Turbine end wall modeling batch automatic design method and system

Abstract

The invention relates to a batch automatic design method and system for turbine end wall modeling, belongs to the technical field of turbine mechanical design, and provides non-axisymmetric end wall modeling design for an axial flow turbine by taking a trigonometric function and a Bezier curve as axial modeling functions and taking a sine function as a circumferential modeling function. Meanwhile, the non-axisymmetric end wall curved surface is accurately drawn through programming, and a point cloud file of the three-dimensional curved surface is generated. And then the point cloud file is imported into three-dimensional modeling software for three-dimensional curved surface modeling, and automatic batch design of the non-axisymmetric end walls of the axial flow turbine is achieved. The end wall near the pressure surface is convex, and the end wall near the suction surface is concave, so that the airflow of the end wall near the pressure surface is accelerated to flow, the static pressure is reduced, the airflow of the end wall near the suction surface is decelerated, the static pressure is increased, and the non-uniformity of circumferential distribution of the static pressure in the end area is reduced; flow separation among the blades is effectively improved, vortex shedding is reduced, pressure loss is reduced, and turbine performance and efficiency are improved.

Description

Technical Field

[0001] The invention relates to a method and system for batch automatic design of turbine end wall molding, belonging to the technical field of turbine machinery design. Background Art

[0002] Turbomachinery has complex three-dimensional flow characteristics, and there are various losses in its flow process, including secondary flow loss, blade profile loss, blade tip clearance loss, etc. Among them, the secondary flow of the end wall will trigger various vortex systems, which will lead to abnormal flow of the working fluid and even separation, and will affect the mainstream flow, resulting in reduced efficiency. Therefore, the key to improving turbine performance is to control the secondary flow, and end wall modeling technology has been proven to be an effective way to control the secondary flow. It mainly refers to the design and optimization of the end wall surface of the turbine or compressor blades, effectively improving the flow separation between blades, reducing vortex shedding, reducing pressure loss, and improving performance and efficiency. Through reasonable end wall modeling design, the optimized design and performance improvement of turbomachinery can be achieved.

[0003] As an important method of end wall shaping technology, non-axisymmetric end wall shaping was studied by Morri, Atkins and others in the last century. Its basic principle is to change the concave and convex degree of the end wall, changing the original smooth surface into an undulating surface. The concave and convex wall surface changes the flow state of the working fluid. The convex wall surface will increase the flow velocity and reduce the static pressure, while the concave wall surface will reduce the flow velocity and increase the static pressure. By reasonably arranging the concave and convex areas of the wall surface, 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 modeling method has been developed for a long time, it also faces some challenges. Non-axisymmetric end wall optimization usually requires a lot of numerical simulation and calculation to evaluate the impact of different end wall shapes on performance. Therefore, a lot of fine design adjustments and three-dimensional modeling of the end wall shape are required, resulting in a large number of shapes. This increases the complexity of the design and requires designers to have an in-depth understanding of the flow field and have high design skills and experience, which may lead to extended design cycles and increased design costs. Therefore, a batch automatic design method for non-axisymmetric end walls is needed to reduce design time and complexity, realize automated design, and facilitate the determination of the best design solution. Summary of the invention

[0005] In view of the shortcomings of the current non-axisymmetric end wall modeling method, which has low design efficiency, cannot generate a large number of models and accurately determine the best modeling scheme, and cannot achieve the best effect of improving flow separation between blades, reducing pressure loss, and improving performance and efficiency, the present invention proposes to use trigonometric functions and Bezier curves as axial modeling functions, and use sine functions as the basis as circumferential modeling functions to design the non-axisymmetric end wall of axial flow turbines. At the same time, programming is used to accurately draw the non-axisymmetric end wall surface, generate a three-dimensional surface, and perform three-dimensional modeling on it, thereby realizing the automatic batch design of the non-axisymmetric end wall of the axial flow turbine. At the same time, it effectively improves the flow separation between blades, reduces vortex shedding, reduces pressure loss, and improves turbine performance and efficiency.

