CN112231836A - Wing profile optimization method based on genetic algorithm and numerical simulation - Google Patents
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Abstract
The invention belongs to the technical field related to airfoil optimization, and discloses an airfoil optimization method based on genetic algorithm and numerical simulation, which comprises the following steps: the method comprises the following steps of (1) carrying out parametric description on an airfoil by adopting a high-order Bezier curve of a plurality of control point control molded lines; obtaining a plurality of airfoils and corresponding angles of attack; obtaining objective function values of a plurality of airfoils under corresponding attack angles through numerical simulation; and sequencing the objective function values by adopting a genetic algorithm, taking the wing profiles and the attack angles corresponding to the objective function values meeting preset rules in the objective function values as target wing profiles and target attack angles, selecting, intersecting and/or varying the coordinates of control points corresponding to the target wing profiles and the target attack angles to obtain an optimized wing profile set, and carrying out repeated value simulation and genetic algorithm processing on the optimized wing profile set until the objective function values reach an optimization termination condition. The method can obtain the airfoil profile and the attack angle with the optimal objective function value in a larger optimizing range by combining a genetic algorithm and a numerical simulation technology.
Description
Technical Field
The invention belongs to the technical field related to airfoil optimization, and particularly relates to an airfoil optimization method based on genetic algorithm and numerical simulation.
Background
Airfoils are one of the important geometric characteristics of structural components of blades, wings, etc. The air-conditioning system is applied to aircrafts in the aerospace field, fans, water pumps and wind turbines in the energy field, and civil equipment such as air conditioners, ventilation fans and other ventilation equipment. With the continuous development of society and the continuous improvement of human requirements, higher requirements are put forward on the performance of wing profiles.
For the optimization of the airfoil profile, the conventional optimization method is to select an initial airfoil profile, perform parametric description on the initial airfoil profile by using an airfoil profile parametric method, select related parameters as optimization variables, apply constraint conditions to the optimization variables, determine an optimization target, seek an extreme value of the optimization target by combining computational fluid dynamics software and an optimization algorithm, and determine specific values of the optimization variables according to the extreme value, so as to achieve the purpose of optimizing the airfoil profile. However, if the optimization process of the airfoil profile is performed on a certain initial airfoil profile, the optimization process is often influenced by the shape of the initial airfoil profile when the constraint conditions of the optimization variables are set, so that the optimization space of the airfoil profile is limited, and a wide shape space is difficult to cover, thereby limiting the optimization effect of the airfoil profile. Moreover, when the airfoil profile line parameterization method based on the function is adopted, the Bessel function is less adopted, the order is lower, and the detailed change of the profile line is limited.
After the airfoil is described in a parameterization mode, the existing research usually considers the influence of profile lines of the upper surface and the lower surface of the airfoil on the performance of the airfoil separately, and neglects the influence of the shapes of the two profile lines of the upper surface and the lower surface of the airfoil at the intersection of the leading edge of the airfoil on the performance of the airfoil. Thus, the airfoil leading edge is often left untreated or is simply transitioned through a circular arc curve and given a value or range of circular arc radii. The former treatment can not guarantee that the upper surface and the lower surface of the airfoil are smooth and continuous at the front edge point, while the latter treatment can guarantee the point but is directly restricted to be in the shape of a circular arc, and the shapes of other airfoil front edges cannot be considered.
Furthermore, the optimization variables are typically determined in accordance with a specific method of parameterization of the airfoil profile. For example, for an airfoil profile line parameterization method based on airfoil geometric characteristics, the optimization variables are mainly taken from geometric characteristic parameters of an airfoil; for the function-based airfoil profile parameterization method, the optimization variables are mainly taken as profile control parameters. In order to ensure the reasonability of the shape of the airfoil, research is carried out by adopting a mode of reducing the optimization range of optimization variables, and the attack angle closely related to the optimization target is often just taken as a given condition or constraint in the whole optimization process. These all restrict the space of optimizing of airfoil profile line to a certain extent, and then restricted the optimal design of airfoil.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides an airfoil profile optimization method based on genetic algorithm and numerical simulation, which is characterized in that the profile of the airfoil profile is parameterized by adopting a high-order Bessel function, an initial airfoil profile does not need to be selected, the optimization range of the airfoil profile is wider, the free design of the airfoil profile leading edge can be realized without being limited to a circular arc, the optimization variables in the optimization of the airfoil profile not only comprise the coordinates of a control point, but also comprise an attack angle, the optimization is more reasonable, and the airfoil profile with a more optimal objective function value and the corresponding attack angle can be obtained by adopting the genetic algorithm to optimize the control point coordinates and the attack angle of the airfoil profile.
