A method for grid generation of viscous internal flow fields with periodic boundary conditions

Abstract

The present invention discloses a method for generating meshes of a viscous internal flow field with periodic boundary conditions, comprising: reading a geometric model of a viscous internal flow field with periodic boundary conditions; assigning boundary conditions to the geometric model, finding primary and secondary boundary lines according to the boundary conditions, and establishing a mapping relationship between the primary and secondary boundary lines and the boundary conditions; establishing a mapping relationship between source surface boundary lines and target surface boundary lines according to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, and calculating an affine transformation matrix from the source surface to the target surface; generating a surface mesh of each surface according to the mapping relationship between the source surface boundary lines and the target surface boundary lines and the affine transformation matrix; generating a boundary layer mesh according to the surface mesh and the affine transformation matrix; reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh and the primary and secondary boundary lines; and generating a volume mesh according to the surface mesh and the boundary layer mesh.

Description

Technical Field

[0001] The invention relates to a method for generating a viscous internal flow field grid with periodic boundary conditions. Background Art

[0002] Aircraft engines, ship gas turbines, back-pressure steam turbines, etc. are all rotating machines. The movement of fluids inside rotating machines is complex. These complex flows are usually caused by the interaction between rotating parts (such as impellers or rotors) and fixed parts (such as stators). In the numerical simulation of internal flow fields, the pre-processing stage with mesh generation as the core is a very time-consuming and complicated process, and the quality of the mesh will directly affect the accuracy and computational efficiency of the numerical simulation. At present, there are few mesh generation software for complex internal flow fields, so there is an urgent need for a customized program that can automatically generate high-quality computational meshes.

[0003] In the numerical simulation of flow fields, structured grids are often used. Although structured grids have fast calculation speed and high solution accuracy, they are insufficient in generating grids for complex structures of rotating machinery. For example, it is difficult to generate effective grids at locations such as blade tips, film cooling holes, and matrix internal cooling channels. Unstructured grids have advantages in dealing with complex flow phenomena and geometric shapes, but their disadvantages are relatively high data storage and computational complexity. In addition, due to the movement of rotating parts in the internal flow field, a certain amount of adhesion and shear force will be generated when the fluid contacts its surface, which will lead to an uneven distribution of fluid velocity. The viscosity effect is particularly significant in areas close to the surface of rotating parts. Both simple structured grids and unstructured grids are difficult to capture this viscous physical information at complex shapes.

[0004] The internal flow field in a rotating machine generally has periodic symmetry, and the flow characteristics on each period will change periodically with the rotational motion. Therefore, the flow characteristics should be the same at the periodic surface position, and the consistency of the periodic surface mesh should be ensured. If the periodic surface mesh is inconsistent, it may cause flow faults, numerical errors, flow instability and other problems, thus affecting the accuracy of the simulation results. Summary of the invention

[0005] Based on this, the present invention proposes a method for generating flow field grids within viscous boundaries with periodic boundary conditions to solve the problems existing in the background technology. This application takes into account the advantages of structured grids and unstructured grids, and generates a flat semi-structured boundary layer grid near the viscous surface, which can not only adapt to the complex geometric shapes parallel to the object surface direction, but also accurately capture the fine flow field characteristics perpendicular to the object surface direction. In addition, a highly reliable affine transformation function is designed to achieve periodic surface consistent grid generation, and the influence of the boundary layer on the periodic surface grid is considered, combined with a general grid algorithm to realize the automatic generation of customized grids in the numerical simulation of complex rotating machinery.

[0006] The present invention discloses a method for generating a viscous internal flow field grid with periodic boundary conditions, comprising:

[0007] Read the geometry model of the viscous internal flow field with periodic boundary conditions;

[0008] Assigning boundary conditions to the geometric model, finding primary and secondary boundary lines according to the boundary conditions, and establishing a mapping relationship between the primary and secondary boundary lines and the boundary conditions;

[0009] According to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, a mapping relationship between the source surface boundary line and the target surface boundary line is established, and an affine transformation matrix from the source surface to the target surface is calculated;

[0010] Generate a surface mesh of each surface according to the mapping relationship between the source surface boundary line and the target surface boundary line and the affine transformation matrix;

[0011] Generate a boundary layer mesh according to the surface mesh and the affine transformation matrix;

[0012] Reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh, and the primary and secondary boundary lines;

[0013] The volume mesh is generated based on the reconstructed surface mesh and boundary layer mesh.

