A periodic boundary layer grid generation method for turbomachinery

Abstract

This invention discloses a method for generating a periodic boundary layer mesh for turbomachinery, comprising: reading the surface mesh of the turbomachinery and constructing a leading edge boundary; constructing a periodic affine transformation function based on the leading edge boundary; constructing a virtual periodic domain based on the leading edge boundary and the affine transformation function using a cell migration method; calculating the periodic travel direction and travel distance based on the virtual periodic domain; pre-generating a layer of triangular prism elements based on the travel direction and travel distance, and establishing a mapping relationship from the bottom node to the top node of the triangular prism elements; checking and periodically deleting invalid elements based on the layer of triangular prism elements, and then updating the leading edge boundary; if the updated leading edge boundary is empty, an initial boundary layer mesh is obtained; checking and repairing the periodic mismatch region caused by transition elements based on the initial boundary layer mesh and the mapping relationship from the bottom node to the top node of the triangular prism elements, to obtain a periodic boundary layer mesh.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery mesh generation technology for aero-engines, and more particularly to a method for generating periodic boundary layer meshes for turbomachinery. Background Technology

[0002] Turbomachinery is a core component of advanced power systems such as aero-engines, gas turbines, and steam turbines, and its design has a decisive impact on the overall system performance. In recent years, computational fluid dynamics (CFD) technology has developed rapidly and has been widely applied to the numerical simulation of turbomachinery. Compared with experimental testing, numerical simulation methods are lower in cost, higher in efficiency, and more suitable for the design and optimization of turbomachinery. This CFD method typically uses the finite volume method to solve partial differential equations, requiring discretization of the flow field region. However, the complex geometry and flow field characteristics of turbomachinery pose significant challenges to mesh generation.

[0003] Turbomachinery typically exhibits periodic structures, thus requiring analysis of individual blade channels rather than complete models. Applying periodic boundary conditions to individual channels significantly saves memory resources and reduces computation time. Periodic boundary conditions have been widely applied in turbomachinery, computational electromagnetics, fiber-reinforced composites, porous media, foam materials, and metal alloys. However, applying periodic boundary conditions requires complex constrained mesh generation processes, as the condition can only be applied when the mesh on the periodic surface is consistent. Some studies have introduced specialized techniques to apply periodic boundary conditions to mismatched meshes, such as the Lagrange multiplier method, slurry decomposition method, and polynomial interpolation. These methods are only recommended when it is difficult to generate completely identical periodic meshes, as they not only require significant additional computational work to implement the periodic boundary conditions but may also lead to interpolation errors and theoretical instabilities. Therefore, it is necessary to develop techniques capable of generating consistent periodic meshes.

[0004] In viscous fluid computation, anisotropic physical phenomena exist in the boundary layer region near the wall, with drastic gradient changes in flow variables. Therefore, it is often necessary to generate anisotropic meshes in this region. Early boundary layer mesh generation methods were based on constructing structured meshes using partial differential equations. Structured meshes possess good orthogonality, which is beneficial for capturing viscous flows. However, this method has limited control over local mesh sizes and low automation. The complex geometry of turbomachinery limits the application of structured meshes. In contrast, unstructured meshes offer greater flexibility in controlling mesh sizes. Some researchers use anisotropic tetrahedral meshes near the wall to capture viscous flow fields, while generating isotropic tetrahedral meshes in the far-field region. However, the lack of orthogonality reduces the accuracy of boundary layer simulations. Currently, hybrid meshes, due to their combination of the advantages of structured and unstructured meshes, are considered the optimal mesh form. The main method for generating hybrid meshes is the propulsion layer mesh generation technique. This method generates semi-structured prismatic elements near the wall and fills the remaining regions with unstructured tetrahedral elements. Although methods for generating boundary layer meshes are relatively mature, ensuring the periodicity of boundary layer elements remains a significant challenge. This requires designing periodic affine transformation functions to achieve mesh matching on periodic boundaries. Furthermore, this places higher demands on various stages of the boundary layer generation process, including element advancement, element detection, and transition element processing. Summary of the Invention

