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 PDF

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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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airfoil
flapping
flapping wing
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frequency
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梅潇
韩国庆
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Shanghai Maritime University
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Abstract

本发明提供一种基于二维平面悬停扑翼气动特性分析方法，所述气动特性分析方法包括如下步骤：步骤1，研究方案的确定；步骤2，二维翼型的建模：选取低速翼型系列中的一标准翼型；步骤3，用户自定义函数UDF的设置：在步骤2的基础上，根据初选扑翼相位角和初选扑翼频率，采用控制变量法编译出多组不同的UDF函数；步骤4，升力系数和阻力系数的计算；步骤5，计算均值以及数值模拟结果分析；本发明提供的二维平面悬停扑翼气动特性分析方法可以模拟真实高频振动的生物薄翼在悬停时的气动特性；通过数值计算分析出平均升阻系数与频率和相位角的关系，从而优选出最合适的扑翼频率和相位角；对目前仿生扑翼飞行器的设计有着不可言表的意义。

The present invention provides a method for analyzing the aerodynamic characteristics of a flapping wing based on a two-dimensional plane. A standard airfoil in the series; Step 3, the setting of the user-defined function UDF: On the basis of step 2, according to the phase angle of the primary flapping wing and the frequency of the primary flapping wing, the control variable method is used to compile multiple groups of different Step 4, calculation of lift coefficient and drag coefficient; Step 5, calculation of mean value and analysis of numerical simulation results; the two-dimensional plane hovering flapping wing aerodynamic characteristic analysis method provided by the present invention can simulate real high-frequency vibration of biological thin The aerodynamic characteristics of the wing when hovering; the relationship between the average lift-drag coefficient and the frequency and the phase angle is analyzed through numerical calculation, so as to select the most suitable flapping-wing frequency and phase angle; it is indescribable for the design of the current bionic flapping-wing aircraft. meaning of the table.

Description

One kind is based on two-dimensional surface hovering flapping wing Aerodynamic characteristics method
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)

