CN111898074B - Airfoil aerodynamic coefficient calculation method and system - Google Patents
Airfoil aerodynamic coefficient calculation method and system Download PDFInfo
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Abstract
The invention relates to a method and a system for calculating airfoil aerodynamic coefficients, wherein the method comprises the following steps: wind tunnel test is carried out on the wing profile according to the set wind attack angle range, and the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle of the wing profile are obtained; polynomial fitting is carried out on the wind attack angle and the lift coefficient corresponding to the wind attack angle, so that a relational expression of the wind attack angle and the lift coefficient is obtained; polynomial fitting is carried out on the wind attack angle and the resistance coefficient corresponding to the wind attack angle, so that a relational expression of the wind attack angle and the resistance coefficient is obtained; and calculating lift coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients. The invention can calculate the corresponding aerodynamic coefficients when different wind attack angles according to the formula, and quicken the acquisition time of the aerodynamic coefficients.
Description
Technical Field
The invention relates to the technical field of aerodynamics of airfoils, in particular to a method and a system for calculating aerodynamic coefficients of airfoils.
Background
The wind turbine blade is composed of a series of wing profiles with different sections, and the quality of the aerodynamic performance of the wing profiles directly influences the capability of the wind turbine blade for absorbing wind energy, thereby influencing the power generation efficiency. The pneumatic performance of the wing profile is improved, so that the power generation efficiency of the wind turbine can be effectively improved. The vortex generator can improve the aerodynamic performance of the wind turbine blade airfoil to different degrees when being arranged at the front edge of the airfoil, and has a simple structure and convenient installation, and has been studied and applied to the wind turbine airfoil in recent years.
The aerodynamics coefficient of the wing profile is changed after the vortex generator is installed at a certain position of the wing profile, test data are usually required to be obtained, the development test cost is high, and the period for obtaining the test data is long, so that the aerodynamics coefficient of the wing profile of the vortex generator installed at different positions is accurately calculated, and the method has important significance for the accuracy and the scientificity of position determination when the vortex generator is installed on an actual wind turbine blade.
Disclosure of Invention
Based on the above, the invention aims to provide a calculation method and a calculation system for airfoil aerodynamic coefficients, which can calculate the corresponding aerodynamic coefficients at different wind attack angles according to a formula, thereby accelerating the acquisition time of the aerodynamic coefficients.
In order to achieve the above object, the present invention provides the following solutions:
a method of airfoil aerodynamic coefficient calculation, the method comprising:
according to the set wind attack angle range, wind tunnel test is carried out on the wing profile, and the set number of data pairs of the wing profile are obtained, wherein the data pairs comprise the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle;
performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient;
performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient;
and calculating lift force coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift force coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients.
Optionally, a vortex generator is installed at a preset position of the airfoil; the preset position comprises a position which is 10 percent of the chord length, 20 percent of the chord length, 30 percent of the chord length or 40 percent of the chord length from the front edge of the airfoil.
Optionally, the performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient specifically includes: according to fitting formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting is performed, wherein x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 Is a first constant, a 2 Is a second constant, a 3 Is a third constant, a 4 A is a fourth constant, a 5 Is a fifth constant.
Optionally, the polynomial fitting is performed on the wind attack angle and the resistance coefficient corresponding to the wind attack angle, so as to obtain a relational expression of the wind attack angle and the resistance coefficient, which specifically includes: according to fitting formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting is performed, wherein x represents the wind angle of attack, f (x) 2 Represents the drag coefficient, a 6 A is a sixth constant, a 7 A is a seventh constant, a 8 Is an eighth constant, a 9 A is a ninth constant, a 10 Is the tenth constant.
Optionally, the wind attack angle ranges from-4 ° to 22 °.
Optionally, the airfoil has a chord length of 300mm.
Optionally, the Reynolds number of the wind tunnel test is 9×10 5 。
The invention also discloses an airfoil aerodynamic coefficient calculation system, which comprises:
parameter acquisition module: when wind tunnel test is carried out on the wing profile according to the set wind attack angle range, the data pairs of the set number of the wing profile are obtained, wherein the data pairs comprise the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle;
a first relation determination module: the method comprises the steps of performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient;
a second relation determination module: the method comprises the steps of performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient;
the calculation module: and calculating lift force coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift force coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients.
Optionally, the first relational expression determining module specifically includes a first relational expression determining unit: for fitting according to formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting is performed, wherein x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 、a 2 、a 3 、a 4 And a 5 Are all constant.
