CN113434961B - Prediction method of fluid-structure interaction characteristics of one-dimensional composite airfoil based on beam theory - Google Patents

Abstract

The invention discloses a one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on beam theory, which belongs to the technical field of composite material airfoil structure deformation and hydrodynamic performance prediction. The realization method of the invention is as follows: establishing a general method for predicting the hydrodynamic performance of the composite material airfoil, establishing a kinematic model of the composite material airfoil based on the force-deformation relationship of the beam theory, and combining the lift line method of hydrodynamic calculation to form a simplified The one-dimensional fluid-structure interaction method analyzes the fluid-structure interaction characteristics of large aspect ratio airfoils in an infinite flow domain, obtains the hydrodynamic performance of composite airfoils with large aspect ratio, and realizes the fluid-structure interaction characteristics of one-dimensional composite airfoils based on beam theory predict. The invention is helpful for in-depth analysis and prediction of the effective mechanical behavior and physical behavior of the composite material, can be applied to the prediction of the hydroelastic properties of the composite material airfoil, and solves the relevant engineering problems such as the strength and stability of the composite material airfoil. The invention has the advantages of high prediction efficiency and high precision.

Description

Prediction method of fluid-structure interaction characteristics of one-dimensional composite airfoil based on beam theory

technical field

The invention relates to a method for predicting the fluid-structure coupling performance of a composite material airfoil, which is suitable for predicting the fluid-solid coupling characteristics of a composite material airfoil with a large aspect ratio, and belongs to the technical field of composite material airfoil structure deformation and hydrodynamic performance prediction.

Background technique

Composite materials have the advantages of high specific stiffness, high specific strength, good fatigue performance, and low magnetic/electrical effects, and have been widely used in all walks of life. In the aerospace field, composite materials have been widely used for vibration and load reduction of helicopter wings. In early marine vessels, composite materials were applied to superstructures, masts or decks to reduce weight. In recent years, composite propellers have become a research hotspot because their passive deformation under off-design conditions can improve performance and fuel efficiency. Due to the large number of design parameters of composite materials, in order to improve the efficiency of composite airfoil optimization, it is necessary to achieve rapid prediction of fluid-structure interaction characteristics.

Most of the previous research on composite materials is based on the uniform beam theory, and the research objects are composite material plates with equal thickness along the width or chord direction, while the propellers used in the field of marine ships are usually airfoil. In order to better predict composite airfoils, based on the theory of anisotropic thin-walled closed-section beams, a modified analytical model for composite airfoils is established to study composite airfoils.

SUMMARY OF THE INVENTION

The technical problem to be solved by the one-dimensional composite material airfoil fluid-solid coupling characteristic prediction method based on the beam theory disclosed in the present invention is: based on the beam theory and the airfoil shape correction model, combined with the lift line method of hydrodynamic calculation, to solve the composite material airfoil The hydrodynamic performance of composite airfoils is predicted by the fluid-structure interaction characteristics of the airfoil. The invention is helpful for in-depth analysis and prediction of the effective mechanical behavior and physical behavior of the composite material. The invention can effectively predict the hydrodynamic characteristics of the composite material airfoil, and has the advantages of high prediction efficiency and high precision.

The purpose of the present invention is achieved through the following technical solutions.

The invention discloses a one-dimensional composite material airfoil fluid-structure coupling characteristic prediction method based on beam theory, establishes a general composite material airfoil hydrodynamic performance prediction method, and establishes a composite material airfoil based on the force-deformation relationship of beam theory. Combined with the lift line method of hydrodynamic calculation, a simplified one-dimensional fluid-structure interaction method is formed to analyze the fluid-structure interaction characteristics of the airfoil with a large aspect ratio in an infinite flow domain, and obtain the hydrodynamic performance of the airfoil with a large aspect ratio of the composite material. Dynamic performance, based on beam theory to realize the prediction of fluid-structure interaction characteristics of one-dimensional composite airfoils. The invention is helpful for in-depth analysis and prediction of the effective mechanical behavior and physical behavior of the composite material, can be applied to the prediction of the hydroelastic properties of the composite material airfoil, and solves the relevant engineering problems such as the strength and stability of the composite material airfoil. The invention can effectively predict the hydrodynamic deformation generated by the composite material airfoil, and has the advantages of high prediction efficiency and high precision.

