CN106227971A - Dynamic derivative fast prediction technology based on harmonic wave equilibrium method - Google Patents

Dynamic derivative fast prediction technology based on harmonic wave equilibrium method Download PDF

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Publication number
CN106227971A
CN106227971A CN201610627801.XA CN201610627801A CN106227971A CN 106227971 A CN106227971 A CN 106227971A CN 201610627801 A CN201610627801 A CN 201610627801A CN 106227971 A CN106227971 A CN 106227971A
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dynamic derivative
solve
harmonic wave
field
harmonic
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陈琦
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63821 People's Liberation Army
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63821 People's Liberation Army
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses dynamic derivative fast prediction technology based on harmonic wave equilibrium method, relate to flight control system design field, a kind of method being specifically related to fast prediction dynamic derivative.Comprise the following steps: one, solve permanent Navier Stokes equation, obtain the steady flow field of original state；Two, using above-mentioned flow field as first field, solve the harmonic balance equation in time domain, obtain Unsteady Flow the most in the same time；Three, by above-mentioned Unsteady Flow, bring fourier progression expanding method formula into, reversely rebuild periodic forced oscillation process；Four, according to rebuilding the aerodynamic moment and the phasor of angle obtained, integration method is used can to pick out dynamic derivative.Solve the problem that the Forecasting Methodology of dynamic derivative calculates overlong time present in prior art.

