Air film hole arrangement method along temperature gradient based on superellipse theory

Abstract

The present invention relates to a method for arranging film holes along a temperature gradient based on hyperellipse theory, comprising the following steps: establishing a hyperellipse curve; establishing a relationship between conjugate temperature lines and temperature difference proportional factors; establishing a hyperellipse curve relating conjugate temperature lines and film hole positions; listing conjugate temperature gradient differences; establishing a film hole optimization arrangement model relating the number of film hole rows and conjugate temperature gradient lines; determining the current film hole position coordinates; determining a film hole position coordinate map; calibrating the actual physical coordinates of each film hole on the turbine end wall; and finally outputting a film hole arrangement plan for the current turbine end wall. The present invention achieves both theoretical and universal applicability of the arrangement strategy; is applicable to a variety of film hole types and all hot-end components with temperature differences; and achieves quantifiable guidance for the arrangement criteria of film holes in hot-end components.

Description

Technical Field

[0001] The present invention relates to the technical field of turbine cooling, and in particular to a method for arranging air film holes along a temperature gradient based on superellipse theory. Background Art

[0002] The film cooling effect on the turbine endwall surface is the result of the interaction of multiple exhaust film holes. The cooling jets within the same exhaust film hole and between different exhaust film holes influence each other, and the cooling effects are coupled and superimposed. Regarding the arrangement of film holes in the endwall area, after Gabriel Lame first proposed the hyperelliptic curve, hyperelliptic theory has been widely applied in graphic design, traffic planning, industrial layout research, and other fields. For example, hyperelliptic curves are used to develop new tank shapes, hyperelliptic methods are used to design S-bend inlets and aircraft fuselage shapes, hyperelliptic curve cryptography is used to create public key cryptosystems, and hyperelliptic curves are used to design signatures and icons. Today, Apple's iOS operating system and Xiaomi's latest logo design both adopt a superelliptic shape.

[0003] For film cooling, Xie Gongnan et al. proposed superelliptical holes to improve adiabatic film efficiency without changing the cross-sectional area of ​​the basic cylindrical hole. On the end wall surface of conjugate heat transfer, the conjugate temperature lines are distributed in an arc-like pattern. Therefore, the conjugate temperature line position of the film hole array can be selected based on the superelliptical curve to control the end wall film cooling effect.

[0004] There are many theories about super ellipse in the existing technology, but there is still a blank on how to arrange the air film holes on the turbine end wall. Instead, it is done purely based on experience and there is no fixed design principle for the air film holes.

[0005] Defects of the existing technology:

[0006] 1. Since the existing technology is based on the designer's experience, the temperature gradient line air film hole arrangement strategy has no theoretical basis;

[0007] 2. Although there are many studies on existing technologies, there is no theoretical basis and it is impossible to quantify the design standards, so it is impossible to put them into practical use, let alone promote their application. Summary of the Invention

[0008] In response to the above problems, the present invention provides a method for arranging air film holes along the temperature gradient based on the superellipse theory, with the aim of achieving the theoretical and universal applicability of the arrangement strategy; being applicable to a variety of air film hole types and all hot end components with temperature differences; and achieving the quantification of the guidelines for the arrangement of air film holes in hot end components.

[0009] In order to solve the above problems, the technical solution provided by the present invention is:

[0010] A method for arranging air film holes along a temperature gradient based on superellipse theory includes the following steps:

[0011] S100. Establish a superelliptic curve;

[0012] S200. Establishing a relationship between the conjugate temperature line and the temperature difference proportional factor;

[0013] S300. Establishing a superelliptic curve about the conjugate temperature line and the air film hole position;

[0014] S400. List the conjugate temperature gradient difference;

[0015] S500. Establishing an optimized arrangement model of film holes with respect to the number of film holes and the conjugate temperature gradient line; the conjugate temperature gradient line is composed of a plurality of the conjugate temperature lines arranged in the order of the conjugate temperature gradient difference;

[0016] S600. Determine the current position coordinates of the air film holes according to the air film hole optimization arrangement model established in S500;

[0017] S700. Determine the air film hole position coordinate diagram by the superelliptic curve established in S300;

[0018] S800. Using the film hole position coordinate diagram in S700, calibrate the actual physical coordinates of each film hole on the turbine end wall; finally output the film hole arrangement plan for the current turbine end wall; the film hole arrangement plan includes the actual physical coordinates.