1.一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述气动特性分析方法包括如下步骤：1. based on a two-dimensional plane hovering flapping wing aerodynamic characteristic analysis method, it is characterized in that, described aerodynamic characteristic analysis method comprises the steps: 步骤1，研究方案的确定：Step 1, the determination of the research plan: 建立扑翼运动二维简化模型及运动方程，并利用FLUENT软件、用户自定义函数UDF和动网格技术，分析二维翼型在不同扑翼频率、不同相位角下的平均升力和阻力系数；Establish two-dimensional simplified model and motion equation of flapping motion, and use FLUENT software, user-defined function UDF and dynamic grid technology to analyze the average lift and drag coefficients of two-dimensional airfoil under different flapping frequencies and different phase angles; 步骤2，二维翼型的建模：Step 2, modeling of the two-dimensional airfoil: 选取低速翼型系列中的一标准翼型，在Gambit中先建立翼型剖面，并确定翼型的上下边界，划分出三角形网格，设置好边界条件；Select a standard airfoil in the low-speed airfoil series, first establish the airfoil section in Gambit, and determine the upper and lower boundaries of the airfoil, divide the triangular mesh, and set the boundary conditions; 步骤3，用户自定义函数UDF的设置：Step 3, the setting of the user-defined function UDF: 在步骤2的基础上，初选扑翼相位角和初选扑翼频率，采用控制变量法编译出多组不同的UDF函数；On the basis of step 2, the initial selection of the flapping phase angle and the primary flapping frequency are used to compile multiple sets of different UDF functions by using the control variable method; 步骤4，升力系数和阻力系数的计算：Step 4, the calculation of lift coefficient and drag coefficient: 将步骤2中所建立的二维翼型模型和步骤3中所编译的UDF函数导入FLUENT中，并定义基本求解器、设置动区域、设置升阻系数监测器以及无量纲化后，进行迭代计算；Import the two-dimensional airfoil model established in step 2 and the UDF function compiled in step 3 into FLUENT, and define the basic solver, set the dynamic area, set the lift-drag coefficient monitor and dimensionless, and then perform iterative calculation ; 步骤5，计算均值以及数值模拟结果分析：Step 5, calculate the mean value and analyze the numerical simulation results: 将步骤4中所得的计算数值导入MATLAB中，选取二维扑翼一个周期的运动数据，键入命令语句得出平均升阻系数与扑翼频率和扑翼相位角的关系图像。Import the calculated values obtained in step 4 into MATLAB, select the motion data of one cycle of the two-dimensional flapping wing, and enter the command statement to obtain the relationship image between the average lift-drag coefficient, the flapping wing frequency and the flapping wing phase angle. 2.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述步骤1具体还包括如下步骤：2. a kind of aerodynamic characteristic analysis method based on two-dimensional plane hovering flapping wing as claimed in claim 1, is characterized in that, described step 1 specifically also comprises the steps: 步骤11，确立计算模型：Step 11, establish the calculation model: 选取薄椭圆面作为二维简化翼型的弦向截面，翼型运动包括平动和转动的复合运动，控制方程为：The thin elliptical surface is selected as the chordwise section of the two-dimensional simplified airfoil. The airfoil motion includes the compound motion of translation and rotation. The governing equation is: 沿Y轴平动：Translation along the Y axis: h(t)＝Am sin(2πft)h(t)=A m sin(2πft) 绕椭圆翼型的几何中心转动：Rotate about the geometric center of an elliptical airfoil: 根据量纲分析可以得到无量纲Reynolds数：According to the dimensional analysis, the dimensionless Reynolds number can be obtained: 式中： where: Am，αm,f和分别为扑动幅值、最大转动幅值、扑翼频率、平动与转动之间的相位差；A m , α m , f and are the flapping amplitude, the maximum rotational amplitude, the flapping frequency, and the phase difference between translation and rotation; ρ，U，μ和c分别为空气的密度、来流速度、黏性系数和翼型弦长；ρ, U, μ and c are the air density, incoming velocity, viscosity coefficient and airfoil chord length, respectively; 步骤12，确立计算方法：Step 12, establish the calculation method: 在数值模拟计算中，翼型的运动是通过控制其平动速度和转动角速度实现的；In the numerical simulation calculation, the motion of the airfoil is realized by controlling its translational velocity and rotational angular velocity; 平动速度：Translation speed: 转动角速度：Rotational angular velocity: 在数值模拟计算中，流体的运动可由下列连续性方程和N-S方程来描述：In the numerical simulation calculation, the motion of the fluid can be described by the following continuity equation and N-S equation: 式中：where: u和v分别为流体沿X轴和Y轴的速度；p为流体的压力。u and v are the velocities of the fluid along the X and Y axes, respectively; p is the pressure of the fluid. 3.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述步骤2具体还包括如下步骤：3. a kind of aerodynamic characteristic analysis method based on two-dimensional plane hovering flapping wing as claimed in claim 1, is characterized in that, described step 2 specifically also comprises the steps: 步骤21，使用坐标点生成NACA0006翼型：Step 21, use the coordinate points to generate the NACA0006 airfoil: 首先确定二维翼型的弦长和中心线位置，再运用厚度的逼近函数，产生上、下翼型曲线，两曲线延长相交就形成了翼型的剖面外形图；翼型剖面前部以切圆处理；First determine the chord length and centerline position of the two-dimensional airfoil, and then use the thickness approximation function to generate upper and lower airfoil curves. The two curves are extended and intersected to form the profile outline of the airfoil; round processing; 步骤22，翼型初始位置确定：Step 22, determine the initial position of the airfoil: 将NACA0006导入GAMBIT建立模型，先分析不同频率对悬停扑翼气动特性的影响；选定初始相位角，选定翼型的中心，计算出翼型在X轴和Y轴的偏移量以及弦长与X轴的夹角；Import NACA0006 into GAMBIT to build a model, first analyze the influence of different frequencies on the aerodynamic characteristics of the hovering flapping wing; select the initial phase angle, select the center of the airfoil, and calculate the offset of the airfoil in the X-axis and Y-axis and the chord The angle between the length and the X axis; 优选地，所述翼型中心定位于弦长的四分之一处；Preferably, the airfoil center is located at a quarter of the chord; 步骤23，在计算区域划分三角网格：Step 23, divide the triangular mesh in the calculation area: 利用布尔运算生成两个圆面，在所生成的圆面区域内划分三角网格；Use Boolean operations to generate two circular surfaces, and divide triangular meshes in the generated circular surface area; 步骤24，设置边界条件：Step 24, set the boundary conditions: 网格划分好之后，进行边界条件的设定，悬停下，翼型表面入口无来流，不用设置入口，直接定义一个出口边界条件。