CN109446688A - One kind is based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method - Google Patents
One kind is based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method Download PDFInfo
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- CN109446688A CN109446688A CN201811317405.2A CN201811317405A CN109446688A CN 109446688 A CN109446688 A CN 109446688A CN 201811317405 A CN201811317405 A CN 201811317405A CN 109446688 A CN109446688 A CN 109446688A
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Abstract
The present invention provides one kind based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, and the Aerodynamic characteristics method includes the following steps: step 1, the determination of research approach；Step 2, the modeling of dimensional airfoil: the standard aerofoil profile in Low Speed Airfoil series is chosen；Step 3, on the basis of step 2, according to primary election flapping wing phase angle and primary election flapping wing frequency, the different UDF function of multiple groups the setting of User-Defined Functions UDF: is compiled out using control variate method；Step 4, the calculating of lift coefficient and resistance coefficient；Step 5, mean value and numerical simulation result analysis are calculated；Two-dimensional surface hovering flapping wing Aerodynamic characteristics method provided by the invention can simulate aerodynamic characteristic of the biological thin wing of true high-frequency vibration in hovering；Go out the average relationship for rising resistance coefficient and frequency and phase angle by numerical Analysis, to it is preferred that go out most suitable flapping wing frequency and phase angle；There is the meaning that can not say table to the design of current bionic flapping-wing flying vehicle.
Description
Technical field
The invention belongs to flight mechanics fields, and in particular to one kind is based on two-dimensional surface hovering flapping wing Aerodynamic characteristics side
Method.
Background technique
Currently, in nature, there is the biologies that can largely fly, wherein the insect and birds that fly are close to one
Million kinds, the birds that can be flown close to 100,000 kinds, these biologies that can fly all be to take the mode of flapping wing to fly, and do not have
Rotor or fixed-wing is taken to fly, rotor and fixed-wing are artificial mechanical traction modes, thus, it can be known that flapping flight is
The elutriation that have passed through the time, the most traditional flying method remained in very long biological evolution, this flapping wing mode
It is the optimal flying method of biology.Flapping flight compared with fixed-wing and rotor flying, flapping flight can by lifting, hovering and
Propulsion functions combine in a sized flap wings system, and aircraft free low speed as the insects such as dragonfly, drosophila is enable to take off, hang
Stop, turn, inverted flight of even turning around.Scientists expect that flying robot helps us to Mars with bionic flapping-wing very early
Carry out more accurate measurement.Since the air on Mars is comparatively than leaner, the magnetic field on Mars is also than tellurian
Magnetic field is faint, existing aircraft, and some is equipped with advanced Mars probe, but if only relying on Magnetic oriented, flies
The flight remote control device of row device will be unable to accurately be positioned and navigated, and this requires aircraft movable on Mars to have
More perfect navigation system, and the navigation for being able to carry out itself and flight control, at this moment flapping flight robot can play instead
Huge effect.
The insect that the living nature overwhelming majority can fly all has the ability of hovering flight, this is the basic skill that they fly
Can, it is this hovering to people it is the most impressive be exactly without going into it deeply when hovering, seem static, its wing is in high frequency in fact
Vibration.Drosophila also has this ability, and when hovering flight, body and horizontal plane can have certain angle for they, and
Angle is generally 30 degree to 60 degree.Although body be it is inclined, it is almost horizontal when their wing is fluttered, wing
Frequency of flapping is generally very big, can achieve several hundred hertz.As drosophila, this kind of insect of dragonfly is obtained by the high-frequency beating of wing
Lift was obtained, this aerodynamic force can balance the weight of itself.Therefore, grinding to the optimal auction of the insect under upper frequency
Study carefully, also just becomes the key for disclosing insect flying mechanism.
Research is in the case where low reynolds number, and on the basis of flapping wing model is built upon two-dimensional, by study its
Aerodynamic characteristics in motion process can make people have deeper understanding to nature insect flying characteristic, to bionical at present
The design of flapping wing aircraft has the meaning that can not say table.
