration analysis program, while taking into account the analysis of complex phenomena of multiphase and multicomponent and pipeline flow behavior, so as to perform more accurate modeling and calculation for lead-based reactor SGTR accidents and improve the accuracy of such accident analysis.

[0004] The present invention adopts the following technical solution:

[0005] A high-precision numerical simulation method for SGTR accident analysis in lead-based reactors is proposed. The method divides the accident area into a piping region and a region with complex interactions (generally near the steam generator rupture or even the core). An integrated severe accident analysis program is used to model the piping region, establishing governing equations for the modeled control volume and solving them using a semi-implicit method. Simultaneously, a core disintegration analysis program is used to model the region with complex interactions. This program divides the material composition, establishes conservation equations for the divided components, and solves these equations using a four-step method. A coupling component is used to transfer data between the two methods, thus completing the modeling and analysis of the SGTR accident.

[0006] First, the piping portion of the system is modeled using an integrated severe accident analysis program. This program models the piping by dividing it into control volumes and connecting them with flow channels. Two control volumes are connected by flow channels, where fluid residence time is not considered, and mass or energy is ignored in all flow channels; that is, the fluid's mass and energy are stored within the control volumes. Within each control volume, "liquid" and "gas" components are distinguished, representing the liquid and gas phases respectively. A two-fluid model is used, applying the laws of conservation of mass, momentum, and energy to both the gas and liquid phases. The mass conservation ordinary differential equation for component m in control volume i can be expressed as follows:

[0007]

[0008] Where: M i,m —Total mass of component m in control volume i / kg, where the subscript m represents water, droplets, or various gaseous components; j —towards the flow control volume; σ ij ——Flow direction, —Going to the control body j The proportion of the phase, The gas or liquid phase in the flow channel, t—time / s. —Density of component m in the outgoing flow control volume j and the incoming flow control volume d / kg·m -3 d represents the flow control body. —In the flow control body j Phase velocity / m·s, A j —Flow area of ​​flow control volume j / m 2 F j —The flow area opening of the flow control volume j. —Non-flowing mass source term of component m in control volume i / kg·s -1 ;

[0009] The energy conservation ordinary differential equation for each phase can be expressed as:

[0010]

[0011] In the formula: —In control body i Total internal energy of phase / J; Enthalpy / J·kg -1 ; —In control body i Non-flowing energy source term of phase / J·s -1 The above equation neglects the gravitational potential energy and volume-average kinetic energy terms of the fluid.

[0012] Neglecting the time derivatives of the gas and liquid phase fractions, the momentum conservation ordinary differential equation for each phase is expressed as follows:

[0013]

[0014] In the formula: L j —Inertial length of the flow channel / m, g —Acceleration due to gravity / m·s -2 ΔP j — Pump head / Pa, K * —Form resistance and wall friction coefficient, f 2,j — Interphase momentum exchange coefficient, L 2,j —Effective length of interphase force action / m —The change in velocity after passing through the flow channel, --for The other phase, density Take the density of the fluid control volume. The terms on the right side of the above equation are the effects of pressure difference, gravity, pump, friction, interphase force, and convection, respectively.

[0015] Furthermore, the integrated severe accident analysis program will employ a semi-implicit method to discretize and solve the control equations. Within each time step, the mass of component m in control volume i at the end of the time step is equal to the sum of the mass of the control volume at the previous time step, the mass of the inflow and outflow control volumes within time Δt, and the mass of the source term. After applying the linear prediction assumption, the unknown terms of the discretized momentum conservation equation are separated, yielding:

[0016]

[0017] In the above formula, k1, k2, and k3 are all known values ​​at the current time. This indicates the pressure within control body i at the previous time step. This indicates the pressure within control body k at the previous time step. Indicates the velocity of the gas at the new time step. The equation representing the velocity of the liquid at the new time step serves as an iterative equation for solving the velocity. Under assumed pressure and cavitation fraction state parameters, it can solve for the velocities of the liquid and gas by simultaneously solving all control volumes. Based on the velocity at the new time step, the mass and energy increments of the gas and liquid within each control volume can be calculated. Then, based on the state equation, the pressure, temperature, and cavitation fraction state parameters within each control volume are calculated. Finally, the difference between the predicted value and the iterative value is determined. The above process is repeated until the predicted value matches the iteratively calculated state parameters, at which point the entire iteration ends, and the solution is completed.

