A turbine end wall profiling batch automatic design method and system

Abstract

The present application relates to a kind of turbine end wall shaping batch automatic design method and system, belong to turbine mechanical design technical field, it is proposed to use trigonometric function and Bezier curve as axial modeling function, with sinusoidal function as the basis as the circumferential modeling function to axial turbine non-axisymmetric end wall shaping design.Meanwhile, programming is used to accurately draw non-axisymmetric end wall surface, generate the point cloud file of three-dimensional surface.Then point cloud file is imported into three-dimensional modeling software and is modeled to three-dimensional surface, the non-axisymmetric end wall batch automatic design of axial turbine is realized.Form the non-axisymmetric end wall shaping of end wall protrusion near pressure surface, end wall recess near suction surface, promote the flow of end wall near pressure surface to accelerate, static pressure reduces, end wall near suction surface airflow deceleration, static pressure rises, reduce the non-uniformity of end area static pressure circumferential distribution, effectively improve the flow separation between blade, reduce vortex shedding, reduce pressure loss, improve turbine performance and efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to a turbine end wall shaping batch automatic design method and system, belonging to the technical field of turbine mechanical design. BACKGROUND

[0002] Turbomachinery has complex three-dimensional flow characteristics, and various losses exist in its flow process, including secondary flow loss, blade profile loss, blade tip clearance loss, etc. Among them, the end wall secondary flow will trigger various vortexes, which will cause abnormal flow of working medium, even separation phenomenon, and will also affect the main flow, leading to efficiency reduction. Therefore, the key to improving turbine performance lies in controlling secondary flow, and end wall shaping technology has been proven to be an effective way to control secondary flow, which mainly refers to the design and optimization of the end wall surface of turbine or compressor blades, effectively improving the flow separation between blades, reducing vortex shedding, reducing pressure loss, improving performance and efficiency, etc. Through reasonable end wall shaping design, the optimization design and performance improvement of turbomachinery can be realized.

[0003] As an important method of end wall shaping technology, non-axisymmetric end wall shaping has been studied by Morri, Atkins and others in the last century. The basic principle is to change the concave-convex degree of the end wall from the original smooth surface to the high-low undulating surface. The concave-convex of the wall changes the flow state of the working medium, where the convex of the wall will promote the flow velocity to rise and reduce the static pressure, and the concave of the wall will reduce the flow velocity and increase the static pressure. By reasonably arranging the concave-convex area of the wall, the flow state can be improved, the secondary flow loss can be reduced, and the turbine efficiency can be improved.

[0004] Although the non-axisymmetric end wall shaping method has been developed for a long time, it also faces some challenges. Non-axisymmetric end wall optimization usually requires a large number of numerical simulations and calculations to evaluate the impact of different end wall shapes on performance, so a large number of fine design adjustments and three-dimensional modeling of end wall shapes are needed, resulting in a large number of shaping. This increases the complexity of the design, which requires the designer to have a deep understanding of the flow field and have high design skills and experience, which may lead to an increase in design period and cost. Therefore, a batch automatic design method of non-axisymmetric end wall is needed, which can reduce the design time and complexity, realize automatic design, and facilitate the determination of the best design scheme. SUMMARY

[0005] The present application is proposed in view of the low design efficiency of the current non-axisymmetric end wall modeling method, the inability to generate a large number of modeling to accurately determine the best modeling scheme, and the inability to achieve the best effect of improving the flow separation between blades, reducing pressure loss, and improving performance and efficiency, and the non-axisymmetric end wall modeling design of the axial turbine is carried out by using the trigonometric function and the Bezier curve as the axial modeling function, and the sinusoidal function as the circumferential modeling function. Meanwhile, the programming is used to accurately draw the non-axisymmetric end wall curve, generate a three-dimensional curve, and perform three-dimensional modeling on it, so as to realize the batch automatic design of the non-axisymmetric end wall of the axial turbine. At the same time, the flow separation between blades is effectively improved, the vortex shedding is reduced, the pressure loss is reduced, and the turbine performance and efficiency are improved.

