A method for optimizing the layout of wear-resistant elbow ceramic liners based on three-dimensional simulation

Abstract

The application provides a kind of wear-resistant elbow ceramic lining plate optimization layout method based on three-dimensional simulation, it is related to ceramic lining plate technical field, including the following steps: establishing the elbow three-dimensional model containing metal matrix and preset ceramic lining plate initial layout, by the coupling simulation of multiple physical fields, the transient thermal stress and structure stress field suffered by ceramic lining plate are obtained;Based on the distribution characteristics of transient thermal stress and structure stress field, multiple regions with different thermal-mechanical failure risks are divided in the elbow three-dimensional model;According to the failure risk level of the region, different reserved assembly gaps are determined for the ceramic lining plate unit of the corresponding region to form a gradient gap layout;Reserved assembly gap refers to the design distance between ceramic lining plate unit and metal matrix mounting surface under normal temperature in the unfixed state.The application realizes precise preventive layout for thermal-mechanical coupling failure, and proposes a gradient reserved gap active stress control means.

Description

Technical Field

[0001] This invention belongs to the field of ceramic liner technology, specifically relating to an optimized layout method for wear-resistant bent pipe ceramic liners based on three-dimensional simulation. Background Technology

[0002] In industrial sectors such as power generation, metallurgy, and mining, wear-resistant bends conveying high-temperature fluids containing solid particles commonly employ ceramic liners to resist wear. Traditional ceramic liner layouts are primarily based on wear experience, employing uniform thickness or simple segmented installation methods, with the core design goal of resisting erosion wear from fluids and particles. However, under high-temperature or significantly variable-temperature conditions, there is a substantial difference in the coefficients of thermal expansion between the ceramic and the metal matrix. When the temperature changes, the expansion or contraction of the metal matrix is ​​constrained by the ceramic liner, generating significant thermal stress within the ceramic and peeling stress at the interface. This thermo-mechanical coupling effect leads to brittle fracture, cracking, or complete spalling of the ceramic liner, with a failure rate often far exceeding the wear process. This results in early structural failure of the ceramic liner under complex thermomechanical loads, becoming a major bottleneck restricting the long-term reliable operation of bend systems. Summary of the Invention

[0003] In view of the above-mentioned defects or deficiencies in the existing technology, a method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation is provided, including the following steps:

[0004] A three-dimensional model of the bent pipe, including the initial layout of the metal substrate and the pre-set ceramic liner, is established. Through multi-physics coupling simulation, the transient thermal stress and structural stress field of the ceramic liner are obtained.

[0005] Based on the distribution characteristics of the transient thermal stress and structural stress field, multiple regions with different thermal-mechanical failure risks are divided in the three-dimensional model of the bent pipe.

[0006] Based on the failure risk level of the area, different reserved assembly gaps are determined for the ceramic liner units in the corresponding area to form a gradient gap layout; the reserved assembly gap refers to the design distance between the ceramic liner unit and the metal substrate mounting surface in the unfastened state at room temperature.

[0007] According to the technical solution provided in this application, obtaining the transient thermal stress and structural stress field of the ceramic liner through multiphysics coupling simulation includes the following steps:

[0008] The transient temperature field and particle impact load distribution of the inner wall of the three-dimensional model of the bent pipe were obtained by coupled simulation of computational fluid dynamics and discrete element method.

[0009] The transient temperature field and particle impact load distribution are used as load conditions and applied to a finite element model that includes the thermophysical properties of the material for thermo-stress coupling calculation, thereby obtaining the transient thermal stress and structural stress field.

[0010] According to the technical solution provided in this application, the step of dividing the three-dimensional model of the bent pipe into multiple regions with different thermal-mechanical failure risks based on the distribution characteristics of the transient thermal stress and structural stress field includes the following steps:

[0011] Extract the maximum principal stress distribution cloud map of the ceramic liner and the normal peel stress distribution cloud map at the interface between the ceramic liner and the metal substrate;

[0012] Areas where the maximum principal stress value exceeds the first threshold of the allowable tensile strength of ceramic materials, or where the interfacial peel stress value exceeds the second threshold of the interfacial bonding strength, are classified as areas of the first risk level.

[0013] The area where the maximum principal stress value and the interface peeling stress value are both lower than their respective thresholds, and the maximum principal stress value exceeds the first threshold by a set proportion, is classified as the second risk level area.

[0014] The remaining areas are classified as third-risk areas.

[0015] According to the technical solution provided in this application, determining different reserved assembly gaps for the ceramic liner units in the corresponding regions based on the failure risk level of the regions to form a gradient gap layout includes the following steps:

[0016] For the ceramic liner unit in the first risk level area, a first gap value is assigned, which is dynamically calculated based on the maximum principal stress peak value and the material thermal expansion coefficient at its location.

[0017] For the ceramic liner unit in the second risk level area, a second gap value smaller than the first gap value is assigned;

[0018] The ceramic liner unit in the third risk level area is given a zero gap or a micro gap smaller than the second gap value.

[0019] According to the technical solution provided in this application, after forming the gradient gap layout, the following steps are also included:

[0020] A digital twin model of the target bend is established, which integrates gradient gap layout, material constitutive relation and working condition parameters;

[0021] Based on the digital twin model, the thermo-mechanical coupling behavior of the pipe bending system is simulated from cold installation, heating to steady-state operation, and then cooling, and the stress evolution and interface contact state of the ceramic liner are predicted at each stage.

[0022] Based on the simulation results, potential areas that may lead to media leakage or increased particle erosion due to gaps under hot working conditions are identified.

[0023] The reserved assembly gap in the potential area is adjusted in reverse to obtain the final target gap layout.

[0024] According to the technical solution provided in this application, the reverse adjustment of the reserved assembly gap in the potential area includes the following steps:

[0025] Based on the data from the full-process simulation of the digital twin model, for the potential region, the equivalent thermal displacement caused by the constraint of thermal expansion at each location, and the sensitivity coefficient of the sealing interface pressure to the gap change are calculated.

[0026] Based on the ratio of the equivalent thermal displacement to the sensitivity coefficient, the gap adjustment priority at each position is determined, wherein positions with large equivalent thermal displacement and low sensitivity coefficient have higher adjustment priority.

