Hybrid fuel pebble bed equilibrium core calculation method

Abstract

This invention relates to a method for calculating a balanced reactor core using a mixed-fuel spherical bed, comprising the following steps: Based on the actual flow state of the fuel spheres, the entire reactor core spherical bed is divided radially into several flow channels, and each flow channel is divided axially into several spherical flow grids of equal volume, thus dividing the entire spherical bed region into several spherical flow grids of equal volume. The fuel spheres within each spherical flow grid are divided into several batches, and the number of batches for each type of fuel sphere is set according to the volume ratio and cycle number of each type. A burnup recursive relationship is established for each spherical flow grid in the reactor core under the actual flow state of the fuel spheres. Burnup recursive calculations are performed on all types and batches of fuel spheres to obtain the nuclide density distribution within each spherical flow grid and all batches of the entire reactor core. Based on the calculated nuclide density distribution of the entire reactor core, the macroscopic cross-section is calculated, and then the coupled solution process of whole-reactor criticality calculation, thermal feedback calculation, and burnup recursive calculation is completed.

Description

Technical Field

[0001] This invention relates to a method for calculating a balanced core in a mixed-fuel pebble bed reactor, and more particularly to a direct calculation method for a balanced core in a mixed-fuel pebble bed reactor of a high-temperature gas-cooled reactor. Background Technology

[0002] Pebble bed high-temperature gas-cooled reactors (HTGRs) feature a fuel cycle characterized by continuous refueling and multiple passes. During operation, if the refueling strategy of the pebble bed core remains constant, the spatial distribution of parameters such as burnup depth, nuclide density, neutron flux, and temperature field within the pebble bed core no longer changes over time, thus reaching a balanced core state. Balanced core characteristics are crucial for the physics design of HTGRs.

[0003] There are two main methods for calculating the balance of a high-temperature gas-cooled reactor (HTGR) core. One is the step-by-step refueling simulation method used in the VSOP program, which simulates the complete refueling and burnup process from initial loading to the final balance of the core. However, this simulation process is computationally expensive. The other method is the direct calculation method for the balance of the core used in the PEBBED program. Its basic idea is to directly obtain the balance of the core state by solving the burnup equation considering the pebble bed flow, based on the spatiotemporal reciprocity of the balance of the core. Those skilled in the art have conducted research on the direct calculation of HTGR balance, developing a series of calculation methods. However, the methods developed in the aforementioned literature are only for single-type fuel spheres. New HTGR designs may employ a mixed fuel cycle with multiple types of fuel spheres, such as a thorium-uranium cycle or a thorium-plutonium cycle. In mixed fuel cycles, different types of fuel spheres may employ different refueling strategies, such as different cycles (number of times through the core).

[0004] The inventors have previously proposed a method for simulating the dumping of mixed-fuel pellet beds. This invention discloses for the first time the direct calculation method for balanced cores using mixed fuels in the PANGU program and its implementation details.

[0005] The pebble bed core burnup equation considering pebble bed flow is as follows:

[0006]

[0007] in For the core The vector consisting of the nuclide densities at time t; The velocity vector of the fuel ball flow; This is the fuel consumption coefficient matrix, where λ is the nuclide decay constant. and Let be the single-group flux and the single-group microscopic cross-section of a nuclide, respectively, defined as follows:

[0008]

[0009] in for The fuel temperature indicates that the microscopic cross-section is temperature-dependent.

[0010] When the core is in equilibrium, equation (1) simplifies to:

[0011]

[0012] Then when the flow velocity is When the distribution is uniform in the vicinity, the following relationship holds:

[0013]

[0014] Physical calculations for high-temperature gas-cooled reactors typically employ methods such as Figure 1 The feeding model shown is as follows: First, the entire pebble bed region is divided radially into several channels, with channel boundaries that can be straight lines or curves. Each channel is then divided axially into several layers, resulting in several pebble flow grids of equal volume. The number of layers can vary between channels to simulate different pebble flow velocities. Within each pebble flow grid, fuel spheres are divided into several batches, with each batch possessing the same physical properties (including material composition, burnup depth, neutron flux density, etc.).

