Curvature fairing method for front edge and rear edge of blade modeling section line

Abstract

The invention relates to the technical field of section line fairing, in particular to a curvature fairing method for the front edge and the rear edge of a blade modeling section line, and the method comprises the following steps: 1, importing a three-dimensional model of an impeller, and obtaining the blade section line of the impeller; step 2, solving discrete points on the section line in an isoparametric manner, and converting Cartesian three-dimensional coordinates of the discrete points into two-dimensional cylindrical coordinates; 3, finding out an initial leading edge endpoint and an initial trailing edge endpoint of the section line by using a central axis algorithm; step 4, according to the curvature of the front edge endpoint and the curvature of the rear edge endpoint, determining a segmentation point of the front edge endpoint and a segmentation point of the rear edge endpoint respectively; 5, the curvature of the front edge and the curvature of the rear edge are smoothed, curve smoothing is carried out in a third-order derivative mode, position constraint and end point constraint are carried out on the basis of an original curve, and the curve can achieve the curve smoothing effect within the minimum range.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cross-section line fairing, and particularly relates to a method for fairing the curvature of the leading edge and the trailing edge of a blade modeling cross-section line. BACKGROUND

[0002] Complex curved surfaces play a vital role in the production and manufacturing of key components such as aero-engine blades, generator blades, and steam turbines. The three-dimensional model of these components is usually constructed based on aerodynamic data or other calculated data, and the blade shape is constructed by using type value points. Specifically, this process involves a method of "cross-section curve interpolation type value point - surface passing through cross-section curve" to construct the blade shape. As shown in FIG. 1, a blade profile is generally composed of four curves of a blade basin, a blade back, a leading edge, and a trailing edge, wherein the shape of the leading edge and the trailing edge of the blade has a significant influence on the aerodynamic performance of the blade profile. Figure 1

[0003] In the traditional design of the leading edge and the trailing edge of the blade, the center and the radius position of the leading edge and the trailing edge are usually given as known conditions, and a cross-section line is created by connecting the first-order geometric continuity of the leading edge and the trailing edge with the blade back and the blade basin, thereby completing the surface modeling. However, with the development of technology, more and more methods begin to directly represent the shape by using type value points, and a second-order geometric continuous cross-section line is created by directly interpolating the type value points. For an axial flow blade, the curvature of the leading edge and the trailing edge of the blade body changes greatly, and the shape has an extremely important influence on the aerodynamic performance of the blade. Therefore, it is necessary to perform curve curvature fairing processing on the leading edge and the trailing edge of the cross-section line of the blade.

[0004] In the fairing of the blade cross-section line, different methods are proposed, including the energy method, the circular rate method, and the local rebound method. The energy method is mainly used for the fairing of spatial curves and spatial net lines, and it studies the deformation of the curve from the perspective of energy. With the decrease of the elastic energy, the curve tends to be fairing. The circular rate method is a point selection modification method, which does not need to interpolate the curve. According to the geometric position of the type value point, the bad point is found out and modified, but this method is mainly suitable for large deflection curves or closed curves. The local rebound method is mainly used for the fairing of planar curves, and can also be used for the fairing of spatial curves. It is a curve fairing method of point selection modification, which simulates the manual fairing process.

[0005] The above-mentioned fairing methods of the blade cross-section line still have some deficiencies. They mainly perform curvature fairing on the overall blade surface, although the overall blade modeling is improved, but the local modeling of the blade is ignored, for example, the significant influence of the leading edge and the trailing edge of the blade on the performance, which leads to the fact that the fairing effect is still difficult to achieve the ideal effect. SUMMARY

[0006] ​The present application aims to avoid the deficiencies in the prior art and provide a method for smoothing the curvature of the leading edge and trailing edge of a blade profile cross-section line, which performs position constraint and end point constraint of the leading edge and trailing edge on the basis of the original curve, so that the curve achieves the curve smoothing effect in the minimum range.

[0007] To achieve the above object, the present application provides the following technical solutions.

