CN110704944B - Variable camber airfoil profile-oriented parametric modeling method - Google Patents
Variable camber airfoil profile-oriented parametric modeling method Download PDFInfo
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Abstract
The invention discloses a variable camber airfoil profile parameterization modeling method, which comprises the steps of establishing a parameterization model of an original airfoil profile, selecting a rigid section and a variable camber section and determining a station, establishing a bending beam model of the variable camber section, determining boundary conditions of a bending beam, establishing a bending beam with parameter representation, establishing a mapping relation between the bending beam and the initial profile, establishing rigidity distribution of the bending beam, and determining mass distribution of the bending beam in the seventh step for a dynamics analysis model. The method is used for: when the variable camber wing is designed, the shape of the variable camber airfoil profile is represented in a parameterization mode, and the parameterization representation is further used for optimizing the wing shape, analyzing structural statics and dynamics and analyzing aeroelasticity. The method has the advantage that the camber process of the real wing can be reasonably represented.
Description
Technical Field
The invention relates to a parametric modeling method for an airfoil profile, in particular to a parametric modeling method for a variable camber airfoil profile
Background
The variable camber wing, also called self-adaptive wing, morphing wing and compliant wing, is a novel wing concept. The wing can automatically change the camber of the wing profile of the wing according to the flight state in the flight process, particularly change the camber of the front edge and the rear edge of the wing so as to keep higher aerodynamic efficiency. For example, chinese patent CN106845019A discloses "an adaptive wing profile design method", which uses a CST (class function and shape function transformation) profile parameterization method to establish a parameterized description of an original wing profile, and optimizes some of the parameters to obtain an optimized profile. The wing profile parameterization method is used for modeling a complex aerodynamic profile of a wing profile of a flight wing in an equation form by using fewer parameters so as to facilitate the optimal design of the profile.
The existing modeling method for parameterization of the profile of the airfoil mostly takes the conventional airfoil as the main: most basically, the coordinate points are stored; some methods, similar to the CST method, characterize an airfoil by using a linear weighted stack of a series of specific curves; some of the wing profiles are created in a changing mode on the basis of the original wing profile. References d.a. masters, n.j.taylor, t.c.s.rendall, c.b.allen, and d.j.poole, "Geometric Comparison of aerol Shape Parameterization Methods", AIAA Journal, vol.55, No.5(2017), pp.1575-1589 introduce a number of modeling approaches to airfoil Parameterization and analyze the performance of the various approaches.
Some specific geometric parameters of the camber airfoil are given as initial design requirements, such as the downtilt angles of the trailing edge and the leading edge, which cannot be conveniently modeled using conventional airfoil parameterization methods. Meanwhile, most of the traditional wing profile parameterization methods are established in a mathematical mode, and physical and practical significance is lacked. In practice, lack of physically meaningful shape may lead to internal structure/construction difficulties.
Disclosure of Invention
According to one aspect of the present invention, there is provided a parametric modeling method for a varying camber airfoil, for parametrically characterizing a varying profile of the varying camber airfoil, comprising:
A) selecting an original airfoil profile, wherein the original airfoil profile refers to an airfoil profile which is selected from an airfoil profile database and has no change of self-curvature, and a characterization model which has a limited number of parameters and can characterize the outline of the original airfoil profile is established;
B) selecting a rigid section and a bending section, and determining a station position, wherein: the rigid section refers to a part which does not participate in bending in the variable-bending wing profile, the variable-bending section refers to a part which participates in bending in the variable-bending wing profile, and the station is a chord-wise distance taking the front edge of the original wing profile as a starting point;
C) establishing a bending beam model of a variable-camber section;
D) determining a first boundary condition and a second boundary condition of a bending beam, wherein the first boundary condition is a boundary constraint condition which needs to be met by a root of the bending beam, the second boundary condition is a boundary constraint condition which needs to be met by a tip of the bending beam, the root of the bending beam is a part close to the camber airfoil, and the tip of the bending beam is a part far away from the camber airfoil;
E) establishing a bending beam with parameter representation;
F) and establishing a mapping relation between the bending beams and the initial shape of the variable camber airfoil, so that the variable camber airfoil is parameterized and characterized by the mapping relation.