[0027] Prioritize adjusting the reserved assembly gaps at positions with higher adjustment priority, and update the digital twin model for verification. Iterate this process until the structural safety and sealing requirements are met, and obtain the target assembly gaps at each position.

[0028] According to the technical solution provided in this application, after obtaining the target assembly gap at each position, the method further includes the following steps:

[0029] Based on the target assembly gaps at each location, generate a digital model of the back surface of the integrated wear-resistant ceramic liner.

[0030] The integrated wear-resistant ceramic liner is configured as a single component that fits against the inner wall of the metal substrate; its working surface is a continuous curved surface adapted to the flow channel, and its back surface includes a gradient cavity structure that forms the target gap layout between itself and the mounting surface of the metal substrate.

[0031] The depth distribution of the gradient cavity structure corresponds to the target assembly gap at each position in the target gap layout, so that when the integrated wear-resistant ceramic liner is installed in place, the target gap layout is naturally formed between its back cavity and the metal substrate.

[0032] According to the technical solution provided in this application, the ceramic liner unit in the second risk level area is given a second gap value that is smaller than the first gap value, which includes the following steps:

[0033] For the second risk level area, extract the stress gradient distribution data within that area from the maximum principal stress distribution cloud map;

[0034] Calculate the standard deviation and mean stress gradient of the maximum principal stress in this region;

[0035] Based on the standard deviation and the average stress gradient, the initial gap value is dynamically calculated using a preset weighting relationship model.

[0036] Determine whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold;

[0037] If so, the initial gap value is used as the second gap value.

[0038] According to the technical solution provided in this application, after determining whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold, the method further includes the following steps:

[0039] If not, then based on the full-process thermo-mechanical coupling behavior simulation data, calculate the transient thermal shock intensity factor of the second risk level region during the critical transient stage of temperature rise. The transient thermal shock intensity factor is positively correlated with the local temperature and stress change rate.

[0040] The initial gap value is weighted and fused with the transient thermal shock intensity factor to obtain the fused gap value;

[0041] The fusion gap value is used as the second gap value.

[0042] According to the technical solution provided in this application, the simulated pipe bending system's entire thermo-mechanical coupling behavior from cold installation, heating to steady-state operation, and then cooling includes the following steps:

[0043] The digital twin model is pre-set with multiple key event trigger points, including: the ceramic liner and the metal substrate begin to contact, the interfacial adhesive reaches the glass transition temperature, the fluid medium temperature undergoes a step change, and the particle impact load reaches a peak.

[0044] During the simulation, when the system state is close to any of the aforementioned key event trigger points, the simulation time step is switched to a more refined first step size for high-resolution calculation; when the system state is far from all key event trigger points, the simulation time step is switched to a second step size larger than the first step size for further calculation.

[0045] The simulation of the entire thermo-mechanical coupling behavior is completed by cyclically switching and calculating the time step.

[0046] Compared with existing technologies, the advantages of this application are as follows: First, it achieves precise preventive layout against thermo-mechanical coupling failure: through multiphysics coupling simulation, the thermo-mechanical coupling stress field of the ceramic liner is quantitatively obtained during the layout design stage, and the failure risk level is classified accordingly. This expands the design objective from a single wear resistance to a synergistic approach of wear resistance and structural failure resistance, fundamentally solving the problem of early brittle failure of ceramic liners caused by thermal stress under high-temperature and variable-temperature conditions. Second, it proposes an active stress control method with gradient reserved gaps: based on different failure risk levels, reserved assembly gaps are differentially determined for liner units. In high-risk areas, the reserved gaps provide controllable release space for thermal expansion, effectively reducing tensile stress and interface peeling stress inside the ceramic, thereby shifting the failure mode from uncontrollable thermal stress fracture to predictable progressive wear, significantly improving the overall reliability and service life of the liner system. At the same time, it achieves optimized utilization of material properties and improved design efficiency: through simulation-driven risk zoning and gap gradient design, it avoids the use of excessive safety margins in low-risk areas (such as blindly increasing the thickness of the liner or using higher-grade materials), so that the material properties are accurately and fully utilized, and costs are reduced. Attached Figure Description

[0047] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0048] Figure 1 The flowchart illustrates the steps of the method for optimizing the layout of wear-resistant curved pipe ceramic liners based on three-dimensional simulation provided in this application. Detailed Implementation

[0049] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0050] 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.

[0051] As mentioned in the background section, this application proposes a method for optimizing the layout of ceramic liners for wear-resistant bent pipes based on three-dimensional simulation. Figure 1 As shown, it includes the following steps:

[0052] S1. Establish a three-dimensional model of the bent pipe including the initial layout of the metal substrate and the pre-set ceramic liner. Through multi-physics coupling simulation, obtain the transient thermal stress and structural stress field of the ceramic liner.

[0053] S2. Based on the distribution characteristics of the transient thermal stress and structural stress field, multiple regions with different thermal-mechanical failure risks are divided in the three-dimensional model of the bent pipe.

[0054] S3. Based on the failure risk level of the area, determine different reserved assembly gaps for the ceramic liner unit in the corresponding area to form a gradient gap layout; the reserved assembly gap refers to the design distance between the ceramic liner unit and the metal substrate mounting surface in the unfastened state at room temperature.

[0055] Specifically, firstly, a precise three-dimensional geometric model of the target wear-resistant bend needs to be created in computer-aided design software. This model must include the metal pipe substrate and a pre-defined initial layout of the ceramic liner. The initial layout of the ceramic liner can be modeled according to experience or the principle of equal thickness. This three-dimensional model is the basic geometric basis for all subsequent simulation analyses.