[0014] Optionally, the geometric model is given boundary conditions, primary and secondary boundary lines are found according to the boundary conditions, and a mapping relationship between the primary and secondary boundary lines and the boundary conditions is established, including:

[0015] Marking casing surface boundary conditions, hub surface boundary conditions, blade surface boundary conditions, source surface boundary conditions and target surface boundary conditions on the boundary surfaces of the geometric model;

[0016] Finding a main boundary line according to the casing surface boundary conditions and the hub surface boundary conditions, and establishing a mapping relationship between the main boundary line and the casing surface boundary conditions;

[0017] A mapping relationship between the main boundary line and the source surface boundary condition is established according to the source surface boundary condition, and a secondary boundary line on the source surface boundary condition is found at the same time.

[0018] Optionally, according to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, a mapping relationship between the source surface boundary line and the target surface boundary line is established, and an affine transformation matrix from the source surface to the target surface is calculated, including:

[0019] According to the mapping relationship between the main boundary line, the secondary boundary line and the boundary conditions, searching for periodic corresponding points on the source surface and the target surface;

[0020] According to the periodic corresponding points, a mapping relationship between a source surface boundary line and a target surface boundary line is established;

[0021] According to the periodic corresponding points, an affine transformation matrix from the source surface to the target surface is calculated.

[0022] Optionally, generating a surface mesh of each surface according to the mapping relationship between the source surface boundary line and the target surface boundary line and an affine transformation matrix includes:

[0023] Generate line meshes of all source surfaces using the endpoints of the boundary lines as constraints;

[0024] According to the affine transformation matrix, projecting the line grid of the source surface to the boundary of the corresponding target surface;

[0025] Generate the remaining boundary line mesh with the endpoints of the boundary line as constraints;

[0026] Traverse all faces, use the boundary line mesh of each face as a constraint, and use the frontier advancing method to generate the triangular surface mesh of each face.

[0027] Optionally, generating a boundary layer mesh according to the surface mesh and the affine transformation matrix includes:

[0028] S51: inputting boundary layer control parameters, and obtaining front boundary points and front triangular facets according to the surface mesh;

[0029] S52: Calculating an initial normal field and a step value according to the front boundary point and the boundary layer control parameter;

[0030] S53: Correcting the initial normal field according to the affine transformation matrix;

[0031] S54: pre-generate a layer of triangular prism units according to the normal field and the step value;

[0032] S55: judging whether the triangular prism unit meets the requirements, deleting the triangular prism unit that does not meet the requirements, and finally establishing a mapping relationship between the bottom layer points and the upper layer points of the triangular prism unit, and updating the front boundary points and the front triangle patch;

[0033] S56: Determine whether the front boundary point is empty. If it is not empty, repeat steps S52-S56. If it is empty, stop generating the boundary layer grid.

[0034] Optionally, reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh, and the primary and secondary boundary lines includes:

[0035] Reconstructing line grids of all main boundary lines according to the boundary layer grids and the main boundary lines;

[0036] Reconstructing the line grids of all secondary boundary lines according to the line grids of the primary boundary lines and the secondary boundary lines;

[0037] The surface mesh of each surface is reconstructed according to the boundary layer mesh, the line mesh and the affine transformation matrix.

[0038] Optionally, a volume mesh is generated based on the reconstructed surface mesh and boundary layer mesh, including:

[0039] Using the reconstructed surface mesh as a constraint boundary of the geometric body to generate internal tetrahedral units;

[0040] The tetrahedral elements and the boundary layer mesh are merged to complete the volume mesh generation.

[0041] The technical solution provided by the embodiments of the present application may have the following beneficial effects:

[0042] The present invention designs a highly reliable affine transformation function. Compared with commercial software such as Pointwise and ICEM, it does not require additional input of user parameters such as rotation / translation axis, rotation angle, translation distance, etc. when processing periodic boundaries, and the degrees of freedom of affine transformation are more flexible.

