Airfoil grid generation method based on RBF and CST

Abstract

The invention provides an airfoil grid generation method based on RBF and CST, and the method comprises the steps: carrying out the geometric parameterization of a reference airfoil through employing a CST method, and obtaining an airfoil profile value point of the reference airfoil; generating a reference airfoil profile grid based on the airfoil profile value point of the reference airfoil profile, and obtaining a space coordinate corresponding to each grid node; updating the airfoil profile value point according to a preset weight value increment to obtain an updated airfoil profile value point; the y-direction coordinate difference between the airfoil profile value point of the reference airfoil profile and the updated airfoil profile value point is obtained; adopting an RBF interpolation method to obtain a weight coefficient matrix based on the y-direction coordinate difference; the y-direction displacement increment of each grid node of the reference airfoil grid is obtained based on the weight coefficient matrix; and obtaining the updated space coordinates corresponding to each grid node based on the space coordinates corresponding to each grid node of the reference airfoil grid and the y-direction displacement increment of each grid node, thereby obtaining the updated airfoil grid.

Description

Technical Field

[0001] The present invention relates to the technical field of airfoil optimization design, and in particular to an airfoil mesh generation method based on RBF and CST. Background Art

[0002] Since the beginning of the 21st century, aerodynamic optimization design methods based on high-reliability computational fluid dynamics (CFD, such as numerical simulation of the Navier-Stokes equations) have been widely used in the development of aircraft. High-reliability computational fluid dynamics aerodynamic analysis is the basis for achieving aerodynamic optimization, which involves four main links: parametric geometric modeling, grid generation, numerical solution of flow field, and post-processing. Among them, high-quality grids help to obtain more reliable numerical simulation results.

[0003] At present, airfoil mesh generation methods are mainly divided into two categories. One is the parametric mesh generation method based on the geometric system. First, geometric parametric modeling is carried out, and then the mesh topology is constructed and the mesh is generated based on the geometry. This type of method relies heavily on geometric topology analysis and mesh distribution optimization. The batch generation of high-quality meshes for aerodynamic optimization design has problems such as low efficiency and poor quality. The other type is the parametric mesh generation method without geometric system support. First, the baseline mesh is generated, and then the mesh is deformed through the free deformation method (FFD). Although it does not rely on geometric topology and has good robustness and high mesh quality, it needs to invert the smooth and continuous aerodynamic shape based on discrete mesh nodes, which also has great difficulties. Summary of the invention

[0004] The present invention provides an airfoil mesh generation method based on RBF and CST, which can solve the technical problems in the prior art.

[0005] According to one aspect of the present invention, a method for generating airfoil mesh based on RBF and CST is provided, the method comprising:

[0006] The CST method is used to geometrically parameterize the reference airfoil and obtain the airfoil value points of the reference airfoil.

[0007] Generate a reference airfoil mesh based on the airfoil value points of the reference airfoil, and obtain the space coordinates corresponding to each mesh node, wherein the reference airfoil mesh includes a surface mesh and a space mesh;

[0008] The airfoil value points are updated according to the preset weight value increment to obtain updated airfoil value points;

[0009] Obtain the y-coordinate difference between the airfoil value point of the reference airfoil and the updated airfoil value point;

[0010] The RBF interpolation method is used to obtain the weight coefficient matrix based on the y-coordinate difference;

[0011] Obtain the y-direction displacement increment of each grid node of the reference airfoil grid based on the weight coefficient matrix;

[0012] Based on the spatial coordinates corresponding to each grid node of the reference airfoil mesh and the y-direction displacement increment of each grid node, the spatial coordinates corresponding to each updated grid node are obtained, thereby obtaining the updated airfoil mesh.

[0013] Preferably, the airfoil value point of the reference airfoil is obtained by the following formula:

[0014]

[0015]

[0016] Where ζ(ψ) is the airfoil value point, ζ is the dimensionless y-axis coordinate, ψ is the dimensionless x-axis coordinate, is the category function, N1 is the first function coefficient, N2 is the second function coefficient, b i is the weight value, n is the order, S(ψ) is the shape function defined by the weighted sum of n-order Besten polynomials, is the Besten polynomial.

[0017] Preferably, the updated airfoil value point is obtained by the following formula:

[0018]

[0019] Where ζ′(ψ) is the updated airfoil value point, S′(ψ) is the updated shape function defined by the weighted sum of n-order Beistein polynomials, and δb i Incremental weight value.

[0020] Preferably, the y-coordinate difference is obtained by the following formula:

[0021] ΔY s =ζ′(ψ)-ζ(ψ);

[0022] In the formula, ΔY s is the y-coordinate difference, ζ′(ψ) is the updated airfoil value point, and ζ(ψ) is the airfoil value point.

