A multi-objective optimization design method of wide-speed-range thin airfoil considering three-dimensional effects

Abstract

The application discloses a wide-speed-range thin airfoil multi-objective optimization design method considering three-dimensional influence, and belongs to the field of aircraft aerodynamic configuration design.The application aims at the problem that the subsonic state resistance of the multi-objective optimization result of the airfoil of a large sweep angle and small aspect ratio thin airfoil is poor in a three-dimensional use environment, and proposes to constrain the height of the upper surface near the leading edge of the airfoil on the basis of a general optimization design method, set the chordwise position range of the height constraint of the upper surface near the leading edge of the airfoil to be 4% to 10% of the chord length, select 1 to 2 chordwise positions to be constrained in height, and the constraint condition is that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil.The application can effectively inhibit the airfoil leading edge separation in the three-dimensional use state.Further, in the case that the airfoil supersonic drag reduction and the resistance divergence Mach number are improved, the subsonic state resistance performance is also ensured, and the application is used for the airfoil aerodynamic design of supersonic transport aircrafts, fighter aircrafts and unmanned aerial vehicles.

Description

Technical Field

[0001] This invention belongs to the field of aircraft aerodynamic shape design, specifically relating to a multi-objective optimization design method for thin airfoils with a wide speed range that takes into account three-dimensional influences. Background Technology

[0002] Drag reduction is the most effective measure to improve the range and flight time of an aircraft, or to enhance its economic efficiency. Supersonic aircraft operate across a wide speed range, requiring designs that balance subsonic low drag, supersonic low drag, and high drag divergence Mach number performance. To reduce shock wave drag, supersonic aircraft generally use wing planforms with large sweep and low aspect ratios. This results in significant three-dimensional flow on the wing surface, with the flow environment of each airfoil profile being completely different from that in the two-dimensional environment. Often, the excellent aerodynamic performance in the two-dimensional environment deteriorates significantly in the three-dimensional environment. The most typical manifestation is the significant increase in wing drag under subsonic conditions. For these reasons, two-dimensional airfoil optimization is rarely performed in supersonic aircraft design; instead, existing classic airfoils are often selected to complete the design, hindering further refinement and improvement of the aircraft's performance.

[0003] With the development of optimization design technology, the technology for directly optimizing three-dimensional airfoils has matured. However, the problem with three-dimensional optimization is the surge in computational workload caused by the significant increase in design parameters. Aircraft design is a process of coordination and iteration among multiple disciplines. During the aircraft design process, the airfoil shape scheme needs to be improved and refined multiple times according to actual needs. High-performance airfoils and effective airfoil optimization methods will continue to play an important role in engineering design for some time to come. Especially given the current generally high performance of aircraft and relatively limited room for further improvement in aerodynamic performance, the design and optimization technology of thin airfoils are even more crucial. Summary of the Invention

[0004] The problem this invention aims to solve is the deterioration of drag in subsonic conditions under three-dimensional operating environments for the multi-objective optimization results of thin airfoils with large sweep and small aspect ratio. It proposes a wide-speed-range thin airfoil multi-objective optimization design method that takes into account three-dimensional effects.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A multi-objective optimization design method for wide-speed-domain thin airfoils considering three-dimensional influences is proposed. Based on general optimization design methods, the height of the upper surface near the leading edge of the airfoil is constrained. The chordal position range of the height constraint on the upper surface near the leading edge of the airfoil is set to 4% to 10% of the chord length. One to two chordal positions are selected for height constraint. The constraint condition is that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil.

[0007] Furthermore, the height of the upper surface of the leading edge with the chordal position at the rear is greater than the height of the upper surface of the leading edge with the chordal position at the front.

[0008] Furthermore, the chordal position range for setting the height constraint on the upper surface near the leading edge of the airfoil is 5% to 10% of the chord length.

[0009] Furthermore, the chordal position range for setting the height constraint on the upper surface near the leading edge of the airfoil is 4% to 8% of the chord length.

[0010] Furthermore, the optimization design method employs one of the following: genetic method, particle swarm optimization method, or surrogate model-based optimization method.

