Pressurized water reactor fuel rod bundle transient nuclear thermal coupling calculation method under two-phase flow condition

Abstract

The invention discloses a pressurized water reactor fuel rod bundle transient nuclear thermal coupling calculation method under a two-phase flow condition. A solid domain model and a fluid domain model are established, and grids are divided; generating a few-group cross section library based on a Monte Carlo program, and parameterizing the cross section into a temperature and density function by using Python interpolation; and a grid is imported into the CFD solving platform, and a two-phase flow thermal hydraulic model is selected. A neutron diffusion equation is discretely solved by adopting a user-defined scalar equation interface, source item, diffusion item and transient item coefficients and neutron physical boundary conditions are defined by utilizing a user-defined function interface, section parameters are updated in real time according to local temperature and density, and meanwhile, a power heat source is calculated according to neutron flux and fed back to thermal hydraulic calculation; and bidirectional coupling is realized. And carrying out steady-state characteristic value calculation, applying disturbance to carry out transient calculation after convergence, and outputting power, temperature, density, void fraction and neutron flux space-time distribution after a termination criterion is met for safety analysis of a nuclear reactor.

Description

Technical Field

[0001] This invention belongs to the field of pressurized water reactor fuel rod bundle and nuclear thermal coupling technology, specifically relating to a transient nuclear thermal coupling calculation method for pressurized water reactor fuel rod bundle under two-phase flow conditions based on a CFD solution platform. Background Technology

[0002] Pressurized water reactors (PWRs) are currently the most widely used commercial nuclear reactor type in the world, characterized by mature technology, rich operational experience, and strong engineering adaptability. As core design evolves towards higher burnup, higher power density, and greater compactness, the thermal margin of fuel assemblies decreases under normal operation and certain transient conditions. This can lead to two-phase flow phenomena such as subcooling and boiling in localized high heat flux density regions, resulting in localized changes in flow heat transfer characteristics and void fraction and density distribution.

[0003] Within a pressurized water reactor (PWR) core, a significant two-way feedback coupling exists between neutron physics and thermal hydraulics: neutron flux affects the reactor power density distribution, thus determining the heat source term of the fuel rods, and consequently influencing fuel temperature, cladding temperature, and coolant temperature and density fields; conversely, changes in thermal hydraulic parameters such as temperature, density, and void fraction alter the neutron cross-section, which in turn affects the neutron flux distribution. If core physics and thermal hydraulic calculations are performed separately using a decoupled approach, it is often difficult to accurately reflect the true response under strong feedback conditions. Especially under conditions of localized boiling, rapid temperature and density changes, or strong transient disturbances, decoupling analysis may introduce significant errors, affecting the assessment of core safety margins and key parameters (such as peak power, peak temperature, and void fraction distribution). Therefore, it is necessary to conduct research on the nuclear-thermal coupling characteristics of PWR fuel rod bundles.

[0004] Nuclear-thermal coupling analysis methods can be broadly categorized into two types: the first type involves cross-software / cross-program coupling calculations, where core physics and thermal-hydraulic equations are solved separately, with parameter exchange and iteration achieved through external interfaces, scripts, or intermediate data files; the second type implements nuclear-thermal coupling within a unified computing platform or the same solver framework, solving the neutronics and thermal-hydraulic equations on a unified platform. Compared to cross-software coupling, unified platform coupling typically reduces errors and resource consumption caused by mesh mapping and data transfer between software programs. Shorter data transfer links and stronger coupling consistency make it more conducive to transient calculations and improve computational stability and robustness.

[0005] Current research and engineering applications show that nuclear-thermal coupling analysis of pressurized water reactor fuel rod bundles primarily relies on single-phase flow or equivalent single-phase assumptions in thermal models. For nuclear-thermal coupling problems involving two-phase flow conditions such as subcooled boiling, research and methods that can simultaneously consider two-phase thermal-hydraulic and core physics feedback within a unified platform are relatively few. Therefore, there is an urgent need for a method that can achieve stable and reliable nuclear-thermal coupling calculations under two-phase flow conditions to improve the accuracy of analysis of steady-state and transient conditions of high-power-density pressurized water reactor fuel rod bundles. Summary of the Invention

