CN105787217B - A kind of optimum design method of aircraft ripple aerofoil profile - Google Patents
A kind of optimum design method of aircraft ripple aerofoil profile Download PDFInfo
- Publication number
- CN105787217B CN105787217B CN201610231176.7A CN201610231176A CN105787217B CN 105787217 B CN105787217 B CN 105787217B CN 201610231176 A CN201610231176 A CN 201610231176A CN 105787217 B CN105787217 B CN 105787217B
- Authority
- CN
- China
- Prior art keywords
- ripple
- ideal
- section
- aerofoil profile
- initial position
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000013461 design Methods 0.000 title claims abstract description 50
- 238000000034 method Methods 0.000 title claims abstract description 36
- 238000005457 optimization Methods 0.000 claims description 16
- 238000004458 analytical method Methods 0.000 claims description 9
- 238000005070 sampling Methods 0.000 claims description 3
- 239000000446 fuel Substances 0.000 abstract description 4
- 238000004422 calculation algorithm Methods 0.000 description 10
- 238000010586 diagram Methods 0.000 description 8
- 238000004364 calculation method Methods 0.000 description 4
- UJCHIZDEQZMODR-BYPYZUCNSA-N (2r)-2-acetamido-3-sulfanylpropanamide Chemical compound CC(=O)N[C@@H](CS)C(N)=O UJCHIZDEQZMODR-BYPYZUCNSA-N 0.000 description 3
- 241001669680 Dormitator maculatus Species 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 239000004744 fabric Substances 0.000 description 3
- 238000012545 processing Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- FKLFBQCQQYDUAM-UHFFFAOYSA-N fenpiclonil Chemical compound ClC1=CC=CC(C=2C(=CNC=2)C#N)=C1Cl FKLFBQCQQYDUAM-UHFFFAOYSA-N 0.000 description 2
- 239000011888 foil Substances 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- 238000005452 bending Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000010425 computer drawing Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000010006 flight Effects 0.000 description 1
- 239000012530 fluid Substances 0.000 description 1
- 229910052751 metal Inorganic materials 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 150000002739 metals Chemical class 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000004064 recycling Methods 0.000 description 1
- 238000007493 shaping process Methods 0.000 description 1
- 230000035939 shock Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Aviation & Aerospace Engineering (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Automation & Control Theory (AREA)
- Turbine Rotor Nozzle Sealing (AREA)
- Structures Of Non-Positive Displacement Pumps (AREA)
Abstract
The present invention relates to a kind of aircraft ripple aerofoil profiles and its optimum design method, it is obtained by being transformed on the basis of primary standard aerofoil profile, the curve parameter of the ripple aerofoil profile is the waviness curve formed that is end-to-end by multistage ripple except the middle section of front and rear edge part, every section of ripple includes a wave crest and a trough, ripple in the waviness curve is uniformly distributed or equal proportion distribution, ripple, which is uniformly distributed, to be referred to: the corrugation length of every section of ripple is equal, the distribution of ripple equal proportion refers to: the corrugation length of every section of ripple is equal with the ratio of the profile thickness of the ripple corresponding position.Compared with prior art, the present invention can improve the resistive energy of liter and structural behaviour of Low Speed Airfoil, can reduce structure size and weight under same task load-up condition, increase fuel economy and flying quality.
Description
Technical field
The present invention relates to a kind of aircraft airfoil structures, more particularly, to a kind of aircraft ripple aerofoil profile and its optimization design
Method.
Background technique
Under the various state of flights of aircraft, wing is the main component that aircraft bears lift, and vertical tail peace tail is winged
The Pneumatic component of machine holding stability and maneuverability.General aircraft has the plane of symmetry, if be parallel to the plane of symmetry wing open up to
Any position partial application, the wing profile scaled off are referred to as wing section or aerofoil profile.Aerofoil profile is wing and empennage forming important set
At part, the aeroperformance and flight quality of aircraft are directly influenced.
For different flying speeds, the air foil shape of wing is different, such as:
For low subsonic aircraft, in order to improve lift coefficient, air foil shape is round end fine stern shape；
Supercritical airfoil is used, its main feature is that leading edge is rich to improve drag divergence Ma number for high subsonic aircraft
It is full, top airfoil is flat, rear is to recessed；
For supersonic aircraft, in order to reduce drag due to shock wave, using tip, fine stern shape aerofoil profile.
Trailing edge geometric modification can aeroperformance in the case of improvement feature, this in transonic plane design by
Pay attention to extensively.Most of reshaping is all using local reshaping design, while most of reshaping result all becomes wing structure
It is weak.The rough inflatable airfoil of upper and lower surface has its Aerodynamic Characteristics, and the inflatable airfoil of top airfoil shaping has significant pneumatic
Advantage.Since inflation aircraft originally belongs to emerging technology, while wavelike structure is difficult to realize on conventional metals wing, therefore
It yet there are no the structure that the wavy aerofoil profile of lower aerofoil is used in rigid wing.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of aircraft corrugated vanes
Type and its optimum design method can improve the resistive energy of liter and structural behaviour of Low Speed Airfoil, can be in same task load item
Reduce structure size and weight under part, increases fuel economy and flying quality.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of aircraft ripple aerofoil profile, is obtained by being transformed on the basis of primary standard aerofoil profile, which is round end
Fine stern shape aerofoil profile, the middle section that the curve parameter of the ripple aerofoil profile removes front and rear edge part is to be end-to-end to be formed by multistage ripple
Waviness curve, every section of ripple includes a wave crest and a trough, and the ripple in the waviness curve is uniformly distributed or waits
Ratio distribution, ripple, which is uniformly distributed, to be referred to: the corrugation length of every section of ripple is equal, and the distribution of ripple equal proportion refers to: every section of wave
The corrugation length of line is equal with the ratio of the profile thickness of the ripple corresponding position.
