Design method of hybrid blade for power station variable-pitch axial flow fan

Abstract

The application discloses a kind of power station dynamic adjustable axial flow fan hybrid blade design method, comprising: first, according to the fan energy-saving reconstruction technical route of fan selection parameter before and after adjustable blade axial flow fan energy-saving reconstruction;Then, according to the fan energy-saving reconstruction technical route, adjustable blade axial flow fan hybrid blade design method is given;Finally, based on the arrangement mode and installation method of the fan hybrid blade on the hub of the designed fan hybrid blade.The application can be customized according to the actual needs of users, personalized development of adjustable axial flow fan small energy-saving blade, and the developed small energy-saving blade is mixed with the original blade and used, and the output of the fan can be reduced after the design of the hybrid blade of the adjustable axial flow fan, realizing the deep energy saving of the fan.

Description

Technical Field

[0001] This invention relates to a movable-blade adjustable axial flow fan used in the flue gas system of a coal-fired power plant, specifically to a hybrid blade design method for a power plant movable-blade axial flow fan. Background Technology

[0002] Currently, adjustable axial flow fans are the most widely used type of thermal power unit in China. However, due to factors such as unreasonable fan selection, large changes in coal quality, and frequent deep peak shaving of units, the fans have various problems in actual operation, such as insufficient fan output, low stall margin, and poor matching with the pipeline system. As a result, the actual operation economy and safety of adjustable axial flow fans are often poor, resulting in high energy consumption of thermal power generating units.

[0003] If the selection margin of an adjustable axial flow fan is too large, problems such as excessive energy consumption and poor low-opening blade adjustment characteristics will occur during actual operation. In this case, energy-saving retrofitting of the adjustable axial flow fan is necessary. Traditional retrofitting solutions involve replacing the entire fan, which not only involves huge investment costs and long payback periods, but also, due to the limited product models from equipment manufacturers, it is difficult to meet the diverse output requirements of adjustable axial flow fans. Therefore, the matching between the retrofitted fan and the system is often not optimal. Therefore, when implementing energy-saving retrofitting of adjustable axial flow fans, considering both the energy-saving effect and investment cost, a method can be adopted: replacing some of the original fan blades with small energy-saving blades, while reusing the remaining blades. This establishes a hybrid design method for the adjustable axial flow fan's original blades and energy-saving blades. Implementing energy-saving retrofitting of adjustable axial flow fans based on this blade design method can achieve significant energy-saving effects while ensuring the safe and stable operation of the fan. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a hybrid blade design method for dynamically adjustable axial flow fans in power plants. The technical solution involves reusing the existing components of the dynamically adjustable axial flow fan while designing energy-saving blades for some of the fan's moving blades. After the design is completed, some of the original moving blades are replaced with small energy-saving blades, while the remaining moving blades are reused. By designing hybrid blades for dynamically adjustable axial flow fans, investment costs are saved, the investment payback period is shortened, and thus deep energy saving of the fan is achieved, while ensuring the safe and reliable operation of the fan.

[0005] This invention is achieved using the following technical solution:

[0006] A method for designing hybrid blades for a dynamically adjustable axial flow fan in a power plant, comprising:

[0007] First, the energy-saving retrofit technology route for the fan is determined based on the fan selection parameters before and after the energy-saving retrofit of the adjustable axial flow fan. Then, based on the energy-saving retrofit technology route, the design method of the hybrid blades for the adjustable axial flow fan is given. Finally, based on the designed hybrid blades, the arrangement and installation method of the hybrid blades on the hub are given.

[0008] A further improvement of this invention is that the method is specifically implemented as follows:

[0009] 1) Determine the energy-saving retrofit technology route for the adjustable-blade axial flow fan based on the fan selection parameters before and after the retrofit; the fan flow rate corresponding to the fan selection parameters at the TB point before the retrofit is q. v1 The unit is m 3 / s, the total pressure of the fan is p t1 The unit is Pa. The fan flow rate corresponding to the TB point selection parameters after the fan energy-saving retrofit is q. v2 The unit is m 3 / s, the total pressure of the fan is p t2 The unit is Pa; when the technical parameters of the fan before and after the modification meet the preset conditions, the design of the mixed blade of the adjustable axial flow fan is implemented.

[0010] When the technical parameters of the fan before and after the modification meet the preset conditions, the energy-saving modification effect of the fan can be achieved by the mixed blade design of the adjustable axial flow fan.

[0011] 2) Determine the design method for the mixing blades of the adjustable axial flow fan. The specific implementation method is as follows:

[0012] (1) The wind turbine's hybrid blade assembly consists of existing blades, small energy-saving blades, and a hub; the existing blades include the old blade body, the old blade root guide circle, and the old blade chassis, while the small energy-saving blades include the new blade body, the new blade root guide circle, and the new blade chassis; the new blade chassis has the same structure as the old blade chassis, and both the new and old blade root guide circles are circular arc surfaces with the same radius of curvature, i.e., R. 22 =R 12 And R 22 ∈[15,25]mm; The new moving blade surface is based on the old moving blade surface, and the surface is reshaped by parametric fitting and adjustment of fitting parameters;

[0013] (2) Parametric fitting of the surface of the old moving blade is performed to obtain the control parameters for surface fitting;

[0014] (3) Determine the surface shape of the new blade based on the parametric fitting results of the old blade surface;

[0015] 3) Based on the designed wind turbine hybrid blades, the arrangement and installation method of the hybrid blades on the hub are given.

[0016] A further improvement of this invention is that, in step 1), the preset conditions that the technical parameters of the wind turbine before and after modification need to meet are as follows:

[0017] The ratio of fan flow rate before and after fan modification meets the requirements.

[0018] The ratio of total pressure of the fan before and after the fan modification meets the requirements.

[0019] Before the wind turbine was modified, the number of blades M in a single-stage moving blade was an even number.

[0020] A further improvement of this invention lies in that, in step 1), the energy-saving retrofit effect of the fan is achieved through the design of the adjustable axial flow fan blades. The specific implementation method is as follows:

[0021] Before and after the modification, the number of single-stage moving blades M of the fan remains unchanged. Before the modification, the number of single-stage moving blades M is an even number. After the modification, M / 2 blades are replaced with small energy-saving blades, while the original M / 2 blades are retained. The small energy-saving blades and the original blades are arranged alternately.

