Indirect generation method and system of cross-sound blade profile based on camber line thickening distribution

Abstract

The application discloses a cross-sound indirect generation method of a blade profile based on a camber line thickness distribution and a related device, and relates to the field of aero-engine design. The method comprises the following steps: extracting a camber line and a thickness distribution based on an original blade profile; adding a control point to fit a camber line parameter; adding a control point to fit a thickness distribution parameter; calling a blade profile generation function to generate a camber line, a thickness distribution and suction surface and pressure surface coordinates according to the fitted parameters; generating an elliptical leading edge and a circular trailing edge to smoothly connect with the pressure surface and the suction surface and generate a complete blade profile. The camber line and the thickness distribution are superimposed to control the change of the blade profile, the camber line and the thickness distribution of the blade profile are fitted after being obtained, control points and control parameters are extracted, the camber line and the thickness distribution can be superimposed to generate a suction surface and a pressure surface of the blade profile, the slope is kept consistent at a connecting point to ensure smooth connection, an elliptical leading edge and a circular trailing edge are adopted, and the complete blade profile is simple and convenient to generate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of transonic blade profile design, and particularly relates to a transonic blade profile indirect generation method and system based on a mean camber line thickening distribution. BACKGROUND

[0002] An axial flow compressor is a multi-stage compression device with airflow flowing in the same direction as the rotating shaft of the working wheel, and is composed of a series of alternating stator-rotor arrangements, and is commonly used in an aero-engine or a gas turbine. The blade of the axial flow compressor is an important part of the airflow passage of the compressor for realizing airflow function conversion and changing the airflow direction. The blade profile is a basic unit of the blade, and the blade is formed by stacking the blade profiles along the stacking line.

[0003] The relative Mach number of the inlet of the transonic compressor at a partial blade height is greater than 1, reaching supersonic speed. The transonic stage has complex flow phenomena such as shock wave and mutual interference with the boundary layer, blade tip leakage, and the like, and the shape of the leading edge has an important influence on the blade profile loss of the cascade and the stable operation range of the cascade, which brings great difficulty to the development process of the transonic stage. Therefore, a blade profile design method is proposed to meet the demand of the transonic working condition.

[0004] The current conventional blade profile design directly defines the pressure surface and the suction surface of the blade profile by using a curve, gives the coordinates and curvature requirements of the control points on the pressure surface and the suction surface, and generates the profile line by using a segmented circular arc, a polynomial or a spline function.

[0005] Another way is to design the blade profile by using a multi-circular-arc blade profile, and the blade profile is generated by splicing 2 or more circular arcs.

[0006] The current high-load blade profile mostly adopts a multi-circular-arc blade profile, a free curve form blade profile without a determined curve form and constraint condition, and the blade profile designed in this way has the following defects:

[0007] 1) The loss is large, and the efficiency of the compression component is low under high-speed working conditions;

[0008] 2) The variable attack angle range is narrow, and the compression component has insufficient surge margin;

[0009] 3) The lag angle increases greatly, and the working state of the compression component is greatly deviated from the design value;

[0010] 4) The transition at the multi-end circular arc connection is unstable.

[0011] 5) The shape of the blade leading edge and trailing edge is complex or insufficient in strength by using the curve design method. SUMMARY

[0012] The purpose of the present application is to provide a cross-sound blade profile indirect generation method and system based on camber line thickening distribution, to solve the problem of large loss in the prior art, low efficiency of the compression component under high speed working conditions, narrow variable angle of attack range, large deviation of working state from the design value, and insufficient strength of the transition at the connection.

[0013] To achieve the above purpose, the present application adopts the following technical solutions:

[0014] The cross-sound blade profile indirect generation method based on camber line thickening distribution comprises:

[0015] Extracting camber line and thickness distribution based on the original blade profile;

[0016] Adding control points to fit the camber line parameters;

[0017] Adding control points to fit the thickness distribution parameters;

[0018] According to the fitted parameters, calling a blade profile generation function to generate camber line, thickness distribution, and suction surface and pressure surface coordinates;

[0019] Generating an elliptical leading edge and a circular trailing edge to smoothly connect with the pressure surface and the suction surface to generate a complete blade profile.

