A parameterization method for airfoil design space with fixed disturbance
By dividing the design space and adding a disturbance function in the airfoil parameterization method, the problem of unsuitable design space in the prior art is solved, and efficient airfoil optimization and accurate geometric design are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-08-31
- Publication Date
- 2026-05-26
AI Technical Summary
Existing airfoil parameterization methods have unsuitable design spaces, leading to problems such as excessive computation or incomplete design scope, which prevents effective optimization of airfoil geometry design.
By mapping the basic airfoil to a Cartesian coordinate system, dividing it into four design spaces, and establishing an orthogonal curvilinear coordinate system in each space, a disturbance function is added to form the disturbed airfoil function curve, and finally the upper and lower curves of the disturbed airfoil are obtained, thus realizing airfoil parameterization.
While ensuring the accuracy of the optimization solution, it saves the airfoil optimization solution time and has the ability to correct local design space, thus improving the efficiency and accuracy of airfoil optimization.
Smart Images
Figure CN117131597B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of airfoil optimization technology, specifically relating to an airfoil parameterization method with a fixed disturbance design space. Background Technology
[0002] The geometry of an airfoil is one of the fundamental geometric characteristics of an airfoil, and its aerodynamics directly affects the aerodynamic characteristics of the airfoil and the entire aircraft. Airfoil shape parameterization defines the airfoil using mathematical equations. Typically, different design variables in airfoil shape parameterization can produce different airfoils, thus the parameterization method directly affects the airfoil design space.
[0003] In existing technologies, the design space of airfoil parametric methods is usually given by the values of design variables. This often results in a design space that differs from the range required for optimization. A limited design space leads to an incomplete scope for the parametric method, while a large design space results in excessive computational overhead. Parametric methods often express the geometric design boundaries of the airfoil through nonlinear constraints. However, airfoil parametric methods with an inappropriate total design space require significant unnecessary computation during optimization and analysis to eliminate invalid airfoils. Therefore, an airfoil parametric method with a defined design space is crucial. Summary of the Invention
[0004] The purpose of this invention is to provide an airfoil parameterization method with a fixed disturbance design space, overcoming the shortcomings of existing parameterization methods that cannot specify the specific shape of the design space, have a limited design space leading to an incomplete design range and thus fail to find the most suitable airfoil; and have a large amount of unsuitable design space leading to a large amount of unnecessary computation; and have an unsuitable total design space leading to a large amount of unnecessary computation in optimization and analysis to eliminate invalid airfoils.
[0005] To achieve the above objectives, the present invention employs the following technical solution:
[0006] This invention provides a method for airfoil parameterization in a fixed disturbance design space, comprising the following steps:
[0007] S1: Map the basic airfoil to the Cartesian coordinate system to obtain the upper and lower curves of the airfoil;
[0008] S2: Based on the upper and lower airfoil curves, obtain the intermediate guide line, the relative upper airfoil curve, and the relative lower airfoil curve;
[0009] S3: Set the upper and lower boundaries of the total design space and divide the total design space into four design spaces according to the intermediate guide line, the upper curve of the relative airfoil, and the lower curve of the relative airfoil. Establish orthogonal curve coordinate systems based on the four design spaces respectively.
[0010] S4: Transform the relative airfoil upper curve and relative airfoil lower curve to orthogonal curvilinear coordinate systems of two adjacent design spaces with the relative airfoil upper curve and relative airfoil lower curve as boundaries to obtain the relative airfoil function curve;
[0011] S5: Add perturbation functions to the relative airfoil function curves respectively to obtain the relative airfoil function curves after perturbation; transform the relative airfoil function curves after perturbation from their respective orthogonal curvilinear coordinate systems to the Cartesian coordinate system to obtain the airfoil function curves after perturbation.
[0012] S6: Based on the perturbation-added airfoil function curve, obtain the perturbation-added airfoil upper curve and the perturbation-added airfoil lower curve, obtain the perturbation airfoil, and complete the airfoil parameterization.
[0013] In the specific implementation process, in S1, the upper curve of the airfoil is greater than the lower curve of the airfoil; in S3, the upper boundary is greater than the upper curve of the relative airfoil, and the lower boundary is less than the lower curve of the relative airfoil.
