CN107644136A - Aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface - Google Patents
Aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface Download PDFInfo
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Abstract
The invention discloses aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface, comprise the following steps：Using wind mill airfoil Generalized Functional integrated presentation and B-spline curves, aerofoil with blunt tail edge molded line parametric control equation group is formed；Calibration method is sat using aerofoil profile leading edge specified location is translated, boss is added in suction surface specified location, to simulate the coarse situation of blade surface；Using the shape function coefficient of aerofoil profile, B-spline curves control parameter and blunt trailing edge thickness and its on the upside of mean camber line distribution ratio as design variable, coarse aerofoil with blunt tail edge molded line optimization, aerofoil with blunt tail edge Optimization Design under the conditions of proposition blade surface is coarse are carried out using particle cluster algorithm coupling XFOIL softwares；For coarse S822R aerofoil profiles (R is coarse) optimization obtains the chord length of trailing edge thickness 2.13%, the blunt trailing edge of thickness distribution ratio 0: 1 is retrofited, liter, resistance coefficient and the lift-drag ratio before and after aerofoil optimization are studied using CFD approach.The aeroperformance of aerofoil with blunt tail edge significantly improves under the conditions of the pneumatic equipment bladess rough surface of the present invention, preferably improves wind energy utilization of the wind energy conversion system under harsh environments.
Description
Technical field
The invention belongs to Airfoil Optimization and remodeling technical field, more particularly, to one kind using Fluid Mechanics Computation with
Aerofoil with blunt tail edge Optimization Design under the conditions of the pneumatic equipment bladess rough surface of optimization algorithm.
Background technology
Wind energy conversion system is operated in the area for the bad environments such as high and cold, coastal, dust storm is frequent more, and its blade surface often adheres to
The dirts such as dust, insect, sleet.Dirt increases the roughness of blade surface, and causes the annual electricity generating capacity of wind energy conversion system to drop significantly
It is low.The design of the aerofoil profile low to roughness sensitiveness is carried out, attachment dirt is mitigated or eliminated to be influenceed on Airfoil Aerodynamic Performance
Effective solution, and then ensure Effec-tive Function of the wind energy conversion system under the conditions of blade surface is coarse.
The direct optimization design of aerofoil profile can solve the problems, such as to be difficult to give appropriate goal pressure and rate distribution very well, but need
Molded line Parameter Expression is carried out to aerofoil profile.Aerofoil profile molded line parametric method mainly has characteristic parameter description, orthogonal basis function, class
Type/shape function conversion and non-homogeneous B spline curve and Generalized Functional integrated presentation etc..Domestic and foreign scholars Ribeiro,
Djavareshkian, Liu, Sanaye, jade pendant Asia equality people construct aerofoil profile ginseng using B é zier functions, Hicks-Henne functions etc.
Numberization expression formula, and set using the optimization of the progress aerofoil profile such as genetic algorithm combination XFOIL softwares and artificial nerve network model
Meter.It is old enter et al. a kind of forms of characterization optimization new aerofoil is integrated based on aerofoil profile Generalized Functional, find compared to other aerofoil profile types
Line expression, it is more easily optimized and extended to form new aerofoil profile molded line, but can not control medium and big thickness aerofoil profile very well
Molded line at trailing edge.Therefore, it is old enter et al. again propose be combined using aerofoil profile Generalized Functional integrated presentation with B-spline curves, enter
The optimization design of row wind mill airfoil molded line.
Blunt trailing edge Transform Type design can also be effectively improved the aeroperformance of rough surface aerofoil profile.Baker et al. experimental studies
The different airfoil profiles symmetrically thickeied, it is found that appropriateness increase trailing edge thickness can increase lift-drag ratio and reduce the coarse susceptibility of leading edge.Yang Rui
Et al. thin, aerofoil with blunt tail edge aeroperformance is simulated using CFD approach, as a result show that aerofoil with blunt tail edge increases maximum lift,
Reduce influence of the leading edge pollution to lift efficiency.
