CN107357976B - Method for calculating dynamic derivative of aircraft - Google Patents

Method for calculating dynamic derivative of aircraft Download PDF

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CN107357976B
CN107357976B CN201710499236.8A CN201710499236A CN107357976B CN 107357976 B CN107357976 B CN 107357976B CN 201710499236 A CN201710499236 A CN 201710499236A CN 107357976 B CN107357976 B CN 107357976B
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aircraft
aerodynamic force
residual error
flow field
boundary condition
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胡国风
周胜
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Sichuan Tengdun Technology Co Ltd
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Abstract

The invention relates to the technical field of fluid dynamics and discloses a method for calculating a dynamic derivative of an aircraft. Determining static flow field boundary conditions b for flight states of an aircraft1The governing equation of the flow field is converged to 0, i.e. R ═ Ax + b1When 0, the flow field is for the boundary condition b1Solution vector x of1Wherein A is a matrix of the governing equation, and when the residual error does not converge to absolute zero, it is set to converge to the allowable residual error R1＝Ax1+b1At this time, the aerodynamic force is
Figure DDA0001333272410000011
Solving equations
Figure DDA0001333272410000012
Wherein F is aerodynamic force, R is residual error, Lambda is adjoint matrix, x is solution vector, and solution vector x is obtained1Conditional corresponding adjoint matrix lambda1(ii) a Increasing a rotation angular speed delta omega around a reference center by the aircraft, generating a normal motion speed on the surface of the aircraft, and calculating a residual error increment delta R generated by the normal speed; the aerodynamic force increment generated by the normal speed is delta F ═ Lambda1Δ R, then the dynamic derivative of the aerodynamic force with respect to the angular velocity can be obtained as
Figure DDA0001333272410000013
The solution scheme of the dynamic derivative is simple and accurate.

