Automatic design method of special aerodynamic contraction profile based on bicubic curve equation

Abstract

The application discloses a special-shaped aerodynamic contraction profile automatic design method based on a bicubic curve equation and belongs to the technical field of aviation aerodynamic wind tunnel test. The method solves the problems of many design parameters of the special-shaped aerodynamic profile, artificial calculation and the problem that existing mechanical software auxiliary design is difficult to complete due to a huge amount of calculation in the prior art. The method comprises the following steps: S1. calculating intersection coordinate values of an entrance profile control equation and calculating polar coordinate values corresponding to a feature point group; S2. dividing the aerodynamic contraction profile according to the feature point group, realizing equal phase and equal distance scattering of each zone in the polar coordinate, obtaining corresponding discrete coordinate point groups of entrance and exit sections and saving the discrete coordinate point groups; S3. using a simultaneous equation set, batch calculating coordinate values of each section space coordinate point group; S4. generating a curve according to the coordinate values of the space coordinate point group, generating a surface according to the curve and obtaining the required aerodynamic contraction profile. The application meets the actual engineering requirements and can be applied to the design of a wind tunnel special-shaped aerodynamic contraction profile.

Description

TECHNICAL FIELD

[0001] The present application relates to the automatic design of special aerodynamic contraction profiles, in particular to a method for the automatic design of special aerodynamic contraction profiles based on bicubic curve equations, and belongs to the technical field of aerodynamic wind tunnel testing. BACKGROUND

[0002] Aerodynamics is a basic science for the development of aerospace technology and other industrial technologies, and wind tunnel testing is one of the basic methods for aerodynamic research. As one of the most basic equipment in wind tunnel testing, wind tunnels play a very important role in aerodynamic research and aircraft aerodynamic design. So far, most aerodynamic experiments have been completed in wind tunnels, and therefore the development of aviation technology is directly related to the development of wind tunnels.

[0003] A wind tunnel is a device that uses a power device to drive a controllable airflow in a pipe system designed according to certain requirements, and performs various aerodynamic tests according to the principles of relativity and similarity. Wind tunnels can be divided into transient wind tunnels and recirculating wind tunnels. A transient wind tunnel consists of an air source, a valve section, a stable section, a nozzle, a test section, an over-expansion section, an under-expansion section, and a silencer tower. A recirculating wind tunnel consists of a driving system, a diffuser section, a test section, a contraction section, a stable section, and a recirculating section. The functions of the various sections of the wind tunnel are different, and the design requirements are also different, resulting in different required profile shapes for each section, which requires transition profiles to change. For some changes in conventional aerodynamic profiles, such as the transition of a circular profile from a large diameter to a small diameter, the design parameters are few and the calculation amount is small, and manual calculation or the use of existing drawing software for auxiliary design can solve the problem well. However, for special wind tunnel design conditions that require special wind tunnels or special wind tunnels, three-dimensional special aerodynamic profiles are required. The profile changes of three-dimensional special aerodynamic profiles are large, the design parameters are many, there are many uncertain factors, and the calculation amount is huge. For example, to calculate a profile with 1000 interpolation points, several thousand two-dimensional quadratic equations and two-dimensional linear equations need to be solved to determine the three-dimensional coordinates of the 1000 interpolation points, and the correct solutions need to be selected manually. Purely manual calculation and existing mechanical design software for auxiliary design are difficult to complete and prone to errors, and it is difficult to meet the needs of engineering practice.

[0004] Therefore, it is necessary to propose a complex special aerodynamic profile automatic design method suitable for wind tunnels, which can efficiently and accurately design complex special aerodynamic profiles through computer language according to given profile design equations and input parameters, to solve the above problems. SUMMARY

[0005] The following presents a simplified summary of the application in order to provide a basic understanding of some aspects of the application. This summary is not an extensive overview of the application. It is not intended to identify key or critical elements of the application or to delineate the scope of the application. Its sole purpose is to present some concepts of the application in a simplified form as a prelude to the more detailed description that is presented later.

[0006] In view of this, in order to solve the problems of many design parameters of special-shaped aerodynamic profile, artificial calculation and difficulty in completing the calculation of existing mechanical design software aided design due to huge calculation amount in the prior art, the application provides an automatic design method of special-shaped aerodynamic contraction profile based on a bicubic curve equation.