[0011] Furthermore, the aforementioned multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influences is implemented based on ARI_OPT software.

[0012] Furthermore, the specific implementation method of the agent-based optimization method includes the following steps:

[0013] S1. Select the NACA64A204 airfoil as the original airfoil for optimization design;

[0014] S2. Parametrically describe the coordinates of the upper and lower surfaces of the airfoil, and perform parametric optimization design of the airfoil based on the Hicks-Henne shape function. The calculation formula is as follows:

[0015]

[0016]

[0017] Among them, y us.basic For the original airfoil upper surface function, y us To optimize the upper surface function of the rear airfoil, y ls.basic For the original airfoil's lower surface function, y ls To optimize the lower surface function of the rear airfoil, f i Let a be the perturbation function. i To optimize the corresponding coefficients of the upper surface function of the rear airfoil, b i To optimize the corresponding coefficients of the lower surface function of the rear airfoil, a i and b i These are design variables for the airfoil optimization process;

[0018] S3. The dynamic mesh in the optimization process is implemented based on the radial basis function method. The formula for calculating the radial basis function is:

[0019]

[0020] Where F(r) is the interpolation function, ||rr i || is the vector from r to ri distance, These are the weighting coefficients corresponding to the radial basis functions;

[0021] S4. Set the surrogate model to the Kring model, set the optimization conditions for the optimization objective, and then transform it into a two-dimensional airfoil. The resulting mathematical expression is:

[0022]

[0023] in, The drag is at Mach number 1.66 and lift coefficient 0.175. The drag is at Mach number 0.8 and lift coefficient 0.44. The drag at Mach number 0.82 and lift coefficient 0.44;

[0024] S5. Set the maximum thickness constraint and the torque constraint in each state during the optimization process. The resulting mathematical expression is:

[0025]

[0026] Among them, T h_max To optimize the maximum thickness of the rear airfoil, For the original airfoil's maximum thickness, |C m|Ma＝1.66 To optimize the pitching moment of the rear airfoil under supersonic conditions, |C m0|Ma＝1.66 |C represents the pitching moment of the original airfoil under supersonic conditions. m|Ma＝0.8 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.8, |C m0|Ma＝0.8 |C represents the pitching moment of the original airfoil at a high subsonic speed of 0.8. m|Ma＝0.82 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.82, |C m0|Ma＝0.82 | represents the pitching moment of the original airfoil at a high subsonic speed of 0.82;

[0027] S6. Select a position with a chordal position range of 4% to 10% of the chord length as the height constraint position of the upper surface near the leading edge of the airfoil. Measure the height of the upper surface at the position and set the constraint condition that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil. Perform the two-dimensional airfoil optimization design of a large sweep and small aspect ratio airfoil.

[0028] The beneficial effects of this invention are as follows:

[0029] The multi-objective optimization design method for wide-speed-domain thin airfoils, as described in this invention, considering three-dimensional influences, can effectively suppress wing leading-edge separation in operational conditions under three-dimensional environments to control drag in subsonic states, and reduce supersonic drag by changing parameters of the lower wing surface near the leading edge. Thus, while achieving supersonic drag reduction and increasing the drag divergence Mach number, drag performance in subsonic states is also guaranteed.

[0030] This invention presents a multi-objective optimization design method for wide-speed-range thin airfoils considering three-dimensional effects, with the core being the control of the upper surface height near the airfoil's leading edge. Due to the significant differences in drag reduction mechanisms between subsonic and supersonic flows, optimization designs that consider drag reduction in supersonic environments often feature a thinning of the leading edge to reduce shock wave drag. Extensive mechanistic analysis of the drag degradation in three-dimensional environments under subsonic conditions reveals that the reduced upper surface height near the leading edge resulting from leading-edge thinning in supersonic optimization weakens the leading-edge anti-separation capability under subsonic conditions, making the leading edge prone to separation and increasing airfoil drag in significant three-dimensional flow environments. However, controlling the height of the upper airfoil surface during optimization and reducing the leading-edge thickness through changes in the lower airfoil shape can maintain the airfoil's subsonic performance while reducing supersonic drag. This, in turn, enhances anti-separation capability in three-dimensional environments, ensuring three-dimensional aerodynamic performance.