Although researcher has carried out numerous studies to the optimization design of aerofoil profile and blunt trailing edge remodeling for many years, and optimization is set
Meter and blunt trailing edge remodeling can improve the aeroperformance of rough surface aerofoil profile, but be wrapped in aerofoil with blunt tail edge molded line Parameter Expression
The influence of distribution ratio and carry out the research of optimization design and be not directed to containing blunt trailing edge thickness and its on the upside of mean camber line.However, grind
Study carefully blade surface it is coarse under the conditions of the optimization of aerofoil with blunt tail edge have great importance for vane design of wind turbines.
The content of the invention
Aerofoil with blunt tail edge optimization is set under the conditions of the problem to be solved in the present invention is to provide a kind of pneumatic equipment bladess rough surface
Meter method, this method can use wind mill airfoil Generalized Functional integrated presentation and B-spline curves, form aerofoil with blunt tail edge molded line ginseng
Numberization governing equation group；Calibration method is sat using aerofoil profile leading edge specified location is translated, boss is added in suction surface specified location,
To simulate the coarse situation of blade surface；With the shape function coefficient of aerofoil profile, B-spline curves control parameter and blunt trailing edge thickness
Distribution ratio is design variable on the upside of mean camber line with it, and coupling XFOIL softwares using particle cluster algorithm carries out the coarse blunt trailing edge wing
Type molded line optimizes, and proposes coarse aerofoil with blunt tail edge Optimization Design, realizes blunt trailing edge under the conditions of pneumatic equipment bladess rough surface
The raising of Airfoil Optimization accuracy.
In order to solve the above technical problems, the technical solution adopted by the present invention is：A kind of pneumatic equipment bladess rough surface condition
Lower aerofoil with blunt tail edge Optimization Design, it is characterised in that：Comprise the following steps：
Step (1), rough surface aerofoil with blunt tail edge molded line expression：Utilize aerofoil profile Generalized Functional integrated presentation and B samples
Bar curve, establish aerofoil with blunt tail edge molded line parametric control equation group；Before the top airfoil of aerofoil profile is away from leading edge 0.4c (c is chord length)
With lower aerofoil away from the molded line before leading edge 0.5c, expressed using the integrated forms of characterization of aerofoil profile Generalized Functional, i.e. the Duan Yi
Type profile coordinate is：
In formula, x is aerofoil profile abscissa, and y is aerofoil profile ordinate, and a is 1/4 aerofoil profile chord length, and θ is argument, and ρ (θ) is aerofoil profile
Shape function, use polynomial expression for：
ρ (θ)=C0+C1θ+C2θ2+…+Ckθk, k=1,2,3 ..., n (2)
In formula, C0, C1, C2..., CkFor shape function coefficient, C0=1；
Upper and lower aerofoil is indicated away from the profile coordinate after leading edge 0.4c, 0.5c using B-spline curves；To make the wing
Type Generalized Functional integrated presentation has continuous, smooth characteristic with B-spline curves at binding site, using B-spline Curve
Matrix form represents coarse aerofoil profile profile coordinate, is：
In formula, P0、P1、P2、P3For the control variable of molded line after top airfoil 0.4c, P '0、P′1、P′2、P′3For lower aerofoil
The control variable of molded line after 0.5c；
Molded line P after top airfoil 0.4c0,3(t) point P0,3(0) upper limb formed by aerofoil profile Generalized Functional integrated presentation
Last coordinate points, P in the molded line of face0,3(1) aerofoil with blunt tail edge top airfoil molded line terminal (1, h × k) is passed through, wherein h is blunt tail
Edge thickness, k are the ratio of top airfoil trailing edge thickness and blunt trailing edge thickness；By formula (3) can inverse go out p0And p3, then upper limb
The control variable of molded line only has p after the 0.4c of face1And p2；Similarly, the control variable of molded line only has P ' after lower aerofoil 0.5c1With
P′2；Molded line after coarse aerofoil profile top airfoil 0.4c, lower aerofoil 0.5c is embodied as：
Calibration method is sat using aerofoil profile leading edge specified location is translated, a high h, wide l are added in suction surface specified location
