Method and device for predicting heat conductivity coefficient of nuclear power plant equipment coating

Abstract

The invention belongs to the technical field of nuclear power, and particularly relates to a nuclear power plant equipment coating heat conductivity coefficient prediction method and device. According to the model building disclosed by the invention, the common defects of pores and macroscopic horizontal cracks in the coating are considered, the coating is used as a tight skeleton, pore and crack three-phase composite system, and after one defect is gradually added into the substrate, the formed system becomes a new substrate in the next step. And repeating the compounding process until the two defects of pores and cracks are added into the system. Therefore, the actual operation state of the thermal barrier coating of the nuclear power equipment can be simulated more vividly. Furthermore, pore shape influence factors and crack shape influence factors corresponding to different porosities and crack rates can be determined through modeling and heat conductivity coefficient simulation calculation, and the actual heat conductivity coefficient of the coating is further predicted. And a theoretical basis is provided for researching the failure behavior of the service thermal barrier coating.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of nuclear power, and particularly relates to a nuclear power plant equipment coating thermal conductivity prediction method and device. BACKGROUND

[0002] The surface of the rotating machinery of a nuclear power plant is coated with a thermal barrier coating (a widely used material is 8% mol yttria (Y2O3) partially stabilized zirconia (ZrO2), referred to as 8YSZ), which will be subjected to the heat, force impact and chemical corrosion of high-temperature gas for a long time in an extremely harsh service environment, and the microstructure thereof will change irreversibly, and in severe cases, the coating will peel off and fail. These irreversible microstructure changes will cause the thermal performance of the coating to degrade, resulting in a decrease in the heat insulation performance of the coating, and thus shortening the service life of the coating, and ultimately leading to damage to the turbine high-temperature blade.

[0003] For many years, research on the internal thermal conductivity of plasma sprayed thermal barrier coatings has mainly focused on the influence of porosity, pore size and shape distribution of the coating on the thermal conductivity of the coating. Still air is a poor conductor of heat, with a thermal conductivity of 0.026 W / (m·K), while the thermal conductivity of zirconia bulk material is 1.8-2.35 W / (m·K), and the introduction of pores will significantly reduce the thermal conductivity of ceramic materials. When heated at high temperatures, some pores and microcracks in the coating come into contact or close, the porosity of the coating decreases, the thermal conductivity increases, and the heat insulation performance decreases.

[0004] Therefore, it is urgent to obtain the local variation law of the thermal conductivity of the coating based on the real microstructure during service, and to explore the optimized coating preparation process and coating structure under specific target conditions. SUMMARY

[0005] To overcome the problems in the related art, a nuclear power plant equipment coating thermal conductivity prediction method and device are provided.

[0006] According to an aspect of an embodiment of the present disclosure, a nuclear power plant equipment coating thermal conductivity prediction method is provided, and the method comprises:

[0007] Step 1: generating a thermal barrier coating model corresponding to different porosities and crack rates;

[0008] Step 2: for each porosity, determining a first thermal conductivity of a thermal barrier coating containing only pores corresponding to the porosity according to formulas three to six, and then determining a pore shape influence factor X corresponding to the porosity from the first thermal conductivity and formula one. p ;

[0009] For each porosity and crack rate, a second thermal conductivity of a thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to formulas three to six, and then the second thermal conductivity and X are used to determine a third thermal conductivity of the thermal barrier coating.p and formula two to determine the crack shape influence factor X c ; thereby obtaining X corresponding to different porosity, crack rate p and X c , establish X p and X c quick query atlas;

[0010] Formula one is used to determine the first effective thermal conductivity k of the digital structure file of the thermal barrier coating containing only pores m+p :

[0011]

[0012] Wherein, X p is the pore shape influence factor, P (pore) is the porosity, k m is the thermal conductivity of the dense state material of the reconstruction area; for example, if the dense state material of the reconstruction area is 8YSZ, then k m is the thermal conductivity of 8YSZ, and the material of the reconstruction area is not limited in the embodiment of the present disclosure;

[0013] Formula two is used to determine the second thermal conductivity k of the nested digital structure file of the thermal barrier coating containing cracks and pores eff :

[0014]