[0031] The present invention describes a multi-objective optimization design method for wide-speed-domain thin airfoils that considers three-dimensional influences, specifically for high subsonic three-dimensional airfoil lift coefficient C. L The effect is obvious when the lift coefficient is ≥0.2, and this range of lift coefficients is the necessary range for supersonic aircraft to fly in subsonic environments.

[0032] The present invention provides a wide-velocity-domain thin airfoil multi-objective optimization design method that considers three-dimensional influences. The constraints can be easily added and can be directly added to the optimization design process without changing the overall optimization design framework. It is applicable to all optimization algorithms.

[0033] The multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influence, as described in this invention, significantly reduces the demand for computational resources compared to three-dimensional optimization, saving more than 90% of resources.

[0034] The present invention describes a multi-objective optimization design method for thin airfoils with a wide speed range that considers three-dimensional influences. This method optimizes airfoils for both subsonic and supersonic operating environments and achieves satisfactory performance under three-dimensional conditions.

[0035] The present invention provides a multi-objective optimization design method for thin airfoils with a wide speed range that considers three-dimensional influences. The optimized airfoil can be used for the aerodynamic design of various military and civilian supersonic aircraft, and has good universality. It can be used for the wing aerodynamic design of supersonic transport aircraft, fighter jets, and drones. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the chordal range of a wide-velocity-domain thin airfoil multi-objective optimization design method considering three-dimensional influences as described in this invention.

[0037] Figure 2 This is a schematic diagram showing the comparison before and after optimization of a wide-velocity-domain thin airfoil multi-objective optimization design method considering three-dimensional influences, as described in this invention.

[0038] Where 2 represents the height of the upper surface near the leading edge of the optimized airfoil, and 3 represents the height of the upper surface near the leading edge of the optimized airfoil. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0040] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0041] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with detailed descriptions in conjunction with the accompanying drawings: Specific implementation method one:

[0043] A multi-objective optimization design method for wide-speed-domain thin airfoils considering three-dimensional influences is proposed. Based on general optimization design methods, the height of the upper surface near the leading edge of the airfoil is constrained. The chordal position range of the height constraint on the upper surface near the leading edge of the airfoil is set to 5% to 10% of the chord length. One to two chordal positions are selected for height constraint. The constraint condition is that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil.

[0044] Furthermore, the height of the upper surface of the leading edge with the chordal position at the rear is greater than the height of the upper surface of the leading edge with the chordal position at the front.

[0045] Furthermore, the optimization design method employs one of the following: genetic method, particle swarm optimization method, or surrogate model-based optimization method.

[0046] Furthermore, the aforementioned multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influences is implemented based on ARI_OPT software.

[0047] Furthermore, the specific implementation method of the agent-based optimization method includes the following steps:

[0048] S1. Select the NACA64A204 airfoil as the original airfoil for optimization design;

[0049] S2. Parametrically describe the coordinates of the upper and lower surfaces of the airfoil, and perform parametric optimization design of the airfoil based on the Hicks-Henne shape function. The calculation formula is as follows:

[0050]

[0051]

[0052] Among them, y us.basic For the original airfoil upper surface function, y us To optimize the upper surface function of the rear airfoil, y ls.basic For the original airfoil's lower surface function, y ls To optimize the lower surface function of the rear airfoil, f i Let a be the perturbation function. i To optimize the corresponding coefficients of the upper surface function of the rear airfoil, b i To optimize the corresponding coefficients of the lower surface function of the rear airfoil, a i and b i These are design variables for the airfoil optimization process;

[0053] S3. The dynamic mesh in the optimization process is implemented based on the radial basis function method. The formula for calculating the radial basis function is:

[0054]

[0055] Where F(r) is the interpolation function, ||rr i || is the vector from r to r i distance, These are the weighting coefficients corresponding to the radial basis functions;

[0056] S4. Set the surrogate model to the Kring model, set the optimization conditions for the optimization objective, and then transform it into a two-dimensional airfoil. The resulting mathematical expression is:

[0057]

