Method and system for predicting flow loss of labyrinth seal

Abstract

The embodiment of the invention discloses a method and a system for predicting flow loss of a labyrinth seal. The method comprises the following steps: defining geometric parameters of the labyrinth seal and physical parameters of a working medium; calculating dimensionless parameters for representing the flow state based on the geometric parameters and the physical parameters; selecting a corresponding flow loss coefficient calculation formula according to the calculation result of the dimensionless parameter; and calculating the flow loss of the labyrinth seal based on the flow loss coefficient. According to the embodiment of the invention, the flow loss of the labyrinth seal can be accurately and quickly predicted, the problem of flow loss evaluation precision of the labyrinth seal is solved, the loss evaluation speed is improved, the design level of the labyrinth seal and even turbine machinery is improved, and the method has wide applicability to different engineering problems.

Description

Technical Field

[0001] This application relates to the technical field of turbine machinery design and analysis, specifically to a method and system for predicting flow loss in labyrinth seals. Background Technology

[0002] Labyrinth seals are widely used in the static-to-rotation clearance of various turbine machinery due to their advantages such as simple structure, low cost and good sealing performance.

[0003] However, under high-speed rotation conditions, the flow losses caused by the relative motion between the moving rotor and the fluid within the labyrinth seal consume a certain amount of mechanical energy, impacting the efficient operation of the turbine. A laboratory, during the operation of a supercritical carbon dioxide prototype, found that various flow losses within the device accounted for approximately 37.5% of the total losses, becoming the main source of losses in small high-speed turbine devices and significantly reducing the device's heat-to-work conversion efficiency. However, research on flow losses within the labyrinth seal is currently quite scarce. Therefore, establishing a predictive model for flow losses in the labyrinth seal has significant engineering application value for improving the optimization design of labyrinth seals and even turbines.

[0004] Existing methods for assessing flow loss are mainly based on numerical solutions of fluid dynamics or simple empirical formulas. While numerical solutions offer high computational accuracy, they are time-consuming and difficult to couple with labyrinth seal optimization design programs. Empirical formula methods offer fast computation speed and strong coupling, but their accuracy is low and their applicability is too limited.

[0005] Therefore, there is an urgent need to develop a prediction scheme for flow loss in labyrinth seals that has high calculation accuracy, fast calculation speed, and wide applicability. Summary of the Invention

[0006] This application proposes a method and system for predicting flow loss in labyrinth seals, which addresses the shortcomings of the prior art.

[0007] According to a first aspect of the embodiments of this application, a method for predicting flow loss in a labyrinth seal is provided, comprising: Define the geometric parameters of the labyrinth seal and the physical parameters of the working fluid; Based on the geometric and physical parameters, dimensionless parameters for characterizing the flow state are calculated. Based on the calculation results of the dimensionless parameters, select the corresponding formula for calculating the flow loss coefficient; The flow loss of the labyrinth seal is calculated based on the aforementioned flow loss coefficient.

[0008] In some embodiments, the geometric parameters of the labyrinth seal include the rotor radius, the sealing gap width, and the sealing axial length; the physical parameters of the working fluid include the gas density, dynamic viscosity, and rotor rotational angular velocity; the sealing gap width is smaller than the rotor radius and the sealing axial length; the working fluid is a Newtonian fluid, and the physical properties of the working fluid are uniformly distributed in the circumferential direction.

[0009] In some embodiments, the dimensionless parameters include the rotating Reynolds number and the gap radius ratio; The rotating Reynolds number is determined based on the linear velocity of the rotor's outer surface and is used to characterize the working fluid flow state; the gap radius ratio is used to characterize the sealing geometry.

[0010] In some embodiments, the formula for calculating the rotating Reynolds number is: ; in, Indicates the rotational Reynolds number; This indicates the density of the gas; This indicates the angular velocity of the rotor. Indicates the rotor radius; This indicates the width of the sealing gap; This indicates the dynamic viscosity of the gas.

