CN102507128B - Prediction method of dynamic aerodynamic characteristics of morphing aircraft - Google Patents

Abstract

The invention discloses a prediction method of dynamic aerodynamic characteristics of a morphing aircraft. The prediction method comprises the steps of: carrying out Fourier series and Taylor series expansion on characteristic physical quantities of the dynamic aerodynamic characteristics of the morphing aircraft; acquiring the dynamic derivative of the characteristic physical quantities of the dynamic aerodynamic characteristics of the aircraft dynamic to the change rate of the wing sweep angle of the morphing aircraft according to the Fourier series and Taylor series of the characteristic physical quantities of the dynamic aerodynamic characteristics of the morphing aircraft; and determining the relation between the characteristic physical quantities of the dynamic aerodynamic characteristics of the morphing aircraft and the change rate of the wing sweep angle of the morphing aircraft by utilizing the obtained dynamic derivative, and then predicting the dynamic aerodynamic characteristics of the morphing aircraft. By adopting the prediction method, the dynamic aerodynamic characteristics of the morphing aircraft can be predicted, and the stability and controllability of the morphing aircraft during the morphing process can be evaluated according to the prediction result.

Description

A kind of prediction method of dynamic aerodynamic characteristics of morphing aircraft

Technical field

The invention belongs to aerodynamic force technical field, relate to a kind of prediction method of dynamic aerodynamic characteristics of morphing aircraft.

Background technology

Economy is the important goal pursued in aircraft industries evolution all the time.Tradition fixed profile aircraft due to taking off, climb, cruise, glide, the stage such as landing keeps comparatively fixing aerodynamic arrangement's profile, is difficult to all have excellent economy in flight overall process.The variant aircraft occurred in recent years, owing to environmentally can change own profile with task, improves the economy of flight overall process significantly.

etc. a series of project, reflect the road of U.S.'s development variant aircraft.Meanwhile, Europe also starts 3AS (Active Aeroelastic Aircraft Structures) project and SMorph (the SmartAircraft Morphing Technologies) project of multiple units cooperation.In these projects, aerodynamics becomes guiding subject, presents many technical matterss urgently to be resolved hurrily.

The full machine aerodynamic characteristic problem of variant aircraft is one of above-mentioned technical matters.Existing correlation technique mostly pays close attention to the aerodynamic characteristic of variant aircraft aerodynamic arrangement and different layout mode, seldom relates to the unsteady aerodynamic characteristic in variant aircraft variant process.

In variant aircraft variant process, because the change of large scale occurs in aerodynamic arrangement, there is significant change in border, flow field, thus can cause significant unsteady aerodynamic effect thereupon, causes the unsteady aerodynamic characteristic in variant process to present significant difference from the aerodynamic characteristic of different layout mode.Set up the quantitative relationship between unsteady aerodynamic characteristic and pseudo steady aerodynamic characteristic, become an important need of current variant aircraft circles.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provides a kind of prediction method of dynamic aerodynamic characteristics of morphing aircraft.Employing the method for the invention can realize the prediction to dynamic aerodynamic characteristics of morphing aircraft, and can realize the assessment to the stability and control in variant aircraft variant process according to predicting the outcome.

Technical solution of the present invention:

A kind of prediction method of dynamic aerodynamic characteristics of morphing aircraft, comprises the following steps:

(1) Fourier expansion is carried out with dynamic aerodynamic characteristics of morphing aircraft feature physical quantity during sine function form mechanical periodicity in variant aircraft wing angle of sweep, and ignore the higher hamonic wave item in Fourier expansion form; Described dynamic aerodynamic characteristics of morphing aircraft feature physical quantity comprises variant aircraft dynamic lift coefficient, variant aircraft dynamic resistance coefficient, variant aircraft dynamic pitching moments coefficient;