[0008] The present application provides a method for smoothing the curvature of the leading edge and trailing edge of a blade profile cross-section line, comprising the following steps.

[0009] Step 1: importing a three-dimensional model of an impeller to obtain a blade cross-section line of the impeller;

[0010] Step 2: obtaining discrete points on the cross-section line at equal parameters, and transforming the Cartesian three-dimensional coordinates of the discrete points into two-dimensional cylindrical coordinates;

[0011] Step 3: finding the initial leading edge end point and the initial trailing edge end point of the cross-section line by using a center axis algorithm;

[0012] Step 4: determining the split point of the leading edge end point and the split point of the trailing edge end point according to the curvature of the leading edge end point and the curvature of the trailing edge end point, respectively, wherein the split point of the leading edge end point is used to determine the shape and position of the leading edge, and the split point of the trailing edge end point is used to determine the shape and position of the trailing edge;

[0013] Step 5: smoothing the curvature of the leading edge according to the split point of the leading edge end point, and smoothing the curvature of the trailing edge according to the split point of the trailing edge end point.

[0014] In some embodiments, the step 1 comprises the following steps.

[0015] In the three-dimensional space, the three-dimensional model of the impeller is intersected with the XY plane to obtain the generatrix N m1 , N m2 , N m1 , N m2 as the upper and lower boundaries of the impeller profile, respectively; other rotating generatrices N m1 , N m2 are obtained by equal parameter interpolation within the range of N i , N i are respectively rotated around the X axis to obtain curved surfaces Nc i , Nc i , and the intersection of the curved surfaces Nc i and the three-dimensional model of the blade of the impeller obtains the cross-section line L i of the blade.

[0016] In some embodiments, the step 2 comprises the following steps.

[0017] In the cross-section line L iThe discrete point P is obtained by using the above parameters. ij (j = 0, 1, ..., m)

[0018] By transforming the coordinates, the discrete point P ij The transformation from Cartesian coordinates to two-dimensional cylindrical coordinates involves the Cartesian coordinates changing from (x...) to (x...) ij ,y ij ,z ij ) represents the two-dimensional cylindrical coordinates, denoted by (r ij ,θ ij ,x ij Its length-preservation transformation formula is as follows:

[0019]

[0020] x ij =x ij ;

[0021] The obtained two-dimensional cylindrical coordinates (m) ij ,r ij *θ ij Projected onto a two-dimensional plane, where m ij Indicates in (x ij ,r ij The arc length along the cross-section line on the plane.

[0022]

[0023] Integrating both sides of the above formula, we get:

[0024]

[0025] Discrete points P of the cross-section line ij Projecting onto a two-dimensional plane yields coordinates P. ij (m ij ,r ij *θ ij ), thus obtaining the coordinates of discrete points on the cross-section line.

[0026] In some implementations, step 3 includes the following steps:

[0027] Step 3.1: Use the centerline algorithm to find the cross-section line L. i The initial leading and trailing edge endpoints are q i h i , with q i h i As the initial dividing point, the cross-section line L i It is divided into an upper cross-section line and a lower cross-section line;

[0028] Step 3.2: When calculating the leading edge of the upper section line, use q iThe curvature of each point on the leading edge curve is calculated as the starting point; then the ratio K is obtained by comparing the curvature of the next point in the leading edge with the curvature of the previous point, and the point represented by the numerator of the maximum K is the initial leading edge split point q i1 ;

[0029] When calculating the leading edge of the lower section line, the lower section line is obtained as q i2 ;

[0030] Step 3.3: Map the leading edge section line into the (m', θ) plane, and the tangent direction is the angle α between the m' axis, which is the blade angle, and the conformal transformation formula is

[0031]

[0032] Find two points q i1 ' and q i2 ', which are along the initial split points q i1 and q i2 of the upper and lower section lines along the leading edge tangent, and the angle between them is the maximum; find a point Q i1 in (q i2 ', q i ) along the leading edge tangent, which has the minimum difference in angle with q i and q i1 along the leading edge tangent, and obtain the leading edge end point Q i2 . i ;

[0033] If the section line L i has a trailing edge, then h i is taken as the starting point to perform the leading edge calculation, and the trailing edge end point H i is obtained.