Specifically, present invention research is fluttered as the unsteady of the insect wings such as dragonfly, drosophila, to influence around aerofoil profile
The UNSTEADY FLOW of air, so that the aerodynamic force affected around aerofoil profile can generate variation.Studying the situation of change can reflect
The stress condition of aerofoil profile out.In turn, pass through the frequency of fluttering of change aerofoil profile, it can be deduced that at different frequencies, around aerofoil profile
The situation of change of lift and resistance.Further, it is fluttered plane with respect to the horizontal plane inclination angle size by changing aerofoil profile, succinctly
Say and namely change its phase angle, it can be deduced that under out of phase angle, the situation of change of lift and resistance around aerofoil profile.
Summary of the invention
The purpose of the present invention is to provide one kind based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method at least to solve
The technical issues of Aerodynamic characteristics can not being carried out to the biological thin wing of high-frequency vibration certainly existing in the prior art.
To achieve the goals above, the invention provides the following technical scheme:
One kind includes as follows based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, the Aerodynamic characteristics method
Step:
Step 1, the determination of research approach:
Flapping motion simplified two-dimensional model and the equation of motion are established, and utilizes FLUENT software, User-Defined Functions UDF
And Dynamic mesh, average lift and resistance coefficient of the analysis of two-dimensional aerofoil profile under different flapping wing frequencies, out of phase angle；
Step 2, the modeling of dimensional airfoil:
The standard aerofoil profile in Low Speed Airfoil series is chosen, aerofoil profile is first established in Gambit, and determine aerofoil profile
Up-and-down boundary marks off triangular mesh, sets boundary condition；
Step 3, the setting of User-Defined Functions UDF:
On the basis of step 2, primary election flapping wing phase angle and primary election flapping wing frequency compile out multiple groups using control variate method
Different UDF functions；
Step 4, the calculating of lift coefficient and resistance coefficient:
The UDF function compiled in the dimensional airfoil model and step 3 established in step 2 is imported in FLUENT, and
After defining basic solver, dynamic region, setting liter resistance coefficient monitor and nondimensionalization being set, it is iterated calculating；
Step 5, mean value and numerical simulation result analysis are calculated:
Evaluation obtained in step 4 is imported in MATLAB, the exercise data of two-dimentional flapping wing a cycle, key are chosen
Enter command statement and obtains the average relationship image for rising resistance coefficient and flapping wing frequency and flapping wing phase angle.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the step 1 is specific
Further include following steps:
Step 11, computation model is established:
Chordwise section of the thin ellipsoid as Simplified two-dimension aerofoil profile is chosen, aerofoil profile movement includes the compound fortune of translation and rotation
It is dynamic, governing equation are as follows:
It is translatable along Y-axis:
H (t)=Am sin(2πft)
Geometric center around oval aerofoil profile rotates:
According to the available dimensionless Reynolds number of dimensional analysis:
In formula:
Am, αm, f andThe phase respectively fluttered between amplitude, maximum rotation amplitude, flapping wing frequency, translation and rotation
Difference；
ρ, U, μ and c are respectively density, speed of incoming flow, viscosity coefficient and the aerofoil profile chord length of air；
Step 12, calculation method is established:
In numerical simulation calculation, the movement of aerofoil profile is realized by controlling its translational velocity and rotational angular velocity；
Translational velocity:
Rotational angular velocity:
In numerical simulation calculation, the movement of fluid can be described by following continuity equation and N-S equation:
In formula:
U and v is respectively speed of the fluid along X-axis and Y-axis；P is the pressure of fluid.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the step 2 is specific
Further include following steps:
Step 21, NACA0006 aerofoil profile is generated using coordinate points:
The chord length and position of center line of blade are determined first, then uses the approximating function of thickness, and it is bent to generate upper and lower aerofoil profile
Line, two curves extend the cross-sectional profile figure that intersection is formed aerofoil profile；Aerofoil profile front is handled with the circle of contact；
Step 22, aerofoil profile initial position determines:
NACA0006 importing GAMBIT is established into model, first analyzes influence of the different frequency to hovering flapping wing aerodynamic characteristic；
Selected starting phase angle, selectes the center of aerofoil profile, calculates aerofoil profile in the offset and chord length of X-axis and Y-axis and the folder of X-axis
Angle；
Preferably, at a quarter of airfoil center positioning chord length；
Step 23, triangle gridding is divided in zoning:
Two discs are generated using Boolean calculation, divide triangle gridding in disc region generated；
Step 24, boundary condition is set:
After grid dividing is good, the setting of boundary condition is carried out, under hovering, airfoil surface entrance does not have to setting without incoming flow
Entrance directly defines one outlet boundary condition.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the step 3 is specific
Further include following steps:
Step 31, control starting phase angle is constant, changes flapping wing frequency:
It is compiled in udf function in the displacement of X-axis, Y-axis as follows
X0=0.0125*0.5*cos (2*80*pi* (time-dtime))
Y0=0.0125*0.5*1.732*cos (2*80*pi* (time-dtime)
It is to be got by x0, y0 to the derivation of time t in X-axis, the speed of Y-axis, is compiled in udf function as follows:
Sing0=-0.0125*2*pi*80*0.5*1*sin (2*80*pi* (time-dtime))；
Sing1=-0.0125*2*pi*80*0.5*1.732*sin (2*80*pi* (time-dtime))；
Wherein angular speed is obtained by angular displacement derivation, is compiled in udf function as follows:
W0=pi*0.25*2*pi*80*sin (2*80*pi* (time-dtime+0.5*pi))
Step 32, control flapping wing frequency is constant, changes flapping wing starting phase angle:
In the function that step 31 is compiled, different differences is added and subtracted behind starting phase angle, to change the initial of flapping wing
Phase angle.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the step 4 is specific
Further include following steps:
Step 41, basic solver definition:
Grid file is read in, 2D two dimension double precision solver is started；And unsteady Unsteady is selected, it is selected in gradient
Tabs under, select Green-Gauss Node Based；
Step 42, parameter setting and calculating:
Dynamic region is created in the triangle gridding that step 2 divides, and lift is set and resistance coefficient detector makes figure window
Mouth can dynamically show lift and resistance coefficient with the variation of iterative process；And it is arranged and calculates time step and time step number；
Preferably, the time step is set as 2.5e-5, the time step number is set as 1000 steps.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that key in the step 5
The sentence entered are as follows:
Y=[3.2258,3.8676,8.0425,10.8660,14.6101]；
X=[80,100,120,140,160]；
plot(X,Y,'k-o')；
ylabel('cl cd')；
Xlabel (' frequency ')；
hold on
Z=[- 1.934, -5.7081, -5.07025, -6.5621, -8.3856]；
plot(X,Z,'k--o')；
Title (' average the relationship for rising resistance coefficient and frequency ')
Legend average lift coefficient cl average resistance coefficient cd
box off。
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the dimensional airfoil
Flutter amplitude be π/3~2 π/3.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the dimensional airfoil
Flapping wing rotation amplitude be π/4~3 π/4.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the dimensional airfoil
Short axle and the ratio between long axis be definite value e.
It is as described above a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, it is preferable that the dimensional airfoil
Frequency of fluttering is 80~160Hz, and phase angle is 70~110 °.
Compared with the immediate prior art, technical solution provided by the invention has following excellent effect:
Two-dimensional surface hovering flapping wing Aerodynamic characteristics method provided by the invention can simulate the life of true high-frequency vibration
Aerodynamic characteristic of the object thin wing in hovering, by simulating the biological thin wing of high-frequency vibration in amplitude and the rotation amplitude one of initially fluttering
Periodically, different flapping wing frequency and phase angle are compared；Go out average rise by numerical Analysis and hinders coefficient and frequency and phase angle
Relationship, thus it is preferred that go out most suitable flapping wing frequency and phase angle；For the understanding to nature insect flying characteristic, to current
The design of bionic flapping-wing flying vehicle has the meaning that can not say table.
Detailed description of the invention
The accompanying drawings constituting a part of this application is used to provide further understanding of the present invention, and of the invention shows
Examples and descriptions thereof are used to explain the present invention for meaning property, does not constitute improper limitations of the present invention.Wherein:
Fig. 1 is that the flapping wing model of the embodiment of the present invention and kinematic parameter define schematic diagram；
Fig. 2 is the aerofoil profile formation basic theory schematic diagram of the embodiment of the present invention；
Fig. 3 be the embodiment of the present invention flap frequency f=80 when, lift coefficient changes with time schematic diagram；
Fig. 4 be the embodiment of the present invention flap frequency f=80 when, resistance coefficient changes with time schematic diagram；
Fig. 5 be the embodiment of the present invention flap frequency f=160 when, phase angle be 90 degree when, the change of lift coefficient at any time
Change schematic diagram；
Fig. 6 be the embodiment of the present invention flap frequency f=160 when, phase angle be 90 degree when, the change of resistance coefficient at any time
Change schematic diagram；
Fig. 7 is that the average liter of the embodiment of the present invention hinders the relation schematic diagram of coefficient and frequency；
Fig. 8 is that the average liter of the embodiment of the present invention hinders the relation schematic diagram of coefficient and phase angle.
