A method for parameterized modeling and interactive design of a blunt trailing edge airfoil

Abstract

A blunt trailing edge airfoil parameterized modeling and interactive design method, in the interactive design system input existing blunt trailing edge airfoil curve coordinate point sequence, based on the blunt trailing edge airfoil parameterized modeling method, get initial fitting curve, the initial fitting curve and each control point are displayed on the interactive interface, operator changes the position of each control point, real-time generation new airfoil curve coordinate point sequence, new airfoil curve and new control point are displayed in real time on the interactive interface of software, and the coordinates of new control point and the coordinate point sequence of new airfoil curve are obtained, the coordinate point sequence of new airfoil curve is input into aerodynamic performance analysis software, and whether the new airfoil meets the aerodynamic performance requirement is calculated and analyzed in real time. The present application is based on Bezier curve for blunt trailing edge airfoil and proposes a simple and feasible parameterized modeling method, the shape of airfoil curve is adjusted and designed by using interactive interface, which is very intuitive and achieves the effect of visual design.

Description

Technical Field

[0001] This invention belongs to the technical field of airfoil design in mechanical engineering, specifically relating to a parametric modeling and interactive design method for blunt trailing edge airfoils. Background Technology

[0002] Airfoils are widely used in aerospace, shipbuilding and marine engineering, renewable energy, and other fields. Zhukovsky first used mathematical methods to draw a series of airfoils. Later, people combined theoretical analysis with wind tunnel tests, and the design theory of airfoils was gradually improved. This work ultimately led to the most widely used NACA airfoil family. The U.S. Renewable Energy Laboratory designed the NREL-S series of airfoils for wind turbines using inverse design methods.

[0003] Currently, experts and scholars employ various methods for parametric modeling of airfoils, including the characteristic parameter method, wall function perturbation method, and B-spline method. In airfoil design, there are multiple methods: using various parametric modeling methods to model the airfoil; changing certain parameters of the airfoil based on intelligent optimization algorithms and conducting extensive calculations to find the corresponding airfoil that meets the specifications; and exploring the impact of different airfoil parameter changes on airfoil performance under specific conditions. The common problems with existing airfoil design methods are: (1) the airfoil modeling process is complex; and (2) interactive design methods are rarely used in the airfoil design process. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to propose a simple and feasible parametric modeling method for airfoils and an interactive airfoil design method based on it, which can bring convenience to airfoil design and provide a foundation for airfoil optimization design.

[0005] To achieve the aforementioned objectives, the present invention adopts the following technical solution:

[0006] A parametric modeling and interactive design method for blunt trailing edge airfoils includes:

[0007] Step 1. Input the sequence of coordinate points of the existing blunt trailing edge airfoil curve (hereinafter referred to as the parent curve) into the computer's interactive design system.

[0008] In this step, the existing blunt trailing edge airfoil curve is usually obtained by processing based on the conventional airfoil curve (such as the NACA series airfoil curve); the coordinate point sequence is the set of the horizontal and vertical coordinates of each point on the parent curve in the rectangular coordinate system.

[0009] Step 2. Obtain the initial fitting curve based on the parametric modeling method for blunt trailing edge airfoils.

[0010] In this step, the specific process of the parametric modeling method for the blunt trailing edge airfoil is as follows: In the input coordinate point sequence, the midpoint of the airfoil chord is selected as the pole, and the ray from the pole to the center point of the airfoil trailing edge is selected as the polar axis, thus constructing a polar coordinate system; the upper trailing edge point of the airfoil is used as the starting point of the control point sequence, and the lower trailing edge point is used as the ending point of the control point sequence. Typically, a control point is selected within different polar angle ranges of the polar coordinate system (see the schematic diagram of this invention). Figure 1 In this method, the polar coordinate system is divided into six polar angle ranges. A control point is selected within each polar angle range, and the polar angle range of each control point lies between the polar angle range of the upper trailing edge point and the polar angle range of the lower trailing edge point. The aforementioned control points, together with the upper and lower trailing edge points, form a control point sequence (the control points in the control point sequence are divided into different polar angle ranges, making subsequent calculations simple and stable, which can be called the "control point partitioning method"). The deviation between the airfoil curve generated based on the control point sequence and the parent curve is used as the fitness. The polar angle and polar radius of each control point of the airfoil curve are used as design variables. The particle swarm optimization algorithm is used to perform least squares fitting on the parent curve to obtain an initial control point sequence composed of multiple control points that meet the fitting requirements, together with the upper and lower trailing edge points. The airfoil curve is generated based on the initial control point sequence and the Bézier curve formula. This airfoil curve is the initial fitted curve.

