Multi-scale coupling determination method and device for the fouling deposition process on fuel rod surfaces in pressurized water reactors

Abstract

The present disclosure belongs to the field of nuclear power technology, and specifically relates to a multi-scale coupling determination method and device for the fouling deposition process on the surface of fuel rods in a pressurized water reactor. The method disclosed herein 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 deposition layer at the micro-mesoscopic scale, and obtain the deposition rate; the required material input parameters are relatively few, and can be adjusted in real time with the operating status of the pressurized water reactor; in addition, the surface temperature, pressure and other parameters of the deposition layer obtained by micro-mesoscopic scale solution can be used as boundary conditions to solve the macroscopic flow equation to achieve a two-way coupling effect, thereby expanding the scope of application of the present disclosure and improving the accuracy of the calculation. The parameter settings of the method disclosed herein can all adopt the physical property change function of the material with changes in temperature, pressure, etc., which improves the versatility and practicality of the program.

Description

Technical Field

[0001] The present disclosure belongs to the field of nuclear power technology, and particularly 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 fuel rod surface in a pressurized water reactor: 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 fuel rod surface; 2. Using micro-mesoscale multi-physics field coupling codes for solution, such as 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 fuel rod surface is in the micron level. At this time, it is difficult to use macroscopic CFD methods 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 according to the actual operating status of the pressurized water reactor. It is an efficient safety assessment method. However, when analyzing the fouling deposition process, existing micro- and mesoscale multi-physics field coupling codes mostly use empirical values ​​for the material properties of sediments, coolants, and other materials. This results in a small scope of application and inability to 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, resulting in inaccurate analysis and prediction results. 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 coupled 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 fuel rod length based on the actual operating conditions of the pressurized water reactor, perform axial and radial meshing of the micro- and mesoscale deposition layer, and set initial boundary conditions and initial states. The initial boundary conditions include the inlet coolant temperature, fuel rod temperature distribution, and fuel rod power distribution; the initial state includes the temperature and pressure fields within each grid, and the initialization of a preset thickness of dirt deposits on the fuel rod surface.

[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 coolant temperature around the fuel rod;

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

[0008] Step 4: Determine the nucleate boiling heat in the fuel rod surface deposits based on the temperature field and pressure field inside the fouling deposit layer obtained in Step 3;

[0009] Step 5: For each time step, the deposition rate of the deposit on the fuel rod surface in the time step is calculated using the deposition rate equation of the deposit in the time step, thereby obtaining the deposition thickness of the deposit in the time step; the deposition rate equation is shown as follows:

[0010]

[0011] Where, 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 coolant turbulence mixing coefficient; 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] Where A cell To calculate 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 is the concentration of dirt particles in the coolant, unit: ppb;

[0014] Step 6: Repeat steps 2 to 5 in each iterative time step to obtain the thickness growth rate in the time step and update the deposition layer thickness until the required calculation time span is reached.

[0015] In one possible implementation, in step 2, the coolant region within the fuel rods and their cells is modeled and the flow control equations and temperature control equations are solved to determine the axial distribution of the turbulent kinetic energy and coolant temperature of the fuel rods and their cells; the spacer grid on the fuel rods is modeled, and the mass conservation equations, momentum conservation equations, and energy conservation equations for controlling the flow of coolant around the fuel rods and the coolant temperature are numerically solved to obtain the turbulent kinetic energy and temperature distribution of the coolant around the fuel rods.

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

[0017]

[0018] Where, is the equivalent thermal conductivity of the dirt deposit, 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 is 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] Where 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 is an inhibitory factor; sub is the boiling factor; h e,surf is the surface evaporation heat coefficient of the sediment layer, unit: W / m 2 K;

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

[0025]

[0026] Where 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 coupled determination apparatus for a fouling deposition process on a fuel rod surface in a pressurized water reactor is provided, the apparatus comprising:

[0032] The first determination module is used to determine the length of the fuel rod based on the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscale 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 within each grid, and the initialization of a preset thickness of dirt deposits on the fuel rod surface;

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

[0035] a fourth determination module, configured to determine the nucleate boiling heat in the fuel rod surface deposits based on the temperature field and pressure field inside the fouling deposit layer obtained by solving the third determination module;

[0036] The fifth determination module is configured to calculate, for each time step, the deposition rate of the deposit on the fuel rod surface in the time step using the deposition rate equation for the deposit in the time step, thereby obtaining the deposition thickness of the deposit in the time step; the deposition rate equation is shown as follows:

[0037]

[0038] Where, 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 coolant turbulence mixing coefficient; 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] Where A cell To calculate 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 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 by repeating the second determination module to the fifth determination module in the time step and update the thickness of the deposition layer until the required calculation time span is reached.

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

[0043] processor;

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

[0045] 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. When the computer program instructions are executed by a processor, the above method is implemented.