The trough of every section of ripple and the curve parameter of primary standard aerofoil profile are tangent in the waviness curve.
The peaks and troughs central symmetry of every section of ripple is distributed in the curve parameter of primary standard aerofoil profile in the waviness curve
Inside and outside.
The ripple amplitude of every section of ripple and the ratio of the profile thickness of the ripple corresponding position are equal in the waviness curve
It is equal.
The waviness curve tangent is obtained or the waviness curve is continuous by multistage sine curve by multi-section circular arc is continuous
It is tangent to obtain.
A kind of optimum design method of above-mentioned aircraft ripple aerofoil profile the following steps are included:
S1: being transformed the lower aerofoil of primary standard aerofoil profile, respectively obtains the equally distributed waviness curve of ripple and ripple
The waviness curve of equal proportion distribution；
S2: respectively to the corresponding ripple aerofoil profile of the equally distributed waviness curve of ripple and ripple equal proportion of step S1 design
The corresponding ripple aerofoil profile of the waviness curve of distribution carries out aeroperformance and Structural Performance Analysis, output analysis result；
S3: establishing the Model for Multi-Objective Optimization of aeroperformance and structural behaviour, is obtained according to the analysis result that step S2 is obtained
To the optimal solution of Model for Multi-Objective Optimization, and export the corresponding ripple aerofoil profile reshaping scheme of optimal solution.
The step S1 specifically:
11: obtaining the curve parameter and chord length of primary standard aerofoil profile, setting ripple is total, and in the lower edge of primary standard aerofoil profile song
Uniform sampling obtains the set AF of raw data points on line；
12: according to the equally distributed definition of ripple, wave being obtained according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in line curve；
13: the definition being distributed according to ripple equal proportion is obtained according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in waviness curve；
14: according to the ripple amplitude of the profile thickness of every section of ripple corresponding position setting ripple, according to every section of ripple
True initial position, corrugation length and ripple amplitude obtain corresponding waviness curve using the method for three strokes and dots arcs.
The step 12 specifically:
121: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum；
122: the ideal initial position of every section of ripple is obtained, following formula is met:
Xideal(1)=w2*C
Xideal(i)=Xideal(1)+(i-1)*λideal
In formula, 0 < w2≤ 5%, 1≤i≤N+1, Xideal(i) the ideal initial position of i-th section of ripple of expression, N+1 sections
The ideal initial position of ripple is the ideal final position of N sections of ripples；
123: the true initial position of every section of ripple is obtained, following formula is met:
K=Find AF (?) .x < Xideal(i) AndAF (? + 1) .x > Xideal(i)}
In formula, Xstart(i) the true initial position of i-th section of ripple is indicated, the true initial position of N+1 sections of ripples is
Do the true final position of N sections of ripples, function Find { } indicate to seek meeting { } interior condition? locate numerical value, AF (k) is indicated
K-th of former data point, AF (k) .x indicate the abscissa of original data point AF (k) in set AF；
124: the corrugation length of every section of ripple is obtained according to the true initial position of every section of ripple.
The step 13 specifically:
131: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum；
132: the ideal initial position X of setting first segment rippleideal(1) and the true final position of N sections of ripples, N
The true final position of Duan Bowen is the true initial position X of N+1 sections of ripplesideal(N+1), meet following formula:
Xideal(1)=w2*C
Xideal(N+1)=(1-w2)*C
In formula, 0 < w2≤ 5%；
133: according to Xideal(1) the true initial position X of first segment ripple is obtainedstart(1) and and Xstart(1) corresponding
Index value I1, and according to Xideal(N+1) the true initial position X of first segment ripple is obtainedstart(N+1) and and Xstart(N+
1) corresponding index value IN+1, meet following formula:
k1=Find AF (?) .x < Xideal(1) AndAF (? + 1) .x > Xideal(1)}
Xstart(1)=AF (I1).x
kN+1=Find AF (?) .x < Xideal(N+1) AndAF (? + 1) .x > Xideal(N+1)}
Xstart(N+1)=AF (IN+1).x
Does function Find { } indicate to seek meeting { } interior condition in formula? locate numerical value, AF (k1)、AF(kN+1) respectively correspond
Indicate kth in set AF1、kN+1A original data point, AF (k1).x、AF(kN+1) .x respectively correspond indicate original data point AF (k1)、AF
(kN+1) abscissa；
134: obtaining the ideal initial position X of a sections of ripplesideal(a), 1 < a≤N, and according to Xideal(a) a sections are obtained
The true initial position X of ripplestart(a) and and Xstart(a) corresponding index value Ia, meet following formula:
Xideal(a)=Xstart(1)+(a-1)*λideal
ka=Find AF (?) .x < Xideal(a) AndAF (? + 1) .x > Xideal(a)}
Xstart(a)=AF (Ia).x
In formula, AF (ka) indicate kth in set AFaA original data point, AF (ka) .x expression original data point AF (ka) horizontal seat
Mark；
135: obtaining the ratio that every section of ripple corresponds to the corrugation length of thickness and the ripple at primary standard aerofoil position
rj, 1≤j≤N, and obtain all rjAverage valueMeet following formula:
rj=avr (AF (I) .y)/(Xstart(j+1)-Xstart(j)),Ij≤I≤Ij+1
In formula, function avr () indicates to seek the average value of all parameters in (), and AF (I) indicates that i-th is former in set AF
Data point, AF (I) .y indicate the ordinate of original data point AF (I)；
136: seeking the ratio r of every section of ripplejWith the difference E of average value rj,By difference EjMiddle maximum value
The index value I of corresponding rippleerrormaxIt is denoted as FlagI, subscript errormax indicates difference EjThe corresponding ripple of middle maximum value
Number, and record difference EjThe sign of middle maximum value is FlagS；
137: judging whether symbol FlagS is positive sign, if so, IerrormaxReduce 1, Ierrormax+1Increase by 1, if it is not,
IerrormaxIncrease by 1, Ierrormax+1Reduce 1, works as Ierrormax=1, then IerrormaxIt is constant, work as Ierrormax=N, then Ierrormax+1No
Become；
138: jump procedure 135 executes circulation next time, the condition of loop termination are as follows: the adjacent FlagI recycled twice
Numerical value is identical, and symbol FlagS is differed；
139: after circulation terminates, obtaining the index value of every section of ripple, every section of ripple is obtained according to the index value of every section of ripple
True initial position and every section of ripple corrugation length.
