A computational method for evaluating uncertainty in fluid-structure interaction dynamics in nuclear engineering

Abstract

The invention discloses a calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering, which relates to the field of nuclear reactor structural mechanics. The grid feature size is selected according to the variable characteristics, and a grid model of different refinement levels and a fluid-solid coupling model thereof are established; the solutions of all grids are classified into three groups according to the continuous grid refinement ratio; the numerical simulation of fluid-solid coupling behavior is carried out, and field variables or integral quantity data are collected; the discrete solutions of three continuous refinement levels are interpolated to the coarsest grid therein to form a solution with a unified post-processing grid; if the variable is an integral quantity, the apparent accuracy order is solved by an iterative method, and the uncertainty is calculated and reported; if the variable belongs to a field variable, node classification, calculation of local apparent order, calculation of global apparent order, calculation of local uncertainty are carried out in sequence, and finally the global uncertainty is calculated by volume weighted average calculation of local uncertainty. The method has good operability and repeatability in actual engineering.

Description

Technical Field

[0001] The invention relates to the technical field of nuclear reactor structural mechanics, and in particular to a calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering. Background Art

[0002] There are a large number of fluid-induced vibrations and fluid-solid coupling phenomena in nuclear engineering. This phenomenon always exists with the operation of nuclear reactors and is related to the safety and reliability of the nuclear reactor structural design. In severe cases, it will lead to structural damage and affect the safe operation of the equipment. For example, in 2012, the San Onofre Nuclear Power Plant in the United States caused excessive flow-induced vibration of the heat transfer tube bundle, which led to the scrapping of the steam generator, and then the nuclear power plant was permanently closed, causing significant economic losses and social impacts.

[0003] Since steam generators, fuel assemblies, reactor internals, nuclear-grade pipelines and other components or equipment in nuclear engineering are very prone to flow-induced vibration, the structural failure problems such as fatigue, collision, noise and wear induced by flow-induced vibration have long plagued the engineering community. At the same time, nuclear engineering has extremely stringent safety requirements, so flow-induced vibration is a factor that must be considered during design and operation. On the other hand, as people's requirements for nuclear reactor performance and efficiency are getting higher and higher, there is an urgent need to adopt more accurate analysis models to characterize the interaction between structure and fluid, so as to reduce the conservatism of traditional analysis and design and improve the engineering usability of analysis results. With the development of computing power and physical models, high-precision numerical models have become a very useful tool for people to better understand and analyze various engineering problems, especially the flow and heat transfer phenomena of various complex structures in nuclear engineering.

[0004] The numerical analysis of fluid-structure interaction is essentially an approximate method, and its errors include rounding errors, iteration errors, and discrete errors, etc., involving structural dynamic response, complex flow field solutions, and fluid-structure interactions. In the analysis process, for the same research object, there may be significant differences in the calculation results due to differences in meshing, model settings, and solution methods. In order to quantitatively evaluate the errors or uncertainties in these calculation processes, and then reach a reasonable convergence solution through iteration to form a reliable numerical model, it is necessary to carry out research on uncertainty calculation methods that match the fluid-structure interaction analysis scenarios in nuclear engineering.

[0005] At present, the assessment of uncertainty in fluid-structure coupling dynamics in nuclear engineering mainly focuses on two aspects: one is grid accuracy, and the other is numerical format. Usually, comparison with experimental data is used to illustrate its rationality, but "reasonable consistency" with experimental data alone is not enough to prove that the calculation of a given model is reasonable. On the other hand, in most cases, no experimental data for comparison can be provided. Therefore, in fluid-structure coupling calculations, there is still a lack of standardized evaluation methods for the reliability of numerical models, the convergence of calculation results, and uncertainty. For example, some studies have not carried out verification of grid independence or numerical methods; some studies have only compared with experimental data to demonstrate the reliability of the method, but have not carried out uncertainty assessment, and there may be situations where the simulation results happen to coincide with the experimental data; some studies have carried out grid independence verification, but they all compare 2 or 3 different calculation grids to obtain the relative difference of the calculation results. When the relative error is small, it is considered that the influence of the grid on the calculation results is small.

