A simplified modeling method and system of a labyrinth for three-dimensional transient simulation of an aircraft engine air system

Abstract

The application discloses a simplified modeling method and system of a labyrinth for three-dimensional transient simulation of an aero-engine air system, and relates to the technical field of aero-engine air system simulation. The method comprises the following steps: simplifying the labyrinth structure into a three-dimensional slit structure; performing three-dimensional numerical simulation on the labyrinth structure before simplification to obtain the drag coefficient and corresponding tooth tip gap, Reynolds number and rotational Reynolds number under each working condition, and generating a drag coefficient database; constructing a functional relationship between the drag coefficient and the tooth tip gap, Reynolds number and rotational Reynolds number; generating a calculation grid according to the three-dimensional slit structure, marking the slit area as a porous medium area, and converting the drag coefficient under the current working condition in the drag coefficient database into a dynamic source term and adding the dynamic source term to the area; and performing three-dimensional transient simulation on the three-dimensional slit structure, in each time step, calculating the current drag coefficient and updating the dynamic source term according to the current tooth tip gap, Reynolds number and rotational Reynolds number through the function until the simulation is completed.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine air system simulation technology, and particularly relates to a simplified modeling method and system for ferrules suitable for three-dimensional transient simulation of aero-engine air systems. Background Technology

[0002] The air system of an aero-engine provides the necessary airflow and pressure for components such as bearing cavity sealing and turbine blade cooling, and is crucial for ensuring reliable engine operation. With the development of computational fluid dynamics (CFD) technology, three-dimensional numerical simulation has become an important tool for analyzing the flow characteristics of air systems, but it still has the following limitations: 1. High computational resource consumption: The air system contains a large number of geometrically complex and small-scale pylon sealing structures. Direct 3D simulation requires the generation of dense meshes, resulting in a 30% to 50% increase in mesh size and a significant increase in computational burden. Especially in transient calculations, where boundary conditions change over time, full 3D analysis requires a large amount of resources, making it difficult to meet the needs of engineering applications.

[0003] 2. The challenge of dynamic changes in gaps and fluid-structure interaction: During engine transitions (such as starting, acceleration, and deceleration), thermal expansion and centrifugal deformation cause dynamic changes in the gaps between the grates. Existing three-dimensional transient simulations struggle to accurately simulate the coupling effect between flow and structural deformation, typically employing unidirectional data transfer or decoupling, which affects simulation accuracy.

[0004] 3. Limited adaptability of simplification methods: Existing simplification methods mainly include the one-dimensional fluid network method and the empirical formula method. The former simplifies the grates into resistance elements and calculates the flow-pressure drop characteristics based on empirical formulas, but it cannot reflect the details of the three-dimensional flow field; the latter is mostly based on steady-state conditions, and has poor adaptability to transient dynamic parameters, thus limiting its accuracy.

[0005] In summary, there is an urgent need to develop a simplified modeling method for pylon structures that balances accuracy and efficiency, in order to achieve high-precision three-dimensional transient simulation of the transition state of air systems. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a simplified modeling method for ferrules in three-dimensional transient simulation of aero-engine air systems, comprising: Parametric analysis was performed on the comb tooth structure, simplifying it into a three-dimensional slit structure; A three-dimensional numerical simulation was performed on the original sieve structure to obtain the drag coefficient and the corresponding tooth tip clearance, Reynolds number and rotational Reynolds number under various working conditions, and a drag coefficient database was generated. By fitting data, a functional relationship is constructed between the drag coefficient and the tooth tip clearance value, the Reynolds number, and the rotational Reynolds number, thus forming a drag coefficient calculation function; A computational mesh is generated based on the three-dimensional slit structure. The slit region of the three-dimensional slit structure is identified as a porous medium region. The drag coefficient under the current working condition is queried from the drag coefficient database. The drag coefficient under the current working condition is converted into a power source item and added to the porous medium region. A three-dimensional transient simulation is performed on the three-dimensional slit structure. In each time step, the drag coefficient is calculated using the drag coefficient calculation function based on the tooth tip gap value, the Reynolds number, and the rotational Reynolds number at the current time. The corresponding power source term is then updated to the porous medium region. This process is repeated until the simulation ends.