Drawings
FIG. 1 is a schematic view of a profile of a variable camber airfoil;
FIG. 2 is a schematic trailing edge view of a variable camber airfoil;
FIG. 3 is a flow chart of a parametric modeling method for a varying camber airfoil profile.
Reference numerals:
1. the method comprises the steps of an upper wing surface of an original wing profile, 2 a lower wing surface of the original wing profile, 3 bending beams of a bending degree part, 4 a normal line of the lower beam in an initial state for marking the bending degree, 5 a bending degree wing profile only considering translation transformation, 6 a bending beam already bent, 7 a normal line for marking the bending degree process after translation and rotation operation, 8 a normal line for marking the bending degree process after translation operation, 9a bending degree wing profile considering both translation and rotation transformation, 10 a first boundary condition of the bending beams, 11 a second boundary condition of the bending beams, 12 a front edge of the bending degree wing profile, 13 a bending degree area standing position, 14 a bending degree area, and 15 a rigid area.
Detailed Description
The invention provides a variable camber airfoil profile-oriented parametric modeling method, which aims to solve the problems that the deflection of the front edge and the rear edge of a variable camber airfoil profile cannot be conveniently represented, the representation mode deviates from the physical significance and the like in the conventional method. According to the method, on the original wing profile, a bending beam is adopted for representing a variable camber area, and a transformation mapping relation between the bending beam and the original wing profile is established. The bending process of the real bending wing profile can be characterized by additionally using relevant statics and dynamics parameters of the bending beam.
According to one aspect of the invention, a parametric modeling method for a variable camber airfoil is provided, which is used for parametrically representing the changed appearance of the variable camber airfoil. The method comprises the following steps:
the first step is as follows: selecting original wing profiles, and establishing a characterization model by adopting a conventional wing profile parameterization method such as a CST (class function and shape function transformation) method, a spline method and the like.
The second step is that: and selecting a rigid section and a bending section to determine the station position.
The third step: and establishing a bending beam model of the variable camber section of the variable camber airfoil.
The fourth step: the boundary conditions of the bending beam are determined.
The fifth step: and establishing the bending beam characterized by parameters.
And a sixth step: and establishing a mapping relation between the bending beam and the variable camber airfoil.
The seventh step: for the static analysis model, determining the rigidity distribution of the bending beam; for the kinetic analysis model, the stiffness distribution and mass distribution of the bending beam are determined.
1) Selecting original airfoil
The original airfoil profile, also called a reference airfoil profile, is an airfoil profile which is selected from an airfoil profile database and has no change in self-curvature. The CST, spline and other parameterization methods refer to the fact that the airfoil profile is expressed as linear combination or nonlinear combination of a series of analyzable functions, and the profile of the airfoil profile can be well characterized. In particular, for the CST method, the airfoil profile parameterization method is as follows:
defining a class function: c (psi) ═ psi0.5(1-ψ)
Where ψ ═ x/c ∈ [0,1], denotes the dimensionless position of the airfoil, and is usually dimensionless using the chord length, where x is the position and c is the original airfoil chord length.
Using a Bernstein polynomial Bi,n(ψ)＝Ki·ψi·(1-ψ)n-iA shape function is defined that is a function of the shape,
wherein K isiIs a binomial coefficient:
where n is the highest order of the binomial, i ═ 0, 1.
And (3) correspondingly multiplying the corresponding shape function and the class function to obtain the shape of each original airfoil:
ζ(ψ)＝C(ψ)·S(ψ)+ψ·ΔζTE
where ζ ═ z/c represents a dimensionless height in the thickness direction, Δ ζTE＝zTEC represents the boundary condition of the trailing edge, zTEIs the position of the original airfoil trailing edge in the thickness direction,
an arbitrary airfoil is represented as a linear superposition of a series of sub-airfoils:
wherein A isiIs all design variables, LEM represents airfoil leading edge modification. The original airfoil profile is represented by points at specific positions on the upper and lower surfaces.
Wherein, when the method is used for parameterizing the original airfoil profile, the proper A is obtained by an optimization methodiThe minimum quadratic distance between the parameterized airfoil profile and the original coordinate point is minimized.
