An integral order combination selection method, system, device and medium for angular coefficient finite element calculation

Abstract

This application relates to the field of radiation heat transfer simulation technology, specifically to a method, system, device, and medium for selecting integration order combinations for finite element method (FEM) calculation of angle coefficients. The method includes: selecting a target geometric configuration based on the target radiation heat transfer problem, and discretizing all internal surfaces of the target geometric configuration into several triangular elements; setting the range of integration order values ​​for finite element calculations, and constructing an integration order combination matrix; for each combination in the integration order combination matrix, calculating the angle coefficient between any two triangular elements in the target geometric configuration using the finite element method; calculating the angle coefficient error value under each integration order combination, filling all error values ​​according to their matrix positions to form an error matrix; and selecting all combinations from the error matrix whose absolute error value does not exceed a preset accuracy threshold as recommended outputs. This application can systematically select integration order combinations, effectively avoiding computational singularities and improving the accuracy of angle coefficient calculations.

Description

Technical Field

[0001] This application relates to the field of radiation heat transfer simulation technology, specifically to a method, system, device, and medium for selecting the combination of integral orders for finite element calculation of angular coefficients. Background Technology

[0002] Radiative heat transfer is one of the fundamental modes of energy transfer and an important research direction in engineering thermophysics, with significant impacts on many industrial fields such as energy and power, metallurgy and chemical engineering, aerospace, and building energy conservation. In the numerical simulation and analysis of radiative heat transfer, the angle factor is a key geometric parameter describing the proportion of radiative energy exchange between two surfaces. Its physical meaning is the proportion of radiative energy emitted by one surface that is directly projected onto the other surface. Accurately determining the angle factor is an important prerequisite for conducting radiative heat transfer analysis in enclosed spaces using radiative heat transfer calculation methods such as the radiation network method and the net heat method.

[0003] Currently, the main numerical methods for calculating angle coefficients include the Monte Carlo method and the finite element method (FEM). The Monte Carlo method simulates the propagation path of light through random sampling, theoretically achieving high accuracy, but it involves enormous computational costs and statistical errors. The FEM, on the other hand, discretizes a continuous surface into a finite number of elements and calculates the angle coefficient by arranging integration points on these elements and performing numerical integration. Its intuitive principle and ease of implementation have led to its widespread application. To improve the accuracy of angle coefficient calculations using the FEM, existing research has proposed various improvement strategies, such as local mesh refinement in singular regions, the use of adaptive mesh subdivision techniques, and the use of mathematical methods to force the calculation results to satisfy the integrity and reciprocity of the angle coefficients.

[0004] However, in existing technologies, the appropriateness of the selected combination of integration orders when calculating angle coefficients using the finite element method significantly affects the accuracy of the calculation results. In practical applications, if the selected combination of integration orders is unsuitable, such as using the same or similar low-order integrals for the radiating and receiving elements, it may lead to large deviations or even singularities in the calculation of angle coefficients under certain geometric configurations. Although increasing the integration order can sometimes improve accuracy, for certain specific geometric configurations, simply increasing the integration order of the radiating and receiving elements simultaneously cannot effectively eliminate this calculation error; instead, it may increase unnecessary computational overhead. Therefore, how to efficiently determine the combination of integration orders that can guarantee the accuracy of angle coefficient calculations for specific radiative heat transfer problems is a problem that urgently needs to be solved in existing technologies. Summary of the Invention

[0005] To address the technical problem that improper selection of the integration order combination of radiating emitting and radiating receiving units can lead to significant deviations or even singularities in the calculation of angle coefficients using the finite element method in existing technologies, this application provides a method, system, device, and medium for selecting integration order combinations in finite element calculation of angle coefficients. By constructing an integration order combination matrix, calculating the error value of the angle coefficient for each combination, and selecting integration order combinations that meet a preset accuracy threshold as recommended combinations, this approach can systematically select suitable integration order combinations, avoiding insufficient calculation accuracy and singularity problems caused by improper selection of integration orders.

