Turbomachine profile method coupling non-axisymmetric endwalls and blade bending

Abstract

This invention discloses a turbine modeling method that couples a non-axisymmetric endwall and blade bending, comprising the steps of: establishing a non-axisymmetric endwall model by applying circumferential and axial control functions to the turbine endwall profile; establishing a blade bending model by adjusting the bend angle and bend height to change the shape of the leading edge overlap line; and coupling the non-axisymmetric endwall model and the blade bending model to obtain an end-bending model. Compared to the independent non-axisymmetric endwall, the end-bending model significantly compresses the radial scale of the channel vortex, compensating for its insufficient control effect; compared to the independent blade bending model, the end-bending model weakens the channel vortex intensity and secondary flow, further compressing the radial height of the channel vortex, compensating for its excessive lateral pressure gradient and poor end-region flow capacity.

Description

Technical Field

[0001] This invention relates to the field of variable geometry turbine technology for aero-engines / gas turbines, and in particular to a turbine modeling method that couples non-axisymmetric endwall and blade bending. Background Technology

[0002] Weight reduction in turbine components significantly improves the thrust-to-weight ratio of aero-engines, especially for high-bypass turbofan engines used in civil applications. High-load design of turbine blades can drastically reduce the number of turbine stage blades and even lower the total number of turbine stages, thereby reducing turbine mass. However, compared to conventional turbine blades, high-load design enhances the lateral pressure gradient within the turbine channel and the adverse pressure gradient on the blade suction surface, making the evolution of the end-zone vortex structure more complex and further exacerbating end-zone flow losses. Therefore, the high-loss problem of turbine blades has become one of the key bottlenecks restricting the development of high-performance aero-engines.

[0003] To address the complex flow within turbine blade passages, numerous scholars have proposed passive control techniques such as non-axisymmetric endwalls, leading-edge trimming, winglets, and blade bending to control losses. Among these, non-axisymmetric endwalls have yielded significant engineering applications and have proven to be an effective means of suppressing end-area flow losses. Rolls-Royce's Brennan et al. used non-axisymmetric endwall technology to redesign the high-pressure turbine stage of the Trent 500 high-bypass turbofan engine, improving turbine stage efficiency by 0.4%. Meanwhile, with the continuous advancement of three-dimensional blade design technology, the application of blade bending technology in turbomachinery has received increasing attention. Academician Wang Zhongqi first elucidated the theory of bent blades: a reasonable inclination angle at the blade endwall can effectively organize the flow of low-energy fluids, achieving the goal of suppressing blade passage losses. However, the individual control effects of non-axisymmetric endwalls or blade bending technology often fail to meet the design requirements of modern high-performance aero-engines: non-axisymmetric endwalls offer limited reduction in passage exit losses, while blade bending increases the lateral pressure gradient near the endwall, weakening its suppression effect on passage vortices. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a turbine modeling method that couples non-axisymmetric endwall and blade bending, comprising the following steps:

[0005] A non-axisymmetric endwall model is established by applying circumferential and axial control functions to the turbine endwall profile.

[0006] By adjusting the bend angle and bend height to change the shape of the leading edge overlap line, a blade bending model can be established; and

[0007] The non-axisymmetric endwall model is coupled with the blade bending model to obtain the end bending model.

[0008] According to some embodiments of the present invention, coupling the non-axisymmetric endwall model with the blade bending model includes:

[0009] This allows the non-axisymmetric endwalls and curved blades to intersect and merge at the endwalls while ensuring the geometric continuity of the end-bending model.

[0010] According to some embodiments of the present invention, the application of circumferential and axial control functions to the turbine endwall profile includes:

[0011] The non-axisymmetric endwall model is controlled by multiple control points distributed on the endwall profile. Among them, m axial control lines are evenly distributed at different circumferential positions, and 2n circumferential control lines are evenly distributed at different axial positions, where m and n are integers greater than 0.

[0012] According to some embodiments of the present invention, the number of control points is 50, the number of axial control lines is 5, and the number of circumferential control lines is 10.

[0013] According to some embodiments of the present invention, changing the shape of the leading edge overlap line by adjusting the bend angle and bend height includes:

[0014] A sinusoidal function is used to construct the distribution pattern of circumferential control points on the non-axisymmetric end wall, so that the peak value of the sinusoidal function in a complete cycle is close to the pressure surface and the valley value is close to the suction surface.