[0014] In the specific implementation process, the process of obtaining the intermediate guide line, the relative upper airfoil curve, and the relative lower airfoil curve based on the upper and lower airfoil curves in S2 is as follows:
[0015]
[0016]
[0017]
[0018] Among them, y mid (x) is the intermediate leading line, y upp (x) represents the curve relative to the airfoil, y low (x) represents the curve relative to the airfoil. For the upper curve of the airfoil, This refers to the lower curve of the airfoil.
[0019] In the specific implementation process, in S3, the four design spaces are respectively the first design space formed by the upper boundary of the total design space and the upper curve of the relative airfoil; the second design space formed by the upper curve of the relative airfoil and the intermediate guide line; the third design space formed by the lower curve of the relative airfoil and the intermediate guide line; and the fourth design space formed by the lower curve of the relative airfoil and the lower boundary of the total design space.
[0020] In the specific implementation process, the step of establishing an orthogonal curvilinear coordinate system in S3 is as follows:
[0021] S31: Use Dirichlet boundary conditions as the boundary conditions;
[0022] S32: Based on the Dirichlet boundary conditions, four design spaces are constructed using the Laplace equation to obtain the field lines and equipotential lines of the vector fields; the field lines and equipotential lines of the vector fields are used as the coordinates u and t of the corresponding orthogonal curvilinear coordinate systems, respectively.
[0023] Wherein, the coordinate u of any point represents the potential of that point, and the value of the coordinate u ranges from [0,1].
[0024] In the specific implementation process, the upper curve of the relative airfoil is transformed into an orthogonal curve coordinate system constructed by the first design space and the second design space, and the lower curve of the relative airfoil is transformed into an orthogonal curve coordinate system constructed by the third design space and the fourth design space.
[0025] In the specific implementation process, in S5, the disturbance function is the disturbance amount along the normal direction of the upper edge of the basic airfoil, and the disturbance function is expressed in the orthogonal curvilinear coordinate system as follows:
[0026]
[0027] Among them, b i The i-th design parameter representing the disturbance amount has a value range of [0,1].
[0028] It is called the k-th order B-spline basis function, where i is from 0 to n;
[0029] Each B-spline basis function is a k-th order piecewise polynomial determined by a sequence T, where the sequence T is a sequence of non-decreasing parameters t;
[0030] The B-spline basis functions described above are defined by the de Boor-Cox formula, as shown below:
[0031]
[0032] Where ψ is the value of the independent variable of the B-spline basis function; k is the order of the B-spline; t i is a non-decreasing parameter in sequence T.
[0033] In the specific implementation process, the formula for the relative airfoil function curve after adding disturbance in S5 is as follows:
[0034] u uu * (t uu )=u upp (tuu )+δ(t uu ,b uu )
[0035] u ul * (t ul )=u upp (t ul )+δ(t ul ,b ul )
[0036] u lu * (t lu )=u low (t lu )+δ(t lu ,b lu )
[0037] u ll * (t ll )=u low (t ll )+δ(t ll ,b ll );
[0038] Among them, u uu * (t uu ) represents the relative airfoil function with added perturbation in the first design space; u ul * (t ul ) represents the relative airfoil function with added perturbation in the second design space; u lu * (t lu ) represents the relative airfoil function with added perturbation in the third design space; u ll * (t ll ) represents the relative airfoil function after adding perturbations in the fourth design space; δ(t) uu ,b uu ) is the perturbation function in the orthogonal curvilinear coordinate system within the first design space; δ(t) ul ,b ul ) represents the perturbation function in the orthogonal curvilinear coordinate system within the second design space; δ(t) lu ,b lu ) represents the perturbation function in the orthogonal curvilinear coordinate system within the third design space; δ(t) ll ,b ll ) represents the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; b uu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the first design space;ul b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the second design space. lu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the third design space. ll The perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; u upp (t uu ) represents the relative airfoil function curve within the first design space; u upp (t ul ) represents the relative airfoil function curve within the second design space; u low (t lu ) represents the relative airfoil function curve within the third design space; u low (t ll ) represents the relative airfoil function curve within the fourth design space.