[0015] Let the flow channel, layer, and batch numbers be i, j, and m, respectively. Let Δt be the time it takes for all fuel balls in the spherical flow grid to fall into the axially lower spherical flow grid (i, j+1). Then, according to equation (4), the recursive expression for the fuel consumption equation of the axially adjacent spherical flow grids is:

[0016]

[0017] Further derivation yields:

[0018]

[0019] Figure 2 The recursive relationship of burnup of fuel spheres in the same batch within adjacent sphere grids of a balanced reactor core is presented. Fuel discharged from the bottom of the core needs to be considered for mixing within the same batch across different channels before returning to the top of the core to become the next batch. During this mixing process, the average nuclide density is obtained by weighting the fuel volume discharged from different channels, as shown in the following formula:

[0020]

[0021] In the formula J i This indicates the number of sphere grids in the i-th flow channel (i.e., the bottom sphere grid number).

[0022] Only the first batch of new fuel of each fuel type needs to be specified for the first layer of the spherical flow grid in each flow channel. The remaining sphere flow grids and batches of fuel nuclides can be determined based on equations (5) and (7). The spatial recursive order of each batch of fuel spheres in the entire reactor core is shown in [reference needed]. Figure 3 .

[0023] The above calculation method only considers a single fuel type. On the other hand, traditional high-temperature gas-cooled reactor calculation programs (such as VSOP) use an average sphere model for all batches of spheres within the sphere flow grid, which cannot distinguish the neutron flux and energy spectrum of each batch. Therefore, the same neutron flux and microscopic single-group cross section can only be approximately used in the burnup process of each batch.

[0024] Therefore, it is hoped that an accurate and efficient direct calculation method for balanced reactor cores with mixed fuel spheres can be proposed, so as to be used for calculations of balanced reactor cores of high-temperature gas-cooled reactors with multiple types of fuel spheres. Summary of the Invention

[0025] To address the aforementioned technical problems, this invention proposes a method for calculating a balanced reactor core using a mixed-fuel pebble bed. The pebble bed contains multiple types of fuel spheres, each type occupying a predetermined volume percentage within the pebble bed region and being circulated a predetermined number of times. The method includes the following steps:

[0026] Based on the actual flow state of the fuel balls, the entire core ball bed is divided into several flow channels in the radial direction. Each flow channel is divided into several ball flow grids with equal volume in the axial direction, so that the entire ball bed area is divided into several ball flow grids with equal volume. The fuel balls in each ball flow grid are divided into several batches, and the number of batches of each type of fuel ball is set according to the volume ratio of each type of fuel ball and the number of cycles.

[0027] Establish the burnup recursion relationship of each spherical flow grid in the reactor core under the actual flow state of the fuel spheres, including: establishing the burnup recursion relationship from the top to the bottom of the spherical bed region for each type of fuel sphere; and establishing the burnup recursion relationship between the batch-by-batch volume weighted average of each type of fuel sphere discharged from the spherical flow grid at the bottom of each flow channel and the next batch of fuel spheres of the same type from the spherical flow grid at the top of each flow channel.

[0028] Based on the established burnup recursion relationship, burnup recursion calculations were performed on all types and batches of fuel balls to obtain the nuclide density distribution in each ball flow grid and for all batches in the entire reactor core.

[0029] Based on the calculated nuclide density distribution of the entire reactor core, the macroscopic cross section is calculated, and then the coupled solution process of whole-reactor criticality calculation, thermal feedback calculation, and burnup recursion calculation is completed. In the process of whole-reactor criticality calculation, the neutron flux and neutron energy spectrum of each batch are calculated independently, and the single-group cross section required for the burnup calculation of each batch is independently merged.

[0030] Setting the batch number for each type of fuel ball based on the volume ratio and cycle number of each type implies that the batch division strategy should be able to reasonably reflect the volume ratio and cycle number of each type of fuel ball.

