An Accelerated Convergence Type Slotting Design Method for Blade Tip Regions

Abstract

The present invention discloses a method for designing slots in the blade tip region with accelerated convergence. The main implementation process includes: Step 1, extracting the original blade geometric profile; Step 2, calculating the curvature of the geometric profile; Step 3, setting the slot outlet position; Step 4, generating the rear wall profile of the slot with accelerated convergence; Step 5, setting the throat width of the slot; Step 6, generating the front wall profile of the slot with accelerated convergence; Step 7, completing the transition between the front wall profile of the slot with accelerated convergence and the blade pressure surface; Step 8, generating the three-dimensional slot geometry. The present invention adjusts the profile design of the slot by introducing profile modeling control parameters, and quickly generates a slot design scheme with a high self-adaptive jet acceleration ratio. The enhanced jet at the slot outlet effectively suppresses the performance degradation caused by the blockage of the compressor blade passage due to the accumulation of low-energy fluid in the compressor blade tip region, improves the aerodynamic performance of the high-load compressor, and has important engineering application prospects.

Description

Technical Field

[0001] The present invention relates to the field of flow control of turbomachinery, and particularly to a design method for slotting at the blade tip region with accelerated convergence. Background Art

[0002] Turbomachinery is widely used in high-tech fields such as aerospace propulsion systems, ship power propulsion systems, energy, and chemical engineering. The compressor is a core component of turbomachinery represented by aeroengines and gas turbines, and is a basic strategic industry in technologically advanced countries. With the development of modern aviation technology, the requirement for the thrust-to-weight ratio of aeroengines is getting higher and higher, which means that on the one hand, the compressor has to increase its overall load, and on the other hand, reduce the number of stages and improve the single-stage load level. Similarly, the research and development of heavy-duty gas turbines also pose significant requirements for the compressor load. However, with the increase in the compressor load level, the adverse pressure gradient in the blade passage gradually intensifies, causing low-energy fluid to gradually accumulate at the blade suction surface tip region, and then developing into three-dimensional corner separation flow, blocking the blade passage and seriously reducing the aerodynamic performance of the compressor. Under high-load conditions, the three-dimensional corner separation flow further evolves into three-dimensional corner stall flow, and even develops into large separation flow covering the entire blade height passage, resulting in a sharp decline in the compressor performance, which has an important impact on the pressure ratio, efficiency, margin, etc. of the compressor. In order to control the three-dimensional corner 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 input and is limited in engineering applications; the passive control method often has a good effect in a single working condition, but it is difficult to be widely applicable to a wide range of working conditions.

[0003] Our research group previously proposed a technology for controlling stator corner separation in compressors by slotting the blade roots (Gas Turbine Experiment and Research, 2007, Vol. 20, No. 3, 28 - 33), also known as the blade tip region slotting technology, and developed a series of channel shaping schemes (CN 105156361B, CN 105179322B, CN 105156356B, CN 105240322B, CN 105298925B), and proposed a method for slotting the blade roots of compressor stators based on an optimization algorithm (CN 105756719B). The proposed blade tip region slotting technology forms an "adaptive" jet to blow away the separated fluid by slotting from the pressure side to the suction side of the blade. Under the conditions of conventional loads, it has a good control effect on large-scale flow separation. The design of the new generation of compressors pursues a greater single-stage aerodynamic load, making the compressor blades have a smaller solidity, a larger bend angle, a thinner thickness, and a more severe blade flow field under high-load conditions. Previously, limited by the understanding of the flow mechanism, the control schemes used were simple forms such as equal-width straight slots, equal-width circular arc slots, and equal-width broken line slots. When the load was not very large, they achieved a good flow control effect of suppressing the corner separation of the compressor, but it was difficult to meet the design requirements of the next generation of high-load compressors. To solve the problem of three-dimensional corner separation in the new generation of high-load compressors, a blade tip region slotting design scheme with different characteristics was further developed according to the research needs of the new generation of high-load compressors. Aiming at the flow phenomenon in the blade tip region of high-load compressors where the endwall underflow migrates upward along the spanwise direction of the blade suction surface due to the strong transverse adverse pressure gradient, forming a low-energy fluid mass that blocks the compressor blade passage, the present invention proposes an accelerated convergence type blade tip region slotting design method. Through reasonable channel profile design, the acceleration ratio of the adaptive jet formed by the channel is increased, so that the enhanced jet at the channel outlet acts on the endwall crossflow that migrates upward along the spanwise direction of the blade suction surface, carrying the low-energy fluid downstream, thereby suppressing the performance degradation caused by the blockage of the compressor blade passage due to the accumulation of low-energy fluid in the blade tip region of the compressor and effectively improving the aerodynamic performance of the high-load compressor. Summary of the Invention

[0004] (1) Technical problems to be solved

[0005] The purpose of the present invention is to provide an accelerated convergence type blade tip region slotting design method, aiming to generate a channel design scheme with a high adaptive jet acceleration ratio quickly through reasonable channel profile design based on the given three-dimensional compressor blade original blade geometry and the channel outlet position, and solve the flow problem that the traditional simple channel design scheme is difficult to effectively control the endwall underflow in the blade tip region of high-load compressors, which migrates upward along the spanwise direction of the blade suction surface due to the strong transverse adverse pressure gradient, forming a low-energy fluid mass that blocks the compressor blade passage.

[0006] (2) Technical solutions

[0007] To solve the above technical problems, the present invention provides an accelerated convergence type blade tip region grooving design method, which includes the following steps:

[0008] Step 1: Extract the original blade geometry.

[0009] Step 2: Calculate the curvature of the geometry.

[0010] Step 3: Set the position of the channel outlet.

[0011] Step 4: Generate the accelerated convergence type channel rear wall geometry.

[0012] Step 5: Set the throat width of the channel.

[0013] Step 6: Generate the accelerated convergence type channel front wall geometry.

[0014] Step 7: Complete the transition between the accelerated convergence type channel front wall geometry and the blade pressure surface.

[0015] Step 8: Generate the three-dimensional channel geometry.