[0039] In the specific implementation process, in S6, the expression for the upper curve of the airfoil after adding disturbance is:
[0040]
[0041] The expression for the lower curve of the airfoil after adding the disturbance is:
[0042]
[0043] in, The generated upper curve of the airfoil after adding perturbations. The lower curve of the generated airfoil after adding perturbations; The function curve on the first airfoil after adding perturbation; The function curve on the second airfoil after adding perturbation; The function curve of the first airfoil after adding perturbation; The function curve of the second airfoil after adding perturbation.
[0044] Compared with the prior art, the present invention has the following beneficial effects:
[0045] This invention provides a parameterization method for airfoil with a fixed disturbance design space. This method transforms geometric boundary constraints into parameterized parameters, eliminating the geometric boundary constraints in the optimization problem. It provides a targeted parameterization method for specific airfoil geometry optimization problems, thereby saving optimization time while ensuring the accuracy of the airfoil optimization solution. Furthermore, the parameterization method provided by this invention can also achieve local parameterization correction of the airfoil by providing a local design space. By specifying a local design space for a certain segment of the airfoil surface and establishing a coordinate system using the airfoil parameterization method with a fixed disturbance design space, airfoil geometry optimization with only local changes can be achieved. Attached Figure Description
[0046] Figure 1 This is a flowchart of the airfoil parameterization method for the design space of the present invention.
[0047] Figure 2 In the figure, Figure (a) shows the upper and lower airfoil curves of the present invention; Figure (b) shows the intermediate guide line, the upper airfoil curve, and the lower airfoil curve of the present invention.
[0048] Figure 3 This is a schematic diagram of the design space for the airfoil parameterization method for the constant disturbance design space of the present invention.
[0049] Figure 4 In the figure, Figure (a) is a schematic diagram of the curve coordinate system of the upper curve of the relative airfoil in the design space; Figure (b) is a schematic diagram of the curve coordinate system of the lower curve of the relative airfoil in the design space.
[0050] Figure 5 In the figure, Figure (a) shows the airfoil upper curve under the influence of the disturbance component; Figure (b) shows the airfoil lower curve under the influence of the disturbance component.
[0051] Figure 6 In the figure, Figure (a) is a schematic diagram of the airfoil update after the upper curve of the relative airfoil is disturbed and corrected according to the curve coordinate system in the design space; Figure (b) is a schematic diagram of the airfoil update after the lower curve of the relative airfoil is disturbed and corrected according to the curve coordinate system in the design space.
[0052] Figure 7 This is a comparison diagram of the original airfoil and the disturbed airfoil of the present invention. Detailed Implementation
[0053] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.
[0054] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0055] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.
[0056] This invention provides a method for airfoil parameterization in a fixed disturbance design space, comprising the following steps:
[0057] S1: Map the basic airfoil to the Cartesian coordinate system to obtain the upper and lower curves of the airfoil;
[0058] S2: Based on the upper and lower airfoil curves, obtain the intermediate guide line, the relative upper airfoil curve, and the relative lower airfoil curve;
[0059] S3: Set the upper and lower boundaries of the total design space and divide the total design space into four design spaces according to the intermediate guide line, the upper curve of the relative airfoil, and the lower curve of the relative airfoil. Establish orthogonal curve coordinate systems based on the four design spaces respectively.
[0060] S4: Transform the relative airfoil upper curve and relative airfoil lower curve to orthogonal curvilinear coordinate systems of two adjacent design spaces with the relative airfoil upper curve and relative airfoil lower curve as boundaries to obtain the relative airfoil function curve;
[0061] S5: Add perturbation functions to the relative airfoil function curves respectively to obtain the relative airfoil function curves after perturbation; transform the relative airfoil function curves after perturbation from their respective orthogonal curvilinear coordinate systems to the Cartesian coordinate system to obtain the airfoil function curves after perturbation.
[0062] S6: Based on the perturbation-added airfoil function curve, obtain the perturbation-added airfoil upper curve and the perturbation-added airfoil lower curve, obtain the perturbation airfoil, and complete the airfoil parameterization.
