A parametric blade slot design method based on Bezier curve

Abstract

The present invention discloses a parameterized blade slot design method based on Bezier curves, and the main process of its implementation includes: step one, giving slot blade geometry design parameters; step two, transforming the original blade geometry to a relative chord length coordinate system; step three, calculating the slot outlet fillet curve; step four, calculating the slot outlet quadratic Bezier curve; step five, calculating the quadratic Bezier curves of the inner walls on both sides of the slot and the slot inlet fillet curve; step six, calculating the slot inlet quadratic Bezier curve; step seven, inversely transforming the slot blade geometry to an absolute coordinate system. By giving the original blade geometry and slot design parameters, the slot geometry of the slotted blade is generated using the Bezier curve, thereby realizing the rapid design of the slot geometry of high-load compressor blades. The designed slotted blade geometry can better regulate the high-load compressor flow field, effectively suppress the three-dimensional corner zone separation flow of the high-load compressor, and has important engineering application prospects.

Description

Technical Field

[0001] The invention relates to the field of compressor flow control of an aero-engine, and in particular to a parameterized blade slotting design method based on a Bezier curve. Background Art

[0002] The compressor is the core component of the aircraft engine and a basic strategic industry for technologically advanced countries. With the development of modern aviation technology, the thrust-to-weight ratio requirements for aircraft engines are becoming higher and higher, which means that the compressor must increase its overall load on the one hand, and reduce the number of stages and increase the single-stage load level on the other hand. However, with the increase of the compressor load level, the adverse pressure gradient in the blade channel gradually intensifies, causing the low-energy fluid to gradually accumulate toward the end area of ​​the blade suction surface, and then develop into a three-dimensional corner zone separation flow, blocking the blade channel and seriously reducing the aerodynamic performance of the compressor. Under high load conditions, the three-dimensional corner zone separation flow further evolves into a three-dimensional corner zone stall flow, and even develops into a large separation flow covering the entire blade height channel, resulting in a sharp decline in compressor performance, which has an important impact on the compressor's pressure ratio, efficiency, margin, etc. In order to control the three-dimensional corner zone separation flow of the compressor, various flow control methods have been introduced. The active control method has a good control effect, but it requires additional energy and is limited in engineering applications; the passive control method often faces the characteristics of good effect in a single condition, but it is difficult to be widely applied to a wide range of conditions.

[0003] Our research group has previously proposed a technology for controlling compressor stator angular separation by blade root slotting (Gas Turbine Test and Research, 2007, Vol. 20, No. 3, 28-33), also known as blade end slotting technology, and developed a series of slot shaping schemes (CN 105156361 B, CN 105179322B, CN 105156356 B, CN 105240322 B, CN 105298925B), and proposed a compressor stator blade root slotting method based on an optimization algorithm (CN 105756719 B). The blade end slotting technology proposed forms an "adaptive" jet to blow away the separated fluid by slotting from the blade pressure surface to the suction surface, and has a good control effect on large-scale flow separation under normal load conditions. The design of the new generation of compressors pursues a larger single-stage aerodynamic load, which makes the compressor blades smaller in density, larger in bend angle, thinner in thickness, and the blade flow field is even worse under high-load conditions. In the early stage, due to the limitations of the understanding of the flow mechanism, the control schemes adopted were simple equal-width straight grooves, equal-width arc grooves, equal-width broken line grooves, etc. When the load was not very large, it played a good flow control effect of suppressing the separation of the compressor corner area, but it was difficult to meet the design requirements of the next generation of high-load compressors. Based on the research on the new generation of high-load blades, it was found that optimizing the groove profile design is an important means to improve the control effect of the groove opening in the blade end area. In order to solve the problem of three-dimensional corner separation in the new generation of high-load compressors, the present invention proposes a parametric blade slotting design method based on Bezier curves, which parameterizes the groove design process that was originally highly dependent on the designer's experience to achieve rapid design of blade slotting geometry. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] The purpose of the present invention is to provide a parametric blade slotting design method based on Bezier curves, which aims to generate the slot geometry of the slotted blade by combining arc curves with Bezier curves based on given original blade geometry, slot inlet and outlet positions and widths, slot profile starting points, slot profile end points, slot inlet inlet angles, slot outlet jet angles, fillet radius and other geometric parameters, so as to achieve rapid design of blade slotting geometry suitable for high-load compressors, effectively suppress the separation flow in the three-dimensional corner area of ​​high-load compressors, and facilitate actual processing for application in engineering practice.

[0006] (II) Technical solution

[0007] In order to solve the above technical problems, the present invention provides a parameterized blade slot design method based on Bezier curves, comprising the following steps:

[0008] Step 1, giving the geometric design parameters of the slotted blade;

[0009] Step 2, transform the original blade geometry into a relative chord length coordinate system;

[0010] Step 3, calculating the fillet curve of the channel outlet;

[0011] Step 4, calculating the quadratic Bezier curve at the channel outlet;

[0012] Step 5, calculating the quadratic Bezier curves of the inner walls on both sides of the channel and the fillet curve of the channel inlet;

[0013] Step 6, calculating the quadratic Bezier curve at the channel inlet;

[0014] Step 7, inversely transform the slotted blade geometry into an absolute coordinate system;

[0015] ① The given slotted blade geometric design parameters include:

[0016] Given the control point coordinates and groove design parameters of the original blade geometry, the original blade geometry is generated from the control point coordinates of the original blade geometry; and the original blade suction surface profile and the original blade pressure surface profile are respectively extracted from the original blade geometry;

[0017] Define the slot design parameters, including: slot inlet relative chord length position SP2, slot outlet relative chord length position EP1, slot profile starting point relative chord length position SP1, slot profile end point relative chord length position EP2, slot inlet width TI, slot outlet width TO, slot inlet fillet radius rin, slot outlet fillet radius rout, slot inlet inlet air intake angle αin and slot outlet jet angle αout;

[0018] ② The transformation of the original blade geometry to the relative chord length coordinate system includes:

[0019] Calculating the chord length c of the original blade geometry, wherein the point with the smallest abscissa value of the original blade geometry is the leading edge point, the point with the largest abscissa value of the original blade geometry is the trailing edge point, and the chord length c of the original blade geometry is the straight-line distance between the leading edge point and the trailing edge point;

[0020] The original blade geometry is subjected to a rotational translation transformation, the leading edge point is set as the origin of the coordinate system (0, 0), and the trailing edge point is transformed to the coordinate point (c, 0); the original blade geometry is scaled at a ratio of 1 / c with the leading edge point as the center to obtain the relative chord length coordinates of the original blade geometry, and a relative chord length coordinate system is established; in the relative chord length coordinate system, the leading edge point is the origin of the coordinate system (0, 0), and the coordinates of the trailing edge point are (1, 0);

[0021] ③ The calculation of the groove outlet fillet curve includes:

[0022] The slot outlet position is selected on the suction surface profile of the original blade, and the fillet radius rout at the slot outlet is set; wherein the value of the fillet radius rout at the slot outlet is not greater than 1 / 2 of the thickness at the trailing edge of the original blade; at the slot outlet position, a vertical line is drawn perpendicular to the suction surface profile of the original blade to the side where the pressure surface profile of the original blade is located, and the length of the vertical line is equal to the fillet radius rout at the slot outlet, and the endpoint of the vertical line is the slot outlet relative chord length position EP1, and the value of the slot outlet relative chord length position EP1 is defined as the ratio of the horizontal coordinate of the slot outlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the end point of the vertical line is the center of the slot outlet fillet curve;

