A parametric blade slot design method based on polynomial curve

Abstract

The present invention discloses a parametric blade slot design method based on polynomial 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 cubic curve; step five, calculating the inner wall arcs on both sides of the slot and the slot inlet fillet curve; step six, calculating the slot inlet cubic 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 polynomial curve and the arc are used to design the slot profile, so as to realize the rapid design of the slot geometry of high-load compressor blades, which is conducive to parametric research. The designed slot 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 polynomial 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 polynomial 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 polynomial curves, which aims to generate the slot geometry of the slotted blade by combining arc curves with cubic polynomial curves based on given original blade geometry, slot inlet and outlet positions and widths, slot profile start and end points, 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 three-dimensional angular zone separation flow 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 parametric blade slot design method based on a polynomial curve, 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 cubic curve of the channel exit;

[0012] Step 5, calculating the inner wall arcs on both sides of the groove and the groove inlet fillet curve;

[0013] Step 6, calculating the cubic curve of 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 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 and the channel exit jet angle α;

[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] Select the slot outlet position on the original blade suction surface line and set the fillet radius r at the slot outlet. 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 slot, a perpendicular line is drawn perpendicular to the suction surface line of the original blade to the side where the pressure surface line of the original blade is located, and the length of the perpendicular line is equal to the fillet radius r at the outlet of the slot out , the endpoint of the vertical line is the relative chord length position EP1 of the slot outlet, and 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;

[0023] Set the slot outlet jet angle α, the unit of the slot outlet jet angle α is °; in the relative chord length coordinate system, take the slot outlet relative chord length position EP1 as the center of the circle and the fillet radius r at the slot outlet as the center of the circle. out As the radius, make an inscribed arc of the original blade suction surface profile line, take the tangent point of the inscribed arc and the original blade suction surface profile line as the starting point, and terminate after including the angle 90°-α as the end point of the groove outlet fillet curve to obtain the groove outlet fillet curve;

[0024] ④ The calculation of the cubic 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 slot outlet cubic curve is obtained according to the end point of the slot outlet fillet curve, the slot outlet width TO, and the slot outlet jet angle α; 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 α, 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 cubic curve;

[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 cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry. The abscissa of the end point of the groove outlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position EP2 of the end point of the groove profile; a point with the same abscissa as the end point of the groove outlet cubic curve is selected on the original blade suction surface profile in the relative chord length coordinate system as the end point of the groove outlet cubic curve;

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

[0029] The channel exit cubic curve is obtained by calculation according to the starting point of the channel exit cubic curve, the end point of the channel exit cubic curve, the starting point slope of the channel exit cubic curve, and the end point slope of the channel exit cubic curve;

[0030] ⑤ The calculation of the inner wall arcs on both sides of the groove and the groove inlet fillet curve includes:

[0031] 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;

[0032] At the inlet of the groove, a perpendicular line is drawn perpendicular to the original blade pressure surface line to the side where the original blade suction surface line is located, and the length of the perpendicular line is equal to the fillet radius r at the inlet of the groove. in , the endpoint 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;

[0033] In the relative chord length coordinate system, according to the starting point of the cubic curve at the slot outlet, the starting point slope of the cubic curve at the slot outlet, the relative chord length position SP2 of the slot inlet, and the fillet radius r at the slot inlet, the slot inlet is in Solve the inner arc of the downstream channel by simultaneous calculation; take the relative chord length position SP2 of the channel inlet as the center, and the fillet radius r at the channel inlet as the center. in As the radius, make an inscribed arc of the original blade pressure surface profile, connect the original blade pressure surface profile and the downstream side slot inner wall arc, and generate a slot inlet fillet curve;

[0034] Connect the relative chord length position SP2 of the slot inlet with the intersection of the slot inlet fillet curve and the downstream slot inner wall arc, 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 intersection of the slot inlet fillet curve and the downstream slot inner wall arc is equal to the slot inlet width TI, and the end point of the extension line is used as the starting point of the upstream slot inner wall arc; the end point of the slot outlet fillet curve in step three is used as the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc is parallel to the slot jet direction determined by the slot outlet jet angle α; the upstream slot inner wall arc can be determined according to the starting point of the upstream slot inner wall arc, the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc;