In figure: 1, the first aerofoil profile；2, the second aerofoil profile；3, aerofoil profile corner；4, aerofoil profile is translatable；5, upper Curve of wing；6, bottom wing
Type curve；7, the circle of contact；8, string；9, aerofoil profile center line.
Specific embodiment
The present invention will be described in detail below with reference to the accompanying drawings and embodiments.It should be noted that in the feelings not conflicted
Under condition, the features in the embodiments and the embodiments of the present application be can be combined with each other.
In the description of the present invention, term " longitudinal direction ", " transverse direction ", "upper", "lower", "front", "rear", "left", "right", " perpendicular
Directly ", the orientation or positional relationship of the instructions such as "horizontal", "top", "bottom" is to be based on the orientation or positional relationship shown in the drawings, and is only
For ease of description the present invention rather than require the present invention that must be constructed and operated in a specific orientation, therefore should not be understood as pair
Limitation of the invention.Term used in the present invention " connected ", " connection " shall be understood in a broad sense, for example, it may be fixedly connected,
It may be a detachable connection；It can be directly connected, can also be indirectly connected by intermediate member, for the common of this field
For technical staff, the concrete meaning of above-mentioned term can be understood as the case may be.
According to a particular embodiment of the invention, the movement of dimensional airfoil can be divided into four ranks within a period of flapping
Section: 1, wing is flapped downwards, and has certain angle of attack.2, wing, along axial torsion, changes the angle of attack and opens when photographing minimum point
Beginning Back stroke.3, wing is with certain angle of attack Back stroke.4, when wing Back stroke to highest point, along axial torsion, under changing the angle of attack and starting
It claps.So in cycles.
According to a particular embodiment of the invention, chordwise section of the thin ellipsoid as Simplified two-dimension wing model is chosen, straight
The motion model of flapping wing is established under angular coordinate system.As shown in Figure 1, (chord length c) is 0.1m to long axis, and the ratio between short axle and long axis e are
0.125, aerofoil profile movement include translation and rotation compound motion, using self-editing program UDF imported into Fluent software come
It improves and resolves performance, the variable during being fluttered by the flapping wing that UDF can control our needs, for example frequency of fluttering, flutter
The various parameters such as amplitude, rotation amplitude, phase angle, and the motion process of fluttering of aerofoil profile can be simulated, these are needed to calculate
Setup parameter be saved in UDF file, the calculation function of Fluent can be improved to greatest extent, make full use of this fluid meter
Calculate software.Wherein, the library function that C language can be not only called in UDF function can also call predefined inside Fluent
It is macro.
According to a particular embodiment of the invention, dynamic mesh model can simulate the flow field under different situations, such as the present invention
In to use the flow field simulating the Boundary motion due to flapping wing to dynamic mesh and changing over time.It has to import needs first
The grid of definition after initialization, imports boundary function UDF to determine the motion mode on boundary.If including movement in flow field
With both no motion of regions, it is necessary to combine them in initial mesh and be identified to them.
According to a particular embodiment of the invention, pass through the power of X suffered by the aerofoil profile in a stable period and Y-direction
Average value can calculate average liter resistance of dimensional airfoil during unsteady flapping motion.If with FLAnd FDCarry out table respectively
Show its lift and resistance, then the lift coefficient C of dimensional airfoilLWith resistance coefficient CDI.e. are as follows:
Wherein: U is the speed of incoming flow on the moment dimensional airfoil surface, since the design is related to two-dimentional flapping wing hovering flight,
So airfoil surface is without incoming flow, therefore herein without the concern for speed of incoming flow.Due to during calculating, parameter is mostly
There is dimension, so it is 2m that NACA0006 aerofoil profile is placed on a radius by we, the center of circle is the border circular areas of origin, is used
Gambit carries out the foundation of flapping wing model and carries out grid dividing appropriate.Calculating process is counted using triangular mesh
It calculates.And in fluent software, relevant parameter is configured, such as defines basic solver, defines dynamic mesh, definition is dynamic
Region defines second order accuracy, then since the present invention is the lift of analysis and the coefficient of resistance, it is therefore desirable in fluent software
Middle carry out nondimensionalization to be said, when calculating upon initialization, time step is configured according to frequency herein
, then a cycle is set calculate 1000 steps, then is arranged and calculates ten periods.