[0006] In a first aspect, this application provides a method for selecting the combination of integration orders for finite element method calculations of angular coefficients, comprising the following steps: S1. Select the target geometric configuration based on the target radiation heat transfer problem, and discretize all the inner surfaces of the target geometric configuration into several triangular units, where the target radiation heat transfer problem is the radiation heat transfer problem in a closed space; S2. Define the range of values ​​for the integration order in the finite element method, and construct the integration order combination matrix, where: Integral order of the radiating emission unit The range of values ​​for is: ; Unit integration order of the radiation receiving unit The range of values ​​for is: ; The integral order combination matrix is The matrix, where the first... The elements are denoted as , representing the radiation emission unit adopting the first The first-order integrator and radiation receiving unit adopts the first-order integrator. Combinations of the orders of integrals of order ; S3. Calculate the angle coefficient between any two triangular elements in the target geometry one by one; In each calculation, the currently calculated triangular element is designated as the radiating element, and the remaining triangular elements are designated as radiating receiving elements. Then, for each integration order combination in the integration order combination matrix... The angular coefficient from a radiating emitting element to a radiating receiving element is calculated using the finite element method. ; S4. Based on the combination of integral orders Calculated value of angle coefficient below The error value under this combination of integral orders is calculated using the principle of integrity of the sum of angle coefficients. All error values ​​are filled into the corresponding positions of the integral order combination matrix to form the error matrix. ; S5. From the error matrix Filter out those that meet the requirements The complete combination of integral orders is output as the recommended combination of integral orders for the target radiative heat transfer problem. This is the preset desired accuracy threshold.

[0007] It should be further noted that in step S1, the target geometric configuration is a closed cavity, and the closed cavity includes a rectangle.

[0008] It should be further explained that, in step S1, discretizing all the inner surfaces of the target geometry into several triangular units specifically includes: Divide all the inner surfaces of the target geometry into Each triangle is divided into three elements, and the node coordinates, area, and normal vector of each triangle are recorded.

[0009] It should be further explained that in step S2, , .

[0010] It should be further noted that in step S3, the finite element method is used to calculate the angle coefficient. The formula is:

[0011] in, For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; The total number of triangular units; Index of the radiating unit; This is the index of the radiation receiving unit; For the first The area of ​​each radiation receiving unit; The integration order used for the radiating emission element is a combination of integration orders. In Sure; The integration order used by the radiating receiving unit is a combination of integration orders. In Sure; For the radiation emission unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; For the radiation receiving unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; This is the index of the integration point on the radiating emission element, with a value ranging from 1 to... ; This is the index of the integration point on the radiating receiving unit, with a value ranging from 1 to... ; For the first On the first radiation emission unit Weighting coefficients for each integration point; For the first On the first radiation receiving unit Weighting coefficients for each integration point; For from the first The first radiation emission unit The integration point points to the first... The first radiation receiving unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiating units; For from the first The first radiation receiving unit The integration point points to the first... The first radiation emission unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiation receiving units; For the first The first radiation emission unit The integration point and the first The first radiation receiving unit Euclidean distance between integration points.

[0012] It should be further explained that in step S3, The calculation formula is:

[0013] in, For the first On the first radiation emission unit The global coordinates of each integration point in three-dimensional space; For the first On the first radiation receiving unit The global coordinates of each integration point in three-dimensional space.

[0014] It should be further noted that in step S3, the total number of integration points on the radiation emission unit... With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points. Total number of integration points on the radiation receiving unit With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points.

[0015] It should be further noted that in step S4, the error value The calculation formula is:

[0016]

[0017] in, For the first The radiating emission elements are combined in the integral order. The total error value below; For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; For the theoretical sum of angle coefficients within a single integral order combination, .

[0018] It should be further explained that the error matrix for The matrix, where the first... Each element is a combination with the integral order. Corresponding error value .

[0019] It should be further noted that in step S5, the expected accuracy threshold... The value range is 1% to 5%.

[0020] It should be further noted that in step S5, if the error matrix... No satisfaction in the middle If the combination of integral orders is such that at least one of the following operations is performed, then return to step S2 and repeat: Increase the maximum value of the integral order of the radiating emission element. ; Increase the maximum value of the integration order of the radiation receiving unit. ; Increase the expected accuracy threshold .

[0021] It should be further noted that step S6 is also included: selecting an integration order combination from the recommended integration order combinations, calculating the angle coefficient of the target radiation heat transfer problem, and using the angle coefficient in the radiation heat transfer calculation of the target radiation heat transfer problem.

[0022] Secondly, this application provides a method for calculating radiative heat transfer of power equipment using the above-mentioned method for selecting combinations of integral orders, comprising the following steps: S61. Treat the radiation heat transfer problem of the target power equipment as the target radiation heat transfer problem, and perform the above-mentioned method for selecting the combination of integral orders to obtain the recommended combination of integral orders; S62. Discretize all the inner surfaces of the target power equipment into... Using a triangular mesh, select one combination of integration orders from the recommended combinations to calculate the angle coefficient matrix of the target radiation heat transfer problem. ; S63. Establish a system of nonlinear equations for the effective radiation of all triangular meshes:

[0023] in, and All are indices of a triangular mesh, with values ​​ranging from 1 to... ; This represents the total number of triangular grids. For the first Effective radiation of a triangular grid; For the first Effective radiation of a triangular grid; For the first Emissivity of a triangular grid; It is the Stefan-Boltzmann constant; For the first The temperature of each triangular grid is either the initial value or the result of the previous iteration step; Angle coefficient matrix The Middle The first triangular grid to the... The angle coefficient of a triangular grid; S64. Iteratively solve the nonlinear equations for effective radiation to obtain the effective radiation for each triangular grid. S65. Substitute the effective radiation of each triangular grid into the radiation heat transfer equation to calculate the radiation heat transfer of each triangular grid. The radiation heat transfer equation is as follows:

[0024] in, For the first Radiative heat transfer of a triangular grid; For the first The area of ​​the triangular grid; S66. Sum up the radiative heat transfer of all the triangular grids to obtain the total radiative heat transfer of the entire target power equipment; S67. Taking the total radiative heat transfer as the heat load, and combining the parameters of conduction and convection heat transfer, the overall energy balance equation of the target power equipment is established. Then, the finite element method is used to discretize and iteratively solve the overall energy balance equation to obtain the temperature of all triangular meshes, thereby realizing the radiative heat transfer calculation of the temperature field of the power equipment.

[0025] Secondly, this application provides a system for selecting the combination of integral orders for finite element method calculations of angular coefficients, used to implement the above-mentioned method for selecting the combination of integral orders, including: The configuration selection and discretization module is used to select the target geometry configuration based on the target radiation heat transfer problem and discretize all the inner surfaces of the target geometry configuration into several triangular elements; The module for constructing the combination matrix of integral orders is used to set the range of values ​​for the integral order in finite element calculations and to construct the combination matrix of integral orders. The angle coefficient calculation module is used to calculate the angle coefficient between any two triangular elements in the target geometric configuration one by one. The error matrix construction module is used to calculate the error value under the integration order combination based on the calculated value of the angle coefficient under the integration order combination and the principle of angle coefficient integrity. All error values ​​are filled in the corresponding positions of the integration order combination matrix to form the error matrix. The recommended integral order combination output module is used to select all integral order combinations from the error matrix whose absolute error value does not exceed a preset accuracy threshold, and use them as the recommended integral order combination output for the target radiation heat transfer problem.

[0026] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method for selecting the combination of integral orders.

[0027] Fourthly, this application provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for selecting the combination of integral orders.

[0028] As can be seen from the above technical solutions, this application has the following advantages: 1. This application constructs an integral order combination matrix for the target geometry, calculates the error between the angle coefficient and its precise value under each integral order combination, and then selects all integral order combinations that meet the requirements as recommended schemes based on a preset accuracy threshold. This provides a clear basis for selecting integral orders and can systematically determine appropriate integral order combinations for different target geometries. This allows the finite element method to effectively avoid computational singularities caused by improper selection of integral orders in the calculation of angle coefficients, and significantly improves computational accuracy and reliability.

[0029] 2. This application, by setting the range of values ​​for the triangular element integration order of the radiating and receiving elements and constructing an integration order combination matrix, includes all possible combinations of the radiating and receiving surfaces under all set integration orders, forming a complete candidate set of integration order combinations. This transforms the selection of integration order from scattered empirical attempts to a systematic exhaustive evaluation, overcoming the shortcomings of existing technologies that lack a complete set of candidate solutions and can only rely on the designer's personal experience for a limited number of attempts. This lays the foundation for accuracy comparison and optimal selection.

[0030] 3. This application covers all pairings of integral order combinations for radiating emitting surfaces and radiating receiving surfaces by calculating each combination of integral orders one by one in the integral order combination matrix. This traversal calculation method ensures that no potentially excellent integral order combination is missed, allowing subsequent error evaluation to be based on complete computational data and avoiding the loss of high-precision solutions due to incomplete candidate combinations.

[0031] 4. This application selects all combinations of integration orders from the error matrix whose absolute error value does not exceed a preset expected accuracy threshold, and outputs these combinations as recommended integration order combinations for the target radiative heat transfer problem. This allows users to directly select a suitable scheme from verified combinations based on the specific accuracy requirements of actual engineering projects, eliminating the need for repeated experimentation. This overcomes the defect in existing technologies where identical integration order combinations easily lead to computational singularities, guiding users to flexibly select appropriate integration order arrays. Thus, even under stringent geometric conditions, high-precision angle factor calculation results can still be obtained. Attached Figure Description To more clearly illustrate the technical solution of this application, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 This is a flowchart of a method for selecting the combination of integration orders for finite element calculation of angular coefficients in one embodiment of this application.

[0033] Figure 2 This is an error comparison chart of various integration order combinations in one embodiment of this application.

[0034] Figure 3 This is a schematic block diagram of an integration order combination selection system for finite element calculation of angular coefficients in one embodiment of this application.