A method for predicting the fluid-solid coupling characteristics of a one-dimensional composite airfoil based on beam theory disclosed in the present invention includes the following steps:

Step 1: According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil section is established by integrating the thin-walled closed section at the dz height.

According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil is expressed as formula (1) by integrating the thin-walled closed section at the height of dz. where N, T, M _x and M _z are the axial force, torque, and bending moment around the x and z axes, respectively, U ₁ , U ₂ and h are the deformations along the x, y and z axes, respectively, and ψ is The twist angle around the y-axis. Commas in kinematic variables indicate differentiation with respect to y.

Among them, the stiffness matrix [C′] is shown in formula (2), and x ₂ (z) and x ₁ (z) are the maximum and minimum values of x for a certain z value in the section.

是单个板的面内刚度系数的简化变换。where A', B', C' are shown in formula (3), the matrix

is a simplified transformation of the in-plane stiffness coefficients for a single plate.

According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil is established by integrating the thin-walled closed section at the height of dz.

Step 2: Consider the superposition of the composite airfoil along the z direction, simplify the stiffness matrix in the force-deformation relationship established in step 1, and obtain the composite airfoil kinematics equation.

When the composite airfoil is superimposed along the z direction, the parameters A', B', and D' are the same in the x direction. The stiffness matrix [C'] component shown in formula (2) is abbreviated as formula (4).

Substitute the simplified stiffness matrix [C′] equation (4) into the force-deformation relationship equation (1), and the kinematic equation of the composite airfoil is obtained as shown in equation (5)

where _{m s} and Is are the mass and mass moments of inertia per unit length, respectively. Sz' and Sx' are the mass moments around the z-axis and the x-axis, respectively, expressed as formula (6), where ρ is the material density. x _a and z _a are the distances between the centroid and the shear center in the x and z directions, respectively.

Step 3: Further simplify the kinematic equation obtained in Step 2 by replacing the components in the simplified stiffness matrix in Step 2.

By replacing C ₂ ′ ₂ , C ₂ ′ ₃ and C ₃ ′ ₃ with GJ, K and EI, the kinematic equation (5) is simplified to the kinematic equation (7).

Step 4: Through the lift line method, analyze the downwash speed and downwash angle induced by the free vortex system on the airfoil to obtain the airfoil geometric angle of attack, and obtain the relationship between the airfoil surface circulation distribution and the geometric angle of attack through the circulation theory transformation .

The downwash velocity v _yi generated by the free vortex system at any point y on the lift line is shown in Eq. (8), where Γ is the circulation, ζ is the coordinates of other points on the lift line, and Δα is the wake vortex line on the lift line The downwash angle caused by the downwash velocity v _yi induced by each point, this angle is opposite to the geometric angle of attack, the expression is shown in Eq. (9), where V _∞ is the incoming flow velocity at infinity, and l is the airfoil extension .

then there are

variable substitution, let

ζ=l-lcosθ ₁ y=l-lcosθ 0≤θ≤π (11)

then there are

Expanding the circular volume into series form yields Eq. (13):

Equation (12) can be rewritten as

get

The first k terms of the series equation are taken to obtain the formula (15), which is substituted into the formula (14) to obtain the coefficient An. Substituting the coefficient An into Equation (13) yields the circulation distribution.

Step 5: Substitute the relationship between the airfoil surface circulation distribution and the geometric angle of attack obtained in step 4 into the relationship between lift and circulation, and obtain the relationship between airfoil lift and attack angle. According to the airfoil bending moment, torque and The relationship of lift; Substitute the lift into the relationship between the airfoil bending moment, torque and lift to obtain the relationship between the bending moment, torque and the airfoil angle of attack, and substitute the bending moment and torque into the kinematics equation simplified in step 3, Get a new angle of attack.

