An optimization design method of an aircraft airfoil

Abstract

The application discloses an optimization design method of an aircraft airfoil, and relates to the technical field of aerospace. First, original coordinate point data of an airfoil boundary is generated according to a theory; then, the original coordinate points are corrected by using a segmented function proposed by the application, so that a sharp corner at a tail end of the airfoil is modified into a round corner; then, the points after the modification are fitted by using a spline curve, so that a new airfoil curve is obtained; finally, a final three-dimensional model of the airfoil is generated according to the airfoil curve. The application can conveniently modify the airfoil with the sharp corner at the tail end into the airfoil with the round corner at the tail end, and generate a smooth airfoil curve, so that the flow field of the airfoil trailing edge can be improved, stress concentration in the airfoil trailing edge region can be reduced, and the processing difficulty of the airfoil can be lowered.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to an optimization design method for aircraft airfoils. Background Technology

[0002] Traditional aircraft airfoils generally employ a sharp-angled trailing edge design, such as the NACA series airfoils, which all have sharp tail tips. While this theoretically reduces drag, it has revealed some drawbacks in practical applications:

[0003] In terms of aerodynamic performance, when an aircraft is cruising, the sudden change in airflow characteristics at sharp corners can easily cause flow separation, forming unstable vortices that interfere with the flow field structure at the trailing edge of the airfoil, resulting in a significant increase in induced drag, which directly affects the aircraft's endurance and fuel efficiency.

[0004] In terms of structural strength, the sharp corner area is a weak link in stress transmission and will produce obvious stress concentration. After being subjected to alternating aerodynamic loads for a long time, it is very easy to develop fatigue cracks, which will lead to airfoil tail fracture and pose a major hidden danger to flight safety.

[0005] In terms of manufacturing process, the forming of sharp corners requires extremely high equipment precision and operating skills, making it difficult to guarantee the accurate forming of sharp corners. Furthermore, the formed sharp corners have poor impact resistance and are easily damaged by collisions during assembly, maintenance, or use. After damage, the delicate structure makes repair extremely difficult, often requiring the replacement of the entire component, which further increases the total life cycle cost.

[0006] To address the aforementioned issues, an optimization design method for aircraft airfoils is proposed. Summary of the Invention

[0007] In view of this, the present invention provides an optimized design method for aircraft airfoils to solve the problems mentioned in the background art.

[0008] The objective of this invention can be achieved through the following technical solution: an optimized design method for aircraft airfoils, comprising:

[0009] Step S1: Generate the original coordinate point data of the airfoil boundary. The original coordinate point data includes the coordinate x of the chord position and the corresponding thickness value y.

[0010] Step S2: Correct the original coordinate point data using a piecewise function, resulting in a three-segment function: the initial segment, the transition segment, and the rounded corner correction segment.

[0011] Step S3: Fit the corrected coordinate point data with spline curves to obtain a new airfoil curve. Cubic spline curves and B-spline curves are preferred. After fitting, calculate the absolute error of the thickness value at each point and the rate of change of curvature of the curve at each point. Count the number of points that exceed the absolute error. Preset the threshold for the number of points that exceed the absolute error and the threshold for the rate of change of curvature. If the number of points that exceed the absolute error and the rate of change of curvature of the curve at each point exceed the corresponding threshold, the curve needs to be refitted.

[0012] Step S4: Generate the final aircraft control surfaces based on the airfoil curves. The two control surfaces are obtained by modifying the airfoil with different chord lengths and maximum thicknesses, and the control surfaces are obtained by sweeping the data points corresponding to the two control surfaces.