[0056] Secondly, based on the aforementioned three-dimensional model, multiphysics sequential coupling simulation analysis is conducted using a professional engineering simulation software platform. This process aims to obtain the comprehensive stress field borne by the ceramic liner under actual working conditions. Specifically, computational fluid dynamics simulation is first used to analyze the flow and heat transfer of high-temperature fluid within the pipe, obtaining the temperature distribution of the pipe wall; simultaneously, the discrete element method can be used to simulate the motion of solid particles and their impact on the wall surface. The calculated transient temperature field and particle impact load distribution are then input into the structural finite element analysis model as load conditions. In the finite element model, the material properties of ceramics and metals must be correctly defined, especially the elastic modulus, Poisson's ratio, density, and, crucially, the coefficient of thermal expansion. Through thermo-stress coupling calculations, the transient thermal stress and structural stress field of the ceramic liner under the combined action of thermal and mechanical loads are finally obtained.

[0057] Then, the stress field data obtained from the simulation calculations were post-processed and analyzed. Based on the distribution characteristics of the stress field, the inner wall surface of the bent pipe model was divided into regions. The division was based on the level of thermo-mechanical coupling failure risk in each region. This identified multiple regions with different thermo-mechanical failure risks in the 3D model.

[0058] Finally, based on the risk level of the aforementioned areas, a specific reserved assembly gap value is determined for each ceramic liner unit within each area, thereby creating a non-uniform, gradient gap layout throughout the entire bend. The reserved assembly gap here specifically refers to the artificially designed and reserved physical distance between the back of the working surface of the ceramic liner unit and the mounting surface of the metal substrate under normal temperature conditions and before final tightening. This gap is a clearly defined dimensional target that must be achieved after subsequent installation.

[0059] The technical principle of this embodiment lies in active stress control. Traditional uniform liners, when heated, experience significant tensile stress within the ceramic due to the difference in expansion between the ceramic and metal, with no outlet for this stress, leading to brittle failure. This embodiment predicts stress concentration areas through simulation and proactively designs larger assembly gaps in high-risk areas. These gaps provide a buffer for the thermal expansion of the metal, effectively reducing the tensile thermal stress on the ceramic after heating. This transforms the failure mechanism from uncontrollable thermal stress fracture to manageable wear after gap closure, preventing early brittle failure of the ceramic liner under high-temperature conditions and significantly extending its service life. Simultaneously, the differentiated design avoids material waste in low-risk areas, achieving a balance between safety and economy.

[0060] In a preferred embodiment, obtaining the transient thermal stress and structural stress field of the ceramic liner through multiphysics coupling simulation includes the following steps:

[0061] The transient temperature field and particle impact load distribution of the inner wall of the three-dimensional model of the bent pipe were obtained by coupled simulation of computational fluid dynamics and discrete element method.

[0062] The transient temperature field and particle impact load distribution are used as load conditions and applied to a finite element model that includes the thermophysical properties of the material for thermo-stress coupling calculation, thereby obtaining the transient thermal stress and structural stress field.

[0063] Specifically, the first step involves importing the previously established 3D model of the bend into dedicated CFD and DEM software or their coupled modules. The physical properties of the fluid medium (such as density, viscosity, and specific heat capacity), inlet boundary conditions (such as flow velocity and temperature), solid particle properties (such as particle size distribution, density, and coefficient of restitution), and particle incident conditions are then set. A transient simulation is run to monitor and output the temperature data (i.e., transient temperature field) at various locations on the inner wall surface of the bend over time, as well as the force load data generated when particles impact the wall (i.e., particle impact load distribution). This step simulates the heat transfer and impact physics processes of the fluid-solid two-phase flow.

[0064] The second step involves performing a thermo-stress coupling simulation. The transient temperature field data and particle impact load distribution data obtained from the first step's CFD-DEM simulation are used as external loads, precisely mapped and applied to another independently established structural finite element analysis model. This finite element model is also based on the same bend geometry, but requires mesh generation and accurate assignment of thermophysical and mechanical properties to the ceramic and metallic materials, such as elastic modulus, Poisson's ratio, coefficient of thermal expansion, and thermal conductivity. A thermo-stress coupling analysis step is set up in the finite element software to superimpose the thermal strain caused by the temperature load and the elastic strain caused by the mechanical load. Through solving, the stress state of the ceramic liner at different times, caused by the combined effects of heat and force, is finally obtained—that is, the transient thermal stress and structural stress field.

[0065] This implementation significantly reduces the computational complexity and resource requirements of direct, fully coupled simulation while ensuring engineering accuracy. It can efficiently and reliably obtain the key loads (thermal and shock) experienced by ceramic liners in real service environments, as well as the resulting stress responses. This provides a solid and quantitative data foundation for subsequent risk assessment and optimization design, and is a prerequisite for the entire method to be realized.

[0066] In a preferred embodiment, the step of dividing the three-dimensional model of the bend into multiple regions with different thermal-mechanical failure risks based on the distribution characteristics of the transient thermal stress and structural stress field includes the following steps:

[0067] Extract the maximum principal stress distribution cloud map of the ceramic liner and the normal peel stress distribution cloud map at the interface between the ceramic liner and the metal substrate;

[0068] Areas where the maximum principal stress value exceeds the first threshold of the allowable tensile strength of ceramic materials, or where the interfacial peel stress value exceeds the second threshold of the interfacial bonding strength, are classified as areas of the first risk level.

[0069] The area where the maximum principal stress value and the interface peeling stress value are both lower than their respective thresholds, and the maximum principal stress value exceeds the first threshold by a set proportion, is classified as the second risk level area.

[0070] The remaining areas are classified as third-risk areas.

[0071] Specifically, firstly, two key types of stress data cloud maps are extracted from the result file generated after the thermo-stress coupling simulation calculation. The first type is the maximum principal stress distribution cloud map of the ceramic liner body. This cloud map reflects the maximum tensile stress value borne by each point inside the ceramic material and is a direct basis for assessing whether the ceramic will undergo tensile fracture. The second type is the normal peel stress distribution cloud map at the interface between the ceramic liner and the metal substrate. This cloud map reflects the magnitude of tensile or compressive stress perpendicular to the bonding surface at various points on the interface. Among them, tensile stress (positive value) is the main cause of interface debonding and liner peeling.

