Method and system for designing steel sealing layer of compressed air energy storage underground artificial reservoir based on isogeometric phase field method

Abstract

The invention discloses a design method and system for a steel sealing layer of a compressed air energy storage underground artificial reservoir based on an isogeometric phase field method, and the method comprises the steps: building a coupling model of air thermodynamics in the reservoir and heat conduction of a wall medium, and carrying out the simulation calculation of the changes of temperature and pressure in the reservoir in the process of inflation-gas storage-deflation-gas storage; establishing a phase field model for thermal coupling fatigue failure analysis of the steel sealing layer, the concrete lining and the surrounding rock; constructing an isogeometric four-order phase field method calculation model for the fatigue failure analysis of the block type steel sealing layer, and performing numerical simulation based on the influence of a block type layout mode, a welding mode, welding defects and welding residual stress of the steel sealing layer on the fatigue failure of the steel sealing layer; and carrying out statistical analysis on a numerical simulation result, and determining a layout method and a welding mode of the steel sealing layer. According to the method, a new thought is provided for design of the steel sealing layer of the compressed air energy storage underground artificial cave depot, and the method assists in solving the electricity abandoning problem of new energy through the CAES technology.

Description

Technical Field

[0001] The invention belongs to the field of the design of a steel sealing layer for an underground artificial cavern of compressed air energy storage, and particularly relates to a design method and system for a steel sealing layer of an underground artificial cavern of compressed air energy storage based on an isogeometric phase field method. Background Art

[0002] New energy represented by wind power and photovoltaic power develops rapidly. However, its inherent intermittency and instability are difficult to fully match the energy demand, resulting in a shortage of supply when the energy demand is high and an oversupply when the energy demand is low. The amount of abandoned wind and photovoltaic power in the country increased significantly from 2020 to 2023. Compressed air energy storage is a large-scale physical energy storage technology with great development potential. It compresses and stores excess electric energy into compressed air during the low electricity consumption period, and releases the stored high-pressure air for power generation during the high electricity consumption peak, so as to realize "peak shaving and valley filling" for unstable energy supply. Compressed air energy storage has the advantages of large installed capacity, long energy storage time, low operating cost, high safety, clean and environmental protection, etc., and is one of the large-scale energy storage technologies expected to achieve commercial operation.

[0003] Salt cavern gas storage has the advantages of good sealing performance and high stability, but it is significantly restricted by the geographical environment. In addition to salt cavern gas storage, underground artificial caverns have become an important form of gas storage for compressed air energy storage power stations. It is a gas storage structure with a certain volume formed by artificial excavation in underground hard rock. The engineering controllability of artificial caverns is strong, and it is the key research and demonstration direction of compressed air energy storage power stations at the present stage. For safety reasons, steel sealing layers are adopted for all the existing / under-construction underground artificial caverns in China. However, the high-frequency charging and discharging cause a large fluctuation in the air temperature in the cavern, and the air pressure is also high. The fatigue durability of the sealing layer has become the key to the sealing performance.

[0004] The isogeometric phase field method combines the advantages of isogeometric analysis and the fracture phase field method, that is: geometric accuracy, high-order continuity, high precision, no traditional grid division process, simple grid refinement, uniformly simulating complex fracture processes such as crack initiation, propagation, bifurcation and aggregation, without fracture criteria, without special technical treatment of non-conforming grids after local refinement, avoiding many difficulties brought by the existence and expansion of cracks, and being able to effectively simulate and reproduce the failure process of the sealing layer of "alternating temperature and pressure load - material property degradation - fatigue damage accumulation - sealing performance failure". Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a design method and system for the steel sealing layer of an underground artificial chamber for compressed air energy storage based on the isogeometric phase field method. The present invention combines the fracture phase field method and the isogeometric analysis theory, adopts the multi-piece modeling method, establishes the isogeometric phase field method model and calculation method of the block-type steel sealing layer, and simulates and reproduces the failure process of the sealing layer of the underground chamber for compressed air energy storage, namely "alternating temperature and pressure load - material property deterioration - fatigue damage accumulation - sealing performance failure". Based on the fatigue durability analysis of the sealing layer, the optimal layout method and welding method of the steel sealing layer are determined. The present invention can obtain the optimal layout method and welding method of the steel sealing layer.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A design method for the steel sealing layer of an underground artificial chamber for compressed air energy storage based on the isogeometric phase field method, the method comprising:

[0008] Establish a coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium, and simulate and calculate the changes in temperature and pressure in the chamber during the processes of "air charging - gas storage - air discharging - gas storage";

[0009] Establish a phase field model for the thermal-mechanical fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock, and realize the fracture analysis inside the sealing layer, lining and surrounding rock and the interface fracture analysis of the sealing layer - lining - surrounding rock;

[0010] Under the framework of isogeometric analysis, combined with the Nitsche method, construct an isogeometric fourth-order phase field method calculation model for the fatigue failure analysis of the block-type steel sealing layer, and numerically simulate the influence of the block layout method, welding method, welding defects and welding residual stress of the steel sealing layer on the fatigue failure of the steel sealing layer;

[0011] Conduct statistical analysis on the numerical simulation results to determine the layout method and welding method of the steel sealing layer.