Parameter w2Value is 2.5%.
Compared with prior art, the invention has the following advantages that
One, be waveform by lower aerofoil macroshape reshaping on the basis of standard aerofoil profile, the ripple aerofoil profile after reshaping by
Vortex can be generated in the ripple in lower aerofoil, formed the differential of air-flow from, can improve Low Speed Airfoil liter it is resistive can, especially
Lift coefficient when can improve Low Angle Of Attack, and resistance coefficient does not significantly rise, thus aerofoil profile liter resistance have it is obvious
Raising, while the design of this ripple struction reshaping increases the effective thickness of wing, can dramatically increase the intensity of wing, improves
The improvement of the structural behaviour of wing, especially bending resistance and torsional property.The promotion of resistive energy is risen in conjunction with the improvement of structural behaviour,
Structure size and weight can be reduced under same task load-up condition, increase fuel economy and flying quality.
Two, a kind of side for being uniformly distributed corrugated design and equal proportion distribution corrugated design for realizing ripple aerofoil profile is proposed
Method can be carried out Fluid Mechanics Computation and wing structure FEM calculation, be convenient for difference with rapid build aerofoil profile controlling curve
The design of type ripple aerofoil profile, wherein equally distributed craftsmanship is more preferable, and the smaller aeroperformance of wavelength is relatively more preferable, and amplitude is more
Big structure performance is relatively more excellent.
Three, the Model for Multi-Objective Optimization of aeroperformance and structural behaviour is proposed, it can be complete by multi-objective optimization design of power
It is calculated at the Pareto optimal of the wavy lower aerofoil reshaping of aerofoil profile, the optimization design aerofoil profile for determining object is obtained, to choose conjunction
Distribution, wavelength and the amplitude of optimal ripple under the conditions of suitable.
Four, the ripple aerofoil profile can be applied to the low speed general-purpose aircraft and unmanned plane using composite structure wing, mention
The resistive energy of the liter of high aircraft and structure efficiency, are widely used.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of round end fine stern shape aerofoil profile；
Fig. 2 is the flow chart of the method for the present invention；
Fig. 3 is the flow chart for being uniformly distributed corrugated design；
Fig. 4 is the flow chart that equal proportion is distributed corrugated design；
Fig. 5 a is the relation schematic diagram of every section of ripple Inner arc under ideal conditions；
Fig. 5 b is the equivalent schematic of circular arc in Fig. 5 a；
Circular arc relational graph at every section of ripple when Fig. 5 c is aerofoil profile actual design；
Fig. 6 a is the structural schematic diagram of CLARK Y standard aerofoil profile；
Fig. 6 b is the equally distributed CLARK Y standard aerofoil profile reshaping design diagram of ripple；
Fig. 7 a is the structural schematic diagram of 16018 standard aerofoil profile of NACA；
Fig. 7 b is the 16018 standard aerofoil profile reshaping design diagram of NACA of ripple equal proportion distribution；
Fig. 8 is the lift-rising Contrast on effect schematic diagram of ripple aerofoil profile of the present invention and primary standard aerofoil profile；
Fig. 9 is the Structure Comparison schematic diagram of ripple aerofoil profile of the present invention and primary standard aerofoil profile.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to
Following embodiments.
A kind of aircraft ripple aerofoil profile, is obtained by being transformed on the basis of primary standard aerofoil profile, the primary standard aerofoil profile such as Fig. 1
It show round end fine stern shape aerofoil profile, which retains the original smooth curve of primary standard aerofoil profile top airfoil, while by bottom wing
Face reshaping is designed as corrugated shape, and lower aerofoil reshaping specifically refers to: the front and rear edge part of the ripple aerofoil profile lower aerofoil retains original
The curve of aerofoil profile, i.e., non-ripple be in primary standard aerofoil profile structure be overlapped, and the middle section of lower aerofoil be ripple struction, i.e., under
The corresponding curve parameter of aerofoil is the waviness curve formed that is end-to-end by multistage ripple except the middle section of front and rear edge part, often
Duan Bowen includes a wave crest and a trough, and wave crest is recessed inwardly in lower aerofoil, and trough is in lower aerofoil outwardly convex, ripple
Ripple in curve is uniformly distributed or equal proportion distribution, and ripple, which is uniformly distributed, to be referred to: the corrugation length of every section of ripple is equal, wave
The distribution of line equal proportion refers to: the corrugation length of every section of ripple is equal with the ratio of the profile thickness of the ripple corresponding position.
Wherein, the trough of every section of ripple and the curve parameter of primary standard aerofoil profile are tangent in waviness curve, such as: every section of ripple
Initial position since trough, terminate after wave crest to trough.Alternatively, in waviness curve every section of ripple peaks and troughs
Central symmetry is distributed in inside and outside the curve parameter of primary standard aerofoil profile, such as: the initial position of every section of ripple is from wave crest and wave
Intermediate point between paddy starts, and successively passes through wave crest, trough, terminates to intermediate point between rich wind and rain trough.Waviness curve is set
Meter can be effectively improved the resistive energy of liter of aerofoil profile.
The ripple amplitude of every section of ripple and the ratio of the profile thickness of the ripple corresponding position are equal in waviness curve.
Compared to primary standard aerofoil profile, improve aerofoil profile liter it is resistive can while can increase the effective thickness of aerofoil profile, guarantee the intensity of wing.
