Energy group structure determination method for physical calculation of reactor core of high-temperature gas cooled reactor
By constructing a physical model of the high-temperature gas-cooled reactor core, performing forward and conjugate neutron transport calculations, and determining the energy group structure, the problem of high memory and time consumption in high-temperature gas-cooled reactor computation was solved, and efficient few-group computation was achieved.
Patent Information
- Application Number
- CN202510989898.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-17
- Publication Date
- 2025-11-28
AI Technical Summary
The calculation of neutron transport in the core of a high-temperature gas-cooled reactor consumes a lot of computational memory and takes a long time, resulting in low simulation efficiency.
A core physics model was constructed, forward and conjugate neutron transport calculations were performed, multi-group flux density was determined, and energy group structure was divided based on average flux weight to achieve the transition from multi-group to few-group.
Reduce computational memory consumption and time, improve computational efficiency, and save resources.
Smart Images
Figure CN121031004A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present disclosure relates to the technical field of nuclear reactor core nuclear design, and particularly relates to a method for determining energy group structure for high-temperature gas-cooled reactor core physical calculation. BACKGROUND
[0002] Pebble-Bed High-Temperature Gas-Cooled Reactor (PB-HTGR) has high inherent safety, superior power generation efficiency, and potential for high-temperature hydrogen production, and has attracted widespread attention. However, due to its complex core structure, fuel elements (coated fuel particles) are randomly stacked to form a pebble bed, and there is a strong multi-physical coupling effect between the coolant (helium) and the graphite moderator and fuel spheres, which poses a great challenge to the core neutron transport calculation.
[0003] In traditional neutron transport calculation, a multi-group approximation method is usually used for processing. However, for high-temperature gas-cooled reactors, if the number of energy groups calculated is large (such as 361 groups), it will lead to problems of large consumption of simulation calculation memory and long required time, thereby greatly affecting the simulation calculation of high-temperature gas-cooled reactors. SUMMARY
[0004] The method for determining energy group structure for high-temperature gas-cooled reactor core physical calculation provided by the present disclosure aims to solve the technical problems of large calculation memory consumption and long calculation time in the prior art.
[0005] According to a first aspect of an embodiment of the present disclosure, a method for determining energy group structure for high-temperature gas-cooled reactor core physical calculation is provided, and the method comprises:
[0006] constructing a core physical model, wherein the core physical model is a core model comprising multiple batches of fuel spheres and graphite spheres;
[0007] performing forward neutron transport calculation on the core physical model to obtain multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physical model;
[0008] performing conjugate neutron transport calculation on the core physical model to obtain multi-group conjugate neutron flux density of each batch of fuel spheres and graphite spheres in the core physical model;
[0009] determining an average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density;
[0010] when the average flux weight meets the division condition, dividing the core physical model based on the boundary line corresponding to the average flux weight to obtain a first group energy group structure.
[0011] Optionally, in the embodiments of the present disclosure, the forward neutron transport calculation on the core physical model to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physical model comprises: performing the forward neutron transport calculation on the core physical model by a first formula to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physical model, wherein the first formula is:
[0012]
[0013] wherein Ω is a unit direction vector of motion, r is a spatial position of a neutron, E is a neutron energy, k eff is a neutron effective multiplication factor, v is a fission neutron number, χ(E) is a fission neutron energy spectrum, ψ is a forward neutron flux density, f(r, Ω', E'→Ω, E) represents a probability that a neutron at a spatial position r, with an energy of E' and a direction of Ω', after interacting with an atom, has an energy falling within a nearby dE and a direction Ω falling within a nearby dΩ, s is scattering, f is fission, and t is a sum of scattering and fission cross sections.
[0014] Optionally, in the embodiments of the present disclosure, the conjugate neutron transport calculation on the core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model comprises: performing the conjugate neutron transport calculation on the core physical model by a second formula to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model, wherein the second formula is:
[0015]
[0016] wherein ψ * is a conjugate neutron flux density, and f(r, Ω, E→Ω', E') represents a probability that a neutron at a spatial position r, with an energy of E and a direction of Ω, after interacting with an atom, has an energy falling within a nearby dE' and a direction Ω' falling within a nearby dΩ'.
[0017] Optionally, in the embodiments of the present disclosure, the determination of the average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density comprises:
[0018] calculating a weight of each energy group in the second group in a flux inner product;
[0019] obtaining a total inner product weight of the second group based on the weight of each energy group in the second group in the flux inner product;
[0020] The total inner product weight of the second group is equally divided as a target to obtain an average flux weight in the first group division.