[0005] Based on this, the present invention proposes a method for generating periodic boundary layer meshes for turbomachinery to address the problems existing in the background art. This method first constructs a periodic affine transformation function based on the input periodic surface mesh. Then, a virtual periodic domain is constructed using an element migration method to generate periodic travel directions and distances. During element detection, periodic invalid elements are recursively eliminated simultaneously. After generating the boundary layer mesh, aperiodic regions caused by transition elements are corrected. This application can generate anisotropic boundary layer meshes on viscous surfaces while ensuring mesh consistency on periodic boundary conditions.

[0006] This invention discloses a method for generating periodic boundary layer meshes for turbomachinery, comprising: S1: Read the periodic surface mesh and boundary conditions of the turbomachinery, and construct the leading edge boundary based on the surface mesh; S2: Construct a periodic affine transformation function based on the boundary conditions and the leading edge boundary; S3: Based on the boundary conditions, leading edge boundary, and affine transformation function, construct a virtual periodic domain using the element migration method; S4: Calculate the periodic direction and distance of travel based on the virtual periodic domain; S5: Generate a layer of triangular prism units in advance according to the travel direction and travel distance, and establish a mapping relationship from the bottom node to the top node of the triangular prism units; S6: Based on the aforementioned layer of triangular prism elements, check and periodically delete invalid elements, and then update the leading edge boundary; S7: If the updated front boundary is empty, the initial boundary layer mesh is obtained; otherwise, repeat steps S3 to S6. S8: Based on the initial boundary layer mesh and the mapping relationship, check and repair the periodic mismatch region caused by the transition unit to obtain a periodic boundary layer mesh.

[0007] Furthermore, the periodic surface mesh and boundary conditions of the turbomachinery are read, and the leading edge boundary is constructed based on the surface mesh, including: Extract the grid point information and element topology information of the periodic surface mesh of the turbomachinery, and define them as leading edge boundary points and leading edge boundary elements; Extract boundary conditions on the surface mesh, including surface boundary conditions and periodic boundary conditions.

[0008] Furthermore, based on the boundary conditions and the leading edge boundary, a periodic affine transformation function is constructed, including: Based on the boundary conditions and the front boundary, construct the source surface point set and the target surface point set; The source and target point sets are decentralized to obtain a point set without translation effect; Construct optimization equations and solve for the optimal rotation matrix based on the set of points without translation effects; Calculate the translation vector based on the set of points without translation effect and the optimal rotation matrix; Based on the optimal rotation matrix and translation vector, construct a periodic affine transformation function.

[0009] Furthermore, based on the aforementioned boundary conditions, leading edge boundary, and affine transformation function, a virtual periodic domain is constructed using a cell migration method, including: Based on the boundary conditions and the leading edge boundary, find the triangular element close to the source surface; Using the periodic affine transformation function, the triangular unit close to the source surface is projected onto the target surface to form a virtual periodic domain.

[0010] Further, based on the virtual periodic domain, the periodic direction of travel and the distance traveled are calculated, including: The boundary containing the virtual periodic domain is partitioned into an inner region and an outer region, and the relationship between the leading edge boundary points of the inner region and the leading edge boundary points of the outer region is established. Calculate the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Smooth the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Remove the virtual periodic domain to obtain the periodic direction and distance of travel.

[0011] Furthermore, based on the aforementioned layer of triangular prism elements, invalid elements are checked and periodically deleted, and then the leading edge boundary is updated, including: Based on the boundary conditions, periodic elements are found in the first-layer triangular prism element, and the duality relationship of the periodic elements is established. The layer of triangular prism elements is inspected, invalid elements are recursively deleted and transition elements are added. At the same time, the synchronous deletion of periodic elements is ensured according to the duality relationship, resulting in a single-layer boundary layer. The top grid points and cells of the single-layer boundary layer are used as the new front boundary.