Boss, as shown in figure 1, translational coordination expression formula is：
In formula, (x, y) is the coordinate at former aerofoil profile molded line control point, and (x ', y ') is that aerofoil profile adds same control after boss
The coordinate of point, θ is shift angle, and：
In formula, (x1, y1)、(x2, y2) start for former aerofoil profile molded line translating sections, the coordinate of end position, and：
Formula (1), (4) and (5) is the rough surface aerofoil with blunt tail edge molded line parametric control equation group that the present invention establishes；
Step (2), rough surface aerofoil with blunt tail edge optimization design：Using maximum lift coefficient and maximum lift-drag ratio as target
Function, choose the 2nd to the 12nd term coefficient, B-spline curves control parameter and blunt trailing edge thickness in the shape function ρ (θ) of aerofoil profile
Distribution ratio is design variable on the upside of mean camber line with it, is coupled using particle swarm optimization algorithm with XFOIL softwares, and it is thick to carry out surface
Rough aerofoil with blunt tail edge molded line optimization, Fig. 2 are optimization design flow chart, and rough surface fine stern edge aerofoil profile obtains the blunt trailing edge wing with optimization
The molded line of type is as shown in Figure 3；
Step (3), the analysis of rough surface aerofoil with blunt tail edge aeroperformance：It is coarse using FLUENT software numerical value gauging surfaces
The front and rear aeroperformance of the blunt trailing edge optimization of aerofoil profile is as shown in Figure 4, Figure 5 and Figure 6；
Step (4), aerofoil with blunt tail edge is excellent under the conditions of realizing pneumatic equipment bladess rough surface to step (3) by step (1)
Change design.
Due to using above-mentioned technical proposal, compared with the conventional method, under the conditions of pneumatic equipment bladess rough surface of the invention
Aerofoil with blunt tail edge Optimization Design, using wind mill airfoil Generalized Functional integrated presentation and B-spline curves, blunt trailing edge can be formed
Aerofoil profile molded line parametric control equation group；Calibration method addition boss is sat using aerofoil profile leading edge specified location is translated, table can be built
The coarse aerofoil with blunt tail edge molded line in face；With the shape function coefficient of aerofoil profile, B-spline curves control parameter and blunt trailing edge thickness and its
Distribution ratio is design variable on the upside of mean camber line, couples XFOIL softwares using particle cluster algorithm, the blunt trailing edge of rough surface can be achieved
Airfoil Optimization；The aerofoil with blunt tail edge that the optimization obtains compared to protocone trailing edge aerofoil profile, its aeroperformance be improved significantly,
So as to improve the wind energy utilization of wind energy conversion system.The inventive method solves the problems, such as described, improves pneumatic equipment bladess surface
The accuracy of aerofoil with blunt tail edge optimization design under the conditions of coarse, technology is provided to operate in bad working environments lower blade Airfoil Design
Support and important references.
Brief description of the drawings
The present invention is specifically described below with reference to accompanying drawing and with reference to example, advantages of the present invention and implementation will
More obvious, wherein content is only used for explanation of the present invention shown in accompanying drawing, without forming to the present invention in all senses
On limitation, in the accompanying drawings：
Fig. 1 is that wind mill airfoil molded line of the present invention forms boss schematic diagram；
Fig. 2 is aerofoil with blunt tail edge optimization design flow chart under the conditions of pneumatic equipment bladess rough surface of the present invention；
Fig. 3 is the front and rear molded lines of the blunt trailing edge optimization of S822R aerofoil profiles of the present invention；
Fig. 4 is S822R of the present invention and S822RBT aerofoil profiles lift coefficient figure；
Fig. 5 is S822R of the present invention and S822RBT aerofoil profiles resistance coefficient figure；
Fig. 6 is S822R of the present invention and S822RBT aerofoil profiles lift-drag ratio figure.
