CN111310282A - Helicopter rotor wing profile generation method and system suitable for plateau environment - Google Patents

Helicopter rotor wing profile generation method and system suitable for plateau environment Download PDF

Info

Publication number
CN111310282A
CN111310282A CN202010222333.4A CN202010222333A CN111310282A CN 111310282 A CN111310282 A CN 111310282A CN 202010222333 A CN202010222333 A CN 202010222333A CN 111310282 A CN111310282 A CN 111310282A
Authority
CN
China
Prior art keywords
airfoil
sample
profile
population
optimal
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.)
Pending
Application number
CN202010222333.4A
Other languages
Chinese (zh)
Inventor
招启军
井思梦
王博
赵国庆
陈希
王清
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN202010222333.4A priority Critical patent/CN111310282A/en
Publication of CN111310282A publication Critical patent/CN111310282A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a helicopter rotor wing profile generation method and system suitable for a plateau environment. The method comprises the following steps: fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile; randomly generating sample points of the sample airfoil profile by adopting a Latin hypercube sampling method; obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points; calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; adopting a kriging model and an EI (enhanced information) point adding strategy to establish a mapping relation between a sample point and flow field characteristics; determining the optimal sample airfoil profile individual parameters by adopting an NSGA-II algorithm based on the mapping relation; generating a rotor wing profile by the optimal sample profile individual parameters and the fitting reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment. The invention can improve the rotor wing aerodynamic performance of the helicopter in the plateau environment and reduce the power burden of the engine.