[0013] In some embodiments, the process of generating the original coordinate point data of the airfoil boundary based on theory specifically includes:

[0014] The aircraft wing is divided into a leading section, a transition section, and a fillet correction section. Original coordinate point data is obtained, including the chordal position x and the thickness value y; where x ranges from 0 to the chord length, and y corresponds to the airfoil thickness at position x. In some embodiments, the process of correcting the original coordinate point data using a piecewise function specifically involves:

[0015] Using the generated original coordinate point data as the correction target, find the maximum value of x in the original coordinate point data, which is the chord length of the airfoil, denoted as . Find the point with the largest y-value; this point is the thickest point of the airfoil. Let its x-coordinate be [x]. p The vertical axis is y p The original airfoil at x= At point y=0, a sharp corner structure is formed, which needs to be corrected to a rounded corner with radius r;

[0016] Using formula Obtain the x-coordinate of the end position of the rounded corner. For the original coordinate point data in Interpolation calculations are performed at the point to obtain the thickness at the end of the fillet. Let the thickness before correction be... The corrected thickness is The coordinate point transformation is performed using the following piecewise function:

[0017]

[0018] when At that time, the coordinates before the thickest point of the airfoil remain unchanged;

[0019] when When the coordinates are at the thickest point of the airfoil and the end of the fillet, the thickness is interpolated using a polynomial. The coefficients of the polynomial have a distribution power n that can be adjusted for interpolation, and its value range is positive real numbers.

[0020] when At that time, the original data will be corrected to a standard arc.

[0021] In some embodiments, selecting the fitted curve specifically means:

[0022] Cubic spline curve: Every two adjacent correction points are connected by a cubic polynomial, and the first and second derivatives of adjacent segments are continuous at the connection point;

[0023] B-spline curves: The shape of the curve is adjusted by controlling the position of the vertices.

[0024] In some embodiments, setting curve parameters and performing fitting specifically involves:

[0025] Set the boundary of the cubic spline curve to a natural boundary, that is, the second derivative of the airfoil leading edge and tail tip is zero; set the B-spline curve to the third order, control the number of vertices to be 2 more than the number of correction points, and control the position of the vertices to minimize the deviation between the curve and the correction points.

[0026] Sort the corrected original coordinate point data in ascending order of chord position x, remove duplicate points or outliers caused by calculation errors, and import the preprocessed data into the fitting tool. The tool automatically generates a continuous curve based on the selected spline curve type.

[0027] In some embodiments, verifying the accuracy of the curve fitting specifically involves:

[0028] Observe the curve state, preset the baseline horizontal line of the curve, use the baseline horizontal line as the reference line, and use the preset fluctuation values ​​above and below as the construction line to construct the upper and lower fluctuation range of the curve. If a point of the curve is higher than the highest value of the fluctuation range, it is judged as a local bulge. If a point of the curve is lower than the lowest value of the fluctuation range, it is judged as a local depression. And gradually increase the point density according to the preset point density increase ratio to correct until the overall trend of the curve is smooth.

[0029] Ten points were randomly selected from the corrected original coordinate data, with each of the front segment, transition segment, and rounded corner correction segment covering at least three points. These ten points were then numbered from 1 to 10 according to the order of selection. Let be the x-coordinate of the extracted point, where i represents the point number, i = 1, 2, ..., 10. Let be the ordinate of the extracted point. In the fitted curve, let the ordinate of the extracted point be denoted as . ,Will and The absolute error at each point is calculated by taking the absolute value of the difference. A threshold is set for the number of points exceeding the absolute error. If the number of points exceeding the absolute error exceeds the threshold, the curve fitting is performed again. The second derivative of the fitted curve is taken to obtain the curvature. The first derivative of the curvature is taken and its absolute value is calculated to determine the rate of change of curvature at each position. A threshold is set for the rate of change of curvature. If the rate of change of curvature at a certain position exceeds the threshold, the curve needs to be refitted. Compared with the prior art, the beneficial effects of this invention are:

[0030] The piecewise function correction method proposed in this invention is based on the original airfoil data points and achieves targeted adjustments through a three-segment function logic. The original data is retained before the thickest point of the airfoil to maintain the core aerodynamic characteristics. The transition segment achieves a smooth and gradual change in thickness through polynomial interpolation. The tail end generates a standard circular arc using a circular equation. No complex iterative calculations are required. The coordinate point correction can be completed through basic mathematical operations. It can be directly automated by data processing software, which greatly reduces the technical threshold for airfoil modification and is especially suitable for the rapid iterative design needs in engineering practice.