[0023] The slot outlet jet angle αout is set, and the unit of the slot outlet jet angle αout is °; in the relative chord length coordinate system, the slot outlet relative chord length position EP1 is used as the starting point of the slot outlet fillet curve, and the fillet radius rout at the slot outlet is used as the radius, and an inscribed arc of the original blade suction surface profile line is made, and the tangent point of the inscribed arc and the original blade suction surface profile line is used as the starting point, and the angle 180°-αout is included and terminated as the end point of the slot outlet fillet curve, so as to obtain the slot outlet fillet curve;

[0024] ④ The calculation of the quadratic Bezier curve of the channel outlet includes:

[0025] Given the groove outlet width TO and the relative chord length position EP2 of the groove profile end point;

[0026] In the relative chord length coordinate system, the starting point of the quadratic Bezier curve at the slot outlet is obtained according to the end point of the slot outlet fillet curve, the slot outlet width TO, and the slot outlet jet angle αout; specifically, with the end point of the slot outlet fillet curve as the starting point, a perpendicular line is drawn perpendicular to the slot jet direction determined by the slot outlet jet angle αout, and the length of the perpendicular line is equal to the slot outlet width TO, and the end point of the obtained perpendicular line is the starting point of the quadratic Bezier curve at the slot outlet;

[0027] The value of the relative chord length position EP2 of the end point of the groove profile is the ratio of the abscissa of the end point of the groove outlet quadratic Bezier curve in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the groove outlet quadratic Bezier curve in the relative chord length coordinate system is obtained from the relative chord length position EP2 of the end point of the groove profile; a point with the same abscissa as the abscissa of the end point of the groove outlet quadratic Bezier curve in the relative chord length coordinate system is selected on the original blade suction surface profile in the relative chord length coordinate system as the end point of the groove outlet quadratic Bezier curve;

[0028] The starting point slope of the quadratic Bezier curve at the slot outlet is determined according to the slot outlet jet angle αout, so that the tangent direction at the starting point of the quadratic Bezier curve at the slot outlet is consistent with the slot jet direction determined by the slot outlet jet angle αout; the end point slope of the quadratic Bezier curve at the slot outlet is the slope of the original blade suction surface profile at the end point of the quadratic Bezier curve at the slot outlet;

[0029] At the starting point of the quadratic Bezier curve at the slot outlet, a ray I is drawn in the direction of the end point of the quadratic Bezier curve at the slot outlet with the starting point slope of the quadratic Bezier curve at the slot outlet; at the end point of the quadratic Bezier curve at the slot outlet, a ray II is drawn in the direction of the starting point of the quadratic Bezier curve at the slot outlet with the end point slope of the quadratic Bezier curve at the slot outlet; the intersection of the drawn ray I and the drawn ray II is selected as the middle control point of the quadratic Bezier curve at the slot outlet;

[0030] The quadratic Bezier curve at the channel outlet is obtained by calculation according to the starting point of the quadratic Bezier curve at the channel outlet, the middle control point of the quadratic Bezier curve at the channel outlet, and the end point of the quadratic Bezier curve at the channel outlet;

[0031] ⑤ The calculation of the quadratic Bezier curves of the inner walls on both sides of the groove and the fillet curve of the groove inlet includes:

[0032] Given a slot inlet width TI and a fillet radius rin at the slot inlet, wherein the fillet radius rin at the slot inlet is not greater than 1 / 2 of the thickness at the leading edge of the original blade;

[0033] At the slot inlet position, a vertical line is drawn perpendicular to the original blade pressure surface profile line toward the side where the original blade suction surface profile line is located, the length of the vertical line is equal to the fillet radius rin at the slot inlet, the starting point of the vertical line is the slot inlet relative chord length position SP2, the value of the slot inlet relative chord length position SP2 is defined as the ratio of the abscissa of the slot inlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the value of the slot inlet relative chord length position SP2 is less than the value of the slot outlet relative chord length position EP1, and the end point of the vertical line is the center of the slot inlet fillet curve;

[0034] The slot inlet air intake angle αin is set, and the unit of the slot inlet air intake angle αout is °; in the relative chord length coordinate system, the slot inlet relative chord length position SP2 is used as the starting point of the slot inlet fillet curve, and the fillet radius rin at the slot inlet is used as the radius to make an inscribed arc of the original blade pressure surface profile, and the inscribed arc takes the tangent point with the original blade pressure surface profile as the starting point and ends after including the angle 180°-αin, so as to obtain the slot inlet fillet curve;

[0035] The quadratic Bezier curves of the inner walls on both sides of the channel include a quadratic Bezier curve of the inner wall of the upstream channel and a quadratic Bezier curve of the inner wall of the downstream channel;

[0036] At the starting point of the quadratic Bezier curve at the slot outlet, a ray III is drawn in the direction of the slot inlet with the starting point slope of the quadratic Bezier curve at the slot outlet; at the end point of the slot inlet fillet curve, a ray IV is drawn in the direction of the slot outlet with the slot inlet air inlet angle αin; the intersection point of the drawn ray III and the drawn ray IV is selected as the middle control point of the quadratic Bezier curve of the inner wall of the downstream slot;

[0037] The quadratic Bezier curve of the inner wall of the downstream channel is obtained by calculation according to the starting point of the quadratic Bezier curve of the channel outlet, the middle control point of the quadratic Bezier curve of the inner wall of the downstream channel, and the end point of the fillet curve of the channel inlet;

[0038] Connect the center of the groove inlet fillet curve and the end point of the groove inlet fillet curve, and make an extension line in the direction of the original blade suction surface profile line, the distance between the end point of the extension line and the end point of the groove inlet fillet curve is equal to the groove inlet width TI, and use the end point of the extension line as the starting point of the quadratic Bezier curve of the upstream groove inner wall; use the end point of the groove outlet fillet curve in step 3 as the end point of the quadratic Bezier curve of the upstream groove inner wall, and determine the end point slope of the quadratic Bezier curve of the upstream groove inner wall according to the groove outlet jet angle αout, so that the tangent direction at the end point of the quadratic Bezier curve of the upstream groove inner wall is consistent with the groove jet direction determined by the groove outlet jet angle αout; determine the starting point slope of the quadratic Bezier curve of the upstream groove inner wall according to the groove inlet inlet angle αin, so that the tangent direction at the starting point of the quadratic Bezier curve of the upstream groove inner wall is consistent with the groove inflow direction determined by the groove inlet inlet angle αin;

[0039] At the starting point of the quadratic Bezier curve of the upstream channel inner wall, a ray V is drawn in the direction of the end point of the quadratic Bezier curve of the upstream channel inner wall with the starting point slope of the quadratic Bezier curve of the upstream channel inner wall; at the end point of the quadratic Bezier curve of the upstream channel inner wall, a ray VI is drawn in the direction of the starting point of the quadratic Bezier curve of the upstream channel inner wall with the end point slope of the quadratic Bezier curve of the upstream channel inner wall; the intersection point of the drawn ray V and the drawn ray VI is selected as the middle control point of the quadratic Bezier curve of the upstream channel inner wall;

[0040] The quadratic Bezier curve of the inner wall of the upstream channel is obtained by calculation according to the starting point of the quadratic Bezier curve of the inner wall of the upstream channel, the middle control point of the quadratic Bezier curve of the inner wall of the upstream channel, and the end point of the quadratic Bezier curve of the inner wall of the upstream channel;

[0041] ⑥ The calculation of the secondary Bezier curve of the channel inlet includes:

[0042] Given a relative chord length position SP1 of the starting point of the groove profile, the value of the relative chord length position SP1 of the starting point of the groove profile is the ratio of the abscissa of the starting point of the groove inlet quadratic Bezier curve in the relative chord length coordinate system to the chord length c of the original blade geometry;

