Airfoil profile optimization design method and system based on segmented geometric parameterization

Abstract

The invention discloses an airfoil optimization design method and system based on segmented geometric parameterization, and the method comprises the steps: S1, employing a segmented geometric parameterization method, carrying out the parameterization fitting of a reference airfoil geometry, and obtaining an airfoil initial parameter vector; s2, according to an optimization requirement, selecting a parameter from the initial parameter vector as an optimization variable; s3, determining an optimization target and constraint conditions, including aerodynamic performance constraint and geometric constraint; and S4, based on an optimization target and constraint conditions, performing iterative optimization on the selected optimization variables, generating an optimal airfoil geometry, and completing the design. According to the airfoil section optimization design method based on airfoil section geometric parameterization, accurate reverse fitting of airfoil section geometry and robust generation of a variant airfoil section can be achieved in airfoil section optimization, geometric features are directly controllable, a designer can rapidly design and optimize the airfoil section according to specific geometric and pneumatic requirements, the number of optimization iterations is remarkably reduced, and the design efficiency is improved. And the airfoil design time of the aircraft and the wind turbine is shortened.

Description

Technical Field

[0001] This invention relates to the field of airfoil optimization design, and specifically to an airfoil optimization design method and system based on piecewise geometric parameterization. Background Technology

[0002] The aerodynamic shape of an airfoil directly determines the aerodynamic performance of aerodynamic equipment such as aircraft wings and wind turbine blades, and its optimized design is a key technology for improving the performance of aerodynamic equipment. Airfoil optimization design methods based on airfoil parameterization are the mainstream technical path in current airfoil design, and are generally divided into two categories: those based on geometric parameterization and those based on non-geometric parameterization.

[0003] Non-geometrically parametric airfoil optimization methods, such as those based on CST, Hicks-Henne, B-spline, NURBS, Bezier, and FFD, as well as machine learning-based methods like VAE and GAN, parameterize airfoil geometry into mathematical parameters without explicit physical meaning. These methods lack direct geometric control during airfoil optimization; there is no clear correspondence between parameter adjustments and airfoil geometric changes, resulting in insufficient geometric interpretability. This makes it difficult for designers to achieve precise control over airfoil geometry through parameter adjustments, hindering the achievement of specific aerodynamic performance requirements.

[0004] The geometric parameterization-based airfoil optimization design method converts airfoil geometry into parameters directly related to geometric features, offering strong geometric intuition and allowing designers to directly control the airfoil shape by adjusting parameters during optimization. However, due to the limitations of existing geometric parameterization methods, airfoil optimization design methods based on geometric parameterization have significant limitations in practical applications, restricting their flexibility and efficiency in airfoil optimization design.

[0005] The PARSEC method describes airfoil geometry using 11 physically meaningful geometric parameters, fitting the entire upper or lower airfoil surface with a single 6th-order polynomial. This single polynomial is constrained by multiple geometric parameters from the leading edge to the trailing edge; therefore, adjusting a single parameter will alter the coefficients of the entire polynomial, leading to global geometric changes. This strong coupling between parameters not only makes precise control of local geometric features difficult, limiting the flexibility of optimization design, but also results in high parameter sensitivity. Small changes can cause significant geometric deviations, and under certain parameter combinations, oscillations can occur, leading to airfoil geometric distortion and the generation of deformed airfoils that do not meet aerodynamic requirements, increasing the optimization difficulty. The iPARSEC method decomposes the leading edge radii of the upper and lower airfoils and optimizes the trailing edge representation in the PARSEC method, but it still uses a single polynomial fitting approach, failing to solve the global coupling problem. It is still prone to generating distorted airfoils during optimization, and its ability to control local airfoil geometric features is limited. The iCST method, building upon iPARSEC, further increases the number of geometric control parameters to 28 and uses a 10th-order CST polynomial instead of a 6th-order polynomial to parameterize the airfoil geometry. While this improves fitting accuracy, the increased number of parameters significantly increases control complexity. Higher-order polynomials are prone to geometric distortion during optimization, leading to more invalid iterations and reduced optimization efficiency. The IGP method, by separating camber and thickness distributions, describes the airfoil with only 8 parameters, achieving direct control over geometric features such as camber and thickness. This enhances airfoil geometric control to some extent, and the fewer parameters improve optimization design efficiency. However, this method also uses a single function to fit camber and thickness distributions and pursues a smaller number of parameters, limiting the ability to fit complex airfoils and finely control local geometric features during the optimization design process.