[0016] ① The extraction of the original blade geometry includes:

[0017] Given the control point coordinates of the original blade geometry of a three-dimensional compressor blade, generate the original blade geometry from the control point coordinates of the original blade geometry; extract the blade section geometry that needs to be grooved from the original blade geometry; divide the extracted blade section geometry into a leading edge section, a blade suction surface section, a blade pressure surface section, and a trailing edge section according to physical characteristics; establish a coordinate system with the point having the smallest abscissa of the blade section geometry as the leading edge point and the point having the largest abscissa of the blade section geometry as the trailing edge point. The line connecting the leading edge point and the trailing edge point of the blade section geometry is the chord length c of the blade section geometry, and the projection of the chord length c of the blade section geometry in the abscissa direction is defined as the axial chord length c of the blade section geometry x ;

[0018] ② The calculation of the geometry curvature includes:

[0019] Adopt a fitting algorithm to encrypt the control points corresponding to the blade suction surface section to obtain an encrypted control point sequence of the blade suction surface section; wherein, the difference in abscissa between any two adjacent control points in the encrypted control point sequence of the blade suction surface section is not greater than 1% of the axial chord length c of the blade section geometry x of;

[0020] Extract the coordinates of each point in the encrypted control point sequence of the blade suction surface section, calculate the relative chord length position of each point in the encrypted control point sequence of the blade suction surface section, calculate the radius of curvature and the coordinates of the center of curvature of each point in the encrypted control point sequence of the blade suction surface section, and store them as the curvature file of the control point sequence of the blade suction surface section;

[0021] Use a fitting algorithm to encrypt the control points corresponding to the blade pressure surface section to obtain an encrypted control point sequence of the blade pressure surface section; wherein, the difference in abscissa between any two adjacent control points in the encrypted control point sequence of the blade pressure surface section is not greater than 1% of the axial chord length c of the blade section profile; x of;

[0022] Extract the coordinates of each point in the encrypted control point sequence of the blade pressure surface section, calculate the relative chord length position of each point in the encrypted control point sequence of the blade pressure surface section, calculate the radius of curvature and the coordinates of the center of curvature of each point in the encrypted control point sequence of the blade pressure surface section, and store them as the curvature file of the control point sequence of the blade pressure surface section;

[0023] ③ The set channel outlet position includes:

[0024] Given the relative chord length position value of the channel outlet position, superimpose a margin value on the relative chord length position value of the channel outlet position as the intended relative chord length position value of the channel outlet tangent point P; wherein, the value range of the margin value is 3%-6% of the axial chord length c value of the blade section profile; x value;

[0025] Calculate the corresponding abscissa according to the intended relative chord length position value of the channel outlet tangent point P, and find the point in the encrypted control point sequence of the blade suction surface section whose abscissa is closest to the abscissa corresponding to the intended relative chord length position value of the channel outlet tangent point P, and define it as the channel outlet tangent point P;

[0026] ④ The generation of the accelerated convergence type channel rear wall profile includes:

[0027] Extract the coordinates P(x P ,y P ), radius of curvature r P and the coordinates of the center of curvature C P (x C_P ,y C_P ) of the channel outlet tangent point P determined in step three from the curvature file of the control point sequence of the blade suction surface section obtained in step two;

[0028] According to the coordinates P(x P ,y P) The curvature center coordinates C of the tangent point P at the outlet of the channel P (x C_P , y C_P ) Calculate the curvature radius angle α of the tangent point P at the outlet of the channel P ; The curvature radius angle a of the tangent point P at the outlet of the channel P is obtained by the following formula:

[0029]

[0030] Set the incoming flow angle of the incoming flow condition to be controlled for the three-dimensional compressor blade as i, and subtract the margin angle from the incoming flow angle i to obtain the channel inlet angle β; among them, the value range of the margin angle is 1-5°, and the greater the difference between the incoming flow angle i of the incoming flow condition to be controlled for the three-dimensional compressor blade and the incoming flow angle of the design condition of the three-dimensional compressor blade, the greater the value of the margin angle;

[0031] Set the channel number value n, where the channel number value n can take any value in {1, 2, 3};

[0032] Calculate the deflection angle θ of the rear wall profile line of the accelerating convergence channel, which is obtained by the following formula:

[0033]

[0034] With the curvature center coordinates C of the tangent point P at the outlet of the channel P (x C_P , y C_P ) as the center, deflect the ray determined by the connection line between the curvature center coordinates C of the tangent point P at the outlet of the channel P (x C_P , y C_P ) and the tangent point P at the outlet of the channel towards the leading edge direction of the blade section profile by the deflection angle θ of the rear wall profile line of the accelerating convergence channel, and the intersection point of the deflected ray and the blade pressure surface section is defined as the starting intention point of the rear wall profile line of the accelerating convergence channel;

[0035] Find the point in the curvature file of the control point sequence of the blade pressure surface section whose abscissa is closest to the abscissa of the starting intention point of the rear wall profile line of the accelerating convergence channel, and define it as the starting point Q of the rear wall profile line of the accelerating convergence channel;

[0036] Extract the coordinates Q(x Q , y Q ), curvature radius r Q and curvature center coordinates C of the starting point Q of the rear wall profile line of the accelerating convergence channel from the curvature file of the control point sequence of the blade pressure surface section obtained in step two Q (x C_Q , y C_Q );

[0037] The control equation of the accelerating convergence type channel rear wall profile is determined in polar coordinates by (θ PQ , ρ PQ ) and is shown as follows:

[0038]

[0039] where the profile shaping control parameter D q is used to regulate the change rate of the accelerating convergence type channel rear wall profile and is obtained by the following formula:

[0040]

[0041] The control equation of the accelerating convergence type channel rear wall profile is used to generate a geometric profile starting from the starting point Q of the accelerating convergence type channel rear wall profile and ending at the tangent point P of the channel outlet as the accelerating convergence type channel rear wall profile;

[0042] At the starting point Q of the accelerating convergence type channel rear wall profile, chamfering is performed on the geometric profile of the accelerating convergence type channel rear wall profile and the blade pressure surface segment, and the corresponding chamfering radius is R Q , and a channel inlet fillet curve is generated; where the chamfering radius R Q is not greater than 1 / 2 of the leading edge thickness of the blade cross-sectional profile;

[0043] ⑤ The setting of the channel throat width includes:

[0044] Specifying a channel throat width d t , and the ratio of the channel throat width d t to the radius of curvature r P of the tangent point P of the channel outlet determined in step three is not less than 0.015;

[0045] ⑥ The generation of the accelerating convergence type channel front wall profile includes:

[0046] With the center of the polar coordinate system corresponding to the control equation of the accelerating convergence type channel rear wall profile as the center, the accelerating convergence type channel rear wall profile is equally offset in the leading edge direction of the blade cross-sectional profile, and the offset amount is equal to the channel throat width d t ; the intersection point of the offset curve and the blade suction surface segment is point M, and the intersection point of the offset curve and the blade pressure surface segment is N;

[0047] At point M, chamfering is performed on the geometric profile of the offset curve and the blade suction surface segment, and the corresponding chamfering radius is R M , and a channel outlet fillet curve is generated; where the chamfering radius R Mnot greater than 1 / 2 of the trailing edge thickness of the blade section profile; the intersection point of the fillet curve at the channel outlet and the offset curve after chamfering is point T;

[0048] With point T as the center, rotate the offset curve towards the leading edge direction of the blade section profile, and the rotation angle is equal to 2 times the allowance angle in step four; the intersection point of the rotated offset curve and the blade pressure surface section is point L; the geometric profile between point L and point T on the rotated offset curve is the leading wall profile of the accelerating convergent channel;

[0049] ⑦ The transition between the leading wall profile of the accelerating convergent channel and the blade pressure surface includes:

[0050] Calculate the slope of the leading wall profile of the accelerating convergent channel to obtain the slopes of the leading wall profile of the accelerating convergent channel at different axial chord lengths;

[0051] Extract the profile between the intersection point of the blade pressure surface section and the leading edge section and the intersection point of the blade pressure surface section and the leading wall profile of the accelerating convergent channel as the blade pressure surface cutting section, and calculate the slope of the blade pressure surface cutting section to obtain the slopes of the blade pressure surface cutting section at different axial chord lengths;

[0052] Select the closest slope values from the slopes of the leading wall profile of the accelerating convergent channel at different axial chord lengths and the slopes of the blade pressure surface cutting section at different axial chord lengths. The closest slope values respectively correspond to the tangent point X of the transition circular arc between the leading wall profile of the accelerating convergent channel and the blade pressure surface on the leading wall profile of the accelerating convergent channel and the tangent point Y on the blade pressure surface cutting section; draw a common tangent circular arc passing through the tangent point X and the tangent point Y, which realizes the transition between the leading wall profile of the accelerating convergent channel and the blade pressure surface section, and completes the grooving scheme corresponding to the blade section profile in step one;

[0053] ⑧ The generation of the three-dimensional channel geometry includes:

[0054] Extract the blade section profiles of the three-dimensional compressor blade at the end wall, and extract multiple groups of blade section profiles of the three-dimensional compressor blade from the end wall to 20% of the blade height at intervals of 5% of the blade height; according to the methods in steps one to seven, keep the channel outlet position the same, and generate the grooving schemes corresponding to the extracted blade section profiles at the end wall and the blade section profiles at different blade heights respectively; from the end wall to 20% of the blade height, smoothly connect the grooving schemes corresponding to the generated blade profile geometries at different blade heights along the blade height direction to complete the modeling of the three-dimensional channel geometry.

[0055] In particular, when the value of the number of channels n described in Step 4 is 2, based on completing the three-dimensional channel geometric modeling using Steps 1 to 8, set the outlet position of the second channel, and repeat Steps 3 to 8 to complete the three-dimensional channel geometric modeling of the second channel.

[0056] In particular, when the value of the number of channels n described in Step 4 is 3, based on completing the three-dimensional channel geometric modeling using Steps 1 to 8, set the outlet position of the second channel, and repeat Steps 3 to 8 to complete the three-dimensional channel geometric modeling of the second channel; set the outlet position of the third channel, and repeat Steps 3 to 8 to complete the three-dimensional channel geometric modeling of the third channel.

[0057] In particular, the accelerated convergence type blade tip region grooving design method can be simultaneously carried out on both end walls of the three-dimensional compressor blade to obtain a double-sided tip region grooving scheme.

[0058] (III) Beneficial effects

[0059] The accelerated convergence type blade tip region grooving design method provided by the present invention has the following beneficial effects: through the given three-dimensional compressor blade original blade geometry and channel outlet position, through reasonable channel profile design, a channel design scheme with a high adaptive jet acceleration ratio is quickly generated, effectively solving the problem that the traditional channel design is difficult to effectively control the flow problem that the end wall underflow migrates upward along the spanwise direction of the blade suction surface due to the strong transverse adverse pressure gradient in the high-load compressor blade tip region, forming a low-energy fluid group that blocks the compressor blade channel.

[0060] The accelerated convergence type blade tip region grooving design method provided by the present invention realizes the channel design effect with a high adaptive jet acceleration ratio by introducing profile modeling control parameters to adjust the channel profile design. The enhanced jet at the channel outlet acts on the end wall cross-flow that migrates upward along the spanwise direction of the blade suction surface, carrying the low-energy fluid downstream, thereby suppressing the performance degradation caused by the blockage of the compressor blade channel due to the accumulation of low-energy fluid in the compressor blade tip region, and effectively improving the aerodynamic performance of the high-load compressor.

[0061] The accelerated convergence type blade tip region grooving design method provided by the present invention can quickly design the blade tip region grooving scheme for the given three-dimensional compressor blade original blade geometry through programming, solve the problem of high empirical dependence of the channel design scheme, and has important engineering application prospects. Description of the drawings

[0062] Figure 1 is a flow chart of the accelerated convergence type blade tip region grooving design method of the present invention;

[0063] Figure 2Schematic diagram of a three-dimensional compressor blade and the cross-sectional position of the blade that needs to be grooved for an accelerated convergence type blade tip region grooving design method of the present invention;

[0064] Figure 3 Profile diagram of the blade cross-section that needs to be grooved for an accelerated convergence type blade tip region grooving design method of the present invention;

[0065] Figure 4 Geometric schematic diagram of the grooved blade cross-section for an accelerated convergence type blade tip region grooving design method of the present invention;

[0066] Figure 5 Compressor blade tip region grooving geometry with three-dimensional channel geometry designed by an accelerated convergence type blade tip region grooving design method of the present invention;

[0067] Figure 6 Streamline diagram of the 10% blade height cross-section of the original blade geometry of a three-dimensional compressor blade for an accelerated convergence type blade tip region grooving design method of the present invention;

[0068] Figure 7 Streamline diagram of the 10% blade height cross-section of the compressor blade tip region grooving geometry with three-dimensional channel geometry designed by an accelerated convergence type blade tip region grooving design method of the present invention;

[0069] In the figure, 1: Three-dimensional compressor blade; 2: Blade cross-section profile; 3: Leading edge section; 4: Blade suction surface section; 5: Blade pressure surface section; 6: Trailing edge section; 7: Accelerated convergence type channel rear wall profile; 8: Channel inlet fillet curve; 9: Channel outlet fillet curve; 10: Accelerated convergence type channel front wall profile; 11: Blade pressure surface cutting section. Detailed implementation method

[0070] The following further elaborates on the detailed implementation method of the present invention in conjunction with the accompanying drawings and embodiments. The following embodiments are only used to illustrate the present invention, but not to limit the scope of the present invention.