After the mesh is divided, the boundary conditions are set, and when the airfoil surface is suspended, there is no incoming flow at the inlet of the airfoil surface, and an outlet boundary condition is directly defined without setting the inlet. 4.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述步骤3具体还包括如下步骤：4. a kind of aerodynamic characteristic analysis method based on two-dimensional plane hovering flapping wing as claimed in claim 1, is characterized in that, described step 3 specifically further comprises the steps: 步骤31，控制初始相位角不变，改变扑翼频率：Step 31, control the initial phase angle to remain unchanged, and change the flapping frequency: 在X轴、Y轴的位移在udf函数中编译如下The displacement on the X axis and the Y axis is compiled as follows in the udf function x0＝0.0125*0.5*cos(2*80*pi*(time-dtime))；x0=0.0125*0.5*cos(2*80*pi*(time-dtime)); y0＝0.0125*0.5*1.732*cos(2*80*pi*(time-dtime)；y0=0.0125*0.5*1.732*cos(2*80*pi*(time-dtime); 在X轴、Y轴的速度是由x0、y0对时间t求导得来的，在udf函数中编译如下：The speed on the X-axis and Y-axis is derived from the time t by x0 and y0, and is compiled in the udf function as follows: sing0＝-0.0125*2*pi*80*0.5*1*sin(2*80*pi*(time-dtime))；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))；sing1=-0.0125*2*pi*80*0.5*1.732*sin(2*80*pi*(time-dtime)); 其中角速度是由角位移求导得到，在udf函数中编译如下：The angular velocity is derived from the angular displacement, which is compiled in the udf function as follows: w0＝pi*0.25*2*pi*80*sin(2*80*pi*(time-dtime+0.5*pi))w0=pi*0.25*2*pi*80*sin(2*80*pi*(time-dtime+0.5*pi)) 步骤32，控制扑翼频率不变，改变扑翼初始相位角：Step 32, control the flapping frequency to remain unchanged, and change the initial phase angle of flapping: 将步骤31编译的函数中，在初始相位角后面加减不同的差值，来改变扑翼的初始相位角。In the function compiled in step 31, different difference values are added or subtracted after the initial phase angle to change the initial phase angle of the flapping wing. 5.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述步骤4具体还包括如下步骤：5. a kind of aerodynamic characteristic analysis method based on two-dimensional plane hovering flapping wing as claimed in claim 1, is characterized in that, described step 4 specifically also comprises the steps: 步骤41，基本求解器定义：Step 41, the basic solver definition: 读入网格文件，启动2D二维双精度求解器；并选择非定常的Unsteady，在梯度选择的选项卡下，选择Green-Gauss Node Based；Read in the grid file, start the 2D 2D double precision solver; and select Unsteady Unsteady, under the gradient selection tab, select Green-Gauss Node Based; 步骤42，参数设置与计算：Step 42, parameter setting and calculation: 在步骤2划分的三角网格中创建动区域，设置升力和阻力系数检测器使得图形窗口可以动态的显示升力和阻力系数随迭代过程的变化；并设置计算时间步长和时间步数；Create a dynamic area in the triangular mesh divided in step 2, set the lift and drag coefficient detectors so that the graph window can dynamically display the changes of the lift and drag coefficients with the iterative process; and set the calculation time step and the number of time steps; 优选地，所述时间步长设置为2.5e-5，所述时间步数设置为1000步。Preferably, the time step size is set to 2.5e -5 , and the time step number is set to 1000 steps. 6.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述步骤5中键入的语句为：6. a kind of aerodynamic characteristic analysis method based on two-dimensional plane hovering flapping wing as claimed in claim 1, is characterized in that, the statement that key-in in described step 5 is: Y＝[3.2258,3.8676,8.0425,10.8660,14.6101]；Y=[3.2258, 3.8676, 8.0425, 10.8660, 14.6101]; X＝[80,100,120,140,160]；X=[80, 100, 120, 140, 160]; plot(X,Y,'k-o')；plot(X,Y,'k-o'); ylabel('cl cd')；ylabel('cl cd'); xlabel('频率')；xlabel('frequency'); hold onhold on Z＝[-1.934,-5.7081,-5.07025,-6.5621,-8.3856]；Z=[-1.934,-5.7081,-5.07025,-6.5621,-8.3856]; plot(X,Z,'k--o')；plot(X,Z,'k--o'); title('平均升阻系数与频率的关系')title('Relationship between average lift-drag coefficient and frequency') legend平均升力系数cl平均阻力系数cdlegend average lift coefficient cl average drag coefficient cd box off。box off. 7.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述二维翼型的扑动幅值为π/3～2π/3。7 . The method for analyzing the aerodynamic characteristics of a flapping wing based on a two-dimensional plane hovering according to claim 1 , wherein the flapping amplitude of the two-dimensional airfoil is π/3˜2π/3. 8 . 8.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述二维翼型的扑翼转动幅值为π/4～3π/4。8 . The method for analyzing the aerodynamic characteristics of a flapping wing based on a two-dimensional plane hovering as claimed in claim 1 , wherein the flapping wing rotation amplitude of the two-dimensional airfoil is π/4˜3π/4. 9 . 9.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述二维翼型的短轴与长轴之比为定值e。9 . The method for analyzing the aerodynamic characteristics of a flapping wing based on a two-dimensional plane hovering as claimed in claim 1 , wherein the ratio of the short axis to the long axis of the two-dimensional airfoil is a fixed value e. 10 . 10.如权利要求1所述的一种基于二维平面悬停扑翼气动特性分析方法，其特征在于，所述二维翼型扑动频率为80～160Hz，相位角为70～110°。10 . The method for analyzing the aerodynamic characteristics of a flapping wing based on a two-dimensional plane hovering according to claim 1 , wherein the flapping frequency of the two-dimensional airfoil is 80-160 Hz, and the phase angle is 70-110°. 11 .
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