[0043] In the relative chord length coordinate system, the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve in the relative chord length coordinate system is obtained by the relative chord length position SP1 of the starting point of the slot profile; a point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve is selected on the original blade pressure surface profile in the relative chord length coordinate system as the starting point of the slot inlet quadratic Bezier curve, and the slope of the point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve is extracted as The starting point slope of the quadratic Bezier curve at the slot inlet; the starting point of the upstream slot inner wall arc in step 5 is used as the end point of the slot inlet quadratic Bezier curve, and the slope at the starting point of the upstream slot inner wall arc in step 5 is used as the end point slope of the slot inlet quadratic Bezier curve; the slot inlet quadratic Bezier curve is tangent to the blade pressure surface profile at the starting point of the slot inlet quadratic Bezier curve, and the slot inlet quadratic Bezier curve is tangent to the upstream slot inner wall arc at the end point of the slot inlet quadratic Bezier curve;

[0044] At the starting point of the quadratic Bezier curve at the slot inlet, a ray VII is drawn in the direction of the end point of the quadratic Bezier curve at the slot inlet with the starting point slope of the quadratic Bezier curve at the slot inlet; at the end point of the quadratic Bezier curve at the slot inlet, a ray VIII is drawn in the direction of the starting point of the quadratic Bezier curve at the slot inlet with the end point slope of the quadratic Bezier curve at the slot inlet; the intersection of the drawn ray VII and the drawn ray VIII is selected as the middle control point of the quadratic Bezier curve at the slot inlet;

[0045] The channel inlet quadratic Bezier curve is obtained by calculation according to the starting point of the channel inlet quadratic Bezier curve, the middle control point of the channel inlet quadratic Bezier curve, and the end point of the channel inlet quadratic Bezier curve;

[0046] ⑦ The inverse transformation of the slotted blade geometry into an absolute coordinate system comprises:

[0047] In the relative chord length coordinate system, the original blade suction surface profile, the original blade pressure surface profile, the slot outlet fillet curve, the slot outlet quadratic Bezier curve, the downstream slot inner wall quadratic Bezier curve, the slot inlet fillet curve, the upstream slot inner wall quadratic Bezier curve, and the slot inlet quadratic Bezier curve together constitute the slotted blade geometry in the relative chord length coordinate system;

[0048] The slotted blade geometry in the relative chord length coordinate system is enlarged at a ratio of c / 1 with the leading edge point as the center to obtain the final slotted blade geometry; the final slotted blade geometry is subjected to an inverse coordinate transformation so that the trailing edge point coordinates are transformed from the coordinate point (c, 0) to the same position as the trailing edge point coordinates of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system.

[0049] In particular, the parameterized blade slotting design method based on Bezier curve is applicable to both the design of two-dimensional compressor blade profiles and the design of three-dimensional compressor blades; when the parameterized blade slotting design method based on Bezier curve is used for the design of three-dimensional compressor blades, the height of the original three-dimensional compressor blade between the upper end wall and the lower end wall is set to H, and a slot stretching line is set along the span direction of the original three-dimensional compressor blade, the slot stretching line is a Bezier curve, and the corresponding slot side wall is a Bezier surface; the slotting height corresponding to the slot stretching line is h; the starting end of the slot stretching line can be located at the lower end wall or the upper end wall, and the corresponding slotting height h ranges from 0 to H, thereby obtaining an end zone slotting scheme.

[0050] In particular, the grooves can be opened simultaneously on the upper end wall side and the lower end wall side of the original three-dimensional compressor blade, thereby obtaining a double-side end zone groove solution.

[0051] In particular, when the value of the slot height h corresponding to the slot stretching line is equal to the height H between the upper end wall and the lower end wall of the original three-dimensional compressor blade, the slot runs through the entire original three-dimensional compressor blade along the span direction to obtain a full-blade height slotting scheme.

[0052] (III) Beneficial effects

[0053] The present invention provides a parametric blade slot design method based on Bezier curve, which has the following beneficial effects: by giving the original blade geometry and slot design parameters, the high-load compressor blade slot geometry can be quickly designed. By giving fewer slot design parameters, the blade slot geometry can be uniquely determined. The slot design parameters are used to perform parametric control on the slot geometry profile, which is conducive to the parametric study of the slot performance of the high-load compressor blade.

[0054] The present invention provides a parametric blade slotting design method based on Bezier curves. By adopting Bezier curves to design the profile of the slot, the designed slotted blade geometry can better regulate the high-load compressor flow field and obtain better aerodynamic performance.

[0055] The present invention provides a parametric blade slotting design method based on Bezier curves, which can quickly generate effective slotted blade geometry by programming given the original blade geometry and slot design parameters, solve the problem of high empirical dependence of slot design schemes, and has important engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of a parameterized blade slot design method based on Bezier curve of the present invention;

[0057] Figure 2 A geometrical schematic diagram of a slotted blade of a parameterized blade slotting design method based on Bezier curves according to the present invention;

[0058] Figure 3 A schematic diagram of three-dimensional compressor blade slotting according to a parameterized blade slotting design method based on Bezier curves of the present invention;

[0059] Figure 4 A flow field diagram of the original blade geometry of a parameterized blade slotting design method based on Bezier curves according to the present invention;

[0060] Figure 5 A flow field diagram of the slotted blade geometry of a parameterized blade slotting design method based on Bezier curves according to the present invention;

[0061] In the figure, 1: quadratic Bezier curve at the slot inlet; 2: quadratic Bezier curve at the inner wall of the upstream slot; 3: fillet curve at the slot outlet; 4: quadratic Bezier curve at the slot outlet; 5: original blade suction surface profile; 6: trailing edge point; 7: original blade pressure surface profile; 8: quadratic Bezier curve at the inner wall of the downstream slot; 9: fillet curve at the slot inlet; 10: leading edge point; 11: three-dimensional compressor blade; 12: lower end wall; 13: full blade height slot; 14: end zone slot. DETAILED DESCRIPTION

[0062] The following is a further detailed description of the specific implementation of the present invention in conjunction with the accompanying drawings and examples. The following examples are only used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0063] like Figure 1 , Figure 2 As shown, the present invention provides a parameterized blade slot design method based on Bezier curve, comprising the following steps:

[0064] Step 1, giving the geometric design parameters of the slotted blade;

[0065] In this step, given the control point coordinates of the original blade geometry and the groove design parameters, the original blade geometry is generated from the control point coordinates of the original blade geometry; the original blade suction surface profile (5) and the original blade pressure surface profile (7) are respectively extracted from the original blade geometry;

[0066] Define the groove design parameters, including: groove inlet relative chord length position SP2, groove outlet relative chord length position EP1, groove profile starting point relative chord length position SP1, groove profile end point relative chord length position EP2, groove inlet width TI, groove outlet width TO, groove inlet fillet radius rin, groove outlet fillet radius rout, groove inlet intake angle αin and groove outlet jet angle αout.

[0067] Step 2, transform the original blade geometry into a relative chord length coordinate system;

[0068] In this step, the chord length c of the original blade geometry is calculated, wherein the point with the smallest abscissa value of the original blade geometry is the leading edge point (10), the point with the largest abscissa value of the original blade geometry is the trailing edge point (6), and the chord length c of the original blade geometry is the straight-line distance between the leading edge point (10) and the trailing edge point (6);

[0069] The original blade geometry is subjected to a rotational translation transformation, the leading edge point (10) is set as the origin of the coordinate system (0, 0), and the trailing edge point (6) is transformed to the coordinate point (c, 0); the original blade geometry is scaled at a ratio of 1 / c with the leading edge point (10) as the center to obtain the relative chord length coordinates of the original blade geometry, and a relative chord length coordinate system is established; in the relative chord length coordinate system, the leading edge point (10) is the origin of the coordinate system (0, 0), and the coordinates of the trailing edge point (6) are (1, 0).