[0012] Further, based on the initial boundary layer mesh and the mapping relationship, the periodic mismatch region caused by the transition unit is checked and repaired to obtain a periodic boundary layer mesh, including: Extract the top-level mesh cells of the initial boundary layer and store the mesh edge information in a hash table; Based on the mapping relationship from the bottom node to the top node of the triangular prism unit and the hash table, all possible cases are divided into triangular candidate units and quadrilateral candidate units. Determine whether the triangular candidate unit and the quadrilateral candidate unit are defective regions. If they are defective regions, then correct the defective regions.

[0013] The technical solutions provided by the embodiments of this application may include the following beneficial effects: This invention can generate anisotropic boundary layer meshes on viscous surfaces while ensuring mesh consistency on periodic boundary conditions.

[0014] This invention constructs a periodic affine transformation function based on an input periodic surface mesh. Commercial software typically calculates rotation matrices or translation vectors based on user-input parameters such as rotation axes, translation axes, angles, and distances to achieve periodic mesh matching. In contrast, the method of this invention requires no additional user input, is more flexible and highly automated, and improves mesh generation efficiency.

[0015] This invention uses a method of constructing a virtual periodic domain by cell migration to calculate the travel distance and direction. This ensures that the leading edge boundary point on the periodic boundary condition is affected by the periodic domains on both sides, and can generate a periodically consistent travel distance and normal, which conforms to the physical law of periodicity.

[0016] This invention employs a periodic recursive deletion method using triangular prism elements and pyramid elements. By establishing a mapping relationship between periodic elements, the synchronous deletion of periodic elements is achieved, ensuring the mesh consistency of periodic boundary conditions during element detection.

[0017] This invention identifies and repairs periodic mismatch regions caused by transition elements by periodically correcting the transition elements, thereby meeting the requirements for mesh consistency on periodic boundary conditions. Attached Figure Description

[0018] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0019] Figure 1 This is a flowchart illustrating a method for generating periodic boundary layer meshes for turbomachinery according to an exemplary embodiment.

[0020] Figure 2 This is a schematic diagram of a turbine surface mesh model and boundary conditions according to an exemplary embodiment.

[0021] Figure 3 This is a schematic diagram of a triangular element close to the source surface boundary, according to an exemplary embodiment.

[0022] Figure 4 This is a schematic diagram of a projected virtual periodic domain according to an exemplary embodiment.

[0023] Figure 5 This is a schematic diagram illustrating the virtual periodic domain partitioning relationship according to an exemplary embodiment.

[0024] Figure 6 This is a schematic diagram illustrating the removal of a virtual periodic domain according to an exemplary embodiment.

[0025] Figure 7 This is a schematic diagram illustrating the duality of periodic units according to an exemplary embodiment.

[0026] Figure 8 This is a schematic diagram illustrating the filling of a transitional pyramid unit according to an exemplary embodiment.

[0027] Figure 9 This is a schematic diagram of a periodic source surface transition unit according to an exemplary embodiment.

[0028] Figure 10 This is a schematic diagram of a periodic target surface transition unit according to an exemplary embodiment.

[0029] Figure 11 This is a schematic diagram illustrating the classification of transition units according to an exemplary embodiment.

[0030] Figure 12 This is a schematic diagram of a tetrahedron repairing a triangular defect region according to an exemplary embodiment.

[0031] Figure 13 This is a schematic diagram illustrating the repair of a tetrahedron with a quadrilateral defect region according to an exemplary embodiment.

[0032] Figure 14 This is a schematic diagram of a pyramid for repairing a quadrilateral defect region, according to an exemplary embodiment.