[0007] Furthermore, simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and the outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction; Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

[0008] Furthermore, the drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

[0009] Furthermore, converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

[0010] Furthermore, local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

[0011] This invention also proposes a simplified modeling system for ferrules suitable for three-dimensional transient simulation of aero-engine air systems, comprising: A simplification module is used to perform parametric analysis on the comb tooth structure, simplifying the comb tooth structure into a three-dimensional slit structure; The database construction module is used to perform three-dimensional numerical simulation on the unsimplified tooth structure, obtain the drag coefficient and corresponding tooth tip clearance value, Reynolds number and rotational Reynolds number under various working conditions, and generate a drag coefficient database. The function generation module is used to construct a functional relationship between the drag coefficient and the tooth tip clearance value, the Reynolds number and the rotational Reynolds number through data fitting, thereby forming a drag coefficient calculation function; The module for adding a power source item is used to generate a computational mesh based on the three-dimensional slit structure, identify the slit region of the three-dimensional slit structure as a porous medium region, query the drag coefficient under the current working condition in the drag coefficient database, and convert the drag coefficient under the current working condition into a power source item and add it to the porous medium region. The update module is used to perform three-dimensional transient simulation of the three-dimensional slit structure. In each time step, based on the tooth tip gap value, the Reynolds number and the rotating Reynolds number at the current time, the drag coefficient at the current time is calculated through the drag coefficient calculation function, and the corresponding power source term is updated to the porous medium region. The simulation is iterated until the simulation ends.

[0012] Furthermore, simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and the outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction; Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

[0013] Furthermore, the drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

[0014] Furthermore, converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

[0015] Furthermore, local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: 1. Significantly improved computational efficiency: By simplifying the complex grating structure into a three-dimensional slit and replacing solid geometry analysis with the momentum source term method, the number of meshes is significantly reduced. Simultaneously, the simplified flow channel is more regular, improving mesh quality and effectively enhancing computational convergence, thus significantly reducing computational resource consumption and solution time.

[0017] 2. Enhanced adaptability of transient state simulation: To address the problem of dynamic changes in clearance under engine transient conditions, this invention constructs a drag coefficient database and establishes a dynamic query and update mechanism, thereby achieving accurate simulation of clearance changes caused by thermal expansion and centrifugal deformation during transient processes, overcoming the shortcomings of traditional simplified methods in terms of dynamic parameter adaptability.

[0018] 3. Balancing computational accuracy and efficiency: This invention establishes a drag coefficient database based on three-dimensional CFD simulation of detailed filament structures, ensuring that the power source terms have a reliable physical basis; while ensuring the accuracy of the model, a simplified model is used for transient calculation, achieving a good balance between high accuracy and high efficiency.

[0019] 4. Good versatility and scalability: This invention is not limited to specific tooth structures; by adjusting the corresponding drag coefficient database, it can be quickly applied to the sealing modeling of different types of tooth structures. Furthermore, the power source term can be easily integrated into existing commercial CFD software through user-defined functions, demonstrating good engineering applicability and operability. Attached Figure Description

[0020] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention; Figure 2 This is a system structure diagram of Embodiment 2 of the present invention; Figure 3 These are comparison diagrams of the comb tooth structure before and after simplification in Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of adding a power source item in Embodiment 1 of the present invention. Detailed Implementation

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0023] Example 1 like Figure 1 As shown in the figure, this embodiment proposes a simplified modeling method for ferrules in three-dimensional transient simulation of aero-engine air systems, which specifically includes the following steps: Step S1: Perform parametric analysis on the comb tooth structure, simplifying the comb tooth structure into a three-dimensional slit structure, such as... Figure 3 As shown; Taking the high-pressure turbine shaft seal grate of a certain type of engine as an example, the grate contains 5 teeth with a tooth tip clearance ranging from 0.1 to 0.5 mm and a grate height of 3 mm. Sensitivity analysis of geometric parameters revealed that the tooth tip clearance and the number of teeth are key parameters affecting flow resistance, while detailed parameters such as tooth root fillet have a smaller impact. Therefore, the grate structure was simplified into a three-dimensional slit structure, reducing the number of meshes in the grate region from approximately 500,000 to approximately 150,000, a reduction of 70%.

[0024] Specifically, simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and the outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction; Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

[0025] Step S2: Perform three-dimensional numerical simulation on the unsimplified tooth structure to obtain the drag coefficient and corresponding tooth tip clearance value, Reynolds number and rotational Reynolds number under each working condition, and generate a drag coefficient database. A systematic three-dimensional CFD simulation was conducted on the detailed grate structure before simplification to explore its flow characteristics under different operating conditions. The tooth tip gaps considered in the calculations were 0.1, 0.2, 0.3, 0.4, and 0.5 mm; the Reynolds number based on the grate hydraulic diameter and average flow velocity ranged from 1000 to 50000; and the rotational Reynolds number based on the grate radius and rotational speed ranged from 0 to 10000.