According to the circulation distribution obtained in step 4, the expression of section lift is obtained as shown in Equation (15).

L=-ρV _∞ Γ(y) (15)

The expressions of the bending moment and torque at the position y _i of the airfoil are shown in Equation (16). Substitute the result of Equation (15) into the simplified kinematics Equation (16) to obtain the bending moment and torque. The moment torque is substituted into Equation (7) to calculate the new angle of attack of the airfoil.

Step 6: After obtaining a new angle of attack, repeat steps 4 and 5 until the angle of attack converges. Substitute the angle of attack that meets the convergence requirements into the relationship between lift and angle of attack obtained in step 5 to obtain the hydrodynamic characteristics of the composite airfoil, that is, to predict the fluid-structure interaction characteristics of the one-dimensional composite airfoil based on beam theory.

It also includes step 7: according to the hydrodynamic characteristics of the composite airfoil obtained in step 6, an in-depth analysis of the effective mechanical behavior, physical behavior and failure mechanism of the composite airfoil can be performed, and related engineering problems can be solved.

Beneficial effects:

1. The method for predicting the fluid-structure interaction characteristics of a one-dimensional composite airfoil based on the beam theory disclosed in the present invention establishes a kinematic model of the composite airfoil based on the beam theory, that is, considering the superposition of the composite airfoil along the z direction, the steps are simplified The stiffness matrix in the established force-deformation relationship is obtained, and the kinematic equation of the composite airfoil is obtained; by replacing the components in the simplified stiffness matrix, the kinematic model obtained in step 2 is further simplified; combined with the lift line calculated by hydrodynamics A simplified one-dimensional fluid-structure interaction method was formed to analyze the fluid-structure interaction characteristics of large aspect ratio airfoils in an infinite flow domain, and to predict the hydrodynamic performance of composite high aspect ratio airfoils. The invention can effectively predict the hydrodynamic deformation of the composite material airfoil with a large aspect ratio, and has the advantages of high prediction efficiency and high precision.

2. The method for predicting the fluid-structure coupling characteristics of one-dimensional composite airfoils based on beam theory disclosed in the present invention, according to the obtained hydrodynamic characteristics of composite airfoils, to predict the effective mechanical behavior, physical behavior and failure mechanism of composite airfoils. In-depth analysis and able to solve related engineering problems.

Description of drawings

1 is a schematic flowchart of a method for predicting the fluid-structure coupling characteristics of a one-dimensional composite airfoil based on beam theory according to the present invention;

FIG. 2 is a schematic diagram of the outline of the NACA0009 composite hydrofoil provided by the embodiment of the present invention.

Detailed ways

In order to better illustrate the purpose and advantages of the present invention, the content of the invention will be further described below with reference to the accompanying drawings and examples.

Example 1:

As shown in Figure 2, a NACA0009 symmetrical geometry, with a spread length of 0.4m and a chord length of 0.1m, is used to predict the fluid-solid coupling characteristics of a single-material single-layer corner composite hydrofoil as an example. The embodiment discloses a method for predicting the fluid-solid coupling characteristics of a one-dimensional composite airfoil based on beam theory, and the specific implementation steps are as follows:

Step 1: According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil section is established by integrating the thin-walled closed section at the dz height.

According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil is expressed as formula (1) by integrating the thin-walled closed section at the height of dz. where N, T, M _x and M _z are the axial force, torque, and bending moment around the x and z axes, respectively, U ₁ , U ₂ and h are the deformations along the x, y and z axes, respectively, and ψ is The twist angle around the y-axis. Commas in kinematic variables indicate differentiation with respect to y.

Among them, the stiffness matrix [C′] is shown in formula (2), and x ₂ (z) and x ₁ (z) are the maximum and minimum values of x for a certain z value in the section.

是单个板的面内刚度系数的简化变换。where A', B', C' are shown in formula (3), the matrix

is a simplified transformation of the in-plane stiffness coefficients for a single plate.

According to the force-deformation relationship of the thin-walled closed section beam, the force-deformation relationship of the composite airfoil is established by integrating the thin-walled closed section at the height of dz.