[0043] The present invention establishes a mapping relationship of geometric boundaries according to defined boundary conditions, reduces manual intervention in the grid generation process, realizes full-automatic grid generation, and improves grid generation efficiency.

[0044] The present invention proposes a boundary layer grid generation method, which can automatically generate high-quality triangular prism units and ensure periodicity on the unit side faces under periodic boundary conditions, and is suitable for numerical simulation of viscous boundaries of flow fields in rotating machinery.

[0045] The present invention proposes an automatic surface mesh reconstruction method, which takes into account the influence of the boundary layer on the periodic boundary, can not only generate boundary layer meshes on the viscous surface to capture flow field characteristics, but also ensure the generation of surface consistent meshes on periodic boundary conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0047] Figure 1 The present invention is a flowchart of a method for generating a flow field grid within a viscous boundary with periodic boundary conditions according to an exemplary embodiment.

[0048] Figure 2 is a diagram of a compressor geometry model according to an exemplary embodiment.

[0049] Figure 3 is a schematic diagram of boundary conditions of a geometric model according to an exemplary embodiment.

[0050] Figure 4is a schematic diagram of a geometric model boundary line according to an exemplary embodiment.

[0051] Figure 5 is a schematic diagram of affine transformation projection according to an exemplary embodiment.

[0052] Figure 6 is a schematic diagram of a first transformation according to an exemplary embodiment.

[0053] Figure 7 is a schematic diagram of a second transformation according to an exemplary embodiment.

[0054] Figure 8 is a schematic diagram of the third transformation according to an exemplary embodiment.

[0055] Fig. 9 is a schematic diagram of the fourth transformation according to an exemplary embodiment.

[0056] Fig.10 is a schematic diagram of surface mesh generation according to an exemplary embodiment.

[0057] Fig.11 is a mapping relationship of triangular prism units shown according to an exemplary embodiment.

[0058] Fig.12 FIG. 4 is a schematic diagram of main boundary line grid reconstruction according to an exemplary embodiment.

[0059] Fig.13 FIG. 4 is a schematic diagram of secondary boundary line mesh reconstruction according to an exemplary embodiment.

[0060] Fig.14 FIG. 4 is a schematic diagram of surface mesh reconstruction according to an exemplary embodiment.

[0061] Fig.15 is a detailed diagram of the interior of a volume mesh according to an exemplary embodiment. DETAILED DESCRIPTION

[0062] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are merely examples of devices and methods consistent with some aspects of the present application as detailed in the appended claims.

[0063] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms of "a", "said" and "the" used in this application and the appended claims are also intended to include plural forms unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0064] Figure 1 is a flow chart of a method for generating a viscous internal flow field grid with periodic boundary conditions according to an exemplary embodiment. Figure 1 As shown, the method may include the following steps:

[0065] S1: Read the geometric model of the viscous internal flow field with periodic boundary conditions;

[0066] Specifically, the periodic boundary condition refers to the situation where the fluid domain of rotating machinery such as turbines, compressors, and steam turbines presents periodic changes. Usually, the grids on the periodic boundaries need to remain consistent. The viscous boundary refers to the viscous fluid movement generated on the near-wall surfaces such as the blade surface, hub surface, and casing surface. The geometry file mainly stores geometric information and topological information based on boundary representation. The topological information describes the connection relationship between points, edges, and surfaces on the shape, and the geometric information defines the equation data of points, edges, and surfaces. Figure 2 As shown, the present application takes the geometric model of the compressor in an aircraft engine as an example for detailed description.