[0035] ⑥ The calculation of the groove inlet cubic curve includes:

[0036] 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 cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry;

[0037] In the relative chord length coordinate system, the horizontal coordinate of the starting point of the groove inlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position SP1 of the starting point of the groove profile; a point with a horizontal coordinate equal to the horizontal coordinate of the starting point of the groove inlet cubic curve is selected on the original blade pressure surface profile in the relative chord length coordinate system as the starting point of the groove inlet cubic curve; the starting point of the upstream groove inner wall arc in step five is used as the end point of the groove inlet cubic curve; the groove inlet cubic curve is tangent to the blade pressure surface profile at the starting point of the groove inlet cubic curve, and the groove inlet cubic curve is tangent to the upstream groove inner wall arc at the end point of the groove inlet cubic curve; the groove inlet cubic curve is generated according to the starting point of the groove inlet cubic curve, the end point of the groove inlet cubic curve, the tangent direction of the starting point of the groove inlet cubic curve, and the tangent direction of the end point of the groove inlet cubic curve;

[0038] ⑦ The inverse transformation of the slotted blade geometry into an absolute coordinate system comprises:

[0039] 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 cubic curve, the downstream slot inner wall arc, the slot inlet fillet curve, the upstream slot inner wall arc, and the slot inlet cubic curve together constitute the slotted blade geometry in the relative chord length coordinate system;

[0040] 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.

[0041] In particular, the parametric blade slotting design method based on polynomial curves is applicable to both the design of two-dimensional compressor blade profiles and the design of three-dimensional compressor blades; when the parametric blade slotting design method based on polynomial curves 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 is set along the span direction of the original three-dimensional compressor blade, and the slotting height of the slot is h; the starting end of the slotting height h can be located at the lower end wall or the upper end wall, and the value range of the slotting height h is 0 to H, thereby obtaining an end area slotting scheme.

[0042] 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.

[0043] In particular, when the slot height h is equal to the height H of the original three-dimensional compressor blade between the upper end wall and the lower end wall, the groove runs through the entire original three-dimensional compressor blade along the span direction to obtain a full-blade height slotting solution.

[0044] (III) Beneficial effects

[0045] The present invention provides a parametric blade slot design method based on a polynomial 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.

[0046] The present invention provides a parametric blade slotting design method based on polynomial curves. By adopting polynomial curves and circular arcs 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.

[0047] The present invention provides a parametric blade slotting design method based on polynomial 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

[0048] Figure 1 It is a flow chart of a parametric blade slot design method based on polynomial curves of the present invention;

[0049] Figure 2 A geometrical schematic diagram of a slotted blade of a parametric blade slotting design method based on a polynomial curve according to the present invention;

[0050] Figure 3 A schematic diagram of three-dimensional compressor blade slotting according to a parametric blade slotting design method based on a polynomial curve of the present invention;

[0051] Figure 4 A flow field diagram of the original blade geometry of a parametric blade slot design method based on a polynomial curve according to the present invention;

[0052] Figure 5 A flow field diagram of the slotted blade geometry of a parametric blade slotting design method based on a polynomial curve according to the present invention;

[0053] In the figure, 1: the cubic curve of the slot inlet; 2: the arc of the inner wall of the slot on the downstream side; 3: the arc of the inner wall of the slot on the upstream side; 4: the fillet curve of the slot outlet; 5: the cubic curve of the slot outlet; 6: the suction surface line of the original blade; 7: the trailing edge point; 8: the pressure surface line of the original blade; 9: the fillet curve of the slot inlet; 10: the leading edge point; 11: the three-dimensional compressor blade; 12: the lower end wall; 13: the full blade height slot; 14: the end area slot. DETAILED DESCRIPTION

[0054] 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.