Embodiment
The present invention is further discussed below with reference to embodiment and its accompanying drawing：
Aerofoil with blunt tail edge Optimization Design is based on following design under the conditions of a kind of pneumatic equipment bladess rough surface of the present invention
Thought：
1st, using wind mill airfoil Generalized Functional integrated presentation and B-spline curves, and by translating aerofoil profile leading edge specific bit
Coordinate addition boss is put, rough surface aerofoil with blunt tail edge molded line parametric control equation group is formed, to prevent aerofoil profile Generalized Functional
Integrated presentation can not be controlled trailing edge shape well；
2nd, with the shape function coefficient of aerofoil profile, B-spline curves control parameter and blunt trailing edge thickness and its on mean camber line
Side distribution ratio is design variable, establishes rough surface aerofoil with blunt tail edge mathematical optimization models, to prevent in terms of not and blunt trailing edge parameter
Cause the accuracy of aerofoil optimization model；
3rd, XFOIL softwares are coupled using particle cluster algorithm, realizes design variable meter and blunt trailing edge thickness and its in mean camber line
The rough surface aerofoil with blunt tail edge molded line optimization of upside distribution ratio, to prevent the blunt trailing edge wing under the conditions of pneumatic equipment bladess rough surface
The accuracy of type optimization design is relatively low.
Solves the technical problem, the present invention represents roughness from aerofoil with blunt tail edge molded line Parameter Expression structure, boss
Innovative design has been carried out with optimization design etc.：
1st, rough surface aerofoil with blunt tail edge molded line expression
In the case where not changing the maximum relative thickness and its position of aerofoil profile, camber and chord length, wind mill airfoil is utilized
Generalized Functional integrated presentation and B-spline curves, and calibration method addition boss is sat by translating aerofoil profile leading edge specified location, establish
Rough surface aerofoil with blunt tail edge molded line parametric control equation group.
2nd, rough surface aerofoil with blunt tail edge optimization design
Optimization program is write by Matlab and XFOIL softwares calculate aeroperformance, carries out rough surface aerofoil with blunt tail edge
Molded line optimizes, and the optimization design of aerofoil with blunt tail edge must take into consideration following several respects problem under the conditions of pneumatic equipment bladess rough surface：
(1) while improves lift coefficient, resistance coefficient change should be smaller；
(2) exponent number of shape function should be able to make the geometry of the aerofoil profile of composition in wind mill airfoils Generalized Functional integrated presentation
Shape can be with quite well, in favor of choosing former term coefficients, B-spline curves in the shape function ρ (θ) of aerofoil profile with former aerofoil profile
Control parameter and blunt trailing edge thickness and its distribution ratio on the upside of mean camber line are design variable；
(3) controls range of variables to need necessarily to be limited, special with shape of the molded line without aerofoil profile avoided the formation of
Sign, and unnecessary iterations can be reduced；
(4) relative thickness of wind mill airfoils is unsuitable excessive or too small, and blade major power should be made to produce aerofoil profile in area
Maximum gauge is 0.12~0.25, to avoid the architectural characteristic of blade from being affected.
3rd, aeroperformance is analyzed before and after the blunt trailing edge optimization of rough surface aerofoil profile
Front and rear liter, resistance coefficient and the lift-drag ratio of the blunt trailing edge optimization of coarse aerofoil profile is calculated using FLUENT softwares.
Aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface of the present invention, including following step
Suddenly：
Step (1), rough surface aerofoil with blunt tail edge molded line expression：Utilize aerofoil profile Generalized Functional integrated presentation and B samples
Bar curve, establish aerofoil with blunt tail edge molded line parametric control equation group；Before the top airfoil of aerofoil profile is away from leading edge 0.4c (c is chord length)
With lower aerofoil away from the molded line before leading edge 0.5c, expressed using the integrated forms of characterization of aerofoil profile Generalized Functional, i.e. the Duan Yi
Type profile coordinate is：
In formula, x is aerofoil profile abscissa, and y is aerofoil profile ordinate, and a is 1/4 aerofoil profile chord length, and θ is argument, and ρ (θ) is aerofoil profile
Shape function, use polynomial expression for：
ρ (θ)=C0+C1θ+C2θ2+…+Ckθk, k=1,2,3 ..., n (2)
In formula, C0, C1, C2..., CkFor shape function coefficient, C0=1；
Upper and lower aerofoil is indicated away from the profile coordinate after leading edge 0.4c, 0.5c using B-spline curves；To make the wing
Type Generalized Functional integrated presentation has continuous, smooth characteristic with B-spline curves at binding site, using B-spline Curve
Matrix form represents coarse aerofoil profile profile coordinate, is：
In formula, P0、P1、P2、P3For the control variable of molded line after top airfoil 0.4c, P '0、P′1、P′2、P′3For lower aerofoil
The control variable of molded line after 0.5c；
Molded line P after top airfoil 0.4c0,3(t) point P0,3(0) upper limb formed by aerofoil profile Generalized Functional integrated presentation
Last coordinate points, P in the molded line of face0,3(1) aerofoil with blunt tail edge top airfoil molded line terminal (1, h × k) is passed through, wherein h is blunt tail
Edge thickness, k are the ratio of top airfoil trailing edge thickness and blunt trailing edge thickness；By formula (3) can inverse go out p0And p3, then upper limb
The control variable of molded line only has p after the 0.4c of face1And p2；Similarly, the control variable of molded line only has P ' after lower aerofoil 0.5c1With
P′2；Molded line after coarse aerofoil profile top airfoil 0.4c, lower aerofoil 0.5c is embodied as：
Calibration method is sat using aerofoil profile leading edge specified location is translated, a high h, wide l are added in suction surface specified location
Boss, as shown in figure 1, translational coordination expression formula is：
In formula, (x, y) is the coordinate at former aerofoil profile molded line control point, and (x ', y ') is that aerofoil profile adds same control after boss
The coordinate of point, θ is shift angle, and：
In formula, (x1, y1)、(x2, y2) start for former aerofoil profile molded line translating sections, the coordinate of end position, and：
Formula (1), (4) and (5) is the rough surface aerofoil with blunt tail edge molded line parametric control equation group that the present invention establishes；
Step (2), rough surface aerofoil with blunt tail edge optimization design：Using maximum lift coefficient and maximum lift-drag ratio as target
Function, choose aerofoil profile shape function coefficient, B-spline curves control parameter and blunt trailing edge thickness and its on the upside of mean camber line point
Match as design variable, coupled using particle swarm optimization algorithm with XFOIL softwares, carry out rough surface aerofoil with blunt tail edge molded line
Optimization design；
Preferably control the molded line of aerofoil with blunt tail edge, preceding 11 term coefficient of selected shape function governing equation, B-spline curves
Control parameter and blunt trailing edge thickness and its distribution ratio are as optimization design variable：
X=(C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, h, k, P1, P2, P1', P2′) (8)
In aerofoil with blunt tail edge optimization process, control range of variables need to be limited, does not have the wing with the molded line avoided the formation of
The shape facility of type, and unnecessary iterations can be reduced, then optimized variable edge-restraint condition is：
Xmin≤X≤Xmax (9)
Most of pneumatic equipment bladess produce area in its major power and are generally 0.12~0.25 using the maximum gauge of aerofoil profile,
Again because influence of the relative thickness to blade construction characteristic of aerofoil profile can not be ignored, then the constraints of profile thickness is：
0.12≤rt≤0.25 (10)
To make aerofoil profile that there is good aeroperformance under wind energy conversion system accidental conditions, the maximum lift system of aerofoil profile is selected
Number and maximum lift-drag ratio are as object function, i.e.,：
F (x)=max (CL/CD) (11)
In formula：CL、CDThe respectively liter of aerofoil profile, resistance coefficient；
Particle swarm optimization algorithm has the advantages that realization is easy, precision is high, convergence is fast, and the efficiency of solving practical problems is very
Height, the algorithm is coupled with XFOIL softwares, carry out the optimization of rough surface aerofoil with blunt tail edge molded line, Fig. 2 is optimization design flow
Figure, the molded line that rough surface fine stern edge aerofoil profile obtains aerofoil with blunt tail edge with optimization are as shown in Figure 3；
Step (3), the analysis of rough surface aerofoil with blunt tail edge aeroperformance：Utilize the coarse aerofoil profile of FLUENT software gauging surfaces
The front and rear aeroperformance of blunt trailing edge optimization is as shown in Figure 4, Figure 5 and Figure 6；
Step (4), aerofoil with blunt tail edge is excellent under the conditions of realizing pneumatic equipment bladess rough surface to step (3) by step (1)
Change design.
