CN113434961B - One-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on beam theory - Google Patents
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Abstract
The invention discloses a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory, and belongs to the technical field of composite material airfoil structural deformation and hydrodynamic performance prediction. The implementation method of the invention comprises the following steps: a universal composite material airfoil hydrodynamic performance prediction method is established, a kinematic model of a composite material airfoil is established based on a beam theory stress-deformation relation, a simplified one-dimensional fluid-solid coupling method is formed by combining a lifting line method of hydrodynamic calculation, the fluid-solid coupling characteristics of a large-aspect-chord-ratio airfoil in an infinite watershed are analyzed, the hydrodynamic performance of the composite material large-aspect-chord-ratio airfoil is obtained, and the fluid-solid coupling characteristic prediction of the one-dimensional composite material airfoil is realized based on the beam theory. The method is beneficial to deep analysis and prediction of effective mechanical behaviors and physical behaviors of the composite material, can be applied to prediction of the water elasticity performance of the composite material airfoil profile, and solves the relevant engineering problems of the strength, the stability and the like of the composite material airfoil profile. The invention has the advantages of high prediction efficiency and high precision.
Description
Technical Field
The invention relates to a method for predicting the fluid-solid coupling performance of a composite material airfoil, which is suitable for predicting the fluid-solid coupling characteristic of a composite material airfoil with a high aspect ratio and belongs to the technical field of composite material airfoil structural deformation and hydrodynamic performance prediction.
Background
The composite material has the advantages of high specific stiffness, high specific strength, good fatigue performance, low magnetic/electric effect and the like, and is widely applied to various industries. In the field of aerospace, composite materials have been widely used for vibration damping and load shedding of helicopter wings. In the early marine vessel field, composite materials were applied to superstructures, masts or decks to reduce weight. In recent years, the performance and the fuel efficiency of the composite propeller can be improved due to the passive deformation of the composite propeller under the non-design working condition, and the composite propeller becomes a research hotspot. Due to the fact that the composite material is provided with more design parameters, in order to improve the composite material airfoil optimization efficiency, the fluid-solid coupling characteristic needs to be rapidly predicted.
In the past, most of researches on composite materials are based on a uniform beam theory, the research objects are composite material plates with equal thickness along the width or the chord direction, and the cross section of the propeller applied to the field of marine ships is usually in a wing shape. In order to better predict the composite material airfoil, a composite material airfoil correction analytical model is established based on the anisotropic thin-wall closed section beam theory, and the composite material airfoil is researched.
Disclosure of Invention
The invention discloses a method for predicting the fluid-solid coupling characteristic of a one-dimensional composite material airfoil based on a beam theory, which aims to solve the technical problems that: based on a beam theory and an airfoil shape correction model, a lift line method of hydrodynamic calculation is combined, the fluid-solid coupling characteristic of the composite material airfoil is solved, and the hydrodynamic performance of the composite material airfoil is predicted. The method is beneficial to deep analysis and prediction of effective mechanical behaviors and physical behaviors of the composite material. The method can effectively predict the hydrodynamic characteristics of the composite material airfoil profile, and has the advantages of high prediction efficiency and high precision.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory, which is used for establishing a universal composite material airfoil hydrodynamic performance prediction method, establishing a kinematic model of a composite material airfoil based on a beam theory stress-deformation relation, forming a simplified one-dimensional fluid-solid coupling method by combining a lifting line method of hydrodynamic calculation, analyzing the fluid-solid coupling characteristic of a high-aspect-chord-ratio airfoil in an infinite basin, obtaining the hydrodynamic performance of the composite material high-aspect-chord-ratio airfoil, and realizing the one-dimensional composite material airfoil fluid-solid coupling characteristic prediction based on the beam theory. The method is beneficial to deep analysis and prediction of effective mechanical behaviors and physical behaviors of the composite material, can be applied to prediction of the water elasticity performance of the composite material airfoil profile, and solves the relevant engineering problems of the strength, the stability and the like of the composite material airfoil profile. The method can effectively predict the hydrodynamic deformation generated by the composite material wing profile, and has the advantages of high prediction efficiency and high precision.
The invention discloses a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory, which comprises the following steps of:
the method comprises the following steps: and establishing a stress-deformation relational expression of the composite material airfoil section by integrating the thin-wall closed section at the dz height according to the stress-deformation relation of the thin-wall closed section beam.