2) Selecting rigid section and bending degree section to determine station position
The rigid section refers to a part which does not participate in the bending process in the bending wing profile, the bending section refers to a part which participates in the bending process in the bending wing profile, and the station is a chord-wise distance taking the front edge of the original wing profile as a starting point.
3) And establishing a bending beam model of the variable-camber section.
The bending beam model is a bending beam which is used for replacing a complex bending section and can simulate a bending process. The curved beam may be a simple euler beam or an accurate ironwood sinco beam; the calculation method can be a material mechanics solution, an elastic mechanics precise solution, or a finite element model solution based on a displacement base or a finite element model solution based on a strain base.
4) The boundary conditions of the bending beam are determined.
The determining of the boundary conditions of the bending beam comprises selecting the boundary conditions which are most in line with physical conditions and can represent the bending process. Taking the variable trailing edge as an example, the operation includes determining the location of the curved beam and the fixed pivot of the variable camber airfoil back wall, the declination angle of the beam curve, the slope of the beam end, and the like.
5) And establishing the bending beam characterized by parameters.
The parameterization representation of the bending beam refers to that partial parameters of the beam are used as adjustable and controllable quantities of the bending beam. The controllable parameter may be a force acting on the node; the rigidity of the section of the bending beam can also be changed, namely the bending beam with variable rigidity; it is also possible to combine the above two parameters.
6) And establishing a mapping relation between the bending beam and the initial shape.
The establishing of the mapping relation between the bending beam and the initial shape comprises the step of connecting points on the initial shape of the variable camber airfoil with the variable camber process of the bending beam. If euler beams are used instead, a plane perpendicular to the neutral plane of the beam is used. When the variable camber beam is bent, the plane also rotates and translates correspondingly, and the points of the upper surface and the lower surface fixedly connected with the plane also rotate and translate correspondingly; the same can be analogized to a shear beam model and the like.
7) For statics analysis purposes, determining the stiffness distribution of a curved beam; for the purpose of kinetic analysis, the stiffness distribution and mass distribution of the bending beam are determined.
The static analysis refers to considering the deformation of the bending beam under the action of static load; the dynamic analysis refers to analysis after inertia force and elastic force of the bending beam are considered, and the analysis model can consider mass of a node and bending rigidity distribution of the beam and is used for further simulating a dynamic process of the wing profile with the bending degree changing capability.
The beneficial effects of the invention include:
the invention adopts a bending beam mapping mode to parameterize and represent the outer contour curve of the variable camber airfoil profile, and the variable camber process of the airfoil profile is replaced by the deformation process of one bending beam. By giving boundary conditions at both ends of the bending beam and using a section stiffness parameter of the bending beam or a distribution force acting on the beam as a parameter, it is possible to satisfy a process of actually expressing a deflection.
The bending beam can be used to simulate static deformation by imparting a realistic stiffness profile.
The bending beam can be used to simulate complex dynamic processes by giving realistic mass and stiffness distributions.
The invention is further illustrated with reference to the following figures and examples.
