CN116579205A - Calculation method for pressurized water reactor nuclear thermal coupling - Google Patents
Calculation method for pressurized water reactor nuclear thermal coupling Download PDFInfo
- Publication number
- CN116579205A CN116579205A CN202310486446.9A CN202310486446A CN116579205A CN 116579205 A CN116579205 A CN 116579205A CN 202310486446 A CN202310486446 A CN 202310486446A CN 116579205 A CN116579205 A CN 116579205A
- Authority
- CN
- China
- Prior art keywords
- grid
- equation set
- phase
- residual
- representing
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000010168 coupling process Methods 0.000 title claims abstract description 47
- 230000008878 coupling Effects 0.000 title claims abstract description 44
- 238000005859 coupling reaction Methods 0.000 title claims abstract description 44
- 238000004364 calculation method Methods 0.000 title claims abstract description 37
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 29
- 238000000034 method Methods 0.000 claims abstract description 102
- 239000011159 matrix material Substances 0.000 claims abstract description 51
- 230000008569 process Effects 0.000 claims abstract description 34
- 238000007781 pre-processing Methods 0.000 claims abstract description 32
- 238000004088 simulation Methods 0.000 claims abstract description 27
- 238000009792 diffusion process Methods 0.000 claims abstract description 15
- 239000012071 phase Substances 0.000 claims description 73
- 239000007791 liquid phase Substances 0.000 claims description 67
- 239000012808 vapor phase Substances 0.000 claims description 67
- 239000013598 vector Substances 0.000 claims description 43
- 230000004907 flux Effects 0.000 claims description 27
- 238000006243 chemical reaction Methods 0.000 claims description 13
- 230000003111 delayed effect Effects 0.000 claims description 12
- 230000004992 fission Effects 0.000 claims description 9
- 230000008859 change Effects 0.000 claims description 6
- 239000002243 precursor Substances 0.000 claims description 6
- 238000011144 upstream manufacturing Methods 0.000 claims description 6
- 230000000593 degrading effect Effects 0.000 claims description 5
- 238000013507 mapping Methods 0.000 claims description 4
- 238000010521 absorption reaction Methods 0.000 claims description 3
- 239000007788 liquid Substances 0.000 claims description 3
- 238000004519 manufacturing process Methods 0.000 claims description 3
- 230000001575 pathological effect Effects 0.000 description 5
- 238000004422 calculation algorithm Methods 0.000 description 4
- 238000000354 decomposition reaction Methods 0.000 description 3
- 238000009795 derivation Methods 0.000 description 3
- 239000012530 fluid Substances 0.000 description 3
- 230000001052 transient effect Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 239000000446 fuel Substances 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- ZOXJGFHDIHLPTG-UHFFFAOYSA-N Boron Chemical compound [B] ZOXJGFHDIHLPTG-UHFFFAOYSA-N 0.000 description 1
- 229910052796 boron Inorganic materials 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 239000002826 coolant Substances 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
-
- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21D—NUCLEAR POWER PLANT
- G21D3/00—Control of nuclear power plant
- G21D3/001—Computer implemented control
- G21D3/002—Core design; core simulations; core optimisation
-
- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21D—NUCLEAR POWER PLANT
- G21D3/00—Control of nuclear power plant
- G21D3/001—Computer implemented control
- G21D3/005—Thermo-hydraulic simulations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/08—Fluids
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E30/00—Energy generation of nuclear origin
- Y02E30/30—Nuclear fission reactors
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- High Energy & Nuclear Physics (AREA)
- Algebra (AREA)
- Geometry (AREA)
- Evolutionary Computation (AREA)
- Computer Hardware Design (AREA)
- Plasma & Fusion (AREA)
- Operations Research (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Fluid Mechanics (AREA)
- Computing Systems (AREA)
- Monitoring And Testing Of Nuclear Reactors (AREA)
Abstract
The application discloses a calculation method of pressurized water reactor nuclear thermal coupling, which comprises the following steps: establishing a neutron diffusion equation set and a thermal hydraulic equation set of a pressurized water reactor core to be analyzed, and coupling the neutron diffusion equation set and the thermal hydraulic equation set to obtain a nuclear thermal coupling equation set; dynamically adjusting the format of the preprocessing matrix and the residual equation set; dynamically updating a preprocessing matrix and a residual equation set; solving a nuclear thermal coupling residual equation set by combining JFNK of the pretreatment matrix; judging the convergence of the JFNK solution and adjusting the simulation step length; and judging whether the simulation process is finished.
Description
Technical Field
The application relates to the technical field of nuclear reactor cores, in particular to a calculation method of pressurized water reactor nuclear thermal coupling.
Background
The reactor nuclear thermal coupling technology can combine a complex neutron diffusion equation set and a thermal hydraulic equation set in the reactor to complete simulation of physical fields such as reactor core neutrons, thermal hydraulic force and the like. Currently, conventional coupling techniques are mainly through the operator decomposition (Operator Splitting, OS) method or Picard iterative method. The OS method takes the partial solutions obtained by the neutron diffusion equation set module and the thermal hydraulic equation set module after the solutions are respectively used as new estimates of boundary conditions of the other side, and the partial solutions are alternately calculated in each time step until the simulation is finished. The method requires smaller coupling time step because of hysteresis in updating of each physical field parameter in transient calculation, otherwise larger error is caused. In each time step, the Picard iterative method requires iteration convergence of the neutron diffusion equation set and the thermodynamic hydraulic equation set, and then the next time step is advanced. The Picard iterative method is a method supporting full implicit coupling, can ensure that convergence is completed in each time step, and can properly increase the time step, but has the problems of low calculation speed and weaker calculation stability.
