Parametric modeling and interactive design method for blunt trailing-edge airfoil

Abstract

A parametric modeling and interactive design method for a blunt trailing-edge airfoil. The method comprises: inputting into an interactive design system a coordinate point sequence of an existing blunt trailing-edge airfoil curve; on the basis of a blunt trailing-edge airfoil parametric modeling method, obtaining an initial fitting curve; displaying the initial fitting curve and each control point on an interactive interface; by means of changing the position of each control point, an operator generating a coordinate point sequence of a new airfoil curve in real time, wherein the new airfoil curve and new control points are displayed in real time on the interactive interface of software, and the coordinates of the new control points and the coordinate point sequence of the new airfoil curve are obtained; and inputting the coordinate point sequence of the new airfoil curve into aerodynamic performance analysis software, and computing and analyzing in real time whether the new airfoil meets aerodynamic performance requirements. The present invention proposes a simple and feasible parametric modeling method for a blunt trailing-edge airfoil on the basis of Bezier curves. An interactive interface is used to adjust and design the shape of the airfoil curve, which is very intuitive and achieves the effect of visual design.

Description

A parametric modeling and interactive design method for blunt trailing edge airfoils Technical Field

[0001] The invention belongs to the technical field of airfoil design in mechanical engineering, and in particular relates to a parametric modeling and interactive design method for a blunt trailing edge airfoil. Background Art

[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 wing airfoils. Later, theoretical analysis combined with wind tunnel testing gradually refined airfoil design theory, ultimately leading to the widely used NACA family of airfoils. The National Renewable Energy Laboratory in the United States used inverse design methods to design the NREL-S series of airfoils for wind turbines.

[0003] Currently, experts and scholars have various methods for parametric modeling of airfoils: characteristic parameter method, wall function perturbation method, B-spline method, etc. There are many methods for designing airfoils: using various parametric modeling methods to model the airfoil; changing certain airfoil parameters based on intelligent optimization algorithms and searching for the corresponding airfoil that meets the requirements through a large number of calculations; exploring the impact of changing different airfoil parameters on airfoil performance under specific conditions, etc. The common problems of existing airfoil design methods are: (1) the airfoil modeling process is complicated; (2) the airfoil design process rarely adopts interactive design methods.

[0004] Summary of the Invention

[0005] In view of the above problems, the purpose of the present invention is to propose a simple and feasible airfoil parametric modeling method and an airfoil interactive design method based on the method, which can facilitate airfoil design and provide a basis for airfoil optimization design.

[0006] To achieve the aforementioned objectives, the present invention adopts the following technical solutions:

[0007] A parametric modeling and interactive design method for a blunt trailing edge airfoil, comprising:

[0008] Step 1. Input the coordinate point sequence of an existing blunt trailing edge airfoil curve (hereinafter referred to as a mother curve) into the interactive design system of a computer.

[0009] In this step, the existing blunt trailing edge airfoil curve is usually obtained based on a conventional airfoil curve (such as a NACA series airfoil curve); the coordinate point sequence is a set of horizontal and vertical coordinates of each point on the mother curve in a rectangular coordinate system.

[0010] Step 2. Based on the parametric modeling method of the blunt trailing edge airfoil, obtain the initial fitting curve.

[0011] In this step, the specific process of the parameterized modeling method of the blunt trailing edge airfoil is as follows: the midpoint of the chord length of the airfoil is selected as the pole in the input coordinate point sequence, and the ray from the pole to the center point of the trailing edge of the airfoil is selected as the polar axis to construct 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 of the airfoil is used as the end point of the control point sequence, and usually a control point is selected in different polar angle ranges of the polar coordinate system (the schematic diagram of the present invention (i.e., Figure 1) divides the polar coordinate system into six polar angle ranges, and a control point is selected in each polar angle range, and the polar angle range of each control point is 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 and The upper trailing edge points and the lower trailing edge points together constitute a control point sequence (the control points that make up the control point sequence are divided into different polar angle ranges, which makes subsequent calculations simple and stable, and can be called the "control point partitioning method"); the deviation between the airfoil curve generated based on the control point sequence and the mother curve is used as the fitness, and the polar angle and polar diameter 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 mother curve to obtain an initial control point sequence consisting of multiple control points that meet the fitting requirements and the upper trailing edge points and the lower trailing edge points; the airfoil curve is generated based on the initial control point sequence and the Bezier curve formula. This airfoil curve is the initial fitting curve.