(2) Taylor series expansion is carried out with dynamic aerodynamic characteristics of morphing aircraft feature physical quantity during sine function form mechanical periodicity in variant aircraft wing angle of sweep; And the single order of the sine function and described sine function that describe wing setting Changing Pattern and second derivative expression formula are substituted into the Taylor series obtained;

(3) utilize the Taylor series obtained in the Fourier series and step (2) obtained in step (1), obtain the dynamic derivative of dynamic aerodynamic characteristics of morphing aircraft feature physical quantity to variant aircraft wing angle of sweep rate of change;

(4) according to the dynamic derivative that step (3) obtains, determine the relation between dynamic aerodynamic characteristics of morphing aircraft feature physical quantity and variant aircraft wing angle of sweep rate of change, dynamic aerodynamic characteristics of morphing aircraft is predicted.

(5) what utilize step (4) to obtain to assess the stability and control in variant aircraft variant process predicting the outcome of dynamic aerodynamic characteristics of morphing aircraft.

Fourier expansion form after ignoring higher hamonic wave item to dynamic aerodynamic characteristics of morphing aircraft feature physical quantity in described step (1) is shown below:

$C=C_0+\stackrel{\‾}{C}\sin \left(\mathrm{\ωt}\right)\cos \mathrm{\α}+\stackrel{\‾}{C}\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}$

Wherein, C is dynamic aerodynamic characteristics of morphing aircraft feature physical quantity; C ₀for the unsteady aerodynamic characteristic feature physical quantity of vibration balancing position; for the amplitude of the unsteady aerodynamic characteristic feature physical quantity of fundamental frequency harmonics component; ω is angle of throw frequency; α is the angle of sweep of vibration and the phase differential of unsteady aerodynamic characteristic feature physical quantity.

The Taylor series of the dynamic aerodynamic characteristics of morphing aircraft feature physical quantity obtained in described step (2) are shown below:

$C=C_0+(C^{\mathrm{\λ}}-{\mathrm{\ω}}^2{C}^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+C^{\stackrel{\·}{\mathrm{\λ}}}\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)$

Wherein, λ is real-time variant aircraft wing angle of sweep, and θ is variant aircraft wing angle of sweep variable quantity, θ ₀for the variant aircraft wing angle of sweep of vibration balancing position.

The dynamic derivative obtained in described step (3) is shown below:

$C^{\stackrel{\·}{\mathrm{\λ}}}=\frac{C_{\left(2\mathrm{k\π}\right)}-C_{\left((2k+1)\mathrm{\π}\right)}}{2\mathrm{\ω}{\mathrm{\θ}}_0}$

Wherein, for variant aircraft wing angle of sweep rate of change.

The present invention compared with prior art tool has the following advantages:

(1) based on dynamic aerodynamic characteristics of morphing aircraft forecast demand, introduce the concept of dynamic aerodynamic characteristics of morphing aircraft feature physical quantity to the dynamic derivative of variant aircraft dynamic profile property feature geometric sense rate of change, and devise the periodicity dynamic profile characteristic of variant aircraft, resolved the equivalence of method of deploying by two kinds, achieve the calculating to dynamic derivative.

(2) according to dynamic aerodynamic characteristics of morphing aircraft feature physical quantity, variant aircraft pseudo steady aerodynamic characteristic feature physical quantity, variant aircraft wing angle of sweep, dynamic aerodynamic characteristics of morphing aircraft feature physical quantity to the physical relation between the dynamic derivative of variant aircraft dynamic profile property feature geometric sense rate of change, establish the prediction method of dynamic aerodynamic characteristics of morphing aircraft based on variant aircraft dynamic profile characteristic, achieve the fast prediction of dynamic aerodynamic characteristics of morphing aircraft.

(3) dynamic derivative of the present invention is adopted to calculate and above-mentioned Forecasting Methodology, can be in flight mechanics and predict that the stability and control in variant aircraft variant process provides critical data, this is significant with improvement flight comfortableness to lifting flight safety.