[0018] Furthermore, the core disintegration analysis program is used to model the region where complex interactions occur. The method for modeling the region where complex interactions occur using the core disintegration analysis program is as follows: the modeled region includes the area near the steam generator rupture and the core part. The above region is modeled by dividing the grid. Since the core disintegration analysis program uses the RZ cylindrical coordinate system for modeling, the heat transfer tube that needs to be considered as the center of rotational symmetry in the cylindrical coordinate system is used to model each component outward. That is, the heat transfer tube part is modeled as a cylinder, and the other parts are modeled as an equivalent ring according to the principle of equal radial effective area.

[0019] The core disintegration analysis program divides the material components as follows: Based on the different densities and temperatures, the different materials are divided into density components and energy components. Based on the different flow behaviors, the fluid is divided into a gas velocity field and two liquid velocity fields. During modeling, the material components need to be distributed in the corresponding positions of the modeling area according to the initial conditions.

[0020] The core disintegration analysis program will establish mass, energy, and momentum conservation equations based on the divided density components, energy components, and velocity fields, respectively, in the following forms:

[0021]

[0022]

[0023]

[0024] The terms in the conservation equations are local means within the required computational grid, where the subscripts m, q, and M represent the density, velocity, and energy components, respectively, and t is time. and Γ m Γ M These are macroscopic density and the mass transfer rate per unit volume originating from the density component m and the energy component M, respectively. It is the velocity field vector q, and p represents pressure. It is the acceleration due to gravity, K. qs K is the momentum exchange function between the velocity field q and the structural components. q′qVM is the momentum exchange function between the velocity fields q and q′. q It is the virtual mass term of the gas phase, H(x) is the step function, and Γ is the dummy mass term of the gas phase. qq′ It is the quality transfer rate between q and q′, e M and α M Q is the specific internal energy and volume fraction of component M. N Q M Q H These are the nuclear heat release rate, the energy exchange rate caused by mass, and the energy transfer rate caused by heat transport, respectively. This represents the term that exists between the gas and average liquid velocity interfaces.

[0025] Furthermore, the core disintegration analysis program is based on the time decomposition method and uses a four-step solution approach, employing high-order spatial difference to reduce numerical diffusion. The four-step solution process is as follows:

[0026] The first step is to solve the mass, momentum and energy conservation equations within each cell defined during modeling. The transport term within the grid is obtained by ignoring the convection term. The transport term within the grid and the convection term between the grids are treated separately. At the same time, the nuclear heating term of all fluid and fuel components is updated.

[0027] The second step is used to solve the fluid convection term. When solving, the source term in the conservation equation is ignored. Then, the conservation equation is integrated. First, the values ​​of each variable at the end of the time step are estimated using the high-order spatial difference method or the first-order donor element grid difference method. Then, the mass and energy are updated, and the derivatives of the state equation and velocity are calculated. For the convection term of the momentum conservation equation, the finite difference method is used.

[0028] The third step is the pressure iteration process, which uses the multivariate Newton-Simpson method to maintain the synchronization of velocity and pressure at the end of the time step. The matrix solution methods used in the pressure iteration are the direct inversion method and the incomplete LU decomposition double conjugate gradient method. The incomplete LU decomposition double conjugate gradient method is more suitable for handling complex problems, especially when the number of grids is greater than 1000. In one-dimensional calculations, Gaussian elimination is used. The residuals in the pressure iteration are derived from the estimates in the second step. The residuals include: the total liquid density, the density of steel, the density of lead and bismuth and the density of control particles, the total density of mixed steam, the steam temperature, and the difference between the grid pressure calculated using the equation of state. By defining the equation of state as a function of the grid pressure, the internal equation of state iteration is eliminated. The above six residuals are expanded to a first-order Taylor series, and the relationship between the six residuals and pressure is obtained using the derivative of the equation of state and the velocity derivative obtained in the second step.

[0029] The fourth step is to maintain the synchronization of the mass, momentum, and energy of the convection term based on the semi-implicit algorithm, while using explicit and first-order donor methods to update the variables of the interface area convection term.