Waviness curve tangent is obtained or waviness curve is continuous tangent by multistage sine curve by multi-section circular arc is continuous
It arrives.Waviness curve design is carried out with circular arc or sine curve, design effect is good, and the ripple struction of lower aerofoil is more smooth, not
It will increase resistance coefficient, and more convenient.Waviness curve can also be multistage similar to circular arc, other sinusoidal curves
Continuous tangent or discontinuous line segment connection.
Because any more preferably single options is not present in the distribution of ripple, wavelength and amplitude, in contrast uniformly divide
The craftsmanship of cloth is more preferable, and the smaller aeroperformance of wavelength is relatively more preferable, and amplitude more big structure performance is relatively more excellent.But reshaping designs
It requires to calculate and determine by aeroperformance and structural behaviour multi-objective optimization design of power method according to aerofoil profile generating algorithm, therefore,
A kind of optimum design method of above-mentioned aircraft ripple aerofoil profile is proposed, as shown in Figure 2, comprising the following steps:
S1: being transformed the lower aerofoil of primary standard aerofoil profile, respectively obtains the equally distributed waviness curve of ripple and ripple
The waviness curve of equal proportion distribution, specifically:
11:, coordinate system is established, using string as x-axis, using leading edge as origin, origin is crossed and makees the y axis vertical with x-axis, obtain
The curve parameter and chord length C of primary standard aerofoil profile, curve parameter can use the function representation of the relative coordinate of string commercial city, ripple are arranged
Total N, and uniform sampling obtains the set AF of raw data points on the curve parameter of primary standard aerofoil profile；
12: according to the equally distributed definition of ripple, wave being obtained according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in line curve；
13: the definition being distributed according to ripple equal proportion is obtained according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in waviness curve；
14: according to the ripple amplitude of the profile thickness of every section of ripple corresponding position setting ripple, according to every section of ripple
True initial position, corrugation length and ripple amplitude obtain corresponding waviness curve using the method for three strokes and dots arcs.
S2: respectively to the corresponding ripple aerofoil profile of the equally distributed waviness curve of ripple and ripple equal proportion of step S1 design
The corresponding ripple aerofoil profile of the waviness curve of distribution carries out aeroperformance and Structural Performance Analysis, output analysis result.
S3: establishing the Model for Multi-Objective Optimization of aeroperformance and structural behaviour, is obtained according to the analysis result that step S2 is obtained
To the optimal solution of Model for Multi-Objective Optimization, and export the corresponding ripple aerofoil profile reshaping scheme of optimal solution.
Ripple is uniformly distributed design and refers to the length value for finding out each ripple according to ripple number N, it is desirable that the length of each ripple
Spend it is identical, can be by set AF, chord length and the ripple of primary standard aerofoil profile it is therefore proposed that a kind of ripple is uniformly distributed algorithm for design
Sum obtains in waviness curve the true initial position and corrugation length of every section of ripple, specifically includes the following steps:
121: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, w1For ratio parameter, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum, this reality
Apply parameter w in example1Value is 5%；
122: the ideal initial position of every section of ripple is obtained, following formula is met:
Xideal(1)=w2*C
Xideal(i)=Xideal(1)+(i-1)*λideal
In formula, w2For ratio parameter, 0 < w2≤ 5%, 1≤i≤N+1, Xideal(i) the ideal starting of i-th section of ripple is indicated
Position, parameter i is integer herein, indicates the number of ripple, the ideal initial position of N+1 sections of ripples is N sections of ripples
Ideal final position, parameter w in the present embodiment2Value is 2.5%；
123: the true initial position of every section of ripple is obtained, following formula is met:
K=Find AF (?) .x < Xideal(i) AndAF (? + 1) .x > Xideal(i)}
In formula, Xstart(i) the true initial position of i-th section of ripple is indicated, the true initial position of N+1 sections of ripples is
Do the true final position of N sections of ripples, function Find { } indicate to seek meeting { } interior condition? locate numerical value, AF (k) is indicated
K-th of former data point in set AF, parameter k is integer herein, indicates the number of former data point, and AF (k) .x indicates former data point
The abscissa of AF (k)；
124: the corrugation length of every section of ripple is obtained according to the true initial position of every section of ripple, meets following formula:
λ (j)=Xstart(j+1)-Xstart(j)
In formula, 1≤j≤N, λ (j) indicate the corrugation length of j-th of ripple, and parameter j is integer herein, and same parameter i's determines
Justice.
Ripple is uniformly distributed algorithm flow chart such as Fig. 3 of algorithm for design, and its essence is find and ideal initial position distance
The abscissa x value of nearest AF, as true ripple initial position, these true ripple initial positions are subtracted each other to obtain corresponding
The actual length of each ripple, in Fig. 3, XidealFor the initial position of ideally each ripple, for the vector of N+1 dimension, i,
J, k is intermediate parameters, XstartFor the initial position of true each ripple, for the vector of N+1 dimension, λ is true each ripple
Length value, be N-dimensional vector, Find { condition } sentence be find out it is qualified? the value at place, it is qualified? value return
Return to left side of the equal sign, AF (?) do .x indicate the in AF? the abscissa x value of a data point, such as AF (15) .x indicate the 15th data
The x value of point.