Accompanying drawing explanation

Fig. 1 is the trigonometric function curve of angle of sweep Changing Pattern;

Fig. 2 is linear modelling result and wind tunnel experimental results comparison curves;

Fig. 3 is invention process flow diagram.

Embodiment

Be illustrated in figure 3 process flow diagram of the present invention, below just according to Fig. 3 and above-mentioned aspect step, the present invention is described further.

Because above-mentioned dynamic aerodynamic characteristics of morphing aircraft feature physical quantity comprises variant aircraft dynamic lift coefficient, variant aircraft dynamic resistance coefficient, variant aircraft dynamic pitching moments coefficient these three kinds, divide three introduction the specific embodiment of the present invention below.

First variant aircraft dynamic lift coefficient C is selected _lfor dynamic aerodynamic characteristics of morphing aircraft feature physical quantity, variant aircraft wing angle of sweep λ is selected to be variant aircraft dynamic profile property feature geometric sense.

Definition variant aircraft dynamic lift coefficient C _lto variant aircraft wing angle of sweep rate of change dynamic derivative be details are as follows for its derivation:

When variant aircraft wing angle of sweep λ changes with cosine function rule (as shown in Figure 1), variant aircraft dynamic lift coefficient can be expressed as fourier expansion form:

$C_L=C_{L0}+{\stackrel{\‾}{C}}_{L\sin }(\mathrm{\ωt}+\mathrm{\α})+h\left(t\right)---\left(1\right)$

In formula, C _lfor real-time dynamic lift coefficient, C _l0for the lift coefficient of vibration balancing position, for the lift coefficient amplitude of fundamental frequency harmonics component, ω represents angle of throw frequency, and the angle of sweep of α representative vibration and the phase differential of lift coefficient, h (t) represents higher harmonic components.

(1) formula of expansion, ignore higher hamonic wave item:

$C_L=C_{L0}+{\stackrel{\‾}{C}}_L\sin \left(\mathrm{\ωt}\right)\cos \mathrm{\α}+{\stackrel{\‾}{C}}_L\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}---\left(2\right)$

According to the concept of pneumatic dynamic derivative, small size forced oscillation done by aircraft, and its dynamic lift coefficient also can be expressed as Taylor expansion form:

$C_L=C_{L0}+C_L^{\mathrm{\λ}}\mathrm{\Δ\λ}+C_L^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}+C_L^{\stackrel{\·\·}{\mathrm{\λ}}}\stackrel{\·\·}{\mathrm{\λ}}+o(\mathrm{\Δ\λ},\stackrel{\·}{\mathrm{\λ}})---\left(3\right)$

The equation of motion of simplify processes forced oscillation:

$\left\{\begin{array}{c}\mathrm{\θ}=\mathrm{\Δ\λ}={\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\\ \stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{\mathrm{\λ}}=\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)\\ \stackrel{\·\·}{\mathrm{\θ}}=\stackrel{\·\·}{\mathrm{\λ}}=-{\mathrm{\ω}}^2{\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\end{array}\right.---\left(4\right)$

In formula, λ is real-time angle of sweep, and θ is angle of sweep variable quantity, θ ₀for the angle of sweep of vibration balancing position, other symbolic significance is the same.

(4) formula substituted into (3) formula and omit higher order term, merging and arrange:

$C_L=C_{L0}+(C_L^{\mathrm{\λ}}-{\mathrm{\ω}}^2{C}_L^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+C_L^{\stackrel{\·}{\mathrm{\λ}}}\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)---\left(5\right)$

Abundant when the cycle of forced oscillation, erased the impact of primary effect, dynamic lift coefficient just reaches the mechanical periodicity of stable state.By (2) and (5) formula, the dynamic derivative of variant aircraft dynamic lift coefficient to variant aircraft wing angle of sweep rate over time can be obtained:

$C_L^{\stackrel{\·}{\mathrm{\λ}}}=\frac{{\stackrel{\‾}{C}}_L\sin \mathrm{\α}}{{\mathrm{\ω\θ}}_0}=\frac{C_{L\left(2\mathrm{k\π}\right)}-C_{L0}}{{\mathrm{\ω\θ}}_0}---\left(6\right)$

In actual computation process, in order to eliminate the little asymmetric of aerodynamic force, take

$C_L^{\stackrel{\·}{\mathrm{\λ}}}=\frac{C_{L\left(2\mathrm{k\π}\right)}-C_{L\left((2k+1)\mathrm{\π}\right)}}{2\mathrm{\ω}{\mathrm{\θ}}_0}---\left(7\right)$

Variant aircraft becomes in sweepback process, and dynamic lift coefficient and quasi-steady lift coefficient have certain quantitative relationship, and rate is relevant over time with wing setting, introduces above-mentioned dynamic derivative, and adopt linear modelling, then this relation can approximate representation be:

$C_L=C_{L0}+C_L^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}---\left(8\right)$

This formula is the linear model of quantitative relationship between variant aircraft dynamic lift coefficient and variant aircraft quasi-steady lift coefficient.

Secondly variant aircraft dynamic resistance coefficient C is selected _dfor dynamic aerodynamic characteristics of morphing aircraft feature physical quantity, variant aircraft wing angle of sweep λ is selected to be variant aircraft dynamic profile property feature geometric sense.

Definition variant aircraft dynamic resistance coefficient C _dto variant aircraft wing angle of sweep rate of change dynamic derivative be details are as follows for its derivation:

When variant aircraft wing angle of sweep λ changes with cosine function rule (as shown in Figure 1), variant aircraft dynamic resistance coefficient can be expressed as fourier expansion form:

$C_D=C_{D0}+{\stackrel{\‾}{C}}_D\sin (\mathrm{\ωt}+\mathrm{\α})+h\left(t\right)---\left(9\right)$

In formula, C _dfor real-time dynamic resistance coefficient, C _d0for the resistance coefficient of vibration balancing position, for the resistance coefficient amplitude of fundamental frequency harmonics component, ω represents angle of throw frequency, and the angle of sweep of α representative vibration and the phase differential of resistance coefficient, h (t) represents higher harmonic components.

(9) formula of expansion, ignore higher hamonic wave item:

$C_D=C_{D0}+{\stackrel{\‾}{C}}_D\sin \left(\mathrm{\ωt}\right)\cos \mathrm{\α}+{\stackrel{\‾}{C}}_D\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}---\left(10\right)$

According to the concept of pneumatic dynamic derivative, small size forced oscillation done by aircraft, and its dynamic resistance coefficient also can be expressed as Taylor expansion form:

$C_D=C_{D0}+C_D^{\mathrm{\λ}}\mathrm{\Δ\λ}+C_D^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}+C_D^{\stackrel{\·\·}{\mathrm{\λ}}}\stackrel{\·\·}{\mathrm{\λ}}+o(\mathrm{\Δ\λ},\stackrel{\·}{\mathrm{\λ}})---\left(11\right)$

The equation of motion of simplify processes forced oscillation:

$\left\{\begin{array}{c}\mathrm{\θ}=\mathrm{\Δ\λ}={\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\\ \stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{\mathrm{\λ}}=\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)\\ \stackrel{\·\·}{\mathrm{\θ}}=\stackrel{\·\·}{\mathrm{\λ}}=-{\mathrm{\ω}}^2{\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\end{array}\right.---\left(12\right)$

In formula, λ is real-time angle of sweep, and θ is angle of sweep variable quantity, θ ₀for the angle of sweep of vibration balancing position, other symbolic significance is the same.