[0006] In summary, existing airfoil optimization design methods based on geometric parameterization suffer from limitations due to the parameterization approach. These limitations include insufficient geometric feature control due to global parameter coupling and susceptibility to distorted airfoils due to high parameter sensitivity, significantly restricting the flexibility and efficiency of airfoil optimization design. Therefore, there is an urgent need for an airfoil optimization design method that can achieve direct and independent control of airfoil geometry, high-precision fitting and reconstruction, and robust airfoil generation during optimization design, in order to improve geometric controllability, optimization robustness, and efficiency in airfoil optimization design. Summary of the Invention

[0007] To address the shortcomings of existing airfoil optimization design methods based on geometric parameterization, such as insufficient control over local geometric features and susceptibility to generating distorted airfoils, this invention aims to provide an airfoil optimization design method based on piecewise geometric parameterization. This method overcomes the limitations of traditional methods, such as parameter coupling and insufficient controllability of geometric features, through piecewise geometric parameterization. It achieves direct and independent control of the airfoil's geometric shape, significantly improving the fine controllability of local geometric features. Simultaneously, it reduces the risk of airfoil geometric distortion to minimize invalid iterations, thereby enhancing geometric controllability, optimization robustness, and efficiency in airfoil optimization design. This provides technical support for the high-performance design of aerodynamic equipment such as aircraft wings and wind turbine blades.

[0008] To achieve the above objectives, this invention provides an airfoil optimization design method based on piecewise geometric parameterization, comprising the following steps:

[0009] Step S1: Use the piecewise geometry parameterization method to perform parameterized fitting on the reference airfoil geometry to obtain the initial parameter vector;

[0010] Step S2: Select parameters as optimization variables from the initial parameter vector according to the optimization requirements;

[0011] Step S3: Determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints;

[0012] Step S4: Based on the optimization objective and constraints, iteratively optimize the selected optimization variables to generate the optimal airfoil geometry and complete the design.

[0013] Preferably, step S1 includes:

[0014] The airfoil geometry is decomposed into the mid-curve distribution C(x) and the thickness distribution T(x);

[0015] With the position of maximum curvature X C and the location of maximum thickness X T Using the segmentation points, piecewise polynomial fitting is performed on the mid-arc line and the thickness line respectively;

[0016] The coefficients of the piecewise polynomial are constrained by 12 geometric parameters to obtain an initial parameter vector; the 12 geometric parameters include: 6 parameters for the mid-arc distribution and 6 parameters for the thickness distribution.

[0017] Preferably, the step of performing piecewise polynomial fitting on the mid-arc line includes:

[0018] The middle arc is divided into a front segment and a back segment. The front segment is fitted with a fourth-order polynomial, and the back segment is fitted with a fifth-order polynomial.

[0019] A set of constraint equations is constructed using six geometric parameters: leading edge direction angle, maximum camber location, maximum camber, curvature at maximum camber, trailing edge location, and trailing edge direction angle. The polynomial coefficients are then solved.

[0020] Preferably, the step of performing polynomial piecewise fitting on the thickness line includes:

[0021] The thickness line is divided into a front section and a back section. The front section uses a line marked with an "x". 0.5 The term is fitted with a fourth-order polynomial to match the leading-edge circular geometry, and the latter part is fitted with a fifth-order polynomial.

[0022] A set of constraint equations is constructed using six geometric parameters: leading edge radius, maximum thickness location, maximum thickness, curvature at maximum thickness, trailing edge angle, and trailing edge thickness. The polynomial coefficients are then solved.