[0034] In some embodiments, the step 4 includes the following steps:

[0035] When determining the split point of the leading edge end point, the following steps are performed:

[0036] Step 4.1: Calculate the leading edge of the upper section line, and take the point P ij (j = 0, 1,.., r) as the starting point to calculate the derivative D ij of the point,

[0037] Step 4.2: Use the starting point P ij and the last three points P i,j+1 , P i,j+2 , and P i,j+3 to fit a straight line and calculate the derivative d of the straight line,

[0038] Step 4.3: Calculate the starting point P ijIf the angle θ' is greater than a set angle threshold, return to step 4.1 and modify the starting point to P i,j+1 , and continue to execute;

[0039] If the angle θ' is not greater than the set angle threshold, find the split point Q i1 of the leading edge of the upper cross-section line

[0040] When calculating the leading edge of the lower cross-section line, obtain the split point Q i2 of the leading edge of the lower cross-section line in the same way as the leading edge of the upper cross-section line

[0041] When calculating the trailing edge of the upper cross-section line, take P ij (j = u, u - 1,..., 0) as the starting point, and then execute the steps of obtaining Q i1 , to obtain the split point H i1 ' of the trailing edge of the upper cross-section line

[0042] When calculating the trailing edge of the lower cross-section line, obtain the split point H i2 of the trailing edge of the lower cross-section line in the same way as the trailing edge of the upper cross-section line

[0043] In some embodiments, the step 5 comprises the following steps:

[0044] When smoothing the curvature of the leading edge, the following steps are executed:

[0045] Step 5.1: Set the objective function E

[0046] min(E) = min(ω1K(t) + ω2D(F))

[0047] ω1, ω2 represent the weights with respect to the rate of change of curvature and the deviation of coordinates; K(t) is the sum of squares of the third derivatives of all points of the smoothed curve, representing the rate of change of curvature; D(F) represents the sum of squares of the deviation between all points of the smoothed curve and the original coordinates;

[0048] Step 5.2: Set the constraint conditions:

[0049] 1) Position constraint: the points of the smoothed curve are smaller than the points of the original cross-section line;

[0050] 2) Shape constraint: the coordinates of the leading edge endpoints Q i , the leading edge split points Q i1 and Q i2 , the maximum curvature points Q ic1 and Q ic2 of the leading edge do not change;

[0051] 3) End point constraint: take the ratio of the arc length of the leading edge of the cross-section line to the arc length of the cross-section line to take the equal proportion arc length of the blade and Q is1 、Q is2 are the end points of the arc length on the airfoil, which ensure the continuity of the second derivative of the points within the two arc lengths;

[0052] For the same cross-sectional line L i , C(t) is the B-spline curve C(t) interpolating the end points Q i , the leading edge split points Q i1 and Q i2 , the maximum curvature points on the leading edge Q ic1 , Q ic2

[0053]

[0054] are the control points of the B-spline curve, are the basis functions of the B-spline curve defined on the node vector U = (u0, u1,..., u n+p+1 );

[0055] Step 5.3: Fair the curvature of the cross-sectional line L i , and propose the objective function E

[0056] Ensure the smoothness of the curvature distribution of the leading edge, i.e. the smoothness of the third derivative of the curve points

[0057]

[0058] Combine the position constraints

[0059]

[0060] are the original points of the leading edge of the cross-sectional line L i ; t are the parameter values of ; l is the chord length of the adjacent discrete points;

[0061] The objective function E is:

[0062]

[0063] Assume that the leading edge end points Q i are at the parameter values t r1 , the maximum curvature points on the leading edge Q ic1 , Q ic2 are at t r2 , t r3 , the leading edge split points Q i1 and Q i2 are at 0 and 1, and the final objective function is expressed as:

[0064] ​

[0065] Solve the high-order equation set E by using the nonlinear least square method, and the C(t) represented in the minimum E is the most smooth leading edge section line;

[0066] When the curvature of the trailing edge is smoothed, the process is performed in the manner of smoothing the curvature of the leading edge as described above, and the most smooth trailing edge section line is obtained.