[0035] Figure 4 This is a schematic diagram of the hardware structure of an electronic device in one embodiment of this application. Detailed Implementation

[0036] To make the purpose, features, and advantages of this application more apparent and understandable, specific embodiments and accompanying drawings will be used to clearly and completely describe the technical solution protected by this application. Obviously, the embodiments described below are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0037] The method for selecting the combination of integral orders involved in this application will be described in detail below. Specific details such as particular system structures and techniques are presented for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details.

[0038] In the method for selecting combinations of integral orders involved in this application, the term "comprising" indicates the presence of the described feature, whole, step, operation, element, and / or component, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or sets thereof. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0039] To facilitate a clear description of the technical solutions of this application, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" do not necessarily imply that they are different.

[0040] The terms "one embodiment" or "some embodiments" used in this application mean that one or more embodiments of this application include the specific features, structures, or characteristics described in that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this application do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0041] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0042] The integration order combination selection method provided in this application embodiment is executed by a computer device, and correspondingly, the integration order combination selection system for angular coefficient finite element calculation runs in the computer device.

[0043] Figure 1 This is a flowchart of a method for selecting the combination of integration orders for finite element calculation of angular coefficients, according to an embodiment of this application. Figure 1 The executing entity can be a combination selection system for integral orders. Depending on different requirements, the order of steps in this flowchart can be changed, and some can be omitted.

[0044] like Figure 1 As shown, the method for selecting the combination of integration orders for finite element calculations of angular coefficients includes: Step S1: Select the target geometric configuration based on the target radiation heat transfer problem, and discretize all the inner surfaces of the target geometric configuration into several triangular units, wherein the target radiation heat transfer problem is the radiation heat transfer problem in a closed space.

[0045] By selecting the corresponding geometric configuration based on the actual heat transfer scenario of the target radiation heat transfer problem and discretizing all its inner surfaces into multiple triangular units, the selection process of the integral order can be carried out for specific geometric configurations, avoiding blind parameter selection detached from the actual physical scenario. Furthermore, the integration operation on the original continuous surface is transformed into a discretization process of numerical integration on each triangular unit, providing a computational carrier for independently arranging integration points and assigning weight coefficients on each triangular unit.

[0046] In some specific embodiments, the target geometry is a closed cavity, which includes a cuboid.

[0047] By limiting the target geometry to a closed cavity or, more specifically, a cuboid, the geometric configuration in radiative heat transfer within a closed space can be covered, thus expanding the applicability of the method.

[0048] In some specific embodiments, discretizing all the inner surfaces of the target geometry into several triangular units specifically includes: Divide all the inner surfaces of the target geometry into Each triangle is divided into three elements, and the node coordinates, area, and normal vector of each triangle are recorded.

[0049] By dividing all the inner surfaces of the target geometry into Each triangular element is represented by a discrete element, and the node coordinates, area, and normal vector of each triangular element are recorded. This allows the geometric information of the surface to be completely converted into a parameterized description of the discrete element, providing the necessary geometric data for the precise positioning of the integration point on the element and the distance and angle calculations involved in the calculation of the angle coefficient.

[0050] Step S2: Define the range of values ​​for the integration order in the finite element calculation, and construct the integration order combination matrix, where: Integral order of the radiating emission unit The range of values ​​for is: ; Unit integration order of the radiation receiving unit The range of values ​​for is: ; The integral order combination matrix is The matrix, where the first... The elements are denoted as , representing the radiation emission unit adopting the first The first-order integrator and radiation receiving unit adopts the first-order integrator. Combinations of integral orders of order integrals.

[0051] By setting the range of integration orders from 1 to the maximum order for the radiating and receiving units respectively, and constructing a complete combination matrix with rows corresponding to the integration orders of the radiating and receiving units and columns corresponding to the integration orders of the radiating and receiving units, all possible pairings of integration orders on the two surfaces are included in the scope of consideration, forming a complete set covering all candidate schemes.

[0052] In some specific embodiments, , .

[0053] By the maximum value of the integration order of the radiating emission element The maximum value of the integration order of the radiating receiver unit All are set to be no less than 6, so that the integral order combination matrix covers at least all combinations from order 1 to order 6, ensuring that high-precision integral order combinations can be included in the candidate set and will not be excluded due to the low upper limit.

[0054] In one specific embodiment, the following is set , The resulting combination matrix of integral orders is shown in Table 1.

[0055] Table 1 Integral order matrix

[0056] Step S3: Calculate the angle coefficient between any two triangular elements in the target geometry one by one; In each calculation, the currently calculated triangular element is designated as the radiating element, and the remaining triangular elements are designated as radiating receiving elements. Then, for each integration order combination in the integration order combination matrix... The angular coefficient from a radiating emitting element to a radiating receiving element is calculated using the finite element method. .