[0071] As Figure 1 shown, the present invention provides an accelerated convergence type blade tip region grooving design method, including the following steps:

[0072] Step 1, extract the original blade geometry profile;

[0073] In this step, as Figure 2 shown, given the control point coordinates of the original blade geometry of the three-dimensional compressor blade (1), generate the original blade geometry from the control point coordinates of the original blade geometry; extract the blade cross-section profile (2) that needs to be grooved from the original blade geometry, and the cross-section taken is as Figure 2 section A-A in Figure 3As shown, the extracted Figure 2 blade cross-sectional profile (2) of the A-A cross-section in Figure 3 is divided into a leading-edge segment (3), a blade suction surface segment (4) ( Figure 3 shown by the red profile line in x ), a blade pressure surface segment (5) (

[0074] shown by the green profile line in

[0075] and a trailing-edge segment (6); a coordinate system is established according to the positional relationship that the point with the smallest abscissa of the blade cross-sectional profile (2) is the leading-edge point and the point with the largest abscissa of the blade cross-sectional profile (2) is the trailing-edge point. The line connecting the leading-edge point and the trailing-edge point of the blade cross-sectional profile (2) is the chord length c of the blade cross-sectional profile (2). The projection of the chord length c of the blade cross-sectional profile (2) in the abscissa direction is defined as the axial chord length c x of the blade cross-sectional profile (2).

[0076]

[0077]

[0078] x of the blade cross-sectional profile (2).

[0079] Extract the coordinates of each point in the encrypted control point sequence of the blade pressure surface segment, calculate the relative chord length position of each point in the encrypted control point sequence of the blade pressure surface segment, calculate the radius of curvature and the coordinates of the center of curvature of each point in the encrypted control point sequence of the blade pressure surface segment, and store them as the curvature file of the control point sequence of the blade pressure surface segment.

[0079] Step 3: Set the position of the channel outlet;

[0080] In this step, given the relative chord length position value at the slot exit position, a margin value is superimposed on the relative chord length position value at the slot exit position as the intended relative chord length position value of the slot exit tangent point P; wherein, the value range of the margin value is 3%-6% of the axial chord length c of the blade section profile (2). x ;

[0081] According to the intended relative chord length position value of the slot exit tangent point P, the corresponding abscissa is calculated, and the point in the encrypted control point sequence of the blade suction surface segment with the abscissa closest to the abscissa corresponding to the intended relative chord length position value of the slot exit tangent point P is defined as the slot exit tangent point P, as Figure 4 shown.

[0082] Step Four, generate the accelerating convergence type slot rear wall profile;

[0083] In this step, the coordinates P(x P , y P ), radius of curvature r P and the coordinates of the center of curvature C P (x C_P , y C_P ) of the slot exit tangent point P determined in Step Three are extracted from the curvature file of the control point sequence of the blade suction surface segment obtained in Step Two;

[0084] According to the coordinates P(x P , y P ) of the slot exit tangent point P and the coordinates of the center of curvature C P (x C_P , y C_P ) of the slot exit tangent point P, calculate the radius of curvature angle α P of the slot exit tangent point P; the radius of curvature angle α P of the slot exit tangent point P is obtained by the following formula:

[0085]

[0086] As Figure 4 shown, set the incoming flow angle of the incoming flow condition to be controlled by the three-dimensional compressor blade (1) as i, and subtract the margin angle from the incoming flow angle i as the slot inlet angle β; wherein, the value range of the margin angle is 1-5°, and the larger the difference between the incoming flow angle i of the incoming flow condition to be controlled by the three-dimensional compressor blade (1) and the incoming flow angle of the design condition of the three-dimensional compressor blade (1), the larger the value of the margin angle;

[0087] Set the number of slots value n, wherein the number of slots value n can take any value in {1, 2, 3};

[0088] Calculate the deflection angle θ of the accelerating convergence type slot rear wall profile, which is obtained by the following formula:

[0089]

[0090] With the coordinates C of the center of curvature of the tangent point P at the outlet of the groove P (x C_P , y C_P ) as the center, deflect the ray determined by the line connecting the coordinates C of the center of curvature of the tangent point P at the outlet of the groove P (x C_P , y C_P ) and the tangent point P at the outlet of the groove by the deflection angle θ of the rear wall profile line of the accelerating convergent groove towards the leading edge direction of the blade cross-section profile line (2). The intersection point of the deflected ray and the blade pressure surface segment (5) is defined as the starting intention point of the rear wall profile line of the accelerating convergent groove;

[0091] Find the point in the curvature file of the control point sequence of the blade pressure surface segment whose abscissa is closest to the abscissa of the starting intention point of the rear wall profile line of the accelerating convergent groove, and define it as the starting point Q of the rear wall profile line of the accelerating convergent groove;

[0092] Extract the coordinates Q(x Q , y Q ), the radius of curvature r Q , and the coordinates C of the center of curvature Q (x C_Q , y C_Q ) of the starting point Q of the rear wall profile line of the accelerating convergent groove from the curvature file of the control point sequence of the blade pressure surface segment obtained in step two;

[0093] The control equation of the rear wall profile line of the accelerating convergent groove is determined by (θ PQ , ρ PQ ) in the polar coordinate system, as shown in the following formula:

[0094]

[0095]

[0096] Among them, the profile control parameter D q is used to regulate the change rate of the rear wall profile line of the accelerating convergent groove and is obtained by the following formula:

[0097]

[0098] Generate a geometric profile line starting from the starting point Q of the rear wall profile line of the accelerating convergent groove and ending at the tangent point P at the outlet of the groove using the control equation of the rear wall profile line of the accelerating convergent groove as the rear wall profile line (7) of the accelerating convergent groove;

[0099] At the starting point Q of the rear wall profile of the accelerating convergent channel, chamfer the geometric profiles of the rear wall profile (7) of the accelerating convergent channel and the blade pressure surface section (5), with a corresponding chamfer radius of R Q , to generate the inlet fillet curve (8) of the channel; among them, the chamfer radius R Q is not greater than 1 / 2 of the thickness of the leading edge section (3) of the blade cross-section profile (2).