[0007] The technical scheme is as follows: the automatic design method of special-shaped aerodynamic contraction profile based on a bicubic curve equation comprises the following steps:

[0008] S1. Calculate the intersection coordinate value of the inlet profile control equation, determine the feature point group, and calculate and store the corresponding polar coordinate value of the feature point group;

[0009] S2. Divide the aerodynamic contraction profile according to the feature point group, realize equal-phase discretization and equal-distance discretization of each zone in polar coordinates, obtain the corresponding discretization coordinate point group of the inlet and outlet cross sections, and save them;

[0010] S3. Use the simultaneous equation set to solve through program loop, and batch calculate the coordinate value of each cross section space coordinate point group;

[0011] S4. Generate a curve according to the coordinate value of the space coordinate point group, generate a surface according to the curve, and obtain the required aerodynamic contraction profile.

[0012] Further, in S1, the following steps are included:

[0013] S11. Design the profile using a bicubic curve equation to obtain a profile control equation, and input the shape equation of the inlet and outlet profiles of the contraction section;

[0014] S12. Call the sympy library in Python, use the solve function to solve the intersection coordinate value of the inlet and outlet profile control equation, determine the feature point group Q, call the math library, and solve and save the corresponding polar coordinate value of the feature point group Q.

[0015] Further, in S11, the profile control equation is expressed as:

[0016] When ,

[0017] When ,

[0018] wherein x is the axial distance, D is the cross-sectional diameter at x, the axial distance, D is the cross-sectional diameter at x, the axial distance is the cross-sectional diameter at x, D1 is the cross-sectional diameter at the inlet of the contraction section, D2 is the cross-sectional diameter at the outlet of the contraction section, L is the length of the contraction section, and X is a constant with a value of 0.5;

[0019] In the S12, the feature point group Q is an inflection point that changes the direction of the curve in the shape equation of the inlet and outlet profile of the contraction section.

[0020] Further, in the S2, the following steps are included:

[0021] S21. The aerodynamic contraction profile is divided according to the angle value of the polar coordinates of the feature point group Q, and the input function is called to input the discretization parameters of each division;

[0022] S22. The discretization parameters in the spatial direction are input, and the cut function in the pandas library is called to divide according to the input discretization parameters, to realize equal-phase discretization and equal-distance discretization of each zone in polar coordinates, to obtain the corresponding discretization coordinate point group O of the inlet and outlet cross sections and to save them.

[0023] Further, in the S3, the following steps are included:

[0024] S31. The sqrt function and for loop statement in the math library are called to calculate the value of the cross-sectional diameter D at the axial distance x, and the first supplementary equation, the specific design criterion equation, and the second supplementary equation are set;

[0025] In the S31, according to the input discretization parameters in the spatial direction and the calculated corresponding discretization coordinate point group O of the inlet and outlet cross sections, the cut function in the pandas library is called to divide to obtain the value of the axial distance x, and the value of the cross-sectional diameter D at the axial distance x is calculated; the axial distance x, the cross-sectional diameter D1 at the inlet of the contraction section, the cross-sectional diameter D2 at the outlet of the contraction section, the length L of the contraction section, and the value of X as 0.5 are substituted into the bicubic curve equation and the specific design criterion equation and solved using the for loop statement to obtain the value of the cross-sectional diameter D at the axial distance x;

[0026] The first supplementary equation is a circular first supplementary equation space profile constructed with the cross-sectional diameter D at the axial distance x, the specific design criterion equation is a specific design criterion equation cross section constructed in parallel with the Z-axis, and the second supplementary equation is a second supplementary equation cross section constructed with the coordinates required by the design and perpendicular to the Z-axis; the Z-axis;​

[0027] The first supplementary equation is expressed as:

[0028]

[0029] The specific design criterion equation is expressed as:

[0030]

[0031] The values of the constants a and b can be obtained by substituting the values of the corresponding discrete coordinate point groups O of the inlet and outlet sections into the equation.

[0032] The second supplementary equation is expressed as:

[0033]

[0034] wherein, The direction section of the coordinate, The coordinate, is a given constant required for design, The direction section is perpendicular to the axis;

[0035] S32. Call the sympy library in Python to solve the values of the constants a and b in the specific design criterion equation using the solve function.

[0036] S33. Call the sympy library in Python to solve the solutions of the equation set consisting of the first supplementary equation, the specific design criterion equation, and the second supplementary equation using the solve function, and use the for loop statement to obtain all the solutions of the equation set, i.e., obtain the coordinate values of the required spatial coordinate point groups.

