CN103942366B - The aerofoil profile and its generation method of the continual curvature represented based on four sections of rational Béziercurves - Google Patents

Abstract

The invention discloses a kind of aerofoil profile of continual curvature that represents of rational Béziercurve for being not less than three times based on four sections of number of times and its generation method, upper molded line leading edge is represented by two rational Béziercurves respectively with trailing edge part, the leading edge of lower profile is also represented by two rational Béziercurves respectively with trailing edge part, four rational Béziercurves are sequentially connected by the position and weights for adjusting the control vertex near splice point, produce the Curve of wing of a continual curvature.Parameter in function has clear and definite geometric meaning, by adjusting parameter value, can generate expected aerofoil profile or family of aerofoil sections, the leading edge radius of curvature of aerofoil profile can be controlled, the position of upper molded line peak and curvature and the afterbody contract angle of aerofoil profile, can generate trailing edge has the aerofoil profile of thickness and closing, realizes reverse design；Four rational Béziercurves can be allowed to approach existing aerofoil profile by adjusting parameter value, to obtain the approximate expression of existing aerofoil profile, can be applicable to positive Aerodynamic optimization design.

Description

The aerofoil profile of the continual curvature represented based on four sections of rational Béziercurves and its generation Method

Technical field

The present invention relates to the aerofoil profile of blade or wing of turbomachine and preparation method thereof, especially blade or wing and its Generation method

Background technology

At present, the aerofoil profile molded line of blade or wing typically determined by coordinate database, that is, provide a series of coordinate datas, so Connect the image lattice that data are represented with smooth curve in order afterwards, generate aerofoil profile molded line in this approach.What this kind of method was generated Molded line exists multi-party not enough：(1) molded line for generating is difficult to ensure that the overall seriality of curvature；(2) parameter in molded line expression formula Number is typically more, while also no clear and definite geometric meaning, and when parameter value changes, image can be difficult to predict Change, or even the air foil shape that is beyond expression；(3) it is difficult to can use similar smooth curve to connect for polytype aerofoil profile data Connect；(4) the aerofoil profile line that this kind of method is produced is only capable of representing an aerofoil profile, it is impossible to represent a family of aerofoil sections.

The content of the invention

For the deficiencies in the prior art in overcoming blade or air-foil making, the invention provides a kind of with four sections of number of times The aerofoil profile and its generation method of the continual curvature that the rational Béziercurve of 3 times is represented are not less than, when the parameter value in function is sent out During changing, a new aerofoil profile is generated as, and in function, the geometric meaning of parameter is very clear and definite, by adjusting parameter value, can Direction as expected generates aerofoil profile, realizes reverse design.

The technical solution adopted for the present invention to solve the technical problems is：The reasonable B é of 3 times are not less than with four sections of number of times Zier curve C₀、C₁、C₂And C₃By the Curve of wing for splicing and combining into a continual curvature, each section of rational Béziercurve by Function

Represent, or represented with its algebraic transformation formula, or represented with its coordinate transform formula, or with its parametric equation table Show, or represented with its polar coordinates type.

P in formula_i ^j=(x_i ^j,y_i ^j) (i=0,1 ..., n_j) it is n_jSecondary rational Béziercurve C_jControl vertex,It is curve C_jThe corresponding power of control vertex, C_jT () is curve C_jThe corresponding point of upper parameter t.Connecting method For：Four sections of curves are sequentially connected, C₀One endIt is set to the trailing edge point of molded line in aerofoil profile, the other endWith C₁One endSpell Connect, C₁The other endWith C₂One endSplicing, C₂The other endWith C₃One endSplicing, C₃The other endArrange For the trailing edge point of aerofoil profile lower profile, and by C₁With C₂Splice point be set to the leading edge point of aerofoil profile.

In order that the aerofoil profile represented by build-up curve is continual curvature, each section of rational Béziercurve needs to meet：WithAbscissa is identical；WithThree point on a straight line；WithThree point on a straight line and abscissa is identical； WithThree point on a straight line；Curve C_jWith C_j+1Curvature identical (j=0,1,2) in stitching portion.

Work as n_jTechnical scheme when=3 (j=0,1,2,3) is：Each section of 3 rational Béziercurves are by function

Represent, or represented with its algebraic transformation formula, or represented with its coordinate transform formula, or with its parametric equation table Show, or represented with its polar coordinates type.