[0023] Preferably, step S2 includes:

[0024] The 12 geometric parameters are divided into selected optimization variables p. s And the parameter p that does not need optimization f ;

[0025] Choose p based on the optimization objective. s The remaining parameters p that do not need optimization f It remains unchanged during optimization;

[0026] Optimize variable p s The range of values ​​is based on the initial parameter vector p. 0 The preset ratio is used to create an optimization space.

[0027] Preferably, step S4 includes:

[0028] A genetic algorithm is used to randomly generate multiple sets of optimization variables within a defined optimization space.

[0029] For each set of variables, the airfoil geometry is generated using a piecewise geometric parameterization method, and the lift-to-drag ratio is calculated using aerodynamic analysis tools.

[0030] The optimization variables are updated through selection, crossover, and mutation operations, iterating until the objective function converges.

[0031] The present invention also provides an airfoil optimization design system based on piecewise geometric parameterization, the system being used to implement the above method, comprising: a fitting module, a selection module, a determination module, and a design module;

[0032] The fitting module is used to perform parametric fitting on the reference airfoil geometry using a piecewise geometric parameterization method to obtain an initial parameter vector;

[0033] The selection module is used to select parameters as optimization variables from the initial parameter vector according to the optimization requirements.

[0034] The determining module is used to determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints;

[0035] The design module is used to iteratively optimize the selected optimization variables based on the optimization objectives and constraints, generate the optimal airfoil geometry, and complete the design.

[0036] Preferably, the workflow of the fitting module includes:

[0037] The airfoil geometry is decomposed into the mid-curve distribution C(x) and the thickness distribution T(x);

[0038] With the position of maximum curvature X C and the location of maximum thickness X T Using the segmentation points, piecewise polynomial fitting is performed on the mid-arc line and the thickness line respectively;

[0039] The coefficients of the piecewise polynomial are constrained by 12 geometric parameters to obtain an initial parameter vector; the 12 geometric parameters include: 6 parameters for the mid-arc distribution and 6 parameters for the thickness distribution.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] This invention presents an airfoil optimization design method based on segmented geometric parameterization. In airfoil optimization, it can achieve accurate inverse fitting of airfoil geometry, robust generation of variant airfoils, and direct controllability. This facilitates designers to quickly design and optimize for specific geometric and aerodynamic requirements, significantly reduces the number of optimization iterations, and lowers the computational cost and time for aircraft and wind turbine airfoil design, thus having significant engineering application value. Attached Figure Description

[0042] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 This is a schematic diagram of SGP airfoil geometry parameterization according to an embodiment of the present invention;

[0044] Figure 2 The parameterized fitting results of the SGP-based airfoil optimization method for the DU93-W-210 airfoil are shown in this embodiment of the invention.

[0045] Figure 3This is a comparative diagram of the variant airfoil generation results of the airfoil optimization methods based on the SGP method and the PARSEC method according to an embodiment of the present invention; wherein, (a) is the variant airfoil generation result based on the SGP method; and (b) is the variant airfoil generation result based on the PARSEC method.

[0046] Figure 4 The results of airfoil geometric controllability optimization based on the SGP airfoil optimization method are as follows: (a) is the optimization of other parameters with fixed thickness, trailing edge position and trailing edge thickness; (b) is the optimization of only the leading edge radius; (c) is the optimization of only the airfoil camber; and (d) is the optimization of only the thickness. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Example 1

[0050] This embodiment provides an airfoil optimization design method based on piecewise geometric parameterization, the steps of which include:

[0051] S1. The piecewise geometric parameterization method is used to perform parametric fitting on the reference airfoil geometry to obtain the initial parameter vector.

