A design method for axial flow turbine blades based on three-dimensional Smith diagram

Abstract

The present invention discloses a method for designing axial turbine blades based on a three-dimensional Smith diagram, comprising the following steps: step 1, performing one-dimensional design for a given working condition to obtain Smith diagrams under different reaction degrees, taking the reaction degree as the third axis, and expanding the original two-dimensional Smith diagram to a three-dimensional space to obtain a three-dimensional Smith diagram; step 2, using the radial reaction degree distribution law of the blade, using the three-dimensional Smith diagram to guide the design of a number of two-dimensional blade profiles with corresponding reaction degrees, and stacking these two-dimensional blade profiles along the center of gravity to obtain a three-dimensional blade profile; step 3, performing three-dimensional numerical simulation on the obtained three-dimensional blade profile, repeating step 2 until the radial reaction degree distribution meets the design requirements, and finally obtaining a turbine blade. According to the present invention, some limitations of the traditional Smith diagram (only applicable to working conditions with a reaction degree of about 0.5) are eliminated, and it is more accurate than the traditional two-dimensional Smith diagram, has a wider range of application, and is repeatedly corrected through three-dimensional numerical simulation, so that the finally obtained three-dimensional blade can obtain better aerodynamic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of power machinery and engineering, and in particular to a design method for axial flow turbine blades based on a three-dimensional Smith diagram. Background Art

[0002] As a prime mover, turbines can convert the energy contained in fluid media into mechanical energy. They are widely used in both aerospace and industrial production. The performance of turbines directly affects the stability of the entire working system. There are many factors that affect the internal flow of turbines, such as the three-dimensional shape of blades, the matching between dynamic and static parts, the thermal properties of the working fluid, the impeller speed and operating status, etc. Among many factors, the three-dimensional shape of blades is one of the most important influencing factors. As turbines continue to develop in the direction of high power, high load, and high flow, the requirements for blades, as the core components of turbines, are getting higher and higher in terms of aerodynamic performance, cooling performance, and material performance, which brings challenges to the flow design of high-performance heavy-duty gas turbines.

[0003] The main purpose of one-dimensional turbine design is to determine the shape of the velocity triangle by setting the airflow angle or selecting three dimensionless parameters: flow coefficient, load coefficient, and reaction. At present, the most widely used method in one-dimensional design is the "Smith diagram", which was proposed by Smith in 1965 after summarizing the experimental data of 70 aviation gas turbines. Designers can quickly evaluate the relationship between the flow coefficient, load coefficient and total efficiency through the Smith diagram, which greatly improves the design efficiency. However, the traditional Smith diagram also has certain limitations, such as being only applicable to working conditions with a reaction degree of about 0.5, and not considering the influence of parameters such as Reynolds number, aspect ratio, and blade tip clearance. Summary of the invention

[0004] In view of the shortcomings of the prior art, the purpose of the present invention is to provide an axial flow turbine blade design method based on a three-dimensional Smith diagram, which eliminates some limitations of the traditional Smith diagram (only applicable to working conditions with a reaction degree of about 0.5), is more accurate than the traditional two-dimensional Smith diagram, has a wider range of applications, and can obtain better aerodynamic performance through repeated corrections of three-dimensional numerical simulation. In order to achieve the above-mentioned purpose and other advantages according to the present invention, a method for designing axial flow turbine blades based on a three-dimensional Smith diagram is provided, comprising the following steps:

[0005] S1. Input design parameters;

[0006] S2, perform one-dimensional design for a given working condition to obtain a three-dimensional Smith diagram;

[0007] S3, using the three-dimensional Smith diagram to obtain the two-dimensional blade shape, and obtaining the three-dimensional blade shape through the two-dimensional blade shape;

[0008] S4. Perform three-dimensional numerical simulation on the three-dimensional blade profile in step S3 to obtain a new radial reaction degree distribution law, repeat S3 until the radial reaction degree distribution meets the design requirements, and finally obtain the turbine blade.

[0009] Preferably, in step S2, the one-dimensional design is used to obtain Smith diagrams under different reaction degrees, and the reaction degree is used as the third axis to expand the original two-dimensional Smith diagram to three-dimensional space to obtain a three-dimensional Smith diagram.

[0010] Preferably, in step S3, the radial reaction degree distribution law of the blade is utilized, and a three-dimensional Smith diagram is used to guide the design of a number of two-dimensional blade profiles with corresponding reaction degrees, and these two-dimensional blade profiles are stacked along the center of gravity to obtain a three-dimensional blade profile.

[0011] Preferably, performing one-dimensional design for a given working condition to obtain Smith diagrams under different reaction degrees comprises the following steps:

[0012] S21, given number of stages N, flow coefficient, load coefficient, degree of reaction, axial speed ratio, ratio of inlet speed c1 to circumferential speed u;

[0013] S22, through the formula:

[0014]

[0015]

[0016]

[0017] The angle values ​​in the velocity triangle are derived, including the absolute air inlet angle α2 of the moving blade, the absolute air outlet angle α3 of the moving blade, the relative air inlet angle β2 of the moving blade, and the relative air outlet angle β3 of the moving blade.