[0070] Step 3, calculating the channel outlet fillet curve (3);

[0071] In this step, the slot outlet position is selected on the original blade suction surface profile (5), and the fillet radius rout at the slot outlet is set; wherein, the value of the fillet radius rout at the slot outlet is not greater than 1 / 2 of the thickness at the trailing edge of the original blade; at the slot outlet position, a vertical line is drawn perpendicular to the original blade suction surface profile (5) to the side where the original blade pressure surface profile (7) is located, and the length of the vertical line is equal to the fillet radius rout at the slot outlet, and the end point of the vertical line is the slot outlet relative chord length position EP1, and the value of the slot outlet relative chord length position EP1 is defined as the ratio of the horizontal coordinate of the slot outlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the end point of the vertical line is the center of the slot outlet fillet curve (3);

[0072] The slot outlet jet angle αout is set, and the unit of the slot outlet jet angle αout is °; in the relative chord length coordinate system, the slot outlet relative chord length position EP1 is used as the starting point of the slot outlet fillet curve (3), and the fillet radius rout at the slot outlet is used as the radius. An inscribed arc of the original blade suction surface profile line (5) is made, and the tangent point of the inscribed arc and the original blade suction surface profile line (5) is used as the starting point, and the angle 180°-αout is included and terminated as the end point of the slot outlet fillet curve (3), thereby obtaining the slot outlet fillet curve (3).

[0073] Step 4, calculating the quadratic Bezier curve (4) at the channel outlet;

[0074] In this step, the channel outlet width TO and the channel profile end point relative to the chord length EP2 are given;

[0075] In the relative chord length coordinate system, the starting point of the slot outlet quadratic Bezier curve (4) is obtained according to the end point of the slot outlet fillet curve (3), the slot outlet width TO, and the slot outlet jet angle αout; specifically, with the end point of the slot outlet fillet curve (3) as the starting point, a perpendicular line is drawn perpendicular to the slot jet direction determined by the slot outlet jet angle αout, and the length of the perpendicular line is equal to the slot outlet width TO, and the end point of the obtained perpendicular line is the starting point of the slot outlet quadratic Bezier curve (4);

[0076] The value of the relative chord length position EP2 of the end point of the groove profile is the ratio of the abscissa of the end point of the groove outlet quadratic Bezier curve (4) in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the groove outlet quadratic Bezier curve (4) in the relative chord length coordinate system is obtained from the relative chord length position EP2 of the end point of the groove profile; a point on the original blade suction surface profile (5) in the relative chord length coordinate system whose abscissa is equal to the abscissa of the end point of the groove outlet quadratic Bezier curve (4) is selected as the end point of the groove outlet quadratic Bezier curve (4);

[0077] The starting point slope of the slot outlet quadratic Bezier curve (4) is determined according to the slot outlet jet angle αout, so that the tangent direction at the starting point of the slot outlet quadratic Bezier curve (4) is consistent with the slot jet direction determined by the slot outlet jet angle αout; the ending point slope of the slot outlet quadratic Bezier curve (4) is the slope of the original blade suction surface profile line (5) at the ending point of the slot outlet quadratic Bezier curve (4);

[0078] At the starting point of the quadratic Bezier curve (4) at the slot outlet, a ray I is drawn in the direction of the end point of the quadratic Bezier curve (4) at the starting point of the slot outlet; at the end point of the quadratic Bezier curve (4) at the slot outlet, a ray II is drawn in the direction of the starting point of the quadratic Bezier curve (4) at the end point of the slot outlet; and the intersection of the drawn ray I and the drawn ray II is selected as the middle control point of the quadratic Bezier curve (4) at the slot outlet;

[0079] The channel outlet quadratic Bezier curve (4) is obtained by calculation according to the starting point of the channel outlet quadratic Bezier curve (4), the middle control point of the channel outlet quadratic Bezier curve (4), and the end point of the channel outlet quadratic Bezier curve (4).

[0080] Step 5, calculating the quadratic Bezier curves of the inner walls on both sides of the channel and the fillet curve of the channel inlet (9);

[0081] In this step, the slot inlet width TI and the fillet radius rin at the slot inlet are given, wherein the value of the fillet radius rin at the slot inlet is not greater than 1 / 2 of the thickness at the leading edge of the original blade;

[0082] At the slot inlet position, a vertical line is drawn perpendicular to the original blade pressure surface profile line (7) toward the side where the original blade suction surface profile line (5) is located. The length of the vertical line is equal to the fillet radius rin at the slot inlet. The starting point of the vertical line is the slot inlet relative chord length position SP2. The value of the slot inlet relative chord length position SP2 is defined as the ratio of the horizontal coordinate of the slot inlet position in the relative chord length coordinate system to the chord length c of the original blade geometry. The value of the slot inlet relative chord length position SP2 is less than the value of the slot outlet relative chord length position EP1. The end point of the vertical line is the center of the slot inlet fillet curve (9).

[0083] The slot inlet air intake angle αin is set, and the unit of the slot inlet air intake angle αout is °; in the relative chord length coordinate system, the slot inlet relative chord length position SP2 is used as the starting point of the slot inlet fillet curve (9), and the fillet radius rin at the slot inlet is used as the radius to draw an inscribed arc of the original blade pressure surface profile line (7). The inscribed arc starts at the tangent point with the original blade pressure surface profile line (7) and ends after including the angle 180°-αin, thereby obtaining the slot inlet fillet curve (9);

[0084] The quadratic Bezier curves on the inner walls of both sides of the channel include a quadratic Bezier curve (2) on the inner wall of the upstream channel and a quadratic Bezier curve (8) on the inner wall of the downstream channel;

[0085] At the starting point of the quadratic Bezier curve (4) at the slot outlet, a ray III is drawn in the direction of the slot inlet with the starting slope of the quadratic Bezier curve (4) at the slot outlet; at the end point of the slot inlet fillet curve (9), a ray IV is drawn in the direction of the slot outlet with the slot inlet air intake angle αin; the intersection of the drawn ray III and the drawn ray IV is selected as the middle control point of the quadratic Bezier curve (8) of the inner wall of the downstream slot;

[0086] The quadratic Bezier curve (8) of the inner wall of the downstream channel is obtained by calculation according to the starting point of the quadratic Bezier curve (4) at the channel outlet, the middle control point of the quadratic Bezier curve (8) of the inner wall of the downstream channel, and the end point of the fillet curve (9) at the channel inlet;

[0087] Connect the center of the groove inlet fillet curve (9) and the end point of the groove inlet fillet curve (9), and make an extension line in the direction of the original blade suction surface line (5), the distance between the end point of the extension line and the end point of the groove inlet fillet curve (9) is equal to the groove inlet width TI, and use the end point of the extension line as the starting point of the secondary Bezier curve (2) of the upstream groove inner wall; use the end point of the groove outlet fillet curve (3) in step 3 as the end point of the secondary Bezier curve (2) of the upstream groove inner wall, according to the groove outlet jet The angle αout determines the end point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel, so that the tangent direction at the end point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is consistent with the channel jet direction determined by the channel outlet jet angle αout; the starting point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel is determined according to the channel inlet air intake angle αin, so that the tangent direction at the starting point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is consistent with the channel inlet flow direction determined by the channel inlet air intake angle αin;

[0088] At the starting point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray V is drawn in the direction of the end point of the quadratic Bezier curve (2) of the upstream channel inner wall with the starting point slope of the quadratic Bezier curve (2) of the upstream channel inner wall; at the end point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray VI is drawn in the direction of the starting point of the quadratic Bezier curve (2) of the upstream channel inner wall with the end point slope of the quadratic Bezier curve (2) of the upstream channel inner wall; the intersection point of the drawn ray V and the drawn ray VI is selected as the middle control point of the quadratic Bezier curve (2) of the upstream channel inner wall;

[0089] The upstream channel inner wall quadratic Bezier curve (2) is obtained by calculation according to the starting point of the upstream channel inner wall quadratic Bezier curve (2), the middle control point of the upstream channel inner wall quadratic Bezier curve (2), and the end point of the upstream channel inner wall quadratic Bezier curve (2).

