A 3D blade design method for axial flow turbines based on optimization of radial speed ratio

Abstract

The present invention provides a three-dimensional blade design method for an axial flow turbine based on radial velocity ratio optimization, including the following steps: 1. For a given working condition, divide the flow passage into n sub-flow passages along the radial direction, and find the optimal velocity ratio χ opt in each sub-flow passage to optimize the total static efficiency η ts of the sub-flow passage, and obtain the distribution law of aerodynamic parameters and total pressure loss coefficient Y p‑loss along the radial direction; 2. Utilize the existing blade profile loss model, query the total pressure loss coefficient Y p‑loss ' in the blade profile loss model, re-give the velocity coefficient ξ', and repeat the steps until the designed Y p‑loss is consistent with Y p‑loss '; 3. Stack the obtained two-dimensional blade profiles along the centroid to obtain a three-dimensional blade, conduct three-dimensional numerical simulation on the three-dimensional blade, and repeat the steps until the designed values of the distribution laws of the velocity coefficient ξ, flow rate G, and trailing angle θ along the radial direction are consistent with the numerical simulation results, and finally obtain the turbine blade. The present invention optimizes the design of each sub-flow passage and introduces a loss model, which is more accurate than the traditional three-dimensional blade design and has better aerodynamic performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of power machinery and engineering, and particularly relates to a three-dimensional blade design method for an axial turbine based on radial speed ratio optimization. Background Technique

[0002] As a prime mover, a turbine is a power machine that can convert the thermal energy in the working medium into mechanical energy, and has a wide range of applications in the fields of energy, chemical industry, aerospace, shipbuilding, automobiles, etc. In the entire working system, the working performance of the turbine is one of the key factors determining the comprehensive performance. There are many influencing factors for the internal flow state of the turbine, such as the geometric shape of the blade, the physical property parameters of the working medium, the matching characteristics between the stationary and rotating components, the impeller speed and the operating state, etc. Among these factors, the geometric shape of the blade is one of the most critical influencing factors. As the turbine continues to develop towards high power and high load, as the core component of the turbine, the length of the blade will inevitably increase, and the flow state of the working medium changes very violently along the radial direction. Precise design of the aerodynamic performance of the turbine blade has become an important part in the design process of high-performance gas turbines. Therefore, it is of great significance to design high-power, high-load and low-loss turbine blades and establish a fast and efficient high-performance turbine blade design method.

[0003] The main purpose of one-dimensional turbine design is to determine the shape of the velocity triangle by setting the flow angle or selecting three dimensionless parameters: flow coefficient, load coefficient and reaction degree. Currently, the method widely used in one-dimensional design is the "Smith chart", which was proposed by Smith in 1965 after summarizing the experimental data of 70 aviation gas turbines. Designers can quickly evaluate the flow coefficient, load coefficient and overall efficiency η tt among the three through the Smith chart, improving the design efficiency. However, limited by material technology and equipment weight, it is necessary to restrict the size of the turbine structure within a certain range, such as the mean diameter, blade length, etc. When using dimensionless parameters for one-dimensional turbine design, the turbine size cannot be directly restricted, and designers need to select the size of the dimensionless parameters according to experience, which has certain requirements for the ability of designers. At the same time, the Smith chart can effectively evaluate the relationship between the overall efficiency η tt and the flow coefficient and load coefficient, but the index determining the turbine power size is the total static efficiency η ts rather than the overall efficiency η tt , and when the design goal is the maximum power, the Smith chart design method is not very applicable. In order to find the velocity triangle with the best total static efficiency, it is necessary to simultaneously optimize the three dimensionless parameters: flow coefficient, load coefficient and reaction degree, which requires a large amount of calculation.

