Multi-scale coupling determination method and device for deposition process of dirt on surface of fuel rod in pressurized water reactor

Abstract

The invention belongs to the technical field of nuclear power, and particularly relates to a multi-scale coupling determination method and device for the deposition process of dirt on the surface of a fuel rod in a pressurized water reactor. According to the method, a multi-scale coupling solution scheme is adopted, fluid turbulence energy and temperature distribution obtained through macro-scale solution are used for solving a sedimentary layer internal temperature and pressure control equation on the micro-mesoscale, and the deposition rate is obtained; the required material input parameters are less and can be adjusted in real time along with the operation state of the pressurized water reactor; besides, parameters such as surface temperature, pressure and the like of the sedimentary layer obtained by micro-mesoscale solution can be used as boundary conditions to solve a macroscopic flow equation, so that a bidirectional coupling effect is realized, the application range of the method is expanded, and the calculation accuracy is improved. The parameter setting of the method disclosed by the invention can adopt a physical property change function of the material along with the change of temperature, pressure and the like, so that the universality and practicability of a program are improved.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear power technology, and in particular relates to a multi-scale coupling determination method and device for a fouling deposition process on a fuel rod surface in a pressurized water reactor. Background Art

[0002] In the related art, there are generally two methods for analyzing the fouling deposition process on the surface of fuel rods in pressurized water reactors: 1. Using CFD (computational fluid dynamics) macroscopic simulation, such as using OpenFOAM, Ansys Fluent and other models to solve the flow and thermal state on the surface of the fuel rods; 2. Using micro-mesoscale multi-physics field coupling codes to solve, such as using BOA, MAMBA, etc.; Among them, the CFD method is good at dealing with larger-scale problems, and according to actual detection, the thickness of the fouling deposition layer on the surface of the fuel rod is in the micron level. At this time, it is difficult to use the macro CFD method to deal with the fouling deposition layer; in contrast, the use of micro-mesoscale multi-physics field coupling codes can reflect and analyze the deposition process of the fouling deposition layer from the principle level, with a faster calculation speed and the ability to change the simulation conditions in real time with the actual operating status of the pressurized water reactor. It is an efficient means of safety assessment. However, when analyzing the fouling deposition process, the existing micro- and mesoscale multi-physics field coupling codes mostly use empirical values ​​for the material properties of sediments, coolants, etc., which makes their application scope small and cannot be flexibly applied to specific operating scenarios. At the same time, commonly used codes (such as BOA) do not consider the erosion of the sediment layer caused by coolant turbulence, making the analysis and prediction results inaccurate. Summary of the invention

[0003] In order to overcome the problems existing in the related art, a multi-scale coupling determination method and device for the fouling deposition process on the surface of fuel rods in a pressurized water reactor are provided.

[0004] According to one aspect of an embodiment of the present disclosure, a multi-scale coupling determination method for a fouling deposition process on a fuel rod surface in a pressurized water reactor is provided, the method comprising:

[0005] Step 1, determine the length of the fuel rod according to the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscopic scale deposition layer area, set initial boundary conditions and initial states, the initial boundary conditions include the inlet coolant temperature, the fuel rod temperature distribution, and the fuel rod power distribution; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness on the surface of the fuel rod;

[0006] Step 2: In each time step, the fuel rod assembly is modeled to determine the axial distribution of the coolant turbulent kinetic energy and the coolant temperature around the fuel rod;

[0007] Step 3, numerically solving the temperature control equation and the pressure control equation in the sediment layer to obtain the temperature field and pressure field inside the dirt sediment layer;

[0008] Step 4, determining the nucleate boiling heat in the deposits on the surface of the fuel rod according to the temperature field and pressure field inside the fouling deposit layer obtained by solving step 3;

[0009] Step 5: For each time step, the deposition rate equation of the deposits in the time step is used to calculate the deposition rate of the deposits on the surface of the fuel rod in the time step, so as to obtain the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows:

[0010]

[0011] In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUD is the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m; where φ p The calculation method is as follows:

[0012]

[0013] In the formula, A cell To calculate the area of ​​the grid unit, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p is the concentration of dirt particles in the coolant, unit: ppb;

[0014] Step 6, by repeating steps 2 to 5 in each iterative time step, the thickness growth rate in the time step is obtained and the thickness of the deposition layer is updated until the required calculation time span is reached.

