A full three-dimensional flow-heat-solid coupling-based calculation method for wear amount of a gullet

Abstract

This invention relates to the field of wear calculation technology, specifically to a method for calculating the wear of a toothed grating based on full three-dimensional fluid-thermal-solid coupling. The method includes constructing a full three-dimensional geometric model of the toothed sealing structure based on multi-physics coupling, and meshing the full three-dimensional geometric model; obtaining the structural field solution results based on a full three-dimensional fluid-thermal-solid bidirectional asynchronous coupling calculation model; determining the contact stress state based on the structural field solution results; and updating the full three-dimensional geometric model in real time according to the wear amount, completing the simulation and quantitative evaluation of the toothed grating wear accumulation process through multiple iterations. This invention deeply integrates multi-physics coupling calculation with the Archard wear model, establishing a quantitative correlation between the coupling effect and the wear amount, simulating the wear accumulation process, and achieving a comprehensive evaluation of the toothed grating wear distribution, wear rate, and remaining life.

Description

Technical Field

[0001] This invention relates to the field of wear calculation technology, specifically to a method for calculating the wear of tooth grates based on full three-dimensional fluid-thermal-solid coupling. Background Technology

[0002] In the field of rotating mechanical seals for aero-engines, accurately predicting the wear of the grating seal structure is crucial, directly impacting the overall efficiency and lifespan of the engine. The grating operates in extremely harsh environments, requiring it to withstand high temperatures, high pressures, and high rotational speeds. Its wear process is a complex result of the combined effects of fluid dynamics, heat transfer, and structural mechanics. Therefore, developing high-precision fluid-thermal-structure interaction (FTH) calculation methods has become a key technological challenge.

[0003] Currently, researchers have mainly developed two technical approaches to balance computational accuracy and efficiency.

[0004] The first approach focuses on improving the computational efficiency of system-level simulations, employing a model simplification strategy. Specifically, they simplify the fluid domain into a one-dimensional airflow network model. Simultaneously, the solid domain, such as the disk and casing, is simulated using a two-dimensional axisymmetric model. These two models are calculated independently. During computation, the fluid model progresses rapidly with a small time step. Only when the accumulated physical time of the fluid calculation reaches the larger time step set by the solid model does the two models pause and exchange data. The fluid transmits parameters such as pressure and temperature to the solid, while the solid feeds back its calculated wall temperature and deformed gap information to the fluid. To further optimize, some advanced methods introduce intelligent control algorithms. These algorithms dynamically adjust the time step of the solid domain based on the rate of change of temperature difference at the fluid-solid interface. When the physical field changes drastically, the step size automatically decreases to ensure accuracy; when the change is gradual, the step size increases to improve efficiency.

[0005] The second approach focuses on achieving high accuracy in component-level simulation, employing fully three-dimensional high-fidelity models. These methods create complete three-dimensional geometric models for key components such as the ferrule, with both fluid and solid components discretized using three-dimensional meshes. A key difference lies in the tightness of coupling. Three-dimensional methods typically employ a tightly coupled strategy, meaning that the fluid and solid components exchange data in real time at each unified time step to ensure strict conservation of energy transfer. This method can accurately capture the complex three-dimensional flow and stress distribution in critical areas such as the ferrule tip.

[0006] Existing technologies have led to different development paths. On the one hand, system-level simplified models have fast computation speeds, making them very suitable for transient performance analysis at the whole-machine level. However, their simplification inevitably results in the loss of complex 3D geometric details and key physical information of the ferrules. On the other hand, component-level 3D high-fidelity models have high accuracy and can clearly reveal local phenomena, but their huge computational resource consumption makes them difficult to apply to wear prediction scenarios that require long-term simulations. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention primarily focuses on the difficulty in predicting the wear of aero-engine ferrules under complex operating conditions in existing technologies. This invention provides a method for calculating ferrule wear based on full three-dimensional fluid-thermal-solid coupling. This method employs full three-dimensional modeling and local dynamic updates, using an adaptive step-size algorithm to obtain the time steps for calculations in both the fluid and solid domains. This constructs an automated bidirectional fluid-thermal-solid coupling calculation method, enabling ferrule wear prediction under complex operating conditions. This further improves analytical accuracy while significantly reducing computational overhead.

[0008] The first objective of this invention is to provide a method for calculating the wear of aero-engine fang teeth based on full three-dimensional fluid-thermal-solid coupling, including: Based on the actual structural parameters of the comb-tooth sealing structure, a full three-dimensional geometric model of the comb-tooth sealing structure based on multi-physics coupling is constructed. The full three-dimensional geometric model includes a solid domain structural model and a fluid domain structural model. Among them, the multi-physics fields include fluid field, temperature field and structural field. Mesh the full 3D geometric model and establish the mesh mapping relationship of the fluid-structure interaction interface; Based on the mesh-based model, the boundary conditions and corresponding material parameters for the fluid field, temperature field, and structural field are set respectively, and the corresponding physical parameters are set based on the selected wear calculation model. A fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model is constructed, and an adaptive step size control algorithm is introduced. The fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model includes a three-dimensional fluid-solid coupled heat transfer transient computational model and a three-dimensional solid domain finite element transient computational model. Based on the meshed model and the set boundary conditions, and based on the full three-dimensional fluid-thermal-solid bidirectional asynchronous coupling calculation model, the fluid field and temperature field are first solved to obtain the fluid-solid coupling calculation results, and then the structural field is solved based on the fluid-solid coupling calculation results to obtain the structural field solution results. The contact stress state is determined based on the structural field solution results. When the contact stress is ≥0, the wear depth and wear volume of the tooth are quantitatively calculated based on the wear calculation model. The coupled calculation step size is adaptively adjusted according to the wear rate change rate. The full three-dimensional geometric model is updated in real time according to the wear amount. The tooth wear accumulation process is simulated and quantitatively evaluated through multiple cycles of iteration.