[0067] The blade modeling section line leading edge and trailing edge curvature smoothing method has the following beneficial effects:

[0068] (1) The blade modeling section line leading edge and trailing edge curvature smoothing method disclosed in the present application divides the leading edge and the trailing edge of the blade, optimizes the curve curvature of the leading edge and the curve curvature of the trailing edge, and then smooths the leading edge and the trailing edge. Specifically, the equidistant two-dimensional section line of the blade is calculated on the three-dimensional model of the blade, the leading and trailing endpoints of the section line are found in the two-dimensional plane by using the center axis algorithm and the three-dimensional shape preserving method, the division of the leading and trailing edges of the section line is completed, and the curvatures of the leading and trailing edges are optimized to find the curve with the most smooth curvature distribution in the search space, so as to realize the curvature smoothing of the leading and trailing edges of the blade section line and improve the quality of the blade.

[0069] (2) The blade modeling section line leading edge and trailing edge curvature smoothing method disclosed in the present application can be operated only by using the three-dimensional model of the blade, has high adaptability, and can be widely applied to the design and manufacturing of blades of different types and sizes. BRIEF DESCRIPTION OF DRAWINGS

[0070] Figure 1 is a schematic diagram of the blade modeling of the embodiment of the present application.

[0071] Figure 2 is a flow route of the blade modeling section line leading edge and trailing edge curvature smoothing method of the embodiment of the present application.

[0072] Figure 3 is a flow diagram of smoothing the curvatures of the leading edge and the trailing edge of the embodiment of the present application.

[0073] Figure 4 is a schematic diagram of the endpoint constraint of the embodiment of the present application. DETAILED DESCRIPTION

[0074] The preferred embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although the preferred embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to make the present application more thorough and complete, and to fully convey the scope of the present application to those skilled in the art.

[0075] Example 1

[0076] The embodiment discloses a method for smoothing the curvature of the leading edge and the trailing edge of a blade profile section line, as shown in the accompanying drawings, comprising the following steps: Figure 2

[0077] Step 1: import a three-dimensional model of an impeller, and obtain a blade section line of the impeller, specifically comprising:

[0078] In a three-dimensional space, the impeller model directly intersects with an XY plane to obtain a parent curve N m1 , N m2 , the parent curve N m1 , N m2 ; N m1 , N m2 as upper and lower boundaries, and other rotating parent curves N i (i = 1, 2,..., n) are obtained by equal parameter interpolation within the range of N m1 , N m2 . N i is respectively rotated around the X axis to obtain a curved surface Nc i , Nc i intersects with the three-dimensional model of the blade to obtain a section line L i of the blade.

[0079] Step 2: obtain discrete points on the section line by equal parameter, and transform the Cartesian three-dimensional coordinates of the discrete points into two-dimensional cylindrical coordinates, specifically comprising:

[0080] Discrete points P ij (j = 0, 1,..., m) are obtained on the section line L i by equal parameter; Cartesian coordinates of the discrete points P ij are changed to cylindrical coordinates by coordinate transformation. Cartesian coordinates are represented by (x ij , y ij , z ij ), and cylindrical coordinates are represented by (r ij , θ ij , x ij ), and the isometric transformation formula is as follows:

[0081]

[0082] x ij = x ij

[0083] The obtained cylindrical coordinates (m ij , r ij * θ ij ) are in the (x ij , r ij ) plane, wherein m ij represents the arc length along the section line in the (x ij , r ij ) plane

[0084]

[0085] Since the cross-section line can be parameterized as a B-spline curve, integrating both sides of the above formula yields:

[0086]

[0087] Based on the discrete point P of this cross-section line ij The coordinates P can be obtained by projecting onto a two-dimensional plane. ij (m ij ,r ij *θ ij ).