[0015] The radial height of the circumferential control points in the first group and the nth group is 0.

[0016] According to some embodiments of the present invention, the circumferential amplitude control function based on a sinusoidal function includes:

[0017]

[0018] Where C(y) represents the circumferential amplitude, A(x) represents the axial amplitude control function, y represents the circumferential coordinate position of the control point, and t represents the distance between the arcs of two adjacent turbine blades.

[0019] According to some embodiments of the present invention, the axial amplitude control function A(x) for a non-axisymmetric end wall includes:

[0020]

[0021] Where R represents the amplitude control coefficient, P PS P is the static pressure near the endwall of the blade pressure surface. SS The static pressure near the endwall of the blade's suction surface is max(P). PS -P SS () represents the maximum pressure difference near the endwall at each axial position;

[0022] It also includes: generating Bézier curves based on discrete points at each axial position, and constructing a non-axisymmetric endwall model by using spline curves to smoothly transition and connect them along the circumference.

[0023] According to some embodiments of the present invention, changing the shape of the leading edge overlap line by adjusting the bend angle and bend height includes:

[0024] The two ends and the middle of the original turbine guide vane's leading edge overlap line are straight lines, and the three straight lines are transitioned by a circular arc. By adjusting the bend angle and bend height, the bending of the turbine blade is controlled, so as to construct a blade bending model.

[0025] According to some embodiments of the present invention, the bend angle is the angle between the straight lines at both ends and the radial direction, and the value of the bend angle ranges from 10° to 20°; the bend height is the radial height of the straight lines at both ends, and the value of the bend height ranges from 10% to 20% of the radial height of the blade.

[0026] According to some embodiments of the present invention, the five axial control lines are evenly distributed between the arc lines of two adjacent turbine blades, and the ten circumferential control lines are evenly distributed at 20%-100% of the axial chord length.

[0027] The turbine modeling method of coupling non-axisymmetric endwall and blade bending in this invention achieves flow control in the turbine passage by fusing the non-axisymmetric endwall model and the blade bending model. Compared with the independent non-axisymmetric endwall, the end bending model significantly compresses the radial scale of the passage vortex, making up for its insufficient control effect. Compared with the independent blade bending model, the end bending model weakens the channel vortex intensity and secondary flow, further compressing the radial height of the channel vortex, making up for its defects of excessive lateral pressure gradient and poor end region flow capacity. Attached Figure Description

[0028] Figure 1 This schematically illustrates the distribution of the non-axisymmetric endwall control lines and control points in the turbine modeling method for coupling non-axisymmetric endwall and blade bending according to an embodiment of the present invention.

[0029] Figure 2 yes Figure 1 A schematic diagram of the circumferential control line of the sinusoidal function of the non-axisymmetric endwall of the turbine modeling method shown;

[0030] Figure 3 yes Figure 1 A schematic diagram of the axial control line of the Bézier curve of the non-axisymmetric endwall of the turbine modeling method shown;

[0031] Figure 4 yes Figure 1 A schematic diagram showing the radial height amplitude variation of the non-axisymmetric endwall in the turbine modeling method shown.

[0032] Figure 5 This is a schematic diagram of the overlapping lines of the bent blade;

[0033] Figure 6 This is a schematic diagram of the impeller after employing a turbine modeling method that couples non-axisymmetric endwall and blade bending; and

[0034] Figure 7 This is a schematic diagram of the total pressure loss after adopting a turbine modeling method that couples non-axisymmetric endwall and blade bending. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0036] However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the invention. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of embodiments of the invention for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the invention.

[0037] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. The term "comprising" as used herein indicates the presence of features, steps, or operations, but does not exclude the presence or addition of one or more other features.

[0038] When using expressions such as "at least one of A, B, and C," the expression should generally be interpreted in accordance with the meaning commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, and C" should include, but is not limited to, systems having A alone, having B alone, having C alone, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.). Similarly, when using expressions such as "at least one of A, B, or C," the expression should generally be interpreted in accordance with the meaning commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, or C" should include, but is not limited to, systems having A alone, having B alone, having C alone, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.).