[0020] Further, extracting camber line and thickness distribution based on the original blade profile:

[0021] According to the definition of camber line, the original blade profile is inscribed in a circle, and then the camber line is obtained by connecting the centers of the inscribed circles, and the thickness distribution is obtained at the corresponding inscribed circle centers. Specifically, by making the normal line of each inscribed circle center intersect with the suction surface and the pressure surface of the blade profile, the thickness distribution is obtained by connecting each point.

[0022] Further, adding control points to fit the camber line parameters:

[0023] The Bezier curve is used to fit the camber line, the order of the Bezier curve is four, the curve contains five control points, which are p0 to p4, the control points p0 and p4 are fixed, and the positions of the other three control points are optimized;

[0024] Where the blade chord length c = constant

[0025] The following six parameters are converted as variables and the related meanings are given:

[0026] Leading edge direction angle alpha and trailing edge direction angle beta:

[0027] From the endpoint property and tangent property of the Bezier curve:

[0028] ;

[0029] Similarly

[0030] ;

[0031] Deflection variation law parameters j, k: where e, f, g, i are the lengths of the line segments;

[0032]

[0033]

[0034] Deflection variation law parameters h1, h2:

[0035] h1 represents the perpendicular distance from P2 to the straight line P0Pd;

[0036] h2 represents the perpendicular distance from P2 to the straight line P4Pd; point pd is the intersection point of the extensions of P0P1 and P4P3.

[0037] Further, the specific solving steps are: according to the coordinates of control points P0 and pd, the straight line equation Ax+By+C=0 passing through two points is solved, the straight line equation parameters are obtained, and then the deflection variation law parameter h1 is obtained according to the distance from the point to the straight line;

[0038]

[0039] Similarly, according to the coordinates of control points P4 and pd, the straight line equation Dx+Ey+F=0 passing through two points is solved, and the deflection variation law parameter h2 is obtained

[0040] .

[0041] Further, add control points to fit the thickness distribution parameters:

[0042] The transonic airfoil thickness distribution curve is composed of two multi-order Bezier curves smoothly connected, the connecting points are the extreme points of the curve, the derivatives on the left and right sides are both 0, and the coordinate ratio of the horizontal coordinate to the airfoil chord length is the relative position of the maximum thickness; the left part of the curve is represented by a four-order Bezier curve, which contains five control points Ph0-Ph4, and the right part is a three-order Bezier curve, which contains four control points Ph4 and Pt1-Pt3;

[0043] Where: maximum thickness = Constant; trailing edge thickness = Constant;

[0044] The following 7 parameters are extracted as variables:

[0045] Head and tail thickness distribution cut angles θ1 and θ2:

[0046] The end point and tangent vector of Bezier curve are used to get

[0047]

[0048] Similarly, we have

[0049]

[0050] Maximum thickness relative position: ;

[0051]

[0052] The greater the value of m, the position of the maximum thickness of the blade moves to the trailing edge;

[0053] Thickness distribution parameters x1, x2:

[0054]

[0055] The greater the value of x1, the slower the thickness change of the front half of the blade, and the smaller the value of x2, the slower the thickness change of the back half of the blade;

[0056] Thickness distribution parameter y1:

[0057]

[0058] The greater the value of y1, the greater the thickness of the front section of the blade;

[0059] Leading edge thickness: r

[0060]

[0061] The greater the value of r, the smaller the ratio of the minor axis to the major axis of the elliptical arc.

[0062] Further, according to the fitted parameters, the blade profile generation function is called to generate the mean camber line, thickness distribution, and coordinates of the suction surface and pressure surface:

[0063] In the optimization process, the mean camber line of transonic and subsonic blade profiles and the thickness distribution rule of transonic blade profiles are controlled; the coordinates of the control points of the mean camber line and thickness distribution of the blade profile are obtained:

[0064] Mean camber line: mid1=[P0x P1x P2x P3x P4x;P0y P1y P2y P3y P4y];

[0065] Left section of thickness distribution: houdu11=[P0xl P1xl P2xl P3xl P4xl;P0yl P1yl P2yl P3ylP4yl];

[0066] Thickness distribution right segment: houdu12=[P0xr P1xr P2xr P3xr; P0yr P1yr P2yr P3yr];

[0067] The middle arc line, thickness distribution, pressure surface and suction surface coordinates are generated by calling the leaf type generation function first blade:

[0068] Specifically, the middle arc line and thickness distribution 60 are equally divided, the Bezier function is called to generate the control curve of the middle arc line and thickness distribution, and the coordinate points are obtained by spline interpolation; the suction surface and pressure surface coordinates are obtained by adding and subtracting the trigonometric function of the base point coordinates at the same time.