[0015] Wherein, P (crack) is the crack rate, and X c is the crack shape influence factor;

[0016] The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in formula three:

[0017]

[0018] In the formula: r is the coordinate vector; e i is the direction vector of discrete velocity; t is time; δt is time step; τ f is the dimensionless relaxation time of fluid; f i (r,t) and are the particle density distribution function and equilibrium state density distribution function corresponding to i direction respectively; i∈[1,n];

[0019] The temperature field distribution function evolution equation of formula three is shown in formula four:

[0020]

[0021] In the formula: τ T is the dimensionless relaxation time of temperature field, τt = a / c s δt+1 / 2; a is the thermal diffusivity; c s is the heat, T i is the temperature distribution function;

[0022] After collision and migration, the macroscopic temperature distribution of the reconstruction area is shown in Equation Five:

[0023]

[0024] The effective thermal conductivity k eff of the thermal barrier coating is determined by Equation Six:

[0025]

[0026] wherein q is the steady-state heat flow through the coating with thickness δ, and ΔT represents the temperature difference between the two ends of the coating;

[0027] Step 3, for the coating whose thermal conductivity needs to be predicted, the thermal conductivity of the coating is predicted according to the porosity, crack rate of the coating and Equation Two.

[0028] In one possible implementation, step 1 comprises:

[0029] Step 11, taking the pores as the first growth phase and the solid skeleton as the non-growth phase, the initial phase of the reconstruction area is the solid skeleton node; according to the nucleation center generation probability a plurality of pore nodes are randomly arranged in the reconstruction area, the size is used to represent the diameter size of the initial pore node and the fineness of the internal structure of the coating;

[0030] Step 12, traversing each pore node in the reconstruction area, controlling each pore node to grow in a random direction, and the adjacent solid skeleton node located in the growth direction of each initial pore node is assigned with a random number, if the random number is less than the corresponding directional growth probability P i , the solid skeleton node is changed into a pore node;

[0031] Step 13, repeating step 12 until the volume fraction of the pores in the reconstruction area reaches the preset volume fraction P (pore) , that is, the porosity of the reconstruction area reaches the preset threshold; and outputting the digital structure file of the thermal barrier coating containing only pores;

[0032] Step 14, inputting and reading the generated digital structure file of the thermal barrier coating containing pores; according to the actual working condition, generating a thermal barrier coating containing cracks in the thermal barrier coating structure, and the crack length is preset as L x , and the crack opening is preset as L z; output the nested digital structure file of the thermal barrier coating containing cracks and pores as a thermal barrier coating model with defects;

[0033] Step 15, repeating steps 11 to 15 to obtain thermal barrier coating models corresponding to different porosities and crack rates.

[0034] According to another aspect of the embodiments of the present disclosure, a nuclear power plant equipment coating thermal conductivity prediction device is provided, and the device comprises:

[0035] A generating module is configured to generate thermal barrier coating models corresponding to different porosities and crack rates.

[0036] A determining module is configured to, for each porosity, determine a first thermal conductivity of a thermal barrier coating containing only pores corresponding to the porosity according to formulas three to six, and then determine a pore shape influence factor X p corresponding to the porosity from the first thermal conductivity and formula one.

[0037] For each porosity and crack rate, a second thermal conductivity of a thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to formulas three to six, and then a crack shape influence factor X p is determined from the second thermal conductivity, X c and formula two; thereby obtaining X p and X c corresponding to different porosities and crack rates, and establishing a rapid query atlas of X p and X c .

[0038] Formula one is used to determine a first effective thermal conductivity k m+p of a digital structure file of a thermal barrier coating containing only pores:

[0039]

[0040] wherein X p is a pore shape influence factor, P (pore) is a porosity, and k m is a thermal conductivity of a dense state material of a reconstruction region; for example, if the dense state material of the reconstruction region is 8YSZ, then k m is a thermal conductivity of 8YSZ, and the embodiments of the present disclosure do not limit the material of the reconstruction region;

[0041] Formula two is used to determine a second thermal conductivity k eff of a nested digital structure file of a thermal barrier coating containing cracks and pores:

[0042]

[0043] wherein P (crack) is a crack rate, and Xc is a crack shape influence factor;