Description

Helicopter rotor wing profile generation method and system suitable for plateau environment
Technical Field
The invention relates to the technical field of rotor wing profile design, in particular to a helicopter rotor wing profile generation method and system suitable for a plateau environment.
Background
The terrain of China is high in the west and low in the east, the average altitude of the Qinghai-Tibet plateau in the west is more than 5000m, and the characteristics of low air temperature, low air density, low air pressure and the like of the plateau environment can greatly influence the performance of an engine and the aerodynamic performance and the operating performance of a rotor wing, so that the method has great difference from the method in the plain environment. At present, altitude flight is realized by a plurality of helicopters at home and abroad, including a blackhawk helicopter in the United states and an AC313 helicopter in China, however, the plateau flight is realized by relying on a higher-power engine mostly, and the improvement on a rotor wing profile is not carried out.
Compared with the plain environment, the air density on the plateau is lower, the same airfoil lift coefficient can only generate smaller lift, and the same rotor wing tension coefficient can only generate smaller tension; at the same time, the stall angle of attack of the airfoil may be reduced due to the reduced reynolds number. Thus, the high altitude environment places demands on the rotor wing profile to have high lift, low drag and torque at lower reynolds numbers. The rotor wing section suitable for the plateau environment can improve the pneumatic performance of the rotor wing in the plateau environment and can reduce the burden of an engine in the plateau environment.
A great deal of research work has been carried out at home and abroad aiming at the design of helicopter rotor wing profiles, and some aeronautical developed countries have established corresponding helicopter special-purpose wing profile libraries, but do not aim at the rotor wing profiles in the plateau environment. The influence of related researchers in China on the aerodynamic characteristics of the rotor wing is analyzed and researched aiming at the plateau environment, but the design work of the rotor wing profile under the plateau environment is basically not available.
Disclosure of Invention
Therefore, there is a need for a method and a system for generating a wing profile of a helicopter rotor suitable for a plateau environment, so as to improve the aerodynamic performance of the wing profile in a plurality of aerodynamic states in the plateau environment, improve the aerodynamic performance of the rotor of the helicopter in the plateau environment, and reduce the power burden of an engine.
In order to achieve the purpose, the invention provides the following scheme:
a helicopter rotor wing section generation method suitable for a plateau environment comprises the following steps:
fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile;
randomly generating sample points of the sample airfoil profile by adopting a Latin hypercube sampling method;
obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points;
calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; the flow field characteristics comprise a lift coefficient, a drag coefficient and a moment coefficient;
adopting a kriging model and an EI (enhanced information) point adding strategy to establish a mapping relation between the sample points and the flow field characteristics;
determining the optimal sample airfoil profile individual parameters by adopting an NSGA-II algorithm based on the mapping relation; the optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient;
generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
Optionally, the generating a rotor wing profile from the optimal sample wing profile individual parameters and the fitting reference wing profile specifically includes:
determining a reference airfoil parameter; the reference airfoil parameters are parameters in the fitting reference airfoil;
obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure BDA0002426524850000021
Wherein the content of the first and second substances,
Figure BDA0002426524850000022
representing a reference airfoil parameter, xoptExpressing the airfoil individual parameters of the optimal sample, and f expressing a function for converting the sample point data into the airfoil parameters;
generating a rotor wing profile from the optimal profile parameters
Figure BDA0002426524850000023
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number.
Optionally, the calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation specifically includes:
determining coordinates of sample points of a sample airfoil from the sample airfoil profile function;
determining an initial grid; the initial mesh is generated from the coordinates;
generating a C-shaped structure body-fitted grid around the wing profile by adopting an elliptic equation grid generation method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure BDA0002426524850000031
Wherein (ξ) represents that the point in the curve coordinate system under the plane is calculated, (ξ) has a mapping relation with the point (x, y) in the straight line coordinate system under the physical plane,
Figure BDA0002426524850000032
p (ξ) is an orthogonality control function, and Q (ξ) is a density control function;
calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure skin grid;
determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure BDA0002426524850000033
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure BDA0002426524850000034
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor viscous stress components acting in a plane perpendicular to the x-axis and along the y-axis, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyAn item for heat conduction;
solving the control equation of the airfoil flow field; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T；
And calculating the flow field characteristic of the sample airfoil under the plateau environment by using the solution of the airfoil flow field control equation.
Optionally, the mapping relationship is:
Figure BDA0002426524850000041
Figure BDA0002426524850000042
Figure BDA0002426524850000043
wherein the content of the first and second substances,
Figure BDA0002426524850000044
is a predicted value of the lift coefficient,
Figure BDA0002426524850000045
is a predicted value of the resistance coefficient,
Figure BDA0002426524850000046
as a prediction of the moment coefficient, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2… Clns]T，Yd＝[Cd1Cd2… Cdns]T，Ym＝[Cm1Cm2… Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure BDA0002426524850000047
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure BDA0002426524850000048
a mapping relationship between fdIs x and
Figure BDA0002426524850000049
a mapping relationship between fmIs x and
Figure BDA00024265248500000410
the mapping relationship between them.
Optionally, the determining the optimal sample airfoil profile individual parameter by using the NSGA-ii algorithm based on the mapping relationship specifically includes:
randomly generating an initial population with the size of N;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation;
performing rapid non-dominated sorting on all individuals in the current generation population according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent generation population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the iteration times of the genetic algorithm;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
performing rapid non-dominated sorting on all individuals in the current generation parent population according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the current generation parent population, and obtaining a current generation offspring population through selection, intersection and variation operations of a genetic algorithm;
merging the current generation parent generation population and the current generation child generation population to obtain a population after the current generation is merged;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population merged by the current generation by adopting the mapping relation;
performing rapid non-dominant sorting on all individuals in the population merged by the current generation according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of each individual in each non-dominant layer;
selecting individuals meeting preset conditions from the population merged by the current generation according to the rapid non-dominated sorting result and the individual crowding degree to form a next generation parent population;
judging whether a population generation number corresponding to the next generation parent population is equal to a preset maximum iteration number or not;
if not, taking the next generation parent population as the current generation parent population, and returning to the step of calculating the lift coefficient, the resistance coefficient and the moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
if so, determining the individuals in the next generation parent population as optimal airfoil profile sample points; the optimal airfoil sample point is a sample point of a sample airfoil corresponding to the optimal flow field characteristic;
and obtaining the individual parameters of the airfoil of the optimal sample from the optimal airfoil sample points.
The invention also provides a helicopter rotor wing section generating system suitable for plateau environment, which comprises:
the fitting module is used for fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile;
the sample point generating module is used for randomly generating sample points of the sample airfoil profile by adopting a Latin hypercube sampling method;
the airfoil profile function determining module is used for obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points;
the flow field characteristic calculation module is used for calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; the flow field characteristics comprise a lift coefficient, a drag coefficient and a moment coefficient;
