CN114004173B - An optimized layout method for electric heating elements of voltage stabilizers in nuclear power plants - Google Patents

Abstract

The invention relates to a method for optimizing the arrangement of electric heating elements of a voltage stabilizer in a nuclear power plant, which includes: firstly performing three-dimensional geometric modeling and meshing of the voltage stabilizer and electric heater; then selecting the RPI wall boiling mathematical model to write UDF, And it is coupled with the Euler-Eulerian two-fluid model to realize the numerical simulation of the supercooled flow boiling phenomenon under ultra-high pressure in the pressurizer; then set up different electric heater arrangements, and calculate the corresponding flow heat transfer control equations Solve it; finally, by comparing the internal temperature field and cavitation share distribution of the voltage stabilizer under different electric heater arrangements, the heating effect is shown to determine the optimal heater arrangement. Compared with the existing technology, the method of the present invention can comprehensively and effectively simulate the complex vapor-liquid two-phase flow in the pressure stabilizer, realize the simulation calculation of the subcooled boiling flow heat transfer process in the three-dimensional pressure stabilizer, and thus can reliably determine Find out the best arrangement of the electric heating elements of the voltage regulator.

Description

An optimized layout method of electric heating elements for voltage stabilizers in nuclear power plants

Technical field

The invention relates to the technical field of optimal design of voltage stabilizers in nuclear power plants, and in particular, to an optimal arrangement method of electric heating elements of voltage stabilizers in nuclear power plants.

Background technique

AP1000 is a million-kilowatt, dual-loop third-generation advanced pressurized water reactor nuclear power unit developed by Westinghouse Company. It is also one of the main models for my country's nuclear power construction for a long time in the future. As of May 2017, China has 4 AP1000 reactors under construction and 12 AP1000 reactors planned to be built. Its planned installed capacity accounts for 53% of the total installed capacity of the reactors planned to be built in my country. At present, there is no mature experience in the operation of AP1000 units in the world. Therefore, it is of great significance to safely and efficiently promote the process of my country's third-generation nuclear power autonomy and ensure the safe and stable operation of the units.

In pressurized water reactor nuclear power plants, the pressure stabilizer is an important device for maintaining system pressure safety. During normal operation, frequent fluid wave in-wave and wave-out processes will occur in the water cavity, accompanied by complex hot and cold fluid mixing and Subcooled boiling heat transfer phenomenon. The electric heater is the core component of the voltage stabilizer equipment. Its main function is to heat the reactor coolant in the voltage stabilizer to maintain it at the saturation temperature that meets the operating pressure during rated operating conditions and variable load operation. Control and regulate pressure fluctuations in the reactor coolant. Since the electric heating element is directly immersed in water, it will withstand harsh tests such as ultra-high water pressure, instantaneous extreme temperature difference changes, high radiation dose, and long-term stable operation. Once a failure occurs, it will affect the power plant's ability to maintain and control the operating pressure of the reactor coolant system. Ability to even cause primary circuit overpressure shutdown. Therefore, the arrangement of the electric heater in the lower head of the voltage stabilizer should be able to ensure that the incoming low-temperature coolant is heated to the saturation temperature in the shortest time, preventing the low-temperature coolant from directly impacting the vapor-liquid interface and aggravating the electric heating. Thermal fatigue on the surface of the reactor causes safety accidents. In recent years, the failure cases of electric heaters in nuclear power plants at home and abroad have attracted more and more scholars' attention.

At present, research on pressure stabilizers at home and abroad mainly focuses on the establishment of mathematical models to study the dynamic characteristics of the pressure stabilizer; the pressure and liquid level control and adjustment systems; and the optimal design of the overall weight of the pressure stabilizer. However, these studies cannot reflect the The complex flow field distribution and thermal-hydraulic characteristics in the voltage stabilizer cannot reflect the heating effect of the electric heating elements inside the voltage stabilizer, making it difficult to provide scientific and effective guidance for the specific layout of the electric heating elements.

Contents of the invention

The purpose of the present invention is to provide an optimized arrangement method of the electric heating elements of the voltage stabilizer of a nuclear power plant in order to overcome the above-mentioned shortcomings of the prior art, and explore the advantages of the electric heating elements in the voltage stabilizer from the perspective of supercooled boiling two-phase heat transfer. Heating uniformity to determine the optimal placement of the voltage regulator's electric heating elements.

The object of the present invention can be achieved through the following technical solutions: an optimized arrangement method of electric heating elements of a nuclear power plant voltage regulator, including the following steps:

S1. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater. Based on the engineering reality, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater, and use CFD pre-processing software for mesh division and Grid independence verification;

S2. Based on the flow, heat transfer and phase change processes in the pressurizer, construct a mathematical physical model for ultra-high pressure supercooled boiling flow heat transfer simulation, and determine the coupling relationship between the Euler-Eulerian two-fluid model and the RPI wall boiling model. ;

S3. Convert the mathematical physical model constructed in step S2 into computer language and embed it into computational fluid dynamics software to realize simulation calculations of boiling heat transfer in a high-pressure environment;

S4. According to the thermal coupling relationship between the electric heater and the coolant, determine the coolant wave inflow speed, temperature and pressure, and set the heating method and power of the electric heater element to determine the initial operating conditions and boundary conditions. ;

S5. According to the actual grouping and number of electric heaters inside the voltage regulator, combined with the typical electric heater layout, set the working modes of on-off electric heaters and proportional electric heaters respectively;

S6. According to the global Courant number, set the iteration time step and solve the flow heat transfer control equations corresponding to different arrangements. When the convergence conditions of the subcooling boiling simulation are met, use CFD post-processing software to analyze the internal differences of the regulator. The flow field, temperature field and cavitation share distribution of the cross section can be used to determine the optimal proportional electric heater arrangement.