[0044] The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in Equation 3:

[0045]

[0046] In the formula, r is a coordinate vector; e i is a discrete velocity direction vector; t is time; δt is a time step; τ f is a dimensionless relaxation time of the fluid; f i (r, t) and are the particle density distribution function and equilibrium state density distribution function corresponding to the i direction respectively; i ∈ [1, n];

[0047] The temperature field distribution function evolution equation of Equation 3 is shown in Equation 4:

[0048]

[0049] In the formula, τ T is a dimensionless relaxation time of the temperature field, τ t = α / c s δt+1 / 2; α is a thermal diffusion coefficient; c s is heat, T i is a temperature distribution function;

[0050] After collision and migration, the macroscopic temperature distribution of the reconstruction region is shown in Equation 5:

[0051]

[0052] The effective thermal conductivity k eff of the thermal barrier coating is determined by Equation 6:

[0053]

[0054] In the formula, q is the steady-state heat flow through the coating with a thickness of δ, and ΔT represents the temperature difference between the two ends of the coating.

[0055] The prediction module is configured to, for a coating for which the thermal conductivity needs to be predicted, predict the thermal conductivity of the coating according to the porosity, crack rate of the coating, and Equation 2.

[0056] In one possible implementation, the generation module includes:

[0057] The initialization module is configured to select pores as a first growth phase, a solid skeleton as a non-growth phase, and the initial phase of the reconstruction region as a solid skeleton node; and according to a nucleation center generation probability randomly arrange a plurality of pore nodes in the reconstruction region, The size is used to represent the diameter size of the initial pore node and the fineness of the internal structure of the coating;

[0058] A pore growth module is configured to traverse each pore node in the reconstruction region and control each pore node to grow in a random direction. An adjacent solid skeleton node located in the growth direction of each initial pore node is assigned a random number. If the random number is less than the corresponding directional growth probability P i , the solid skeleton node is changed to a pore node.

[0059] A pore iteration module is configured to repeatedly execute the pore growth module until the volume fraction of the pores in the reconstruction region reaches a preset volume fraction P (pore) , i.e., the porosity of the reconstruction region reaches a preset threshold. A digital structure file of the porous thermal barrier coating is output.

[0060] A crack nesting module is configured to input and read the generated digital structure file of the porous thermal barrier coating. According to actual working conditions, a crack-containing thermal barrier coating is nested in the porous thermal barrier coating structure, the crack length is preset as L x , and the crack opening is preset as L z . A nested digital structure file of the thermal barrier coating containing cracks and pores is output as a thermal barrier coating model with defects.

[0061] An output module is configured to repeatedly initialize the initialization module, the pore growth module, the pore iteration module, and the crack nesting module to obtain thermal barrier coating models corresponding to different porosities and crack rates.

[0062] According to another aspect of the embodiments of the present disclosure, a nuclear power plant equipment coating thermal conductivity prediction device is provided, and the device comprises:

[0063] A processor;

[0064] A memory for storing processor-executable instructions;

[0065] The processor is configured to execute the above method.

[0066] According to another aspect of the embodiments of the present disclosure, a non-volatile computer-readable storage medium is provided, which stores computer program instructions, and the computer program instructions are executed by a processor to implement the above method.

[0067] The beneficial effects of the present disclosure are that the model building of the present disclosure considers the common defects of the coating, i.e. pores and macro-level cracks, and regards the coating as a three-phase composite system of a compact skeleton, pores and cracks, and then gradually adds a defect to the substrate, and the system formed will become a new substrate for the next step. Repeat this composite process until both pores and cracks are added to the system. Thus, the actual running state of the thermal barrier coating of the nuclear power equipment can be more realistically simulated. Further, the present disclosure can determine the pore shape influence factor and the crack shape influence factor corresponding to different porosities and crack rates through modeling and simulation of the thermal conductivity coefficient, and further predict the thermal conductivity coefficient of the actual coating. This provides a theoretical basis for studying the failure behavior of the service thermal barrier coating. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 is a flowchart of a nuclear power plant equipment coating thermal conductivity prediction method according to an embodiment of the present disclosure.