In order that the aerofoil profile represented by build-up curve is continual curvature, each section of rational Béziercurve needs to meet (see figure 1)：WithAbscissa is identical；WithThree point on a straight line；WithThree point on a straight line and abscissa phase Together；WithThree point on a straight line；Curve C_jWith C_j+1Curvature identical (j=0,1,2) in stitching portion.Due to for 3 Secondary rational Béziercurve C_j, can be on the premise of curve shape not be changed by control vertex corresponding power It is adjusted to 1,1(WithIt is separate and byUniquely determine), therefore the curve in the technical program Function can be reduced to

So as to according to the curvature at two end points of every section of curve, uniquely determine as the following formulaWith

Here k_j+1Represent curve C_jWith C_j+1Stitching portion curvature (j=0,1,2), k₀Represent molded line trailing edge point in aerofoil profile Curvature, k₄Represent the curvature of aerofoil profile lower profile trailing edge point.

In the aerofoil profile generating function that the present invention is given, parameter is selected as the control vertex coordinate of reasonable B é zier functions With the curvature of splice point, it is 3 times in four curves, andWith3 points of place straight lines andWithWhen 3 points of place straight lines are each parallel to x-axis, the parameter that is mutually related is removed, 23 final separate parameters are：Ginseng Number 1 (WithAbscissa), parameter 2 (Vertical coordinate), parameter 3 (Abscissa), parameter 4 (Vertical coordinate), parameter 5 ( Abscissa), parameter 6 (Vertical coordinate), parameter 7 (Abscissa), parameter 8 (Abscissa), parameter 9 ( Vertical coordinate), parameter 10 (Abscissa), parameter 11 (Vertical coordinate), parameter 12 (Abscissa), parameter 13 (Vertical coordinate), parameter 14 (Abscissa), parameter 15 (Abscissa), parameter 16 (Abscissa), ginseng Number 17 (Vertical coordinate), parameter 18 (Vertical coordinate), parameter 19 (Place's curvature), parameter 20 (OrPlace curvature), parameter 21 (OrPlace's curvature), parameter 22 (OrPlace's curvature), parameter 23 (Place's curvature).

In above-mentioned 23 parameters, there are 15 parameters to correspond to the geometrical property of aerofoil profile：Parameter 1-2 (Coordinate) correspondence Trailing edge upper side position, parameter 1-4 (WithCoordinate) determine afterbody contract angle, the coordinate of camber line peak in parameter 6-7 correspondence, Parameter 10 (Abscissa) correspondence leading edge point abscissa, parameter 1,16-18 (WithCoordinate) determine afterbody contract Angle, parameter 19-23 correspond to the curvature of relevant position.

The generation method of the aerofoil profile of the continual curvature represented with four sections of rational Béziercurves is：First determine above-mentioned corresponding letter Number, or its algebraic transformation formula, or its coordinate transform formula, or its parametric equation, or its polar coordinates type embodies Formula, then presses the respective function, or its algebraic transformation formula, or its coordinate transform formula, or its parametric equation again respectively, or The expression of person its polar coordinates type generates aerofoil profile.Determine expression method be to parameter assignment, then can be respectively Obtain by the Curve of wing of a continual curvature of four sections of rational Béziercurve combination producings, giving different parameter class values can Different types of aerofoil profile is generated, also four rational Béziercurves can be allowed to approach existing aerofoil profile by adjusting parameter value, be given The approximate expression of existing aerofoil profile.

Beneficial effects of the present invention:By setup parameter excursion just can control generate aerofoil profile leading edge radius of curvature, on The position of molded line peak and curvature, the adjustment at afterbody contract angle and thickness, the different types of aerofoil profile of generation, the aerofoil profile curvature of generation Continuously, be not in any rough phenomenon.

Description of the drawings

The present invention is further described with example below in conjunction with the accompanying drawings.

Fig. 1 is the symbol diagram of four sections of three rational Béziercurves and its each control vertex.

Fig. 2 is one of aerofoil profile image embodiment with four three rational Béziercurves generations.

Fig. 3 is the two of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 4 is the three of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 5 is the four of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 6 is the five of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 7 is the six of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 8 is the seven of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Fig. 9 is the eight of the aerofoil profile image embodiment generated with four three rational Béziercurves.

Specific embodiment

For each group four three reasonable B é zier functions, some with the parameter value for determining are provided as embodiment Expression, and draw corresponding aerofoil profile image.

One of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate NACA0012 aerofoil profiles shown in Fig. 2.

The two of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate NACA63A010 aerofoil profiles shown in Fig. 3.

The three of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate NACA16018 aerofoil profiles shown in Fig. 4.

The four of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate RAE822 aerofoil profiles shown in Fig. 5.

The five of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate (2) -0010 supercritical airfoils of SC shown in Fig. 6.

The six of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate (2) -0414 supercritical airfoils of SC shown in Fig. 7.