(12) formula substituted into (11) formula and omit higher order term, merging and arrange:

$C_D=C_{D0}+(C_D^{\mathrm{\λ}}-{\mathrm{\ω}}^2{C}_D^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+C_D^{\stackrel{\·}{\mathrm{\λ}}}\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)---\left(13\right)$

Abundant when the cycle of forced oscillation, erased the impact of primary effect, dynamic resistance coefficient just reaches the mechanical periodicity of stable state.By (10) and (13) formula, the dynamic derivative of variant aircraft dynamic resistance coefficient to variant aircraft wing angle of sweep rate over time can be obtained:

$C_D^{\stackrel{\·}{\mathrm{\λ}}}=\frac{{\stackrel{\‾}{C}}_D\sin \mathrm{\α}}{{\mathrm{\ω\θ}}_0}=\frac{C_{D\left(2\mathrm{k\π}\right)}-C_{D0}}{{\mathrm{\ω\θ}}_0}---\left(14\right)$

In actual computation process, in order to eliminate the little asymmetric of aerodynamic force, take

$C_D^{\stackrel{\·}{\mathrm{\λ}}}=\frac{C_{D\left(2\mathrm{k\π}\right)}-C_{D\left((2k+1)\mathrm{\π}\right)}}{2\mathrm{\ω}{\mathrm{\θ}}_0}---\left(15\right)$

Variant aircraft becomes in sweepback process, and dynamic resistance coefficient and pseudo steady resistance coefficient have certain quantitative relationship, and rate is relevant over time with wing setting, introduces above-mentioned dynamic derivative, and adopt linear modelling, then this relation can approximate representation be:

$C_D=C_{D0}+C_D^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}---\left(16\right)$

This formula is the linear model of quantitative relationship between variant aircraft dynamic resistance coefficient and variant aircraft pseudo steady resistance coefficient.

Finally select variant aircraft dynamic pitching moments coefficient Cm _zfor dynamic aerodynamic characteristics of morphing aircraft feature physical quantity, variant aircraft wing angle of sweep λ is selected to be variant aircraft dynamic profile property feature geometric sense.

Definition variant aircraft dynamic pitching moments coefficient Cm _zto variant aircraft wing angle of sweep rate of change dynamic derivative be details are as follows for its derivation:

When variant aircraft wing angle of sweep λ changes with cosine function rule (as shown in Figure 1), variant aircraft dynamic pitching moments coefficient can be expressed as fourier expansion form:

${\mathrm{Cm}}_Z={\mathrm{Cm}}_{Z0}+{\stackrel{\‾}{\mathrm{Cm}}}_Z\sin (\mathrm{\ωt}+\mathrm{\α})+h\left(t\right)---\left(17\right)$

In formula, Cm _zfor real-time dynamic pitching moments coefficient, Cm _z0for the pitching moment coefficient of vibration balancing position, for the pitching moment coefficient amplitude of fundamental frequency harmonics component, ω represents angle of throw frequency, and the angle of sweep of α representative vibration and the phase differential of pitching moment coefficient, h (t) represents higher harmonic components.

(17) formula of expansion, ignore higher hamonic wave item:

${\mathrm{Cm}}_Z={\mathrm{Cm}}_{Z0}+{\stackrel{\‾}{\mathrm{Cm}}}_Z\sin \left(\mathrm{\ωt}\right)\cos \mathrm{\α}+{\stackrel{\‾}{\mathrm{Cm}}}_Z\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}---\left(18\right)$

According to the concept of pneumatic dynamic derivative, small size forced oscillation done by aircraft, and its dynamic pitching moments coefficient also can be expressed as Taylor expansion form:

${\mathrm{Cm}}_Z=C_{Z0}+{\mathrm{Cm}}_D^{\mathrm{\λ}}\mathrm{\Δ\λ}+{\mathrm{Cm}}_D^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}+{\mathrm{Cm}}_D^{\stackrel{\·\·}{\mathrm{\λ}}}\stackrel{\·\·}{\mathrm{\λ}}+o(\mathrm{\Δ\λ},\stackrel{\·}{\mathrm{\λ}})---\left(19\right)$