[0055] like Figure 1 , Figure 2 As shown, the present invention provides a parametric blade slot design method based on a polynomial curve, comprising the following steps:

[0056] Step 1, giving the geometric design parameters of the slotted blade;

[0057] 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 (6) and the original blade pressure surface profile (8) are respectively extracted from the original blade geometry;

[0058] 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 and the channel exit jet angle α.

[0059] Step 2, transform the original blade geometry into a relative chord length coordinate system;

[0060] 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 (7), 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 (7);

[0061] 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 (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 (7) are (1, 0).

[0062] Step 3, calculating the channel outlet fillet curve (4);

[0063] In this step, the slot outlet position is selected on the original blade suction surface profile (6), and the fillet radius r at the slot outlet is set. out ; Among them, 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 slot outlet, a vertical line is drawn perpendicular to the original blade suction surface line (6) toward the side where the original blade pressure surface line (8) is located, and the length of the vertical line is equal to the fillet radius r at the slot outlet out , the endpoint of the vertical line is the relative chord length position EP1 of the slot outlet, and the value of the relative chord length position EP1 of the slot outlet 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;

[0064] Set the slot outlet jet angle α, the unit of the slot outlet jet angle α is °; in the relative chord length coordinate system, take the slot outlet relative chord length position EP1 as the center of the circle and the fillet radius r at the slot outlet as the center of the circle. outAs the radius, an inscribed arc is made on the original blade suction surface profile line (6). The inscribed arc is made with its tangent point with the original blade suction surface profile line (6) as the starting point and ends after including an angle of 90°-α as the end point of the groove outlet fillet curve, thereby obtaining the groove outlet fillet curve (4).

[0065] Step 4, calculating the channel exit cubic curve (5);

[0066] In this step, the channel outlet width TO and the channel profile end point relative to the chord length EP2 are given;

[0067] In the relative chord length coordinate system, the starting point of the cubic curve of 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 α; 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 α, 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 cubic curve of the slot outlet;

[0068] 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 cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry. The abscissa of the end point of the groove outlet cubic curve in the relative chord length coordinate system can be 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 (6) in the relative chord length coordinate system whose abscissa is equal to the abscissa of the end point of the groove outlet cubic curve is selected as the end point of the groove outlet cubic curve;

[0069] The starting point slope of the slot outlet cubic curve is determined according to the slot outlet jet angle α, so that the tangent direction at the starting point of the slot outlet cubic curve is consistent with the slot jet direction determined by the slot outlet jet angle α; the ending point slope of the slot outlet cubic curve is the slope of the original blade suction surface profile line (6) at the ending point of the slot outlet cubic curve;

[0070] The channel exit cubic curve (5) is obtained by calculation according to the starting point of the channel exit cubic curve, the end point of the channel exit cubic curve, the starting point slope of the channel exit cubic curve, and the end point slope of the channel exit cubic curve.

[0071] Step 5, calculating the inner wall arcs on both sides of the groove and the groove inlet fillet curve (9);

[0072] In this step, the slot inlet width TI and the fillet radius r at the slot inlet are given. in , where the fillet radius r at the channel inlet is in The value of is not greater than 1 / 2 of the thickness at the leading edge of the original blade;

[0073] At the slot inlet, a vertical line is drawn perpendicular to the original blade pressure surface line (8) toward the original blade suction surface line (6), and the length of the vertical line is equal to the fillet radius r at the slot inlet. in , the endpoint 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;

[0074] In the relative chord length coordinate system, according to the starting point of the cubic curve at the slot outlet, the starting slope of the cubic curve at the slot outlet, the relative chord length position SP2 of the slot inlet, and the fillet radius r at the slot inlet, in Solve the arc of the inner wall of the downstream channel by simultaneous calculation (2); take the position SP 2 of the channel inlet relative to the chord length as the center, and the radius of the fillet at the channel inlet r in As the radius, an inscribed arc is made for the original blade pressure surface profile line (8), and the original blade pressure surface profile line (8) is connected with the downstream side channel inner wall arc (2) to generate a channel inlet fillet curve (9);

[0075] Connect the relative chord length position SP2 of the slot inlet with the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2), and make an extension line in the direction of the original blade suction surface profile line (6), the distance between the end point of the extension line and the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2) is equal to the slot inlet width TI, and use the end point of the extension line as the starting point of the upstream slot inner wall arc; use the end point of the slot outlet fillet curve in step 3 as the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc is parallel to the slot jet direction determined by the slot outlet jet angle α; the upstream slot inner wall arc (3) can be determined according to the starting point of the upstream slot inner wall arc, the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc.