Further, step S1 specifically includes the following steps:

S11. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater, including the detailed size structure of the voltage stabilizer’s upper head, cylinder, lower head, and electric heater;

S12. Based on the actual engineering, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater, and simplify the internal part of the voltage stabilizer and the electric heating element. The geometric model includes the voltage stabilizer and the components connected to the voltage stabilizer. fluctuating tube pipe;

S13. Carry out tetrahedral meshing on the established three-dimensional full-scale geometric model of the voltage regulator, and use the average cavitation share of the axial section and the average temperature of the section as reference objects to verify the grid independence.

Further, the specific process of simplifying the internal part of the voltage regulator and the electric heating element in step S12 is as follows: ignoring the cold section, end plug and sealed end connector, only retaining the heating section, regardless of its internal structure, Simplify it into a cylinder;

Ignore the electric heater support plate, guide plate, screen, wave tube and the take-over structure of the voltage stabilizer in the voltage stabilizer, and establish a coordinate system with the center of the intersection surface between the lower head of the voltage stabilizer and the cylinder as the coordinate origin. The fluid enters from the positive y direction, and the gravity direction is the negative y direction;

Cut off the cylinder with a height of 1m above the lower head for modeling.

Further, the mathematical physical model constructed in step S2 is specifically:

Among them, the subscript k represents gas or liquid, the subscript i represents non-k phase, α _k , ρ _k , H _k are the volume fraction, density, velocity, and enthalpy of each phase, /> For the mass transfer from k phase to i phase, the first term on the right side of the mathematical physical model equation represents the enthalpy change caused by pressure; the second term is the combination of molecular heat flux and turbulent heat flux; the third term represents diffusion The change in enthalpy caused by mass flux; the last term represents the wall heat flux, which requires the introduction of a boiling model. The present invention uses the RPI wall boiling model to calculate the heat flux.

Further, the RPI wall boiling model in step S2 includes a convection heat transfer term, a quenching heat flow term and an evaporation heat flow term, in which the bubble nucleation density adopts the LC model, the detachment diameter adopts the Unal model, and the detachment frequency adopts the Cole model. .

Further, the step S3 is specifically to compile the UDF (User-DefineFunction, user-defined function) of the RPI wall boiling model, which is written in C language and defined using the DEFINE macro, by calling the fluid speed, temperature, pressure, pressure gradient, Turbulent kinetic energy, velocity gradient, heat flow on the wall, boundary, convective heat transfer coefficient, and coupling the Euler-Eulerian two-fluid model to convert the RPI wall boiling model into computer language and embed it into computational fluid dynamics software to enable high-pressure The calculation of boiling heat transfer in ambient conditions is realized.

Further, the step S4 specifically includes the following steps:

S41. Use the transient thermal function test data of the starting loop of the pressurized water reactor nuclear power plant as the simulated working condition to determine the speed, temperature and operating pressure of the coolant flowing into the surge tube;

S42. Set the heating form of the electric heater as a surface heat source, and realize the heat transfer phenomenon by defining the heat flux of different cylinders;

S43. Set the thermal boundary of the regulator wall to a stationary, smooth and non-slip adiabatic boundary;

Set the calculation domain and initial pressure corresponding to the water phase and vapor phase.

Further, typical electric heater arrangements in step S5 include but are not limited to cross arrangement, inner ring arrangement, inner middle ring arrangement, inner and outer ring arrangement, middle ring arrangement, middle outer ring arrangement and outer ring arrangement.

Further, the step S6 specifically includes the following steps:

S61. According to the global Courant number, set the iteration time step, and iteratively solve the flow heat transfer control equations corresponding to different arrangements;

S62. After the convergence conditions of the subcooled boiling simulation are met, the CFD post-processing software is used to analyze the flow field, temperature field and cavitation share distribution along the axial direction of the stabilizer in different internal cross-sections under different arrangements to filter out The optimal arrangement of heating efficiency and heating performance is the optimal proportional electric heater arrangement.

Further, step S61 specifically includes the following steps:

S611. Select the VOF two-phase flow model and the Realizable k-ε turbulence model;

The SIMPLEC algorithm is used to process the pressure-velocity coupling relationship of the continuity equation and the momentum equation, and the volumetric vapor content rate in the discrete format of the convection term adopts the second-order upwind format;

The interphase heat transfer uses the RM correlation, the drag force model uses the IZ correlation, the lift model uses the Moraga correlation, the wall lubrication force uses the Antal model, and the turbulent dissipation force uses the Burns model;

S612. Based on the mathematical physical model constructed in step S2, import the UDF function of the RPI wall boiling model into the FLUENT software to simulate the boiling heat transfer of the coolant in the regulator, and set the time step for iterative solution;

S613. Set the changing trend of hot and cold fluid density with temperature according to the polynomial function, and set the vapor phase density to change according to the ideal gas law;

S614. Compare the average cavitation share of the outlet cross-section at each time iteration step with the cavitation share of the previous time. If the difference between the two is less than the preset threshold, it indicates that the coupling calculation has converged and the corresponding calculation result is output; otherwise, continue Iterative calculation.