[0022] A further improvement of the present invention is that, in step 2), (2) of the present invention, firstly, the old moving blade is uniformly divided into N blade profile sections along the blade height direction in a polar coordinate system, where 3≤N≤10, N is an integer, the first section is the blade root section, the Nth section is the blade tip section, and the curve of each blade profile section is formed by the pressure surface profile PS. i Suction surface profile SS i Composition, through the PS pressure surface profile i Suction surface profile SS i The method of curve fitting at discrete points on the curve is used to obtain the curve control parameters for each airfoil section; then, the centroid O of the curve for each airfoil section is used as the reference point. i Using discrete points, an n-order Bézier curve is used to fit the old moving blade stacking curve, and the old moving blade stacking curve SL and curve control parameters are obtained by solving.

[0023] A further improvement of the present invention is that, in step 2), (2) the specific implementation method is as follows:

[0024] ① Using a second-order Bézier curve, the mid-arc C of the i-th airfoil section of the old moving blade is... i Perform curve fitting, where 1≤i≤N, and fit the middle arc C. i Placed horizontally in a Cartesian coordinate system, the mid-arc C i Leading edge point LE i Let the origin be (0,0) and the mid-arc C be... i String length is Cord i Mid-arc C iTail edge point TE i Coordinates are (Cord) i ,0), mid-arc C i N is selected uniformly above C N discrete points, where 90 ≤ N C The standard deviation (RSD) of the curve fitting is ≤150, and the standard deviation (RSD) of the curve fitting satisfies RSD≤1E-3. The control points P of the Bézier curve are obtained by solving the second-order Bézier curve fitting problem. i The coordinates and the fitted curve function equation: y = f(x); then, based on the control points P of the Bézier curve... i And the middle arc C i Leading edge point LE i C, middle arc i Tail edge point TE i The coordinates are used to solve for the inlet geometric angle β of the i-th airfoil section. 1,i Exit geometric angle β 2,i and leaf chord length Cord i ;

[0025] ② Using an n-th order Bézier curve, n≥3, the pressure surface profile PS of the i-th airfoil section of the old moving blade is... i Suction surface profile SS i Perform curve fitting; the formula for an nth-order Bézier curve is as follows:

[0026]

[0027] In the formula, j is the control point number of the Bézier curve, and P j Let B(t) be the j-th control point, j = 0, 1, ..., n, where n is the order of the Bézier curve, t is the time parameter between [0, 1], and B(t) is the coordinate of the point on the Bézier curve corresponding to parameter t. j,n (t) are n-order Bernstein basis functions. For combinations,

[0028] The middle arc C i Placed horizontally in a Cartesian coordinate system, the mid-arc C i Leading edge point LE i Let the origin be (0,0) and the mid-arc C be... i String length is Cord i Mid-arc C i Tail edge point TE i Coordinates are (Cord) i ,0), pressure surface profile PS i Suction surface profile SS i N are selected uniformly above P N S There are discrete points, 100≤NP =N S ≤160, during the fitting process, maintain the leading edge point LE of the blade. i TE at the trailing edge of the blade i The position remains unchanged, and the centering arc C is used. i Applying the same blade thickness distribution to both sides to adjust the pressure surface profile PS i Suction surface profile SS i Curve fitting is performed on discrete points on the curve; the least squares method is used, based on the Bezier fitting curve and the mid-arc C. i Solving for the control points P of the Bézier curve by minimizing the sum of squared errors between discrete points. i , i = 0, 1, ..., n, and obtain the order n of the Bézier curve. After the fitting is completed, the nth order Bézier fitting curve of the leaf thickness distribution and the fitting curve function equation are obtained: y = b(x);

[0029] ③The centroid O of the i-th airfoil section curve i For discrete points, with N discrete points, an n-order Bézier curve is used to fit the old moving blade stacking curve, where n≥3; during the fitting process, the least squares method is used, based on the Bézier fitting curve and the blade centroid O. i Solve for the control points P of the Bézier curve by minimizing the sum of squared errors. i , i = 0, 1, ..., n, and obtain the order n of the Bézier curve. After fitting, the old moving leaf stacking curve SL is obtained.

[0030] A further improvement of the present invention is that, in step 2) (3), the specific implementation method is as follows:

[0031] ① By adjusting the arc C in the i-th airfoil section of the original moving blade i By obtaining the parameters of the Bessel fitting curve, the Bessel fitting curve of the arc in the i-th airfoil section of the small energy-saving blade is obtained, thus completing the arc C′ in the i-th airfoil section of the small energy-saving blade. i The shape;

[0032] The inlet geometry angle of the curved Bezier fitting curve in the small energy-saving blade is β′. 1,i The exit geometry angle is β′ 2,i and leaf chord length Cord′ i Determine using the following formula:

[0033]

[0034] In the formula, ε1 is the blade angle adjustment coefficient, and ε2 is the blade length adjustment coefficient;

[0035] Having determined the above parameters, the mid-arc line C of the i-th airfoil section of the small energy-saving blade is thus determined. iLeading edge point LE′ i C, middle arc i Tail edge point TE′ i Control point P′ i and the middle arc C′ i Second-order Bézier curves;

[0036] ②The mid-arc line C′ based on the i-th airfoil section of the small energy-saving blade i The pressure surface profile PS′ of the i-th airfoil section of the small energy-saving blade is determined by superimposing the blade thickness distribution on both sides of the profile curve and shaping the leading and trailing arc curves on the leading and trailing edges of the airfoil section. i and suction surface profile SS′ i The shape is then used to complete the shape of the leaf curve of the i-th leaf section;

[0037] ③ Stack the airfoil profiles of N airfoil sections of the small energy-saving blade along the blade height direction to generate a three-dimensional shape of the small energy-saving blade, wherein the airfoil profiles include the pressure surface profile PS′. i and suction surface profile SS′ i , i = 1, ..., N; Determine the centroid O′ of the i-th airfoil section based on the airfoil profile of the small energy-saving blade. i Starting from the centroid O′1 of the first blade section, the centroids O′ of the N blade sections of the small energy-saving blade are... i The blades, i = 1, ..., N, are arranged along the SL direction of the old moving blade stacking curve, thus determining the centroid O′ of the N blade sections. i And the position of the blade profile; then, the blade profile of the i-th blade section of the small energy-saving blade is superimposed along the blade height direction through the old moving blade superposition curve SL, thus completing the three-dimensional model of the small energy-saving blade.

