CN103942366B - The aerofoil profile and its generation method of the continual curvature represented based on four sections of rational Béziercurves - Google Patents
The aerofoil profile and its generation method of the continual curvature represented based on four sections of rational Béziercurves Download PDFInfo
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- CN103942366B CN103942366B CN201410109556.4A CN201410109556A CN103942366B CN 103942366 B CN103942366 B CN 103942366B CN 201410109556 A CN201410109556 A CN 201410109556A CN 103942366 B CN103942366 B CN 103942366B
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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
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 formulai j=(xi j,yi j) (i=0,1 ..., nj) it is njSecondary rational Béziercurve CjControl vertex,It is curve CjThe corresponding power of control vertex, CjT () is curve CjThe 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 CjWith Cj+1Curvature identical (j=0,1,2) in stitching portion.
Work as njTechnical 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 CjWith Cj+1Curvature identical (j=0,1,2) in stitching portion.Due to for 3
Secondary rational Béziercurve Cj, 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 kj+1Represent curve CjWith Cj+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
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 formulai j(i=0,1 ..., nj) it is njSecondary rational Béziercurve CjControl vertex,It is curve CjThe corresponding power of control vertex, CjT () is curve CjThe 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 CjWith Cj+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
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 CjWith Cj+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
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 CjWith Cj+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
Frequency nj, 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
Frequency nj, 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
Frequency nj, 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.
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CN104863799A (en) * | 2015-04-17 | 2015-08-26 | 湖北工业大学 | Method for designing wind turbine airfoil by using Bessel function curve |
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US7928984B1 (en) * | 2007-08-31 | 2011-04-19 | Adobe Systems Incorporated | Efficient data packaging for rendering bézier curves on a GPU |
CN103049593A (en) * | 2012-10-05 | 2013-04-17 | 李英明 | Method for calculating Hausdorff distance between two parameter curves |
CN103136341A (en) * | 2013-02-04 | 2013-06-05 | 北京航空航天大学 | Lane line reconstruction device based on Bezier curve |
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US7928984B1 (en) * | 2007-08-31 | 2011-04-19 | Adobe Systems Incorporated | Efficient data packaging for rendering bézier curves on a GPU |
CN103049593A (en) * | 2012-10-05 | 2013-04-17 | 李英明 | Method for calculating Hausdorff distance between two parameter curves |
CN103136341A (en) * | 2013-02-04 | 2013-06-05 | 北京航空航天大学 | Lane line reconstruction device based on Bezier curve |
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