[0009] In one embodiment, boundary conditions and corresponding material parameters are set for the fluid field, temperature field, and structural field, respectively, including: Fluid field boundary conditions: Input the physical parameters of the working medium, set the inlet pressure, temperature, flow rate, and outlet pressure of the fluid domain, adopt no-slip boundary conditions between the grate teeth and the base wall, and set the coupling interface as the fluid-solid heat transfer and pressure transmission boundary. Temperature field boundary conditions: Set the initial temperature of the solid domain, ensure the continuity of heat flux density at the coupling interface, and input the temperature-related parameters of the material; Structural field boundary conditions: Set the boundary conditions for the grate sealing structure, apply a rotational angular velocity to the grate rotor, and input the mechanical parameters of the material.

[0010] In one embodiment, the implementation method of the full three-dimensional flow-thermal-solid bidirectional asynchronous coupling calculation model is as follows: The fluid field and temperature field are solved by a three-dimensional fluid-structure interaction heat transfer transient calculation model to obtain the fluid-structure interaction calculation results; the fluid-structure interaction calculation results include fluid pressure load and solid domain temperature load; The fluid-structure interaction calculation results are synchronously transferred to the three-dimensional solid domain finite element transient calculation model for structural field solution, completing the structural deformation solution of one coupled time step, and obtaining the solid domain deformation and contact stress. Then, the deformation of the solid domain is used to correct the structure model and boundary conditions of the fluid domain, forming an asynchronous closed-loop coupled iteration. Each physical field is solved according to an independent adaptive step size. The step size coordination coefficient can accurately receive the data between physical fields and eliminate asynchronous transmission deviation.

[0011] In one embodiment, the fluid field is solved by combining the three-dimensional compressible Navier-Stokes equations with the standard k-ε three-dimensional turbulence model to obtain the temperature field, heat flux density, and fluid pressure load at the fluid-structure interaction surface.

[0012] In one embodiment, the temperature field is solved by using the three-dimensional unsteady heat conduction equation and the convection heat transfer equation. The convection heat transfer boundary of the coupling interface is defined based on Newton's cooling formula. The temperature field and heat flux density of the fluid-structure interaction surface transferred by the fluid field are combined to perform a coupled solution to obtain the temperature load of the solid domain.

[0013] In one embodiment, the structural field solution is based on the three-dimensional elasticity equations, combined with the fluid pressure load transmitted by the fluid field and the temperature load of the solid domain transmitted by the temperature field, to solve the stress field, strain field and displacement field of the solid domain, and obtain the deformation and contact stress of the solid domain.

[0014] In one embodiment, the wear calculation model adopts the temperature-pressure dual-parameter modified Archard wear calculation model, which corrects the basic wear coefficient by introducing temperature correction coefficient and pressure correction coefficient.

[0015] In one embodiment, the adaptive step size control rule specifically includes: defining the wear rate change rate of adjacent coupled steps; when the wear rate is stable, keeping the calculation step size unchanged; when the wear rate increases sharply, triggering a step size reduction mechanism to reduce the iteration step size and improve calculation accuracy; when the wear rate decreases sharply, triggering a step size amplification mechanism to increase the iteration step size and improve calculation efficiency, and all adjusted step sizes are limited to a preset threshold range; wherein, defining Indicates the rate of change of wear, when The time is a stable state; The time is a period of rapid increase; It was a period of sudden drop.

[0016] In one embodiment, the iterative update process is as follows: after completing the wear amount solution and geometric model correction by single-step coupling calculation, the multi-physics coupling solution, wear calculation, and geometric update process are repeated to realize the dynamic cumulative simulation of the wear morphology of the sieve teeth and accurately restore the wear failure characteristics of the sieve teeth under different working durations.

[0017] In one embodiment, the partitioned meshing strategy specifically includes: the fluid domain structure model adopts a tetrahedral unstructured mesh, and the mesh is locally refined in the region where the velocity gradient changes abruptly in the gap between the comb teeth; the solid domain structure model adopts a hexahedral structured mesh, and the mesh is locally refined in the wear-sensitive region.

[0018] The present invention has at least the following beneficial effects: This invention provides a method for calculating the wear of sieve teeth based on full three-dimensional fluid-thermal-solid coupling. This method uses a full three-dimensional geometric model and a two-way coupling algorithm to fully preserve the structural details of the sieve teeth and the three-dimensional spatial distribution characteristics of multiple physical fields, revealing the interaction mechanism of fluid, heat and solid, overcoming the problem of insufficient accuracy caused by the simplification of two-dimensional models, and greatly improving the accuracy of wear prediction.

[0019] This invention employs a bidirectional asynchronous coupling algorithm. Its core logic is based on the asynchronous logic of "fluid-structure interaction heat transfer to obtain temperature field + solid surface pressure load transfer → structural field solution for single-step deformation → geometric correction feedback". This eliminates the inter-field waiting constraints of traditional synchronous coupling. With adaptive step size control, it can solve the wear amount according to the appropriate step size, avoiding the drawbacks of "insufficient accuracy" or "low efficiency" of fixed step size. Compared with traditional synchronous coupling algorithms, the computational efficiency is improved by more than 30%, while ensuring the computational accuracy of the wear abrupt change stage and the multi-field coupling region.

[0020] This invention deeply integrates multiphysics coupling calculation with the Archard wear model to establish a quantitative correlation between coupling effect and wear amount. It can simulate the wear accumulation process and achieve a comprehensive assessment of the wear distribution, wear rate and remaining life of the toothed filaments, adapting to the wear analysis needs under complex working conditions. Furthermore, through adaptive mesh updating and coupled iterative optimization, it balances computational accuracy and efficiency, without relying on a large number of physical experiments. It can quickly complete toothed filament wear simulation and structural optimization during the design stage, shortening the R&D cycle and reducing costs.

