Rapid processing method for airfoil trailing edge step
By constructing a continuously differentiable perturbation function, the thickness distribution of the wing trailing edge is modified, which solves the problem of inconsistent thickness of the wing trailing edge step, realizes flexible adjustment of the airfoil trailing edge thickness, improves design and manufacturing efficiency, and maintains the consistency of the airfoil's aerodynamic characteristics.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-04
- Publication Date
- 2026-03-31
AI Technical Summary
When adjusting the trailing edge thickness of an airfoil, conventional methods can affect the continuity of the airfoil chord length or derivative, leading to increased manufacturing difficulty and decreased aerodynamic characteristics.
By constructing a continuously differentiable perturbation function, the thickness distribution of the airfoil trailing edge is modified to achieve local adjustment of the step thickness. The new airfoil coordinates are then calculated from the camber and thickness distributions to ensure the continuity of the airfoil curve and the invariance of the chord length.
It enables flexible adjustment of the wing trailing edge thickness, improves design efficiency and processing accuracy, reduces manufacturing difficulty, and maintains the overall aerodynamic characteristics of the airfoil.
Smart Images
Figure CN121765833A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aerodynamics, specifically a method for rapid treatment of trailing edge steps in airfoils. Background Technology
[0002] The wing is the core aerodynamic component of an aircraft, and its design directly affects flight performance, economy, safety, and environmental adaptability. The key to wing design lies in the design of the airfoil, also known as the air section.
[0003] Normally, airfoil data adopts a standard format, with a closed trailing edge or a fixed thickness. However, due to different layout forms in engineering, directly using the standard format airfoil will lead to inconsistent thickness of the trailing edge step, resulting in a wavy trailing edge or an excessively thin trailing edge step, which will cause difficulties in manufacturing and affect the design and production efficiency of the aircraft. Common methods for handling the trailing edge step of the airfoil include (1) direct truncation method: the designer needs to truncate the airfoil along the chord direction to the required thickness of the trailing edge based on experience. This method can ensure the continuity of the airfoil curve, but it will change the chord length of the airfoil and bring other problems; (2) direct thickening method: starting from the position of maximum thickness, the airfoil coordinates are directly and symmetrically thickened according to a quadratic function. This method can ensure that the airfoil chord length remains unchanged, but it will cause the derivative of the airfoil to be discontinuous at the position of maximum thickness, affecting the smoothness of the airfoil, thereby affecting the aerodynamic characteristics of the wing and the difficulty of processing. Summary of the Invention
[0004] The purpose of this invention is to propose a rapid and concise method for treating the trailing edge step of airfoils. This method solves the problem of adjusting the trailing edge thickness of airfoils in engineering practice for ease of manufacturing. It allows for arbitrary adjustment of the trailing edge thickness while maintaining the continuity of the airfoil curve and the airfoil chord length, thus ensuring the smoothness of the airfoil shape and the basic stability of its overall aerodynamic characteristics. This provides an engineering-applicable analytical method for the rapid treatment of trailing edge steps in airfoils, improving the design efficiency of airfoils and wings. The technical solution of the present invention: A rapid processing method for trailing edge steps in airfoils is proposed. First, the airfoil data is standardized, and the thickness and camber distribution curves of the airfoil are calculated using airfoil coordinates. Then, a new continuous perturbation function is constructed. This perturbation function is a continuously differentiable function, and the perturbation amount at the trailing edge is exactly the required step thickness. Furthermore, it rapidly decays to 0 from the trailing edge of the airfoil, reducing the impact on other parts of the airfoil. By superimposing this smooth and continuous perturbation function on the thickness distribution, the local rapid adjustment of the trailing edge step thickness of the airfoil is achieved. Finally, the airfoil coordinates are calculated back from the camber and thickness distributions to obtain the required airfoil shape.