[0031] This invention corrects the sharp corner of the airfoil tail end to a rounded corner of a specified size. Through parametric design, the rounded corner radius is precisely matched with the machining process. This flexible adjustment not only reduces tool wear and dimensional deviation during sharp corner machining, but also disperses the tail end stress through the rounded corner transition, significantly reducing the risk of fatigue cracks.

[0032] This invention corrects the sharp corner of the tail end to a rounded corner and combines it with spline curves for high-precision fitting, forming a smooth and continuous airfoil tail section curve. The rounded corner structure weakens the abrupt change effect of airflow at the tail end from the source. Combined with the hybrid fitting of cubic splines and B splines, the pressure gradient change of the airfoil tail section flow field is made more gradual, effectively improving the aerodynamic efficiency and flight stability of the aircraft. Attached Figure Description

[0033] Further details, features, and advantages of this application are disclosed in the following description of exemplary embodiments in conjunction with the accompanying drawings, in which:

[0034] Figure 1 This is a flowchart of a method for modifying an aircraft airfoil according to the present invention;

[0035] Figure 2 This is a comparative schematic diagram showing the aircraft airfoil modification proposed in this invention before and after.

[0036] Figure 3 This is an example diagram illustrating the use of a modified airfoil to establish the control surfaces of an aircraft according to the present invention. Detailed Implementation

[0037] Several embodiments of this application will now be described in more detail with reference to the accompanying drawings to enable those skilled in the art to implement this application. This application may be embodied in many different forms and for various purposes and should not be limited to the embodiments set forth herein. These embodiments are provided to make this application thorough and complete, and to fully convey the scope of this application to those skilled in the art. The embodiments described do not limit this application.

[0038] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It will be further understood that terms such as those defined in commonly used dictionaries shall be interpreted as having a meaning consistent with their meaning in the relevant field and / or the context of this specification, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0039] Please see Figure 1 As shown, an optimization design method for an aircraft airfoil includes:

[0040] Step S1: Generate the original coordinate point data of the airfoil boundary based on the theory, specifically:

[0041] If the original coordinate point data of the airfoil boundary is generated based on existing theories, then the appropriate NACA airfoil is selected according to the flight characteristics of the aircraft, including the speed range, lift requirements, and flight attitude. For example, for aircraft components with symmetrical flight attitudes (such as control surfaces and missile wings), NACA 00 series symmetrical airfoils (such as NACA 0012 and NACA 0015) are preferred, as the thickness of the upper and lower surfaces is symmetrical about the chord in their original coordinate data. For wings that need to optimize the cruise lift-to-drag ratio, NACA 44 series asymmetrical airfoils can be selected to improve aerodynamic efficiency by utilizing their camber characteristics.

[0042] Coordinate data was obtained from authoritative aerospace engineering databases (such as public documents from the National Advisory Committee on Aeronautics (NACA) and the built-in database of professional airfoil design software). The obtained data consisted of discrete points with chordal positions (x) and thickness values ​​(y). The value of x ranged from 0 to the chord length, and the value of y corresponded to the thickness of the airfoil at position x. It is important to note that the spacing between the points in the original data must meet the requirements for airfoil modification to ensure that the detailed features of the airfoil curve are fully preserved. If the spacing between the data points is too large, selective interpolation must be used to supplement intermediate points to ensure the continuity of subsequent corrections.

[0043] If the original coordinate point data is designed based on aerodynamic simulation, then the original airfoil boundary coordinates need to be designed using aerodynamic simulation tools for specific flight conditions (such as high altitude and low Reynolds number environments in near space) or special performance requirements (such as high lift-to-drag ratio and low radar cross-section); specifically:

[0044] The design conditions of the aircraft are clearly defined as the simulation input conditions. The design conditions of the aircraft include, but are not limited to, cruise Mach number, flight altitude and target lift number.

[0045] Using a basic model (such as the NACA series) as the initial model, import computational fluid dynamics software (such as Fluent, XFOIL) and perform multiple rounds of aerodynamic performance simulation by adjusting the thickness distribution, camber, and leading edge radius of the airfoil.