[0033] Figure 15 This is a detailed diagram of a periodic boundary layer mesh according to an exemplary embodiment. Detailed Implementation

[0034] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0035] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0036] Figure 1 This is a flowchart illustrating a method for generating periodic boundary layer meshes for turbomachinery according to an exemplary embodiment, such as... Figure 1 As shown, the method may include the following steps: S1: Read the periodic surface mesh and boundary conditions of the turbomachinery, and construct the leading edge boundary based on the surface mesh; specifically, this may include the following sub-steps: S11: Extract the grid point information and element topology information of the periodic surface mesh of the turbomachinery, and define them as leading edge boundary points and leading edge boundary elements; Specifically, this application uses a turbine surface mesh model in an aero-engine as an example for detailed explanation. Assuming each surface has N mesh points, the mesh points of each surface are stored in a set P = {P1, P2, ..., P...}. N}, where each P i ={x i , y i , z i Let} represent the three-dimensional coordinates of the i-th point on the face, where i ∈ [1, N]; store the element topology information of each face in the set T = {T1, T2, ..., T}. N}, where each T i ={P m , P j , P k Let} represent the topology of the i-th triangular element on the face, including the m-th, j-th, and k-th points, where m∈[1,N], j∈[1,N], and k∈[1,N]. Then, the set P of each face is the set of front boundary points, and the set T of each face is the set of front boundary elements. The front boundary constructed from the face mesh will serve as the initial front for generating the boundary layer mesh.

[0037] S12: Extract boundary conditions on the surface mesh, including surface boundary conditions and periodic boundary conditions; Specifically, the boundary conditions for the turbomachinery are set as follows: Figure 2 As shown, boundary conditions include surface boundary conditions and periodic boundary conditions. Each type of boundary has different physical properties, imposing specific requirements on mesh generation. For example, surface boundary conditions typically require the generation of anisotropic boundary layer meshes; periodic boundary conditions include source and target surfaces, and the mesh topology and geometry of the source and target surfaces must be kept consistent.

[0038] S2: Based on the boundary conditions and the leading edge boundary, construct a periodic affine transformation function; specifically, this may include the following sub-steps: S21: Based on the boundary conditions and the leading edge boundary, construct the source surface point set and the target surface point set; Specifically, based on the extracted boundary conditions, the source surface and the target surface are found, and the set of grid points P on the source surface is... s ={P s1 , P s2 , ... , P sN} as the source surface point set, the set of grid points P on the target surface t ={P t1 , P t2 , ... , P tNThe target surface is represented by a set of points. This step aims to transform the abstract geometric boundary into a discrete set of points that can be used for mathematical calculations, providing structured input data for subsequent algorithm implementation. By explicitly distinguishing between the source and target surfaces and establishing one-to-one corresponding mesh point pairs, the subsequent rigid body transformation solution has a clear physical correspondence and numerical feasibility.

[0039] S22: Decentralize the source surface point set and the target surface point set to obtain a point set without translation effect; Specifically, the purpose of this step is to decompose and simplify the complex spatial registration problem into two independent sub-problems: translation and rotation. By calculating the centroid of the point set and translating it to the origin, the translational degree of freedom is eliminated first, allowing the subsequent algorithm to focus on solving the pure rotation transformation.

[0040]

[0041]

[0042]

[0043]

[0044] here and Let represent the centroids of the source and target point sets, respectively. and These are the i-th points in the source and target point sets, respectively. and These are the i-th point in the decentralized source and target point sets, respectively, and N is the number of points in the source and target surfaces.

[0045] S23: Construct the optimization equation and solve for the optimal rotation matrix based on the set of points without translation effect; Find an affine transformation matrix that minimizes the root mean square deviation between the transformed source and target point sets. This problem can be reduced to solving the following optimization model:

[0046] Here R is the rotation matrix, since and Since all are constants, minimizing the equation is equivalent to maximizing the following function:

[0047] Its goal is to solve for RH Rotation matrix that takes the maximum value of trace R The covariance matrix is ​​processed using singular value decomposition. H= The matrix can be obtained.U and V :

[0048] here Let U be a diagonal matrix containing the singular values ​​of the covariance matrix, and let U and V be orthogonal matrices.