the mapping relation establishing module is used for establishing the mapping relation between the sample points and the flow field characteristics by adopting a kriging model and an EI (enhanced information element) point adding strategy;
the individual parameter determining module is used for determining the optimal sample airfoil individual parameters by adopting an NSGA-II algorithm based on the mapping relation; the optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient;
a rotor wing profile determination module for generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
Optionally, the rotor wing profile determining module specifically includes:
the reference airfoil parameter determining unit is used for determining reference airfoil parameters; the reference airfoil parameters are parameters in the fitting reference airfoil;
an optimal airfoil profile parameter determining unit for obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure BDA0002426524850000061
Wherein the content of the first and second substances,
Figure BDA0002426524850000062
representing a reference airfoil parameter, xoptExpressing the airfoil individual parameters of the optimal sample, and f expressing a function for converting the sample point data into the airfoil parameters;
a rotor profile determination unit for generating a rotor profile from the optimal profile parameters
Figure BDA0002426524850000063
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number.
Optionally, the flow field characteristic calculating module specifically includes:
a coordinate determination unit for determining coordinates of sample points of the sample airfoil from the sample airfoil profile function;
an initial grid determining unit for determining an initial grid; the initial mesh is generated from the coordinates;
the skin grid generating unit is used for generating a C-shaped structure skin grid around the wing section by adopting an elliptic equation grid generating method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure BDA0002426524850000064
Wherein (ξ) represents that the point in the curve coordinate system under the plane is calculated, (ξ) has a mapping relation with the point (x, y) in the straight line coordinate system under the physical plane,
Figure BDA0002426524850000065
p (ξ) is an orthogonality control function, and Q (ξ) is a density control function;
the grid parameter calculation unit is used for calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure body-fitted grid;
the airfoil flow field control equation determining unit is used for determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure BDA0002426524850000071
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure BDA0002426524850000072
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor acting on a plane perpendicular to the x-axis and along the y-axisComponent of sexual stress, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyAn item for heat conduction;
the solving unit is used for solving the airfoil flow field control equation; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T；
And the flow field characteristic determining unit is used for calculating the flow field characteristic of the sample airfoil under the plateau environment according to the solution of the airfoil flow field control equation.
Optionally, the mapping relationship in the mapping relationship establishing module is:
Figure BDA0002426524850000073
Figure BDA0002426524850000074
Figure BDA0002426524850000075
wherein the content of the first and second substances,
Figure BDA0002426524850000081
is a predicted value of the lift coefficient,
Figure BDA0002426524850000082
is a predicted value of the resistance coefficient,
Figure BDA0002426524850000083
as a prediction of the moment coefficient, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2… Clns]T，Yd＝[Cd1Cd2… Cdns]T，Ym＝[Cm1Cm2… Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure BDA0002426524850000084
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure BDA0002426524850000085
a mapping relationship between fdIs x and
Figure BDA0002426524850000086
a mapping relationship between fmIs x and
Figure BDA0002426524850000087
the mapping relationship between them.
Optionally, the individual parameter determining module specifically includes:
the initial population generating unit is used for randomly generating an initial population with the size of N;
the first calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation;
the first sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the iteration times of the genetic algorithm;
the second calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
the second sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation parent population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation parent population, and obtaining a current generation offspring population through selection, intersection and variation operations of a genetic algorithm;
the population merging unit is used for merging the current generation parent population and the current generation child population to obtain a population after the current generation is merged;
the third calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population merged by the current generation by adopting the mapping relation;
the third sequencing unit is used for performing rapid non-dominant sequencing on all individuals in the population merged by the current generation according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of the individuals in each non-dominant layer;
the individual selecting unit is used for selecting individuals meeting preset conditions from the population combined by the current generation according to the rapid non-dominated sorting result and the individual crowding degree to form a next generation parent population;
the judging unit is used for judging whether the population generation number corresponding to the next generation parent population is equal to the preset maximum iteration number or not; if not, the next generation parent population is used as the current generation parent population and returns to the second computing unit; if so, determining the individuals in the next generation parent population as optimal airfoil profile sample points, and executing an individual parameter determination unit; the optimal airfoil sample point is a sample point of a sample airfoil corresponding to the optimal flow field characteristic;
and the individual parameter determining unit is used for obtaining the optimal sample airfoil individual parameters from the optimal airfoil sample points.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a helicopter rotor wing section generating method and a system suitable for a plateau environment, wherein the method comprises the following steps: obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points; calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; adopting a kriging model and an EI (enhanced information) point adding strategy to establish a mapping relation between a sample point and flow field characteristics; determining the optimal sample airfoil profile individual parameters by adopting an NSGA-II algorithm based on the mapping relation; and generating the helicopter rotor wing profile suitable for the plateau environment by the optimal sample wing profile individual parameters and the fitting reference wing profile. The invention simultaneously considers the aerodynamic characteristics of a plurality of flight states in the plateau environment, improves the aerodynamic performance of the wing profile in the plateau environment in the plurality of aerodynamic states, improves the aerodynamic performance of the rotor wing of the helicopter in the plateau environment, and reduces the power burden of the engine.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method for generating a helicopter rotor wing profile suitable for a plateau environment according to an embodiment of the present invention;
FIG. 2 is a schematic view of an airfoil coordinate system and airfoil profile;
FIG. 3 is a comparison of the profile of an SC1095 airfoil profile with an OPT975 airfoil profile;
FIG. 4 is a graph comparing lift coefficient curves for an SC1095 airfoil and an OPT975 airfoil at Ma 0.3;
FIG. 5 is a polar-curve comparison plot of the SC1095 airfoil and the OPT975 airfoil at Ma 0.3;
FIG. 6 is a comparison graph of the moment coefficient curves of the SC1095 airfoil and the OPT975 airfoil when Ma is 0.3;
FIG. 7 is a graph comparing lift coefficient curves for an SC1095 airfoil and an OPT975 airfoil at Ma 0.4;
FIG. 8 is a polar-curve comparison plot of the SC1095 airfoil and the OPT975 airfoil at Ma 0.4;
FIG. 9 is a comparison of torque coefficient curves for an SC1095 airfoil and an OPT975 airfoil at Ma 0.4;
FIG. 10 is a graph comparing the lift coefficient curves for an SC1095 airfoil and an OPT975 airfoil at Ma 0.5;
FIG. 11 is a polar-curve comparison plot of the SC1095 airfoil and the OPT975 airfoil at Ma 0.5;
FIG. 12 is a comparison of torque coefficient curves for an SC1095 airfoil and an OPT975 airfoil at Ma 0.5;
FIG. 13 is a plot of pull coefficient and hover efficiency FM versus collective pitch for a rotor using the SC1095 airfoil and a rotor using the OPT975 airfoil;
FIG. 14 is a graph of pull coefficient versus torque coefficient for a rotor using the SC1095 airfoil and a rotor using the OPT975 airfoil;
FIG. 15 is a plot of hover efficiency FM as a function of coefficient of tension for a rotor using the SC1095 airfoil and a rotor using the OPT975 airfoil;
fig. 16 is a schematic structural diagram of a helicopter rotor wing profile generating system suitable for use in a plateau environment according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of a method for generating a helicopter rotor wing profile suitable for a plateau environment according to an embodiment of the present invention. Referring to fig. 1, the method for generating a helicopter rotor wing profile suitable for a plateau environment of the present embodiment includes:
step 101: and fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile.
In this embodiment, a classic rotor wing type SC1095 wing type is selected as a reference wing type, and the wing type is fitted by using a Class-Shape Transformation (CST) method to obtain a fitting reference wing type.
