Method and device for calculating equivalent neutron diffusion coefficient of cavity of pebble-bed high-temperature gas cooled reactor

Abstract

The invention provides a method and a device for calculating an equivalent neutron diffusion coefficient of a cavity of a pebble-bed high-temperature gas cooled reactor. Wherein the pebble-bed high-temperature gas cooled reactor comprises a cavity area; the calculation method comprises the following steps: determining a neutron diffusion equation of a cavity area under two-dimensional R-Z cylinder geometry according to geometrical characteristics of the pebble-bed high-temperature gas cooled reactor; according to a neutron diffusion equation of the cavity area under the two-dimensional R-Z cylinder geometry, performing Taylor expansion on the neutron-flux density to obtain a Taylor expansion of the neutron-flux density; respectively substituting the Taylor expansion of the neutron flux density into the diffusion solution and the transport integral analytical solution of the net neutron current on the surface of the cavity; and performing similar term analogy on the diffusion solution of the net neutron current on the surface of the cavity and the transport integral analytical solution to obtain an axial diffusion coefficient calculation formula and a radial diffusion coefficient calculation formula of the cavity region.

Description

Technical Field

[0001] This application relates to the field of nuclear reactor physics calculations, and in particular to a method and apparatus for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity. Background Technology

[0002] Neutron physics calculations for pebble-bed high-temperature gas-cooled reactor (HTGR) cores employ diffusion calculations. However, the upper part of a pebble-bed HTGR contains a cavity region. Within this region, the approximations used in the neutron diffusion equations introduce larger errors, affecting the accuracy of HTGR physics calculations. Diffusion coefficients generated using traditional methods and core neutron diffusion calculations offer good accuracy for pressurized water reactors (PWRs), supporting the design and operation of existing PWR nuclear power plants. However, HTGRs have unique design characteristics, employing helium cooling and featuring a cavity region in the upper part of the core. The neutron diffusion equations rely on several approximations, one of which is the assumption of an "infinitely homogeneous medium." This makes calculation errors from fuel to the cavity region more pronounced, impacting the accuracy of HTGR calculations. Summary of the Invention

[0003] This application provides a method and apparatus for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity.

[0004] In a first aspect, embodiments of this application provide a method for calculating the equivalent neutron diffusion coefficient of a cavity in a pebble bed high-temperature gas-cooled reactor. The pebble bed high-temperature gas-cooled reactor is in a clean reactor state, and includes a dry graphite sphere region at the bottom of the pebble bed, a mixed sphere region of fuel spheres and graphite spheres at the top of the pebble bed, and a cavity region at the top of the pebble bed. The calculation method includes:

[0005] Based on the geometric characteristics of the pebble bed high-temperature gas-cooled reactor, the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry is determined;

[0006] Based on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, a Taylor expansion of the neutron flux density is performed to obtain the Taylor expansion of the neutron flux density;

[0007] Substitute the Taylor expansion of the neutron flux density into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively;

[0008] By comparing the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms, the formulas for calculating the axial diffusion coefficient and radial diffusion coefficient of the cavity region are obtained.

[0009] Secondly, embodiments of this application provide a device for calculating the equivalent neutron diffusion coefficient of a pebble bed high-temperature gas-cooled reactor cavity. The pebble bed high-temperature gas-cooled reactor is in a clean reactor state. The pebble bed high-temperature gas-cooled reactor includes a dry graphite sphere region at the bottom of the pebble bed, a mixed sphere region of fuel spheres and graphite spheres at the top of the pebble bed, and a cavity region at the top of the pebble bed. The calculation device includes:

[0010] The determination module is used to determine the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry based on the geometric characteristics of the pebble bed high-temperature gas-cooled reactor.

[0011] The expansion module is used to perform a Taylor expansion of the neutron flux density based on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, so as to obtain the Taylor expansion of the neutron flux density.

[0012] The substitution module is used to substitute the Taylor expansion of the neutron flux density into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively.

[0013] The analogy module is used to compare the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms to obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0014] Thirdly, embodiments of this application provide an electronic device, including:

[0015] One or more processors;

[0016] The processor is used to invoke instructions to cause the electronic device to perform the method described in the first aspect above.