[0038] A further improvement of the present invention is that, in step 2), (3)-②, the specific implementation method is as follows:

[0039] First, based on the Bessel fitting curve y = b(x) of the blade thickness distribution of the i-th blade section obtained in step (2), the blade thickness distribution function b(x) = f1(x), 0 ≤ x ≤ Cord is obtained. i ,make The abscissa of the blade thickness distribution function is dimensionless, resulting in the function b(k) = f2(k), 0 ≤ k ≤ 1. The thickness of the blade section of the small energy-saving blade is multiplied by a thickness adjustment coefficient ε3, where ε3 ∈ [0.7, 1], i.e., b(k) = ε3·f2(k), 0 ≤ k ≤ 1. Let the abscissa of the i-th blade section of the small energy-saving blade be x′, and the chord length of the blade section be Cord′.i ,but This can be organized into the blade thickness distribution function of the i-th blade section of the small energy-saving blade, b(x′)=f3(x′),0≤x′≤Cord′; thus, the blade thickness distribution law of the i-th blade section of the small energy-saving blade is determined.

[0040] Then, the blade thickness distribution law of the i-th blade section determined in the above steps is superimposed on the mid-arc line C′ of that blade section. i On the airfoil profile, pressure surface curves and suction surface curves are generated. Leading edge and trailing edge circular arc curves are constructed at the leading and trailing edges of the airfoil section, respectively. Both the leading and trailing edge circular arc curves are arc segments, tangent to the pressure and suction surface curves generated above. Furthermore, at this airfoil section, the radius R′ of the leading edge circular arc curve of the small energy-saving blade is... 1,i Satisfy: 0 < R′ 1,i ≤5%·Cord′ i Small energy-saving blade trailing edge arc curve radius R′ 2,i Satisfy: 0 < R′ 2,i ≤3%·Cord′ i Thus, the pressure surface profile PS′ of the i-th airfoil section of the small energy-saving blade is determined. i and suction surface profile SS′ i The pressure surface profile PS′ i and suction surface profile SS′ i When combined, the airfoil profile of the i-th airfoil section of the small energy-saving blade is constructed.

[0041] A further improvement of the present invention is that, in step 3), the specific implementation method is as follows:

[0042] (1) Before and after the modification, the number of single-stage moving blades M of the fan remains unchanged, where M is an even number. After the modification, M / 2 blades are replaced with small energy-saving blades, while the original M / 2 moving blades remain unchanged. The small energy-saving blades and the original blades are arranged alternately in sequence.

[0043] (2) The centroid O1 of the first blade section of the original old blade, i.e. the blade root section, is located on the rotation center line of the old blade chassis, and the centroid O′1 of the first blade section of the small energy-saving blade is located on the rotation center line of the new blade chassis. During the operation of the fan, the installation angle of the first blade section of the small energy-saving blade is consistent with the installation angle of the first blade section of the original old blade, and is adjusted synchronously.

[0044] The present invention has at least the following beneficial technical effects:

[0045] This invention provides a hybrid blade design method for a dynamic axial flow fan in a power plant. It can customize small energy-saving blades for dynamic axial flow fans according to the actual needs of users, and mix and install the developed small energy-saving blades with the original dynamic blades. After the hybrid blade design of the dynamic axial flow fan is completed, the fan output can be reduced, achieving deep energy saving of the fan. At the same time, it can effectively improve the fan's regulation performance, expand the fan's operating range, and significantly improve the fan's operating economy and safety. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of a three-dimensional model of the present invention;

[0047] Figure 2 This is a schematic diagram of the original three-dimensional model of the moving blade of the present invention;

[0048] Figure 3 This is a schematic diagram of a three-dimensional model of the small energy-saving blade of the present invention;

[0049] Figure 4 This is a schematic diagram of the arc shape in the cross-section of the blade of the present invention;

[0050] Figure 5 This is a schematic diagram of the blade profile and shape of the present invention.

[0051] Figure 1 In the middle, 1. the original moving blades, 2. small energy-saving blades, and 3. the hub.

[0052] Figure 2 In the middle, 11. old leaf body, 12. old leaf root guide circle, 13. old leaf base plate.

[0053] R 12 The radius of curvature of the old leaf root guide circle 12 is in mm.

[0054] Figure 3 In the middle, 21. New leaf body, 22. New leaf root guide circle, 23. New leaf base plate.

[0055] R 22 The radius of curvature of the new leaf root guide circle 22 is in mm.

[0056] Figure 4 The parameters of the mid-arc line of the i-th blade section are given by LE. i For the leading edge of the leaf shape, TE i C is the leaf-shaped trailing edge point. i The airfoil is a curved profile, P i Let f(x) be the control point of the Bézier curve, and let y = f(x) be the arc C in the leaf shape. i The fitted curve function equation, N C This represents the number of discrete points uniformly selected along the arc of the blade.

[0057] β 1,i The leading edge inlet geometry angle of the airfoil, β 2,i The exit geometry angle of the blade trailing edge is given; all units are in degrees.

[0058] Cord i The chord length of the leaf shape is in mm.

[0059] Figure 5 The parameters in the figure are the shaping curve parameters of the i-th blade section of the original blade, where PS i For the airfoil pressure surface profile, SS i For the suction surface profile of the leaf shape, N P PS for airfoil pressure surface profile i The number of discrete points uniformly selected above, N S For the suction surface profile SS i The number of discrete points selected uniformly on the blade leading edge (LE) i Let the origin be 0, and x be the arc C of the leaf shape. i b(x) is the distance from a point on the x-axis to the origin 0, and b(x) is the blade thickness distribution corresponding to the x-axis position.

[0060] R 1,i R is the radius of the original blade leading edge arc curve. 2,i The radius of the original blade trailing edge arc is given; all units are in mm.

[0061] Where N is the total number of blade profile sections, i is the blade profile section number, M is the number of single-stage moving blades of the wind turbine before and after the modification, and RSD is the standard deviation of the curve fitting.

[0062] j is the control point number of the Bézier curve, P j Let B(t) be the j-th control point (j = 0, 1, ..., n), where n is the order of the Bézier curve, t is the time parameter between [0, 1], and B(t) is the coordinate of the point on the Bézier curve corresponding to parameter t. j,n (t) are n-order Bernstein basis functions. It is the combination number.