[0006] The technical scheme of the present application is as follows:

[0007] A batch automatic design method for turbine end wall modeling, wherein the moving blades and the stationary blades of the axial turbine are alternately arranged along the end wall axis, uniformly distributed in the circumferential direction, and the end wall shapes of the adjacent circumferential blades are the same; the method designs the end wall between the adjacent circumferential blades as a period, and finally forms an end wall modeling with a protruding end wall near the pressure surface and a recessed end wall near the suction surface, which at least includes the following steps:

[0008] Step 1: determining the end wall curve range with the adjacent circumferential blades as the two boundary arcs;

[0009] Step 2: determining the circumferential modeling function based on the sinusoidal function, and proposing the circumferential modeling function under different frequency coefficients, and the formula is as follows:

[0010]

[0011] In the formula, alpha is the frequency coefficient; y0 is the start point of the cascade pitch, y n is the end point of the cascade pitch;

[0012] Step 3: since the sinusoidal curve is convex around the horizontal straight line and concave, it cannot realize the convex and concave around the curved straight line. However, in the actual turbine hub, there is a curved surface with curvature between the pressure surface and the suction surface of the hub end wall. Therefore, the circumferential modeling function is represented in the form of polar coordinates, and the sinusoidal function is used to realize the convex and concave, and the formula form is as follows:

[0013]

[0014] In the formula, alpha still represents the frequency coefficient, which can adjust the corresponding positions of the peak points and the valley points of the non-axisymmetric end wall curve along the axis by different values; n represents the number of blades; r dThe radius of the blade root is represented by r, and θ is the polar angle. The curves at different frequency coefficients also intersect at a point, which is controlled by the phase π / n. When the frequency coefficient α = 1, the blade spacing is exactly one period of a sine function, and when the blade has a certain thickness, the root of the pressure surface of the blade is entirely on the convex end wall surface, and the root of the suction surface of the blade is entirely on the concave end wall surface. By changing the value of the frequency coefficient, the greater the value of α, the farther the convex position is from the pressure surface, and the farther the concave position is from the suction surface, thereby achieving the movement of the concave position and the convex position in the circumferential direction by controlling the value of α.

[0015] The improved circumferential function changes the horizontal dashed line originally surrounded by the convex and concave into a dashed line with curvature, which is consistent with the curvature structure of the real hub.

[0016] The improved circumferential modeling function adds an adjustment parameter of the number of blades n, which can achieve accurate non-axisymmetric end wall modeling of the end wall surface of any hub radius and any number of blades.

[0017] The frequency coefficient is changed based on the periodicity between the blade spacing, for example: α = 1 represents that there is a periodic sine curve between the blade spacing.

[0018] Step 4: Considering that the airflow inside the channel changes most dramatically, and is also the main area where secondary flow and various vortex systems are generated and developed, the axial modeling function is applied to the end wall of the inlet and outlet flow channels of the blade, and the hub end wall surface between the leading edge and the trailing edge of the blade is finally determined to be an axial modeling range of the non-axisymmetric end wall surface.

[0019] Step 5: The method proposes a "single-peak" modeling amplitude control function of the trigonometric function in the axial direction, which is as follows:

[0020]

[0021] In the formula: the coefficient C is used to control the amplitude, which is given by the designer; z LE represents the axial position of the leading edge of the blade; z TE represents the axial position of the trailing edge of the blade;

[0022] Step 6: The method also uses a Bezier curve-based end wall modeling design method as the axial function, which uses selected n control points to construct the axial function. Considering the correlation of the Bezier curve, the axial modeling function h BCPM in the method is selected as a fourth-order Bezier curve composed of five control points, which is as follows:

[0023]

[0024] In the formula: P i represents the i-th control point (zi h i ),z i is the coordinate of the i-th control point in the axial direction of the z-axis, h i is the height of the i-th control point; B i,4 (t) represents a quartic Bernstein polynomial, and its definition is as follows:

[0025]