Optionally, the second relation determining module specifically includes a second relation determining unit: for fitting according to formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting is performed, wherein x represents the wind angle of attack, f (x) 2 Represents the drag coefficient, a 6 、a 7 、a 8 、a 9 And a 10 Are all constant.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a wing section aerodynamic coefficient calculation method and a wing section aerodynamic coefficient calculation system, which are characterized in that wind tunnel tests are carried out on wing sections according to a set wind attack angle range, polynomial fitting is carried out on the obtained wind attack angle and lift coefficients corresponding to the wind attack angle, and a relational expression of the wind attack angle and the lift coefficients is determined; and performing polynomial fitting on the obtained wind attack angle and the resistance coefficient corresponding to the wind attack angle, determining a relation between the wind attack angle and the resistance coefficient, and calculating the corresponding aerodynamic coefficient when different wind attack angles according to each relation, thereby accelerating the acquisition time of the aerodynamic coefficient.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a method for calculating aerodynamic coefficients of an airfoil according to an embodiment of the present invention;
FIG. 2 is a schematic view of a vortex generator mounting location according to an embodiment of the present invention;
FIG. 3 is a graph of experimental values of lift coefficient of an airfoil according to an embodiment of the invention;
FIG. 4 is a graph of experimental values of drag coefficients of an airfoil according to an embodiment of the invention;
FIG. 5 is a graph of a parametric representation of a lift coefficient fitting equation according to an embodiment of the present invention;
FIG. 6 is a graph showing parameters of a drag coefficient fitting equation according to an embodiment of the present invention;
FIG. 7 is a graph of fitted values of lift coefficients of airfoils according to an embodiment of the present invention;
FIG. 8 is a graph of fit values of drag coefficients for an airfoil according to an embodiment of the invention;
FIG. 9 is a schematic flow chart of an airfoil aerodynamic coefficient calculation system according to an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a wing section aerodynamic coefficient calculation method and a wing section aerodynamic coefficient calculation system, which can calculate corresponding aerodynamic coefficients at different wind attack angles according to a formula, and accelerate the acquisition time of the aerodynamic coefficients.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
FIG. 1 is a schematic flow chart of an airfoil aerodynamic coefficient calculation method, as shown in FIG. 1, the airfoil aerodynamic coefficient calculation method includes:
step 101: and carrying out wind tunnel test on the wing profile according to the set wind attack angle range, and obtaining data pairs of the set number of the wing profile, wherein the data pairs comprise the wind attack angle, a lift coefficient corresponding to the wind attack angle and a resistance coefficient corresponding to the wind attack angle.
Step 102: and performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient, namely a lift coefficient calculation formula.
Step 103: and performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient, namely a resistance coefficient calculation formula.
Step 104: and calculating lift force coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift force coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients.
In step 101, when wind tunnel test is performed on the airfoil, selecting an airfoil with model number NACA4418 in a wind turbine blade, wherein the chord length c=300 mm of the airfoil, and the test Reynolds number Re=9×10 5 The wind attack angle range is selected to be-4 degrees to 22 degrees based on the principle that the range of the test wind attack angle can contain the wind attack angle state of the actual wind turbine blade in the running process, and the data pairs with the set number are specifically 14 pairs.
Vortex generators are arranged at preset positions of the wing profile, the vortex generators with different sizes are arranged on the surface of the wing profile, the effects of improving the lift coefficient of the wing profile and reducing the drag coefficient of the wing profile are different, and the sizes of the vortex generators effective for improving the lift coefficient of the wing profile and reducing the drag coefficient of the wing profile are selected. The dimensional parameters of the vortex generator are shown in table 1.
TABLE 1 parameters of vortex generators
As shown in fig. 2, the preset positions include positions 10%, 20%, 30% or 40% of the chord length from the leading edge of the airfoil.
The data obtained through wind tunnel tests show that when vortex generators are arranged at different positions of the wing profile, the variation trend of the aerodynamic lift coefficient of the wing profile along with the wind attack angle is consistent, the lift coefficient of the wing profile firstly linearly grows along with the increase of the wind attack angle, and when the wind attack angle is increased to a certain value, the lift coefficient of the wing profile starts to sharply decline, and the wing profile generates stall phenomenon. Except that the vortex generators are installed at different positions, the values of the attack angles of the wind, in which the lift coefficient starts to decrease, are different, and the specific change curves are shown in fig. 3.
In fig. 3, the abscissa represents the wind attack angle, and the ordinate represents the lift coefficient, wherein a curve 1a represents the lift coefficient experimental value change curve when a smooth airfoil (no vortex generator is mounted on the airfoil) is shown, a curve 2a represents the lift coefficient experimental value change curve when a vortex generator is mounted at a position 10% chord length from the airfoil leading edge, a curve 3a represents the lift coefficient experimental value change curve when a vortex generator is mounted at a position 20% chord length from the airfoil leading edge, a curve 4a represents the lift coefficient experimental value change curve when a vortex generator is mounted at a position 30% chord length from the airfoil leading edge, and a curve 5a represents the lift coefficient experimental value change curve when a vortex generator is mounted at a position 40% chord length from the airfoil leading edge.