[0005] Furthermore, the method and process are as follows: Step 1: Classify the airfoil coordinates according to XY, where X is the chord coordinate and Y is the corresponding normal coordinate. Then, divide the coordinates from the leading edge of the airfoil and separate the coordinate data into upper surface data. , and lower wing surface data , ; Step 2: Normalize the coordinate data to facilitate data standardization. The normalization formula is as follows: ,
[0006] ,
[0007] in , , , These are the normalized chord and normal coordinates, with subscripts up and low representing the upper and lower surfaces, respectively. , For the leading edge coordinates of the airfoil, , The coordinates are for the trailing edge of the airfoil; Step 3: Interpolate the normalized coordinates, interpolating the normal coordinates onto uniformly distributed chord coordinates to improve the accuracy of the airfoil curve description. The interpolation formula is as follows:
[0008]
[0009]
[0010] in The coordinates are uniformly distributed from 0 to 1. for The dimension of a vector For the corresponding interpolated upper wing surface coordinates, For the corresponding interpolated lower wing surface coordinates, This is the interpolation formula; Step 4: Calculate the camber and thickness distribution curves of the airfoil based on the interpolated airfoil coordinates. These curves are used to modify the airfoil thickness through perturbation. The calculation formula is as follows:
[0011]
[0012] in Indicates the airfoil thickness distribution. Indicates the airfoil camber distribution; Step 5: Based on the required adjustment of the trailing edge thickness, superimpose the following construction formula onto the thickness distribution to calculate the new thickness distribution;
[0013]
[0014] in This is the location of the airfoil's maximum thickness. For the trailing edge step thickness that needs adjustment, The decay rate of the disturbance curve. This represents the thickness disturbance. For a new thickness distribution; Step 6, Obtain the new airfoil coordinates
[0015] Among them New airfoil upper surface coordinates For the new airfoil's lower surface coordinates.
[0016] Furthermore, before step 1, it is necessary to obtain the original coordinates of the airfoil that needs to be adjusted. This can be obtained through an airfoil database or by extracting the airfoil profile using modeling software. Furthermore, standard format airfoils obtained through airfoil databases and other means can skip step 2; Furthermore, before step 3, the airfoil coordinates need to be sorted. The coordinates should be arranged in a clockwise or counterclockwise circle starting from the airfoil's head or tail. Furthermore, the interpolation formula used in step 3 can be any interpolation algorithm, including but not limited to spline interpolation and shape-preserving interpolation, but the smoothness and continuity of the interpolated data must be guaranteed. Furthermore, in step 3... The dimension should be large enough to ensure that the airfoil curve can be accurately described; Furthermore, after step 5, the airfoil needs to be restored to the required chord length. This can be done by directly scaling the coordinates before importing them into the modeling software, or by scaling them within the modeling software itself.
[0017] The beneficial effects of this invention are as follows: This invention proposes a fast and simple method for treating the trailing edge step of an airfoil, solving the problem of adjusting the trailing edge thickness of an airfoil in engineering practice for ease of manufacturing. The advantages of this invention are: the disturbance attenuation function constructed in this invention results in a trailing edge disturbance amount that is precisely equal to the trailing edge thickness, which is intuitive and clear. Furthermore, the attenuation degree of the disturbance thickness can be freely adjusted through an attenuation factor, facilitating customized airfoil shaping. It achieves precise adjustment of the local trailing edge step thickness without affecting the airfoil camber and overall airfoil continuity. The method is simple, practical, and convenient, easily programmable, and can quickly adjust the airfoil to adapt to different wing chord lengths, improving the efficiency and accuracy of airfoil and wing design. It avoids the strong reliance on designer experience in traditional methods, reduces manufacturing difficulty and cost, and provides support for the ever-increasing demands of aircraft production. It has positive significance for the fields of aerodynamic design and manufacturing, especially in aerospace and other fields with extremely high R&D cycle sensitivity, demonstrating significant application value. Attached Figure Description
[0018] Figure 1 The present invention is implemented using the following steps and procedures.
[0019] Figure 2 This is the thickness disturbance curve for Example 2.
[0020] Figure 3 Comparison of the trailing edge steps of the airfoil in Example 2.
[0021] Figure 4 This is a comparison of the subsonic lift coefficient curves before and after the airfoil adjustment in Example 2.
[0022] Figure 5 This is a comparison of the subsonic drag coefficient curves before and after the airfoil adjustment in Example 2.
[0023] Figure 6 This is a comparison of the subsonic pitching moment coefficient curves before and after airfoil adjustment in Example 2.
[0024] Figure 7 The image shows a comparison of the supersonic lift coefficient curves before and after the airfoil adjustment in Example 2.
[0025] Figure 8 This is a comparison of the supersonic drag coefficient curves before and after airfoil adjustment in Example 2.
[0026] Figure 9 This is a comparison of the supersonic pitching moment coefficient curves before and after airfoil adjustment in Example 2. Detailed Implementation
[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.
[0028] The technical solution of this invention: Several technical difficulties involved in airfoil design and processing: 1) How to construct the perturbation function 2) How to ensure the continuity of the airfoil.