[0021] This invention is applicable to different types of toothed structures (straight teeth, helical teeth, honeycomb teeth) and different working conditions (start-stop, variable load, high temperature and high pressure), and can be extended to various power equipment with toothed sealing structures such as aero engines and gas turbines, with a wide range of application scenarios. Attached Figure Description

[0022] Figure 1 A flowchart of a method for calculating the wear of comb teeth based on full three-dimensional fluid-thermal-solid coupling provided by the present invention; Figure 2 Flowchart of the fluid-thermal-solid coupling computational framework; Figure 3 This is a schematic diagram of an adaptive asynchronous iterative computation framework; Figure 4 Schematic diagrams of the fluid domain (a) and the solid domain (b); Figure 5 This is a full three-dimensional geometric model of the comb-tooth sealing structure. Detailed Implementation

[0023] In order to illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following detailed description is provided in conjunction with the embodiments.

[0024] In aero-engines, the ferrule sealing structure is crucial, and its wear prediction directly impacts overall engine efficiency and lifespan. The ferrules operate in high-temperature, high-pressure, and high-speed environments. The wear process involves complex interactions between fluids, temperature fields, and structural deformation; therefore, high-precision fluid-thermal-structure interaction (FTH) calculation methods are required.

[0025] Existing technologies mainly fall into two categories. One approach prioritizes computational efficiency and is used for system-level analysis. These methods employ simplified models: a one-dimensional airflow path model is used to simulate the fluid domain, while a two-dimensional axisymmetric model is used to handle the solid domain. The two models are calculated separately. The fluid model performs rapid calculations with a small time step. When the fluid calculation time accumulates to the time step of the solid model, the two models exchange data: the fluid transmits pressure and temperature information to the solid, and the solid provides feedback to the fluid regarding wall temperature and the resulting gap after deformation. Some methods also incorporate intelligent algorithms, such as PID controllers. These algorithms dynamically adjust the time step based on changes in the fluid-solid temperature difference. When the physical field changes rapidly, the step size automatically decreases; when the change is slow, the step size increases, thereby improving computational efficiency.

[0026] Another type of method pursues high accuracy and is used for component-level analysis. These methods employ a full 3D high-fidelity model, with both the fluid and solid domains using 3D meshes. The coupling is tighter, and the fluid and solid exchange data in real time at each time step, which ensures the conservation of heat flux and temperature transfer. The 3D method can accurately capture the complex flow and stress details in the local area of ​​the grating.

[0027] Existing technologies each have their own advantages and disadvantages. System-level simplified models have fast calculation speed and are suitable for whole-machine analysis, but model simplification will lose three-dimensional geometric details and physical information. Component-level three-dimensional models have high accuracy and can clearly show local phenomena, but the calculation cost is very high and it is difficult to use for long-term wear prediction.

[0028] This invention aims to overcome the shortcomings of existing technologies and provide a full three-dimensional fluid-thermal-structure coupling calculation method for tooth wear. By constructing a full three-dimensional multiphysics coupling model, it reveals the interaction mechanism of fluid field, temperature field and structural field, establishes a quantitative correlation between coupling effect and tooth wear, realizes efficient simulation of tooth wear process, working condition wear prediction and life assessment, and provides reliable theoretical support for the optimized design of tooth sealing structure.

[0029] See Figure 1 As shown, a method for calculating the wear of aero-engine fang teeth based on full three-dimensional fluid-thermal-structure coupling is presented, which is used to calculate the wear of aero-engine fang teeth. The method includes: S1. Constructing the full 3D geometric model and mesh generation of the comb-tooth sealing structure: Based on the actual structural parameters of the comb-tooth sealing structure, a full three-dimensional geometric model of the comb-tooth sealing structure based on multi-physics coupling is constructed. The full three-dimensional geometric model includes a solid domain structural model and a fluid domain structural model. Among them, the multi-physics fields include fluid field, temperature field and structural field. Mesh the full 3D geometric model and establish the mesh mapping relationship of the fluid-structure interaction interface; The specific strategies for partitioning the mesh include: using a tetrahedral unstructured mesh for the fluid domain structure model, and locally refining the mesh in areas where the velocity gradient changes abruptly in the gaps between the comb teeth; and using a hexahedral structured mesh for the solid domain structure model, and locally refining the mesh in wear-sensitive areas.

[0030] For example, the actual structural parameters of the toothed seal structure include the disk cavity structural parameters and tooth profile parameters; a full three-dimensional geometric model of the toothed seal structure is constructed using three-dimensional modeling software, in which the wear area of ​​the toothed seal is parametrically modeled, and irrelevant redundant structures such as chamfers and roundings are eliminated to optimize computational efficiency. After establishing the solid domain structural model of the toothed seal, Boolean operations are used to extract the fluid domain model. In this invention, the fluid domain includes the mainstream fluid domain and the secondary fluid domain; the solid domain includes the disk cavity structure and the toothed structure.

[0031] During the mesh generation process, the mesh is refined in areas with large velocity gradients, such as the gaps between the grates; the mesh density is optimized in wear-sensitive areas such as the tooth tips and contact interfaces to ensure the accuracy of stress calculation; and a mesh mapping relationship for the fluid-structure interaction interface is established to ensure the continuous transfer of physical quantities such as temperature, pressure, heat transfer coefficient, and velocity during the coupling process.