The equation of motion of simplify processes forced oscillation:

$\left\{\begin{array}{c}\mathrm{\θ}=\mathrm{\Δ\λ}={\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\\ \stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{\mathrm{\λ}}=\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)\\ \stackrel{\·\·}{\mathrm{\θ}}=\stackrel{\·\·}{\mathrm{\λ}}=-{\mathrm{\ω}}^2{\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\end{array}\right.---\left(20\right)$

In formula, λ is real-time angle of sweep, and θ is angle of sweep variable quantity, θ ₀for the angle of sweep of vibration balancing position, other symbolic significance is the same.

(20) formula substituted into (19) formula and omit higher order term, merging and arrange:

${\mathrm{Cm}}_Z={\mathrm{Cm}}_{Z0}+({\mathrm{Cm}}_Z^{\mathrm{\λ}}-{\mathrm{\ω}}^2{\mathrm{Cm}}_Z^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+{\mathrm{Cm}}_Z^{\stackrel{\·}{\mathrm{\λ}}}\mathrm{\ω}{\mathrm{\θ}}_0\cos \left(\mathrm{\ωt}\right)---\left(21\right)$

Abundant when the cycle of forced oscillation, erased the impact of primary effect, dynamic pitching moments coefficient just reaches the mechanical periodicity of stable state.By (18) and (21) formula, the dynamic derivative of variant aircraft dynamic pitching moments coefficient to variant aircraft wing angle of sweep rate over time can be obtained:

${\mathrm{Cm}}_Z^{\stackrel{\·}{\mathrm{\λ}}}=\frac{{\stackrel{\‾}{\mathrm{Cm}}}_z\sin \mathrm{\α}}{{\mathrm{\ω\θ}}_0}=\frac{{\mathrm{Cm}}_{z\left(2\mathrm{k\π}\right)}-{\mathrm{Cm}}_{z0}}{{\mathrm{\ω\θ}}_0}---\left(22\right)$

In actual computation process, in order to eliminate the little asymmetric of aerodynamic force, take

${\mathrm{Cm}}_Z^{\stackrel{\·}{\mathrm{\λ}}}=\frac{{\mathrm{Cm}}_{z\left(2\mathrm{k\π}\right)}-{\mathrm{Cm}}_{z\left((2k+1)\mathrm{\π}\right)}}{2\mathrm{\ω}{\mathrm{\θ}}_0}---\left(23\right)$

Variant aircraft becomes in sweepback process, dynamic pitching moments coefficient and pseudo steady pitching moment coefficient have certain quantitative relationship, and rate is relevant over time with wing setting, introduces above-mentioned dynamic derivative, adopt linear modelling, then this relation can approximate representation be:

$C_{\mathrm{Mz}}=C_{\mathrm{Mz}0}+C_{\mathrm{Mz}}^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}---\left(24\right)$

This formula is the linear model of quantitative relationship between variant aircraft dynamic pitching moments coefficient and variant aircraft pseudo steady pitching moment coefficient.

Based on dynamic aerodynamic characteristics of morphing aircraft feature physical quantity Forecasting Methodology of the present invention, real-time lift coefficient, resistance coefficient, the pitching moment coefficient in the full airborne period of aircraft can be obtained, in conjunction with real-time quality distribution character, moment of inertia characteristics in the full airborne period of aircraft, and the real-time thrust in the full airborne period of aircraft, can according to " aircraft flight dynamics " (Fang Zhenping work, publishing house of BJ University of Aeronautics & Astronautics) method of flight mechanics that records realizes the prediction of flight stability and maneuverability, and promote flight safety and improve flight comfortableness.

