A sealing tooth non-uniform distribution straight-through type labyrinth seal structure design method and sealing structure based on agent model optimization

Abstract

The application discloses a design method and a sealing structure of a straight-through labyrinth sealing structure based on an agent model optimization and a non-uniform distribution of sealing teeth, and relates to a design method and a sealing structure of a straight-through labyrinth sealing structure. In order to solve the problems that the existing labyrinth sealing optimization depends on complex structure changes or additional components, is high in cost and is not suitable for old unit reconstruction, and a non-uniform distribution lacks a systematic design method and mechanism guidance, the design method comprises the following steps: determining design variables and constraint conditions, wherein the design variables comprise an axial total length L, a tooth number n and an axial coordinate of a middle tooth; generating sample points by using a Latin hypercube sampling; obtaining a leakage amount by CFD simulation; constructing a Kriging agent model; and optimizing by using a genetic algorithm and iteratively verifying until the accuracy is met. The application belongs to the technical field of rotary machinery sealing.

Description

Technical Field

[0001] This invention relates to a design method and sealing structure for a straight-through labyrinth seal, belonging to the field of rotary mechanical seal technology. Background Technology

[0002] Labyrinth seals are widely used in interstage sealing of rotating machinery such as steam turbines, gas turbines, and aero engines due to their advantages of simple structure, non-contact operation, high temperature resistance, and high pressure resistance. Their performance directly affects the overall efficiency of the machine. Research shows that optimizing the labyrinth seal structure to reduce leakage flow is an important way to improve the efficiency of rotating machinery.

[0003] Currently, optimization research on labyrinth seals mainly focuses on the geometric parameters of the sealing teeth (such as tooth shape, tooth height, tooth thickness, etc.). Figure 11 ) and the combination of sealing teeth and corresponding wall surfaces (such as labyrinth-honeycomb seals, such as Figure 12 However, the aforementioned optimization methods often involve complex structural changes or the introduction of additional sealing components, which not only increases manufacturing costs but also poses reliability challenges under high-temperature and high-speed conditions due to the sensitivity of the relative positions between components. For example, labyrinth-honeycomb seals are extremely sensitive to the relative positions of the sealing teeth and the honeycomb structure; high-temperature deformation can easily cause them to deviate from the design values, thus deteriorating the sealing performance.

[0004] It is worth noting that, in addition to the methods mentioned above, adjusting the axial position of the sealing teeth to change the size distribution of each chamber can also significantly affect sealing performance. However, existing research mostly focuses on cases where the sealing teeth are evenly distributed, with less research on structures with non-uniform distribution (i.e., inconsistent chamber sizes). In fact, for many old units in service, the flow passage structure is basically fixed, making it difficult to make significant geometric modifications or add new components. However, adjusting the axial position of the sealing teeth is a near-zero-cost modification based on the existing structure. If a non-uniform distribution can be achieved by optimizing the axial position of the sealing teeth, it can not only be used for the efficient design of new units, but also provide a low-cost and highly feasible solution for the efficiency improvement and retrofitting of many old steam turbines of 300MW class and below that use traditional insert-pipe steam inlet structures and were put into operation relatively early.

[0005] Furthermore, while existing research has revealed some flow characteristics of labyrinth seals through flow field analysis, it has rarely established the intrinsic relationship between chamber geometry (such as aspect ratio) and sealing performance (such as leakage and energy dissipation). This lack of mechanistic understanding results in a lack of theoretical guidance for the design of non-uniformly distributed seals, making it difficult to quickly and effectively obtain optimal solutions.

[0006] In summary, existing technologies lack a method for optimizing the non-uniform distribution of sealing teeth that is applicable to both the efficient design of new units and the low-cost retrofitting of old units. They also lack an in-depth understanding of the relationship between chamber geometry and sealing performance to guide structural design. Summary of the Invention

[0007] To address the problems of existing labyrinth seal optimization relying on complex structural changes or additional components, high costs, and unsuitability for retrofitting old units, as well as the lack of system design methods and mechanism guidance for non-uniform distribution, this invention proposes a design method and sealing structure for a straight-through labyrinth seal with non-uniformly distributed sealing teeth based on surrogate model optimization.