[0067] S2: assigning boundary conditions to the geometric model, finding primary and secondary boundary lines according to the boundary conditions, and establishing a mapping relationship between the primary and secondary boundary lines and the boundary conditions; specifically, the following sub-steps may be included:

[0068] S21: marking a casing surface boundary condition, a hub surface boundary condition, a blade surface boundary condition, a source surface boundary condition, and a target surface boundary condition on the boundary surface of the geometric model;

[0069] Specifically, the boundary conditions in this example are set as follows: Figure 3 As shown in the figure, some specific boundary lines can be found according to the set boundary conditions; in addition, the user needs to establish a mapping relationship when specifying the source surface and the target surface. In the example, source surfaces 1, 2, and 3 correspond to target surfaces 1, 2, and 3 respectively. According to the mapping relationship, the target surface of the corresponding period can be quickly found by the number of any source surface.

[0070] S22: finding a main boundary line according to the casing surface boundary conditions and the hub surface boundary conditions, and establishing a mapping relationship between the main boundary line and the casing surface boundary conditions;

[0071] Specifically, all casing surfaces and hub surfaces are traversed, and the boundary lines of each surface are found according to the topological relationship. These boundary lines are called main boundary lines. At the same time, a mapping relationship between the main boundary lines on the casing surface and the casing surface boundary conditions is established. The main boundary lines on the casing surface can be quickly found through the mapping relationship. Figure 4 As shown, the boundary lines represented by the solid lines in the example are the main boundary lines, among which main boundary lines No. 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 establish a mapping relationship with the boundary conditions of the casing surface.

[0072] S23: establishing a mapping relationship between a main boundary line and the source surface boundary condition according to the source surface boundary condition, and simultaneously searching for a secondary boundary line on the source surface boundary condition;

[0073] Specifically, all source surfaces are traversed, and the boundary line of each surface is found according to the topological relationship to determine whether it is the main boundary line. If it is the main boundary line, a mapping relationship between it and the boundary condition of the source surface is established. If it is not the main boundary line, it is called a secondary boundary line. The main boundary line on the source surface can be quickly found through the mapping relationship. Figure 4 As shown, the boundary lines represented by the dotted lines in the example are secondary boundary lines, among which the main boundary lines 2, 5, 8, 11, 15, and 18 establish a mapping relationship with the source surface boundary conditions.

[0074] S3: According to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, a mapping relationship between the source surface boundary line and the target surface boundary line is established, and an affine transformation matrix from the source surface to the target surface is calculated; specifically, the following sub-steps may be included:

[0075] S31: searching for periodic corresponding points on the source surface and the target surface according to the mapping relationship between the primary boundary line, the secondary boundary line and the boundary conditions;

[0076] Specifically, assuming that the number of boundary lines between the source and target surfaces is n, the set of boundary line endpoints of the source surface is X = {x i}∈R 3 (i=0,1,...,n), the corresponding target surface boundary line endpoint set is Y={y i}∈R 3 (i=0,1,...,n), then the coordinates of the center points of the source and target surfaces are:

[0077]

[0078] Here C X is the coordinate of the center point of the source surface, C Y is the coordinate of the center point of the target surface.

[0079] Find the main boundary line on the source and target surfaces that has a mapping relationship with the boundary conditions of the casing surface. Assuming that the endpoints of the boundary line on the source surface are S1 and S2, and the endpoints of the boundary line on the target surface are T1 and T2, calculate:

[0080] s=C X S1×C X S2

[0081] t=C Y T1×C Y T2

[0082] Here s is the vector product of the vectors from the center point of the source surface to the two endpoints of the main boundary line, and t is the vector product of the vectors from the center point of the target surface to the two endpoints of the main boundary line.

[0083] C X , C Y , S1, S2, T1, T2 are the corresponding points of the period, among which C X The corresponding point is C Y , if the sign of s and t is consistent, then the corresponding points of S1 and S2 are T1 and T2; if the sign of s and t is inconsistent, then the corresponding points of S1 and S2 are T2 and T1. According to the periodic corresponding points of the source surface and the target surface, the mapping relationship between the source surface boundary line and the target surface boundary line can be automatically established without manual intervention, and the affine transformation matrix from the source surface to the target surface can be calculated.