The Jacobian-Free Newton-Krylov (JFNK) method is a strong coupling algorithm, and a diffusion equation set and a thermal hydraulic equation set to be coupled are placed in a large matrix to be solved uniformly, so that uniform updating of parameters in an iterative solving process is ensured, the convergence speed is improved, and the iterative error is reduced. Generally, the JFNK method has a faster convergence speed, a higher convergence accuracy, and a better calculation stability than the conventional operator decomposition method or Picard iteration method. Therefore, the JFNK method is beneficial to improving the calculation efficiency of the pressurized water reactor nuclear thermal coupling simulation. However, in transient simulation, when the pressurized water reactor coolant changes phase, if the two-phase fluid equation is uniformly used to be compatible with the single-phase fluid equation, the phenomenon of distortion caused by pathological state and even degradation into an indefinite equation set may occur. And if the phase change occurs, corresponding equations are listed according to specific conditions, and then the problem of the pathological equation set and the indefinite equation set can be solved by simultaneous solving. However, the JFNK method is complex in calculation flow and weak in expansion capability when large-scale matrixes are solved simultaneously. When the number and the format of the physical field equation set are changed, the whole matrix to be solved is changed, and the method is a challenge for JFNK algorithm. Therefore, how to solve the two-phase nuclear thermal coupling of the pressurized water reactor stably and efficiently by using the JFNK method is a technical problem to be solved.
Disclosure of Invention
The application provides a calculation method of pressurized water reactor nuclear thermal coupling, which is used for overcoming at least one technical problem in the prior art.
The embodiment of the application provides a calculation method of pressurized water reactor nuclear thermal coupling, which comprises the following steps:
step S1, establishing a neutron diffusion equation set and a thermal hydraulic equation set of a pressurized water reactor core to be analyzed, and coupling the neutron diffusion equation set and the thermal hydraulic equation set to obtain a nuclear thermal coupling equation set; discretizing the neutron diffusion equation set by using an expansion joint block method to obtain a first grid set sum, and discretizing the thermal hydraulic equation set by using a sub-channel method to obtain a second grid set sum; establishing a mapping relation between the first grid set and the second grid set; the first grid set and the second grid set are obtained based on the same grid division mode of the pressurized water reactor core;
initializing parameters of a physical field of the reactor core according to boundary conditions and initial conditions of the physical field of the pressurized water reactor core, and initializing physical quantities including a transport section, a scattering section, an absorption section, a fission section, a neutron production section and other reaction sections by using a few-group section library;
the initial time step is calculated according to the following formula:
wherein the symbol Δt represents the maximum time step allowed; symbol Deltax i Representing the cell grid size in m; symbol U i Representing the maximum speed in the cell grid in m/s; the symbol η represents an empirical coefficient greater than 0;
step S2, dynamically adjusting the format of the preprocessing matrix and the residual equation set, and specifically comprising the following steps:
s21, reading each physical parameter at the previous moment relative to the moment to be analyzed, calculating a process parameter, and storing the process parameter into a computer memory;
step S22, judging the phase states of each grid in the first grid set and the second grid set, and for any first grid in the first grid set, if any first grid is a liquid phase, degrading a two-phase residual equation set corresponding to the grid into a liquid-phase residual equation set, and deleting vapor phase physical quantities in corresponding vectors to be solved; if any one of the first grids is a vapor phase, degrading a two-phase residual equation set corresponding to the grid into a vapor phase residual equation set, and deleting liquid phase physical quantity in a corresponding vector to be solved; if the first arbitrary grid is two phases, the two-phase residual equation set and the vector to be solved are unchanged; traversing phase parameters of all grids in the first grid set and the second grid set, counting the number of equations to be solved and physical quantities to be solved, and determining the scale and the generation form of a corresponding preprocessing matrix and residual equation set;
step S3, dynamically updating a preprocessing matrix and a residual equation set, wherein the method specifically comprises the following steps:
step S31, reading all physical parameters and process parameters of the previous moment from a memory;
step S32, judging the phase states of each grid in the first grid set and the second grid set, for a second arbitrary grid in the first grid set and the second grid set, if the second arbitrary grid is two-phase, filling a residual equation set and a vector to be solved of the grid based on a two-phase physical parameter database, if the second arbitrary grid is liquid phase, filling the residual equation set and the vector to be solved of the grid based on the liquid phase physical parameter database, if the second arbitrary grid is vapor phase, filling the residual equation set and the vector to be solved of the grid based on the vapor phase physical parameter database until the residual equation set and the vector to be solved are completed;
s4, solving a nuclear thermal coupling residual equation set by combining JFNK of a pretreatment matrix;
s5, judging the convergence of JFNK solution and adjusting the simulation step length;
and S6, judging whether the simulation process is finished.
Preferably, if the second arbitrary grid is two-phase, filling out a residual equation set and a vector to be solved of the grid based on a two-phase physical parameter database, including:
based on the physical parameters including neutron flux density, pressure, temperature, flow rate and section gas content of the two phases at the previous moment read from the memory, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, heat exchange coefficient of the two phases, wall thermal power and wall resistance coefficient are calculated.
Preferably, if the second arbitrary grid is a liquid phase, filling out a residual equation set and a vector to be solved of the grid based on a liquid phase physical parameter database, including:
based on the physical parameters including neutron flux density, liquid phase pressure, temperature and flow velocity read from the memory at the previous moment, process parameters including neutron flux density, macroscopic reaction section, total heat power density, liquid phase heat exchange coefficient, wall heat power and wall resistance coefficient are calculated.