To achieve the above object, according to one aspect of the present invention, there is provided a method for optimizing an airfoil profile based on genetic algorithm and numerical simulation, the method comprising: s1, parameterizing the profiles of the upper surface and the lower surface of the airfoil respectively by adopting a high-order Bezier curve so that the profiles of the upper surface and the lower surface of the airfoil are controlled by a plurality of control points respectively, wherein the order of the Bezier curve is greater than or equal to 4; s2, generating coordinates and corresponding attack angles of a plurality of groups of control points, and further obtaining a plurality of wing profiles and corresponding attack angles; s3, obtaining objective function values of the airfoils under the corresponding attack angles through numerical simulation; s4, sequencing the objective function values by adopting a genetic algorithm, taking the airfoils and the attack angles corresponding to the objective function values meeting preset rules in the objective function values as target airfoils and target attack angles, selecting, intersecting and/or varying the coordinates of control points and the target attack angles corresponding to the target airfoils to obtain an optimized airfoil set, repeatedly executing S3 and S4 on the optimized airfoil set until the objective function values reach optimization termination conditions, and outputting the profile line coordinates and the corresponding attack angles of the optimized airfoils.
Preferably, before the numerical simulation in step S3, the method further includes: and eliminating the wing profiles which do not meet the preset conditions in the plurality of wing profiles.
Preferably, before the numerical simulation in step S3, the method specifically includes: and obtaining coordinates of each point on the airfoil profile line, and removing airfoils with negative thickness and zero thickness.
Preferably, the sorting of the objective function values by using a genetic algorithm in step S4 specifically includes: and sequencing the objective function values according to the fitness by adopting a genetic algorithm.
Preferably, the parameterized description formula of the profile of the upper surface or the lower surface of the airfoil is as follows:
the number n is the order of the upper surface molded line or the lower surface molded line of the airfoil, and the orders of the upper surface molded line and the lower surface molded line can be equal or unequal; i is a control point, BiFor the coordinates corresponding to the ith control point, t ∈ [0, 1 ]]And B (t) is the coordinate of the profile.
Preferably, two ends of the profile line of the upper surface and the profile line of the lower surface of the airfoil are respectively a leading edge point and a trailing edge point, and the abscissa of the control point closest to the leading edge point in the control points of the upper surface and the lower surface is selected to be the same as the leading edge point, so that the leading edge is smooth and continuous.
Preferably, step S2 is specifically: generating the coordinates and the attack angles of a plurality of groups of control points in a preset range according to one of a factorial test, a full factor test, a Latin hypercube, an orthogonal test or a random generation method, and further obtaining a plurality of airfoils and corresponding attack angles.
Preferably, the objective function value comprises one or more combinations of lift-drag ratio, lift coefficient or drag coefficient.
In general, compared with the prior art, the wing profile optimization method based on the genetic algorithm and the numerical simulation provided by the invention has the following beneficial effects that:
1. by means of a high-order Bezier curve, the order is greater than or equal to 4, the molded line which is more sensitive to the coordinate change of the control point can be obtained, and therefore the requirement for fine adjustment and optimization of the molded line is met;
2. the method comprises the steps that a Bezier curve is adopted to describe the upper surface and the lower surface of an airfoil profile, therefore, leading edge points and tail edge points of the airfoil profile are two end points of an upper surface profile line and a lower surface profile line, the abscissa of a control point closest to the leading edge point in the control points of the upper surface and the lower surface is selected to be the same as the leading edge point to realize smooth transition of the leading edge of the airfoil profile, the defect that the leading edge is designed to be in a circular arc shape or not smooth and continuous in the leading edge in the existing airfoil profile is overcome, and the optimization range of the shape design of the leading edge of the airfoil;
3. the coordinates and the attack angle of the control point (without the leading edge point and the trailing edge point) are simultaneously used as optimization variables, so that the influence of the molded line and the attack angle on the objective function can be simultaneously considered, and a better design scheme is obtained;
4. the genetic algorithm is adopted to screen the optimal airfoil profile and the attack angle in the objective function value, so that the coordinate and the attack angle corresponding to the screened airfoil profile can be selected, crossed and/or varied to obtain the optimized airfoil profile, and the objective function can be iteratively calculated on the optimized airfoil profile again, so that the airfoil profile with the more excellent objective function value and the corresponding attack angle thereof can be obtained;
5. by eliminating unreasonable wing profiles such as negative thickness or zero thickness and the like in the generated wing profiles, the calculation amount in the optimization process is reduced, and the optimization efficiency and the rationality of the optimization result are improved.