[0069] Further, the elliptical leading edge and the circular trailing edge are generated to smoothly connect with the pressure surface and the suction surface to generate a complete blade profile:

[0070] The elliptical leading edge is generated by solving the elliptical equation and the major axis equation:

[0071]

[0072]

[0073] The coordinates of the trailing edge are obtained by solving the equation composed of the circle and the suction surface and pressure surface; the slope is kept consistent at the connection point to obtain the transonic blade profile with the middle arc line and thickness distribution, the elliptical leading edge and the circular trailing edge.

[0074] Further, an indirect generation system of a transonic blade profile based on a middle arc line and thickness distribution, comprising:

[0075] A data extraction module for extracting the middle arc line and thickness distribution based on the original blade profile;

[0076] A parameter fitting module for adding control points to fit the parameters of the middle arc line and thickness distribution;

[0077] A coordinate generation module for generating the middle arc line, thickness distribution, and suction surface and pressure surface coordinates by calling the blade profile generation function according to the fitted parameters;

[0078] A blade profile generation module for generating an elliptical leading edge and a circular trailing edge to smoothly connect with the pressure surface and the suction surface to generate a complete blade profile.

[0079] Further, a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to realize the steps of the indirect generation method of the transonic blade profile based on the middle arc line and thickness distribution.

[0080] Further, a computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of the cross-sound blade indirect generation method based on the mid-chord line thickening distribution.

[0081] Compared with the prior art, the present application has the following technical effects:

[0082] The present application is mainly used for parameterization processing and modeling of transonic blades, based on the construction method of the mid-chord line and the thickness distribution, aiming at the characteristics of large thickness variation and complex mid-chord line of transonic blades, the mid-chord line is superimposed with the thickness distribution to control the variation of the blade profile, after obtaining the mid-chord line and the thickness distribution of the blade profile, fitting is performed, 13 control variables are extracted, the suction surface and the pressure surface of the blade profile can be generated by superimposing the mid-chord line and the thickness distribution, the leading edge adopts an ellipse, and the trailing edge adopts a circular arc to generate a complete blade profile.

[0083] 1) The present application is used for transonic working conditions, but is suitable for various working conditions, and the blade profile designed by the method has small leading edge thickness, which reduces the shock wave to a certain extent;

[0084] 2) The present application parameterizes the blade profile parameters, and uses 13 control variables to control the mid-chord line and the thickness distribution, which meets the characteristics of large thickness variation and complex mid-chord line of transonic blades;

[0085] 3) The blade profile curve generated by the present application is smooth, smooth and coherent, and also improves the problems of strange and low strength of the blade profile generated by other modeling methods.

[0086] 4) The main reason for the high requirement of transonic blade design is high load and the influence of shock wave, the designed blade profile can control the influence of shock wave through numerical calculation verification (CFD), and the shock wave strength is reduced to a certain extent, and the loss is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0087] Figure 1 A flowchart for generating a mid-chord line thickening blade profile.

[0088] Figure 2 A drawing for extracting a blade profile mid-chord line.

[0089] Figure 3 A drawing for extracting a blade profile thickness distribution.

[0090] Figure 4 A modeling schematic diagram of a blade profile mid-chord line.

[0091] Figure 5 A modeling schematic diagram of a blade profile thickness distribution curve.

[0092] Figure 6 A performance curve comparison between a transonic blade profile prototype and a representative scheme.

[0093] Figure 7 Contrast the suction surface Mach number cloud of the transonic blade profile prototype and the representative scheme. DETAILED DESCRIPTION

[0094] The application is further described below in conjunction with the accompanying drawings:

[0095] Please refer to Figures 1 to 5 , the application is mainly used for parameterization processing and modeling of transonic blades, based on the construction method of camber line and thickness distribution of blades, aiming at the characteristics of large thickness variation and complex camber line of transonic blades, the variation of the blade profile is controlled by superimposing the camber line and the thickness distribution, after obtaining the camber line and the thickness distribution of the blade profile, fitting is performed, 13 control variables are extracted, the camber line and the thickness distribution can be superimposed to generate the suction surface and the pressure surface of the blade profile, the leading edge adopts an ellipse, and the trailing edge adopts a circular arc to generate a complete blade profile.