Preferably, if the second arbitrary grid is a vapor phase, filling out a residual equation set and a vector to be solved of the grid based on a vapor phase physical parameter database, and specifically including:
based on the physical parameters including neutron flux density, vapor phase pressure, temperature and flow rate read from the memory at the previous time, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, vapor phase heat exchange coefficient, wall thermal power and wall resistance coefficient are calculated.
Preferably, when the phase is two-phase, the set of nuclear thermal coupling equations is:
x＝[Φ,C,Q,P,α g ,u g ,u l ,w g ,w l ,h g ,h l ] T
wherein f Φ Representing a neutron flux residual equation set; f (f) C Representing a delayed neutron concentration residual equation set; f (f) Q Representing a system of residual equations of the fracture energy; f (f) P Representing a set of vapor phase mass residual equations;representing a liquid phase mass residual equation set; />Representing a set of vapor phase axial momentum residual equations; />Representing a liquid phase axial momentum residual equation set; />Representing a set of vapor phase lateral momentum residual equations;representing a liquid phase lateral momentum residual equation set; />Representing a set of vapor phase energy residual equations; />Representing a liquid phase energy residual equation set; the superscript n+1 is the variable value of the current time step, and the superscript n is the variable value of the previous time step; Δt is the time step in s; phi is neutron flux density in cm -2 s -1 The method comprises the steps of carrying out a first treatment on the surface of the v is neutron velocity in cm/s; c is the density of the delayed neutron precursor nuclei in cm -3 The method comprises the steps of carrying out a first treatment on the surface of the J is neutron flux density in cm -2 s -1 ；a 1 、a 2 、a 3 、a 4 Is the correlation coefficient of the expansion block method; lambda (lambda) d Is the decay constant of the delayed neutron precursor nucleus, and has the unit of t -1 ；Σ f Is a fissile section in cm -1 ；β、k eff The neutron fraction and the effective multiplication factor are delayed respectively; e (E) f Is energy generated by single fission, and the unit is J; q is fission generating energy, and the unit is W; v is the volume of the mesh in m 3 ；A u 、A w Flow areas orthogonal to the axial and transverse velocities, respectively, in m 2 ；ρ g 、ρ l The density of the vapor phase and the liquid phase, respectively, in kg/m 3 ；α g 、α l The cross section steam content and the cross section liquid content are respectively; h is a g 、h l Specific enthalpy of vapor phase and liquid phase, respectively, in kJ/kg; u (u) g 、u l The axial flow rates of the vapor phase and the liquid phase are respectively expressed in m/s; w (w) g 、w l The lateral flow rates, m/s, of the vapor and liquid phases, respectively; Γ is the phase change mass flow in kg/s of the liquid phase vaporized into the vapor phase; p (P) J 、P J+1 The pressures of the axially upstream and downstream grids, respectively, in Pa; p (P) ii 、P jj The pressures of the transverse upstream and downstream grids are Pa; τ wg,u 、τ wl,u Wall resistance in kg.m/s for the axial vapor and liquid phases, respectively 2 ；τ wg,w 、τ wl,w Wall drag in kg.m/s for the transverse vapor and liquid phases, respectively 2 ；τ gl Is the resistance of the vapor phase and the liquid phase, and the unit is kg.m/s 2 ；q g 、q l The total heat transferred to the vapor phase and the liquid phase in the grid is W; n is n j Representing the total number of adjacent grids in the axial direction; n is n gap Representing the total number of adjacent grids in the transverse direction.
One embodiment of the present disclosure can achieve at least the following advantages:
(1) The pressurized water reactor nuclear thermal coupling calculation method can calculate the pressurized water reactor two-phase nuclear thermal coupling problem efficiently and stably, and avoid the problems of pathological states, indefinite solutions and the like.
(2) According to the application, the JFNK method is utilized to carry out two-phase nuclear thermal coupling simultaneous solution on the pressurized water reactor core, and each physical field variable is updated simultaneously in JFNK iteration, so that compared with the traditional methods such as an OS method and a Picard, the method has higher convergence accuracy, higher convergence speed and better stability.
(3) According to the dynamic Jacobi preprocessing method and the dynamic residual equation set method, the scale and format of the preprocessing matrix and the residual equation set are dynamically adjusted according to the phase states in each discrete grid, so that infinitesimal quantities are avoided, pathological conditions are reduced, an uncertain equation set is eliminated, and an uncertain solution is avoided.
(4) The application provides an intelligent calculation time step scheme, fully utilizes the full implicit iteration characteristic supported by the JFNK algorithm, improves the simulation time step, reduces the simulation times and greatly improves the calculation efficiency.
(5) The application does not need to limit the discrete form of neutron diffusion equation and thermodynamic hydraulic equation set, and only needs to describe the physical variable relation among the cells by using the discrete equation so as to construct a corresponding Jacobi preprocessing matrix and a differential equation set.
Drawings
In order to more clearly illustrate the embodiments of the application or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 shows a schematic flow chart of a method for calculating nuclear thermal coupling of a pressurized water reactor;
FIG. 2 shows a flow chart for dynamically adjusting the pretreatment matrix and the format of the equation set to be solved in the calculation method of the nuclear thermal coupling of the pressurized water reactor provided by the application;
FIG. 3 shows a flow chart for dynamically updating a pretreatment matrix and a system of equations to be solved in a method for calculating nuclear thermal coupling of a pressurized water reactor.
Detailed Description
For the purposes of making the objects, technical solutions and advantages of one or more embodiments of the present specification more clear, the technical solutions of one or more embodiments of the present specification will be clearly and completely described below in connection with specific embodiments of the present specification and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, of the embodiments of the present specification. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without undue burden, are intended to be within the scope of one or more embodiments herein.
It should be understood that although the terms first, second, third, etc. may be used in this document to describe various information, these information should not be limited to these terms. These terms are only used to distinguish one type of information from another.