[0023] Preferably, the weight coefficient matrix is ​​obtained by the following formula:

[0024] ΔY s =ΦW Y ;

[0025]

[0026] In the formula, ΔY s is the y-coordinate difference, Φ is the conditional matrix, WY is the weight coefficient matrix, is the radial basis function, r1, r m 、r s 、r N They are the radius vectors formed by the coordinates of the 1st, mth, sth, and Nth nodes of the object surface grid.

[0027] Preferably, the y-direction displacement increment of each grid node of the reference airfoil grid is obtained by the following formula:

[0028]

[0029] In the formula, Δy j is the y-direction displacement increment of the j-th grid node of the base airfoil grid, w l is the lth weight coefficient of a single type value point, is the radial basis function, r l is the radius vector formed by the coordinates of the lth node of the object surface grid, r j is the radius vector formed by the coordinates of the jth grid node of the reference airfoil grid.

[0030] Preferably, the space coordinates corresponding to each updated grid node are obtained by the following formula:

[0031] X new =X

[0032] Y new =Y+ΔY

[0033] Among them, ΔY=[Δy1 Δy2 … Δy M ],

[0034] In the formula, X new is the x-axis coordinate corresponding to each grid node after update, X is the x-axis coordinate corresponding to each grid node of the reference airfoil grid, and Y is new is the y-axis coordinate corresponding to each grid node after the update, Y is the y-axis coordinate corresponding to each grid node of the reference airfoil grid, ΔY is the y-axis displacement increment of each grid node of the reference airfoil grid, Δy1, Δy2, …, Δy M are the y-displacement increments of the 1st, 2nd, ..., Mth grid nodes of the benchmark airfoil grid respectively.

[0035] According to another aspect of the present invention, a computer device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any of the above methods when executing the computer program.

[0036] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0037] 1. The CST method is used to establish the airfoil geometry model, which has the airfoil shape characteristics of "front round tail tip", which is suitable for engineering applications;

[0038] 2. Realize parametric deformation of airfoil mesh based on geometric system, without the need to reconstruct continuous geometry based on discrete mesh after optimization, which has the advantage of retaining geometric optimization design features to the greatest extent;

[0039] 3. Based on the high-quality reference grid, the airfoil parametric grid generation is realized through RBF interpolation, which does not rely on grid topology reconstruction and has high grid generation quality and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The included drawings are used to provide a further understanding of the embodiments of the present invention, which constitute a part of the specification, are used to illustrate the embodiments of the present invention, and together with the text description, explain the principles of the present invention. Obviously, the drawings in the following description are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0041] Figure 1 A flow chart of a method for generating an airfoil mesh based on RBF and CST according to an embodiment of the present invention is shown;

[0042] Figure 2a A reference airfoil mesh provided according to an embodiment of the present invention is shown;

[0043] Figure 2b An updated airfoil mesh provided according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0044] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0047] like Figure 1 As shown, the present invention provides an airfoil mesh generation method based on RBF and CST, the method comprising:

[0048] The CST method is used to geometrically parameterize the reference airfoil and obtain the airfoil value points of the reference airfoil.

[0049] Generate a reference airfoil mesh based on the airfoil value points of the reference airfoil, such as Figure 2a As shown, the spatial coordinates corresponding to each grid node are obtained, wherein the reference airfoil grid includes a surface grid and a space grid;

[0050] The airfoil value points are updated according to the preset weight value increment to obtain updated airfoil value points;

[0051] Obtain the y-coordinate difference between the airfoil value point of the reference airfoil and the updated airfoil value point;

[0052] The RBF interpolation method is used to obtain the weight coefficient matrix based on the y-coordinate difference;

[0053] Obtain the y-direction displacement increment of each grid node of the reference airfoil grid based on the weight coefficient matrix;

[0054] Based on the spatial coordinates corresponding to each grid node of the reference airfoil mesh and the y-direction displacement increment of each grid node, the spatial coordinates corresponding to each updated grid node are obtained, thereby obtaining the updated airfoil mesh, such as Figure 2b shown.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. The CST method is used to establish the airfoil geometry model, which has the airfoil shape characteristics of "front round tail tip", which is suitable for engineering applications;

[0057] 2. Realize parametric deformation of airfoil mesh based on geometric system, without the need to reconstruct continuous geometry based on discrete mesh after optimization, which has the advantage of retaining geometric optimization design features to the greatest extent;

[0058] 3. Based on the high-quality reference grid, the airfoil parametric grid generation is realized through RBF interpolation, which does not rely on grid topology reconstruction and has high grid generation quality and efficiency.