[0069] Figure 2 is a schematic diagram of a nested digital structure file of a thermal barrier coating containing cracks and pores according to an embodiment of the present disclosure.

[0070] Figure 3 is a block diagram of a nuclear power plant equipment coating thermal conductivity prediction device according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0071] The present disclosure will be described in further detail below with reference to the drawings and specific embodiments.

[0072] Unless otherwise defined, technical and scientific terms used in the present disclosure have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs; the terminology used in the present disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure; the term "comprising", and any variation thereof, is intended to cover a non-exclusive inclusion; it is apparent that the embodiments described in the present disclosure are only a part of the embodiments of the present disclosure, and not all the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present disclosure.

[0073] In the present disclosure, the phrase "embodiment" means that the specific features, structures or characteristics described in connection with the embodiment can be included in at least one embodiment of the present disclosure. The appearance of this phrase in various places in the specification does not necessarily mean the same embodiment, nor is it an independent or alternative embodiment to other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0074] Figure 1FIG. 1 is a flowchart of a method for predicting a thermal conductivity of a coating of a nuclear power plant equipment according to an embodiment of the present disclosure. The method can be executed by a terminal device, which can be a server, a desktop computer, a notebook computer, or the like, and the type of the terminal device is not limited in the present disclosure. As shown in FIG. 1, the method includes the following steps. Figure 1

[0075] Step 1: generating a thermal barrier coating model corresponding to different porosities and crack rates.

[0076] Step 11: selecting pores as a first growth phase and a solid skeleton as a non-growth phase, and the initial phase of the reconstruction region is a solid skeleton node. According to the nucleation center generation probability , a plurality of pore nodes are randomly arranged in the reconstruction region. The size is used to represent the diameter size of the initial pore node and the fineness of the internal structure of the coating. The greater the value, the greater the pore size.

[0077] Step 12: traversing each pore node in the reconstruction region, controlling each pore node to grow in a random direction, and assigning a random number to the adjacent solid skeleton node located in the growth direction of each initial pore node. If the random number is less than the corresponding directional growth probability P i , the solid skeleton node is changed to a pore node.

[0078] Step 13: repeating step 12 until the volume fraction of the pores in the reconstruction region reaches a preset volume fraction P (pore) , that is, the porosity of the reconstruction region reaches a preset threshold; and outputting a digital structure file of the thermal barrier coating containing only pores.

[0079] Step 14: inputting and reading the generated digital structure file of the thermal barrier coating containing pores; according to the actual working condition, generating a thermal barrier coating containing cracks in the thermal barrier coating structure, and presetting the crack length as L x , and the crack opening as L z ; and outputting a nested digital structure file of the thermal barrier coating containing cracks and pores as a thermal barrier coating model with defects, as shown in FIG. 2. Figure 2

[0080] Step 15: repeating steps 11 to 14 to obtain thermal barrier coating models corresponding to different porosities.

[0081] In one possible implementation, in step 1, the thermal barrier coating model corresponding to different porosities and crack rates can also be generated by modeling through image acquisition according to the actual operation of the coating of the nuclear power plant equipment.

[0082] ​​Step 2, for each porosity, the first thermal conductivity of the thermal barrier coating containing only pores corresponding to the porosity is determined according to Formulas Three to Six, and then the first thermal conductivity and Formula One are used to determine the pore shape influence factor X corresponding to the porosity p .

[0083] For each porosity and crack rate, the second thermal conductivity of the thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to Formulas Three to Six, and then the second thermal conductivity, X p and Formula Two are used to determine the crack shape influence factor X c ; thereby obtaining X p and X c corresponding to different porosities and crack rates, and establishing a rapid query atlas of X p and X c .

[0084] Formula One is used to determine the first effective thermal conductivity k m+p of the digital structure file of the thermal barrier coating containing pores:

[0085]

[0086] wherein X p is the pore shape influence factor, P (pore) is the porosity, and k m is the thermal conductivity of the dense state material of the reconstruction region. For example, if the dense state material of the reconstruction region is 8YSZ, then k m is the thermal conductivity of 8YSZ, and the material of the reconstruction region is not limited in the embodiments of the present disclosure.