[0049] Based on the singular value decomposition results, the formula for calculating the rotation matrix R is:

[0050] The resulting rotation matrix R It will serve as a core component in the subsequent assembly of affine transformation functions.

[0051] S24: Calculate the translation vector based on the set of points without translation effect and the optimal rotation matrix; Specifically, after calculating the optimal rotation matrix, the translation properties also need to be considered. The formula for calculating the translation vector is:

[0052] The resulting translation vector T It will serve as a core component in the subsequent assembly of affine transformation functions.

[0053] S25: Construct a periodic affine transformation function based on the optimal rotation matrix and translation vector. Specifically, the translation and rotation components, which were solved independently in the previous steps, are reintegrated to form a complete rigid body transformation that can be applied to the original actual coordinates, from which the periodic affine transformation function can be obtained. :

[0054] here Let be the grid points on the source surface. Using a periodic affine transformation function, any element and grid point on the source surface can be projected onto the corresponding target surface.

[0055] S3: Based on the boundary conditions, leading edge boundary, and affine transformation function, construct a virtual periodic domain using a cell migration method; specifically, this may include the following sub-steps: S31: Based on the boundary conditions and the leading edge boundary, find the triangular element close to the source surface; Specifically, for a surface mesh on an object's boundary condition, all triangular elements are traversed, and elements whose mesh edges lie on the periodic boundary source surface are identified and marked, such as... Figure 3 As shown, the triangular elements of the source surface found will serve as the parent elements of the virtual periodic domain.

[0056] S32: Using the periodic affine transformation function, the triangular unit close to the source surface is projected onto the target surface to form a virtual periodic domain; Specifically, assuming the set of source face triangle units of the marker is The k-th triangular unit is represented by the coordinates of its three vertices (grid points):

[0057] The set of triangular units contained in the virtual periodic domain after projection is: ={ }, where the vertices of each mapped triangle unit are:

[0058] The projected virtual periodic domain is as follows Figure 4 As shown. After constructing the virtual periodic domain, the leading edge boundary points on the target surface will be jointly affected by the elements on both sides of the periodic surface, and the travel distance and direction calculated as a result will be more in line with the physical laws of periodicity.

[0059] S4: Calculate the periodic direction and distance of travel based on the virtual periodic domain; specifically, this may include the following sub-steps: S41: The boundary containing the virtual periodic domain is partitioned into an inner region and an outer region, and the relationship between the leading edge boundary points of the inner region and the leading edge boundary points of the outer region is established. Specifically, such as Figure 5 As shown, the virtual periodic domain is divided into an inner region and an outer region. For example, a mapping relationship is established between the leading edge boundary points on the source surface of the outer region and the corresponding points on the target surface of the inner region, and a mapping relationship is established between the virtual points of the outer region and their parent points in the inner region. Partitioning is to facilitate the use of different computational logics for the leading edge boundary points in different regions.

[0060] S42: Calculate the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Specifically, the direction of travel of a leading edge boundary point is the average of the normal vectors of its adjacent elements; the travel distance of a leading edge boundary point can be calculated using the following formula:

[0061] here, The current layer height. For growth rate, c This is the current floor number. h 0 For the first height, is the smoothing coefficient for concave and convex angles.

[0062] The method described above is used to calculate the direction and distance of travel for the leading edge boundary points of the inner region. Although the leading edge boundary points of the outer region do not directly participate in the calculation, their values ​​will be updated to match those of the corresponding points in the inner region. Maintaining the values ​​of the leading edge boundary points of the outer region is for subsequent smoothing operations.

[0063] S43: Smooth the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Specifically, Laplacian smoothing is applied to the direction and distance of travel to avoid abrupt changes between adjacent leading edge points. The smoothing process iterates only on the leading edge boundary points of the inner region, but the points outside the region are still updated synchronously according to the changes in the leading edge boundary points of the inner region, and will in turn affect the calculation of the leading edge boundary points of the inner region.