[0063] q v1 The fan flow rate corresponding to the TB point selection parameters of the fan before the upgrade, q v2 The above figures represent the fan flow rate corresponding to the selected parameters at the TB point of the upgraded fan. All units are in meters (m³). 3 / s.

[0064] p t1 To determine the total pressure of the fan corresponding to the TB point selection parameters before the upgrade, p t2The total pressure of the fan is the total pressure of the fan corresponding to the selection parameters of the fan at TB point after the modification. All units are Pa.

[0065] SL is the blade stacking curve, O i The centroid of the i-th blade section of the original moving blade.

[0066] b(x) = f1(x) is the blade thickness distribution function of the i-th blade section of the original blade, b(x) = f2(x) is the dimensionless blade thickness distribution function of the i-th blade section of the original blade, and b(x) = f3(x) is the thickness distribution function of the i-th blade section of the small energy-saving blade.

[0067] The following parameters are all parameters of the i-th blade section of the small energy-saving blade:

[0068] C′ 1,i The leaf-shaped mid-curve profile, PS′ i For the airfoil pressure surface profile, SS′ i It is the suction surface profile of the leaf shape.

[0069] β′ 1,i β′ is the leading edge inlet geometry of the airfoil. 2,i ε1 is the blade tip exit geometry angle, and all units are °; ε2 is the blade length adjustment coefficient, and ε3 is the blade thickness adjustment coefficient.

[0070] Cord′ i For the leaf chord length, R′ 1,i R′ is the radius of the arc of the leading edge curve of the airfoil. 2,i The radius of the trailing edge arc curve of the blade is given in mm.

[0071] x′ is the mid-arc line C′ of the leaf shape. 1,i Let b(x′) be the distance from the origin O to a point in the x-direction, and let b(x′) be the blade thickness distribution corresponding to the x-coordinate position x′. i The center of gravity of the leaf shape. Detailed Implementation

[0072] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0073] This invention provides a design method for hybrid blades of a power plant adjustable axial flow fan, comprising: first, determining the energy-saving retrofit technology route of the fan based on the fan selection parameters before and after the energy-saving retrofit of the adjustable axial flow fan; then, providing a design method for hybrid blades of the adjustable axial flow fan based on the energy-saving retrofit technology route; and finally, providing the arrangement and installation method of the hybrid blades on the hub based on the designed hybrid blades.

[0074] The specific implementation method of this invention is as follows:

[0075] 1. Determine the energy-saving retrofit technology route for the adjustable-blade axial flow fan based on the fan selection parameters before and after the retrofit. The fan flow rate corresponding to the fan selection parameters at point TB before the retrofit is q. v1 (Unit is m) 3 / s), the total pressure of the fan is p t1 (Unit: Pa), the fan flow rate corresponding to the TB point selection parameters after the fan energy-saving retrofit is q. v2 (Unit is m) 3 / s), the total pressure of the fan is p t2 (Unit: Pa). When the technical parameters of the fan before and after modification meet the following conditions, a hybrid blade design for an adjustable-blade axial flow fan can be implemented:

[0076] (1) The ratio of fan flow rate before and after fan modification meets the requirements.

[0077] (2) The ratio of the total pressure of the fan before and after the fan modification meets the requirements.

[0078] (3) Before the wind turbine was modified, the number of blades M of a single-stage moving blade was an even number.

[0079] When the technical parameters of the fan before and after the modification meet the above conditions, the energy-saving modification effect of the fan can be achieved by designing a hybrid blade for an adjustable axial flow fan. The specific implementation method is as follows:

[0080] Before and after the modification, the number of single-stage moving blades M of the wind turbine remains unchanged. Before the modification, the number of single-stage moving blades M is an even number. After the modification, M / 2 blades are replaced with small energy-saving blades, while the original M / 2 blades are retained. The small energy-saving blades and the original blades are arranged alternately. The arrangement and installation method of the mixed blades on the hub are described below.

[0081] 2. Determine the design method for the mixing blades of the adjustable axial flow fan. The implementation method for the fan mixing blade design is as follows:

[0082] (1) As Figure 1 As shown, the hybrid rotor blade assembly of the wind turbine consists of the original rotor blades 1, small energy-saving blades 2, and a hub 3. Among them, as... Figure 2As shown, the original moving blade 1 includes the old moving blade body 11, the old blade root guide circle 12, and the old blade base 13; as Figure 3 As shown, the small energy-saving blade 2 includes a new moving blade body 21, a new blade root guide circle 22, and a new blade chassis 23. The structure of the new blade chassis 23 is completely identical to that of the old blade chassis 13. Both the new blade root guide circle 22 and the old blade root guide circle 12 are curved surfaces with the same radius of curvature, i.e., R. 22 =R 12 And usually R 22 ∈[15,25]mm. The new moving blade surface 21 is based on the old moving blade surface 11. It is reshaped by parametric fitting of the surface and adjustment of the fitting parameters. The specific implementation method is described below.

[0083] (2) Parametric fitting is performed on the surface of the old moving blade 11 to obtain the control parameters for surface fitting. First, the old moving blade 11 is uniformly divided into N (3≤N≤10, N is an integer) blade profile sections along the blade height direction in the polar coordinate system (the first section is the blade root section, and the Nth section is the blade tip section). The curve of each blade profile section is formed by the pressure surface profile PS. i Suction surface profile SS i Composition, through the PS pressure surface profile i Suction surface profile SS i The method of curve fitting at discrete points on the curve is used to obtain the curve control parameters for each airfoil section; then, the centroid O of the curve for each airfoil section is used as the reference point. i For discrete points, an nth-order Bézier curve is used to fit the old rotor blade stacking curve, and the old rotor blade stacking curve SL and curve control parameters are obtained by solving. Thus, the control parameters for fitting the old rotor blade surface are obtained. The specific implementation method is as follows:

[0084] ① Using a second-order Bézier curve, the mid-arc line C of the i-th (1≤i≤N) blade section of the old moving blade is... i Perform curve fitting (see) Figure 4 ).like Figure 4 As shown, the middle arc C i Placed horizontally in a Cartesian coordinate system, the mid-arc C i Leading edge point LE i Let the origin be (0,0) and the mid-arc C be... i String length is Cord i Mid-arc C i Tail edge point TE i Coordinates are (Cord) i ,0), mid-arc C i N is selected uniformly above C (90≤N) CFor discrete points ≤150, the standard deviation (RSD) of the curve fitting should satisfy RSD≤1E-3. The control points P of the Bézier curve are obtained by fitting a second-order Bézier curve. i The coordinates and the fitted curve function equation: y = f(x). Then, based on the control points P of the Bézier curve... i And the middle arc C i Leading edge point LE i C, middle arc i Tail edge point TE i The coordinates can be used to solve for the inlet geometric angle β of the i-th airfoil section. 1,i Exit geometric angle β 2,i and leaf chord length Cord i .