[0026] Step S3: Construct a functional relationship between the drag coefficient and the tooth tip clearance value, the Reynolds number, and the rotational Reynolds number through data fitting to form a drag coefficient calculation function; Specifically, the drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

[0027] Preferably, by obtaining the Reynolds number and rotating Reynolds number in each direction, the drag coefficient in each direction can be calculated using the drag coefficient calculation function.

[0028] Step S4: Generate a computational mesh (i.e., a three-dimensional computational mesh for the air system) based on the three-dimensional slit structure. Identify the slit region of the three-dimensional slit structure as a porous medium region. Query the drag coefficient database for the current operating condition and convert the drag coefficient under the current operating condition into a power source item, adding it to the porous medium region. Figure 4 As shown; Specifically, local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

[0029] Specifically, converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

[0030] Preferably, the formula for calculating the power source can be easily integrated into existing commercial CFD software through user-defined functions or other means.

[0031] Step S5: Perform three-dimensional transient simulation on the three-dimensional slit structure. In each time step, calculate the drag coefficient at the current time based on the tooth tip gap value, the Reynolds number and the rotating Reynolds number at the current time through the drag coefficient calculation function, and update the corresponding power source term to the porous medium region. Iterate cyclically until the simulation ends.

[0032] To verify the accuracy of steps S1-S5, a transient simulation of the air system was performed on the acceleration process of a certain type of aero-engine (0-100% speed, time 20s) (step S5 is the transient simulation). Compared with the experimental results, the deviation of the main parameters (flow rate, pressure) obtained by calculation was less than 5%. This not only realized the transient flow heat transfer simulation considering the change of the tooth gap, but also greatly shortened the calculation time and significantly reduced the consumption of computing resources.

[0033] Example 2 like Figure 2 As shown, this embodiment proposes a simplified modeling system for ferrules in three-dimensional transient simulation of aero-engine air systems, specifically including the following modules: A simplification module is used to perform parametric analysis on the comb tooth structure, simplifying the comb tooth structure into a three-dimensional slit structure; Specifically, simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and the outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction; Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

[0034] The database construction module is used to perform three-dimensional numerical simulation on the unsimplified tooth structure, obtain the drag coefficient and corresponding tooth tip clearance value, Reynolds number and rotational Reynolds number under various working conditions, and generate a drag coefficient database. The function generation module is used to construct a functional relationship between the drag coefficient and the tooth tip clearance value, the Reynolds number and the rotational Reynolds number through data fitting, thereby forming a drag coefficient calculation function; Specifically, the drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

[0035] The module for adding a power source item is used to generate a computational mesh based on the three-dimensional slit structure, identify the slit region of the three-dimensional slit structure as a porous medium region, query the drag coefficient under the current working condition in the drag coefficient database, and convert the drag coefficient under the current working condition into a power source item and add it to the porous medium region. Specifically, local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

[0036] Specifically, converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

[0037] The update module is used to perform three-dimensional transient simulation of the three-dimensional slit structure. In each time step, based on the tooth tip gap value, the Reynolds number and the rotating Reynolds number at the current time, the drag coefficient at the current time is calculated through the drag coefficient calculation function, and the corresponding power source term is updated to the porous medium region. The simulation is iterated until the simulation ends.

[0038] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A simplified modeling method for ferrules in three-dimensional transient simulation of aero-engine air systems, characterized in that, include: Parametric analysis was performed on the comb tooth structure, simplifying it into a three-dimensional slit structure; A three-dimensional numerical simulation was performed on the original sieve structure to obtain the drag coefficient and the corresponding tooth tip clearance, Reynolds number and rotational Reynolds number under various working conditions, and a drag coefficient database was generated. By fitting data, a functional relationship is constructed between the drag coefficient and the tooth tip clearance value, the Reynolds number, and the rotational Reynolds number, thus forming a drag coefficient calculation function; A computational mesh is generated based on the three-dimensional slit structure. The slit region of the three-dimensional slit structure is identified as a porous medium region. The drag coefficient under the current working condition is queried from the drag coefficient database. The drag coefficient under the current working condition is converted into a power source item and added to the porous medium region. A three-dimensional transient simulation is performed on the three-dimensional slit structure. In each time step, the drag coefficient is calculated using the drag coefficient calculation function based on the tooth tip gap value, the Reynolds number, and the rotational Reynolds number at the current time. The corresponding power source term is then updated to the porous medium region. This process is repeated until the simulation ends.