[0011] In some embodiments, the formula for calculating the gap radius ratio is: ; in, This indicates the ratio of the gap radii; Indicates the rotor radius; This indicates the width of the sealing gap.

[0012] In some embodiments, the method further includes: The range of the rotating Reynolds number is divided into at least region I and region II. The flow loss coefficient is calculated based on region I and region II. The formula for calculating the flow loss coefficient is as follows: ; in, This represents the flow loss coefficient.

[0013] In some implementations, the selection of the appropriate flow loss coefficient calculation formula includes: Based on the range of the rotating Reynolds number from 10 to 100,000 and the range of the gap radius ratio from 0.02 to 0.10, the corresponding flow loss coefficient calculation formula is selected.

[0014] In some implementations, the range of region I is greater than or equal to 10 and less than 1000, and the range of region II is greater than or equal to 1000 and less than or equal to 100000.

[0015] In some implementations, the formula for calculating the flow loss is: ; in, The value represents flow loss (in W); L represents the axial length of the seal (in m).

[0016] According to a second aspect of this application, a system for predicting flow loss in a labyrinth seal is provided, comprising: The initial parameter definition module is used to define the geometric parameters of the labyrinth seal and the physical parameters of the working fluid; The parameter processing module is used to calculate dimensionless parameters characterizing the flow state based on the geometric and physical parameters. The formula matching module is used to select the corresponding flow loss coefficient calculation formula based on the calculation results of the dimensionless parameters. The flow loss calculation module is used to calculate the flow loss of the labyrinth seal based on the flow loss coefficient.

[0017] The beneficial effects of the method and system for predicting flow loss in labyrinth seals according to embodiments of this application include at least the following: This application's embodiments first construct a complete and standardized input parameter system by defining the geometric parameters of the labyrinth seal and the physical parameters of the working fluid, laying a solid foundation for subsequent quantitative calculations. This ensures that the method has a consistent parameter framework when handling labyrinth seals of different specifications, improving the systematicness and standardization of the method. Based on these parameters, dimensionless parameters used to characterize the flow state are calculated, effectively simplifying complex physical phenomena and extracting essential characteristics. The use of dimensionless parameters allows the method to transcend the limitations of specific sizes and working fluids, significantly improving the versatility and applicability of the prediction model. The selection of the corresponding flow loss coefficient calculation formula based on the calculation results of the dimensionless parameters reflects the method's fine differentiation and adaptive capability for different flow states. This selection mechanism ensures that the calculation model can dynamically match actual working conditions, thereby logically improving the accuracy and reliability of the prediction results. Finally, the flow loss of the labyrinth seal is calculated based on the selected flow loss coefficient, achieving rapid and quantitative evaluation of key sealing performance indicators. This transforms all the aforementioned theoretical calculations into specific engineering application value, providing direct and efficient data support for the optimized design of turbomachinery. Attached Figure Description

[0018] Figure 1This is a flowchart illustrating the method for predicting flow loss in a labyrinth seal according to an embodiment of this application. Figure 2 This is a comparison diagram of the fitted formula plane and the numerical calculation value for region I in an embodiment of this application. Figure 3 This is a comparison diagram of the fitting formula plane and the numerical calculation value for region II in an embodiment of this application. Figure 4 This is a comparative diagram showing the calculated values ​​and numerical calculation results of the flow loss coefficient prediction method at different Reynolds numbers in this application embodiment; Figure 5 This is a diagram illustrating the predicted value of flow loss and its relative deviation from the numerically calculated value in an embodiment of this application. Figure 6 This is a schematic diagram of the overall architecture of the labyrinth seal flow loss prediction system according to an embodiment of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the following method and system for predicting flow loss in labyrinth seals will be described clearly and completely in conjunction with the accompanying drawings of the embodiments of this application. Obviously, the described embodiments are only some embodiments of the embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0020] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed embodiments of the present application, but merely to illustrate selected embodiments of the present application. Other embodiments obtained by those skilled in the art based on the embodiments of the present application without inventive effort are all within the scope of protection of the embodiments of the present application.

[0021] It can be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it will not be further defined and explained in subsequent figures according to the embodiments of this application.