[0058] in, The drag is at Mach number 1.66 and lift coefficient 0.175. The drag is at Mach number 0.8 and lift coefficient 0.44. The drag at Mach number 0.82 and lift coefficient 0.44;

[0059] S5. Set the maximum thickness constraint and the torque constraint in each state during the optimization process. The resulting mathematical expression is:

[0060]

[0061] Among them, T h_max To optimize the maximum thickness of the rear airfoil, For the original airfoil's maximum thickness, |C m|Ma＝1.66 To optimize the pitching moment of the rear airfoil under supersonic conditions, |C m0|Ma＝1.66 |C represents the pitching moment of the original airfoil under supersonic conditions. m|Ma＝0.8 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.8, |C m0|Ma＝0.8 |C represents the pitching moment of the original airfoil at a high subsonic speed of 0.8. m|Ma＝0.82 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.82, |C m0|Ma＝0.82 | represents the pitching moment of the original airfoil at a high subsonic speed of 0.82;

[0062] S6. Select the chordal position range as the height constraint position of the upper surface near the leading edge of the airfoil, measure the height of the upper surface at the position, and set the constraint condition that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil, and carry out the two-dimensional airfoil optimization design of a large sweep and small aspect ratio airfoil.

[0063] Furthermore, the constraint expression for ensuring that the height of the upper leading edge surface of the optimized airfoil is not lower than the height of the upper leading edge surface of the original airfoil is as follows:

[0064] y-y0>0

[0065] Where y0 is the height of the upper leading edge surface of the original airfoil, and y is the height of the upper leading edge surface of the optimized airfoil;

[0066] Furthermore, when selecting two chord-direction points x1 and x2 for optimization design, x1 is the position where the chord is in front relative to x2. The height of the upper surface of the airfoil at position x1 is y1, and the height of the upper surface of the airfoil at position x2 is y2. Then, the constraint expression for ensuring that the height of the leading edge upper surface of the optimized airfoil is not lower than the height of the leading edge upper surface of the original airfoil is:

[0067] y x＝x1 ≥y1

[0068] y x＝x2 ≥y2

[0069] y x＝x1 >y x＝x2

[0070] Among them, y x＝x1 After optimizing the height of the upper surface of the leading edge of the airfoil at position x1, y x＝x2 The height of the upper leading edge surface of the airfoil is optimized for position x2.

[0071] This embodiment describes a multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influences. By constraining the height, it maintains or increases the flow velocity on the upper surface near the leading edge of the airfoil, thereby reducing the three-dimensional lateral flow component and suppressing leading-edge separation. The longitudinal coordinate of the upper surface of the airfoil within the chord length range at this position is set to be no less than the longitudinal coordinate value of the original airfoil at the response position. Samples that do not meet the constraints are automatically screened out during optimization. Within this chord length range, selecting 1 to 2 chord positions for height constraints can meet the design requirements. Specific Implementation Method Two:

[0073] A multi-objective optimization design method for wide-speed-domain thin airfoils considering three-dimensional influences is proposed. Based on general optimization design methods, the height of the upper surface near the leading edge of the airfoil is constrained. The chordal position range of the height constraint of the upper surface near the leading edge of the airfoil is set to 4% to 8% of the chord length. One to two chordal positions are selected for height constraint. The constraint condition is that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil.

[0074] Furthermore, the height of the upper surface of the leading edge with the chordal position at the rear is greater than the height of the upper surface of the leading edge with the chordal position at the front.

[0075] Furthermore, the optimization design method employs one of the following: genetic method, particle swarm optimization method, or surrogate model-based optimization method.

[0076] Furthermore, the aforementioned multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influences is implemented based on ARI_OPT software.