[0084] S32: establishing a mapping relationship between a source surface boundary line and a target surface boundary line according to the periodic corresponding points;

[0085] Specifically, find boundary lines with S1 and S2, T1 and T2 as endpoints on the source surface and the target surface respectively, use these two boundaries as the starting boundaries of the source surface and the target surface, and use breadth-first search to wind the boundaries on the source surface and the target surface into a ring in the same direction in sequence. Finally, establish a mapping relationship between the source surface boundary line and the target surface boundary line according to the starting boundary and the winding order. Through the mapping relationship, the target surface boundary line of the corresponding period can be quickly found according to the number of any source surface boundary line.

[0086] S33: Calculating an affine transformation matrix from the source surface to the target surface according to the periodic corresponding points;

[0087] Specifically, Figure 5 As shown, with S∈R 3 Represents the source surface, with T∈R 3 represents the target surface, assuming that the grid point set of the source surface is X = {x i}∈R 3 (i=0,1,...,n), the grid point set of the target surface is Y={y i}∈R 3 (i=0,1,...,n), find the affine transformation function Project the mesh on the source face onto the target face:

[0088]

[0089] like Figure 6 The first transformation is shown, which moves the source surface along Vector translation, surface by S1S2S3C X Become OS2'S3'C X ', and move the target surface along Vector translation, surface by T1T2T3C Y becomes OT2'T3'C Y ', at this time, the grid point set of the source surface and the grid point set of the target surface after transformation are X'={x' i}∈R 3 (i=0,1,...,n) and Y'={y' i}∈R 3 (i=0,1,...,n), satisfying the formula:

[0090]

[0091] like Figure 7 This is the second transformation. First, find and Then find the angle α between and The vector product of and normalized to get vector n, according to the Rodrigues rotation formula, the rotation matrix M around the n vector can be obtained α :

[0092]

[0093] M α =I+(1-cosα)·KK T +K·sinα

[0094] Here I is the identity matrix, α is the rotation angle, and K is:

[0095]

[0096] The surface OS2'S3'C X 'Rotate around vector n by angle α to obtain surface OT2'S3"C X ”. At this time, the grid point set of the transformed surface is X”={x” i}∈R 3 (i=0,1,...,n), satisfying the formula:

[0097] x” i =M α x' i (i=0,1,...,n)

[0098] like Figure 8 This is the third transformation. First, find and The angle β between them and the rotation axis r, according to the Rodriguez rotation formula, the rotation matrix M around the r vector can be obtained β :

[0099]

[0100] here

[0101] M β =I+(1-cosβ)·RR T +R·sinβ

[0102] Here I is the identity matrix, β is the rotation angle, and R is:

[0103]

[0104] The surface OT2'S3"C X "Rotate β around the vector r to obtain the surface OT2'T3'CY'. The grid point set of the transformed surface is X"'={x"' i}∈R 3 (i=0,1,...,n), satisfying the formula:

[0105] x"' i =M β x” i (i=0,1,...,n)

[0106] like Fig. 9 The fourth transformation is shown, which transforms the surface OT2'T3'C Y 'Along the vector Translate to get the surface O'T2"T3"C Y ”, and the initial target surface T1T2T3C Y The mesh point set of the transformed surface is X””={x”” i}∈R 3 (i=0,1,...,n), satisfying the formula:

[0107]

[0108] This gives the affine transformation function for:

[0109]

[0110] By calculating the affine transformation function, any line grid or surface grid point on the source surface can be projected onto the target surface of the corresponding period.

[0111] S4: Generate a surface mesh of each surface according to the mapping relationship between the source surface boundary line and the target surface boundary line and the affine transformation matrix; specifically, the following sub-steps may be included:

[0112] S41: Generate line meshes of all source surfaces using the endpoints of the boundary lines as constraints;

[0113] Specifically, Fig.10 As shown in (a), assuming that the starting point of the curve is P0 and the end point is P n , the curve is represented by C(t)=(x(t),y(t),z(t)), t∈[P0,P n ], starting from the starting point P0, assuming that the current discrete point is P t , the next discrete point position to be calculated is P t+1 , then it satisfies Where L is P t The grid size value of the point position is calculated by the Newton-Simpson numerical iteration method to obtain the point coordinates at the t+1 discrete point, and then P t+1 The discrete point is used as the current discrete point for a new round of iteration. If the value is smaller than the minimum grid size, the next discrete point is P. n The discretization is ended and the generated source surface boundary line mesh is used as the constraint boundary for the source surface mesh generation.