[0019] Preferably, the hyperelliptic curve in S100 is expressed as follows:

[0020]

[0021] Wherein: a is the length of the major semi-axis of the superellipse; b is the length of the minor semi-axis of the superellipse; x is the row number of the air film holes; y is the value of x corresponding to the conjugate temperature line; θ is used to characterize the auxiliary angle in the coordinate system; n is the number of terms in the general expression; m is the number of terms in the general expression.

[0022] Preferably, the relationship between the conjugate temperature line and the temperature difference proportional factor in S200 is expressed as follows:

[0023] y=T min +ΔT·κ

[0024] Where: T min is the lowest conjugate temperature in the blade channel on the turbine end wall surface; ΔT is the conjugate temperature gradient difference, which is used to characterize the spacing between two adjacent rows of film holes; κ is the temperature difference proportional factor.

[0025] Preferably, the superelliptic curve about the conjugate temperature line and the air film hole position in S300 is expressed as follows:

[0026]

[0027] The hyperelliptic curve of the conjugate temperature line and the air film hole position is a hyperelliptic curve about (x, κ).

[0028] Preferably, the conjugate temperature gradient difference in S400 is expressed as follows:

[0029]

[0030] Where: T max is the maximum conjugate temperature in the blade channel on the turbine end wall surface; i is a counter for the number of rows of film holes.

[0031] Preferably, the air film hole optimization arrangement model in S500 is expressed as follows:

[0032]

[0033] Among them: when n>2, the graph of the hyperelliptic curve is a hyperellipse; when n=2, the graph of the hyperelliptic curve is an ellipse; when 1<n<2, the graph of the hyperelliptic curve is a subellipse; when n=1, the graph of the hyperelliptic curve is a rhombus; when n<1, the graph of the hyperelliptic curve is a star.

[0034] Preferably, S600 specifically includes the following steps:

[0035] S610. The temperature of the blade leading edge stagnation point close to the blade suction surface in the cascade channel on the turbine end wall surface is taken as the maximum temperature; then the first conjugate temperature line is fixed to this maximum temperature;

[0036] S620. The temperature at the middle position of the blade suction surface is taken as the minimum temperature; and then the last conjugate temperature line is fixed as the minimum temperature;

[0037] S630. Calculate the conjugate temperature gradient difference;

[0038] S640. Take different values ​​for a, b, n, and m and combine them to obtain specific expressions of the Hole pattern on the (x, y) hyperelliptic curve under different combinations.

[0039] Preferably, the air film hole position coordinate diagram in S700 is a set of the position coordinates of the air film holes corresponding to the arrangement of the air film holes on the shape of the superelliptical curve of the hole pattern when the air film holes take different values ​​for different combinations.

[0040] Preferably, in S800, the actual physical coordinates of each film hole are calibrated by mapping the hole pattern under different values ​​of n onto the turbine end wall.

[0041] Preferably, the film hole arrangement scheme in S800 further includes the angle between the axis of each film hole and the section of the surface of the turbine end wall where the film hole is located, the number of film holes per exhaust, and the diameter of each film hole.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] 1. The present invention introduces superellipse theory into the layout strategy of air film holes along the conjugate temperature gradient and further optimizes it, thus achieving the theoretical and universal applicability of the layout strategy;

[0044] 2. Since the air film hole optimization arrangement criterion of the present invention is based on the superellipse theory, it can be applied to various air film hole types and all hot end components with temperature differences;

[0045] 3. Since the air film hole optimization arrangement criterion of the present invention is also combined with the conjugate heat transfer calculation method to evaluate the optimization arrangement criterion, it ultimately achieves the quantification of the arrangement criterion guiding the air film holes in the hot end components, laying a solid foundation for the subsequent automatic generation of design solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic flow chart of an arrangement method according to a specific embodiment of the present invention;