[0030] Furthermore, the method for transferring data between the integrated severe accident analysis program and the core disintegration analysis program using coupling components is as follows: three synchronization events are used to achieve time step exchange, rollback, and data exchange. The three synchronization events are implemented as follows: The first synchronization involves reading the initial time steps of the integrated severe accident analysis program and the core disintegration analysis program, exchanging their information, selecting the smaller value of the two program time steps, and using this value as the common time step length for calculation. The second synchronization involves halving the time step values ​​determined in the first step when the calculated time steps of the two programs are inconsistent, using this value as the new time step length for both programs, and returning to the first step to recalculate. This step is repeated until the calculated time steps of the two programs are consistent. The third synchronization involves exchanging data with each other. During the data exchange, the two programs first write the data to be transferred into shared memory and then send a write completion signal. After both programs receive the write completion signal from the other, they begin to read the required data from the other's shared memory and send a data read completion signal. After both programs receive the data read completion signal from the other, they return to the initial calculation process.

[0031] Compared with the prior art, the present invention has at least the following beneficial effects:

[0032] This invention provides a high-precision numerical simulation method for SGTR accident analysis in lead-based reactors. It combines the advantages of an integrated severe accident analysis program and a core disintegration analysis program. For the SGTR accident in lead-based reactors, the accident area is divided into a pipe region and a region with complex interactions. The integrated severe accident analysis program and the core disintegration analysis program are used for modeling respectively, and a coupling component is used to achieve data interaction between the programs. This largely ensures the integrity of the modeling region, significantly improves the modeling refinement, and ensures the accuracy of the calculation results.

[0033] Furthermore, using an integrated severe accident analysis program, the pipeline is modeled by connecting the control volume and the flow channel, and mass, energy, and momentum conservation equations are established for the gas and liquid phases within the control volume, respectively, to ensure accurate modeling and calculation of the pipeline portion in SGTR accident analysis.

[0034] Furthermore, the core disintegration analysis program is used to model the region where complex interactions occur. Based on the density composition, energy composition and velocity field, the mass, energy and momentum conservation equations are established and solved using the four-step method to ensure a detailed analysis of the accident zone.

[0035] Furthermore, by using a coupling component, data exchange between the integrated severe accident analysis program and the core disintegration analysis program is achieved through three synchronous events. Finally, the modeling and analysis of the lead-based reactor SGTR accident is completed, ensuring the correctness of data exchange and thus obtaining more accurate calculation results.

[0036] In summary, this invention fully leverages the advantages of the integrated severe accident analysis program and core disintegration analysis program, ensuring the integrity of the SGTR accident modeling region for lead-based reactors. It utilizes coupling components to achieve accurate data exchange between programs, and can yield precise calculation results for pipe flow problems and complex multiphase / multifluid interactions involved in accidents. The accuracy of the calculation results is guaranteed.

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0038] Figure 1a and Figure 1b These are longitudinal and transverse cross-sectional views of the ALFERD reactor;

[0039] Figure 2 Schematic diagram of SGTR accident modeling for the ALFERD reactor;

[0040] Figure 3 This is a schematic diagram of the internal control unit in an integrated critical incident analysis program.

[0041] Figure 4 A schematic diagram of the flow path in an integrated severe accident analysis program;

[0042] Figure 5 The solution process for the integrated severe accident analysis program;

[0043] Figure 6 The calculation process is a four-step method;

[0044] Figure 7 Diagram of parallel coupling mode for MpCCI;

[0045] Figure 8 This is a schematic diagram of the synchronization principle for coupled signals.

[0046] Figure 9 This is a flowchart of the module-coupled computation process;

[0047] Figure 10 This is a graph showing the pressure changes in the steam generator when seven heat transfer tubes ruptured during the SGTR accident at the ALFERD reactor. Detailed Implementation

[0048] This invention discloses a high-precision numerical simulation method for analyzing lead-based reactor SGTR accidents. Taking the modeling and calculation analysis of the SGTR accident in the ALFERD reactor as an example, the analysis steps for lead-based reactor SGTR accidents in this invention are explained below:

[0049] ALFRED is a 300 MWth (~120 MWe) monolithic pool-type lead-cooled fast reactor. All major components are contained within the reactor vessel, and the flow of liquid lead within the reactor is as follows: Figure 1a and Figure 1b As shown, the flow path of lead is indicated by arrows. When an SGTR accident occurs, water at approximately 180 bar and a temperature below 7 K saturation interacts with low-pressure, high-temperature molten lead. This calculation simulates the extreme condition of simultaneous rupture of seven heat transfer tubes to study the changes in pressure and other parameters within the steam generator after an SGTR accident.