[0004] To eliminate these limitations, scholars at home and abroad have conducted a lot of research. Some scholars use the speed ratio χ, that is, the ratio of the absolute velocity c1 at the outlet of the stator blade to the circumferential velocity u as a reference for design. However, at this time, the speed ratio χ is used as a single index for the overall performance of the turbine stage, and no research has been found to use the speed ratio χ as a parameter varying along the radial direction and the speed ratio χ as a dimensionless number to be optimized for the three-dimensional blade design of the turbine. Summary of the Invention

[0005] Aiming at the defects of the prior art, the purpose of the present invention is to provide a three-dimensional blade design method for an axial-flow turbine based on radial speed ratio optimization, including the following steps:

[0006] S1: For a given working condition, given the dimensional parameters of the axial-flow turbine and generate a flow passage structure;

[0007] S2: According to the above flow passage structure, divide the flow passage into n sub-flow passages along the radial direction, and assume the distribution laws of the stator-rotor blade velocity coefficient ξ, the flow rate G, and the stagger angle θ along the radial direction;

[0008] S3: Find the optimal speed ratio χ for each sub-flow passage opt , so that the total static efficiency η of each sub-flow passage ts reaches the optimum, and obtain the aerodynamic parameters of the two-dimensional airfoil and the distribution law of the total pressure loss coefficient Y of the airfoil p-loss along the radial direction;

[0009] S4: Use the existing airfoil loss model, according to the obtained aerodynamic parameters, query the total pressure loss coefficient Y in the airfoil loss model p-loss ';

[0010] S5: Judge whether the total pressure loss coefficient Y in the airfoil loss model p-loss ' is consistent with the total pressure loss coefficient Y of the airfoil p-loss . If Y p-loss ' is consistent with Y p-loss , then proceed to the next step. If Y p-loss ' is inconsistent with Y p-loss , then re-give the velocity coefficient ξ and return to S3 until the total pressure loss coefficient Y in the airfoil loss model p-loss ' is consistent with the total pressure loss coefficient Y of the airfoil p-loss , and obtain a new two-dimensional airfoil;

[0011] S6: Stack the above new two-dimensional airfoils along the centroid to obtain a three-dimensional blade, and perform three-dimensional numerical simulation on the obtained three-dimensional blade, so as to obtain the latest distribution laws of the stator-rotor blade velocity coefficient ξ, the flow rate G, and the stagger angle θ along the radial direction;

[0012] S7: Using the latest radial distribution laws of the static and moving blade velocity coefficients ξ, the flow rate G, and the stagger angle θ, repeat S3 - S6, and determine whether the latest radial distribution laws of the static and moving blade velocity coefficients ξ, the flow rate G, and the stagger angle θ are consistent with the results of the three-dimensional numerical simulation in the current S6. When they are inconsistent, repeat S3 - S6 until they are consistent; when they are consistent, output the three-dimensional turbine blade.

[0013] Further, a judgment condition is also set between S3 and S4, and the judgment condition is: determine whether the current radial distribution laws of the static and moving blade velocity coefficients ξ, the flow rate G, and the stagger angle θ have undergone three-dimensional numerical simulation. When the judgment result is that they have not undergone three-dimensional numerical simulation, enter S4; when the judgment result is that they have undergone three-dimensional numerical simulation, directly enter S6.

[0014] Further, in S1, the given operating conditions include the total inlet temperature T 01 、the total pressure P 01 、the outlet static pressure P 3 and the flow rate G; the dimensional parameters of the axial flow turbine include the mean diameter d Ν of the stator blade, the hub ratio λ Ν of the stator blade, the aspect ratio AR N of the stator blade, the aspect ratio AR R of the rotor blade, the tip expansion angle θ Ntop of the stator blade, the root expansion angle θ Nhub of the stator blade, the tip expansion angle θ Rtop of the rotor blade, the root expansion angle θ Rhub of the rotor blade, the installation angle AA N of the stator blade, the installation angle AA R of the rotor blade, and the axial clearance δ between the stator and rotor blades, and derive the inlet and outlet heights of the stator and rotor blades through the dimensional parameters of the axial flow turbine.

[0015] Further, the inlet and outlet heights of the stator and rotor blades include the tip height d inNtop of the inlet of the stator blade, the root height d inNhub of the inlet of the stator blade, the tip height d outNtop of the outlet of the stator blade, the root height d outNhub of the outlet of the stator blade, the tip height d inRtop of the inlet of the rotor blade, the root height d inRhub of the inlet of the rotor blade, the tip height d outRtop of the outlet of the rotor blade, and the root height d outRhub of the outlet of the rotor blade; the tip height d inNtop of the inlet of the stator blade is derived through Formula 1, and Formula 1 is:

[0016]

[0017] The root height d inNhubDerivation through Formula 2, and the Formula 2 is as follows:

[0018]

[0019] The height d of the top of the stator blade outlet outNtop Derivation through Formula 3, and the Formula 3 is as follows:

[0020]

[0021] The height d of the root of the stator blade outlet outNhub Derivation through Formula 4, and the Formula 4 is as follows:

[0022]

[0023] The height d of the top of the rotor blade inlet inRtop Derivation through Formula 5, and the Formula 5 is as follows:

[0024] d inRtop = d outNtop + δ[tan(θ Ntop ) + tan(θ Rtop )];

[0025] The height d of the root of the rotor blade inlet inRhub Derivation through Formula 6, and the Formula 6 is as follows:

[0026] d inRhub = d outNhub - δ[tan(θ Nhub ) + tan(θ Rhub )];

[0027] The height d of the top of the rotor blade outlet outRtop Derivation through Formula 7, and the Formula 7 is as follows:

[0028]

[0029] The height d of the root of the rotor blade outlet outRhub Derivation through Formula 8, and the Formula 8 is as follows:

[0030]

[0031] Furthermore, in the S3, it specifically includes the following steps:

[0032] S31: Search for the optimal speed ratio χ opt for one of the single flow channels, so that the total static efficiency η ts of the current single flow channel reaches the optimum;

[0033] S32: Repeat the design process of a single sub-channel for each sub-channel, and output the final aerodynamic parameters of the two-dimensional blade profile and the radial design results of the total pressure loss coefficient.

[0034] Furthermore, the design process of the single flow channel specifically includes the following steps:

[0035] S311: a set of speed ratios χ is given to the single flow channel, with an interval of 0.005;

[0036] S312: Based on the speed ratio χ, the average diameter d and the stationary blade speed coefficient ξ N Get the stator blade outlet velocity C 2 and gas state and according to flow rate G, flow area A 2 and density ρ 2 Get the stator blade outlet airflow angle α 2 , and thus the total pressure loss coefficient Y of the stationary blade is calculated P-lossN ;

[0037] S313: According to the moving blade speed coefficient ξ R , outlet pressure P 3 Get the relative velocity W of the moving blade outlet 3 and gas state and according to flow rate G, flow area A 3 and density ρ 3 Get the blade outlet airflow angle α 3 , and thus the total pressure loss coefficient Y of the moving blade is calculated P-lossR ;

[0038] S314: Finding the best speed ratio in the given set of speed ratios x so that the total static efficiency reaches the maximum value;

[0039] S315: Determine the optimal speed ratio x opt Is it on the boundary of the given set of speed ratios? If so, the optimal value is outside the interval. According to the optimal speed ratio χ opt The speed ratio range is reset, and S312-S314 are repeated to obtain a new optimal speed ratio and then a judgment is made until the optimal speed ratio x opt Or the new optimal speed ratio is not within the optimal speed ratio x opt Or on the boundary of this set of speed ratio ranges given by the new optimal speed ratio, at this point, the design of this sub-flow channel is completed.

[0040] Compared with the prior art, the beneficial effects of the present invention are mainly reflected in:

[0041] 1. The turbine size is directly restricted, the design method is intuitive and convenient, and the speed ratio χ is used as the dimensionless number to be optimized, with fewer optimization variables and faster design speed.

[0042] 2. Optimize the design of each sub-channel of the blade and introduce a loss model, which is more accurate than the traditional three-dimensional blade design and has better aerodynamic performance.

[0043] 3. Through repeated correction by three-dimensional numerical simulation, the finally obtained three-dimensional blade can achieve excellent aerodynamic performance in the design results. Brief Description of the Drawings

[0044] Figure 1 It is a schematic flow chart of a three-dimensional blade design method for an axial flow turbine based on radial speed ratio optimization according to the present invention;

[0045] Figure 2 It is a schematic flow chart of speed ratio optimization according to the present invention;

[0046] Figure 3 It is a schematic diagram of the relationship between the total static efficiency and the speed ratio at different radial positions according to the present invention;

[0047] Figure 4 It is a schematic diagram of the optimization result of the total static efficiency at different radial positions according to the present invention and its corresponding optimal speed ratio;

[0048] Figure 5 It is a schematic diagram of the optimization result of the total pressure loss coefficient at different radial positions according to the present invention and its corresponding optimal speed ratio;

[0049] Figure 6 It is a schematic diagram of the two-dimensional airfoil designed according to the present invention;

[0050] Figure 7 It is a schematic diagram of the three-dimensional blade designed according to the present invention. Detailed Embodiment

[0051] The following will describe in more detail a three-dimensional blade design method for an axial flow turbine based on radial speed ratio optimization according to the present invention with reference to the schematic diagrams, in which the preferred embodiments of the present invention are shown. It should be understood that those skilled in the art can modify the present invention described herein while still achieving the advantageous effects of the present invention. Therefore, the following description should be understood as a broad guidance for those skilled in the art and not as a limitation to the present invention.