[0057] In some specific embodiments, the finite element method is used to calculate the angle coefficient. The formula is:

[0058] in, For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; The total number of triangular units; Index of the radiating unit; This is the index of the radiation receiving unit; For the first The area of ​​each radiation receiving unit; The integration order used for the radiating emission element is a combination of integration orders. In Sure; The integration order used by the radiating receiving unit is a combination of integration orders. In Sure; For the radiation emission unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; For the radiation receiving unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; This is the index of the integration point on the radiating emission element, with a value ranging from 1 to... ; This is the index of the integration point on the radiating receiving unit, with a value ranging from 1 to... ; For the first On the first radiation emission unit Weighting coefficients for each integration point; For the first On the first radiation receiving unit Weighting coefficients for each integration point; For from the first The first radiation emission unit The integration point points to the first... The first radiation receiving unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiating units; For from the first The first radiation receiving unit The integration point points to the first... The first radiation emission unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiation receiving units; For the first The first radiation emission unit The integration point and the first The first radiation receiving unit Euclidean distance between integration points.

[0059] By clarifying the finite element calculation formula, the calculation of the angle coefficient can automatically adapt to the corresponding integration point distribution and weight configuration based on different integration order combinations, thereby achieving accurate acquisition of the angle coefficient values ​​under different integration order combinations.

[0060] In some specific embodiments, the total number of integration points on the radiation emission unit With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points. Total number of integration points on the radiation receiving unit With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points. The specific weighting coefficients and the area coordinates of the corresponding integration points within their respective triangular units are shown in Table 2.

[0061] Table 2. Correspondence between the number of integration points, area coordinates, and weighting coefficients.

[0062] By the total number of points and Let them be the order of integration, respectively. and The specific values ​​are determined, and the weight coefficients of each integration point and the area coordinates within the corresponding triangular unit are determined, so that the position and weight of the integration point corresponding to each combination of integration orders have clear and uniform values, ensuring that the same integration parameters are used in different calculation instances for the same combination of integration orders.

[0063] In some specific embodiments, The calculation formula is:

[0064] in, For the first On the first radiation emission unit The global coordinates of each integration point in three-dimensional space; For the first On the first radiation receiving unit The global coordinates of each integration point in three-dimensional space.

[0065] By employing the Euclidean distance formula in three-dimensional space to calculate the distance between the integration points of the radiating emitting unit and the radiating receiving unit, and using the coordinates of each integration point in the global coordinate system for solution, the distance parameter calculation can accurately reflect the true spatial interval between the two integration points, providing a reliable numerical input for the accurate calculation of the denominator term in the angle coefficient calculation formula.

[0066] Step S4, based on the combination of integral orders Calculated value of angle coefficient below The error value under this combination of integral orders is calculated using the principle of integrity of the sum of angle coefficients. All error values ​​are filled into the corresponding positions of the integral order combination matrix to form the error matrix. .

[0067] By using the principle of angular coefficient integrity—that the sum of the angular coefficients of all radiating emission elements within a closed cavity should be 1—as a benchmark, the error value of the angular coefficient calculation under each combination of integral orders is calculated. All error values ​​are then filled in according to the corresponding positions of each combination in the matrix, forming an error matrix of the same type as the integral order combination matrix, where each element represents the calculation deviation under that combination. This presents the calculation accuracy of each combination of integral orders in a complete form of quantitative data.

[0068] In some specific embodiments, the error value The calculation formula is:

[0069]

[0070] in, For the first The radiating emission elements are combined in the integral order. The total error value below; For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; For the theoretical sum of angle coefficients within a single integral order combination, .

[0071] By defining error values The calculation formula allows the error value to be measured in the form of relative deviation to measure the calculation accuracy of each combination of integral orders, eliminating the influence of different angular systems and numerical values ​​on the error evaluation scale.

[0072] In some specific embodiments, the error matrix for The matrix, where the first... Each element is a combination with the integral order. Corresponding error value .

[0073] By using the error matrix Constructed as The matrix and the first The elements at each position are assigned the combination of integral orders. The corresponding error value This ensures that the error matrix and the integral order combination matrix maintain a completely consistent correspondence in structure, and each position in the matrix can be directly traced back to the corresponding integral order combination by its row number and column number.

[0074] Step S5, from the error matrix Filter out those that meet the requirements The complete combination of integral orders is output as the recommended combination of integral orders for the target radiative heat transfer problem. This is the preset desired accuracy threshold.

[0075] By using a preset expected accuracy threshold as the screening criterion to traverse each element in the error matrix and extracting the combination of integral orders corresponding to all elements whose absolute error value does not exceed the threshold as the recommended output, the final recommended combination is quantitatively verified to ensure that its calculation error is within an acceptable range.

[0076] In some specific embodiments, the desired accuracy threshold The value range is 1% to 5%.