[0052] For the parametric description of airfoil geometry, this embodiment designs a segmented geometric parameterization (SGP) method. The airfoil geometry is decomposed into independent mid-curve distribution curves and thickness distribution curves, and a piecewise function fitting strategy is adopted to replace the traditional global fitting method using a single function. The specific method is as follows:

[0053] ① Definition of airfoil geometry:

[0054] The SGP method decomposes the geometry of the airfoil into the mid-curve distribution C(x) and the thickness distribution T(x):

[0055]

[0056] Among them, z up (x) and z low (x) represents the coordinate distribution of the upper and lower surfaces, respectively:

[0057]

[0058] like Figure 1 As shown, the SGP method describes airfoil geometry using 12 parameters with explicit physical meaning:

[0059] [α LE ,X C ,C,Cxx c Z TE ,α TE ,R LE ,X T ,T,Txx t ,β TE ,ΔZ TE ].

[0060] These parameters include: six geometric parameters describing the arc distribution: leading edge direction angle α LE Location of maximum curvature X C Maximum curvature C, curvature Cxx at the point of maximum curvature c Trailing edge direction angle α TE Tail edge position Z TE And six geometric parameters describing the thickness line distribution: leading edge radius R LE Location of maximum thickness X T Maximum thickness T, curvature Txx at maximum thickness t Tail edge angle β TE Trailing edge thickness ΔZ TE .

[0061] The mid-curve and thickness lines are obtained by solving the piecewise polynomial expressions of C(x) and T(x) based on the geometric parameter constraints of the mid-curve and thickness line piecewise fitting models, respectively. Then, the coordinate distribution of the upper and lower surfaces of the airfoil is obtained by equation (2). The mid-curve piecewise fitting model and the thickness line fitting model are described below.

[0062] ② Piecewise fitting model of the middle arc

[0063] Use X C Divide the middle arc C(x) into two segments;

[0064] The first segment of the middle arc, x∈[0,X] C Using C f (x) Fitting:

[0065] C f (x)=a1x+a2x 2 +a3x 3 +a4x 4 (3)

[0066] The latter segment of the middle arc, x∈[X] C [1] Using C r (x) Fitting:

[0067] C r (x)=b1x+b2x 2 +b3x 3 +b4x 4 +b5x 5 (4)

[0068] Front C f (x) and the latter part C r In (x), the coefficients of the arc are determined by satisfying the constraints of 6 curvature geometric parameters.

[0069] The first part is in x=X C The value at that location is equal to C:

[0070] C f (X C )=a1X C +a2X C 2 +a3X C 3 +a4X C 4 =C (5)

[0071] The first part is in x=X C The first derivative at point 0 is 0:

[0072] C' f (X C )=a1+2a2X C +3a3X C 2 +4a4X C 3 =0 (6)

[0073] The first part is in x=X C The second derivative is equal to the airfoil at x = X C The curvature Cxx at the point c :

[0074] C” f (X C )=2a2+6a3X C +12a4X C 2 =Cxx c (7)

[0075] The front segment is at the leading edge x = X LE The first derivative is equal to the leading edge angle α LE Tangent:

[0076]

[0077] To maintain continuity, the first and second segments must be at x = X C The mid-arc value, first derivative, and curvature are equal.

[0078] The latter part is in x=X C The value at that location is equal to C:

[0079] C r (X C )=b1X C +b2X C 2 +b3X C 3 +b4X C 4 +b5X C 5 =C (9)

[0080] The latter part is in x=X C The first derivative at point 0 is 0:

[0081] C' r (X C )=b1+2b2X C +3b3X C 2 +4b4X C 3 +5b5X C 4 =0 (10)

[0082] The latter part is in x=X C The second derivative is equal to the airfoil at x = X C The curvature Cxx at the point c :

[0083] C” r (X C ) = 2b² + 6b³X C +12b4X C 2 +20b5X C 3 =Cxx c (11)

[0084] The latter part is at the trailing edge x = X TE The value is equal to the airfoil trailing edge position Z. TE :

[0085]

[0086] The latter part is at the trailing edge x = X TE The slope is equal to the trailing direction angle α.TE Tangent:

[0087]

[0088] The above-mentioned arc constraint forms the following equation:

[0089]