[0006] The technical solution of the present invention is as follows:

[0007] A method for batch automatic design of turbine end wall shape, wherein the moving blades and the stationary blades of the axial flow turbine are alternately arranged along the end wall axial direction and evenly distributed circumferentially, and the end wall shapes between adjacent circumferential blades are the same; the method designs the end wall between adjacent circumferential blades as a cycle, and finally forms an end wall shape with the characteristics of convex end wall near the pressure surface and concave end wall near the suction surface, which at least includes the following steps:

[0008] Step 1: Use the mid-arcs of adjacent circumferential blades as the boundaries on both sides to determine the range of the end wall surface;

[0009] Step 2: Based on the sine function, determine the circumferential modeling function and propose the circumferential modeling function under different frequency coefficients. The formula is:

[0010]

[0011] Where α is the frequency coefficient; y0 is the starting point of the blade pitch, y n is the end point of the blade cascade pitch;

[0012] Step 3: Since the sine curve is convex and concave around a horizontal straight line, it cannot achieve convexity and concave around a curved straight line. However, in the actual turbomachinery hub, there is a curved surface with curvature on the hub end wall between the pressure surface and the suction surface. Therefore, the circumferential modeling function is expressed in the form of polar coordinates, and the sine function is used to achieve convexity and concave, and its formula form is as follows:

[0013]

[0014] In the formula, α still represents the frequency coefficient, and the corresponding positions of the peak and valley points of the non-axisymmetric end wall surface along the axial direction can be adjusted by taking different values; n represents the number of blades; r drepresents the blade root radius, and θ is the polar angle of polar coordinates; the curves under different frequency coefficients also intersect at one point, which is controlled by the phase π / n; when the frequency coefficient α=1, the blade cascade pitch is just one period of the sine function, and when the blade has a certain thickness, the root of the pressure side of the blade is all on the convex end wall, and the suction side of the blade is also all on the concave end wall; the value of the frequency coefficient is changed, the larger α is, the farther the convex position is from the pressure surface, and the farther the concave position is from the suction surface, and the movement of the concave position and the convex position in the circumferential direction is achieved by controlling the value of α;

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

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

[0017] The frequency coefficient is changed according to the periodicity between the blade pitches. For example, α=1 means that there is a periodic sinusoidal curve between the blade pitches.

[0018] Step 4: Considering that the airflow changes most drastically inside the channel, and it is also the main area for the generation and development of secondary flow and various vortex systems, the axial modeling function is applied to the end wall of the blade inlet and outlet flow channels, and finally it is determined that the hub end wall between the leading edge and the trailing edge of the blade is the axial modeling range of the non-axisymmetric end wall;

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

[0020]

[0021] Where: coefficient C is used to control the amplitude and is given by the designer; 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;

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

[0023]

[0024] Where: P i represents the i-th control point (zi ,h i ), z i is the coordinate of the i-th control point on the z-axis, h i is the height of the i-th control point; B i,4 (t) represents the quartic Bernstein polynomial, which is defined as:

[0025]

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

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

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

[0029] Where: C h Represents the amplitude coefficient; H B represents the blade height; i represents the modeling function of various axial modeling schemes after unitization, i = TFPM, BCPM, z LE Indicates the axial position of the leading edge of the blade; z TE represents the axial position of the blade trailing edge; h(z) is the h in step 5 TFPM or h in step 6 BCPM For a selected blade channel, the amplitude coefficient C h To determine the peak and valley values ​​of the convex and concave surfaces on the non-axisymmetric end wall; the amplitude coefficient C h The most important role is to determine the height of the peak and the valley, by increasing the amplitude coefficient C h The value of makes the concave-convex degree of the non-axisymmetric end wall change more obviously, and the amplitude coefficient C h Controls the radial variation of the non-axisymmetric end wall;

[0030] The various axial modeling functions are unified, and an integrated axial modeling function is given, so that a more flexible design scheme can be adopted in batch design of non-axisymmetric end wall modeling.

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

[0032] Orthogonal circumferential and axial modeling functions are realized by programming and expressed in programming language. The design scheme can be quickly adjusted by adjusting the control parameters of the program, while reducing the design difficulty. The method of inputting the control function range can realize batch design of modeling schemes.

[0033] Preferably, in step 8, different axial flow turbine models have different blade root radius, blade number, blade leading edge axial position and trailing edge axial position. For different axial flow turbine models, the position parameters and period parameters in the program can be adjusted to adapt. By adjusting r in formula (2), d , n, z in formula (3) and formula (6) LE With z TE , realizing batch design of axial flow turbines of various types and sizes.