[0077] Furthermore, the specific implementation method of the agent-based optimization method includes the following steps:

[0078] S1. Select the NACA64A204 airfoil as the original airfoil for optimization design;

[0079] S2. Airfoil parametric optimization design based on Hicks-Henne shape function, the calculation formula is as follows:

[0080]

[0081]

[0082] Among them, yus.basic For the original airfoil upper surface function, y us To optimize the upper surface function of the rear airfoil, y ls.basic For the original airfoil's lower surface function, y ls To optimize the lower surface function of the rear airfoil, f i Let a be the perturbation function. i To optimize the corresponding coefficients of the upper surface function of the rear airfoil, b i To optimize the corresponding coefficients of the lower surface function of the rear airfoil, a i and b i These are design variables for the airfoil optimization process;

[0083] S3. The dynamic mesh in the optimization process is implemented based on the radial basis function method. The formula for calculating the radial basis function is:

[0084]

[0085] Where F(r) is the interpolation function, ||rr i || is the vector from r to r i distance, These are the weighting coefficients corresponding to the radial basis functions;

[0086] S4. Set the surrogate model to the Kring model, set the optimization conditions for the optimization objective, and then transform it into a two-dimensional airfoil. The resulting mathematical expression is:

[0087]

[0088] in, The drag is at Mach number 1.66 and lift coefficient 0.175. The drag is at Mach number 0.8 and lift coefficient 0.44. The drag at Mach number 0.82 and lift coefficient 0.44;

[0089] S5. Set the maximum thickness constraint and the torque constraint in each state during the optimization process. The resulting mathematical expression is:

[0090]

[0091] Among them, T h_max To optimize the maximum thickness of the rear airfoil, For the original airfoil's maximum thickness, |C m|Ma＝1.66 To optimize the pitching moment of the rear airfoil under supersonic conditions, |C m0|Ma＝1.66 |C represents the pitching moment of the original airfoil under supersonic conditions. m|Ma＝0.8 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.8, |C m0|Ma＝0.8|C represents the pitching moment of the original airfoil at a high subsonic speed of 0.8. m|Ma＝0.82 To optimize the pitching moment of the rear airfoil under high subsonic speed of 0.82, |C m0|Ma＝0.82 | represents the pitching moment of the original airfoil at a high subsonic speed of 0.82;

[0092] S6. Select the chordal position range as the height constraint position of the upper surface near the leading edge of the airfoil, measure the height of the upper surface at the position, and set the constraint condition that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil, and carry out the two-dimensional airfoil optimization design of a large sweep and small aspect ratio airfoil.

[0093] Furthermore, the calculation expression for ensuring that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil is as follows:

[0094] y / y0>1

[0095] Where y0 is the height of the upper leading edge surface of the original airfoil, and y is the height of the upper leading edge surface of the optimized airfoil;

[0096] Furthermore, when selecting two chord-direction points x1 and x2 for optimization design, x1 is the position where the chord is in front relative to x2. The height of the upper surface of the airfoil at position x1 is y1, and the height of the upper surface of the airfoil at position x2 is y2. Then, the constraint expression for ensuring that the height of the leading edge upper surface of the optimized airfoil is not lower than the height of the leading edge upper surface of the original airfoil is:

[0097] y x＝x1 ≥y1

[0098] y x＝x2 ≥y2

[0099] y x＝x1 >y x＝x2

[0100] Among them, y x＝x1 After optimizing the height of the upper surface of the leading edge of the airfoil at position x1, y x＝x2 The height of the upper leading edge surface of the airfoil is optimized for position x2.

[0101] A comparison was made between airfoils OPT1 and OPT2 obtained without optimization using the method of this invention, and airfoils OPT3 and OPT4 obtained using the method of this invention. The drag of these airfoils is comparable in two dimensions, but the results of verification in a three-dimensional environment with a small aspect ratio airfoil and a 50° sweep are shown in Table 1. In the table, the corresponding values ​​for subsonic and supersonic drag reduction are the drag reduction values ​​relative to the original airfoil, with drag reduction being positive; among the increases in drag divergence Mach number relative to the original airfoil, the increase in divergence Mach number is positive. It can be seen that by applying the method of this invention, the subsonic drag performance of the optimized airfoil in a three-dimensional environment is significantly improved.

[0102] Table 1 Comparison of the effects of airfoils with and without the application of this invention in a three-dimensional environment.