[0064] S44: Remove the virtual periodic domain to obtain the periodic travel direction and travel distance; Specifically, such as Figure 6 As shown, if all virtual periodic domain units are removed, then the direction and distance of travel of all leading edge boundary points will have a periodic effect and there will be no redundant nodes.

[0065] S5: Generate a layer of triangular prism units in advance according to the travel direction and travel distance, and establish a mapping relationship from the bottom node to the top node of the triangular prism units; Specifically, the dual point of each leading edge boundary point can be calculated based on the direction and distance of travel. By connecting each leading edge boundary point with its dual point, a layer of triangular prism elements can be pre-generated, and a mapping relationship between the leading edge boundary points and their dual points can be established. Based on this mapping relationship, all elements in the top layer can be quickly found from the bottom layer of the boundary layer, and the layer number of each leading edge point can also be identified.

[0066] S6: Based on the aforementioned layer of triangular prism elements, check and periodically delete invalid elements, and then update the leading edge boundary; S61: Based on the boundary conditions, find periodic elements in the first-layer triangular prism element and establish the duality relationship of the periodic elements. Specifically, such as Figure 7 As shown, elements close to the periodic boundary are found in the pre-generated triangular prism elements, and a periodic correspondence is established. Based on this periodic correspondence, the synchronous deletion of periodic invalid elements can be achieved.

[0067] S62: Check the layer of triangular prism units, recursively delete invalid units and supplement transition units, and at the same time ensure the synchronous deletion of periodic units according to the duality relationship to obtain a single-layer boundary layer. Specifically, three criteria were established to evaluate the validity of a cell. If any criterion is not met, the cell will be removed, and the advancement of the relevant front boundary point will be terminated. First, the quality of prism cells is evaluated using a scaling aspect ratio; if the scaling aspect ratio of a prism cell is lower than a set threshold, the cell is marked as invalid. Second, a global intersection check is performed on each cell; all cells with intersections are marked as invalid. Furthermore, if the difference in layer number between adjacent points is greater than one, low-quality tetrahedral or pyramidal cells may be generated. Therefore, if any adjacent point in the previous layer has been marked as stopping advancement, the cell at the current position will also be marked as invalid. If a cell on a periodic boundary is removed, its dual cells will also be removed simultaneously.

[0068] After removing the prism element, the quadrilateral faces of the adjacent elements will be exposed. For example... Figure 8 As shown, these quadrilateral faces are typically converted into triangular faces by inserting pyramid elements. This is because the top surface mesh of the boundary layer serves as input to a tetrahedral mesh generator, which only accepts triangular elements. If the inserted pyramid element causes global intersections or results in poor quality, the pyramid element and its dependent prism elements must be removed. It's important to note that if the dependent prism element is a periodic element, its corresponding periodic mapping element will also be removed simultaneously. Furthermore, new pyramid elements need to be added to the positions of the removed prism elements, and checks must be performed. This entire process is executed recursively until the number of prism elements to be deleted is empty.

[0069] S63: Use the top grid points and cells of the single-layer boundary layer as the new front boundary; Specifically, after generating one layer of cells and removing invalid cells, it is determined whether the current layer number meets the maximum layer number. If the maximum layer number is not reached, the top layer point and top layer mesh cell will be used as the new front boundary point and front boundary cell for subsequent advancement.

[0070] S7: If the updated leading edge boundary is empty, then the initial boundary layer mesh is obtained; otherwise, repeat steps S3 to S6. Specifically, this step is designed as a cyclical process for determining the termination condition and the final output control point. Its core logic lies in the fact that the leading edge boundary represents the geometric surface region in the current boundary layer mesh that has not yet been covered by triangular prism elements and needs to continue generating new elements. Through iterative execution of steps S3 to S6, the program continuously pushes the leading edge boundary into the flow field and generates new triangular prism element layers, while dynamically updating the leading edge boundary until the entire computational domain is completely filled within the preset boundary layer thickness.