[0029] Overall approach: This method does not directly process the airfoil curve coordinates. Instead, it first standardizes the airfoil data and calculates the thickness and camber distribution curves of the airfoil using the airfoil coordinates. Then, this invention constructs a new continuous perturbation function, which is a continuously differentiable function. The perturbation amount of this function at the trailing edge is exactly the required step thickness and decays rapidly to 0 from the trailing edge of the airfoil, reducing the impact on other parts of the airfoil. By superimposing this smooth and continuous perturbation function on the thickness distribution, the local rapid adjustment of the step thickness at the trailing edge of the airfoil is achieved. Finally, the airfoil coordinates are calculated from the camber and thickness distributions to obtain the required airfoil shape. Since the camber distribution and maximum thickness of the airfoil remain unchanged after modification by this method, and the continuity requirement of the shape is met, the overall aerodynamic characteristics of the airfoil before and after adjustment are basically consistent.
[0030] Example 1 Please refer to Figure 1. A method for rapid treatment of airfoil trailing edge steps is described below: Step 1: Extract the airfoil coordinates from the wing model that needs adjustment. Classify the airfoil coordinates according to XY, where X is the chord coordinate and Y is the corresponding normal coordinate. Then, segment the airfoil from the leading edge and divide the coordinate data into upper surface data. , and lower wing surface data , ; Step 2: To standardize the coordinate data, the coordinate data obtained in Step 1 is normalized. The normalization calculation formula is as follows: ,
[0031] ,
[0032] in , , , These are the normalized chord and normal coordinates, with subscripts up and low representing the upper and lower surfaces, respectively. , For the leading edge coordinates of the airfoil, , The coordinates are for the trailing edge of the airfoil; Step 3: Perform interpolation on the normalized coordinates, interpolating the normal coordinates onto the uniformly distributed chord coordinates. The interpolation formula is as follows:
[0033]
[0034]
[0035] in The coordinates are uniformly distributed from 0 to 1. For the corresponding interpolated upper wing surface coordinates, For the corresponding interpolated lower wing surface coordinates, use any common interpolation formula; Step 4: Calculate the camber distribution curve and thickness distribution curve of the airfoil based on the airfoil coordinates;
[0036]
[0037] in Indicates the airfoil thickness distribution. Indicates the airfoil camber distribution; Step 5: Based on the required adjustment of the trailing edge thickness, superimpose the following construction formula onto the thickness distribution to calculate the new thickness distribution;
[0038]
[0039] in This is the location of the airfoil's maximum thickness. For the trailing edge step thickness that needs adjustment, The decay rate of the disturbance curve. This represents the thickness disturbance. For a new thickness distribution; Step 6: Obtain the new airfoil coordinates that meet the requirements.
[0040] Among them New airfoil upper surface coordinates For the new airfoil's lower surface coordinates.
[0041] In this embodiment, the airfoil is obtained by 3D wing cropping. Step 2 is required to normalize the data so that the data format is standardized and easy to process. In this embodiment, before step 3, the airfoil coordinates need to be sorted, and the coordinates are arranged in a clockwise or counterclockwise circle starting from the airfoil head or tail. In this embodiment, the interpolation formula used in step 3 is a common interpolation algorithm such as spline interpolation or shape-preserving interpolation, which ensures the smoothness and continuity of the interpolated data; In this embodiment, in step 3 The dimension is large enough to ensure that the airfoil curve can be accurately described; In this embodiment, after step 5, the airfoil needs to be restored to the required chord length. This can be done by directly scaling the coordinates before importing them into the modeling software, or by scaling them within the modeling software. The specific implementation methods of the present invention are described below with reference to specific data: Example 2 1) Extract the airfoil section that needs adjustment from the modeling software and export the airfoil coordinates as follows: Table 1 Lower wing surface coordinates
[0042] Table 2 Upper wing surface coordinates
[0043] 2) Normalize the airfoil coordinates according to the following formula. The normalized coordinates are... , , , See the table below ,
[0044] ,
[0045] Table 3 Normalized lower wing surface coordinates
[0046] Table 4 Normalized upper wing surface coordinates
[0047] 3) To , Interpolation is performed according to the following formula, using the PCHIP conformal interpolation method, and the values are taken. The interpolated coordinate data of the upper and lower wing surfaces are obtained. and
[0048]
[0049]
[0050]
[0051] Table 5. Interpolated airfoil coordinate data (partial)
[0052] 4) Substitute the airfoil data into the formula
[0053]
[0054] The thickness and camber distributions of the airfoil were calculated. Table 6. Coordinates of Thickness and Curvature Curves (Partial)
[0055] 5) Calculate the disturbance amount Values , The calculated disturbance is as follows:
[0056]
[0057] Table 7. Thickness disturbance and new thickness distribution data (partial)
[0058] 6) Calculate the adjusted airfoil coordinates based on the new thickness distribution and the original camber distribution. The formula and specific values are as follows:
[0059] Table 8. Coordinate data points of the new airfoil (partial)
[0060] Numerical simulations of the subsonic and supersonic aerodynamic characteristics of the modified airfoil and the reference airfoil were performed. The results are shown in curves 4 and 9. The relative thickness of the airfoil step increased from 0.00136 to 0.00186. It can be seen that the airfoil modified by this method not only meets the requirements for trailing edge thickness modification, but also has minimal impact on the overall aerodynamic characteristics.