[0031] In a first preferred embodiment of this batching strategy in the mixed-fuel pebble bed core balancing calculation method according to the present invention, the number of batches for each type of fuel sphere is equal to the number of cycles. Batches of the same type of fuel sphere have the same volume fraction, while batches of different types of fuel spheres can have different volume fractions, thereby ensuring that the volume ratio of different types of fuel spheres conforms to the actual loading conditions. According to this batching strategy, the volume fraction of a single batch of different types of fuel spheres may be different. For example, suppose the pebble bed contains uranium spheres and thorium spheres with a volume ratio of 3:1, and both uranium and thorium spheres pass through the core 5 times. Under this batching strategy, each sphere flow grid contains 10 batches of fuel spheres, with uranium and thorium spheres each divided into 5 batches. The volume fraction of each uranium sphere batch is 15%, and the volume fraction of each thorium sphere batch is 5%. That is, the volume fraction of each uranium sphere batch is the same, and the volume fraction of each thorium sphere batch is also the same, but the volume fraction of each uranium sphere batch and the volume fraction of each thorium sphere batch are different.

[0032] In a second preferred embodiment of this batching strategy of the mixed-fuel pebble bed core balancing calculation method according to the present invention, each batch of each type of fuel sphere has the same volume fraction, the ratio of the number of batches of each type of fuel sphere is equal to the volume ratio of each type of fuel sphere, and the number of batches of each type of fuel sphere is an integer multiple of its cycle number. It should be understood that when the number of batches is M times the cycle number, then every M batches represents one cycle number. For example, in the same example case, assuming the pebble bed contains uranium spheres and thorium spheres with a volume ratio of 3:1, and both uranium and thorium spheres pass through the core 5 times, the fuel spheres in each sphere flow grid can be divided into 20 batches, each batch having the same volume fraction, with uranium spheres occupying 15 batches and thorium spheres occupying 5 batches, i.e., the ratio of the number of batches of uranium spheres to thorium spheres is also equal to 3:1, the same as its volume ratio. Wherein, batches 1-3 of uranium spheres represent the 1st pass, batches 4-6 represent the 2nd pass, ..., batches 13-15 represent the 5th pass. In other words, not only are the volume fractions of each batch of uranium spheres the same, but the volume fractions of each batch of thorium spheres are also the same. Furthermore, the volume fractions of each batch of uranium spheres and each batch of thorium spheres are also the same. In this case, the ratio of their batch numbers is their volume ratio.

[0033] It should be understood that these two batching strategies can also be used in combination in different channels of the reactor core, but this would establish a more complex burnup recursion relationship for each type of fuel ball, and therefore, although feasible, it is not the preferred option.

[0034] However, any batching strategy that can reasonably simulate the volume ratio and number of cycles of various types of fuel balls based on the above batching strategy or similar strategies derived therefrom should obviously fall within the scope of this invention.

[0035] The mixed-fuel pebble bed balanced reactor core calculation method of the present invention can be solved by either iterative methods or by directly solving a system of simultaneous equations.

[0036] The following formula is used to establish a recursive relationship for the fuel consumption of each type of fuel pellet, from the top to the bottom of the pellet bed area:

[0037]

[0038] In the formula, the subscript k represents the fuel type number.

[0039] A batch-by-batch volume-weighted average of the different types of fuel balls discharged from the bottom ball flow grid of each flow channel in the reactor core is used to establish a recursive relationship with the same type of fuel balls passing through the top ball flow grid of each flow channel in the next batch. When the fuel ball batching strategy adopts the first preferred implementation, the recursive relationship is as follows:

[0040]

[0041] When the fuel ball batching strategy adopts the second preferred implementation, and the number of batches of the k-th type of fuel balls is M times its cycle number, the subscript m in formula (9) is... k +1 is replaced with m accordingly. k +M. In other words, the first preferred implementation of the batching strategy for the next batch of fuel balls of the same type passing through the top ball flow grid of each channel is the next batch of fuel balls of the same type passing through the top ball flow grid of each channel, and the second preferred implementation of the batching strategy is the next M batches of fuel balls of the same type passing through the top ball flow grid of each channel.

[0042] Then, the burnup of all types and batches of fuel balls is calculated by recursion according to formulas (8) and (9) to obtain the nuclide density distribution of all batches in each ball flow grid of the entire core.

[0043] Figure 4 It describes the recursive relationship of fuel consumption for adjacent sphere flow grids of the same type and with the same number of passes (cycles). Figure 5 The spatial recursive order of fuel spheres of various types and batches is described. It should be noted that if the latter batching strategy is adopted as described above, the subscript j in formula (8) represents the number of passes, which may include multiple batches. For simplicity, the former batching strategy will be used in the following description, that is, the number of batches for each type of fuel sphere is equal to its number of cycles.

[0044] In one embodiment of the mixed-fuel sphere bed balanced reactor core calculation method according to the present invention, in the steps of completing the coupled solution process of whole-reactor criticality calculation, thermal feedback calculation, and burnup recursive calculation, an iterative method is adopted to solve the problem, repeating the following steps ① and ② until the calculation of neutron flux, temperature, and nuclide density distribution in the reactor core converges: ① First, perform whole-reactor criticality calculation and thermal feedback calculation to obtain the power distribution and microscopic cross-section of all types and batches of fuel spheres; ② Then, perform burnup recursive calculation on all types and batches of fuel spheres to update the whole-reactor nuclide density distribution and the macroscopic cross-section required for the next whole-reactor criticality calculation.

[0045] In another embodiment of the mixed-fuel pebble bed balanced reactor core calculation method according to the present invention, during the coupled solution process of completing the whole reactor criticality calculation, thermal feedback calculation, and fuel consumption recursive calculation, a system of simultaneous equations relating the whole reactor criticality, thermal feedback, and fuel consumption recursive relationship is established and the system of simultaneous equations is solved directly. Attached Figure Description

[0046] Embodiments of the present invention are illustrated below with reference to the accompanying drawings. In the drawings:

[0047] Figure 1 This is a schematic diagram of the core pouring model for a pebble bed stack.

[0048] Figure 2 The diagram illustrates the burnup recursion in direct calculations for a single-fuel-balanced reactor core.

[0049] Figure 3 The spatial recursive order in direct calculation of a single fuel-balanced reactor core is illustrated schematically.

[0050] Figure 4 The diagram illustrates the burnup recursion in the direct calculation of a mixed-fuel balanced reactor core.

[0051] Figure 5 The spatial recursive order in the direct calculation of a mixed-fuel balanced reactor core is illustrated schematically. Detailed Implementation

[0052] Assume the pebble bed core contains uranium, thorium, and plutonium fuel spheres (numbered 1, 2, and 3 respectively) in a volume ratio of 5:3:1. The number of times each fuel sphere passes through the core is: 5 times for uranium, 3 times for thorium, and 1 time for plutonium. For simplicity, assume the core is radially divided into two channels: channel 1, located on the inner side, contains 10 sphere flow grids; channel 2, located on the outer side, contains 15 sphere flow grids. The refueling time step is Δt.

[0053] Step (1): The uranium, thorium, and plutonium spheres are divided into batches of 5, 3, and 1 with equal volume ratios, so each sphere flow grid contains a total of 9 batches. Assume that the initial state of the reactor core consists entirely of new fuel spheres.

[0054] Step (2): Establish the recursive relationship of fuel consumption for each channel and sphere flow grid for different types of fuel spheres. Taking the third batch of thorium fuel spheres (fuel type number 2) in channel 1 as an example, the nuclide density expression for each sphere flow grid is as follows:

[0055]

[0056] The batch of fuel balls discharged from the bottom spherical flow grids (numbered 10 and 15) of the two flow channels was volume-weighted and mixed. A burnup recursion relationship was established with the fourth batch of thorium fuel balls from the first layer spherical flow grid of the two flow channels. The expression for the burnup recursion relationship is as follows:

[0057]

[0058] Step (3): Conduct full-reactor criticality calculation and thermal feedback coupled calculation to obtain parameters such as flux, temperature, and burnup cross section of all batches of fuel balls of the three types, which are used for burnup recursive calculation.

[0059] Step (4): According to equations (8) and (9), and Figure 5 The given recursive order is used to perform burnup recursive calculations on all batches of fuel balls of the three types, update the total reactor nuclide density, and use it for the next total reactor criticality and thermal feedback coupling calculation.