[0059] According to an embodiment of the present invention, the CST method is used to geometrically parameterize the reference airfoil, and obtaining the airfoil value points of the reference airfoil specifically includes: selecting the reference airfoil geometry according to a specific optimization scenario, and normalizing the coordinates of the reference airfoil geometry. Since the number of airfoil value points is large, it is not conducive to the optimization algorithm to carry out calculations, and the relevant geometric shapes need to be represented using a limited number of parameters. Therefore, the CTS method is used to perform dimensionality reduction processing to achieve geometric parameterization to obtain the airfoil value points of the reference airfoil.

[0060] Specifically, the airfoil value point of the reference airfoil is obtained by the following formula:

[0061]

[0062]

[0063] Where ζ(ψ) is the airfoil value point, ζ is the dimensionless y-axis coordinate, ψ is the dimensionless x-axis coordinate, is the category function, which is used to determine the type of geometric shapes that can be expressed by CST parameterization. N1 is the coefficient of the first function, N2 is the coefficient of the second function, and b i is the weight value, n is the order, S(ψ) is the shape function defined by the weighted sum of n-order Besten polynomials, is the Besten polynomial.

[0064] Among them, ζ=y / c, ψ=x / c;

[0065]

[0066]

[0067] In the formula, x and z are the x-axis and z-axis coordinates of the airfoil, respectively, and c is the chord length of the airfoil.

[0068] According to an embodiment of the present invention, the updated airfoil value point is obtained by the following formula:

[0069]

[0070] Where ζ′(ψ) is the updated airfoil value point, S′(ψ) is the updated shape function defined by the weighted sum of n-order Beistein polynomials, and δb i Incremental weight value.

[0071] According to an embodiment of the present invention, the y-coordinate difference is obtained by the following formula:

[0072] ΔY s =ζ′(ψ)-ζ(ψ);

[0073] In the formula, ΔY s is the y-coordinate difference, ζ′(ψ) is the updated airfoil value point, and ζ(ψ) is the airfoil value point.

[0074] According to an embodiment of the present invention, an RBF (Radial Basis Function) interpolation method is used to perform airfoil mesh deformation, and its basic form is:

[0075]

[0076] Where F(r) is the interpolation function, N represents the total number of nodes of the object surface mesh, and w l is the lth weight coefficient of a single type value point, is the radial basis function, r is the radius vector of a single point, r l It is the radius vector formed by the coordinates of the lth node of the object surface mesh.

[0077] In this embodiment, the radial basis function can adopt Wendland's C 2 Function, which is suitable for mesh deformation interpolation, and its calculation method is as follows:

[0078]

[0079]

[0080] Where d is the radius of action of the radial basis function, and η is the parameter of the radial basis function.

[0081] The interpolation condition of the above radial basis function interpolation problem is described in the following matrix form to obtain the weight coefficient matrix:

[0082] ΔY s =ΦW Y ;

[0083]

[0084] In the formula, ΔY s is the y-coordinate difference, Φ is the conditional matrix, W Y is the weight coefficient matrix, is the radial basis function, r1, r m 、r s 、r N They are the radius vectors formed by the coordinates of the 1st, mth, sth, and Nth nodes of the object surface grid.

[0085] According to an embodiment of the present invention, the y-direction displacement increment of each grid node of the reference airfoil grid is obtained by the following formula:

[0086]

[0087] In the formula, Δy j is the y-direction displacement increment of the j-th grid node of the base airfoil grid, w l is the lth weight coefficient of a single type value point, is the radial basis function, r l is the radius vector formed by the coordinates of the lth node of the object surface grid, r j is the radius vector formed by the coordinates of the jth grid node of the reference airfoil grid.

[0088] The key link of the radial basis function mesh deformation method is to approximate the object surface deformation displacement through radial basis function interpolation.

[0089] According to an embodiment of the present invention, the space coordinates corresponding to each updated grid node are obtained by the following formula:

[0090] X new =X

[0091] Y new =Y+ΔY

[0092] Among them, ΔY=[Δy1 Δy2 … Δy M ],

[0093] In the formula, X new is the x-axis coordinate corresponding to each grid node after update, X is the x-axis coordinate corresponding to each grid node of the reference airfoil grid, and Y is new is the y-axis coordinate corresponding to each grid node after the update, Y is the y-axis coordinate corresponding to each grid node of the reference airfoil grid, ΔY is the y-axis displacement increment of each grid node of the reference airfoil grid, Δy1, Δy2, …, ΔyM are the y-displacement increments of the 1st, 2nd, ..., Mth grid nodes of the benchmark airfoil grid respectively.

[0094] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements any of the above methods when executing the computer program.