[0037] In the S33, the solutions of the equation set consisting of the first supplementary equation, the specific design criterion equation, and the second supplementary equation are ( , , ).

[0038] Further, in the S4, the geopandas library in Python is called to create a curve with the obtained coordinate values of the spatial coordinate point groups at each section, and the curves created by each section are used to form a surface, thereby obtaining the required aerodynamic contraction surface.

[0039] ​​The beneficial effects of the present application are as follows: the present application inputs a contraction section profile end face shape equation, inputs discretization calculation parameters; determines characteristic points and calculates characteristic point coordinates, partitions the aerodynamic contraction profile according to the end face characteristic points; judges whether each zone satisfies the equal phase discretization condition, if yes, discretizes according to the equal phase, if not, discretizes according to the equal distance; inputs a profile control equation and a specific design criterion equation composed of spatial Z direction discrete points at the same position, according to the profile control equation, the specific design criterion equation and the cross section position equation, batch automatically calculates the values of the spatial cross section discrete coordinate points; generates a curve according to the coordinate points, generates a surface according to the curve, so as to obtain the required aerodynamic contraction profile. The present application realizes the automatic calculation of the special aerodynamic contraction profile with large profile change and multiple control parameters through computer language, for example, for coordinate point encryption or design change such as increasing or reducing the design cross section, only the input parameters need to be changed, and the required result can be automatically calculated; and the present application partitions, sets the characteristic points, so that the automatic calculation does not disappear the typical characteristics of the profile due to interpolation, and is more accurate for different profiles. BRIEF DESCRIPTION OF DRAWINGS

[0040] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and serve to explain the principles of the application. In the drawings:

[0041] Figure 1 It is a flowchart of the automatic design method of the special aerodynamic contraction profile based on the bicubic curve equation;

[0042] Figure 2 It is a schematic diagram for characteristic point group capture and partition;

[0043] Figure 3 It is a schematic diagram of the cross section of the special aerodynamic contraction profile equation group;

[0044] Figure 4 It is a schematic diagram of an example of an inlet circular cross section and an outlet 90° fan-shaped cross section;

[0045] Figure 5 It is a schematic diagram of an example of an inlet circular cross section and an outlet 180° fan-shaped cross section.

[0046] FIG. 1 is a first partition; FIG. 2 is a second partition; FIG. 3 is a third partition; FIG. 4 is a fourth partition; FIG. 5 is a first outlet cross section profile line; FIG. 6 is a second outlet cross section profile line; FIG. 7 is a third outlet cross section profile line; FIG. 8 is a fourth outlet cross section profile line; FIG. 9 is a ridge line; FIG. 10 is a first characteristic point; FIG. 11 is a second characteristic point; FIG. 12 is a third characteristic point; FIG. 13 is a fourth characteristic point; 3-1 is a first supplementary equation space profile; 3-2 is a specific design criterion equation cross section; 3-3 is a second supplementary equation cross section; and 3-4 is an intersection point. DETAILED DESCRIPTION

[0047] In order to make the technical solutions and advantages of the embodiments of the present application clearer, the exemplary embodiments of the present application are further described in detail below with reference to the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0048] Reference Figures 1-5 The automatic design method of the special-shaped aerodynamic contraction profile based on the bicubic curve equation includes the following steps:

[0049] S1. Calculate the intersection coordinate value of the inlet profile control equation, determine the feature point group, and calculate and store the polar coordinate value corresponding to the feature point group;

[0050] The specific steps are as follows:

[0051] S11. Design the profile by using the bicubic curve equation to obtain the profile control equation, and input the shape equation of the inlet and outlet profiles of the contraction section;

[0052] S12. Call the sympy library in Python, use the solve function to solve the intersection coordinate value of the inlet and outlet profile control equation, determine the feature point group Q, call the math library, and calculate and save the polar coordinate value corresponding to the feature point group Q;

[0053] Specifically, the object in the present embodiment is the complex special-shaped aerodynamic contraction section profile of a certain wind tunnel. The inlet of the contraction section is a circular cross section, and the outlet is a 90° sector cross section. Therefore, the contraction profile from each point on the inlet to the outlet is different, so the inlet and outlet are discretized, and each corresponding point of the inlet and outlet has a contraction curve. The entire contraction section is fitted by multiple curves.