[0047] Figure 2 Schematic diagram of the position distribution of air film holes with different layouts on a superelliptical curve according to a specific embodiment of the present invention;

[0048] Figure 3a A schematic diagram of Holepattern 1 showing the spatial distribution of air film holes with different layouts on the end wall surface according to a specific embodiment of the present invention;

[0049] Figure 3b A schematic diagram of Holepattern II showing the spatial distribution of air film holes with different layouts on the end wall surface according to a specific embodiment of the present invention;

[0050] Figure 3c A schematic diagram of Holepattern III showing the spatial distribution of air film holes with different layouts on the end wall surface according to a specific embodiment of the present invention;

[0051] Figure 3d A schematic diagram of Holepattern IV showing the spatial distribution of air film holes with different layouts on the end wall surface according to a specific embodiment of the present invention;

[0052] Figure 3e Schematic diagram of Holepattern V showing the spatial distribution of air film holes with different layouts on the end wall surface according to a specific embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0054] It should be noted that the present invention combines the applicant's previous extensive experiments and calculations on the specific structure of gas turbine blades and end walls and the number of film holes, comprehensively considers and optimizes the layout of film holes on the surface of turbine components, and proposes a turbine guide vane and end wall film hole arrangement strategy along the conjugate temperature gradient to obtain a more uniform and efficient cooling film distribution, while minimizing the temperature gradient inside the hot end components to reduce thermal stress, thereby improving the film cooling efficiency at the lowest cost.

[0055] like Figure 1 As shown, a method for arranging air film holes along a temperature gradient based on superellipse theory includes the following steps:

[0056] S100. Establish a hyperelliptic curve.

[0057] It should be noted that the superellipse is a multi-parameter curve model, and changing the parameters will result in a configuration that is better than the circular structure.

[0058] Currently, super-elliptical structures have attracted the attention of researchers in the fields of mechanics and thermal research, but there is no actual application of super-elliptical structures on turbine blades. The present invention is the first breakthrough and practically applicable technical solution in this field.

[0059] In this specific embodiment, the hyperelliptic curve in S100 is expressed as follows:

[0060]

[0061] Where: a is the length of the major semi-axis of the superellipse; b is the length of the minor semi-axis of the superellipse; x is the row number of the air film holes; y is the value of the conjugate temperature line corresponding to x; θ is used to represent the auxiliary angle in the coordinate system; n is the number of terms in the general expression; m is the number of terms in the general expression.

[0062] S200. Establish a relationship between the conjugate temperature line and the temperature difference proportional factor.

[0063] In this specific embodiment, the relationship between the conjugate temperature line and the temperature difference proportional factor in S200 is expressed as follows:

[0064] y=T min +ΔT·κ

[0065] Where: T min is the lowest conjugate temperature in the blade channel on the turbine end wall surface; ΔT is the conjugate temperature gradient difference, which is used to characterize the spacing between two adjacent rows of film holes; κ is the temperature difference proportional factor.

[0066] It should be noted that, through a large number of experiments and calculations conducted by the applicant in the early stage, the following conclusion can be drawn: the air film holes arranged along the temperature gradient line can achieve a better cooling effect than the air film holes arranged according to the flow direction.

[0067] Therefore, the technical solution of the present invention is to combine the superellipse theory with the temperature gradient line air film hole arrangement strategy on the basis of the above research results, thereby solving the problem that the temperature gradient line air film hole arrangement strategy in the prior art has no theoretical basis; this problem of the prior art has led to the fact that although there are many studies in this field, it cannot be put into practical use.

[0068] In order to better demonstrate the practical effects and principles of the present invention, this specific embodiment assigns numerical values ​​to specific parameters for reference.

[0069] In this specific embodiment, x=1, 2, 3, 4, representing the first isotherm Row1, the second isotherm Row2, the third isotherm Row3, and the fourth isotherm Row4, respectively; accordingly, the relationship between the conjugate temperature lines and the temperature difference proportional factor is established.