[0006] Existing uncertainty analysis of fluid-structure interaction dynamics for nuclear engineering mainly determines whether the numerical model converges by comparing the relative influence of different grids and solution accuracy on the calculation results. There is a lack of judgment indicators for evaluating grid-independent solutions or grid convergence, which makes the evaluation of numerical models rely on manual experience. At present, most numerical simulation error estimates are based on experimental data or theoretical precise solutions, but in actual engineering, experimental data or theoretical solutions are often not available, and the method of comparison with experimental data is not sufficient to prove the rationality of the numerical model, and it is impossible to accurately give the uncertainty of the calculation results, which makes it difficult to adapt to actual engineering needs. Summary of the invention

[0007] Based on the problems existing in the prior art, the purpose of the present invention is to provide a calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering, and to provide a judgment index for evaluating grid independent solutions or grid convergence, so that the grid convergence research does not rely on manual experience, and has the advantages of unified standards and elimination of human factors. In the analysis of flow-induced vibration and fluid-solid coupling, it can give a reasonable and reliable uncertainty or error estimate for the numerical simulation results, and then reach a converged solution through iteration to form a reliable numerical model. The proposed uncertainty calculation method is also applicable to flow field dynamics simulations of other engineering applications, and is also applicable to a wide range of methods, such as acoustic boundary element method, structural dynamics finite element method, etc.

[0008] The present invention is achieved through the following technical solutions:

[0009] In a first aspect, the present application provides a computational method for evaluating the uncertainty of fluid-solid interaction dynamics in nuclear engineering, comprising the following steps:

[0010] The grid feature size is selected according to the variable characteristics, and the grid models with different refinement levels and their fluid-structure coupling models are established. Then, all grid solutions are classified into groups of three according to the continuous grid refinement ratios.

[0011] Conduct numerical simulation of fluid-structure interaction behavior and collect field variable or integral quantity data;

[0012] If the variable is an integral quantity, an iterative method is used to solve for the apparent order of accuracy and the uncertainty is calculated and reported;

[0013] If the variable is a field variable, the discrete solutions of three consecutive refinement levels are first interpolated to the coarsest grid to form a solution with a unified post-processing grid. Then, node classification, calculation of local apparent order, calculation of local apparent accuracy order, and calculation of local uncertainty are performed in sequence. Finally, the global uncertainty is obtained by volume weighted average of the local uncertainties.

[0014] Furthermore, the grid characteristic size is defined as:

[0015] If the grid model is a three-dimensional calculation, for the integral quantity and field variables, the global grid characteristic size is calculated using the following formula:

[0016]

[0017] h=(ΔnΔsΔl) 1 / 3 (2);

[0018] Where: ΔV i is the volume of the i-th unit; N is the number of grids; Δn, Δs and Δl are the normal distance, axial distance and radial distance of the local grid of interest respectively;

[0019] If the grid model is a two-dimensional calculation, the corresponding grid feature size is calculated using the following formula:

[0020]

[0021] h=(ΔhΔs) 1 / 2 (4);

[0022] Where: ΔA i is the area of ​​the ith unit.

[0023] Furthermore, grid models with different refinement levels and their fluid-solid coupling models are established, including the following steps:

[0024] Using geometrically similar elements, systematically build mesh models with different refinement ratios, where the refinement ratio is r = h coarse / h fine , where h coarse represents the coarse grid, h finerepresents a fine grid;

[0025] According to the thermal-hydraulic conditions and structural dynamic characteristics, based on the established grid models with different refinement levels, flow field analysis models, structural motion equations or finite element models are formed respectively; the vibration and flow field are coupled and solved through sequential coupling and data transfer.

[0026] Furthermore, grouping the solutions of meshes of different refinement levels means classifying the meshes of different refinement levels into groups of three according to continuous mesh refinement ratios.

[0027] Furthermore, the collection of integral quantity or field variable data requires:

[0028] For the integral quantity, collect the global variables to be evaluated;

[0029] For field variables, local variables to be evaluated are collected in the flow field area to be evaluated and output in ASCII format. Each data file also contains the number and coordinates of each grid center point or each grid node.

[0030] Furthermore, if the variable is an integral quantity, the steps to evaluate the uncertainty are:

[0031] 1) Calculate and report the apparent order of accuracy:

[0032] Let h1 <h2<h3,r 21 =h2 / h1, r 32 =h3 / h2, use the iterative method to solve formula (5) and calculate the apparent accuracy order p:

[0033]

[0034] In the formula, s=1·sign(ε 32 / ε 21 ), ε 32 =φ3-φ2,ε 21 =φ2-φ1,φ k represents the solution of the kth grid, and the subscript 1 in h and φ indicates the finest grid;

[0035] 2) Calculate and report uncertainty:

[0036] Taking the safety factor into account, the uncertainty based on the finest grid is:

[0037]

[0038] In the formula, the safety factor F s It is usually taken as 1.25, and the subscript 1 in φ indicates the finest grid;

[0039] 3) Determination of apparent accuracy order:

[0040] The uncertainty based on the intermediate precision grid is:

[0041]

[0042] Furthermore, if the variable is a field variable, the steps for evaluating uncertainty are:

[0043] 1) Interpolation at the post-processing grid: The discrete solutions of three consecutive refinement levels are interpolated to the coarsest grid to form a solution with a unified post-processing grid;

[0044] 2) Classify the computing nodes into three categories: progressive nodes, convergent nodes, and oscillating nodes, and count and report the percentages of each type of nodes;

[0045] 3) Calculate the local apparent order p at all progressive nodes of the post-processing grid;

[0046] 4) At all nodes corresponding to p(x)>0, calculate the mean and standard deviation of the local apparent order, the local uncertainty, and the global uncertainty.