Description

Method for calculating dynamic derivative of aircraft
Technical Field
The invention relates to the technical field of fluid dynamics, in particular to a method for calculating a dynamic derivative of an aircraft.
Background
The calculation of aircraft aerodynamic forces by the CFD method is usually solved in the form of
Ax+b＝0 (1)
The matrix A is a matrix representing a control equation, b represents a boundary condition, and x is a vector to be solved.
The method for solving the flow field control equation (1) is mainly a time correlation method, and an initial value x is set for a vector x to be solved0Over a time-varying course
Figure BDA0001333272390000011
Finally, the solution of the formula (1) is obtained. Wherein R is the residual, and the process of solving is the process of gradually converging the residual to 0. The existing methods comprise tests and calculations, and the methods for solving the dynamic derivative are all that the aircraft is subjected to periodic forced vibration (rotation around the gravity center when the derivative of angular velocity is solved, translation when the derivative of the change rate of the angle of attack/sideslip angle is solved), the time history of the aerodynamic force change is obtained through the calculations or tests, and the corresponding dynamic derivative is obtained according to the phase relation between the aerodynamic force change and the change rate of the angular velocity/angle of attack.
The following is an example of the derivative of the pitch moment with respect to the pitch angle rate and the rate of change of the angle of attack. Setting the aircraft (model) at equilibrium position alpha0The nearby part is in pitching sinusoidal vibration, and the state equation is
Figure BDA0001333272390000012
Where A is the angular amplitude, T is the period of vibration, and T is the time. Then there is
Figure BDA0001333272390000013
Figure BDA0001333272390000021
Where Δ α is the angle of attack deviation amplitude, ω is the angular velocity,
Figure BDA0001333272390000022
is the rate of change of angle of attack. The aerodynamic force at small amplitude rotation/oscillation satisfies the following relation:
F＝F(α0)+ΔαFα+ω(Fω+Fα) (4)
after the change course of the aerodynamic force F is obtained, the integral is carried out on a complete period
Figure BDA0001333272390000023
The sum of the angular velocity and the derivative of the angle of attack change rate of the aerodynamic force can be obtained
Figure BDA0001333272390000024
These two terms cannot be separately obtained with forced rotation only. If the aircraft (model) is subjected to up-and-down sinusoidal vibration, the state equation is
Figure BDA0001333272390000025
Wherein Y is the amplitude. Then there is
Figure BDA0001333272390000026
Figure BDA0001333272390000027
Where is the v flight velocity. Only influencing the aerodynamic force during this movement
Figure BDA0001333272390000028
The magnitude of the deviation, ω is the angular velocity,
Figure BDA0001333272390000029
is the rate of change of angle of attack. Formula (A), (B) and4) the following steps are changed:
Figure BDA00013332723900000210
after the change course of the aerodynamic force F is obtained, the integral is carried out on a complete period
Figure BDA00013332723900000211
The derivative of the aerodynamic force to the change rate of the angle of attack can be obtained
Figure BDA0001333272390000031
When the dynamic derivative is calculated by adopting a numerical calculation method, the unsteady aerodynamic force change course of the forced oscillation process needs to be calculated, and then the dynamic derivative term is distinguished by using the phase component of the aerodynamic force change. The calculation in the unsteady process has high precision requirement, long time consumption and great resource consumption, and if the amplitude of vibration is overlarge, the calculation result contains excessive high-order terms, so that the precision is poor; if the amplitude is too small, the amount of variation may be too small, and the calculation error may introduce a large deviation. Wind tunnel tests are subject to test accuracy, as are conflicts in amplitude selection.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: in view of the existing problems, a method for calculating the dynamic derivative of the aircraft is provided.
The technical scheme adopted by the invention is as follows: a method for calculating the dynamic derivative of an aircraft specifically comprises the following processes:
step 1, determining static flow field boundary condition b aiming at flight state of aircraft1The governing equation of the flow field is converged to 0, i.e. R ═ Ax + b1When 0, the flow field is for the boundary condition b1Solution vector x of1Wherein A is a matrix of the governing equation, and when the residual error does not converge to absolute zero, it is set to converge to the allowable residual error R1＝Ax1+b1At this time, it is pneumaticForce is
Figure BDA0001333272390000032
Step 2, solving equation
Figure BDA0001333272390000033
Wherein F is aerodynamic force, R is residual error, Lambda is adjoint matrix, x is solution vector, and solution vector x is obtained1Conditional corresponding adjoint matrix lambda1；
Step 3, increasing a rotation angular velocity delta omega around the reference center by the aircraft, generating a normal motion velocity on the surface of the aircraft, and calculating a residual error increment delta R generated by the normal velocity;
and 4, increasing the aerodynamic force generated by the normal speed to delta F ═ Lambda1Δ R, then the dynamic derivative of the aerodynamic force with respect to the angular velocity can be obtained as
Figure BDA0001333272390000034
Further, the calculation method of the dynamic derivative of the line former further comprises the following processes: (a) a tiny rotation angular velocity delta omega is added around the reference center by the aircraft, the normal motion velocity is generated on the surface of the aircraft, and a corresponding boundary condition b is obtained2(ii) a (b) With x1Is the initial field, corresponds to b2As a boundary condition, there is a residual R2＝Ax1+b2(ii) a (c) Boundary condition becomes b2The aerodynamic force at the initial moment of the flow field is still the aerodynamic force of the static flow field
Figure BDA0001333272390000041
In the process that the residual R converges to 0, satisfy
Figure BDA0001333272390000042
Figure BDA0001333272390000043
Then
Figure BDA0001333272390000044
(d) When the residual error converges to 0, it can be obtained
Figure BDA0001333272390000045
Is corresponding to the boundary condition b2The aerodynamic force of (a); (f) similarly, if the solution in step 1 is continuously calculated and converged to the residual error equal to 0, the solution can also be obtained
Figure BDA0001333272390000046
(g) The amount of change Δ F in aerodynamic force is represented by a adjoint matrix as F2-F1＝Λ1Δ R; wherein Δ R ═ R2-R1＝(Ax1+b2)-(Ax1+b1)＝b2-bx; (h) obtaining the dynamic derivative of the aerodynamic force to the angular velocity as
Figure BDA0001333272390000047
Compared with the prior art, the beneficial effects of adopting the technical scheme are as follows: the technical scheme of the invention can obtain the dynamic derivative of the aerodynamic force to the angular velocity only by requiring a solution field and an adjoint matrix thereof without calculating unsteady motion. According to the principle of the method, the obtained dynamic derivative is only related to residual variation delta R caused by the change of the boundary condition, and the residual existing in the initial flow field has no influence, so that the degree of residual convergence in the calculation of the initial flow field can be properly relaxed. The method greatly reduces resource consumption, obtains a strict dynamic derivative, does not contain the influence of other factors such as high-order components, incidence angle change rate and the like, improves the accuracy, and does not have the limitation of vibration amplitude and frequency.
Drawings
Fig. 1 is a schematic flow chart of the method for calculating the dynamic derivative of the aircraft according to the invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, a method for calculating a dynamic derivative of an aircraft specifically includes the following processes:
step 1, determining static flow field boundary condition b aiming at flight state of aircraft1The governing equation of the flow field is converged to 0, i.e. R ═Ax+b1When 0, the flow field is for the boundary condition b1Solution vector x of1Wherein A is a matrix of the governing equation, and when the residual error does not converge to absolute zero, it is set to converge to the allowable residual error R1＝Ax1+b1At this time, the aerodynamic force is
Figure BDA0001333272390000051
Step 2, solving equation
Figure BDA0001333272390000052
Wherein F is aerodynamic force, R is residual error, Lambda is adjoint matrix, x is solution vector, and solution vector x is obtained1Conditional corresponding adjoint matrix lambda1；
Step 3, increasing a rotation angular velocity delta omega around the reference center by the aircraft, generating a normal motion velocity on the surface of the aircraft, and calculating a residual error increment delta R generated by the normal velocity;
and 4, increasing the aerodynamic force generated by the normal speed to delta F ═ Lambda1Δ R, then the dynamic derivative of the aerodynamic force with respect to the angular velocity can be obtained as
Figure BDA0001333272390000053
When the aircraft increases a rotation angular speed delta omega around the reference center, a corresponding boundary condition b is introduced2. The calculation method of the dynamic derivative of the line former further comprises the following processes: (a) a tiny rotation angular velocity delta omega is added around the reference center by the aircraft, the normal motion velocity is generated on the surface of the aircraft, and a corresponding boundary condition b is obtained2(ii) a (b) With x1Is the initial field, corresponds to b2As a boundary condition, there is a residual R2＝Ax1+b2(ii) a (c) Boundary condition becomes b2The aerodynamic force at the initial moment of the flow field is still the aerodynamic force of the static flow field
Figure BDA0001333272390000054
In the process that the residual R converges to 0, satisfy
Figure BDA0001333272390000055
Then
Figure BDA0001333272390000056
(d) When the residual error converges to 0, it can be obtained
Figure BDA0001333272390000057
Is corresponding to the boundary condition b2The aerodynamic force of (a); (f) similarly, if the solution in step 1 is continuously calculated and converged to the residual error equal to 0, the solution can also be obtained
Figure BDA0001333272390000058
(g) The amount of change Δ F in aerodynamic force is represented by a adjoint matrix as F2-F1＝Λ1Δ R; wherein Δ R ═ R2-R1＝(Ax1+b2)-(Ax1+b1)＝b2-b1(ii) a (h) Obtaining the dynamic derivative of the aerodynamic force to the angular velocity as
Figure BDA0001333272390000059
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed. Those skilled in the art to which the invention pertains will appreciate that insubstantial changes or modifications can be made without departing from the spirit of the invention as defined by the appended claims.

