CN107357976A - A kind of computational methods of the dynamic derivative of aircraft - Google Patents
A kind of computational methods of the dynamic derivative of aircraft Download PDFInfo
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- CN107357976A CN107357976A CN201710499236.8A CN201710499236A CN107357976A CN 107357976 A CN107357976 A CN 107357976A CN 201710499236 A CN201710499236 A CN 201710499236A CN 107357976 A CN107357976 A CN 107357976A
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- aerodynamic force
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Abstract
The present invention relates to fluid dynamics techniques field, discloses a kind of computational methods of the dynamic derivative of aircraft.Passive flow field boundary condition b is determined for the state of flight of aircraft1, ask the governing equation in flow field to converge on 0 i.e. R=Ax+b1When=0, flow field is directed to boundary condition b1Solution vector x1, wherein A is the matrix of governing equation, and residual error is not converged when arriving absolute zero, if it converges on the residual error R of permission1=Ax1+b1, now aerodynamic force beSolve equationWherein F is aerodynamic force, and R is residual error, and Λ is adjoint matrix, and x is solution vector, is obtained with solution vector x1Adjoint matrix Λ corresponding to condition1；Aircraft increases a rotational angular velocity Δ ω around reference center, and aircraft surface produces normal direction movement velocity, calculates residual error increment Delta R caused by normal velocity；Aerodynamic force increment caused by normal velocity is Δ F=Λ1Δ R, the then dynamic derivative that can obtain aerodynamic force angular velocity areThe solution scheme of this programme dynamic derivative is simply accurate.
Description
Technical field
The present invention relates to fluid dynamics techniques field, particularly a kind of computational methods of the dynamic derivative of aircraft.
Background technology
With CFD approach calculating aircraft aerodynamic force be generally to solve for shaped like
Ax+b=0 (1)
Large-scale matrix equation, wherein matrix A is to represent the matrix of governing equation, and b represents boundary condition, x for wait to ask to
Amount.
The method for solving flow field control equation (1) is mainly time matching method, treats and asks vector x to set an initial value x0, experience
One course changed over time
Finally give the solution of formula (1).Wherein R is residual error, and the process of solution is exactly the process for making residual error gradually converge to 0.
Existing method, including test and calculate, the method for solving dynamic derivative are all to make aircraft carry out periodicity forced vibration (to ask pair
Rotated during the derivative of angular speed around center of gravity, make translation when seeking the derivative to the angle of attack/sideslip angular rate of change), by calculating or trying
The time history for obtaining changes in aerodynamic forces is tested, phase is obtained according to changes in aerodynamic forces and the phase relation of angular speed/angle-of-attack rate
The dynamic derivative answered.
Illustrated below so that pitching moment is to rate of pitch and angle-of-attack rate derivative as an example.If aircraft
(model) is in equilbrium position α0Nearby make pitching sinusoidal vibration, its state equation is
Wherein A is angle amplitude, and T is the vibration period, and t is the time.Then have
Wherein Δ α is angle of attack deviation oscillation, and ω is angular speed,For angle-of-attack rate.The gas when rotating/swinging by a small margin
Power meets following relational expression：
F=F (α0)+ΔαFα+ω(Fω+Fα) (4)
After the change course for obtaining aerodynamic force F, a complete cycle is integrated
It can obtain the sum of aerodynamic force angular velocity and angle-of-attack rate derivative
Only with forcing rotation to respectively obtain this two.If making aircraft (model) carry out sinusoidal vibration up and down,
Its state equation is
Wherein Y is amplitude.Then have
Wherein it is v flying speeds.Only having for aerodynamic force is influenceed in the motion processDeviation oscillation, ω are angular speed,For angle-of-attack rate.Formula (4) is changed into：
After the change course for obtaining aerodynamic force F, a complete cycle is integrated
It can obtain derivative of the aerodynamic force to angle-of-attack rate
Gone through when calculating dynamic derivative using numerical computation method, it is necessary to calculate and force the unsteady aerodynamic force of concussion process to change
Journey, then tell dynamic derivative item with the phase component of changes in aerodynamic forces.Unsteady process is calculated to required precision height, is taken
It is long, it is very big to resource consumption, and if the amplitude of vibration is excessive, result of calculation can include excessive higher order term, deterioration in accuracy；
If amplitude is too small, variable quantity is possible and too small, and calculation error can bring larger deviation again.Wind tunnel test is limited by test
Precision, equally also deposit the contradiction of amplitude selection.
The content of the invention
The technical problems to be solved by the invention are：For above-mentioned problem, there is provided a kind of the dynamic of aircraft is led
Several computational methods.