[0047] Furthermore, computing nodes are divided into three categories according to the following conditions:

[0048]

[0049]

[0050] Where the superscript * indicates that the solution is dimensionless using the maximum absolute value of φ(x), and C0 is a positive real number.

[0051] Furthermore, if the mesh refinement ratio r is a fixed value, the local apparent accuracy order at each post-processing mesh node is calculated by the following formula:

[0052]

[0053] If the mesh refinement ratio is not a fixed value, the local apparent accuracy order is obtained by iteratively solving the following formula:

[0054]

[0055] In the formula, s=1·sign(ε 32 (x) / ε 21 (x)), ε 32 (x) = φ3(x) - φ2(x), ε 21 (x)=φ2(x)-φ1(x),φ k (x) represents the solution of the kth grid at node x.

[0056] Furthermore, in all P L At the nodes corresponding to (x)>0, the local uncertainty based on the finest grid is calculated using the following formula:

[0057]

[0058] In the formula, F s =1.25, P L (x) is the local apparent accuracy order at node x; at the convergence node, the uncertainty U(x) = 0.

[0059] Furthermore, the global uncertainty is calculated by taking the volume-weighted average of the local uncertainties:

[0060]

[0061] Where n is all P L The number of nodes corresponding to (x)>0 and the total number of convergent nodes.

[0062] In a second aspect, the present application provides a computer program, which can implement the steps of the method described above.

[0063] In a third aspect, the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above method.

[0064] In a fourth aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0065] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0066] (1) The present invention provides a quantitative index for evaluating grid-independent solutions or grid-converged solutions, so that the grid convergence research in numerical analysis no longer relies on manual experience, and has the advantages of unified standards and elimination of human factors;

[0067] (2) The uncertainty assessment method of the present invention can provide reasonable and reliable uncertainty and error estimates for numerical simulation results during flow-induced vibration and fluid-solid coupling analysis, and then reach a convergent solution through iteration to form a reasonable and reliable numerical model;

[0068] (3) The present invention is applicable to both the case of a fixed mesh refinement ratio and the case of a non-fixed mesh refinement ratio. In actual engineering, the corresponding computational mesh and numerical model can be conveniently established according to the specific object, thereby alleviating the contradiction between the complexity of the model and the ease of analysis and design.

[0069] (4) The present invention is applicable to both global uncertainty assessment of integral quantities and local uncertainty assessment of field variables. The global estimate is used to report the global accuracy of the numerical solution, and the local estimate can identify local error sources, such as insufficient grid density or unreasonable boundary conditions, and thus improve the model.

[0070] (5) The uncertainty calculation method proposed in the present invention is applicable to both the case where fluid-solid coupling is considered and the case where fluid-solid coupling is not considered, such as separate flow field analysis and other methods, such as the acoustic boundary element method, the structural dynamics finite element method, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0072] Figure 1 It is a flow chart of a calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering according to the present invention;

[0073] Figure 2 It is a schematic diagram of the geometric structure and mesh division of Examples 2 to 4 of the present invention;

[0074] Figure 3 is a three-dimensional flow field geometric model of the tube bundle structure of Example 5 of the present invention;

[0075] Figure 4 It is the local grid detail of Example 5 of the present invention. DETAILED DESCRIPTION

[0076] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0077] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0078] The terms "comprises," "comprising," or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0079] Example 1

[0080] This embodiment provides a calculation method for evaluating the uncertainty of fluid-solid interaction dynamics in nuclear engineering, and the specific steps are:

[0081] S1: Carry out mesh refinement. The specific implementation steps are as follows:

[0082] S1-1: Select the grid feature size according to the variable characteristics. For three-dimensional calculations, for the integral quantity, the global grid feature size is calculated using the formula; for the field variable, the local grid feature size is calculated using the formula:

[0083]

[0084] h=(ΔnΔsΔl) 1 / 3 (2);

[0085] Where: ΔV i is the volume of the i-th unit; N is the number of grids; Δn, Δs and Δl are the normal distance, axial distance and radial distance of the local grid of interest, respectively.