[0088] Step 3: Use the centerline algorithm to find the initial leading and trailing endpoints of the cross-section line, specifically including:

[0089] Using the centerline algorithm, find all cross-sectional lines L. i The leading and trailing edge endpoints Q i H i Follow these steps:

[0090] Step 3.1: Use the centerline algorithm to find the cross-section line L. i The initial leading and trailing edge endpoints q i h i . with q i h i As the dividing point, the cross-section line L i It is divided into two parts, upper and lower.

[0091] Step 3.2: Taking the leading edge of the above cross-section line as an example, with q... i Calculate the curvature at each point on the curve, starting from the initial point; then, calculate the numerator of the curvature at each subsequent point and compare it with the curvature at the previous point to obtain the ratio K. The point represented by the largest numerator of K is the initial leading edge split point q. i1 The lower cross-section line is q. i2 .

[0092] Step 3.3: Map the leading edge section line onto the (m', θ) plane. The angle α between its tangent direction and the m' axis is the blade angle. The conformal transformation formula is:

[0093]

[0094] Find two points q i1 '、q i2 ', the initial dividing point q of the two points along the tangent to the leading edge and the upper and lower section lines. i1 q i2 The angle between the tangents along the leading edge is the largest; at (q i1 ',q i2 Find a point Q within ')i , Q i along the tangent of the leading edge and q i1 , q i2 along the tangent of the leading edge has the smallest difference, Q i is the end point of the leading edge.

[0095] If the section line has a trailing edge, take h i as the start point and perform the same method above to obtain the end point H i .

[0096] Step 4: Determine the split point of the leading edge end point and the split point of the trailing edge end point according to the curvature of the leading edge end point and the curvature of the trailing edge end point, specifically including:

[0097] Take the section line L is above as an example to complete the split of the leading edge and the trailing edge, and perform the following steps:

[0098] Step 4.1: Take the leading edge L is1 as an example, and calculate the derivative D ij of the point P ij (j = 0, 1,..., r) as the start point.

[0099] Step 4.2: Use the start point P ij and the next three points P i,j+1 , P i,j+2 , P i,j+3 fit a straight line and calculate the derivative d of the straight line.

[0100] Step 4.3: Calculate the angle θ' between the tangent of the section line and the fitted straight line at the start point P ij . If the angle θ' is greater than a set angle threshold, return to the first step and modify the start point to P i,j+1 , and continue to execute.

[0101] If the angle θ' is not greater than the set angle threshold, it is considered that the split point Q i1 of the leading edge is found.

[0102] For the split point H is2 ' of the trailing edge L i1 , search in the opposite direction and perform the above steps, that is, the start point P ij (j = u, u-1,..., 0); for the lower section line L ix , the above steps can complete the split of the leading edge Q i2 and the trailing edge H i2 .

[0103] Step 5: Smooth the curvature of the leading edge and the curvature of the trailing edge, specifically including:

[0104] Take the leading edge of the blade as an example, as shown in Figure 3The figure shows that n is the number of the rotating generatrixes:

[0105] Step 5.1: Set the objective function E

[0106] min(E) = min(ω1K(t) + ω2D(F))

[0107] ω1, ω2 represent the weight of the rate of change of curvature and the coordinate deviation; K(t) is the sum of squares of the third derivative of all points of the smoothed curve, representing the rate of change of curvature; D(F) represents the sum of squares of the deviation between all points of the smoothed curve and the original coordinates;

[0108] Step 5.2: Set the constraint condition: such as Figure 4 as shown,

[0109] 1) Position constraint: the deviation between the points of the smoothed curve and the original section line points is small.

[0110] 2) Shape constraint: the coordinates of the leading edge end point Q i , the leading edge split point Q i1 and Q i2 , the maximum curvature points of the leading edge Q ic1 , Q ic2 do not change;

[0111] 3) End point constraint: as shown, Figure 4 the equal proportion arc length of the blade is taken as the ratio of the arc length of the leading edge of the section line to the arc length of the section line and Q is1 , Q is2 are the end points of the arc length on the blade; it is ensured that the first and second derivatives of the points within the two arc lengths are continuous.