[0026] Five control points P i (i = 0, 1, …, 4) are uniformly distributed from the blade leading edge to the blade trailing edge in the axial direction, and only the central control point P2 among the five control points can change in the radial direction, and the value of the height h i also determines the degree of convexity and concavity of the non-axisymmetric end wall surface;

[0027] Step 7: In order to unify various axial modeling functions and facilitate future unified design, the integrated axial modeling function is given by referring to the current research method, and its form is as follows:

[0028] h i (z) = C h · H B · h(z), z LE ≤ z ≤ z TE (6)

[0029] In the formula: C h represents the amplitude coefficient; H B represents the blade height; i represents the unitized modeling function of various axial modeling schemes, i = TFPM, BCPM, z LE represents the axial position of the blade leading edge; z TE represents the axial position of the blade trailing edge; h(z) is h TFPM in step 5 or h BCPM in step 6; for a selected blade passage, the peak and valley values of the non-axisymmetric end wall surface can be determined according to the amplitude coefficient C h ; the amplitude coefficient C h plays the most important role in determining the height of the peak and valley; by increasing the value of the amplitude coefficient C h , the concave-convex degree of the non-axisymmetric end wall surface changes more obviously, and the amplitude coefficient C h controls the radial change of the non-axisymmetric end wall;

[0030] Various axial modeling functions are unified, and the integrated axial modeling function is given, so that more flexible design schemes can be selected when designing non-axisymmetric end wall modeling in batches.

[0031] Step 8: precise drawing of the non-axisymmetric end wall surface is realized by multiplying the orthogonal circumferential modeling function and the axial modeling function using MATLAB programming, and the point cloud files of the three-dimensional surfaces of the "trigonometric function method" and "Bezier curve method" are obtained;

[0032] The orthogonal circumferential and axial modeling functions are realized by programming and expressed by a programming language. By adjusting the control parameters of the program, the design scheme can be quickly adjusted, and the design difficulty is reduced. By using the method of inputting the control function range, batch design of the modeling scheme can be realized.

[0033] Preferably, in step 8, different axial turbine models have different blade root radii, blade numbers, blade leading edge axial positions and trailing edge axial positions. For different axial turbine models, the position parameters and periodic parameters in the program can be adjusted for adaptation. By adjusting r d , n in formula (2), z LE and z TE in formula (3) and formula (6), batch design of multiple types of different size axial turbines can be realized.

[0034] Step 9: In the three-dimensional modeling software, the surface is generated using the point cloud file. First, import the point cloud file, use the "mesh" function to create a mesh surface, and select the mesh surface to create a solid surface. After the surface is created, edit the surface to adjust the shape and properties of the surface to meet the design requirements.

[0035] Preferably, in step 9, the three-dimensional modeling software is SolidWorks. First, import the point cloud file, use the "mesh" function to create a mesh surface, and select the mesh surface to create a solid surface. After the surface is created, import SolidWorks to generate two non-axisymmetric end walls of the flow channel. To reduce the subsequent calculation amount, single-flow numerical simulation is used in subsequent numerical calculation, so only one non-axisymmetric end wall of the flow channel is left after editing the surface to adjust the shape and properties of the surface to meet the design requirements. The modeling scheme designed by programming is constructed in three dimensions to realize three-dimensional modeling of the modeling scheme, which can be directly imported into the subsequent CFD calculation software for performance evaluation and calculation.

[0036] Preferably, step 10 is also included to ensure the accuracy of the blade profile. Based on the non-axisymmetric end wall, the original turbine blade CAD file is imported into the three-dimensional modeling software to draw the static blade and the moving blade. Then, a series of operation commands such as segmentation, combination, stretching, cutting, and array are used to complete the three-dimensional modeling of the entire turbine.

[0037] A turbine end wall modeling batch automatic design system has a program stored thereon, which, when executed by a processor, implements the steps in the turbine end wall modeling batch automatic design method as described above.