[0063] This invention calculates the intermediate guide line based on the basic airfoil, and divides the design space into four design spaces by setting the upper and lower boundaries of the design space relative to the upper and lower airfoil curves. Orthogonal curve coordinate systems are constructed for each space, and the upper and lower airfoil curves are transformed into the orthogonal curve coordinate systems of the four design spaces. A disturbance is added to the transformed airfoil curves to form new curves, which are then transformed into Cartesian coordinates to form the disturbed upper and lower airfoil curves. This achieves the beneficial effect of improving the aerodynamic performance of the airfoil in a given design space with as few parameters as possible.
[0064] The present invention will now be described in further detail with reference to the accompanying drawings:
[0065] See Figure 1 As shown, the present invention provides a method for airfoil parameterization in a fixed disturbance design space, comprising the following steps:
[0066] Step 1: Map the basic airfoil to a Cartesian coordinate system. The upper part of the basic airfoil's y-axis is the upper curve of the airfoil. The lower part of the y-axis is the lower curve of the airfoil. Among them, the upper curve of the airfoil is larger than the lower curve of the airfoil, that is...
[0067] Step 2: Based on the airfoil curve and the lower curve of the airfoil Obtain the intermediate guide line y mid (x), relative airfoil curve y upp (x) and the relative airfoil curve y low (x);
[0068] The process of obtaining the intermediate guide line, relative to the upper airfoil curve, and relative to the lower airfoil curve based on the upper and lower airfoil curves is as follows:
[0069]
[0070]
[0071]
[0072] Among them, y mid (x) is the intermediate leading line, y upp (x) represents the curve relative to the airfoil, y low (x) represents the curve relative to the airfoil. For the upper curve of the airfoil, This refers to the lower curve of the airfoil.
[0073] Step 3: Set the upper boundary y of the overall design space DBCu (x) and lower boundary y DBCl (x) and according to the intermediate guide line y mid (x), relative airfoil curve y upp (x) and the relative airfoil curve y low (x) Divide the total design space into four design spaces, and establish orthogonal curvilinear coordinate systems based on the four design spaces respectively; where the upper boundary y DBCu (x) is greater than the curve y on the relative airfoil. upp (x), lower boundary y DBCl (x) is less than the relative airfoil curve y low (x);
[0074] The upper boundary y of the total design space DBCu (x) and the curve y on the relative airfoil upp The first design space Ω formed by (x) UU , relative airfoil curve y upp (x) and the intermediate leading line y mid The second design space Ω constituted by (x) UL y-curve relative to airfoil l o w (x) and the intermediate leading line y mid The third design space Ω constituted by (x) LU y-curve relative to airfoil l o w (x) and the lower boundary y of the total design space DBCl The fourth design space Ω constituted by (x) LL In the first design space Ω UU Second design space Ω UL Third design space Ω LU Fourth Design Space Ω LL Construct orthogonal curvilinear coordinate systems respectively.
[0075] Establishing an orthogonal curvilinear coordinate system involves the following steps:
[0076] Step S31: Define the potential energy on the initial curve boundary as 0, and define the potential energy on the perturbation boundary as 1;
[0077] Step S32: Solve the Laplace equation in each design space according to the boundary conditions in step S31, and obtain the vector field distribution in the design space through numerical solution; the field lines and equipotential lines of the vector field obtained by solving the Laplace equation in the design space are used as two coordinates u and t in the curvilinear coordinate system; where the coordinate u of any point represents the potential of that point, and the value range is [0,1].
[0078] Specifically, Dirichlet boundary conditions are used as boundary conditions; four design spaces are constructed using the Laplace equation based on the Dirichlet boundary conditions to obtain the field lines and equipotential lines of the vector fields; the field lines and equipotential lines of the vector fields are used as the coordinates u and t of the corresponding orthogonal curvilinear coordinate systems, respectively.
[0079] Wherein, the coordinate u of any point represents the potential of that point, and the value of the coordinate u ranges from [0,1].