[0006] To overcome the problems of the existing technology, the present invention aims to provide a transient nuclear-thermal coupling calculation method for pressurized water reactor fuel rod bundles under two-phase flow conditions based on a CFD solution platform. Addressing the issues of two-phase flow phenomena such as supercooled boiling that may occur in pressurized water reactor fuel rod bundles at high power densities, the strong feedback coupling between temperature / density / cavitation fraction distribution and neutron physics characteristics leading to difficulties in accurately reflecting actual physical effects through decoupling analysis, and the problems of mesh mapping and data transfer errors, as well as insufficient consistency and stability in transient calculations during cross-program coupling, the present invention solves the two-phase thermal-hydraulic control equations and neutron diffusion equations simultaneously on the same mesh within a CFD solution platform. It also combines a Monte Carlo program to generate a minority section library under different operating conditions and establishes the functional relationship between the minority sections and temperature and density through Python interpolation. This enables bidirectional information exchange and steady-state / transient coupling calculation between neutron physics and thermal-hydraulic processes, thereby obtaining the spatiotemporal distribution characteristics of physical quantities such as power, temperature, density, cavitation fraction, and neutron flux, applicable to nuclear reactor safety analysis.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for transient nuclear-thermal coupling calculation of fuel rod bundles in a pressurized water reactor under two-phase flow conditions, comprising the following steps: Step 1: Establish a three-dimensional geometric model containing the fuel rod bundle and the surrounding coolant flow channels, and mesh the three-dimensional geometric model to obtain the computational mesh for subsequent coupled solution; Step 2: Establish a three-dimensional geometric model of the fuel rod bundle and its surrounding coolant channels in the Monte Carlo program, consistent with Step 1; perform Monte Carlo calculations under multiple temperature and density conditions covering the target operating range to obtain minority cross-section data under the corresponding operating conditions and form a minority cross-section database; based on the minority cross-section database, use Python interpolation methods to construct the minority cross-sections into continuous functions of temperature and density, so as to obtain the minority cross-section parameters in real time according to the local temperature and density during the nuclear thermal coupling calculation, and realize the feedback effect of thermal hydraulic parameters on neutron physical properties; Step 3: Since the CFD solution platform has a built-in thermal-hydraulic calculation model but does not include a neutron physics solution model, the neutron diffusion equation is embedded in the CFD solution platform to achieve nuclear thermal coupling analysis of the fuel rod bundle. The neutron diffusion equation is solved using the CFD solution platform's User-Defined Scalar (UDS) framework. The neutron diffusion equation is mapped to the UDS through equivalent transformations: transient terms are mapped to UDS transient terms, diffusion terms to UDS diffusion terms, and the remaining terms are treated as UDS source terms. The transient term coefficients, diffusion coefficients, and source term coefficients of the UDS are determined by the User-Defined Function (UDS) interface. The UDF is implemented and combined with the continuous function of the minority cross section with temperature and density constructed in step two, so that the neutron physics parameters can be updated in real time according to the local temperature and density during the calculation process; the transient term coefficients, diffusion coefficients, source term coefficients and boundary conditions corresponding to the UDS are defined through the UDF interface, and the UDF is loaded into the CFD solution platform to participate in the solution, so as to realize the synchronous solution of the thermal hydraulic control equation and the neutron diffusion equation on the same computing grid; Step 4: Select a thermal-hydraulic calculation model that matches the calculation conditions in the CFD solution platform; considering the high power density of the fuel rod bundle, the coolant may undergo subcooling boiling, so a two-phase flow model needs to be enabled in the thermal-hydraulic calculation model to characterize the boiling-related phase change and heat transfer processes; at the same time, enable UDS to provide a calculation framework for solving the neutron diffusion equation. Step 5: Set the material property parameters for the solid domain and fluid domain in the CFD solution platform respectively; set the thermophysical property parameters such as density, specific heat capacity, and thermal conductivity for the solid domain, and set the parameters such as density, specific heat capacity, thermal conductivity, viscosity, molar mass, and standard enthalpy for the fluid domain, and set the diffusivity parameter defined in UDF that is related to the UDS solution. Step 6: Set the computational domain boundary conditions and perform global standard initialization in the CFD solution platform, and start the steady-state nuclear thermal coupling calculation; realize the bidirectional feedback coupling of neutron physics and thermal hydraulics during the steady-state solution process, and iterate until the preset convergence criterion is met; Step 7: After the steady-state nuclear thermal coupling calculation reaches convergence, save the calculation results and perform post-processing analysis; after introducing a disturbance, start the transient nuclear thermal coupling calculation, maintain the bidirectional feedback coupling of neutron physics and thermal hydraulics during the transient solution process, and terminate the calculation and output the results after the set physical time or preset termination criterion is reached.