Description

Dynamic derivative fast prediction technology based on harmonic wave equilibrium method
Technical field
The present invention relates to flight control system design field, a kind of method being specifically related to fast prediction dynamic derivative.
Background technology
Dynamic derivative is one of important parameter in flight control system design, dynamic stability and the flight to aircraft Quality has a major impact, and along with modern advanced aircraft is more and more higher to the requirement of mobility and agility, the weight of dynamic derivative The property wanted highlights the most day by day.Currently, the Forecasting Methodology of dynamic derivative mainly has engineering approximation method, method for numerical simulation and wind tunnel test Method.Wherein method for numerical simulation due to precision of prediction higher, expense between engineering approximation method and wind tunnel test methods, Thus be used widely.But when traditional method for numerical simulation predicts dynamic derivative, general employing dual time-stepping method Numerical-Mode Intend the forced oscillation process in 2-3 cycle, calculate the time longer.
Summary of the invention
The present invention provides dynamic derivative fast prediction technology based on harmonic wave equilibrium method, solves present in prior art dynamic The problem that the Forecasting Methodology of derivative calculates overlong time.
For solving the problems referred to above, the present invention adopts the following technical scheme that dynamic derivative fast prediction based on harmonic wave equilibrium method Technology, uses harmonic wave equilibrium method to solve aircraft forced oscillation process, then identification dynamic derivative, comprises the following steps:
Step one: solve stationary Navier-Stokes equations, obtains the steady flow field of original state；
Step 2: using above-mentioned flow field as first field, solves the harmonic balance equation in time domain, obtainsN T=2N H+ 1 different time The Unsteady Flow carved；DescribedN H=1,2,3 ...,N HFor harmonic number；
Step 3: by above-mentionedN TIndividual Unsteady Flow, brings fourier progression expanding method formula into:
, reverse reconstruction periodically forces Oscillatory process；
Step 4: according to rebuilding the aerodynamic moment and the phasor of angle obtained, use integration method can pick out dynamic derivative, i.e.。
Advantages of the present invention has: harmonic wave equilibrium method is incorporated into the solution procedure in periodically flow field by the present invention, only needs coupling Solve the flow field in several equidistant moment in the cycle, the oscillatory process in whole cycle, and then identification dynamic derivative can be rebuild.It calculates Precision is consistent with traditional dual time-stepping method, but owing to without solving whole oscillatory process, computational efficiency typically can promote one Individual magnitude is the highest；And the calculating time of the present invention is unrelated with aircraft frequency of oscillation, measurable any given frequency Dynamic Stability Derivatives of The Aircraft.To reduce Flight Vehicle Design cost, shorten system development cycle significant.
Accompanying drawing explanation
Fig. 1 is the flow chart of the present invention；
Fig. 2 is that the dynamic derivative of the present invention predicts the outcome and test value, the broken line graph that predicts the outcome of traditional method；
Fig. 3 is dynamic derivative predictive efficiency efficiency comparative's form with traditional method of the present invention.
Detailed description of the invention
By optimal embodiment, the present invention is described in detail below.
As it is shown in figure 1, this technology realize principle:
Navier-Stockes equation under generalized curvilinear coordinate is abbreviated as following form
(1)
Wherein,QFor conservation variable, by all remainders of Navier-Stockes equation it isR (Q).Lead owing to numerical prediction is dynamic Number needs numerical simulation to force pure oscillation process, is typical periodic process, thus, it is believed thatQWithRIn oscillatory process In be also periodic, the cycleT = 2 π / ω, thus,QWithRThe form of deployable one-tenth Fourier space superposition:
(2)
In formula (2), whereinn=1,2 ...,N H ,N HRepresent Fourier space item,、、；、、 ；、、It is respectively Fourier coefficient.Convolution (1) and formula (2), and utilize the integral characteristic of trigonometric function, hold It is easy to get:
(3)
Formula (3) constitutesN T=2N HThe equation group of+1 variable, is abbreviated into following form by formula (3):
(4)
WhereinAIt isN T×N TKnown coefficient matrix,WithRefer to respectively containN TThe vector of individual flow field variable:
(5)
On frequency domain, directly solve (4) formula extremely difficult, for this reason, it may be necessary to be converted into the harmonic balance equation of time domain, conversion formula For:
(6)
Wherein, time domain variableQWithNIt is similarly and containsN TThe vector of individual flow field variable:
(7)
EFor Fourier transform matrix:
(8)
Then, bring (6) formula into (4) formula, just obtain the harmonic balance equation in time domain:
(9)
The both sides of above formula premultiplication simultaneouslyEInverse matrix, abbreviation obtains
(10)
Wherein, matrixDEach term coefficient be:
(11)
Noticing, formula (10) and formula (4) are of equal value, but are more easy to solve.Meanwhile, the explicit time stepping method of formula (10) Form is conditional stability, for this reason, it may be necessary to source itemMake the process of an implicit expression, to avoid the instability calculated Property.Final time stepping method formula is:
(12)
Formula (12), at the left end virtual time derivative term of formula (10), uses the way solving standing state equation the most availableQ 。
ComprisedN T The variable of individual instantaneous flow field solutionQAfter, according to formula (6), utilize inverse fourier transform, i.e. Can obtain containing the variable of fourier series item；Recycling fourier progression expanding method formula, it may be assumed that
(13)
Thus complete the process of " reconstruction ", obtain flow field variable time dependent course curve in whole oscillatory process, with Sample have also been obtained the sluggish circle that aerodynamic moment changes with oscillation angle.According to sluggishness circle, use integration method, can identification set out to lead Number:
(14)
The step that realizes of this technology is:
The harmonic balance method is applied to existing unsteady flo w Navier-Stockes solver, it is only necessary to following step Can realize:
Step one: expand array.Equation (10) containsIndividual flow field variableQ, therefore, original Navier-Stockes asks The array solving code to expandTimes, simultaneously plus " Do circulation " before all solvers.
Step 2: to flow field variable the most in the same timeQ (t), solve and obtain correspondence The position coordinates in moment.
Step 3: owing to flow field coordinate position the most in the same time is the most different, mesh point need to be recalculated respectively to the time Derivative term.
Step 4: in view of the impact of mesh motion, the computing formula of flux is also required to carry out suitable amendment, by formula (1) without viscous logical vector in Navier-StockesVector is led to viscosityUse respectivelyEReplacing, other both directions are identical, Can write a Chinese character in simplified form into:
(15)
Step 5: dynamic wall boundary condition, directly makes each point velocity component on wall
(16)
As above step is when operation, and step 2 and step 3 can obtain by direct solution before iteration starts, it is only necessary to calculate one Secondary.If existing program is unsteady flo w calculation procedure, then step 4 and step 5 have been contemplated that, at application the harmonic balance method Time need not revise the most separately, only need to adjust data structure makes it be applicable to the harmonic balance method.
The application effect of this technology is shown in Fig. 2 and Fig. 3.In fig. 2, the dynamic derivative of this technology predicts the outcome and test value, biography Predicting the outcome of system method all coincide preferably, demonstrates the precision of prediction of this technology.In figure 3, the dynamic derivative prediction of this technology Efficiency is compared with traditional method, it was predicted that precision typically promotes a more than magnitude, demonstrates the predictive efficiency of this technology.
It is last that it is noted that obviously above-described embodiment is only for clearly demonstrating example of the present invention, and also The non-restriction to embodiment.For those of ordinary skill in the field, can also do on the basis of the above description Go out change or the variation of other multi-form.Here without also cannot all of embodiment be given exhaustive.And thus drawn What Shen went out obviously changes or changes among still in protection scope of the present invention.