[0011] The formula for Bézier curves is:

[0012]

[0013] In this formula, k is the control point number, n is the number of control points, and t is a parameter that takes values ​​from 0 to 1; P k Let be the coordinates of the k-th control point in the polar coordinate system, which can be expressed as (ρ k ,α k ), where ρ and α are the polar radius and polar angle in the polar coordinate system, respectively; the sequence of all control points arranged in order is called the control point sequence, which can be represented as [P1, P2, P3…P…]. n B(t) is the obtained Bézier curve.

[0014] Considering that interactive computer design systems typically use a standard Cartesian coordinate system, it is necessary to convert the x and y coordinates of each control point in the control point sequence from the Cartesian coordinate system to the polar radius and polar angle in the polar coordinate system to generate the airfoil curve. The specific conversion formula is as follows:

[0015]

[0016]

[0017]

[0018] In this formula, x and y are the horizontal and vertical coordinates of each control point in the rectangular coordinate system, respectively, and ρ and α are the polar radius and polar angle of each control point in the polar coordinate system, respectively.

[0019] In the process of least-squares fitting of the parent curve using the particle swarm optimization algorithm, the deviation between the airfoil curve generated based on the control point sequence and the parent curve is used as the fitness, and the polar angle and polar radius of each control point of the airfoil curve are used as design variables.

[0020] Step 3. Display the initial fitted curve and each control point on the interactive interface of the interactive design system.

[0021] Step 4. The operator changes the position of each control point by long-pressing and dragging the mouse, and confirms the new position of each control point by releasing the mouse; by capturing the real-time position of the control points, the coordinate point sequence of the new airfoil curve is generated in real time. The new airfoil curve and the new control points are displayed in real time on the interactive interface of the software, and the coordinates of the new control points and the coordinate point sequence of the new airfoil curve are obtained.

[0022] During the interactive design process in this step, the coordinates of the new leading edge point of the final airfoil curve may not be (0,0). To address this issue, this application proposes an airfoil coordinate normalization transformation method, the specific process of which is as follows:

[0023] The coordinates of the new leading edge point of the new airfoil curve are (a, b). The coordinates of any point on the new airfoil curve are defined as (x, b). i ,y i ), calculate the distance l from this point to the center point of the trailing edge. i :

[0024]

[0025] Calculate the distance l from the new leading edge point to the center point of the trailing edge. m (This value is the maximum distance from each point on the new airfoil curve to the center point of the trailing edge):

[0026] l m =max(l i )

[0027] Calculate the angle θ0 between the line connecting the new leading edge point and the center point of the trailing edge and the x-axis:

[0028]

[0029] (x) can be obtained through the following formula. i ,y i Transformed coordinates (x) j ,y j ):

[0030]

[0031] Step 5. Input the coordinate point sequence of the new airfoil curve into the aerodynamic performance analysis software, and calculate and analyze in real time whether the new airfoil meets the aerodynamic performance requirements such as lift and drag coefficients. If the new airfoil meets the aerodynamic performance requirements, extract the coordinate point sequence of the current new airfoil curve as the airfoil shape data.

[0032] By employing the aforementioned technical solution, the parametric modeling and interactive design method for blunt trailing edge airfoils of the present invention has the following beneficial effects:

[0033] First, this invention proposes a simple and feasible parametric modeling method based on Bézier curves for blunt trailing edge airfoils.