Fig. 2 is unsteady aerodynamic characteristic linear modelling result and the comparing of pseudo steady wind tunnel experimental results and dynamic wind tunnel experimental results.In figure, horizontal ordinate is angle of sweep, ordinate is pitching moment coefficient, solid dotted line represents the pseudo steady pitching moment coefficient of testing and obtaining, and open circles dotted line represents the pitching moment coefficient that linear model obtains, and open triangles dotted line represents the unsteady flo w pitching moment coefficient of testing and obtaining.Unsteady aerodynamic characteristic linear modelling result and experimental result have consistance as seen from the figure, and the error of the two is less than 5%, this demonstrate beneficial effect of the present invention.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (1)

1. a prediction method of dynamic aerodynamic characteristics of morphing aircraft, is characterized in that comprising the following steps:

(1) Fourier expansion is carried out with dynamic aerodynamic characteristics of morphing aircraft feature physical quantity during sine function form mechanical periodicity in variant aircraft wing angle of sweep, and ignore the higher hamonic wave item in Fourier expansion form; Described dynamic aerodynamic characteristics of morphing aircraft feature physical quantity comprises variant aircraft dynamic lift coefficient, variant aircraft dynamic resistance coefficient, variant aircraft dynamic pitching moments coefficient;

(2) Taylor series expansion is carried out with dynamic aerodynamic characteristics of morphing aircraft feature physical quantity during sine function form mechanical periodicity in variant aircraft wing angle of sweep; And the single order of the sine function and described sine function that describe wing setting Changing Pattern and second derivative expression formula are substituted into the Taylor series obtained;

(3) utilize the Taylor series obtained in the Fourier series and step (2) obtained in step (1), obtain the dynamic derivative of dynamic aerodynamic characteristics of morphing aircraft feature physical quantity to variant aircraft wing angle of sweep rate of change;

(4) according to the dynamic derivative that step (3) obtains, determine the relation between dynamic aerodynamic characteristics of morphing aircraft feature physical quantity and variant aircraft wing angle of sweep rate of change, dynamic aerodynamic characteristics of morphing aircraft is predicted;

Fourier expansion form after ignoring higher hamonic wave item to dynamic aerodynamic characteristics of morphing aircraft feature physical quantity in described step (1) is shown below:

$C=C_0+\stackrel{\‾}{C}\sin \left(\mathrm{\ωt}\right)\cos \mathrm{\α}+\stackrel{\‾}{C}\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}$

Wherein, C is dynamic aerodynamic characteristics of morphing aircraft feature physical quantity; C ₀for the unsteady aerodynamic characteristic feature physical quantity of vibration balancing position; for the amplitude of the unsteady aerodynamic characteristic feature physical quantity of fundamental frequency harmonics component; ω is angle of throw frequency; α is the angle of sweep of vibration and the phase differential of unsteady aerodynamic characteristic feature physical quantity;

The Taylor series of the dynamic aerodynamic characteristics of morphing aircraft feature physical quantity obtained in described step (2) are shown below:

$C=C_0+(C^{\mathrm{\λ}}-{\mathrm{\ω}}^2{C}^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+C^{\stackrel{\·}{\mathrm{\λ}}}{\mathrm{\ω\θ}}_0\cos \left(\mathrm{\ωt}\right)$

Wherein, λ is real-time variant aircraft wing angle of sweep, and θ is variant aircraft wing angle of sweep variable quantity, θ ₀for the variant aircraft wing angle of sweep of vibration balancing position;

The dynamic derivative obtained in described step (3) is shown below:

$C^{\stackrel{\·}{\mathrm{\λ}}}=\frac{C_{\left(2\mathrm{k\π}\right)}-C_{\left((2k+1)\mathrm{\π}\right)}}{{2\mathrm{\ω\θ}}_0}$

Wherein, for variant aircraft wing angle of sweep rate of change;

What utilize step (4) to obtain to assess the stability and control in variant aircraft variant process predicting the outcome of dynamic aerodynamic characteristics of morphing aircraft;

Described variant aircraft dynamic resistance coefficient is defined as C _d, to variant aircraft wing angle of sweep rate of change dynamic derivative be