[0052] The overall design process is as Figure 1 shown.

[0053] S1. First, for a given working condition, after giving the structural dimensions of the turbine, divide the axial flow turbine flow channel into multiple sub-channels along the radial direction, assume the velocity coefficient ξ of the stator and rotor blades, and find the optimal speed ratio χ opt in each sub-channel to make the total static efficiency η ts of the current sub-channel reach the optimum, and obtain the aerodynamic parameters of the two-dimensional airfoil and the distribution law of the total pressure loss coefficient Y p-loss along the radial direction as shown in Figure 4 and5 As shown, the calculation process is as follows Figure 2 shown below:

[0054] S1.1. According to the design conditions, the total inlet temperature T 01 of the turbine, the total pressure P 01 , the static pressure P 3 at the outlet, and the flow rate G are known.

[0055] S1.2. Then, given the average diameter d Ν of the stator blades, the hub ratio λ Ν of the stator blades, the aspect ratio AR N of the rotor blades, the aspect ratio AR R of the stator blades, the tip expansion angle θ Ntop of the stator blades, the root expansion angle θ Nhub of the stator blades, the tip expansion angle θ Rtop of the rotor blades, the root expansion angle θ Rhub of the rotor blades, the installation angle AA N of the stator blades, the installation angle AA R of the rotor blades, and the axial clearance δ between the stator and rotor blades, the inlet and outlet heights of the stator and rotor blades (the tip height d inNtop of the stator blade inlet, the root height d inNhub of the stator blade inlet, the tip height d outNtop of the stator blade outlet, the root height d outNhub of the stator blade outlet, the tip height d inRtop of the rotor blade inlet, the root height d inRhub of the rotor blade inlet, the tip height d outRtop of the rotor blade outlet, and the root height d outRhub ) can be derived from the formulas in the following text.

[0056]

[0057]

[0058]

[0059]

[0060] d inRtop = d outNtop + δ[tan(θ Ntop ) + tan(θ Rtop )] (5)

[0061] d inRhub = d outNhub - δ[tan(θ Nhub ) + tan(θ Rhub )] (6)

[0062]

[0063]

[0064] S1.3. Given the velocity coefficients ξ of the stator and rotor blades, the lag angle θ, and the law of the radial distribution of the flow rate G, divide the flow path into n sub-flow paths with the same flow area along the radial direction.

[0065] S1.4. For a certain sub-flow path, given a set of speed ratios χ with an interval of 0.005. According to the speed ratio χ, the mean diameter d, and the velocity coefficient ξ of the stator blade N obtain the outlet velocity C of the stator blade 2 and the gas state. Then, according to the flow rate G, the flow area A 2 and the density ρ 2 obtain the outlet gas flow angle α of the stator blade 2 , and thus the total pressure loss coefficient Y of the stator blade can be calculated P-lossN . Similarly, according to the velocity coefficient ξ of the rotor blade R , the outlet pressure P 3 obtain the relative velocity W at the outlet of the rotor blade 3 and the gas state. Then, according to the flow rate G, the flow area A 3 and the density ρ 3 obtain the outlet gas flow angle α of the rotor blade 3 , and thus the total pressure loss coefficient Y of the rotor blade can be calculated P-lossR . Finally, among a given set of speed ratios χ, find the optimal speed ratio χ opt to maximize the total static efficiency η ts . If the optimal speed ratio χ opt is on the boundary of the given speed ratio range, it means that the optimal value is outside the interval. At this time, the speed ratio range will be re-given according to the position of the optimal speed ratio χ opt until the optimal speed ratio χ opt is not on the boundary, as shown in Figure 3 .

[0066] S1.5. Repeat the single sub-flow path design process for each sub-flow path, and output the aerodynamic parameters of the final output two-dimensional blade profile and the design results of the total pressure loss coefficient along the radial direction.