[0034] Secondly, the present invention uses an interactive interface to adjust and design the shape of the airfoil curve, which is very intuitive and achieves the effect of visual design.

[0035] Third, this invention proposes a method for normalizing and transforming airfoil coordinates for non-standard airfoil coordinate points. Attached Figure Description

[0036] Figure 1 This is a schematic diagram illustrating the principle of the parametric modeling method for blunt trailing edge airfoils in this invention.

[0037] Figure 2 It is an interactive interface that generates the initial fitted curve and its control points by fitting the mother curve.

[0038] Figure 3 It refers to the shape of a new airfoil curve obtained by dragging several control points in an interactive interface.

[0039] Figure 4 This is a schematic diagram illustrating the principle of the airfoil coordinate normalization transformation method.

[0040] Figure 5 This is a diagram showing the lift and drag coefficients of a new airfoil during the interactive design process. Detailed Implementation

[0041] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments.

[0042] Please see Figures 2 to 4 This embodiment of a parametric modeling and interactive design method for blunt trailing edge airfoils includes:

[0043] Step 1. Run the Matlab interactive design system on the computer and input the coordinate point sequence of the blunt trailing edge airfoil curve generated based on a certain airfoil of the NACA series (see Table 1 below) into the aforementioned Matlab system;

[0044] Table 1. Coordinate point sequence of the blunt trailing edge airfoil curve generated based on a certain airfoil from the NACA series.

[0045] 1 1 0.005 19 0.09887 0.03736 37 0.30066 -0.03892 2 0.95012 0.009843 20 0.07387 0.03248 38 0.35049 -0.0395 3 0.90024 0.015356 21 0.0489 0.02656 39 0.40032 -0.03917 4 0.85033 0.021307 22 0.02401 0.01884 40 0.45015 -0.03751 5 0.80039 0.027407 23 0.01163 0.01354 41 0.5 -0.03497 6 0.7504 0.033465 24 0.00673 0.01056 42 0.54987 -0.03174 7 0.70038 0.039243 25 0.00431 0.00867 43 0.59975 -0.02804 8 0.65033 0.04462 26 0 0 44 0.64967 -0.02402 9 0.60025 0.049467 27 0.00569 -0.00767 45 0.69962 -0.0198 10 0.55014 0.053643 28 0.00827 -0.00916 46 0.7496 -0.01556 11 0.5 0.057029 29 0.01337 -0.0114 47 0.79962 -0.01148 12 0.44985 0.059415 30 0.02599 -0.01512 48 0.84968 -0.00784 13 0.39968 0.06059 31 0.0511 -0.02024 49 0.89977 -0.00501 14 0.34951 0.0601 32 0.07613 -0.024 50 0.94988 -0.00352 15 0.29934 0.05836 33 0.10113 -0.02702 51 1 -0.005 16 0.24919 0.05533 34 0.15106 -0.03168 52 1 0.005 17 0.19905 0.05097 35 0.20095 -0.03505 18 0.14894 0.04514 36 0.25081 -0.03743

[0046] Step 2. Obtain the initial fitting curve based on the parametric modeling method for blunt trailing edge airfoils.

[0047] The specific process of the parametric modeling method for blunt trailing edge airfoils is as follows: In the coordinate point sequence input in step 1, the midpoint of the airfoil chord is selected as the pole, and the ray from the pole to the center point of the airfoil trailing edge is taken as the polar axis, thus constructing a polar coordinate system. The upper trailing edge point is used as the starting point of the control point sequence, and the lower trailing edge point is used as the ending point. The polar coordinate system is divided into 10 different polar angle ranges, with one control point in each polar angle range. The 10 control points, along with the upper and lower trailing edge points, form the control point sequence. The deviation between the airfoil curve generated based on the control point sequence and the parent curve is used as the fitness. The polar angle and polar radius of each control point on the airfoil curve are used as design variables. The particle swarm optimization algorithm is used to perform least-squares fitting on the parent curve. This yields an initial control point sequence consisting of 10 control points that meet the fitting requirements (the coordinate data of the 10 control points are shown in Tables 2 and 3) and the upper and lower trailing edge points. The airfoil curve (i.e., the initial fitted curve) is generated based on the initial control point sequence and the Bézier curve formula.