[0022] This application discloses a method for predicting flow loss in labyrinth seals. This method is based on a labyrinth seal flow loss prediction system and can accurately and quickly predict the flow loss of labyrinth seals. It has the advantages of simple calculation, high calculation accuracy, and good coupling, solving the problem of accuracy in labyrinth seal flow loss assessment while improving the speed of loss assessment. This enhances the design level of labyrinth seals and even turbine machinery, and has wide applicability to various engineering problems. (See attached figure) Figure 1As shown, the method includes steps 110-140.

[0023] Step 110: Define the geometric parameters of the labyrinth seal and the physical parameters of the working fluid.

[0024] For example, the geometric parameters of the labyrinth seal include the rotor radius, the seal gap width, and the seal axial length; the physical parameters of the working fluid include the gas density, dynamic viscosity, and rotor rotational angular velocity.

[0025] The sealing gap width is defined based on the distance between the sealing tooth surface and the outer surface of the rotor, and the sealing axial length is defined based on the distance between the first and last sealing tooth surfaces. The sealing gap width is much smaller than the rotor radius and the sealing axial length. The working fluid is a Newtonian fluid, and the physical properties of the working fluid are uniformly distributed in the same direction in the circumferential direction.

[0026] Step 120: Based on the geometric and physical parameters, calculate the dimensionless parameters used to characterize the flow state.

[0027] The flow loss within the labyrinth seal is related to the flow state of the working fluid inside and the sealing geometry parameters. The working fluid flow parameters are represented by the dimensionless rotating Reynolds number, and the labyrinth seal geometry parameters are represented by the dimensionless gap radius ratio.

[0028] In some implementations, the dimensionless parameter includes the rotating Reynolds number and the gap radius ratio.

[0029] For example, the rotating Reynolds number is determined based on the linear velocity of the rotor's outer surface and is used to characterize the working fluid flow state; the gap radius ratio is used to characterize the sealing geometry, and the characteristic length of this geometry is taken as the width of the labyrinth seal gap.

[0030] In some implementations, the rotating Reynolds number is calculated using the following formula: ; in, This represents the rotational Reynolds number; This indicates the density of the gas (unit: kg / m³). This indicates the angular velocity of the rotor (in rad / s). This indicates the rotor radius (in meters). This indicates the width of the sealing gap (in meters). This indicates the dynamic viscosity of a gas (unit: Pa·s).

[0031] In some implementations, the formula for calculating the gap radius ratio is: ; in, This indicates the ratio of the gap radius; This indicates the rotor radius; This indicates the width of the sealing gap.

[0032] Step 130: Based on the calculation result of the dimensionless parameter, select the corresponding formula for calculating the flow loss coefficient.

[0033] In some implementations, the method further includes: The range of the rotating Reynolds number is divided into at least region I and region II, and the flow loss coefficient is calculated based on region I and region II.

[0034] For example, the formula for calculating the flow loss coefficient is as follows: ; in, This represents the flow loss coefficient.

[0035] In some implementations, the selection of the appropriate flow loss coefficient calculation formula includes: selecting the appropriate flow loss coefficient calculation formula based on the range of the rotating Reynolds number from 10 to 100,000 and the range of the gap radius ratio from 0.02 to 0.10.

[0036] For example, the range of region I is greater than or equal to 10 and less than 1000, and the range of region II is greater than or equal to 1000 and less than or equal to 100000.

[0037] Step 140: Calculate the flow loss of the labyrinth seal based on the flow loss coefficient.

[0038] In some implementations, the formula for calculating the flow loss is: ; in, The value represents flow loss (in W); L represents the axial length of the seal (in m).