[0067] S2. Using the existing blade profile loss model, according to the aerodynamic parameters of the two-dimensional blade profile in the S1 design results, query the total pressure loss coefficient Y p-loss ' in the blade profile loss model, re-give the velocity coefficient ξ', and repeat S1 until the total pressure loss coefficient Y p-loss of the designed blade profile is consistent with the total pressure loss coefficient Y p-loss ' in the blade profile loss model, and obtain a new set of two-dimensional blade profiles, as shown in Figure 6 .

[0068] S3. Stack the obtained new two-dimensional blade profiles along the centroid to obtain a three-dimensional blade. As shown in Figure 7 , perform three-dimensional numerical simulation on the obtained three-dimensional blade, so as to obtain a new distribution law of the velocity coefficient ξ, flow rate G, and stagger angle θ along the radial direction. Use the new distribution law of the velocity coefficient ξ, flow rate G, and stagger angle θ along the radial direction, and repeat S1 until the design values of the distribution laws of the velocity coefficient ξ, flow rate G, and stagger angle θ along the radial direction are consistent with the numerical simulation results, and finally obtain the turbine blade.

[0069] The above is only the preferred embodiment of the present invention and does not impose any limitation on the present invention. Any person skilled in the art within the technical field, without departing from the technical solution of the present invention, makes any form of equivalent substitution or modification and other changes to the technical solution and technical content disclosed in the present invention, which are all within the content of the technical solution of the present invention and still fall within the protection scope of the present invention.

Claims

1. A three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization, characterized in that, it includes the following steps: S1: For a given working condition, given the dimensional parameters of the axial flow turbine and generate the flow passage structure; S2: According to the above flow passage structure, divide the flow passage into n sub-flow passages along the radial direction, and assume the radial distribution laws of the stator and rotor blade velocity coefficients ξ, the flow rate G, and the stagger angle θ; S3: Find the optimal speed ratio χ for each sub-channel opt , so that the total static efficiency η of each sub-channel ts reaches the optimum, and obtain the aerodynamic parameters of the two-dimensional blade profile and the radial distribution law of the total pressure loss coefficient Y of the blade profile p-loss ; S4: Using the existing blade profile loss model, according to the obtained aerodynamic parameters, query the total pressure loss coefficient Y in the blade profile loss model p-loss '; S5: Determine the total pressure loss coefficient Y in the blade profile loss model p-loss ’ and the total pressure loss coefficient Y of the blade profile p-loss Whether they are consistent. If Y p-loss ’ and Y p-loss are consistent, proceed to the next step. If Y p-loss ’ and Y p-loss are inconsistent, re - specify the velocity coefficient ξ and return to S3 until the total pressure loss coefficient Y p-loss ’ in the blade profile loss model and the total pressure loss coefficient Y of the blade profile p-loss are consistent to obtain a new two - dimensional blade profile; S6: Stack the above new two-dimensional airfoils along the centroid to obtain a three-dimensional blade, and perform three-dimensional numerical simulation on the obtained three-dimensional blade, so as to obtain the latest radial distribution laws of the stator and rotor blade velocity coefficients ξ, the flow rate G, and the stagger angle θ; S7: Use the latest radial distribution laws of the stator and rotor blade velocity coefficients ξ, the flow rate G, and the stagger angle θ, repeat S3 - S6, and judge whether the latest radial distribution laws of the stator and rotor blade velocity coefficients ξ, the flow rate G, and the stagger angle θ are consistent with the results of the three-dimensional numerical simulation in the current S6. When they are inconsistent, repeat S3 - S6 until they are consistent; when they are consistent, output the three-dimensional blade of the turbine.

2. The three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization according to claim 1, characterized in that, a judgment condition is also set between S3 and S4, and the judgment condition is: judge whether the current radial distribution laws of the stator and rotor blade velocity coefficients ξ, the flow rate G, and the stagger angle θ have passed three-dimensional numerical simulation. When the judgment result is that it has not passed three-dimensional numerical simulation, enter S4; when the judgment result is that it has passed three-dimensional numerical simulation, directly enter S6.