[0086] For two-dimensional calculations, the corresponding grid characteristic size is expressed as:

[0087]

[0088] h=(ΔnΔs) 1 / 2 (4);

[0089] S1-2: Establish mesh models with different refinement levels.

[0090] Using geometrically similar elements, a mesh model with different refinement ratios is systematically established. The mesh refinement ratio is defined as: r = h coarse / h fine , where h coarse represents the coarse grid, h fine Represents a fine grid.

[0091] All meshes can use fixed or non-fixed refinement ratios.

[0092] S1-3: Establish a fluid-structure coupling numerical model.

[0093] According to the thermal-hydraulic conditions and structural dynamic characteristics of the analysis object, based on the established grid models with different refinement levels, flow field analysis models, structural motion equations or finite element models are formed respectively; the vibration and flow field are coupled and solved through sequential coupling and data transfer.

[0094] Among them, professional software for thermal-hydraulic analysis is used to calculate the flow field in which the structure is located, and the corresponding flow velocity, density and pressure are obtained as boundary conditions for fluid-solid coupling simulation; general CFD (computational fluid dynamics) software or open source CFD program is used to establish a flow field analysis model, and general finite element software or motion equations are used to describe the movement of the structure.

[0095] S1-4: Group solutions of different mesh refinement levels.

[0096] According to the continuous mesh refinement ratio, meshes of different refinement levels are classified into groups of three. For example, three meshes can only analyze one set of solutions, four meshes can analyze two sets of solutions, and so on.

[0097] S2: Collect integral quantity or field variable data.

[0098] Carry out numerical simulations of fluid-structure interaction behavior and collect field variable or integral quantity data.

[0099] Among them, for the integral quantity, the global variables such as resistance, lift, vibration displacement, etc. that need to be evaluated are output.

[0100] Among them, for field variables, the local variables that need to be evaluated (such as surface pressure, spatial flow velocity, etc.) are collected in the flow field area that needs to be evaluated and saved as a text document in ASCII format. Each data file also contains the number and coordinates of each grid center point (each grid node can also be selected as a data sampling point).

[0101] S3: If the variable is an integral quantity, the specific implementation steps for evaluating uncertainty are:

[0102] S3-1: Calculate and report the apparent order of accuracy.

[0103] Let h1 <h2<h3,r 21 =h2 / h1, r 32 =h3 / h2, use the iterative method to solve the following formula and calculate the apparent accuracy order p:

[0104]

[0105] In the formula, s=1·sign(ε 32 / ε 21 ), ε32 = φ3 - φ2, ε 21 = φ2 - φ1, φ k represents the solution of the k-th grid, and the subscript 1 represents the finest grid.

[0106] where, if r 21 = r 32 = r, then the apparent accuracy order p simplifies to the following formula and can be directly calculated:

[0107]

[0108] where, ε 32 / ε 21 < 0 indicates oscillatory convergence, |ε 32 × ε 21 | < C0 indicates that the solution may have converged, where C0 is a very small positive real number, such as C0 = 10 -30 .

[0109] where, the consistency between the apparent accuracy order and the theoretical accuracy order of the numerical format used is a good indicator for judging the convergence of the solution and the reliability of the numerical model. If the apparent accuracy order is basically consistent with the theoretical accuracy order, it indicates that the numerical solution converges asymptotically and the corresponding uncertainty estimate is reliable.

[0110] where, if the formula has no real solution, the reported result indicates that the uncertainty of this set of solutions cannot be obtained, but it does not necessarily strictly mean that the calculation result is bad or the numerical model is unreliable.

[0111] S3-2: Calculate and report the uncertainty.

[0112] Considering the safety factor, the uncertainty based on the finest grid is:

[0113]

[0114] In the formula, the safety factor F s is usually taken as 1.25, and the subscript 1 represents the finest grid.

[0115] S3-3: Judgment of the apparent accuracy order.

[0116] The uncertainty based on the medium-accuracy grid is:

[0117]

[0118] Calculate If α ≈ r p , then p is the apparent accuracy order.

[0119] S4: If the variable belongs to a field variable, the specific implementation steps for evaluating the uncertainty are:

[0120] S4-1: Interpolation at the post-processing grid.

[0121] The discrete solutions of three successively refined levels are interpolated onto the coarsest grid to form a solution with a uniform post-processing grid. To avoid introducing additional uncertainties during post-processing, interpolation methods with better than second-order accuracy are used.

[0122] Among them, interpolation can be conveniently implemented based on general numerical analysis software (such as Matlab, Mathematics) or programming languages ​​(such as FORTRAN, Python, etc.).

[0123] S4-2: Classify nodes and report the proportion of each type of node.