[0087] Formula Two is used to determine the second thermal conductivity k eff of the nested digital structure file of the thermal barrier coating containing cracks and pores:

[0088]

[0089] wherein P (crack) is the crack rate, and X c is the crack shape influence factor.

[0090] The lattice Boltzmann model (LBM) is adopted to determine the thermal conductivities of different microstructure coatings by replacing the complex macroscopic second-order convection heat transfer equation set with two first-order partial differential equations. The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in Formula Three:

[0091]

[0092] In the formula, r is a coordinate vector; e i is a direction vector of discrete velocity; t is time; and δt is a time step.f is the dimensionless relaxation time of the fluid; f i (r, t) and f i eq (r, t) are the particle density distribution function and equilibrium state density distribution function corresponding to the i direction respectively; i e [1, n].

[0093] The temperature field distribution function evolution equation of formula three is shown in formula four:

[0094]

[0095] In the formula: τ T is the dimensionless relaxation time of the temperature field, τ t = a / c s delta t + 1 / 2; a is the thermal diffusivity; c s is the heat, T i is the temperature distribution function.

[0096] After collision and migration, the macroscopic temperature distribution of the reconstruction area is shown in formula five:

[0097]

[0098] The effective thermal conductivity k eff of the thermal barrier coating is determined by formula six:

[0099]

[0100] Wherein: q is the steady-state heat flow through the coating with a thickness of delta, and delta T represents the temperature difference between the two ends of the coating.

[0101] Step 3, for the coating whose thermal conductivity needs to be predicted, the thermal conductivity of the coating is predicted according to the porosity, crack rate of the coating and formula two.

[0102] The model of the present disclosure considers that the common defects in the coating are pores and macroscopic cracks, and the coating is regarded as a three-phase composite system of compact skeleton, pores and cracks. After adding a kind of defect to the base gradually, the system formed will become the new base of the next step. Repeat this composite process until both the pores and cracks are added to the system. Thus, the actual running state of the thermal barrier coating of the nuclear power equipment can be simulated more realistically. Further, the present disclosure can determine the pore shape influence factor and crack shape influence factor corresponding to different porosity and crack rate by modeling and simulating the thermal conductivity, and further predict the thermal conductivity of the actual coating.

[0103] According to another aspect of the embodiment of the present disclosure, a nuclear power plant equipment coating thermal conductivity prediction device is provided, which comprises:

[0104] The generating module is configured to generate thermal barrier coating models corresponding to different porosities and crack rates;

[0105] The determining module is configured to determine, for each porosity, a first thermal conductivity coefficient of the thermal barrier coating containing only pores corresponding to the porosity according to formulas three to six, and then determine a pore shape influence factor X p corresponding to the porosity from the first thermal conductivity coefficient and formula one;

[0106] For each porosity and crack rate, a second thermal conductivity coefficient of the thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to formulas three to six, and then a crack shape influence factor X p is determined from the second thermal conductivity coefficient, X c ; thereby obtaining X p and X c corresponding to different porosities and crack rates, and establishing a rapid query atlas of X p and X c .

[0107] Formula one is used to determine the first effective thermal conductivity coefficient k m+p of the digital structure file of the thermal barrier coating containing only pores:

[0108]

[0109] wherein, X p is a pore shape influence factor, P (pore) is a porosity, and k m is a thermal conductivity coefficient of the dense state material of the reconstruction area; for example, if the dense state material of the reconstruction area is 8YSZ, k m is the thermal conductivity coefficient of 8YSZ, and the material of the reconstruction area is not limited in the embodiments of the present disclosure;

[0110] Formula two is used to determine the second thermal conductivity coefficient k eff of the nested digital structure file of the thermal barrier coating containing cracks and pores:

[0111]

[0112] wherein, P (crack) is a crack rate, and X c is a crack shape influence factor;

[0113] The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in formula three:

[0114]

[0115] In the formula, r is a coordinate vector, e i is a direction vector of a discrete velocity, t is time, and δt is a time step.f is the dimensionless relaxation time of the fluid; f i (r, t) and f i eq (r, t) are the particle density distribution function and equilibrium density distribution function corresponding to the i direction respectively; i ∈ [1, n];