[0100] Step Five, set the throat width of the channel;

[0101] In this step, as Figure 4 shown, given the throat width d t of the channel, the ratio of the throat width d t of the channel to the radius of curvature r P of the outlet tangent point P of the channel determined in Step Three is not less than 0.015.

[0102] Step Six, generate the front wall profile of the accelerating convergent channel;

[0103] In this step, as Figure 4 shown, with the center of the polar coordinate system corresponding to the control equation of the rear wall profile of the accelerating convergent channel as the center, offset the rear wall profile (7) of the accelerating convergent channel equidistantly towards the leading edge direction of the blade cross-section profile (2), and the offset amount is equal to the throat width d t of the channel; the intersection point of the offset curve and the blade suction surface section (4) is point M, and the intersection point of the offset curve and the blade pressure surface section (5) is point N;

[0104] At point M, chamfer the geometric profiles of the offset curve and the blade suction surface section (4), with a corresponding chamfer radius of R M , to generate the outlet fillet curve (9) of the channel; among them, the chamfer radius R M is not greater than 1 / 2 of the thickness of the trailing edge section (6) of the blade cross-section profile (2); the intersection point of the outlet fillet curve (9) of the channel and the offset curve after chamfering is point T;

[0105] With point T as the center, rotate the offset curve towards the leading edge direction of the blade cross-section profile (2), and the rotation angle is equal to 2 times the remaining angle in Step Four; the intersection point of the rotated offset curve and the blade pressure surface section is point L; the geometric profile between point L and point T of the rotated offset curve is the front wall profile (10) of the accelerating convergent channel.

[0106] Step Seven, complete the transition between the front wall profile of the accelerating convergent channel and the blade pressure surface;

[0107] In this step, the slope of the accelerating convergence channel front wall profile (10) is calculated to obtain the slopes of the accelerating convergence channel front wall profile at different axial chord length positions.

[0108] As Figure 4 shown, the profile between the intersection point of the blade pressure surface section (5) and the leading edge section (3) and the intersection point of the blade pressure surface section (5) and the accelerating convergence channel front wall profile (10) is extracted as the blade pressure surface cutting section (11) ( Figure 4 shown as the magenta profile in the figure), and the slope of the blade pressure surface cutting section (11) is calculated to obtain the slopes of the blade pressure surface cutting section at different axial chord length positions.

[0109] The closest slope values are selected from the slopes of the accelerating convergence channel front wall profile at different axial chord length positions and the slopes of the blade pressure surface cutting section at different axial chord length positions. The selected closest slope values respectively correspond to the tangent point X of the transition circular arc between the accelerating convergence channel front wall profile (10) and the blade pressure surface on the accelerating convergence channel front wall profile (10) and the tangent point Y on the blade pressure surface cutting section (11). A common tangent circular arc passing through the tangent point X and the tangent point Y is made, thus realizing the transition between the accelerating convergence channel front wall profile (10) and the blade pressure surface, and completing the grooving scheme corresponding to the blade section profile (2) described in Step 1.

[0110] Step 8, generate the three-dimensional channel geometry;

[0111] In this step, the blade section profile (2) of the three-dimensional compressor blade at the end wall is extracted, and multiple groups of blade section profiles (2) of the three-dimensional compressor blade from the end wall to 20% of the blade height are extracted at intervals of 5% of the blade height; the extracted blade section profiles (2) are processed according to the methods in Step 1 to Step 7, keeping the channel outlet position the same, and the grooving schemes corresponding to the extracted blade section profiles (2) at the end wall and the blade section profiles (2) at different blade heights are generated respectively (such as Figure 4 section B-B in the figure); the Figure 4 generated grooving scheme (section B-B) is restored to the position of the blade section profile (2) of the original blade geometry that needs to be grooved, replacing the Figure 2 shown section A-A; as Figure 5 shown, starting from the end wall to 20% of the blade height, the grooving schemes corresponding to the blade section profiles (2) at different blade heights are smoothly connected along the blade height direction to complete the modeling of the three-dimensional channel geometry.

[0112] Particularly, when the value of the channel number n described in Step 4 is 2, on the basis of completing the three-dimensional channel geometry modeling by using Step 1 to Step 8, the outlet position of the second channel is set, and Step 3 to Step 8 are repeated to complete the three-dimensional channel geometry modeling of the second channel.

[0113] Particularly, when the value of the number n of the channels described in Step 4 is 3, on the basis of completing the three-dimensional channel geometric modeling by using Steps 1 to 8, set the outlet position of the second channel, and repeat Steps 3 to 8 to complete the three-dimensional channel geometric modeling of the second channel; set the outlet position of the third channel, and repeat Steps 3 to 8 to complete the three-dimensional channel geometric modeling of the third channel.

[0114] Particularly, the accelerated convergence type blade tip region grooving design method can be simultaneously carried out on both end walls of the three-dimensional compressor blade to obtain a double-sided tip region grooving scheme.

[0115] Example 1:

[0116] Taking a certain high-speed and high-load compressor cascade studied by the research group as an example, a double-sided tip region grooving scheme of the three-dimensional compressor blade was carried out by using the accelerated convergence type blade tip region grooving design method of the present invention, and the value of the number n of the grooves opened was 1. Numerical simulations were carried out on the original blade geometry of the three-dimensional compressor blade and the tip region grooving geometry of the compressor blade with three-dimensional grooves, and the control effect of the accelerated convergence type blade tip region grooving design method of the present invention on the three-dimensional corner separation of the compressor was verified.

[0117] As Figure 4 shown is the schematic diagram of the grooved blade cross-section geometry of the accelerated convergence type blade tip region grooving design method of the present invention. In this embodiment, the relative chord length position value of the given channel outlet position is 35%, and a margin value of 5% is superimposed on the relative chord length position value of the channel outlet position as the intended relative chord length position value of the channel outlet tangent point P; calculate the corresponding abscissa according to the intended relative chord length position value of the channel outlet tangent point P, and find the point in the encrypted control point sequence of the blade suction surface segment whose abscissa is closest to the abscissa corresponding to the intended relative chord length position value of the channel outlet tangent point P, and define it as the channel outlet tangent point P. Extract the coordinates P(0.0019, 0.0005) of the determined channel outlet tangent point P from the curvature file of the control point sequence of the blade suction surface segment obtained in Step 2, the curvature radius r P = 0.06 and the curvature center coordinates C P (0.0157, 0.0589); calculate the curvature radius angle α of the channel outlet tangent point P P = 13.28°.