[0039] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0040] According to some embodiments of the present invention, the turbine shape includes an endwall profile and a plurality of turbine blades uniformly arranged circumferentially on the endwall profile, and the area between two adjacent turbine blades is a blade channel; one side of the channel is the pressure surface (PS) of one turbine blade, and the other side of the channel is the suction surface (SS) of another turbine blade.

[0041] According to some embodiments of the present invention, under certain operating conditions, numerical calculations are performed on the turbine blade flow channel without applying turbine styling methods to obtain the vortex structure in the end region of the blade flow channel and the total outlet loss. The calculation of the total loss λ includes:

[0042]

[0043] Among them, P o,i P represents the average total pressure at the inlet mass flow rate of the flow field. o,loc P represents the local total pressure within the flow field. o,plane1 P represents the average total pressure at the mass flow rate of section Plane1. s,plane1 This represents the average static pressure of the mass flow rate at section Plane1.

[0044] According to some embodiments of the present invention, optionally, the distance between the Plane1 section and the trailing edge of the blade cascade is 40% of the axial chord length of the blade.

[0045] According to one aspect of the present invention, a turbine modeling method for coupling non-axisymmetric endwall and blade bending is provided, comprising steps S1 to S3.

[0046] According to some embodiments of the present invention, step S1 includes: establishing a non-axisymmetric endwall model by applying circumferential and axial control functions to the turbine endwall profile.

[0047] According to some embodiments of the present invention, step S2 includes: changing the shape of the leading edge overlap line by adjusting the bend angle and bend height to establish a blade bending model.

[0048] According to some embodiments of the present invention, step S3 includes: coupling the non-axisymmetric endwall model with the blade bending model to obtain the end bending model.

[0049] In this embodiment, flow control of the turbine passage is achieved by fusing the non-axisymmetric endwall model and the blade bending model. Compared with the independent non-axisymmetric endwall, the end bending model significantly compresses the radial scale of the passage vortex, making up for its insufficient control effect. Compared with the independent blade bending model, the end bending model weakens the channel vortex intensity and secondary flow, further compressing the radial height of the channel vortex, making up for its defects of excessive lateral pressure gradient and poor end region flow capacity.

[0050] According to some embodiments of the present invention, coupling the non-axisymmetric endwall model with the blade bending model includes: making the non-axisymmetric endwall and the bent blade intersect and merge at the endwall while ensuring the geometric continuity of the end-bending model.

[0051] Figure 1 The diagram illustrates the distribution of the non-axisymmetric endwall control lines and control points in the turbine modeling method for coupling non-axisymmetric endwall and blade bending according to an embodiment of the present invention.

[0052] According to some embodiments of the present invention, such as Figure 1 As shown, the control functions applied to the turbine endwall profile include: using multiple control points distributed on the endwall profile to control the non-axisymmetric endwall model, wherein m axial control lines (dashed lines) are evenly distributed at different circumferential positions, and 2n circumferential control lines (solid lines) are evenly distributed at different axial positions, where m and n are integers greater than 0.

[0053] According to some embodiments of the present invention, the number of control points is 50, the number of axial control lines is 5, and the number of circumferential control lines is 10.

[0054] According to some embodiments of the present invention, the radial heights of discrete points on the first and fifth axial control lines are consistent to ensure the circumferential continuity of the non-axisymmetric end wall.

[0055] According to some embodiments of the present invention, the radial height of the 1st, 2nd, 9th and 10th control points on each axial control line is set to 0 to ensure the geometric continuity of the blade passage inlet and outlet.

[0056] According to some embodiments of the present invention, optionally, the radial height of the discrete control points on the 1st, 3rd, and 5th axial control lines is all set to 0, which satisfies the sinusoidal function and ensures the circumferential continuity of the non-axisymmetric end wall.

[0057] According to some embodiments of the present invention, changing the shape of the leading edge overlap line by adjusting the bend angle and bend height includes:

[0058] A sinusoidal function is used to construct the distribution pattern of circumferential control points on the non-axisymmetric end wall, so that the peak value of the sinusoidal function in a complete cycle is close to the pressure surface and the valley value is close to the suction surface; wherein, the radial height of the circumferential control points in the first group and the nth group is 0.

[0059] Figure 2 yes Figure 1 A schematic diagram of the circumferential control line of the sinusoidal function of the non-axisymmetric endwall of the turbine modeling method shown.