As stated previously, current system simulations have difficulty expanding high-dimensional, multi-physical field objects due to traditional pipeline node and thermodynamic component modeling methods. Thus, how to efficiently model and couple objects in a manner that is individually suitable to form a multi-object, multi-scale, multi-physical field system is a current research hotspot. Classical coupling methods include an operator decomposition (OS) method, a Picard iteration method, and the like. The conventional OS coupling method may cause the physical field parameters to not converge in the time step, so that the accurate model calculates inaccurate or even erroneous results. The Picard method can enable the physical field parameters in each step to be converged, but the calculated amount is large, the convergence stability is poor, and the calculation efficiency is low. Therefore, the system simulation method compatible with multiple objects, multiple scales and multiple physical fields and high in convergence speed and stability is worthy of research. The application provides a calculation method of pressurized water reactor nuclear thermal coupling, which is used for solving the technical problems in the prior art.
As shown in fig. 1, the simulation method flow may include the following steps:
step S1: initializing a system of equations, a time step and physical field parameters:
step S11: initializing a system of equations. The application can combine neutron diffusion equation set and thermal hydraulic equation set into a large-scale nuclear thermal coupling equation set. Taking a pressurized water reactor typical reactor core modeling as an example, discretizing a middle diffusion equation set by using an expansion joint block method to obtain a first grid set sum, discretizing a thermal hydraulic equation set by using a subchannel method to obtain a second grid set sum, and then establishing a mapping relation between the first grid set and the second grid set sum. When specific grid division is carried out, the first grid set sum and the second grid set sum can be obtained based on the same grid division mode for the pressurized water reactor core, so that the mapping relation between the discrete grids of the expansion joint block method and the discrete grids of the sub-channels is conveniently established. Wherein the nuclear thermal coupling equation when the phase is two phases is as follows:
x＝[Φ,C,Q,P,α g ,u g ,u l ,w g ,w l ,h g ,h l ] T
wherein f Φ Representing a neutron flux residual equation set; f (f) C Representing a delayed neutron concentration residual equation set; f (f) Q Representing a system of residual equations of the fracture energy; f (f) P Representing a set of vapor phase mass residual equations;representing a liquid phase mass residual equation set; />Representing a set of vapor phase axial momentum residual equations; />Representing a liquid phase axial momentum residual equation set; />Representing a set of vapor phase lateral momentum residual equations;representing a liquid phase lateral momentum residual equation set; />Representing a set of vapor phase energy residual equations; />Representing a liquid phase energy residual equation set; the superscript n+1 is the variable value of the current time step, and the superscript n is the variable value of the previous time step; Δt is the time step in s; phi is neutron flux density in cm -2 s -1 The method comprises the steps of carrying out a first treatment on the surface of the v is neutron velocity in cm/s; c is the density of the delayed neutron precursor nuclei in cm -3 The method comprises the steps of carrying out a first treatment on the surface of the J is neutron flux density in cm -2 s -1 ；a 1 、a 2 、a 3 、a 4 Is the correlation coefficient of the expansion block method; lambda (lambda) d Is the decay constant of the delayed neutron precursor nucleus, and has the unit of t -1 ；Σ f Is a fissile section in cm -1 ；β、k eff The neutron fraction and the effective multiplication factor are delayed respectively; e (E) f Is energy generated by single fission, and the unit is J; q is fission generating energy, and the unit is W; v is the volume of the mesh in m 3 ；A u 、A w Flow areas orthogonal to the axial and transverse velocities, respectively, in m 2 ；ρ g 、ρ l The density of the vapor phase and the liquid phase, respectively, in kg/m 3 ；α g 、α l The cross section steam content and the cross section liquid content are respectively; h is a g 、h l Specific enthalpy of vapor phase and liquid phase, respectively, in kJ/kg; u (u) g 、u l The axial flow rates of the vapor phase and the liquid phase are respectively expressed in m/s; w (w) g 、w l The lateral flow rates, m/s, of the vapor and liquid phases, respectively; Γ is the phase change mass flow in kg/s of the liquid phase vaporized into the vapor phase; p (P) J 、P J+1 The pressures of the axially upstream and downstream grids, respectively, in Pa; p (P) ii 、P jj The pressures of the transverse upstream and downstream grids are Pa; τ wg,u 、τ wl,u Wall resistance in kg.m/s for the axial vapor and liquid phases, respectively 2 ；τ wg,w 、τ wl,w Wall resistance in kg.m/s for the transverse vapor and liquid phases, respectively 2 ；τ gl Is the resistance of the vapor phase and the liquid phase, and the unit is kg.m/s 2 ；q g 、q l The total heat transferred to the vapor phase and the liquid phase in the grid is W; n is n j Representing the total number of adjacent grids in the axial direction; n is n gap Representing the total number of adjacent grids in the transverse direction.
Step S12: the physical field parameters are initialized. According to boundary conditions and initial conditions of the reactor core physical field, initializing parameters of the reactor core physical field, and initializing physical quantities such as a reaction section by using a few macroscopic section libraries. The core physical field boundary conditions and initial conditions are typically physical quantities such as flow rate, pressure, temperature, specific enthalpy, etc., which are chosen in this example as flow rate at the core inlet, specific enthalpy, and core outlet pressure. The minority group macroscopic reaction section generally includes a transport section, a scattering section, an absorption section, a fission section, a neutron production section, and the like. The few-group macroscopic section library can query corresponding section data according to the information such as the density, the temperature, the boron concentration and the temperature of the fuel of the fluid.