[0017] Fourthly, embodiments of this application provide a storage medium storing instructions that, when executed on an electronic device, cause the electronic device to perform the method described in the first aspect above.

[0018] Fifthly, embodiments of this application provide a program product, including at least one of a program and instructions, wherein when the program and instructions are executed by an electronic device, they implement the steps of the method described in the first aspect.

[0019] According to the technical solution of this application, by performing a Taylor expansion of the neutron flux density and substituting it into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, and by analogy with similar terms, the calculation formula corresponding to the diffusion coefficient in the diffusion equation can be obtained. This can solve the problem that the calculation error from fuel to cavity region becomes prominent due to the assumption of "infinite homogeneous medium" in traditional methods, thereby improving the accuracy of calculation and analysis of pebble bed high-temperature gas-cooled reactors.

[0020] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0021] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0022] Figure 1 A schematic flowchart illustrating the method for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity provided in an embodiment of this application;

[0023] Figure 2 This is an example diagram of a pebble bed type high-temperature gas-cooled reactor model provided in the embodiments of this application;

[0024] Figure 3 A block diagram of the device for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity provided in the embodiments of this application;

[0025] Figure 4 This is a block diagram of an electronic device according to an embodiment of this application. Detailed Implementation

[0026] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0027] The following describes, with reference to the accompanying drawings, a method and apparatus for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity according to embodiments of this application.

[0028] It should be noted that the execution subject of the pebble bed type high temperature gas-cooled reactor cavity equivalent neutron diffusion coefficient calculation method in this application embodiment can be a pebble bed type high temperature gas-cooled reactor cavity equivalent neutron diffusion coefficient calculation device. This device can be implemented by software and / or hardware. This device can be configured in an electronic device, which may include, but is not limited to, a terminal, a server, etc.

[0029] Figure 1 This is a schematic flowchart illustrating the method for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity provided in an embodiment of this application. In some embodiments, such as Figure 2 As shown, the pebble bed high-temperature gas-cooled reactor is in a clean reactor state (without control rods and absorber spheres). The pebble bed high-temperature gas-cooled reactor includes a dry graphite sphere region 201 at the bottom of the pebble bed, a mixed sphere region 202 of fuel spheres and graphite spheres at the top of the pebble bed, and a cavity region 203 at the top of the pebble bed. Figure 1As shown, the method for calculating the equivalent neutron diffusion coefficient of the cavity in this pebble bed type high-temperature gas-cooled reactor may include the following steps.

[0030] In step 101, the neutron diffusion equation for the cavity region under two-dimensional RZ cylindrical geometry is determined based on the geometric characteristics of the pebble bed type high-temperature gas-cooled reactor.

[0031] For example, for such Figure 2 The geometric characteristics of the pebble bed high-temperature gas-cooled reactor shown allow us to derive the neutron diffusion equation for the cavity region under a two-dimensional RZ cylindrical geometry. As an example, the formula for this neutron diffusion equation for the cavity region under this two-dimensional RZ cylindrical geometry is as follows:

[0032]

[0033] Among them, D z D is the axial diffusion coefficient of the cavity region. r denoted as , where is the radial diffusion coefficient of the cavity region; r is the radial position coordinate; and z is the axial position coordinate. denoted as neutron flux density.

[0034] In step 102, the neutron flux density is expanded using Taylor expansion based on the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry, resulting in the Taylor expansion of the neutron flux density.

[0035] In some embodiments, based on the neutron diffusion equation for the cavity region under two-dimensional RZ cylindrical geometry, the interface between the cavity region and the hybrid sphere region can be selected as the expansion point to perform a Taylor expansion of the neutron flux density, resulting in a Taylor expansion of the neutron flux density. For example, based on the neutron diffusion equation for the cavity region under two-dimensional RZ cylindrical geometry, a Taylor expansion of the neutron flux density is performed at the cavity boundary to obtain a Taylor expansion of the neutron flux density, which is expressed as follows:

[0036]

[0037] in, Neutron flux density; This is the zeroth-order term in the Taylor expansion of the neutron flux density; This is a first-order term in the Taylor expansion of the neutron flux density; This is the second-order term in the Taylor expansion of the neutron flux density.