Compared with the existing technology, the present invention explores the heating uniformity of the electric heating element in the voltage stabilizer from the perspective of supercooled boiling two-phase heat transfer, and proposes a method based on the Euler-Eulerian two-fluid theory and the RPI wall boiling model. A three-dimensional simulation method for simulating the boiling phenomenon of supercooled flow under ultra-high pressure in a voltage regulator, and using UDF compilation method to realize the simulation calculation of boiling heat transfer in a high-pressure environment, thus solving the problem that the existing technology cannot reflect the complex internal problems of the voltage regulator. The problem of high-pressure subcooled boiling flow heat transfer phenomenon can effectively simulate the heat transfer process of subcooled boiling flow in a three-dimensional pressure stabilizer, and then obtain its internal flow field, temperature field and cavitation share distribution, which can be used for electric heaters. The layout implementation theory guides the optimal arrangement of electric heaters to maximize the role of electric heaters and enhance the heating effect.

Description of the drawings

Figure 1 is a schematic flow diagram of the method of the present invention;

Figure 2 is a schematic diagram of the application process of the embodiment;

Figure 3a is a schematic structural diagram of the voltage regulator of the embodiment;

Figure 3b is a schematic structural diagram of the wave tube of the embodiment;

Figure 4 is a schematic structural diagram of the electric heater according to the embodiment;

Figure 5 is a schematic diagram of the calculation area of the embodiment;

Figure 6 is a verification experiment of the RPI wall boiling heat transfer model in the embodiment;

Figure 7 is a schematic cross-sectional view of the proportional electric heater according to the embodiment;

Figure 8 is the cavitation share distribution in the axial cross-section of the embodiment;

Figure 9 is the average temperature distribution of the axial cross-section of the embodiment;

Figure 10 is a cloud diagram of the temperature distribution of different sections under the cross arrangement of the embodiment;

Figure 11 is a cloud diagram of the temperature distribution in different sections under the arrangement of the inner and outer rings of the embodiment;

Figure 12 is a cloud diagram of the temperature distribution of different sections under the inner ring arrangement of the embodiment.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Example

As shown in Figure 1, an optimized arrangement method for electric heating elements of a nuclear power plant voltage regulator includes the following steps:

S1. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater. Based on the engineering reality, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater, and use CFD pre-processing software for mesh division and Grid independence verification;

S2. Based on the flow, heat transfer and phase change processes in the pressurizer, construct a mathematical physical model for ultra-high pressure supercooled boiling flow heat transfer simulation, and determine the coupling relationship between the Euler-Eulerian two-fluid model and the RPI wall boiling model. ;

S3. Convert the mathematical physical model constructed in step S2 into computer language and embed it into computational fluid dynamics software to realize simulation calculations of boiling heat transfer in a high-pressure environment;

S4. According to the thermal coupling relationship between the electric heater and the coolant, determine the coolant wave inflow speed, temperature and pressure, and set the heating method and power of the electric heater element to determine the initial operating conditions and boundary conditions. ;

S5. According to the actual grouping and number of electric heaters inside the voltage regulator, combined with the typical electric heater layout, set the working modes of on-off electric heaters and proportional electric heaters respectively;

S6. According to the global Courant number, set the iteration time step and solve the flow heat transfer control equations corresponding to different arrangements. When the convergence conditions of the subcooling boiling simulation are met, use CFD post-processing software to analyze the internal differences of the regulator. The flow field, temperature field and cavitation share distribution of the cross section can be used to determine the optimal proportional electric heater arrangement.

In specific applications, this technical solution mainly includes the following contents:

1. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater, including the detailed size and structure of the voltage stabilizer's upper head, cylinder, lower head, and electric heater. According to the actual engineering practice, a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater was established. The internal part of the voltage stabilizer and the electric heating element were reasonably simplified. CFD pre-processing software was used to divide the mesh and select appropriate parameters for meshing. Lattice irrelevance verification.

Among them, the geometric model includes the entire pressure stabilizer (upper head, cylinder, lower head), and the wave tube pipeline connected to the pressure stabilizer. The simplification method of the electric heating element in the voltage regulator is to ignore the cold section, end plug and sealed end connector, retain only the heating section, ignore its internal structure, and simplify it into a cylinder; and ignore the internal structure of the voltage regulator. The structure of the electric heater support plate, guide plate, screen, surge tube and voltage stabilizer takeover is used to establish a coordinate system with the center of the circle interface between the lower head of the voltage stabilizer and the cylinder as the origin of the coordinate system. The fluid flows from y positive direction, the gravity direction is the negative y direction; in order to save computing resources, only the 1m-high cylinder above the lower head is intercepted for modeling calculations.