[0080] Step 4: Adjust the curve y on the relative airfoil upp (x), relative airfoil curve y low (x) are transformed into the orthogonal curvilinear coordinate system of the two adjacent design spaces with x as the boundary to obtain the relative airfoil function curve;
[0081] In the specific implementation process, the curve y on the relative airfoil will be... upp (x) are respectively transformed into the first design space Ω UU With the second design space Ω UL The constructed orthogonal curvilinear coordinate system is relative to the lower airfoil curve y l o w (x) respectively transform the third design space Ω LU With the fourth design space Ω LL The constructed orthogonal curvilinear coordinate system is transformed relative to the airfoil curve as follows: u upp (t uu ), u upp (t ul ), u low (t lu ), u low (t ll ), where the coordinate u represents the potential at that point, with a value range of [0,1]. The relative airfoil functions one, two, three, and four in the relative airfoil function curves are: u upp (t uu ), u upp (t ul ), u low (t lu), u low (t ll ).
[0082] Specifically, the relative airfoil function curves include the relative airfoil function curves u within the first design space. upp (t uu The relative airfoil function curve u in the second design space upp (t ul The relative airfoil function curve u in the third design space low (t lu ) and the relative airfoil function curve u in the fourth design space low (t ll ).
[0083] Step 5: On the relative airfoil function curve: u upp (t uu ), u upp (t ul ), u low (t lu ), u low (t ll Add perturbations to each of the following, and obtain the relative airfoil function curves after adding perturbations;
[0084] The relative airfoil function curve after adding perturbation is u uu * (t uu ), u ul * (t ul ), u lu * (t lu ), u ll * (t ll ); where u uu * (t uu ) represents the relative airfoil function with added perturbation in the first design space; u ul * (t ul ) represents the relative airfoil function with added perturbation in the second design space; u lu * (t lu ) represents the relative airfoil function with added perturbation in the third design space; u ll * (t ll ) represents the relative airfoil function after adding perturbations within the fourth design space;
[0085] The airfoil function formula after adding perturbation is:
[0086] uuu * (t uu )=u upp (t uu )+δ(t uu ,b uu )
[0087] u ul * (t ul )=u upp (t ul )+δ(t ul ,b ul )
[0088] u lu * (t lu )=u low (t lu )+δ(t lu ,b lu )
[0089] u ll * (t ll )=u low (t ll )+δ(t ll ,b ll )
[0090] Among them, u uu * (t uu ) represents the relative airfoil function with added perturbation in the first design space; u ul * (t ul ) represents the relative airfoil function with added perturbation in the second design space; u lu * (t lu ) represents the relative airfoil function with added perturbation in the third design space; u ll * (t ll ) represents the relative airfoil function after adding perturbations in the fourth design space; δ(t) uu ,b uu ) is the perturbation function in the orthogonal curvilinear coordinate system within the first design space; δ(t) ul ,b ul ) represents the perturbation function in the orthogonal curvilinear coordinate system within the second design space; δ(t) lu ,b lu ) represents the perturbation function in the orthogonal curvilinear coordinate system within the third design space; δ(t) ll ,b ll) represents the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; b uu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the first design space; ul b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the second design space. lu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the third design space. ll The perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; u upp (t uu ) represents the relative airfoil function curve within the first design space; u upp (t ul ) represents the relative airfoil function curve within the second design space; u low (t lu ) represents the relative airfoil function curve within the third design space; u low (t ll () represents the relative airfoil function curve within the fourth design space;
[0091] The disturbance function is the disturbance amount along the normal direction of the basic airfoil. The disturbance function is expressed in an orthogonal curvilinear coordinate system as follows:
[0092]
[0093] Among them, b i The i-th design parameter represents the disturbance amount, and its value ranges from [0,1]. These are called k-th (k-1) degree B-spline basis functions. Each B-spline basis function is a k-th degree piecewise polynomial defined on a sequence T of non-decreasing parameters t, where the sequence T is a sequence of non-decreasing parameters t. The above B-spline basis functions are defined by the de Boor-Cox formula, as shown below:
[0094]
[0095] Where ψ is the value of the independent variable of the B-spline basis function; k is the order of the B-spline; t i is a non-decreasing parameter in sequence T.