[0072] Secondly, based on the aforementioned cloud map data, automated region division is performed using pre-set material strength thresholds. Specifically, a script or application tool is written in the post-processing module of the data processing or simulation software to scan the entire ceramic liner area. Units or node sets whose maximum principal stress exceeds the allowable tensile strength of the ceramic material (the first threshold) are marked. Simultaneously, areas where the interface normal peel stress exceeds the interface bonding strength (e.g., adhesive strength or the holding force of a mechanical locking structure, the second threshold) are also marked. All marked areas, regardless of which condition is triggered, are uniformly classified as first-risk level areas. These areas represent the highest failure risk, with stress levels exceeding the material or interface's tolerance capacity, and are areas that must be prioritized in the design.

[0073] Next, areas not classified as first-risk level are further screened. Areas whose maximum principal stress values, while not exceeding the first threshold, have exceeded it by a specific percentage (e.g., 70% or 80%, this is the set percentage) are identified. Simultaneously, the interfacial peel stress in these areas must be below the second threshold. Areas meeting both conditions are classified as second-risk level areas. These areas, while not immediately failing, are close to the safety boundary and pose a potential risk.

[0074] Finally, all remaining areas—those with low maximum principal stress values ​​(below the set percentage of the first threshold) and safe interface peel stress—are classified as third-risk level areas. These areas have the lowest risk.

[0075] This implementation divides the complex surface of the pipe liner into a limited number of graded areas with clear risk connotations, providing a precise action map for subsequent implementation of differentiated and refined design countermeasures. This allows the optimization design work to be targeted, concentrating resources on the high-risk areas that require the most attention.

[0076] In a preferred embodiment, determining different reserved assembly gaps for the ceramic liner units in the corresponding regions based on the failure risk level of the regions to form a gradient gap layout includes the following steps:

[0077] For the ceramic liner unit in the first risk level area, a first gap value is assigned, which is dynamically calculated based on the maximum principal stress peak value and the material thermal expansion coefficient at its location.

[0078] For the ceramic liner unit in the second risk level area, a second gap value smaller than the first gap value is assigned;

[0079] The ceramic liner unit in the third risk level area is given a zero gap or a micro gap smaller than the second gap value.

[0080] Specifically, for the first risk level region: the calculation of the first gap value (denoted as G1) is crucial for releasing thermal stress. This calculation is based on the peak value of the maximum principal stress (σ) in this region. max The unit is MPa (derived from the maximum principal stress distribution cloud map) and the thermal expansion characteristics of the material. The construction principle of the specific calculation formula is as follows:

[0081] Under ideal conditions of complete constraint (zero clearance), the ceramic liner experiences a thermal stress σ. thermal It can be approximated as:

[0082] σ thermal =Ec·Δα·ΔT;

[0083] Where Ec is the elastic modulus of the ceramic, Δα is the difference in thermal expansion coefficients between the metal and the ceramic, and ΔT is the operating temperature rise. When a uniform pre-reserved gap G exists, this gap allows the metal matrix to expand freely relative to the ceramic, thereby reducing the thermal stress generated by the actual constraint. The relationship can be simplified as follows:

[0084] σ actual ∝(Ec·Δα·ΔT-k·G);

[0085] Where k is a stiffness coefficient related to the structure and constraints.

[0086] Therefore, in order to make the actual working stress σ in the high-risk area actual To reduce the gap to below the allowable tensile strength [σ] of the ceramic (i.e., the first threshold) while retaining a certain safety margin n, the required first gap value G1 can be estimated by the following formula:

[0087] ;

[0088] In practical engineering applications, the coefficient k can be obtained through parametric analysis and calibration of the finite element model. A more direct approach is to set the initial contact condition of the target region as a gap in the thermo-stress coupling simulation model and parameterize this gap value. Through several simulation trials, a value that maximizes the peak principal stress σ in the region can be found. maxThe minimum gap value that drops below the safety threshold is determined as G1. This process embodies the meaning of dynamic calculation, that is, determining the solution in real time based on the stress state at a specific location.

[0089] For the second risk level region: the second gap value (denoted as G2) is explicitly required to be less than G1. Its determination is not a simple proportionality, but rather related to the stress level of the region. A specific implementation method is to calculate the average value of the maximum principal stress σ in the region. avg And based on its ratio to the allowable strength [σ], it is interpolated linearly or nonlinearly between 0 and G1. For example:

[0090] ;

[0091] Where, σ low This is the stress threshold (i.e., the set ratio of [σ]) used to divide the second and third risk levels. This means that the higher the stress level (the closer to the first risk zone), the closer the obtained G2 is to G1; the lower the stress level (the closer to the third risk zone), the smaller the obtained G2 is.

[0092] For the third risk level area: the third gap value (denoted as G3) is set to be close to zero. In 3D modeling, the curved surface of the ceramic backing plate in this area can be directly designed to conform to the mounting surface of the metal substrate (i.e., zero gap). In some cases where assembly precision is extremely high or to prevent fretting wear, a fixed micro-gap can be assigned, such as a minimum value between 0.05 mm and 0.15 mm. This value G3 should be much smaller than the typical G2 (e.g., G3 < 0.3 × G2) to ensure that it still functionally approximates a fitted state.

[0093] In a preferred embodiment, after forming the gradient gap layout, the following step is further included:

[0094] A digital twin model of the target bend is established, which integrates gradient gap layout, material constitutive relation and working condition parameters;

[0095] Based on the digital twin model, the thermo-mechanical coupling behavior of the pipe bending system is simulated from cold installation, heating to steady-state operation, and then cooling, and the stress evolution and interface contact state of the ceramic liner are predicted at each stage.

[0096] Based on the simulation results, potential areas that may lead to media leakage or increased particle erosion due to gaps under hot working conditions are identified.

[0097] The reserved assembly gap in the potential area is adjusted in reverse to obtain the final target gap layout.

[0098] Specifically, Step 1: In a multiphysics simulation platform such as ANSYS, COMSOL, or Abaqus, construct a higher-precision digital twin model that surpasses the initial design model. This model integrates the following elements: Geometry: A detailed 3D assembly containing defined gradient gap values. This means that the contact surface between the ceramic liner and the metal matrix is ​​accurately modeled as a curved surface with initial gaps. Material Constitutive: Input the realistic properties of the ceramic, metal, and the bonding layer between them (if present) as a function of temperature. For example, a table of data on the elastic modulus, thermal conductivity, and coefficient of thermal expansion of the ceramic as a function of temperature; plastic deformation curves of the metal; viscoelastic models of the adhesive or temperature-dependent failure criteria. Operating Parameters: Define a complete transient load history. This includes fluid inlet temperature-time curves, pressure-time curves, and particle mass flow rate-time curves, simulating realistic start-up, steady-state operation, shutdown, or load fluctuation processes.