[0048] Table 2 shows the coordinate data of the 10 control points after fitting (in rectangular coordinates).

[0049] 1 0.834961 0.020782 6 0.275127 -0.15378 2 0.541563 0.045207 7 0.482303 -0.01351 3 0.477692 0.111201 8 0.500448 -0.00138 4 0.43302 0.106931 9 0.530425 -0.09168 5 -1.37788 0.010798 10 0.500143 -6.9E-05

[0050] Table 3. Coordinate data of the 10 control points after fitting (in polar coordinates)

[0051] 1 0.061964 0.335606 6 3.741396 0.272425 2 0.827377 0.06141 7 3.793591 0.022264 3 1.768775 0.113417 8 5.026397 0.00145 4 2.130395 0.126176 9 5.032811 0.096599 5 3.135843 1.877907 10 5.833728 0.000158

[0052] Step 3. Display the initial fitted curve and control points obtained in Step 2 on the interactive interface of the Matlab system, such as... Figure 2 As shown in Table 4, the coordinate point sequence of the initial fitted curve is shown in Table 4, and the coordinate data of each control point is shown in Table 2.

[0053] Table 4. Coordinate point sequence of the initial fitted curve

[0054]

[0055]

[0056] Step 4. The operator changes the position of each control point by long-pressing and dragging the mouse, and confirms the new position of each control point by releasing the mouse; by capturing the real-time position of the control points, the coordinate point sequence of the new airfoil curve is generated in real time, and the new airfoil curve and the new control points are displayed in real time on the interactive interface of the Matlab system (e.g., Figure 3 As shown in Table 5), the coordinates of the new control points and the coordinate point sequence of the new airfoil curve are obtained (as shown in Table 6).

[0057] Table 5. Coordinate data of the new control point sequence

[0058] 1 1 0.005 7 0.2616 -0.2156 2 0.835 0.0208 8 0.4823 -0.0135 3 0.5416 0.0452 9 0.5004 -0.0014 4 0.4777 0.1112 10 0.5304 -0.0917 5 0.433 0.1069 11 0.5001 -0.0001 6 -1.3779 0.0108 12 1 -0.005

[0059] Table 6. Coordinate point sequence of the new airfoil curve

[0060]

[0061]

[0062] Through the interactive design in step 4, the final coordinates of the new leading edge point of the new airfoil curve obtained in this embodiment (i.e., point 60 in Table 6) are (-0.0025, -0.0079), not (0, 0). To address this issue, the airfoil coordinate normalization transformation method proposed in this application (see [link to application]) is used. Figure 4 The sequence of coordinate points after the transformation of the new airfoil curve is shown in Table 7.

[0063] Table 7. Coordinate point sequence after the transformation of the new airfoil curve.

[0064]

[0065]

[0066]

[0067] Step 5. Input the coordinate point sequence after the new airfoil curve is transformed into aerodynamic performance analysis software to calculate and analyze in real time whether the new airfoil meets the aerodynamic performance requirements such as lift and drag coefficients (e.g., Figure 5 As shown, if the new airfoil meets the user's performance requirements or requires further analysis, the coordinate point sequence of the current new airfoil curve is extracted as the airfoil shape data, thereby achieving the purpose of interactive and visual adjustment and design of the airfoil.