[0050] First, the pipeline section is modeled using an integrated critical accident analysis program, such as... Figure 2 As shown in the left half, a single heat transfer tube is modeled, with control volumes PIPE121 to PIPE128 serving as the flow channels for liquid lead. PIPE129 and PIPE120 are set as time-dependent control volumes as boundary conditions to control the flow of liquid lead. Control volumes PIPE101 to PIPE110 serve as the water channel, where liquid water absorbs heat and gradually vaporizes. A thermal structure is added between the two channels to simulate the heat exchange between liquid lead and water.

[0051] A schematic diagram of the control body is shown below. Figure 3 As shown, the schematic diagram of the flow channel is as follows: Figure 4 As shown, the two control volumes are connected by flow channels. The residence time of the fluid in these channels is not considered, and mass or energy is ignored in all channels; that is, the mass and energy of the fluid are stored within the control volumes. The control volumes are divided into "liquid" and "gas" components, representing the liquid and gas phases respectively. A two-fluid model is used, applying the laws of conservation of mass, momentum, and energy to the gas and liquid phases respectively. The mass conservation ordinary differential equation for component m in control volume i can be expressed as follows:

[0052]

[0053] Where: M i,m —Total mass of component m in control volume i / kg, where the subscript m represents water, droplets, or various gaseous components; j —towards the flow control volume; σ ij ——Flow direction, —Going to the control body j The proportion of the phase, The gas or liquid phase in the flow channel, t—time / s. —Density of component m in the outgoing flow control volume j and the incoming flow control volume d / kg·m -3 d represents the flow control body. —In the flow control body j Phase velocity / m·s, A j —Flow area of ​​flow control volume j / m 2 F j —The flow area opening of the flow control volume j. —Non-flowing mass source term of component m in control volume i / kg·s -1 The energy conservation ordinary differential equation for each phase can be expressed as:

[0054]

[0055] In the formula: —In control body i Total internal energy of phase / J; Enthalpy / J·kg -1 ; —In control body i Non-flowing energy source term of phase / J·s -1 The above equation neglects the gravitational potential energy and volume-average kinetic energy terms of the fluid.

[0056] Neglecting the time derivatives of the gas and liquid phase fractions, the momentum conservation ordinary differential equation for each phase is expressed as follows:

[0057]

[0058] In the formula: L j —Inertial length of the flow channel / m, g —Acceleration due to gravity / m·s -2 ΔP j — Pump head / Pa, K * —Form resistance and wall friction coefficient, f 2,j — Interphase momentum exchange coefficient, L 2,j —Effective length of interphase force action / m —The change in velocity after passing through the flow channel, --for The other phase, density Take the density of the fluid control volume. The terms on the right side of the above equation are the effects of pressure difference, gravity, pump, friction, interphase force, and convection, respectively.

[0059] The integrated severe accident analysis program employs a semi-implicit method to discretize and solve the control equations. At each time step, the mass of component m in control volume i at the end of the time step is equal to the sum of the mass of the control volume at the previous time step, the mass of the inflow and outflow control volumes within time Δt, and the mass of the source term. After applying the linear prediction assumption, the unknown terms of the discretized momentum conservation equation are separated, yielding:

[0060]

[0061] In the above formula, k1, k2, and k3 are all known values ​​at the current time. This indicates the pressure within control body i at the previous time step. This indicates the pressure within control body k at the previous time step. Indicates the velocity of the gas at the new time step. This represents the velocity of the liquid at the new time step. This equation, serving as an iterative equation for solving the velocity, can be solved by simultaneously solving all control volumes under assumed state parameters such as pressure and cavitation fraction. Based on the velocity at the new time step, the mass and energy increments can be calculated. Then, based on the state equation, state parameters such as pressure, temperature, and cavitation fraction are calculated. Finally, the difference between the predicted values ​​(such as pressure) and the iterative values ​​is determined. This process is repeated until the predicted values ​​match the iteratively calculated state parameters, at which point the entire iteration ends, completing the solution. The solution flow of the integrated severe accident analysis program is as follows: Figure 5 As shown.