[0034] Step 9: In the 3D modeling software, use the point cloud file to generate the surface; 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 3D modeling software is SolidWorks, first import the point cloud file, use the "grid" function to create a mesh surface, and select the mesh surface to create a solid surface; after the surface is created, two non-axisymmetric end walls of the flow channel are generated after importing SolidWorks. In order to reduce the subsequent calculation amount, the subsequent numerical calculation adopts single flow channel numerical simulation, so the surface is edited to leave only one non-axisymmetric end wall of the flow channel to adjust the shape and properties of the surface to meet the design requirements. The modeling scheme designed by programming is constructed at the three-dimensional level to realize the 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 shape, on the basis of obtaining the non-axisymmetric end wall, the original CAD file of the turbine blade shape is imported into the 3D modeling software to draw the stationary blades and the moving blades. Then, a series of operation commands such as splitting, combining, stretching, cutting, and arraying are used to complete the 3D modeling of the entire turbine.

[0037] A system for batch automatic design of turbine end wall molding is provided, on which a program is stored. When the program is executed by a processor, the steps in the method for batch automatic design of turbine end wall molding as described above are realized.

[0038] Through the improvement and parameterization of circumferential and axial modeling functions, multiple axial modeling functions are integrated and unified. Under the premise of considering the curvature of the end wall surface, accurate drawing is achieved by programming, and three-dimensional modeling is performed to form a non-axisymmetric end wall modeling, which accelerates the end wall airflow near the pressure surface, reduces the static pressure, slows down the end wall airflow near the suction surface, increases the static pressure, reduces the unevenness of the circumferential distribution of the static pressure in the end area, effectively improves the flow separation between the blades, reduces vortex shedding, reduces pressure loss, and improves turbine performance and efficiency.

[0039] The beneficial effects of the present invention are:

[0040] The present invention proposes a non-axisymmetric end wall modeling method based on a sine function as a circumferential modeling function, and a trigonometric function and a Bezier curve as an axial modeling function. In particular, the circumferential function is improved. The improved circumferential function changes the horizontal dotted line originally surrounded by the convex and concave into a dotted line surrounding the curvature, which is consistent with the curvature structure of the real hub. At the same time, a variety of axial modeling functions are integrated to unify the form, providing convenience for the subsequent increase of axial modeling function types and adaptation of more design methods. Each function is converted into a programming language, and the non-axisymmetric end wall surface is accurately drawn by multiplying the orthogonal circumferential function with the axial direction. Combined with 3D modeling software, the design difficulty is reduced through programming and 3D modeling, and the non-axisymmetric end wall of the axial turbine is flexible and convenient. The batch automatic design is realized, and the designed modeling scheme can effectively improve the flow separation between blades, reduce vortex shedding, reduce pressure loss, and improve turbine performance and efficiency.

[0041] Getting rid of the dependence on commercial turbine design software will help with subsequent self-iteration and the construction of an independent intellectual property system, and promote the development of domestic CFD software. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 : Schematic diagram of the non-axisymmetric end wall curved surface boundary;

[0043] Figure 2 :Schematic diagram of axial flow turbine direction regulation;

[0044] Figure 3 : Schematic diagram of non-axisymmetric end wall modeling function;

[0045] Figure 4 : Improved circumferential modeling function;

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

[0047] Figure 6 : Schematic diagram comparing the axial modeling function curves of the “trigonometric function method” and the “Bezier curve method”;

[0048] Figure 7 : Schematic diagram of non-axisymmetric end wall surface after programming by “trigonometric function method”;

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

[0050] Fig. 9 : Schematic diagram of three-dimensional surface modeling using the trigonometric function method;

[0051] Fig.10 : Schematic diagram of 3D modeling of surfaces using the Bezier curve method;

[0052] Fig.11 : "Trigonometric function method" is used to create a schematic diagram of the three-dimensional model of the turbine stator blade;

[0053] Fig.12 : "Bezier curve method" creates a schematic diagram of the three-dimensional model of the turbine stator blade;

[0054] Fig.13 : Schematic diagram of comparison of total pressure loss coefficient of stationary blades. DETAILED DESCRIPTION

[0055] The present invention is further described below through examples and in conjunction with the accompanying drawings, aiming to demonstrate the technical features, implementation steps and expected effects of the present invention, but is not limited thereto.