[0076] Step 6, calculating the channel inlet cubic curve (1);

[0077] 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 cubic curve (1) in the relative chord length coordinate system to the chord length c of the original blade geometry;

[0078] In the relative chord length coordinate system, the horizontal coordinate of the starting point of the groove inlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position SP1 of the starting point of the groove profile; a point with a horizontal coordinate equal to the horizontal coordinate of the starting point of the groove inlet cubic curve is selected on the original blade pressure surface profile (8) in the relative chord length coordinate system as the starting point of the groove inlet cubic curve; the starting point of the upstream groove inner wall arc in step 5 is used as the end point of the groove inlet cubic curve; the groove inlet cubic curve (1) is tangent to the blade pressure surface profile at the starting point of the groove inlet cubic curve), and the groove inlet cubic curve (1) is tangent to the upstream groove inner wall arc (3) at the end point of the groove inlet cubic curve; the groove inlet cubic curve (1) is generated according to the starting point of the groove inlet cubic curve, the end point of the groove inlet cubic curve, the tangent direction of the starting point of the groove inlet cubic curve, and the tangent direction of the end point of the groove inlet cubic curve.

[0079] Step 7, inversely transform the slotted blade geometry into an absolute coordinate system;

[0080] In this step, in the relative chord length coordinate system, the original blade suction surface profile (6), the original blade pressure surface profile (8), the slot outlet fillet curve (4), the slot outlet cubic curve (5), the downstream slot inner wall arc (2), the slot inlet fillet curve (9), the upstream slot inner wall arc (3), and the slot inlet cubic curve (1) together constitute the slotted blade geometry in the relative chord length coordinate system;

[0081] 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 (7) is transformed from the coordinate point (c, 0) to the same position as the coordinate of the trailing edge point (7) of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system.

[0082] Furthermore, the parametric blade slotting design method based on polynomial curves proposed in the present invention is applicable to the design of two-dimensional compressor blade profiles as well as the design of three-dimensional compressor blades (11); when the parametric blade slotting design method based on polynomial curves 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 (12) is set to H, and a slot is set along the span direction of the original three-dimensional compressor blade (11), and the slotting height of the set slot is h; the starting end of the slotting height h can be located at the lower end wall (12) or the upper end wall, and the value range of the slotting height h is 0 to H, thereby obtaining an end zone slotting (14) scheme.

[0083] 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.

[0084] 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.

[0085] Embodiment 1:

[0086] Taking a high-load compressor blade row studied by the research group as an example, a parametric blade slotting design method based on polynomial curves proposed in the present invention was used to design the slotting scheme on both sides of the blade end area, and the flow field of the prototype blade row and the slotted blade row was numerically simulated to verify the control effect of the slotting scheme on both sides of the blade end area.

[0087] like Figure 2 The figure shows a geometrical schematic diagram of a slotted blade of a parametric blade slotting design method based on a polynomial curve of the present invention. In this embodiment, the value of the slot inlet relative to the chord length position SP2 is 23%, the value of the slot outlet relative to the chord length position EP1 is 30%, 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 50%, the slot inlet width TI is 1.4 mm, the slot outlet width TO is 1 mm, and the fillet radius r at the slot inlet is 1.4 mm. in The value of is 0.2mm, and the radius of the fillet at the groove outlet is r out The value of is 0.2 mm, the value of the jet angle α at the channel outlet is 10°, and the chord length of the original blade geometry is c = 50 mm.

[0088] 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 (50, 0); the original blade geometry is scaled at a ratio of 1 / 50 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).