[0096] The variation of the blade profile is controlled by superimposing the camber line and the thickness distribution, after obtaining the camber line and the thickness distribution of the blade profile, fitting is performed, control points and control parameters are extracted, the camber line and the thickness distribution can be superimposed to generate the suction surface and the pressure surface of the blade profile, in order to ensure smooth connection, the slope is kept consistent at the connection point, the leading edge adopts an ellipse, and the trailing edge adopts a circular arc, and the complete blade profile has the characteristics of simplicity and convenience.

[0097] Next, each step of the blade profile generation process is described in detail.

[0098] 1) Extracting camber line and thickness distribution based on original blade profile

[0099] First, the camber line and thickness distribution of the original blade profile need to be extracted. According to the definition of the camber line, the original blade profile needs to be inscribed with a circle, and then connecting the centers of the inscribed circles can obtain the camber line (as shown in Figure 2 ). The thickness distribution can be obtained at the corresponding centers of the inscribed circles (as shown in Figure 3 ).

[0100] 2) Adding control points for fitting of camber line parameters

[0101] The camber line modeling diagram of the blade profile is shown in Figure 4 .

[0102] Since the Bezier curve of the fitted camber line is of the fourth order, the curve contains five control points, p0 to p4, and the point pd is the intersection point of the extended lines of p0p1 and p4p3. In order to ensure that the chord length of the blade profile remains unchanged during the optimization process, the control points p0 and p4 are fixed, and the positions of the other three control points are optimized.

[0103] where the chord length c = constant

[0104] The following six parameters are converted as variables and the related meanings are given:

[0105] The leading edge direction angle a and the trailing edge direction angle β:

[0106] The end point and tangent vector of the Bezier curve can be obtained:

[0107] ;

[0108] Similarly

[0109] ;

[0110] The deflection change rule parameters j, k: where e, f, g, i are the lengths of the line segments;

[0111]

[0112]

[0113] Deflection change rule parameters h1, h2:

[0114] h1 represents the perpendicular distance from point P2 to the straight line P0Pd;

[0115] h2 represents the perpendicular distance from point P2 to the straight line P4Pd.

[0116] The specific solving steps are: according to the coordinates of the control points p0 and pd, the straight line equation Ax+By+C=0 passing through the two points is obtained, and the straight line equation parameters are obtained, then according to the distance from the point to the straight line, the deflection change rule parameter h1 is obtained,

[0117]

[0118] Similarly, according to the coordinates of the control points p4 and pd, the straight line equation Dx+Ey+F=0 passing through the two points can be obtained, and the deflection change rule parameter h2 can be obtained

[0119]

[0120] 3) Add control points to fit the thickness distribution parameters

[0121] The leaf profile thickness distribution modeling schematic diagram is shown in Figure 5 .

[0122] The cross-sonic airfoil thickness distribution curve is composed of two multi-order Bezier curves smoothly connected, the connecting point is the extreme point of the curve, the derivative of the left and right sides is 0, and the coordinate of the horizontal coordinate is the maximum thickness relative position. The left part of the curve is represented by a four-order Bezier curve, which contains five control points Ph0-Ph4, and the right part is a three-order Bezier curve, which contains four control points Ph4 and Pt1-Pt3.

[0123] Wherein: maximum thickness = Constant; trailing edge thickness = Constant;

[0124] Due to the complexity of the thickness distribution law and the large number of curve control points, in order to simplify the model, the following 7 parameters are extracted as variables:

[0125] The thickness distribution cut angles θ1 and θ2 at the beginning and end:

[0126] Using the endpoint property and tangent property of Bezier curve, we can get

[0127]

[0128] Similarly, we have

[0129]

[0130] The maximum thickness relative position: ;

[0131]

[0132] The larger the value of m is, the more the position of the maximum thickness of the blade moves to the trailing edge;

[0133] The thickness distribution parameters x1 and x2:

[0134]

[0135] The larger the value of x1 is, the slower the thickness change of the front half of the blade is, and the smaller the value of x2 is, the slower the thickness change of the back half of the blade is;

[0136] The thickness distribution parameter y1:

[0137]

[0138] The larger the value of y1 is, the greater the thickness of the front part of the blade is;

[0139] The thickness of the leading edge: r

[0140]

[0141] The larger the value of r is, the smaller the ratio of the major axis to the minor axis of the elliptic arc length is.