Step S13: the time step is initialized. And calculating an initial time step according to the Brownian number, and storing the initial time step in a memory for subsequent calculation and calling. The formula for the time step is as follows:
where Δt is the maximum time step allowed; Δx i Is a unitGrid size, m; u (U) i Is the maximum speed in the cell grid, m/s; η is an empirical coefficient greater than 0 and can take a value of 3 or even higher when the system of equations is in the fully hidden format.
Step S2: the dynamic adjustment of the preprocessing matrix and the residual equation set format, as shown in fig. 2, may specifically include:
step S21: and reading the solution vector parameter at the previous moment, calculating the process parameter, and storing the process parameter into a memory for convenient reading in other steps. Because the nuclear thermal coupling is a simulation of multiple physical fields, considering the number of grids and the number of equation sets to be solved, if all physical quantities are used as the to-be-solved quantities and written into a large to-be-solved vector, the residual equation and the preprocessing matrix are huge, and the calculation is difficult. The application takes the heat conduction equation set of the solid structural members such as the fuel rod, the control rod guide pipe, the positioning grid and the like as the process parameter equation set, thereby being beneficial to ensuring the calculation accuracy, reducing the calculation amount and improving the calculation efficiency. Because the process parameter equation set completes updating and solving after each JFNK nuclear thermal coupling non-precise Newton iteration, participates in the next non-precise Newton iteration until convergence, and the vector to be solved and the process parameters are updated, thereby meeting the requirement of full implicit coupling and having smaller calculation precision. And the process parameter equation set is independently solved, so that the scale of the nuclear thermal coupling equation set is reduced, the calculated amount of JFNK nuclear thermal coupling is greatly reduced, and the calculation efficiency is improved.
Step S22: and determining the composition format of the preprocessing matrix and the residual equation set. The number and the format of the residual equation set change due to the change of the phase state in each cell in transient calculation, and the corresponding vector to be solved changes. So that the pre-processing matrix also changes. Therefore, all the phase parameters of the grids need to be traversed, the number of equations to be solved and the number of physical quantities to be solved are counted, and the corresponding preprocessing matrix and residual equation set scale and generation form are determined.
In the step, the phase state of each grid in the first grid set and the second grid set can be judged, and for any first grid in the first grid set, if any first grid is a liquid phase, the two-phase residual equation set corresponding to the grid is degenerated into the liquid phase residual equation set, and the vapor phase physical quantity in the corresponding vector to be solved is deleted; if the first arbitrary grid is vapor phase, degrading the two-phase residual equation set corresponding to the grid into a vapor phase residual equation set, and deleting the liquid phase physical quantity in the corresponding vector to be solved; if the first arbitrary grid is two phases, the two-phase residual equation set and the vector to be solved are unchanged; traversing phase parameters of all grids in the first grid set and the second grid set, counting the number of equations to be solved and physical quantities to be solved, and determining the corresponding preprocessing matrix and residual equation set scale and generation form.
More specifically, the application can judge which phase the grid is in according to the section steam-containing rate value result of each grid in the last step, and dynamically adjust the corresponding equation set form. If the two phases are two phases, the two-phase residual equation set and the vector to be solved are unchanged. If the vector is a liquid phase, the two-phase residual equation set corresponding to the grid is degenerated into a liquid phase residual equation set, and the vapor phase physical quantity in the corresponding vector to be solved is deleted, as shown in the following formula:
similarly, if the vector is a vapor phase, the two-phase residual equation set corresponding to the grid is degenerated into a vapor phase residual equation set, and the liquid phase physical quantity in the corresponding vector to be solved is deleted, as shown in the following formula:
the application adopts Jacobi matrix as JFNK preprocessing matrix, the preprocessing matrix is generated by the discrete equation sets of all grids and the variables to be solved through the bias derivative, and the block matrix form is as follows:
when a certain grid phase is single-phase, the residual equation is only the equation of the single-phase. When the Jacobi matrix is formed, the independent variables of the Jacobi matrix are subjected to partial derivation by using the single-phase residual equation to obtain partial derivation terms, and the partial derivation terms are placed at corresponding positions of the Jacobi matrix.
Therefore, when the grid in the single-phase state exists, the two-phase equation set is degenerated into the single-phase equation, and the whole residual equation set and the pretreatment matrix scale can be reduced, so that the calculation amount is reduced, and the calculation speed can be improved.
Step S3: the dynamically updating the preprocessing matrix and the residual equation set, as shown in fig. 3, may specifically include:
step S31: and reading the solution vector parameters, the process parameters and the time step at the last moment from the memory.
Step S32: and (3) updating the parameters of the residual equation set according to the format of the residual equation set generated in the step (2). And updating a residual equation set by using the solution vector parameter, the process parameter and the time step of the last moment read from the memory.
Specifically, as shown in fig. 3, if any one of the first grid set and the second grid set is two-phase, filling in the residual equation set and the vector to be solved of the grid based on the two-phase physical parameter database may specifically include:
based on the physical parameters including neutron flux density, pressure, temperature, flow rate and section gas content of the two phases at the previous moment read from the memory, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, heat exchange coefficient of the two phases, wall thermal power and wall resistance coefficient are calculated.
If the second arbitrary grid is a liquid phase, filling out a residual equation set and a vector to be solved of the grid based on a liquid phase physical parameter database, which specifically may include:
based on the physical parameters including neutron flux density, liquid phase pressure, temperature and flow velocity read from the memory at the previous moment, process parameters including neutron flux density, macroscopic reaction section, total heat power density, liquid phase heat exchange coefficient, wall heat power and wall resistance coefficient are calculated.
If the second arbitrary grid is vapor phase, filling out a residual equation set and a vector to be solved of the grid based on a vapor phase physical parameter database, which specifically may include:
based on the physical parameters including neutron flux density, vapor phase pressure, temperature and flow rate read from the memory at the previous time, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, vapor phase heat exchange coefficient, wall thermal power and wall resistance coefficient are calculated.