[0038] In step 103, the Taylor expansion of the neutron flux density is substituted into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively.

[0039] In some embodiments, the Taylor expansion of the neutron flux density is substituted into the diffusion solution of the net neutron flux at the cavity surface to obtain the expression for the net neutron flux under diffusion theory; the Taylor expansion of the neutron flux density is substituted into the analytical solution of the transport integral of the net neutron flux at the cavity surface to obtain the expression for the net neutron flux under transport theory.

[0040] As an example, the diffusion solution of net neutron flux at a cavity surface is expressed as follows:

[0041]

[0042] The analytical solution for the transport integral of the net neutron flow at the cavity surface is expressed as follows:

[0043] j trans (r)=∫ 4π ψ(r,Ω)ΩdΩ

[0044] Where, j diff The diffusion solution for the net neutron flux at the cavity surface; j trans ψ(r,Ω) is the analytical solution of the transport integral of the net neutron flux on the cavity surface; r is the spatial variable; Ω is the angular variable; and ψ(r,Ω) is the neutron angular flux density.

[0045] In step 104, the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface are compared with similar terms to obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0046] In some embodiments, the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface are matched with similar terms based on Taylor expansion, and the coefficients of the same power are made equal to establish equations for the axial diffusion coefficient and the radial diffusion coefficient. Solving the equations for the axial diffusion coefficient and the radial diffusion coefficient yields the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0047] For example, performing similar operations means rearranging the analytical solutions for the diffusion and transport integrals of the net neutron flow according to the same power of the independent variable (position coordinates (r, z)), making the coefficients of corresponding terms equal. Since the focus is on the equivalent diffusion coefficient, the diffusion coefficient (including the axial and radial diffusion coefficients) needs to be analytically derived from these equations. As an example, the expression for the axial diffusion coefficient of the cavity region is as follows:

[0048]

[0049] The formula for calculating the radial diffusion coefficient of the cavity region is as follows:

[0050]

[0051] Where R is the radius of the cavity region; H is the height of the cavity region; and h is the height-to-diameter ratio of the cavity region.

[0052] For example, since the diffusion solution of the net neutron flux at the cavity surface incorporates the Taylor expansion of the neutron flux density, the diffusion solution j of the net neutron flux at the cavity surface... diff It will be expressed as a polynomial, including the Taylor expansion coefficients and diffusion coefficients (including axial and radial diffusion coefficients). Since the analytical solution of the transport integral of the net neutron flux at the cavity surface incorporates the Taylor expansion of the neutron flux density, the analytical solution of the transport integral of the net neutron flux at the cavity surface will also be expressed as a polynomial, including the Taylor expansion coefficients and geometric parameters (such as R, H, etc.). Because the net neutron flux should be equal at the cavity surface (i.e., the net neutron flux under the diffusion approximation should be equal to the net neutron flux under the more accurate transport theory), we can let: j diff (r)=j trans By rearranging both sides into polynomial form with respect to the position coordinates (r, z), and then comparing the coefficients of the same power, equations for the axial diffusion coefficient and the radial diffusion coefficient can be established. Solving these equations yields the formulas for calculating the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0053] The inventor targeted Figure 2 The pebble bed high-temperature gas-cooled reactor model shown was compared and verified using both conventional methods and the method designed in this application's embodiment. This pebble bed high-temperature gas-cooled reactor model was a clean reactor (without control rods and absorber spheres). The bottom of the pebble bed (excluding the unloading pipe) was pre-loaded with approximately 232,000 dry graphite spheres to a height of 605 cm. These were then topped with a 275 cm high mixture of fuel spheres (7:8 ratio of 4.2% enriched fuel spheres and graphite spheres). All spheres in the mixture region contained 600 ppm of water in their graphite. The effective neutron multiplication factor of the reactor core was compared at this point. Table 1 below shows that the deviations of the calculation method in this application's embodiment were 20 pcm and -8 pcm, respectively, for the two examples at 30°C vacuum and 30°C saturated air, which are very close to the reference solution, proving the feasibility and correctness of the method for handling the upper cavity problem of the pebble bed.