[0070] It should be noted that T min It is the lowest conjugate temperature in the blade channel on the turbine end wall surface, generally located in the middle area of ​​the suction surface.

[0071] S300. Establish a superelliptic curve about the conjugate temperature line and the air film hole position.

[0072] In this specific embodiment, the superelliptic curve regarding the conjugate temperature line and the air film hole position in S300 is expressed as follows:

[0073]

[0074] The hyperelliptic curve of the conjugate temperature line and the air film hole position is the hyperelliptic curve about (x,κ).

[0075] S400. List the conjugate temperature gradient differences.

[0076] In this specific embodiment, the conjugate temperature gradient difference in S400 is expressed as follows:

[0077]

[0078] Where: T max is the maximum conjugate temperature in the blade channel on the turbine end wall surface; i is a counter for the number of rows of film holes.

[0079] S500. Establishing an optimal arrangement model of air film holes with respect to the number of air film hole rows and conjugate temperature gradient lines; the conjugate temperature gradient lines are composed of a plurality of conjugate temperature lines arranged in order of conjugate temperature gradient differences.

[0080] In this specific embodiment, the air film hole optimization arrangement model in S500 is expressed as follows:

[0081]

[0082] Among them: when n>2, the graph of the hyperelliptic curve is a hyperellipse; when n=2, the graph of the hyperelliptic curve is an ellipse; when 1<n<2, the graph of the hyperelliptic curve is a subellipse; when n=1, the graph of the hyperelliptic curve is a rhombus; when n<1, the graph of the hyperelliptic curve is a star.

[0083] It should be noted that the above formula is the optimal arrangement criterion for film holes based on the superellipse theory, which is obtained by combining the above formulas with respect to the number of film hole rows and the conjugate temperature gradient line.

[0084] It should be noted that the values ​​of n and m affect the shape of the hyperelliptic curve and greatly influence the final film cooling effect.

[0085] S600. Determine the current position coordinates of the air film holes according to the air film hole optimization arrangement model established in S500.

[0086] In this specific embodiment, S600 specifically includes the following steps:

[0087] S610. Take the temperature of the blade leading edge stagnation point close to the blade suction surface in the blade cascade channel on the turbine end wall surface as the maximum temperature; then fix the first conjugate temperature line to this maximum temperature.

[0088] S620. Take the temperature at the middle position of the blade suction surface as the lowest temperature; then fix the last conjugate temperature line as this lowest temperature.

[0089] S630. Calculate the conjugate temperature gradient difference.

[0090] S640. Take different values ​​for a, b, n, and m and combine them to obtain specific expressions of the Hole pattern on the (x, y) hyperelliptic curve under different combinations.

[0091] In this specific embodiment, the temperature at the leading edge of the blade near the suction surface in the cascade channel is the highest, which is 1540K, and the temperature in the middle of the blade suction surface is the lowest, which is 1510K. In this specific embodiment, a total of four exhaust film holes are arranged; therefore, it can be obtained:

[0092] ΔT = (1540-1510) / 4 = 7.5

[0093] Therefore, formula (xxx) can be further expressed as follows:

[0094] y=1510+7.5κ

[0095] Then, in this specific embodiment, the first conjugate temperature line is fixed to 1540K, and the fourth conjugate temperature line, that is, the last conjugate temperature line, is fixed to 1517.5K; therefore, the first isotherm x=1 corresponds to the point (4, 1540), and the fourth isotherm x=4 corresponds to the point (1, 1517.5).