[0015] In a possible implementation, in step 2, the coolant region in the fuel rod and its unit is modeled and the flow control equation and the temperature control equation are solved to determine the turbulent kinetic energy of the fuel rod and its unit and the axial distribution of the coolant temperature; the positioning grid on the fuel rod is modeled, and the mass conservation equation, momentum conservation equation and energy conservation equation for the control rod coolant flow and the coolant temperature are numerically solved to obtain the turbulent kinetic energy and the axial distribution of the temperature of the coolant around the fuel rod.

[0016] In a possible implementation, in step 3, the temperature control equation is as follows:

[0017]

[0018] In the formula, is the equivalent thermal conductivity of the dirt deposits, unit: W / m·K; is the equivalent volume heat capacity of the dirt deposits, unit: J / m 3 ·K; T is temperature, unit: K; τ is the tortuosity of the dirt deposit; κ is the permeability of the dirt deposit; μ w is the dynamic viscosity of the coolant, unit: Pa·s; ε is the porosity; P is the pressure, unit: Pa; r c is the radius of the chimney in the core boiling structure inside the sediment, unit: m; n c The chimney density of the core boiling structure inside the sediment, unit: # / m 2 ;h e,chim is the evaporation heat transfer coefficient of the chimney surface in the core-boiler structure, unit: W / m 2 ·K;T sat is the coolant saturation temperature, unit: K;

[0019] The first boundary condition of the temperature control equation is as follows:

[0020]

[0021] The second boundary condition of the temperature control equation is as follows:

[0022]

[0023] In the formula, q ′ c ′ lad is the heat flux on the fuel rod, unit: W / m 2 ; F R is the Reynolds coefficient; h c is the convection heat transfer coefficient of the sediment layer surface, unit: W / m 2 ·K;T b The coolant temperature determined in step 2, unit: K; Sfc S sub is the boiling factor; h e,surf is the evaporation heat coefficient of the deposition layer surface, unit: W / m 2 K;

[0024] The pressure control equation inside the sediment layer is as follows:

[0025]

[0026] In the formula, h fg is the vaporization enthalpy of the coolant, unit: J / mol; ρ w is the density of the coolant, unit: kg / m 3 ; The boundary conditions of the pressure control equation are as follows:

[0027]

[0028] P=P B

[0029] Where P B is the coolant pressure, unit: Pa. When solving the pressure control equation, the temperature distribution in the deposition layer obtained by solving the temperature control equation must be used. The steady-state solution of the pressure control equation is also used to solve the temperature equation in the next time step.

[0030] In one possible implementation, in step 3, the temperature control equation and the pressure control equation are discretized using the finite difference method, the grid is radially divided inside the deposition layer for one-dimensional solution, and different difference formats are used according to the direction of the pressure gradient inside the deposition layer: when the capillary flow direction is from the coolant region to the inside of the deposition layer, the forward difference format is used for the convection term of the control equation; when the capillary flow direction is from the deposition layer to the coolant region, the backward difference format is used for the convection term of the control equation.

[0031] According to another aspect of an embodiment of the present disclosure, a multi-scale coupling determination device for a fouling deposition process on a fuel rod surface in a pressurized water reactor is provided, the device comprising:

[0032] The first determination module is used to determine the length of the fuel rod according to the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscopic scale deposition layer area, and set initial boundary conditions and initial states. The initial boundary conditions include the inlet coolant temperature, the fuel rod temperature distribution, and the fuel rod power distribution; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness on the surface of the fuel rod;

[0033] The second determination module is used to model the fuel rod assembly in each time step and determine the axial distribution of the turbulent kinetic energy and the coolant temperature of the coolant around the fuel rod;

[0034] The third determination module is used to numerically solve the temperature control equation and the pressure control equation in the sediment layer to obtain the temperature field and the pressure field inside the dirt sediment layer;

[0035] A fourth determination module is used to determine the nucleate boiling heat in the fuel rod surface deposits according to the temperature field and pressure field inside the fouling deposition layer solved by the third determination module;

[0036] The fifth determination module is used to calculate the deposition rate of the deposits on the surface of the fuel rod in each time step by using the deposition rate equation of the deposits in the time step, so as to obtain the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows:

[0037]

[0038] In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUD is the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m; where φ p The calculation method is as follows:

[0039]

[0040] In the formula, A cell To calculate the area of ​​the grid unit, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p is the concentration of dirt particles in the coolant, unit: ppb;

[0041] The sixth determination module is used to obtain the thickness growth rate in each iterative time step and update the thickness of the deposition layer by repeating the second determination module to the fifth determination module in each iterative time step until the required calculation time span is reached.