[0089] At the slot outlet, a vertical line is drawn perpendicular to the original blade suction surface line (6) toward the original blade pressure surface line (8), and the length of the vertical line is equal to the fillet radius r at the slot outlet. out =0.2 / 50mm, the endpoint of the perpendicular line is the relative chord length position EP1 of the slot outlet. In the relative chord length coordinate system, the relative chord length position EP1 of the slot outlet is the center of the circle, and the fillet radius r at the slot outlet is the center of the circle. out=0.2 / 50mm as the radius, make an inscribed arc of the original blade suction surface profile line (6), the inscribed arc takes the tangent point with the original blade suction surface profile line (6) as the starting point, ends after including an angle of 80°, and serves as the end point of the groove outlet fillet curve, thereby obtaining the groove outlet fillet curve (4).

[0090] 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 slot outlet jet angle α. The length of the vertical line is equal to the slot outlet width TO=1 / 50mm. The end point of the obtained vertical line is the starting point of the slot outlet cubic curve. The value of the relative chord length position EP2 of the slot profile end point is 50%, so the abscissa of the end point of the slot outlet cubic curve in the relative chord length coordinate system is 0.5. The point with the same abscissa as the end point of the slot outlet cubic curve on the original blade suction surface profile (6) in the relative chord length coordinate system is selected as The end point of the slot outlet cubic curve; the starting point slope of the slot outlet cubic curve is determined according to the slot outlet jet angle α=10°, so that the tangent direction at the starting point of the slot outlet cubic curve is consistent with the slot jet direction determined by the slot outlet jet angle α=10°; the end point slope of the slot outlet cubic curve is the slope of the original blade suction surface profile line (6) at the end point of the slot outlet cubic curve; the slot outlet cubic curve (5) is obtained by calculation according to the starting point of the slot outlet cubic curve, the end point of the slot outlet cubic curve, the starting point slope of the slot outlet cubic curve, and the end point slope of the slot outlet cubic curve.

[0091] At the slot inlet, a vertical line is drawn perpendicular to the original blade pressure surface line (8) toward the original blade suction surface line (6), and the length of the vertical line is equal to the fillet radius r at the slot inlet. in =0.2 / 50mm, the endpoint of the vertical line is the relative chord length position SP2 of the slot inlet, and in this embodiment, the horizontal coordinate of the relative chord length position SP2 of the slot inlet is 0.23. In the relative chord length coordinate system, according to the starting point of the slot outlet cubic curve, the starting point slope of the slot outlet cubic curve, the relative chord length position SP2 of the slot inlet, and the fillet radius r at the slot inlet, in Solve the arc of the inner wall of the downstream channel (2) by combining the two methods; take the position SP2 of the channel inlet relative to the chord length as the center, and the radius r of the fillet at the channel inlet as the center. in =0.2 / 50mm as the radius, make an inscribed arc of the original blade pressure surface profile (8), connect the original blade pressure surface profile (8) and the downstream side channel inner wall arc (2), and generate the channel inlet fillet curve (9);

[0092] The relative chord length position SP2 of the slot inlet is connected to the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2), and an extension line is made in the direction of the original blade suction surface profile line (6), the distance between the end point of the extension line and the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2) is equal to the slot inlet width TI = 1.4 / 50mm, and the end point of the extension line is used as the starting point of the upstream slot inner wall arc; the end point of the slot outlet fillet curve is used as the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc is parallel to the slot jet direction determined by the slot outlet jet angle α = 10°; the upstream slot inner wall arc (3) can be determined according to the starting point of the upstream slot inner wall arc, the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc.

[0093] A point whose abscissa is equal to the abscissa of the starting point of the slot inlet cubic curve is selected on the original blade pressure surface profile (8) in the relative chord length coordinate system as the starting point of the slot inlet cubic curve; the starting point of the upstream slot inner wall arc is taken as the end point of the slot inlet cubic curve; the slot inlet cubic curve (1) is tangent to the blade pressure surface profile at the starting point of the slot inlet cubic curve, and the slot inlet cubic curve (1) is tangent to the upstream slot inner wall arc (3) at the end point of the slot inlet cubic curve; the slot inlet cubic curve (1) is generated according to the starting point of the slot inlet cubic curve, the end point of the slot inlet cubic curve, the tangent direction of the starting point of the slot inlet cubic curve, and the tangent direction of the end point of the slot inlet cubic curve.