The fitted reference airfoil profile may be represented as
Figure BDA0002426524850000111
Wherein, yscDenotes the ordinate, x, of the upper and lower airfoil surfaces of the SC1095 airfoilscRepresenting the abscissa of the upper and lower airfoil surfaces of an SC1095 airfoil, the reference airfoil parameters
Figure BDA0002426524850000112
See table 1.
TABLE 1
Figure BDA0002426524850000113
Step 102: and randomly generating sample points of the sample airfoil by adopting a Latin hypercube sampling method.
In this embodiment, a Latin Hypercube Sampling (LHS) method is used to generate sample points
Figure BDA0002426524850000114
Where the superscript j denotes the sample point number of the sample airfoil and the subscript i denotes the design variable number.
Step 103: and obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points.
The present embodiment utilizes reference airfoil parameters
Figure BDA0002426524850000115
And sample point
Figure BDA0002426524850000116
Parameters of the sample airfoil profile can be obtained
Figure BDA0002426524850000117
Further obtaining a sample airfoil profile function, wherein the specific formula is as follows:
Figure BDA0002426524850000118
Figure BDA0002426524850000121
wherein, yjDenotes the ordinate, x, of the upper and lower airfoils of the j-th sample airfoiljThe abscissa of the upper and lower airfoils of the jth sample airfoil is shown, and f is a function for converting the sample point data into airfoil parameters.
Step 104: and calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation.
The flow field characteristics include lift coefficient, drag coefficient, and moment coefficient.
The step 104 specifically includes:
41) determining coordinates (x) of sample points of a sample airfoil from the sample airfoil profile functionj,yj)。
42) Determining an initial grid; the initial mesh is generated from the coordinates.
43 generating a C-shaped structure body-fitted grid around the wing profile by adopting an elliptic equation grid generation method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure BDA0002426524850000123
Wherein (ξ) represents that the point in the curve coordinate system under the plane is calculated, (ξ) has a mapping relation with the point (x, y) in the straight line coordinate system under the physical plane,
Figure BDA0002426524850000122
p (ξ) is the orthogonality control function and Q (ξ) is the density control function, so that the grid point coordinates (x, y) around the sample airfoil can be obtained.
44) And calculating the area, the volume and the plane normal vector of the airfoil grid unit based on the grid point coordinates (x, y) of the airfoil of the sample. Based on the method, the density, the pressure intensity, the speed and the like of the flow field around the sample airfoil in the plateau environment can be obtained through solving according to the airfoil flow field control equation, and then the lift coefficient Cl, the resistance coefficient Cd and the moment coefficient Cm of the airfoil are obtained through calculation. Specifically, the method comprises the following steps:
and calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure skin grid.
Determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure BDA0002426524850000131
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure BDA0002426524850000132
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor viscous stress components acting in a plane perpendicular to the x-axis and along the y-axis, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyIs a term for heat conduction.
Solving the control equation of the airfoil flow field; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T。
And calculating the flow field characteristic of the sample airfoil under the plateau environment by using the solution of the airfoil flow field control equation.
Step 105: and establishing a mapping relation between the sample point and the flow field characteristic by adopting a kriging model and an EI (edge-added) point strategy.
The present embodiment is based on sample points
Figure BDA0002426524850000133
And the lift coefficient Cl, the drag coefficient Cd and the moment coefficient Cm of the airfoil profile of the sample, and according to a kriging model and an EI point adding strategy, an unknown point x and an airfoil lift coefficient predicted value can be respectively established
Figure BDA0002426524850000134
x and predicted airfoil drag coefficient values
Figure BDA0002426524850000135
x and moment coefficient prediction
Figure BDA0002426524850000136
The mapping relation f betweenl，fd，fmThe formula is as follows:
Figure BDA0002426524850000137
Figure BDA0002426524850000138
Figure BDA0002426524850000139
wherein the content of the first and second substances,
Figure BDA00024265248500001310
is a predicted value of the lift coefficient,
Figure BDA00024265248500001311
is a predicted value of the resistance coefficient,
Figure BDA00024265248500001312
as a function of moment coefficientMeasured value, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2… Clns]T，Yd＝[Cd1Cd2… Cdns]T，Ym＝[Cm1Cm2… Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure BDA0002426524850000141
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure BDA0002426524850000142
a mapping relationship between fdIs x and
Figure BDA0002426524850000143
a mapping relationship between fmIs x and
Figure BDA0002426524850000144
the mapping relationship between them.
Step 106: and determining the optimal sample airfoil profile individual parameters by adopting an NSGA-II algorithm based on the mapping relation.
The optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient.
The step 106 specifically includes:
61) an initial population of size N was randomly generated.
62) And calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation.
63) Performing rapid non-dominated sorting on all individuals in the current generation population according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent generation population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the number of iterations of the genetic algorithm.
64) And calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation.
65) And performing rapid non-dominated sorting on all individuals in the current generation parent population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation parent population, and obtaining the current generation offspring population through selection, intersection and variation operations of a genetic algorithm.
66) And merging the current generation parent generation population and the current generation child generation population to obtain a population after the current generation is merged.
67) And calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population combined by the current generation by adopting the mapping relation.
68) And performing rapid non-dominant sequencing on all the individuals in the population merged by the current generation according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of the individuals in each non-dominant layer.
68) And selecting individuals meeting preset conditions from the population merged by the current generation according to the quick non-dominated sorting result and the individual crowding degree to form a next generation parent population.
69) And judging whether the population generation number corresponding to the next generation parent population is equal to a preset maximum iteration number. If not, taking the next generation parent population as the current generation parent population, and returning to the step 64). If so, determining individuals in the next generation parent population as optimal airfoil profile sample points, and obtaining optimal airfoil profile individual parameters of the samples from the optimal airfoil profile sample points; and the optimal airfoil sample point is a sample point of the sample airfoil corresponding to the optimal flow field characteristic.
Idea based on the aboveA specific process for determining the optimal sample airfoil individual parameters by adopting the NSGA-II algorithm is as follows: (1) randomly generating an initial population x of size N1,x2,...,xN(ii) a (2) Calculating Cl, Cd and Cm of each individual in the population by using a mapping relation established by a Kriging model; (3) according to the values of Cl, Cd and Cm, carrying out non-dominated sorting on individuals in the population, and obtaining a first generation parent population through three basic operations of selection, crossover and mutation of a genetic algorithm
Figure BDA0002426524850000151
(4) Repeating the step (2) and the step (3) to obtain a second generation filial population
Figure BDA0002426524850000152
(5) Merging the parent population and the offspring population; (6) calculating each individual Cl, Cd and Cm in the combined population according to a mapping relation established by a Kriging model; (7) performing rapid non-dominant sorting according to Cl, Cd and Cm, and simultaneously performing crowding degree calculation on individuals in each non-dominant layer; (8) selecting proper individuals to form a new parent population according to the non-dominant relationship and the crowding degree of the individuals
Figure BDA0002426524850000153
(9) Repeating the step (2) and the step (3) to obtain a new filial generation population
Figure BDA0002426524850000154
(10) Repeating the steps (5) to (9) until the number of iteration steps reaches a set value, and finally obtaining the optimal airfoil profile individual parameter xopt。
Step 107: generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
The step 107 specifically includes:
71) determining a reference airfoil parameter; the reference airfoil parameters are parameters in the fitted reference airfoil.
72) Obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure BDA0002426524850000155
Wherein the content of the first and second substances,
Figure BDA0002426524850000156
representing a reference airfoil parameter, xoptThe optimal sample airfoil individual parameter is represented, and f represents a function for converting the sample point data into the airfoil parameter.
73) Generating a rotor wing profile from the optimal profile parameters