Claims (2)

1. A method for calculating a dynamic derivative of an aircraft is characterized by specifically comprising the following processes:
step 1, determining static flow field boundary condition b aiming at flight state of aircraft1The governing equation of the flow field is converged to 0, i.e. R ═ Ax + b1When 0, the flow field is for the boundary condition b1Solution vector x of1Wherein A is a matrix of the governing equation, and when the residual error does not converge to absolute zero, it is set to converge to the allowable residual error R1＝Ax1+b1At this time, the aerodynamic force is
Figure FDA00013332723800000110
Step 2, solving equation
Figure FDA0001333272380000012
Wherein F is aerodynamic force, R is residual error, Lambda is adjoint matrix, x is solution vector, and solution vector x is obtained1Conditional corresponding adjoint matrix lambda1；
Step 3, increasing a rotation angular velocity delta omega around the reference center by the aircraft, generating a normal motion velocity on the surface of the aircraft, and calculating a residual error increment delta R generated by the normal velocity;
and 4, increasing the aerodynamic force generated by the normal speed to delta F ═ Lambda1Δ R, then the dynamic derivative of the aerodynamic force with respect to the angular velocity can be obtained as
Figure FDA0001333272380000011
2. The method of calculating the dynamic derivatives of an aircraft according to claim 1, characterized in that it further comprises the following processes: (a) a tiny rotation angular velocity delta omega is added around the reference center by the aircraft, the normal motion velocity is generated on the surface of the aircraft, and a corresponding boundary condition b is obtained2(ii) a (b) With x1Is the initial field, corresponds to b2As a boundary condition, there is a residual R2＝Ax1+b2(ii) a (c) Boundary condition becomes b2The aerodynamic force at the initial moment of the flow field is still the aerodynamic force of the static flow field
Figure FDA0001333272380000019
In the process that the residual R converges to 0, satisfy
Figure FDA0001333272380000014
Figure FDA0001333272380000013
Then
Figure FDA0001333272380000018
(d) When the residual error converges to 0, it can be obtained
Figure FDA0001333272380000017
Is corresponding to the boundary condition b2The aerodynamic force of (a); (f) similarly, if the solution in step 1 is continuously calculated and converged to the residual error equal to 0, the solution can also be obtained
Figure FDA0001333272380000015
(g) The amount of change Δ F in aerodynamic force is represented by a adjoint matrix as F2-F1＝Λ1Δ R; wherein Δ R ═ R2-R1＝(Ax1+b2)-(Ax1+b1)＝b2-b1(ii) a (h) Obtaining the dynamic derivative of the aerodynamic force to the angular velocity as
Figure FDA0001333272380000016
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CN110619160B (en) * 2019-09-02 2022-12-02 四川腾盾科技有限公司 Implicit solution method based on accompanying residual sorting
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