[0062] Then, a core dismantling analysis program was used to model the area surrounding the breach in the steam generator and the core portion, such as... Figure 2 As shown in the right half, since multiphase and multicomponent modeling is based on the RZ cylindrical coordinate system, the principle of equivalent radial effective area must be followed during modeling. In this problem, the ruptured heat transfer tube is the key consideration, so it is placed at the center to restore its cylindrical geometry. Other components are modeled as rings according to the principle of equivalent area, distributed around the ruptured heat transfer tube. The reactor is divided into 28 radial grids and 50 axial grids. Figure 2 In the diagram, region 1 represents lead, region 2 represents water, region 3 represents heat transfer tubes and grid structures, region 4 represents argon, and region 5 represents the non-calculation region. The breach location is at grid 11 along the axis. Finally, to enable smooth data exchange between the two programs, a control body PIPE100 was added to the integrated severe accident analysis program to receive boundary information from the core disintegration analysis program and transmit it to the integrated severe accident analysis program.

[0063] The core disintegration analysis program divides the components into density and energy components based on differences in density and temperature, and the fluid into a gas velocity field and two liquid velocity fields based on differences in flow behavior. During modeling, the material components need to be distributed in appropriate locations according to initial conditions. The program will then establish mass, energy, and momentum conservation equations based on the divided density, energy, and velocity fields, in the following forms:

[0064]

[0065]

[0066]

[0067] The terms in the conservation equations are local means within the required computational grid, where the subscripts m, q, and M represent the density, velocity, and energy components, respectively, and t is time. and Γ m Γ M These are macroscopic density and the mass transfer rate per unit volume originating from the density component m and the energy component M, respectively. It is the velocity field vector q, and p represents pressure. It is the acceleration due to gravity, K. qs K is the momentum exchange function between the velocity field q and the structural components. q′q VM is the momentum exchange function between the velocity fields q and q′. q It is the virtual mass term of the gas phase, H(x) is the step function, and Γ is the dummy mass term of the gas phase. qq′ It is the quality transfer rate between q and q′, e M and α M Q is the specific internal energy and volume fraction of component M. N Q M Q H These are the nuclear heat release rate, the energy exchange rate caused by mass, and the energy transfer rate caused by heat transport, respectively. This indicates the items present at the gas-to-mean-liquid velocity interface. Specific component tables are shown in Tables 1 through 3.

[0068] Table 1 Structural components

[0069]

[0070]

[0071] Table 2 Liquid Components

[0072]

[0073] Continued from Table 2 Liquid Components

[0074]

[0075] Table 3 Gas Components

[0076]

[0077] The reactor core disintegration analysis program is based on the time decomposition method and uses a four-step solution approach, employing high-order spatial difference to reduce numerical diffusion. The four-step solution process is as follows: Figure 6 As shown. The first step is to solve the mass, momentum, and energy conservation equations within the cell, and obtain the intra-cell transport term while neglecting the convection term. Intra-cell transport and inter-cell convection are treated separately, and the nuclear heating terms of all fluid and fuel components are updated at the same time.

[0078] The second step is used to solve for the fluid convection term. During the solution process, the source term in the conservation equation is ignored, and then the conservation equation is integrated. First, the values ​​of each variable at the end of the time step are estimated using a higher-order spatial difference method or a first-order donor element grid difference method. Then, the mass and energy are updated, and the derivatives of the state equation and velocity are calculated. The convection term of the momentum conservation equation is handled using the finite difference method.

[0079] The third step is the pressure iteration process, which uses the multivariate Newton-Simpson method to maintain the synchronization of velocity and pressure at the end of the time step. The matrix solution methods used in the pressure iteration are the direct inversion method and the incomplete LU decomposition double conjugate gradient method. The incomplete LU decomposition double conjugate gradient method is more suitable for handling complex problems, especially when the number of grids is greater than 1000. In one-dimensional calculations, Gaussian elimination is used. The residuals in the pressure iteration are derived from the estimates in the second step. The residuals include: the total liquid density, the density of steel, the density of lead and bismuth and the density of control particles, the total density of mixed steam, the steam temperature, and the difference between the grid pressure calculated using the equation of state. By defining the equation of state as a function of the grid pressure, the internal equation of state iteration is eliminated. The above six residuals are expanded to a first-order Taylor series, and the relationship between the six residuals and pressure is obtained using the derivative of the equation of state and the velocity derivative obtained in the second step.