[0118] Set the incoming flow angle of the incoming flow condition to be controlled of the three-dimensional compressor blade (1) as i = 41.91°, and subtract the margin angle 1.91° from the incoming flow angle i as the channel inlet angle β = 40°. Set the number value of the channels n = 1, and calculate the deflection angle θ = 18.36° of the rear wall profile of the accelerated convergence type channel

[0119] With the coordinates C of the center of curvature of the tangent point P at the outlet of the channel P Taking (0.0157, 0.0589) as the center, the coordinates C of the center of curvature of the tangent point P at the outlet of the channel P The ray determined by the line connecting (0.0157, 0.0589) and the tangent point P at the outlet of the channel is deflected by an angle θ = 18.36° in the leading edge direction of the blade cross-sectional profile (2) to accelerate the convergence of the rear wall profile of the channel. The intersection point of the deflected ray and the blade pressure surface section (5) is taken as the starting intention point of the rear wall profile of the accelerating convergent channel.

[0120] Find the point in the curvature file of the control point sequence of the blade pressure surface section with the abscissa closest to the abscissa of the starting intention point of the rear wall profile of the accelerating convergent channel, and define it as the starting point Q of the rear wall profile of the accelerating convergent channel. Extract the coordinates Q(-0.0136, 0.0069), the radius of curvature r Q = 0.046 and the coordinates C of the center of curvature Q (0.0111, 0.0459) of the starting point Q of the rear wall profile of the accelerating convergent channel from the curvature file of the control point sequence of the blade pressure surface section obtained in step two; calculate the profile modeling control parameter D q = 0.136, which is used to regulate the change rate of the rear wall profile of the accelerating convergent channel. Calculate the control equation (θ PQ , ρ PQ ) of the rear wall profile of the accelerating convergent channel:

[0121] ρ PQ = 0.06 - 0.136·[θ PQ - 4.48] 2

[0122] θ PQ ∈[4.48, 2.91]

[0123] Use the control equation of the rear wall profile of the accelerating convergent channel to generate a geometric profile starting from the starting point Q of the rear wall profile of the accelerating convergent channel and ending at the tangent point P at the outlet of the channel, as the rear wall profile (7) of the accelerating convergent channel. Chamfer the geometric profiles of the rear wall profile (7) of the accelerating convergent channel and the blade pressure surface section (5) at the starting point Q of the rear wall profile of the accelerating convergent channel, and the corresponding chamfer radius is R Q = 0.0002 to generate the inlet fillet curve (8) of the channel.

[0124] Given the throat width d t = 0.007.

[0125] Centering around the center of the polar coordinate system corresponding to the control equation of the accelerating-converging channel rear wall profile, the accelerating-converging channel rear wall profile (7) is equally offset in the leading edge direction of the blade section profile (2) by an offset amount equal to the channel throat width d t = 0.007; the intersection point of the offset curve and the blade suction surface section (4) is point M, and the intersection point of the offset curve and the blade pressure surface section (5) is N; at point M, chamfering is performed on the geometric profiles of the offset curve and the blade suction surface section (4), with a corresponding chamfer radius of R M = 0.0002 to generate the channel outlet fillet curve (9), and the intersection point of the channel outlet fillet curve (9) and the offset curve after chamfering is point T.

[0126] Centering around point T, the offset curve is rotated in the leading edge direction of the blade section profile (2), and the rotation angle is equal to twice the remaining angle in step four; the intersection point of the rotated offset curve and the blade pressure surface section is point L; the geometric profile of the rotated offset curve between point L and point T is the accelerating-converging channel front wall profile (10).

[0127] Calculate the slope of the accelerating-converging channel front wall profile (10) to obtain the slopes of the accelerating-converging channel front wall profile at different axial chord lengths; extract the profile between the intersection point of the blade pressure surface section (5) and the leading edge section (3) and the intersection point of the blade pressure surface section (5) and the accelerating-converging channel front wall profile (10) as the blade pressure surface cutting section (11), and calculate the slope of the blade pressure surface cutting section (11) to obtain the slopes of the blade pressure surface cutting section at different axial chord lengths; select the closest slope values from the slopes of the accelerating-converging channel front wall profile at different axial chord lengths and the slopes of the blade pressure surface cutting section at different axial chord lengths, which respectively correspond to the tangent point X of the transition circular arc between the accelerating-converging channel front wall profile (10) and the blade pressure surface on the accelerating-converging channel front wall profile (10) and the tangent point Y on the blade pressure surface cutting section (11); draw a common tangent circular arc passing through the tangent points X and Y, thus realizing the transition between the accelerating-converging channel front wall profile (10) and the blade pressure surface section (5), and completing the slotting scheme corresponding to the blade section profile (2) described in step one.

[0128] As Figure 2 shown, extract the blade section profile (2) of the three-dimensional compressor blade (1) at the end wall, and extract multiple groups of blade section profiles (2) of the three-dimensional compressor blade from the end wall to 20% of the blade height at intervals of 5% of the blade height; according to the methods of steps one to seven for the extracted blade section profiles (2), while keeping the channel outlet position the same, respectively generate the slotting schemes corresponding to the extracted blade section profiles (2) at the end wall and the blade section profiles (2) at different blade heights; as Figure 5As shown, from the end wall to 20% of the blade height, the grooving schemes corresponding to the blade section profiles (2) of different blade heights smoothly connected along the blade height direction are completed to form the geometry of the three-dimensional channel.

[0129] In this embodiment, channels with a height of 20% of the blade are opened on both end walls of a certain high-speed and high-load compressor cascade under study. The value of the number of channels n is taken as 1, and a grooving scheme for the bilateral end regions of the three-dimensional compressor blade is obtained. The computational fluid dynamics method is used to numerically simulate the original blade geometry of the three-dimensional compressor blade and the grooving geometry of the end region of the compressor blade with three-dimensional channels in this embodiment. Figure 6 The streamline diagram of the 10% blade height section of the original blade geometry of the three-dimensional compressor blade is given. Figure 7 The streamline diagram of the 10% blade height section of the grooving geometry of the end region of the compressor blade with three-dimensional channels designed by using an accelerated convergence type blade end region grooving design method of the present invention is given. It can be seen from the result comparison that the channels designed by using an accelerated convergence type blade end region grooving design method of the present invention significantly suppress the three-dimensional corner separation flow on the suction surface side of the blade and improve the flow capacity of the blade channel.