[0071] S8: Based on the initial boundary layer mesh and the mapping relationship, check and repair the periodic mismatch region caused by the transition unit to obtain a periodic boundary layer mesh; specifically, this may include the following sub-steps: S81: Extract the top-level mesh cells of the initial boundary layer and store the mesh edge information in a hash table; Specifically, all triangular cells on the top surface of the boundary layer are identified, and then the three undirected edges of each triangular cell are stored in a hash table container, which is then deduplicated. This hash table container will be used to determine the construction status of the transition unit region.

[0072] S82: Based on the mapping relationship from the bottom node to the top node of the triangular prism unit and the hash table, all possible cases are divided into triangular candidate units and quadrilateral candidate units. Specifically, if the number of adjacent boundary layer units on the surface is different, a stepped structure will be formed, and as mentioned earlier, pyramid units need to be inserted at these locations for transition. Figure 9 and Figure 10 As shown, if the vertex of the inserted pyramid element is located on the plane of symmetry, the region is classified as a benign defect region; otherwise, it is a non-defect region. Similarly, it can be observed that if one side of the periodic boundary is a defect region and the other side is a non-defect region, the mesh on the periodic boundary will lose its consistency. Therefore, we need to locate the defect regions and periodically repair them.

[0073] Based on the mapping relationship from the bottom node to the top node of the triangular prism element, the maximum number of layers at each point on the periodic boundary condition is first determined. If the maximum number of layers of adjacent points is different, the top triangle is recorded as a candidate triangular element in a preset order, such as... Figure 11 The triangular units abc in (a)-(b) are shown in the diagram; conversely, if adjacent points have the same maximum layer number, the corresponding quadrilaterals are recorded as candidate quadrilateral units according to a preset order, such as... Figure 11 The cells (c)-(f) are shown in cells abcd. Candidate cells will be further screened to find defective areas for repair.

[0074] S83: Determine whether the triangular candidate unit and the quadrilateral candidate unit are defective regions. If they are defective regions, correct the defective regions. Specifically, for a candidate triangle unit abc, if its hypotenuse ac cannot be retrieved from the hash table, such as Figure 11 As shown in (a), this region is identified as a defect region. In this case, a tetrahedral element needs to be added, with its base being triangle abc and its vertices being the interior points of the corresponding triangle at the top layer, as shown in (a). Figure 12 As shown. If the hypotenuse ac can be retrieved from the hash table, such as... Figure 11As shown in (b) above, this area does not require additional repair.

[0075] For a candidate quadrilateral cell abcd, if its top edge cd cannot be retrieved from the hash table, such as Figure 11 As shown in (d) and (e), the region is determined to be a defect region; conversely, if the top edge cd can be retrieved, as shown in... Figure 11 As shown in (c) and (f) in Figure 11, no repair is required. Furthermore, for quadrilateral-related defect areas, further discussion is needed to determine the appropriate repair element type: if opposite edges ac or bd can be retrieved from the hash table, as shown in (e) of Figure 11, then add a tetrahedral element with a base of triangle adc or bcd and vertices that are the interior points of the corresponding top-level triangle, such as... Figure 13 As shown; if neither edge ac nor edge bd can be retrieved, as Figure 11 As shown in (d), a pyramid unit is added, with its base being a quadrilateral abcd and its vertices being the interior points of the corresponding triangle at the top layer, as shown in (d). Figure 14 As shown. The repaired transition unit region will maintain consistency under periodic boundary conditions. The resulting periodic boundary layer mesh is shown below. Figure 15 As shown.