[0112] For the same section line L i , C(t) is the B-spline curve C(t) i , Q i1 and Q i2 , Q ic1 , Q ic2 interpolated by the end points Q

[0113]

[0114] is the control point of the B-spline curve, is the basis function of the B-spline curve defined in the node vector U = (u0, u1,..., u n+p+1 );

[0115] Thirdly, the section line L i is smoothed in curvature, and the objective function E is proposed

[0116] For example, the curvature distribution of the leading edge is ensured to be smooth, i.e. the third derivative of the curve point is smooth

[0117]

[0118] Combined position constraint

[0119]

[0120] is the section line L i The original point of the leading edge; is the parameter value of ; l is the chord length of the adjacent discrete points, because is the equal parameter taking point l can be regarded as a constant.

[0121] The objective function E can be expressed as:

[0122]

[0123] Therefore, the final objective function can be expressed as, assuming the leading edge end point Q i The in the leading edge parameter value is t r1 , the maximum point Q ic1 , Q ic2 of the upper and lower curvatures of the leading edge t r2 , t r3 , the leading edge split point Q i1 and Q i2 are 0 and 1.

[0124]

[0125] The high-order equation set E is solved by using the nonlinear least square method, and C(t) represented in the minimum E is the most smooth leading edge section line.

[0126] The above proposes a method for smoothing the leading edge and trailing edge curvatures of the blade modeling section line. The leading edge and trailing edge end points are found by the center axis algorithm, length preserving and shape preserving algorithm, and then the first derivative of the section line calculation point is compared with the first derivative of the straight line fitted by the three points after the point, the leading edge and trailing edge range is found within the angle threshold, the third derivative is used to construct the objective function within the leading edge and trailing edge range, and the shape constraint, position constraint and end point constraint are set, and then the nonlinear least square method is used to solve. The curve represented in the minimum value of the objective function is the most smooth curve. Compared with other commonly used methods, this method uses the third derivative to smooth the curve, and position constraint and end point constraint are added based on the original curve, which can make the curve reach the curve smoothing effect in the smallest range.

[0127] The above smoothing method focuses on the curvature smoothing of the leading and trailing edges of the blade section line. On the basis of extracting the leading and trailing edges of the blade two-dimensional section line on the three-dimensional model of the impeller, the curve smoothing method for finding the optimal curvature distribution in the coordinate space is realized. The working angle of the existing literature is mostly on the overall curvature smoothing of the blade surface. Although the overall blade modeling is improved, the local modeling such as the leading and trailing edges has a significant influence on the performance. The targeted optimization of these key local areas can achieve similar or even better performance than the overall optimization. In addition, some literature focuses on the segmentation of the leading and trailing edges of the blade, but does not optimize the curvature to improve the blade modeling.

[0128] In the embodiment, the equidistant two-dimensional section line of the blade is calculated by using the shape preserving method on the three-dimensional model of the blade. The mid-axis algorithm and the three-dimensional shape preserving method are used to find the leading and trailing end points of the section line in the two-dimensional plane. The angle between the tangent of the point on the section line and the straight line fitted by the three points behind the point is calculated. The segmentation of the leading and trailing edges of the section line is completed by setting the angle threshold. The position, shape and end point constraints are set. The third derivative of the curve is used to establish the objective function E. The most smooth curve with the optimal curvature distribution in the search space is found.

[0129] The embodiment only needs the three-dimensional model of the blade and has high adaptability.

[0130] In addition, it should be noted that the use of "first", "second" and the like to limit parts is only for the convenience of distinguishing the corresponding parts, and the above words have no special meaning without further declaration, so it cannot be understood as a limitation on the protection scope of the present application.