[0085] ② Using an nth-order (n≥3) Bézier curve, the pressure surface profile PS of the i-th airfoil section of the old moving blade is... i Suction surface profile SS i Perform curve fitting (see) Figure 5 The formula for an nth-order Bézier curve is as follows:

[0086]

[0087] In the formula, j is the control point number of the Bézier curve, and P j Let B(t) be the j-th control point, j = 0, 1, ..., n, where n is the order of the Bézier curve, t is the time parameter between [0, 1], and B(t) is the coordinate of the point on the Bézier curve corresponding to parameter t. j,n (t) are n-order Bernstein basis functions. For combinations,

[0088] like Figure 5 As shown, the middle arc C i Placed horizontally in a Cartesian coordinate system, the mid-arc C i Leading edge point LE i Let the origin be (0,0) and the mid-arc C be... i String length is Cord i Mid-arc C i Tail edge point TE i Coordinates are (Cord) i ,0), pressure surface profile PS i Suction surface profile SS i N are selected uniformly above P N S (100≤N) P =N S Discrete points ≤160. During the fitting process, the leading edge point LE of the blade is maintained. iTE at the trailing edge of the blade i The position remains unchanged, and the centering arc C is used. i Applying the same blade thickness distribution to both sides to adjust the pressure surface profile PS i Suction surface profile SS i Curve fitting is performed on discrete points on the curve; the least squares method is used, based on the Bezier fitting curve and the mid-arc C. i Solving for the control points P of the Bézier curve by minimizing the sum of squared errors between discrete points. i , i = 0, 1, ..., n, and obtain the order n of the Bézier curve. After the fitting is completed, the nth order Bézier fitting curve of the blade thickness distribution and the fitting curve function equation are obtained: y = b(x).

[0089] ③The centroid O of the i-th airfoil section curve i For discrete points, with N discrete points, an nth-order (n≥3) Bézier curve is used to fit the old moving blade stacking curve; during the fitting process, the least squares method is used, based on the Bézier fitting curve and the blade centroid O. i Solve for the control points P of the Bézier curve by minimizing the sum of squared errors. i , i = 0, 1, ..., n, and obtain the order n of the Bézier curve. After fitting, the old moving leaf stacking curve SL is obtained.

[0090] (3) Based on the parametric fitting results of the old blade 11, determine the surface shape of the new blade 21. The specific implementation method is as follows:

[0091] ① By adjusting the arc C in the i-th airfoil section of the original moving blade i By obtaining the parameters of the Bessel fitting curve, the Bessel fitting curve of the arc in the i-th airfoil section of the small energy-saving blade is obtained, thus completing the arc C′ in the i-th airfoil section of the small energy-saving blade. i Its shape.

[0092] The inlet geometry angle of the curved Bezier fitting curve in the small energy-saving blade is β′. 1,i The exit geometry angle is β′ 2,i and leaf chord length Cord′ i Determine using the following formula:

[0093]

[0094] In the formula, ε1 is the blade angle adjustment coefficient and ε2 is the blade length adjustment coefficient.

[0095] Having determined the above parameters, the mid-arc line C of the i-th airfoil section of the small energy-saving blade is thus determined. i Leading edge point LE′ i C, middle arc i Tail edge point TE′i Control point P′ i and the middle arc C′ i The second-order Bezier curve.

[0096] ②The mid-arc line C′ based on the i-th airfoil section of the small energy-saving blade i The pressure surface profile PS′ of the i-th airfoil section of the small energy-saving blade is determined by superimposing the blade thickness distribution on both sides of the profile curve and shaping the leading and trailing arc curves on the leading and trailing edges of the airfoil section. i and suction surface profile SS′ i The shape is then determined to complete the blade curve shape for the i-th blade section. The specific implementation method is as follows:

[0097] First, such as Figure 5 As shown, based on the Bessel fitting curve y=b(x) of the blade thickness distribution of the i-th blade section obtained in step (2), the blade thickness distribution function b(x)=f1(x),0≤x≤Cord can be obtained. i ,make The abscissa of the blade thickness distribution function is dimensionless, resulting in the function b(k) = f2(k), 0 ≤ k ≤ 1. The thickness of the blade section of the small energy-saving blade is multiplied by a thickness adjustment coefficient ε3, where ε3 ∈ [0.7, 1], i.e., b(k) = ε3·f2(k), 0 ≤ k ≤ 1. Let the abscissa of the i-th blade section of the small energy-saving blade be x′, and the chord length of the blade section be Cord′. i ,but This can be summarized as the blade thickness distribution function of the i-th blade section of the small energy-saving blade: b(x′)=f3(x′), 0≤x′≤Cord′. This determines the blade thickness distribution pattern of the i-th blade section of the small energy-saving blade.

[0098] Then, the blade thickness distribution law of the i-th blade section determined in the above steps is superimposed on the mid-arc line C′ of that blade section. i On the profile, pressure surface curves and suction surface curves are generated. For example... Figure 5 As shown, leading-edge and trailing-edge circular arcs are constructed at the leading and trailing edges of the blade section, respectively. Both the leading-edge and trailing-edge circular arcs are arc segments, tangent to the pressure and suction surface curves generated above, respectively. Furthermore, at this blade section, the radius R′ of the leading-edge circular arc of the small energy-saving blade... 1,i Satisfy: 0 < R′ 1,i ≤5%·Cord′ i Small energy-saving blade trailing edge arc curve radius R′ 2,i Satisfy: 0 < R′2,i ≤3%·Cord′ i This determines the pressure surface profile PS′ of the i-th airfoil section of the small energy-saving blade. i and suction surface profile SS′ i The pressure surface profile PS′ i and suction surface profile SS′ i When combined, the airfoil profile of the i-th airfoil section of the small energy-saving blade is constructed.