And (3) according to the stress-deformation relation of the thin-wall closed section beam, expressing the stress-deformation relation of the composite material airfoil as an expression (1) by integrating the thin-wall closed section at the dz height. In the formula, N, T, M x And M z Axial force, torque, bending moment around the x and z axes, U 1 ,U 2 And h are deformations along the x, y and z axes, respectively, and ψ is the twist angle about the y axis. Commas in kinematic variables represent the differentiation with respect to y.
Wherein, the rigidity matrix [ C']As shown in formula (2), x 2 (z) and x 1 (z) is the maximum and minimum of x for a certain z value in the section.
Wherein A ', B ' and C ' are shown as formula (3), and matrix
Is a simplified transformation of the in-plane stiffness coefficient of a single plate.
And establishing a stress-deformation relation of the composite material airfoil profile by integrating the height dz of the thin-wall closed section according to the stress-deformation relation of the thin-wall closed section beam.
Step two: and (4) considering the composite material wing profile to be overlapped along the z direction, and simplifying the rigidity matrix in the stress-deformation relation established in the step one to obtain the composite material wing profile kinematic equation.
And (3) if the composite material airfoil is overlapped along the z direction, the parameters A ', B' and D 'are the same in the x direction, and the component of the stiffness matrix [ C' ] shown in the formula (2) is abbreviated as a formula (4).
Substituting the simplified rigidity matrix [ C' ] formula (4) into the stress-deformation relational expression (1) to obtain the composite material airfoil kinematic equation shown in the formula (5)
Wherein m is s And I s Mass and mass moment of inertia per unit length, respectively. Sz 'and Sx' are mass moments around the z-axis and x-axis, respectively, and are represented by equation (6), where ρ is the material density. x is the number of a And z a The distances of the centroid from the shear center in the x-direction and the z-direction, respectively.
Step three: and (5) further simplifying the kinematic equation obtained in the step two by replacing the component in the stiffness matrix simplified in the step two.
C is to be 2 ′ 2 ,C 2 ′ 3 And C 3 ′ 3 Replacing GJ, K and EI, then the kinematic equation (5) is simplified to the kinematic equation (7).
Step four: and analyzing the lower washing speed and the lower washing angle induced by the free vortex system on the airfoil by a lift line method to obtain the geometric attack angle of the airfoil, and obtaining the relationship between the surface circulation distribution of the airfoil and the geometric attack angle by the circulation theoretical transformation.
The lower washing speed v generated by the free vortex system at any point y on the lifting line yi As shown in formula (8), wherein Γ is the loop quantity, ζ is the coordinates of other points on the lift line, and Δ α is the wash-down velocity v induced by the wake vortex line at each point on the lift line yi The resulting wash-down angle, which is the inverse of the geometric angle of attack, is expressed as formula (9), where V ∞ The incoming flow velocity at infinity, l is the airfoil span length.
Then there is
A variable is substituted, such that
ζ＝l-lcosθ 1 y＝l-lcosθ 0≤θ≤π (11)
Then there is
Expanding the ring size into a series form to obtain formula (13):
then the formula (12) is rewritten as
Namely obtain
The series equation takes the first k term to obtain equation (15), and substitutes equation (14) to obtain a coefficient An. The ring weight distribution is obtained by substituting the coefficient An into the formula (13).
Step five: substituting the relationship between the airfoil surface circulation distribution and the geometric attack angle obtained in the step four into a relationship between lift force and circulation to obtain a relationship between airfoil lift force and attack angle, and obtaining the relationship between airfoil bending moment, torque and lift force according to the relationship between airfoil bending moment and torque; and substituting the lift force into the relationship among the wing section bending moment, the torque and the lift force to obtain the relationship among the bending moment, the torque and the wing section attack angle, and substituting the bending moment and the torque into the kinematic equation obtained by the step three, so as to obtain a new attack angle.
And (4) obtaining a section lift force expression formula shown in a formula (15) according to the circulation distribution obtained in the fourth step.
L＝-ρV ∞ Γ(y) (15)
Wing type y i The expression of the bending moment and the torque at the position is shown as a formula (16), the result of the formula (15) is substituted into a kinematic equation (16) obtained through simplification, the bending moment and the torque are obtained, the obtained bending moment and torque are substituted into a formula (7), and the wing profile is obtained through calculationNew angle of attack.