[0047] The beneficial effects of the present disclosure are as follows: in order to address the defects of existing micro-mesoscale methods that mostly use empirical formulas and have a small scope of application, and cannot accurately consider the influence of coolant turbulence effects on the fouling deposition process, the present disclosure adopts a multi-scale coupling solution scheme, using the fluid turbulent kinetic energy and temperature distribution obtained from the macroscale 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 status of the pressurized water reactor; in addition, the surface temperature, pressure and other parameters of the deposition layer obtained from the micro-mesoscale solution can be used as boundary conditions to solve the macroscopic flow equation to achieve a two-way coupling effect, thereby expanding the scope of application of the present disclosure and improving the accuracy of the calculation. The parameter settings of the present disclosure method can all adopt the physical property change function of the material with changes in 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, which can be used for subsequent element enrichment analysis and prediction of fouling-induced axial power offset. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This 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 This 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 This 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 will be 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 this disclosure have the same meanings as those generally understood by those skilled in the art to which this disclosure belongs; the terms used in this disclosure are only for the purpose of describing specific embodiments and are not intended to limit this disclosure; the term "including" and any variations thereof in this disclosure are intended to cover non-exclusive inclusions. Obviously, the embodiments described in this disclosure are only some of the embodiments of this disclosure, not all of them. Based on the embodiments in this disclosure, all other embodiments obtained by those of ordinary skill in the art without making any creative work are within the scope of protection of this disclosure.

[0053] References to "embodiments" in this disclosure mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the disclosure. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, 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 the fouling deposition process on the 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-mesoscale deposition layer area is divided into axial and radial grids, and 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 within each grid and the dirt deposition of a preset thickness initialized on the fuel rod surface, where the preset thickness can be, for example, 1 micron, and an applicable preset thickness value can be selected according to actual needs.

[0056] Step 2: At each time step, the fuel rod assembly is modeled to determine the axial distribution of the coolant turbulent kinetic energy and coolant temperature around the fuel rods. In step 2, the coolant region within the fuel rods and their cells is modeled and the flow and temperature control equations are solved to determine the axial distribution of the turbulent kinetic energy and coolant temperature within the fuel rods and their cells. The spacer grid on the fuel rods is modeled, and the mass, momentum, and energy conservation equations governing the coolant flow and coolant temperature are numerically solved to obtain the axial distribution of the coolant turbulent kinetic energy and temperature around the fuel rods. The finite volume method or other suitable methods can be used to solve the problem in step 2.

[0057] Step 3: Numerically solve the temperature control equation and pressure control equation within the sediment layer to obtain the heat of nucleate boiling in the sediment layer and the temperature and pressure fields inside the fouling sediment layer. The temperature control equation is shown below. The temperature control equation takes into account the porous characteristics of the fouling, convective heat transfer, and temperature control of boiling heat transfer.

[0058]

[0059] Where, is the equivalent thermal conductivity of the dirt deposit, 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 is 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] Where 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 is an inhibitory factor; sub is the boiling factor; h e,surf is the surface evaporation heat coefficient of the sediment layer, unit: W / m 2 ·K.

[0065] The first boundary condition acts on the fuel rod surface, taking into account the heat input from the fuel rod; the second boundary condition acts on the sediment layer and the coolant surface. The T b The first and second boundary conditions, derived from the coolant temperature distribution determined at the macroscale in step 2, account for convective heat transfer and evaporative heat transfer between the deposit surface and the coolant. The deposit temperature distribution, obtained using the temperature equation in the current time step, is used to solve the energy equation at the macroscale in the next time step.

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

[0067]

[0068] Where 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 used to determine the capillary flow driven by pressure inside the deposition layer, while also considering the mass loss caused by the vaporization of the coolant due to nucleate boiling inside the deposition layer. 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, in Pa. The temperature distribution within the deposition layer, obtained by solving the temperature control equation, is used when solving the pressure control equation. The steady-state solution of the pressure control equation is also used to solve the temperature equation for the next time step. The temperature control equation and pressure control equation within the deposition layer disclosed herein comprehensively consider the diffusion heat transfer within the sediment, the convective heat transfer caused by capillary flow, and the evaporative heat transfer process caused by nucleate boiling that may occur within the core boiling structure within the deposition layer.

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

[0075] c1T 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 the 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 the grid in the axial direction are determined. 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 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: Based on the temperature field and pressure field inside the fouling deposit layer obtained in step 3, the nucleate boiling heat in the deposit on the fuel rod surface is determined using 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 fuel rod surface 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] Where, 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 coolant turbulence mixing coefficient; 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] Where 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, within each time step, the sediment thickness growth rate 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 coolant turbulent kinetic energy intensity and other parameters determined in step 2.

[0092] Step 6: Repeat steps 2 to 5 in each iterative time step to obtain the thickness growth rate in the time step and update the thickness of the deposited layer until the required time span is reached.

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

[0094] The first determination module is used to determine the length of the fuel rod based on the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscale 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 within each grid, and the initialization of a preset thickness of dirt deposits on the fuel rod surface;

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

[0097] a fourth determination module, configured to determine the nucleate boiling heat in the fuel rod surface deposits based on the temperature field and pressure field inside the fouling deposit layer obtained by solving the third determination module;

[0098] The fifth determination module is configured to calculate, for each time step, the deposition rate of the deposit on the fuel rod surface in the time step using the deposition rate equation for the deposit in the time step, thereby obtaining the deposition thickness of the deposit in the time step; the deposition rate equation is shown as follows:

[0099]

[0100] Where, 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 coolant turbulence mixing coefficient; 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] Where A cell To calculate 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 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 by repeating the second determination module to the fifth determination module in the time step and update the thickness of the deposition layer 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 fuel rod surface fouling process in a pressurized water reactor according to an embodiment of the present disclosure. For example, the device 1900 can 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 the instructions to perform the above-described 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 that can be executed by the processing component 1922 of the apparatus 1900 to perform the above-described method.