Wavelength refers to the length value that each ripple is found out according to ripple number N to the design of the scores cloth such as profile thickness, and aerofoil profile is got over
The corrugation length in thick place is longer, and the thickness of length and corresponding position is directly proportional.It is therefore proposed that a kind of ripple equal proportion point
Cloth algorithm can obtain the true starting of every section of ripple in waviness curve by the set AF of primary standard aerofoil profile, chord length and ripple sum
Position and corrugation length, specifically includes the following steps:
131: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum, parameter w in the present embodiment1
Value is 5%；
132: the ideal initial position X of setting first segment rippleideal(1) and the true final position of N sections of ripples, N
The true final position of Duan Bowen is the true initial position X of N+1 sections of ripplesideal(N+1), meet following formula:
Xideal(1)=w2*C
Xideal(N+1)=(1-w2)*C
In formula, 0 < w2≤ 5%, parameter w in the present embodiment2Value is 2.5%；
133: according to Xideal(1) the true initial position X of first segment ripple is obtainedstart(1) and and Xstart(1) corresponding
Index value I1, index value I is the number of former data point in the AF of the true initial position value of ripple, the subscript of index value I
For the number of index value, the as number of ripple, and according to Xideal(N+1) the true initial position of first segment ripple is obtained
Xstart(N+1) and and Xstart(N+1) corresponding index value IN+1, meet following formula:
k1=Find AF (?) .x < Xideal(1) AndAF (? + 1) .x > Xideal(1)}
Xstart(1)=AF (I1).x
kN+1=Find AF (?) .x < Xideal(N+1) AndAF (? + 1) .x > Xideal(N+1)}
Xstart(N+1)=AF (IN+1).x
Does Find { } indicate to seek meeting { } interior condition in formula? locate numerical value, AF (k1)、AF(kN+1) respectively correspond expression
Kth in set AF1、kN+1A original data point, k1、kN+1For intermediate variable, AF (k1).x、AF(kN+1) to respectively correspond expression former by .x
Data point AF (k1)、AF(kN+1) abscissa；
134: obtaining the ideal initial position X of a sections of ripplesideal(a), 1 < a≤N, a are the number of ripple, and according to
Xideal(a) the true initial position X of a sections of ripples is obtainedstart(a) and and Xstart(a) corresponding index value Ia, meet with
Lower formula:
Xideal(a)=Xstart(1)+(a-1)*λideal
ka=Find AF (?) .x < Xideal(a) AndAF (? + 1) .x > Xideal(a)}
Xstart(a)=AF (Ia).x
In formula, AF (ka) indicate kth in set AFaA original data point, kaFor intermediate variable, AF (ka) the former data of .x expression
Point AF (ka) abscissa；
135: obtaining the ratio that every section of ripple corresponds to the corrugation length of thickness and the ripple at primary standard aerofoil position
rj, 1≤j≤N, j are the number of ripple, and obtain all rjAverage valueMeet following formula:
rj=avr (AF (I) .y)/(Xstart(j+1)-Xstart(j)),Ij≤I≤Ij+1
In formula, avr () indicates to seek the average value of all parameters in (), and AF (I) indicates i-th original data in set AF
Point, AF (I) .y indicate the ordinate of original data point AF (I)；
136: seeking the ratio r of every section of ripplejWith average valueDifference Ej,By difference EjMiddle maximum value
The index value I of corresponding rippleerrormaxIt is denoted as mark value FlagI, subscript errormax indicates difference EjMiddle maximum value is corresponding
The number of ripple, and record difference EjThe sign of middle maximum value is symbol FlagS；
137: judging whether symbol FlagS is positive sign, if so, IerrormaxReduce 1, Ierrormax+1Increase by 1, if it is not,
IerrormaxIncrease by 1, Ierrormax+1Reduce 1, works as Ierrormax=1, then IerrormaxIt is constant, work as Ierrormax=N, then Ierrormax+1No
Become；
138: jump procedure 135 executes circulation next time, the condition of loop termination are as follows: the adjacent FlagI recycled twice
Numerical value is identical, and the adjacent symbol FlagS recycled twice is differed；
139: after circulation terminates, obtaining the index value of every section of ripple, every section of ripple is obtained according to the index value of every section of ripple
True initial position and every section of ripple corrugation length, with the formula of step 124.
Ripple is uniformly distributed algorithm flow chart such as Fig. 4 of algorithm for design, and its essence is the horizontal seats for presetting suitable AF
Initial position of the x value as ripple is marked, repeatedly realizes that ripple corresponds to thickness and the wave at primary standard aerofoil position by recycling
The equal proportion of the ratio of the corrugation length of line, finally using the abscissa x value of the AF obtained after circulation terminates as true ripple
The actual length of corresponding each ripple is subtracted each other to obtain in initial position, these true ripple initial positions, in Fig. 3, a, FlagI,
FlagS, j, errormax etc. are intermediate parameters, and max () sentence is the maximum value for finding out " () " interior numerical value, Find { max
(?) do be sentence corresponding when finding the maximum value for taking " () " interior numerical value? value, and will? value return to left side of the equal sign, sign
() indicates to take the symbol of numerical value in " () ", and avr () indicates to take several or array average values in " () ".
Above-mentioned ripple equal proportion Distribution Algorithm and ripple are uniformly distributed the true of the available every section of ripple of algorithm for design and rise
Beginning position and corrugation length, it is further assumed that the ripple amplitude of every section of ripple and the aerofoil profile of the ripple corresponding position are thick in waviness curve
The ratio of degree is equal, then the ripple amplitude of the profile thickness setting ripple of available every section of ripple corresponding position, by every
True initial position, corrugation length and the ripple amplitude of Duan Bowen obtains corresponding waviness curve using the method for three strokes and dots arcs,
So as to determine circular arc drawn (three strokes and dots arcs methods can guarantee computer drawing during, between circular arc, circular arc with before
The continuity of the spline curve of Fang Houfang, and the data that other methods have calculating be it is discrete, having certain error causes
Discontinuously).
In case where the curve parameter of the trough of every section of ripple in waviness curve and primary standard aerofoil profile is tangent, a Duan Bo
The geometrical relationship of three sections of circular arcs is as shown in Figure 5 a in line, O1、O2For the center of circle of circular arc, A, B are cutting for standard aerofoil profile and corrugated vane
Point, to be approximated as straightway for AB section convenient for calculating, we term it wave crest line, C, D are cut AB for circular arc and circular arc
Point.