[0012] The Bezier curve formula is:

[0013] In this formula, k is the number of the control point, n is the number of control points, and t is a parameter with a value from 0 to 1; P k is the coordinate of the kth control point in the polar coordinate system, which can be expressed as (ρ k ,α k ), 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 expressed as [P1, P2, P3…P n ]; B(t) is the obtained Bezier curve.

[0014] Considering that the computer interactive design system usually adopts the ordinary rectangular coordinate system, it is necessary to convert the horizontal and vertical coordinates of each control point in the rectangular coordinate system into the polar diameter and polar angle in the polar coordinate system to generate the airfoil curve. The specific conversion formula is:

[0015] In this formula, x and y are the horizontal and vertical coordinates of each control point in the rectangular coordinate system, and ρ and α are the polar diameter and polar angle of each control point in the polar coordinate system.

[0016] In the process of least square fitting of the mother curve using the particle swarm optimization algorithm, the deviation between the airfoil curve generated based on the control point sequence and the mother curve is used as the fitness, and the polar angle and polar diameter of each control point of the airfoil curve are used as design variables.

[0017] Step 3. Display the initial fitting curve and each control point on the interactive interface of the interactive design system.

[0018] 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 point, the coordinate point sequence of the new airfoil curve is generated in real time. The new airfoil curve and the new control point are displayed in real time on the interactive interface of the software, and the coordinates of the new control point and the coordinate point sequence of the new airfoil curve are obtained.

[0019] During the interactive design process of this step, the coordinates of the new leading edge point of the new airfoil curve may not be (0,0). To address this problem, this application proposes a method for normalizing the airfoil coordinates. The specific process is as follows:

[0020] The new leading edge coordinates of the new airfoil curve are (a, b). The coordinates of any point on the new airfoil curve are defined as (x i ,y i ), calculate the distance l from this point to the center of the trailing edge i :

[0021] Calculate the distance l from the new leading edge point to the trailing edge center point m (This value is the maximum distance from each point on the new airfoil curve to the center point of the trailing edge): m =max (l i )

[0022] Calculate the angle θ0 between the line connecting the new leading edge point and the trailing edge center point and the x-axis:

[0023] The following formula is used to obtain (x i ,y i )The transformed coordinates (x j ,y j ):

[0024] 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 the lift and drag coefficient. 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.

[0025] By means of the above technical solution, the parametric modeling and interactive design method of a blunt trailing edge airfoil of the present invention has the following beneficial effects:

[0026] First, the present invention proposes a simple and feasible parameterized modeling method based on Bezier curve for blunt trailing edge airfoils;

[0027] Second, the present invention uses an interactive interface to adjust and design the airfoil curve shape, which is very intuitive and achieves a visual design effect;

[0028] Third, the present invention proposes a method for normalizing airfoil coordinates for non-standard airfoil coordinate points. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] FIG1 is a schematic diagram showing the principle of the parameterized modeling method of the blunt trailing edge airfoil in the present invention.

[0030] FIG2 is an initial fitting curve generated by fitting the mother curve, and an interactive interface of each control point.

[0031] FIG3 shows the shape of the new airfoil curve obtained by dragging several control points in the interactive interface.

[0032] FIG4 is a schematic diagram showing the principle of the airfoil coordinate normalization transformation method.

[0033] Figure 5 is a graph of the lift and drag coefficients of a new airfoil during the interactive design process. DETAILED DESCRIPTION

[0034] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and preferred embodiments.

[0035] Referring to FIG. 2 to FIG. 4 , a method for parameterized modeling and interactive design of a blunt trailing edge airfoil according to this embodiment includes:

[0036] Step 1. Run the Matlab interactive design system on a 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;

[0037] Table 1 Coordinate point sequence of the blunt trailing edge airfoil curve generated based on a NACA series airfoil

[0038] Step 2. Based on the parametric modeling method of the blunt trailing edge airfoil, obtain the initial fitting curve.

[0039] The specific process of the parametric modeling method for blunt-trailing-edge airfoils is as follows: From 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 of the airfoil's trailing edge is used as the polar axis to construct 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 end point of the control point sequence. The polar coordinate system is divided into 10 different polar angle ranges, each with one control point. 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 value. The polar angle and polar radius of each control point of the airfoil curve are used as design variables. The parent curve is fitted with a particle swarm optimization algorithm using least squares fitting. 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 is obtained. The airfoil curve (i.e., the initial fitting curve) is generated based on the initial control point sequence and the Bezier curve formula.