[0054] Table 1

[0055]

[0056] In the above embodiments, by performing a Taylor expansion of the neutron flux density and substituting it into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, and by analogy with similar terms, the calculation formula corresponding to the diffusion coefficient in the diffusion equation can be obtained. This can solve the problem that the calculation error from fuel to cavity region becomes prominent due to the assumption of "infinite homogeneous medium" in traditional methods, thereby improving the accuracy of calculation and analysis of pebble bed high-temperature gas-cooled reactors.

[0057] Figure 3 A block diagram of the device for calculating the equivalent neutron diffusion coefficient of a pebble bed-type high-temperature gas-cooled reactor cavity provided in an embodiment of this application. Figure 3 As shown, the device for calculating the equivalent neutron diffusion coefficient of the cavity of the pebble bed type high-temperature gas-cooled reactor may include: a determination module 301, an expansion module 302, a substitution module 303, and a similar term analogy module 304.

[0058] Among them, the determination module 301 is used to determine the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry based on the geometric characteristics of the pebble bed type high-temperature gas-cooled reactor.

[0059] The expansion module 302 is used to perform Taylor expansion of the neutron flux density according to the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry, so as to obtain the Taylor expansion of the neutron flux density.

[0060] Substitute module 303, which is used to substitute the Taylor expansion of the neutron flux density into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively.

[0061] The analogy module 304 is used to compare the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms to obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0062] In some embodiments, the expansion module 302 is used to: select the interface between the cavity region and the hybrid sphere region as the expansion point according to the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry, and perform Taylor expansion on the neutron flux density to obtain the Taylor expansion of the neutron flux density.

[0063] In some embodiments, the neutron diffusion equation for the cavity region under two-dimensional RZ cylindrical geometry is expressed as follows:

[0064]

[0065] The Taylor expansion of the neutron flux density is expressed as follows:

[0066]

[0067] Among them, D z D is the axial diffusion coefficient of the cavity region.r denoted as , where is the radial diffusion coefficient of the cavity region; r is the radial position coordinate; and z is the axial position coordinate. Neutron flux density; This is the zeroth-order term in the Taylor expansion of the neutron flux density; This is a first-order term in the Taylor expansion of the neutron flux density; This is the second-order term in the Taylor expansion of the neutron flux density.

[0068] In some embodiments, the analogy module 304 is used to: match like terms of the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface based on Taylor expansion, make the coefficients of the same power equal, so as to establish equations about the axial diffusion coefficient and the radial diffusion coefficient, solve the equations about the axial diffusion coefficient and the radial diffusion coefficient, and obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

[0069] In some embodiments, the diffusion solution of the net neutron flow at the cavity surface is expressed as follows:

[0070]

[0071] The analytical solution for the transport integral of the net neutron flow at the cavity surface is expressed as follows:

[0072] j trans (r)=∫ 4π ψ(r,Ω)ΩdΩ

[0073] Where, j diff The diffusion solution for the net neutron flux at the cavity surface; j trans ψ(r,Ω) is the analytical solution of the transport integral of the net neutron flux on the cavity surface; r is the spatial variable; Ω is the angular variable; and ψ(r,Ω) is the neutron angular flux density.

[0074] In some embodiments, the formula for calculating the axial diffusion coefficient of the cavity region is expressed as follows:

[0075]

[0076] The formula for calculating the radial diffusion coefficient of the cavity region is as follows:

[0077]

[0078] Where R is the radius of the cavity region; H is the height of the cavity region; and h is the height-to-diameter ratio of the cavity region.

[0079] It should be noted that the explanation of the above-described embodiment of the method for calculating the equivalent neutron diffusion coefficient of the cavity in a pebble bed type high-temperature gas-cooled reactor also applies to the device for calculating the equivalent neutron diffusion coefficient of the cavity in this embodiment of the pebble bed type high-temperature gas-cooled reactor, and will not be repeated here.

[0080] According to embodiments of this application, this application also provides an electronic device and a readable storage medium.