For demonstration purpose, arc AC is connected to the rear end DB, as shown in Figure 5 b.But due to positions most in airfoil profile
Wave crest line is not parallel with chord length direction, and there are an angles, so, the situation of majority of case be as shown in Figure 5 c, can
To prove, △ DEF ∽ △ GDF, then FGFE=FD2, and then obtain:
In formula, i is the number of ripple, and R (i) indicates the corresponding radius of i-th section of ripple medium wave peak, 2R (i)=FG, λ (i) table
Show that the corrugation wavelength of i-th section of ripple, λ (i)=CH, k ' (i) indicate the slope of the wave crest line of i-th section of ripple, k ' (i)=tan
θ, θ are the angle of wave crest line and horizontal line (string), i.e. θ=∠ HCA, h (i) indicate the corresponding ripple amplitude of i-th section of ripple
(i.e. wave height, the distance of wave crest to trough), h (i)=2EF.
It may further obtain:
In formula, (xO,yO) indicate the coordinate of center of circle O in i-th section of ripple in Fig. 5 c,I-th section is indicated in Fig. 5 a
Center of circle O in ripple2Coordinate.
After obtaining the center of circle of corresponding three circular arcs of each section of ripple, according to Pythagorean theorem, three points on circular arc are found out,
Input data as three strokes and dots arcs.
Through checking, airfoil geometry building method error of the invention is 10-4The order of magnitude is even lower, guarantees aerofoil profile gas enough
Geometric accuracy needed for dynamic performance and structural behaviour simulation calculation.
Reshaping design based on different airfoil profiles, performance has larger difference under various boundary, and optimization design needs big
The basic data of amount calculates.In order to efficiently carry out simulation calculation, present invention determine that efficient calculation process, utilizes code
Batch processing is carried out, since simulation time cost is big, operating quantity is big, and each example reaches convergence and needs number of iterations thousand times even more
More, each reshaping design needs thousands of a examples, and workload quantity is very big, too low using the gimmick efficiency being manually entered, because
The method that this present invention uses code, records the journal file of Gambit, Fluent and Ansys respectively, utilizes
Journal file carries out automatic processing, what the text only formatted in journal file was automatically generated, remaining is all
It is parameter, all parameters are set according to the specific requirement of each example, to guarantee the validity of each numerical results.
The process of code is realized by Matlab, and Matlab can export arbitrary form fixation and unfixed text, no
The rule that fixed text need to only edit text can export.
Realize code, it is necessary first to complete under primary correctly Gambit gridding operation and Fluent, Ansys
Corresponding journal file, analyzes the meaning of sentence in journal file, finds out the setting sentence of relevant parameter, as needed
Example, it is edited, the code needed, carries out batch processing, then efficient multi-objective optimization design of power process are as follows:
A) Curve of wing after the design of rapid build reshaping；
B) complete program code is devised, finite element grid is divided according to airfoil geometry curve automatically, is respectively adopted
Fluent and Ansys software calculates the aeroperformance of different airfoil profiles automatically and structural behaviour and exports result；
C) multi-objective optimization algorithm is used, solves the noninferior solution of aeroperformance and structural behaviour multi-objective optimization design of power, really
Determine design scheme, completes aerofoil profile reshaping and optimization design.
Ripple struction is carried out to CLARK Y standard aerofoil profile and 16018 standard aerofoil profile of NACA respectively using the method for the present invention
Reshaping, before modified after structure as shown in Fig. 6 a, Fig. 6 b, Fig. 7 a and Fig. 7 b, by verification experimental verification, lower aerofoil macroshape is changed
Shape be waveform after, vortex can be generated in the ripple of lower aerofoil, forms the differential of air-flow from as a result, the wing can be significantly improved
The aeroperformance of type, especially within the scope of Low Angle Of Attack, as shown in Figure 8 and Figure 9, dotted line is not have ripply standard aerofoil profile, left
The n at upper angle is ripple number, CLIndicate lift coefficient, CDIndicate resistance coefficient, CL/CDLift resistance ratio is indicated, from different ripple numbers
It can be seen that in Low Angle Of Attack model in lower lift coefficient-angle of attack curve, resistance coefficient-angle of attack curve and lift resistance ratio-angle of attack curve
In enclosing, ripple number is more, and lift coefficient and lift resistance ratio are bigger, and resistance coefficient does not significantly rise, and increase in the angle of attack
Afterwards, vortex is blown flat by front incoming flow, therefore will gradually lose lift-rising effect.
To sum up, corrugated vane reshaping can effectively improve the resistive energy of liter of aerofoil profile, while the design of this reshaping increases wing
Effective thickness can dramatically increase the intensity of wing.The two combine, can reduce under same task load-up condition structure size with
Weight increases fuel economy and flying quality.
