LBM-based simulation method for long-distance pipeline bellows compensator

Abstract

The application discloses a kind of long pipe wave tube compensator simulation methods based on LBM, it is related to long heat supply pipeline safety simulation technical field, comprising the following steps: S1, the three-dimensional geometric model of wave tube compensator is established and LBM lattice space mapping;S2, solving transient temperature field and pressure field;S3, based on temperature field calculation thermal strain, displacement field and stress field are solved by LBM elastic model;S4, simulate full cycle start-stop cycle: temperature rise, high temperature keeps, temperature drop stage;S5, output maximum von Mises equivalent stress, maximum axial deformation, residual stress and residual deformation;S6, according to pressure vessel safety criterion evaluation compensator safety.The application uses the above-mentioned long pipe wave tube compensator simulation methods based on LBM, and parallel efficiency is high, complex boundary adaptability is strong, transient temperature gradient is captured stable, and can be used for long heat supply pipeline wave tube compensator safety evaluation and operation strategy optimization.

Description

Technical Field

[0001] This invention relates to the field of safety simulation technology for long-distance heating pipelines, and in particular to a simulation method for bellows compensators in long-distance pipelines based on LBM. Background Technology

[0002] Long-distance heating pipelines are the core infrastructure of urban centralized heating systems. Corrugated pipe compensators are used to absorb the thermal expansion and contraction displacement of the pipeline caused by temperature changes, and are a key component ensuring the safe operation of the pipeline. In actual operation, especially during start-up and shutdown cycles, the pipeline temperature rises rapidly from ambient temperature (e.g., 20°C) to high temperature (e.g., 130°C) in a short period, and then cools back to ambient temperature. This drastic temperature change triggers significant thermal expansion and contraction effects, leading to complex thermal stress and deformation inside the corrugated pipe. If stress concentration exceeds the material's limits or deformation exceeds the design range, it may cause the corrugated pipe to crack, become unstable, or fail to seal, resulting in energy leakage and heating interruption.

[0003] Currently, the finite element method (FEM) is mainly used in engineering to perform thermal-structural coupling analysis of bellows. However, FEM has the following shortcomings when dealing with transient large temperature gradients, complex geometric boundaries (such as multi-layered bellows), and long-term cyclic simulations: (1) The transient temperature gradient analysis capability is limited, and numerical oscillations are prone to occur, especially under rapid start-up and shutdown conditions.

[0004] (2) The modeling of contact and sliding boundaries in multi-layer structures is complex and computationally expensive.

[0005] (3) Poor parallel scalability makes it difficult to meet the needs of large-scale parameter scanning or real-time simulation. Summary of the Invention

[0006] The purpose of this invention is to provide a simulation method for bellows compensators in long-distance pipelines based on LBM, which solves the problems of low computational efficiency, weak analytical ability of transient temperature gradient, and difficulty in efficiently coupling temperature-deformation-stress fields in the existing FEM method mentioned in the background art.

[0007] To achieve the above objectives, this invention provides a simulation method for bellows compensators in long-distance pipelines based on LBM, comprising the following steps: S1. Establish a three-dimensional geometric model of the bellows compensator and discretize the three-dimensional geometric model into an LBM lattice space; S2. Using the dual distribution function LBM, establish the LBM evolution equations for the temperature field and pressure field, and solve for the transient temperature field and pressure field respectively; S3. Calculate thermal strain based on temperature field, and solve displacement and stress fields using LBM elastic model; S4. Simulates the full-cycle start-stop cycle and outputs the maximum von Mises equivalent stress, maximum axial deformation, residual stress, and residual deformation. S5. Assess the safety of the compensator according to the pressure vessel safety guidelines; S6. Perform slow start-stop simulation and fast start-stop simulation respectively, and output the recommended upper limit of start-stop rate by comparing the impact of start-stop rate.

[0008] Preferably, the specific steps of S1 are as follows: S11. Obtain the structural parameters of the bellows, including nominal diameter, wave height, wave pitch, total length, number of layers, and equivalent wall thickness. S12. Use 3D modeling software to construct a 3D geometric model and export the 3D geometric model as an STL format; S13. The three-dimensional geometric model is discretized into an LBM lattice space using a discrete velocity model. S14. Map the material parameters to the lattice nodes. The material parameters include density, specific heat capacity, thermal conductivity, coefficient of thermal expansion, elastic modulus and Poisson's ratio.