[0021] Optionally, in the embodiment of the present disclosure, the weight of each energy group in the second group in the flux inner product is calculated, comprising: calculating the weight of each energy group in the second group in the flux inner product by a third formula, wherein the third formula is:
[0022]
[0023] Wherein, ψ g，r is the forward neutron flux of the gth energy group in the rth region, is the conjugate neutron flux of the gth energy group in the rth region, g is the gth energy group, r is the rth region, K1, K2, …, K n is the flux inner product weight of each energy group in the second group division, is the average flux inner product weight obtained by the second group division.
[0024] Optionally, in the embodiment of the present disclosure, before the first group energy group structure is obtained by dividing the core physical model based on the corresponding boundary line of the average flux weight when the average flux weight meets the division condition, the method further comprises:
[0025] The flux inner product weights of the plurality of energy groups in the second group are added to obtain a total of the second group;
[0026] If the average flux weight is equal to the total of the second group, it is determined that the average flux weight meets the division condition.
[0027] Optionally, in the embodiment of the present disclosure, the fuel spheres have different enrichment, burnup level and temperature attributes.
[0028] Optionally, in the embodiment of the present disclosure, the first group is a 4-group.
[0029] Optionally, in the embodiment of the present disclosure, the second group is a 361-group.
[0030] Optionally, in the embodiment of the present disclosure, the target division is a 4-division.
[0031] The technical scheme provided by the embodiment of the present disclosure can include the following beneficial effects:
[0032] The method for determining the energy group structure for the core physics calculation of the high-temperature gas-cooled reactor comprises the following steps: constructing a core physics model, wherein the core physics model is a core model comprising multiple batches of fuel balls and graphite balls; performing forward neutron transport calculation on the core physics model to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physics model; performing conjugate neutron transport calculation on the core physics model to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physics model; determining the average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density; and when the average flux weight meets the division condition, dividing the core physics model based on the boundary line corresponding to the average flux weight to obtain the first group energy group structure. Thus, the present disclosure provides a method for determining the few-group energy group structure of the high-temperature gas-cooled reactor, realizes the transition from multi-group to few-group calculation, and thus realizes the low memory consumption and short calculation time of the calculation of the pebble bed high-temperature gas-cooled reactor, thereby saving the calculation time and calculation resources.
[0033] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF DRAWINGS
[0034] The accompanying drawings, which are incorporated into and form part of the specification, illustrate embodiments consistent with the present disclosure and, together with the specification, serve to explain the principles of the present disclosure.
[0035] Figure 1 FIG. 1 is a flowchart of a method for determining the energy group structure for the core physics calculation of the high-temperature gas-cooled reactor according to some embodiments of the present disclosure;
[0036] Figure 2 FIG. 2 is a schematic diagram of the radial cross-section of the core of the high-temperature gas-cooled reactor according to some embodiments of the present disclosure;
[0037] Figure 3 FIG. 3 is a schematic diagram of the axial cross-section of the core of the high-temperature gas-cooled reactor according to some embodiments of the present disclosure. DETAILED DESCRIPTION
[0038] Some embodiments of the present disclosure will be described in detail herein with reference to the drawings, in which some embodiments of the present disclosure are shown by way of illustration. The following description is, therefore, not to be taken in a limiting sense, but is made merely for the purpose of describing the general principles of the present disclosure. The method, apparatus and / or system described herein can be used with any number of different devices and / or systems, and are not limited to the devices and / or systems set forth herein.
[0039] The implementations described below with respect to some embodiments of the present disclosure are not meant to be representative of all implementations consistent with the present disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of the present disclosure as detailed in the appended claims.
[0040] Figure 1 is a flowchart of a method for determining a group structure for a high temperature gas cooled reactor core physics calculation according to some embodiments of the present disclosure, as shown in Figure 1 The method can include the following steps:
[0041] Step 101, constructing a core physics model, wherein the core physics model is a core model including a plurality of batches of fuel spheres and graphite spheres.
[0042] In the embodiments of the present disclosure, the fuel spheres have different enrichment levels, burnup levels and temperature properties.
[0043] In the embodiments of the present disclosure, the core physics model can further include a reflector layer. Figure 2 A high temperature gas cooled reactor core radial cross-sectional view is provided for the embodiments of the present disclosure, Figure 3 A high temperature gas cooled reactor core axial cross-sectional view is provided for the embodiments of the present disclosure. As shown in Figure 2 and Figure 3 The core physics model includes a standard reflector layer, an absorber channel containing reflector layer, a gap containing reflector layer and a cold helium channel containing reflector layer.
[0044] Step 102, performing a forward neutron transport calculation on the core physics model to obtain a multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physics model.
[0045] In the embodiments of the present disclosure, after obtaining the core physics model through the above steps, a forward neutron transport calculation can be performed on the core physics model to obtain a multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physics model.