[0068] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The features described in the above embodiments and specification are only illustrative of the principles of the present invention. Various changes and modifications can be made to the present invention without departing from the spirit and scope of the present invention. All such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A parametric modeling and interactive design method for blunt trailing edge airfoils, characterized in that... include: Step 1. Input the sequence of coordinate points of the existing blunt trailing edge airfoil curve (hereinafter referred to as the parent curve) into the computer's interactive design system; Step 2. Obtain the initial fitting curve based on the parametric modeling method for blunt trailing edge airfoils; Step 3. Display the initial fitted curve and each control point on the interactive interface of the interactive design system; Step 4. The operator changes the position of each control point by long-pressing and dragging the mouse, and confirms the new position of each control point by releasing the mouse; by capturing the real-time position of the control points, the coordinate point sequence of the new airfoil curve is generated in real time. The new airfoil curve and the new control points are displayed in real time on the interactive interface of the software, and the coordinates of the new control points and the coordinate point sequence of the new airfoil curve are obtained. Step 5. Input the coordinate point sequence of the new airfoil curve into the aerodynamic performance analysis software, and calculate and analyze in real time whether the new airfoil meets the aerodynamic performance requirements. If the new airfoil meets the aerodynamic performance requirements, extract the coordinate point sequence of the current new airfoil curve as the airfoil shape data. In step 2, the specific process of the parametric modeling method for the blunt trailing edge airfoil is as follows: In the input coordinate point sequence, select the midpoint of the airfoil chord as the pole, and the ray from the pole to the center point of the airfoil trailing edge as the polar axis to construct a polar coordinate system; take the upper trailing edge point of the airfoil as the starting point of the control point sequence, and the lower trailing edge point of the airfoil as the ending point of the control point sequence. Select one control point in different polar angle ranges of the polar coordinate system. The selected multiple control points, together with the upper trailing edge point and the lower trailing edge point, form the control point sequence. The deviation between the airfoil curve generated based on the control point sequence and the parent curve is used as the fitness. The polar angle and polar radius of each control point of the airfoil curve are used as design variables. The particle swarm optimization algorithm is used to perform least squares fitting on the parent curve to obtain an initial control point sequence composed of multiple control points that meet the fitting requirements, the upper trailing edge point, and the lower trailing edge point. An airfoil curve is generated based on the initial control point sequence and the Bézier curve formula; this airfoil curve is the initial fitted curve.

2. The parametric modeling and interactive design method for blunt trailing edge airfoils according to claim 1, characterized in that... The formula for Bézier curves is: ； In this formula, For the control point numbering, The number of control points, The parameter takes values ​​from 0 to 1; For the first The coordinates of each control point in the polar coordinate system are expressed as follows: ρ and α are the polar radius and polar angle in polar coordinates, respectively; the sequence of all control points arranged in order is called the control point sequence, denoted as [ ]; The obtained Bézier curve.

3. The parametric modeling and interactive design method for blunt trailing edge airfoils according to claim 2, characterized in that... Among the selected multiple control points, the polar angle range of each control point lies between the polar angle range of the upper tail edge point and the polar angle range of the lower tail edge point.

4. The parametric modeling and interactive design method for blunt trailing edge airfoils according to claim 2, characterized in that... Since the interactive design system uses a rectangular coordinate system, it is necessary to convert the x and y coordinates of each control point in the rectangular coordinate system to the polar radius and polar angle in the polar coordinate system to generate the airfoil curve. The specific conversion formula is as follows: ； ； ； In this formula, x and y are the horizontal and vertical coordinates of each control point in the rectangular coordinate system, respectively, and ρ and α are the polar radius and polar angle of each control point in the polar coordinate system, respectively.

5. The parametric modeling and interactive design method for blunt trailing edge airfoils according to claim 1, characterized in that... In the interactive design process of step 4, the coordinate point sequence of the new airfoil curve is transformed using the airfoil coordinate transformation method. The specific process is as follows: The coordinates of the new leading edge point of the new airfoil curve are: Define the coordinates of any point on the new airfoil curve as... Calculate the distance l from this point to the center of the trailing edge. i : ； Calculate the distance from the new leading edge point to the center point of the trailing edge. : ； Calculate the angle between the line connecting the new leading edge point and the center point of the trailing edge and the x-axis. : ； The following formula is used to obtain... Transformed coordinates : 。

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