A semi-parametric airfoil leading edge design and reshaping method

Abstract

The application discloses a semi-parameterized airfoil leading edge design and modification method, which comprises the following steps: designing or fitting the leading edge of an initial airfoil as a circular arc tangent to the trailing edge and the root of the hub; determining a setting angle and a rotation point, and transforming the airfoil to a positioning coordinate system through rotation and translation; constructing an elliptic line as a leading edge line in the positioning coordinate system, wherein the elliptic line passes through the trailing edge and the root of the hub, is tangent to the airfoil at the trailing edge and has a continuous second derivative; calculating characteristic parameters of the elliptic line based on the geometric information of the trailing edge; and splicing the elliptic line after reverse transformation with the original airfoil to obtain a final airfoil. The application improves the first-order continuity of the leading edge profile to the second-order continuity, effectively reduces the over-acceleration of the leading edge, improves the variable attack angle performance, meanwhile, retains the physical characteristics and parameterized expression of the leading edge wedge angle, and balances the aerodynamic performance and the engineering design requirement.

Description

Technical Field

[0001] This invention relates to the field of airfoil design technology, and more particularly to a semi-parametric airfoil leading edge design and modification method. Background Technology

[0002] The leading edge of airfoils, such as those in compressors, turbines, and aircraft, is a crucial region affecting their aerodynamic performance. It influences the over-acceleration of high-speed incoming flow, fluid separation, and transition. Studies have shown that leading edge curves with second-order continuous smoothness exhibit better aerodynamic performance. Furthermore, as industrial products, engineers and manufacturers desire airfoils with curves that can be easily parametrically expressed for ease of design, manufacturing, and control. Therefore, a leading edge design and modification method that balances smoothness and parametric expression is essential. Summary of the Invention

[0003] (a) Technical problems to be solved To address the shortcomings of existing technologies, the present invention aims to improve airfoil design capabilities, thereby enhancing the smoothness of the airfoil's leading edge profile, reducing over-acceleration of the leading edge flow, improving variable angle of attack performance, while retaining physical characteristics such as the leading edge wedge angle and geometric parameterized expression.

[0004] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a semi-parametric airfoil leading edge design and modification method, comprising the following steps: S1. Obtain the initial leaf shape, design or fit the leading edge of the initial leaf shape into an arc that is tangent to both the starting point of the leaf back and the starting point of the leaf base, and obtain the first and second derivatives at the starting point of the leaf back. S2. Determine the placement angle and rotation point of the leading edge design. The placement angle is the angle between the perpendicular bisector of the line connecting the starting point of the leaf back and the starting point of the leaf basin and the reference direction. The rotation point is the intersection of the line connecting the two perpendicular bisectors. S3. Using the rotation point as the rotation center, rotate the initial blade shape according to the placement angle so that the perpendicular bisector is parallel to the reference direction to obtain the placement blade shape; S4. Translate the placed blade shape so that the rotation point coincides with the origin of the coordinate system to obtain the positioning blade shape, and record the ordinate of the starting point of the back of the positioning blade shape. S5. Calculate the first and second derivatives at the starting point of the blade back in the positioning blade shape; S6. Construct an elliptical line as the leading edge line in the coordinate system of the positioning leaf shape. The elliptical line passes through the starting point of the leaf back and the starting point of the leaf basin, and is tangent to the positioning leaf shape at the starting point of the leaf back and has a continuous second derivative. S7. Calculate the characteristic parameters of the ellipse line based on the ordinate, first derivative, and second derivative of the starting point on the back of the blade in the positioning blade shape. S8. Determine the parameter range of the leading edge line, and generate the leading edge line based on the characteristic parameters of the elliptical line; S9. The leading edge line is transformed in reverse according to the translation amount and the rotation angle to obtain the final leading edge line; S10. The final leading edge line is spliced ​​with the leaf basin line, leaf back line and trailing edge line of the initial leaf shape to obtain the final leaf shape.

[0005] As a preferred embodiment, the reference direction in S2 is the X-axis direction of the initial blade shape, and the placement angle is the angle between the perpendicular bisector and the X-axis direction.

[0006] As a preferred embodiment, in the rotated placement of the blade in S3, the vertical line is rotated to the X-axis direction.