[0032] S2. Set the multiphysics coupling boundary conditions and physical parameters: Based on the mesh-based model, the boundary conditions and corresponding material parameters for the fluid field, temperature field, and structural field are set respectively, and the corresponding physical parameters are set based on the selected wear calculation model. Set the boundary conditions and corresponding material parameters for the fluid field, temperature field, and structural field, respectively, including: Fluid field boundary conditions: Input the physical parameters of the working medium, set the inlet pressure, temperature, flow rate, and outlet pressure of the fluid domain, adopt no-slip boundary conditions between the grate teeth and the base wall, and set the coupling interface as the fluid-solid heat transfer and pressure transmission boundary; physical parameters include density, viscosity, specific heat capacity, and thermal conductivity.

[0033] Temperature field boundary conditions: Set the initial temperature of the solid domain to ensure the continuity of heat flux density at the coupling interface, and input the temperature-related parameters of the material; the purpose of setting the initial temperature of the solid domain is to consider fluid convection heat transfer and solid heat conduction. The temperature-related parameters include the material's thermal conductivity, coefficient of thermal expansion, and other temperature-dependent parameters.

[0034] Structural field boundary conditions: Set the boundary conditions for the grate seal structure, apply a rotational angular velocity to the grate rotor, and input the mechanical parameters of the material. Consider centrifugal force, thermal stress, and fluid pressure loads. The input mechanical parameters of the material include elastic modulus, Poisson's ratio, yield strength, and wear coefficient. The wear calculation model adopts the temperature-pressure dual-parameter modified Archard wear calculation model, which corrects the basic wear coefficient by introducing temperature correction coefficient and pressure correction coefficient.

[0035] S3. Construct a fully three-dimensional fluid-thermal-solid bidirectional coupled computational model: A fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model is constructed, and an adaptive step size control algorithm is introduced. The fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model includes a three-dimensional fluid-solid coupled heat transfer transient computational model and a three-dimensional solid domain finite element transient computational model. Based on the meshed model and the set boundary conditions, and based on the full three-dimensional fluid-thermal-solid bidirectional asynchronous coupling calculation model, the fluid field and temperature field are first solved to obtain the fluid-solid coupling calculation results, and then the structural field is solved based on the fluid-solid coupling calculation results to obtain the structural field solution results. In this invention, a fluid-heat-solid bidirectional asynchronous coupled computational framework is constructed based on the finite element and finite volume coupling algorithm. An adaptive step size control algorithm is incorporated to realize asynchronous feedback and dynamic step size optimization of multiple physics fields. The principle of the construction is as follows: the temperature field of the solid domain is first obtained through fluid-solid coupled heat transfer calculation, and the fluid pressure load on the solid surface is extracted at the same time. The temperature field and pressure load are synchronously transferred to the structural field calculation to complete the structural deformation solution of one coupled time step. The deformation result is then used to correct the geometry and boundary conditions of the fluid domain, forming an asynchronous closed-loop coupling of "fluid-solid coupled heat transfer to obtain temperature field + solid surface pressure load transfer → structural field solution of single-step deformation → geometric correction feedback".

[0036] Among them, the core advantage of bidirectional asynchronous is that it does not require waiting for the synchronous convergence of each physical field. It can solve independently according to its own adaptive step size, and realize the inter-field linkage through the timed transmission of load and temperature, thus balancing coupling accuracy and computational efficiency.

[0037] The adaptive step size control algorithm is designed with an asynchronous mechanism and adopts a multi-field step size decoupling and cooperative strategy, setting the basic time step size of the fluid-structure interaction field separately. Structural field foundation time step Through step size coordination coefficient ( Establish a correlation to satisfy the structural field step size adaptation relationship: (Equation 1) ensures that the structural field step size can accurately receive the load and temperature data transmitted by the fluid-structure interaction field, and avoids asynchronous transmission deviation caused by step size mismatch.

[0038] The implementation method of the full three-dimensional flow-thermal-solid bidirectional asynchronous coupling calculation model is as follows: The fluid field and temperature field are solved by a three-dimensional fluid-structure interaction heat transfer transient calculation model to obtain the fluid-structure interaction calculation results; the fluid-structure interaction calculation results include fluid pressure load and solid domain temperature load; The fluid-structure interaction calculation results are synchronously transferred to the three-dimensional solid domain finite element transient calculation model for structural field solution, completing the structural deformation solution of one coupled time step, and obtaining the solid domain deformation and contact stress. Then, the deformation of the solid domain is used to correct the structure model and boundary conditions of the fluid domain, forming an asynchronous closed-loop coupled iteration. Each physical field is solved according to an independent adaptive step size. The step size coordination coefficient can accurately receive the data between physical fields and eliminate asynchronous transmission deviation.

[0039] The fluid field solution is obtained by combining the three-dimensional compressible Navier-Stokes equations with the standard k-ε three-dimensional turbulence model to obtain the temperature field, heat flux density and fluid pressure load at the fluid-structure interaction surface.

[0040] The temperature field is solved by using the three-dimensional unsteady heat conduction equation and the convection heat transfer equation. Based on Newton's cooling formula, the convection heat transfer boundary of the coupling interface is defined. The temperature field and heat flux density of the fluid-structure interaction surface transferred by the fluid field are combined to obtain the temperature load of the solid domain.

[0041] The structural field solution is based on the three-dimensional elasticity equations, combined with the fluid pressure load transmitted by the fluid field and the temperature load of the solid domain transmitted by the temperature field, to solve the stress field, strain field and displacement field of the solid domain, and obtain the deformation and contact stress of the solid domain.