[0046] When the simulation results meet the design objectives, the discrete coordinate points of the airfoil boundary are extracted from the simulation model, including the chord position x and the thickness value y. During extraction, it is necessary to ensure that the coordinate points cover the entire chord length of the airfoil, and to increase the density of the points (x interval ≤ 0.01m) in aerodynamically sensitive areas (such as the maximum thickness point and near the trailing edge) to accurately capture the key geometric features of the airfoil.

[0047] Additional notes: The choice between the two data sources should be based on the actual application scenario: For general-purpose aircraft components, using existing theoretical airfoil data can reduce design costs; for customized requirements (such as the special aerodynamic environment of near-space aircraft), data generated through aerodynamic simulation can better match performance indicators and lay an optimization foundation for subsequent tail radius modification.

[0048] Step S2: Correct the original coordinate points using a piecewise function, and correct the sharp corners at the airfoil's tail end to smooth rounded corners. Specifically:

[0049] like Figure 2 As shown, using the generated original coordinate point data as the correction object, the tail of the aircraft airfoil is a sharp angle (x= (where y=0), the correction goal is to transform the sharp corner into a rounded corner with radius r, while ensuring the continuity of the airfoil curve;

[0050] Find the maximum value of x in the original coordinate data; this is the chord length of the airfoil, denoted as . Find the point with the largest y-value; this point is the thickest point of the airfoil. Let its x-coordinate be [x]. p The vertical axis is y p The original airfoil at x= At point y=0, a sharp corner structure is formed, which needs to be corrected to a rounded corner with a radius of r; the value of r is selected according to the specific processing technology.

[0051] Using formula Obtain the x-coordinate of the end position of the rounded corner. For the original data Interpolation calculations are performed at the point to obtain the thickness at the end of the fillet. ;

[0052] Let the thickness before correction be... The corrected thickness is The coordinate point transformation is performed using the following piecewise function:

[0053]

[0054] Here, a three-part piecewise function is used to correct the original coordinate point data, as follows:

[0055] (1) When At that time, the coordinates of the points before the thickest point of the airfoil remain unchanged;

[0056] The leading edge of the airfoil is the main area for lift generation, and its thickness distribution directly affects the lift characteristics. Therefore, maintaining the original thickness ensures that the aerodynamic characteristics of the leading edge of the airfoil are consistent with the original design, and avoids affecting the main performance due to modification.

[0057] (2) When At that time, the thickness of the coordinate point at the thickest point of the airfoil and the end of the fillet is interpolated using a polynomial. The coefficient of the polynomial has a distribution power n that can be adjusted for interpolation. Its value range is positive real numbers, and its specific value can be adjusted according to the actual situation. When n is larger, the earlier corrected data is closer to the original data.

[0058] From the thickest point to the end of the rounded corner, the thickness must be smoothly transitioned from its maximum value to a minimum using polynomial interpolation. This avoids gas diversion caused by abrupt changes in thickness, and the curvature is continuous and without abrupt changes, providing a smooth basis for subsequent rounded corner transitions;

[0059] (3) When At this time, the original data will be corrected to a standard arc to meet the requirements of the fillet radius r;

[0060] The last segment of the airfoil's tail end generates a circular arc with radius r using the circular equation, transforming sharp corners into smooth rounded corners, thus improving aerodynamic performance and structural strength.

[0061] Step S3: Fit the corrected points using spline curves to obtain a new airfoil curve, specifically:

[0062] Based on the continuity requirements of the airfoil curve (which must meet the stringent requirements of aerodynamic performance for surface smoothness), the following two types of curves are preferred:

[0063] Cubic spline curve: Every two adjacent correction points are connected by a cubic polynomial, and the first derivative (slope) and second derivative (curvature) of adjacent segments are continuous at the connection point, which can completely avoid the curve from having inflection points or abrupt changes, and ensure smooth airflow on the airfoil surface; this type is suitable for scenarios with high requirements for overall smoothness, especially for fitting the leading section and transition section of the airfoil;

[0064] B-spline curves: By controlling the position of the vertices, the shape of the curve can be adjusted. They have the characteristic that local adjustments do not affect the overall shape, making them suitable for fine fitting of the tail edge rounded corner correction segment.