When real-time variant aircraft wing angle of sweep λ changes with cosine function rule, variant aircraft dynamic resistance coefficient can be expressed as fourier expansion form:

$C_D=C_{D0}+{\stackrel{\‾}{C}}_D\sin (\mathrm{\ωt}+\mathrm{\α})+h\left(t\right)$

Wherein, C _dfor variant aircraft dynamic resistance coefficient, C _d0for the resistance coefficient of vibration balancing position, for the resistance coefficient amplitude of fundamental frequency harmonics component, ω represents angle of throw frequency, the angle of sweep of α representative vibration and the phase differential of resistance coefficient, and h (t) represents higher harmonic components;

Ignore the higher hamonic wave item in above formula:

$C_D=C_{D0}{+{\stackrel{\‾}{C}}_{D}s}_{}\mathrm{in}\left(\mathrm{\ωt}\right)\cos \mathrm{\α}+{\stackrel{\‾}{C}}_D\cos \left(\mathrm{\ωt}\right)\sin \mathrm{\α}$

Dynamic resistance coefficient is expressed as Taylor expansion form:

$C_D=C_{D0}+C_D^{\mathrm{\λ}}\mathrm{\Δ\λ}+C_D^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}+C_D^{\stackrel{\·\·}{\mathrm{\λ}}}\stackrel{\·\·}{\mathrm{\λ}}+o(\mathrm{\Δ\λ},\stackrel{\·}{\mathrm{\λ}})$

The equation of motion of simplify processes forced oscillation:

$\left\{\begin{array}{c}\mathrm{\θ}=\mathrm{\Δ\λ}={\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\\ \stackrel{\·}{\mathrm{\θ}}=\stackrel{\·}{\mathrm{\λ}}={\mathrm{\ω\θ}}_0\cos \left(\mathrm{\ωt}\right)\\ \stackrel{\·\·}{\mathrm{\θ}}=\stackrel{\·\·}{\mathrm{\λ}}=-{\mathrm{\ω}}^2{\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)\end{array}\right.$

Wherein, λ is real-time variant aircraft wing angle of sweep, and θ is variant aircraft wing angle of sweep variable quantity, θ ₀for the variant aircraft wing angle of sweep of vibration balancing position;

Upper two formulas merge omits higher order term, obtains:

$C_D=C_{D0}+(C_D^{\mathrm{\λ}}-{\mathrm{\ω}}^2{C}_D^{\stackrel{\·\·}{\mathrm{\λ}}}){\mathrm{\θ}}_0\sin \left(\mathrm{\ωt}\right)+C_D^{\stackrel{\·}{\mathrm{\λ}}}{\mathrm{\ω\θ}}_0\cos \left(\mathrm{\ωt}\right)$

Variant aircraft dynamic resistance coefficient is to the dynamic derivative of variant aircraft wing angle of sweep rate over time:

$C_D^{\stackrel{\·}{\mathrm{\λ}}}=\frac{{\stackrel{\‾}{C}}_D\sin \mathrm{\α}}{{\mathrm{\ω\θ}}_0}=\frac{C_{D\left(2\mathrm{k\π}\right)}-C_{D0}}{{\mathrm{\ω\θ}}_0}$

In actual computation process, in order to eliminate the little asymmetric of aerodynamic force, following formula is taked to calculate the linear model of quantitative relationship between variant aircraft dynamic resistance coefficient and variant aircraft pseudo steady resistance coefficient:

$C_D^{\stackrel{\·}{\mathrm{\λ}}}=\frac{C_{D\left(2\mathrm{k\π}\right)}-C_{D\left((3k+1)\mathrm{\π}\right)}}{{2\mathrm{\ω\θ}}_0}$

$C_D=C_{D0}+C_D^{\stackrel{\·}{\mathrm{\λ}}}\stackrel{\·}{\mathrm{\λ}}.$