Step 2: Consider the superposition of the composite airfoil along the z direction, simplify the stiffness matrix in the force-deformation relationship established in step 1, and obtain the composite airfoil kinematics equation.

When the composite airfoil is superimposed along the z direction, the parameters A', B', and D' are the same in the x direction. The stiffness matrix [C'] component shown in formula (2) is abbreviated as formula (4).

Substitute the simplified stiffness matrix [C′] equation (4) into the force-deformation relationship equation (1), and the kinematic equation of the composite airfoil is obtained as shown in equation (5)

where _{m s} and Is are the mass and mass moments of inertia per unit length, respectively. Sz' and Sx' are the mass moments around the z-axis and the x-axis, respectively, expressed as formula (6), where ρ is the material density. x _a and z _a are the distances between the centroid and the shear center in the x and z directions, respectively.

Step 3: Further simplify the kinematic equation obtained in Step 2 by replacing the components in the simplified stiffness matrix in Step 2.

By replacing C ₂ ′ ₂ , C ₂ ′ ₃ and C ₃ ′ ₃ with GJ, K and EI, the kinematic equation (5) is simplified to the kinematic equation (7).

Step 4: Through the lift line method, analyze the downwash speed and downwash angle induced by the free vortex system on the airfoil to obtain the airfoil geometric angle of attack, and obtain the relationship between the airfoil surface circulation distribution and the geometric angle of attack through the circulation theory transformation .

The downwash velocity v _yi generated by the free vortex system at any point y on the lift line is shown in Eq. (8), where Γ is the circulation, ζ is the coordinates of other points on the lift line, and Δα is the wake vortex line on the lift line The downwash angle caused by the downwash velocity v _yi induced by each point, this angle is opposite to the geometric angle of attack, the expression is shown in Eq. (9), where V _∞ is the incoming flow velocity at infinity, and l is the airfoil extension .

then there are

variable substitution, let

ζ=l-lcosθ ₁ y=l-lcosθ 0≤θ≤π (11)

then there are

Expanding the circular volume into series form yields Eq. (13):

Equation (12) can be rewritten as

get

The first k terms of the series equation are taken to obtain the formula (15), which is substituted into the formula (14) to obtain the coefficient An. Substituting the coefficient An into Equation (13) yields the circulation distribution.

Step 5: Substitute the relationship between the airfoil surface circulation distribution and the geometric angle of attack obtained in step 4 into the relationship between lift and circulation, and obtain the relationship between airfoil lift and attack angle. According to the airfoil bending moment, torque and The relationship of lift; Substitute the lift into the relationship between the airfoil bending moment, torque and lift to obtain the relationship between the bending moment, torque and the airfoil angle of attack, and substitute the bending moment and torque into the kinematics equation simplified in step 3, Get a new angle of attack.

According to the circulation distribution obtained in step 4, the expression of section lift is obtained as shown in Equation (15).

L=-ρV _∞ Γ(y) (15)

The expressions of the bending moment and torque at the position y _i of the airfoil are shown in Equation (16). Substitute the result of Equation (15) into the simplified kinematics Equation (16) to obtain the bending moment and torque. The moment torque is substituted into Equation (7) to calculate the new angle of attack of the airfoil.

Step 6: After obtaining a new angle of attack, repeat steps 4 and 5 until the angle of attack converges. Substitute the angle of attack that meets the convergence requirements into the relationship between lift and angle of attack obtained in step 5 to obtain the hydrodynamic characteristics of the composite airfoil, that is, to predict the fluid-structure interaction characteristics of the one-dimensional composite airfoil based on beam theory.

It also includes step 7: according to the hydrodynamic characteristics of the composite airfoil obtained in step 6, an in-depth analysis of the effective mechanical behavior, physical behavior and failure mechanism of the composite airfoil can be performed, and related engineering problems can be solved.

The above-mentioned specific descriptions further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above-mentioned descriptions are only specific embodiments of the present invention, and are not intended to limit the protection of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection 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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