The wing profile is installed at different positions, and the drag coefficient of the wing profile gradually increases with the increase of the attack angle of wind, as shown in fig. 4. In fig. 4, the abscissa represents the wind attack angle, the ordinate represents the drag coefficient, wherein the curve 6a represents the drag coefficient experimental value variation curve when the vortex generator is installed at a position 10% of the chord length from the airfoil leading edge, the curve 7a represents the drag coefficient experimental value variation curve when the vortex generator is installed at a position 20% of the chord length from the airfoil leading edge, the curve 9a represents the drag coefficient experimental value variation curve when the vortex generator is installed at a position 30% of the chord length from the airfoil leading edge, and the curve 10a represents the drag coefficient experimental value variation curve when the vortex generator is installed at a position 40% of the chord length from the airfoil leading edge.
The step 103 specifically includes: fitting formula f (x) 1 For the fourth order polynomial, according to fitting formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting the wind angle of attack and the lift coefficient, where x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 Is a first constant, a 2 Is a second constant, a 3 Is a third constant, a 4 A is a fourth constant, a 5 Is a fifth constant.
The step 104 specifically includes: fitting formula f (x) 2 For the fourth order polynomial, according to fitting formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting the wind attack angle and the resistance coefficient, wherein x represents the wind attack angle, f (x) 2 Represents the drag coefficient, a 6 A is a sixth constant, a 7 A is a seventh constant, a 8 Is an eighth constant, a 9 A is a ninth constant, a 10 Is the tenth constant.
And respectively acquiring wind attack angles in the ranges of-4 degrees to 14 degrees and 14 degrees to 22 degrees, setting a number of wind attack angles, lift coefficients corresponding to the wind attack angles and resistance coefficients corresponding to the wind attack angles, and fitting through a fitting formula to acquire parameters of the lift coefficient fitting formula shown in figure 5 and parameters of the resistance coefficient fitting formula shown in figure 6.
Fig. 7 is a graph of a fitted value corresponding to an airfoil lift coefficient calculation formula, wherein the abscissa represents a wind attack angle, the ordinate represents a lift coefficient, curve 1b represents a fitted value change curve of the lift coefficient when a smooth airfoil is formed, curve 2b represents a fitted value change curve of the lift coefficient when a vortex generator is mounted at a position 10% chord length from the airfoil leading edge, curve 3b represents a fitted value change curve of the lift coefficient when a vortex generator is mounted at a position 20% chord length from the airfoil leading edge, curve 4b represents a fitted value change curve of the lift coefficient when a vortex generator is mounted at a position 30% chord length from the airfoil leading edge, and curve 5b represents a fitted value change curve of the lift coefficient when a vortex generator is mounted at a position 40% chord length from the airfoil leading edge.
Fig. 8 is a fitted value curve corresponding to an airfoil drag coefficient calculation formula, wherein the abscissa represents a wind attack angle, the ordinate represents a drag coefficient, a curve 6b represents a drag coefficient fitted value change curve when a vortex generator is installed at a position 10% chord length from the airfoil leading edge, a curve 7b represents a drag coefficient fitted value change curve when a vortex generator is installed at a position 20% chord length from the airfoil leading edge, a curve 9b represents a drag coefficient fitted value change curve when a vortex generator is installed at a position 30% chord length from the airfoil leading edge, and a curve 10b represents a drag coefficient fitted value change curve when a vortex generator is installed at a position 40% chord length from the airfoil leading edge, as shown in fig. 8.
The lift and drag coefficients associated with vortex generators mounted at various locations on the NACA4418 airfoil can be intuitively derived from FIGS. 7 and 8.
The invention provides a calculation method of airfoil aerodynamic coefficient, according to the wind attack angle range set, wind tunnel test is carried out on airfoil, polynomial fitting is carried out on the obtained wind attack angle and lift coefficient corresponding to the wind attack angle, and the relation between the wind attack angle and lift coefficient is determined; and performing polynomial fitting on the obtained wind attack angle and the resistance coefficient corresponding to the wind attack angle, determining a relation between the wind attack angle and the resistance coefficient, and calculating the corresponding aerodynamic coefficient when different wind attack angles according to each relation, thereby accelerating the acquisition time of the aerodynamic coefficient. According to different positions of the vortex generator, which are arranged at the front edge of the airfoil, a set number of wind attack angles, lift force coefficients and drag force coefficients are obtained for fitting, a calculation formula corresponding to each position is determined, and when the vortex generator is arranged at different positions of the front edge of the airfoil, the lift force coefficients and the drag force coefficients corresponding to different wind attack angles are calculated through the calculation formula corresponding to each position. The time and the cost of the test are saved, and the lift coefficient and the resistance coefficient of the wing profile of the vortex generator installed at different positions in the actual engineering can be calculated according to the lift coefficient calculation formula and the resistance coefficient calculation formula. The method has important significance for the accuracy and the scientificity of position determination when the vortex generator is installed on the actual wind turbine blade, and provides basis and method for engineering design and related research.