[0081] like Figure 4 The diagram shown is a block diagram of an electronic device according to an embodiment of this application. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present application described and / or claimed herein.

[0082] like Figure 4 As shown, the electronic device includes one or more processors 401, a memory 402, and interfaces for connecting the components, including high-speed interfaces and low-speed interfaces. The components are interconnected via different buses and can be mounted on a common motherboard or otherwise as required. The processors can process instructions executed within the electronic device, including instructions stored in or on memory to display graphical information of a GUI on an external input / output device (such as a display device coupled to the interface). In other embodiments, multiple processors and / or multiple buses can be used with multiple memories and multiple memory modules, if desired. Similarly, multiple electronic devices can be connected, each providing some of the necessary operations (e.g., as a server array, a group of blade servers, or a multiprocessor system). Figure 4 Take a processor 401 as an example.

[0083] The memory 402 is the non-transient computer-readable storage medium provided in this application. The memory stores instructions executable by at least one processor to cause the at least one processor to execute the method for calculating the equivalent neutron diffusion coefficient of the cavity in a pebble-bed high-temperature gas-cooled reactor provided in this application. The non-transient computer-readable storage medium of this application stores computer instructions for causing a computer to execute the method for calculating the equivalent neutron diffusion coefficient of the cavity in a pebble-bed high-temperature gas-cooled reactor provided in this application.

[0084] Memory 402, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the method for calculating the equivalent neutron diffusion coefficient of the cavity in a pebble bed type high-temperature gas-cooled reactor in the embodiments of this application (e.g., attached). Figure 3 The determination module 301, expansion module 302, substitution module 303, and analogy module 304 are shown. The processor 401 executes various server functions and data processing by running non-transient software programs, instructions, and modules stored in the memory 402, thereby realizing the method for calculating the equivalent neutron diffusion coefficient of the cavity in the pebble bed type high-temperature gas-cooled reactor in the above method embodiment.

[0085] Memory 402 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created based on the use of the electronic device. Furthermore, memory 402 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory 402 may optionally include memory remotely located relative to processor 401, and these remote memories can be connected to the electronic device via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0086] The electronic device may also include an input device 403 and an output device 404. The processor 401, memory 402, input device 403, and output device 404 can be connected via a bus or other means. Figure 4 Taking the example of a connection between China and Israel via a bus.

[0087] Input device 403 can receive input numerical or character information, and generate key signal inputs related to user settings and function control of the electronic device, such as touch screens, keypads, mice, trackpads, touchpads, joysticks, one or more mouse buttons, trackballs, joysticks, etc. Output device 404 may include display devices, auxiliary lighting devices (e.g., LEDs), and haptic feedback devices (e.g., vibration motors). The display device may include, but is not limited to, liquid crystal displays (LCDs), light-emitting diode (LED) displays, and plasma displays. In some embodiments, the display device may be a touch screen.

[0088] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transferring data and instructions to the storage system, the at least one input device, and the at least one output device.

[0089] These computational programs (also referred to as programs, software, software applications, or code) include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms “machine-readable medium” and “computer-readable medium” refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device (PLD)) used to provide machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term “machine-readable signal” refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0090] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0091] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), the Internet, and blockchain networks.

[0092] Computer systems can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. A server can be a cloud server, also known as a cloud computing server or cloud host, a hosting product within the cloud computing service ecosystem, addressing the shortcomings of traditional physical hosts and VPS (Virtual Private Server, or simply "VPS") services, such as high management difficulty and weak business scalability. Servers can also be servers for distributed systems or servers incorporating blockchain technology.

[0093] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0094] In the description of this application, "multiple sets" means at least two sets, such as two sets, three sets, etc., unless otherwise explicitly specified.

[0095] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0096] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0097] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0098] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0099] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0100] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity, characterized in that, The pebble bed type high-temperature gas-cooled reactor includes a cavity region; the calculation method includes: Based on the geometric characteristics of the pebble bed high-temperature gas-cooled reactor, the neutron diffusion equation of the cavity region under two-dimensional RZ cylindrical geometry is determined; Based on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, a Taylor expansion of the neutron flux density is performed to obtain the Taylor expansion of the neutron flux density; Substitute the Taylor expansion of the neutron flux density into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively; By comparing the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms, the formulas for calculating the axial diffusion coefficient and radial diffusion coefficient of the cavity region are obtained.