[0116] The temperature field distribution function evolution equation of formula three is shown in formula four:

[0117]

[0118] In the formula: τ T is the dimensionless relaxation time of the temperature field, τ t = α / c s δt+1 / 2; α is the thermal diffusion coefficient; c s is the heat, T i is the temperature distribution function;

[0119] After collision and migration, the macroscopic temperature distribution of the reconstruction area is shown in formula five:

[0120]

[0121] The effective thermal conductivity k eff of the thermal barrier coating is determined by formula six:

[0122]

[0123] Wherein: q is the steady-state heat flow through the coating with a thickness of δ, ΔT represents the temperature difference of the two ends of the coating;

[0124] The prediction module is configured to, for a coating for which the thermal conductivity needs to be predicted, predict the thermal conductivity of the coating according to the porosity, crack rate of the coating and formula two.

[0125] In one possible implementation, the generation module comprises:

[0126] The initialization module is configured to select pores as the first growth phase and solid skeletons as the non-growth phase, and the initial phase of the reconstruction area is all the solid skeleton nodes; according to the nucleation center generation probability randomly arrange a plurality of pore nodes in the reconstruction area, The size of the pore node is used to represent the diameter size of the initial pore node and the fineness of the internal structure of the coating;

[0127] The pore growth module is configured to traverse each pore node in the reconstruction area, control each pore node to grow in a random direction, and assign a random number to an adjacent solid skeleton node located in the growth direction of each initial pore node, if the random number is less than the corresponding directional growth probability P i, then the solid skeleton node becomes a pore node;

[0128] The pore iteration module is used to repeatedly execute the pore growth module until the volume fraction of pores in the reconstructed area reaches the preset volume fraction P. (pore) That is, the porosity of the reconstructed area reaches the preset threshold; the digital structure file containing only the porous thermal barrier coating is output;

[0129] The crack nesting module is used to input and read the generated digital structure file of the thermal barrier coating containing pores; according to the actual working conditions, the thermal barrier coating containing cracks is nested in the thermal barrier coating containing pores, and the crack length is preset to L x , the crack opening is preset to L z ; Output the nested digital structure file of the thermal barrier coating containing cracks and pores as a thermal barrier coating model with defects;

[0130] The output module is used to repeat the initialization module, pore growth module, pore iteration module, and crack nesting module to obtain thermal barrier coating models corresponding to different porosity and crack rates.

[0131] 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.

[0132] Figure 3 1900 is a block diagram of a device for predicting thermal conductivity of a coating on a nuclear power plant equipment according to 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 the instructions to perform the above-described method.

[0133] 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.

[0134] In an example embodiment, there is also provided a non-transitory computer- readable storage medium, such as the memory 1932 including computer program instructions, which can be executed by the processing component 1922 of the apparatus 1900 to implement the above-described methods.

[0135] The present disclosure can be a system, a method, and / or a computer program product. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0136] The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium can be, for example, but is not limited to, an electronic 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. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, 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 mechanically encoded device such as punch-cards or punched tape, a

[0137] The computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0138] Computer readable program instructions for carrying out operations of the present disclosure can be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate array (FPGA), or programmable logic array (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0139] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0140] These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can include random access memory (RAM), read only memory (ROM), electrically erasable programmable read only memory (EEPROM), flash memory or other data storage device. When the computer readable program instructions are loaded into the computer and other programmable data processing apparatus, a series of operational steps are implemented that provide processes such that the computer or other programmable apparatus provide processes for implementing the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0141] The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus or other device to produce a computer implemented process such that the instructions which execute on the computer, other programmable data processing apparatus, or other device implement the functions / acts specified in the flowchart and / or block diagram block or blocks.

[0142] The flow diagrams and the block diagrams in the drawings are presented to illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flow diagrams and the block diagrams can represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logic functions. In some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks can sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flow diagrams, and combinations thereof, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and

[0143] Embodiments of the present disclosure have been described above, and the description is intended to be illustrative of the embodiments and not restrictive. Many modifications and variations of the described embodiments are possible and are within the scope of the disclosure. The selection of the terms to be used in the description is not intended to limit the scope of the embodiments described herein, but rather to best describe the principles of the embodiments in the context of the specific applications of the technology.