[0095] In summary, the present invention provides an airfoil mesh generation method based on RBF and CST, which has the following beneficial effects compared with the prior art:

[0096] 1. The CST method is used to establish the airfoil geometry model, which has the airfoil shape characteristics of "front round tail tip", which is suitable for engineering applications;

[0097] 2. Realize parametric deformation of airfoil mesh based on geometric system, without the need to reconstruct continuous geometry based on discrete mesh after optimization, which has the advantage of retaining geometric optimization design features to the greatest extent;

[0098] 3. Based on the high-quality reference grid, the airfoil parametric grid generation is realized through RBF interpolation, which does not rely on grid topology reconstruction and has high grid generation quality and efficiency.

[0099] In the description of the present invention, it is necessary to understand that the directions or positional relationships indicated by directional words such as "front, back, up, down, left, right", "lateral, vertical, perpendicular, horizontal" and "top, bottom" are usually based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description. Unless otherwise specified, these directional words do not indicate or imply that the devices or elements referred to must have a specific direction or be constructed and operated in a specific direction. Therefore, they cannot be understood as limiting the scope of protection of the present invention. The directional words "inside and outside" refer to the inside and outside relative to the contours of each component itself.

[0100] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used here to describe the spatial positional relationship between a device or feature and other devices or features as shown in the figure. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figure. For example, if the device in the accompanying drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0101] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. If not otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for generating airfoil mesh based on RBF and CST, characterized in that: The method comprises: The CST method is used to geometrically parameterize the reference airfoil and obtain the airfoil value points of the reference airfoil. Generate a reference airfoil mesh based on the airfoil value points of the reference airfoil, and obtain the space coordinates corresponding to each mesh node, wherein the reference airfoil mesh includes a surface mesh and a space mesh; The airfoil value points are updated according to the preset weight value increment to obtain updated airfoil value points; Obtain the y-coordinate difference between the airfoil value point of the reference airfoil and the updated airfoil value point; The RBF interpolation method is used to obtain the weight coefficient matrix based on the y-coordinate difference; Obtain the y-direction displacement increment of each grid node of the reference airfoil grid based on the weight coefficient matrix; Based on the space coordinates corresponding to each grid node of the reference airfoil mesh and the y-direction displacement increment of each grid node, the space coordinates corresponding to each updated grid node are obtained, thereby obtaining the updated airfoil mesh.

2. The method according to claim 1, characterized in that: The airfoil value point of the reference airfoil is obtained by the following formula: Where ζ(ψ) is the airfoil value point, ζ is the dimensionless y-axis coordinate, ψ is the dimensionless x-axis coordinate, is the category function, N1 is the first function coefficient, N2 is the second function coefficient, b i is the weight value, n is the order, S(ψ) is the shape function defined by the weighted sum of n-order Besten polynomials, is the Besten polynomial.

3. The method according to claim 1 or 2, characterized in that: The updated airfoil value point is obtained by the following formula: Where ζ′(ψ) is the updated airfoil value point, S′(ψ) is the updated shape function defined by the weighted sum of n-order Beistein polynomials, and δb i Incremental weight value.

4. The method according to any one of claims 1 to 3, characterized in that: The y-coordinate difference is obtained by the following formula: Y s =ζ′(ψ)-ζ(ψ); In the formula, ΔY s is the y-coordinate difference, ζ′(ψ) is the updated airfoil value point, and ζ(ψ) is the airfoil value point.

5. The method according to claim 1, characterized in that The weight coefficient matrix is ​​obtained by the following formula: ΔY s =ΦW Y ; In the formula, ΔY s is the y-coordinate difference, Φ is the conditional matrix, W Y is the weight coefficient matrix, is the radial basis function, r1, r m 、r s 、r N They are the radius vectors formed by the coordinates of the 1st, mth, sth, and Nth nodes of the object surface grid.

6. The method according to claim 1, characterized in that The y-direction displacement increment of each grid node of the reference airfoil grid is obtained by the following formula: In the formula, Δy j is the y-direction displacement increment of the j-th grid node of the base airfoil grid, w l is the lth weight coefficient of a single type value point, is the radial basis function, r l is the radius vector formed by the coordinates of the lth node of the object surface grid, r j is the radius vector formed by the coordinates of the jth grid node of the reference airfoil grid.

7. The method according to claim 1, characterized in that The space coordinates corresponding to each updated grid node are obtained by the following formula: X new =X Y new =Y+ΔY Where, ΔY=[Δy1 Δy2...Δy M ], Where, X new is the x-axis coordinate corresponding to each grid node after update, X is the x-axis coordinate corresponding to each grid node of the reference airfoil grid, and Y is new is the y-axis coordinate corresponding to each grid node after the update, Y is the y-axis coordinate corresponding to each grid node of the reference airfoil grid, ΔY is the y-axis displacement increment of each grid node of the reference airfoil grid, Δy1, Δy2, ..., Δy M are the y-displacement increments of the 1st, 2nd, ..., Mth grid nodes of the benchmark airfoil grid respectively.

8. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the method according to any one of claims 1 to 7 when executing the computer program.

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