[0142] 4) call the function of generating blade profile to generate camber line, thickness distribution and coordinates of suction surface and pressure surface;

[0143] The above 13 parameters are selected as the optimization variables of the blade profile, and the camber line of the transonic and subsonic blade profile and the thickness distribution law of the transonic blade profile are controlled in the optimization process.

[0144] The coordinates of the control points of the camber line and the thickness distribution of the blade profile can be obtained:

[0145] Camber line: mid1=[P0x P1x P2x P3x P4x;P0y P1y P2y P3y P4y];

[0146] Left segment of thickness distribution: houdu11=[P0xl P1xl P2xl P3xl P4xl;P0yl P1yl P2yl P3yl P4yl];

[0147] Right segment of thickness distribution: houdu12=[P0xr P1xr P2xr P3xr;P0yr P1yr P2yr P3yr];

[0148] Call the blade profile generation function first blade to generate camber line, thickness distribution, pressure surface and suction surface coordinates:

[0149] Specifically, the camber line and the thickness distribution are equally divided into 60 parts, the Bezier function is called to generate the control curves of the camber line and the thickness distribution, and the spline interpolation is performed to obtain the coordinate points. The coordinates of the suction surface and the pressure surface are obtained by adding and subtracting the trigonometric function of the base point coordinates.

[0150] 5) Generate an elliptical leading edge and a circular trailing edge to smoothly connect with the pressure surface and the suction surface to generate a complete blade profile.

[0151] The generation of the elliptical leading edge uses the simultaneous elliptic equation and the major axis equation to obtain:

[0152]

[0153]

[0154] In order to ensure smooth connection, the equation composed of the circle and the suction surface and the pressure surface is solved to obtain the coordinates of the trailing edge

[0155] In order to ensure smooth connection, the slope is kept consistent at the connection point, and through the above steps, a transonic blade profile with camber line and thickness distribution, elliptical leading edge and circular trailing edge can be obtained.

[0156] In order to verify the design method, CFD numerical calculation is used for verification, two-dimensional numerical simulation analysis is carried out on the original cascade of Germany DLR and the blade profile designed by the method, and the numerical simulation results show that the total pressure loss coefficient of the blade profile designed by the method is reduced compared with the original blade profile, such as Figure 6 ; at the same time, it can be seen from the Mach number cloud chart that the shock wave intensity of the blade profile designed by the method is weakened, such as Figure 7 .

[0157] In another embodiment of the application, a transonic blade profile indirect generation system based on camber line thickness distribution is provided, which can be used to realize the above-mentioned transonic blade profile indirect generation method based on camber line thickness distribution.

[0158] The data extraction module is used for extracting the camber line and thickness distribution based on the original blade profile.

[0159] The parameter fitting module is used for adding control points to fit the camber line parameters and adding control points to fit the thickness distribution parameters.

[0160] The coordinate generation module is used for generating the camber line, thickness distribution and suction surface and pressure surface coordinates according to the fitted parameters by calling the blade profile generation function.

[0161] The blade profile generation module is used for generating an elliptical leading edge and a circular trailing edge, so as to smoothly connect the pressure surface and the suction surface, and generate a complete blade profile.

[0162] The division of the modules in the embodiments of the application is illustrative, and is only a logical function division, and when actually implemented, another division mode can be used, and in addition, the function modules in each embodiment of the application can be integrated in one processor, or can be physically separated, or two or more modules can be integrated in one module. The integrated module can be realized in the form of hardware or in the form of a software function module.

[0163] In still another embodiment of the present application, a computer device is provided, which comprises a processor and a memory, the memory being configured to store a computer program, the computer program comprising program instructions, and the processor being configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions in the computer storage medium to implement a corresponding method flow or corresponding function; the processor in the embodiments of the present application can be used for the operation of the indirect generation method of the cross-sound blade profile based on the distribution of the thickness of the middle camber line.