[0007] As a preferred embodiment, the calculation method for the first and second derivatives at the starting point of the blade back in the positioning blade shape in S5 is as follows: in, The placement angle is... and These are the first and second derivatives at the starting point of the initial leaf shape on the back of the leaf, obtained in S1.

[0008] As a preferred embodiment, in S6, the major axis of the ellipse is aligned with the X-axis of the positioning leaf shape coordinate system, and the minor axis is aligned with the Y-axis. The center of the ellipse is located on the X-axis, and its parametric equation is: in, For the semi-major axis, It is a semi-minor axis. The x-coordinate of the circle's center is... For angle parameters.

[0009] As a preferred embodiment, the characteristic parameters of the elliptical line in S7 , , and the angle parameters corresponding to the starting point of the blade back. Calculated using the following formula: in, The ordinate of the starting point on the back of the blade in the aforementioned positioning blade shape is... and These are the first and second derivatives at the starting point on the back of the blade in the aforementioned positioning blade shape, respectively.

[0010] As a preferred embodiment, the parameter range of the leading edge line in S8 is the angle parameter corresponding to the starting point on the back of the blade. The angle parameter corresponding to the starting point of the leaf basin The angle parameter corresponding to the starting point of the leaf basin. Based on symmetry, it is determined to be .

[0011] As a preferred embodiment, the second derivatives at the leaf back starting point and the leaf basin starting point of the initial leaf shape in S1 are both less than or equal to zero.

[0012] As a preferred embodiment, the initial airfoil includes a compressor airfoil or a turbine airfoil.

[0013] (III) Beneficial Effects Compared with the prior art, the present invention provides a semi-parametric airfoil leading edge design and modification method, which has the following beneficial effects: This invention constructs an elliptical line as the leading edge and utilizes the first and second derivatives at the blade back initiation point to ensure that the leading edge and blade back lines are not only tangentially continuous but also curvature continuous at the connection point, achieving an improvement in the leading edge profile from first-order continuity to second-order continuity. Compared to a traditional circular arc leading edge, this effectively reduces flow overacceleration near the leading edge, lowers flow losses, and improves variable angle of attack performance. Blades designed or modified using this invention, compared to blades with a circular arc leading edge, show a significant reduction in flow overacceleration near the leading edge and a significant improvement in variable angle of attack performance because the leading edge is geometrically improved from first-order continuous smoothness to second-order continuous smoothness. Compared to blades with an arbitrary continuous curve leading edge, it retains physical characteristics such as the leading edge wedge angle and geometric parametric expression, ensuring the parametric design level of the blade. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram of the initial blade shape of the present invention; Figure 3 This is a schematic diagram of the leaf arrangement of the present invention; Figure 4 This is a schematic diagram of the positioning blade type of the present invention; Figure 5 This is a schematic diagram of the elliptical leading edge design of the present invention; Figure 6This is a schematic diagram of the final blade shape of the present invention; Figure 7 This is a schematic diagram comparing the surface isentropic Mach number distribution effect calculated by the simulation of this invention. Detailed Implementation

[0015] To better understand the purpose, structure, and function of this invention, the following will further explain a semi-parametric airfoil leading edge design and modification method of this invention in conjunction with the accompanying drawings and specific embodiments.

[0016] refer to Figure 1-7 This invention discloses a semi-parametric airfoil leading edge design and modification method, which improves the leading edge profile from first-order continuity to second-order continuity, effectively reducing leading edge over-acceleration and improving variable angle of attack performance, while retaining physical characteristics and parametric expressions such as the leading edge wedge angle, thus balancing aerodynamic performance and engineering design requirements. The method includes the following steps: S1. Design or scan the initial leaf shape. Design or fit the leading edge of the initial leaf shape into an arc tangent to both the leaf back start point and the leaf base start point. Denote the leaf back start point tangent to the arc as point B, and the leaf base start point tangent to the arc as point P. Obtain the first derivative of the initial leaf back start point B. and second derivative .