According to a particular embodiment of the invention, as shown in Figure 1, the first aerofoil profile 1 be initial aerofoil position of the invention, second
Aerofoil profile 2 is the obtained position of aerofoil profile corner 3 that the first aerofoil profile 1 is fluttered certain, the airfoil center of 1 second aerofoil profile 2 of the first aerofoil profile
In the displacement that the displacement of vertical direction is aerofoil profile translation 4, wherein aerofoil profile corner 3 is denoted as αm, aerofoil profile translation 4 is denoted as Am；Such as Fig. 2 institute
Show, upper Curve of wing 6 and Airfoil curve 7 are tangent on left side head and the circle of contact 7, and 7 radius of the circle of contact is denoted as r, upper 5 He of Curve of wing
There is aerofoil profile center line 9 between Airfoil curve 6, string 9 is located at 9 lower section of aerofoil profile center line；
According to a particular embodiment of the invention, a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, pneumatically
Characteristic analysis method includes the following steps:
Step 1, the determination of research approach:
Flapping motion simplified two-dimensional model and the equation of motion are established, and utilizes FLUENT software, User-Defined Functions UDF
And Dynamic mesh, average lift and resistance coefficient of the analysis of two-dimensional aerofoil profile under different flapping wing frequencies, out of phase angle.
Step 2, the modeling of dimensional airfoil:
The standard aerofoil profile in Low Speed Airfoil series is chosen, aerofoil profile is first established in Gambit, and determine aerofoil profile
Up-and-down boundary marks off triangular mesh, sets boundary condition.
Step 3, the setting of User-Defined Functions UDF:
On the basis of step 2, according to primary election flapping wing phase angle and primary election flapping wing frequency, compiled out using control variate method
The different UDF function of multiple groups.
Step 4, the calculating of lift coefficient and resistance coefficient:
The UDF function compiled in the dimensional airfoil model and step 3 established in step 2 is imported in FLUENT, and
After defining basic solver, dynamic region, setting liter resistance coefficient monitor and nondimensionalization being set, it is iterated calculating.
Step 5, mean value and numerical simulation result analysis are calculated:
Evaluation obtained in step 4 is imported in MATLAB, the exercise data of two-dimentional flapping wing a cycle, key are chosen
Enter command statement and obtains the average relationship image for rising resistance coefficient and flapping wing frequency and flapping wing phase angle.
According to a particular embodiment of the invention, step 1 specifically further includes following steps:
Step 11, computation model is established:
Chordwise section of the thin ellipsoid as Simplified two-dimension aerofoil profile is chosen, aerofoil profile movement includes the compound fortune of translation and rotation
It is dynamic, governing equation are as follows:
It is translatable along Y-axis:
H (t)=Am sin(2πft)
Geometric center around oval aerofoil profile rotates:
According to the available dimensionless Reynolds number of dimensional analysis:
In formula:
Am, αm, f andThe phase respectively fluttered between amplitude, maximum rotation amplitude, flapping wing frequency, translation and rotation
Difference.
ρ, U, μ and c are respectively density, speed of incoming flow, viscosity coefficient and the aerofoil profile chord length of air.
Step 12, calculation method is established:
In numerical simulation calculation, the movement of aerofoil profile is realized by controlling its translational velocity and rotational angular velocity.
Translational velocity:
Rotational angular velocity:
In numerical simulation calculation, the movement of fluid can be described by following continuity equation and N-S equation:
In formula:
U and v is respectively speed of the fluid along X-axis and Y-axis.P is the pressure of fluid.