[0103] state Original airfoil OPT1 OPT2 OPT3 OPT4 Subsonic drag reduction 0 -8 -5 +6 -1 Supersonic drag reduction 0 +16 +19 +17 +7 Increased Mach number due to drag divergence 0 +0.02 +0.02 +0.02 +0.04

[0104] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0105] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for multi-objective optimization design of wide speed range thin airfoils considering three-dimensional effects, characterized in that: Based on the general optimization design method, the height of the upper surface near the leading edge of the airfoil is constrained. The chord position range of the height constraint of the upper surface near the leading edge of the airfoil is set to 4%~10% of the chord length. One or two chord positions are selected for height constraint. The constraint condition is that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil. The optimization design method adopts an optimization approach based on a surrogate model; The specific implementation method of the optimization method based on the surrogate model includes the following steps: S1. Select the original airfoil and optimize its design; S2. Parametrically describe the coordinates of the upper and lower surfaces of the airfoil, and perform parametric optimization design of the airfoil based on the Hicks-Henne shape function. The calculation formula is as follows: ； wherein, is the original airfoil upper surface function, is the optimized airfoil upper surface function, is the original airfoil lower surface function, is the optimized airfoil lower surface function, is the perturbation function, is the optimized airfoil upper surface function corresponding coefficient, is the optimized airfoil lower surface function corresponding coefficient, and is the design variable of the airfoil optimization process; S3. The dynamic mesh in the optimization process is implemented based on the radial basis function method. The formula for calculating the radial basis function is: ； in, It is an interpolation function. It is vector r to distance, These are the weighting coefficients corresponding to the radial basis functions; S4. Set the surrogate model to the Kring model, set the optimization conditions for the optimization objective, and then transform it into a two-dimensional airfoil. The resulting mathematical expression is: ； in, The drag is at Mach number 1.66 and lift coefficient 0.

175. The drag is at Mach number 0.8 and lift coefficient 0.

44. The drag at Mach number 0.82 and lift coefficient 0.44; S5. Set the maximum thickness constraint and the torque constraint in each state during the optimization process. The resulting mathematical expression is: ； in, To optimize the maximum thickness of the rear airfoil, This is the maximum thickness of the original airfoil. To optimize the pitching moment of the rear airfoil under supersonic conditions, This represents the pitching moment of the original airfoil under supersonic conditions. To optimize the pitching moment of the rear airfoil under high subsonic speed condition of 0.8, The pitching moment of the original airfoil at a high subsonic speed of 0.8 is given. To optimize the pitching moment of the rear airfoil under high subsonic speed condition of 0.82, The pitching moment of the original airfoil at a high subsonic speed of 0.82; S6. Select a position with a chordal position range of 4% to 10% of the chord length as the height constraint position of the upper surface near the leading edge of the airfoil. Measure the height of the upper surface at the position and set the constraint condition that the height of the upper surface of the leading edge of the optimized airfoil is not lower than the height of the upper surface of the leading edge of the original airfoil. Perform a two-dimensional airfoil optimization design for a large sweep and small aspect ratio airfoil.

2. The multi-objective optimization design method for wide-velocity thin airfoils considering three-dimensional influences according to claim 1, characterized in that: The height of the upper surface of the leading edge with the chord direction at the rear is greater than the height of the upper surface of the leading edge with the chord direction at the front.

3. The multi-objective optimization design method for wide-velocity thin airfoils considering three-dimensional influences according to claim 2, characterized in that: The chordal position range for setting the height constraint on the upper surface near the leading edge of the airfoil is 5% to 10% of the chord length.

4. The multi-objective optimization design method for wide-velocity thin airfoils considering three-dimensional influences according to claim 2, characterized in that: The chordal position range for setting the height constraint on the upper surface near the leading edge of the airfoil is 4% to 8% of the chord length.

5. A multi-objective optimization design method for wide-velocity-range thin airfoils considering three-dimensional influences according to claim 3 or 4, characterized in that: The optimization design method employs either the genetic method or the particle swarm optimization method.

6. The multi-objective optimization design method for wide-velocity thin airfoils considering three-dimensional influences according to claim 5, characterized in that: The multi-objective optimization design method for wide-velocity thin airfoils that considers three-dimensional influences is implemented based on ARI_OPT software.

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