Figure BDA0002426524850000161
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number. Wherein the parameters
Figure BDA0002426524850000162
See table 2:
TABLE 2
Figure BDA0002426524850000163
Profile data for the rotor wing profile are shown in table 3:
TABLE 3
Figure BDA0002426524850000164
Figure BDA0002426524850000171
The maximum relative thickness of the rotor wing profile is 9.75% c, the maximum relative thickness position is 23.64% c, the maximum relative camber is 4.87% c, the maximum relative camber position is 25.42% c, wherein c represents the chord length of the rotor wing, and c is 1.
The rotor wing profile obtained by the helicopter rotor wing profile generation method suitable for the plateau environment can be called an OPT975 wing profile, can obviously improve the aerodynamic performance of the helicopter in a plurality of aerodynamic states in the plateau environment, can improve the rotor wing aerodynamic performance of the helicopter in the plateau environment, and can reduce the power burden of an engine. When the airfoil is applied to a conventional rectangular blade rotor, the airfoil has better hovering aerodynamic performance under the plateau condition, namely a larger tension coefficient and higher hovering efficiency.
The front edge of the upper wing surface of the wing profile is gradually transited, then is raised upwards, the radius of the front edge of the lower wing surface is smaller, and the front edge of the lower wing surface is gradually transited to the middle of the wing profile, so that the wing profile resistance is reduced and the resistance divergence is delayed while the wing profile curvature is effectively increased and the wing profile lift force is improved; the curves of the middle part and the tail part of the wing profile are smooth, the tail load is weakened, and the stall attack angle is delayed. The airfoil coordinate system and airfoil profile are shown in FIG. 2.
Fig. 3 shows a comparison of the profile of the OPT975 airfoil profile and the SC1095 airfoil profile generated using the method provided by the example, and fig. 4 to 12 show a comparison of the aerodynamic characteristics of the OPT975 airfoil profile and a classic rotor wing profile used by a eagle helicopter generated using the method provided by the example. As can be seen from the figure, the OPT975 airfoil has better lift, lift-drag and moment characteristics than the SC1095 airfoil. Specifically, fig. 4 to 12 show the lift coefficient curve, the polar curve and the moment coefficient curve of the OPT975 airfoil and the classic rotor airfoil SC1095 airfoil at a altitude of 5000m and 0.3, 0.4 and 0.5, respectively. As can be seen from the figure, the OPT975 airfoil has a greater lift coefficient when the angles of attack are the same; the coefficient of drag of the OPT975 airfoil is smaller when the coefficient of lift is the same; when the mach number is small, the absolute value of the moment coefficient of the OPT975 airfoil is smaller and the moment coefficient divergence angle of attack is larger.
Fig. 13-15 show aerodynamic performance comparison plots for two pairs of rectangular blade rotors using the OPT975 and SC1095 airfoils, respectively. Rotor parameters are shown in table 4. The two rotors only use different wing profiles, and other parameters are the same. As can be seen from fig. 13 to 15, the rotor using the OPT975 airfoil has better hovering performance in a plateau environment, and has a greater drag coefficient and hovering efficiency when the collective pitch is the same; under the condition of high tension coefficient, the rotor has smaller torque coefficient and larger hovering efficiency, and the OPT975 airfoil is a helicopter rotor airfoil suitable for plateau environment.
TABLE 4
Rotor diameter 16.3576m Tip speed 200m/s
Aspect ratio 13.4 Root cutting 0.2R
Number of blades 4 Reynolds number 5.546*106(H＝5000m)
Blade shape Rectangle Negative torsion 12°
The invention also provides a helicopter rotor wing section generating system suitable for the plateau environment, and fig. 16 is a schematic structural diagram of the helicopter rotor wing section generating system suitable for the plateau environment in the embodiment of the invention. Referring to fig. 16, the system includes:
and the fitting module 201 is configured to fit the reference airfoil profile by using a class shape function transformation method to obtain a fitting reference airfoil profile.
And the sample point generating module 202 is used for randomly generating sample points of the sample airfoil by adopting a Latin hypercube sampling method.
And the airfoil profile function determining module 203 is configured to obtain a sample airfoil profile function according to the fitting reference airfoil and the sample point.
The flow field characteristic calculation module 204 is used for calculating the flow field characteristic of the sample airfoil profile in the plateau environment according to the sample airfoil profile function and the airfoil flow field control equation; the flow field characteristics include lift coefficient, drag coefficient, and moment coefficient.
A mapping relation establishing module 205, configured to establish a mapping relation between the sample point and the flow field characteristic by using a kriging model and an EI adding point strategy.
An individual parameter determination module 206, configured to determine an optimal sample airfoil individual parameter based on the mapping relationship by using an NSGA-ii algorithm; the optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient.
A rotor wing profile determination module 207 for generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
As an optional embodiment, the rotor wing profile determining module 207 specifically includes:
the reference airfoil parameter determining unit is used for determining reference airfoil parameters; the reference airfoil parameters are parameters in the fitted reference airfoil.
An optimal airfoil profile parameter determining unit for obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure BDA0002426524850000191
Wherein the content of the first and second substances,
Figure BDA0002426524850000192
representing a reference airfoil parameter, xoptThe optimal sample airfoil individual parameter is represented, and f represents a function for converting the sample point data into the airfoil parameter.
A rotor profile determination unit for generating a rotor profile from the optimal profile parameters
Figure BDA0002426524850000193
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number.
As an optional implementation manner, the flow field characteristic calculating module 204 specifically includes:
a coordinate determination unit for determining coordinates of sample points of the sample airfoil from the sample airfoil profile function.
An initial grid determining unit for determining an initial grid; the initial mesh is generated from the coordinates.
The skin grid generating unit is used for generating a C-shaped structure skin grid around the wing section by adopting an elliptic equation grid generating method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure BDA0002426524850000201
Wherein (ξ) represents that the point in the curve coordinate system under the plane is calculated, (ξ) has a mapping relation with the point (x, y) in the straight line coordinate system under the physical plane,
Figure BDA0002426524850000202
p (ξ) is the orthogonality control function, Q (ξ) is the density control functionAnd (4) counting.
And the grid parameter calculation unit is used for calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure body-fitted grid.
The airfoil flow field control equation determining unit is used for determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure BDA0002426524850000203
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure BDA0002426524850000204
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor viscous stress components acting in a plane perpendicular to the x-axis and along the y-axis, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyIs a term for heat conduction.
The solving unit is used for solving the airfoil flow field control equation; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T。
And the flow field characteristic determining unit is used for calculating the flow field characteristic of the sample airfoil under the plateau environment according to the solution of the airfoil flow field control equation.
As an optional implementation manner, the mapping relationship in the mapping relationship establishing module 205 is:
Figure BDA0002426524850000211
Figure BDA0002426524850000212
Figure BDA0002426524850000213
wherein the content of the first and second substances,
Figure BDA0002426524850000214
is a predicted value of the lift coefficient,
Figure BDA0002426524850000215
is a predicted value of the resistance coefficient,
Figure BDA0002426524850000216
as a prediction of the moment coefficient, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2… Clns]T，Yd＝[Cd1Cd2… Cdns]T，Ym＝[Cm1Cm2… Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure BDA0002426524850000217
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure BDA0002426524850000218
the relationship betweenCorrelation of radiation, fdIs x and
Figure BDA0002426524850000219
a mapping relationship between fmIs x and
Figure BDA00024265248500002110
the mapping relationship between them.
As an optional implementation manner, the individual parameter determining module 206 specifically includes:
and the initial population generating unit is used for randomly generating an initial population with the size of N.
And the first calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation.
The first sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the number of iterations of the genetic algorithm.
And the second calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation.
And the second sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation parent population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation parent population, and obtaining the current generation offspring population through selection, intersection and variation operations of a genetic algorithm.