[0080] The fourth step uses a semi-implicit algorithm to maintain synchronization of the mass, momentum, and energy of the convection term, while simultaneously updating the variables of the interfacial area convection term using explicit and first-order donor methods. Table 4 summarizes the variable updates in the four-step method, where ρ... (1) ρ (2) ρ (3) and ρ (4) The densities ρ are the updated densities after steps 1, 2, 3, and 4, respectively. (n) ρ is the density at the start of the time step. (n+1) Let v be the density at the end of the time step. (1) v (2) v (3) and v (4)These represent the speeds after updates in steps 1, 2, 3, and 4, respectively, v. (n) v is the initial velocity at the start of the time step. (n+1) Let be the velocity at the end of the time step, t be time, and e be the specific internal energy.

[0081] Table 4. Four-step variable update process

[0082]

[0083]

[0084] Continued from Table 4: Four-Step Variable Update Process

[0085]

[0086] To ensure that the integrated severe accident analysis program and the core disintegration analysis program can be performed synchronously and in parallel, it is essential to guarantee strict uniformity in their time step progression and data exchange. During coupled computation, the two programs need to have the same time step and number of loop steps, and the timing of data exchange must be reasonable. To achieve these points, this invention references the program scheduling order in MpCCI, such as... Figure 7 As shown, three synchronization events are used simultaneously to achieve time step exchange, rollback time step exchange, and data exchange.

[0087] The integrated severe accident analysis program and the core disintegration analysis program are largely the same in their calculation flow, including four steps: determining the initial values ​​of system parameters, predicting or determining the time step size, performing thermal-hydraulic calculations, checking convergence, and advancing the time step. However, there are some differences in the order in which these steps are implemented between the integrated severe accident analysis program and the core disintegration analysis program. Therefore, it is necessary to determine whether the time step is consistent within the coupled program. The specific method is as follows: First, read the initial time step of both the integrated severe accident analysis program and the core disintegration analysis program, and exchange their information. This completes the first synchronization between the two programs. Next, the smaller of the two program time steps is selected and used as the unified time step for both programs. Since the solution methods in the two programs are different, there is a possibility that the time steps will be inconsistent after convergence checks. At this point, a rollback is needed, which is the second synchronization. Specifically, the time step value determined in the first step is halved, and this value is used as the new time step for both programs. The program then returns to the first step and recalculates. When the time steps of the two programs reach a consensus after calculation and convergence, the second step is considered complete, and the third synchronization begins. This involves updating the calculated state parameters of both programs and exchanging data. During this process, both programs first write the data to be transferred to shared memory and then send a write completion signal. Once both programs receive the write completion signal from the other, they begin reading the required data from the other's shared memory and send a data read completion signal. Once both programs receive the data read completion signal from the other, they return to the initial calculation flow. The diagram illustrating the signal synchronization principle between programs is shown below. Figure 8 As shown. This completes the three synchronization events in the calculation of one time step. The calculation flowchart is as follows. Figure 9 As shown.

[0088] As mentioned earlier, this paper applies the technical solution of the present invention to model and calculate the SGTR accident of the ALFERD reactor. The pressure change curve at the breach location is presented here, as shown in the figure. Figure 10 As shown in the graph, the pressure change trend of the calculated results is consistent with that of the reference program. However, because the technical solution of this invention can model the entire steam generator, while the reference program only models a portion of the steam generator, the decreasing trend of the pressure calculated by applying this invention is slower. This also reflects that the technical solution of this invention can completely model the entire problem area, fully leveraging the advantages of both programs and avoiding their shortcomings.

[0089] In summary, the method established in this invention combines the advantages of an integrated severe accident analysis program and a core disintegration analysis program. For the lead-based reactor SGTR accident, the accident area is divided into a pipe region and a region with complex interactions. The integrated severe accident analysis program, adept at calculating flow problems within pipes, is used to model and calculate the pipe region, while the core disintegration analysis program, adept at calculating complex interactions involving multiple phases and fluids, is used to model and calculate the region with complex interactions. This largely ensures the completeness of the modeling of the accident area and significantly improves the modeling refinement. Furthermore, the use of coupling components enables accurate data transfer between the two programs, ensuring the accuracy of the calculation results.