Step S33: and (3) updating the preprocessing matrix according to the preprocessing matrix format generated in the step (2). And updating the preprocessing matrix by using the solution vector parameter, the process parameter and the time step of the last moment read from the memory. The present example uses Jacobi matrices as preprocessing matrices. The Jacobi matrix is a large matrix formed by the partial derivatives of all elements in the to-be-solved vector by each residual equation set. The format is as follows:
the Jacobi matrix is used for preprocessing calculation of the Krylov subspace in the JFNK so as to improve the calculation efficiency of the Krylov subspace method. If left preprocessing is used, the Jacobi matrix is decomposed by incomplete LU and then is subjected to inverse operation, and then is multiplied on the matrix to be solved.
Step S4: solving the nuclear thermal coupling residual equation set by using JFNK in combination with the preprocessing matrix comprises:
step S41: non-exact newton iterations. The non-accurate Newton iteration method is an outer loop of JFNK iteration solution, and the non-accurate Newton iteration method comprises the following steps: and constructing a Jacobi matrix vector product linear equation set, updating iteration solution, judging iteration convergence and the like. Wherein the iterative solution update includes an update to the Krylov subspace solution and an update to the process parameters. The iteration convergence judgment refers to whether the equation residual meets the convergence requirement or not in the outer loop, if so, the loop is exited, and if not, the outer loop is continued. Constructing a Jacobi matrix-vector product linear equation set refers to deforming a nonlinear equation set according to a form of a non-precise Newton equation, and differentiating the Jacobi matrix-vector product to form a linear equation set so as to solve the Krylov subspace iteration. The non-exact newton equation is shown below:
wherein F (x) k ) Is the value of the k iteration function, F' (x) k ) Is the Jacobi matrix value of the kth iteration,is the iteration step length, eta of the solution k Is a mandatory item. However, since Jacobi matrix solution is difficult, and Jacobi matrix and iteration step length appear in the form of matrix vector product in the inaccurate newton equation, the JFNK method adopts the differential approximation process as follows:
where ε is a small constant. Therefore, the complex inaccurate Newton equation is converted into a linear equation set, and the equation set can be effectively solved by the Krylov subspace method in the next step.
Step S42: the Krylov subspace iteratively solves a linear system of equations. In the JFNK solving process, the Krylov subspace iteration method is an inner loop algorithm for JFNK iteration solving and is used for solving a large linear equation set. The application can stably and efficiently solve the iteration step length by using the pretreatment matrix of the step 3 and combining the Krylov subspace iteration method. The left preprocessing matrix is recorded as M, and the inaccurate Newton equation after left preprocessing is:
in one iteration step, except for the iteration stepOther numbers are known in addition to the unknowns. The calculation of the iteration step can be completed at a higher convergence rate by using the Krylov subspace iteration method.
Step S5: judging the convergence of the JFNK solution and adjusting the simulation step length comprises the following steps:
and (5) judging the convergence of the JFNK solution. In the JFNK solution process, if the preset iteration number (for example, in a possible embodiment technical solution, the iteration number may be set to 1 thousand times) does not converge, it is determined that the equation solution does not converge. When the equation calculation is not converged, dividing the current simulation time step by 2, updating the time step value in the memory, and re-executing the 3 rd step (dynamically updating the preprocessing matrix and the residual equation set) to update the preprocessing matrix and the residual equation set. If the equation calculation is converged, the physical field parameter calculation at the simulation moment is considered to be completed, and the next step is performed.
Step S6: judging the simulation ending time and adjusting the corresponding simulation process, which can specifically include:
judging the simulation ending time: comparing the current simulation time with the required simulation time, if the required simulation time is not reached, calculating a simulation step length according to the Brownian number, and executing the step 2 (determining the composition form of the preprocessing matrix and the residual equation set). If the required simulation time is reached, the program is terminated.
In the technical scheme of the application, when the JFNK method is used for solving the process of the large-scale nuclear thermal coupling equation set, physical quantities such as a neutron field, a temperature field, a pressure field, a flow velocity field and the like are updated simultaneously in each non-precise Newton iteration step, and compared with the OS method and the Picard method for separately solving the physical fields, the method has higher nuclear thermal coupling calculation precision. Compared with the first-order convergence speed of the OS method and the Picard method, the JFNK method adopted by the application has the second-order convergence speed and has higher calculation speed. In addition, the method dynamically adjusts the corresponding equation set according to the phase states of the discrete grids, compared with modeling by using the two-phase equations without distinguishing the phase states of each grid, the method has fewer equations and smaller calculated quantity, and can avoid the pathological problems generated when the two-phase equations calculate the single-phase physical field.
Those of ordinary skill in the art will appreciate that: the drawing is a schematic diagram of one embodiment and the modules or flows in the drawing are not necessarily required to practice the application.
Those of ordinary skill in the art will appreciate that: the modules in the apparatus of the embodiments may be distributed in the apparatus of the embodiments according to the description of the embodiments, or may be located in one or more apparatuses different from the present embodiments with corresponding changes. The modules of the above embodiments may be combined into one module, or may be further split into a plurality of sub-modules.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application.