[0164] In still another embodiment of the present application, the present application further provides a storage medium, specifically a computer readable storage medium (Memory), which is a memory device in the computer device, and is configured to store programs and data. It can be understood that the computer readable storage medium herein can include the built-in storage medium in the computer device, and of course can also include the expansion storage medium supported by the computer device. The computer readable storage medium provides a storage space, and the storage space stores the operating system of the terminal. Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and the instructions can be one or more computer programs (including program codes). It should be noted that the computer readable storage medium herein can be a high-speed RAM memory, or a non-volatile memory such as at least one disk memory. One or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the indirect generation method of the cross-sound blade profile based on the distribution of the thickness of the middle camber line in the above embodiments.

[0165] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0166] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processing device or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0167] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0168] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0169] Finally, it should be noted that the above-mentioned embodiments are merely intended for describing the technical solutions of the present application, but not for limiting it. Although the present application is described in detail with reference to the above embodiments, those skilled in the field should understand that the specific embodiments of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and any modification or equivalent replacement without departing from the spirit and scope of the present application should be covered in the protection scope of the claims of the present application.

Claims

1. An indirect generation method of a transonic airfoil based on camber line thickening distribution, characterized in that, include: Extraction of mid-curve and thickness distribution based on the original airfoil shape; Add control points to fit the parameters of the mid-arc line; Add control points to fit the thickness distribution parameters; Based on the fitted parameters, the airfoil generation function is called to generate the mid-curve, thickness distribution, and coordinates of the suction and pressure surfaces; An elliptical leading edge and a round trailing edge are generated to smoothly connect with the pressure surface and suction surface, thus creating a complete blade shape; Add control points to fit the parameters of the mid-arc line: The Bezier curve was used to fit the arc. The Bezier curve is of order four and contains five control points, p0 to p4. Control points p0 and p4 were fixed, and the positions of the other three control points were optimized. Where the leaf chord length c = constant The following six parameters are calculated and used as variables, with their respective meanings provided: Leading edge direction angle α and trailing edge direction angle β: From the endpoint properties and tangent properties of the Bezier curve, we get: ； Similarly ； Deflection variation parameters j and k: where e, f, g, and i are the lengths of the line segment; Deflection variation parameters h1, h2: h1 represents the perpendicular distance from point P2 to line P0Pd; h2 represents the perpendicular distance from point P2 to line P4Pd; point pd is the intersection of the extensions of p0p1 and p4p3; Add control points to fit the thickness distribution parameters: The transonic blade thickness distribution curve is formed by two multi-order Bezier curves smoothly connected. The connection point is the extreme point of the curve, and the derivatives on both sides are 0. The ratio of the horizontal axis coordinate to the blade chord length is the relative position of the maximum thickness. The left side of the curve is represented by a fourth-order Bezier curve, which contains five control points from Ph0 to Ph4. The right side is a third-order Bezier curve, which contains four control points from Ph4 to Pt1 to Pt3. Where: maximum thickness = Constant; trailing edge thickness = Constant; Extract the following 7 parameters as variables: The thickness distribution at the beginning and end is tangent at angles θ1 and θ2. Using the endpoints and tangent properties of the Bezier curve, we obtain Maximum thickness relative position : Thickness distribution parameters x1, x2: Thickness distribution parameter y1: Leading edge thickness r: 。 2. The method for indirect generation of transonic blade shape based on the thickness distribution of the mid-arc line according to claim 1, characterized in that, Extraction of mid-curve and thickness distribution based on the original airfoil: According to the definition of the middle arc, an inscribed circle is drawn for the original blade shape, and then the center of the inscribed circle is connected to obtain the middle arc. The thickness distribution is obtained at the corresponding center of the inscribed circle. Specifically, the intersection of the line drawn through the center of each inscribed circle with the suction surface and pressure surface of the blade shape is obtained by connecting the points.