[0060] According to some embodiments of the present invention, the circumferential hydrostatic pressure distribution inside the turbine blade is similar to a sinusoidal function distribution, conforming to the circumferential control profile of a sinusoidal function, such as... Figure 2 As shown, the geometric convex curvature of the non-axisymmetric endwall near the blade pressure side can accelerate the flow and reduce the local static pressure, while the geometric concave curvature of the endwall near the blade suction side can delay the flow and increase the local static pressure.

[0061] According to some embodiments of the present invention, the circumferential amplitude control function based on a sinusoidal function includes:

[0062]

[0063] Where C(y) represents the circumferential amplitude, A(x) represents the axial amplitude control function, y represents the circumferential coordinate position of the control point, and t represents the distance between the arcs of two adjacent turbine blades.

[0064] Figure 3 yes Figure 1 A schematic diagram of the axial control line of the Bézier curve of the non-axisymmetric endwall of the turbine modeling method shown.

[0065] According to some embodiments of the present invention, such as Figure 3 As shown, the axial amplitude of the non-axisymmetric endwall is calculated based on the distribution of the pressure difference between the suction and pressure surfaces of the turbine end region blades along the axial direction.

[0066] Figure 4 yes Figure 1 A schematic diagram showing the radial height amplitude variation of the non-axisymmetric endwall in the turbine styling method illustrated.

[0067] According to some embodiments of the present invention, only the following is required: Figure 1 The radial height of the 12 solid discrete points shown is controlled, while the radial height of the remaining hollow discrete points is 0. Based on the discrete points at each axial position, Bézier curves are generated, and spline curves are used to smoothly connect them along the circumferential direction to construct a non-axisymmetric endwall model, resulting in the model shown below. Figure 4 The diagram shows the concave-convex structure of the non-axisymmetric end wall.

[0068] According to some embodiments of the present invention, the axial amplitude control function A(x) for a non-axisymmetric end wall includes:

[0069]

[0070] Where R represents the amplitude control coefficient, with a value ranging from 3mm to 8mm, and P... PS P is the static pressure near the endwall of the blade pressure surface. SS The static pressure near the endwall of the blade's suction surface is max(P). PS -P SS () represents the maximum pressure difference near the endwall at each axial position;

[0071] It also includes: generating Bézier curves based on discrete points at each axial position, and constructing a non-axisymmetric endwall model by using spline curves to smoothly transition and connect them along the circumference.

[0072] According to some embodiments of the present invention, changing the shape of the leading edge overlap line by adjusting the bend angle and bend height includes:

[0073] The two ends and the middle of the original turbine guide vane's leading edge overlap line are straight lines, and the three straight lines are transitioned by a circular arc. By adjusting the bend angle and bend height, the bending of the turbine blade is controlled, so as to construct a blade bending model.

[0074] According to some embodiments of the present invention, the bend angle is the angle between the straight lines at both ends and the radial direction, and the value of the bend angle includes 10° to 20°; the bend height is the radial height of the straight lines at both ends, and the value of the bend height includes 10% to 20% of the radial height of the blade.

[0075] Figure 5 This is a schematic diagram of the overlapping lines of the bent blade.

[0076] According to some embodiments of the present invention, such as Figure 5 As shown, the two ends and the middle of the original leading edge overlap line are straight lines, and the three straight lines are transitioned by a circular arc. By defining the bending angle α and the bending height h, the bending of the turbine blade is precisely controlled, and the blade bending model is constructed. The blade bending is divided into positive bending, where the pressure surface and the end wall form an acute angle, and negative bending, where the pressure surface and the end wall form an acute angle, thus obtaining the shape of the leading edge overlap line of the negative bending blade.

[0077] Figure 6 This is a schematic diagram of the impeller after adopting a turbine modeling method that couples non-axisymmetric endwalls and blade bending.

[0078] According to some embodiments of the present invention, such as Figure 6 As shown, an end-bending model is constructed by coupling a non-axisymmetric endwall model with a blade bending model. The endwall of the end-bending model protrudes near the pressure surface and is concave near the suction surface, and the blade bending at the root is very obvious. Compared with the independent non-axisymmetric endwall, the end-bending model significantly compresses the radial scale of the channel vortex, making up for its insufficient control effect. Compared with the independent blade bending model, the end-bending model weakens the channel vortex intensity and secondary flow, further compressing the radial height of the channel vortex, making up for its defects of excessive transverse pressure gradient and poor end region flow capacity.