[0108] The present disclosure may be a system, method and / or 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 can be a tangible device that can hold and store instructions for use by an instruction execution device. A computer-readable storage medium can 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 thereof. More specific examples (a non-exhaustive list) of computer-readable storage media 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 disc 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 thereof. As used herein, a computer-readable storage medium is not to be construed 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 an electrical 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, fiber optic transmission, wireless transmission, 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 to be stored in the computer-readable storage medium in each computing / processing device.

[0111] The computer program instructions for performing the operations of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent 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++, and conventional procedural programming languages ​​such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely 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 entirely 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., utilizing 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 personalized by utilizing the state information of the computer-readable program instructions. 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 flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each block of the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, 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 is generated that implements the functions / actions specified in one or more blocks in the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium, where these instructions cause the computer, programmable data processing device, and / or other device to operate in a specific manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing various aspects of the functions / actions specified in one or more blocks 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 operational 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 blocks in the flowchart and / or block diagram.

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

[0116] While various embodiments of the present disclosure have been described above, the above descriptions are illustrative, non-exhaustive, and not intended to be limiting of the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, their practical applications, or improvements to existing technologies, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A multi-scale coupled determination method for the fouling deposition process on the fuel rod surface in a pressurized water reactor, characterized in that: The method comprises: Step 1: Determine the fuel rod length based on the actual operating conditions of the pressurized water reactor, perform axial and radial meshing of the micro- and mesoscale deposition layer, and set initial boundary conditions and initial states. The initial boundary conditions include the inlet coolant temperature, fuel rod temperature distribution, and fuel rod power distribution; the initial state includes the temperature and pressure fields within each grid, and the initialization of a preset thickness of dirt deposits on the fuel rod surface. Step 2: In each time step, the fuel rod assembly is modeled to determine the axial distribution of the coolant turbulent kinetic energy and coolant temperature around the fuel rod; Step 3, numerically solving the temperature control equation and pressure control equation in the sediment layer to obtain the temperature field and pressure field inside the dirt sediment layer; Step 4: Determine the nucleate boiling heat in the fuel rod surface deposits based on the temperature field and pressure field inside the fouling deposit layer obtained in Step 3; Step 5: For each time step, the deposition rate of the deposit on the fuel rod surface in the time step is calculated using the deposition rate equation of the deposit in the time step, thereby obtaining the deposition thickness of the deposit in the time step; the deposition rate equation is shown as follows: Where, 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 coolant turbulence mixing coefficient; 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: Where A cell To calculate 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 is the concentration of dirt particles in the coolant, unit: ppb; Step 6: Repeat steps 2 to 5 in each iterative time step to obtain the thickness growth rate in the time step and update the deposition layer thickness until the required calculation time span is reached.

2. The method according to claim 1, characterized in that In step 2, the coolant area within the fuel rod and its unit is modeled and the flow control equations and temperature control equations 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 equations, momentum conservation equations, and energy conservation equations for the control rod coolant flow and coolant temperature are numerically solved to obtain the turbulent kinetic energy and axial distribution of the temperature 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: Where, is the equivalent thermal conductivity of the dirt deposit, 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 is 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: Where 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 is an inhibitory factor; sub is the boiling factor; h e,surf is the surface evaporation heat coefficient of the sediment layer, unit: W / m 2 K; The pressure control equation inside the sediment layer is as follows: Where 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, wherein In step 3, the temperature control equation and the pressure control equation are discretized using 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 fuel rod surface 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 based on the actual operating conditions of the pressurized water reactor, perform axial and radial grid division on the micro-mesoscale 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 within each grid, and the initialization of a preset thickness of dirt deposits on the fuel rod surface; The second determination module is used to model the fuel rod assembly in each time step and determine the axial distribution of the coolant turbulent kinetic energy and the coolant temperature 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 pressure field inside the dirt sediment layer; a fourth determination module, configured to determine the nucleate boiling heat in the fuel rod surface deposits based on the temperature field and pressure field inside the fouling deposit layer obtained by solving the third determination module; The fifth determination module is configured to calculate, for each time step, the deposition rate of the deposit on the fuel rod surface in the time step using the deposition rate equation for the deposit in the time step, thereby obtaining the deposition thickness of the deposit in the time step; the deposition rate equation is shown as follows: Where, 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 coolant turbulence mixing coefficient; 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: Where A cell To calculate 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 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 by repeating the second determination module to the fifth determination module in the time step and update the thickness of the deposition layer until the required calculation time span is reached.

6. A multi-scale coupled determination device for the fouling deposition process on the fuel rod surface 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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