[0096] Furthermore, in order to simplify the problem, this specific embodiment adopts a standard hyperelliptic curve. Therefore, the following conditions are given in this specific embodiment:

[0097]

[0098] Therefore, the formula (yyy) can be simplified as follows:

[0099]

[0100] then:

[0101] Let n = 1, a = 5, and the hyperelliptic curve of Hole pattern I with respect to (x, y) is expressed as follows:

[0102]

[0103] Let n = 2, a = 4.1, and the hyperelliptic curve of Hole pattern II about (x, y) is expressed as follows:

[0104]

[0105] Let n = 3, a = 4, and the hyperelliptic curve of Hole pattern III about (x, y) is expressed as follows:

[0106]

[0107] Let n = 0.5, a = 9, and the hyperelliptic curve of Hole pattern IV about (x, y) is expressed as follows:

[0108]

[0109] Let n = 0.25, a = 33.9, and the hyperelliptic curve of Hole pattern V about (x, y) is expressed as follows:

[0110]

[0111] S700. Determine the air film hole position coordinate diagram using the superelliptic curve established in S300.

[0112] In this specific embodiment, the air film hole position coordinate diagram in S700 is a set of air film hole position coordinates corresponding to the arrangement of the air film holes on the shape of the superelliptical curve of the hole pattern when different values ​​of a, b, n, and m are combined.

[0113] like Figure 2 As shown in FIG. 1 , the position distribution of the air film holes of different layouts on the superelliptical curve in this specific embodiment is shown. Specifically:

[0114] Hole pattern I has n=1, and the superellipse shape is a "diamond".

[0115] Hole pattern II has n=2, and the superelliptical shape is "ellipse".

[0116] For Hole pattern III, n>2, the superellipse shape is a rectangle with rounded corners, called a "superellipse", and the vertex curvature is 0.

[0117] For Hole patterns IV and V, 0<n<1, and the superellipse has a four-pointed star shape with four sides concave inward, called a "star shape", and the curvature of the vertex approaches infinity.

[0118] S800. Using the film hole position coordinate diagram in S700, calibrate the actual physical coordinates of each film hole on the turbine end wall; finally output the film hole arrangement plan for the current turbine end wall; the film hole arrangement plan includes the actual physical coordinates.

[0119] In this specific embodiment, in S800 , the actual physical coordinates of each film hole are calibrated by mapping the hole patterns under different values ​​of n onto the turbine end wall.

[0120] In this specific embodiment, the film hole arrangement scheme in S800 also includes the angle between the axis of each film hole and the cross-section of the surface of the turbine end wall where the film hole is located, the number of film holes per exhaust, and the diameter of each film hole.

[0121] In this specific embodiment, the air film hole positions corresponding to each arrangement are shown in Table 1:

[0122] Table 1. Comparison table of air film hole layout, flow direction and temperature

[0123]

[0124] like Figure 3a to Figure 3e The figure shows the spatial distribution of different layouts on the end wall surface, corresponding to Hole pattern I to Hole pattern V. Specifically:

[0125] When n=1, the conjugate temperature gradient difference (ΔT) between the rows of air film holes in Hole pattern I is 7.5 K, and the arrangement of the air film holes adopts a strategy of isothermal gradient.

[0126] When n>1, the ΔT between the rows of Hole pattern II air film holes is 2.5K, 7.5K, and 12.5K. The ΔT between the rows of Hole pattern III air film holes is 1.3K, 3.7K, and 12.5K. The arrangement of the air film holes is dense in the front and sparse in the back.

[0127] When n < 1, the ΔT between the rows of Hole pattern IV air film holes is 11 K, 7.0 K, and 4.5 K. The ΔT between the rows of Hole pattern V air film holes is 14.0 K, 5.0 K, and 3.5 K. The arrangement of the air film holes is sparse in the front and dense in the back.

[0128] The film holes are classic cylindrical. The hole axis forms a 35° angle with the end wall surface. The hole diameter is D = 1 mm. The number of film holes per exhaust is 17, 12, 10, and 8, respectively, for a total of 47 film holes.

[0129] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0130] The above description of the disclosed embodiments is intended to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present disclosure is not limited to the embodiments presented herein but is intended to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0131] The foregoing description includes examples of one or more embodiments. Of course, it is not possible to describe all possible combinations of components or methods for the purposes of describing the above embodiments, but one of ordinary skill in the art will recognize that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to encompass all such changes, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including," as explained in terms of "including," used as a transitional word in the claims. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or."