[0008] The technical solution adopted by the present invention to solve the above problems is as follows: The steps of the design method of a straight-through labyrinth seal structure with non-uniform distribution of sealing teeth based on surrogate model optimization described in the present invention include: Step 1: Determine the design variables; Step 2: Use experimental design methods to generate several sample points within the range of values ​​for the design variables; Step 3: Establish a corresponding labyrinth seal geometric model for each sample point and perform computational fluid dynamics numerical simulation to obtain the leakage amount of the sealing structure corresponding to each sample point. Step 4: Using the design variables of the sample points as input and the corresponding leakage amount as output, construct the surrogate model; Step 5: Using an optimization algorithm with the goal of minimizing leakage, the algorithm seeks the optimal solution in the mapping relationship constructed by the surrogate model. The optimal solution is the combination of design variables that minimizes the leakage predicted by the surrogate model. Step 6: Perform CFD verification on the optimal solution and calculate the relative error between the leakage amount predicted by the surrogate model and the leakage amount obtained from CFD verification. If the relative error is less than the preset threshold, the optimal solution is output as the final design result. Otherwise, the optimal solution and its corresponding CFD verification results are added to the sample set as new sample points, and the process returns to step 4 to rebuild the surrogate model. Steps 4 to 6 are executed iteratively until the accuracy requirements are met.

[0009] Furthermore, the design variables include the total axial length L of the sealing structure, the total number of sealing teeth n, and the absolute axial coordinates of the intermediate sealing teeth excluding the sealing teeth at the beginning and end. , , …, Wherein, along the flow direction, the leading edge coordinate of the first sealing tooth is defined as... =0, the coordinate of the last sealing tooth is defined as x n= L, and the coordinates of the intermediate sealing teeth satisfy the recurrence constraint < < L, where i = 2, 3, …, n - 1; meanwhile, the design variables also satisfy the geometric feasibility constraint n*w ≤ a *L, where w is the axial width of the root of a single sealing tooth, a is a coefficient determined by the engineering application conditions and satisfies 0 < a ≤ 1.

[0010] Furthermore, the experimental design method in step 2 is Latin hypercube sampling, and the number of generated sample points is at least 15 * (n - 2), where n is the total number of sealing teeth and (n - 2) is the number of intermediate sealing teeth.

[0011] Furthermore, the surrogate model in step 4 is a Kriging model, and the correlation function of the Kriging model is a linear correlation function.

[0012] Furthermore, the optimization algorithm in step 5 is a genetic algorithm, and the population size of this genetic algorithm is set to 50, and the maximum number of evolutionary generations is set to 100.

[0013] Furthermore, the preset threshold in step ⑥ is that the relative error is less than 1.5%.

[0014] Furthermore, the design variables in step 1 also include one or more of the tooth height, root width, tip width of the sealing teeth, and the sealing gap.

[0015] Furthermore, after constructing the Kriging model, the leave-one-out cross-validation is used to evaluate the prediction accuracy of the surrogate model.

[0016] In the straight-through labyrinth seal structure with non-uniform distribution of sealing teeth optimized based on the surrogate model described in the present invention, along the flow direction, a plurality of sealing chambers are jointly formed by adjacent sealing teeth and between the sealing teeth and the rotor, where: For the first chamber formed by the first sealing tooth and the second sealing tooth, the aspect ratio satisfies 2.25 ≤ ≤ 3.75, and the defined aspect ratio is the ratio of the axial length l of this chamber to the tooth height h of the sealing tooth, that is = ( ) / h; For at least one sealing chamber in the middle region, the aspect ratio is less than 1, that is, the axial length of this chamber is less than the tooth height h of the sealing tooth; The aspect ratio of the last sealing chamber is jointly determined by the total axial length L of the seal structure, the axial coordinates of each intermediate sealing tooth, and the tooth height h of the sealing tooth.

[0017] The beneficial effects of the present invention are: 1. This invention achieves high-efficiency sealing simply by adjusting the axial position of the sealing teeth. It is suitable for new unit design and low-cost efficiency improvement retrofit of old units, and can be extended to rotating machinery such as steam turbines, gas turbines, and aero engines.

[0018] 2. This invention establishes a systematic optimization process based on Latin hypercube sampling, Kriging surrogate models, and genetic algorithms. Compared with traditional full-parameter scanning methods and successive trial-and-error methods, it can significantly reduce the amount of CFD numerical computation. In the embodiment, the relative error between surrogate model prediction and CFD verification is only 0.29%. While ensuring high accuracy, it shortens the design cycle from several weeks to several days, significantly improving engineering design efficiency.

[0019] 3. Under the same number of teeth, same total axial length, and same operating conditions, the optimized non-uniformly distributed sealing structure of this invention reduces leakage by up to 4.5% compared to the traditional uniformly distributed structure. For large rotating machinery, the reduction in leakage directly translates into increased unit efficiency and reduced energy consumption, resulting in significant economic benefits and social benefits of energy conservation and emission reduction.