[0038] By improving and parameterizing the circumferential and axial modeling functions, a plurality of axial modeling functions are integrated and unified. Under the premise of considering the curvature of the end wall surface, precise drawing is realized by programming, and three-dimensional modeling is performed to form a non-axially symmetric end wall modeling, so as to promote the acceleration of the end wall airflow near the pressure surface, reduce the static pressure, decelerate the end wall airflow near the suction surface, increase the static pressure, reduce the non-uniformity of the static pressure circumferential distribution in the end region, effectively improve the flow separation between blades, reduce vortex shedding, reduce pressure loss, improve turbine performance and efficiency.

[0039] The present application has the following advantages:

[0040] The present application proposes a non-axially symmetric end wall modeling method based on a sine function as a circumferential modeling function, a trigonometric function and a Bezier curve as axial modeling functions, especially the improved circumferential function, which changes the originally convex and concave horizontal dotted line around it into a dotted line with curvature, which is consistent with the curvature structure of the real hub. At the same time, a plurality of axial modeling functions are integrated and unified, which provides convenience for subsequent addition of axial modeling function types and adaptation to more design methods. Each function is converted into a programming language, and the orthogonal circumferential function and the axial function are multiplied to realize precise drawing of the non-axially symmetric end wall surface. Combined with three-dimensional modeling software, programming and three-dimensional modeling reduce the design difficulty, realize flexible and convenient batch automatic design of the non-axially symmetric end wall of the axial flow turbine, and the designed modeling scheme can effectively improve the flow separation between blades, reduce vortex shedding, reduce pressure loss, improve turbine performance and efficiency.

[0041] It is free from dependence on commercial turbine design software, which is helpful for subsequent self-iteration and independent intellectual property system construction, and promotes the development of domestic CFD software. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 : Non-axially symmetric end wall surface boundary schematic diagram;

[0043] Figure 2 : Axial flow turbine direction specification schematic diagram;

[0044] Figure 3 : Non-axially symmetric end wall modeling function schematic diagram;

[0045] Figure 4 : Improved circumferential modeling function;

[0046] Figure 5: Schematic diagram of concave-convex region comparison of axial modeling function between "trigonometric function method" and "Bezier curve method";

[0047] Figure 6 : Schematic diagram of curve comparison of axial modeling function between "trigonometric function method" and "Bezier curve method";

[0048] Figure 7 : Schematic diagram of non-axial symmetric end wall surface after programming of "trigonometric function method";

[0049] Figure 8 : Schematic diagram of non-axial symmetric end wall surface after programming of "Bezier curve method";

[0050] Figure 9 : Schematic diagram of three-dimensional modeling of surface of "trigonometric function method";

[0051] Figure 10 : Schematic diagram of three-dimensional modeling of surface of "Bezier curve method";

[0052] Figure 11 : Schematic diagram of creating three-dimensional model of turbine stator vane of "trigonometric function method";

[0053] Figure 12 : Schematic diagram of creating three-dimensional model of turbine stator vane of "Bezier curve method";

[0054] Figure 13 : Schematic diagram of comparison of total pressure loss coefficient of stator vane. DETAILED DESCRIPTION

[0055] The present application is further described below by way of examples and with reference to the accompanying drawings, which are intended to illustrate the technical features, implementation steps and expected effects of the present application, but are not limited thereto.

[0056] Example 1

[0057] A batch automatic design method of non-axial symmetric end wall of an axial flow turbine is provided for constructing a non-axial symmetric end wall modeling of a stator vane of an axial flow turbine, wherein the blades are uniformly distributed in the circumferential direction, and the end wall shapes of adjacent circumferential blades are the same, and the end wall between adjacent circumferential blades is designed as a period, and the design process specifically includes the following steps:

[0058] Step 1: determining the end wall surface range ( ) with the camber line of adjacent circumferential blades as the two boundary lines. Figure 1

[0059] Step 2: determining the circumferential modeling function (the direction of the modeling function is defined as shown in Figure 2 、 Figure 3 ), and proposing the circumferential modeling function under different frequency coefficients, and the formula is:

[0060] ​

[0061] In the formula, α is the frequency coefficient; y0 is the starting point of the blade cascade pitch, y n This is the endpoint of the leaf cascade pitch.