Step six: and after a new attack angle is obtained, repeating the fourth step and the fifth step until the attack angle is converged. And substituting the attack angle meeting the convergence requirement into the relation between the lift force and the attack angle obtained in the step five to obtain the hydrodynamic characteristic of the composite material airfoil, namely realizing the prediction of the fluid-solid coupling characteristic of the one-dimensional composite material airfoil based on the beam theory.
The method also comprises the seventh step: and (5) deeply analyzing the effective mechanical behavior, physical behavior and failure mechanism of the composite material airfoil according to the hydrodynamic characteristics of the composite material airfoil obtained in the step six, and solving the related engineering problems.
Has the advantages that:
1. the invention discloses a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory.A kinematic model of a composite material airfoil is established based on the beam theory, namely, the composite material airfoil is considered to be overlapped along the z direction, and a rigidity matrix in a stress-deformation relation established in the first step is simplified to obtain a kinematic equation of the composite material airfoil; further simplifying the kinematic model obtained in the step two by replacing components in the simplified rigidity matrix; and combining a lifting line method of hydrodynamic calculation to form a simplified one-dimensional fluid-solid coupling method, analyzing the fluid-solid coupling characteristics of the high-aspect-ratio wing profile in an infinite basin, and predicting the hydrodynamic performance of the composite material high-aspect-ratio wing profile. The method can effectively predict the hydrodynamic deformation generated by the high aspect ratio composite material airfoil profile, and has the advantages of high prediction efficiency and high precision.
2. The invention discloses a one-dimensional composite material wing section fluid-solid coupling characteristic prediction method based on a beam theory, which deeply analyzes effective mechanical behavior, physical behavior and failure mechanism of a composite material wing section according to the obtained hydrodynamic characteristic of the composite material wing section and can solve related engineering problems.
Drawings
FIG. 1 is a schematic flow chart of a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory according to the invention;
fig. 2 is a schematic external view of a NACA0009 composite hydrofoil according to an embodiment of the present invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in fig. 2, a single-material single-lay-angle composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory disclosed in this embodiment is, as shown in fig. 1, implemented by taking a symmetric geometry of NACA0009, an span length of 0.4m, a chord length of 0.1m, and a fluid-solid coupling characteristic prediction of a single-material single-lay-angle composite material airfoil as an embodiment, and specifically includes the following steps:
the method comprises the following steps: and establishing a stress-deformation relational expression of the composite material airfoil section by integrating the thin-wall closed section at the dz height according to the stress-deformation relation of the thin-wall closed section beam.
And (3) according to the stress-deformation relation of the thin-wall closed section beam, expressing the stress-deformation relation of the composite material airfoil as an expression (1) by integrating the thin-wall closed section at the dz height. In the formula, N, T, M x And M z Axial force, torque, bending moment around the x and z axes, U 1 ,U 2 And h are deformations along the x, y and z axes, respectively, and ψ is the twist angle about the y axis. Commas in kinematic variables represent the differentiation with respect to y.
Wherein, the rigidity matrix [ C']Such asIs represented by the formula (2), x 2 (z) and x 1 (z) is the maximum and minimum of x for a certain z value in the section.
Wherein A ', B ' and C ' are shown as formula (3), and matrix
Is a simplified transformation of the in-plane stiffness coefficient of a single plate.
And establishing a stress-deformation relational expression of the composite material airfoil profile by integrating the dz height of the thin-wall closed section according to the stress-deformation relation of the thin-wall closed section beam.
Step two: and (4) considering the composite material wing profile to be overlapped along the z direction, and simplifying the rigidity matrix in the stress-deformation relation established in the step one to obtain the composite material wing profile kinematic equation.
And (3) if the composite material airfoil is overlapped along the z direction, the parameters A ', B' and D 'are the same in the x direction, and the component of the stiffness matrix [ C' ] shown in the formula (2) is abbreviated as a formula (4).
Substituting the simplified rigidity matrix [ C' ] formula (4) into the stress-deformation relational expression (1) to obtain the composite material airfoil kinematic equation shown in the formula (5)
Wherein m is s And I s Mass and mass moment of inertia per unit length, respectively. Sz 'and Sx' are mass moments around the z-axis and x-axis, respectively, and are represented by equation (6), where ρ is the material density. x is the number of a And z a The distances of the centroid from the shear center in the x-direction and the z-direction, respectively.
Step three: and (5) further simplifying the kinematic equation obtained in the step two by replacing the component in the stiffness matrix simplified in the step two.