[0020] 4. This invention reveals for the first time the intrinsic relationship between the aspect ratio of the sealed chamber and shear stress and energy dissipation, and clarifies the bimodal distribution law of sealing performance as the aspect ratio of the chamber changes, providing a solid theoretical foundation for the design of non-uniform toothed labyrinth seals. It completely changes the traditional situation where non-uniform distribution design relies on empirical trial and error, realizing a shift from "blind optimization" to "theoretical guidance." Attached Figure Description

[0021] Figure 1 This is a structural comparison diagram of the traditional uniform distribution and the non-uniform distribution sealing structure of the present invention, wherein (a) is the traditional uniform distribution and (b) is the non-uniform distribution of the present invention; Figure 2 This is a schematic diagram illustrating the design variable definitions of the present invention; Figure 3 This is an overall optimized flowchart of the method of the present invention; Figure 4 This is a comparison chart of leakage before and after the optimization of this invention; Figure 5 This is a diagram showing the aspect ratio distribution of the chamber in the optimized sealing structure of this invention; Figure 6 This is a schematic diagram of the distribution of sample points in the Latin hypercube sampling method; Figure 7 This is a schematic diagram of a CFD computational model, where (a) is the geometric model and (b) is the mesh generation. Figure 8 This is a comparison chart of the CFD calculation results of the optimized solution and the prediction results of the surrogate model; Figure 9The image shows a comparison of the flow field cloud maps before and after optimization, where (a) represents a uniform distribution and (b) represents a non-uniform distribution. Figure 10 This is a schematic diagram of the flow field structure under different chamber aspect ratios and its relationship with the variation of turbulent kinetic energy; Figure 11 This is a schematic diagram illustrating existing research directions for optimizing maze sealing. Figure 12 This is a schematic diagram of an existing combination of labyrinth sealing structures.

[0022] Example like Figures 1 to 12 As shown in the figure, the steps of the design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization in this embodiment include: Step 1: Determine the design variables and their constraints; Step 2: Generate sample points using Latin hypercube sampling; Step 3: Obtain the leakage amount at each sample point through CFD simulation; Step 4: Construct the Kriging agent model; Step 5: Use a genetic algorithm to find the optimal solution and perform CFD verification. If the accuracy is met, output the result; otherwise, add the verification result to the sample set for iterative optimization.

[0023] The basic structural parameters of the labyrinth seal are as follows: Radius of the surface of revolution: r = 350mm Sealing tooth height: h = 3mm Width at the root of the sealing tooth: wr = 0.48mm Width of sealing tooth tip: wt = 0.18mm Sealing tooth clearance (radial clearance): c = 0.3mm Total axial length of the seal: L = 15mm Total number of sealing teeth: n = 5 Calculate the geometric feasibility constraint coefficient α based on the number of teeth n, the root width wr, and the total axial length L: The sum of the widths of all sealing tooth roots: n * wr = 2.4mm By the constraint n * wr ≤ a L can be obtained as follows: a ≥ (n * wrt) / L = 2.4 / 15 = 0.16 (satisfies 0 < a ≤1).

[0024] like Figure 2 The design variables in step 1 include: The total axial length L of the sealing structure (in this embodiment, L=15mm is a fixed value and is not considered a variable); The total number of sealing teeth n (in this embodiment, n=5 is a fixed value and is not considered a variable); The axial absolute coordinates of the remaining intermediate sealing teeth, excluding the sealing teeth at both ends. ; The coordinate definition rules are as follows: Along the flow direction, the leading edge coordinates of the first sealing tooth are defined as follows: ; The coordinates of the last sealing tooth are defined as follows: = L = 15mm; The coordinates of the intermediate sealing tooth must satisfy the recursive constraint: ; Design variables are , , There are a total of 3 design variables.

[0025] In step 2, the Latin hypercube sampling method is used to generate sample points within the range of values ​​of the design variables. Based on the dimensions of the design variables, the number of sample points is at least 15*(n-2) = 15*3 = 45. like Figure 6 As shown, the sample points uniformly cover the entire design space, ensuring the reliability of the proxy model construction; In step 3, for each sample point, a corresponding labyrinth seal geometry model is generated in the 3D modeling software. The sealing tooth cross-section is a right trapezoid, with a root width wr=0.48mm, a tip width wt=0.18mm, a tooth height h=3mm, and a radial clearance c=0.3mm.

[0026] like Figure 7 As shown, Ansys meshing is used for unstructured mesh generation, where... Figure 7 (a) is a geometric model. Figure 7 (b) Mesh generation, with the total number of meshes controlled at around 5.5 million, and local densification of the tooth tip gap area to ensure calculation accuracy.