Claims

1. A method for predicting thermal conductivity of coatings for nuclear power plant equipment, characterized in that: The method comprises: Step 1: Generate thermal barrier coating models corresponding to different porosity and crack rates; Step 2: For each porosity, determine the first thermal conductivity of the thermal barrier coating containing only pores corresponding to the porosity according to equations 3 to 6, and then determine the pore shape influence factor X corresponding to the porosity according to the first thermal conductivity and equation 1. p ; For each porosity and crack rate, the second thermal conductivity of the thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to equations 3 to 6, and then the second thermal conductivity, X p The crack shape influencing factor X is determined by formula 2 c ; Thus, we can obtain X corresponding to different porosity and crack rate p and X c , build X p and X c Quick query graph; Formula 1 is used to determine the first effective thermal conductivity k of the digital structure file of the thermal barrier coating containing only pores m+p : Among them, X p is the pore shape influencing factor, P (pore) is the porosity, k m is the thermal conductivity of the material in the dense state of the reconstructed region; for example, if the material in the dense state of the reconstructed region is 8YSZ, then k m is the thermal conductivity of 8YSZ. The disclosed embodiment does not limit the material of the reconstruction area; Formula 2 is used to determine the second thermal conductivity k of the nested digital structure file of the thermal barrier coating containing cracks and pores eff : Among them, P (crack) is the crack rate, X c is the crack shape influencing factor; The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in Equation 3: Where: r is the coordinate vector; e i is the direction vector of the discrete velocity; t is time; δt is the time step; τ f is the dimensionless relaxation time of the fluid; f i (r,t) and f i eq (r, t) are the particle density distribution function and equilibrium density distribution function corresponding to the direction i, respectively; i∈[1,n]; The evolution equation of the temperature field distribution function of Equation 3 is shown in Equation 4: Where: τ T is the dimensionless relaxation time of the temperature field, τ t =α / c s δt+1 / 2; α is the thermal diffusion coefficient; c s is heat, T i is the temperature distribution function; After collision and migration, the macroscopic temperature distribution of the reconstructed area is shown in Equation 5: The effective thermal conductivity k of the thermal barrier coating is determined using formula 6: eff : Where: q is the steady-state heat flux through the coating with a thickness of δ, ΔT represents the temperature difference between the two ends of the coating; Step 3: For the coating whose thermal conductivity needs to be predicted, the thermal conductivity of the coating is predicted based on the porosity, crack rate and formula 2 of the coating.

2. The method according to claim 1, characterized in that Step 1 includes: Step 11: Select pores as the first growth phase, solid skeleton as the non-growth phase, and the initial phases of the reconstruction area are all solid skeleton nodes; according to the nucleation center generation probability P c m Multiple pore nodes are randomly arranged in the reconstruction area, P c m The size of is used to indicate the diameter of the initial pore nodes and the fineness of the internal structure of the coating; Step 12: traverse each pore node in the reconstruction area and control each pore node to grow in a random direction. The adjacent solid skeleton nodes located in the growth direction of each initial pore node are assigned a random number. If the random number is less than the corresponding directional growth probability P in the direction, i , then the solid skeleton node becomes a pore node; Step 13: Repeat step 12 until the volume fraction of pores in the reconstructed area reaches the preset volume fraction P. (pore) That is, the porosity of the reconstructed area reaches the preset threshold; the digital structure file containing only the porous thermal barrier coating is output; Step 14: input and read the generated digital structure file of the thermal barrier coating containing pores; according to the actual working conditions, generate the thermal barrier coating containing cracks in the thermal barrier coating containing pores structure, and the crack length is preset to L x , the crack opening is preset to L z ; Output the nested digital structure file of the thermal barrier coating containing cracks and pores as a thermal barrier coating model with defects; Step 15: Repeat steps 11 to 15 to obtain thermal barrier coating models corresponding to different porosities and crack rates.