[0042] For example, the fluid field solution is achieved using the three-dimensional compressible Navier-Stokes equations, specifically in Cartesian coordinates using tensor form combined with the standard k-ε three-dimensional turbulence model. This fully characterizes the fluid density changes and triaxial flow characteristics under high temperature and high pressure conditions. The three-dimensional compressible Navier-Stokes equations are as follows: 1) Three-dimensional compressible continuity equation: (Equation 1) In the formula, The instantaneous density of the fluid. For velocity tensor components, For spatial coordinate tensor components, For time.

[0043] 2) Three-dimensional compressible momentum equation: (Equation 2) In the formula, For hydrostatic pressure, These are the components of the gravitational acceleration tensor. For the tensor components of the volume force source term, For the three-dimensional viscous stress tensor, For velocity components, These are spatial coordinate components.

[0044] 3) Three-dimensional compressible energy equation: (Equation 3) In the formula, The total energy per unit mass of fluid. The thermal conductivity of the fluid, For temperature, To correct the viscous dissipation tensor, The intensity of the internal heat source.

[0045] The standard k-ε three-dimensional turbulence model includes the three-dimensional turbulent kinetic energy k equation and the three-dimensional dissipation rate ε equation, as follows: Three-dimensional turbulent kinetic energy k-equation: (Equation 4) Three-dimensional dissipation rate ε equation: (Equation 5) In the formula, For three-dimensional turbulent viscosity, The turbulent kinetic energy tensor generated by the three-dimensional average velocity gradient. The turbulent kinetic energy generated by three-dimensional buoyancy. For compressibility effect term, Turbulent dissipation rate refers to the rate at which the kinetic energy of turbulent fluctuations is converted into heat energy per unit mass of fluid. Turbulent kinetic energy refers to the turbulent pulsating kinetic energy per unit mass of fluid. , , , These are empirical constants, for example, with values ​​of 0.09, 1.44, 1.92, and 0.85.

[0046] Based on the boundary conditions of the fluid field and the solid field, the three-dimensional compressible tensor equations are discretized using the finite volume method. The pressure-velocity-density coupled problem is solved using the SIMPLEC algorithm, combined with the ideal gas law. , Assuming the gas constant, we correlate density with pressure and temperature to ultimately obtain the temperature field of the fluid-structure interaction surface, as well as the heat flux density and fluid pressure load.

[0047] Temperature field solution: Based on the coupled solution of the three-dimensional unsteady heat conduction equation and the convection heat transfer equation, the temperature field and heat flux density characteristics of the fluid-structure interaction surface are adapted to the fluid field solution. The core formula is as follows: 1) Solid domain heat conduction equation: (Equation 6) In the formula, This is the density of the solid (a constant). For isobaric specific heat capacity, Thermal conductivity of solids It serves as an internal heat source.

[0048] 2) Fluid domain convective heat transfer equation: (Equation 7) In the formula, For fluid density, For the convective heat transfer tensor term, For isobaric specific heat capacity, The thermal conductivity of the fluid, For fluid viscosity dissipation tensor.

[0049] 3) The convective heat transfer boundary conditions at the coupled interface follow Newton's law of cooling: (Equation 8) In the formula, For heat flux density, The convective heat transfer coefficient is... The solid wall temperature, This refers to the mainstream temperature of the compressible fluid.

[0050] This invention combines the three-dimensional heat flux density boundary of the fluid field and uses the finite element method to solve the tensor equation to obtain the basic data of temperature gradient and thermal stress distribution of the comb teeth and the matrix. That is, the temperature load of the solid domain provides accurate thermal load for the structural field solution.

[0051] Structural field solution: Based on the three-dimensional elasticity equations, considering the temperature load, fluid pressure load, and the set rotational centrifugal load in the solid domain, the core formulas are as follows: 1) Equations of motion: (Equation 9) In the formula, For Cauchy stress tensor, These are the volume force vector tensor components (including fluid pressure load and centrifugal force). For the density of solid materials, These are the components of the acceleration tensor.

[0052] 2) Geometric equations: (Equation 10) In the formula, For the total strain tensor, For thermal strain tensor, The volumetric expansion coefficient refers to the strain rate generated by the isotropic expansion / contraction of a fluid element due to temperature changes. The Kronecker delta function is a coefficient that describes the change in volume / length of a fluid as its temperature changes. Temperature change refers to the temperature change of a fluid element. These are the components of the elastic strain tensor.

[0053] 3) Constitutive equation: (Equation 11) In the formula, , Let Lamé constant be . For elastic modulus, Poisson's ratio, Let be the volumetric strain tensor.

[0054] 4) Formula for calculating centrifugal load: (Equation 12) In the formula, For rotating centrifugal loads, Angular velocity of rotation Let be the tensor component of the distance from the particle to the axis of rotation. ρ is the density of the solid material.

[0055] The finite element method is used to solve the tensor equations to obtain the stress, strain, and displacement fields of the solid domain of the comb-tooth sealing structure. The contact pressure and relative sliding distance between the comb tooth tip and the bushing are calculated, representing the deformation and contact stress of the solid domain. Local stress concentrations in the contact pressure are corrected using Hertzian contact theory. (Equation 13) In the formula, For contact load, For contact width, , These are the radii of curvature of the two contacting bodies at the point of contact, i.e. Let be the radius of the first cylinder or contact body 1. The radius of the second cylinder or contact body 2.

[0056] S4. Coupled Iterative Calculation and Quantitative Assessment of Wear: The contact stress state is determined based on the structural field solution results. When the contact stress is greater than 0, the wear depth and wear volume of the tooth are quantitatively calculated based on the wear calculation model. The coupled calculation step size is adaptively adjusted according to the wear rate change rate. The full three-dimensional geometric model is updated in real time according to the wear amount. The tooth wear accumulation process is simulated and quantitatively evaluated through multiple cycles of iteration.