[0017] S2. Calculate the leading edge design placement angle and rotation point. The specific method is as follows: Calculate the perpendicular bisector of the line connecting the starting point B on the back of the leaf and the starting point P on the leaf base, and calculate the angle between the perpendicular bisector and the leaf shape about the X-axis. that angle The point where the front edge is designed for placement is the rotation point T, and the intersection of the line connecting the two edges is the rotation point T.

[0018] S3. Using the rotation point as the rotation center, rotate the initial leaf shape according to the placement angle designed at the leading edge to obtain the placement leaf shape, so that the perpendicular bisector of the line connecting the starting point of the leaf back and the starting point of the leaf basin is placed in the X-axis direction.

[0019] S4. Translate and position the blade profile so that the rotation point T coincides with the origin o of the coordinate system to obtain the positioning blade profile. Record the ordinate of the starting point B on the back of the positioning blade profile. .

[0020] S5. Calculate the first derivative of the starting point B on the back of the positioning leaf shape. and second derivative The calculation method is as follows: ; .

[0021] S6. Construct a leading edge ellipse in the positioning leaf shape and its coordinate system, such that the ellipse passes through the leaf back starting point B and the leaf base starting point P, and is tangent to both the leaf back starting point B and the leaf base starting point P. The second derivative is continuous at the leaf back starting point B. The major axis of the ellipse is the X-axis direction, the minor axis is the Y-axis direction, and the center of the ellipse is on the X-axis with coordinates (c, 0). Let the parametric equation of the ellipse be: ; .

[0022] S7. The ordinate y of the starting point B on the back of the positioning blade obtained through S5, and its first derivative. and second derivative Calculate the characteristic parameters of the leading edge ellipse equation in S6. , , The specific method is as follows: First, calculate the angle parameter values ​​of the ellipse equation corresponding to the starting point B on the leaf back. ... (I); Secondly, calculate the semi-minor axis of the equation of the leading edge ellipse. ... (II); Then, calculate the semi-major axis of the equation of the leading edge ellipse. ... (III); Finally, calculate the x-coordinate of the center of the leading edge ellipse. ... (IV).

[0023] Specifically, the feature parameters in S7 are obtained based on the following elliptic parameterization expression: ...(1) …………(2) The first derivative can be obtained: ………………………………(3) The second derivative can be obtained: ………(4) From equations (2), (3), and (4) above, we can obtain: …………………………(5) According to equation (5), we can obtain: according to Figure 4 It can be seen that point B corresponds to The value ranges from 90° to 180°, so ……………………(6) According to equations (3) and (4), we can obtain: ………………(7) Equation (7) yields equation (8). ………………(8) Equation (9) is derived from equation (3). …………………………(9) Substituting the value of point B into equation (6) yields equation (I) in S7. Substituting the value of point B into equation (8) yields equation (II) in S7. Substituting the value of point B into equation (9) yields equation (III) in S7.

[0024] According to the Ming Shu Figure 4 Point B corresponds to At that time, …………………………(10) Therefore, there is ……………………………(11) According to equation (5), we get And then according to Figure 4 It can be seen that point B corresponds to The value is negative, so Substituting this into equation (11), we obtain equation (12). ……………………………(12) Substituting the value of point B into equation (12) gives equation (IV) in S7.

[0025] S8. Calculate the angle parameter values ​​of the ellipse equation corresponding to the starting point P of the leaf basin. (Symbols have been modified) Because the starting point B on the underside of the locating leaf shape and the starting point P on the leaf base of the locating leaf shape are symmetrical about the Y-axis, therefore .

[0026] S9. Determine the range of angle parameters for the corresponding ellipse equation of the leading edge ellipse as ( , ), calculate the angle range according to the ellipse equation of S6 and the characteristic parameters of S7 (). , The corresponding elliptic curve is the leading edge line.

[0027] S10. Translate the leading edge line in the reverse direction according to the translation amount in S4, and then rotate it according to the rotation angle in S3. Rotate in the opposite direction to obtain the final leading edge line.

[0028] S11. Connect the final leading edge line with the leaf basin line, leaf back line, and trailing edge line of the initial leaf shape to obtain a complete and closed final leaf shape. Define the angle between the tangent at the starting point of the leaf back and the tangent at the starting point of the leaf basin as the leading edge wedge angle of the final leaf shape.