[0054] In the present embodiment, the center of the circular cross section of the inlet of the contraction section is taken as the coordinate origin to establish a space rectangular coordinate system, and the coordinate axes are represented by three axes perpendicular to each other. 、 、 The axis is perpendicular to the circular cross section of the inlet of the contraction section. The present contraction section profile design uses the bicubic curve equation to design the profile to obtain the profile control equation.

[0055] The profile control equation is expressed as:

[0056] When ,

[0057] When ,

[0058] wherein x is a Cartesian coordinate system axial distance, D is axial distance is the cross-sectional diameter at x, D1 is the cross-sectional diameter at the entrance of the contraction section, D2 is the cross-sectional diameter at the exit of the contraction section, L is the length of the contraction section, and X is a constant with a value of 0.5;

[0059] According to the shapes of the two end faces of the contraction section, i.e., the circular entrance and the fan-shaped exit, the shape equation of the end face of the contraction section is inputted into the embodiment.

[0060] The shape equation of the entrance of the end face of the contraction section is represented as:

[0061]

[0062] wherein the entrance shape of the end face of the contraction section is a circular entrance cross-sectional profile, is the radius of the entrance cross-sectional profile, is the coordinate point of the entrance cross-sectional profile;

[0063] The shape equation of the exit of the end face of the contraction section is represented as:

[0064]

[0065] wherein the exit cross section is a 90° fan-shaped annulus formed by four lines represented by the shape equation of the exit of the end face of the contraction section, i.e., the first exit cross-sectional profile 5, the second exit cross-sectional profile 6, the third exit cross-sectional profile 7, and the fourth exit cross-sectional profile 8, , is the radius of the second exit cross-sectional profile 6 and the fourth exit cross-sectional profile 8, is the coordinate point of the second exit cross-sectional profile 6, is the coordinate point of the second exit cross-sectional profile 8, is the coordinate point of the second exit cross-sectional profile 5, is the coordinate point of the second exit cross-sectional profile 7;

[0066] In the embodiment, the feature point group Q is the inflection point of the four lines represented by the shape equation of the exit, i.e., the first feature point 10, the second feature point 11, the third feature point 12, and the fourth feature point 13.

[0067] S2. According to the feature point group, the aerodynamic contraction profile is divided into zones, the equal-phase discretization and equal-distance discretization in polar coordinates are realized, and the corresponding discretized coordinate point groups of the entrance and exit cross sections are saved.

[0068] The specific steps are as follows:

[0069] S21. Partition the aerodynamic convergent profile according to the angle value of the polar coordinates of the feature point group Q, and call the input function to input the discrete parameters of each partition;

[0070] S22. Input the discrete parameters in the space z direction, and according to the input discrete parameters, call the cut function in the pandas library to divide, realize the equal phase discretization and equal distance discretization of each zone in the polar coordinates, obtain the corresponding discrete coordinate point group O of the inlet and outlet cross sections and save them;

[0071] Specifically, according to the shapes of the first outlet cross section profile 5, the second outlet cross section profile 6, the third outlet cross section profile 7 and the fourth outlet cross section profile 8, the first feature point 10, the second feature point 11, the third feature point 12 and the fourth feature point 13 are extracted, the entire convergent section is divided into the first partition 1, the second partition 2, the third partition 3 and the fourth partition 4, the discrete parameters are input, the spatial phase of the discrete coordinate points of each zone is automatically calculated by using the cut function in the pandas library, and the division is judged, so that each zone that can be discretized in equal phase is discretized in equal phase, the discrete coordinate point values of each zone end surface are automatically calculated according to the spatial phase, the density of the discrete coordinate points of each zone is determined, and if each zone cannot be discretized in equal phase, the horizontal coordinate or vertical coordinate equal distance discretization is performed. In the embodiment, the first partition 1, the second partition 2 and the third partition 3 are discretized in equal phase, and the fourth partition 4 is discretized in equal distance of the horizontal coordinate, and the discrete method is that each cross section is discretized into n coordinate points, and each cross section is discretized into m discrete coordinate points, including m cross sections between the inlet section and the outlet section.