FIG. 9 is a schematic structural diagram of an airfoil aerodynamic coefficient calculation system, as shown in FIG. 9, comprising:
parameter acquisition module 201: and the data pairs are used for acquiring the set number of the wing profiles when wind tunnel tests are carried out on the wing profiles according to the set wind attack angle range, and the data pairs comprise the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle.
The first relationship determination module 202: and the method is used for performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient.
The second relation determination module 203: and the method is used for performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient.
The calculation module 204: and calculating lift force coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift force coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients.
The first relational expression determination module 202 specifically includes a first relational expression determination unit: for fitting according to formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting is performed, wherein x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 、a 2 、a 3 、a 4 And a 5 Are all constant.
The second relational expression determining module 203 specifically includes a second relational expression determining unit: for fitting according to formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting is performed, wherein x represents the wind angle of attack, f (x) 2 Represents the drag coefficient, a 6 、a 7 、a 8 、a 9 And a 10 Are all constant.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (6)
1. A method of airfoil aerodynamic coefficient calculation, the method comprising:
according to the set wind attack angle range, wind tunnel test is carried out on the wing profile, and the set number of data pairs of the wing profile are obtained, wherein the data pairs comprise the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle;
performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient;
performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient;
calculating lift coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients;
the method for obtaining the relation between the wind attack angle and the lift coefficient specifically comprises the following steps of: according to fitting formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting is performed, wherein x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 Is a first constant, a 2 Is a second constant, a 3 Is a third constant, a 4 A is a fourth constant, a 5 Is a fifth constant;
and performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient, wherein the method specifically comprises the following steps of: according to fitting formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting is performed, wherein x represents the wind angle of attack, f (x) 2 Represents the drag coefficient, a 6 A is a sixth constant, a 7 A is a seventh constant, a 8 Is an eighth constant, a 9 A is a ninth constant, a 10 Is the tenth constant.
2. The airfoil aerodynamic coefficient calculation method according to claim 1, wherein a vortex generator is installed at a preset position of the airfoil; the preset position comprises a position which is 10 percent of the chord length, 20 percent of the chord length, 30 percent of the chord length or 40 percent of the chord length from the front edge of the airfoil.
3. The airfoil aerodynamic coefficient calculation method of claim 1, wherein said wind attack angle ranges from-4 ° to 22 °.
4. The airfoil aerodynamic coefficient calculation method according to claim 1, wherein a chord length of the airfoil is 300mm.
5. The method of claim 1, wherein the reynolds number of the wind tunnel test is 9 x 10 5 。
6. An airfoil aerodynamic coefficient calculation system, said system comprising:
parameter acquisition module: when wind tunnel test is carried out on the wing profile according to the set wind attack angle range, the data pairs of the set number of the wing profile are obtained, wherein the data pairs comprise the wind attack angle, the lift coefficient corresponding to the wind attack angle and the resistance coefficient corresponding to the wind attack angle;
a first relation determination module: the method comprises the steps of performing polynomial fitting on the wind attack angle and the lift coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the lift coefficient;
a second relation determination module: the method comprises the steps of performing polynomial fitting on the wind attack angle and the resistance coefficient corresponding to the wind attack angle to obtain a relational expression of the wind attack angle and the resistance coefficient;
the calculation module: calculating lift coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the lift coefficients, and calculating resistance coefficients corresponding to different wind attack angles according to the relation between the wind attack angles and the resistance coefficients;
the first relation determining module specifically includes a first relation determining unit: for fitting according to formula f (x) 1 ＝a 1 x 4 +a 2 x 3 +a 3 x 2 +a 4 x+a 5 Fitting is performed, wherein x represents the wind angle of attack, f (x) 1 Representing the lift coefficient, a 1 、a 2 、a 3 、a 4 And a 5 Are all constants;
the second relation determining module specifically includes a second relation determining unit: for fitting according to formula f (x) 2 ＝a 6 x 4 +a 7 x 3 +a 8 x 2 +a 9 x+a 10 Fitting is performed, wherein x represents the wind angle of attack, f (x) 2 Represents the drag coefficient, a 6 、a 7 、a 8 、a 9 And a 10 Are all constant.
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| CN111898074A (en) | 2020-11-06 |
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