2. The simplified modeling method for ferrules applicable to three-dimensional transient simulation of aero-engine air systems as described in claim 1, characterized in that, Simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction. Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

3. The simplified modeling method for ferrules applicable to three-dimensional transient simulation of aero-engine air systems as described in claim 1, characterized in that, The drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

4. The simplified modeling method for ferrules applicable to three-dimensional transient simulation of aero-engine air systems as described in claim 3, characterized in that, Converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

5. The simplified modeling method for ferrules applicable to three-dimensional transient simulation of aero-engine air systems as described in claim 2, characterized in that, Local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

6. A simplified modeling system for ferrules suitable for three-dimensional transient simulation of aero-engine air systems, characterized in that, include: A simplification module is used to perform parametric analysis on the comb tooth structure, simplifying the comb tooth structure into a three-dimensional slit structure; The database construction module is used to perform three-dimensional numerical simulation on the unsimplified tooth structure, obtain the drag coefficient and corresponding tooth tip clearance value, Reynolds number and rotational Reynolds number under various working conditions, and generate a drag coefficient database. The function generation module is used to construct a functional relationship between the drag coefficient and the tooth tip clearance value, the Reynolds number and the rotational Reynolds number through data fitting, thereby forming a drag coefficient calculation function; The module for adding a power source item is used to generate a computational mesh based on the three-dimensional slit structure, identify the slit region of the three-dimensional slit structure as a porous medium region, query the drag coefficient under the current working condition in the drag coefficient database, and convert the drag coefficient under the current working condition into a power source item and add it to the porous medium region. The update module is used to perform three-dimensional transient simulation of the three-dimensional slit structure. In each time step, based on the tooth tip gap value, the Reynolds number and the rotating Reynolds number at the current time, the drag coefficient at the current time is calculated through the drag coefficient calculation function, and the corresponding power source term is updated to the porous medium region. The simulation is iterated until the simulation ends.

7. The simplified modeling system for ferrules suitable for three-dimensional transient simulation of aero-engine air systems as described in claim 6, characterized in that, Simplifying the comb structure into a three-dimensional slit structure includes: retaining the inlet-end contraction structure and outlet-end expansion structure of the comb structure in the two-dimensional cross-section of the comb structure; replacing the middle section tooth structure of the comb structure with a slit structure of equal axial length; the slit width of the slit structure is equal to the tooth tip gap value of the comb structure; and the slit length of the slit structure is equal to the axial length of the comb structure, thereby generating a two-dimensional cross-section of the slit, wherein the axial length is the distance between the outermost points of the two ends of the tooth tip of the comb structure along the axial direction. Maintaining the same rotation axis, rotation radius, and rotation angle as the comb structure, the two-dimensional cross-section of the slit is rotated and swept to generate the three-dimensional slit structure.

8. The simplified modeling system for ferrules applicable to three-dimensional transient simulation of aero-engine air systems as described in claim 6, characterized in that, The drag coefficient calculation function includes: in, The drag coefficient is... Based on the tooth tip clearance value Let be the first polynomial function of the independent variable. Let Reynolds number be the number in question. Based on the tooth tip clearance value Let be the second polynomial function of the independent variable. Based on the tooth tip clearance value Let be the third polynomial function of the independent variable. Let the rotational Reynolds number be , Based on the tooth tip clearance value The fourth polynomial function of the independent variable is determined by least-squares fitting of the simulation data from the three-dimensional numerical simulation. , , and .

9. A simplified modeling system for ferrules suitable for three-dimensional transient simulation of aero-engine air systems as described in claim 8, characterized in that, Converting the drag coefficient under the current operating condition into a power source includes: The drag coefficient Divide by the distance at which the pressure drop occurs to obtain the pressure gradient per unit dynamic head, and calculate the power source: in, The power source item in the direction of the main leakage. The velocity component in the main leakage direction of the tooth tip gap Pressure gradient component in the main leakage direction For the density of the fluid medium, The velocity component in the main leakage direction of the tooth tip gap is represented. The modulus of the total velocity, The velocity component perpendicular to the main leakage direction Pressure gradient component in the main leakage direction For the power source term perpendicular to the main leakage direction, The velocity component in the main leakage direction of the tooth tip gap The pressure gradient component perpendicular to the main leakage direction The velocity component perpendicular to the main leakage direction The pressure gradient component perpendicular to the main leakage direction.

10. A simplified modeling system for ferrules used in three-dimensional transient simulation of aero-engine air systems as described in claim 7, characterized in that, Local mesh refinement is performed near the interface between the porous medium region and the surrounding flow field, and the mesh size of the refined region is no greater than one-fifth of the slit width.

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