[0131] The above only describes the preferred embodiments of the application and is not intended to limit the application. For those skilled in the art, the application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method of fairing the curvature of the leading edge and the trailing edge of a profiled cross-section of a blade, characterized in that, The method comprises the following steps: Step 1: importing a three-dimensional model of an impeller, and obtaining a blade section line of the impeller; Step 2: obtaining discrete points on the section line at equal parameters, and transforming Cartesian three-dimensional coordinates of the discrete points into two-dimensional cylindrical coordinates; Step 3: finding initial leading edge end points and initial trailing edge end points of the section line by using a center axis algorithm; Step 4: determining a split point of the leading edge end points and a split point of the trailing edge end points according to curvatures of the leading edge end points and curvatures of the trailing edge end points respectively, wherein the split point of the leading edge end points is used to determine a shape and a position of a leading edge, and the split point of the trailing edge end points is used to determine a shape and a position of a trailing edge; Step 5: smoothing curvatures of the leading edge according to the split point of the leading edge end points, and smoothing curvatures of the trailing edge according to the split point of the trailing edge end points.

2. The method of fairing the curvature of the leading and trailing edges of a profiled cross-sectional line of a blade according to claim 1, characterized in that, The step 1 comprises the following steps: In three-dimensional space, intersect the impeller three-dimensional model with XY plane to obtain the generatrix N m1 , N m2 , N m1 , N m2 respectively as the upper and lower boundaries of the impeller profile; in the range of N m1 , N m2 as the upper and lower boundaries, other rotating generatrix N i (i=1, 2,..., n) is obtained by equal parameter interpolation; N i is respectively rotated around the X axis to obtain the curved surface Nc i , Nc i is intersected with the blade three-dimensional model of the impeller three-dimensional model to obtain the cross section line L i of the blade.

3. The method of fairing the curvature of the leading and trailing edges of a profiled cross-sectional line of a blade according to claim 2, characterized in that, The step 2 comprises the following steps: At the cross section line L i The upper parameter obtains the discrete point P ij (j = 0, 1,..., m) By coordinate transformation, the Cartesian coordinates of the discrete points P ij are changed to two-dimensional cylindrical coordinates, which are represented by (x ij ,y ij ,z ij ) and two-dimensional cylindrical coordinates are represented by (r ij ,θ ij ,x ij ). The conformal transformation formula is as follows: x ij = x ij ; The obtained two-dimensional cylindrical coordinates (m ij ,r ij *θ ij ) are projected onto a two-dimensional plane, wherein m ij represents an arc length along a cross-sectional line on the (x ij ,r ij ) plane, Integrating both sides of the above formula to obtain: The discrete points P of the cross-section line ij are projected to a two-dimensional plane to obtain coordinates P ij (m ij ,r ij *θ ij ), obtaining the discrete point coordinates of the cross-section line.

4. The method of fairing the curvature of the leading and trailing edges of a profiled cross-sectional line of a blade according to claim 3, wherein, The step 3 comprises the following steps: Step 3.1: Find the section line L using the center axis algorithm i with initial leading and trailing edge end points q i , h i , and with q i , h i as initial split points, split the section line L i into an upper section line and a lower section line; Step 3.2: When calculating the leading edge of the upper section line, calculate the curvature of each point on the leading edge curve with q i as the starting point; then take the ratio K of the curvature of the next point on the leading edge to the curvature of the previous point; the point represented by the numerator of the largest K is the initial leading edge split point q i1 ; When calculating the leading edge of the lower cross-section line, the lower cross-section line is obtained as q i2 ; Step 3.3: mapping the leading edge section line into an (m', θ) plane, and an angle α between a tangent direction of the leading edge section line and the m' axis is a blade angle, wherein a conformal transformation formula is Finding two points q i1 ', q i2 ', the initial segmentation points of the upper and lower section lines along the leading edge tangent i1 ', q i2 The angle along the leading edge tangent is maximum; find a point Q i1 ', q i2 ' within (q i ', Q i ' along the leading edge tangent and q i1 ', q i2 The difference of the angle along the leading edge tangent is minimum, and the leading edge end point Q i is obtained; If the section line L i h i is the starting point, the trailing edge end point H i is obtained in the same way as for the leading edge.