[0096] Step Six: Add perturbation to the four curves u uu * (t uu ), u ul * (t ul ), u lu * (t lu ), u ll *(t ll Transform from their respective curvilinear coordinate systems to Cartesian coordinate systems to obtain the perturbation-added airfoil function curves; the perturbation-added airfoil function curves are as follows: in, The function curve on the first airfoil after adding perturbation; The function curve on the second airfoil after adding perturbation; The function curve of the first airfoil after adding perturbation; The function curve of the second airfoil after adding perturbation;
[0097] Step 7: Based on the perturbation-added airfoil function curve, obtain the perturbation-added airfoil upper curve and the perturbation-added airfoil lower curve to obtain the perturbation airfoil and complete the airfoil parameterization;
[0098] The upper and lower curves of the airfoil after adding perturbation are as follows:
[0099]
[0100]
[0101] in, For the generated upper curve of the perturbation airfoil, The generated lower curve of the airfoil after perturbation; The function curve on the first airfoil after adding perturbation; The function curve on the second airfoil after adding perturbation; The function curve of the first airfoil after adding perturbation; The function curve of the second airfoil after adding perturbation.
[0102] Example
[0103] This embodiment provides a method for parameterizing airfoil design space with a fixed disturbance, including the following steps:
[0104] Step S1: As Figure 2 (a) shows the basic airfoil, model number NLF0416. Mapping the basic airfoil to a Cartesian coordinate system, the upper part of the basic airfoil's y-axis is the upper curve of the airfoil. The lower part of the y-axis is the lower curve of the airfoil.
[0105] Step S2: Calculate the intermediate guide line y mid (x), relative airfoil curve y upp (x), relative airfoil curve y low (x); such as Figure 2 As shown in (b).
[0106] y mid (x)=(y upp (x)+y low (x)) / 2;
[0107]
[0108]
[0109] Step S3: As Figure 3 As shown, the upper boundary y of the total design space is set. DBCu (x), lower boundary y DBCl (x), the design space can be freely chosen, that is, the upper boundary y DBCu (x), lower boundary y DBCl (x) can be any curve, encompassing the entire wing or only a portion thereof; y corresponds to the upper and lower boundaries of the design space on the airfoil, respectively. DBCu (x) and y mid (x); The upper and lower boundaries of the design space under the airfoil are y mid (x) and y DBCl (x); then, the relative upper airfoil curve, the intermediate guide line, and the relative lower airfoil curve divide the design space into four design spaces; the upper airfoil curve y upp (x) and its upper boundary y DBCu (x) constitutes the design space Ω UU That is, the first design space; the upper curve y of the airfoil upp (x) and y mid (x) constitutes the design space Ω UL That is, the second design space; the lower airfoil curve y l o w (x) and y mid (x) constitutes the design space Ω LU That is, the third design space; the lower airfoil curve y l o w (x) and its lower boundary y DBCl (x) constitutes the design space Ω LL That is, the fourth design space; construct orthogonal curvilinear coordinate systems in the four design spaces respectively; the curve y on the airfoil upp (x) design space Ω U From Ω UU and Ω UL Composition, lower airfoil curve y l o w (x) design space Ω L From Ω LU and Ω LL composition;
[0110] Preferably, the design space is a rectangular design space; other design spaces can be designed using the same method.
[0111] Four design spaces each construct an orthogonal curvilinear coordinate system, such as Figure 4 As shown, where y DBCu (x) is greater than y upp (x), y DBCl (x) is less than y low (x), the specific process:
[0112] Vector fields were constructed in four design spaces using the Laplace equations, with the boundary conditions defined as Dirichlet boundary conditions. The potential on the original relative airfoil was defined as 0, and the potential at the perturbation design boundary was defined as 1. The vector fields were solved using the finite element method in the MATLAB toolbox. Based on the solved vector fields, equipotential lines and field lines were calculated, as follows: Figure 4 As shown, the field lines and equipotential lines are used as the coordinates u and t of the corresponding orthogonal curvilinear coordinate system, respectively. That is, the equipotential lines and field lines are used as the abscissa and ordinate of the curvilinear coordinate system, respectively.
[0113] Step S4: Adjust the curve y on the relative airfoil upp (x), relative airfoil curve y low (x) respectively transform to the orthogonal curvilinear coordinate system of the two adjacent design spaces with it as the boundary. upp (t), u low (t), to obtain the relative airfoil function for the corresponding design space: u upp (t uu ), u upp (t ul ), u low (t lu ), u low (t ll );
[0114] Step S5: Obtain the perturbation curve by solving for the perturbation parameters in four curvilinear coordinate systems. The perturbation function in the curvilinear coordinate system is as follows: Figure 5 As shown in Figures (a) and (b), the disturbance function is composed of a linear superposition of polynomials. In particular, when all design parameters are 0, it represents the original airfoil curve, and when all design parameters are 1, it represents the situation where the design boundary is reached.