[0076] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0077] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for generating periodic boundary layer meshes for turbomachinery, characterized in that, include: S1: Read the periodic surface mesh and boundary conditions of the turbomachinery, and construct the leading edge boundary based on the surface mesh; S2: Construct a periodic affine transformation function based on the boundary conditions and the leading edge boundary; S3: Based on the boundary conditions, leading edge boundary, and affine transformation function, construct a virtual periodic domain using the element migration method; S4: Calculate the periodic direction and distance of travel based on the virtual periodic domain; S5: Generate a layer of triangular prism units in advance according to the travel direction and travel distance, and establish a mapping relationship from the bottom node to the top node of the triangular prism units; S6: Based on the aforementioned layer of triangular prism elements, check and periodically delete invalid elements, and then update the leading edge boundary; S7: If the updated front boundary is empty, the initial boundary layer mesh is obtained; otherwise, repeat steps S3 to S6. S8: Based on the initial boundary layer mesh and the mapping relationship, check and repair the periodic mismatch region caused by the transition unit to obtain a periodic boundary layer mesh.

2. The method according to claim 1, characterized in that, Read the periodic surface mesh and boundary conditions of the turbomachinery, and construct the leading edge boundary based on the surface mesh, including: Extract the grid point information and element topology information of the periodic surface mesh of the turbomachinery, and define them as leading edge boundary points and leading edge boundary elements; Extract boundary conditions on the surface mesh, including surface boundary conditions and periodic boundary conditions.

3. The method according to claim 1, characterized in that, Based on the boundary conditions and the leading edge boundary, a periodic affine transformation function is constructed, including: Based on the boundary conditions and the front boundary, construct the source surface point set and the target surface point set; The source and target point sets are decentralized to obtain a point set without translation effect; Construct optimization equations and solve for the optimal rotation matrix based on the set of points without translation effects; Calculate the translation vector based on the set of points without translation effect and the optimal rotation matrix; Based on the optimal rotation matrix and translation vector, construct a periodic affine transformation function.

4. The method according to claim 1, characterized in that, Based on the aforementioned boundary conditions, leading edge boundary, and affine transformation function, a virtual periodic domain is constructed using a cell migration method, including: Based on the boundary conditions and the leading edge boundary, find the triangular element close to the source surface; Using the periodic affine transformation function, the triangular unit close to the source surface is projected onto the target surface to form a virtual periodic domain.

5. The method according to claim 1, characterized in that, Based on the virtual periodic domain, the periodic direction of travel and the distance traveled are calculated, including: The boundary containing the virtual periodic domain is partitioned into an inner region and an outer region, and the relationship between the leading edge boundary points of the inner region and the leading edge boundary points of the outer region is established. Calculate the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Smooth the travel direction and distance of the leading edge boundary points of the inner region, and simultaneously update the travel direction and distance of the leading edge boundary points of the outer region according to the relationship; Remove the virtual periodic domain to obtain the periodic direction and distance of travel.

6. The method according to claim 1, characterized in that, Based on the aforementioned layer of triangular prism elements, invalid elements are checked and periodically deleted, and then the leading edge boundary is updated, including: Based on the boundary conditions, periodic elements are found in the first-layer triangular prism element, and the duality relationship of the periodic elements is established. The layer of triangular prism elements is inspected, invalid elements are recursively deleted and transition elements are added. At the same time, the synchronous deletion of periodic elements is ensured according to the duality relationship, resulting in a single-layer boundary layer. The top grid points and cells of the single-layer boundary layer are used as the new front boundary.

7. The method according to claim 1, characterized in that, Based on the initial boundary layer mesh and the mapping relationship, the periodic mismatch region caused by the transition unit is checked and repaired to obtain a periodic boundary layer mesh, including: Extract the top-level mesh cells of the initial boundary layer and store the mesh edge information in a hash table; Based on the mapping relationship from the bottom node to the top node of the triangular prism unit and the hash table, all possible cases are divided into triangular candidate units and quadrilateral candidate units. Determine whether the triangular candidate unit and the quadrilateral candidate unit are defective regions. If they are defective regions, then correct the defective regions.

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