[0057] The adaptive step size control rules specifically include: defining the wear rate change rate of adjacent coupled steps; keeping the calculation step size unchanged when the wear rate is stable; triggering the step size reduction mechanism when the wear rate increases sharply to reduce the iteration step size and improve calculation accuracy; and triggering the step size amplification mechanism when the wear rate decreases sharply to increase the iteration step size and improve calculation efficiency. All adjusted step sizes are limited to the preset threshold range.

[0058] Among them, the definition Indicates the rate of change of wear, when The time is a stable state; The time is a period of rapid increase; It was a period of sudden drop.

[0059] The iterative update process is as follows: after completing the wear amount solution and geometric model correction in single-step coupled calculation, the multiphysics field coupled solution, wear calculation, and geometric update process are repeated to realize the dynamic cumulative simulation of the wear morphology of the tooth and accurately restore the wear failure characteristics of the tooth under different working durations; among them, geometric model correction refers to the correction of the morphology of the wear area at the tooth tip.

[0060] See Figure 2 As shown, in the step-by-step time-series solution of the fluid-thermal-solid-wear multi-field coupling, the entire calculation is divided into two main modules: the left box (fluid-solid coupled heat transfer field solution) and the right box (structural field solution). A step-by-step time coupling strategy is adopted: first, the fluid field and temperature field are solved, and then the structural mechanics and wear calculations are performed simultaneously, with time steps... The transient simulation is carried out cyclically across the entire time domain.

[0061] Solving for fluid-structure interaction heat transfer fields specifically includes: Construct a three-dimensional fluid-structure interaction transient heat transfer calculation model: geometry, fluid / solid domain partitioning, boundary conditions (fluid inlet pressure / temperature, initial solid temperature, rotational angular velocity, etc.) and material parameters (density, thermal conductivity, elastic modulus, hardness, etc.). initialization Physical quantities of the entire field at any given time: given initial temperature, flow rate, pressure, and initial field; Read Transient boundary conditions at any time: fluid inlet pressure / temperature, initial solid temperature, rotational angular velocity, etc. Solve The fluid domain field and solid domain temperature field at any time: The three-dimensional compressible Navier-Stokes equations combined with the standard k-ε turbulence model are used to solve for the velocity field, pressure field, temperature field and heat flux density of the fluid domain; Output The fluid-structure interaction results at any given time combine the hydrostatic load P obtained from the fluid field solution and the solid temperature load obtained from the temperature field solution. T sSimultaneously transferred to the solid domain finite element model; Time progress: Then, proceed to the next heat flow iteration, where... This is the current calculation time. This represents the time step for fluid-structure-thermal coupling. Decision branch Once the thermal field completes a time step update, the temperature data at that moment is transmitted to the right-side structural field as a thermal load.

[0062] The solution of the structural field specifically includes: Three-dimensional transient finite element model of solids: solid structure mesh, constitutive model, and contact pair modeling; Receive data from the left: Read Three types of loads at any given time: Thermal load (from the fluid-structure heat transfer temperature field in the left frame), centrifugal load (centrifugal force of rotating parts), fluid pressure load; Read Time-boundary constraints: structural fixed constraints and contact constraints inherit the results from the previous step; Finite element solution Solid deformation and contact stress; Based on the structural field solution results, the contact stress between the tooth tip and the bushing is extracted. If contact stress If there is no contact, wear is not calculated, and the process proceeds directly to the next coupling step; if... If there is contact, wear calculation is triggered.

[0063] Wear increment calculation specifically includes: Read the wear calculation boundary conditions: wear coefficient, friction coefficient, contact range and other wear model parameters; Solve to Material wear within a single step: Based on the Archard wear formula, the material removal thickness at this time step is calculated using the current contact stress; Obtain solid wear results: Wear causes changes in structural geometry, and the wear results are fed back to the final output.

[0064] See Figure 3 As shown, during the fluid-structure interaction iteration, one coupling time step is first solved. and transmit to the structural field Temperature field in the solid domain and pressure load on the wall at any given time; Read after initializing the structural field Structural calculations are performed under constant load. Based on the structural field calculation results, wear calculations are not performed when the contact stress is <0. The coupling time step size remains unchanged, and the next coupling time step is directly entered to perform fluid-thermal-structure coupling iterative calculations. When the contact stress is ≥0, the wear amount is calculated; the modified Archard wear model is used to quantitatively calculate the wear amount.

[0065] For example, based on an adaptive step size control algorithm, intelligent step size adjustment is achieved, with the following specific rules: Wear Conditions and Asynchronous Adaptation: Defining the Wear Rate Change Rate: (Equation 14) In the formula, , These represent the wear depths of two adjacent steps, The rate of change of wear rate, This represents the coupling time step size corresponding to the current time step. when At this time, the calculation step size remains unchanged, and the next coupled time step calculation is performed; when When the time step is reduced, the step size reduction mechanism is triggered to perform the calculation for the next coupled time step. The new step size is calculated according to the formula: (Equation 15) Update, for example, The time step reduction correction factor is defined empirically and all satisfy the following conditions: To avoid a sharp drop in efficiency due to excessively small step sizes; when At that time, the step size amplification mechanism is triggered to perform the calculation for the next coupling time step, according to the formula: (Equation 16) Enlarged, for example, The time step magnification correction factor is defined empirically and all satisfy the following conditions. This avoids a sharp drop in accuracy due to excessively large step sizes.

[0066] Wear Calculation: Based on the converged structural field stress and displacement results, the contact pressure and relative sliding distance between the tooth tip and the substrate are extracted. The modified Archard wear model is used to quantitatively calculate the wear amount. The calculation formula is as follows: 1) Wear volume formula: (Equation 17) In the formula, For wear volume, The wear coefficient (related to material pairing and surface condition). For normal contact force, This is the relative sliding distance. The Brinell hardness of the material.