[0008] Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. The method of this invention solves the two-phase thermal-hydraulic control equations and the neutron diffusion equations simultaneously on the same grid within a unified platform, avoiding the errors and complexities caused by grid mapping and data transfer during cross-program coupling, facilitating steady-state and transient calculations and improving computational consistency and stability; 2. The method of this invention uses UDS of the CFD solution platform to realize the implantation of the neutron physics solution model, and uses UDF to realize the definition of source terms, diffusion terms, transient terms and boundary conditions, which facilitates bidirectional information exchange between neutron physics and thermo-hydraulics, with short coupling links and clear implementation methods; 3. The method of this invention generates a database of minority cross sections under different operating conditions based on the Monte Carlo program, and establishes the functional relationship between the minority cross sections and temperature and density through Python interpolation method. This allows the neutron physics parameters to be updated in real time based on local temperature, density and cavitation fraction during the coupled calculation process, and can consider the feedback effect of thermal parameters on neutron physics under two-phase flow conditions. 4. The method of the present invention has good versatility and can be applied to the nuclear thermal coupling calculation of fuel rod bundles with different fuel element geometries. At the same time, the method is also applicable to transient nuclear thermal coupling calculation under different perturbation forms. By introducing the corresponding transient perturbation and calculating to a preset physical time, the corresponding transient response characteristics can be obtained. Attached Figure Description

[0009] Figure 1 This is an overall flowchart of the nuclear thermal coupling calculation method of the present invention.

[0010] Figure 2 The flowchart shows the steady-state and transient nuclear thermal coupling iterative calculation process. Detailed Implementation

[0011] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments: This invention presents a transient two-way nuclear-thermal coupling calculation method for pressurized water reactor fuel rod bundles under two-phase flow conditions based on a CFD solution platform. It addresses the problems of strong two-way feedback coupling between the thermal-hydraulic and neutron physics characteristics of pressurized water reactor fuel rod bundles, which makes decoupling analysis difficult to accurately reflect actual physical effects, and the issues of mesh mapping and data transfer errors, and insufficient consistency and stability in transient calculations during cross-program coupling. This invention achieves two-way information exchange between neutron physics and thermal-hydraulic processes and steady-state and transient nuclear-thermal coupling calculations by simultaneously solving the two-phase thermal-hydraulic control equations and the neutron diffusion equations on the same mesh within the CFD solution platform, combined with a minority group cross-section library generated by a Monte Carlo program and its temperature-density parameterized function relationship. The iterative calculation process for steady-state and transient nuclear-thermal coupling is shown in the attached figure. Figure 2 As shown; the overall flowchart of the nuclear thermal coupling calculation method of this invention is attached. Figure 1 As shown.

[0012] The method includes the following steps: Step 1: Establish a three-dimensional geometric model containing the fuel rod bundle and the surrounding coolant flow channels, and mesh the three-dimensional geometric model to obtain the computational mesh for subsequent coupled solution.

[0013] Step 2: Establish a three-dimensional geometric model of the fuel rod bundle and its surrounding coolant channels in the Monte Carlo program, consistent with that in Step 1; perform Monte Carlo calculations under multiple temperature and density conditions covering the target operating range to obtain minority cross-section data under the corresponding operating conditions, forming a minority cross-section database; based on the above minority cross-section database, use a two-dimensional interpolation method implemented in Python to construct the minority cross-sections as continuous functions of temperature and density, so as to obtain the minority cross-section parameters in real time according to the local temperature and density during the nuclear thermal coupling calculation, thereby realizing the feedback effect of thermal-hydraulic parameters on neutron physics properties.