[0124] Compute nodes are divided into three categories based on the following criteria:

[0125]

[0126]

[0127] In the formula, the superscript * indicates that the solution is dimensionless by using the maximum absolute value of φ(x), and C0 is a very small positive real number, such as C0 = 10 -30 .

[0128] Furthermore, the percentage of each type of nodes is counted and reported.

[0129] S4-3: Calculate the local apparent accuracy order.

[0130] At all progressive nodes of the postprocessed mesh, the local apparent accuracy order p is calculated.

[0131] Where, if the mesh refinement ratio r is a fixed value, the local appearance at each post-processing mesh node is calculated by the following formula:

[0132]

[0133] If the mesh refinement ratio is not a fixed value, the local apparent accuracy order is obtained by iteratively solving the following formula:

[0134]

[0135] In the formula, s=1·sign(ε 32 (x) / ε 21 (x)), ε 32 (x) = φ3(x) - φ2(x), ε 21 (x)=φ2(x)-φ1(x),φ k (x) represents the solution of the kth grid at node x.

[0136] If p≤0 or is not a real number, its percentage in the progressive nodes is counted and reported, and the corresponding nodes and their related variables are removed from the progressive nodes.

[0137] S4-4: Calculate and report the local apparent order of accuracy.

[0138] In all P L At the nodes corresponding to (x)>0, the mean and standard deviation of the local apparent accuracy order are calculated and reported.

[0139] Among them, the local apparent accuracy order is P L The average value of (x); use P L The standard deviation of (x) is used to measure how close the solution is to the asymptotic bounds, and thus to measure the confidence in the estimates obtained from the postprocessing procedure.

[0140] S4-5: Calculate local uncertainty.

[0141] In all P L At the nodes corresponding to (x)>0, the local uncertainty based on the finest grid is calculated using the following formula:

[0142]

[0143] In the formula, F s =1.25, P L (x) is the local apparent accuracy order at node x. At the convergence node, the uncertainty U(x) = 0.

[0144] S4-6: Calculate and report global uncertainty.

[0145] The global uncertainty is calculated as the volume-weighted average of the local uncertainties:

[0146]

[0147] Where n is all P L The number of nodes corresponding to (x)>0 and the total number of convergent nodes.

[0148] Example 2

[0149] This embodiment first analyzes the uncertainty of field variables for relatively simple working conditions, two-dimensional laminar flow, considering only flow field dynamics, with a fixed grid refinement ratio of r=2, and a numerical model with first-order accuracy (the pressure term is in a linear format and the momentum term is in a first-order upwind format).

[0150] Select the two-dimensional cavity flow with top wall moving, Reynolds number Re = 10 2 The cavity is a laminar forced flow, and the top surface of the cavity moves at a uniform speed along the x direction in its own plane. Figure 2The geometric structure and mesh division diagram are given.

[0151] In this embodiment, the x-direction velocity and y-direction velocity of the entire flow field area are selected as local variables to be evaluated, which are field variables. For a two-dimensional grid, the grid characteristic size is defined as h = (ΔnΔs) 1 / 2 , Δn and Δs are the normal distance and axial distance of the local grid of interest, respectively. For simplicity, this embodiment uses n×n uniform grid discretization ( Figure 2 ).

[0152] In this embodiment, a fixed mesh refinement ratio r=2 is taken, and n=10, 20, 40, 80 and 160 are taken respectively to establish meshes of six refinement levels. For each mesh, a flow field analysis model is established. The solutions of the six refinement levels are classified into three groups according to the continuous mesh refinement ratios, three in a group, and can be divided into three groups: n=10, 20, 40; n=20, 40, 80; n=40, 80, 160.

[0153] The general CFD software ANSYS Fluent is used to calculate the flow field. All working conditions are calculated for 30,000 steps, and all calculations reach the convergence standard. The x-direction velocity, y-direction velocity, unit volume, node number and coordinates at all nodes are output and saved as an ASCII file. Table 1 shows an example of the flow field data output by ANSYS Fluent.

[0154] Table 1

[0155] nodenumber x-coordinate y-coordinate cell-volume x-velocity y-velocity 1 2.00E-02 0.00E+00 4.00E-04 0.00E+00 0.00E+00 2 2.00E-02 2.00E-02 4.00E-04 -3.93E-02 3.24E-02 3 0.00E+00 2.00E-02 4.00E-04 0.00E+00 0.00E+00 4 0.00E+00 0.00E+00 4.00E-04 0.00E+00 0.00E+00 5 2.00E-02 4.00E-02 4.00E-04 -5.76E-02 8.09E-02

[0156] The quantity to be evaluated in this embodiment is a field variable, so the original flow field data is first read using Matlab software, and the griddata command is used to interpolate the discrete solutions of three consecutive refinement levels to the coarsest grid to form a solution with a unified post-processing grid. The interpolation uses the V4 method with second-order accuracy.