[0062] Step 3: Represent the circumferential modeling function using polar coordinates. Figure 4 The upper convexity and lower concavity are achieved using a sine function to match the curvature structure of a real wheel hub. The formula is shown below:

[0063]

[0064] In the formula, α still represents the frequency coefficient, which can be adjusted by different values ​​to change the corresponding axial positions of the peak and valley points of the non-axisymmetric endwall surface; n represents the number of blades; r d The radius of the leaf root is represented by θ, which is the polar angle in polar coordinates. The curves under different frequency coefficients also intersect at a point, which is controlled by the phase π / n. In this embodiment, seven values ​​of α are selected for design: 0, 0.25, 0.5, 0.75, 1, 1.25, and 1.5.

[0065] Step 4: The axial shaping function is applied to the endwall of the blade inlet and outlet flow channels to finally determine the axial shaping range of the hub endwall between the leading and trailing edges of the blade as the non-axisymmetric endwall.

[0066] Step 5: The axial shaping function adopts an integrated unified form. In this embodiment, two types are selected for design: the trigonometric function "single-peak" shaping amplitude control function and the fourth-order Bezier curve axial function, such as... Figure 5 , Figure 6 As shown.

[0067] The trigonometric function's "single-peak" modeling amplitude control function takes the following form:

[0068]

[0069] In the formula: the coefficient C is used to control the amplitude, which is given by the designer; in this method, C is set to 1; z LE Indicates the axial position of the blade's leading edge; z TE Indicates the axial position of the trailing edge of the blade;

[0070] Step 6: The endwall shaping design method based on Bezier curves is used as the axial function. This method uses n selected control points to construct the axial function. Considering the relevant properties of Bezier curves, the axial shaping function h in this method... BCPM We select a fourth-order Bezier curve consisting of five control points, in the following form:

[0071]

[0072] In the formula: P i Represents the i-th control point (z) i ,h i ), z i Let h be the coordinate of the i-th control point along the z-axis. i B is the height of the i-th control point; i,4 (t) represents a fourth-degree Bernstein polynomial, defined as:

[0073]

[0074] Five control points P i (i = 0, 1, ..., 4) are uniformly distributed along the axial direction from the leading edge to the trailing edge of the blade. Among the five control points, only the central control point P2 can vary radially, and its height h is... i The value of also determines the degree of upward convexity and downward concavity of the non-axisymmetric end wall;

[0075] Step 7: Provide the integrated axial modeling function, which has the following form:

[0076] h i (z)=C h ·H B ·h(z),z LE ≤z≤z TE (6).

[0077] In the formula: C h This represents the amplitude coefficient; in this embodiment, C is selected. h The design uses six values: 0%, 1%, 2%, 3%, 4%, and 5%. H B The blade height is represented by ; ... LE Indicates the axial position of the blade's leading edge; z TE This indicates the axial position of the trailing edge of the blade; h(z) is the h from step 5. TFPM Or h in step 6 BCPM For a selected blade channel, the amplitude coefficient C can be used as a reference. h To determine the peak and valley values ​​of the convex and concave surfaces on the non-axisymmetric endwalls; amplitude coefficient C h Its most important function is to determine the height of peaks and troughs by increasing the amplitude coefficient C. h The value of makes the unevenness of the non-axisymmetric end wall more obvious, and the amplitude coefficient C h It controls the radial variation of the non-axisymmetric endwall.

[0078] Step 8: Precise drawing of the non-axisymmetric endwall surface is realized by multiplying the orthogonal circumferential and axial modeling functions using MATLAB programming, then the relevant data is extracted to generate the three-dimensional surface of the trigonometric function method and the Bezier curve method as shown in Figs. 8 and 9. A total of 84 endwall modeling is generated according to different values of a, C and the type of axial modeling function, and is exported in the form of a point cloud file. Figure 7 、 Figure 8 h