[0029] This invention constructs an elliptical line as the leading edge and utilizes the first and second derivative information at the blade back initiation point to ensure that the leading edge line and the blade back line are not only tangentially continuous but also curvature continuous at the connection point, thus achieving an improvement in the leading edge profile from first-order continuity to second-order continuity. Compared to the traditional circular arc leading edge, this effectively reduces flow over-acceleration near the leading edge, lowers flow losses, and improves variable angle of attack performance.

[0030] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A semi-parametric airfoil leading edge design and modification method, characterized in that, Includes the following steps: S1. Obtain the initial leaf shape, design or fit the leading edge of the initial leaf shape into an arc that is tangent to both the starting point of the leaf back and the starting point of the leaf base, and obtain the first and second derivatives at the starting point of the leaf back. S2. Determine the placement angle and rotation point of the leading edge design. The placement angle is the angle between the perpendicular bisector of the line connecting the starting point of the leaf back and the starting point of the leaf basin and the reference direction. The rotation point is the intersection of the line connecting the two perpendicular bisectors. S3. Using the rotation point as the rotation center, rotate the initial blade shape according to the placement angle so that the perpendicular bisector is parallel to the reference direction to obtain the placement blade shape; S4. Translate the placed blade shape so that the rotation point coincides with the origin of the coordinate system to obtain the positioning blade shape, and record the ordinate of the starting point of the back of the positioning blade shape. S5. Calculate the first and second derivatives at the starting point of the blade back in the positioning blade shape; S6. Construct an elliptical line as the leading edge line in the coordinate system of the positioning leaf shape. The elliptical line passes through the starting point of the leaf back and the starting point of the leaf basin, and is tangent to the positioning leaf shape at the starting point of the leaf back and has a continuous second derivative. S7. Calculate the characteristic parameters of the ellipse line based on the ordinate, first derivative, and second derivative of the starting point on the back of the blade in the positioning blade shape. S8. Determine the parameter range of the leading edge line, and generate the leading edge line based on the characteristic parameters of the elliptical line; S9. The leading edge line is transformed in reverse according to the translation amount and the rotation angle to obtain the final leading edge line; S10. The final leading edge line is spliced ​​with the leaf basin line, leaf back line and trailing edge line of the initial leaf shape to obtain the final leaf shape.

2. The semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, The reference direction in S2 is the X-axis direction of the initial airfoil.

3. The semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, In the rotated leaf shape in S3, the vertical line is rotated to the X-axis direction.

4. The semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, The calculation method for the first and second derivatives at the starting point of the blade back in the positioning blade shape in S5 is as follows: in, The placement angle is... and These are the first and second derivatives at the starting point of the initial leaf shape on the back of the leaf, obtained in S1.

5. The semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, In S6, the major axis of the ellipse is aligned with the X-axis of the positioning leaf shape coordinate system, and the minor axis is aligned with the Y-axis. The center of the ellipse is located on the X-axis, and its parametric equation is: in, For the semi-major axis, It is a semi-minor axis. The x-coordinate of the circle's center is... For angle parameters.

6. A semi-parametric airfoil leading edge design and modification method according to claim 5, characterized in that... The characteristic parameters of the elliptical line in S7 , , and the angle parameters corresponding to the starting point of the blade back. Calculated using the following formula: in, The ordinate of the starting point on the back of the blade in the aforementioned positioning blade shape is... and These are the first and second derivatives at the starting point on the back of the blade in the aforementioned positioning blade shape, respectively.

7. A semi-parametric airfoil leading edge design and modification method according to claim 6, characterized in that, The parameter range of the leading edge line mentioned in S8 is the angle parameter corresponding to the starting point on the back of the blade. The angle parameter corresponding to the starting point of the leaf basin The angle parameter corresponding to the starting point of the leaf basin. Based on symmetry, it is determined to be .

8. The semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, In S1, the second derivatives at the leaf back starting point and the leaf basin starting point of the initial leaf shape are both less than or equal to zero.

9. A semi-parametric airfoil leading edge design and modification method according to claim 1, characterized in that, The initial airfoil includes either a compressor airfoil or a turbine airfoil.

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