[0042] According to another aspect of an embodiment of the present disclosure, a multi-scale coupling determination device for a fouling deposition process on a fuel rod surface in a pressurized water reactor is provided, the device comprising:

[0043] processor;

[0044] a memory for storing processor-executable instructions;

[0045] Wherein, the processor is configured to execute the above method.

[0046] According to another aspect of an embodiment of the present disclosure, a non-volatile computer-readable storage medium is provided, on which computer program instructions are stored, and the computer program instructions implement the above method when executed by a processor.

[0047] The beneficial effects of the present disclosure are: in view of the defects that the existing micro-mesoscale methods mostly use empirical formulas, have a small application scope, and cannot accurately consider the influence of the coolant turbulence effect on the fouling deposition process, the present disclosure method adopts a multi-scale coupling solution scheme, and uses the fluid turbulent kinetic energy and temperature distribution obtained by macroscopic scale solution to solve the temperature and pressure control equations inside the micro-mesoscale deposition layer, and obtain the deposition rate; the required material input parameters are relatively few, and can be adjusted in real time with the operating state of the pressurized water reactor; in addition, the surface temperature, pressure and other parameters of the deposition layer obtained by micro-mesoscale solution can be used as boundary conditions to solve the macroscopic flow equation to achieve a two-way coupling effect, which expands the scope of application of the present disclosure and improves the accuracy of the calculation. The parameter settings of the present disclosure method can all use the physical property change function of the material with temperature, pressure, etc., which improves the versatility and practicality of the program. A simulation method for the distribution of fouling deposition thickness on the surface of fuel rods in pressurized water reactors is provided, so as to be used for subsequent element enrichment analysis and prediction of fouling-induced axial power offset. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a flow chart of a multi-scale coupling determination method for a fouling deposition process on a fuel rod surface in a pressurized water reactor shown in an embodiment of the present disclosure.

[0049] Figure 2 It is a schematic diagram of grid division in a multi-scale coupling method for a fouling deposition process on a fuel rod surface in a pressurized water reactor shown in an embodiment of the present disclosure.

[0050] Figure 3 It is a block diagram of a multi-scale coupling determination device for a fouling deposition process on a fuel rod surface in a pressurized water reactor shown in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0051] The present disclosure is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0052] Unless otherwise defined, the technical and scientific terms used in the present disclosure have the same meanings as those generally understood by those skilled in the art to which the present disclosure belongs; the terms used in the present disclosure are only for the purpose of describing specific embodiments and are not intended to limit the present disclosure; the term "including" and any variations thereof in the present disclosure are intended to cover non-exclusive inclusions. Obviously, the embodiments described in the present disclosure are only part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making creative efforts are within the scope of protection of the present disclosure.

[0053] Reference to "embodiments" in this disclosure means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the disclosure. The appearance of the phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0054] Figure 1 This is a flowchart of a multi-scale coupling determination method for a fouling deposition process on a fuel rod surface in a pressurized water reactor shown in an embodiment of the present disclosure. The method can be executed by a terminal device, wherein the terminal device can be a server, a desktop computer, etc. The embodiment of the present disclosure does not limit the type of terminal device. Figure 1 As shown, the method includes:

[0055] Step 1: Determine the length of the fuel rods according to the actual operating conditions of the pressurized water reactor, and Figure 2 As shown, the micro-mesoscopic scale deposition layer area is divided into axial and radial grids, and the initial boundary conditions and initial states are set. The initial boundary conditions include the inlet coolant temperature, fuel rod temperature distribution, and fuel rod power distribution in the initial state; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness initialized on the fuel rod surface, wherein the preset thickness can be, for example, 1 micron, and the applicable preset thickness value can be selected according to actual needs.