[0114] S42: Projecting the line grid of the source surface onto the corresponding target surface boundary according to the affine transformation matrix;

[0115] Specifically, Fig.10 As shown in (b), the target surface boundary line corresponding to the source surface boundary line is found according to the mapping relationship between the source surface boundary line and the target surface boundary line, and the grid points on the source surface boundary line are projected to the corresponding target surface boundary line through the affine transformation matrix to generate a target surface boundary line grid, and the generated target surface boundary line grid is used as the constraint boundary for generating the target surface grid.

[0116] S43: Generate the remaining boundary line meshes with the endpoints of the boundary line as constraints;

[0117] Specifically, Fig.10 As shown in (c) in FIG. 4 , all boundary lines are traversed to find the boundary lines that have not been discretized, and then the discretization of the boundary lines is completed by the method in S41.

[0118] S44: traverse all faces, take the boundary line mesh of each face as a constraint, and use the frontier advancing method to generate the triangular face mesh of each face;

[0119] Specifically, Fig.10As shown in (d) in the figure, the surface boundary line mesh is projected into the parameter space to generate the initial frontier boundary. Then, the two-dimensional frontier advancing technique is used to generate a triangular mesh in the parameter space. The distribution of mesh points is optimized by the Laplace smoothing method. Finally, the mesh generated in the parameter space is mapped back to the physical space to output the triangular surface mesh.

[0120] S5: Generate a boundary layer mesh according to the surface mesh and the affine transformation matrix; specifically, the following sub-steps may be included:

[0121] S51: inputting boundary layer control parameters, and obtaining front boundary points and front triangular facets according to the surface mesh;

[0122] Specifically, the surface mesh points on the hub surface, casing surface and blade surface are used as the first-layer frontier boundary points, and the surface mesh triangles are used as the frontier triangle patches; the boundary layer control parameters include the number of layers, the first-layer height and the growth rate. In this example, the number of boundary layers is 25, the first-layer height is 0.001, and the growth rate is 1.2; the frontier boundary points and boundary layer control parameters are used to calculate the normal field and step value, and the frontier triangle patches, normal field and step value are used to guide the generation of triangular prism units.

[0123] S52: Calculating an initial normal field and a step value according to the front boundary point and the boundary layer control parameter;

[0124] Specifically, the average normal value of the triangular units around the frontier boundary point is taken as the normal of the point. After the normals of all points are calculated, Laplace smoothing is used to obtain an initial normal field. In order to ensure the periodicity of the side of the boundary layer on the periodic boundary, the normal field needs to be corrected later; the step value of each layer calculation is:

[0125] h n =α n-1 h0

[0126] Here, h n is the current layer height, α is the boundary layer growth rate, n is the current layer number, and h0 is the first layer height.

[0127] S53: Correcting the initial normal field according to the affine transformation matrix;

[0128] Specifically, the normal of the front boundary point on the source surface is projected to the front boundary point on the corresponding target surface through the affine transformation matrix, and the original normal is replaced to generate a new normal field for guiding the generation of the triangular prism unit;

[0129] S54: pre-generate a layer of triangular prism units according to the normal field and the step value;

[0130] Specifically, the side edges of the frontier boundary points are generated according to the normal and step value of the frontier boundary points, all frontier triangular facets are traversed, a layer of triangular prism units are pre-generated according to the side edges, and a mapping relationship between the triangular prism units with the side on the source surface and the triangular prism units with the side on the target surface is established. Through the mapping relationship, the triangular prism on the target surface corresponding to the triangular prism on the source surface can be quickly found, such as Fig.11 As shown;

[0131] S55: judging whether the triangular prism unit meets the requirements, deleting the triangular prism unit that does not meet the requirements, and finally establishing a mapping relationship between the bottom layer points and the upper layer points of the triangular prism unit, and updating the front boundary points and the front triangle patch;