[0014] Step 3: Since the CFD solution platform has a built-in thermal-hydraulic calculation model required for nuclear-thermal coupling, but does not include a neutron physics solution model, it is necessary to embed two groups of neutron diffusion equations into the CFD solution platform to realize the nuclear-thermal coupling analysis of fuel rod bundles. The calculation method proposed in this invention uses the UDS framework of the CFD solution platform to solve the neutron diffusion equation. The equation form of UDS is consistent with the standard transport-diffusion equation, and the neutron diffusion equation can be mapped to UDS through equivalent equation transformation: the transient terms of the neutron diffusion equation are matched with the transient terms of UDS, the diffusion terms are matched with the diffusion terms of UDS, and the remaining terms are uniformly treated as source terms of UDS, thereby realizing the solution of the neutron diffusion equation in the CFD solution platform.

[0015] The transient coefficients, diffusion coefficients, and source coefficients of the UDS are specifically defined through a UDF. Combined with the continuous functions of the minority group cross section with temperature and density constructed in step two, this allows for real-time updates of neutron physics parameters based on local temperature and density during the calculation process, thereby characterizing the feedback effect of thermal-hydraulic parameters on neutron physics properties. Based on the geometric characteristics, boundary conditions, and minority group cross section function form of the research object, the transient coefficients, diffusion coefficients, source coefficients, and boundary conditions corresponding to the UDS are defined through the UDF interface. The UDF is then loaded into the CFD solution platform to participate in the solution process, enabling simultaneous solving of the thermal-hydraulic control equations and the neutron diffusion equations on the same computational grid, providing a foundation for steady-state and transient nuclear thermal coupling calculations.

[0016] Step 4: Select a thermal-hydraulic calculation model that matches the calculation conditions in the CFD solution platform. Considering the high power density of the fuel rod bundle, the coolant may undergo subcooled boiling. Therefore, a two-phase flow model needs to be enabled in the thermal-hydraulic calculation model to characterize the boiling-related phase change and heat transfer processes; at the same time, UDS should be enabled to provide a computational framework for solving the neutron diffusion equation.

[0017] Step 5: Set the material property parameters for the solid domain and fluid domain in the CFD solution platform. Solid domain material properties include thermophysical parameters such as density, specific heat capacity, and thermal conductivity, and the diffusivity parameter defined in the UDF that is relevant to the UDS solution. Fluid domain material properties include parameters such as density, specific heat capacity, thermal conductivity, viscosity, molar mass, and standard enthalpy, and the diffusivity parameter defined in the UDF that is relevant to the UDS solution.

[0018] Step Six: Set the boundary conditions of the computational domain in the CFD solution platform, perform global standard initialization of the computational domain, and then start the steady-state nuclear thermal coupling calculation. The steady-state calculation is performed at rated power. During the iteration process, the effective multiplication factor (k) is calculated based on the results of the equation solution. eff ), and calculate the power distribution of the fuel rod bundle based on the neutron flux, and input the power distribution as a heat source term into the thermal-hydraulic control equation; determine k eff The system checks whether the power distribution or other relevant field quantities meet the preset convergence criteria. If convergence fails, it uses the minority group cross-sectional function constructed in step two based on the local temperature and density to update the coefficients and source terms of the neutron diffusion equation, achieving bidirectional feedback coupling between neutron physics and thermo-hydraulic dynamics. The iterative solution continues until the preset convergence criteria are met. The specific iterative solution process is as follows: Figure 2 As shown.

[0019] Step 7: After the steady-state nuclear thermal coupling calculation converges, save the calculation results for post-processing and analysis. Introduce a perturbation to initiate transient nuclear thermal coupling calculations, i.e., solve the thermal-hydraulic and neutron physics equations. Calculate the change in total power based on the fission rate, calculate the power distribution of the fuel rod bundle based on the neutron flux and use it as a heat source term. Simultaneously, update the coefficients and source terms of the neutron diffusion equations based on the small group cross-section function constructed in Step 2, according to the local temperature and density. After the set physical time is reached, terminate the calculation and output the calculation results of power, temperature, density, cavitation fraction, and spatiotemporal distribution of neutron flux. The specific iterative solution process is as follows: Figure 2 As shown.