[0046] Specifically, in the embodiments of the present disclosure, the method for performing forward neutron transport calculation on the core physical model to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physical model can include the following steps: performing forward neutron transport calculation on the core physical model by a first formula to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physical model, wherein the first formula is:
[0047]
[0048] wherein Ω is a unit direction vector of motion, r is a spatial position of a neutron, E is a neutron energy, k eff is a neutron effective multiplication factor, v is a number of fission neutrons, χ(E) is a fission neutron energy spectrum, ψ is a forward neutron flux density, f(r, Ω', E'→Ω, E) represents a probability that a neutron at a spatial position r, with an energy of E' and a direction of Ω', after interacting with an atom, has an energy falling within a nearby dE and a direction Ω falling within a nearby dΩ, s is scattering, f is fission, and t is a sum of scattering and fission cross sections.
[0049] Step 103, performing conjugate neutron transport calculation on the core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model.
[0050] In the embodiments of the present disclosure, after obtaining the core physical model through the above steps, the core physical model can be subjected to conjugate neutron transport calculation to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model.
[0051] Specifically, in the embodiments of the present disclosure, the method for performing conjugate neutron transport calculation on the core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model can include the following steps: performing conjugate neutron transport calculation on the core physical model by a second formula to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model, wherein the second formula is:
[0052]
[0053] wherein ψ * is a conjugate neutron flux density, and f(r, Ω, E→Ω', E') represents a probability that a neutron at a spatial position r, with an energy of E and a direction of Ω, after interacting with an atom, has an energy falling within a nearby dE' and a direction Ω' falling within a nearby dΩ'.
[0054] Step 104, determining an average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density.
[0055] In the embodiments of the present disclosure, after the multi-group forward neutron flux density and the multi-group conjugate neutron flux density are determined through the above steps, the average flux weight in the first group division can be determined based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density.
[0056] In the embodiments of the present disclosure, the first group can be a 4-group.
[0057] In the embodiments of the present disclosure, the method for determining the average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density can include the following steps:
[0058] Step 1041, the weight of each energy group in the second group on the flux inner product is calculated.
[0059] In the embodiments of the present disclosure, the method for calculating the weight of each energy group in the second group on the flux inner product can include: calculating the weight of each energy group in the second group on the flux inner product through a third formula, wherein the third formula is:
[0060]
[0061] wherein ψ g，r is the forward neutron flux of the gth energy group in the rth region, is the conjugate neutron flux of the gth energy group in the rth region, g is the gth energy group, r is the rth region, K1, K2, …, K n is the flux inner product weight of each energy group in the second group division, is the average flux inner product weight obtained by the second group division.
[0062] In the embodiments of the present disclosure, the second group can be a 361-group.
[0063] Step 1042, based on the weight of each energy group in the second group on the flux inner product, the total inner product weight of the second group is obtained.
[0064] In the embodiments of the present disclosure, after the weight of each energy group in the second group on the flux inner product is obtained through the above steps, the weight of each energy group in the second group on the flux inner product is added to obtain the total inner product weight of the second group
[0065] Step 1043, the total inner product weight of the second group is equally divided to obtain the average flux weight in the first group division.
[0066] In the embodiments of the present disclosure, after the total inner product weight of the second group is obtained through the above steps, the total inner product weight of the second group can be equally divided to obtain the average flux weight in the first group division.
[0067] In the embodiments of the present disclosure, the target equal division can be a 4-way equal division.
[0068] In the embodiments of the present disclosure, the total inner product weight of the second group is divided into 4 parts, that is, the average flux weight in the first group division is
[0069] In step 105, when the average flux weight meets the division condition, the core physical model is divided based on the division line corresponding to the average flux weight, to obtain the first group energy group structure.
[0070] In the embodiments of the present disclosure, after the average flux weight is determined by the above steps, before the core physical model is divided based on the division line corresponding to the average flux weight to obtain the first group energy group structure, the method can further include the following steps:
[0071] Step 1, the flux inner product weights of the plurality of energy groups in the second group are added to obtain the total sum K1+K2+…+K n ;
[0072] Step 2, if the average flux weight is equal to the total sum of the second group, it is determined that the average flux weight meets the division condition. In the embodiments of the present disclosure, if the average flux weight is equal to the total sum of the second group, that is, At this time, it can be determined that the average flux weight meets the division condition.
[0073] In the embodiments of the present disclosure, after it is determined that the average flux weight meets the division condition by the above steps, the core physical model can be divided based on the division line corresponding to the average flux weight to obtain the first group energy group structure.
[0074] The present disclosure provides an energy group structure determination method for high-temperature gas-cooled reactor core physical calculation, which comprises constructing a core physical model, wherein the core physical model is a core model comprising multiple batches of fuel balls and graphite balls; performing forward neutron transport calculation on the core physical model to obtain the multi-group forward neutron flux density of each batch of fuel balls and graphite balls in the core physical model; performing conjugate neutron transport calculation on the core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel balls and graphite balls in the core physical model; determining the average flux weight in the first group division based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density; and when the average flux weight meets the division condition, dividing the core physical model based on the division line corresponding to the average flux weight to obtain the first group energy group structure. Thus, the present disclosure provides a method for determining the few-group energy group structure of the high-temperature gas-cooled reactor, realizes the conversion from multi-group to few-group calculation, and thus realizes the low memory consumption and short calculation time of the calculation of the pebble bed high-temperature gas-cooled reactor, saving the calculation time and calculation resources.