[ example 1 ]: parametric modeling method for camber airfoil with a camber trailing edge in the form of a compliant rib
As shown in fig. 1 and 2. The present case uses the RAE 2822 supercritical airfoil as the initial airfoil profile, which includes an upper airfoil surface 1 and a lower airfoil surface 2. The original airfoil profile is generally determined by the form of a given point. Firstly, parameterizing by a CST (class function and shape function transformation) method, and obtaining proper A by an optimization methodiThe least squares error between the parameterized airfoil profile and the original coordinate points is minimized. Then, in a second step, the rigid zone 14, the camber zone 15 and the camber zone station 13 of the camber airfoil are determined. The rigid region 15 is a region where bending deformation does not occur in the bending deformation airfoil profile, and the bending deformation region 14 is bending deformationThe camber airfoil is a region where camber deformation occurs. Further, in a third step, the trailing edge portion of the camber is parameterized to create a bending beam 3. When the bending beam 3 is established, an Euler beam model is used for description, parameters are the section shape of the beam, a finite element analysis method is used for calculation, and the nonlinear phenomenon when the structure is subjected to geometric large deformation is considered. Fourthly, determining boundary conditions of two ends of the bending beam 3: the first boundary condition 10 is a boundary constraint condition that the bending beam needs to meet at the root, and a clamped position is used; the second boundary condition 11 is the boundary constraint that the bending beam tip needs to satisfy, where the downward deflection angle and the slope of the bending beam are determined. Fifth, the deformation result 9 of the bending beam 3 under the boundary condition and the sectional shape distribution can be obtained by means of finite element calculation. And finally, establishing a mapping relation between the variable camber airfoil upper airfoil surface 1 and the variable camber airfoil lower airfoil surface 2 relative to the bending beam 3. During the bending process of the bending beam 3, any section can be translated and rotated. The mapping relation may only consider translation, and the normal 4 of the beam for identifying the initial state of the camber is a straight line perpendicular to the bending beam 3 connecting the upper airfoil surface 1 of the original profile and the lower airfoil surface 2 of the original profile for describing the bending deformation mapping process of the camber area 14 in detail. If only the translation mapping is considered, the normal 4 of the beam in the initial state for identifying camber is subjected to translation transformation to become the normal 8 subjected to translation operation for identifying camber, and the original airfoil profiles 1 and 2 are also synchronously mapped to the profile 5 only subjected to translation transformation. If the translation mapping and the rotation mapping are considered comprehensively, the normal 4 of the beam in the initial state for identifying the camber becomes the normal 7 subjected to the translation operation and the rotation operation for identifying the camber after the translation transformation and the rotation transformation, and the original airfoil profiles 1 and 2 are also synchronously mapped into the profile 9 considering both the translation transformation and the rotation transformation. To this end, a parametric modeling method for a camber airfoil having a camber trailing edge in the form of a compliant rib may be performed by a in the CST parametric modeling methodiAnd several cross-sectional shapes and corresponding boundary conditions for describing the bending beam. By adjusting the downward deflection angle of the second boundary condition 11 of the beam, a difference can be obtainedTrailing edge profile at edge deflection angle.
[ example 2 ]: further use of the parametric modeling method: aerodynamic profile optimization and static and dynamic analysis
As shown in fig. 3, a basic flow for the pneumatic profile optimization analysis and the static and dynamic analysis using the parametric modeling method is shown. For the pneumatic shape optimization analysis, after selecting an original airfoil profile, determining a variable camber section station, establishing a bending beam model, parameterizing a bending beam and establishing a beam-profile mapping relation, the variable camber area 14 and the parameterized variable camber airfoil profile describing the rigid area 15 are expressed for the pneumatic shape optimization analysis module to call. For static and dynamic analysis, the actual physical implementation mode of the variable camber airfoil profile needs to be considered firstly. The concrete actual physical modes refer to an internal structure and/or mechanism mode for realizing the bending change function, a related joint rib implementation mode, a compliant mechanism implementation mode and the like. For the implementation mode of the compliant mechanism, determining the sectional shape parameters and mass distribution of the bending beam 3 according to the topological structure of the compliant mechanism; the first boundary condition 10 of the bending beam 3 is determined according to the connection way of the compliant mechanism and the rigid area 15. During static and dynamic analysis, the deformation of the bending beam 3 obtains the corresponding changed camber outline 9 and the change trend of the outline 9 through the determined mapping relation. And calculating aerodynamic force acting on the airfoil profile 9 by methods such as computational fluid mechanics and the like or aerodynamic force obtained by a wind tunnel test, and applying the aerodynamic force on an elastomer dynamic model to perform static and dynamic analysis.