[0132] Specifically, traverse each triangular prism unit to determine whether it has quality or intersection problems. If it meets the requirements, keep the triangular prism unit; if it does not meet the requirements, delete the triangular prism unit. In addition, the triangular prism unit on the source or target surface needs to meet the requirements of the mapping unit at the same time to be retained, otherwise all will be deleted; finally, the top-level point is used as the new frontier boundary point, the top-level triangle patch is used as the new frontier triangle patch, and a mapping relationship from the bottom-level point of the triangular prism to the upper-level point is established. The top-level grid point can be found from the first-level grid point of the boundary layer through the mapping relationship;

[0133] S56: Determine whether the front boundary point is empty, if not, repeat steps S52-S56, if it is empty, stop generating the boundary layer grid;

[0134] S6: Reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh, and the primary and secondary boundary lines; specifically, the following sub-steps may be included:

[0135] S61: reconstructing line grids of all main boundary lines according to the boundary layer grids and the main boundary lines;

[0136] Specifically, Fig.12 As shown, all grid points on the main boundary line are traversed, and according to the mapping relationship between the bottom layer points and the upper layer points of the triangular prism, the next mapping point is continuously searched until the search is empty, and the last mapping point found is used as the new grid point;

[0137] S62: reconstructing the line meshes of all the secondary boundary lines according to the line meshes of the primary boundary lines and the secondary boundary lines;

[0138] Specifically, the endpoints on the main boundary line of the source surface are used as the new endpoints of its adjacent secondary boundary line, and the secondary boundary line of the source surface is discretized again with the new endpoints as constraint points, such as Fig.13 As shown in (a) in FIG. 1 ; then the source surface secondary boundary line grid is reprojected to the corresponding target surface boundary through the affine transformation matrix, as shown in FIG. Fig.13 As shown in (b) in .

[0139] S63: reconstructing a surface mesh of each surface according to the boundary layer mesh, the line mesh and the affine transformation matrix;

[0140] Specifically, the surface meshes on the boundary conditions of the hub surface, casing surface and blade surface are first reconstructed, and the bottom surface meshes are replaced by the top frontier triangular facets of the boundary layer, such as Fig.14 As shown in (a) in ; then, the triangular surface mesh of the source surface is regenerated using the frontier advancement technique with the reconstructed boundary line mesh as a constraint, as shown in Fig.14 As shown in (b) in FIG. 1 ; the surface mesh of the source surface is then reprojected to the corresponding target surface through the affine transformation matrix, as shown in FIG. Fig.14 Finally, the frontier advancement technique is used to regenerate the triangular mesh of the remaining faces, as shown in (c) in the figure. Fig.14 As shown in (d) in the figure, all the reconstructed surface meshes are used as constraint boundaries for volume mesh generation.

[0141] S7: Generate a volume mesh according to the surface mesh and the boundary layer mesh; specifically, the following sub-steps may be included:

[0142] S71: Using the surface mesh as a constraint boundary of the geometric body, generating internal tetrahedral units;

[0143] Specifically, the BW interpolation method is used to tetrahedronize the interior of the geometric body. After the division, all tetrahedrons are traversed to determine whether they intersect with the constraint boundary. If they intersect, these tetrahedrons are split and merged to restore the constraint boundary. Finally, the Laplace smoothing method is used to improve the distribution of grid points.

[0144] S72: merging the tetrahedral unit and the boundary layer mesh to complete volume mesh generation;

[0145] Specifically, the tetrahedron and boundary layer triangular prism elements are combined to generate a hybrid mesh. The total number of elements in the example is 2885283, of which the number of tetrahedron elements is 1403789 and the number of triangular prism elements is 1481494. The internal details are as follows: Fig.15 shown.

[0146] Those skilled in the art will readily appreciate other embodiments of the present application after considering the description and practicing the contents disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The description and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the claims.