[0090] Step 6, calculating the quadratic Bezier curve (1) at the channel inlet;

[0091] In this step, the relative chord length position SP1 of the starting point of the groove profile is given, and the value of the relative chord length position SP1 of the starting point of the groove profile is the ratio of the horizontal coordinate of the starting point of the groove inlet quadratic Bezier curve (1) in the relative chord length coordinate system to the chord length c of the original blade geometry;

[0092] In the relative chord length coordinate system, the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) in the relative chord length coordinate system is obtained from the relative chord length position SP1 of the starting point of the slot profile; a point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) is selected on the original blade pressure surface profile (7) in the relative chord length coordinate system as the starting point of the slot inlet quadratic Bezier curve (1); the slope of the point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) selected on the original blade pressure surface profile (7) is extracted as the slot inlet quadratic Bezier curve. The starting point slope of the inlet quadratic Bezier curve (1); the starting point of the upstream side slot inner wall arc in step 5 is used as the end point of the slot inlet quadratic Bezier curve (1), and the slope at the starting point of the upstream side slot inner wall arc in step 5 is used as the end point slope of the slot inlet quadratic Bezier curve (1); the slot inlet quadratic Bezier curve (1) is tangent to the blade pressure surface profile at the starting point of the slot inlet quadratic Bezier curve (1), and the slot inlet quadratic Bezier curve (1) is tangent to the upstream side slot inner wall arc at the end point of the slot inlet quadratic Bezier curve (1);

[0093] At the starting point of the slot inlet quadratic Bezier curve (1), a ray VII is drawn in the direction of the end point of the slot inlet quadratic Bezier curve (1) with the starting point slope of the slot inlet quadratic Bezier curve (1); at the end point of the slot inlet quadratic Bezier curve (1), a ray VIII is drawn in the direction of the starting point of the slot inlet quadratic Bezier curve (1) with the end point slope of the slot inlet quadratic Bezier curve (1); the intersection of the drawn ray VII and the drawn ray VII I is selected as the middle control point of the slot inlet quadratic Bezier curve (1). According to the starting point of the slot inlet quadratic Bezier curve (1), the middle control point of the slot inlet quadratic Bezier curve (1), and the end point of the slot inlet quadratic Bezier curve (1), the slot inlet quadratic Bezier curve (1) is obtained by calculation.

[0094] Step 7, inversely transform the slotted blade geometry into an absolute coordinate system;

[0095] In this step, in the relative chord length coordinate system, the original blade suction surface profile (5), the original blade pressure surface profile (7), the slot outlet fillet curve (3), the slot outlet quadratic Bezier curve (4), the downstream slot inner wall quadratic Bezier curve (8), the slot inlet fillet curve (9), the upstream slot inner wall quadratic Bezier curve (2), and the slot inlet quadratic Bezier curve (1) together constitute the slotted blade geometry in the relative chord length coordinate system;

[0096] The slotted blade geometry in the relative chord length coordinate system is enlarged by a ratio of c / 1 with the leading edge point (10) as the center to obtain the final slotted blade geometry; the final slotted blade geometry is subjected to an inverse coordinate transformation so that the coordinate of the trailing edge point (6) is transformed from the coordinate point (c, 0) to the same position as the coordinate of the trailing edge point (6) of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system;

[0097] Furthermore, the parameterized blade slotting design method based on Bezier curve proposed in the present invention is applicable to the design of two-dimensional compressor blade profiles and the design of three-dimensional compressor blades (11); when the parameterized blade slotting design method based on Bezier curve proposed in the present invention is used for the design of three-dimensional compressor blades (11), the height of the original three-dimensional compressor blade (11) between the upper end wall and the lower end wall is set to H, and a slot stretching line is set along the span direction of the original three-dimensional compressor blade (11), the slot stretching line is a Bezier curve, and the corresponding slot side wall is a Bezier surface; the slotting height corresponding to the slot stretching line is h; the starting end of the slot stretching line can be located at the lower end wall or the upper end wall, and the corresponding slotting height h has a value range of 0 to H, thereby obtaining an end zone slotting scheme.

[0098] In particular, the grooves can be opened simultaneously on the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11), thereby obtaining a double-sided end zone groove scheme.

[0099] In particular, when the value of the slot height h is equal to the height H of the original three-dimensional compressor blade (11) between the upper end wall and the lower end wall (12), the slot runs through the entire original three-dimensional compressor blade (11) along the span direction, obtaining a full-blade height slot (13) solution.

[0100] Embodiment 1:

[0101] Taking a high-load compressor blade row studied by the research group as an example, a parameterized blade slotting design method based on Bezier curve proposed in the present invention was used to design the slotting scheme of the double-sided end areas of the blade, and the flow field of the prototype blade row and the slotted blade row was numerically simulated to verify the control effect of the double-sided end area slotting scheme.

[0102] like Figure 2The figure shows a schematic diagram of the slotted blade geometry of a parametric blade slotting design method based on Bezier curves of the present invention. In this embodiment, the value of the slot inlet relative to the chord length position SP2 is 30%, the value of the slot outlet relative to the chord length position EP1 is 55%, the value of the slot profile start point relative to the chord length position SP1 is 10%, the value of the slot profile end point relative to the chord length position EP2 is 70%, the slot inlet width TI is 4mm, the slot outlet width TO is 3.2mm, the fillet radius rin at the slot inlet is 0.2mm, the fillet radius rout at the slot outlet is 0.2mm, the slot inlet inlet angle αin is 17°, and the slot outlet jet angle αout is 9°. The chord length c of the original blade geometry is 151.5mm.

[0103] The original blade geometry is subjected to a rotational translation transformation, the leading edge point (10) is set as the origin of the coordinate system (0, 0), and the trailing edge point (7) is transformed to the coordinate point (151.5, 0); the original blade geometry is scaled at a ratio of 1 / 151.5 with the leading edge point (10) as the center to obtain the relative chord length coordinates of the original blade geometry, and a relative chord length coordinate system is established; in the relative chord length coordinate system, the leading edge point (10) is the origin of the coordinate system (0, 0), and the coordinates of the trailing edge point (7) are (1, 0).

[0104] At the slot outlet, a vertical line is drawn perpendicular to the original blade suction surface profile line (5) toward the side where the original blade pressure surface profile line (7) is located. The length of the vertical line is equal to the fillet radius rout=0.2 / 151.5 mm at the slot outlet, and the starting point of the vertical line is the slot outlet relative chord length position EP1. In the relative chord length coordinate system, the slot outlet relative chord length position EP1 is used as the starting point of the slot outlet fillet curve (3), and the fillet radius rout=0.2 / 151.5 mm at the slot outlet is used as the radius to draw an inscribed arc of the original blade suction surface profile line (5). The inscribed arc starts from the tangent point with the original blade suction surface profile line (5), and ends after including an angle of 171°, as the end point of the slot outlet fillet curve, thereby obtaining the slot outlet fillet curve (3).