[0056] Embodiment 1:

[0057] A method for batch automatic design of non-axisymmetric end walls of axial flow turbines is provided. The method is to construct a non-axisymmetric end wall shape of a stator blade of an axial flow turbine. The blades in the turbine are evenly distributed in the circumferential direction, and the end wall shapes between adjacent circumferential blades are the same. The end wall between adjacent circumferential blades is designed as a cycle. The design process specifically includes the following steps:

[0058] Step 1: Use the arc lines of adjacent circumferential blades as the boundaries on both sides to determine the end wall surface range ( Figure 1 ).

[0059] Step 2: Based on the sine function, determine the circumferential shaping function (the shaping function direction is defined as Figure 2 , Figure 3 As shown in Figure 2, a circumferential shaping function under different frequency coefficients is proposed, and its formula is:

[0060]

[0061] Where α is the frequency coefficient; y0 is the starting point of the blade pitch, y n is the end point of the blade pitch.

[0062] Step 3: Express the circumferential modeling function in polar coordinates ( Figure 4 ), the sine function is used to realize the convexity and concavity, so that it is consistent with the curvature structure of the real wheel hub. The formula is as follows:

[0063]

[0064] In the formula, α still represents the frequency coefficient, and the corresponding positions of the peak and valley points of the non-axisymmetric end wall surface along the axial direction can be adjusted by taking different values; n represents the number of blades; r d represents the blade root radius, θ is the polar angle of polar coordinates, and the curves under different frequency coefficients also intersect at one point, which is controlled by the phase π / n; this embodiment selects seven values ​​of α=0, 0.25, 0.5, 0.75, 1, 1.25, and 1.5 for design.

[0065] Step 4: The axial modeling function is applied to the end walls of the blade inlet and outlet flow channels, and finally it is determined that the hub end wall between the leading edge and the trailing edge of the blade is the axial modeling range of the non-axisymmetric end wall.

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

[0067] The "single-peak" shaping amplitude control function of the trigonometric function has the following form:

[0068]

[0069] Where: coefficient C is used to control the amplitude and is given by the designer. In this method, the value of C is 1; 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;

[0070] Step 6: The end wall modeling design method based on Bezier curve is used as the axial function. The method uses the selected n control points to construct the axial function. Considering the relevant properties of the Bezier curve, the axial modeling function h in the method is BCPM A fourth-order Bezier curve consisting of five control points is selected as follows:

[0071]

[0072] Where: P i represents the i-th control point (z i ,h i ), z i is the coordinate of the i-th control point on the z-axis, h i is the height of the i-th control point; B i,4 (t) represents the quartic Bernstein polynomial, which is defined as:

[0073]

[0074] Five control points P i (i=0,1,…,4) are evenly 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 change along the radial direction. Its height h i The value of also determines the degree of convexity and concavity of the non-axisymmetric end wall;

[0075] Step 7: Give the integrated axial modeling function, which is as follows:

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

[0077] Where: C h Indicates the amplitude coefficient. In this embodiment, C is selected h =0, 1%, 2%, 3%, 4%, 5% six values ​​are designed. B represents the blade height; i represents the modeling function of various axial modeling schemes after unitization, i = TFPM, BCPM, z LE Indicates the axial position of the leading edge of the blade; z TE represents the axial position of the blade trailing edge; h(z) is the h in step 5 TFPM or h in step 6 BCPM For a selected blade channel, the amplitude coefficient C h To determine the peak and valley values ​​of the convex and concave surfaces on the non-axisymmetric end wall; the amplitude coefficient C h The most important role is to determine the height of the peak and the valley, by increasing the amplitude coefficient C h The value of makes the concave-convex degree of the non-axisymmetric end wall change more obviously, and the amplitude coefficient C h Controls the radial variation of the non-axisymmetric end wall.

[0078] Step 8: Using MATLAB programming, the non-axisymmetric end wall surface is accurately drawn by multiplying the orthogonal circumferential modeling function with the axial modeling function, and then the relevant data is extracted to generate the "trigonometric function method" and "Bezier curve method" three-dimensional surface ( Figure 7 , Figure 8 As shown), according to different α, C h A total of 84 end wall shapes were generated by using the axial modeling function type and exported as point cloud files.