According to a particular embodiment of the invention, step 2 specifically further includes following steps:
Step 21, NACA0006 aerofoil profile is generated using coordinate points:
The chord length and position of center line of blade are determined first, then use the approximating function of thickness, Curve of wing 5 in generation,
Airfoil curve 6, two curves extend the cross-sectional profile figure that intersection is formed aerofoil profile.Aerofoil profile front is handled with the circle of contact 7.
Step 22, aerofoil profile initial position determines:
NACA0006 importing GAMBIT is established into model, first analyzes influence of the different frequency to hovering flapping wing aerodynamic characteristic.
Selected starting phase angle, selectes the center of aerofoil profile, calculates aerofoil profile in the offset and chord length of X-axis and Y-axis and the folder of X-axis
Angle.
Preferably, at a quarter of airfoil center positioning chord length.
Step 23, triangle gridding is divided in zoning:
Two discs are generated using Boolean calculation, divide triangle gridding in disc region generated.
Step 24, boundary condition is set:
After grid dividing is good, the setting of boundary condition is carried out, under hovering, airfoil surface entrance does not have to setting without incoming flow
Entrance directly defines one outlet boundary condition.
According to a particular embodiment of the invention, step 3 specifically further includes following steps:
Step 31, control starting phase angle is constant, changes flapping wing frequency:
It is compiled in udf function in the displacement of X-axis, Y-axis as follows
X0=0.0125*0.5*cos (2*80*pi* (time-dtime))
Y0=0.0125*0.5*1.732*cos (2*80*pi* (time-dtime)
It is to be got by x0, y0 to the derivation of time t in X-axis, the speed of Y-axis, is compiled in udf function as follows:
Sing0=-0.0125*2*pi*80*0.5*1*sin (2*80*pi* (time-dtime))；
Sing1=-0.0125*2*pi*80*0.5*1.732*sin (2*80*pi* (time-dtime))；
Wherein angular speed is obtained by angular displacement derivation, is compiled in udf function as follows:
W0=pi*0.25*2*pi*80*sin (2*80*pi* (time-dtime+0.5*pi))
Step 32, control flapping wing frequency is constant, changes flapping wing starting phase angle:
In the function that step 31 is compiled, different differences is added and subtracted behind starting phase angle, to change the initial of flapping wing
Phase angle.
According to a particular embodiment of the invention, step 4 specifically further includes following steps:
Step 41, basic solver definition:
Grid file is read in, 2D two dimension double precision solver is started.And unsteady Unsteady is selected, it is selected in gradient
Tabs under, select Green-Gauss Node Based.
Step 42, parameter setting and calculating:
Dynamic region is created in the triangle gridding that step 2 divides, and lift is set and resistance coefficient detector makes figure window
Mouth can dynamically show lift and resistance coefficient with the variation of iterative process.And it is arranged and calculates time step and step number.
Preferably, time step is set as 2.5e-5, time step number is set as 1000 steps.
According to a particular embodiment of the invention, the sentence keyed in step 5 are as follows:
Y=[3.2258,3.8676,8.0425,10.8660,14.6101]；
X=[80,100,120,140,160]；
plot(X,Y,'k-o')；
ylabel('cl cd')；
Xlabel (' frequency ')；
hold on
Z=[- 1.934, -5.7081, -5.07025, -6.5621, -8.3856]；
plot(X,Z,'k--o')；
Title (' average the relationship for rising resistance coefficient and frequency ')
Legend average lift coefficient cl average resistance coefficient cd
box off。
According to a particular embodiment of the invention, the amplitude of fluttering of dimensional airfoil is π/3~2 π/3.The flapping wing of dimensional airfoil turns
Dynamic amplitude is π/4~3 π/4.The ratio between the short axle of dimensional airfoil and long axis are definite value e.Dimensional airfoil flutter frequency be 80~
160Hz, phase angle are 70~110 °.