[0079] Step 9: In the three-dimensional modeling software SolidWorks, the surface is generated using the point cloud file. First, the point cloud file is imported, and the mesh function is used to create a mesh surface, and the mesh surface is selected to create a solid surface. After the surface is created, the SolidWorks is imported, and two non-axisymmetric endwall surfaces of the flow channel are generated. To reduce the subsequent calculation amount, the single-flow numerical simulation is used in the subsequent numerical calculation, and therefore the surface is edited to leave only one non-axisymmetric endwall surface of the flow channel to adjust the shape and properties of the surface to meet the design requirements, and the final modeling is shown in Figs. 10 and 11. Figure 9 、 Figure 10

[0080] Step 10: To ensure the accuracy of the blade profile, the original turbine blade CAD file is directly imported into the three-dimensional modeling software to draw the stationary blade and the moving blade. Then a series of operation commands such as segmentation, combination, stretching, cutting, and array are used to complete the three-dimensional modeling of the turbine as shown in Figs. 12 and 13. Figure 11 、 Figure 12

[0081] The model of the endwall surface generated in Step 9 needs to be increased with turbine blades to form a complete turbine model to explore the influence of the endwall surface on the performance of the turbine. The turbine blade CAD file imported in Step 10 is the original turbine blade of the original turbine model before the non-axisymmetric endwall modeling.

[0082] Step 11: The complete turbine three-dimensional model is imported into the CFD software for meshing and numerical simulation calculation to test the performance of the turbine with the designed non-axisymmetric endwall modeling and the changes of the internal flow field.

[0083] Through comparison, the non-axisymmetric endwall modeling constructed by this method effectively improves the flow separation between the blades, reduces the vortex shedding, reduces the pressure loss, and improves the performance and efficiency of the turbine. The best design scheme of the turbine compared with the original turbine improves the total isentropic efficiency η ts by nearly 0.5%, and the calculation formula is as follows: where, ΔW x and ΔW max ​​​​respectively, represent actual specific work and ideal specific work; h 01 and h 02 respectively, represent actual total enthalpy at inlet and outlet of the passage; h 2s respectively, represent actual total pressure at inlet and outlet of the passage; p 01 respectively, represent actual total pressure at inlet and outlet of the passage; p 1s respectively, represent actual total pressure at inlet and outlet of the passage; p Figure 13 respectively, represent actual total pressure at inlet and outlet of the passage; p respectively, represent actual total pressure at inlet and outlet of the passage; p

[0084] Embodiment 2

[0085] A non-axisymmetric end wall batch automatic design system of an axial turbine, which has a program stored thereon, the program being executed by a processor to implement the steps of the non-axisymmetric end wall batch automatic design method of the axial turbine according to Embodiment 1.

[0086] Through the above embodiments, the purposes of the present application are completely achieved. Those skilled in the art can understand that the present application includes but is not limited to the contents described in the drawings and the above detailed embodiments. Although the present application has been described with respect to the presently preferred embodiments, it will be apparent that many modifications and changes can be made by those skilled in the art without departing from the spirit and broad scope of the present application.