Drawings
FIG. 1 schematically illustrates a step diagram of a method of wing profile optimization based on genetic algorithms and numerical simulations according to an embodiment of the present disclosure;
FIG. 2 schematically illustrates an airfoil profile parameterization according to an embodiment of the present disclosure;
fig. 3 schematically illustrates reynolds number Re 3 × 10 according to an embodiment of the disclosure6The profile line schematic diagram of the time-optimized airfoil profile;
fig. 4 schematically illustrates reynolds number Re of 3 × 10 according to an embodiment of the disclosure6The lift-drag characteristic diagram of the airfoil profile and several common airfoil profiles is optimized;
fig. 5 schematically illustrates reynolds number Re 3 × 10 according to an embodiment of the disclosure5The profile line schematic diagram of the time-optimized airfoil profile;
fig. 6 schematically illustrates reynolds number Re 3 × 10 according to an embodiment of the disclosure5And the lift-drag characteristic diagram of the airfoil profile and several common airfoil profiles is optimized.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1, the present invention provides a method for optimizing a wing profile based on genetic algorithm and numerical simulation, the method including steps S1 to S4.
S1, parameterizing the profiles of the upper surface and the lower surface of the airfoil respectively by adopting a high-order Bezier curve so that the profiles of the upper surface and the lower surface of the airfoil are controlled by a plurality of control points respectively, wherein the order of the Bezier curve is greater than or equal to 4;
in the embodiment of the disclosure, the parameterized description formula of the profile of the upper surface or the lower surface of the airfoil is as follows:
the number n is the order of the upper surface molded line or the lower surface molded line of the airfoil, and the orders of the upper surface molded line and the lower surface molded line can be equal or unequal; i is a control point, BiFor the coordinates corresponding to the ith control point, t ∈ [0, 1 ]]B (t) is the coordinate of the molded line, n is more than or equal to 4, and a plurality of different t values can be selected to generate points on a plurality of molded lines.
The airfoil leading edge point is O, the coordinates are (0, 0), the unit chord length is taken, the airfoil trailing edge point is E, the coordinates are (1, 0), the upper surface of the airfoil is a p-order Bezier curve composed of control points O, U1, U2, …, Ui, …, Up-1 and E, the lower surface of the airfoil is a q-order Bezier curve composed of control points O, D1, D2, …, Di, …, Dq-1 and E, n is p when the upper surface linear type is described, and n is q when the lower surface linear type is described.
For example, as shown in fig. 2, the upper surface of the airfoil is a 5 th order bezier curve fit controlled by six control points O, U1, U2, U3, U4, E, the lower surface of the airfoil is a4 th order bezier curve controlled by five control points O, D1, D2, D3, E, and the intersection of the two is a leading edge point O (0, 0) and a trailing edge point E (1, 0).
Since the bezier curve is tangent to the control line at the origin, the abscissa of the control point closest to the leading point of the control points of the upper and lower surfaces is chosen to be the same as the leading point, i.e. the abscissas of control points U1 and D1 are chosen to be the same as the abscissa of leading point O, i.e. Xo ═ XU1＝XD1The molded lines of the upper surface and the lower surface of the airfoil are smooth and continuous at the front edge point, so that the smooth transition of the front edge of the airfoil is ensured, and the shape of the generated front edge is not limited to the arc shape.
The generation of Bezier curve is closely related to the coordinates of control points, the order of control points is restricted to ensure the reasonability of airfoil shape, and the abscissa of the latter control point is larger than that of the former control pointI.e. Xo < XU1＜...＜XUi＜...＜XE，Xo＜XD1＜...＜XDi＜...＜XE。
S2, generating coordinates and corresponding attack angles of a plurality of groups of control points, and further obtaining a plurality of wing profiles and corresponding attack angles;
in the present application, the coordinates and the angle of attack of the control points of the airfoil profile are generated according to one of a factorial test, a full factor test, a latin hypercube, an orthogonal test or a random generation method. For the embodiment, the control point coordinates and the attack angle of the airfoil profile are generated by a random generation method.
In order to better control the generation of the airfoil profile line, the coordinates and the attack angle of each control point (without leading edge point and trailing edge point) are selected as optimization variables X, namely:
X＝(U1，U1，U3，U4，D1，D2，D3，α.....)
in order to ensure that each optimization variable has a larger optimization range, for the airfoil with unit chord length, the airfoil is limited to be positioned in a square with the length of 1 and the heights of the upper surface and the lower surface of the airfoil of 0.5 respectively, and the ordinate of any point on the airfoil profile line needs to be between-0.5 and 0.5, so that the abscissa range of each point on the airfoil profile line is 0 to 1, and the ordinate range is-0.5 to 0.5.