The seven of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate (2) -0606 supercritical airfoils of SC shown in Fig. 8.

The eight of embodiment：Fol-lowing values are given respectively by the control vertex of four three reasonable B é zier functions and power

Substitute in mapping software, and merge image, generate (2) -0714 supercritical airfoils of SC shown in Fig. 9.

Claims (6)

1. a kind of aerofoil profile of the continual curvature for using four sections of rational Béziercurves to represent, is characterized in that：3 are not less than by four sections of number of times Secondary rational Béziercurve C₀、C₁、C₂And C₃Splice and combine into the Curve of wing of a continual curvature, each section of reasonable B é zier Curve function

$C_j\left(t\right)=\frac{\underset{i=0}{\overset{n_j}{\Σ}}{\mathrm{\ω}}_i^j{P}_i^j{B}_{i,n_j}\left(t\right)}{\underset{i=0}{\overset{n_j}{\Σ}}{\mathrm{\ω}}_i^j{B}_{i,n_j}\left(t\right)},0\≤t\≤1,n_j\≥3,j=0,1,2,3$

Represent, or represented with its algebraic transformation formula, or represented with its coordinate transform formula, or represented with its parametric equation, Or represented with its polar coordinates type；P in formula_i ^j(i=0,1 ..., n_j) it is n_jSecondary rational Béziercurve C_jControl vertex,It is curve C_jThe corresponding power of control vertex, C_jT () is curve C_jThe corresponding point of upper parameter t；

Connecting method is：Four sections of curves are sequentially connected, C₀One endIt is set to the trailing edge point of molded line in aerofoil profile, the other endWith C₁One endSplicing, C₁The other endWith C₂One endSplicing, C₂The other endWith C₃One endSplicing, C₃'s The other endIt is set to the trailing edge point of aerofoil profile lower profile, and by C₁With C₂Splice point be set to the leading edge point of aerofoil profile；

In order that the aerofoil profile represented by build-up curve is continual curvature, each section of rational Béziercurve needs to meet：WithIt is horizontal Coordinate is identical；With P₁ ¹Three point on a straight line；With P₁ ²Three point on a straight line and abscissa is identical； With P₁ ³Three point on a straight line；Curve C_jWith C_j+1Curvature identical (j=0,1,2) in stitching portion.

2. the aerofoil profile of the continual curvature for using four sections of rational Béziercurves to represent according to claim 1, is characterized in that：By Four sections of 3 rational Béziercurve C₀、C₁、C₂And C₃Splice and combine into the Curve of wing of a continual curvature, each section of reasonable B é Zier curves are by function

$C_j\left(t\right)=\frac{\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^j{P}_i^j{B}_{i,3}\left(t\right)}{\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^j{B}_{i,3}\left(t\right)},0\≤t\≤1,j=0,1,2,3$

Represent, or represented with its algebraic transformation formula, or represented with its coordinate transform formula, or represented with its parametric equation, Or represented with its polar coordinates type；

In order that the aerofoil profile represented by build-up curve is continual curvature, each section of rational Béziercurve needs to meet：WithIt is horizontal Coordinate is identical；With P₁ ¹Three point on a straight line；With P₁ ²Three point on a straight line and abscissa is identical； With P₁ ³Three point on a straight line；Curve C_jWith C_j+1Curvature identical (j=0,1,2) in stitching portion.

3. the aerofoil profile of the continual curvature for using four sections of rational Béziercurves to represent according to claim 1 and 2, its feature It is：By four sections of 3 rational Béziercurve C₀、C₁、C₂And C₃The Curve of wing of a continual curvature is spliced and combined into, each section has Reason Bézier curve is by function

$C_j\left(t\right)=\frac{P_0^j{B}_{0,3}\left(t\right)+{\mathrm{\ω}}_1^j{P}_1^j{B}_{1,3}\left(t\right)+{\mathrm{\ω}}_2^j{P}_2^j{B}_{2,3}\left(t\right)+P_3^j{B}_{3,3}\left(t\right)}{B_{0,3}\left(t\right)+{\mathrm{\ω}}_1^j{B}_{1,3}\left(t\right)+{\mathrm{\ω}}_2^j{B}_{2,3}\left(t\right)+B_{3,3}\left(t\right)},0\≤t\≤1,j=0,1,2,3$

Represent, or represented with its algebraic transformation formula, or represented with its coordinate transform formula, or represented with its parametric equation, Or represented with its polar coordinates type；

In order that the aerofoil profile represented by build-up curve is continual curvature, each section of rational Béziercurve needs to meet：WithIt is horizontal Coordinate is identical；With P₁ ¹Three point on a straight line；With P₁ ²Three point on a straight line and abscissa is identical； With P₁ ³Three point on a straight line；Curve C_jWith C_j+1Curvature identical (j=0,1,2) in stitching portion.