Claims (1)

1. dynamic derivative fast prediction technology based on harmonic wave equilibrium method, it is characterised in that use harmonic wave equilibrium method to solve aircraft Forced oscillation process, then identification dynamic derivative, comprise the following steps:
Step one, solve stationary Navier-Stokes equations, obtain the steady flow field of original state；
Step 2, using above-mentioned flow field as first field, solve the harmonic balance equation in time domain, obtainN T=2N H+ 1 the most in the same time Unsteady Flow；DescribedN H=1,2,3 ...,N HFor harmonic number；
Step 3, by above-mentionedN TIndividual Unsteady Flow, brings fourier progression expanding method formula into, and reverse reconstruction periodically forces shakes Swing process；
Step 4, the aerodynamic moment obtained according to reconstruction and the phasor of angle, use integration method can pick out dynamic derivative.
CN201610627801.XA 2016-08-03 2016-08-03 Dynamic derivative fast prediction technology based on harmonic wave equilibrium method Pending CN106227971A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
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
CN116384290A (en) * 2023-06-06 2023-07-04 中国空气动力研究与发展中心计算空气动力研究所 Hypersonic aircraft dynamic derivative prediction method considering real gas effect

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102507128A (en) * 2011-09-29 2012-06-20 中国航天空气动力技术研究院 Prediction method of dynamic aerodynamic characteristics of morphing aircraft
CN103218481A (en) * 2013-03-26 2013-07-24 东南大学 Simulation method of wind-induced disaster whole process of long-span bridge
CN104850759A (en) * 2015-06-16 2015-08-19 中国空气动力研究与发展中心高速空气动力研究所 Method for processing forced vibration dynamic stability derivative test data of wind tunnel

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Publication number Priority date Publication date Assignee Title
CN102507128A (en) * 2011-09-29 2012-06-20 中国航天空气动力技术研究院 Prediction method of dynamic aerodynamic characteristics of morphing aircraft
CN103218481A (en) * 2013-03-26 2013-07-24 东南大学 Simulation method of wind-induced disaster whole process of long-span bridge
CN104850759A (en) * 2015-06-16 2015-08-19 中国空气动力研究与发展中心高速空气动力研究所 Method for processing forced vibration dynamic stability derivative test data of wind tunnel

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Cited By (3)

* Cited by examiner, † Cited by third party
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
CN116384290A (en) * 2023-06-06 2023-07-04 中国空气动力研究与发展中心计算空气动力研究所 Hypersonic aircraft dynamic derivative prediction method considering real gas effect
CN116384290B (en) * 2023-06-06 2023-08-22 中国空气动力研究与发展中心计算空气动力研究所 Hypersonic aircraft dynamic derivative prediction method considering real gas effect

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Application publication date: 20161214