[0027] The boundary conditions are set as follows: Working fluid: superheated steam; Total inlet pressure: 10.684 MPa; Import total temperature: 513 ℃; Outlet static pressure: 8.9 MPa; Speed: 3000 rpm; Wall conditions: The rotor surface is a rotating wall surface, and the stator surface is a stationary wall surface; Steady-state solutions were obtained using CFX software, with the SST kw model chosen for turbulence. The leakage rate Q (unit: kg / s) at each sample point was obtained through simulation. 45 groups ( The corresponding Q is then combined to form the initial dataset.

[0028] In step 4, design variables ( With input Q and output Q, a proxy model is constructed using a Kriging model. In this embodiment, the correlation function of the Kriging model is a linear correlation function.

[0029] After the model was built, leave-one-out cross-validation was used to evaluate its accuracy. The average error of the cross-validation was 0.81%, indicating that the surrogate model has high prediction accuracy and can be used for subsequent optimization.

[0030] In step 5, with the goal of minimizing leakage, a genetic algorithm is used to optimize the surrogate model. The genetic algorithm parameters are set as follows: Population size: 50 Maximum number of generations: 100 Crossover probability: 0.8 The mutation probability is automatically adjusted based on the population situation, including the mutation step size and range (the mutation function is Gaussian mutation). The optimal solution is obtained after optimization. ).

[0031] In step 5, CFD simulation is performed on the optimal solution to obtain the actual leakage amount. The relative error between the surrogate model prediction and the actual leakage amount is calculated: Relative error = (predicted value – CFD) / CFD like Figure 8 As shown, Figure 8 The comparison between the CFD calculation results of the optimized solution and the prediction results of the surrogate model is shown, and the two agree well. In this embodiment, the relative error is 0.29%, which is less than the preset threshold of 1.5%, so this optimal solution is accepted as the final design result.

[0032] If the relative error is greater than or equal to 1.5%, the optimal solution and its CFD results are added to the sample set as new sample points. Then, return to step 4 to rebuild the surrogate model and continue iterative optimization until the accuracy requirements are met or the preset maximum number of iterations is reached.

[0033] Analysis of optimization results in this embodiment The final optimized sealing structure parameters obtained in this embodiment are: = 7.62mm = 9.83mm = 10.94mm Calculate the axial length of each chamber based on the above parameters: First chamber (between tooth 1 and tooth 2): = = 7.62 - 0 = 7.62mm Second chamber (between teeth 2 and 3): = 9.83 - 7.62 = 2.21mm Third chamber (between teeth 3 and 4): = 10.94 - 9.83 = 1.11mm Fourth chamber (between teeth 4 and 5): = 15 - 10.94 = 4.06mm Calculate the aspect ratio of each chamber (the ratio of the axial length of the chamber to the tooth height h, where h = 3 mm), such as Figure 5 As shown: The aspect ratio of the first chamber: = / h = 7.62 / 3 = 2.54 The aspect ratio of the second chamber: = / h = 2.21 / 3 = 0.74 The aspect ratio of the third chamber: = / h = 1.11 / 3 = 0.37 The aspect ratio of the fourth chamber is: = / h = 4.06 / 3 = 1.35 The results above show that: The length-to-width ratio of the first chamber =2.54, its aspect ratio Satisfies 2.25 ≤ ≤ 3.75.

[0034] The length-to-width ratios of the second and third chambers are both less than 1, which is consistent with the characteristic that the middle chamber is compressed. The aspect ratio of the fourth chamber is slightly greater than 1, which is determined by the first three chambers. The aspect ratio of the first chamber is not close to 3 because the total axial length L=15mm in this embodiment is relatively short, making it impossible to achieve a larger first chamber.

[0035] The optimized non-uniform distribution structure ( Figure 1 b) A uniformly distributed structure with the same number of teeth and the same axial length ( Figure 1a) CFD comparison was performed. With a uniform distribution, the tooth spacing is equal, and the axial length between every two teeth is L / (n-1)=15 / 4=3.75mm, resulting in a calculated leakage rate of 0.0614 kg / s. After optimization, the leakage rate of the non-uniformly distributed structure is 0.0584 kg / s, a reduction of 5.14%. Figure 4 As shown.

[0036] Figure 9 The comparison of flow field cloud maps before and after optimization is shown, among which Figure 9 (a) is a uniform distribution. Figure 9 (b) shows a non-uniform distribution. It can be seen that the non-uniform distribution structure generates stronger and longer turbulent kinetic energy within the cavity, making dissipation more significant.