And the population merging unit is used for merging the current generation parent population and the current generation child population to obtain a population after the current generation is merged.
And the third calculating unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population combined by the current generation by adopting the mapping relation.
And the third sequencing unit is used for performing rapid non-dominant sequencing on all the individuals in the population merged by the current generation according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of the individuals in each non-dominant layer.
And the individual selecting unit is used for selecting individuals meeting preset conditions from the population combined by the current generation according to the rapid non-dominated sorting result and the individual crowding degree to form a next generation parent population.
The judging unit is used for judging whether the population generation number corresponding to the next generation parent population is equal to the preset maximum iteration number or not; if not, the next generation parent population is used as the current generation parent population and returns to the second computing unit; if so, determining the individuals in the next generation parent population as optimal airfoil profile sample points, and executing an individual parameter determination unit; and the optimal airfoil sample point is a sample point of the sample airfoil corresponding to the optimal flow field characteristic.
And the individual parameter determining unit is used for obtaining the optimal sample airfoil individual parameters from the optimal airfoil sample points.
The helicopter rotor wing section generating system suitable for the plateau environment of this embodiment considers the aerodynamic characteristics of a plurality of flight states under the plateau environment simultaneously, has improved the aerodynamic performance of wing section under a plurality of aerodynamic states in the plateau environment, has improved the rotor aerodynamic performance of helicopter under the plateau environment to the power burden of engine has been alleviateed.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. A helicopter rotor wing section generation method suitable for a plateau environment is characterized by comprising the following steps:
fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile;
randomly generating sample points of the sample airfoil profile by adopting a Latin hypercube sampling method;
obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points;
calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; the flow field characteristics comprise a lift coefficient, a drag coefficient and a moment coefficient;
adopting a kriging model and an EI (enhanced information) point adding strategy to establish a mapping relation between the sample points and the flow field characteristics;
determining the optimal sample airfoil profile individual parameters by adopting an NSGA-II algorithm based on the mapping relation; the optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient;
generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
2. A method according to claim 1, wherein said generating a rotor wing profile from said optimal sample profile individual parameters and said fitting reference profile, comprises:
determining a reference airfoil parameter; the reference airfoil parameters are parameters in the fitting reference airfoil;
obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure FDA0002426524840000011
Wherein the content of the first and second substances,
Figure FDA0002426524840000012
representing a reference airfoil parameter, xoptExpressing the airfoil individual parameters of the optimal sample, and f expressing a function for converting the sample point data into the airfoil parameters;
generating a rotor wing profile from the optimal profile parameters
Figure FDA0002426524840000013
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number.
3. The method according to claim 1, wherein the calculating the flow field characteristics of the sample airfoil profile in the plateau environment according to the sample airfoil profile function and the airfoil flow field control equation specifically comprises:
determining coordinates of sample points of a sample airfoil from the sample airfoil profile function;
determining an initial grid; the initial mesh is generated from the coordinates;
generating a C-shaped structure body-fitted grid around the wing profile by adopting an elliptic equation grid generation method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure FDA0002426524840000021
Wherein (ξ) represents the points in the curvilinear coordinate system under the calculation plane, (ξ) and the straight line under the physical planeThe points (x, y) in the line coordinate system have a mapping relation,
Figure FDA0002426524840000022
p (ξ) is an orthogonality control function, and Q (ξ) is a density control function;
calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure skin grid;
determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure FDA0002426524840000023
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure FDA0002426524840000024
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor viscous stress components acting in a plane perpendicular to the x-axis and along the y-axis, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyAn item for heat conduction;
solving the control equation of the airfoil flow field; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T；
And calculating the flow field characteristic of the sample airfoil under the plateau environment by using the solution of the airfoil flow field control equation.
4. A method according to claim 1, wherein the mapping relationship is:
Figure FDA0002426524840000031
Figure FDA0002426524840000032
Figure FDA0002426524840000033
wherein the content of the first and second substances,
Figure FDA0002426524840000034
is a predicted value of the lift coefficient,
Figure FDA0002426524840000035
is a predicted value of the resistance coefficient,
Figure FDA0002426524840000036
as a prediction of the moment coefficient, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2…Clns]T，Yd＝[Cd1Cd2…Cdns]T，Ym＝[Cm1Cm2…Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure FDA0002426524840000037
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure FDA0002426524840000038
a mapping relationship between fdIs x and
Figure FDA0002426524840000039
a mapping relationship between fmIs x and
Figure FDA00024265248400000310
the mapping relationship between them.
5. A method for generating a helicopter rotor wing profile suitable for use in a high altitude environment according to claim 1 wherein said determining optimal sample wing profile individual parameters based on said mapping relationship using the NSGA-ii algorithm specifically comprises:
randomly generating an initial population with the size of N;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation;
performing rapid non-dominated sorting on all individuals in the current generation population according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent generation population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the iteration times of the genetic algorithm;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
performing rapid non-dominated sorting on all individuals in the current generation parent population according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the current generation parent population, and obtaining a current generation offspring population through selection, intersection and variation operations of a genetic algorithm;
merging the current generation parent generation population and the current generation child generation population to obtain a population after the current generation is merged;
calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population merged by the current generation by adopting the mapping relation;
performing rapid non-dominant sorting on all individuals in the population merged by the current generation according to a lift coefficient, a resistance coefficient and a moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of each individual in each non-dominant layer;
selecting individuals meeting preset conditions from the population merged by the current generation according to the rapid non-dominated sorting result and the individual crowding degree to form a next generation parent population;
judging whether a population generation number corresponding to the next generation parent population is equal to a preset maximum iteration number or not;
if not, taking the next generation parent population as the current generation parent population, and returning to the step of calculating the lift coefficient, the resistance coefficient and the moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
if so, determining the individuals in the next generation parent population as optimal airfoil profile sample points; the optimal airfoil sample point is a sample point of a sample airfoil corresponding to the optimal flow field characteristic;
and obtaining the individual parameters of the airfoil of the optimal sample from the optimal airfoil sample points.
6. A helicopter rotor wing profile generation system suitable for use in a plateau environment comprising:
the fitting module is used for fitting the reference airfoil profile by adopting a class shape function transformation method to obtain a fitting reference airfoil profile;
the sample point generating module is used for randomly generating sample points of the sample airfoil profile by adopting a Latin hypercube sampling method;
the airfoil profile function determining module is used for obtaining a sample airfoil profile function according to the fitting reference airfoil and the sample points;
the flow field characteristic calculation module is used for calculating the flow field characteristic of the sample airfoil under the plateau environment according to the sample airfoil shape function and the airfoil flow field control equation; the flow field characteristics comprise a lift coefficient, a drag coefficient and a moment coefficient;