[0060] Repeat steps (3) and (4) until the calculations of neutron flux, temperature, and nuclide density in the reactor core converge.

[0061] The preferred embodiments of the present invention have been described above, but the spirit and scope of the present invention are not limited to the specific contents disclosed herein. Those skilled in the art can make many more implementations and applications based on the teachings of the present invention, including any combination of the various technical features of the above embodiments. These implementations and applications are all within the spirit and scope of the present invention. The spirit and scope of the present invention are not limited by the specific embodiments, but by the claims.

Claims

1. A method for calculating a balanced reactor core using a mixed-fuel pebble bed, wherein the pebble bed contains multiple types of fuel pebbles, each type of fuel pebbles occupying a predetermined volume ratio within the pebble bed region and being circulated a predetermined number of times, the method comprising the following steps: Based on the actual flow state of the fuel spheres, the entire core pebble bed is divided radially into several flow channels. Each flow channel is further divided axially into several sphere flow grids of equal volume, resulting in the entire pebble bed region being divided into several sphere flow grids of equal volume. The fuel balls within each ball flow grid are divided into several batches, and the number of batches for each type of fuel ball is set according to the volume ratio of each type of fuel ball and the number of cycles. Establish the burnup recursion relationship of each spherical flow grid in the reactor core under the actual flow state of the fuel spheres, including: establishing the burnup recursion relationship from the top to the bottom of the spherical bed region for each type of fuel sphere; and establishing the burnup recursion relationship between the batch-by-batch volume weighted average of each type of fuel sphere discharged from the spherical flow grid at the bottom of each flow channel and the next batch of fuel spheres of the same type from the spherical flow grid at the top of each flow channel. Based on the established burnup recursion relationship, burnup recursion calculations were performed on all types and batches of fuel balls to obtain the nuclide density distribution in each ball flow grid and for all batches in the entire reactor core. Based on the calculated nuclide density distribution of the entire reactor core, the macroscopic cross section is calculated, and then the coupled solution process of whole-reactor criticality calculation, thermal feedback calculation, and burnup recursion calculation is completed. In the process of whole-reactor criticality calculation, the neutron flux and neutron energy spectrum of each batch are calculated independently, and the single-group cross section required for the burnup calculation of each batch is independently merged.

2. The method for calculating balanced core composition of a mixed-fuel pebble bed according to claim 1, characterized in that, The number of batches for each type of fuel ball is equal to the number of cycles. Each batch of the same type of fuel ball has the same volume share, while batches of different types of fuel balls can have different volume shares, thus ensuring that the volume ratio of different types of fuel balls conforms to the actual loading conditions.

3. The method for calculating a balanced reactor core using a mixed-fuel pebble bed according to claim 1, characterized in that, Each batch of each type of fuel ball has the same volume fraction, the ratio of the number of batches of each type of fuel ball is equal to the volume ratio of each type of fuel ball, and the number of batches of each type of fuel ball is an integer multiple of the number of cycles of each type of fuel ball.

4. The method for calculating a balanced reactor core using a mixed-fuel pebble bed according to claim 2 or 3, characterized in that, In the coupled solution process of completing the full-reactor criticality calculation, thermal feedback calculation, and burnup recursion calculation, an iterative method is used to solve the problem, repeating the following steps ① and ② until the calculations of core neutron flux, temperature, and nuclide density distribution converge: ① First, perform full-reactor criticality calculations and thermal feedback calculations to obtain the power distribution and micro-sections of all types and batches of fuel pellets; ②Then, burnup recursion calculations are performed on all types and batches of fuel balls to update the nuclide density distribution of the entire reactor and the macroscopic cross section required for the next reactor criticality calculation.

5. The method for calculating balanced core composition of a mixed-fuel pebble bed according to claim 2 or 3, characterized in that, In the coupled solution process of completing the full reactor criticality calculation, thermal feedback calculation, and fuel consumption recursion calculation, a system of simultaneous equations relating full reactor criticality, thermal feedback, and fuel consumption recursion is established and the system of simultaneous equations is solved directly.

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