[0147] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A method for generating a mesh for a viscous internal flow field with periodic boundary conditions, characterized in that: include: Read the geometry model of the viscous internal flow field with periodic boundary conditions; Assigning boundary conditions to the geometric model, finding primary and secondary boundary lines according to the boundary conditions, and establishing a mapping relationship between the primary and secondary boundary lines and the boundary conditions; According to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, a mapping relationship between the source surface boundary line and the target surface boundary line is established, and an affine transformation matrix from the source surface to the target surface is calculated; Generate a surface mesh of each surface according to the mapping relationship between the source surface boundary line and the target surface boundary line and the affine transformation matrix; Generate a boundary layer mesh according to the surface mesh and the affine transformation matrix; Reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh, and the primary and secondary boundary lines; Generate volume mesh according to the reconstructed surface mesh and boundary layer mesh; The step of assigning boundary conditions to the geometric model, finding the primary and secondary boundary lines according to the boundary conditions, and establishing a mapping relationship between the primary and secondary boundary lines and the boundary conditions includes: Marking casing surface boundary conditions, hub surface boundary conditions, blade surface boundary conditions, source surface boundary conditions and target surface boundary conditions on the boundary surfaces of the geometric model; Finding a main boundary line according to the casing surface boundary conditions and the hub surface boundary conditions, and establishing a mapping relationship between the main boundary line and the casing surface boundary conditions; A mapping relationship between the main boundary line and the source surface boundary condition is established according to the source surface boundary condition, and a secondary boundary line on the source surface boundary condition is found at the same time.

2. The method according to claim 1, characterized in that According to the mapping relationship between the primary and secondary boundary lines and the boundary conditions, a mapping relationship between the source surface boundary line and the target surface boundary line is established, and an affine transformation matrix from the source surface to the target surface is calculated, including: According to the mapping relationship between the main boundary line, the secondary boundary line and the boundary conditions, searching for periodic corresponding points on the source surface and the target surface; According to the periodic corresponding points, a mapping relationship between a source surface boundary line and a target surface boundary line is established; According to the periodic corresponding points, an affine transformation matrix from the source surface to the target surface is calculated.

3. The method according to claim 1, characterized in that Generate a surface mesh of each surface according to the mapping relationship between the source surface boundary line and the target surface boundary line and the affine transformation matrix, including: Generate line meshes of all source surfaces using the endpoints of the boundary lines as constraints; According to the affine transformation matrix, projecting the line grid of the source surface to the boundary of the corresponding target surface; Generate the remaining boundary line mesh with the endpoints of the boundary line as constraints; Traverse all faces, use the boundary line mesh of each face as a constraint, and use the frontier advancing method to generate the triangular surface mesh of each face.

4. The method according to claim 1, characterized in that: Generate a boundary layer mesh according to the surface mesh and the affine transformation matrix, including: S51: inputting boundary layer control parameters, and obtaining front boundary points and front triangular facets according to the surface mesh; S52: Calculating an initial normal field and a step value according to the front boundary point and the boundary layer control parameter; S53: Correcting the initial normal field according to the affine transformation matrix; S54: pre-generate a layer of triangular prism units according to the normal field and the step value; S55: judging whether the triangular prism unit meets the requirements, deleting the triangular prism unit that does not meet the requirements, and finally establishing a mapping relationship between the bottom layer points and the upper layer points of the triangular prism unit, and updating the front boundary points and the front triangle patch; S56: Determine whether the front boundary point is empty. If it is not empty, repeat steps S52-S56. If it is empty, stop generating the boundary layer grid.

5. The method according to claim 1, characterized in that Reconstructing the surface mesh of each surface according to the affine transformation matrix, the boundary layer mesh, and the primary and secondary boundary lines, including: Reconstructing line grids of all main boundary lines according to the boundary layer grids and the main boundary lines; Reconstructing the line grids of all secondary boundary lines according to the line grids of the primary boundary lines and the secondary boundary lines; The surface mesh of each surface is reconstructed according to the boundary layer mesh, the line mesh and the affine transformation matrix.

6. The method according to claim 1, characterized in that Based on the reconstructed surface mesh and boundary layer mesh, a volume mesh is generated, including: Using the reconstructed surface mesh as a constraint boundary of the geometric body to generate internal tetrahedral units; The tetrahedral elements and the boundary layer mesh are merged to complete the volume mesh generation.

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