[0072] S3. Batch calculate the coordinate values of the space coordinate point group of each cross section by using the simultaneous equation set and program loop solving;

[0073] The specific steps are as follows:

[0074] S31. Calculate the value of the cross section diameter D at the axial distance x by calling the sqrt function in the math library and the for loop statement, and set the first supplementary equation, the specific design criterion equation and the second supplementary equation;

[0075] S32. Call the sympy library in Python, and use the solve function to solve the values of the constants a and b in the specific design criterion equation;

[0076] S33. Call the sympy library in Python, use the solve function to solve the simultaneous equation set of the first supplementary equation, the specific design criterion equation and the second supplementary equation, and use the for loop statement to obtain the solutions of all the equation sets, that is, the coordinate values of the required space coordinate point group;

[0077] ​Specifically, the contraction section inlet section diameter D1 in the profile control equation of each inlet section discrete coordinate point is determined according to the distance from the inlet coordinate to the coordinate origin on the inlet section, the contraction section outlet section diameter D2 in the profile control equation of each outlet section discrete coordinate point is determined according to the distance from the outlet coordinate to the coordinate origin on the outlet section, and the section position is determined according to the axial distance x The value of the axial distance x is substituted into the profile control equation to obtain the section diameter D at the axial distance x, and a total of D values are obtained.

[0078] In the embodiment, the first supplementary equation is represented as the first supplementary equation space profile 3-1, the specific design criterion equation is represented as the specific design criterion equation section 3-2, and the second supplementary equation is represented as the second supplementary equation section 3-3.

[0079] The first supplementary equation is represented as:

[0080]

[0081] Reference Figure 3 To ensure the consistency of the projection of the space coordinate points and ensure that the lines connecting the corresponding coordinate points in each space do not intersect each other, it is required that the specific design criterion equation section 3-2 and the first supplementary equation space profile 3-1 are parallel to the axis.

[0082] The specific design criterion equation is represented as:

[0083]

[0084] The values of the constants a and b are obtained by substituting the values of the corresponding discrete coordinate point groups O of the inlet and outlet sections into the equation, and a total of values of the parameter a and values of the parameter b are obtained.

[0085] The second supplementary equation is represented as:

[0086]

[0087] Wherein, is the coordinate of the directional section, is a given constant required for design, in the embodiment, 10 directional sections are selected, and the values of the coordinates of the 10 directional sections are 50 mm, 100 mm, 150 mm, 200 mm, 250 mm, 300 mm, 350 mm, 400 mm, 450 mm, and 500 mm, respectively, and the 10 sections are all perpendicular to the axis, and reference is made to Figure 3 ​​, the second supplementary equation section 3-3 is one of the direction sections;

[0088] The first supplementary equation, the specific design criterion equation and the second supplementary equation are combined, and the parameters D, a and b are transformed to solve the equation group. The solution of the embodiment is , , According to different engineering environment needs, different conditions can be set, unreasonable solutions can be discarded, and reference Figure 3 The intersection point 3-4 of the first supplementary equation space profile 3-1, the specific design criterion equation section 3-2 and the second supplementary equation section 3-3 is the coordinate value of the space coordinate point group obtained by the solution of the embodiment.

[0089] S4. Call the geopandas library in Python to create a curve with the obtained coordinate values of each section space coordinate point group, and construct a surface with the curves created by each section to obtain the required aerodynamic contraction profile;

[0090] Specifically, each section space coordinate point is connected into a curve by spline interpolation, and each section curve is generated into a surface by spline interpolation to obtain the generated contraction segment space surface, i.e. the aerodynamic contraction profile, as shown in Figure 4 The entrance is a circular section, and the exit is a 90° fan-shaped section. The above obtained aerodynamic contraction profile has been verified by wind tunnel test, the contraction surface flow field is uniform, the aerodynamic performance is good, and meets the needs of engineering practice. Figure 5 The entrance is a circular section, and the exit is a 180° fan-shaped section. The above obtained aerodynamic contraction profile has been verified by wind tunnel test, the contraction surface flow field is uniform, the aerodynamic performance is good, and meets the needs of engineering practice.

[0091] Although the present application is described according to a limited number of embodiments, those skilled in the art, with the benefit of the above description, will understand that other embodiments can be conceived within the scope of the application described herein, and that the method of the present application is not limited to a specific computing language, and is satisfied with this design method. In addition, it should be noted that the language used in this specification is mainly selected for readability and teaching purposes, rather than for explaining or limiting the subject matter of the present application. Therefore, many modifications and changes are obvious to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the present application is illustrative, not limiting, and the scope of the present application is defined by the appended claims.