[0105] In the relative chord length coordinate system, with the end point of the slot outlet fillet curve as the starting point, a vertical line is drawn perpendicular to the slot outlet jet direction determined by the jet angle αout of the slot outlet. The length of the vertical line is equal to the slot outlet width TO=3.2 / 151.5mm. The end point of the vertical line is the starting point of the quadratic Bezier curve of the slot outlet. The value of the relative chord length position EP2 of the end point of the slot profile is 70%, and the horizontal coordinate of the end point of the quadratic Bezier curve of the slot outlet in the relative chord length coordinate system is 0.7. The original blade suction surface profile in the relative chord length coordinate system is A point on the line (5) whose abscissa is equal to the abscissa of the end point of the quadratic Bezier curve at the slot outlet is selected as the end point of the quadratic Bezier curve at the slot outlet; the starting point slope of the quadratic Bezier curve at the slot outlet is determined according to the slot outlet jet angle α=10°, so that the tangent direction at the starting point of the quadratic Bezier curve at the slot outlet is consistent with the slot jet direction determined by the slot outlet jet angle αout=9°; the end point slope of the quadratic Bezier curve at the slot outlet is the slope of the original blade suction surface profile line (5) at the end point of the quadratic Bezier curve at the slot outlet.

[0106] At the starting point of the channel exit quadratic Bezier curve (4), a ray I is drawn in the direction of the end point of the channel exit quadratic Bezier curve (4) with the starting point slope of the channel exit quadratic Bezier curve (4); at the end point of the channel exit quadratic Bezier curve (4), a ray II is drawn in the direction of the starting point of the channel exit quadratic Bezier curve (4) with the end point slope of the channel exit quadratic Bezier curve (4); the intersection of the drawn ray I and the drawn ray II is selected as the middle control point of the channel exit quadratic Bezier curve (4). The channel exit quadratic Bezier curve (4) is obtained by calculation according to the starting point of the channel exit quadratic Bezier curve (4), the middle control point of the channel exit quadratic Bezier curve (4), and the end point of the channel exit quadratic Bezier curve (4).

[0107] At the slot inlet position, a vertical line is drawn perpendicular to the original blade pressure surface profile line (7) toward the side where the original blade suction surface profile line (5) is located. The length of the vertical line is equal to the fillet radius rin at the slot inlet = 0.2 / 151.5 mm. The starting point of the vertical line is the slot inlet relative chord length position SP2 = 70%, and the end point of the vertical line is the center of the slot inlet fillet curve (9). With the slot inlet relative chord length position SP2 as the starting point of the slot inlet fillet curve (9), and with the fillet radius rin at the slot inlet = 0.2 / 151.5 mm as the radius, an inscribed arc of the original blade pressure surface profile line (7) is drawn. The inscribed arc starts from the tangent point with the original blade pressure surface profile line (7) and ends after including an angle of 163°, thereby obtaining the slot inlet fillet curve (9).

[0108] At the starting point of the quadratic Bezier curve (4) at the slot outlet, a ray III is drawn in the direction of the slot inlet with the starting slope of the quadratic Bezier curve (4) at the slot outlet; at the end point of the slot inlet fillet curve (9), a ray IV is drawn in the direction of the slot outlet with the slot inlet air intake angle αin=17°; the intersection point of the drawn ray III and the drawn ray IV is selected as the middle control point of the quadratic Bezier curve (8) of the downstream slot inner wall; based on the starting point of the quadratic Bezier curve (4) at the slot outlet, the middle control point of the quadratic Bezier curve (8) of the downstream slot inner wall, and the end point of the slot inlet fillet curve (9), the quadratic Bezier curve (8) of the downstream slot inner wall is obtained by calculation.

[0109] Connect the center of the groove inlet fillet curve (9) and the end point of the groove inlet fillet curve (9), and make an extension line in the direction of the original blade suction surface line (5), the distance between the end point of the extension line and the end point of the groove inlet fillet curve (9) is equal to the groove inlet width TI = 4 / 151.5mm, and use the end point of the extension line as the starting point of the upstream side groove inner wall quadratic Bezier curve (2); use the end point of the groove outlet fillet curve (3) in step 3 as the end point of the upstream side groove inner wall quadratic Bezier curve (2), according to the groove outlet jet angle α out=9° to determine the end point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel, so that the tangent direction at the end point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is consistent with the channel jet direction determined by the channel outlet jet angle αout=9°; the starting point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel is determined according to the channel inlet air intake angle αin=17°, so that the tangent direction at the starting point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is consistent with the channel inlet flow direction determined by the channel inlet air intake angle αin=17°.

[0110] At the starting point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray V is drawn with the starting point slope of the upstream channel inner wall quadratic Bezier curve (2) in the direction of the end point of the upstream channel inner wall quadratic Bezier curve (2); at the end point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray VI is drawn with the end point slope of the upstream channel inner wall quadratic Bezier curve (2) in the direction of the starting point of the upstream channel inner wall quadratic Bezier curve (2); the intersection of the drawn ray V and the drawn ray VI is selected as the middle control point of the upstream channel inner wall quadratic Bezier curve (2). The upstream channel inner wall quadratic Bezier curve (2) is obtained by calculation according to the starting point of the upstream channel inner wall quadratic Bezier curve (2), the middle control point of the upstream channel inner wall quadratic Bezier curve (2), and the end point of the upstream channel inner wall quadratic Bezier curve (2).

[0111] In the relative chord length coordinate system, the geometry of the slotted blade in the relative chord length coordinate system is jointly constituted by the original blade suction surface profile (5), the original blade pressure surface profile (7), the slot outlet fillet curve (3), the slot outlet quadratic Bezier curve (4), the downstream slot inner wall quadratic Bezier curve (8), the slot inlet fillet curve (9), the upstream slot inner wall quadratic Bezier curve (2), and the slot inlet quadratic Bezier curve (1);

[0112] The slotted blade geometry in the relative chord length coordinate system is enlarged by a ratio of c / 1 with the leading edge point (10) as the center to obtain the final slotted blade geometry; the final slotted blade geometry is subjected to an inverse coordinate transformation so that the coordinate of the trailing edge point (6) is transformed from the coordinate point (c, 0) to the same position as the coordinate of the trailing edge point (6) of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system.

[0113] In this embodiment, grooves with a groove height of 20% of the blade height are respectively arranged on the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11), thereby obtaining a double-side end zone groove scheme.

[0114] A computational fluid dynamics method is used to numerically simulate an original three-dimensional compressor blade (11) and a double-side end region slotting scheme designed using a Bezier curve-based parameterized blade slotting design method of the present invention. Figure 4 The geometry and streamline diagram of the original three-dimensional compressor blade (11) at 10% blade height are given. Figure 5 The geometry and streamline diagram of the 10% blade height section of the double-side end slot scheme designed by the parametric blade slot design method based on Bezier curve of the present invention are given. From the comparison of the results, it can be seen that the slot designed by the parametric blade slot design method based on Bezier curve of the present invention significantly suppresses the three-dimensional corner zone separation flow on the suction side of the blade and improves the flow capacity of the blade channel. The generated slot jet has good wall adhesion.

[0115] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0116] In summary, the parametric blade slot design method based on Bezier curve provided by the present invention, by giving the original blade geometry and fewer slot design parameters, uses Bezier curve to design the slot profile, realizes the rapid design of high-load compressor blade slot geometry, and is conducive to the parametric study of high-load compressor blade slot performance. The designed slotted blade geometry can better regulate the high-load compressor flow field, effectively suppress the three-dimensional corner zone separation flow of the high-load compressor, and obtain better aerodynamic performance, which has important engineering application prospects.