[0056] Step 2, in each time step, the fuel rod assembly is modeled to determine the axial distribution of the turbulent kinetic energy and the coolant temperature of the coolant around the fuel rod; in step 2, the coolant area in the fuel rod and its unit is modeled and the flow control equation and the temperature control equation are solved to determine the axial distribution of the turbulent kinetic energy and the coolant temperature of the fuel rod and its unit; the positioning grid on the fuel rod is modeled, and the mass conservation equation, momentum conservation equation and energy conservation equation for the control rod coolant flow and the coolant temperature are numerically solved to obtain the turbulent kinetic energy and the axial distribution of the temperature of the coolant around the fuel rod. In step 2, the finite volume method can be used for solution, or other applicable methods can be used for solution.

[0057] Step 3: Numerically solve the temperature control equation and pressure control equation in the sediment layer to obtain the heat of nucleate boiling in the sediment layer, the temperature field and pressure field inside the dirt sediment layer; the temperature control equation is shown in the following equation, which takes into account the porous characteristics of the dirt, convective heat transfer and temperature control of boiling heat transfer.

[0058]

[0059] In the formula, is the equivalent thermal conductivity of the dirt deposits, unit: W / m·K; is the equivalent volume heat capacity of the dirt deposits, unit: J / m 3 ·K; T is temperature, unit: K; τ is the tortuosity of the dirt deposit; κ is the permeability of the dirt deposit; μ w is the dynamic viscosity of the coolant, unit: Pa·s; ε is the porosity; P is the pressure, unit: Pa; r c is the radius of the chimney in the core boiling structure inside the sediment, unit: m; n c The chimney density of the core boiling structure inside the sediment, unit: # / m 2 ;h e,chim is the evaporation heat transfer coefficient of the chimney surface in the core-boiler structure, unit: W / m 2 ·K;T sat is the coolant saturation temperature, unit: K.

[0060] The first boundary condition of the temperature control equation is as follows:

[0061]

[0062] The second boundary condition of the temperature control equation is as follows:

[0063]

[0064] In the formula, q ′ c ′lad is the heat flux on the fuel rod, unit: W / m 2 ; F R is the Reynolds coefficient; h c is the convection heat transfer coefficient of the sediment layer surface, unit: W / m 2 ·K;T b is the coolant temperature, unit: K; S fc S sub is the boiling factor; h e,surf is the evaporation heat coefficient of the deposition layer surface, unit: W / m 2 ·K.

[0065] The first boundary condition acts on the surface of the fuel rod, taking into account the heat input from the fuel rod; the second boundary condition acts on the surface of the deposition layer and the coolant. b The first and second boundary conditions take into account the convective heat transfer and evaporative heat transfer between the surface of the deposit layer and the coolant, which are derived from the coolant temperature distribution determined at the macroscopic scale in step 2. The temperature distribution of the deposit layer obtained by the temperature equation in the current time step will be used to solve the energy equation at the macroscopic scale in the next time step.

[0066] The pressure control equation inside the sediment layer is as follows:

[0067]

[0068] In the formula, h fg is the vaporization enthalpy of the coolant, unit: J / mol; ρ w is the density of the coolant, unit: kg / m 3 .

[0069] In the deposition layer, Darcy's law is considered to determine the capillary flow driven by the internal pressure of the deposition, and the mass loss caused by the evaporation of the coolant due to nucleate boiling inside the deposition is also considered. The boundary conditions of the pressure control equation are shown as follows:

[0070]

[0071] P=P B

[0072] Where P B is the coolant pressure, unit: Pa. When solving the pressure control equation, the temperature distribution in the deposition layer obtained by solving the temperature control equation must be used. The steady-state solution of the pressure control equation is also used to solve the temperature equation in the next time step. The temperature control equation and the pressure control equation in the deposition layer disclosed in the present invention comprehensively consider the diffusion heat transfer in the sediment, the convection heat transfer brought by the capillary flow, and the evaporation heat transfer process brought by the nucleate boiling that may occur in the core boiling structure inside the deposition layer.

[0073] In a possible implementation, the temperature control equation and the pressure control equation may be discretized by using a finite difference method, for example: Figure 2 As shown in the figure, the grid is radially divided inside the deposition layer for one-dimensional solution, and different difference formats are used according to the direction of the pressure gradient inside the deposition layer: when the capillary flow direction is from the coolant area to the inside of the deposition layer, the forward difference format is used for the convection term of the control equation; when the capillary flow direction is from the deposition layer to the coolant area, the backward difference format is used for the convection term of the control equation.