[0130] The above are only the preferred embodiments of the invention patent of the present invention, and are not used to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0131] In summary, an accelerated convergence type blade end region grooving design method provided by the present invention adjusts the grooving profile design by introducing profile modeling control parameters, quickly generates a grooving design scheme with a high adaptive jet acceleration ratio, and effectively solves the flow problem that in the traditional grooving design, it is difficult to effectively control the end wall underflow along the suction surface of the blade due to the strong transverse adverse pressure gradient in the end region of the high-load compressor blade, resulting in the formation of a low-energy fluid mass that blocks the compressor blade channel. The enhanced jet at the channel outlet acts on the end wall cross-flow migrating upward along the suction surface of the blade, carrying the low-energy fluid downstream, thereby suppressing the performance degradation caused by the blockage of the compressor blade channel due to the accumulation of low-energy fluid in the end region of the compressor blade and improving the aerodynamic performance of the high-load compressor. Further, an accelerated convergence type blade end region grooving design method provided by the present invention can be realized by programming to quickly design a blade end region grooving scheme for a given original blade geometry of a three-dimensional compressor blade, solve the problem of high empirical dependence of the grooving design scheme, and has important engineering application prospects.

Claims

1. An accelerated convergence type blade tip region slotting design method, characterized in that, Including the following steps: Step 1, extract the original blade geometric profile; Step 2, calculate the curvature of the geometric profile; Step 3, set the position of the channel outlet; Step 4, generate the geometric profile of the accelerating and converging channel rear wall; Step 5, set the width of the channel throat; Step 6, generate the geometric profile of the accelerating and converging channel front wall; Step 7, complete the transition between the geometric profile of the accelerating and converging channel front wall and the blade pressure surface; Step 8, generate the three-dimensional channel geometry; ① The extraction of the original blade geometric profile includes: Given the control point coordinates of the original blade geometry of the three-dimensional compressor blade (1), generate the original blade geometry from the control point coordinates of the original blade geometry; extract the blade section profile (2) that needs to be grooved from the original blade geometry; divide the extracted blade section profile (2) into a leading edge section (3), a blade suction surface section (4), a blade pressure surface section (5), and a trailing edge section (6) according to physical characteristics; establish a coordinate system with the point with the smallest abscissa of the blade section profile (2) as the leading edge point and the point with the largest abscissa of the blade section profile (2) as the trailing edge point. The line connecting the leading edge point and the trailing edge point of the blade section profile (2) is the chord length c of the blade section profile (2), and the projection of the chord length c of the blade section profile (2) in the abscissa direction is defined as the axial chord length cx of the blade section profile (2); ② The calculation of the geometric profile curvature includes: Use a fitting algorithm to encrypt the control points corresponding to the blade suction surface section (4) to obtain an encrypted control point sequence of the blade suction surface section; wherein, the abscissa difference between any two adjacent control points in the encrypted control point sequence of the blade suction surface section is not greater than 1% of the axial chord length cx of the blade section profile (2); Extract the coordinates of each point in the encrypted control point sequence of the blade suction surface section, calculate the relative chord length position of each point in the encrypted control point sequence of the blade suction surface section, calculate the radius of curvature and the coordinates of the curvature center of each point in the encrypted control point sequence of the blade suction surface section, and store them as the curvature file of the control point sequence of the blade suction surface section; Use a fitting algorithm to encrypt the control points corresponding to the blade pressure surface section (5) to obtain an encrypted control point sequence of the blade pressure surface section; wherein, the abscissa difference between any two adjacent control points in the encrypted control point sequence of the blade pressure surface section is not greater than 1% of the axial chord length cx of the blade section profile (2); Extract the coordinates of each point in the encrypted control point sequence of the blade pressure surface section, calculate the relative chord length position of each point in the encrypted control point sequence of the blade pressure surface section, calculate the radius of curvature and the coordinates of the curvature center of each point in the encrypted control point sequence of the blade pressure surface section, and store them as the curvature file of the control point sequence of the blade pressure surface section; ③ The setting of the channel outlet position includes: Given the relative chord length position value of the slot exit position, a margin value is superimposed on the relative chord length position value of the slot exit position as the intended relative chord length position value of the slot exit tangent point P; wherein, the value range of the margin value is 3%-6% of the axial chord length cx value of the blade section profile (2). Calculate the corresponding abscissa according to the intended relative chord length position value of the slot exit tangent point P, and find the point in the encrypted control point sequence of the blade suction surface segment whose abscissa is closest to the abscissa corresponding to the intended relative chord length position value of the slot exit tangent point P, and define it as the slot exit tangent point P. ④ The generation of the accelerated convergence type slot rear wall profile includes:[[]] Extract the coordinates P(xP, yP), the radius of curvature rP, and the coordinates of the center of curvature C (xC_P, yC_P) of the tangent point P at the outlet of the channel determined in step three from the curvature file of the control point sequence of the blade suction surface segment obtained in step two. P (xC_P, yC_P); Based on the coordinates P(xP, yP) of the tangent point P at the outlet of the channel and the coordinates C P (xC_P, yC_P) of the center of curvature of the tangent point P at the outlet of the channel, calculate the curvature radius angle αP of the tangent point P at the outlet of the channel; the curvature radius angle αP of the tangent point P at the outlet of the channel is obtained by the following formula: Set the incoming flow angle of the incoming flow condition to be controlled by the three-dimensional compressor blade (1) as i, and subtract the margin angle from the incoming flow angle i to obtain the slot inlet angle β; wherein, the value range of the margin angle is 1-5°, and the greater the difference between the incoming flow angle i of the incoming flow condition to be controlled by the three-dimensional compressor blade (1) and the incoming flow angle of the design condition of the three-dimensional compressor blade (1), the greater the value of the margin angle. Set the slot number value n, where the slot number value n can take any value in {1, 2, 3}. Calculate the deflection angle θ of the accelerated convergence type slot rear wall profile, which is obtained by the following formula: With the coordinates C of the center of curvature of the tangent point P at the outlet of the channel P (xC_P, yC_P) as the center, the coordinates C of the center of curvature of the tangent point P at the outlet of the channel P The ray determined by the connection line between the coordinates (xC_P, yC_P) of the center of curvature of the tangent point P at the outlet of the channel and the tangent point P is deflected by the turning angle θ of the rear wall profile of the accelerating and converging channel in the leading edge direction of the blade cross-section profile (2), and the intersection point of the deflected ray and the blade pressure surface segment (5) is defined as the starting intention point of the rear wall profile of the accelerating and converging channel; Find the point in the curvature file of the control point sequence of the blade pressure surface segment whose abscissa is closest to the abscissa of the starting intended point of the accelerated convergence type slot rear wall profile, and define it as the starting point Q of the accelerated convergence type slot rear wall profile. Extract the coordinates Q(xQ, yQ), the radius of curvature rQ, and the coordinates of the center of curvature C of the starting point Q of the accelerating converging channel rear wall profile from the leaf pressure surface segment control point sequence curvature file obtained in step two Q (xC_Q, yC_Q); The control equation of the accelerated convergence type slot rear wall profile is determined by (θPQ, ρPQ) in the polar coordinate system, as shown in the following formula: Among them, the profile shaping control parameter Dq is used to regulate the change rate of the accelerated convergence type slot rear wall profile, and is obtained by the following formula: Use the control equation of the accelerated convergence type slot rear wall profile to generate a geometric profile starting from the starting point Q of the accelerated convergence type slot rear wall profile and ending at the slot exit tangent point P, as the accelerated convergence type slot rear wall profile (7). At the starting point Q of the accelerated convergence type slot rear wall profile, chamfer the geometric profiles of the accelerated convergence type slot rear wall profile (7) and the blade pressure surface segment (5), and the corresponding chamfer radius is RQ, to generate a slot inlet fillet curve (8); wherein, the chamfer radius RQ is not greater than 1 / 2 of the thickness of the leading edge segment (3) of the blade section profile (2). ⑤ The setting of the slot throat width includes:[[]] Given the slot throat width dt, the ratio of the slot throat width dt to the curvature radius rP of the slot exit tangent point P determined in step three is not less than 0.