[0065] Additional notes: Both types of curves can be used simultaneously. Cubic spline curves can be used in the leading edge and transition sections of the airfoil, while B-spline curves are used in the trailing edge fillet correction section, balancing overall continuity and local accuracy.

[0066] The cubic spline curve boundary is set to a natural boundary, meaning the second derivative of the airfoil leading edge and trailing edge is zero, to avoid abrupt curvature changes at the endpoints. The interpolation node spacing is consistent with the spacing of the corrected data points to ensure that the fitted curve and the correction trend are the same. The B-spline curve order is set to third, and the number of vertices is controlled to be two more than the number of correction points. The software automatically optimizes the control of the vertex positions to minimize the deviation between the curve and the correction points.

[0067] Sort the corrected original coordinate point data in ascending order of chord position x, remove duplicate points or outliers caused by calculation errors, and import the preprocessed data into the fitting tool. The tool will automatically generate a continuous curve based on the selected spline curve type.

[0068] After the fitting tool is run, observe the curve status. Set a baseline horizontal line for the curve. Use the baseline horizontal line as a reference line and set the upper and lower preset fluctuation values ​​as the construction line to construct the upper and lower fluctuation range of the curve. If a point on the curve is higher than the highest value of the fluctuation range, it is judged as a local bulge. If a point on the curve is lower than the lowest value of the fluctuation range, it is judged as a local depression. Gradually increase the point density according to the preset point density increase ratio to make corrections until the overall trend of the curve is smooth.

[0069] Ten points were randomly selected from the corrected original coordinate data, with each of the front segment, transition segment, and rounded corner correction segment covering at least three points. These ten points were then numbered from 1 to 10 according to the order of selection. Let be the x-coordinate of the extracted point, where i represents the point number, i = 1, 2, ..., 10. Let be the ordinate of the extracted point. In the fitted curve, let the ordinate of the extracted point be denoted as . ,Will and Calculate the absolute error at each point by taking the absolute value of the difference. Set a threshold for the number of points exceeding the absolute error. If the number of points exceeding the absolute error exceeds the threshold, refit the curve. Calculate the curvature of the fitted curve by taking its second derivative. Calculate the rate of change of curvature at each position by taking the first derivative of the curvature and taking its absolute value. Set a threshold for the rate of change of curvature. If the rate of change of curvature at a certain position exceeds the threshold, refit the curve. Step S4: Generate the final 3D model based on the airfoil curve, specifically:

[0070] like Figure 3 100 represents the main body of the rudder; 1 represents the top surface of the rudder; 2 represents the bottom surface of the rudder; 3 represents the side surface of the rudder. The aircraft control rudder generated from the airfoil curves obtained in steps S1 to S3 has a top surface and a bottom surface with different chord lengths. and maximum thickness The airfoil was modified to obtain the two airfoil tails with smooth rounded corners. The two airfoil curves have the same number of data points and correspond one-to-one. The rudder side is obtained by sweeping the corresponding data points of the rudder top and bottom surfaces, and its surface property is ruled surface.

[0071] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method of optimised design of an aircraft airfoil, characterised in that, The method comprises the following steps: Step S1: generating original coordinate point data of the airfoil boundary, the original coordinate point data comprising coordinate x of chordwise position and corresponding thickness value y; Step S2: modifying the original coordinate point data by using a piecewise function, and modifying into three piecewise functions, namely a front piece, a transition piece and a round corner modification piece; Step S3: fitting the modified coordinate point data by using a cubic spline curve or a B spline curve to obtain a new airfoil curve; After the fitting is completed, the absolute error of the thickness value at each point and the curvature change rate of the curve at each point are calculated, the number of points exceeding the preset absolute error is counted, a number threshold of the points exceeding the preset absolute error and a change threshold of the curvature change rate are set, if the number of the points exceeding the absolute error is more than the number threshold, the curve fitting is re-performed, and if the curvature change rate at a position exceeds the change threshold, the curve needs to be re-fitted; The cubic spline curve: each two adjacent modified points are connected by a cubic polynomial, and the first derivative and the second derivative of the adjacent segments at the connection points are continuous; The B spline curve: the curve shape is adjusted by controlling the positions of the control points; Step S4: generating a final aircraft control rudder according to the airfoil curve, wherein two rudder surfaces are obtained by modifying the airfoils with different chord lengths and maximum thicknesses, and a rudder side surface is obtained by sweeping the data points corresponding to the two rudder surfaces.