Claims

1. A high-precision numerical simulation method for SGTR accident analysis of lead-based reactors, characterized in that, The area where a SGTR accident occurs in a lead-based reactor is divided into the piping region and the region of complex interaction, namely the area near the steam generator rupture and the core. An integrated severe accident analysis program is used to model the piping region. The integrated severe accident analysis program establishes control equations for the modeled control volume and solves the control equations discretly. At the same time, a core disintegration analysis program is used to model the region of complex interaction. The core disintegration analysis program divides the material composition, establishes conservation equations, and solves the conservation equations. A coupling component is used to realize the data transfer between the integrated severe accident analysis program and the core disintegration analysis program, thus completing the modeling and analysis of the SGTR accident. The method for transferring data between the integrated severe accident analysis program and the core disintegration analysis program using coupling components is as follows: Three synchronization events are used to achieve time step exchange, rollback, and data exchange. The three synchronization events are implemented as follows: The first synchronization involves reading the initial time steps of both the integrated severe accident analysis program and the core disintegration analysis program, exchanging their information, selecting the smaller value of the two program time steps, and using this value as the common time step length for calculation. The second synchronization occurs when the calculated time steps of the two programs are inconsistent. The initially determined time step values ​​are halved, and this value is used as the new time step for both programs. The program then returns to the first step to recalculate, repeating this process until the calculated time steps of the two programs are consistent. The third synchronization involves data exchange. During data exchange, both programs first write the data to be transferred to shared memory and then send a write completion signal. Once both programs receive the write completion signal from the other, they begin reading the required data from the other's shared memory and send a data read completion signal. Once both programs receive the data read completion signal from the other, they return to the initial calculation process.

2. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The method for modeling a pipeline region using an integrated critical accident analysis program is as follows: when modeling and calculating a pipeline using an integrated critical accident analysis program, the pipeline is simulated by connecting the control volume and the flow channel.

3. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The integrated severe accident analysis program establishes control equations for the modeled control volume as follows: The control volume is divided into liquid and gaseous components, representing the liquid and gaseous phases respectively. A two-fluid model is used, and control equations are established for the gaseous and liquid phases respectively using the laws of conservation of mass, momentum, and energy. The control volume... i Middle components The mass conservation ordinary differential equation is expressed by the following equation: In the formula: — Control System i medium density components m Total mass / kg, subscript m Representing the density components of water, droplets, or various gases. —De-flow control body, — Flow direction, —To the Control Entity j In The proportion of the phase, The gas or liquid phase in the flow channel — Time / s — De-flow control system j and incoming flow control body d medium density components m Density / kg·m -3 , Represents the flow control system. ——De-flow control system j middle Phase velocity / m·s ——De-flow control system j Flow area / m 2 , ——De-flow control system j The flow area opening, ——Control body i medium density components m Non-flowing mass source term / kg·s -1 ; The energy conservation ordinary differential equation for each phase is expressed by the following equation: In the formula: ——Control body i middle Total internal energy of phase / J; —— Enthalpy / J·kg -1 ; ——Control body i middle Non-flow energy source term of phase / J·s -1 The above equation neglects the gravitational potential energy and volume-average kinetic energy terms of the fluid. Neglecting the time derivatives of the gas and liquid phase fractions, the momentum conservation ordinary differential equation for each phase is expressed as follows: In the formula: ρ is density, — Flow channel inertial length / m — Gravitational acceleration / m·s -2 , — Pump head / Pa, — Form resistance and wall friction coefficient, — Interphase momentum exchange coefficient, — Effective length of interphase force action / m — The change in velocity after passing through the flow channel, — For The other phase, density Taking the density of the fluid control volume, the terms on the right side of the above equation are the effects of pressure difference, gravity, pump, friction, interphase force, and convection, respectively.

4. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The integrated severe accident analysis program uses a semi-implicit method to discretize and solve the control equations. Within each time step, the control volume at the end of the time step... i Middle components m The mass is equal to the mass of the control body at the previous moment. The sum of the inflow and outflow control volume mass and the source term mass within a given time interval, after applying the linear prediction assumption, allows us to separate the unknown terms of the discretized momentum conservation equation, resulting in: In the above formula k 1, k 2, k 3 are all known values ​​at the current moment. Indicates the previous time step control body i Internal pressure, Indicates the previous time step control body k Internal pressure, Indicates the velocity of the gas at the new time step. The equation representing the velocity of the liquid at the new time step serves as an iterative equation for solving the velocity. Under assumed pressure and cavitation fraction state parameters, it can solve for the velocities of the liquid and gas by simultaneously solving all control volumes. Based on the velocity at the new time step, the mass and energy increments of the gas and liquid within each control volume can be calculated. Then, based on the state equation, the pressure, temperature, and cavitation fraction state parameters within each control volume are calculated. Finally, the difference between the predicted value and the iterative value is determined. The above process is repeated until the predicted value matches the iteratively calculated state parameters, at which point the entire iteration ends, and the solution is completed.

5. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The core disintegration analysis program models regions with complex interactions as follows: the modeling region includes the vicinity of the steam generator rupture and the core portion. The above regions are modeled by dividing them into meshes. Since the core disintegration analysis program uses the RZ cylindrical coordinate system for modeling, the heat transfer tubes that need to be considered as the center of rotational symmetry in the cylindrical coordinate system are used as the modeling point for each component. That is, the heat transfer tube part is modeled as a cylinder, and the other parts are modeled as an equivalent ring according to the principle of equal radial effective area.

6. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The core disintegration analysis program divides the material components as follows: Based on the different densities and temperatures, the different materials are divided into density components and energy components. Based on the different flow behaviors, the fluid is divided into a gas velocity field and two liquid velocity fields. During modeling, the material components need to be distributed in the corresponding positions of the modeling area according to the initial conditions.

7. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The method for establishing conservation equations in the core disintegration analysis program is as follows: The core disintegration analysis program will establish mass, energy, and momentum conservation equations based on the divided density components, energy components, and velocity fields, respectively, in the following form: The terms in the conservation equations are the local means within the grid to be computed. t It is time. , and , These are macroscopic density and density-derived components, respectively. m With energy components M The mass transfer rate per unit volume, It is a velocity field velocity field vector, Represents pressure, It is gravitational acceleration. It is a velocity field The momentum exchange function between structural components. It is a velocity field and The momentum exchange function between them It is a virtual mass term in the gas phase. It is a step function. yes and The quality of transmission rate between them and It is an energy component Specific internal energy and volume fraction, These are the nuclear heat release rate, the energy exchange rate caused by mass, and the energy transfer rate caused by heat transport, respectively. This represents the term that exists between the gas and average liquid velocity interfaces.

8. The high-precision numerical simulation method for SGTR accident analysis of lead-based reactors according to claim 1, characterized in that, The core dismantling analysis program solves the conservation equations using a time decomposition method, employing a four-step solution process. The four-step solution flow is as follows: The first step is to solve the mass, momentum and energy conservation equations within each cell defined during modeling. The transport term within the grid is obtained by ignoring the convection term. The transport term within the grid and the convection term between the grids are treated separately. At the same time, the nuclear heating term of all fluid and fuel components is updated. The second step is used to solve the fluid convection term. When solving, the source term in the conservation equation is ignored. Then, the conservation equation is integrated. First, the values ​​of each variable at the end of the time step are estimated using the high-order spatial difference method or the first-order donor element grid difference method. Then, the mass and energy are updated, and the derivatives of the state equation and velocity are calculated. For the convection term of the momentum conservation equation, the finite difference method is used. The third step is the pressure iteration process, which uses the multivariate Newton-Simpson method to maintain the synchronization of velocity and pressure at the end of the time step. The matrix solution methods used in the pressure iteration are the direct inversion method and the incomplete LU decomposition double conjugate gradient method. The incomplete LU decomposition double conjugate gradient method is more suitable for handling complex problems, especially when the number of grids is greater than 1000. In one-dimensional calculations, Gaussian elimination is used. The residuals in the pressure iteration are derived from the estimates in the second step. The residuals include: the total liquid density, the density of steel, the density of lead and bismuth and the density of control particles, the total density of mixed steam, the steam temperature, and the difference between the grid pressure calculated using the equation of state. By defining the equation of state as a function of the grid pressure, the internal equation of state iteration is eliminated. The above six residuals are expanded to a first-order Taylor series, and the relationship between the six residuals and pressure is obtained using the derivative of the equation of state and the velocity derivative obtained in the second step. The fourth step is to maintain the synchronization of the mass, momentum, and energy of the convection term based on the semi-implicit algorithm, while using explicit and first-order donor methods to update the variables of the interface area convection term.

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