Claims (7)
1. a kind of aircraft optimum design method of ripple aerofoil profile, the ripple aerofoil profile on the basis of primary standard aerofoil profile by being transformed
It obtains, which is round end fine stern shape aerofoil profile, which is characterized in that the curve parameter of the ripple aerofoil profile removes front and back edge
The middle section divided is the waviness curve formed that is end-to-end by multistage ripple, and every section of ripple includes a wave crest and a wave
Paddy, the ripple in the waviness curve is uniformly distributed or equal proportion distribution, and ripple, which is uniformly distributed, to be referred to: the ripple of every section of ripple is long
Degree is equal, and the distribution of ripple equal proportion refers to: the profile thickness of the corrugation length of every section of ripple and the ripple corresponding position
Ratio is equal；
The optimum design method the following steps are included:
S1: being transformed the lower aerofoil of primary standard aerofoil profile, respectively obtains the ratio such as the equally distributed waviness curve of ripple and ripple
The waviness curve of example distribution；
S2: the corresponding ripple aerofoil profile of the equally distributed waviness curve of ripple and ripple equal proportion of step S1 design are distributed respectively
The corresponding ripple aerofoil profile of waviness curve carry out aeroperformance and Structural Performance Analysis, output analysis result；
S3: establishing the Model for Multi-Objective Optimization of aeroperformance and structural behaviour, is obtained according to the analysis result that step S2 is obtained more
The optimal solution of objective optimization model, and export the corresponding ripple aerofoil profile reshaping scheme of optimal solution；
The step S1 specifically:
11: obtaining the curve parameter and chord length of primary standard aerofoil profile, setting ripple is total, and on the curve parameter of primary standard aerofoil profile
Uniform sampling obtains the set AF of raw data points；
12: according to the equally distributed definition of ripple, ripple song being obtained according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in line；
13: the definition being distributed according to ripple equal proportion obtains ripple according to the set AF of primary standard aerofoil profile, chord length and ripple sum
The true initial position of every section of ripple and corrugation length in curve；
14: according to the ripple amplitude of the profile thickness of every section of ripple corresponding position setting ripple, according to the true of every section of ripple
Initial position, corrugation length and ripple amplitude obtain corresponding waviness curve using the method for three strokes and dots arcs；
The step 12 specifically:
121: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, w1For ratio parameter, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum；
122: the ideal initial position of every section of ripple is obtained, following formula is met:
Xideal(1)=w2*C
Xideal(i)=Xideal(1)+(i-1)*λideal
In formula, w2For ratio parameter, 0 < w2≤ 5%, 1≤i≤N+1, Xideal(i) the ideal initial position of i-th section of ripple is indicated,
The ideal initial position of N+1 sections of ripples is the ideal final position of N sections of ripples；
123: the true initial position of every section of ripple is obtained, following formula is met:
K=Find AF (?) .x < Xideal(i) AndAF (? + 1) .x > Xideal(i)}
In formula, Xstart(i) the true initial position of i-th section of ripple is indicated, the true initial position of N+1 sections of ripples is N
Do the true final position of Duan Bowen, function Find { } indicate to seek meeting { } interior condition? locate numerical value, AF (k) indicates set
K-th of former data point in AF, And indicate that its front and back function is two conditions arranged side by side, and AF (k) .x indicates original data point AF (k)
Abscissa；
124: the corrugation length of every section of ripple is obtained according to the true initial position of every section of ripple.
2. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1, which is characterized in that the ripple
The trough of every section of ripple and the curve parameter of primary standard aerofoil profile are tangent in curve.
3. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1, which is characterized in that the ripple
The peaks and troughs central symmetry of every section of ripple is distributed in inside and outside the curve parameter of primary standard aerofoil profile in curve.
4. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1, which is characterized in that the ripple
The ripple amplitude of every section of ripple and the ratio of the profile thickness of the ripple corresponding position are equal in curve.
5. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1, which is characterized in that the ripple
Curve tangent is obtained or the waviness curve tangent is obtained by multistage sine curve is continuous by multi-section circular arc is continuous.
6. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1, which is characterized in that the step
13 specifically:
131: setting ripple total length L, and theoretical corrugation length λ is obtained according to Lideal, meet following formula:
L=(1-w1)*C
λideal=L/N
In formula, 0 < w1≤ 10%, C indicate the chord length of primary standard aerofoil profile, and N indicates ripple sum；
132: the ideal initial position X of setting first segment rippleideal(1) and the true final position of N sections of ripples, N sections of waves
The true final position of line is the true initial position X of N+1 sections of ripplesideal(N+1), meet following formula:
Xideal(1)=w2*C
Xideal(N+1)=(1-w2)*C
In formula, 0 < w2≤ 5%；
133: according to Xideal(1) the true initial position X of first segment ripple is obtainedstart(1) and and Xstart(1) corresponding rope
Draw value I1, and according to Xideal(N+1) the true initial position X of N sections of ripples is obtainedstart(N+1) and and Xstart(N+1) right
The index value I answeredN+1, meet following formula:
k1=Find AF (?) .x < Xideal(1) AndAF (? + 1) .x > Xideal(1)}
Xstart(1)=AF (I1).x
kN+1=Find AF (?) .x < Xideal(N+1) AndAF (? + 1) .x > Xideal(N+1)}
Xstart(N+1)=AF (IN+1).x
Does function Find { } indicate to seek meeting { } interior condition in formula? locate numerical value, AF (k1)、AF(kN+1) respectively correspond expression
Kth in set AF1、kN+1A original data point, AF (k1).x、AF(kN+1) .x respectively correspond indicate original data point AF (k1)、AF
(kN+1) abscissa；
134: obtaining the ideal initial position X of a sections of ripplesideal(a), 1 < a≤N, and according to Xideal(a) a sections of ripples are obtained
True initial position Xstart(a) and and Xstart(a) corresponding index value Ia, meet following formula:
Xideal(a)=Xstart(1)+(a-1)*λideal
ka=Find AF (?) .x < Xideal(a) AndAF (? + 1) .x > Xideal(a)}
Xstart(a)=AF (Ia).x
In formula, AF (ka) indicate kth in set AFaA original data point, AF (ka) .x expression original data point AF (ka) abscissa；
135: obtaining the ratio r that every section of ripple corresponds to the corrugation length of thickness and the ripple at primary standard aerofoil positionj, 1≤j
≤ N, and obtain all rjAverage valueMeet following formula:
rj=avr (AF (I) .y)/(Xstart(j+1)-Xstart(j)),Ij≤I≤Ij+1
In formula, function avr () indicates to seek the average value of all parameters in (), and AF (I) indicates i-th original data in set AF
Point, AF (I) .y indicate the ordinate of original data point AF (I)；
136: seeking the ratio r of every section of ripplejWith average valueDifference Ej,By difference EjMiddle maximum value is corresponding
Ripple index value IerrormaxIt is denoted as FlagI, subscript errormax indicates difference EjThe number of the corresponding ripple of middle maximum value,
And record difference EjThe sign of middle maximum value is FlagS；
137: judging whether symbol FlagS is positive sign, if so, IerrormaxReduce 1, Ierrormax+1Increase by 1, if it is not, IerrormaxIncrease
Add 1, Ierrormax+1Reduce 1, works as Ierrormax=1, then IerrormaxIt is constant, work as Ierrormax=N, then Ierrormax+1It is constant；
138: jump procedure 135 executes circulation next time, the condition of loop termination are as follows: the adjacent FlagI numerical value recycled twice
It is identical, and symbol FlagS is differed；
139: after circulation terminates, obtaining the index value of every section of ripple, the true of every section of ripple is obtained according to the index value of every section of ripple
The corrugation length of real initial position and every section of ripple.