[0018] Preferably, in step S3, two-dimensional blade profiles with different reaction degrees are obtained according to a given radial reaction degree distribution and a three-dimensional Smith diagram, and these blade profiles are stacked along the center of gravity to obtain a three-dimensional blade.

[0019] Compared with the prior art, the present invention has the following beneficial effects: it eliminates some limitations of the traditional Smith diagram (only applicable to working conditions with a reaction degree of about 0.5), is more accurate than the traditional two-dimensional Smith diagram, has a wider range of applications, and through repeated corrections through three-dimensional numerical simulation, the final three-dimensional blade can obtain better aerodynamic performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a flow chart of an axial flow turbine blade design method based on a three-dimensional Smith diagram according to the present invention;

[0021] Figure 2 A conventional two-dimensional Smith diagram of an axial-flow turbine blade according to the axial-flow turbine blade design method based on a three-dimensional Smith diagram of the present invention;

[0022] Figure 3 A schematic diagram of a one-dimensional design process of an axial-flow turbine blade according to the axial-flow turbine blade design method based on a three-dimensional Smith diagram of the present invention;

[0023] Figure 4 A schematic diagram of a three-dimensional Smith diagram of an axial-flow turbine blade according to the axial-flow turbine blade design method based on the three-dimensional Smith diagram of the present invention;

[0024] Figure 5 A schematic diagram of radial reaction distribution of an axial flow turbine blade design method based on a three-dimensional Smith diagram according to the present invention;

[0025] Figure 6 A schematic diagram of a two-dimensional blade profile of an axial flow turbine blade design method based on a three-dimensional Smith diagram according to the present invention;

[0026] Figure 7 It is a schematic diagram of a three-dimensional blade profile of an axial flow turbine blade design method based on a three-dimensional Smith diagram according to the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Reference Figure 1-7 , an axial flow turbine blade design method based on a three-dimensional Smith diagram, comprising the following steps: S1, inputting design parameters;

[0029] S2, perform one-dimensional design for a given working condition to obtain a three-dimensional Smith diagram;

[0030] S3, using the three-dimensional Smith diagram to obtain the two-dimensional blade shape, and obtaining the three-dimensional blade shape through the two-dimensional blade shape;

[0031] S4. Perform three-dimensional numerical simulation on the three-dimensional blade profile in step S3 to obtain a new radial reaction degree distribution law, repeat S3 until the radial reaction degree distribution meets the design requirements, and finally obtain the turbine blade.

[0032] Eliminate some limitations of the Smith diagram (the range is about 0.5 of reaction degree), use the reaction degree as the third axis, expand the original two-dimensional Smith diagram to three-dimensional space, and obtain a three-dimensional Smith diagram to guide the design of two-dimensional blades under different reaction degrees. Then use the radial reaction degree distribution law of the blade and use the three-dimensional Smith diagram to guide the design of several two-dimensional blades with corresponding reaction degrees. Stack these two-dimensional blades along the center of gravity to obtain a three-dimensional blade. Perform three-dimensional numerical simulation on the obtained three-dimensional blade to obtain a new radial reaction degree distribution law. Repeat the above steps until the radial reaction degree distribution meets the design requirements. Finally, a three-dimensional blade with better aerodynamic performance is obtained.

[0033] Furthermore, in step S2, the one-dimensional design is used to obtain Smith diagrams under different reaction degrees, and the reaction degree is used as the third axis to expand the original two-dimensional Smith diagram to three-dimensional space to obtain a three-dimensional Smith diagram.

[0034] Furthermore, in step S3, the radial reaction degree distribution law of the blade is utilized, and a three-dimensional Smith diagram is used to guide the design of a number of two-dimensional blade profiles with corresponding reaction degrees, and these two-dimensional blade profiles are stacked along the center of gravity to obtain a three-dimensional blade profile.

[0035] Furthermore, performing one-dimensional design for a given working condition to obtain Smith diagrams under different reaction degrees includes the following steps:

[0036] S21, given number of stages N, flow coefficient, load coefficient, degree of reaction, axial speed ratio, ratio of inlet speed c1 to circumferential speed u;

[0037] S22, through the formula:

[0038]

[0039]

[0040]

[0041] The angle values ​​in the velocity triangle are derived, including the absolute air inlet angle α2 of the moving blade, the absolute air outlet angle α3 of the moving blade, the relative air inlet angle β2 of the moving blade, and the relative air outlet angle β3 of the moving blade.

[0042] Furthermore, in step S3, according to the given radial reaction degree distribution and the three-dimensional Smith diagram, two-dimensional blade profiles with different reaction degrees are obtained, and these blade profiles are stacked along the center of gravity to obtain a three-dimensional blade.

[0043] Example 1

[0044] S1, first, perform a one-dimensional design and calculate the two-dimensional Smith diagram (such as Figure 2), the calculation process is as follows Figure 3 As shown, the reaction degree is used as the third axis, and the original two-dimensional Smith diagram is expanded to three-dimensional space to obtain a three-dimensional Smith diagram (as shown in Figure 4 ):

[0045] S1.1, according to the design conditions, we can know the turbine inlet total temperature T01, total pressure P01, outlet total pressure P0end, and flow rate G.