[0099] Step Two: Transient Simulation of Full-Process Thermo-Mechanical Coupled Behavior: A transient analysis is set up to simulate the complete cycle from installation at room temperature (e.g., 20°C) (cold state), through startup heating, reaching the maximum operating temperature (e.g., 800°C) and stabilizing (steady state), to shutdown and cooling back to room temperature. The analysis type is a fully coupled thermo-stress analysis, considering: Heat conduction: heat transfer between metal and ceramic. Heat convection and radiation: heat transfer between fluid and walls, and in the gaps within the cavity. Structural contact nonlinearity: defining the "hard contact" normal behavior and "friction" tangential behavior between the ceramic and metal contact surfaces to realistically simulate gap closure under pressure, interface sliding, and separation. Equivalent pressure load of particle impact load (applied as a time-series load).

[0100] Step 3: Identification of Potential Problem Areas: Post-processing simulation results, focusing on two key failure modes during the thermally stable operating phase (when the temperature is highest and the load is stable):

[0101] Leakage risk identification: This is achieved by analyzing contact pressure distribution contour maps. Areas where the contact pressure is below the medium permeation pressure threshold (e.g., 0.1 MPa for high-temperature gases) are identified as potential areas for seal failure. These areas may form channels for medium leakage due to excessive gaps or poor contact.

[0102] Scouring aggravation risk identification: By analyzing the wall shear force contour map or particle trajectory density map output by the fluid simulation module, areas where the wall shear force or particle impact frequency is significantly higher than the average level due to local geometric abrupt changes (such as steps or cavities caused by gaps) are identified as potential areas for scouring aggravation.

[0103] Step 4: Reverse Adjustment and Iterative Optimization: For the identified "potential areas," initiate an optimization loop. The adjustment targets are the design values ​​of the reserved assembly clearances determined for these areas. The adjustment strategy is: for leakage risks due to insufficient contact pressure, reduce the clearance value at that location; for scouring risks due to flow field distortion, it may be necessary to adjust the clearance value or optimize the geometric chamfer of the liner edge at that location. After each adjustment, update the geometric parameters of the digital twin model and rerun the simulations in Steps 2 and 3. This process is repeated until simulation predictions show that the contact pressure in all areas is higher than the sealing threshold throughout the entire work cycle, and there are no abnormal local scouring hotspots. The final converged set of clearance values ​​is the final target clearance layout.

[0104] The technical advantage of this implementation method is that it achieves self-improvement and robustness verification of the design scheme. It not only greatly saves costs and time, but more importantly, it ensures that the optimized gradient gap layout is reliable and durable in complex real-world service environments, significantly reducing the risk of product failure in practical applications.

[0105] In a preferred embodiment, the reverse adjustment of the reserved assembly gap in the potential area includes the following steps:

[0106] Based on the data from the full-process simulation of the digital twin model, for the potential region, the equivalent thermal displacement caused by the constraint of thermal expansion at each location, and the sensitivity coefficient of the sealing interface pressure to the gap change are calculated.

[0107] Based on the ratio of the equivalent thermal displacement to the sensitivity coefficient, the gap adjustment priority at each position is determined, wherein positions with large equivalent thermal displacement and low sensitivity coefficient have higher adjustment priority.

[0108] Prioritize adjusting the reserved assembly gaps at positions with higher adjustment priority, and update the digital twin model for verification. Iterate this process until the structural safety and sealing requirements are met, and obtain the target assembly gaps at each position.

[0109] Specifically, step one: For each finite element mesh element or node i within the identified potential region, perform the following calculations:

[0110] Calculate the equivalent thermal displacement Di: This is the theoretical driving force calculated based on thermodynamic principles. The formula is:

[0111] Di=(αm-αc)·ΔT·Li·Ci;

[0112] Where αm and αc are the thermal expansion coefficients of the metal and ceramic, respectively; ΔT is the operating temperature rise; Li is the characteristic length at this location (which can be simplified to 1); Ci is the constraint coefficient (between 0 and 1), obtained by simulation by extracting the ratio of the actual strain to the free thermal expansion strain at this location during the heating process. The larger Di is, the stronger the tendency to push away at this point due to thermal expansion mismatch.

[0113] Calculate the sensitivity coefficient S i The numerical perturbation method is employed. In the digital twin model, the design value of the gap corresponding to the unit is increased by a tiny amount δ (e.g., 0.01 mm), and the interfacial contact pressure P under thermal stability is recalculated quickly. i ’ The sensitivity coefficient is defined as:

[0114] ;

[0115] Among them, P i,原始 This is the contact pressure under the original gap. The larger Si is, the faster the sealing pressure drops due to a slight increase in gap, meaning that this position is more sensitive to gap changes and the adjustment cost is higher.

[0116] Step 2: Calculate the priority index R for each calculation point i. i :

[0117] ;

[0118] in, R is a very small positive number, used to prevent the denominator from being zero. i The physical meaning of R is the thermal stress relief benefit that can be obtained in exchange for a unit loss of sealing performance. i A higher value indicates a higher cost-effectiveness in releasing thermal stress by increasing the gap, and therefore should be given a higher adjustment priority.

[0119] Step 3: Sorting and Selection: Sort and select all points within the potential region according to their priority index R. i Sort from highest to lowest priority. Incremental adjustment: Select the top N (e.g., top 10%) high-priority points and increase their corresponding reserved assembly gap values ​​by a fixed adjustment step ΔG (e.g., 0.05 mm). Verification and update: Apply these adjustments, update the digital twin model, and perform a rapid verification simulation under hot conditions. Recalculate the contact pressure and stress distribution of the adjusted model. Convergence judgment: Check whether the contact pressure in all areas is higher than the sealing threshold and the stress is lower than the safety threshold. If satisfied, stop the iteration, and the current gap value is the target assembly gap. If not satisfied, recalculate D for all affected points based on the new simulation results. i and S i (Because the system state has changed), update R.i Sort the data and proceed to the next adjustment cycle. Termination condition: The iteration process continues until the convergence condition is met, the maximum number of iterations is reached, or the gap between all adjustable points has reached the preset upper limit.