7. a kind of optimum design method of aircraft ripple aerofoil profile according to claim 1 or 6, which is characterized in that parameter w2
Value is 2.5%.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610231176.7A CN105787217B (en) | 2016-04-14 | 2016-04-14 | A kind of optimum design method of aircraft ripple aerofoil profile |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610231176.7A CN105787217B (en) | 2016-04-14 | 2016-04-14 | A kind of optimum design method of aircraft ripple aerofoil profile |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105787217A CN105787217A (en) | 2016-07-20 |
| CN105787217B true CN105787217B (en) | 2019-07-12 |
Family
ID=56396575
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610231176.7A Expired - Fee Related CN105787217B (en) | 2016-04-14 | 2016-04-14 | A kind of optimum design method of aircraft ripple aerofoil profile |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105787217B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106777977B (en) * | 2016-12-15 | 2019-08-02 | 中国航空工业集团公司西安飞机设计研究所 | A kind of pneumatic distribution surface approximating method of plane airfoil |
| CN112395688A (en) * | 2020-11-18 | 2021-02-23 | 哈尔滨工程大学 | Method for calculating optimal attack angle of sail of ship |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1080608A (en) * | 1992-07-03 | 1994-01-12 | 北京航空航天大学 | The method of a kind of raising aerofoil profile (blade profile) lift |
| CN101885381A (en) * | 2010-07-15 | 2010-11-17 | 沈阳航空航天大学 | Wing with recesses |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1317163C (en) * | 2000-12-01 | 2007-05-23 | 周子健 | Wave-shaped straight wing |
| CN102032215B (en) * | 2010-12-30 | 2012-07-04 | 北京理工大学 | Method for designing blade type with waveform surface |
| CN104108462A (en) * | 2014-08-03 | 2014-10-22 | 佛山市神风航空科技有限公司 | Corrugated wings |
-
2016
- 2016-04-14 CN CN201610231176.7A patent/CN105787217B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1080608A (en) * | 1992-07-03 | 1994-01-12 | 北京航空航天大学 | The method of a kind of raising aerofoil profile (blade profile) lift |
| CN101885381A (en) * | 2010-07-15 | 2010-11-17 | 沈阳航空航天大学 | Wing with recesses |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105787217A (en) | 2016-07-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Johansen et al. | Aerodynamic investigation of winglets on wind turbine blades using CFD | |
| Tang et al. | Passive separation control with blade-end slots in a highly loaded compressor cascade | |
| CN110566506B (en) | Design method for simulating S1 flow surface inverse problem of axial flow compressor | |
| CN107742011B (en) | Design method of impeller blade drag reduction micro-texture | |
| CN112883503B (en) | Numerical simulation method based on influence of PTFE (polytetrafluoroethylene) membrane on aerodynamic characteristics of fan blade | |
| Li et al. | Aerodynamic optimization of wind turbine airfoils using response surface techniques | |
| CN108829970A (en) | Axial fan blade optimum design method and optimization system based on vortex dynamics | |
| CN106050739A (en) | High-performance wing section for cooling fan | |
| CN105404743A (en) | Wind turbine airfoil design method combining B spline with curvature smooth continuity | |
| Xu et al. | Correlation of solidity and curved blade in compressor cascade design | |
| CN113553671A (en) | Bionic anti-cavitation axial flow impeller design method | |
| Crawford | Re‐examining the precepts of the blade element momentum theory for coning rotors | |
| CN104863799A (en) | Method for designing wind turbine airfoil by using Bessel function curve | |
| CN105787217B (en) | A kind of optimum design method of aircraft ripple aerofoil profile | |
| JP2022515453A (en) | Modeling method for aero engine fan assembly | |
| CN104317992A (en) | Positive design method of wind turbine airfoil and wind turbine airfoil family | |
| CN113536458B (en) | Quick geometric modeling method of deformable wing based on class shape function transformation | |
| CN112926132B (en) | Fixed wing airfoil aerodynamic shape design method considering influence of three-dimensional effect | |
| CN103939283B (en) | Blade special for vertical axis wind turbine | |
| CN110287647A (en) | A kind of design method of transonic compressor plane cascade shock wave control | |
| CN114169103A (en) | Propeller modeling method and system based on large propeller disc load working condition | |
| CN105298912A (en) | Bump front edge inlet guider blade | |
| CN109779971B (en) | High-load compressor blade profile radial stacking modeling optimization method based on curvature control | |
| CN113090580A (en) | Centrifugal impeller blade with S-shaped front edge and modeling method thereof | |
| Madsen | An analytical linear two-dimensional actuator disc model and comparisons with computational fluid dynamics (CFD) simulations |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20191217 Address after: 313300 floor 5, building 2, modern industrial park, tianzihu Town, Anji County, Huzhou City, Zhejiang Province Co-patentee after: TONGJI University Patentee after: ZHEJIANG RUISI AUTOMATION TECHNOLOGY Co.,Ltd. Address before: 201204, room 1432, 319 Pu Jian Road, Shanghai, Pudong New Area Co-patentee before: Tongji University Patentee before: SHANGHAI YITIAN UNMANNED AERIAL VEHICLE TECHNOLOGY Co.,Ltd. |
|
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20190712 |