Claims (5)
1. The calculation method of the pressurized water reactor nuclear thermal coupling is characterized by comprising the following steps:
step S1, establishing a neutron diffusion equation set and a thermal hydraulic equation set of a pressurized water reactor core to be analyzed, and coupling the neutron diffusion equation set and the thermal hydraulic equation set to obtain a nuclear thermal coupling equation set; discretizing the neutron diffusion equation set by using an expansion joint block method to obtain a first grid set sum, and discretizing the thermal hydraulic equation set by using a sub-channel method to obtain a second grid set sum; establishing a mapping relation between the first grid set and the second grid set; the first grid set and the second grid set are obtained based on the same grid division mode of the pressurized water reactor core;
initializing parameters of a physical field of the reactor core according to boundary conditions and initial conditions of the physical field of the pressurized water reactor core, and initializing physical quantities including a transport section, a scattering section, an absorption section, a fission section, a neutron production section and other reaction sections by using a few-group section library;
the initial time step is calculated according to the following formula:
wherein the symbol Δt represents the maximum time step allowed; symbol Deltax i Representing the cell grid size in m; symbol U i Representing the maximum speed in the cell grid in m/s; the symbol η represents an empirical coefficient greater than 0;
step S2, dynamically adjusting the format of the preprocessing matrix and the residual equation set, and specifically comprising the following steps:
s21, reading each physical parameter at the previous moment relative to the moment to be analyzed, calculating a process parameter, and storing the process parameter into a computer memory;
step S22, judging the phase states of each grid in the first grid set and the second grid set, and for any first grid in the first grid set, if any first grid is a liquid phase, degrading a two-phase residual equation set corresponding to the grid into a liquid-phase residual equation set, and deleting vapor phase physical quantities in corresponding vectors to be solved; if any one of the first grids is a vapor phase, degrading a two-phase residual equation set corresponding to the grid into a vapor phase residual equation set, and deleting liquid phase physical quantity in a corresponding vector to be solved; if the first arbitrary grid is two phases, the two-phase residual equation set and the vector to be solved are unchanged; traversing phase parameters of all grids in the first grid set and the second grid set, counting the number of equations to be solved and physical quantities to be solved, and determining the scale and the generation form of a corresponding preprocessing matrix and residual equation set;
step S3, dynamically updating a preprocessing matrix and a residual equation set, wherein the method specifically comprises the following steps:
step S31, reading all physical parameters and process parameters of the previous moment from a memory;
step S32, judging the phase states of each grid in the first grid set and the second grid set, for a second arbitrary grid in the first grid set and the second grid set, if the second arbitrary grid is two-phase, filling a residual equation set and a vector to be solved of the grid based on a two-phase physical parameter database, if the second arbitrary grid is liquid phase, filling the residual equation set and the vector to be solved of the grid based on the liquid phase physical parameter database, if the second arbitrary grid is vapor phase, filling the residual equation set and the vector to be solved of the grid based on the vapor phase physical parameter database until the residual equation set and the vector to be solved are completed;
s4, solving a nuclear thermal coupling residual equation set by combining JFNK of a pretreatment matrix;
s5, judging the convergence of JFNK solution and adjusting the simulation step length;
and S6, judging whether the simulation process is finished.
2. The method for calculating nuclear thermal coupling of pressurized water reactor according to claim 1, wherein if the second arbitrary grid is two-phase, filling out a residual equation set and a vector to be solved of the grid based on a two-phase physical parameter database, specifically comprising:
based on the physical parameters including neutron flux density, pressure, temperature, flow rate and section gas content of the two phases at the previous moment read from the memory, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, heat exchange coefficient of the two phases, wall thermal power and wall resistance coefficient are calculated.
3. The method for calculating nuclear thermal coupling of pressurized water reactor according to claim 1, wherein if the second arbitrary grid is a liquid phase, filling out a residual equation set and a vector to be solved of the grid based on a liquid phase physical parameter database, specifically comprising:
based on the physical parameters including neutron flux density, liquid phase pressure, temperature and flow velocity read from the memory at the previous moment, process parameters including neutron flux density, macroscopic reaction section, total heat power density, liquid phase heat exchange coefficient, wall heat power and wall resistance coefficient are calculated.
4. The method for calculating nuclear thermal coupling of pressurized water reactor according to claim 1, wherein if said second arbitrary grid is a vapor phase, filling out a residual equation set and a vector to be solved of the grid based on a vapor phase physical parameter database, specifically comprising:
based on the physical parameters including neutron flux density, vapor phase pressure, temperature and flow rate read from the memory at the previous time, process parameters including neutron flux density, macroscopic reaction section, total thermal power density, vapor phase heat exchange coefficient, wall thermal power and wall resistance coefficient are calculated.