[0040] Table 2 Coordinate data of 10 control points after fitting (in rectangular coordinate system)

[0041] Table 3 Coordinate data of 10 control points after fitting (in polar coordinate system)

[0042] Step 3. Display the initial fitting curve and each control point obtained in step 2 on the interactive interface of the Matlab system, as shown in Figure 2, where the coordinate point sequence of the initial fitting curve is shown in Table 4, and the coordinate data of each control point is shown in Table 2.

[0043] Table 4 Coordinate point sequence of the initial fitting curve

[0044] 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 point, 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 Matlab system (as shown in Figure 3), and the coordinates of the new control points (as shown in Table 5) and the coordinate point sequence of the new airfoil curve (as shown in Table 6) are obtained.

[0045] Table 5 Coordinate data of the new control point sequence

[0046] Table 6 Coordinate point sequence of the new airfoil curve

[0047] Through the interactive design in step 4, the new leading edge coordinates of the new airfoil curve ultimately obtained in this embodiment (i.e., point number 60 in Table 6) are (-0.0025, -0.0079), not (0, 0). To address this phenomenon, according to the airfoil coordinate normalization transformation method proposed in this application (see Figure 4), the coordinate point sequence of the new airfoil curve after transformation is shown in Table 7.

[0048] Table 7 Coordinate point sequence after conversion of the new airfoil curve

[0049] Step 5. Input the converted 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 the lift and drag coefficient (as shown in Figure 5). If the new airfoil meets the user's performance requirements or needs 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 visual adjustment and airfoil design.

[0050] The basic principles, main features and advantages of the present invention are shown and described above. 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 the specification are only for illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which shall fall within the scope of the present invention to be protected. 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 a blunt trailing edge airfoil, characterized in that include: Step 1. Input the coordinate point sequence of an existing blunt trailing edge airfoil curve (hereinafter referred to as a mother curve) into the interactive design system of the computer; Step 2. Based on the parameterized modeling method of the blunt trailing edge airfoil, an initial fitting curve is obtained; Step 3. Display the initial fitting 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 point, a coordinate point sequence of the new airfoil curve is generated in real time, the new airfoil curve and the new control point are displayed in real time on the interactive interface of the software, and the coordinates of the new control point 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.

2. A method for parameterized modeling and interactive design of a blunt trailing edge airfoil according to claim 1, characterized in that In step 2, the specific process of the blunt trailing edge airfoil parameterized modeling method is as follows: The midpoint of the chord length of the airfoil is selected as the pole in the input coordinate point sequence, and the ray from the pole to the center point of the trailing edge of the airfoil is selected as the polar axis to construct 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 of the airfoil is used as the end point of the control point sequence. Usually, one control point is selected in different polar angle ranges of the polar coordinate system, and the selected multiple control points and the upper trailing edge point and the lower trailing edge point together constitute a control point sequence; The deviation between the airfoil curve generated based on the control point sequence and the mother curve is used as the fitness, the polar angle and polar diameter of each control point of the airfoil curve are used as design variables, and the particle swarm optimization algorithm is used to perform least squares fitting on the mother curve to obtain an initial control point sequence consisting of multiple control points that meet the fitting requirements and the upper trailing edge points and the lower trailing edge points; Generate an airfoil curve based on the initial control point sequence and the Bezier curve formula, and the airfoil curve is the initial fitting curve; The Bezier curve formula is: In this formula, k is the number of the control point, n is the number of control points, and t is a parameter with a value ranging from 0 to 1; P k is the coordinate of the kth control point in the polar coordinate system, expressed as (ρ k ,α k ), 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 is expressed as [P1, P2, P3…P n ]; B(t) is the obtained Bezier curve.

3. A method for parameterized modeling and interactive design of a blunt trailing edge airfoil according to claim 2, characterized in that Among the selected multiple control points, the polar angle range of each control point is between the polar angle range of the upper trailing edge point and the polar angle range of the lower trailing edge point.

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

5. The method for parameterized modeling and interactive design of a blunt trailing edge airfoil according to claim 1, characterized in that In the interactive design process of step 4, the coordinates of the new leading edge point of the new airfoil curve may not be (0,0). To address this phenomenon, the coordinate point sequence of the new airfoil curve is transformed by the airfoil coordinate normalization transformation method. The specific process is as follows: The new leading edge coordinates of the new airfoil curve are (a, b); the coordinates of any point on the new airfoil curve are defined as (x i ,y i ), calculate the distance l from this point to the center of the trailing edge i : Calculate the distance l from the new leading edge point to the center point of the trailing edge m : L m =max(l i ) Calculate the angle θ0 between the line connecting the new leading edge point and the trailing edge center point and the x-axis: The following formula is used to obtain (x i ,y i )The transformed coordinates (x j ,y j ):

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