C is to be 2 ′ 2 ,C 2 ′ 3 And C 3 ′ 3 Replacing GJ, K and EI, then the kinematic equation (5) is simplified to the kinematic equation (7).
Step four: and analyzing the lower washing speed and the lower washing angle induced by the free vortex system on the airfoil by a lift line method to obtain the geometric attack angle of the airfoil, and obtaining the relationship between the surface circulation distribution of the airfoil and the geometric attack angle by the circulation theoretical transformation.
The lower washing speed v generated by the free vortex system at any point y on the lifting line yi As shown in formula (8), wherein Γ is the loop quantity, ζ is the coordinates of other points on the lift line, and Δ α is the wash-down velocity v induced by the wake vortex line at each point on the lift line yi The resulting wash-down angle, which is the inverse of the geometric angle of attack, is expressed as formula (9), where V ∞ The incoming flow velocity at infinity, l is the airfoil span length.
Then there is
A variable is substituted, such that
ζ＝l-lcosθ 1 y＝l-lcosθ 0≤θ≤π (11)
Then there is
Expanding the ring size into a series form to obtain formula (13):
then the formula (12) is rewritten as
Namely obtain
The series equation takes the first k term to obtain equation (15), and substitutes equation (14) to obtain a coefficient An. The ring weight distribution is obtained by substituting the coefficient An into the formula (13).
Step five: substituting the relationship between the airfoil surface circulation distribution and the geometric attack angle obtained in the step four into a relationship between lift force and circulation to obtain a relationship between airfoil lift force and attack angle, and obtaining the relationship between airfoil bending moment, torque and lift force according to the relationship between airfoil bending moment and torque; and substituting the lift force into the relationship among the wing section bending moment, the torque and the lift force to obtain the relationship among the bending moment, the torque and the wing section attack angle, and substituting the bending moment and the torque into the kinematic equation obtained by the step three, so as to obtain a new attack angle.
And (5) obtaining a section lift force expression formula shown in a formula (15) according to the circulation distribution obtained in the fourth step.
L＝-ρV ∞ Γ(y) (15)
Wing type y i The expression of the bending moment and the torque at the position is shown as a formula (16), the result of the formula (15) is substituted into a kinematic equation (16) obtained through simplification, the bending moment and the torque are obtained, and the obtained bending moment and the torque are substituted into a formula (7) to obtain a new attack angle of the airfoil profile through calculation.
Step six: and after a new attack angle is obtained, repeating the fourth step and the fifth step until the attack angle is converged. And substituting the attack angle meeting the convergence requirement into the relation between the lift force and the attack angle obtained in the step five to obtain the hydrodynamic characteristic of the composite material airfoil, namely realizing the prediction of the fluid-solid coupling characteristic of the one-dimensional composite material airfoil based on the beam theory.
The method also comprises the seventh step: and (5) deeply analyzing the effective mechanical behavior, physical behavior and failure mechanism of the composite material airfoil according to the hydrodynamic characteristics of the composite material airfoil obtained in the step six, and solving the related engineering problems.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (2)
1. A one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on a beam theory is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: according to the stress-deformation relation of the thin-wall closed section beam, establishing a stress-deformation relation of the composite material airfoil section by integrating the thin-wall closed section in the dz height direction;
the first implementation method comprises the following steps of,
according to the stress-deformation relation of the thin-wall closed section beam, integrating the thin-wall closed section in the dz height direction, and expressing the stress-deformation relation of the composite material wing profile as an expression (1); in the formula, N, T, M x And M z Axial force, torque, bending moment around the x and z axes, U 1 ,U 2 And h are deformations along the x, y and z axes, respectively, and ψ is the twist angle about the y axis; commas in kinematic variables represent the differential with respect to y;
wherein, the rigidity matrix [ C']As shown in formula (2), x 2 (z) and x 1 (z) is the maximum and minimum values of x for a certain z value in the profile;
wherein A ', B ' and C ' are shown as formula (3), and matrix
Is a simplified transformation of the in-plane stiffness coefficient of a single plate;
according to the stress-deformation relation of the thin-wall closed section beam, establishing a stress-deformation relation formula of the composite material wing section through the integral of the thin-wall closed section at the dz height;
step two: the composite material wing profiles are overlapped along the z direction, and a rigidity matrix in the stress-deformation relation established in the step one is simplified to obtain a composite material wing profile kinematic equation;