2. The method as described in claim 1, characterized in that, The Taylor expansion of the neutron flux density is obtained by performing a Taylor expansion on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, including: Based on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, the interface between the cavity region and the hybrid sphere region is selected as the expansion point, and the neutron flux density is subjected to Taylor expansion to obtain the Taylor expansion of the neutron flux density.

3. The method as described in claim 1 or 2, characterized in that, The neutron diffusion equation for the cavity region under the two-dimensional RZ cylindrical geometry is expressed as follows: The Taylor expansion of the neutron flux density is expressed as follows: Among them, D z D is the axial diffusion coefficient of the cavity region. r denoted as , where r is the radial diffusion coefficient of the cavity region; r is the radial position coordinate; and z is the axial position coordinate. Neutron flux density; This is the zeroth-order term in the Taylor expansion of the neutron flux density; , is a first-order term in the Taylor expansion of the neutron flux density; is the second-order term in the Taylor expansion of the neutron flux density.

4. The method as described in claim 1, characterized in that, The step of comparing the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms to obtain the calculation formulas for the axial diffusion coefficient and radial diffusion coefficient of the cavity region includes: The diffusion solution of the net neutron flow on the cavity surface and the analytical solution of the transport integral are matched with similar terms based on Taylor expansion, and the coefficients of the same power are made equal to establish equations for the axial diffusion coefficient and the radial diffusion coefficient. The equations for the axial diffusion coefficient and the radial diffusion coefficient are solved to obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

5. The method as described in claim 1 or 4, characterized in that, The diffusion solution of the net neutron flow at the cavity surface is expressed as follows: The analytical solution for the transport integral of the net neutron flow at the cavity surface is expressed as follows: j trans (r)=∫ 4π ψ(r,Ω)ΩdΩ Where, j diff The diffusion solution of the net neutron flux at the cavity surface; j trans ψ(r,Ω) is the analytical solution of the transport integral of the net neutron flux on the cavity surface; r is a spatial variable; Ω is an angular variable; and ψ(r,Ω) is the neutron angular flux density.

6. The method as described in claim 1 or 4, characterized in that, The formula for calculating the axial diffusion coefficient of the cavity region is as follows: The formula for calculating the radial diffusion coefficient of the cavity region is as follows: Where R is the radius of the cavity region; H is the height of the cavity region; and h is the height-to-diameter ratio of the cavity region.

7. A device for calculating the equivalent neutron diffusion coefficient of a pebble bed type high-temperature gas-cooled reactor cavity, characterized in that, The pebble bed type high-temperature gas-cooled reactor includes a cavity region; the computing device includes: The determination module is used to determine the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry based on the geometric characteristics of the pebble bed high-temperature gas-cooled reactor. The expansion module is used to perform a Taylor expansion of the neutron flux density based on the neutron diffusion equation of the cavity region under the two-dimensional RZ cylindrical geometry, so as to obtain the Taylor expansion of the neutron flux density. The substitution module is used to substitute the Taylor expansion of the neutron flux density into the diffusion solution and transport integral analytical solution of the net neutron flux at the cavity surface, respectively. The analogy module is used to compare the diffusion solution and transport integral analytical solution of the net neutron flow on the cavity surface with similar terms to obtain the calculation formulas for the axial diffusion coefficient and the radial diffusion coefficient of the cavity region.

8. An electronic device, characterized in that, include: One or more processors; The processor is used to invoke instructions to cause the electronic device to perform the method of any one of claims 1-6.

9. A storage medium storing instructions, characterized in that, When the instructions are executed on an electronic device, the electronic device causes the electronic device to perform the method of any one of claims 1-6.

10. A program product comprising at least one of a program and instructions, characterized in that, When at least one of the programs or instructions is executed by an electronic device, it implements the steps of the method according to any one of claims 1-6.

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