[0099] ③ The airfoil profiles (including the pressure surface profile PS′) of the N airfoil sections of the small energy-saving blades i and suction surface profile SS′ i (i = 1, ..., N) are stacked along the blade height direction to generate a three-dimensional shape of a small energy-saving blade. Based on the blade profile of the i-th blade section, the centroid O′ of that blade section can be determined. i Starting from the centroid O′1 of the first blade section, the centroids O′ of the N blade sections of the small energy-saving blade are... i (i=1,…,N), arranged along the SL direction of the old moving blade stacking curve, thus determining the centroid O′ of the N blade sections. i (i = 1, ..., N) and the position of the blade profile. Then, the blade profile of the i-th blade section of the small energy-saving blade is superimposed along the blade height direction through the old moving blade superposition curve SL, thus completing the three-dimensional model of the small energy-saving blade.

[0100] After the above steps, the curved shape of the new leaf blade 21 is completed.

[0101] 3. Based on the designed wind turbine hybrid blades, the arrangement and installation method of the hybrid blades on the hub are given. The specific implementation method is as follows:

[0102] (1) As Figure 1 As shown, the number of single-stage moving blades M of the fan remains unchanged before and after the modification (M is an even number). After the modification, M / 2 blades are replaced with small energy-saving blades, while the original M / 2 moving blades remain unchanged. The small energy-saving blades and the original blades are arranged alternately in sequence.

[0103] (2) The centroid O1 of the first airfoil section (i.e., the blade root section) of the original old blade is located on the rotation center line of the old blade chassis 13, and the centroid O′1 of the first airfoil section (i.e., the blade root section) of the small energy-saving blade is located on the rotation center line of the new blade chassis 23. During the operation of the fan, the installation angle of the first airfoil section (i.e., the blade root section) of the small energy-saving blade is consistent with the installation angle of the first airfoil section of the original old blade, and is adjusted synchronously.

[0104] Example

[0105] A domestic 600MW unit's blower is a single-stage adjustable axial flow fan with 22 blades and an impeller diameter of 2660mm. The motor's rated speed is 990r / min, and the fan's flow rate at point TB is q. v1 232m 3 / s, TB point pressure p t1 The Pa is 4730. After the energy-saving renovation, the flow rate q at the TB point of the fan is... v2 210m 3 / s, TB point pressure p t2 The pressure is 3400 Pa. The following steps should be followed to design the mixing blades of the dynamically adjustable axial flow fan:

[0106] 1. The ratio of fan flow rate before and after fan modification meets the requirements. The ratio of total pressure of the fan before and after the fan modification meets the requirements. Before the fan modification, the number of single-stage moving blades M=22, which is an even number, meeting the implementation conditions of this invention. Therefore, the dynamic adjustment axial flow fan hybrid blade design method is adopted to implement the fan energy-saving modification.

[0107] 2. According to the method of the present invention, the number of single-stage moving blades of the fan remains unchanged at M=22 before and after the modification. After the modification, M / 2=11 blades are replaced with small energy-saving blades, while the original M / 2=11 blades are retained. The small energy-saving blades and the original blades are arranged alternately in sequence.

[0108] 3. Perform parametric fitting on the surface of the old blade 11 to obtain the control parameters for surface fitting.

[0109] (1) Select N=7, and divide the old moving blade 11 into 7 blade profile sections evenly along the blade height direction in the polar coordinate system. The specific implementation method is as follows:

[0110] (2) Using a second-order Bézier curve, the mid-arc C of the i-th (1≤i≤7) blade section of the old moving blade is... i Curve fitting is performed, with the mid-arc C i N is selected uniformly above C =100 (90≤N) C For discrete points ≤150, the standard deviation (RSD) of the curve fitting must satisfy RSD≤1E-3. After fitting, the arc C in the i-th leaf section is obtained. i Bézier curve control point P i and leading edge point LE i C i Tail edge point TE i The coordinates of the blade section and the inlet geometry β. 1,i Exit geometric angle β 2,i and leaf chord length Cord i .

[0111] (3) Using an nth-order (n≥3) Bezier curve, the pressure surface profile PS of the i-th airfoil section of the old moving blade is... i Suction surface profile SS i Curve fitting is performed. During the fitting process, the airfoil pressure surface profile PS i Suction surface profile SS i N are selected uniformly above P =N S =120 discrete points. After fitting, the control points P of the Bezier curve of the airfoil are obtained. i Let i = 0, 1, ..., n, and let y = b(x) be the nth-order Bezier curve for the leaf thickness distribution.

[0112] (4) Taking the centroid O of the i-th airfoil section curve as an example i The points are discrete, with N=7 points. An n-order (n≥3) Bézier curve is used to fit the old blade stacking curve. After fitting, the old blade stacking curve SL and the Bézier curve control points P of the curve are obtained. i , i = 0, 1, ..., n and the order n of the Bézier curve.

[0113] 4. Based on the parametric fitting results of the old blade 11, determine the surface shape of the new blade 21.

[0114] (1) By adjusting the arc C of the i-th airfoil section of the original moving blade i By obtaining the parameters of the Bessel fitting curve, the Bessel fitting curve of the arc in the i-th airfoil section of the small energy-saving blade is obtained, thus completing the arc C′ in the i-th airfoil section of the small energy-saving blade. i In terms of design and implementation, the blade angle adjustment coefficient ε1 = 0.7 and the blade length adjustment coefficient ε2 = 0.7.

[0115] (2) The mid-arc C′ based on the i-th airfoil section of the small energy-saving blade i The pressure surface profile PS′ of the i-th airfoil section of the small energy-saving blade is determined by superimposing the blade thickness distribution on both sides of the profile curve and shaping the leading and trailing arc curves on the leading and trailing edges of the airfoil section. i and suction surface profile SS′ i The shape is then determined, thus completing the blade profile curve shape for the i-th blade section. During implementation, the blade thickness adjustment coefficient ε3 = 0.9, and the leading edge arc radius R′... 1,i =3.5%·Cord′ i The radius of the trailing edge arc curve is R′ 2,i =2.5%·Cord′ i .

[0116] (3) The airfoil profiles (including the pressure surface profile PS′) of the small energy-saving blades with N=7 airfoil sections. i and suction surface profile SS′ i (i = 1, ..., N) are stacked along the leaf height direction to generate a three-dimensional shape of a small energy-saving blade. In this way, the curved surface shape of the new blade 21 is completed.