[0039] This application's embodiments first construct a complete and standardized input parameter system by defining the geometric parameters of the labyrinth seal and the physical parameters of the working fluid, laying a solid foundation for subsequent quantitative calculations. This ensures that the method has a consistent parameter framework when handling labyrinth seals of different specifications, improving the systematicness and standardization of the method. Based on these parameters, dimensionless parameters used to characterize the flow state are calculated, effectively simplifying complex physical phenomena and extracting essential characteristics. The use of dimensionless parameters allows the method to transcend the limitations of specific sizes and working fluids, significantly improving the versatility and applicability of the prediction model. The selection of the corresponding flow loss coefficient calculation formula based on the calculation results of the dimensionless parameters reflects the method's fine differentiation and adaptive capability for different flow states. This selection mechanism ensures that the calculation model can dynamically match actual working conditions, thereby logically improving the accuracy and reliability of the prediction results. Finally, the flow loss of the labyrinth seal is calculated based on the selected flow loss coefficient, achieving rapid and quantitative evaluation of key sealing performance indicators. This transforms all the aforementioned theoretical calculations into specific engineering application value, providing direct and efficient data support for the optimized design of turbomachinery.

[0040] In a specific process of a method for predicting flow loss in a labyrinth seal according to an embodiment of this application, the flow loss of a certain labyrinth seal is predicted, as follows: First, based on the geometric parameters of the labyrinth seal shown in Table 1 below, the flow loss of a certain labyrinth seal was predicted, and the proposed prediction method was verified by numerical calculation method to verify the accuracy of the embodiments of this application.

[0041] Table 1 Geometric parameters of the labyrinth seal

[0042] Based on the above-described method, this application calculates the flow loss coefficient and flow loss of a labyrinth seal under different rotational speeds and clearance widths. It also calculates the relative deviations between the predicted values ​​and the values ​​calculated using the original empirical formulas, and the numerically calculated values. The maximum relative deviation is only 6.5%, which fully verifies the accuracy and reliability of the labyrinth seal flow loss calculation. Compared to traditional numerical solutions or simple empirical formulas, this application's embodiments are computationally simple, have high accuracy, and good coupling. It solves both the accuracy problem of labyrinth seal flow loss assessment and improves the speed of loss assessment, thereby enhancing the design level of labyrinth seals and even turbine machinery. It has broad applicability to various engineering problems.

[0043] See attached document Figure 2 As shown, a comparison between the fitted formula plane and the numerical calculation values ​​for region I is presented. Figure 2It can be observed that the numerical calculation results in region I are uniformly distributed and fit the formula plane, and the sum of squared residuals of the fitting formula is 1.02 × 10⁻⁶. -6 This demonstrates the accuracy of the prediction formula.

[0044] See attached document Figure 3 As shown, a comparison between the fitted formula plane and the numerical calculation values ​​for region II is presented. Figure 3 It can be observed that the numerical calculation results in region II are uniformly distributed and fit the formula plane, and the sum of squared residuals of the fitting formula is 4.90 × 10⁻⁶. -6 This demonstrates the accuracy of the prediction formula.

[0045] See attached document Figure 4 As shown, this paper presents a comparison between the calculated and numerical results of the predicted flow loss coefficient within the labyrinth seal at different Reynolds numbers. Figure 4 It can be observed that the flow loss coefficient decreases with the increase of the Reynolds number, and the numerical calculation results are very close to the values ​​calculated by the prediction method.

[0046] See attached document Figure 5 As shown, the predicted flow loss within a labyrinth seal and its relative deviation from the numerically calculated value are illustrated. Figure 4 It can be seen that the maximum prediction deviation verified by the embodiments of this application is 6.5%, which can meet the application requirements of labyrinth seals and turbine machinery.

[0047] In summary, the method described in this application not only solves the problem of accurately assessing the flow loss of labyrinth seals in turbine machinery, but also further improves the optimization design level of labyrinth seals and turbine machinery. It has a fast calculation speed and the calculation results have high reliability, which can meet different engineering design requirements and has wide applicability to various engineering problems.

[0048] See attached document Figure 6 As shown, this application also discloses a prediction system for flow loss in a labyrinth seal, including: an initial parameter definition module 610, a parameter processing module 620, a formula matching module 630, and a flow loss calculation module 640.

[0049] The initial parameter definition module 610 is used to define the geometric parameters of the labyrinth seal and the physical parameters of the working fluid.