[0132] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for arranging air film holes along a temperature gradient based on superellipse theory, characterized by: The following steps are involved: S100. Establish a superelliptic curve; S200. Establishing a relationship between the conjugate temperature line and the temperature difference proportional factor; S300. Establishing a superelliptic curve about the conjugate temperature line and the air film hole position; S400. List the conjugate temperature gradient difference; S500. Establishing an optimized arrangement model of film holes with respect to the number of film holes and the conjugate temperature gradient line; the conjugate temperature gradient line is composed of a plurality of the conjugate temperature lines arranged in the order of the conjugate temperature gradient difference; S600. Determine the current position coordinates of the air film holes according to the air film hole optimization arrangement model established in S500; S700. Determine the air film hole position coordinate diagram by the superelliptic curve established in S300; S800. Using the film hole position coordinate map in S700, calibrate the actual physical coordinates of each film hole on the turbine end wall; and finally output a film hole arrangement plan for the current turbine end wall; the film hole arrangement plan includes the actual physical coordinates; The hyperelliptic curve in S100 is expressed as follows: Where: a is the length of the major semi-axis of the superellipse; b is the length of the minor semi-axis of the superellipse; x is the row number of the air film holes; y is the value of x corresponding to the conjugate temperature line; θ is used to represent the auxiliary angle in the coordinate system; n is the number of terms in the general expression; m is the number of terms in the general expression; The relationship between the conjugate temperature line and the temperature difference proportional factor in S200 is expressed as follows: y=T min +ΔT·k Where: T min is the lowest conjugate temperature in the blade channel on the turbine end wall surface; ΔT is the conjugate temperature gradient difference, which is used to characterize the spacing between two adjacent rows of film holes; κ is the temperature difference proportional factor.

2. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 1, characterized in that: In S300, the superelliptic curve regarding the conjugate temperature line and the air film hole position is expressed as follows: The hyperelliptic curve of the conjugate temperature line and the air film hole position is a hyperelliptic curve about (x, κ).

3. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 2, characterized in that: The conjugate temperature gradient difference in S400 is expressed as follows: Where: T max is the maximum conjugate temperature in the blade channel on the turbine end wall surface; i is a counter for the number of rows of film holes.

4. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 3, characterized in that: The air film hole optimization arrangement model in S500 is expressed as follows: Among them: when n>2, the graph of the hyperelliptic curve is a hyperellipse; when n=2, the graph of the hyperelliptic curve is an ellipse; when 1<n<2, the graph of the hyperelliptic curve is a subellipse; when n=1, the graph of the hyperelliptic curve is a rhombus; when n<1, the graph of the hyperelliptic curve is a star.

5. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 4, characterized in that: S600 specifically includes the following steps: S610. The temperature of the blade leading edge stagnation point close to the blade suction surface in the cascade channel on the turbine end wall surface is taken as the maximum temperature; then the first conjugate temperature line is fixed to this maximum temperature; S620. The temperature at the middle position of the blade suction surface is taken as the minimum temperature; and then the last conjugate temperature line is fixed as the minimum temperature; S630. Calculate the conjugate temperature gradient difference; S640. Take different values ​​for a, b, n, and m and combine them to obtain specific expressions of the Hole pattern on the (x, y) hyperelliptic curve under different combinations.

6. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 5, characterized in that: The air film hole position coordinate diagram in S700 is a set of the position coordinates of the air film holes corresponding to the arrangement of the air film holes on the shape of the superelliptical curve of the hole pattern when different values ​​of a, b, n, and m are combined.

7. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 6, characterized in that: In S800, the actual physical coordinates of each film hole are calibrated by mapping the hole patterns under different n values ​​onto the turbine end wall.

8. The method for arranging air film holes along a temperature gradient based on superellipse theory according to claim 7, characterized in that: The film hole arrangement scheme described in S800 also includes the angle between the axis of each film hole and the tangent plane of the surface of the turbine end wall where the film hole is located, the number of film holes per exhaust, and the diameter of each film hole.

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