[0074] For example, taking the forward difference format as an example, the temperature discrete equation of the forward difference format is as follows:

[0075] 1T i-1 +[c3(Δx) 2 -2c1-c2P ′ Δx]T i +(c1+c2P ′ Δx)T i+1 =c4(Δx) 2

[0076] The pressure discretization equation in forward difference format is as follows:

[0077] P i-1 -2P i +P i+1 =S P,i

[0078] Where: c4=c3T sat ;P ′ is the pressure gradient at the grid point; (Δx) 2 is the radial grid size;

[0079] like Figure 2 As shown, the fuel rod power boundary conditions and coolant temperature boundary conditions in each layer of grid in the axial direction are determined, where the fuel rod power boundary conditions are given by the actual pressurized water reactor operating state, and the coolant temperature is obtained by solving the energy conservation equation in step 2; under the working conditions where the accuracy requirement is not high but the determination speed requirement is high, the coolant temperature can also be indirectly given by the energy conservation method:

[0080]

[0081] Where: ΔT is the coolant temperature rise, unit: K; q is the heat flux per unit area of ​​the fuel rod, unit: W / m 2 ;c p is the specific heat capacity of the coolant, unit: J / kg·K; is the coolant flow rate, unit: m 3 / s.

[0082] Step 4, according to the temperature field and pressure field inside the fouling deposit layer obtained by solving step 3, the nucleate boiling heat in the deposit on the surface of the fuel rod is determined by the following formula;

[0083] q surf =S fc S sub h e,surf (T n -T sat )·2πr c dx

[0084]

[0085] Step 5: For each time step, the deposition rate equation of the deposits in the time step is used to determine the deposition rate of the deposits on the surface of the fuel rod in the time step, thereby obtaining the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows:

[0086]

[0087] In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUD is the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m.

[0088] Among them, φ p The method for determining is as follows:

[0089]

[0090] In the formula, A cell To determine the area of ​​the grid cell, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p It is the concentration of dirt particles in the coolant, unit: ppb.

[0091] In step 5, in each time step, the growth rate of the deposit thickness is determined based on the temperature field and pressure field inside the fouling deposit layer obtained in step 3, the nucleate boiling heat obtained in step 4, and the parameters such as the turbulent kinetic energy intensity of the coolant determined in step 2.

[0092] Step 6, by repeating steps 2 to 5 in each iterative time step, the thickness growth rate in the time step is obtained and the thickness of the deposited layer is updated until the required determined time span is reached.

[0093] According to another aspect of an embodiment of the present disclosure, a multi-scale coupling determination device for a fouling deposition process on a fuel rod surface in a pressurized water reactor is provided, the device comprising:

[0094] The first determination module is used to determine the length of the fuel rod according to the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscopic scale deposition layer area, and set initial boundary conditions and initial states. The initial boundary conditions include the inlet coolant temperature, the fuel rod temperature distribution, and the fuel rod power distribution; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness on the surface of the fuel rod;

[0095] The second determination module is used to model the fuel rod assembly in each time step and determine the axial distribution of the turbulent kinetic energy and the coolant temperature of the coolant around the fuel rod;

[0096] The third determination module is used to numerically solve the temperature control equation and the pressure control equation in the sediment layer to obtain the temperature field and the pressure field inside the dirt sediment layer;

[0097] A fourth determination module is used to determine the nucleate boiling heat in the fuel rod surface deposits according to the temperature field and pressure field inside the fouling deposition layer solved by the third determination module;

[0098] The fifth determination module is used to calculate the deposition rate of the deposits on the surface of the fuel rod in each time step by using the deposition rate equation of the deposits in the time step, so as to obtain the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows:

[0099]

[0100] In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUDis the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m; where φ p The calculation method is as follows:

[0101]

[0102] In the formula, A cell To calculate the area of ​​the grid unit, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p is the concentration of dirt particles in the coolant, unit: ppb;

[0103] The sixth determination module is used to obtain the thickness growth rate in each iterative time step and update the thickness of the deposition layer by repeating the second determination module to the fifth determination module in each iterative time step until the required calculation time span is reached.