[0075] It should be understood that the various forms of flow shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, in series, or in a different order, as long as the desired results of the technology disclosed in the present disclosure are achieved, which is not limited herein.
[0076] The specific implementation described above does not constitute a limitation on the protection scope of the present disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present disclosure shall be included in the protection scope of the present disclosure.
Claims
1. A method for determining the energy group structure for physical calculations of a high-temperature gas-cooled reactor core, characterized in that, The method includes: Construct a core physical model, wherein the core physical model is a core model including multiple batches of fuel balls and graphite balls; Forward neutron transport calculations were performed on the core physics model to obtain the multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physics model. Conjugate neutron transport calculations were performed on the core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel spheres and graphite spheres in the core physical model. Based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density, the average flux weight in the first group partition is determined. When the average flux weight satisfies the partitioning condition, the core physical model is partitioned based on the boundary line corresponding to the average flux weight to obtain the first energy group structure.
2. The method as described in claim 1, characterized in that, The step of performing forward neutron transport calculations on the core physical model to obtain the multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physical model includes: performing forward neutron transport calculations on the core physical model using a first formula to obtain the multi-group forward neutron flux density of each batch of fuel spheres and graphite spheres in the core physical model, wherein the first formula is: Where Ω is the unit direction vector of motion, r is the spatial position of the neutron, E is the neutron energy, and k eff denoted as the effective neutron multiplication coefficient, v as the number of fission neutrons, χ(E) as the fission neutron energy spectrum, ψ as the forward neutron flux density, and f(r,Ω′,E′→Ω,E) representing the energy change of a neutron at spatial position r with energy E' and direction Ω' after interacting with an atom and falling within the vicinity dE, where direction Ω is the probability of falling within the vicinity dΩ, s is scattering, f is fission, and t is the sum of the scattering and fission cross sections.
3. The method as described in claim 1, characterized in that, The step of performing conjugate neutron transport calculations on the reactor core physical model to obtain the multi-group conjugate neutron flux density of each batch of fuel spheres and graphite spheres in the reactor core physical model includes: performing conjugate neutron transport calculations on the reactor core physical model using a second formula to obtain the multi-group conjugate neutron flux density of each batch of fuel spheres and graphite spheres in the reactor core physical model, wherein the second formula is: Where, ψ * Let f(r,Ω,E→Ω′,E′) be the conjugate neutron flux density, and let f(r,Ω,E→Ω′,E′) represent the probability that a neutron with energy E and direction Ω at spatial position r interacts with an atom, and its energy changes to E′ and falls within the vicinity dE′, and its direction Ω′ falls within the vicinity dΩ′.
4. The method as described in claim 1, characterized in that, The determination of the average flux weight in the first group partition based on the multi-group forward neutron flux density and the multi-group conjugate neutron flux density includes: Calculate the weight of each energy group in the second group on the flux inner product; Based on the weight of each energy group in the second group in the flux inner product, the total inner product weight of the second group is obtained. The total inner product weight of the second group is divided equally to obtain the average flux weight in the first group partition.
5. The method as described in claim 4, characterized in that, The calculation of the weight of each energy group in the second group on the flux inner product includes: calculating the weight of each energy group in the second group on the flux inner product using a third formula, wherein the third formula is: Where, ψ g，r Let g be the forward neutron flux in the r-th region of the g-th energy group. Let K1, K2, ..., K be the conjugate neutron flux of the r-th region in the g-th energy group, where g is the g-th energy group and r is the r-th region. n This represents the flux inner product weight for each energy group during the second group partitioning. The average flux inner product weight is obtained from the second group partition.
6. The method as described in claim 1, characterized in that, Before dividing the core physical model based on the boundary line corresponding to the average flux weight to obtain the first energy group structure when the average flux weight satisfies the partitioning condition, the method further includes: The flux inner product weights of multiple energy groups in the second group are added together to obtain the sum of the fluxes in the second group; If the average flux weight is equal to the sum of the second group, then the average flux weight is determined to satisfy the partitioning condition.
7. The method as described in claim 1, characterized in that, The fuel balls have different enrichment levels, burnup levels, and temperature properties.
8. The method according to any one of claims 1-6, characterized in that, The first group is group 4.
9. The method according to any one of claims 1-6, characterized in that, The second group is group 361.
10. The method as described in claim 4, characterized in that, The target is divided into four equal parts.