[0079] Step 9: In the 3D modeling software SolidWorks, use the point cloud file to generate the surface. 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, it is imported into SolidWorks to generate two non-axisymmetric end walls of the flow channel. In order to reduce the subsequent calculation amount, the subsequent numerical calculation uses a single flow channel numerical simulation. Therefore, the surface is edited to leave only one non-axisymmetric end wall of the flow channel to adjust the shape and properties of the surface to meet the design requirements. The final shape is as follows Fig. 9 , Fig.10 shown.

[0080] Step 10: To ensure the accuracy of the blade shape, the original turbine blade shape CAD file is directly imported into the 3D modeling software to draw the stationary and moving blades. Then, a series of operation commands such as splitting, combining, stretching, cutting, and arraying are used to complete the 3D modeling of the turbine ( Fig.11 , Fig.12 shown).

[0081] The model generated in step 9 is the end wall surface model. To explore the impact of the end wall surface on the turbine performance, it is necessary to build an entire turbine model with a non-axisymmetric end wall. Therefore, it is necessary to add turbine blades on the basis of the end wall surface to form a complete turbine model. The turbine blade CAD file imported in step 10 is the blade of the original turbine model before the non-axisymmetric end wall modeling is performed in this method.

[0082] Step 11: Import the complete turbine 3D model into the CFD software for meshing and numerical simulation calculations to test the turbine performance and internal flow field changes under the designed non-axisymmetric end wall shape.

[0083] By comparison, the non-axisymmetric end wall shape constructed by this method effectively improves the flow separation between blades, reduces vortex shedding, reduces pressure loss, and improves turbine performance and efficiency. The turbine with the best design has a total static isentropic efficiency η compared with the original turbine. ts The increase is nearly 0.5%, and the calculation formula is: In the formula, ΔW x and ΔW maxThey represent actual specific work and ideal specific work respectively; h 01 and h 02 represent the actual total enthalpy at the channel inlet and outlet respectively; h 2s Indicates the actual static enthalpy at the channel outlet; the total pressure loss coefficient is relatively reduced by 9.85% ( Fig.13 ), and its calculation formula is: In the formula, p0 and p 01 Respectively represent the actual total pressure at the channel inlet and outlet; p 1s Indicates the actual static pressure at the channel outlet. In addition, the design time spent by this method is reduced by about 30% compared with the traditional method, while reducing the design difficulty, and can well realize the batch automatic design of the non-axisymmetric end wall of the axial flow turbine.

[0084] Example 2

[0085] A system for automatic batch design of non-axisymmetric end walls of axial flow turbines has a program stored thereon, which, when executed by a processor, implements the steps in the method for automatic batch design of non-axisymmetric end walls of axial flow turbines as described in Example 1.

[0086] Through the above embodiments, the purpose of the present invention is fully and effectively achieved. Those skilled in the art can understand that the present invention includes but is not limited to the contents described in the drawings and the above specific embodiments. Although the present invention has been described with respect to the most practical and preferred embodiments currently considered, it should be understood that the present invention is not limited to the disclosed embodiments, and any modification that does not deviate from the functional and structural principles of the present invention will be included in the scope of the claims.