The present invention also provides, the aerofoil profile coordinate point data of NACA0006, coordinate point data is as follows:
The self-defining udf function of the present invention is as follows:
In addition to this, the present invention also provides the relationships and different phases of different frequency and average lift coefficient and resistance coefficient
The relationship of parallactic angle and different lift coefficients and resistance coefficient；It is as shown in the table:
Average lift coefficient and resistance coefficient and lift resistance ratio under 5.1 different frequency of table
Average lift coefficient and resistance coefficient and lift resistance ratio under 5.2 out of phase angle of table
According to a particular embodiment of the invention, for dimensional airfoil during fluttering, suitable flapping wing frequency flies aerofoil profile
Row plays the role of vital.The variation of average lift and resistance coefficient is as shown in figure 5, work as flapping wing under different flapping wing frequencies
When frequency increases gradually, average resistance coefficient reduces gradually, and absolute value increases gradually, average lift coefficient with frequency increasing
Increasing greatly and constantly also found by calculating, and for lift resistance ratio with the increase first increases and then decreases of frequency, absolute value is first to reduce
After increase, since the lift resistance ratio under normal circumstances described in us is all its absolute value said, when lift resistance ratio maximum, frequency
Rate is 100Hz, so in several frequencies in invention, determines that optimal frequency is 100Hz, herein it should be noted that
The analysis at phase angle, which is built upon, to be carried out on the basis of optimal frequency.Dimensional airfoil is during fluttering, due to aerofoil profile phase
The variation at angle, the position of maximum rotational velocity also change therewith, therefore average ascending aorta banding is caused also to change.It is different
The variation of average lift and resistance coefficient is as shown in Figure 6 under translation rotation phase difference.Change model in entire translation rotation phase difference
In enclosing, average resistance coefficient is negative value, average lift coefficient is positive value, shows that aerofoil profile by lift, works as phase in the vertical direction
At 70-110 °, average resistance coefficient first reduces and increases afterwards potential difference, and average lift coefficient first increases and then decreases, absolute value
It is first to reduce to increase afterwards；While phase angle increases, lift resistance ratio is first to reduce to increase afterwards, and absolute value is first to increase to subtract again
It is small.
The above description is only a preferred embodiment of the present invention, is not intended to restrict the invention, for those skilled in the art
For member, the invention may be variously modified and varied.All within the spirits and principles of the present invention, it is made it is any modification,
Equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (10)
1. one kind is based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that the Aerodynamic characteristics side
Method includes the following steps:
Step 1, the determination of research approach:
Flapping motion simplified two-dimensional model and the equation of motion are established, and using FLUENT software, User-Defined Functions UDF and is moved
Grid, average lift and resistance coefficient of the analysis of two-dimensional aerofoil profile under different flapping wing frequencies, out of phase angle；
Step 2, the modeling of dimensional airfoil:
The standard aerofoil profile in Low Speed Airfoil series is chosen, aerofoil profile is first established in Gambit, and determination aerofoil profile is upper and lower
Boundary marks off triangular mesh, sets boundary condition；
Step 3, the setting of User-Defined Functions UDF:
On the basis of step 2, primary election flapping wing phase angle and primary election flapping wing frequency compile out multiple groups difference using control variate method
UDF function；
Step 4, the calculating of lift coefficient and resistance coefficient:
The UDF function compiled in the dimensional airfoil model and step 3 established in step 2 is imported in FLUENT, and is defined
Basic solver after dynamic region, setting liter resistance coefficient monitor and nondimensionalization is arranged, is iterated calculating；
Step 5, mean value and numerical simulation result analysis are calculated:
Evaluation obtained in step 4 is imported in MATLAB, the exercise data of two-dimentional flapping wing a cycle is chosen, keys in life
Sentence is enabled to obtain the average relationship image for rising resistance coefficient and flapping wing frequency and flapping wing phase angle.
2. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
Stating step 1 specifically further includes following steps:
Step 11, computation model is established:
Chordwise section of the thin ellipsoid as Simplified two-dimension aerofoil profile is chosen, aerofoil profile movement includes the compound motion of translation and rotation,
Governing equation are as follows:
It is translatable along Y-axis:
H (t)=Am sin(2πft)
Geometric center around oval aerofoil profile rotates:
According to the available dimensionless Reynolds number of dimensional analysis:
In formula:
Am, αm, f andThe phase difference respectively fluttered between amplitude, maximum rotation amplitude, flapping wing frequency, translation and rotation；
ρ, U, μ and c are respectively density, speed of incoming flow, viscosity coefficient and the aerofoil profile chord length of air；
Step 12, calculation method is established:
In numerical simulation calculation, the movement of aerofoil profile is realized by controlling its translational velocity and rotational angular velocity；
Translational velocity:
Rotational angular velocity:
In numerical simulation calculation, the movement of fluid can be described by following continuity equation and N-S equation:
In formula:
U and v is respectively speed of the fluid along X-axis and Y-axis；P is the pressure of fluid.
3. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
Stating step 2 specifically further includes following steps:
Step 21, NACA0006 aerofoil profile is generated using coordinate points:
The chord length and position of center line of dimensional airfoil are determined first, then uses the approximating function of thickness, and it is bent to generate upper and lower aerofoil profile
Line, two curves extend the cross-sectional profile figure that intersection is formed aerofoil profile；Aerofoil profile front is handled with the circle of contact；
Step 22, aerofoil profile initial position determines:
NACA0006 importing GAMBIT is established into model, first analyzes influence of the different frequency to hovering flapping wing aerodynamic characteristic；It is selected
Starting phase angle selectes the center of aerofoil profile, calculates aerofoil profile in the offset and chord length of X-axis and Y-axis and the angle of X-axis；
Preferably, the airfoil center is positioned at a quarter of chord length；
Step 23, triangle gridding is divided in zoning:
Two discs are generated using Boolean calculation, divide triangle gridding in disc region generated；
Step 24, boundary condition is set:
After grid dividing is good, the setting of boundary condition is carried out, under hovering, airfoil surface entrance does not have to inlet porting without incoming flow,
Directly define one outlet boundary condition.
4. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
Stating step 3 specifically further includes following steps:
Step 31, control starting phase angle is constant, changes flapping wing frequency:
It is compiled in udf function in the displacement of X-axis, Y-axis as follows
X0=0.0125*0.5*cos (2*80*pi* (time-dtime))；
Y0=0.0125*0.5*1.732*cos (2*80*pi* (time-dtime)；
It is to be got by x0, y0 to the derivation of time t in X-axis, the speed of Y-axis, is compiled in udf function as follows:
Sing0=-0.0125*2*pi*80*0.5*1*sin (2*80*pi* (time-dtime))；
Sing1=-0.0125*2*pi*80*0.5*1.732*sin (2*80*pi* (time-dtime))；
Wherein angular speed is obtained by angular displacement derivation, is compiled in udf function as follows:
W0=pi*0.25*2*pi*80*sin (2*80*pi* (time-dtime+0.5*pi))
Step 32, control flapping wing frequency is constant, changes flapping wing starting phase angle:
In the function that step 31 is compiled, different differences is added and subtracted behind starting phase angle, to change the initial phase of flapping wing
Angle.
5. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
Stating step 4 specifically further includes following steps:
Step 41, basic solver definition:
Grid file is read in, 2D two dimension double precision solver is started；And unsteady Unsteady is selected, in the choosing of gradient selection
Under item card, Green-Gauss Node Based is selected；
Step 42, parameter setting and calculating:
Dynamic region is created in the triangle gridding that step 2 divides, and lift is set and resistance coefficient detector makes graphical window can
Dynamically to show lift and resistance coefficient with the variation of iterative process；And it is arranged and calculates time step and time step number；
Preferably, the time step is set as 2.5e-5, the time step number is set as 1000 steps.
6. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
State the sentence keyed in step 5 are as follows:
Y=[3.2258,3.8676,8.0425,10.8660,14.6101]；
X=[80,100,120,140,160]；
plot(X,Y,'k-o')；
ylabel('cl cd')；
Xlabel (' frequency ')；
hold on
Z=[- 1.934, -5.7081, -5.07025, -6.5621, -8.3856]；
plot(X,Z,'k--o')；
Title (' average the relationship for rising resistance coefficient and frequency ')
Legend average lift coefficient cl average resistance coefficient cd
box off。
7. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
The amplitude of fluttering for stating dimensional airfoil is π/3~2 π/3.
8. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
The flapping wing rotation amplitude for stating dimensional airfoil is π/4~3 π/4.
9. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that institute
Stating the ratio between short axle and long axis of dimensional airfoil is definite value e.
10. as described in claim 1 a kind of based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method, which is characterized in that
The dimensional airfoil flutters frequency as 80~160Hz, and phase angle is 70~110 °.
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