[0115] This shows that the design space of this method is consistent with the initially set design space range. It can be proven that when the design parameter b... iWhen the number of possible values approaches infinity, this method can traverse all single-valued function curves passing through both endpoints within the design space under an orthogonal curvilinear coordinate system. This ensures that the design space is fully and effectively utilized, guaranteeing that curves within the design space can be searched without including unwanted curves from outside the design space.
[0116] Step S6; Add perturbation to the four curves u uu * (t uu ), u ul * (t ul ), u lu * (t lu ), u ll * (t ll Transform from their respective curvilinear coordinate systems to Cartesian coordinate systems to obtain the airfoil function curves after adding perturbations, as follows:
[0117] Step S7: Based on the perturbation-added airfoil function curve, obtain the perturbation-added airfoil upper curve and the perturbation-added airfoil lower curve. The perturbation-added airfoil upper and lower curves are expressed as follows:
[0118]
[0119]
[0120] in, The generated upper curve of the airfoil after adding perturbations. The lower curve of the generated airfoil after adding perturbations.
[0121] like Figure 6 Figure (a) shows the two disturbance curves of the basic airfoil's upper curve within its design space, and Figure 6 Figure (b) shows the two disturbance curves of the basic airfoil within its design space. The new airfoil after disturbance is obtained based on these disturbance curves, as shown below. Figure 7 As shown, the comparison diagram of the original airfoil and the disturbed airfoil of the present invention shows the basic airfoil (original airfoil) and the airfoil curve after disturbance (disturbed airfoil), achieving the beneficial effect of improving the aerodynamic performance of the airfoil in a given design space with as few parameters as possible.
[0122] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.
Claims
1. A method for parameterizing airfoil design space with a fixed disturbance, characterized in that, Includes the following steps: S1: Map the basic airfoil to the Cartesian coordinate system to obtain the upper and lower curves of the airfoil; S2: Based on the upper and lower airfoil curves, obtain the intermediate guide line, the relative upper airfoil curve, and the relative lower airfoil curve; S3: Set the upper and lower boundaries of the total design space and divide the total design space into four design spaces according to the intermediate guide line, the upper curve of the relative airfoil, and the lower curve of the relative airfoil. Establish orthogonal curve coordinate systems based on the four design spaces respectively. S4: Transform the relative airfoil upper curve and relative airfoil lower curve to orthogonal curvilinear coordinate systems of two adjacent design spaces with the relative airfoil upper curve and relative airfoil lower curve as boundaries to obtain the relative airfoil function curve; S5: Add perturbation functions to the relative airfoil function curves respectively to obtain the relative airfoil function curves after perturbation; transform the relative airfoil function curves after perturbation from their respective orthogonal curvilinear coordinate systems to the Cartesian coordinate system to obtain the airfoil function curves after perturbation. S6: Based on the perturbation-added airfoil function curve, obtain the perturbation-added airfoil upper curve and the perturbation-added airfoil lower curve, obtain the perturbation airfoil, and complete the airfoil parameterization.
2. The airfoil parameterization method for a constant disturbance design space according to claim 1, characterized in that, In S1, the upper curve of the airfoil is greater than the lower curve of the airfoil; in S3, the upper boundary is greater than the upper curve of the relative airfoil, and the lower boundary is less than the lower curve of the relative airfoil.
3. The airfoil parameterization method for a fixed disturbance design space according to claim 2, characterized in that, In S2, the process of obtaining the intermediate guide line, the relative upper airfoil curve, and the relative lower airfoil curve based on the upper and lower airfoil curves is as follows: Among them, y mid (x) is the intermediate leading line, y upp (x) represents the curve relative to the airfoil, y low (x) represents the curve relative to the airfoil. For the upper curve of the airfoil, This refers to the lower curve of the airfoil.