the mapping relation establishing module is used for establishing the mapping relation between the sample points and the flow field characteristics by adopting a kriging model and an EI (enhanced information element) point adding strategy;
the individual parameter determining module is used for determining the optimal sample airfoil individual parameters by adopting an NSGA-II algorithm based on the mapping relation; the optimal sample airfoil individual parameter is determined by a sample point of a sample airfoil corresponding to the optimal flow field characteristic; the optimal flow field characteristics comprise an optimal lift coefficient, an optimal resistance coefficient and an optimal moment coefficient;
a rotor wing profile determination module for generating a rotor wing profile from the optimal sample profile individual parameters and the fitted reference profile; the rotor wing section is a helicopter rotor wing section suitable for plateau environment.
7. A helicopter rotor profile generating system adapted for use in a high altitude environment according to claim 6 wherein said rotor profile determining module specifically comprises:
the reference airfoil parameter determining unit is used for determining reference airfoil parameters; the reference airfoil parameters are parameters in the fitting reference airfoil;
an optimal airfoil profile parameter determining unit for obtaining optimal airfoil profile parameters from the reference airfoil profile parameters and the optimal sample airfoil profile individual parameters
Figure FDA0002426524840000051
Wherein the content of the first and second substances,
Figure FDA0002426524840000052
representing a reference airfoil parameter, xoptExpressing the airfoil individual parameters of the optimal sample, and f expressing a function for converting the sample point data into the airfoil parameters;
a rotor profile determination unit for generating a rotor profile from the optimal profile parameters
Figure FDA0002426524840000053
yoptIndicating the longitudinal coordinate, x, of the upper and lower wing surfaces of the rotor wing profileoptAnd (3) an abscissa representing the upper and lower airfoils of the rotor wing profile, and i represents a design variable number.
8. A helicopter rotor airfoil generation system suitable for use in a plateau environment according to claim 6 wherein said flow field characteristics calculation module specifically includes:
a coordinate determination unit for determining coordinates of sample points of the sample airfoil from the sample airfoil profile function;
an initial grid determining unit for determining an initial grid; the initial mesh is generated from the coordinates;
the skin grid generating unit is used for generating a C-shaped structure skin grid around the wing section by adopting an elliptic equation grid generating method based on a Poisson equation according to the coordinates and the initial grid; the Poisson equation is
Figure FDA0002426524840000061
Wherein (ξ) represents that the point in the curve coordinate system under the plane is calculated, (ξ) has a mapping relation with the point (x, y) in the straight line coordinate system under the physical plane,
Figure FDA0002426524840000062
p (ξ) is an orthogonality control function, and Q (ξ) is a density control function;
the grid parameter calculation unit is used for calculating the area of each grid unit and the volume of each grid unit in the C-shaped structure body-fitted grid;
the airfoil flow field control equation determining unit is used for determining an airfoil flow field control equation according to the area, the volume, the conservation variable, the convection flux term and the viscous flux term; the control equation of the airfoil flow field is
Figure FDA0002426524840000063
Wherein t is physical time, FcFor the convective flux term, FvIs a viscous flux term, omega is the volume of a grid cell, S is the area of a grid cell, W is a conservation variable,
Figure FDA0002426524840000064
ρ is air density, E is total energy, H is total enthalpy, p is pressure, u is velocity component in x-axis direction, V is velocity component in y-axis direction, V is total enthalpy, H is total enthalpy, p is pressure, V is air density, E is air density, H is air density, V isrAs relative speed of movement, VtIs the moving speed of the grid, (n)x,ny) Is a grid cell surface unit normal vector, tauxxFor viscous stress components acting in a plane perpendicular to the x-axis and along the x-axis, τxyFor viscous stress components acting in a plane perpendicular to the x-axis and along the y-axis, τyyFor the viscous stress component acting in a plane perpendicular to the y-axis and along the y-axis direction, ΘxAs a viscous stress-acting term, ΘyAn item for heat conduction;
the solving unit is used for solving the airfoil flow field control equation; solving the control equation of the airfoil flow field by [ rho u rho v rho E ═ W ═]T；
And the flow field characteristic determining unit is used for calculating the flow field characteristic of the sample airfoil under the plateau environment according to the solution of the airfoil flow field control equation.
9. A helicopter rotor wing profile generating system adapted for use in a high altitude environment according to claim 6 wherein said mapping relationship in said mapping relationship establishing module is:
Figure FDA0002426524840000071
Figure FDA0002426524840000072
Figure FDA0002426524840000073
wherein the content of the first and second substances,
Figure FDA0002426524840000074
is a predicted value of the lift coefficient,
Figure FDA0002426524840000075
is a predicted value of the resistance coefficient,
Figure FDA0002426524840000076
as a prediction of the moment coefficient, YlVector, Y, formed by lift coefficients Cl corresponding to sample points of a sample airfoildIs a vector consisting of resistance coefficients Cd corresponding to sample points of a sample airfoil, YmA vector consisting of moment coefficients Cm corresponding to sample points of the sample airfoil, Yl＝[Cl1Cl2…Clns]T，Yd＝[Cd1Cd2…Cdns]T，Ym＝[Cm1Cm2…Cmns]TNs denotes the number of sample points of the sample airfoil, x denotes the data vector of the airfoil to be predicted,
Figure FDA0002426524840000077
a j sample point corresponding to the ith design variable representing the sample airfoil, i being the design variable number, j being the sample point number of the sample airfoil, flIs x and
Figure FDA0002426524840000078
a mapping relationship between fdIs x and
Figure FDA0002426524840000079
a mapping relationship between fmIs x and
Figure FDA00024265248400000710
the mapping relationship between them.
10. A helicopter rotor wing profile generating system adapted for use in a high altitude environment according to claim 6 wherein said individual parameter determination module specifically comprises:
the initial population generating unit is used for randomly generating an initial population with the size of N;
the first calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation population by adopting the mapping relation;
the first sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation population, and obtaining the current generation parent population through selection, intersection and variation operations of a genetic algorithm; the algebra of the population is equal to the iteration times of the genetic algorithm;
the second calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the current generation parent population by adopting the mapping relation;
the second sequencing unit is used for performing rapid non-dominated sequencing on all individuals in the current generation parent population according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the current generation parent population, and obtaining a current generation offspring population through selection, intersection and variation operations of a genetic algorithm;
the population merging unit is used for merging the current generation parent population and the current generation child population to obtain a population after the current generation is merged;
the third calculation unit is used for calculating a lift coefficient, a resistance coefficient and a moment coefficient corresponding to each individual in the population merged by the current generation by adopting the mapping relation;
the third sequencing unit is used for performing rapid non-dominant sequencing on all individuals in the population merged by the current generation according to the lift coefficient, the resistance coefficient and the moment coefficient corresponding to the individuals in the population merged by the current generation, and calculating the crowding degree of the individuals in each non-dominant layer;
the individual selecting unit is used for selecting individuals meeting preset conditions from the population combined by the current generation according to the rapid non-dominated sorting result and the individual crowding degree to form a next generation parent population;
the judging unit is used for judging whether the population generation number corresponding to the next generation parent population is equal to the preset maximum iteration number or not; if not, the next generation parent population is used as the current generation parent population and returns to the second computing unit; if so, determining the individuals in the next generation parent population as optimal airfoil profile sample points, and executing an individual parameter determination unit; the optimal airfoil sample point is a sample point of a sample airfoil corresponding to the optimal flow field characteristic;
and the individual parameter determining unit is used for obtaining the optimal sample airfoil individual parameters from the optimal airfoil sample points.
CN202010222333.4A 2020-03-26 2020-03-26 Helicopter rotor wing profile generation method and system suitable for plateau environment Pending CN111310282A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010222333.4A CN111310282A (en) 2020-03-26 2020-03-26 Helicopter rotor wing profile generation method and system suitable for plateau environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010222333.4A CN111310282A (en) 2020-03-26 2020-03-26 Helicopter rotor wing profile generation method and system suitable for plateau environment