Since there are many heating cylinders in the model and the model is complex, it is divided into tetrahedral meshes. In order to ensure the heat transfer effect, a boundary layer mesh is set around each cylinder. The average cavitation share of the axial section and the average temperature of the section are used as reference objects to verify the grid independence to ensure the accuracy of the calculation.

2. Construct a mathematical physical model for ultra-high pressure supercooled boiling flow heat transfer simulation based on the flow, heat transfer, phase change and other processes in the pressurizer, and establish a coupling relationship between the Euler-Eulerian two-fluid model and the RPI wall boiling model. Among them, the Euler-Eulerian two-fluid model coupled RPI wall boiling model was used to numerically simulate the subcooled boiling heat transfer phenomenon in the pressurizer to explore the heating uniformity under different arrangements of the heater.

The transient flow at the vapor-liquid interface is described by the RANS equation based on the VOF multiphase flow model. The coupled Realizable k-ε turbulence model makes the entire solution system closed. Water vapor compressibility is described by the ideal gas law. In order to reduce the calculation time and simplify the model, the heat conduction effect between the fluid and the tube wall and the inside direction of the tube wall is ignored.

In order to describe the supercooled boiling phenomenon, the wall heat flow correlation in the energy conservation equation adopts the RPI wall boiling model, which divides the heat flow transferred from the electric heater wall to the fluid into three parts, which are the convective heat transfer Q between the wall and the fluid. _c , quenching heat flow Q _q , evaporation heat flow Q _e . The convective heat transfer term is as follows:

Q _c = h _c (T _w -T _l ) (1-A _b )

In the formula, h _c is the relative liquid heat transfer coefficient, T _w and T _l are the wall temperature and the temperature of the fluid close to the wall respectively. _Na is the nucleation density, d _bw is the bubble detachment diameter. Under normal circumstances, the K value can be set to 4. For different applications, K can vary between 1.8-5.

The quench heat flow term is as follows:

In the formula, t _w is the bubble waiting time, k _l is the liquid phase thermal conductivity, ρ _l is the liquid phase density, and C _pl is the liquid phase constant pressure specific heat capacity.

The evaporation heat flow term is as follows:

In the formula, the detachment frequency of wall bubbles is f, and the replenishment period of the surrounding liquid after the bubbles detach is 1/f. d _bw is the bubble detachment diameter, _Na is the nucleation density, ρ _v is the gas phase density, h _lv is the latent heat of evaporation.

The bubble active nucleation density depends on factors such as wall roughness, local fluid parameters, wall superheat, wall and liquid wettability, etc. The present invention selects a nucleation density correlation (LC correlation) suitable for high-pressure boiling conditions, as follows :

N _a =(C ⁿ ·(T _w -T _sat )) ⁿ

In the formula, n=1.805, C=210. The Unal model is selected as the bubble escape diameter. This model is suitable for pressures of 0.1-17.7MPa, heat flow rates of 0.47-10.64MW/m ² , speeds of 0.08-9.15m/s, subcooling degrees of 3-86K, and bubble average values. The case where the diameter is 0.08-1.24mm is as follows:

In the formula, ΔT _sup =T _w -T _sat is the wall superheat, U _b is the near-wall velocity, U ₀ =0.61m/s, and the subscripts s, l and v represent the solid phase, liquid phase and gas phase respectively.

The Cole model is selected for the bubble detachment frequency. This model has not only been widely verified under low pressure, but has also been extended to medium and high pressure experimental conditions, as shown below:

The diameter of the bubble is a function of local subcooling:

In the formula, d _min =0.00015m, d _max =0.001m, ΔT _min =0K, ΔT _max =13.5K.

In summary, in the numerical simulation of subcooled boiling heat transfer in the regulator, the LC model is used for the bubble nucleation density, the Unal model is used for the detachment diameter, and the Cole model is used for the detachment frequency.

3. Convert the mathematical physical model constructed above and the summarized semi-empirical theoretical calculation formula into computer language and embed it into commercial software to realize the calculation of boiling heat transfer and verify the accuracy and practicability of the model. The boiling heat transfer model that comes with general commercial CFD (computational fluid dynamics) software has great limitations. It is only suitable for low pressure situations and cannot be used to simulate high-pressure boiling heat transfer in a pressurizer. The present invention applies the boiling heat transfer model under high pressure to the voltage stabilizer, and prepares UDF (User-Define Function) for the empirical correlation of the above-mentioned RPI wall boiling heat transfer model. It is written in C language and uses the DEFINE macro to Definition, call the fluid velocity, temperature, pressure, pressure gradient, turbulent kinetic energy, velocity gradient, heat flow and convection heat transfer coefficient of the wall and boundary in the main program of the software, and couple the Euler two-fluid model to convert it The computer language is embedded into commercial software to enable the calculation of boiling heat transfer in high-pressure environments.

In this embodiment, in order to verify the accuracy of the written UDF, CFD software is used to compile it, and the Euler two-fluid model is coupled to conduct a numerical simulation of a supercooled flow boiling experiment under a certain ultra-high pressure condition to compare the difference with the experimental results. .