[0077] By setting the desired accuracy threshold The value range is set between 1% and 5%, so that the threshold can cover the general requirements for the accuracy of radiation heat transfer calculation in engineering practice. This avoids both overly strict thresholds that would lead to the elimination of a large number of effective combinations and overly wide thresholds that would allow combinations with insufficient accuracy to be retained.

[0078] In some specific embodiments, if the error matrix No satisfaction in the middle If the combination of integral orders is such that at least one of the following operations is performed, then return to step S2 and repeat: Increase the maximum value of the integral order of the radiating emission element. ; Increase the maximum value of the integration order of the radiation receiving unit. ; Increase the expected accuracy threshold .

[0079] When there is no combination of integral orders in the error matrix that satisfies the condition that the absolute value of the error does not exceed the desired accuracy threshold, the maximum value of the integral order of the radiating emission unit or the maximum value of the integral order of the radiating receiving unit or the desired accuracy threshold is increased, and the integral order combination matrix construction step is returned to be re-executed. This allows the method to expand the search range or relax the constraints when the first screening is unsuccessful, providing further opportunities to obtain a combination of integral orders that meets the requirements.

[0080] In one specific embodiment, the target geometry is set as a cube with a side length of 1. , ,set up The aforementioned method was repeated multiple times, and the error comparison graph for each combination of integral orders is shown below. Figure 2 As shown, the error value exist Figure 2 The Chinese character is represented as .

[0081] according to Figure 2 It can be seen that when using the combination of the two integral orders O1O6 and O2O6, The ranges are -1.32% ~ 0.13% and -2.27% ~ 0.0003%, respectively, both satisfying the requirements. Given the given conditions, O1O6 and O2O6 are therefore used as the recommended combination of integration orders for the target radiative heat transfer problem corresponding to this target geometry.

[0082] In some specific embodiments, the calculation of radiative heat transfer of power equipment using the above-described method for selecting the combination of integral orders includes the following steps: S61. Treat the radiation heat transfer problem of the target power equipment as the target radiation heat transfer problem, and perform the above-mentioned method for selecting the combination of integral orders to obtain the recommended combination of integral orders; S62. Discretize all the inner surfaces of the target power equipment into... Using a triangular mesh, select one combination of integration orders from the recommended combinations to calculate the angle coefficient matrix of the target radiation heat transfer problem. ; S63. Establish a system of nonlinear equations for the effective radiation of all triangular meshes:

[0083] in, and All are indices of a triangular mesh, with values ​​ranging from 1 to... ; This represents the total number of triangular grids. For the first Effective radiation of a triangular grid; For the first Effective radiation of a triangular grid; For the first Emissivity of a triangular grid; It is the Stefan-Boltzmann constant; For the first The temperature of each triangular grid is either the initial value or the result of the previous iteration step; Angle coefficient matrix The Middle The first triangular grid to the... The angle coefficient of a triangular grid; S64. Iteratively solve the nonlinear equations for effective radiation to obtain the effective radiation for each triangular grid. S65. Substitute the effective radiation of each triangular grid into the radiation heat transfer equation to calculate the radiation heat transfer of each triangular grid. The radiation heat transfer equation is as follows:

[0084] in, For the first Radiative heat transfer of a triangular grid; For the first The area of ​​the triangular grid; S66. Sum up the radiative heat transfer of all the triangular grids to obtain the total radiative heat transfer of the entire target power equipment; S67. Taking the total radiative heat transfer as the heat load, and combining the parameters of conduction and convection heat transfer, the overall energy balance equation of the target power equipment is established. Then, the finite element method is used to discretize and iteratively solve the overall energy balance equation to obtain the temperature of all triangular meshes, thereby realizing the radiative heat transfer calculation of the temperature field of the power equipment.

[0085] The following are embodiments of an integral order combination selection system for finite element calculation of angular coefficient provided in this application. This integral order combination selection system for finite element calculation of angular coefficient belongs to the same inventive concept as the integral order combination selection method in the above embodiments. For details not described in the embodiments of the integral order combination selection system, please refer to the embodiments of the integral order combination selection method for finite element calculation of angular coefficient provided in the above embodiments.

[0086] like Figure 3 As shown, the system for selecting the combination of integral orders for finite element method calculations of angular coefficients includes: The configuration selection and discretization module is used to select the target geometry configuration based on the target radiation heat transfer problem and discretize all the inner surfaces of the target geometry configuration into several triangular elements; The module for constructing the combination matrix of integral orders is used to set the range of values ​​for the integral order in finite element calculations and to construct the combination matrix of integral orders. The angle coefficient calculation module is used to calculate the angle coefficient between any two triangular elements in the target geometric configuration one by one. The error matrix construction module is used to calculate the error value under the integration order combination based on the calculated value of the angle coefficient under the integration order combination and the principle of angle coefficient integrity. All error values ​​are filled in the corresponding positions of the integration order combination matrix to form the error matrix. The recommended integral order combination output module is used to select all integral order combinations from the error matrix whose absolute error value does not exceed a preset accuracy threshold, and use them as the recommended integral order combination output for the target radiation heat transfer problem.