[0120] In a preferred embodiment, after obtaining the target assembly gaps at each location, the method further includes the following step:

[0121] Based on the target assembly gaps at each location, generate a digital model of the back surface of the integrated wear-resistant ceramic liner.

[0122] The integrated wear-resistant ceramic liner is configured as a single component that fits against the inner wall of the metal substrate; its working surface is a continuous curved surface adapted to the flow channel, and its back surface includes a gradient cavity structure that forms the target gap layout between itself and the mounting surface of the metal substrate.

[0123] The depth distribution of the gradient cavity structure corresponds to the target assembly gap at each position in the target gap layout, so that when the integrated wear-resistant ceramic liner is installed in place, the target gap layout is naturally formed between its back cavity and the metal substrate.

[0124] Specifically, step one: Obtain the target assembly gap dataset output above. This dataset defines the three-dimensional reference surface S on the bent pipe metal matrix. base On (u,v), the target gap value G corresponding to each pair of parameter coordinates (u,v) (or each discrete point). target (u,v). This dataset typically exists as an interpolation table or in the form of a finite element mesh node.

[0125] Step 2: Generate the digital model of the back surface of the liner: In CAD software (such as SolidWorks, CATIA, or via scripting), perform the following geometric operations: Using the theoretical design surface S of the inner wall of the metal matrix... base This serves as a reference surface. A new surface S is generated by offsetting along the inner normal direction (pointing towards the interior of the pipe / ceramic liner) at each point on this reference surface. back The offset distance d(u,v) is not a constant, but is exactly equal to the target gap value G at that point. target (u,v).

[0126] ;

[0127] in, It is the unit normal vector. The S generated in this way... back This refers to the back profile of the liner. It interacts with the base surface S. base The normal distance between them is everywhere equal to G. target This space is the gradient cavity structure.

[0128] Step 3: Constructing an integrated 3D solid liner: Design the working surface of the ceramic liner as a smooth, continuous curved surface S that perfectly matches the designed flow path of the pipeline. wear S usually wear It can be in S base Based on this, it is obtained by uniformly offsetting inward along the normal direction by the nominal thickness t of the lining plate. Using the solid modeling functions of CAD software (such as lofting, generating solids from stitched surfaces, or Boolean operations), the working surface S is... wear and back shape S back As the boundary, a closed, single 3D solid model with variable thickness is constructed. This solid is the digital model of the integrated wear-resistant ceramic liner. Its thickness T(u,v) is:

[0129] T(u,v)=t+G target (u,v);

[0130] As can be seen, the thickness of the liner plate changes synchronously with the target gap value. Where the gap is large, the liner plate is thin (the cavity is deep), and where the gap is small, the liner plate is thick (the cavity is shallow).

[0131] Step 4: Export the generated integrated 3D solid model of the liner plate to a common format such as STEP or IGES for direct use: Mold Design: If using processes such as slip casting or gel casting, this model is used to manufacture the corresponding cavities for plaster molds, rubber molds, or metal molds. CNC Machining Programming: If using large ceramic blocks for CNC machining, this model is used to generate machining toolpaths for five-axis CNC machine tools. 3D Printing Slicing: If using ceramic additive manufacturing technology, this model is used for slicing and generating printing paths.

[0132] In a preferred embodiment, assigning a second gap value smaller than the first gap value to the ceramic liner unit in the second risk level area includes the following steps:

[0133] For the second risk level area, extract the stress gradient distribution data within that area from the maximum principal stress distribution cloud map;

[0134] Calculate the standard deviation and mean stress gradient of the maximum principal stress in this region;

[0135] Based on the standard deviation and the average stress gradient, the initial gap value is dynamically calculated using a preset weighting relationship model.

[0136] Determine whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold;

[0137] If so, the initial gap value is used as the second gap value.

[0138] In practice, firstly, in the post-processing environment where the simulation has been completed, the maximum principal stress data of all nodes or elements in the region marked as the second risk level are extracted to form a dataset. Next, two key statistical characteristics of this dataset are calculated: first, its standard deviation, which quantifies the dispersion of stress values ​​around the average value. A larger standard deviation indicates a more uneven stress distribution, potentially indicating localized stress high points that are close to the threshold but not yet reached it; second, the average stress gradient, which requires first calculating the absolute value of the stress difference between adjacent elements and then averaging all such differences. A larger gradient indicates more drastic spatial stress changes, which may physically correspond to locations of geometric or load abrupt changes.

[0139] Based on the calculated standard deviation and average stress gradient, the initial gap value is dynamically calculated using a pre-defined weighted relationship model. This model can be a linear equation, for example: Initial gap value = K1 × Standard deviation + K2 × Average stress gradient + Base value. Here, K1 and K2 are positive weighting coefficients, their magnitudes reflecting the importance of the corresponding characteristics to the gap requirement, and can be determined through historical data fitting or expert experience. The base value is a benchmark gap set according to the average stress level of the second risk level. The design principle of this model is that the more uneven and drastic the stress distribution, the larger the calculated initial gap value. This is because uneven and rapidly changing stress fields are more sensitive to thermal cycling and local deformation, requiring greater displacement tolerance to ensure safety.

[0140] Next, a judgment step is set up. Two thresholds need to be determined beforehand through statistical analysis or engineering experience: a first preset threshold corresponds to the upper limit of acceptable stress distribution uniformity, and a second preset threshold corresponds to the upper limit of acceptable stress variation smoothness. The calculated standard deviation is compared with the first preset threshold, and the average stress gradient is compared with the second preset threshold. If both are below their respective thresholds, the stress field in the second risk region is determined to be in a relatively mild and stable state. At this point, the initial gap value calculated by the weighted relationship model is sufficient to handle the risk and can be directly determined as the final second gap value adopted for this unit.