[0104] The description of the above-mentioned device has been explained in detail in the description of the above-mentioned method, and will not be repeated here.

[0105] Figure 3 1900 is a block diagram of a multi-scale coupling device for a fouling deposition process on a fuel rod surface in a pressurized water reactor shown in an embodiment of the present disclosure. For example, the device 1900 may be provided as a server. Figure 3 , the apparatus 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions, such as an application, that can be executed by the processing component 1922. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute instructions to perform the above method.

[0106] The device 1900 may also include a power supply component 1926 configured to perform power management of the device 1900, a wired or wireless network interface 1950 configured to connect the device 1900 to a network, and an input / output (I / O) interface 1958. The device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server™, MacOS X™, Unix™, Linux™, FreeBSD™, or the like.

[0107] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the device 1900 to perform the above method.

[0108] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0109] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0110] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0111] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0112] Various aspects of the present disclosure are described herein with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to the embodiments of the present disclosure. It should be understood that each box in the flowchart and / or block diagram and the combination of each box in the flowchart and / or block diagram can be implemented by computer-readable program instructions.

[0113] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0114] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0115] The flow chart and block diagram in the accompanying drawings show the possible architecture, function and operation of the system, method and computer program product according to multiple embodiments of the present disclosure. In this regard, each square box in the flow chart or block diagram can represent a part of a module, program segment or instruction, and a part of the module, program segment or instruction includes one or more executable instructions for realizing the specified logical function. In some alternative implementations, the function marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two continuous square boxes can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or action, or can be implemented with a combination of special hardware and computer instructions.

[0116] The embodiments of the present disclosure have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or improvements to the technology in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A multi-scale coupled determination method for the fouling deposition process on the surface of fuel rods in a pressurized water reactor, characterized in that: The method comprises: Step 1, determine the length of the fuel rod according to the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscopic scale deposition layer area, set initial boundary conditions and initial states, the initial boundary conditions include the inlet coolant temperature, the fuel rod temperature distribution, and the fuel rod power distribution; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness on the surface of the fuel rod; Step 2: In each time step, the fuel rod assembly is modeled to determine the axial distribution of the coolant turbulent kinetic energy and the coolant temperature around the fuel rod; Step 3, numerically solving the temperature control equation and the pressure control equation in the sediment layer to obtain the temperature field and the pressure field inside the dirt sediment layer; Step 4, determining the nucleate boiling heat in the deposits on the surface of the fuel rod according to the temperature field and pressure field inside the fouling deposit layer obtained by solving step 3; Step 5: For each time step, the deposition rate equation of the deposits in the time step is used to calculate the deposition rate of the deposits on the surface of the fuel rod in the time step, so as to obtain the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows: In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUD is the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m; where φ p The calculation method is as follows: In the formula, A cell To calculate the area of ​​the grid unit, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p is the concentration of dirt particles in the coolant, unit: ppb; Step 6, by repeating steps 2 to 5 in each iterative time step, the thickness growth rate in the time step is obtained and the thickness of the deposition layer is updated until the required calculation time span is reached.

2. The method according to claim 1, characterized in that In step 2, the coolant area in the fuel rod and its unit is modeled and the flow control equation and temperature control equation are solved to determine the axial distribution of the turbulent kinetic energy and coolant temperature of the fuel rod and its unit; the positioning grid on the fuel rod is modeled, and the mass conservation equation, momentum conservation equation and energy conservation equation for the control rod coolant flow and coolant temperature are numerically solved to obtain the turbulent kinetic energy and temperature axial distribution of the coolant around the fuel rod.