3. The method for indirect generation of transonic blade shape based on the thickness distribution of the mid-arc line according to claim 1, characterized in that, The specific solution steps are as follows: Based on the coordinates of control points p0 and pd, find the equation of the straight line passing through the two points Ax+By+C=0, obtain the parameters of the straight line equation, and then obtain the deflection variation law parameter h1 based on the distance from the point to the straight line. Similarly, based on the coordinates of control points p4 and pd, the equation of the straight line passing through these two points, Dx + Ey + F = 0, can be obtained, and the deflection variation parameter h2 can be calculated. 。 4. The method for indirect generation of transonic blade shape based on the thickness distribution of the mid-arc line according to claim 3, characterized in that, Based on the fitted parameters, the airfoil generation function is called to generate the mid-curve, thickness distribution, and coordinates of the suction and pressure surfaces: During the optimization process, the curvature of the transonic and subsonic airfoils and the thickness distribution of the transonic airfoils were controlled; the coordinates of the control points for the curvature and thickness distribution of the airfoils were obtained. Mid-arc line: mid1=[P0x P1x P2x P3x P4x; P0y P1y P2y P3y P4y]; Thickness distribution left segment: houdu11=[P0xl P1xl P2xl P3xl P4xl; P0yl P1yl P2yl P3yl P4yl]; Thickness distribution right segment: houdu12=[P0xr P1xr P2xr P3xr; P0yr P1yr P2yr P3yr]; The blade shape generation function `first blade` is called to generate the mid-curve, thickness distribution, and coordinates of the pressure and suction surfaces. Specifically, the middle arc and thickness distribution are divided into 60 equal parts, and the Bessel function is called to generate the control curves of the middle arc and thickness distribution. Spline interpolation is then performed to obtain the coordinate points. The coordinates of the suction surface and the pressure surface are obtained by adding and subtracting trigonometric functions from the base point coordinates.

5. The method for indirect generation of transonic blade shape based on the thickness distribution of the mid-arc line according to claim 1, characterized in that, Generate an elliptical leading edge and a rounded trailing edge, smoothly connecting them with the pressure and suction surfaces to create a complete blade shape: The leading edge of the ellipse is generated by solving the equations of the ellipse and its major axis simultaneously: Solve the equations formed by the circle and the suction / pressure surfaces to obtain the coordinates of the trailing edge; maintain a consistent slope at the connection point to obtain a transonic leaf shape with a thickened distribution of the middle arc, an elliptical leading edge, and a circular trailing edge.

6. A transonic blade indirect generation system based on mid-arc line thickness distribution, characterized in that, include: The data extraction module is used to extract the mid-curve and thickness distribution based on the original blade shape; The parameter fitting module is used to add control points to fit the parameters of the mid-curve and to add control points to fit the parameters of the thickness distribution. The coordinate generation module is used to generate the coordinates of the mid-arc line, thickness distribution, suction surface and pressure surface by calling the airfoil generation function based on the fitted parameters. The blade shape generation module is used to generate an elliptical leading edge and a round trailing edge, so that they can be smoothly connected with the pressure surface and the suction surface to generate a complete blade shape. Add control points to fit the parameters of the mid-arc line: The Bezier curve was used to fit the arc. The Bezier curve is of order four and contains five control points, p0 to p4. Control points p0 and p4 were fixed, and the positions of the other three control points were optimized. Where the leaf chord length c = constant The following six parameters are calculated and used as variables, with their respective meanings provided: Leading edge direction angle α and trailing edge direction angle β: From the endpoint properties and tangent properties of the Bezier curve, we get: ； Similarly ； Deflection variation parameters j and k: where e, f, g, and i are the lengths of the line segment; Deflection variation parameters h1, h2: h1 represents the perpendicular distance from point P2 to line P0Pd; h2 represents the perpendicular distance from point P2 to line P4Pd; point pd is the intersection of the extensions of p0p1 and p4p3; Add control points to fit the thickness distribution parameters: The transonic blade thickness distribution curve is formed by two multi-order Bezier curves smoothly connected. The connection point is the extreme point of the curve, and the derivatives on both sides are 0. The ratio of the horizontal axis coordinate to the blade chord length is the relative position of the maximum thickness. The left side of the curve is represented by a fourth-order Bezier curve, which contains five control points from Ph0 to Ph4. The right side is a third-order Bezier curve, which contains four control points from Ph4 to Pt1 to Pt3. Where: maximum thickness = Constant; trailing edge thickness = Constant; Extract the following 7 parameters as variables: The thickness distribution at the beginning and end is tangent at angles θ1 and θ2. Using the endpoints and tangent properties of the Bezier curve, we obtain Relative position of maximum thickness : Thickness distribution parameters x1, x2: Thickness distribution parameter y1: Leading edge thickness r: 。 7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the indirect generation method for transonic leaf shape based on the thickness distribution of the middle arc line as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the indirect generation method of transonic leaf shape based on the thickness distribution of the middle arc line as described in any one of claims 1 to 5.

Images