4. Based on the serious thermal coupling relationship between electric heaters and coolants, determine the coolant wave inflow speed, temperature and pressure based on actual industrial measurements or experience, and define the heating method and power of the electric heater elements to determine the initial working conditions. conditions and boundary conditions. Specifically, the speed, temperature and operating pressure of the coolant flowing into the surge tube are determined based on the transient thermal function test data of the startup loop of the pressurized water reactor nuclear power plant as the simulated working condition. The heating form of the electric heater is defined as a surface heat source, and the heat transfer phenomenon is realized by defining the heat flux of different cylinders. The thermal boundary of the wall of the pressurizer is set as an adiabatic boundary, which is stationary, smooth and without slip; the calculation domain and initial pressure corresponding to the water phase and vapor phase are set.

5. Based on the actual grouping and number of electric heaters inside the voltage regulator, enumerate typical electric heater arrangements, and set the working modes of on-off electric heaters and proportional electric heaters respectively. First determine the number of groups of on-off electric heaters and proportional electric heaters in the actual voltage regulator. At the moment of startup, all on-off electric heaters work, while the proportional electric heaters are all off. List the different arrangements of electric heaters, including but not limited to cross arrangement, inner ring arrangement, inner and middle ring arrangement, inner and outer ring arrangement, middle ring arrangement, middle and outer ring arrangement, outer ring arrangement, etc., to compare the heating effects of different arrangements. .

6. Solve the flow heat transfer control equation and determine the appropriate time step based on the global Courant number. After meeting the convergence conditions of the subcooled boiling simulation, CFD post-processing software was used to analyze the flow field, temperature field and cavitation share distribution of different cross-sections inside the regulator, and the optimal proportional electric heater layout was obtained, which provided the basis for the project. Application provides theoretical basis. Specifically, the SIMPLEC algorithm is used to process the pressure-velocity coupling relationship of the continuity equation and the momentum equation, and the volumetric vapor content rate in the discrete format of the convection term adopts the second-order upwind format. The interphase heat transfer uses the RM correlation, the drag force model uses the IZ correlation, the lift model uses the Moraga correlation, the wall lubrication force uses the Antal model, and the turbulence dissipation force uses the Burns model. The time step is set for iterative solution.

Since simulated boiling involves two-phase flow, direct temperature field simulation is not easy to converge. This invention first calculates the flow field. After the flow field converges, the energy equation is opened and the UDF function of the RPI wall boiling model is imported into FLUENT. Simulate the boiling heat transfer of the coolant in the voltage regulator. The iterative decision is whether the difference between the average cavitation share of the outlet cross-section of the voltage regulator obtained by the two previous calculations is less than a predetermined value. In subsequent analysis, the cross-sectional average void fraction and the cross-sectional average temperature distribution along the axial direction of the stabilizer are used to characterize the heating performance of the stabilizer.

This embodiment applies the above technical solution to illustrate the modeling example of the AP1000 nuclear power plant voltage regulator, as shown in Figure 2, including the following steps:

Step 1. Based on the actual project, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage regulator including the electric heater, reasonably simplify the internal part of the voltage regulator and the electric heating elements, and use CFD pre-processing software to mesh and select appropriate Parameters are verified for grid independence.

(1) Figure 3a and Figure 3b are schematic diagrams of the AP1000 voltage regulator and its wave tube. It adopts an electrically heated vertical cylindrical structure design, consisting of an upper head, three cylinders (upper, middle and lower cylinders) and a belt It consists of the lower head of the support, which is the same thickness as the cylinder. It is a metal container that can withstand high pressure inside. The upper part is the steam space, equipped with a sprayer that can reduce temperature and pressure, and the upper head is equipped with a spray nozzle, which is connected to the cold pipe section of the coolant system; the lower part is the water space, with a total of 78 electric heaters installed in three circles. Arranged in concentric circles, 20 electric heaters are installed in the inner ring, 26 electric heaters are installed in the middle ring, and 32 electric heaters are installed in the outer ring, which are installed vertically in the heater casing of the lower head of the voltage stabilizer. Among them, 60 are on-off electric heaters, mainly used for reactor startup or transient processes; 18 are proportional electric heaters, mainly used to compensate for steady-state waste heat loss. There is no clear guideline for the layout of on-off and proportional electric heaters. Most of them arrange 78 electric heater elements into 78 casings according to engineering experience and the requirements of electric heater circuits, lacking theoretical guidance.

(2) Figure 4 is a schematic structural diagram of the AP1000 electric heater. It is a direct-insertion immersion tube cladding type. Each electric heater is an independent unit, and part of it is inserted into the voltage regulator to perform the heating function. It is composed of mechanical components and The electrical components consist of a corrosion-resistant 316L stainless steel housing and end plugs, and the mechanical components include sealed end connectors (auxiliary pressure boundaries). Electrical components mainly include spiral nickel-chromium alloy resistance wire, sealed terminals, conductors and insulating materials. The heating section of the resistance wire is the heating section, and the non-heating section of the outer casing of the electric heater is the cold section. The vertical arrangement length of the electric heater in the voltage regulator is generally 1591mm (based on the height of the internal bottom of the voltage regulator), and the effective heating section is about 1060mm. In the present invention, it is simplified into a cylinder with a length of 1060 mm and a diameter of 22 mm, with a total of 78 cylinders.