the second step is realized by the method that,
if the composite material airfoil is overlapped along the z direction, the parameters A ', B' and D 'are the same in the x direction, and the component of the stiffness matrix [ C' ] shown in the formula (2) is abbreviated as a formula (4);
substituting the simplified rigidity matrix [ C' ] formula (4) into the stress-deformation relational expression (1) to obtain the composite material airfoil kinematic equation shown in the formula (5)
Wherein m is s And I s Mass and mass moment of inertia per unit length, respectively; sz 'and Sx' are mass moments around the z-axis and x-axis, respectively, and are represented by formula (6), where ρ is the material density; x is a radical of a fluorine atom a And z a The distances between the centroid and the shearing center in the x direction and the z direction respectively;
step three: further simplifying the kinematic equation obtained in the second step by replacing the component in the stiffness matrix simplified in the second step;
the third step is to realize the method as follows,
c' 22 ,C′ 23 And C' 33 Replacing GJ, K and EI, and then simplifying the kinematic equation (5) into a kinematic equation (7);
step four: analyzing the lower washing speed and the lower washing angle induced by the free vortex system on the airfoil by a lift line method to obtain the geometric attack angle of the airfoil, and obtaining the relationship between the surface circulation distribution of the airfoil and the geometric attack angle by the circulation theoretical transformation;
the implementation method of the fourth step is that,
the lower washing speed v generated by the free vortex system at any point y on the lifting line yi As shown in formula (8), wherein Γ is the loop quantity, ζ is the coordinates of other points on the lift line, and Δ α is the wash-down velocity v induced by the wake vortex line at each point on the lift line yi The resulting wash-down angle, which is the inverse of the geometric angle of attack, is expressed as formula (9), where V ∞ The incoming flow velocity at infinity, l is the airfoil span length;
then there is
A variable is replaced by
ζ＝l-lcosθ 1 y＝l-lcosθ 0≤θ≤π (11)
Then there is
Expanding the ring size into a series form to obtain formula (13):
then the formula (12) is rewritten as
Namely obtain
Taking the first k terms in the series equation to obtain a formula (15), and substituting the formula (15) into a formula (14) to obtain a coefficient An; substituting the coefficient An into the formula (13) to obtain the distribution of the ring weight;
step five: substituting the relationship between the airfoil surface circulation distribution and the geometric attack angle obtained in the step four into a relationship between lift force and circulation to obtain a relationship between airfoil lift force and attack angle, and obtaining the relationship between airfoil bending moment, torque and lift force according to the relationship between airfoil bending moment and torque; substituting the lift force into the relationship among the wing section bending moment, the torque and the lift force to obtain the relationship among the bending moment, the torque and the wing section attack angle, and substituting the bending moment and the torque into the kinematic equation obtained by the step three in a simplified way to obtain a new attack angle;
the fifth step is to realize that the method is that,
according to the circulation distribution obtained in the fourth step, a section lift force expression formula is obtained and is shown as a formula (15);
L＝-ρV ∞ Γ(y) (15)
wing type y i The expression of the bending moment and the torque at the position is shown as a formula (16), the result of the formula (15) is substituted into a kinematic equation (16) obtained through simplification, the bending moment and the torque are obtained, and the obtained bending moment and the torque are substituted into a formula (7) to obtain a new attack angle of the wing section through calculation;
step six: after a new attack angle is obtained, repeating the fourth step and the fifth step until the attack angle is converged; and substituting the attack angle meeting the convergence requirement into the relation between the lift force and the attack angle obtained in the step five to obtain the hydrodynamic characteristic of the composite material airfoil, namely realizing the prediction of the fluid-solid coupling characteristic of the one-dimensional composite material airfoil based on the beam theory.
2. The method for predicting the fluid-solid coupling characteristic of the one-dimensional composite material airfoil based on the beam theory as claimed in claim 1, wherein the method comprises the following steps: and seventhly, deeply analyzing the effective mechanical behavior, the physical behavior and the failure mechanism of the composite material airfoil according to the hydrodynamic characteristics of the composite material airfoil obtained in the step six.
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| CN110837677A (en) * | 2019-11-08 | 2020-02-25 | 扬州大学 | Modeling method of binary airfoil nonlinear flutter time domain model |
| CN110837678A (en) * | 2019-11-08 | 2020-02-25 | 扬州大学 | Binary airfoil frequency domain flutter model modeling method based on multi-body system transfer matrix method |
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