[0157] Data reading, processing and interpolation can also be conveniently implemented based on other general numerical analysis software (such as Mathematics) or programming languages ​​(such as FORTRAN, Python, etc.).

[0158] Then, according to formula (8), the computing nodes are divided into three categories: progressive nodes, convergent nodes, and oscillating nodes. The percentage of each type of node is counted and reported, see Table 2.

[0159] Table 2

[0160]

[0161] At all progressive nodes, the local apparent accuracy order is calculated. The mesh refinement ratio r in this embodiment is a fixed value. The local apparent accuracy order p at each post-processing mesh node is calculated by formula (9). Nodes with p≤0 and corresponding variables are eliminated from the progressive nodes, and their percentage of progressive nodes is counted and reported, as shown in Table 3.

[0162] Table 3

[0163] Grid x-speed Y speed 10 / 20 / 40 18.99％ 12.35％ 20 / 40 / 80 13.68％ 5.43％ 40 / 80 / 160 8.57％ 4.39％

[0164] At all nodes corresponding to p(x)>0, the mean and standard deviation of the local apparent accuracy order are calculated, and the local uncertainty is calculated by the formula. The global uncertainty is calculated by the formula. The results are shown in Table 4. With the increase of the refinement level, the apparent accuracy order tends to be consistent with the theoretical accuracy order of the numerical model, indicating that the numerical solution converges asymptotically and the corresponding uncertainty estimate is reliable.

[0165] Table 4

[0166]

[0167] Example 3

[0168] On the basis of Example 2, the numerical model takes the second-order accuracy (the pressure term is the second-order format, the momentum term is the second-order upwind format), takes n=5, 10, 20, 40, 80 and 160 respectively, establishes 6 levels of grid refinement, and the numerical solution can be divided into 4 groups: n=5, 10, 20; n=10, 20, 40; n=20, 40, 80; n=40, 80, 160. All other parameters are exactly the same as in Example 2, and the calculated local apparent accuracy order and global uncertainty are shown in Table 5.

[0169] Table 5

[0170]

[0171]

[0172] Example 4

[0173] On the basis of Example 2, the case of non-fixed mesh refinement ratio is analyzed, and all other parameters are exactly the same as those of Example 2. Take n=10, 20, 27, 40, 80 respectively, establish 5 mesh refinement levels, and the numerical solutions can be divided into 3 groups: n=10, 20, 27; n=20, 27, 40; n=27, 40, 80.

[0174] The steps of grid interpolation and computing node classification are the same as those in Example 2. The percentage of each type of node is shown in Table 6.

[0175] Table 6

[0176]

[0177] In this embodiment, the mesh refinement ratio r is a non-fixed value, and the local apparent accuracy order p at each post-processing mesh node is calculated by iteratively solving formula (10). In the progressive nodes, nodes with p≤0 and non-real numbers and corresponding variables are eliminated, and their percentage of progressive nodes is counted and reported, as shown in Table 7.

[0178] Table 7

[0179] Grid x-speed Y speed 10 / 20 / 27 6.67％ 5.41％ 20 / 27 / 40 9.93％ 5.16％ 27 / 40 / 80 5.16％ 4.69％

[0180] The calculation of the local apparent accuracy order and the global uncertainty is the same as that of Example 2. The results are shown in Table 8. The average value of the local apparent accuracy order of n=10, 20, and 27 is 2.96, which is much larger than the theoretical accuracy order of 1. Therefore, the uncertainty obtained by this group of solutions is not credible. However, with the increase of the refinement level, the apparent accuracy order tends to be consistent with the theoretical accuracy order of the numerical model, indicating that the numerical solution converges asymptotically and the corresponding uncertainty estimate is reliable. The uncertainty given by the solution group of n=27, 40, and 80 is 1.18% (x-direction velocity).

[0181] Table 8

[0182]

[0183] Example 5

[0184] This embodiment aims at relatively complex working conditions, three-dimensional turbulence, consideration of fluid-solid coupling, non-fixed grid refinement ratio, and numerical accuracy of second-order accuracy (pressure term is in second-order format, momentum term is in second-order upwind format) to analyze the uncertainty of integral quantities (drag, lift).