The present invention does not address part and is applied to prior art.
Embodiment：
1st, S822 aerofoil profiles are widely used in the major power generation area of pneumatic equipment bladess, have at 39.2%c most
Big relative thickness 16%, and the relative camber 1.92% of maximum at 59.5%c；A high h is added at top airfoil 2%c
=0.003c, wide l=3mm boss.
2nd, optimization primary condition is：It is 5 × 10 to take reynolds number Re5, Mach number Ma is 0.11, and population scale 20 is maximum
Evolutionary generation was 300 generations, Studying factors S1、S2For 0.5, dimension 20；To enable the existing stronger search of algorithm routine
Power, there is preferable convergence again, and inertia weight w reduces adaptive adjustment formula using linear：
In formula, wmaxAnd wminThe maximum and minimum value of inertia weight are represented, 0.9 and 0.4 is chosen according to design experiences；t
And tmaxRepresent the evolutionary generation currently with maximum.
3rd, aerofoil with blunt tail edge optimization and pneumatic performance evaluation
Using optimization method of the present invention, optimization program is write by Matlab and XFOIL softwares calculate aeroperformance, is carried out
Blunt trailing edge optimization when the intermediate gauge Special Airfoil of Wind Turbine S822 of National Renewable Energy lab design is coarse is set
Meter, and carry out aeroperformance calculating using FLUENT softwares.
S822R aerofoil profiles of aerofoil with blunt tail edge optimization design and its excellent under the conditions of pneumatic equipment bladess rough surface of the present invention
The shape for changing aerofoil profile S822RBT is as shown in Figure 3.It is risen, resistance coefficient and lift-drag ratio carry out analysis shows：(1) the S822RBT wings
The trailing edge thickness of type is 2.13%c, and upper and lower aerofoil trailing edge thickness distribution ratio is 0: 1.(2) the lift system of S822RBT aerofoil profiles
Number is before 14.23 ° of angles of attack and after 16 ° of angles of attack apparently higher than S822R aerofoil profiles；Resistance coefficient before 8.19 ° of angles of attack with
S822R aerofoil profiles are very close, and S812R aerofoil profiles are higher than after 8.19 ° of angles of attack；The stall angle of S822R and S822RBT aerofoil profiles is equal
For 14.23 °.(3) lift-drag ratio of S822RBT aerofoil profiles when the angle of attack is less than 8.19 ° apparently higher than S822R aerofoil profiles；8.19 °~16 °
In range of angles of attack, less than S822R aerofoil profiles；After 16 ° of angles of attack, it is sufficiently close to S822R aerofoil profiles；S822RBT aerofoil profiles most rise higher
Resistance ratio is higher than S822R aerofoil profiles.