Claims (7)
1. A parametric modeling method facing a variable camber airfoil profile, which is used for parametrically characterizing the changed appearance of the variable camber airfoil profile, is characterized by comprising the following steps:
A) selecting an original airfoil profile, wherein the original airfoil profile refers to an airfoil profile which is selected from an airfoil profile database and has no change of self-curvature, and a characterization model which has a limited number of parameters and can characterize the outline of the original airfoil profile is established;
B) selecting a rigid section (15) and a bending section (14) and determining a station (13), wherein: the rigid section refers to a part which does not participate in bending in the variable-bending wing profile, the variable-bending section refers to a part which participates in bending in the variable-bending wing profile, and the station is a chord-wise distance taking the front edge of the original wing profile as a starting point;
C) establishing a bending beam model of the variable-camber section, wherein the bending beam model is a bending beam which is used for replacing a complex variable-camber section and can simulate a variable-camber process;
D) determining a first boundary condition (10) and a second boundary condition (11) of the bending beam, wherein the first boundary condition refers to a boundary constraint condition which needs to be met by a root of the bending beam, the second boundary condition refers to a boundary constraint condition which needs to be met by a tip of the bending beam, the root of the bending beam refers to a part close to the variable camber airfoil, and the tip of the bending beam refers to a part far away from the variable camber airfoil;
E) establishing a parametrically characterized bending beam, wherein the parametrically characterized bending beam is formed by taking partial parameters of the bending beam as adjustable and controllable quantities of the bending beam;
F) and establishing a mapping relation between the bending beams and the initial shape of the variable camber airfoil profile, and then parameterizing and representing the variable camber airfoil profile by using the mapping relation.
2. The variable camber airfoil-oriented parametric modeling method according to claim 1, wherein the operation of establishing a characterization model of an original airfoil comprises:
the airfoil is characterized by a linear or non-linear combination of a series of resolvable functions.
3. The variable camber airfoil-oriented parametric modeling method according to claim 2, wherein the operation of establishing a characterization model of an original airfoil comprises:
A1) defining a class function: c (psi) ═ psi0.5(1-ψ)
Wherein psi ═ x/c ∈ [0,1], represents a dimensionless station of the airfoil, chord length is adopted for dimensionless, wherein x is the station, c is the original airfoil chord length,
A2) using a Bernstein polynomial Bi,n(ψ)＝Ki·ψi·(1-ψ)n-iA shape function is defined that is a function of the shape,
wherein KiIs a binomial coefficient:
n is the highest order of the binomial, i is 0,1,., n,
A3) and multiplying the corresponding shape function and the corresponding class function to obtain the shape of each airfoil:
ζ(ψ)＝C(ψ)·S(ψ)+ψ·ΔζTE
where ζ ═ z/c represents a dimensionless height in the thickness direction, Δ ζTE＝zTEC represents the boundary condition of the trailing edge, zTEIs the position of the original airfoil trailing edge in the thickness direction,
A4) an arbitrary airfoil is represented as a linear superposition of a series of sub-airfoils:
wherein A isiIs all design variables, LEM represents the airfoil leading edge correction, the original airfoil is represented by points of specific positions of the upper surface and the lower surface,
wherein, when the method is used for parameterizing the original airfoil profile, the proper A is obtained by an optimization methodiThe minimum quadratic distance between the parameterized airfoil profile and the original coordinate point is minimized.
4. The variable camber airfoil-oriented parametric modeling method according to claim 1, wherein the mapping comprises a translational mapping and a rotational mapping and a linear or non-linear combination of the two mapping.
5. The variable camber airfoil-oriented parametric modeling method according to claim 1, characterized in that:
the operation of establishing a characterization model of the original airfoil profile in step a) comprises: establishing a characterization model of the original airfoil profile by adopting a conventional airfoil profile parameterization method of a class function and shape function transformation method and a spline method,
the bending beam is at least one selected from a simple euler beam and a precision ironwood sinco beam,
the operation of establishing the parameter representation of the bending beam in the step E) adopts at least one selected from a material mechanics solution, an elastic mechanics precise solution, a finite element model solution based on a displacement base and a finite element model solution based on a strain base,
said step F) comprises associating points on the initial profile of the variform profile with a variform course of the bending beam.
6. Use of the parametric modeling method for a varying camber airfoil according to any of claims 1-5 in profile aerodynamic optimization analysis.
7. The variogram airfoil-oriented parametric modeling method according to one of claims 1-5, further comprising:
G) determining the rigidity distribution of the bending beam facing to statics analysis; and determining the rigidity and mass distribution of the bending beam facing the dynamic analysis.
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