Claims

1. A method for batch automatic design of turbine endwall shapes, characterized in that, In an axial flow turbine, the moving and stationary blades are arranged alternately along the endwall axially and uniformly distributed circumferentially, with adjacent circumferential blades having the same endwall shape. The method designs the endwall between adjacent circumferential blades as a cycle, ultimately forming an endwall shape with endwall protrusions near the pressure surface and endwall concavities near the suction surface, including the following steps: Step 1: Determine the range of the endwall curved surface using the mid-arc lines of adjacent circumferential blades as the two side boundaries; Step 2: Based on the sine function, determine the circumferential shaping function and propose the circumferential shaping function for different frequency coefficients. The formula is as follows: In the formula, α is the frequency coefficient; y0 is the starting point of the blade cascade pitch, y n This is the endpoint of the cascade pitch. Step 3: Represent the circumferential shaping function in polar coordinates, and use a sine function to achieve the convex and concave shapes. The formula is shown below: In the formula, α adjusts the corresponding axial positions of the peak and valley points of the non-axisymmetric endwall surface by different values; n represents the number of blades; r d Let α represent the blade root radius, and θ be the polar angle in polar coordinates. The curves under different frequency coefficients intersect at a single point, which is controlled by the phase π / n. When the frequency coefficient α = 1, the blade cascade pitch is exactly one sine function period, and the entire pressure surface root of the blade is on the convex end wall, while the suction surface of the blade is entirely on the concave end wall. By changing the value of the frequency coefficient α, the larger the value, the further the convex position is from the pressure surface, and the further the concave position is from the suction surface. By controlling the value of α, the circumferential movement of the concave and convex positions can be achieved. Step 4: The axial shaping function is applied to the endwall of the blade inlet and outlet flow channels to finally determine the axial shaping range of the hub endwall between the leading and trailing edges of the blade. Step 5: Extract the single-peak modeling amplitude control function of trigonometric functions along the axis, in the following form: In the formula: coefficient C is used to control the amplitude and is given by the designer; z LE Indicates the axial position of the leading edge of the blade; z TE Indicates the axial position of the trailing edge of the blade; Step 6: The endwall shaping design method based on Bezier curves is used as the axial function. This method uses n selected control points to construct the axial function; the axial shaping function h BCPM We select a fourth-order Bezier curve consisting of five control points, in the following form: In the formula: P i Represents the i-th control point (z) i ,h i ), z i Let h be the coordinate of the i-th control point along the z-axis. i B is the height of the i-th control point; i,4 (t) represents a fourth-degree Bernstein polynomial, defined as: Five control points P i (i = 0, 1, ..., 4) are uniformly distributed along the axial direction from the leading edge to the trailing edge of the blade. Among the five control points, only the central control point P2 varies radially, and its height h is... i The value of also determines the degree of upward convexity and downward concavity of the non-axisymmetric end wall; Step 7: Provide the integrated axial modeling function, which has the following form: h i (z)=C h ·H B ·h(z),z LE ≤z≤z TE (6) In the formula: C h H represents the amplitude coefficient; B The blade height is represented by ; i represents the modeling function after normalization for various axial modeling schemes, i = TFPM, BCPM; h(z) is the h from step 5. TFPM Or h in step 6 BCPM Select a blade channel, based on the amplitude coefficient C h To determine the peak and valley values ​​of the convex and concave surfaces on the non-axisymmetric endwalls; amplitude coefficient C h Its function is to determine the height of the peak and trough by increasing the amplitude coefficient C. h The value of causes a change in the unevenness of the non-axisymmetric end wall, with an amplitude coefficient C. h It controls the radial variation of the non-axisymmetric endwall; Step 8: Using programming, multiply the orthogonal circumferential modeling function with the axial modeling function to draw the non-axisymmetric end wall surface, and obtain the point cloud file of the three-dimensional surface using the trigonometric function method and the Bezier curve method. Step 9: In 3D modeling software, generate a surface using the point cloud file; adjust the shape and properties of the surface to meet the design requirements.

2. The method for batch automatic design of turbine endwall shapes according to claim 1, characterized in that, In step 8, different axial flow turbine models have different blade root radii, number of blades, and axial positions of the leading and trailing edges. For different axial flow turbine models, the r value in formula (2) is adjusted. d , n, z in formula (3) and formula (6) LE With z TE This enables the batch design of axial flow turbines of various types and sizes.

3. The method for batch automatic design of turbine endwall shapes according to claim 1, characterized in that, In step 9, first import the point cloud file, use the mesh function to create a mesh surface, and at the same time select the mesh surface to create a solid surface; after the surface is created, edit the surface to leave only the non-axisymmetric end wall of one flow channel, and adjust the shape and properties of the surface to meet the design requirements.

4. The method for batch automatic design of turbine endwall shapes according to claim 1, characterized in that, It also includes step 10, which involves importing the original turbine blade CAD file into the 3D modeling software based on the non-axisymmetric endwall, drawing the stationary blades and moving blades, and then using a series of operation commands such as segmentation, combination, stretching, cutting, and arraying to complete the 3D modeling of the entire turbine.

5. A batch automated design system for turbine endwall molding, characterized in that, It stores a program that, when executed by a processor, implements the steps in the batch automatic design method for turbine endwall styling as described in any one of claims 1-4.

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