S3, obtaining objective function values of the airfoils under the corresponding attack angles through numerical simulation;
unreasonable wing profiles with zero thickness or negative thickness can be generated in the optimization process, and the wing profiles can be removed through programming. For example, the coordinates of each point on the airfoil profile line can be read through a program, unreasonable airfoil profile lines such as negative thickness and zero thickness can be eliminated through judgment of geometric relations, and reasonable airfoil profile lines are reserved for further processing.
According to the embodiment of the disclosure, firstly, the airfoil profile line coordinate is obtained, the airfoil profile line coordinate is imported into preprocessing software, automatic division of grids is realized through a script file, then, automatic setting of calculation conditions (including an attack angle) and export of an objective function value are realized through a script macro file of the numerical simulation software, and the objective function value of the airfoil is obtained.
According to different application situations, the objective function may be one or more combination of a lift-drag ratio function, a lift coefficient function or a drag coefficient function, and in the embodiment of the present disclosure, the objective function is a lift-drag ratio function, and the expression is:
wherein, ClAnd CdRespectively, the lift coefficient and the drag coefficient of the airfoil profile.
In the embodiment of the disclosure, during numerical simulation, a turbulence model is selected as an SST k-omega model, a working medium is calculated to be incompressible air, a SIMPLE algorithm is adopted to couple a speed field and a pressure field, discrete formats are both second-order windward, the conditions of an inlet and an outlet are set as a speed inlet and a free outflow, and all convergence residual errors are set as 10-8。
S4, sequencing the objective function values by adopting a genetic algorithm, taking the airfoils and the attack angles corresponding to the objective function values meeting preset rules in the objective function values as target airfoils and target attack angles, selecting, intersecting and/or varying the coordinates of control points and the target attack angles corresponding to the target airfoils to obtain an optimized airfoil set, repeatedly executing S3 and S4 on the optimized airfoil set until the objective function values reach optimization termination conditions, and outputting the profile line coordinates and the corresponding attack angles of the optimized airfoils.
In the embodiment of the disclosure, the objective function values are sorted according to fitness by using a genetic algorithm, and part of the airfoil profiles and the corresponding attack angles which meet the conditions are selected as the objective airfoil profiles and the objective attack angles which need to be subsequently processed. And (3) selecting, intersecting and/or mutating the coordinates and the target attack angle of the control points corresponding to the sorted and screened target airfoils by using a genetic algorithm to obtain a better optimized airfoil set, wherein the airfoil set is finally optimized if the target function value of the optimized airfoil set meets a termination condition, and the operation in the steps S3 and S4 is continuously repeated to perform numerical simulation if the target function value of the optimized airfoil set does not meet the termination condition, so that the genetic algorithm is processed again until the optimization termination condition is reached.
In the embodiment of the disclosure, a multi-island genetic algorithm is adopted for solving, and the parameters of the multi-island genetic algorithm are set as follows: the number of the islands is 4, the population number of each island is 30, the iteration algebra is 20, the migration is carried out at the probability of 0.05 every 5 generations, and the cross probability and the mutation probability are 0.8 and 0.1 respectively.
The optimization method in the application is particularly suitable for the Reynolds number of 105～108And (4) optimizing the airfoil under the condition. The method is adopted for the embodiment of the disclosure, and the Reynolds numbers are respectively 3 multiplied by 105And 3X 106The airfoil profile is optimized.
FIG. 3 shows Reynolds number 3X 10 obtained by the method of the present application6And optimizing the obtained airfoil profile. FIG. 4 shows Reynolds number of 3X 106In time, the lift-drag characteristic curve graph of the obtained wing profile and several common wing profiles is optimized. As can be seen, the maximum lift-drag ratio of the optimized airfoil of the application appears at the attack angle position of 6.05 degrees, and the maximum lift-drag ratio is 79.4. In contrast, the maximum lift-drag ratios of several conventional airfoils, such as c72, CLARKY, NACA4412, occur at 4 °, 8 °, and 7 ° angles of attack, respectively, and are 75.0, 73.5, and 72.9, respectively. Compared with a plurality of common airfoils, the optimized airfoil has higher lift-drag ratio in the range of attack angles of 3-10 degrees, and the performance of the airfoil obtained by optimization through the method is better.