[0009] Preferably, the specific steps of S2 are as follows: S21. Set the boundary conditions for the temperature field, adopt the double distribution function (LBM), establish the evolution equation of the temperature distribution function, define the temperature equilibrium distribution function, and solve for the temperature field. S22. Introduce pressure boundary conditions, establish the evolution equation of the density distribution function, define the density equilibrium distribution function, and solve for the pressure field.

[0010] Preferably, the temperature field boundary conditions in S21 are as follows: the inner wall temperature changes with time according to a linear start-stop curve; the outer wall is a convective heat transfer boundary with a heat transfer coefficient of 10 W / (m²). 2 ·K), with an ambient temperature of 20℃.

[0011] Preferably, the pressure field boundary condition in S22 is: the internal pressure is constant at 3 MPa.

[0012] Preferably, the specific steps of S3 are as follows: S31. Calculate the thermal strain of each cell based on the temperature field; S32. Calculate stress by coupling thermal strain using the generalized Hooke's law; S33. Employ the displacement distribution function to evolve the LBM elasticity model; S34. Solve for the displacement and stress fields using the LBM elastic model.

[0013] Preferably, the specific steps of S4 are as follows: S41. Initialize the temperature, pressure, displacement, and stress of all grid cells; S42. Simulate the full-cycle start-stop loop, using time-stepping loop iteration; The entire start-stop cycle includes a heating phase, a high-temperature holding phase, and a cooling phase, specifically: Heating phase: linearly increases from 20℃ to 130℃; High-temperature holding section: maintained at 130℃; Cooling phase: linearly decreasing from 130℃ to 20℃; In this case, the heating rate and the cooling rate are the same; S43. When the time step iteration reaches the total simulation duration, the simulation ends.

[0014] Preferably, the specific steps of S42 are as follows: S421. Update the temperature field boundary conditions, and assign the inner wall temperature according to the start-stop curve; S422, Perform collision migration of the temperature distribution function evolution equation; S423, Perform collision migration of the density distribution function evolution equation; S424. Calculate the thermal strain based on the current temperature field; S425. Perform collision migration of the displacement distribution function and update the displacement field; S426 Calculate the stress field and output the maximum von Mises equivalent stress and maximum axial deformation; S427. When the iteration reaches the output time point, save the result.

[0015] Preferably, the safety criteria in S5 are: If the combined strength range of primary and secondary stresses is ≤3 times the allowable stress of the material at the design temperature, then the structure is safe. If the residual stress at the end of cooling is ≤0.2 times the yield strength and the residual deformation is ≤0.001mm, then the structure has no cumulative plastic damage.

[0016] Preferably, the specific steps of S6 are as follows: S61. Perform slow start-stop simulation and fast start-stop simulation respectively, where the slow start-stop simulation rate is 0.275℃ / s and the fast start-stop simulation rate is 0.55℃ / s. S62. Compare the peak value of maximum equivalent stress, residual stress, peak value of deformation, and stress-deformation decoupling behavior. S63, the recommended start / stop rate for output is 0.3℃ / s.

[0017] Therefore, the present invention employs the above-mentioned simulation method for bellows compensators in long-distance pipelines based on LBM, which has the following beneficial effects: (1) Compared with the traditional FEM, the LBM method has higher numerical stability under transient large temperature gradients and no oscillations.

[0018] (2) This invention is naturally parallel and can be accelerated on GPU, making it suitable for long-term cyclic simulation.

[0019] (3) The present invention can naturally handle the complex geometric boundaries of multi-layered corrugated pipes without the need for additional contact algorithms.

[0020] (4) The present invention successfully captured the stress redistribution and deformation-stress decoupling phenomenon during the high temperature holding stage, which is consistent with the experimental and FEM results.

[0021] (5) This invention can quantitatively assess the impact of start-up and shutdown rates on thermal shock intensity, providing a clear basis for engineering operation strategies.

[0022] (6) This invention combines safety criteria to achieve rapid safety assessment of the entire life cycle of the bellows compensator.