The technical solution adopted by the present invention is as follows：A kind of computational methods of the dynamic derivative of aircraft, specifically include following mistake
Journey：
Step 1, the state of flight for aircraft determine passive flow field boundary condition b1, ask the governing equation in flow field to restrain
In 0 i.e. R=Ax+b1When=0, flow field is directed to boundary condition b1Solution vector x1, wherein A is the matrix of governing equation, and residual error is not received
When holding back absolute zero, if it converges on the residual error R of permission1=Ax1+b1, now aerodynamic force be
Step 2, solve equationWherein F is aerodynamic force, and R is residual error, and Λ is adjoint matrix, and x is solution
Vector, obtain with solution vector x1Adjoint matrix Λ corresponding to condition1；
Step 3, aircraft increase a rotational angular velocity Δ ω around reference center, and aircraft surface produces normal direction motion speed
Degree, calculate residual error increment Delta R caused by normal velocity；
Aerodynamic force increment caused by step 4, normal velocity is Δ F=Λ1Δ R, then it can obtain aerodynamic force angular velocity
Dynamic derivative be
Further, the computational methods of the dynamic derivative of the row device also include procedure below：(a) aircraft increases around reference center
Add a small rotational angular velocity Δ ω, aircraft surface produces normal direction movement velocity, boundary condition b corresponding to acquisition2；(b)
With x1For first field, corresponding b2For boundary condition, then there is residual error R2=Ax1+b2；(c) boundary condition is changed into b2Initial time aerodynamic force
Still it is the aerodynamic force in static flow fieldDuring residual error R converges to 0, meet Then(d) when residual error converges to 0, can obtain
For corresponding boundary condition b2Aerodynamic force；If the solution in step 1 similarly (f) is continued into calculating converges to residual error equal to 0, can also obtain(g) the variation delta F=F of aerodynamic force is represented with adjoint matrix2-F1=Λ1ΔR；, wherein Δ R=
R2-R1=(Ax1+b2)-(Ax1+b1)=b2-bx；(h) dynamic derivative of acquisition aerodynamic force angular velocity is
Compared with prior art, having the beneficial effect that using above-mentioned technical proposal：Technical scheme only needs to ask
Flow field and its adjoint matrix are solved, the dynamic derivative of aerodynamic force angular velocity can be obtained, without calculating non-stationary motion.And
According to its Method And Principle, residual error variation delta R caused by obtained dynamic derivative only changes with boundary condition is relevant, and initial flow-field is deposited
Residual error do not influence, therefore calculate initial flow-field when the convergent degree of residual error can suitably relax.This method greatly reduces
Resource consumption, and what is obtained is strict dynamic derivative, the influence not comprising the other factors such as high order component and angle-of-attack rate,
Accuracy improves, and the limitation of Oscillation Amplitude and frequency is secondly not present.
Brief description of the drawings
Fig. 1 is the schematic flow sheet of the computational methods of the dynamic derivative of aircraft of the present invention.
Embodiment
The present invention is described further below in conjunction with the accompanying drawings.
As shown in figure 1, a kind of computational methods of the dynamic derivative of aircraft, specifically include procedure below：
Step 1, the state of flight for aircraft determine passive flow field boundary condition b1, ask the governing equation in flow field to restrain
In 0 i.e. R=Ax+b1When=0, flow field is directed to boundary condition b1Solution vector x1, wherein A is the matrix of governing equation, and residual error is not received
When holding back absolute zero, if it converges on the residual error R of permission1=Ax1+b1, now aerodynamic force be
Step 2, solve equationWherein F is aerodynamic force, and R is residual error, and Λ is adjoint matrix, and x is solution
Vector, obtain with solution vector x1Adjoint matrix Λ corresponding to condition1；
Step 3, aircraft increase a rotational angular velocity Δ ω around reference center, and aircraft surface produces normal direction motion speed
Degree, calculate residual error increment Delta R caused by normal velocity；
Aerodynamic force increment caused by step 4, normal velocity is Δ F=Λ1Δ R, then it can obtain aerodynamic force angular velocity
Dynamic derivative be
When aircraft increases a rotational angular velocity Δ ω, boundary condition b corresponding to introducing around reference center2.The row
The computational methods of the dynamic derivative of device also include procedure below：(a) aircraft increases a small rotational angular velocity Δ around reference center
ω, aircraft surface produce normal direction movement velocity, boundary condition b corresponding to acquisition2；(b) with x1For first field, corresponding b2For boundary condition,
Then there is residual error R2=Ax1+b2；(c) boundary condition is changed into b2Initial time aerodynamic force still be static flow field aerodynamic forceIn residual error R
During converging to 0, meetThen(d) when residual error converges to 0, can obtainFor corresponding boundary condition b2's
Aerodynamic force；If the solution in step 1 similarly (f) is continued into calculating converges to residual error equal to 0, can also obtain
(g) the variation delta F=F of aerodynamic force is represented with adjoint matrix2-F1=Λ1ΔR；, wherein Δ R=R2-R1=(Ax1+b2)-(Ax1
+b1)=b2-b1；(h) dynamic derivative of acquisition aerodynamic force angular velocity isThe invention is not limited in preceding
The embodiment stated.The present invention expands to any new feature disclosed in this manual or any new combination, and
The step of any new method or process for disclosing or any new combination.If those skilled in the art, this hair is not being departed from
The unsubstantiality that bright spirit is done is altered or modified, and should all belong to the scope of the claims in the present invention protection.