Claims (4)
- A kind of 1. aerofoil with blunt tail edge Optimization Design under the conditions of pneumatic equipment bladess rough surface, it is characterised in that：Including following Step：Step (1), rough surface aerofoil with blunt tail edge molded line expression：It is bent using aerofoil profile Generalized Functional integrated presentation and B-spline Line, establish aerofoil with blunt tail edge molded line parametric control equation group；The top airfoil of aerofoil profile away from before leading edge 0.4c (c is chord length) and under Aerofoil is expressed, i.e. this section of aerofoil profile type away from the molded line before leading edge 0.5c using the integrated forms of characterization of aerofoil profile Generalized Functional Line coordinates is：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>=</mo> <mi>a</mi> <mrow> <mo>(</mo> <mi>&rho;</mi> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> <mo>/</mo> <mi>&rho;</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>)</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <mi>a</mi> <mrow> <mo>(</mo> <mi>&rho;</mi> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> <mo>/</mo> <mi>&rho;</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>)</mo> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&theta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>In formula, x is aerofoil profile abscissa, and y is aerofoil profile ordinate, and a is 1/4 aerofoil profile chord length, and θ is argument, and ρ (θ) is the shape of aerofoil profile Function, use polynomial expression for：ρ (θ)=C0+C1θ+C2θ2+…+Ckθk, k=1,2,3 ..., n (2)In formula, C0, C1, C2..., CkFor shape function coefficient, C0=1；Upper and lower aerofoil is indicated away from the profile coordinate after leading edge 0.4c, 0.5c using B-spline curves；To make aerofoil profile wide Adopted functional integration expression has continuous, smooth characteristic with B-spline curves at binding site, using B-spline Curve matrix Form represents coarse aerofoil profile profile coordinate, is：<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>t</mi> <mo>,</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>,</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> <mo>&rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>P</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>P</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>P</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>P</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>3</mn> </mrow> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>t</mi> <mo>,</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>,</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> <mo>&rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msup> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>&prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>P</mi> <mn>3</mn> </msub> <mo>&prime;</mo> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>In formula, P0、P1、P2、P3For the control variable of molded line after top airfoil 0.4c, P '0、P′1、P′2、P′3For lower aerofoil 0.5c it The control variable of molded line afterwards；Molded line P after top airfoil 0.4c0,3(t) point P0,3(0) the top airfoil type formed by aerofoil profile Generalized Functional integrated presentation Last coordinate points, P in line0,3(1) aerofoil with blunt tail edge top airfoil molded line terminal (1, h × k) is passed through, wherein h is that blunt trailing edge is thick Degree, k are the ratio of top airfoil trailing edge thickness and blunt trailing edge thickness；By formula (3) can inverse go out p0And p3, then top airfoil The control variable of molded line only has p after 0.4c1And p2；Similarly, the control variable of molded line only has P ' after lower aerofoil 0.5c1And P ′2；Molded line after coarse aerofoil profile top airfoil 0.4c, lower aerofoil 0.5c is embodied as：<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>t</mi> <mo>,</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>,</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> <mo>&rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>6</mn> <mi>P</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>-</mo> <mn>4</mn> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>P</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>P</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>P</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>6</mn> <mi>P</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mn>4</mn> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>P</mi> <mrow> <mn>0</mn> <mo>,</mo> <mn>3</mn> </mrow> <mo>&prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>&lsqb;</mo> <mn>1</mn> <mo>,</mo> <mi>t</mi> <mo>,</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> <mo>,</mo> <msup> <mi>t</mi> <mn>3</mn> </msup> <mo>&rsqb;</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>6</mn> <mi>P</mi> <msup> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mo>-</mo> <mn>4</mn> <msubsup> <mi>P</mi> <mn>1</mn> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>P</mi> <mn>2</mn> <mo>&prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>P</mi> <mn>1</mn> <mo>&prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>P</mi> <mn>2</mn> <mo>&prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>6</mn> <mi>P</mi> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>&prime;</mo> </msup> <mo>-</mo> <mn>4</mn> <msubsup> <mi>P</mi> <mn>2</mn> <mo>&prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>P</mi> <mn>1</mn> <mo>&prime;</mo> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Using