[0023] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 This is a flowchart illustrating an embodiment of the simulation method for bellows compensators for long-distance pipelines based on LBM according to the present invention. Figure 2 This is a bellows compensator mesh model, which is an embodiment of the LBM-based simulation method for bellows compensators in long-distance pipelines according to the present invention. Figure 3 This is a time curve illustrating the axial deformation of a bellows compensator for long-distance pipelines based on LBM, according to an embodiment of the present invention. Figure 4 The following are temperature field distribution cloud maps at different time steps in an embodiment of the simulation method for bellows compensators in long-distance pipelines based on LBM of the present invention: (a) is t=20s, (b) is t=100s, (c) is t=400s, (d) is t=500s, (e) is t=700s, and (f) is t=900s. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0027] Please see Figures 1-4 This invention provides a simulation method for bellows compensators in long-distance pipelines based on Lattice Boltzmann (LBM). This method is an efficient, stable, and parallelizable simulation approach based on LBM. In recent years, the Lattice Boltzmann (LBM) method, as a mesoscopic numerical method, has been widely used in computational fluid dynamics and heat transfer due to its inherent parallelism, strong ability to handle complex geometric boundaries, and ease of coupling multiple physics fields (flow, heat transfer, and elasticity). However, there is still a significant gap in research on applying LBM to the thermo-structural coupled transient simulation of bellows compensators, especially the stress and deformation analysis under full-cycle start-stop cycles. This method includes the following steps: S1. Establish the three-dimensional geometric model of the bellows compensator and map it to the LBM lattice space.

[0028] Obtain the following structural parameters for the corrugated pipe: nominal diameter DN80, wave height 10 mm, wave pitch 15 mm, total length 150 mm, number of layers 3 (316L-304-316L), and equivalent wall thickness 2.0 mm.

[0029] Use 3D modeling software (such as SolidWorks) to build the geometric model and export it as an STL file.

[0030] The model is discretized into an LBM lattice space, using either the D3Q19 or D3Q27 discrete velocity model. Each lattice size Δx is ≤ 1 / 5 of the smallest geometric feature size (e.g., 1 / 5 of the trough curvature radius).

[0031] Material parameters are mapped to lattice nodes: density ρ = 7930 kg / m³ 3 Specific heat capacity c p =500 J / (kg·K), thermal conductivity k=16.3 W / (m·K), coefficient of thermal expansion α=1.70×10-5 K -1 The elastic modulus E = 1.94 × 10⁻⁶ 11 Pa, Poisson's ratio ν = 0.3.

[0032] S2. Establish the LBM evolution equation for the temperature field.

[0033] The double distribution function LBM is used, where the temperature distribution function g i The evolution equation for (x,t) is: ; in, For time step, It is a discrete velocity vector.

[0034] Equilibrium distribution function: ; in, For macroscopic speed, T For macroscopic temperature, ω i These are the weighting coefficients. c s For the speed of sound in a grid, τ T The dimensionless relaxation time is related to the thermal diffusivity. α T The relationship is: ; Boundary conditions: Inner wall surface (in contact with the heat medium): Temperature changes linearly with time; simulated start-up and shutdown curves: Slow start-stop: 0-400 s from 20℃ to 130℃, 400-500 s maintain 130℃, 500-900 s drop to 20℃.

[0035] Rapid start-stop: 0-200 s to rise from 20℃ to 130℃, 200-250 s to maintain 130℃, and 250-450 s to drop to 20℃.

[0036] Outer wall surface (in contact with air): convective heat transfer boundary, heat transfer coefficient h = 10 W / (m²) 2 ·K), ambient temperature T amb =20℃. Use the LBM convection boundary scheme (such as the non-equilibrium extrapolation scheme).

[0037] S3. Establish the LBM evolution equation for the pressure field.

[0038] The internal pressure P = 3 MPa is introduced through pressure boundary conditions. The evolution equation of the density distribution function fi(x,t) is: ; Equilibrium state: ; Macro density Macro speed ,pressure Set density values ​​at the inlet / outlet boundaries to achieve a pressure of 3 MPa.

[0039] S4, Thermo-structural coupling LBM elastic model.

[0040] The displacement and stress fields are solved using a spring lattice model or the elastic distribution function method.

[0041] Calculate the thermal strain of each cell from the temperature field: in, For thermal strain, This is a reference temperature.

[0042] Total strain: ; in, For total strain, For elastic strain, This is thermal strain.

[0043] Stress is calculated using the generalized Hooke's law: ; in, For stress tensor, For strain tensor, For the Kronecker function, For elastic modulus, Poisson's ratio, The coefficient of thermal expansion is This represents the change in temperature.

[0044] Displacement distribution function in the LBM elastic model evolution: ; in, Let be the dimensionless relaxation time of the displacement distribution function. This is the equilibrium distribution function.

[0045] Displacement field by The zeroth moment is obtained, and the stress field is calculated through displacement gradient.

[0046] Coupling method: weak coupling, that is, the temperature field affects the stress-strain field, but the reaction of stress on the temperature field is ignored.

[0047] S5, Full-cycle start-stop cycle simulation process.

[0048] Initialization: Temperature of all cells T=20℃, pressure P=3 MPa, displacement u=0, stress σ=0.