[0117] 5. Based on the invention of this invention, and referring to the dimensions of the old blade root guide circle 12 and the old blade chassis 13 of the original moving blade 1, the design of the new blade root guide circle 22 and the new blade chassis 23 of the small energy-saving blade 2 is completed. The radius of curvature R of the new blade root guide circle 22 is... 22 And the radius of curvature R of the old leaf root guide circle 12 12 Satisfy R 22 =R 12 =20mm. After the above steps, the three-dimensional model of the small energy-saving blade 2 is completed.

[0118] 6. Based on the designed small energy-saving blades and the existing moving blades, determine the arrangement and installation method of the hybrid blades on the hub. The specific implementation method is as follows:

[0119] (1) Before and after the modification, the number of single-stage moving blades of the fan M=22 remained unchanged. After the modification, M / 2=11 blades were replaced with small energy-saving blades. The original moving blades M / 2=11 remained unchanged. The small energy-saving blades and the original blades were arranged alternately.

[0120] (2) The centroid O1 of the first airfoil section (i.e., the blade root section) of the original old blade is located on the rotation center line of the old blade chassis 13, and the centroid O′1 of the first airfoil section (i.e., the blade root section) of the small energy-saving blade is located on the rotation center line of the new blade chassis 23. During the operation of the fan, the installation angle of the first airfoil section (i.e., the blade root section) of the small energy-saving blade is consistent with the installation angle of the first airfoil section of the original old blade, and is adjusted synchronously.

[0121] After the above steps, the design and shaping of the hybrid blades for the dynamically adjustable axial flow fan are complete. When the designed hybrid blades are applied to the dynamically adjustable axial flow fan, the fan not only meets the output requirements of the newly selected operating point after the energy-saving retrofit, but also reduces the overall energy consumption of the fan by more than 10%. The fan's operating economy and equipment applicability are significantly improved, demonstrating the remarkable effectiveness of this energy-saving retrofit.

[0122] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for designing hybrid blades for a dynamically adjustable axial flow fan in a power plant, characterized in that, include: First, the technical route for energy-saving retrofit of the fan is determined based on the fan selection parameters before and after the energy-saving retrofit of the adjustable blade axial flow fan. Then, based on the technical roadmap for energy-saving retrofitting of wind turbines, a design method for the hybrid blades of an adjustable axial flow fan is presented. Finally, based on the designed hybrid blades, the arrangement and installation method of the hybrid blades on the hub are given. The specific implementation method is as follows: 1) Determine the energy-saving retrofit technical route for the adjustable-blade axial flow fan based on the fan selection parameters before and after the retrofit; the fan flow rate corresponding to the fan TB point selection parameters before the retrofit is: The unit is m 3 / s, the total pressure of the fan is The unit is Pa. The fan flow rate corresponding to the TB point selection parameters after the fan energy-saving retrofit is... The unit is m 3 / s, the total pressure of the fan is The unit is Pa; when the technical parameters of the fan before and after the modification meet the preset conditions, the design of the mixed blade of the adjustable axial flow fan is implemented. When the technical parameters of the fan before and after the modification meet the preset conditions, the energy-saving modification effect of the fan can be achieved by the mixed blade design of the adjustable axial flow fan. 2) Determine the design method for the mixing blades of the adjustable axial flow fan. The specific implementation method is as follows: (1) The wind turbine's hybrid moving blade assembly consists of the original moving blades, small energy-saving blades, and a hub; the original moving blades include the old moving blade body, the old blade root guide circle, and the old blade chassis, while the small energy-saving blades include the new moving blade body, the new blade root guide circle, and the new blade chassis; the structure of the new blade chassis is completely identical to that of the old blade chassis, and both the new and old blade root guide circles are circular arc surfaces with the same radius of curvature. ,and mm; The new moving blade surface is based on the old moving blade surface, and the surface shape is reshaped by parametric fitting and adjustment of fitting parameters; (2) Parametric fitting of the surface of the old moving blade is performed to obtain the control parameters for surface fitting; firstly, the old moving blade is uniformly divided along the blade height direction in the polar coordinate system into One leaf-shaped cross section, of which , The values ​​are integers, the first section is the leaf root section, and the second section is the leaf root section. Each section is the blade tip section, and the profile curve of each blade section is formed by the pressure surface profile. Suction surface profile Composition, through the pressure surface profile Suction surface profile The method of curve fitting at discrete points on the curve is used to obtain the curve control parameters for each airfoil section; then, the centroid of the curve for each airfoil section is used as the reference point. For discrete points, use The old blade stacking curve is obtained by fitting a Bézier curve to the old blade stacking curve. And curve control parameters; (3) Determine the surface shape of the new blade based on the parametric fitting results of the old blade surface; 3) Based on the designed wind turbine hybrid blades, the arrangement and installation method of the hybrid blades on the hub are given. The specific implementation method is as follows: (1) Number of single-stage moving blades of the fan before and after the modification Remain unchanged, where If it is an even number, after the modification it will be The blades were replaced with smaller, energy-saving blades. The original moving blades remain unchanged, while small energy-saving blades are arranged alternately with the original blades. (2) The centroid of the first leaf shape section of the original old leaf, i.e., the leaf root section. Located on the rotation centerline of the old blade chassis, the centroid of the first airfoil section of the small energy-saving blade. Located on the rotation center line of the new blade chassis; during the operation of the wind turbine, the installation angle of the first airfoil section of the small energy-saving blade is kept consistent with the installation angle of the first airfoil section of the original old blade, and is adjusted synchronously.

2. The hybrid blade design method for a power plant dynamically adjustable axial flow fan according to claim 1, characterized in that, In step 1), the preset conditions that the technical parameters of the wind turbine before and after the modification need to meet are as follows: The ratio of fan flow rate before and after fan modification meets the requirements. ; The ratio of total pressure of the fan before and after the fan modification meets the requirements. ; Number of blades per stage before wind turbine modification It is an even number.

3. The hybrid blade design method for a power plant dynamically adjustable axial flow fan according to claim 2, characterized in that, In step 1), the energy-saving retrofit effect of the fan is achieved through the design of the adjustable axial flow fan blades. The specific implementation method is as follows: Number of single-stage moving blades of the fan before and after modification The number of blades in a single-stage moving blade remains unchanged. If it is an even number, after the modification it will be Replace the original blades with smaller, energy-saving blades, while retaining the original ones. The blades are arranged alternately with small energy-saving blades and the original blades.