[0046] S1.2, then give the number of stages N and flow coefficient The load coefficient ψ, reaction degree Ω, axial speed ratio γ, and the ratio of the inlet speed c1 to the circumferential speed u χ can be used to derive the angle values ​​(α2, α3, β2, β3) in the speed triangle from the formula below.

[0047]

[0048]

[0049]

[0050]

[0051] S1.3, assuming the efficiency of the whole stage ηtt, the velocity triangle can be derived. At this time, the state of point 2 (stationary blade outlet) has not been determined (pressure is unknown). Assuming the pressure P2 at point 2 (stationary blade outlet), the total pressure loss coefficient (YN, YR) of the stationary and moving blades is determined based on the given geometric parameters of the stationary and moving blades (blade tip clearance, aspect ratio, installation angle, etc.). Then all points can be determined, and we get a new efficiency value ηtt′.

[0052] S1.4, compare the difference between the newly obtained efficiency ηtt′ and the originally assumed efficiency ηtt, and perform iterative calculation until the difference between the two meets the accuracy requirements. At this point, the single-stage turbine solution process has been completed.

[0053] S1.5, for multi-stage turbines, it is only necessary to repeat the single-stage calculation. It should be noted that multi-stage turbines have the problem of supercriticality, that is, each stage of the turbine may be supersonic, but for the entire stage, there can only be one critical flow. To address this problem, in the program, we assume that for supercritical conditions, the only place where supersonic occurs is the last stage of the moving blades. When actually running the program, first assume the total pressure at the outlet of the first stage moving blades, run the single-stage solution process, and determine whether it is supercritical. If it is supercritical, change the total pressure at the outlet of the first stage moving blades until there is no supercriticality in the first stage. If there is no supercriticality, continue to calculate the next stage. Repeat this process to calculate the first N-1 stages. For the last stage, since the total pressure at the outlet of the entire stage is given, if a supercritical situation occurs, the supercritical situation is only caused by changing the reaction degree to appear in the last stage of the moving blades.

[0054] S2, using the radial reaction distribution law of the blade ( Figure 5 ), using the three-dimensional Smith diagram to guide the design of several two-dimensional blade profiles with corresponding reaction degrees ( Figure 6 ), these two-dimensional blades are stacked along the center of gravity to obtain a three-dimensional blade ( Figure 7 );

[0055] S3, performing three-dimensional numerical simulation on the obtained three-dimensional blade profile to obtain a new radial reaction degree distribution law, repeating step 2 until the radial reaction degree distribution meets the design requirements, and finally obtaining the turbine blade.

[0056] The number of devices and processing scales described here are used to simplify the description of the present invention, and the application, modification and variation of the present invention will be obvious to those skilled in the art.

[0057] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and implementation modes. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for designing axial flow turbine blades based on a three-dimensional Smith diagram, characterized in that: The following steps are involved: S1. Input design parameters; S2. Perform one-dimensional design for a given working condition to obtain a three-dimensional Smith diagram. The one-dimensional design obtains Smith diagrams under different reaction degrees. The reaction degree is used as the third axis, and the original two-dimensional Smith diagram is expanded to three-dimensional space to obtain a three-dimensional Smith diagram. The one-dimensional design for a given working condition to obtain the Smith diagram under different reaction degrees includes the following steps: S21, given number of stages N, flow coefficient Load coefficient ψ, reaction degree Ω, axial speed ratio γ, ratio of inlet speed c1 to circumferential speed u χ; S22, through the formula: The angle values ​​in the velocity triangle are derived, including the absolute inlet angle of the moving blade α2, the absolute outlet angle of the moving blade α3, the relative inlet angle of the moving blade β2, and the relative outlet angle of the moving blade β3; S3, using the three-dimensional Smith diagram to obtain the two-dimensional blade shape, and obtaining the three-dimensional blade shape through the two-dimensional blade shape; S4. Perform three-dimensional numerical simulation on the three-dimensional blade profile in step S3 to obtain a new radial reaction degree distribution law, repeat S3 until the radial reaction degree distribution meets the design requirements, and finally obtain the turbine blade.

2. The axial flow turbine blade design method based on three-dimensional Smith diagram according to claim 1, characterized in that: In step S3, the radial reaction degree distribution law of the blade is utilized, and a three-dimensional Smith diagram is used to guide the design of a number of two-dimensional blade profiles with corresponding reaction degrees, and these two-dimensional blade profiles are stacked along the center of gravity to obtain a three-dimensional blade profile.

3. The axial flow turbine blade design method based on three-dimensional Smith diagram according to claim 1, characterized in that: In step S3, two-dimensional blade profiles with different reaction degrees are obtained according to the given radial reaction degree distribution and the three-dimensional Smith diagram, and these blade profiles are stacked along the center of gravity to obtain a three-dimensional blade.

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