[0049] Time stepping loop (Δt=1×10) -5 (s, total number of steps is determined based on total time): (1) Update the temperature field boundary conditions (assign values ​​to the inner wall temperature according to the start-stop curve); (2) Execute the temperature distribution function g i Collision-Migrating; (3) Execute the density distribution function f i Collision-Migrating; (4) Calculate the thermal strain from the current temperature field; (5) Execute the displacement distribution function Collision-migration, updating the displacement field; (6) Calculate the stress field and output the maximum von Mises equivalent stress σ. vM Maximum axial deformation δ max ; (7) If the output time point is reached (e.g., every 0.1 s), save the result.

[0050] Simulation termination condition: Reaching the total simulation time (900 s for slow simulation, 450 s for fast simulation).

[0051] S6. Stress assessment and safety criteria.

[0052] According to the pressure vessel safety guidelines (JB 4732 / ASME VIII-2): If the combined strength range of primary stress (generated by pressure) and secondary stress (generated by thermal constraint) is ≤ 3 times the allowable stress of the material at the design temperature, then the structure is safe.

[0053] Calculate the residual stress σ at the end of cooling. res and residual deformation δ res .

[0054] Judgment criterion: σ res ≤0.2 times the yield strength, δ res If the thickness is ≤0.001 mm, the structure is considered to have no cumulative plastic damage.

[0055] S7, Comparison of the impact of start-stop rate.

[0056] Perform slow (0.275℃ / s) and fast (0.55℃ / s) start-stop simulations respectively.

[0057] Compare the peak value of maximum equivalent stress, residual stress, peak value of deformation, and stress-deformation decoupling behavior.

[0058] Output recommendation: Start-stop rate ≤ 0.3℃ / s.

[0059] Example 1 This embodiment uses a slow start-stop cycle (0.275℃ / s).

[0060] The geometric and material parameters are as described above.

[0061] LBM lattice size: Δx = 0.5 mm, total number of lattices approximately 12 million (can be halved due to symmetry).

[0062] Computing platform: NVIDIA A100 GPU, CUDA parallel LBM solver.

[0063] Simulation time: approximately 4.5 hours (900 s physical time, time step 1e-5 s, total 9e7 steps).

[0064] Output results: Temperature field: The overall temperature reaches 130℃ at 400 s, and the radial temperature difference is <1℃.

[0065] Maximum axial deformation: 0.0606 mm at 500 s, residual deformation after cooling: 0.00085 mm.

[0066] Maximum equivalent stress: 332.78 MPa at 500 s, residual stress at the end of cooling: 8.86 MPa.

[0067] Safety assessment: 332.78 MPa < 3 × 203 MPa = 609 MPa, which meets the safety criteria.

[0068] Decoupling phenomenon: Deformation stabilizes within 400-500 s, and stress slowly increases from 315 MPa to 332.78 MPa.

[0069] Example 2 This embodiment uses a rapid start-stop cycle (0.55℃ / s).

[0070] Total duration 450 s, heating rate 0.55℃ / s, hold for 50 s, cooling rate 0.55℃ / s.

[0071] The remaining parameters are the same as in Example 1.

[0072] Simulation time: Approximately 2.3 hours.

[0073] Output results: Maximum axial deformation: 0.121 mm (99% increase compared to slow speed).

[0074] Maximum equivalent stress: 499.16 MPa (50% higher than slow speed).

[0075] Residual stress: 25.37 MPa (186% higher than at slower speeds).

[0076] Residual deformation: 0.00092 mm (still very small).

[0077] Safety assessment: 499.16 MPa < 609 MPa, still meets safety requirements, but the stress margin is reduced.

[0078] Conclusion: Rapid start-stop significantly increases the risk of thermal shock and should be avoided.