(3) Use the SpaceClaim module of the ANSYS software to create a three-dimensional full-scale geometric model of the voltage regulator including the electric heater component. In this model, the center of the circle at the interface between the lower head and the cylinder is the coordinate origin to establish a coordinate system. The fluid enters from the positive y direction. The direction of gravity is the negative y direction. In order to save computing resources, only the cylinder with a height of 1m above the lower head is cut out for modeling calculation, see Figure 5.

(4) Import the model into the ICEM module of ANSYS software and define each boundary surface. Since there are many heating cylinders in the model and the model is complex, it is divided into tetrahedral meshes. In order to ensure the heat transfer effect, each cylinder is A boundary layer grid is set around it. The distance from the first boundary layer to the wall is 0.05mm. The boundary layer thickness growth coefficient is 1.15. A total of 10 boundary layers are set up. When verifying the grid independence, five types of grids were divided into 3548221, 3979844, 4334370, 5003512, and 6104898 numbers. The average cavitation share of the axial section and the average temperature of the section were used as reference objects to verify the grid independence.

Step 2: Construct a mathematical physical model for ultra-high pressure supercooled boiling flow heat transfer simulation, and establish a coupling relationship between the Euler-Eulerian two-fluid model and the RPI wall boiling model.

(1) The Euler-Eulerian two-fluid model establishes the mass, momentum and energy conservation equations of the liquid phase and the vapor phase respectively. The continuity, momentum and energy equations for each phase are solved separately, making the system of equations closed. Its energy equation is:

In the formula, the subscript k represents gas or liquid, and the subscript i represents non-k phase. α _k ,ρ _k , H _k represents the volume fraction, density, velocity, and enthalpy of each phase respectively. /> Represents the mass transfer from phase k to phase i. The first term on the right represents the enthalpy change due to pressure. The second term is a combination of molecular and turbulent heat fluxes. The third term represents the change in enthalpy caused by diffusive mass flux (evaporation and condensation). The last term represents the wall heat flux and requires the introduction of the boiling model. The present invention uses the RPI wall boiling model to calculate the heat flux, in which the bubble nucleation density uses the LC model, the detachment diameter uses the Unal model, and the detachment frequency uses the Cole model.

Step 3. Writing and verification of UDF.

(1) Use the Visual studio 2015 platform to write the UDF of the RPI wall ultra-high pressure boiling model, convert it into a computer language and embed it into commercial software to realize the calculation of boiling heat transfer.

(2) In order to verify the accuracy of the written UDF, it was compiled with CFD software and coupled with the Euler two-fluid model to numerically simulate the supercooled flow boiling experiment of Liu et al. under ultrahigh pressure conditions. Figure 6 is a simulation diagram of the experimental test section. The dark part is the heating section. There are three sections in total, and the heating power of each section is 95kW/m2. Water is used as the working medium, the inlet is set as the mass flow inlet, the outlet is the pressure outlet, the operating pressure is 15MPa, and the Realizable k-ε turbulence model is selected. The comparison between the simulation results and the experimental results is shown in Table 1. The simulation results and experimental results The error is within the acceptable range, which shows that the RPI boiling model coupled with the Euler two-fluid model can well predict the boiling phenomenon of subcooled flow in the pipeline, and also proves the correctness of the UDF written.

Table 1 Experimental example verification results

Step 4. Determine the initial working conditions and boundary conditions.

(1) Select the transient thermal functional test data of the starting loop as the simulation working condition, that is, the speed of the coolant flowing into the wave tube is 0.1m/s, the temperature is 595K, the operating pressure is 15.5MPa, and the inlet is set to the speed inlet. The outlet is a pressure outlet. The electric heater is defined as a surface heat source heating form with a heat flux of 0.264w/mm ² , which is achieved by defining different cylindrical heat sources.

(2) The thermal boundary of the wall of the voltage regulator is set as an adiabatic boundary, which is stationary, smooth and without slip. The physical properties of the flowing medium are shown in Table 2.

Table 2 Physical properties of coolant and saturated steam

parameter value Initial water temperature of voltage regulator, K 617.95 Wave entry water temperature, K 595 Wave inflow velocity, m/s 5.5 Coolant density, kg/m ³ 737.9063+1.81776T-0.00322T ² Coolant specific heat capacity at constant pressure, J/kg·K 5458.3 Coolant dynamic viscosity, kg/m·s 5.122× ^10-5 Density of saturated steam, kg/m ³ 100.86 Specific heat capacity of saturated steam at constant pressure, J/kg·K 13803.5 Saturated steam dynamic viscosity, kg/m·s 2.55× ^10-5 Latent heat of saturated steam, J/kg 973.31×10 ³ Richardson number R _i 0.022 Reynolds number _Re 26997662

Step 5. Typical layout plan of electric heater.

(1) This example lists 7 proportional electric heater arrangements for comparison, namely cross arrangement, inner ring arrangement, inner and middle ring arrangement, inner and outer ring arrangement, middle ring arrangement, middle and outer ring arrangement, outer ring arrangement, specifically The layout of the holes is shown in Table 3. Figure 7 shows the schematic diagram and scope of the cross arrangement, with a total of 78 holes, in which the dark circles represent proportional electric heaters.