[0087] The integral order combination selection system in this embodiment is used to implement the integral order combination selection method for angular coefficient finite element calculation.

[0088] This application also provides an electronic device for implementing the various embodiments of this application. Figure 4 To illustrate the hardware structure of an electronic device according to various embodiments of this application, as shown in the following diagram... Figure 4 As shown, the electronic device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor.

[0089] Those skilled in the art will understand that the electronic device structure involved in the embodiments of this application does not constitute a limitation on the electronic device. The electronic device may include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements.

[0090] In embodiments of this application, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments of this application described and / or claimed herein.

[0091] In this application embodiment, the processor can be implemented using at least one of an Application-Specific Integrated Circuit (ASIC), a Digital Signal Processor (DSP), a Digital Signal Processing Device (DSPD), a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such implementations can be implemented within a controller. For software implementations, implementations such as processes or functions can be implemented with separate software modules that allow the performance of at least one function or operation. The software code can be implemented by a software application (or program) written in any suitable programming language, and the software code can be stored in memory and executed by the controller.

[0092] In addition, the electronic device includes some functional modules not shown, which will not be described in detail here.

[0093] Those skilled in the art will understand that the various aspects of the electronic device provided in this application can be implemented as a system, method, or program product. Therefore, the various aspects of this application can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0094] This application also provides a storage medium storing a program product capable of implementing a method for selecting the combination of integral orders for angular coefficient finite element calculations. In some possible implementations, various aspects of this application may also be implemented as a program product comprising program code that, when run on a terminal device, causes the terminal device to perform the steps described in the foregoing "Exemplary Methods" section of this specification according to various exemplary embodiments of this application.

[0095] The storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0096] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for selecting the combination of integration orders for finite element method calculations of angular coefficients, characterized in that, include: S1. Select the target geometric configuration based on the target radiation heat transfer problem, and discretize all the inner surfaces of the target geometric configuration into several triangular units, where the target radiation heat transfer problem is the radiation heat transfer problem in a closed space; S2. Define the range of values ​​for the integration order in the finite element method, and construct the integration order combination matrix, where: Integral order of the radiating emission unit The range of values ​​for is: ; Unit integration order of the radiation receiving unit The range of values ​​for is: ; The integral order combination matrix is The matrix, where the first... The elements are denoted as , representing the radiation emission unit adopting the first The first-order integrator and radiation receiving unit adopts the first-order integrator. Combinations of the orders of integrals of order ; S3. Calculate the angle coefficient between any two triangular elements in the target geometry one by one; In each calculation, the currently calculated triangular element is designated as the radiating element, and the remaining triangular elements are designated as radiating receiving elements. Then, for each integration order combination in the integration order combination matrix... The angular coefficient from a radiating emitting element to a radiating receiving element is calculated using the finite element method. ; S4. Based on the combination of integral orders Calculated value of angle coefficient below The error value under this combination of integral orders is calculated using the principle of integrity of the sum of angle coefficients. All error values ​​are filled into the corresponding positions of the integral order combination matrix to form the error matrix. ; S5. From the error matrix Filter out those that meet the requirements The complete combination of integral orders is output as the recommended combination of integral orders for the target radiative heat transfer problem. This is the preset desired accuracy threshold.

2. The method for selecting the combination of integral orders as described in claim 1, characterized in that, Calculation of angle coefficient using the finite element method The formula is: in, For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; The total number of triangular units; Index of the radiating unit; This is the index for the radiation receiving unit; For the first The area of ​​each radiation receiving unit; The integration order used for the radiating emission element is a combination of integration orders. In Sure; The integration order used by the radiating receiving unit is a combination of integration orders. In Sure; For the radiation emission unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; For the radiation receiving unit to adopt the first The total number of integration points corresponding to the order of integration, based on the order of integration. Sure; This is the index of the integration point on the radiating emission element, with a value ranging from 1 to... ; This is the index of the integration point on the radiating receiving unit, with a value ranging from 1 to... ; For the first On the first radiation emission unit Weighting coefficients for each integration point; For the first On the first radiation receiving unit Weighting coefficients for each integration point; For from the first The first radiation emission unit The integration point points to the first... The first radiation receiving unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiating units; For from the first The first radiation receiving unit The integration point points to the first... The first radiation emission unit The vector at the nth integration point, and the vector at the th integration point The angle between the normals of the radiation receiving units; For the first The first radiation emission unit The integration point and the first The first radiation receiving unit Euclidean distance between integration points.