[0185] Figure 3 The three-dimensional flow field geometric model of the tube bundle structure of a specific embodiment is shown in FIG. Using geometrically similar units, a grid model with different refinement ratios is systematically established. The local grid details are as follows: Figure 4 As shown in Table 9, the grid conditions of this embodiment are listed, size represents the size of each tube circumferential grid, N Total represents the total number of units, and r is the mesh refinement ratio. The number of boundary layers for each tube is set to 15, and the first grid is 0.1%D away from the tube bundle wall to ensure that y+≤1. An expansion factor of 1.01 is used to transition from boundary layer units to tetrahedral units. Formula (1) is used to calculate the global mesh characteristic size. The global mesh characteristic size is expressed as a function of the total number of mesh units, and the mesh refinement ratio r can be easily obtained.

[0186] Table 9

[0187]

[0188] To better illustrate this embodiment, the moving tube is forced to vibrate in a sinusoidal form, and the displacement form of the moving tube is specified as: y(t) = y0sin(2πft), where y0 = 3mm is the amplitude of the tube, and f = 10Hz is the oscillation frequency of the tube. The flow field simulation is based on the open source CFD tool OpenFOAM, and the turbulence simulation uses the SST model

[0189] This embodiment has a non-fixed mesh refinement ratio and five mesh refinement levels, and its numerical solutions can be divided into three groups: mesh1, mesh2, mesh3; mesh2, mesh3, mesh4; mesh3, mesh4, mesh5.

[0190] Numerical simulation of fluid-solid coupling behavior is carried out, and the drag coefficient and lift coefficient of each grid model are output (see Table 10).

[0191] Table 10

[0192] mesh <![CDATA[N Total ]]> Drag coefficient Lift coefficient mesh1 6.51E+05 6.70 3.61 mesh2 3.35E+05 6.69 3.17 mesh3 2.49E+05 6.60 2.94 mesh4 1.59E+05 6.35 2.78 mesh5 1.13E+05 5.89 2.55

[0193] The apparent accuracy order is calculated by solving formula (5) by iteration method, and the uncertainty is calculated by formula (7), and the results are shown in Table 11. For the drag coefficient, all meshes did not obtain a reasonable apparent order, so the obtained uncertainties were not credible; for the lift coefficient, the p obtained by mesh1, mesh2, and mesh3 was close to α, and was also close to the theoretical accuracy order 1 of this embodiment. It can be considered that the mesh convergence solution was obtained, the numerical model was reasonable, and its uncertainty was 2.24%.

[0194] Table 11

[0195]

[0196] Example 6

[0197] This embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of a calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering in the above-mentioned embodiment 1.

[0198] The computer device may be a desktop computer, a notebook, a PDA, a cloud server, etc. The computer device may interact with the user through a keyboard, a mouse, a remote control, a touch pad, or a voice control device.

[0199] The storage includes at least one type of readable storage medium, and the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or D interface display memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory can be an internal storage unit of the computer device, for example, a hard disk or memory of the computer device. In other embodiments, the memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. Of course, the memory can also include both the internal storage unit of the computer device and an external storage device. In this embodiment, the memory is often used to store the operating system and various application software installed on the computer device, such as the program code for running the calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering, etc. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.

[0200] The processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code stored in the memory or process data, such as running the program code of the calculation method for evaluating the uncertainty of fluid-solid coupling dynamics in nuclear engineering.

[0201] Example 7

[0202] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the above-mentioned calculation method for evaluating the uncertainty of fluid-structure coupling dynamics in nuclear engineering.

[0203] The computer-readable storage medium stores an interface display program, which can be executed by at least one processor to enable the at least one processor to perform the steps of a method for evaluating the calculation method of fluid-solid coupling dynamics uncertainty in nuclear engineering.

[0204] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, computer, server or network device, etc.) to execute the methods described in each embodiment of the present application.

[0205] The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only the specific embodiments of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention. For those skilled in the art, it is obvious that the present application is not limited to the details of the above exemplary embodiments, and the present application can be implemented in other specific forms without departing from the spirit or basic features of the present application. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present application is limited by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present application.