(2) When the loop starts transiently, all 60 on-off electric heaters in the voltage regulator are working, while the 18 proportional electric heaters in the control group are all off, that is, only the on-off electric heaters are working. A heat source is set on the electric heater and the position of the proportional electric heater is changed, thereby realizing different electric heater arrangements.

Table 3 Different arrangements of proportional electric heaters

Step 6. Solve the flow heat transfer control equation.

(1) Based on the above steps, select the transient solver;

(2) The time step is selected as 2ms based on the global Courant number. At this time, the global Courant number of each time step is below 2, which can fully meet the requirements of simulation calculations.

(3) Select the VOF two-phase flow model and the Realizable k-ε turbulence model; use the SIMPLEC algorithm to process the pressure-velocity coupling relationship of the continuity equation and the momentum equation. The volumetric vapor content rate in the discrete format of the convection term adopts the second-order upwind format. The interphase heat transfer uses the RM correlation, the drag force model uses the IZ correlation, the lift model uses the Moraga correlation, the wall lubrication force uses the Antal model, and the turbulent dissipation force uses the Burns model.

(4) Open the energy equation, import the UDF function of the RPI wall boiling model into FLUENT to simulate the boiling heat transfer of the coolant in the regulator, and set the time step for iterative solution.

(5) Set the changing trend of hot and cold fluid density with temperature according to the polynomial function, and set the vapor phase density to change according to the ideal gas law;

(6) Compare the average cavitation share of the outlet cross-section at each time iteration step with the cavitation share of the previous time. If the difference between the two is less than 1%, the coupling calculation can be considered to have converged and the corresponding calculation results will be output. Otherwise, continue the iteration. .

Step 7. Analysis of calculation results

(1) After the calculation, use CFD post-processing software to analyze the average cavitation share of the internal section of the regulator and the distribution of the average cross-section temperature along the axial direction, as shown in Figures 8 and 9.

(2) Figures 10, 11, and 12 show the temperature distribution cloud diagrams of different sections in three typical arrangements. Six sections are selected along the vertical direction of the heater, y=-0.5, -0.25, 0, 0.25, respectively. 0.5, 0.75.

(3) Analyze the distribution of the cross-sectional average cavitation share and the cross-sectional average temperature along the axial direction of the voltage stabilizer under different arrangements of the proportional electric heater. The results show that the average temperature of the cross section increases with the increase of the void fraction, but the relationship between the two is not a simple linear relationship. When the heaters are arranged in a cross pattern, they can heat the incoming low-temperature cold fluid to the saturation temperature as quickly as possible. This arrangement has the best heating efficiency and performance; when the proportional electric heater is arranged in a single circle (inner circle , middle ring, outer ring), the U-shaped heating area is small and the temperature gradient is relatively large, which seriously affects the uniformity of temperature distribution and heating effect of the outlet fluid. Therefore, the single-circle arrangement of proportional electric heaters should be avoided as much as possible.

In summary, it can be seen that this technical solution can effectively simulate the heat transfer process of subcooled boiling flow in a three-dimensional voltage regulator, obtain its internal flow field, temperature field and cavitation share distribution, and realize the theory of the layout of electric heaters. Guidance, so as to find the best arrangement of electric heaters, maximize the role of electric heaters, and enhance the heating effect.

Claims (10)