Claims

1. A method for batch automatic design of turbine end wall molding, characterized in that: The moving blades and the stationary blades in the axial flow turbine are alternately arranged along the axial direction of the end wall and are evenly distributed circumferentially, and the end wall shapes between adjacent circumferential blades are the same; the method is designed with the end wall between adjacent circumferential blades as a cycle, and finally forms an end wall shape with the characteristics of a convex end wall near the pressure surface and a concave end wall near the suction surface, including the following steps: Step 1: Use the mid-arcs of adjacent circumferential blades as the boundaries on both sides to determine the range of the end wall surface; Step 2: Based on the sine function, determine the circumferential modeling function and propose the circumferential modeling function under different frequency coefficients. The formula is: Where α is the frequency coefficient; y0 is the starting point of the blade pitch, y n is the end point of the blade cascade pitch; Step 3: Express the circumferential modeling function in polar coordinates, and use the sine function to achieve convexity and concavity. The formula is as follows: In the formula, α still represents the frequency coefficient, and the corresponding positions of the peak point and the valley point of the non-axisymmetric end wall surface along the axial direction are adjusted by taking different values; n represents the number of blades; r d represents the blade root radius, and θ is the polar angle of polar coordinates; the curves under different frequency coefficients intersect at one point, which is controlled by the phase π / n; when the frequency coefficient α=1, the blade cascade pitch is just one period of the sine function, and the pressure side root of the blade is all on the convex end wall, and the suction side of the blade is also all on the concave end wall; the value of the frequency coefficient is changed, the larger α is, the farther the convex position is from the pressure surface, and the farther the concave position is from the suction surface, and the movement of the concave position and the convex position in the circumferential direction is achieved by controlling the value of α; Step 4: The axial modeling function is applied to the end wall of the blade inlet and outlet flow passages, and finally the hub end wall surface between the leading edge and the trailing edge of the blade is determined to be the axial modeling range of the non-axisymmetric end wall surface; Step 5: Propose a single-peak shaping amplitude control function of the trigonometric function along the axial direction, in the following form: Where: coefficient C is used to control the amplitude and is given by the designer; LE Indicates the axial position of the leading edge of the blade; z TE Indicates the axial position of the blade trailing edge; Step 6: The end wall modeling design method based on Bezier curve is used as the axial function. This method uses the selected n control points to construct the axial function; the axial modeling function h BCPM A fourth-order Bezier curve consisting of five control points is selected as follows: Where: P i represents the i-th control point (z i ,h i ), z i is the coordinate of the i-th control point on the z-axis, h i is the height of the i-th control point; B i,4 (t) represents the quartic Bernstein polynomial, which is defined as: Five control points P i (i=0,1,…,4) are evenly 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 changes along the radial direction. Its height h i The value of also determines the degree of convexity and concavity of the non-axisymmetric end wall; Step 7: Give the integrated axial modeling function, which is as follows: h i (z)=C h ·H B ·h(z),z LE ≤z≤z TE (6) Where: C h Represents the amplitude coefficient; H B represents the blade height; i represents the modeling function of various axial modeling schemes after unitization, i = TFPM, BCPM, z LE Indicates the axial position of the leading edge of the blade; z TE represents the axial position of the blade trailing edge; h(z) is the h in step 5 TFPM or h in step 6 BCPM , select a blade channel, according to the amplitude coefficient C h To determine the peak and valley values ​​of the convex and concave surfaces on the non-axisymmetric end wall; the amplitude coefficient C h The role is to determine the height of the peak and the valley, by increasing the amplitude coefficient C h The value of makes the concave-convex degree of the non-axisymmetric end wall change, and the amplitude coefficient C h Controls the radial variation of the non-axisymmetric end wall; Step 8: Using programming, draw the non-axisymmetric end wall surface by multiplying the orthogonal circumferential modeling function and the axial modeling function, and obtain the point cloud file of the three-dimensional surface using the trigonometric function method and the Bezier curve method; Step 9: In the 3D modeling software, use the point cloud file to generate a surface; adjust the shape and properties of the surface to meet the design requirements.

2. The method for batch automatic design of turbine end wall molding according to claim 1 is characterized in that: In step 8, different axial flow turbine models have different blade root radius, number of blades, leading edge axial position of blades and trailing edge axial position. For different axial flow turbine models, by adjusting r in formula (2) d , n, z in formula (3) and formula (6) LE With z TE , realizing batch design of axial flow turbines of various types and sizes.

3. The method for batch automatic design of turbine end wall molding according to claim 1 is characterized in that: In step 9, 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 and leave only the non-axisymmetric end wall of one flow channel to adjust the shape and properties of the surface to meet the design requirements.

4. The method for batch automatic design of turbine end wall molding according to claim 1 is characterized in that: The method also includes step 10, in which, on the basis of obtaining the non-axisymmetric end wall, the original CAD file of the turbine blade shape is imported into the 3D modeling software to draw the stationary blades and the moving blades, and then a series of operation commands such as splitting, combining, stretching, cutting and arraying are used to complete the 3D modeling of the entire turbine.

5. A batch automatic design system for turbine end wall molding, characterized in that: A program is stored thereon, and when the program is executed by a processor, the steps in the method for batch automatic design of turbine end wall molding as claimed in any one of claims 1 to 4 are implemented.

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