[0079] According to some embodiments of the present invention, five axial control lines are evenly distributed between the arc lines of two adjacent turbine blades, and ten circumferential control lines are evenly distributed at 20%-100% of the axial chord length.

[0080] The turbine modeling method of coupling non-axisymmetric endwall and blade bending in this invention can give full play to the advantages of non-axisymmetric endwall method and blade bending method. While compressing the radial scale of the channel vortex, it suppresses the magnitude of the transverse pressure gradient in the end region, significantly reduces the total loss of the outlet flow field, and improves the performance of turbine blades. It provides technical reserves and theoretical support for modern turbine aerodynamic design and end region flow control.

[0081] The technical solution of the present invention will be further described below with reference to a specific embodiment implemented by a university. It should be understood that the specific embodiment is only for the purpose of enabling those skilled in the art to better understand the technical solution of the present invention, and should not be construed as an inappropriate limitation on the scope of protection of the present invention.

[0082] To fully leverage the suppressive effect of the non-axisymmetric endwall on the transverse pressure gradient in the end region and the characteristics of blade bending in rationally organizing low-energy fluid flow, this invention combines non-axisymmetric endwall control technology and blade bending technology to construct an end-bending model. Numerical simulation results show that the end-bending model, which integrates non-axisymmetric endwall and blade bending, maximizes advantages and minimizes disadvantages. It drastically compresses the size of the channel vortex, and the significant enhancement of the flow capacity in the middle of the channel compensates for the losses caused by the accumulation of low-energy fluid near the endwall. It also suppresses the upward migration of low-energy fluid to form a recirculation zone, eliminates low-energy fluid clusters in front of the trailing edge, and reduces the size of the closed separation bubble.

[0083] According to some embodiments of the present invention, a certain low-pressure turbine blade cascade is selected for flow control, and its flow control effect is verified by numerical simulation.

[0084] Numerical calculations were performed on the turbine cascade without turbine modeling at an inlet blade chord Re=200000. The data confirmed the anisotropy of the flow field. Here, only the low-pressure turbine blade cascade with half-blade height was modeled and numerically calculated to obtain the total pressure loss coefficient at the outlet. The vortex system structure of the blade cascade cascade was also constructed, clarifying that the cascade vortex migrates towards the suction surface of the blade cascade under the action of the transverse pressure gradient in the end region, which is the main loss in the end region of the low-pressure turbine. The low-energy fluid in the endwall boundary layer is excessively deflected towards the suction surface and rises upward to the cascade vortex, forming a recirculation zone in front of the trailing edge of the suction surface.

[0085] Following the above-described process for coupling the non-axisymmetric endwall and blade bending, non-axisymmetric endwall models, blade bending models, and end-bending models for this low-pressure turbine blade cascade were constructed. The amplitude control coefficient R was set to 3.85 mm; a reverse-bending blade profile was adopted, with the bending angle α set to 15° and the bending height h set to 15 mm. The turbine flow channel was meshed using the same mesh structure as the original low-pressure turbine blade cascade, and the initial field was set to be consistent with it for numerical calculations. Based on the numerical calculation results, the total pressure loss coefficient under each control method was obtained, and the vortex system structure of the blade cascade channel was constructed.

[0086] The control effects of end-bending coupling technology, non-axisymmetric endwall technology, and blade bending technology on turbine blade passage losses were compared. The relative reduction value Δλ of the total pressure loss coefficient is defined as follows:

[0087]

[0088] Where, λ Ref λ is the total pressure loss coefficient of the original turbine blade cascade. Opt This represents the total pressure loss coefficient after employing various flow control methods.

[0089] Figure 7 This is a schematic diagram of the total pressure loss after adopting a turbine modeling method that couples non-axisymmetric endwall and blade bending.

[0090] According to some embodiments of the present invention, in combination Figure 7 As shown in Table 1, the non-axisymmetric endwall model and the blade bending model reduced the total pressure loss coefficient by 4.36% and 5.82% respectively, while the end bending model reduced the total pressure loss coefficient by 9.46%, which is almost the sum of the effects of the first two flow control methods.