1. A method for optimizing the arrangement of electric heating elements of a voltage regulator in a nuclear power plant, which is characterized in that it includes the following steps: S1. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater. Based on the engineering reality, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater, and use CFD pre-processing software for mesh division and Grid independence verification; S2. Based on the flow, heat transfer and phase change processes in the pressurizer, construct a mathematical physical model for ultra-high pressure supercooled boiling flow heat transfer simulation, and determine the coupling relationship between the Euler-Eulerian two-fluid model and the RPI wall boiling model. ; S3. Convert the mathematical physical model constructed in step S2 into computer language and embed it into computational fluid dynamics software to realize simulation calculations of boiling heat transfer in a high-pressure environment; S4. According to the thermal coupling relationship between the electric heater and the coolant, determine the coolant wave inflow speed, temperature and pressure, and set the heating method and power of the electric heater element to determine the initial operating conditions and boundary conditions. ; S5. According to the actual grouping and number of electric heaters inside the voltage regulator, combined with the typical electric heater layout, set the working modes of on-off electric heaters and proportional electric heaters respectively; S6. According to the global Courant number, set the iteration time step and solve the flow heat transfer control equations corresponding to different arrangements. When the convergence conditions of the subcooling boiling simulation are met, use CFD post-processing software to analyze the internal differences of the regulator. The flow field, temperature field and cavitation share distribution of the cross section can be used to determine the optimal proportional electric heater arrangement. 2. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that step S1 specifically includes the following steps: S11. Determine the structure of the pressurized water reactor nuclear power station voltage stabilizer and its internal electric heater, including the detailed size structure of the voltage stabilizer’s upper head, cylinder, lower head, and electric heater; S12. Based on the actual engineering, establish a three-dimensional full-scale geometric model of the nuclear power plant voltage stabilizer including the electric heater, and simplify the internal part of the voltage stabilizer and the electric heating element. The geometric model includes the voltage stabilizer and the components connected to the voltage stabilizer. fluctuating tube pipe; S13. Carry out tetrahedral meshing on the established three-dimensional full-scale geometric model of the voltage regulator, and use the average cavitation share of the axial section and the average temperature of the section as reference objects to verify the grid independence. 3. A method for optimizing the arrangement of electric heating elements of a voltage stabilizer in a nuclear power plant according to claim 2, characterized in that the specific process of simplifying the interior of the voltage stabilizer and the electric heating elements in step S12 is: ignoring cold segments, end plugs and sealed end connectors, only the heating segment is retained, and its internal structure is not considered, simplifying it into a cylinder; Ignore the electric heater support plate, guide plate, screen, wave tube and the take-over structure of the voltage stabilizer in the voltage stabilizer, and establish a coordinate system with the center of the intersection surface between the lower head of the voltage stabilizer and the cylinder as the coordinate origin. The fluid enters from the positive y direction, and the gravity direction is the negative y direction; Cut off the cylinder with a height of 1m above the lower head for modeling. 4. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that the mathematical physical model constructed in step S2 is specifically: Among them, the subscript k represents gas or liquid, the subscript i represents non-k phase, α _k , ρ _k , H _k are the volume fraction, density, velocity, and enthalpy of each phase, /> For the mass transfer from k phase to i phase, the first term on the right side of the mathematical physical model equation represents the enthalpy change caused by pressure; the second term is the combination of molecular heat flux and turbulent heat flux; the third term represents diffusion The change in enthalpy caused by mass flux; the last term represents the wall heat flux. Specifically, the RPI wall boiling model is used to calculate the heat flux. 5. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage stabilizer according to claim 4, characterized in that the RPI wall boiling model in step S2 includes a convection heat transfer term, a quenching heat flow term and an evaporation heat flow. item, in which the bubble nucleation density adopts the LC model, the detachment diameter adopts the Unal model, and the detachment frequency adopts the Cole model. 6. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that step S3 specifically involves UDF compilation of the RPI wall boiling model, written in C language and using the DEFINE macro. Definition, by calling the fluid velocity, temperature, pressure, pressure gradient, turbulent kinetic energy, velocity gradient, wall, boundary heat flow, convective heat transfer coefficient, and coupling the Euler-Eulerian two-fluid model to convert the RPI wall boiling model The computer language is embedded into computational fluid dynamics software to enable the calculation of boiling heat transfer in high-pressure environments. 7. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that step S4 specifically includes the following steps: S41. Use the transient thermal function test data of the starting loop of the pressurized water reactor nuclear power plant as the simulated working condition to determine the speed, temperature and operating pressure of the coolant flowing into the surge tube; S42. Set the heating form of the electric heater as a surface heat source, and realize the heat transfer phenomenon by defining the heat flux of different cylinders; S43. Set the thermal boundary of the regulator wall to a stationary, smooth and non-slip adiabatic boundary; Set the calculation domain and initial pressure corresponding to the water phase and vapor phase. 8. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that typical electric heater arrangements in step S5 include but are not limited to cross arrangement, inner ring arrangement, Inner and middle ring layout, inner and outer ring layout, middle ring layout, middle and outer ring layout and outer ring layout. 9. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 1, characterized in that step S6 specifically includes the following steps: S61. According to the global Courant number, set the iteration time step, and iteratively solve the flow heat transfer control equations corresponding to different arrangements; S62. After the convergence conditions of the subcooled boiling simulation are met, the CFD post-processing software is used to analyze the flow field, temperature field and cavitation share distribution along the axial direction of the stabilizer in different internal cross-sections under different arrangements to filter out The optimal arrangement of heating efficiency and heating performance is the optimal proportional electric heater arrangement. 10. A method for optimizing the arrangement of electric heating elements of a nuclear power plant voltage regulator according to claim 9, characterized in that step S61 specifically includes the following steps: S611. Select the VOF two-phase flow model and the Realizable k-ε turbulence model; The SIMPLEC algorithm is used to process the pressure-velocity coupling relationship of the continuity equation and the momentum equation, and the volumetric vapor content rate in the discrete format of the convection term adopts the second-order upwind format; The interphase heat transfer uses the RM correlation, the drag force model uses the IZ correlation, the lift model uses the Moraga correlation, the wall lubrication force uses the Antal model, and the turbulent dissipation force uses the Burns model; S612. Based on the mathematical physical model constructed in step S2, import the UDF function of the RPI wall boiling model into the FLUENT software to simulate the boiling heat transfer of the coolant in the regulator, and set the time step for iterative solution; S613. Set the changing trend of hot and cold fluid density with temperature according to the polynomial function, and set the vapor phase density to change according to the ideal gas law; S614. Compare the average cavitation share of the outlet cross-section at each time iteration step with the cavitation share of the previous time. If the difference between the two is less than the preset threshold, it indicates that the coupling calculation has converged and the corresponding calculation result is output; otherwise, continue Iterative calculation.