2. The method of claim 1, wherein, The process of generating the original coordinate point data of the airfoil boundary according to the theory is as follows: The aircraft wing is divided into a front piece, a transition piece and a round corner modification piece, and the original coordinate point data comprising chordwise position x and thickness value y are obtained; wherein the value range of x is 0 to chord length, and the value of y corresponds to the thickness of the airfoil at the position x.

3. The method of claim 2, wherein, The process of modifying the original coordinate point data by using a piecewise function is as follows: The generated original coordinate point data is taken as a correction object, the maximum value of x in the original coordinate point data is found, that is, the chord length of the airfoil, and is denoted as ; the point with the maximum y value is found, which is the thickest point of the airfoil, the abscissa at this time is denoted as x p , and the ordinate is denoted as y p ; the original airfoil is a sharp corner structure at x= and y=0, and needs to be corrected into a round corner with a radius r; Using the formula the end position horizontal coordinate of the rounded corner is obtained , the original coordinate point data is interpolated at to obtain the thickness of the end position of the rounded corner ; the thickness before correction is , the thickness after correction is , and the following piecewise function is used for coordinate point transformation: ； When the coordinate before the thickest point of the airfoil remains unchanged; When the thickness of the coordinate at the thickest point of the airfoil and the end of the fillet is interpolated by a polynomial, the coefficients of the polynomial have a distribution power n that can adjust the interpolation, and the value range is a positive real number; When the original data will be corrected to a standard arc.

4. The method of claim 3, wherein, The curve parameters are set and fitting is performed, and the specific process is as follows: The boundary of the cubic spline curve is set as a natural boundary, that is, the second derivative of the leading edge and the tail end of the airfoil is zero; the order of the B spline curve is set as three, the number of control points is more than that of the modified points by two, and the positions of the control points are controlled to make the curve deviate from the modified points as little as possible; The modified original coordinate point data are sorted according to the chordwise position x from small to large, and the repeated points or abnormal points caused by calculation errors are removed, the pretreated data are imported into a fitting tool, and the tool automatically generates a continuous curve according to the selected spline curve type.

5. The method of claim 4, wherein, The fitting accuracy of the curve is verified, and the specific process is as follows: The state of the curve is observed, a reference line is set as a reference line, a fluctuation range is constructed by setting a preset fluctuation value above and below the reference line, if a point of the curve is higher than the highest value of the fluctuation range, it is determined as a local convex, if a point of the curve is lower than the lowest value of the fluctuation range, it is determined as a local concave; and the point density is gradually increased according to a preset point density increase ratio for modification until the overall trend of the curve is smooth. 10 points are randomly extracted from the modified original coordinate point data, at least 3 points are covered in each of the front section, transition section and round corner correction section, the 10 points are numbered from 1 to 10 according to the extraction order, and the corresponding abscissa of the extracted points is denoted as xi, i represents the number of each point, i = 1, 2, …, 10, the ordinate of the extracted points is denoted as yi, in the fitting curve, the ordinate of the extracted points is denoted as yi, the absolute error at each point is calculated by taking the absolute value of the difference between xi and xi, and yi and yi, a preset number threshold of the number of points exceeding the absolute error is set, if the number of points exceeding the preset absolute error is more than the number threshold, the curve fitting is performed again, the curvature of the fitted curve is obtained by taking the second derivative of the fitted curve, the first derivative of the curvature is taken and the absolute value is taken, the curvature change rate of the fitted curve at each position is calculated, a preset change threshold of the curvature change rate of the curve is set, if the curvature change rate at a position exceeds the change threshold, the curve needs to be fitted again.​

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