[0037] Figure 10 Further details were revealed regarding the flow field structure characteristics under different chamber aspect ratios: When the length and width of the chamber are relatively small (as in this embodiment) = 0.74), due to the limitation of the axial length inside the cavity, the axial velocity of the vortex inside the cavity is almost 0, which increases the velocity gradient between the vortex and the mainstream (leakage flow), thereby exacerbating energy dissipation; When the length-to-width ratio of the chamber is close to 1 ( = 1.35), the flow inside the cavity gradually transitions to a structure with full vortices and the vortex core located in the center of the cavity, and the dissipation capacity is relatively weakened; When the axial length of the chamber allows for the formation of a larger chamber (length-to-width ratio close to 3), the vortex core inside the chamber oscillates, thereby exacerbating energy dissipation.

[0038] As the chamber further enlarges, the vortices within the chamber fail to develop into a full structure. Instead, they are suppressed in the radial direction, exhibiting a flattened characteristic. This weakens the momentum exchange between the mainstream and the depths of the chamber, and consequently reduces the dissipation capacity.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization, characterized in that, The specific steps include: Step 1: Determine the design variables; Step 2: Use experimental design methods to generate several sample points within the range of values ​​for the design variables; Step 3: Establish a corresponding labyrinth seal geometric model for each sample point and perform computational fluid dynamics numerical simulation to obtain the leakage amount of the sealing structure corresponding to each sample point. Step 4: Using the design variables of the sample points as input and the corresponding leakage amount as output, construct the surrogate model; Step 5: Using an optimization algorithm with the goal of minimizing leakage, the algorithm seeks the optimal solution in the mapping relationship constructed by the surrogate model. The optimal solution is the combination of design variables that minimizes the leakage predicted by the surrogate model. Step 6: Perform CFD verification on the optimal solution and calculate the relative error between the leakage amount predicted by the surrogate model and the leakage amount obtained from CFD verification. If the relative error is less than the preset threshold, the optimal solution is output as the final design result. Otherwise, the optimal solution and its corresponding CFD verification results are added to the sample set as new sample points, and the process returns to step 4 to rebuild the surrogate model. Steps 4 to 6 are executed iteratively until the accuracy requirements are met.

2. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, The design variables include the total axial length L of the sealing structure, the total number n of sealing teeth, and the absolute axial coordinates of the remaining intermediate sealing teeth except the first and last sealing teeth , , …, ; among which, along the flow direction, the leading edge coordinate of the first sealing tooth is defined as =0, the coordinate of the last sealing tooth is defined as =L, and the coordinates of the intermediate sealing teeth satisfy the recurrence constraint < <L, where i = 2, 3, …, n - 1; meanwhile, the design variables also satisfy the geometric feasibility constraint n*w ≤ a *L, where w is the axial width of the root of a single sealing tooth, a is a coefficient determined by the engineering application conditions and satisfies 0 < a ≤ 1.

3. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, In step 2, the experimental design method is Latin hypercube sampling, and the number of sample points generated is at least 15 * (n-2), where n is the total number of sealing teeth and (n-2) is the number of intermediate sealing teeth.

4. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, In step 4, the surrogate model is a Kriging model, and the correlation function of the Kriging model is a linear correlation function.

5. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, The optimization algorithm in step 5 is a genetic algorithm, with a population size of 50 and a maximum number of generations of evolution of 100.

6. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, The preset threshold in step 6 is a relative error of less than 1.5%.

7. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 1, characterized in that, The design variables in step 1 also include one or more of the following: tooth height, tooth root width, tooth tip width, and sealing gap.

8. The design method for a straight-through labyrinth seal structure with non-uniformly distributed sealing teeth based on surrogate model optimization according to claim 4, characterized in that, After constructing the Kriging model, leave-one-out cross-validation was used to evaluate the prediction accuracy of the surrogate model.

9. A sealing structure designed using the method described in any one of claims 1 to 8, characterized in that, The sealing structure, along the flow direction, comprises multiple sealing chambers formed by adjacent sealing teeth and the space between the sealing teeth and the rotor, wherein: The first chamber formed by the first sealing tooth and the second sealing tooth has a length-to-width ratio of Satisfies 2.25 ≤ ≤ 3.75, the length-to-width ratio is defined as the ratio of the axial length l of the chamber to the tooth height h of the sealing tooth, i.e. = ( ) / h; At least one sealed chamber located in the middle region has an aspect ratio of less than 1, that is, the axial length of the chamber is less than the tooth height h of the sealing tooth; The aspect ratio of the final sealing chamber is determined by the total axial length L of the sealing structure, the axial coordinates of each intermediate sealing tooth, and the tooth height h of the sealing tooth.

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