[0091] Table 1 Comparison of End-Bend Coupling Control Effects

[0092]

[0093] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. It should be noted that implementations not illustrated or described in the drawings or the main text of the specification are forms known to those skilled in the art and are not described in detail. Furthermore, the definitions of the components described above are not limited to the various specific structures, shapes, or methods mentioned in the embodiments, and those skilled in the art can easily modify or substitute them.

[0094] It should also be noted that, in specific embodiments of the present invention, unless otherwise stated otherwise, the numerical parameters in this specification and the appended claims are approximate values ​​and can be changed according to the desired characteristics obtained from the content of the present invention. Specifically, all numbers used in the specification and claims to indicate dimensions, range conditions, etc., of the composition should be understood to be modified by the term "about" in all cases. Generally, this means that there may be variations of ±10% in some embodiments, ±5% in some embodiments, ±1% in some embodiments, and ±0.5% in some embodiments.

[0095] Those skilled in the art will understand that the features described in the various embodiments and / or claims of the present invention can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, the features described in the various embodiments and / or claims of the present invention can be combined or combined in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

[0096] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are 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 within the protection scope of the present invention.

Claims

1. A turbine modeling method for coupling non-axisymmetric endwall and blade bending, characterized in that, Including the following steps: A non-axisymmetric endwall model is established by applying circumferential and axial control functions to the turbine endwall profile. By adjusting the bend angle and bend height, the shape of the leading edge overlap line is changed to establish a blade bending model; as well as The non-axisymmetric endwall model is coupled with the blade bending model to obtain the end bending model; The coupling of the non-axisymmetric endwall model with the blade bending model includes: This ensures that the non-axisymmetric endwalls and curved blades intersect and merge at the endwalls while maintaining the geometric continuity of the end-bend model. The control functions applied to the turbine endwall profile include: A sinusoidal function is used to construct the distribution pattern of circumferential control points on the non-axisymmetric end wall, so that the peak value of the sinusoidal function in a complete cycle is close to the pressure surface and the valley value is close to the suction surface; wherein, the radial height of the circumferential control points in the first group and the nth group is 0; Circumferential amplitude control functions based on sinusoidal functions include: Where C(y) represents the circumferential amplitude, A(x) represents the axial amplitude control function, y represents the circumferential coordinate position of the control point, and t represents the distance between the arcs of two adjacent turbine blades; The axial magnitude control function A(x) for a non-axisymmetric end wall includes: Where R represents the amplitude control coefficient, PPS is the static pressure on the near-end wall of the blade pressure surface, PSS is the static pressure on the near-end wall of the blade suction surface, and max(PPS-PSS) is the maximum value of the near-end wall pressure difference at each axial position. It also includes: generating Bézier curves based on discrete points at each axial position, and constructing a non-axisymmetric endwall model by using spline curves to smoothly transition and connect them along the circumference. The method of changing the shape of the leading edge overlap line by adjusting the bend angle and bend height includes: The two ends and the middle of the original turbine guide vane's leading edge overlap line are straight lines, and the three straight lines are transitioned by a circular arc. By adjusting the bend angle and bend height, the bending of the turbine blade is controlled, so as to construct a blade bending model.

2. The turbine design method according to claim 1, characterized in that, The control functions applied to the turbine endwall profile include: The non-axisymmetric endwall model is controlled by multiple control points distributed on the endwall profile. Among them, m axial control lines are evenly distributed at different circumferential positions, and 2n circumferential control lines are evenly distributed at different axial positions, where m and n are integers greater than 0.

3. The turbine styling method according to claim 2, characterized in that, The number of control points is 50, the number of axial control lines is 5, and the number of circumferential control lines is 10.

4. The turbine design method according to claim 1, characterized in that, The bend angle is the angle between the straight lines at both ends and the radial direction, and the value of the bend angle ranges from 10° to 20°; the bend height is the radial height of the straight lines at both ends, and the value of the bend height ranges from 10% to 20% of the radial height of the blade.

5. The turbine styling method according to claim 3, characterized in that, The five axial control lines are evenly distributed between the arc lines of two adjacent turbine blades, and the ten circumferential control lines are evenly distributed at 20%-100% of the axial chord length.

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