[0067] 2) Wear depth per unit time Calculation formula: (Equation 18) In the formula, For wear volume, For contact area, For average contact pressure, This is the relative sliding distance. The wear coefficient is... The Brinell hardness of the material.

[0068] 3) Considering the multiphysics coupling effect, the wear coefficient... Make corrections: (Equation 19) In the formula, The wear coefficient of the base under normal temperature and pressure. This is the temperature correction factor. This is the pressure correction factor. The reference value is the room temperature. The amplitude of the contact pressure is used. The wear depth and wear volume per unit time are calculated using the above formulas to clarify the wear distribution pattern in three-dimensional space. It should be noted that during the structural field solution process, when the calculation residual reaches a certain standard, the structural field calculation is considered accurate, and the calculation is said to have converged.

[0069] To further illustrate the method for calculating tooth wear based on full three-dimensional fluid-thermal-solid coupling provided by this invention, specific examples and accompanying drawings are used for explanation.

[0070] Example Calculation of interstage tooth wear in aero-engine compressors, including: Geometric modeling and mesh generation: (1) Establish a solid domain model. Considering the axisymmetric properties of the comb and stator casing model and the mesh complexity of the complete cycle, the solid domain part is constructed as a 1 / 36 cycle model of the comb and stator casing, such as... Figure 4 As shown, monitoring surfaces are set on the tooth tip and bushing surface of the grates to detect the radial deformation of the grates. Specifically, in step n (n≥2), a local dynamic update strategy is used for reconstruction. The grate radius is adjusted to update the geometry, keeping the dimensions and structure of the disk cavity and other parts unchanged. This approach preserves the accuracy of the 3D model while reducing the computational load during model and mesh reconstruction.

[0071] (2) Establish the corresponding fluid domain model, such as Figure 4 As shown, the boundary of the fluid domain model is defined as follows: Figure 4 As shown, the model has two inlets and outlets, where INLET1 and OUTLET1 are the inlet and outlet of the cold airflow path in the disc cavity, respectively, and INLET2 and OUTLET2 are the inlet and outlet of the airflow in the sealed cavity, respectively.

[0072] (3) Figure 4 The solid domain (b) shown in the figure shares topology with the fluid domain (a) to form a coupled model suitable for fluid-structure heat transfer calculations, such as... Figure 5 As shown. The mesh was then created, with the toothed portion refined, and fluid and solid wall boundary layers added to meet the computational requirements.

[0073] Boundary conditions and physical parameter settings: The working medium in both the main flow domain and the secondary flow domain is air, with pressure boundary conditions at the inlet and outlet. The inlet and outlet pressures of both the main flow and secondary flow domains change over time. The initial temperature of the solid domain is 300 K, and the solid domain material is a high-temperature alloy such as Inconel 718, with an elastic modulus of 200 GPa, Poisson's ratio of 0.3, and a coefficient of thermal expansion of 12 × 10⁻⁶. -6 / ℃, wear coefficient K=2×10 - 15 m 3 / (N·m), solid domain rotor rotational angular velocity 10000r / min, considering centrifugal load.

[0074] Construction of a coupled computational model: Based on the ANSYS multiphysics coupling platform, Fluent is used to solve the fluid-structure interaction field, and ANSYS Mechanical is used to solve the structural field, thus building a bidirectional asynchronous coupling framework.

[0075] Setting basic parameters: Basic step size for fluid-structure interaction field , structural field foundation step length The fluid-structure interaction field is in one coupling time step per iteration. It transmits the solid-domain temperature field and wall pressure load to the structural field.

[0076] Coupled Iteration and Wear Calculation: See Figure 2 and Figure 3 As shown, the fluid-structure interaction field is first iterated to solve for one coupling time step. and transmit to the structural field Temperature field in the solid domain and pressure load on the wall at any given time; Read after initializing the structural field Structural calculations are performed under constant load. Based on the structural field calculation results, wear calculations are not performed when the contact stress is <0. The coupling time step size remains unchanged, and the next coupling time step is directly entered to perform fluid-thermal-structure coupling iterative calculations. When the contact stress is ≥0, the wear amount is calculated; the modified Archard wear model is used to quantitatively calculate the wear amount.

[0077] An adaptive step size control algorithm enables intelligent step size adjustment, with the following specific rules: when At this time, the calculation step size remains unchanged; when When the step size reduction mechanism is triggered, the next coupled time step calculation is performed, and the new step size is adjusted accordingly. (Equation 15) Update, for example, And all satisfy To avoid a sharp drop in efficiency due to excessively small step sizes; when At that time, the step size amplification mechanism is triggered to perform the next coupled time step calculation, according to... (Equation 16) Enlarged, for example, And all satisfy This avoids a sharp drop in accuracy due to excessively large step sizes.

[0078] Based on the calculation results of wear and structural deformation, the geometry is updated, and the next coupling time step is performed. The fluid-thermal-solid coupling calculation continues until the runtime ends.

[0079] The bidirectional asynchronous algorithm provided by this invention improves efficiency by more than 30% compared with traditional synchronous algorithms while ensuring accuracy through asynchronous interaction between fields and differential control of step size.

[0080] In summary, this invention provides a full three-dimensional fluid-thermal-structure coupling calculation method for tooth wear. By constructing a full three-dimensional multiphysics coupling model, it reveals the interaction mechanism of the fluid field, temperature field, and structural field, establishes a quantitative correlation between the coupling effect and the tooth wear, and realizes efficient simulation of the tooth wear process, working condition wear prediction, and life assessment, providing reliable theoretical support for the optimized design of tooth sealing structures.