[0090] Solving the above equations for the coefficients a1, a2, a3, a4, b1, b2, b3, b4, and b5 yields the piecewise expression for the airfoil's mid-curve:

[0091]

[0092] ③ Piecewise fitting model for thickness lines

[0093] Use X T Divide the thickness line T(x) into two segments:

[0094] The first segment x∈[0,X T Using T f (x) Fitting:

[0095] T f (x)=c1x 0.5 +c2x 2 +c3x 3 +c4x 4 (16)

[0096] The latter part x∈[X T ,1] Using T r (x) Fitting:

[0097] T r (x)=d1x 0.5 +d2x 2 +d3x 3 +d4x 4 +d5x 5 (17)

[0098] front section T f (x) and the latter part T r (x) The coefficients of the thickness line are determined by satisfying constraints of 6 thickness parameters:

[0099] The first part is in x=X LE The radius of curvature at that point is equal to For detailed derivation, see section ④A below. Due to the thickness line leading edge constraint, c1 is set to...

[0100]

[0101] The first part is in x=XT The value at point T is equal to:

[0102] T f (X T )=c1X T 0.5 +c2X T 2 +c3X T 3 +c4X T 4 =T (19)

[0103] The first part is in x=X T The first derivative is 0:

[0104]

[0105] The first part is in x=X T The second derivative is equal to the airfoil at x = X T curvature Txx at the point t :

[0106]

[0107] To maintain continuity, the first and second segments must be at x = X T The thickness, first derivative, and curvature are equal.

[0108] The latter part is in x=X T The value is equal to T:

[0109] T r (X T )=d1X T 0.5 +d2X T 2 +d3X T 3 +d4X T 4 +d5X T 5 =T (22)

[0110] The latter part is in x=X T The first derivative is 0:

[0111]

[0112] The latter part is in x=X T The second derivative is equal to the airfoil at x = X T curvature Txx at the point t :

[0113]

[0114] The latter part is in x=X TE The value is equal to the airfoil trailing edge thickness ΔZ TE :

[0115]

[0116] The latter part is in x=X TE The slope and the angle between the airfoil's trailing edge satisfy For detailed derivation, please refer to the following section ④B thickness line tail edge constraint:

[0117]

[0118] The above thickness line constraints form the following equation:

[0119]

[0120] Solving the above system of equations yields the expression for the airfoil's camber line:

[0121]

[0122] ④Thickness line leading edge constraint and trailing edge constraint

[0123] A. Thickness line leading edge constraint

[0124] In airfoil design, the leading edge of the airfoil is typically approximated as circular. In the SGP method, the airfoil thickness distribution curve T(x) represents the vertical distance between the upper and lower surfaces of the airfoil.

[0125] T(x) = z up (x)-z low (x) (29)

[0126] For the leading edge of the airfoil, assume it is a radius of R. LE The center of the circle is (R) LE The equation of a circle with x, y, y = 0 is:

[0127]

[0128] Therefore, the expressions for the upper and lower surfaces of the circle near the leading edge can be obtained:

[0129]

[0130] The thickness distribution curve of the airfoil near the leading edge is as follows:

[0131]

[0132] At the leading edge of the airfoil, x→0, x>>x 2 Therefore, x can be ignored. 2 item:

[0133]

[0134] For the fitting function of the thickness curve in the first segment, x→0, x 0.5 >>x 2 x 3 x 4 Therefore, the higher-order term x is ignored. 2 x 3 x 4 :

[0135]

[0136] Therefore, the coefficients in the airfoil thickness distribution curve T(x) in the SGP method

[0137] B. Thickness line trailing edge constraint

[0138] The thickness line T(x) is at the trailing edge x = X TE The first derivative is:

[0139] T'(X TE )=z' up (X TE )-z' low (X TE (36)

[0140] Airfoil trailing edge angle β TE For the upper and lower surfaces at x = X TE The included angle at that point is symmetrical with respect to the middle arc, meaning the angle between the upper and lower surfaces is:

[0141]

[0142] In x = X TE The first derivative is equal to the slope at that point:

[0143]

[0144] Airfoil trailing edge angles are generally small. The value of is negligible compared to 1, therefore, under the small-angle approximation assumption:

[0145]

[0146] Similarly, the lower surface at x = X TE The first derivative at point is:

[0147]

[0148] therefore:

[0149]

[0150] Furthermore, because the thickness curve T(x) is at x = X TE The expression decreases at each position, therefore T'(X) TE ) < 0; while the trailing edge angle is positive, tan(β) TE / 2) is a positive value. To ensure consistency between the constraints and the geometric definitions, a negative sign is introduced:

[0151]

[0152] Reference airfoil parameter initialization: Select the reference airfoil to be optimized, and determine the initial parameter vector p through geometric fitting based on the SGP method described above. 0 :

[0153]

[0154] Let p satisfy the geometric fitting accuracy requirement be denoted as p. 0 .

[0155] p 0 =[α LE 0 ,X C 0 C 0 ,Cxx c 0 Z TE 0 ,α TE 0 ,R LE 0 ,X T 0 ,T 0 ,Txx t 0 ,β TE 0 ,ΔZ TE 0 ] T (44)

[0156] Step S2: Select parameters as optimization variables from the initial parameter vector according to the optimization requirements.

[0157] The 12 geometric parameters of the SGP method are used as airfoil optimization design variables:

[0158] p i =[α LE i ,X C i C i ,Cxx c i Z TEi ,α TE i ,R LE i ,X T i ,T i ,Txx t i ,β TE i ,ΔZ TE i ] T (45)

[0159] The SGP airfoil parameterization method used in this method has a one-to-one correspondence between its control parameters and the airfoil's geometric features. Furthermore, adjusting the geometric feature controlled by one parameter will not cause changes to the geometric features controlled by other parameters. Therefore, during airfoil optimization, it is possible to select and fix geometric features according to optimization requirements. The selected optimization variable is denoted as p. s Variables that do not require optimization are denoted as fixed variables p. f The airfoil geometry design variable p is expressed as:

[0160] p i =[p s i ,p f ] T (46)

[0161] Where, p i p is the design variable for the i-th variant airfoil during the optimization process. s i p is the optimization variable corresponding to the i-th variant airfoil. f This remains unchanged during the optimization process. If only the airfoil leading edge radius is optimized, then:

[0162] p s =[R LE ], p f =[α LE ,X C ,C,Cxx c Z TE ,α TE ,X T ,T,Txx t ,β TE ,ΔZ TE (47)

[0163] The design variables for the i-th variant airfoil are:

[0164]

[0165] Step S3: Determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints.

[0166] To maximize the airfoil lift-to-drag ratio C under target operating conditions l / C d To optimize the objective, where C l C is the lift coefficient. d This is the drag coefficient.

[0167]

[0168] Maximize f(p) s (50)

[0169] Aerodynamic performance constraints: drag coefficient not higher than initial value, lift coefficient not lower than initial value.

[0170] subject to C d (p s ,p f )≤C d0 C l (p s ,p f )≥C l0 (51)

[0171] Geometric constraints: Initial parameter vector p 0 The selected optimization variables 1.25 times is used as the upper bound of the optimization variable range. 0.75 times is used as the lower bound of the optimization variable range, thus forming the optimization design space.

[0172] Step S4: Based on the optimization objective and constraints, iteratively optimize the selected optimization variables to generate the optimal airfoil geometry and complete the design.

[0173] Use a genetic algorithm to iteratively optimize p s The optimal solution is searched using the following steps:

[0174] Initialization: in P s Multiple sets of p are randomly generated within the inner circle. s This forms the initial population, with p in each group. s and fixed variable p f Different variant airfoil design variables p i =[p s i ,p f ] T ;

[0175] Objective function evaluation: The objective function value f(p) for each corresponding variant airfoil is calculated using XFOIL;

[0176] Parameter Update: Generate a new generation of p through selection, crossover, and mutation operations. s Iterate until the objective function converges.