3. The method for selecting the combination of integral orders as described in claim 2, characterized in that, In step S3, The calculation formula is: in, For the first On the first radiation emission unit The global coordinates of each integration point in three-dimensional space; For the first On the first radiation receiving unit The global coordinates of each integration point in three-dimensional space.

4. The method for selecting the combination of integral orders as described in claim 1, characterized in that, In step S3, the total number of integration points on the radiation emission unit With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points. Total number of integration points on the radiation receiving unit With the order of integration The correspondence is as follows: The first order corresponds to 1 integration point, the second order corresponds to 3 integration points, the third order corresponds to 4 integration points, the fourth order corresponds to 6 integration points, the fifth order corresponds to 7 integration points, and the sixth order corresponds to 12 integration points.

5. The method for selecting the combination of integral orders as described in claim 1, characterized in that, Error value The calculation formula is: in, For the first The radiative emission elements are combined in the integral order. The total error value below; For the first The radiation emission unit to the first Calculated angle factor values ​​for each radiating receiving unit; For the theoretical sum of angle coefficients within a single integral order combination, .

6. The method for selecting the combination of integral orders as described in claim 1, characterized in that, In step S5, if the error matrix No satisfaction in the middle If the combination of integral orders is such that at least one of the following operations is performed, then return to step S2 and repeat: Increase the maximum value of the integral order of the radiating emission element. ; Increase the maximum value of the integration order of the radiation receiving unit. ; Increase the expected accuracy threshold .

7. A method for calculating radiative heat transfer in power equipment using the integration order combination selection method as described in any one of claims 1-6, characterized in that, Includes the following steps: S61. Treat the radiation heat transfer problem of the target power equipment as the target radiation heat transfer problem, and perform the above-mentioned method for selecting the combination of integral orders to obtain the recommended combination of integral orders; S62. Discretize all the inner surfaces of the target power equipment into... Using a triangular mesh, select one combination of integration orders from the recommended combinations to calculate the angle coefficient matrix for the target radiation heat transfer problem. ; S63. Establish a system of nonlinear equations for the effective radiation of all triangular meshes: in, and All are indices of a triangular mesh, with values ​​ranging from 1 to... ; This represents the total number of triangular grids. For the first Effective radiation of a triangular grid; For the first Effective radiation of a triangular grid; For the first Emissivity of a triangular grid; It is the Stefan-Boltzmann constant; For the first The temperature of each triangular grid is either the initial value or the result of the previous iteration step; Angle coefficient matrix Middle The first triangular grid to the... The angle coefficient of a triangular grid; S64. Iteratively solve the nonlinear equations for effective radiation to obtain the effective radiation for each triangular grid. S65. Substitute the effective radiation of each triangular grid into the radiation heat transfer equation to calculate the radiation heat transfer of each triangular grid. The radiation heat transfer equation is as follows: in, For the first Radiative heat transfer of a triangular grid; For the first The area of ​​the triangular grid; S66. Sum up the radiative heat transfer of all the triangular grids to obtain the total radiative heat transfer of the entire target power equipment; S67. Taking the total radiative heat transfer as the heat load, and combining the parameters of conduction and convection heat transfer, the overall energy balance equation of the target power equipment is established. Then, the finite element method is used to discretize and iteratively solve the overall energy balance equation to obtain the temperature of all triangular meshes, thereby realizing the radiative heat transfer calculation of the temperature field of the power equipment.

8. A system for selecting the combination of integral orders for finite element method calculations of angular coefficients, characterized in that, A method for implementing the combination selection of integral orders as described in any one of claims 1-6 includes: The configuration selection and discretization module is used to select the target geometry configuration based on the target radiation heat transfer problem and discretize all the inner surfaces of the target geometry configuration into several triangular elements; The module for constructing the combination matrix of integral orders is used to set the range of values ​​for the integral order in finite element calculations and to construct the combination matrix of integral orders. The angle coefficient calculation module is used to calculate the angle coefficient between any two triangular elements in the target geometry one by one. The error matrix construction module is used to calculate the error value under the integration order combination based on the calculated value of the angle coefficient under the integration order combination and the principle of angle coefficient integrity. All error values ​​are filled in the corresponding positions of the integration order combination matrix to form the error matrix. The recommended integral order combination output module is used to select all integral order combinations from the error matrix whose absolute error value does not exceed a preset accuracy threshold, and use them as the recommended integral order combination output for the target radiation heat transfer problem.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When a processor executes a computer program, it implements the steps of the method for selecting the combination of integral orders as described in any one of claims 1-6.

10. A storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the steps of the method for selecting the combination of integral orders as described in any one of claims 1-6.

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