Claims

1. A method for transient nuclear thermal coupling calculation of fuel rod bundles in a pressurized water reactor under two-phase flow conditions, characterized in that: In the CFD solution platform, a unified grid is used to solve the neutron diffusion equation and the thermal-hydraulic control equation simultaneously to reduce errors caused by data transfer and grid mapping and to facilitate transient calculations. At the same time, the minority group cross section is fitted as a function of temperature and density, so that the feedback effect of thermal parameters on neutron physics can be reflected in the coupled calculation process, thereby studying the temperature Doppler effect and the influence of the density reduction of the coolant caused by temperature increase and boiling on the neutron physics properties. The method includes the following steps: Step 1: Establish a three-dimensional geometric model containing the fuel rod bundle and the surrounding coolant flow channels, and mesh the three-dimensional geometric model to obtain the computational mesh for subsequent coupled solution; Step 2: Establish a three-dimensional geometric model of the fuel rod bundle and its surrounding coolant channels in the Monte Carlo program, consistent with Step 1; perform Monte Carlo calculations under multiple temperature and density conditions covering the target operating range to obtain minority cross-section data under the corresponding operating conditions and form a minority cross-section database; based on the minority cross-section database, use Python interpolation methods to construct the minority cross-sections into continuous functions of temperature and density, so as to obtain the minority cross-section parameters in real time according to the local temperature and density during the nuclear thermal coupling calculation, and realize the feedback effect of thermal hydraulic parameters on neutron physical properties; Step 3: Since the CFD solution platform has a built-in thermal-hydraulic calculation model but does not include a neutron physics solution model, the neutron diffusion equation is embedded in the CFD solution platform to achieve nuclear thermal coupling analysis of fuel rod bundles. The neutron diffusion equation is solved using the CFD solution platform's user-defined scalar equation interface (UDS) framework. The neutron diffusion equation is mapped to the UDS through equivalent transformation of the equation: transient terms are mapped to UDS transient terms, diffusion terms are mapped to UDS diffusion terms, and the remaining terms are treated as UDS source terms. The transient term coefficients, diffusion coefficients, and source term coefficients of the UDS are implemented by the user-defined function interface (UDF), and combined with the continuous functions of the minority group cross section and temperature and density constructed in Step 2, the neutron physics parameters are updated in real time according to the local temperature and density during the calculation process. The transient term coefficients, diffusion coefficients, source term coefficients, and boundary conditions corresponding to the UDS are defined through the UDF interface, and the UDF is loaded into the CFD solution platform to participate in the solution, so as to achieve synchronous solution of the thermal-hydraulic control equation and the neutron diffusion equation on the same computational grid. Step 4: Select a thermal-hydraulic calculation model that matches the calculation conditions in the CFD solution platform; considering the high power density of the fuel rod bundle, the coolant will undergo subcooling boiling, so a two-phase flow model needs to be enabled in the thermal-hydraulic calculation model to characterize the boiling-related phase change and heat transfer processes; at the same time, enable UDS to provide a calculation framework for solving the neutron diffusion equation. Step 5: Set the material property parameters for the solid domain and fluid domain in the CFD solution platform respectively; set the thermophysical property parameters such as density, specific heat capacity, and thermal conductivity for the solid domain, and set the parameters such as density, specific heat capacity, thermal conductivity, viscosity, molar mass, and standard enthalpy for the fluid domain, and set the diffusivity parameter defined in UDF that is related to the UDS solution. Step 6: Set the computational domain boundary conditions and perform global standard initialization in the CFD solution platform, and start the steady-state nuclear thermal coupling calculation; realize the bidirectional feedback coupling of neutron physics and thermal hydraulics during the steady-state solution process, and iterate until the preset convergence criterion is met; Step 7: After the steady-state nuclear thermal coupling calculation reaches convergence, save the calculation results and perform post-processing analysis; after introducing a disturbance, start the transient nuclear thermal coupling calculation, maintain the bidirectional feedback coupling of neutron physics and thermal hydraulics during the transient solution process, and terminate the calculation and output the results after the set physical time or preset termination criterion is reached.

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