translate aerofoil profile leading edge specified location sit calibration method, suction surface specified location add a high h, wide l it is convex Platform, as shown in figure 1, translational coordination expression formula is：<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>x</mi> <mo>-</mo> <mi>h</mi> <mi> </mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>y</mi> <mo>+</mo> <mi>h</mi> <mi> </mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mrow> <mo>(</mo> <mi>&theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>In formula, (x, y) is the coordinate at former aerofoil profile molded line control point, and (x ', y ') is that aerofoil profile adds same control point after boss Coordinate, θ are shift angle, and：<mrow> <mi>&theta;</mi> <mo>=</mo> <mi>a</mi> <mi>r</mi> <mi>c</mi> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>In formula, (x1, y1)、(x2, y2) start for former aerofoil profile molded line translating sections, the coordinate of end position, and：<mrow> <mi>l</mi> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Formula (1), (4) and (5) is the rough surface aerofoil with blunt tail edge molded line parametric control equation group that the present invention establishes；Step (2), rough surface aerofoil with blunt tail edge optimization design：Using maximum lift coefficient and maximum lift-drag ratio as target letter Number, choose in the shape function ρ (θ) of aerofoil profile the 2nd to the 12nd term coefficient, B-spline curves control parameter and blunt trailing edge thickness and Its distribution ratio on the upside of mean camber line is design variable, is coupled using particle swarm optimization algorithm with XFOIL softwares, carries out rough surface Aerofoil with blunt tail edge molded line optimizes, and Fig. 2 is optimization design flow chart, and rough surface fine stern edge aerofoil profile obtains aerofoil with blunt tail edge with optimization Molded line it is as shown in Figure 3；Step (3), the analysis of rough surface aerofoil with blunt tail edge aeroperformance：Utilize the coarse aerofoil profile of FLUENT software numerical value gauging surfaces The front and rear aeroperformance of blunt trailing edge optimization is as shown in Figure 4, Figure 5 and Figure 6；Step (4), realize that aerofoil with blunt tail edge optimization is set under the conditions of pneumatic equipment bladess rough surface by step (1) to step (3) Meter.
- 2. aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface according to claim 1, It is characterized in that：After the foundation of step (1) rough surface aerofoil with blunt tail edge molded line expression formula, with shape function coefficient, the B of aerofoil profile SPL control parameter and blunt trailing edge thickness and its distribution ratio on the upside of mean camber line are design variable, and it is blunt to carry out rough surface Trailing edge aerofoil profile molded line optimizes.
- 3. aerofoil with blunt tail edge optimization design side under the conditions of a kind of pneumatic equipment bladess rough surface according to claim 1 or 2 Method, it is characterised in that：The coarse aerofoil profile is optimized using particle cluster algorithm with the method that XFOIL softwares are combined and set Meter.
- 4. aerofoil with blunt tail edge Optimization Design under the conditions of a kind of pneumatic equipment bladess rough surface according to claim 3, It is characterized in that：The blunt trailing edge thickness of the S822RBT aerofoil profiles (R is coarse, and BT is blunt trailing edge) is 2.13%c, and upper and lower Aerofoil trailing edge thickness distribution ratio is 0: 1.
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| CN112541298A (en) * | 2020-11-03 | 2021-03-23 | 西安交通大学 | Turbine mechanical blade profile automatic parameterization generation method based on deep learning |
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| CN112329170B (en) * | 2020-11-04 | 2022-11-01 | 山东省科学院海洋仪器仪表研究所 | Blade airfoil section optimization design method for tidal current energy water turbine |
| CN112329170A (en) * | 2020-11-04 | 2021-02-05 | 山东省科学院海洋仪器仪表研究所 | Blade airfoil optimization design method of tidal current energy water turbine |
| CN112329359B (en) * | 2020-11-12 | 2022-07-08 | 天津工业大学 | Neural network prediction method for aerodynamic performance of wing section of wind turbine under open ice condition |
| CN112329359A (en) * | 2020-11-12 | 2021-02-05 | 天津工业大学 | Neural network prediction method for aerodynamic performance of wing section of wind turbine under open ice condition |
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