[0141] In a preferred embodiment, after determining whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold, the method further includes the following steps:

[0142] If not, then based on the full-process thermo-mechanical coupling behavior simulation data, calculate the transient thermal shock intensity factor of the second risk level region during the critical transient stage of temperature rise. The transient thermal shock intensity factor is positively correlated with the local temperature and stress change rate.

[0143] The initial gap value is weighted and fused with the transient thermal shock intensity factor to obtain the fused gap value;

[0144] The fusion gap value is used as the second gap value.

[0145] In practice, if the judgment result is negative, meaning that either the standard deviation or the average stress gradient of the region exceeds a preset threshold, it indicates that the stress field in this region exhibits significant inhomogeneity or drastic changes. In this case, calculations based solely on steady-state stress distribution characteristics may be insufficient, and it is necessary to examine its dynamic behavior during the heating process.

[0146] Next, data for the critical transient phase of temperature rise in this region needs to be extracted from the transient results of the full-process thermo-mechanical coupling simulation. This phase typically refers to the period with the fastest temperature change rate between the cold state and the steady-state operating temperature. For a representative point within this region, its transient thermal shock intensity factor is calculated. Calculating this factor requires obtaining the rate of change of temperature over time (dT / dt) and the rate of change of stress over time (dσ / dt) at that point. A feasible calculation formula is: Transient thermal shock intensity factor = sqrt( (A×dT / dt) 2 + (B× dσ / dt) 2 ), where A and B are normalization coefficients used to balance the dimensions and influence weights of temperature and stress change rates. This factor comprehensively characterizes the intensity of the dynamic thermal and force shock experienced by the point during startup; the larger the factor value, the stronger the thermal shock experienced by the point.

[0147] Then, this transient thermal shock intensity factor is fused with the previously calculated initial gap value to obtain a more comprehensive fused gap. The fusion can be performed using a weighted summation method: Fusion gap value = W1 × Initial gap value + W2 × Transient thermal shock intensity factor. Where W1 and W2 are weighting coefficients, and W1 + W2 = 1. The weighting coefficients can be adjusted according to the specific extent of exceedance in this region: if the standard deviation exceeds the limit significantly, W1 can be appropriately increased; if the average stress gradient exceeds the limit significantly, both W1 and W2 can be increased simultaneously; if both exceed the limit only slightly, a balanced weighting can be used. Finally, this fused gap value is used as the second gap value for the ceramic liner unit. In this way, for the second risk region with complex internal stress states or severe start-up processes, the designed gap value will simultaneously cover steady-state distribution characteristics and transient impact intensity, thus providing more reliable protection.

[0148] In a preferred embodiment, the simulated pipe bending system's thermo-mechanical coupling behavior throughout the entire process from cold installation, heating to steady-state operation, and cooling includes the following steps:

[0149] The digital twin model is pre-set with multiple key event trigger points, including: the ceramic liner and the metal substrate begin to contact, the interfacial adhesive reaches the glass transition temperature, the fluid medium temperature undergoes a step change, and the particle impact load reaches a peak.

[0150] During the simulation, when the system state is close to any of the aforementioned key event trigger points, the simulation time step is switched to a more refined first step size for high-resolution calculation; when the system state is far from all key event trigger points, the simulation time step is switched to a second step size larger than the first step size for further calculation.

[0151] The simulation of the entire thermo-mechanical coupling behavior is completed by cyclically switching and calculating the time step.

[0152] Before implementation, a series of key event trigger points need to be predefined in the solver settings of the digital twin model. These events are critical points where the system state may change abruptly, determined by physical process analysis, and include at least: the moment when the ceramic liner and the metal substrate begin to contact (the instant the gap closes), the interfacial adhesive reaches its glass transition temperature (abrupt change in material properties), the inlet temperature of the fluid medium undergoes a preset step change (abrupt change in thermal load), and the moment when the particle impact load reaches its peak within a cycle (abrupt change in mechanical load). Each event point corresponds to a calculable physical quantity threshold or a preset time point.

[0153] After initiating the transient simulation, the solver does not use a fixed time step, but instead employs this method. At the start of each calculation step, the solver calls a monitoring function to evaluate the distance between the current system state and all preset key event trigger points. This distance can be temporal (e.g., how long until the preset temperature step) or state-related (e.g., how much difference is there between the current adhesive temperature and its glass transition temperature). The system sets a proximity range, such as a few seconds before or after in time, or a percentage of the state-related parameters.

[0154] If the monitoring function determines that the current state is not approaching any critical events, the solver advances the calculation using a larger second step size. This step size is maximized while ensuring numerical stability, allowing for rapid transitions through periods of relative calm in the physical process and saving computation time. Once the monitoring function detects that the system state is approaching a critical event, the solver immediately and automatically switches the time step to a finer first step size. This first step size is an order of magnitude or more smaller than the second step size to ensure accurate capture of rapid nonlinear changes in stress, contact state, etc., before and after the event. After the event process has ended (e.g., the contact state has stabilized and the temperature has passed the transition zone), the monitoring function determines that the state is far from the event point, and the solver switches back to a larger second step size to continue the calculation.

[0155] The entire simulation process is completed through automatic, cyclical switching between large-step progression and small-step fine-grained capture. This method precisely allocates valuable computational resources (small time steps) to the short periods when the physical process is most complex and requires the highest resolution, while using economical large step sizes for the long periods of slow change. This significantly reduces the total computation time required to complete a full simulation of a cold-hot-cold process without sacrificing the accuracy of the key physical processes.