4. The airfoil parameterization method for a constant disturbance design space according to claim 3, characterized in that, In S3, the four design spaces are: the first design space formed by the upper boundary of the total design space and the upper curve of the relative airfoil; the second design space formed by the upper curve of the relative airfoil and the intermediate guide line; the third design space formed by the lower curve of the relative airfoil and the intermediate guide line; and the fourth design space formed by the lower curve of the relative airfoil and the lower boundary of the total design space.
5. The airfoil parameterization method for a constant disturbance design space according to claim 4, characterized in that, In step S3, the step of establishing an orthogonal curvilinear coordinate system is as follows: S31: Use Dirichlet boundary conditions as the boundary conditions; S32: Based on the Dirichlet boundary conditions, four design spaces are constructed using the Laplace equation to obtain the field lines and equipotential lines of the vector fields; the field lines and equipotential lines of the vector fields are used as the coordinates u and t of the corresponding orthogonal curvilinear coordinate systems, respectively. Wherein, the coordinate u of any point represents the potential of that point, and the value of the coordinate u ranges from [0,1].
6. The airfoil parameterization method for a constant disturbance design space according to claim 5, characterized in that, The upper curve of the relative airfoil is transformed into an orthogonal curve coordinate system constructed by the first design space and the second design space, and the lower curve of the relative airfoil is transformed into an orthogonal curve coordinate system constructed by the third design space and the fourth design space.
7. The airfoil parameterization method for a constant disturbance design space according to claim 6, characterized in that, In S5, the disturbance function is the disturbance amount along the normal direction of the upper edge of the basic airfoil. The disturbance function is expressed in an orthogonal curvilinear coordinate system as follows: Among them, b i The i-th design parameter representing the disturbance amount has a value range of [0,1]. It is called the k-th order B-spline basis function, where i is from 0 to n; Each B-spline basis function is a k-th order piecewise polynomial determined by a sequence T, where the sequence T is a sequence of non-decreasing parameters t; The B-spline basis functions described above are defined by the de Boor-Cox formula, as shown below: Where ψ is the value of the independent variable of the B-spline basis function; k is the order of the B-spline; t i is a non-decreasing parameter in sequence T.
8. The airfoil parameterization method for a constant disturbance design space according to claim 7, characterized in that, In S5, the formula for the relative airfoil function curve after adding the disturbance is as follows: u uu * (t uu )=u upp (t uu )+δ(t uu ,b uu ) u ul * (t ul )=u upp (t ul )+δ(t ul ,b ul ) u lu * (t lu )=u low (t lu )+δ(t lu ,b lu ) u ll * (t ll )=u low (t ll )+δ(t ll ,b ll ); Among them, u uu * (t uu ) represents the relative airfoil function with added perturbation in the first design space; u ul * (t ul ) represents the relative airfoil function with added perturbation in the second design space; u lu * (t lu ) represents the relative airfoil function with added perturbation in the third design space; u ll * (t ll ) represents the relative airfoil function after adding perturbations in the fourth design space; δ(t) uu ,b uu ) is the perturbation function in the orthogonal curvilinear coordinate system within the first design space; δ(t) ul ,b ul ) represents the perturbation function in the orthogonal curvilinear coordinate system within the second design space; δ(t) lu ,b lu ) represents the perturbation function in the orthogonal curvilinear coordinate system within the third design space; δ(t) ll ,b ll ) represents the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; b uu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the first design space; ul b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the second design space. lu b represents the perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the third design space. ll The perturbation parameters of the perturbation function in the orthogonal curvilinear coordinate system within the fourth design space; u upp (t uu ) represents the relative airfoil function curve within the first design space; u upp (t ul ) represents the relative airfoil function curve within the second design space; u low (t lu ) represents the relative airfoil function curve within the third design space; u low (t ll ) represents the relative airfoil function curve within the fourth design space.
9. The airfoil parameterization method for a constant disturbance design space according to claim 8, characterized in that, In step S6, the expression for the upper curve of the airfoil after adding the disturbance is: The expression for the lower curve of the airfoil after adding the disturbance is: in, The generated upper curve of the airfoil after adding perturbations. The lower curve of the generated airfoil after adding perturbations; The function curve on the first airfoil after adding perturbation; The function curve on the second airfoil after adding perturbation; The function curve of the first airfoil after adding perturbation; The function curve of the second airfoil after adding perturbation.