[0094] The geometry of the slotted blade in the relative chord length coordinate system is jointly constituted by the original blade suction surface profile (6), the original blade pressure surface profile (8), the slot outlet fillet curve (4), the slot outlet cubic curve (5), the downstream slot inner wall arc (2), the slot inlet fillet curve (9), the upstream slot inner wall arc (3), and the slot inlet cubic curve (1).

[0095] The slotted blade geometry in the relative chord length coordinate system is enlarged by a ratio of 50 / 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 (7) is transformed from the coordinate point (50,0) to the same position as the coordinate of the trailing edge point (7) of the original blade geometry, thereby obtaining the slotted blade geometry in the original blade geometry coordinate system.

[0096] 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.

[0097] 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 parameterized blade slotting design method based on a polynomial curve according to 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 polynomial curves 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 polynomial curves 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.

[0098] 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.

[0099] In summary, the parametric blade slot design method based on polynomial curves provided by the present invention, by given the original blade geometry and fewer slot design parameters, uses polynomial curves and arcs to design the profile of the slot, thereby realizing the rapid design of the slot geometry of high-load compressor blades, which is conducive to the parametric study of the slot performance of high-load compressor blades. The designed slotted blade geometry can better regulate the flow field of the high-load compressor, 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 polynomial 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 (4); Step 4, calculating the channel exit cubic curve (5); Step 5, calculating the inner wall arcs on both sides of the groove and the groove inlet fillet curve (9); Step 6, calculating the channel inlet cubic curve (1); 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 (6) and the original blade pressure surface profile (8) 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 and the channel exit jet angle α; 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 (7), 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 (7); 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 (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 (7) are (1, 0); ③ The calculation of the channel outlet fillet curve (4) includes: The slot outlet position is selected on the original blade suction surface line (6), 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 slot, a perpendicular line is drawn perpendicular to the suction surface line (6) of the original blade to the side where the pressure surface line (8) of the original blade is located, and the length of the perpendicular line is equal to the fillet radius r at the outlet of the slot out , the endpoint of the vertical line is the relative chord length position EP1 of the slot outlet, and 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; Set the slot outlet jet angle α, the unit of the slot outlet jet angle α is °; in the relative chord length coordinate system, take the slot outlet relative chord length position EP1 as the center of the circle and the fillet radius r at the slot outlet as the center of the circle. out As the radius, an inscribed arc is made for the original blade suction surface profile line (6), the inscribed arc takes the tangent point with the original blade suction surface profile line (6) as the starting point, ends after including an angle of 90°-α, and serves as the end point of the groove outlet fillet curve, thereby obtaining the groove outlet fillet curve (4); ④ The calculation of the channel exit cubic curve (5) 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, the starting point of the slot outlet cubic curve is obtained according to the end point of the slot outlet fillet curve, the slot outlet width TO, and the slot outlet jet angle α; 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 α, 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 cubic curve; 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 cubic curve in the relative chord length coordinate system to the chord length c of the original blade geometry. The abscissa of the end point of the groove outlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position EP2 of the end point of the groove profile; a point whose abscissa is equal to the abscissa of the end point of the groove outlet cubic curve in the relative chord length coordinate system is selected on the original blade suction surface profile (6) as the end point of the groove outlet cubic curve; The starting point slope of the slot outlet cubic curve is determined according to the slot outlet jet angle α, so that the tangent direction at the starting point of the slot outlet cubic curve is consistent with the slot jet direction determined by the slot outlet jet angle α; the ending point slope of the slot outlet cubic curve is the slope of the original blade suction surface profile line (6) at the ending point of the slot outlet cubic curve; The channel exit cubic curve (5) is obtained by calculation according to the starting point of the channel exit cubic curve, the end point of the