Claims

1. A computational method for evaluating the uncertainty of fluid-structure interaction dynamics in nuclear engineering, characterized in that: The following steps are involved: The grid feature size is selected according to the thermal hydraulic conditions and structural dynamic characteristics of the analysis object, and the corresponding flow velocity, density and pressure are obtained as the boundary conditions of the fluid-solid coupling simulation. Grid models with different refinement levels and their fluid-solid coupling models are established, and then all grid solutions are classified into groups of three according to the continuous grid refinement ratio. Conduct numerical simulation of fluid-structure interaction behavior and collect field variable or integral quantity data; If the variable is an integral quantity, an iterative method is used to solve for the apparent order of accuracy and the uncertainty is calculated and reported; If the variable is a field variable, the discrete solutions of three consecutive refinement levels are first interpolated to the coarsest grid to form a solution with a unified post-processing grid, and then node classification, local apparent order calculation, global apparent order calculation, local uncertainty calculation are performed in sequence, and finally the global uncertainty is obtained by volume weighted average of local uncertainties; Requirements for collecting integral quantity or field variable data: For the integral quantity, collect the global variables to be evaluated; For field variables, local variables to be evaluated are collected in the flow field area to be evaluated and output in ASCII format. Each data file also contains the number and coordinates of each grid center point or each grid node; If the variable is an integral quantity, the steps to assess uncertainty are: 1) Calculate and report the apparent order of accuracy: Let h1 <h2<h3,r 21 =h2 / h1, r 32 =h3 / h2, use the iterative method to solve formula (5) and calculate the apparent accuracy order p: In the formula, s=1·sign(ε 32 / ε 21 ), ε 32 =φ3-φ2,ε 21 =φ2-φ1,φ k represents the solution of the kth grid, and the subscript 1 in h and φ indicates the finest grid; 2) Calculate and report uncertainty: Taking the safety factor into account, the uncertainty based on the finest grid is: In the formula, the safety factor F s is taken as 1.25, and the subscript 1 in φ indicates the finest grid; 3) Determination of apparent accuracy order: The uncertainty based on the intermediate fine grid is: If the variable is a field variable, the steps to assess uncertainty are: 1) Interpolation at the post-processing grid: The discrete solutions of three consecutive refinement levels are interpolated to the coarsest grid to form a solution with a unified post-processing grid; 2) Classify the computing nodes into three categories: progressive nodes, convergent nodes, and oscillating nodes, and count and report the percentages of each type of nodes; 3) Calculate the local apparent accuracy order pL at all progressive nodes of the post-processing grid; 4) At all nodes corresponding to pL(x)>0, calculate the mean value and standard deviation, local uncertainty, and global uncertainty of the local apparent accuracy order pL; x is a grid node; Compute nodes are divided into three categories based on the following criteria: In the formula, the superscript * indicates that the solution is dimensionless using the maximum absolute value of φ(x), and C0 is a positive real number; If the mesh refinement ratio r is a fixed value, the local apparent accuracy order at each post-processing mesh node is calculated as follows: If the mesh refinement ratio is not a fixed value, the local apparent accuracy order is obtained by iteratively solving the following formula: In the formula, s=1·sign(ε 32 (x) / ε 21 (x)), ε 32 (x) = φ3(x) - φ2(x), ε 21 (x)=φ2(x)-φ1(x),φ k (x) represents the solution of the kth grid at node x; At all nodes where pL(x)>0, the local uncertainty based on the finest grid is calculated using the following formula: In the formula, F s =1.25, P L (x) is the local apparent accuracy order at node x; at the convergence node, the uncertainty U(x) = 0; The global uncertainty is calculated as the volume-weighted average of the local uncertainties: Where n is all P L (x)>0 corresponding nodes and the total number of convergent nodes, ΔV i is the volume of the ith unit.

2. A calculation method for evaluating the uncertainty of fluid-structure interaction dynamics in nuclear engineering according to claim 1, characterized in that: The grid feature size is defined as: If the grid model is a three-dimensional calculation, for the integral quantity and field variables, the global grid characteristic size is calculated using the following formula: h=(ΔnΔsΔl) 1 / 3 (2); Where: ΔV i is the volume of the i-th unit; N is the number of grids; Δn, Δs and Δl are the normal distance, axial distance and radial distance of the local grid of interest respectively; If the grid model is a two-dimensional calculation, the corresponding grid feature size is calculated using the following formula: h=(ΔnΔs) 1 / 2 (4); Where: ΔA i is the area of ​​the ith unit.

3. A calculation method for evaluating the uncertainty of fluid-structure interaction dynamics in nuclear engineering according to claim 1, characterized in that: Establishing mesh models with different refinement levels and their fluid-structure interaction models includes the following steps: Using geometrically similar elements, systematically build mesh models with different refinement ratios, where the refinement ratio is r = h coarse / h fine , where h coarse represents the coarse grid, h fine represents a fine grid; According to the thermal-hydraulic conditions and structural dynamic characteristics, based on the established grid models with different refinement levels, flow field analysis models, structural motion equations or finite element models are formed respectively; the vibration and flow field are coupled and solved through sequential coupling and data transfer.

4. A calculation method for evaluating the uncertainty of fluid-structure interaction dynamics in nuclear engineering according to claim 1, characterized in that: Grouping the solutions of meshes of different refinement levels means classifying the meshes of different refinement levels into groups of three according to continuous mesh refinement ratios.

5. A computer program, characterized in that The computer program can implement the steps of the method according to any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes the steps of the method according to any one of claims 1 to 4.

7. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 4.

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