3. The three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization according to claim 1, characterized in that, In S1, the given operating conditions include the total temperature T at the turbine inlet 01 , the total pressure P 01 , the static pressure P at the outlet 3 , and the flow rate G; the dimensional parameters of the axial turbine include the mean diameter d of the stator blades Ν , the hub ratio λ of the stator blades Ν , the aspect ratio AR of the stator blades N , the aspect ratio AR of the rotor blades R , the tip expansion angle θ of the stator blades Ntop , the root expansion angle θ of the stator blades Nhub , the tip expansion angle θ of the rotor blades Rtop , the root expansion angle θ of the rotor blades Rhub , the installation angle AA of the stator blades N , the installation angle AA of the rotor blades R , and the axial clearance δ between the stator and rotor blades, and the inlet and outlet heights of the stator and rotor blades are derived from the dimensional parameters of the axial turbine.

4. The three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization according to claim 3, characterized in that, The inlet and outlet heights of the stationary and moving blades include the tip height d of the inlet of the stationary blade inNtop , the root height d of the inlet of the stationary blade inNhub , the tip height d of the outlet of the stationary blade outNtop , the root height d of the outlet of the stationary blade outNhub , the tip height d of the inlet of the moving blade inRtop , the root height d of the inlet of the moving blade inRhub , the tip height d of the outlet of the moving blade outRtop and the root height d of the outlet of the moving blade outRhub ; the tip height d of the inlet of the stationary blade inNtop is derived by Formula 1, and the Formula 1 is as follows: The height d of the root of the stator blade at the inlet inNhub Derived from Formula 2, the Formula 2 is as follows: The height d of the top of the stator blade outlet outNtop Derived by Formula 3, the Formula 3 is as follows: The root height d of the stator blade outlet outNhub Derived by Equation 4, where Equation 4 is as follows: The inlet tip height d of the moving blade inRtop Derived through Formula 5, the Formula 5 is as follows: d inRtop = d outNtop + δ[tan(θ Ntop ) + tan(θ Rtop )]; The height d of the blade root at the inlet of the moving blade inRhub Derived through Formula VI, where Formula VI is as follows: d inRhub = d outNhub - δ[tan(θ Nhub ) + tan(θ Rhub )]; The height d of the top of the moving blade outlet outRtop Derived by Formula 7, the Formula 7 is as follows: The height d of the blade root at the outlet of the moving blade outRhub Derived by Formula VIII, where Formula VIII is as follows:

5. The three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization according to claim 1, characterized in that, in S3, it specifically includes the following steps: S31: Search for the optimal speed ratio χ for one of the single sub-channels opt , so that the total static efficiency η ts of the current single sub-channel reaches the optimum; S32: Repeat the design process of a single sub-flow passage for each sub-flow passage, and output the aerodynamic parameters of the final two-dimensional airfoil and the radial design results of the total pressure loss coefficient.

6. The three-dimensional blade design method for axial flow turbines based on radial velocity ratio optimization according to claim 5, characterized in that, the design process of the single sub-flow passage specifically includes the following steps: S311: Given a set of velocity ratios χ for the single sub-flow passage, with an interval of 0.005; S312: Obtain the outlet velocity C of the stator blade according to the speed ratio χ, the mean diameter d, and the stator blade velocity coefficient ξ N and the gas state, and obtain the outlet gas flow angle α of the stator blade according to the flow rate G, the flow area A 2 and the density ρ 2 2 2 so as to calculate the total pressure loss coefficient Y of the stator blade P-lossN ;​​ S313: According to the moving blade velocity coefficient ξ R , the outlet pressure P 3 to obtain the relative velocity W at the outlet of the moving blade 3 and the gas state, and according to the flow rate G, the flow area A 3 and the density ρ 3 to obtain the flow angle α at the outlet of the moving blade 3 , thereby calculating the total pressure loss coefficient Y of the moving blade P-lossR ; S314: Among the given set of speed ratios χ, find the optimal speed ratio χ opt to maximize the total static efficiency; S315: Determine the optimal speed ratio x opt Is it on the boundary of the given set of speed ratios? If so, the optimal value is outside the interval. According to the optimal speed ratio χ opt The speed ratio range is reset, and S312-S314 are repeated to obtain a new optimal speed ratio and then a judgment is made until the optimal speed ratio x opt Or the new optimal speed ratio is not within the optimal speed ratio x opt Or on the boundary of this set of speed ratio ranges given by the new optimal speed ratio, at this point, the design of this sub-flow channel is completed.

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