FIG. 5 shows Reynolds number 3X 10 obtained by the method of the present application5And optimizing the obtained airfoil profile. FIG. 6 shows Reynolds number of 3X 105In the time, the lift-drag characteristic curve diagrams of the airfoil profile optimized by the application and several common airfoil profiles are shown in the figure, the maximum lift-drag ratio of the optimized airfoil profile of the application is 52.22 when the attack angle AOA is 7.25 degrees, the maximum lift-drag ratio of the optimized airfoil profile of the application is 48.92, 47.2 and 46.72 when the c72, CLARKY and NACA4412 airfoil profiles are respectively 5 degrees, 7 degrees and 8 degrees, and the optimized airfoil profile has the lift-drag ratio higher than that of the common airfoil profiles in the range of the attack angles of 5 degrees to 12 degrees.
Analysis of the two specific embodiments shows that the optimized airfoil profile with the high lift-drag ratio can be obtained by the method, and the optimized airfoil profile has the high lift-drag ratio in a large attack angle range, so that the airfoil profile obtained by optimization by the method has better performance.
In summary, according to the airfoil optimization method based on the genetic algorithm and the numerical simulation, the profile of the airfoil is parameterized by the high-order bessel function, the initial airfoil is not required to be designed, so that the optimization range of the profile of the airfoil is wider, the high-order bessel function is more suitable for fine adjustment of the profile, the free design of the leading edge of the airfoil can be realized without being limited to a circular arc, the coordinate and the attack angle of a control point are considered when the airfoil is optimized, and the control point coordinate and the attack angle of the airfoil are optimized by the genetic algorithm, so that the profile of the airfoil with a better objective function value and the corresponding attack angle can be obtained.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A method for optimizing wing profiles based on genetic algorithm and numerical simulation, which is characterized by comprising the following steps:
s1, parameterizing the profiles of the upper surface and the lower surface of the airfoil respectively by adopting a high-order Bezier curve so that the profiles of the upper surface and the lower surface of the airfoil are controlled by a plurality of control points respectively, wherein the order of the Bezier curve is greater than or equal to 4;
s2, generating coordinates and corresponding attack angles of a plurality of groups of control points, and further obtaining a plurality of wing profiles and corresponding attack angles;
s3, obtaining objective function values of the airfoils under the corresponding attack angles through numerical simulation;
s4, sequencing the objective function values by adopting a genetic algorithm, taking the airfoils and the attack angles corresponding to the objective function values meeting preset rules in the objective function values as target airfoils and target attack angles, selecting, intersecting and/or varying the coordinates of control points and the target attack angles corresponding to the target airfoils to obtain an optimized airfoil set, repeatedly executing S3 and S4 on the optimized airfoil set until the objective function values reach optimization termination conditions, and outputting the profile line coordinates and the corresponding attack angles of the optimized airfoils.
2. The optimization method of claim 1, wherein the numerical simulation in step S3 further comprises: and eliminating the wing profiles which do not meet the preset conditions in the plurality of wing profiles.
3. The optimization method according to claim 2, wherein the numerical simulation in step S3 specifically includes: and obtaining coordinates of each point on the airfoil profile line, and removing airfoils with negative thickness and zero thickness.
4. The optimization method according to claim 1, wherein the step S4 of sorting the objective function values by using a genetic algorithm specifically comprises: and sequencing the objective function values according to the fitness by adopting a genetic algorithm.
5. The optimization method according to claim 1, wherein the parameterized description formula of the profile of the upper surface or the lower surface of the airfoil is as follows:
the number n is the order of the upper surface molded line or the lower surface molded line of the airfoil, and the orders of the upper surface molded line and the lower surface molded line can be equal or unequal; i is a control point, BiFor the coordinates corresponding to the ith control point, t ∈ [0, 1 ]]And B (t) is the coordinate of the profile.
6. The optimization method according to claim 1, wherein two ends where the profile lines of the upper surface and the lower surface of the airfoil intersect are a leading edge point and a trailing edge point respectively, and the abscissa of the control point closest to the leading edge point in the control points of the upper surface and the lower surface is selected to be the same as the leading edge point so as to realize smooth and continuous leading edges.
7. The optimization method according to claim 1, wherein the step S2 specifically includes: generating the coordinates and the corresponding attack angles of a plurality of groups of control points in a preset range according to one of a factorial test, a full factor test, a Latin hypercube, an orthogonal test or a random generation method, and further obtaining a plurality of airfoils and corresponding attack angles.
8. The optimization method of claim 1, wherein the objective function values comprise one or more combinations of lift-to-drag ratios, lift coefficients, or drag coefficients.
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