[0177] Convergence and Output: When the optimization algorithm converges, it outputs the optimal variable. Optimal variables and fixed variables generate optimal design At this point, the following condition is met:

[0178] f(p * )≥(C l +C d )0,C d (p * )≤C d0 C1(p * )≤C l0 (52)

[0179] Example 2

[0180] The specific technical effects of the airfoil optimization design method based on airfoil segmented geometric parameterization provided by this invention are as follows:

[0181] The airfoil optimization design method based on the SGP parameterization method uses 12 geometric parameters to accurately fit and reconstruct the baseline airfoil during airfoil optimization, such as... Figure 2 As shown, the RMSE of the fitting accuracy is 0.00032. This precise fitting capability gives the airfoil optimization results good reliability.

[0182] The airfoil optimization design method based on segmented geometric parameterization avoids generating distorted airfoils during the optimization process, prevents invalid iterations, and shortens the optimization design time. For example... Figure 3 The airfoils generated during the optimization process all maintain continuous curvature, reasonable shape, and no geometric distortion, while the airfoils generated under the same conditions based on PARSEC are mostly distorted. In multiple optimizations, the optimization design method of this invention reduces the optimization time by 60%.

[0183] The airfoil optimization design method based on segmented geometric parameterization uses the SGP parameterization method to directly associate 12 parameters with the airfoil's geometric features. The segmented modeling of the arc and thickness lines reduces the coupling between parameters, ensuring that adjusting a single parameter only affects the corresponding geometric feature. This enables direct control of the airfoil's geometric features and further allows for controllable optimization of these features. Without altering other geometric characteristics, specific geometric features can be optimized to meet aerodynamic requirements, such as... Figure 4As shown in (a), with the thickness, trailing edge position, and trailing edge thickness remaining constant, optimizing other parameters improves the lift-to-drag ratio by 3.7%. Figure 4 (b) Only the leading edge radius was optimized, decreasing from 0.025 to 0.018, resulting in a 2.3% improvement in lift-to-drag ratio; Figure 4 (c) Only the airfoil camber was optimized, increasing from 0.028 to 0.031, resulting in a 4.2% improvement in lift-to-drag ratio; Figure 4 (d) Only the thickness was optimized, reducing the thickness from 0.21 to 0.19, resulting in a 3.3% improvement in lift-to-drag ratio.

[0184] Example 3

[0185] This embodiment also provides an airfoil optimization design system based on piecewise geometric parameterization, including: a fitting module, a selection module, a determination module, and a design module; the fitting module is used to perform parametric fitting on the reference airfoil geometry using a piecewise geometric parameterization method to obtain an initial parameter vector; the selection module is used to select parameters as optimization variables from the initial parameter vector according to optimization requirements; the determination module is used to determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints; the design module is used to iteratively optimize the selected optimization variables based on the optimization objective and constraints to generate the optimal airfoil geometry and complete the design.

[0186] The fitting module's workflow includes: decomposing the airfoil geometry into a mid-curvature distribution C(x) and a thickness distribution T(x); and using the maximum camber position X... C and the location of maximum thickness X T Using the segmentation points, piecewise polynomial fitting is performed on the mid-arc line and the thickness line respectively; the coefficients of the piecewise polynomial are constrained by 12 geometric parameters to obtain the initial parameter vector; the 12 geometric parameters include: 6 parameters of the mid-arc line distribution and 6 parameters of the thickness distribution.

[0187] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An airfoil optimization design method based on piecewise geometric parameterization, characterized in that, Includes the following steps: Step S1: Use the piecewise geometry parameterization method to perform parameterized fitting on the reference airfoil geometry to obtain the initial parameter vector; Step S2: Select parameters as optimization variables from the initial parameter vector according to the optimization requirements; Step S3: Determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints; Step S4: Based on the optimization objective and constraints, iteratively optimize the selected optimization variables to generate the optimal airfoil geometry and complete the design.