channel exit cubic curve, the starting point slope of the channel exit cubic curve, and the end point slope of the channel exit cubic curve; ⑤ The calculation of the inner wall arcs on both sides of the groove and the groove inlet fillet curve (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 (8) toward the side where the original blade suction surface line (6) is located, and the length of the perpendicular line is equal to the fillet radius r at the inlet of the groove. in , the endpoint 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; In the relative chord length coordinate system, according to the starting point of the cubic curve at the slot outlet, the starting point slope of the cubic curve at the slot outlet, the relative chord length position SP2 of the slot inlet, and the fillet radius r at the slot inlet, the slot inlet is in Solve the downstream side channel inner wall arc (2) by combining the two methods; take the channel inlet relative chord length position SP2 as the center of the circle and the fillet radius r at the channel inlet as the center of the circle. in As the radius, an inscribed arc is made for the original blade pressure surface profile line (8), the original blade pressure surface profile line (8) is connected with the downstream side channel inner wall arc (2), and a channel inlet fillet curve (9) is generated; Connect the relative chord length position SP2 of the slot inlet with the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2), and make an extension line in the direction of the original blade suction surface profile line (6), the distance between the end point of the extension line and the intersection of the slot inlet fillet curve (9) and the downstream slot inner wall arc (2) is equal to the slot inlet width TI, and the end point of the extension line is used as the starting point of the upstream slot inner wall arc; the end point of the slot outlet fillet curve in step 3 is used as the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc is parallel to the slot jet direction determined by the slot outlet jet angle α; the upstream slot inner wall arc (3) can be determined according to the starting point of the upstream slot inner wall arc, the end point of the upstream slot inner wall arc, and the tangent direction at the end point of the upstream slot inner wall arc; ⑥ The calculation of the channel inlet cubic 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 cubic curve 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 groove inlet cubic curve in the relative chord length coordinate system can be obtained from the relative chord length position SP1 of the starting point of the groove profile; a point whose horizontal coordinate is equal to the horizontal coordinate of the starting point of the groove inlet cubic curve is selected on the original blade pressure surface profile (8) in the relative chord length coordinate system as the starting point of the groove inlet cubic curve; the starting point of the upstream groove inner wall arc in step 5 is used as the end point of the groove inlet cubic curve; the groove inlet cubic curve (1) is tangent to the blade pressure surface profile at the starting point of the groove inlet cubic curve, and the groove inlet cubic curve (1) is tangent to the upstream groove inner wall arc (3) at the end point of the groove inlet cubic curve; the groove inlet cubic curve (1) is generated according to the starting point of the groove inlet cubic curve, the end point of the groove inlet cubic curve, the tangent direction of the starting point of the groove inlet cubic curve, and the tangent direction of the end point of the groove inlet cubic curve; 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 (6), the original blade pressure surface profile line (8), the slot outlet fillet curve (4), the slot outlet cubic curve (5), the downstream slot inner wall arc (2), the slot inlet fillet curve (9), the upstream slot inner wall arc (3), and the slot inlet cubic 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 (7) are transformed from the coordinate point (c, 0) to the same position as the coordinates of the trailing edge point (7) of the original blade geometry to obtain the slotted blade geometry in the original blade geometry coordinate system.

2. A parametric blade slot design method based on polynomial curve according to claim 1, characterized in that: The parametric blade slotting design method based on polynomial curves is applicable to the design of two-dimensional compressor blade profiles and also to the design of three-dimensional compressor blades (11); when the parametric blade slotting design method based on polynomial curves 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 (12) is set to H, and a slot is set along the span direction of the original three-dimensional compressor blade (11), and the slotting height of the slot is h; the starting end of the slotting height h can be located at the lower end wall (12) or the upper end wall, and the value range of the slotting height h is 0 to H, thereby obtaining an end zone slotting (14) scheme.

3. A parametric blade slot design method based on polynomial curve according to 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 parametric blade slot design method based on polynomial curve according to claim 2, characterized in that: When the value of the slot 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 slot (13) solution.

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