Claims

1. A parametric blade slot design method based on Bezier curve, characterized in that: The steps include: Step 1, giving the geometric design parameters of the slotted blade; Step 2, transform the original blade geometry into a relative chord length coordinate system; Step 3, calculating the channel outlet fillet curve (3); Step 4, calculating the quadratic Bezier curve (4) at the channel outlet; Step 5, calculating the quadratic Bezier curves of the inner walls on both sides of the channel and the fillet curve of the channel inlet (9); Step 6, calculating the quadratic Bezier curve (1) at the channel inlet; Step 7, inversely transform the slotted blade geometry into an absolute coordinate system; ① The given slotted blade geometric design parameters include: Given the control point coordinates and groove design parameters of the original blade geometry, the original blade geometry is generated from the control point coordinates of the original blade geometry; and the original blade suction surface profile (5) and the original blade pressure surface profile (7) are respectively extracted from the original blade geometry; Define the groove design parameters, including: groove inlet relative chord length position SP2, groove outlet relative chord length position EP1, groove profile start point relative chord length position SP1, groove profile end point relative chord length position EP2, groove inlet width TI, groove outlet width TO, groove inlet fillet radius r in , the radius of the fillet at the groove outlet r out 、Slot inlet angle α in and the channel outlet jet angle α out ; ② The transformation of the original blade geometry to the relative chord length coordinate system includes: Calculating the chord length c of the original blade geometry, wherein the point with the smallest abscissa value of the original blade geometry is the leading edge point (10), the point with the largest abscissa value of the original blade geometry is the trailing edge point (6), and the chord length c of the original blade geometry is the straight-line distance between the leading edge point (10) and the trailing edge point (6); The original blade geometry is subjected to a rotational translation transformation, the leading edge point (10) is set as the origin of the coordinate system (0, 0), and the trailing edge point (6) is transformed to the coordinate point (c, 0); the original blade geometry is scaled at a ratio of 1 / c with the leading edge point (10) as the center to obtain the relative chord length coordinates of the original blade geometry, and a relative chord length coordinate system is established; in the relative chord length coordinate system, the leading edge point (10) is the origin of the coordinate system (0, 0), and the coordinates of the trailing edge point (6) are (1, 0); ③ The calculation of the channel outlet fillet curve (3) includes: The slot outlet position is selected on the original blade suction surface line (5), and the fillet radius r at the slot outlet is set. out ; Wherein, the fillet radius r at the groove outlet out The value of is not greater than 1 / 2 of the thickness at the trailing edge of the original blade; at the outlet of the groove, a vertical line is drawn perpendicular to the suction surface line (5) of the original blade to the side where the pressure surface line (7) of the original blade is located, and the length of the vertical line is equal to the fillet radius r at the outlet of the groove out , the endpoint of the vertical line is the relative chord length position EP1 of the slot outlet, the value of the relative chord length position EP1 of the slot outlet is defined as the ratio of the abscissa of the slot outlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the end point of the vertical line is the center of the slot outlet fillet curve (3); Set the channel outlet jet angle α out , the jet angle α at the channel outlet out The unit is °; in the relative chord length coordinate system, the relative chord length position EP1 of the groove outlet is taken as the starting point of the groove outlet fillet curve (3), and the fillet radius r at the groove outlet is taken as the starting point of the groove outlet fillet curve (3). out As the radius, make an inscribed arc of the original blade suction surface profile line (5), take the tangent point of the inscribed arc and the original blade suction surface profile line (5) as the starting point, including the angle 180°-α out The groove outlet fillet curve (3) is terminated as the end point of the groove outlet fillet curve (3); ④ The calculation of the channel outlet quadratic Bezier curve (4) comprises: Given the groove outlet width TO and the relative chord length position EP2 of the groove profile end point; In the relative chord length coordinate system, according to the end point of the channel outlet fillet curve (3), the channel outlet width TO, the channel outlet jet angle α out The starting point of the quadratic Bezier curve (4) at the channel outlet is obtained; specifically, the end point of the channel outlet fillet curve (3) is taken as the starting point, perpendicular to the channel outlet jet angle α out A perpendicular line is drawn to the determined channel jet direction, the length of which is equal to the channel outlet width TO, and the end point of the obtained perpendicular line is the starting point of the quadratic Bezier curve (4) at the channel outlet; The value of the relative chord length position EP2 of the end point of the groove profile is the ratio of the abscissa of the end point of the groove outlet quadratic Bezier curve (4) in the relative chord length coordinate system to the chord length c of the original blade geometry, and the abscissa of the end point of the groove outlet quadratic Bezier curve (4) in the relative chord length coordinate system is obtained from the relative chord length position EP2 of the end point of the groove profile; a point on the original blade suction surface profile (5) in the relative chord length coordinate system whose abscissa is equal to the abscissa of the end point of the groove outlet quadratic Bezier curve (4) is selected as the end point of the groove outlet quadratic Bezier curve (4); According to the channel outlet jet angle α out Determine the starting point slope of the quadratic Bezier curve (4) at the channel outlet so that the tangent direction at the starting point of the quadratic Bezier curve (4) at the channel outlet is inversely proportional to the jet angle α at the channel outlet. out The determined channel jet directions are consistent; the end point slope of the channel outlet quadratic Bezier curve (4) is the slope of the original blade suction surface profile (5) at the end point of the channel outlet quadratic Bezier curve (4); At the starting point of the quadratic Bezier curve (4) at the channel outlet, a ray I is drawn in the direction of the end point of the quadratic Bezier curve (4) at the starting point of the channel outlet; at the end point of the quadratic Bezier curve (4) at the channel outlet, a ray II is drawn in the direction of the starting point of the quadratic Bezier curve (4) at the end point of the channel outlet; and the intersection of the drawn ray I and the drawn ray II is selected as the middle control point of the quadratic Bezier curve (4) at the channel outlet; The channel outlet quadratic Bezier curve (4) is obtained by calculation according to the starting point of the channel outlet quadratic Bezier curve (4), the middle control point of the channel outlet quadratic Bezier curve (4), and the end point of the channel outlet quadratic Bezier curve (4); ⑤ The calculation of the quadratic Bezier curves of the inner walls on both sides of the channel and the fillet curve of the channel inlet (9) includes: Given the groove inlet width TI and the fillet radius r at the groove inlet in , wherein the fillet radius r at the inlet of the groove in The value of is not greater than 1 / 2 of the thickness at the leading edge of the original blade; At the inlet of the groove, a perpendicular line is drawn perpendicular to the original blade pressure surface line (7) toward the side where the original blade suction surface line (5) is located, and the length of the perpendicular line is equal to the fillet radius r at the inlet of the groove. in , the starting point of the vertical line is the relative chord length position SP2 of the slot inlet, the value of the relative chord length position SP2 of the slot inlet is defined as the ratio of the abscissa of the slot inlet position in the relative chord length coordinate system to the chord length c of the original blade geometry, and the value of the relative chord length position SP2 of the slot inlet is less than the value of the relative chord length position EP1 of the slot outlet, and the end point of the vertical line is the center of the slot inlet fillet curve (9); Set the channel inlet angle α in , the slot inlet angle α out The unit is °; in the relative chord length coordinate system, the relative chord length position SP2 of the groove inlet is the starting point of the groove inlet fillet curve (9), and the fillet radius r at the groove inlet is in As the radius, an inscribed arc is made of the original blade pressure surface profile line (7), the inscribed arc takes the tangent point with the original blade pressure surface profile line (7) as the starting point, and includes an angle of 180°-α in Then the groove inlet fillet curve (9) is obtained; The quadratic Bezier curves of the inner walls on both sides of the channel include a quadratic Bezier curve (2) of the inner wall of the upstream channel and a quadratic Bezier curve (8) of the inner wall of the downstream channel; At the starting point of the quadratic Bezier curve (4) at the slot outlet, a ray III is drawn in the direction of the slot inlet with the starting slope of the quadratic Bezier curve (4) at the slot outlet; at the end point of the slot inlet fillet curve (9), a ray III is drawn in the direction of the slot inlet with the starting slope of the quadratic Bezier curve (4) at the slot inlet. in Draw ray IV in the direction of the channel outlet; select the intersection of ray III and ray IV as the middle control point of the quadratic Bezier curve (8) of the inner wall of the downstream channel; The quadratic Bezier curve (8) of the inner wall of the downstream channel is obtained by calculation according to the starting point of the quadratic Bezier curve (4) at the channel outlet, the middle control point of the quadratic Bezier curve (8) of the inner wall of the downstream channel, and the end point of the fillet curve (9) at the channel inlet; Connect the center of the groove inlet fillet curve (9) and the end point of the groove inlet fillet curve (9), and make an extension line in the direction of the original blade suction surface profile line (5), the distance between the end point of the extension line and the end point of the groove inlet fillet curve (9) is equal to the groove inlet width TI, and use the end point of the extension line as the starting point of the upstream groove inner wall quadratic Bezier curve (2); use the end point of the groove outlet fillet curve (3) in step 3 as the end point of the upstream groove inner wall quadratic Bezier curve (2), according to the groove outlet jet angle α out Determine the end point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel so that the tangent direction at the end point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is in line with the jet angle α at the outlet of the channel. out The determined channel jet direction is consistent; according to the channel inlet inlet angle α in Determine the starting point slope of the quadratic Bezier curve (2) of the inner wall of the upstream channel so that the tangent direction at the starting point of the quadratic Bezier curve (2) of the inner wall of the upstream channel is in line with the inlet angle α of the channel inlet. in The flow direction of the determined channel is consistent; At the starting point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray V is drawn in the direction of the end point of the quadratic Bezier curve (2) of the upstream channel inner wall with the starting point slope of the quadratic Bezier curve (2) of the upstream channel inner wall; at the end point of the quadratic Bezier curve (2) of the upstream channel inner wall, a ray VI is drawn in the direction of the starting point of the quadratic Bezier curve (2) of the upstream channel inner wall with the end point slope of the quadratic Bezier curve (2) of the upstream channel inner wall; the intersection point of the drawn ray V and the drawn ray VI is selected as the middle control point of the quadratic Bezier curve (2) of the upstream channel inner wall; The upstream channel inner wall quadratic Bezier curve (2) is obtained by calculation according to the starting point of the upstream channel inner wall quadratic Bezier curve (2), the middle control point of the upstream channel inner wall quadratic Bezier curve (2), and the end point of the upstream channel inner wall quadratic Bezier curve (2); ⑥ The calculation of the channel inlet quadratic Bezier curve (1) comprises: Given a relative chord length position SP1 of the starting point of the groove profile, the value of the relative chord length position SP1 of the starting point of the groove profile is the ratio of the abscissa of the starting point of the groove inlet quadratic Bezier curve (1) in the relative chord length coordinate system to the chord length c of the original blade geometry; In the relative chord length coordinate system, the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) in the relative chord length coordinate system is obtained from the relative chord length position SP1 of the starting point of the slot profile; a point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) is selected on the original blade pressure surface profile (7) in the relative chord length coordinate system as the starting point of the slot inlet quadratic Bezier curve (1), and the slope of the point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the slot inlet quadratic Bezier curve (1) is extracted as the starting point of the slot inlet quadratic Bezier curve (1). The starting point slope of the slot inlet quadratic Bezier curve (1); the starting point of the upstream slot inner wall arc in step 5 is used as the end point of the slot inlet quadratic Bezier curve (1), and the slope at the starting point of the upstream slot inner wall arc in step 5 is used as the end point slope of the slot inlet quadratic Bezier curve (1); the slot inlet quadratic Bezier curve (1) is tangent to the blade pressure surface profile at the starting point of the slot inlet quadratic Bezier curve (1), and the slot inlet quadratic Bezier curve (1) is tangent to the upstream slot inner wall arc at the end point of the slot inlet quadratic Bezier curve (1); At the starting point of the channel inlet quadratic Bezier curve (1), a ray VII is drawn in the direction of the end point of the channel inlet quadratic Bezier curve (1) with the starting point slope of the channel inlet quadratic Bezier curve (1); at the end point of the channel inlet quadratic Bezier curve (1), a ray VIII is drawn in the direction of the starting point of the channel inlet quadratic Bezier curve (1) with the end point slope of the channel inlet quadratic Bezier curve (1); and the intersection of the drawn ray VII and the drawn ray VIII is selected as the middle control point of the channel inlet quadratic Bezier curve (1); The channel inlet quadratic Bezier curve (1) is obtained by calculation according to the starting point of the channel inlet quadratic Bezier curve (1), the middle control point of the channel inlet quadratic Bezier curve (1), and the end point of the channel inlet quadratic Bezier curve (1); ⑦ The inverse transformation of the slotted blade geometry into an absolute coordinate system comprises: In the relative chord length coordinate system, the original blade suction surface profile line (5), the original blade pressure surface profile line (7), the slot outlet fillet curve (3), the slot outlet quadratic Bezier curve (4), the downstream slot inner wall quadratic Bezier curve (8), the slot inlet fillet curve (9), the upstream slot inner wall quadratic Bezier curve (2), and the slot inlet quadratic Bezier curve (1) together constitute the slotted blade geometry in the relative chord length coordinate system; The slotted blade geometry in the relative chord length coordinate system is enlarged at a ratio of c / 1 with the leading edge point (10) as the center to obtain a final slotted blade geometry; the final slotted blade geometry is subjected to an inverse coordinate transformation so that the coordinates of the trailing edge point (6) are transformed from the coordinate point (c, 0) to the same position as the coordinates of the trailing edge point (6) of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system.