3. A device for predicting thermal conductivity of coatings for nuclear power plant equipment, characterized in that: The method comprises: Generation module, used to generate thermal barrier coating models corresponding to different porosity and crack rates; A determination module is used to determine the first thermal conductivity of the thermal barrier coating containing only pores corresponding to each porosity according to equations 3 to 6, and then determine the pore shape influence factor X corresponding to the porosity according to the first thermal conductivity and equation 1. p ; For each porosity and crack rate, the second thermal conductivity of the thermal barrier coating containing pores and cracks corresponding to the porosity and crack rate is determined according to equations 3 to 6, and then the second thermal conductivity, X p The crack shape influencing factor X is determined by formula 2 c ; Thus, we can obtain X corresponding to different porosity and crack rate p and X c , build X p and X c Quick query graph; Formula 1 is used to determine the first effective thermal conductivity k of the digital structure file of the thermal barrier coating containing only pores m+p : Among them, X p is the pore shape influencing factor, P (pore) is the porosity, k m is the thermal conductivity of the material in the dense state of the reconstructed region; for example, if the material in the dense state of the reconstructed region is 8YSZ, then k m is the thermal conductivity of 8YSZ. The disclosed embodiment does not limit the material of the reconstruction area; Formula 2 is used to determine the second thermal conductivity k of the nested digital structure file of the thermal barrier coating containing cracks and pores eff : Among them, P (crack) is the crack rate, X c is the crack shape influencing factor; The velocity field distribution function evolution equation in the lattice Boltzmann method is shown in Equation 3: Where: r is the coordinate vector; e i is the direction vector of the discrete velocity; t is time; δt is the time step; τ f is the dimensionless relaxation time of the fluid; f i (r,t) and f i eq (r, t) are the particle density distribution function and equilibrium density distribution function corresponding to the direction i, respectively; i∈[1,n]; The evolution equation of the temperature field distribution function of Equation 3 is shown in Equation 4: Where: τ T is the dimensionless relaxation time of the temperature field, τ t =α / c s δt+1 / 2; α is the thermal diffusion coefficient; c s is heat, T i is the temperature distribution function; After collision and migration, the macroscopic temperature distribution of the reconstructed area is shown in Equation 5: The effective thermal conductivity k of the thermal barrier coating is determined using formula 6: eff : Where: q is the steady-state heat flux through the coating with a thickness of δ, ΔT represents the temperature difference between the two ends of the coating; The prediction module is used to predict the thermal conductivity of a coating for which thermal conductivity prediction is required, based on the porosity, crack rate and formula 2 of the coating.

4. The device according to claim 2, characterized in that The generated modules include: The initialization module is used to select pores as the first growth phase, solid skeleton as the non-growth phase, and the initial phases of the reconstruction area are all solid skeleton nodes; according to the nucleation center generation probability P c m Multiple pore nodes are randomly arranged in the reconstruction area, P c m The size of is used to indicate the diameter of the initial pore nodes and the fineness of the internal structure of the coating; The pore growth module is used to traverse each pore node in the reconstruction area and control each pore node to grow in a random direction. The adjacent solid skeleton nodes located in the growth direction of each initial pore node are assigned a random number. If the random number is less than the corresponding directional growth probability P in this direction, the pore node will be regenerated. i , then the solid skeleton node becomes a pore node; The pore iteration module is used to repeatedly execute the pore growth module until the volume fraction of pores in the reconstructed area reaches the preset volume fraction P. (pore) That is, the porosity of the reconstructed area reaches the preset threshold; the digital structure file containing only the porous thermal barrier coating is output; The crack nesting module is used to input and read the generated digital structure file of the thermal barrier coating containing pores; according to the actual working conditions, the thermal barrier coating containing cracks is nested in the thermal barrier coating containing pores, and the crack length is preset to L x , the crack opening is preset to L z ; Output the nested digital structure file of the thermal barrier coating containing cracks and pores as a thermal barrier coating model with defects; The output module is used to repeat the initialization module, pore growth module, pore iteration module, and crack nesting module to obtain thermal barrier coating models corresponding to different porosity and crack rates.

5. A device for predicting thermal conductivity of coatings for nuclear power plant equipment, characterized in that: The device comprises: processor; a memory for storing processor-executable instructions; The processor is configured to execute the method of claim 1 or 2.

6. 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 claim 1 or 2 is implemented.

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