[0079] Therefore, this invention employs the aforementioned LBM-based simulation method for bellows compensators in long-distance pipelines to simulate their transient thermo-structural coupling response during start-stop cycles (20℃→130℃→20℃). The temperature and pressure fields are solved separately using a dual-distribution function LBM, and the displacement and stress fields are solved through thermal strain coupling. It can completely simulate the entire cycle of heating, high-temperature holding, and cooling, outputting axial deformation, von Mises equivalent stress, residual stress, and residual deformation. Structural safety is assessed according to pressure vessel safety criteria. By comparing the responses under slow (0.275℃ / s) and rapid (0.55℃ / s) start-stop conditions, the deformation-stress decoupling phenomenon during the high-temperature holding stage is revealed, and the thermal shock risk is quantitatively provided. This invention has advantages such as high parallel efficiency, strong adaptability to complex boundaries, and stable transient temperature gradient capture, and can be used for safety assessment and operational strategy optimization of bellows compensators in long-distance heating pipelines.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A simulation method for bellows compensators in long-distance pipelines based on LBM, characterized in that, Includes the following steps: S1. Establish a three-dimensional geometric model of the bellows compensator and discretize the three-dimensional geometric model into an LBM lattice space; S2. Using the dual distribution function LBM, establish the LBM evolution equations for the temperature field and pressure field, and solve for the transient temperature field and pressure field respectively; S3. Calculate thermal strain based on temperature field, and solve displacement and stress fields using LBM elastic model; S4. Simulates the full-cycle start-stop cycle and outputs the maximum von Mises equivalent stress, maximum axial deformation, residual stress, and residual deformation. S5. Assess the safety of the compensator according to the pressure vessel safety guidelines; S6. Perform slow start-stop simulation and fast start-stop simulation respectively, and output the recommended upper limit of start-stop rate by comparing the impact of start-stop rate.

2. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific steps of S1 are as follows: S11. Obtain the structural parameters of the bellows, including nominal diameter, wave height, wave pitch, total length, number of layers, and equivalent wall thickness. S12. Use 3D modeling software to construct a 3D geometric model and export the 3D geometric model as an STL format; S13. The three-dimensional geometric model is discretized into an LBM lattice space using a discrete velocity model. S14. Map the material parameters to the lattice nodes. The material parameters include density, specific heat capacity, thermal conductivity, coefficient of thermal expansion, elastic modulus and Poisson's ratio.

3. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific steps of S2 are as follows: S21. Set the boundary conditions for the temperature field, adopt the double distribution function (LBM), establish the evolution equation of the temperature distribution function, define the temperature equilibrium distribution function, and solve for the temperature field. S22. Introduce pressure boundary conditions, establish the evolution equation of the density distribution function, define the density equilibrium distribution function, and solve for the pressure field.

4. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 3, characterized in that, The temperature field boundary conditions in S21 are as follows: the inner wall temperature changes with time according to a linear start-stop curve; the outer wall is a convective heat transfer boundary with a heat transfer coefficient of 10 W / (m²). 2 ·K), with an ambient temperature of 20℃.

5. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 3, characterized in that, The pressure field boundary condition in S22 is: the internal pressure is constant at 3 MPa.

6. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific steps of S3 are as follows: S31. Calculate the thermal strain of each cell based on the temperature field; S32. Calculate stress by coupling thermal strain using the generalized Hooke's law; S33. Employ the displacement distribution function to evolve the LBM elasticity model; S34. Solve for the displacement and stress fields using the LBM elastic model.

7. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific steps of S4 are as follows: S41. Initialize the temperature, pressure, displacement, and stress of all grid cells; S42. Simulate the full-cycle start-stop loop, using time-stepping loop iteration; The entire start-stop cycle includes a heating phase, a high-temperature holding phase, and a cooling phase, specifically: Heating phase: linearly increases from 20℃ to 130℃; High-temperature holding section: maintained at 130℃; Cooling phase: linearly decreasing from 130℃ to 20℃; In this case, the heating rate and the cooling rate are the same; S43. When the time step iteration reaches the total simulation duration, the simulation ends.

8. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 7, characterized in that, The specific steps of S42 are as follows: S421. Update the temperature field boundary conditions, and assign the inner wall temperature according to the start-stop curve; S422, Perform collision migration of the temperature distribution function evolution equation; S423, Perform collision migration of the density distribution function evolution equation; S424. Calculate the thermal strain based on the current temperature field; S425. Perform collision migration of the displacement distribution function and update the displacement field; S426 Calculate the stress field and output the maximum von Mises equivalent stress and maximum axial deformation; S427. When the iteration reaches the output time point, save the result.

9. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific safety criteria in S5 are as follows: If the combined strength range of primary and secondary stresses is ≤3 times the allowable stress of the material at the design temperature, then the structure is safe. If the residual stress at the end of cooling is ≤0.2 times the yield strength and the residual deformation is ≤0.001mm, then the structure has no cumulative plastic damage.

10. The simulation method for bellows compensators in long-distance pipelines based on LBM according to claim 1, characterized in that, The specific steps of S6 are as follows: S61. Perform slow start-stop simulation and fast start-stop simulation respectively, where the slow start-stop simulation rate is 0.275℃ / s and the fast start-stop simulation rate is 0.55℃ / s. S62. Compare the peak value of maximum equivalent stress, residual stress, peak value of deformation, and stress-deformation decoupling behavior. S63, the recommended start / stop rate for output is 0.3℃ / s.

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