015. ⑥ The generation of the accelerated convergence type slot front wall profile includes:[[]] Taking the center of the polar coordinate system corresponding to the control equation of the accelerated convergence type slot rear wall profile as the center, offset the accelerated convergence type slot rear wall profile (7) equidistantly towards the leading edge direction of the blade section profile (2), and the offset amount is equal to the slot throat width dt; the intersection point of the offset curve and the blade suction surface segment (4) is point M, and the intersection point of the offset curve and the blade pressure surface segment (5) is point N. At point M, chamfer the geometric profile of the offset curve and the blade suction surface section (4), with a corresponding chamfer radius of RM, to generate a channel outlet fillet curve (9); wherein, the chamfer radius RM is not greater than 1 / 2 of the thickness of the trailing edge section (6) of the blade cross-sectional profile (2); the intersection point of the channel outlet fillet curve (9) and the offset curve after chamfering is point T; With point T as the center, rotate the offset curve towards the leading edge direction of the blade cross-sectional profile (2), and the rotation angle is equal to twice the remaining angle in step four; the intersection point of the rotated offset curve and the blade pressure surface section is point L; the geometric profile between point L and point T of the rotated offset curve is the accelerating converging channel front wall profile (10); ⑦ The completion of the transition between the accelerating converging channel front wall profile and the blade pressure surface includes: Calculate the slope of the accelerating converging channel front wall profile (10) to obtain the slopes of the accelerating converging channel front wall profile at different axial chord lengths; Extract the profile between the intersection point of the blade pressure surface section (5) and the leading edge section (3) and the intersection point of the blade pressure surface section (5) and the accelerating converging channel front wall profile (10) as the blade pressure surface cutting section (11), and calculate the slope of the blade pressure surface cutting section (11) to obtain the slopes of the blade pressure surface cutting section at different axial chord lengths; Select the closest slope values from the slopes of the accelerating converging channel front wall profile at different axial chord lengths and the slopes of the blade pressure surface cutting section at different axial chord lengths. The closest slope values respectively correspond to the tangent point X of the transition arc between the accelerating converging channel front wall profile (10) and the blade pressure surface on the accelerating converging channel front wall profile (10) and the tangent point Y on the blade pressure surface cutting section (11); draw a common tangent arc passing through the tangent point X and the tangent point Y, which realizes the transition between the accelerating converging channel front wall profile (10) and the blade pressure surface, and completes the grooving scheme corresponding to the blade cross-sectional profile (2) in step one; ⑧ The generation of the three-dimensional channel geometry includes: Extract the blade cross-sectional profile (2) of the three-dimensional compressor blade (1) at the end wall, and extract multiple groups of blade cross-sectional profiles (2) of the three-dimensional compressor blade from the end wall to 20% of the blade height at intervals of 5% of the blade height; according to the methods of steps one to seven, keep the channel outlet position the same, and respectively generate the grooving schemes corresponding to the extracted blade cross-sectional profiles (2) at the end wall and the blade cross-sectional profiles (2) at different blade heights; from the end wall to 20% of the blade height, smoothly connect the grooving schemes corresponding to the blade cross-sectional profiles (2) at different blade heights along the blade height direction to complete the modeling of the three-dimensional channel geometry.

2. The accelerated convergence type blade tip region grooving design method according to claim 1, wherein When the value of the number of channels \(n\) described in Step 4 is 2, based on completing the 3D channel geometric modeling using Steps 1 to 8, set the outlet position of the second channel, and repeat Steps 3 to 8 to complete the 3D channel geometric modeling of the second channel.

3. The accelerated convergence type blade tip region grooving design method according to claim 1, characterized in that, When the value of the number of channels \(n\) described in Step 4 is 3, based on completing the 3D channel geometric modeling using Steps 1 to 8, set the outlet position of the second channel, and repeat Steps 3 to 8 to complete the 3D channel geometric modeling of the second channel; set the outlet position of the third channel, and repeat Steps 3 to 8 to complete the 3D channel geometric modeling of the third channel.

4. A method for designing a slotted blade tip region with accelerated convergence, as described in any one of claims 1 - 3, characterized in that The described accelerated convergence type blade tip region grooving design method can be simultaneously carried out on both end walls of the 3D compressor blade to obtain a bilateral tip region grooving scheme.

Images