4. The hybrid blade design method for a power plant dynamically adjustable axial flow fan according to claim 1, characterized in that, In step 2), (2) the specific implementation method is as follows: ① Using second-order Bézier curves, the 11th section of the old moving blade was... The mid-arc line of each leaf section Perform curve fitting, where , the middle arc Placed horizontally in a Cartesian coordinate system, the middle arc Leading edge point The origin is (0,0), and the middle arc is... chord length is Mid-arc line Tail edge point The coordinates are ( ,0), middle arc line Selecting uniformly from above discrete points, of which The standard deviation RSD of the curve fit satisfies The control points of the Bézier curve are obtained by fitting the second-order Bézier curve. The coordinates and the equation of the fitted curve function: ; Then, based on the control points of the Bézier curve and the middle arc Leading edge point Mid-arc line Tail edge point The coordinates of the first element are obtained by solving the problem. Inlet geometry of each airfoil section Exit geometry and leaf chord length ; ② Adopt Bézier curve of order 1, , for the old leaf body 11th Pressure surface profile of each air-shaped section Suction surface profile Perform curve fitting; The formula for a Bézier curve is as follows: In the formula, These are the control point numbers for the Bézier curve. For the first One control point, , Let be the order of the Bézier curve. for The time parameters between For parameters The coordinates of the corresponding point on the Bézier curve, For n-order Bernstein basis functions, For combinations, ; middle arc Placed horizontally in a Cartesian coordinate system, the middle arc Leading edge point The origin is (0,0), and the middle arc is... chord length is Mid-arc line Tail edge point The coordinates are ( ,0), pressure surface profile Suction surface profile Select evenly from above , discrete points, During the fitting process, the leading edge point of the blade is maintained. , leaf trailing edge point The position remains unchanged, and a centering arc is used. Applying the same blade thickness distribution to both sides to adjust the pressure surface profile Suction surface profile Curve fitting is performed on discrete points on the curve; the least squares method is used, based on the Bézier fitting curve and the mid-arc line. Solving for the control points of a Bézier curve by minimizing the sum of squared errors between discrete points. , And obtain the order of the Bézier curve. After fitting, the leaf thickness distribution is obtained. Bézier curve and its function equation: ; ③ With the first The centroid of the airfoil section curve Let be discrete points, and the number of discrete points is . ,use The Bézier curve is used to fit the old leaf accumulation curve. During the fitting process, the least squares method was used, based on the Bezier fitting curve and the centroid of the leaf shape. Solving for the control points of the Bézier curve by minimizing the sum of squared errors. , And obtain the order of the Bézier curve. After fitting, the old moving blade stacking curve is obtained. .

5. The hybrid blade design method for a power plant dynamically adjustable axial flow fan according to claim 4, characterized in that, In step 2), (3), the specific implementation method is as follows: ① By adjusting the original moving blades The mid-arc line of the leaf-shaped section The parameters of the Bessel fitting curve were used to obtain the first step of the small energy-saving blade. The Bessel fitting curve of the arc in the first blade section completes the first small energy-saving blade. The mid-arc line of the leaf-shaped section The shape; The inlet geometry angle of the curved Bezier fitting curve in the small energy-saving blade is... The exit geometry is Leaf chord length Determine using the following formula: In the formula, This is the blade angle adjustment coefficient. This is the leaf length adjustment coefficient; Having determined the above parameters, the first step of the small energy-saving blade was thus determined. The mid-arc line of each leaf section Leading edge point Mid-arc line Tail edge point Control points and the middle arc Second-order Bézier curves; ②Based on small energy-saving blades The mid-arc line of each leaf section The shape curves are superimposed on both sides of the blade thickness distribution, and the leading and trailing edge arc curves are shaped at the leading and trailing edges of the blade section. This determines the shape of the small energy-saving blade. Pressure surface profile of each air-shaped section and suction surface profile The shape, thus completing the first The shape of the leaf curve in the cross section; ③Incorporate small energy-saving blades The airfoil profiles of individual blade sections are stacked along the blade height direction to generate a three-dimensional shape of a small energy-saving blade, wherein the airfoil profiles include pressure surface profiles. and suction surface profile , According to the small energy-saving blades Determine the airfoil profile of each airfoil section to identify its centroid. The centroid of the first blade section Starting with small energy-saving blades Center of gravity of each airfoil section , Along the old leaf accumulation curve Arrange them in the correct directions, and that's how you determine the orientation. Center of gravity of each airfoil section and the position of the blade profile; then, the small energy-saving blades... The airfoil profile of each airfoil section passes through the accumulated curve of the old moving blade. By stacking the layers along the height of the blade, the three-dimensional shape of the small energy-saving blade is completed.

6. The hybrid blade design method for a power plant dynamically adjustable axial flow fan according to claim 5, characterized in that, In step 2), (3)-②, the specific implementation method is as follows: First, based on the original moving blade obtained in step (2), Bessel fitting curves for the thickness distribution of individual airfoil sections The thickness distribution function of the airfoil at this cross section is obtained. ,make The abscissa of the blade thickness distribution function is dimensionless, and the result is a simplified function. The thickness of the small energy-saving blade profile section is multiplied by a thickness adjustment coefficient based on the original thickness of the moving blade profile section. , ,Right now ;Let the small energy-saving blades The x-coordinate of each leaf section is The chord length of the blade section is ,but , Organize them into small energy-saving blades. Airfoil thickness distribution function ; Thus, the first small energy-saving blade was determined. The distribution pattern of blade thickness in each blade section; Then, the small energy-saving blades determined in the above steps are... The thickness distribution pattern of each airfoil cross-section is superimposed on the mid-arc line of that airfoil cross-section. On the airfoil profile, pressure surface curves and suction surface curves are generated. Leading edge and trailing edge circular arc curves are constructed at the leading and trailing edges of the airfoil section, respectively. Both leading and trailing edge circular arc curves are arc segments, tangent to the pressure and suction surface curves generated above. Furthermore, at this airfoil section, the radius of the leading edge circular arc curve of the small energy-saving blade is... satisfy: ; Small energy-saving blade trailing edge arc radius satisfy: Thus, the first small energy-saving blade was determined. Pressure surface profile of each air-shaped section and suction surface profile , pressure surface profile and suction surface profile When combined, this completes the first small energy-saving blade. The construction of the airfoil profile of each airfoil section.

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