2. The airfoil optimization design method based on piecewise geometric parameterization according to claim 1, characterized in that, Step S1 includes: The airfoil geometry is decomposed into the mid-curve distribution C(x) and the thickness distribution T(x); With the position of maximum curvature X C and the location of maximum thickness X T Using the segmentation points, piecewise polynomial fitting is performed on the mid-arc line and the thickness line respectively; The coefficients of the piecewise polynomial are constrained by 12 geometric parameters to obtain an initial parameter vector; the 12 geometric parameters include: 6 geometric parameters for the mid-arc distribution and 6 geometric parameters for the thickness line distribution.

3. The airfoil optimization design method based on piecewise geometric parameterization according to claim 2, characterized in that, The steps for piecewise polynomial fitting of the mid-arc line include: The middle arc is divided into a front segment and a back segment. The front segment is fitted with a fourth-order polynomial, and the back segment is fitted with a fifth-order polynomial. A set of constraint equations is constructed using six geometric parameters: leading edge direction angle, maximum camber location, maximum camber, curvature at maximum camber, trailing edge location, and trailing edge direction angle. The polynomial coefficients are then solved.

4. The airfoil optimization design method based on piecewise geometric parameterization according to claim 2, characterized in that, The steps for polynomial piecewise fitting of the thickness line include: The thickness line is divided into a front section and a back section. The front section uses a line marked with an "x". 0.5 The fourth-order polynomial fit of the term, x 0.5 The term is matched with the leading edge circular geometry, and the latter part is fitted using a fifth-order polynomial; A set of constraint equations is constructed using six geometric parameters: leading edge radius, maximum thickness location, maximum thickness, curvature at maximum thickness, trailing edge angle, and trailing edge thickness. The polynomial coefficients are then solved.

5. The airfoil optimization design method based on piecewise geometric parameterization according to claim 2, characterized in that, Step S2 includes: The 12 geometric parameters are divided into selected optimization variables p. s And the parameter p that does not need optimization f ; Choose p based on the optimization objective. s The remaining parameters p that do not need optimization f It remains unchanged during optimization; Optimize variable p s The range of values ​​is based on the initial parameter vector p. 0 The preset ratio is used to create an optimization space.

6. The airfoil optimization design method based on piecewise geometric parameterization according to claim 1, characterized in that, Step S4 includes: Genetic algorithms are used to randomly generate multiple sets of offspring with optimization variables within a defined optimization space. Each group of offspring and the parameter p that does not need optimization f The parameters are combined into a set of SGP parameters, the airfoil geometry is generated by a piecewise geometry parameterization method, and the lift-to-drag ratio is calculated using aerodynamic analysis tools. The optimization variables are updated through selection, crossover, and mutation operations, iterating until the objective function converges.

7. An airfoil optimization design system based on piecewise geometric parameterization, said system being used to implement the method described in any one of claims 1-6, characterized in that, include: Fitting module, selection module, determination module, and design module; The fitting module is used to perform parametric fitting on the reference airfoil geometry using a piecewise geometric parameterization method to obtain an initial parameter vector; The selection module is used to select parameters as optimization variables from the initial parameter vector according to the optimization requirements. The determining module is used to determine the optimization objective and constraints, including aerodynamic performance constraints and geometric constraints; The design module is used to iteratively optimize the selected optimization variables based on the optimization objectives and constraints, generate the optimal airfoil geometry, and complete the design.

8. The airfoil optimization design system based on piecewise geometric parameterization according to claim 7, characterized in that, The workflow of the fitting module includes: The airfoil geometry is decomposed into the mid-curve distribution C(x) and the thickness distribution T(x); With the position of maximum curvature X C and the location of maximum thickness X T Using the segmentation points, piecewise polynomial fitting is performed on the mid-arc line and the thickness line respectively; The coefficients of the piecewise polynomial are constrained by 12 geometric parameters to obtain an initial parameter vector; the 12 geometric parameters include: 6 geometric parameters for the mid-arc distribution and 6 geometric parameters for the thickness distribution.

Images