[0156] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for optimizing the layout of ceramic liners for wear-resistant bent pipes based on three-dimensional simulation, characterized in that, Includes the following steps: A three-dimensional model of the bent pipe, including the initial layout of the metal substrate and the pre-set ceramic liner, is established. Through multi-physics coupling simulation, the transient thermal stress and structural stress field of the ceramic liner are obtained. Based on the distribution characteristics of the transient thermal stress and structural stress field, multiple regions with different thermal-mechanical failure risks are divided in the three-dimensional model of the bent pipe. Based on the failure risk level of the area, different reserved assembly gaps are determined for the ceramic liner units in the corresponding area to form a gradient gap layout; The reserved assembly gap refers to the designed distance between the ceramic liner unit and the metal substrate mounting surface in the unfastened state at room temperature. Based on the distribution characteristics of the transient thermal stress and structural stress field, multiple regions with different thermal-mechanical failure risks are divided in the three-dimensional model of the bent pipe, including the following steps: Extract the maximum principal stress distribution cloud map of the ceramic liner and the normal peel stress distribution cloud map at the interface between the ceramic liner and the metal substrate; Areas where the maximum principal stress value exceeds the first threshold of the allowable tensile strength of ceramic materials, or where the interfacial peel stress value exceeds the second threshold of the interfacial bonding strength, are classified as areas of the first risk level. The area where the maximum principal stress value and the interface peeling stress value are both lower than their respective thresholds, and the maximum principal stress value exceeds the first threshold by a set proportion, is classified as the second risk level area. The remaining areas are classified as Level 3 risk areas; The step of determining different reserved assembly gaps for ceramic liner units in the corresponding regions based on the failure risk level of the regions to form a gradient gap layout includes the following steps: For the ceramic liner unit in the first risk level area, a first gap value is assigned, which is dynamically calculated based on the maximum principal stress peak value and the material thermal expansion coefficient at its location. For the ceramic liner unit in the second risk level area, a second gap value smaller than the first gap value is assigned; The ceramic liner unit in the third risk level area is given a zero gap or a micro gap smaller than the second gap value.

2. The method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation according to claim 1, characterized in that, The method of obtaining the transient thermal stress and structural stress field of the ceramic liner through multiphysics coupling simulation includes the following steps: The transient temperature field and particle impact load distribution of the inner wall of the three-dimensional model of the bent pipe were obtained by coupled simulation of computational fluid dynamics and discrete element method. The transient temperature field and particle impact load distribution are used as load conditions and applied to a finite element model that includes the thermophysical properties of the material for thermo-stress coupling calculation, thereby obtaining the transient thermal stress and structural stress field.

3. The method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation according to claim 1, characterized in that, Following the formation of the gradient gap layout, the following steps are also included: A digital twin model of the target bend is established, which integrates gradient gap layout, material constitutive relation and working condition parameters; Based on the digital twin model, the thermo-mechanical coupling behavior of the pipe bending system is simulated from cold installation, heating to steady-state operation, and then cooling, and the stress evolution and interface contact state of the ceramic liner are predicted at each stage. Based on the simulation results, potential areas that may lead to media leakage or increased particle erosion due to gaps under hot working conditions are identified. The reserved assembly gap in the potential area is adjusted in reverse to obtain the final target gap layout.

4. The method for optimizing the layout of wear-resistant curved pipe ceramic liners based on three-dimensional simulation according to claim 3, characterized in that, The reverse adjustment of the reserved assembly gap in the potential area includes the following steps: Based on the data from the full-process simulation of the digital twin model, for the potential region, the equivalent thermal displacement caused by the constraint of thermal expansion at each location, and the sensitivity coefficient of the sealing interface pressure to the gap change are calculated. Based on the ratio of the equivalent thermal displacement to the sensitivity coefficient, the gap adjustment priority at each position is determined, wherein positions with large equivalent thermal displacement and low sensitivity coefficient have higher adjustment priority. Prioritize adjusting the reserved assembly gaps at positions with higher adjustment priority, and update the digital twin model for verification. Iterate this process until the structural safety and sealing requirements are met, and obtain the target assembly gaps at each position.

5. The method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation according to claim 4, characterized in that, After obtaining the target assembly clearance at each position, the following steps are also included: Based on the target assembly gaps at each location, generate a digital model of the back surface of the integrated wear-resistant ceramic liner. The integrated wear-resistant ceramic liner is configured as a single component that fits against the inner wall of the metal substrate; its working surface is a continuous curved surface adapted to the flow channel, and its back surface includes a gradient cavity structure that forms the target gap layout between itself and the mounting surface of the metal substrate. The depth distribution of the gradient cavity structure corresponds to the target assembly gap at each position in the target gap layout, so that when the integrated wear-resistant ceramic liner is installed in place, the target gap layout is naturally formed between its back cavity and the metal substrate.

6. The method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation according to claim 1, characterized in that, The ceramic liner unit for the second risk level area is given a second gap value that is smaller than the first gap value, including the following steps: For the second risk level area, extract the stress gradient distribution data within that area from the maximum principal stress distribution cloud map; Calculate the standard deviation and mean stress gradient of the maximum principal stress in this region; Based on the standard deviation and the average stress gradient, the initial gap value is dynamically calculated using a preset weighting relationship model. Determine whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold; If so, the initial gap value is used as the second gap value.

7. The method for optimizing the layout of wear-resistant curved pipe ceramic liners based on three-dimensional simulation according to claim 6, characterized in that, After determining whether the standard deviation is lower than a first preset threshold and whether the average stress gradient is lower than a second preset threshold, Includes the following steps: If not, then based on the full-process thermo-mechanical coupling behavior simulation data, calculate the transient thermal shock intensity factor of the second risk level region during the critical transient stage of temperature rise. The transient thermal shock intensity factor is positively correlated with the local temperature and stress change rate. The initial gap value is weighted and fused with the transient thermal shock intensity factor to obtain the fused gap value; The fusion gap value is used as the second gap value.

8. The method for optimizing the layout of wear-resistant bent pipe ceramic liners based on three-dimensional simulation according to claim 3, characterized in that, The simulated pipe bending system exhibits thermo-mechanical coupling behavior throughout the entire process from cold installation, heating to steady-state operation, and cooling, including the following steps: The digital twin model is pre-set with multiple key event trigger points, including: the ceramic liner and the metal substrate begin to contact, the interfacial adhesive reaches the glass transition temperature, the fluid medium temperature undergoes a step change, and the particle impact load reaches a peak. During the simulation, when the system state is close to any of the aforementioned key event trigger points, the simulation time step is switched to a more refined first step size for high-resolution calculation; when the system state is far from all key event trigger points, the simulation time step is switched to a second step size larger than the first step size for further calculation. The simulation of the entire thermo-mechanical coupling behavior is completed by cyclically switching and calculating the time step.

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