2. A parameterized blade slot design method based on Bezier curve according to claim 1, characterized in that: The parameterized blade slotting design method based on Bezier curve is applicable to the design of two-dimensional compressor blade profiles and the design of three-dimensional compressor blades (11); when the parameterized blade slotting design method based on Bezier curve is used for the design of three-dimensional compressor blades (11), the height of the original three-dimensional compressor blade (11) between the upper end wall and the lower end wall is set to H, and a slot stretching line is set along the span direction of the original three-dimensional compressor blade (11), the slot stretching line is a Bezier curve, and the corresponding slot side wall is a Bezier surface; the slotting height corresponding to the slot stretching line is h; the starting end of the slot stretching line can be located at the lower end wall or the upper end wall, and the corresponding slotting height h has a value range of 0 to H, thereby obtaining an end zone slotting scheme.

3. A parameterized blade slot design method based on Bezier curve as claimed in claim 2, characterized in that: The grooves can be simultaneously opened on the upper end wall side and the lower end wall side of the original three-dimensional compressor blade (11), thereby obtaining a double-side end zone groove scheme.

4. A parameterized blade slot design method based on Bezier curve as claimed in claim 2, characterized in that: When the value of the slotting height h is equal to the height H between the upper end wall and the lower end wall (12) of the original three-dimensional compressor blade (11), the groove runs through the entire original three-dimensional compressor blade (11) along the span direction, obtaining a full-blade height slotting solution.

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