[0081] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the wear amount of a gullet based on full three-dimensional flow-heat-solid coupling, characterized by, Used to calculate the wear of aero-engine tooth grates, including: Based on the actual structural parameters of the comb-tooth sealing structure, a full three-dimensional geometric model of the comb-tooth sealing structure based on multi-physics coupling is constructed. The full three-dimensional geometric model includes a solid domain structural model and a fluid domain structural model. Among them, the multi-physics fields include fluid field, temperature field and structural field. Mesh the full 3D geometric model and establish the mesh mapping relationship of the fluid-structure interaction interface; Based on the mesh-based model, the boundary conditions and corresponding material parameters for the fluid field, temperature field, and structural field are set respectively, and the corresponding physical parameters are set based on the selected wear calculation model. A fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model is constructed, and an adaptive step size control algorithm is introduced. The fully three-dimensional fluid-thermal-solid bidirectional asynchronous coupled computational model includes a three-dimensional fluid-solid coupled heat transfer transient computational model and a three-dimensional solid domain finite element transient computational model. Based on the meshed model and the set boundary conditions, and based on the full three-dimensional fluid-thermal-solid bidirectional asynchronous coupling calculation model, the fluid field and temperature field are first solved to obtain the fluid-solid coupling calculation results, and then the structural field is solved based on the fluid-solid coupling calculation results to obtain the structural field solution results. The contact stress state is determined based on the structural field solution results. When the contact stress is ≥0, the wear depth and wear volume of the tooth are quantitatively calculated based on the wear calculation model. The coupled calculation step size is adaptively adjusted according to the wear rate change rate. The full three-dimensional geometric model is updated in real time according to the wear amount. The tooth wear accumulation process is simulated and quantitatively evaluated through multiple cycles of iteration.

2. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, Set the boundary conditions and corresponding material parameters for the fluid field, temperature field, and structural field, respectively, including: Fluid field boundary conditions: Input the physical parameters of the working medium, set the inlet pressure, temperature, flow rate, and outlet pressure of the fluid domain, adopt no-slip boundary conditions between the grate teeth and the base wall, and set the coupling interface as the fluid-solid heat transfer and pressure transmission boundary. Temperature field boundary conditions: Set the initial temperature of the solid domain, ensure the continuity of heat flux density at the coupling interface, and input the temperature-related parameters of the material; Structural field boundary conditions: Set the boundary conditions for the grate sealing structure, apply a rotational angular velocity to the grate rotor, and input the mechanical parameters of the material.

3. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, The implementation method of the full three-dimensional fluid-thermal-solid bidirectional asynchronous coupling calculation model is as follows: The fluid field and temperature field are solved by a three-dimensional fluid-structure interaction heat transfer transient calculation model to obtain the fluid-structure interaction calculation results; the fluid-structure interaction calculation results include fluid pressure load and solid domain temperature load; The fluid-structure interaction calculation results are synchronously transferred to the three-dimensional solid domain finite element transient calculation model for structural field solution, completing the structural deformation solution of one coupled time step, and obtaining the solid domain deformation and contact stress. Then, the deformation of the solid domain is used to correct the structure model and boundary conditions of the fluid domain, forming an asynchronous closed-loop coupled iteration. Each physical field is solved according to an independent adaptive step size. The step size coordination coefficient can accurately receive the data between physical fields and eliminate asynchronous transmission deviation.

4. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, The fluid field is solved by combining the three-dimensional compressible Navier-Stokes equations with the standard k-ε three-dimensional turbulence model to obtain the temperature field, heat flux density and fluid pressure load at the fluid-structure interaction surface.

5. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 4, characterized in that, The temperature field is solved by using the three-dimensional unsteady heat conduction equation and the convection heat transfer equation. Based on Newton's cooling formula, the convection heat transfer boundary of the coupling interface is defined. The temperature field and heat flux density of the fluid-structure interaction surface transferred by the fluid field are combined to obtain the temperature load of the solid domain.

6. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 5, characterized in that, The structural field solution is based on the three-dimensional elasticity equations, combined with the fluid pressure load transmitted by the fluid field and the temperature load of the solid domain transmitted by the temperature field, to solve the stress field, strain field and displacement field of the solid domain, and obtain the deformation and contact stress of the solid domain.

7. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, The wear calculation model adopts the temperature-pressure dual-parameter modified Archard wear calculation model, which corrects the basic wear coefficient by introducing temperature correction coefficient and pressure correction coefficient.

8. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, The adaptive step size control rules specifically include: defining the wear rate change rate of adjacent coupled steps; keeping the calculation step size unchanged when the wear rate is stable; triggering the step size reduction mechanism when the wear rate increases sharply to reduce the iteration step size and improve calculation accuracy; and triggering the step size amplification mechanism when the wear rate decreases sharply to increase the iteration step size and improve calculation efficiency. All adjusted step sizes are limited to the preset threshold range. wherein, the definition represents the wear change rate, when is a stable state; is a sudden increase state; is a sudden decrease state. 9.The full three-dimensional flow-thermal-solid coupling based calculation method of the gullet wear amount according to claim 1, wherein, The iterative update process is as follows: after completing the wear amount solution and geometric model correction in a single-step coupled calculation, the multi-physics field coupled solution, wear calculation, and geometric update process are repeated to realize the dynamic cumulative simulation of the wear morphology of the sieve teeth and accurately restore the wear failure characteristics of the sieve teeth under different working durations.

10. The full three-dimensional flow-thermal-solid coupling-based gullet wear amount calculation method according to claim 1, characterized in that, The specific strategies for partitioning the mesh include: using a tetrahedral unstructured mesh for the fluid domain structure model, and locally refining the mesh in areas where the velocity gradient changes abruptly in the gaps between the comb teeth; and using a hexahedral structured mesh for the solid domain structure model, and locally refining the mesh in wear-sensitive areas.

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