Claims

1. A method for automatic design of a profile of a special aerodynamic convergent surface based on a bicubic curve equation, characterized in that, The method comprises the following steps: S1. Calculate the intersection coordinate values of the inlet profile control equation, determine the feature point group, and calculate and store the corresponding polar coordinate values of the feature point group; S2. Divide the aerodynamic contraction surface according to the feature point group, realize equal-phase discretization and equal-distance discretization of each zone in the polar coordinate, obtain the corresponding discretized coordinate point group of the inlet and outlet cross sections, and save them; S3. Use the simultaneous equation set to solve through program loops to batch calculate the coordinate values of the spatial coordinate point group of each cross section; S4. Generate a curve according to the coordinate values of the spatial coordinate point group, generate a surface according to the curve, and obtain the required aerodynamic contraction surface; In S2, the following steps are included: S21. Divide the aerodynamic contraction surface according to the angle values of the polar coordinates of the feature point group Q, and call the input function to input the discretization parameters of each zone; S22. Input space The discretization parameter of the direction is divided according to the input discretization parameter, the cut function in the pandas library is called to realize the equal phase discretization and the equal distance discretization of each area in the polar coordinate, and the corresponding discretization coordinate point group O of the exit and entrance section is obtained and saved. In S3, the following steps are included: S31. Call the sqrt function in math library and for loop statement to calculate The value of the cross-sectional diameter D at the axial distance x is determined and the first supplementary equation, the specific design criterion equation and the second supplementary equation are set. In the S31, according to the input space The discrete parameter of the direction and the corresponding discrete coordinate point group O of the calculated inlet and outlet section are called to divide and obtain The value of the axial distance x, the value of the section diameter D at the axial distance x The value of the axial distance x, the value of the section diameter D at the axial distance x The value of the axial distance x, the value of the section diameter D at the axial distance x The value of the axial distance x, the value of the section diameter D at the axial distance x The first supplementary equation is as follows: The first supplementary equation spatial surface of the circle is constructed by the diameter D of the cross-section at an axial distance of x. The specific design criterion equation is the cross-section constructed parallel to the Z-axis. The second supplementary equation is based on the design requirements. Coordinate construction and The second supplementary equation section perpendicular to the axis; The first supplementary equation is represented as: ； The specific design criterion equation is represented as: ； wherein the values of the constants a and b can be obtained by substituting the values of the corresponding discretized coordinate point group O of the inlet and outlet cross sections into the equation; The second supplementary equation is represented as: ； in, for directional section coordinate, Given the constants required for the design, Directional section and The axis is perpendicular; S32. Call the sympy library in Python, and use the solve function to solve the values of the constants a and b in the specific design criterion equation; S33. Call the sympy library in Python, use the solve function to solve the solutions of the specific design criterion equation, the supplementary equation, and the equation set determined by the position of the cross section and the coordinate points on the cross section satisfying the equation, and use the for loop statement to obtain the solutions of all the equation sets, that is, the coordinate values of the required spatial coordinate point array; In S33, the solution to the system of equations formed by the first supplementary equation, the specific design criterion equation, and the second supplementary equation is ( , , ).

2. The automatic design method of a special-shaped aerodynamic contraction profile based on a bicubic curve equation according to claim 1, characterized in that, In S1, the following steps are included: S11. Use a bicubic curve equation to design the surface to obtain a profile control equation, and input the shape equation of the inlet and outlet surfaces of the contraction section; S12. Call the sympy library in Python, use the solve function to solve the intersection coordinate values of the inlet profile control equation, determine the feature point group Q, call the math library, and obtain and save the corresponding polar coordinate values of the feature point group Q.

3. The method of automatic design of a profile of aero-contraction of a special shape based on a bicubic curve equation according to claim 2, characterized in that, In S11, the profile control equation is represented as: When time; When time; Wherein, x is the Cartesian coordinate system Axial distance, D is Axial distance is the cross-sectional diameter at x, D1 is the cross-sectional diameter at the entrance of the contraction section, D2 is the cross-sectional diameter at the exit of the contraction section, L is the length of the contraction section, and X is a constant with a value of 0.

5. In S12, the feature point group Q is the inflection point of the shape equation of the inlet and outlet surfaces of the contraction section that changes the direction of the curve.

4. The method of automatic design of a profile of aerofoils of variable geometry based on bicubic curve equation according to claim 3, characterized in that, In S4, call the geopandas library in Python to create a curve with the coordinate values of the spatial coordinate point group at each cross section, construct a surface with the curves created by each cross section, and thus obtain the required aerodynamic contraction surface.

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