3. The method according to claim 1, characterized in that In step 3, the temperature control equation is as follows: In the formula, is the equivalent thermal conductivity of the dirt deposits, unit: W / m·K; is the equivalent volume heat capacity of the dirt deposits, unit: J / m 3 ·K; T is temperature, unit: K; τ is the tortuosity of the dirt deposit; κ is the permeability of the dirt deposit; μ w is the dynamic viscosity of the coolant, unit: Pa·s; ε is the porosity; P is the pressure, unit: Pa; r c is the radius of the chimney in the core boiling structure inside the sediment, unit: m; n c The chimney density of the core boiling structure inside the sediment, unit: # / m 2 ; h e,chim is the evaporation heat transfer coefficient of the chimney surface in the core-boiler structure, unit: W / m 2 ·K;T sat is the coolant saturation temperature, unit: K; The first boundary condition of the temperature control equation is as follows: The second boundary condition of the temperature control equation is as follows: In the formula, q ′ c ′ lad is the heat flux on the fuel rod, unit: W / m 2 ; F R is the Reynolds coefficient; h c is the convection heat transfer coefficient of the sediment layer surface, unit: W / m 2 ·K;T b The coolant temperature determined in step 2, unit: K; S fc S sub is the boiling factor; h e,surf is the evaporation heat coefficient of the deposition layer surface, unit: W / m 2 K; The pressure control equation inside the sediment layer is as follows: In the formula, h fg is the vaporization enthalpy of the coolant, unit: J / mol; ρ w is the density of the coolant, unit: kg / m 3 ; The boundary conditions of the pressure control equation are as follows: P=P B Where P B is the coolant pressure, unit: Pa. When solving the pressure control equation, the temperature distribution in the deposition layer obtained by solving the temperature control equation must be used. The steady-state solution of the pressure control equation is also used to solve the temperature equation in the next time step.

4. The method according to claim 1, characterized in that: In step 3, the temperature control equation and the pressure control equation are discretized by the finite difference method, and the grid is radially divided inside the deposition layer for one-dimensional solution. Different difference formats are used according to the direction of the pressure gradient inside the deposition layer: when the capillary flow direction is from the coolant area to the inside of the deposition layer, the forward difference format is used for the convection term of the control equation; when the capillary flow direction is from the deposition layer to the coolant area, the backward difference format is used for the convection term of the control equation.

5. A multi-scale coupled determination device for the fouling deposition process on the surface of fuel rods in a pressurized water reactor, characterized in that: The device comprises: The first determination module is used to determine the length of the fuel rod according to the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscopic scale deposition layer area, and set initial boundary conditions and initial states. The initial boundary conditions include the inlet coolant temperature, the fuel rod temperature distribution, and the fuel rod power distribution; the initial state includes the temperature field and pressure field in each grid and the dirt deposition of the preset thickness on the surface of the fuel rod; The second determination module is used to model the fuel rod assembly in each time step and determine the axial distribution of the turbulent kinetic energy and the coolant temperature of the coolant around the fuel rod; The third determination module is used to numerically solve the temperature control equation and the pressure control equation in the sediment layer to obtain the temperature field and the pressure field inside the dirt sediment layer; A fourth determination module is used to determine the nucleate boiling heat in the fuel rod surface deposits according to the temperature field and pressure field inside the fouling deposition layer solved by the third determination module; The fifth determination module is used to calculate the deposition rate of the deposits on the surface of the fuel rod in each time step by using the deposition rate equation of the deposits in the time step, so as to obtain the deposition thickness of the deposits in the time step; the deposition rate equation is shown as follows: In the formula, is the growth rate of the deposition layer thickness, unit: m / s; η is the adsorption probability of dirt particles in the coolant; φ p is the flux related to nucleate boiling and the turbulent mixing coefficient of the coolant; M p is the molar mass of the dirt particles, unit: kg / mol; ρ CRUD is the average density of the sediment layer, unit: kg / m 3 ; α is the erosion coefficient of the deposit layer related to the turbulent kinetic energy intensity of the coolant; δ CRUD is the thickness of the deposited layer on the fuel rod surface, unit: m; where φ p The calculation method is as follows: In the formula, A cell To calculate the area of ​​the grid unit, unit: m 2 ; A chim.t is the cross-sectional area of ​​the chimney structure, unit: m 2 ;q SNB,chim is the nucleate boiling heat inside the sediment; q SNB,surf is the nucleate boiling heat on the sediment surface; k mp is the turbulent mass transfer coefficient; C p is the concentration of dirt particles in the coolant, unit: ppb; The sixth determination module is used to obtain the thickness growth rate in each iterative time step and update the thickness of the deposition layer by repeating the second determination module to the fifth determination module in each iterative time step until the required calculation time span is reached.

6. A multi-scale coupled determination device for the fouling deposition process on the surface of fuel rods in a pressurized water reactor, characterized in that: The device comprises: processor; a memory for storing processor-executable instructions; The processor is configured to execute the method according to any one of claims 1 to 4.

7. A non-volatile computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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