[0061] The above description is merely a specific embodiment of the present invention, providing a detailed description of the invention. Parts not covered herein are conventional techniques. However, the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method of rapid treatment of an airfoil trailing edge step, characterized in that, First, the airfoil data is standardized, the thickness distribution curve and the camber distribution curve of the airfoil are calculated through the airfoil coordinates, then a new continuous disturbance function is constructed, which is a continuous and derivable function, the disturbance quantity at the trailing edge of this function is exactly the required step thickness, and it quickly decays to 0 from the trailing edge of the airfoil, reducing the influence on other positions of the airfoil, by superimposing a smooth and continuous disturbance function on the thickness distribution, the local and rapid adjustment of the step thickness of the trailing edge of the airfoil is realized, finally the airfoil coordinates are calculated through the camber distribution and the thickness distribution, and the required airfoil shape is obtained.
2. The method of claim 1, wherein, The method flow is as follows: Step 1, the airfoil coordinates are classified according to XY, where X is chordwise coordinate and Y is corresponding normal coordinate, and the coordinates are divided from the airfoil leading edge, and the coordinate data are divided into upper surface data , and lower surface data , ; Step 2, normalize the coordinate data for easy standardization of data, the normalization formula is as follows: ， ， wherein , , , are the normalized chordwise and normal coordinates, the subscripts up and low denote the upper and lower wing surface, respectively, , is the airfoil leading edge coordinate, , is the airfoil trailing edge coordinate; Step 3, interpolate the normalized coordinates, interpolate the normal coordinates to the uniform chord coordinates, which is used to improve the description accuracy of the airfoil curve, the interpolation formula is as follows: wherein is a coordinate uniformly distributed between 0 and 1, is is the dimension of the vector, is the corresponding interpolated upper surface coordinate, is the corresponding interpolated lower surface coordinate, is the interpolation formula; Step 4, calculate the camber distribution curve and the thickness distribution curve of the airfoil according to the interpolated airfoil coordinates, which is used for airfoil thickness modification disturbance processing, the calculation formula is as follows: wherein denotes the airfoil thickness distribution, denotes the airfoil camber distribution; Step 5, according to the required adjustment of the trailing edge thickness, superimpose the following construction formula on the thickness distribution to calculate the new thickness distribution; wherein is the position of the maximum thickness of the airfoil, is the thickness of the trailing edge step that needs to be adjusted, is the decay rate of the perturbation curve, is the amount of thickness perturbation, is the new thickness distribution; Step 6, get the new airfoil coordinates wherein new airfoil upper surface coordinates, are new airfoil lower surface coordinates.
3. The method of claim 2, wherein, Before step 1, the original airfoil coordinates that need to be adjusted are needed, which can be obtained through the airfoil database or by intercepting the airfoil profile through modeling software.
4. The method of claim 2, wherein, The standard format airfoil obtained through the airfoil database method can skip step 2.
5. The method of claim 2, wherein, Before step 3, the airfoil coordinates need to be sorted, the coordinates should be arranged in a clockwise or counterclockwise circle starting from the head or tail of the airfoil.
6. The method of claim 2, wherein, The interpolation formula used in step 3 can be any interpolation algorithm, including but not limited to spline interpolation and shape-preserving interpolation, but it must ensure the smoothness and continuity of the interpolated data.
7. The method of claim 2, wherein, In said step 3 The dimensionality of the matrix should be large enough to ensure that the airfoil curve can be accurately described.
8. The method of claim 2, wherein, After step 5, the airfoil needs to be restored to the required chord length, which can be scaled directly on the coordinates before importing into the modeling software, or scaled in the modeling software.