5. The method of claim 1, wherein when the phase is two phases, the set of nuclear thermal coupling equations is:
x＝[Φ,C,Q,P,α g ,u g ,u l ,w g ,w l ,h g ,h l ] T
wherein f Φ Representing a neutron flux residual equation set; f (f) C Representing a delayed neutron concentration residual equation set; f (f) Q Representing a system of residual equations of the fracture energy; f (f) P Representing a set of vapor phase mass residual equations;representing a liquid phase mass residual equation set; />Representing a set of vapor phase axial momentum residual equations; />Representing a liquid phase axial momentum residual equation set; />Representing a set of vapor phase lateral momentum residual equations; />Representing a liquid phase lateral momentum residual equation set; />Representing a set of vapor phase energy residual equations; />Representing a liquid phase energy residual equation set; the superscript n+1 is the variable value of the current time step, and the superscript n is the variable value of the previous time step; Δt is the time step in s; phi is neutron flux density in cm -2 s -1 The method comprises the steps of carrying out a first treatment on the surface of the v is neutron velocity in cm/s; c is the density of the delayed neutron precursor nuclei in cm -3 The method comprises the steps of carrying out a first treatment on the surface of the J is neutron flux density in cm -2 s -1 ；a 1 、a 2 、a 3 、a 4 Is the correlation coefficient of the expansion block method; lambda (lambda) d Is the decay constant of the delayed neutron precursor nucleus, and has the unit of t -1 ；Σ f Is a fissile section in cm -1 ；β、k eff The neutron fraction and the effective multiplication factor are delayed respectively; e (E) f Is energy generated by single fission, and the unit is J; q is fission generating energy, and the unit is W; v is the volume of the mesh in m 3 ；A u 、A w Flow areas orthogonal to the axial and transverse velocities, respectively, in m 2 ；ρ g 、ρ l The density of the vapor phase and the liquid phase, respectively, in kg/m 3 ；α g 、α l The cross section steam content and the cross section liquid content are respectively; h is a g 、h l Specific enthalpy of vapor phase and liquid phase, respectively, in kJ/kg; u (u) g 、u l The axial flow rates of the vapor phase and the liquid phase are respectively expressed in m/s; w (w) g 、w l The lateral flow rates, m/s, of the vapor and liquid phases, respectively; Γ is the phase change mass flow in kg/s of the liquid phase vaporized into the vapor phase; p (P) J 、P J+1 The pressures of the axially upstream and downstream grids, respectively, in Pa; p (P) ii 、P jj The pressures of the transverse upstream and downstream grids are Pa; τ wg,u 、τ wl,u Wall resistance in kg.m/s for the axial vapor and liquid phases, respectively 2 ；τ wg,w 、τ wl,w Wall drag in kg.m/s for the transverse vapor and liquid phases, respectively 2 ；τ gl Is the resistance of the vapor phase and the liquid phase, and the unit is kg.m/s 2 ；q g 、q l The total heat transferred to the vapor phase and the liquid phase in the grid is W; n is n j Representing the total number of adjacent grids in the axial direction; n is n gap Representing the total number of adjacent grids in the transverse direction.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310486446.9A CN116579205A (en) | 2023-04-28 | 2023-04-28 | Calculation method for pressurized water reactor nuclear thermal coupling |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310486446.9A CN116579205A (en) | 2023-04-28 | 2023-04-28 | Calculation method for pressurized water reactor nuclear thermal coupling |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116579205A true CN116579205A (en) | 2023-08-11 |
Family
ID=87535155
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310486446.9A Pending CN116579205A (en) | 2023-04-28 | 2023-04-28 | Calculation method for pressurized water reactor nuclear thermal coupling |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116579205A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117473873A (en) * | 2023-11-13 | 2024-01-30 | 上海交通大学 | Nuclear thermal coupling realization method based on deep M & Mnet neural network |
-
2023
- 2023-04-28 CN CN202310486446.9A patent/CN116579205A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117473873A (en) * | 2023-11-13 | 2024-01-30 | 上海交通大学 | Nuclear thermal coupling realization method based on deep M & Mnet neural network |
| CN117473873B (en) * | 2023-11-13 | 2024-04-26 | 上海交通大学 | Nuclear thermal coupling realization method based on DeepM & Mnet neural network |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107066745B (en) | Method for obtaining three-dimensional neutron flux density distribution in fast neutron reactor core transient process | |
| CN112906271B (en) | Reactor transient physical thermal full-coupling fine numerical simulation method and system | |
| Zhang et al. | An assessment of coupling algorithms in HTR simulator TINTE | |
| CN105653869A (en) | Three-dimensional transient performance analysis method for supercritical water reactor core | |
| CN116579205A (en) | Calculation method for pressurized water reactor nuclear thermal coupling | |
| CN112906272B (en) | Reactor steady-state physical thermal full-coupling fine numerical simulation method and system | |
| Valtavirta et al. | Coupled neutronics–fuel behavior calculations in steady state using the Serpent 2 Monte Carlo code | |
| CN114444413A (en) | Sub-channel-level three-dimensional thermal hydraulic analysis method for plate-shaped fuel reactor core | |
| CN112052579A (en) | Floating grid-based nuclear-thermal-force multi-physical coupling calculation method | |
| Yu et al. | Fuel performance analysis of BEAVRS benchmark Cycle 1 depletion with MCS/FRAPCON coupled system | |
| Yoon et al. | A multiscale and multiphysics PWR safety analysis at a subchannel scale | |
| Ma et al. | A novel analytical unified energy flow calculation method for integrated energy systems based on holomorphic embedding | |
| Park et al. | BEAVRS benchmark analyses by DeCART stand-alone calculations and comparison with DeCART/MATRA multi-physics coupling calculations | |
| García et al. | Serpent2-SUBCHANFLOW pin-by-pin modelling capabilities for VVER geometries | |
| Nizet et al. | Optimal control applied to air conditioning in buildings | |
| Kang et al. | Investigation on the nonintrusive multi-fidelity reduced-order modeling for PWR rod bundles | |
| Yue et al. | Coupled neutronics, thermal-hydraulics, and fuel performance analysis of dispersion plate-type fuel assembly in a cohesive way | |
| CN116090260A (en) | System simulation method for full coupling of reactor | |
| CN110705184B (en) | Virtual volume momentum source method for fine numerical solution of reactor core | |
| Alsayyari et al. | Analysis of the Molten Salt Fast Reactor using reduced-order models | |
| CN114169203B (en) | Two-phase flow total hidden numerical method for transient safety analysis of nuclear power plant | |
| Hancox et al. | Analysis of transient flow boiling: Application of the method of characteristics | |
| Ellis et al. | Progress in the development of an implicit steady state solution in the coupled code TRACE/PARCS | |
| Bullerwell | A Multiphysics Coupling Scheme Between OpenMC and OpenFOAM for High-Fidelity, Flexible Multi-Physics Analysis of Nuclear Reactors | |
| Zhang et al. | Calculation of two-fluid subchannels model of pressurized water reactor: Picard Krylov method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |