An equivalent modeling method and system suitable for special-shaped fuels

Abstract

An equivalent modeling method and system suitable for special-shaped fuels, relating to the field of fuel element modeling in nuclear reactor design. To solve the problem that the design program used in the prior art nuclear design is aimed at simple cylindrical fuel elements and is difficult to handle complex geometric models, the equivalent modeling method includes: calculating the effective proliferation coefficient of the special-shaped cross spiral fuel model, initializing the volume of the central fuel cylinder to half of the total volume of the special-shaped cross spiral fuel; initializing an equivalent model equal to the effective proliferation coefficient of the special-shaped cross spiral fuel, and setting the initial value of the equivalent model; using the Monte Carlo method to calculate the effective proliferation coefficient of the equivalent model, and comparing it with the effective proliferation coefficient of the special-shaped cross spiral fuel model, using the Monte Carlo method to calculate the effective proliferation coefficients of the special-shaped cross spiral model and the equivalent model at different burnup points and compare them; it is also applicable to the fields of special-shaped cross spiral fuel analysis and reactor fuel assembly design.

Description

Technical Field

[0001] The invention relates to the field of fuel element modeling in nuclear reactor design, and in particular to an equivalent modeling method and system suitable for special-shaped fuels. Background Art

[0002] In recent years, with the continuous development of reactors, the fuel elements in nuclear reactor design have become more diversified, with the emergence of special-shaped geometries such as rods, spheres, rings, plates, crosses, and wire windings. Among them, the special-shaped cross spiral fuel assembly improves its thermal hydraulic performance and power density by increasing the heat exchange area. Compared with traditional pressurized water reactor fuel elements, spiral structural elements can maintain material strength and structural integrity under operating conditions while ensuring strong heat exchange capacity, thereby improving the safety and economy of the reactor. However, since the objects of traditional reactor neutron physics analysis are mostly regular geometries, it is difficult to apply them to special-shaped geometries. Therefore, for special-shaped spiral elements, it is necessary to establish a corresponding equivalent model to simplify their geometric features so that they can adapt to traditional neutron analysis software.

[0003] The method used by Monte Carlo programs such as Serpent and OpenMC to describe geometry is structural solid geometry (CSG). This method uses Boolean operations on equation surfaces to represent solid geometry. Commonly used geometric shapes include regular shapes such as planes, circles, hexagons, and rectangles. The CSG method can accurately describe the geometric characteristics of a single two-dimensional cross-helical fuel, such as Figure 2 As shown in the figure (the yellow part is the fuel, the blue and orange parts are the coolant, and the gray part is the cladding), the discrete two-dimensional cross sections are axially stretched and stacked to obtain the final axial slice stacking model of the special-shaped cross spiral fuel. Its xz cross-section diagram is shown in Figure 1 shown.

[0004] However, the spiral surface expression of the special-shaped cross spiral fuel element contains transcendental functions such as sine and cosine, which makes the spiral geometry unable to be effectively described in the common CSG modeling method. Therefore, in the traditional Monte Carlo program, the stacked model of axial slices is usually used to approximate the special-shaped cross spiral fuel. When there are many axial slices, the discrete spiral stretching surface can be regarded as a continuous spiral surface. This method improves the accuracy of modeling, but it also increases the complexity of the model.

[0005] To solve the problem of CSG modeling method in dealing with spiral surfaces, the University of Wisconsin developed the Direct Accelerated Monte Carlo method (DAGMC), which realizes the particle positioning and transport calculation based on CAD model. DAGMC can use CAD models created by AutoCAD, SolidWorks, COMSOL Multiphysics and other software after being processed by CUBIT. This method has strong modeling freedom and accuracy.

[0006] Since the geometry of DAGMC is composed of a large number of triangular patch entities, a large number of geometric calculations are needed to determine the location of particles and possible boundary intersections when performing particle transport calculations. Therefore, there are problems with computational efficiency and it is difficult to directly apply it to reactor design.

[0007] In summary, the design programs used in nuclear design in the prior art are generally APOLLO, CASMO, etc., which are mostly aimed at simple cylindrical fuel elements and are difficult to handle complex geometric models. Therefore, it is necessary to equate the complex spiral geometry of the special-shaped cross spiral fuel element to a simple circular geometry and ensure the accuracy of the effective proliferation coefficient in the burnup calculation under different conditions. Summary of the invention

[0008] The present invention aims at the design procedure adopted in the nuclear design in the prior art, which is aimed at simple cylindrical fuel elements and is difficult to handle complex geometric models. Therefore, it is necessary to equate the complex spiral geometry of the special-shaped cross spiral fuel element to a simple circular geometry and ensure the accuracy of the effective proliferation coefficient in the fuel consumption calculation under different conditions.

[0009] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0010] Solution 1: An equivalent modeling method applicable to special-shaped fuels, the equivalent modeling method comprising the following steps:

[0011] Step 1: Calculate the effective multiplication coefficient Keff under the initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions

[0012] Step 2: Construct an equivalent model and set the initial value of the equivalent model, which includes initializing the central fuel volume of the equivalent model. iter and Fuel during the search min , Fuel max Among them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel;

[0013] Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , among which Water min =0;

[0014] Step 3: Use the Monte Carlo method to calculate the effective proliferation coefficient Keff of the equivalent model described in step 2eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in step 1 hex Compare them. When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated.

[0015] Step 4: Use the Monte Carlo method to calculate the effective multiplication coefficients of the special-shaped cross-helix model in step 1 and the equivalent model described in step 2 at different burnup points And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in step 2, otherwise update the size of the central fuel of the equivalent model in step 2.

[0016] Furthermore, a preferred embodiment is provided, in which the special-shaped cross-spiral fuel model described in step one is implemented by using a CSG stacking model with ten axial slices.

[0017] Further, a preferred embodiment is provided, in which the method for updating the volume of the intermediate layer coolant in step 3 is: Water iter =(Water min +Water max ) / 2

[0018] If Keff eq >Keff hex , then Water max =Water iter , update Water iter ;

[0019] If Keff eq <Keff hex , then Water min =Water iter , update Water iter .

[0020] Further, a preferred embodiment is provided, in which the method for updating the volume of the central fuel in step 4 is: iter =(Fuel min +Fuel max ) / 2

[0021] Calculate the error between the effective multiplication coefficient of the special-shaped cross-helical fuel and the equivalent model at all fuel points, and calculate the mean of the error

[0022] If Err>0, then Fuel max =Fuel iter, Update Fuel iter ;

[0023] If Err>0, then Fuel min =Fuel iter , Update Fuel iter .

[0024] Furthermore, a preferred embodiment is provided, in which the arrangement of the equivalent model equal to the effective proliferation coefficient of the special-shaped cross spiral fuel described in step 2 is central fuel, middle layer coolant, outer layer fuel, cladding and outer layer coolant in sequence.

[0025] Furthermore, a preferred embodiment is provided, which includes, after setting the arrangement of the equivalent model described in step 2 that is equal to the effective proliferation coefficient of the special-shaped cross spiral fuel, the step of determining the geometric parameters of the central fuel, the middle layer coolant, the outer layer fuel, the cladding and the outer layer coolant.

[0026] Furthermore, a preferred embodiment is provided, wherein the geometric parameters of the central fuel and the intermediate coolant are determined by a dichotomy method, and the geometric parameters of the outer fuel, the cladding and the outer coolant are calculated by the principle of material conservation.

[0027] Solution 2: An equivalent modeling system suitable for special-shaped fuels, the system comprising:

[0028] Calculation module for calculating the effective multiplication coefficient Keff under initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions

[0029] Initialization module, used to build an equivalent model and set the initial value of the equivalent model, the initial value includes initializing the central fuel volume of the equivalent model Fuel iter and Fuel during the search min , Fuel max Among them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel;

[0030] Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , among which Water min =0;

[0031] The update module is used to calculate the effective proliferation coefficient Keff of the equivalent model described in the initialization module using the Monte Carlo method eqand the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in the calculation module hex Compare them. When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated.

[0032] Correction module, used to calculate the effective multiplication coefficient of the special-shaped cross spiral model in the calculation module and the equivalent model described in the initialization module at different burnup points using the Monte Carlo method And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in the initialization module, otherwise the size of the central fuel of the equivalent model in the initialization module is updated.

[0033] Solution three: A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes any one of the methods described in Solution one.

[0034] Solution 4: A computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described in any one of Solution 1 are implemented.

[0035] The present invention is beneficial in that:

[0036] The equivalent modeling method suitable for special-shaped fuels described in the present invention reduces the modeling complexity of special-shaped cross-spiral fuel elements while ensuring that the effective proliferation coefficients at different burnup depths are equal, making it applicable to traditional nuclear design programs and expanding the analysis method of special-shaped cross-spiral fuels. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the xz cross section of the axial 10-layer stacking model described in the prior art.

[0038] Figure 2 It is a schematic diagram of a two-dimensional cross-section model described in the prior art.

[0039] Figure 3 It is a cross-sectional schematic diagram of using a concentric circle geometric structure to replace a cross-shaped blade in the embodiment 10. Among them, (a) is a schematic diagram of the material partition of the special-shaped cross spiral fuel model, and (b) is a schematic diagram of the material partition of the equivalent model.

[0040] Figure 4 A schematic flow chart of an equivalent modeling method applicable to special-shaped fuels as described in Implementation Method 1.

[0041] Figure 5 This is a geometric diagram of the tenth embodiment.

[0042] Figure 6 It is a schematic diagram of the iterative search for the interlayer coolant parameters of the equivalent model described in the tenth embodiment.

[0043] Figure 7 It is a schematic diagram comparing the calculation results of the equivalent model described in the tenth embodiment and the special-shaped cross-screw fuel benchmark model under burnup conditions.

[0044] Figure 8 It is a schematic diagram comparing the calculation results of the special-shaped cross-screw fuel model and the equivalent model at different burnup points under different calculation parameters described in Implementation Example 10.

[0045] Figure 8 In the figure, (a) is a schematic diagram of the change of HZP in the hot state when the boron concentration is 0 ppm and the enrichment is 2.3; (b) is a schematic diagram of the change of HZP in the hot state when the boron concentration is 0 ppm and the enrichment is 4.5; (c) is a schematic diagram of the change of HFP in the hot state when the boron concentration is 0 ppm and the enrichment is 4.5; (d) is a schematic diagram of the change of HFP in the hot state when the boron concentration is 600 ppm and the enrichment is 2.3; (e) is a schematic diagram of the change of HZP in the hot state when the boron concentration is 600 ppm and the enrichment is 2.3; (f) is a schematic diagram of the change of HFP in the hot state when the boron concentration is 600 ppm and the enrichment is 4.5; (g) is a schematic diagram of the change of HZP in the hot state when the boron concentration is 600 ppm and the enrichment is 4.5. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the implementation methods of the present application clearer, the technical solutions in the implementation methods of the present application will be clearly and completely described below in conjunction with the drawings in the implementation methods of the present application. Obviously, the described implementation methods are only part of the implementation methods of the present application, not all of the implementation methods.

[0047] Embodiment 1: This embodiment provides an equivalent modeling method applicable to special-shaped fuels, and the equivalent modeling method comprises the following steps:

[0048] Step 1: Calculate the effective multiplication coefficient Keff under the initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions

[0049] Step 2: Construct an equivalent model and set the initial value of the equivalent model, which includes initializing the central fuel volume of the equivalent model. iter and Fuel during the search min , Fuel maxAmong them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel;

[0050] Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , among which Water min =0;

[0051] Step 3: Use the Monte Carlo method to calculate the effective proliferation coefficient Keff of the equivalent model described in step 2 eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in step 1 hex Compare them. When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated.

[0052] Step 4: Use the Monte Carlo method to calculate the effective multiplication coefficients of the special-shaped cross-helix model in step 1 and the equivalent model described in step 2 at different burnup points And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in step 2, otherwise update the size of the central fuel of the equivalent model in step 2.

[0053] Among them, see Figure 3 As shown, Water iter and Water max The blue part is the coolant volume, the yellow part is the fuel, the orange part is the coolant, and the gray part is the cladding.

[0054] Embodiment 2: This embodiment further limits the equivalent modeling method applicable to special-shaped fuels described in embodiment 1. The special-shaped cross-spiral fuel model described in step 1 is implemented by using a CSG stacking model with ten axial slices.

[0055] Embodiment 3: This embodiment further limits the equivalent modeling method applicable to special-shaped fuels described in embodiment 1. The method for updating the volume of the intermediate layer coolant in step 3 is:

[0056] Water iter =(Water min +Water max ) / 2

[0057] If Keff eq >Keff hex , then Watermax =Water iter , update Water iter ;

[0058] If Keff eq <Keff hex , then Water min =Water iter , update Water iter .

[0059] Embodiment 4: This embodiment further limits the equivalent modeling method applicable to special-shaped fuels described in embodiment 1. The method for updating the central fuel volume in step 4 is:

[0060] Fuel iter =(Fuel min +Fuel max ) / 2

[0061] Calculate the error between the effective multiplication coefficient of the special-shaped cross-helical fuel and the equivalent model at all fuel points, and calculate the mean of the error

[0062] If Err>0, then Fuel max =Fuel iter , Update Fuel iter ;

[0063] If Err>0, then Fuel min =Fuel iter , Update Fuel iter .

[0064] Embodiment 5. This embodiment is a further limitation of the equivalent modeling method applicable to special-shaped fuels described in embodiment 1. The arrangement of the equivalent model equal to the effective proliferation coefficient of the special-shaped cross-spiral fuel described in step 2 is, in sequence, the central fuel, the middle layer coolant, the outer layer fuel, the cladding and the outer layer coolant.

[0065] Embodiment 6. This embodiment is a further limitation of the equivalent modeling method suitable for special-shaped fuels described in embodiment 1. After setting the arrangement of the equivalent model equal to the effective proliferation coefficient of the special-shaped cross spiral fuel described in step 2, it also includes the step of determining the geometric parameters of the central fuel, the middle layer coolant, the outer layer fuel, the cladding and the outer layer coolant.

[0066] Embodiment 7. This embodiment is a further limitation of the equivalent modeling method applicable to special-shaped fuels described in embodiment 6. The geometric parameters of the central fuel and the middle layer coolant are determined by the dichotomy method; the geometric parameters of the outer fuel, cladding and outer coolant are calculated by the principle of material conservation.

[0067] Embodiment 8: This embodiment proposes an equivalent modeling system suitable for special-shaped fuels, the system comprising:

[0068] Calculation module for calculating the effective multiplication coefficient Keff under initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions

[0069] Initialization module, used to build an equivalent model and set the initial value of the equivalent model, the initial value includes initializing the central fuel volume of the equivalent model Fuel iter and Fuel during the search min , Fuel max Among them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel;

[0070] Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , among which Water min =0;

[0071] The update module is used to calculate the effective proliferation coefficient Keff of the equivalent model described in the initialization module using the Monte Carlo method eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in the calculation module hex Compare them. When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated.

[0072] Correction module, used to calculate the effective multiplication coefficient of the special-shaped cross spiral model in the calculation module and the equivalent model described in the initialization module at different burnup points using the Monte Carlo method And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in the initialization module, otherwise update the size of the central fuel of the equivalent model in the initialization module and repeat the update module.

[0073] The initial value of the equivalent model in this embodiment includes Fuelmax , Fuel min , Fuel iter , Water max , Water min and Water iter ;

[0074] Embodiment 9: A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in any one of embodiments 1 to 7.

[0075] Embodiment 10: A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described in any one of embodiments 1 to 7 are implemented.

[0076] Implementation eleven: This implementation provides an example, which is used to explain the above implementations one to ten. The specific example is as follows:

[0077] See also Figures 1 to 8 To explain this embodiment, this embodiment proposes an equivalent modeling method for a special-shaped cross spiral fuel element, simplifies the complex spiral cross geometric model into a simple concentric circle model, and proposes the use of a dichotomy method to determine the geometric parameters of the central fuel and the middle layer coolant of the equivalent model. It mainly uses a method of using a concentric circle geometric structure to equivalently replace the cross-shaped blades, and the criterion is to keep the effective proliferation coefficient equal. The layout of this method is to expand radially from the center to the outside, in order of the central fuel, the middle layer coolant, the outer fuel, the cladding and the outer coolant. Its geometric schematic diagram is shown as follows: Figure 3 As shown in (b);

[0078] This implementation also provides a method for determining the geometric parameters of the equivalent model, namely the dichotomy method, and the specific method is described below.

[0079] The equivalent model needs to be adapted to the traditional nuclear design program, so only the concentric circle geometry is retained. At the same time, considering that in the special-shaped cross spiral model, neutrons may escape from the cross-blade fuel and pass through the cladding and coolant and then return to the fuel, the intermediate coolant and outer fuel are introduced into the equivalent model to simulate this physical process, that is, Figure 3 The blue and yellow circles in (b) are shown in the figure, but the process of neutrons passing through the cladding and returning to the fuel is ignored for the principle of simplification. The parameters that need to be searched in the equivalent model are the radius of the central fuel and the intermediate coolant. The remaining parameters can be calculated based on the principle that the equivalent model and the original cross-shaped spiral fuel model are the same in material composition and total amount.

[0080] In this embodiment, two Monte Carlo models are established, and except for the different geometric shapes, the other calculation conditions of the two models are the same.

[0081] The special-shaped cross-spiral fuel adopts a CSG stacking model with ten layers of axial slices. The specific layered cross-section diagram is as follows Figure 2 As shown, the xz cross-section diagram is Figure 1 , the slices in the model have the same layer height; the equivalent model uses concentric circle geometry, and the specific geometric parameter search steps are as follows:

[0082] Step 1: Calculate the effective multiplication coefficient Keff under the initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions

[0083] Step 2: Initialize the equivalent model center fuel volume Fuel iter and Fuel during the search min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross spiral fuel. Initialize the equivalent model interlayer coolant volume Water iter and Water max The blue part volume, Water min =0;

[0084] Step 3: Use the Monte Carlo method to calculate the effective proliferation coefficient Keff of the equivalent model described in step 2 eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in step 1 hex Compare them. When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and updated.

[0085] The volume update formula of the intermediate layer coolant is Water iter =(Water min +Water max ) / 2

[0086] If Keff eq >Keff hex , then Water max =Water iter , update Water iter ;

[0087] If Keff eq <Keff hex , then Water min =Water iter, update Water iter .

[0088] According to the principle that the total amount of material is the same, that is, the volume remains unchanged, the radii corresponding to the outer fuel, cladding, and outer coolant are calculated, the input card of the equivalent model is modified, and Keff is calculated again. eq This process is called dichotomy, and ultimately results in an equivalent model that is equal to the effective proliferation coefficient of the cross-helical fuel.

[0089] Step 4: Use the Monte Carlo method to calculate the effective multiplication coefficient of the special-shaped cross spiral model in step 1 and the equivalent model described in step 2 at different burnup points And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in step 2, otherwise the size of the central fuel of the equivalent model in step 2 is updated.

[0090] The updating method is: calculate the error between the effective multiplication coefficient of the special-shaped cross-helical fuel and the equivalent model at all fuel points, and calculate their mean

[0091] If Err>0, then Fuel max =Fuel iter , Update Fuel iter ;

[0092] If Err>0, then Fuel min =Fuel iter , Update Fuel iter .

[0093] For a detailed flowchart, see Figure 4 shown.

[0094] The above implementation mode is explained below with reference to specific examples:

[0095] First, the schematic diagram and specific parameters of the geometric model are as follows:

[0096] Table 1 Geometric parameters

[0097]

[0098]

[0099] Table 2 Material parameters

[0100]

[0101] The cross-sectional diagram of the special-shaped cross-spiral fuel element and the equivalent model element is shown in Figure 3As shown. The boundary conditions of the two models are the same, both are periodic boundary conditions (all around and above and below are periodic boundary conditions). The number of particles put into the simulation calculation is 30,000, the inactive generation is 30 generations, and the active generation is 300 generations. After the radius of the central fuel is initially selected, the binary search method is used to search for the intermediate coolant radius of the equivalent model. The convergence condition is the Keff of the special-shaped cross fuel element. hex and the Keff of the equivalent model eq The difference is within 20pcm. The specific iteration value of the effective multiplication coefficient is as follows: Figure 6 shown.

[0102] After obtaining the equivalent model under the initial conditions, the fuel consumption of the special-shaped cross spiral model and the equivalent model was calculated to verify the accuracy of the equivalent model at different fuel consumption points. The power was taken as 0.04kW / g and the fuel consumption depth was 60MWd / kgHM. The Keff at different fuel consumption points was calculated. i And the error value is Figure 7 The maximum error between the two is 100.9pcm, which is within 300pcm, so the models can be considered equivalent.

[0103] In order to verify the applicability of the model, Figure 8 The model was designed under three different parameter conditions: fuel enrichment, boric acid concentration and reactor operating conditions (hot full power HFP; hot zero power HZP) for verification.

[0104] The calculation results of the special-shaped cross-helix fuel model and the equivalent model at different burnup points under different calculation parameters are compared as follows Figure 8 As shown (B600 in the figure represents a boric acid concentration of 600ppm):

[0105] According to the calculation results, within the error range of 300pcm, the equivalent model is relatively accurate under different calculation conditions and has strong adaptability.

[0106] Figure 4Any process or method description in the flowchart described in or otherwise described herein can be understood as representing a module, fragment or portion of a code including one or more executable instructions for implementing the steps of a custom logic function or process, and the scope of the preferred embodiment of the present invention includes other implementations, in which the functions may be performed in a substantially simultaneous manner or in a reverse order according to the functions involved, which should be understood by a person skilled in the art of the present invention. The logic and / or steps represented in the flowchart or otherwise described herein illustrate the possible implementation architecture, functions and operations of the apparatus and methods according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the above-mentioned module, program segment, or a part of a code contains one or more executable instructions for implementing the specified logic function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in reverse order, depending on the functions involved. It is also noted that each block in the block diagram or flowchart, and combinations of blocks in the block diagram or flowchart, may be implemented by a dedicated hardware-based system that performs the specified functions or operations, or may be implemented by a combination of dedicated hardware and computer instructions. For example, what may be considered as an ordered list of executable instructions for implementing a logical function may 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 system including a processor, or other system that can fetch instructions from and execute instructions in an instruction execution system, apparatus, or device).

[0107] For the purposes of the present specification, "computer-readable medium" may be any device that can contain, store, communicate, propagate or transmit a program for use with an instruction execution system, device or equipment or in conjunction with these instruction execution systems, devices or equipment. More specific examples of computer-readable media (non-exhaustive list) include the following: an electrical connection with one or N wirings (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and editable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program may be printed, because the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting or processing in other suitable ways as necessary, and then stored in a computer memory. It should be understood that the various parts of the present invention may be implemented in hardware, software, firmware or a combination thereof. In the above embodiments, the N steps or methods may be implemented in software or firmware stored in a 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 of the following technologies known in the art or a combination thereof: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0108] Those skilled in the art will appreciate that the above are only preferred embodiments of the present invention, and the various embodiments of the present disclosure and / or the features described in the claims may be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments, or perform equivalent substitutions on some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