[0050] The parameter processing module 620 is used to calculate dimensionless parameters characterizing the flow state based on the geometric and physical parameters.

[0051] The formula matching module 630 is used to select the corresponding flow loss coefficient calculation formula based on the calculation result of the dimensionless parameter.

[0052] The flow loss calculation module 640 is used to calculate the flow loss of the labyrinth seal based on the flow loss coefficient.

[0053] The system in this embodiment of the application realizes the process and automation of flow loss prediction for labyrinth seals through a modular architecture. It establishes a standardized input foundation through the initial parameter definition module, improves the model's versatility by using dimensionless parameter processing, ensures the accuracy of calculations through intelligent selection by the formula matching module, and finally outputs reliable evaluation results efficiently through the flow loss calculation module. Thus, the overall computational efficiency and engineering applicability of labyrinth seal design and analysis are significantly improved.

[0054] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of this application, and this application is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and substance of this application, and these modifications and improvements are also considered to be within the scope of protection of this application.

Claims

1. A method of predicting flow loss of a labyrinth seal, characterized by, The method comprises: defining geometric parameters of the labyrinth seal and physical parameters of the working medium; calculating dimensionless parameters for characterizing flow states based on the geometric parameters and the physical parameters; selecting a corresponding flow loss coefficient calculation formula according to a calculation result of the dimensionless parameters; calculating flow loss of the labyrinth seal based on the flow loss coefficient.

2. The method of claim 1, wherein, The geometric parameters of the labyrinth seal comprise a rotor radius, a sealing gap width and a sealing axial length; the physical parameters of the working medium comprise gas density, dynamic viscosity and a rotor rotation angular velocity; the sealing gap width is smaller than the rotor radius and the sealing axial length; the working medium is a Newtonian fluid, and physical properties of the working medium are uniformly distributed in a circumferential direction.

3. The method of claim 2, wherein, The dimensionless parameters comprise a rotational Reynolds number and a gap radius ratio; wherein the rotational Reynolds number is determined based on a linear velocity of an outer surface of the rotor and is used for characterizing a flow state of the working medium; the gap radius ratio is used for characterizing geometric characteristics of the seal.

4. The method of claim 3, wherein, The calculation formula of the rotational Reynolds number is: ； wherein, represents the rotational Reynolds number; represents the gas density; represents the rotor angular velocity of rotation; represents the rotor radius; represents the seal gap width; represents the gas dynamic viscosity.

5. The method of claim 4, wherein, The calculation formula of the gap radius ratio is: ； wherein, represents the gap radius ratio; represents the rotor radius; represents the seal gap width.

6. The method of claim 5, wherein, The method further comprises: dividing a range of the rotational Reynolds number into at least region I and region II, and calculating the flow loss coefficient according to the region I and the region II, wherein a calculation formula of the flow loss coefficient is: ； wherein represents the flow loss coefficient.

7. The method of claim 6, wherein, The selecting a corresponding flow loss coefficient calculation formula comprises: based on an interval range of the rotational Reynolds number being 10 to 100000 and an interval range of the gap radius ratio being 0.02 to 0.10, selecting a corresponding flow loss coefficient calculation formula.

8. The method of claim 6, wherein, The interval range of the region I is greater than or equal to 10 to less than 1000, and the interval range of the region II is greater than or equal to 1000 to less than or equal to 100000.

9. The method of claim 6, wherein, The calculation formula of the flow loss is: ； wherein represents the flow loss; L represents the sealing axial length.

10. A system for predicting flow losses of a labyrinth seal, characterized by, The method comprises: an initial parameter definition module configured to define geometric parameters of the labyrinth seal and physical parameters of the working medium; a parameter processing module configured to calculate dimensionless parameters for characterizing flow states based on the geometric parameters and the physical parameters; a formula matching module configured to select a corresponding flow loss coefficient calculation formula according to a calculation result of the dimensionless parameters; a flow loss calculation module configured to calculate flow loss of the labyrinth seal based on the flow loss coefficient.

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