Claims (2)
1. a kind of computational methods of the dynamic derivative of aircraft, it is characterised in that specifically include procedure below：
Step 1, the state of flight for aircraft determine passive flow field boundary condition b1, ask the governing equation in flow field to converge on 0 i.e.
R=Ax+b1When=0, flow field is directed to boundary condition b1Solution vector x1, wherein A is the matrix of governing equation, and residual error is not converged to be arrived
During absolute zero, if it converges on the residual error R of permission1=Ax1+b1, now aerodynamic force be
Step 2, solve equationWherein F is aerodynamic force, and R is residual error, and Λ is adjoint matrix, and x is solution vector,
Obtain with solution vector x1Adjoint matrix Λ corresponding to condition1；
Step 3, aircraft increase a rotational angular velocity Δ ω around reference center, and aircraft surface produces normal direction movement velocity,
Calculate residual error increment Delta R caused by normal velocity；
Aerodynamic force increment caused by step 4, normal velocity is Δ F=Λ1Δ R, then it can obtain the dynamic of aerodynamic force angular velocity and lead
Number is
2. the computational methods of the dynamic derivative of aircraft as claimed in claim 1, it is characterised in that also including procedure below：(a)
Aircraft increases a small rotational angular velocity Δ ω around reference center, and aircraft surface produces normal direction movement velocity, obtains
Corresponding boundary condition b2；(b) with x1For first field, corresponding b2For boundary condition, then there is residual error R2=Ax1+b2；(c) boundary condition
It is changed into b2Initial time aerodynamic force still be static flow field aerodynamic forceDuring residual error R converges to 0, meet Then
(d) when residual error converges to 0, can obtainFor corresponding boundary condition b2Aerodynamic force；If (f) similarly by step 1
In solution continue calculating and converge to residual error equal to 0, can also obtain(g) aerodynamic force is represented with adjoint matrix
Variation delta F=F2-F1=Λ1ΔR；, wherein Δ R=R2-R1=(Ax1+b2)-(Ax1+b1)=b2-b1；(h) aerodynamic force is obtained
The dynamic derivative of angular velocity is
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Cited By (5)
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| CN109063391A (en) * | 2018-09-30 | 2018-12-21 | 上海机电工程研究所 | Dynamic derivative under rotating condition calculates detection method and dynamic derivative wind tunnel test methods |
| CN110619160A (en) * | 2019-09-02 | 2019-12-27 | 四川腾盾科技有限公司 | Implicit solution method based on accompanying residual sorting |
| CN110674607A (en) * | 2019-09-02 | 2020-01-10 | 四川腾盾科技有限公司 | Implicit solution method based on residual magnitude ordering |
| CN112393876A (en) * | 2019-08-16 | 2021-02-23 | 北京空天技术研究所 | Dynamic pneumatic derivative prediction method suitable for internal and external flow integrated appearance |
| CN114088330A (en) * | 2021-11-19 | 2022-02-25 | 中国航空工业集团公司哈尔滨空气动力研究所 | Longitudinal dynamic derivative low-speed wind tunnel continuous measurement test method |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109063391A (en) * | 2018-09-30 | 2018-12-21 | 上海机电工程研究所 | Dynamic derivative under rotating condition calculates detection method and dynamic derivative wind tunnel test methods |
| CN112393876A (en) * | 2019-08-16 | 2021-02-23 | 北京空天技术研究所 | Dynamic pneumatic derivative prediction method suitable for internal and external flow integrated appearance |
| CN112393876B (en) * | 2019-08-16 | 2022-04-12 | 北京空天技术研究所 | Dynamic pneumatic derivative prediction method suitable for internal and external flow integrated appearance |
| CN110619160A (en) * | 2019-09-02 | 2019-12-27 | 四川腾盾科技有限公司 | Implicit solution method based on accompanying residual sorting |
| CN110674607A (en) * | 2019-09-02 | 2020-01-10 | 四川腾盾科技有限公司 | Implicit solution method based on residual magnitude ordering |
| CN110674607B (en) * | 2019-09-02 | 2022-11-18 | 四川腾盾科技有限公司 | Implicit solution method based on residual magnitude ordering |
| 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 |
| CN114088330A (en) * | 2021-11-19 | 2022-02-25 | 中国航空工业集团公司哈尔滨空气动力研究所 | Longitudinal dynamic derivative low-speed wind tunnel continuous measurement test method |
| CN114088330B (en) * | 2021-11-19 | 2023-03-17 | 中国航空工业集团公司哈尔滨空气动力研究所 | Longitudinal dynamic derivative low-speed wind tunnel continuous measurement test method |
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