[0109] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. An equivalent modeling method suitable for special-shaped fuels, characterized in that: The equivalent modeling method comprises the following steps: Step 1: Calculate the effective multiplication coefficient Keff under the initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions Step 2: Construct an equivalent model and set the initial value of the equivalent model, which includes initializing the central fuel volume of the equivalent model. iter and Fuel during the search min , Fuel max Among them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel; Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , Water min =0; Step 3: Use the Monte Carlo method to calculate the effective proliferation coefficient Keff of the equivalent model described in step 2 eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in step 1 hex When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated. Step 4: Use the Monte Carlo method to calculate the effective multiplication coefficients of the special-shaped cross-helix model in step 1 and the equivalent model described in step 2 at different burnup points And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in step 2, otherwise update the size of the central fuel of the equivalent model in step 2; The method for iterative volume update of the intermediate coolant in step 3 is: Water iter =(Water min +Water max ) / 2 If Keff eq >Keff hex , then Water max =Water iter , update Water iter ; If Keff eq <Keff hex , then Water min =Water iter , update Water iter .

2. The equivalent modeling method applicable to special-shaped fuels according to claim 1, characterized in that: The special-shaped cross-spiral fuel model described in step 1 is implemented using a CSG stacking model with ten layers of axial slicing.

3. The equivalent modeling method applicable to special-shaped fuels according to claim 1, characterized in that: The method for updating the volume of the central fuel in step 4 is: Fuel iter =(Fuel min +Fuel max ) / 2 Calculate the error between the effective multiplication coefficient of the special-shaped cross-helical fuel and the equivalent model at all fuel points, and calculate the mean of the error If Err>0, then Fuel max =Fuel iter , Update Fuel iter ; If Err>0, then Fuel min =Fuel iter , Update Fuel iter .

4. The equivalent modeling method applicable to special-shaped fuels according to claim 1, characterized in that: The arrangement of the equivalent model constructed in step 2 is central fuel, middle layer coolant, outer layer fuel, cladding and outer layer coolant.

5. The equivalent modeling method applicable to special-shaped fuels according to claim 1, characterized in that: After setting the arrangement of building the equivalent model described in step 2, the step of determining the geometric parameters of the central fuel, the middle layer coolant, the outer layer fuel, the cladding and the outer layer coolant is also included.

6. The equivalent modeling method applicable to special-shaped fuels according to claim 5, characterized in that: The geometric parameters of the central fuel and the middle layer coolant are determined by the dichotomy method, and the geometric parameters of the outer layer fuel, the cladding and the outer layer coolant are calculated by the principle of material conservation.

7. An equivalent modeling system suitable for special-shaped fuels, characterized in that: The system comprises: Calculation module for calculating the effective multiplication coefficient Keff under initial conditions of the special-shaped cross-helix fuel model hex and effective multiplication coefficient under burnup conditions Initialization module, used to build an equivalent model and set the initial value of the equivalent model, the initial value includes initializing the central fuel volume of the equivalent model Fuel iter and Fuel during the search min , Fuel max Among them, Fuel min It is half the volume of the cross-spiral fuel. max is the total volume of the special-shaped cross-spiral fuel; Initialize the equivalent model intermediate layer coolant volume Water iter and Water max , Water min =0; The update module is used to calculate the effective proliferation coefficient Keff of the equivalent model described in the initialization module using the Monte Carlo method eq and the effective multiplication coefficient Keff of the special-shaped cross-helix fuel model described in the calculation module hex When the difference between the two is less than 20pcm, they are considered equivalent. If the difference between the two is greater than 20pcm, the volume of the intermediate layer coolant of the equivalent model needs to be recalculated and the volume of the intermediate layer coolant needs to be updated. Correction module, used to calculate the effective multiplication coefficient of the special-shaped cross spiral model in the calculation module and the equivalent model described in the initialization module at different burnup points using the Monte Carlo method And compare; if the difference between the two is less than 300pcm at all burnup points, it is equivalent to the model constructed in the initialization module, otherwise the size of the central fuel of the equivalent model in the initialization module is updated; The method for iterative volume update of the intermediate coolant in step 3 is: Water iter =(Water min +Water max ) / 2 If Keff eq >Keff hex , then Water max =Water iter , update Water iter ; If Keff eq <Keff hex , then Water min =Water iter , update Water iter .

8. A computer device comprising a memory and a processor, characterized in that A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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