4. the generation method of the aerofoil profile of the continual curvature for being represented with four sections of rational Béziercurves, is characterized in that：Including following step Suddenly

1) first determine each section of rational Béziercurve

$C_j\left(t\right)=\frac{\underset{i=0}{\overset{n_j}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^j{P}_i^j{B}_{i,n_j}\left(t\right)}{\underset{i=0}{\overset{n_j}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^j{B}_{i,n_j}\left(t\right)},0\≤t\≤1,n_j\≥3,j=0,1,2,3$

Frequency n_j, control vertex coordinateAnd each splice point and the curvature at upper lower profile trailing edge point, or The value of the relevant parameter in its algebraic transformation formula, or its coordinate transform formula, or its parametric equation, or its polar coordinates type； In order that the aerofoil profile represented by build-up curve is continual curvature, need to expire when each section of rational Béziercurve apex coordinate is established Foot：WithAbscissa is identical,With P₁ ¹Three point on a straight line；With P₁ ²Three point on a straight line and abscissa It is identical, With P₁ ³Three point on a straight line, and determined in each section of curve controlled summit by given curvatureOrOr AndOrOrCorresponding power, the two power can not correspond to identical control vertex；

2) the corresponding power of each section of curve other control vertex is determined again；

3) and then above-mentioned expression formula, or its algebraic transformation formula, or its coordinate transform formula, or its parametric equation are pressed, or Its polar coordinates type, generates aerofoil profile.

5. the generation method of the aerofoil profile of the continual curvature for being represented with four sections of 3 rational Béziercurves, is characterized in that：

First determine each section of rational Béziercurve

$C_j\left(t\right)=\frac{\underset{i=0}{\overset{3}{\Σ}}{\mathrm{\ω}}_i^j{P}_i^j{B}_{i,3}\left(t\right)}{\underset{i=0}{\overset{3}{\Σ}}{\mathrm{\ω}}_i^j{B}_{i,3}\left(t\right)},0\≤t\≤1,j=0,1,2,3$

Frequency n_j, control vertex coordinateAnd splice point and the curvature at upper lower profile trailing edge point, Huo Zheqi The value of the relevant parameter in algebraic transformation formula, or its coordinate transform formula, or its parametric equation, or its polar coordinates type；For The aerofoil profile represented by build-up curve is made to be continual curvature, each section of rational Béziercurve needs to meet：WithAbscissa phase Together； With P₁ ¹Three point on a straight line,With P₁ ²Three point on a straight line and abscissa is identical,With P₁ ³ Three point on a straight line；And the power of any two control vertex in each section of curve controlled summit is determined by given curvature, it is then determined that respectively The corresponding power of other control vertexs of section curve, finally by above-mentioned expression formula, or its algebraic transformation formula, or its coordinate transform Formula, or its parametric equation, or its polar coordinates type, generate aerofoil profile.

6. the generation method of the aerofoil profile of the continual curvature for being represented with four sections of 3 rational Béziercurves, is characterized in that：

First determine each section of rational Béziercurve

$C_j\left(t\right)=\frac{P_0^j{B}_{0,3}\left(t\right)+{\mathrm{\ω}}_1^j{P}_1^j{B}_{1,3}\left(t\right)+{\mathrm{\ω}}_2^j{P}_2^j{B}_{2,3}\left(t\right)+P_3^j{B}_{3,3}\left(t\right)}{B_{0,3}\left(t\right)+{\mathrm{\ω}}_1^j{B}_{1,3}\left(t\right)+{\mathrm{\ω}}_2^j{B}_{2,3}\left(t\right)+B_{3,3}\left(t\right)},0\≤t\≤1,j=0,1,2,3$

Frequency n_j, control vertex coordinateAnd splice point and the curvature at upper lower profile trailing edge point, Huo Zheqi The value of the relevant parameter in algebraic transformation formula, or its coordinate transform formula, or its parametric equation, or its polar coordinates type；For The aerofoil profile represented by build-up curve is made to be continual curvature, each section of rational Béziercurve needs to meet：WithAbscissa phase Together； With P₁ ¹Three point on a straight line；With P₁ ²Three point on a straight line and abscissa is identical；With P₁ ³ Three point on a straight line；And power in each section of curve is determined by given curvatureWithValue；

Then above-mentioned expression formula, or its algebraic transformation formula, or its coordinate transform formula, or its parametric equation, Huo Zheqi are pressed Polar coordinates type, generates aerofoil profile.