Publications (1)

Publication Number Publication Date
CN111310282A true CN111310282A (en) 2020-06-19

Family

ID=71147489

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010222333.4A Pending CN111310282A (en) 2020-03-26 2020-03-26 Helicopter rotor wing profile generation method and system suitable for plateau environment

Country Status (1)

Country Link
CN (1) CN111310282A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113353285A (en) * 2021-07-13 2021-09-07 南京航空航天大学 Method and system for determining rotor wing profile
CN117022588A (en) * 2023-08-08 2023-11-10 中山大学 Hydrofoil structure optimization method, system, equipment and medium based on Kriging model

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4776531A (en) * 1986-09-05 1988-10-11 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration High lift, low pitching moment airfoils
CN109376418A (en) * 2018-10-16 2019-02-22 湘潭大学 A kind of pneumatic Robust Optimal Design method of small wind airfoil type suitable for turbulent flow operating condition
CN110110384A (en) * 2019-04-12 2019-08-09 电子科技大学 A kind of application method based on the non-dominant genetic algorithm of concentration strategy in the optimization of aircraft wing-type design
CN110705126A (en) * 2019-10-24 2020-01-17 南京航空航天大学 Helicopter rotor wing profile determining method and system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4776531A (en) * 1986-09-05 1988-10-11 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration High lift, low pitching moment airfoils
CN109376418A (en) * 2018-10-16 2019-02-22 湘潭大学 A kind of pneumatic Robust Optimal Design method of small wind airfoil type suitable for turbulent flow operating condition
CN110110384A (en) * 2019-04-12 2019-08-09 电子科技大学 A kind of application method based on the non-dominant genetic algorithm of concentration strategy in the optimization of aircraft wing-type design
CN110705126A (en) * 2019-10-24 2020-01-17 南京航空航天大学 Helicopter rotor wing profile determining method and system

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
QINGWANG: "Rotor aerodynamic shape design for improving performance of an unmanned helicopter", 《AEROSPACE SCIENCE AND TECHNOLOGY》 *
蔡文杰: "基于偏最小二乘法的翼型稳健设计替代模型", 《计算机测量与控制》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113353285A (en) * 2021-07-13 2021-09-07 南京航空航天大学 Method and system for determining rotor wing profile
CN113353285B (en) * 2021-07-13 2022-06-10 南京航空航天大学 Method and system for determining rotor wing profile
CN117022588A (en) * 2023-08-08 2023-11-10 中山大学 Hydrofoil structure optimization method, system, equipment and medium based on Kriging model
CN117022588B (en) * 2023-08-08 2024-03-26 中山大学 Hydrofoil structure optimization method, system, equipment and medium based on Kriging model

Similar Documents

Publication Publication Date Title
WO2021077855A1 (en) Helicopter rotor airfoil determination method and system
CN109190283B (en) Wind turbine airfoil aerodynamic optimization method considering high turbulence free inflow effect
CN109460566B (en) Aerodynamic robust optimization design method for thick airfoil section on inner side of wind turbine blade
CN109766604B (en) Blade high-rigidity design method based on random isogeometric analysis
Wang et al. Aerodynamic design of multi-propeller/wing integration at low Reynolds numbers
CN111310282A (en) Helicopter rotor wing profile generation method and system suitable for plateau environment
CN110516318A (en) Airfoil Design method based on radial basis function neural network agent model
Amato et al. Numerical Analysis of the Influence of Tip Devices on the Power Coefficient of a VAWT
Klimczyk et al. Robust design and optimization of UAV empennage
Smith et al. The design of a joined wing flight demonstrator aircraft
CN105787217B (en) A kind of optimum design method of aircraft ripple aerofoil profile
Junge et al. Optimizing spanwise lift distributions yacht sails using extended lifting line analysis
Ivanov et al. Influence of selected turbulence model on the optimization of a class-shape transformation parameterized airfoil
Kumar et al. Aerodynamic Performance Optimization of Multiple Slat Airfoil based on Multi-Objective Genetic Algorithm
Basom et al. Inviscid analysis of horizontal-axis wind turbines using distributed vorticity elements
Wu et al. Using the combined flow control accessory to the aerodynamic performance enhancement of bio-inspired seagull airfoils
Oda et al. Studies on wingtip geometries by optimum spanwise lift distribution design method
Chuang et al. Effects of Reynolds number and inclined angle of stroke plane on aerodynamic characteristics of flapping corrugated airfoil
Zhang et al. Multi-objective optimization design for airfoils with high lift-to-drag ratio based on geometric feature control
CN113536458B (en) Quick geometric modeling method of deformable wing based on class shape function transformation
Lee et al. Active flow control bump design using hybrid Nash-game coupled to evolutionary algorithms
Galbraith et al. Aspects of unsteady aerodynamics in wind turbines
Mukherjee et al. Corrugation assisted enhancement of aerodynamic characteristics of delta wing for micro aerial vehicle
Rimi et al. Optimizing Aerodynamic Performance of Selig S3014 Airfoil through Dimensional Parametric Analysis
Lupp et al. Aeroelastic tailoring for maximizing sailplane average cross-country speed

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20200619