5. The method of fairing the curvature of the leading and trailing edges of a profiled cross-sectional line of a blade according to claim 4, characterized in that, The step 4 comprises the following steps: When the split point of the leading edge end points is determined, the following steps are performed: Step 4.1: Calculate the leading edge time of the upper cross section line with point P ij (j = 0, 1,.., r) as the starting point to calculate the derivative D of the point ij , Step 4.2: Using starting point P ij The last three points P i,j+1 , P i,j+2 , P i,j+3 Fit a straight line and calculate the derivative d of this line, Step 4.3: Calculate the starting point P ij the angle θ' between the tangent of the section line and the fitting straight line, if the angle θ' is greater than a set angle threshold, return to step 4.1 and modify the starting point as P i,j+1 , continue to execute; If the included angle θ' is not greater than a set angle threshold, a split point Q of the leading edge of the upper cross section line is found i1 , When the leading edge of the lower cross-section line is calculated, the split point Q of the leading edge of the lower cross-section line is obtained in the same way as the leading edge of the upper cross-section line i2 ; When the trailing edge of the upper cross section line is calculated, the point P ij (j = u, u - 1,..., 0) is taken as a starting point, and the steps of obtaining Q i1 are executed again to obtain the division point H i1 ' of the trailing edge of the upper cross section line. When the trailing edge of the lower cross-sectional line is calculated, the split point H of the trailing edge of the lower cross-sectional line is obtained in the same manner as the trailing edge of the upper cross-sectional line i2 .

6. The method of fairing the curvature of the leading and trailing edges of a profiled cross-sectional line of a blade according to claim 5, wherein The step 5 comprises the following steps: When the curvatures of the leading edge are smoothed, the following steps are performed: Step 5.1: setting a target function E min(E) = min(ω1K(t) + ω2D(F)) ω1 and ω2 represent weights about a curvature change rate and a coordinate deviation; K(t) is a sum of squares of third derivatives of all points of a smoothed curve, and represents the curvature change rate; D(F) represents a sum of squares of deviations between all points of the smoothed curve and original coordinates; Step 5.2: setting constraint conditions: 1) position constraint: points of the smoothed curve are smaller than points of the original section line; 2) Shape constraints: leading edge end point Q i , leading edge split point Q i1 , and Q i2 , leading edge upper and lower curvature maxima Q ic1 , Q ic2 coordinates do not change; 3) End constraint: take the equal proportion arc length of blade with the ratio of the arc length of the leading edge of the section line and the arc length of the section line and Q is1 , Q is2 The end points of the arc length on the blade ensure the continuity of the first and second derivatives of the points within the two arc lengths. For the same section line L i , C(t) is the B-spline curve C(t) interpolated at the end points Q i , the leading edge split point Q i1 , and Q i2 , the maximum upper and lower curvature points on the leading edge Q ic1 , Q ic2 ​ are the control points of a B-spline curve, are the basis functions of a B-spline curve defined on the knot vector U = (u0, u1,..., u n+p+1 ). Step 5.3: On section line L i Curvature fairing, objective function E guaranteeing curvature distribution smoothing of the leading edge, that is, smoothing of the third derivative of the curve points combining the position constraint is the cross-sectional line L i the point of the leading edge as originally; is the parameter value; l is the chord length of the adjacent discrete point; The target function E is: Assume the leading edge end point Q i At the leading edge parameter value t r1 , the leading edge upper and lower curvature maximum points Q ic1 , Q ic2 At t r2 , t r3 , the leading edge split points Q i1 and Q i2 0 and 1, the final objective function is expressed as: a high-order equation group E is solved by using a nonlinear least square method, and C(t) represented in the minimum E is the most smoothed leading edge section line; When the curvatures of the trailing edge are smoothed, the curvatures of the leading edge are smoothed in the above manner, and the most smoothed trailing edge section line is obtained.

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