[0012] Preferably, the method for establishing the coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium includes:

[0013] Improve the convective heat transfer model between the chamber wall and the compressed air, correct the convective heat transfer coefficient, and improve the Kushnir model to establish the air thermodynamics model in the chamber;

[0014] According to the heat conduction theory, establish the heat conduction models of the chamber wall media in the steel sealing layer, concrete lining and surrounding rock respectively;

[0015] Combine the air thermodynamics model in the chamber and the heat conduction model of the chamber wall medium to obtain the coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium.

[0016] Preferably, the method for simulating the changes in temperature and pressure in the cavern during the "inflation - gas storage - deflation - gas storage" process includes:

[0017] Using the finite difference method to solve the air thermodynamic model in the cavern and the isogeometric analysis method to solve the heat conduction model of the cavern wall medium, and simulating the changes in temperature and pressure in the cavern during the "inflation - gas storage - deflation - gas storage" process.

[0018] Preferably, the method for establishing a phase - field model for thermo - mechanical coupling fatigue failure analysis of a steel seal layer - concrete lining - surrounding rock includes:

[0019] Based on the phase - field model for fatigue failure analysis of steel and rock - like materials under thermo - mechanical coupling, combined with an additional interface phase - field model, establish a phase - field model for thermo - mechanical coupling fatigue failure analysis of a steel seal layer - concrete lining - surrounding rock, and simulate the internal fractures of the seal layer, lining, and surrounding rock, as well as the interface fractures between the seal layer - lining - surrounding rock.

[0020] Preferably, the method for constructing an isogeometric fourth - order phase - field method calculation model for fatigue failure analysis of a segmented steel seal layer and numerically simulating the effects of the segmented layout method, welding method, welding defects, and welding residual stress of the steel seal layer on its fatigue failure includes:

[0021] Based on the established phase - field model for thermo - mechanical coupling fatigue failure analysis of a steel seal layer - concrete lining - surrounding rock, obtain the weak form of the governing equation, use the isogeometric analysis method based on TH - NURBS to discretize the field variables, and derive the discrete governing equation;

[0022] Use the Nitsche method with variational consistency characteristics to impose the coupling constraints between two - piece phase - field models;

[0023] Based on the Nitsche method, respectively derive the multi - piece isogeometric analysis governing equations for the displacement field, phase field, and temperature field; estimate the stabilizing term coefficient value through local eigenvalues, then calculate the influence of the stabilizing term coefficient value on the results, and finally determine the values of the stabilizing term coefficients in the multi - piece isogeometric analysis governing equations for the displacement field, phase field, and temperature field respectively;

[0024] The steel seal layer is designed in a segmented manner, and the blocks are welded together during construction. The welding methods include two - pass welds and three - pass welds. Using the multi - piece modeling method, each block is regarded as one or more pieces, and each weld is regarded as a piece, to establish an isogeometric phase - field method model and calculation method for the segmented steel seal layer;

[0025] Adopt adaptive analysis, global - local technology, and loop skipping algorithm acceleration schemes;

[0026] Determine the initial stress / strain state of the weld through welding process modeling, and then conduct fatigue analysis of the seal layer.

[0027] The present invention also provides a steel seal layer design system for an underground artificial cavern for compressed air energy storage based on the isogeometric phase field method. The system is used to implement the foregoing method, and the system includes: a thermal module, an analysis module, a calculation module, and a statistics module;

[0028] The thermal module is used to establish a coupling model of air thermodynamics in the cavern and heat conduction of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the processes of "air filling - gas storage - gas release - gas storage";

[0029] The analysis module is used to establish a phase field model for the thermo - mechanical coupling fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock, and realize the fracture analysis inside the seal layer, lining and surrounding rock and the interface fracture analysis of the seal layer - lining - surrounding rock;

[0030] The calculation module is used to construct an isogeometric fourth - order phase field method calculation model for the fatigue failure analysis of the segmented steel seal layer under the framework of isogeometric analysis, and in combination with the Nitsche method, numerically simulate the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel seal layer on the fatigue failure of the steel seal layer;

[0031] The statistics module is used to perform statistical analysis on the numerical simulation results to determine the layout method and welding method of the steel seal layer.

[0032] Preferably, the process of establishing the coupling model of air thermodynamics in the cavern and heat conduction of the cavern wall medium includes:

[0033] Improve the convective heat transfer model between the cavern wall and the compressed air, correct the convective heat transfer coefficient, and improve the Kushnir model to establish the air thermodynamics model in the cavern;

[0034] According to the heat conduction theory, establish the heat conduction models of the cavern wall media in the steel seal layer, concrete lining and surrounding rock respectively;

[0035] Combine the air thermodynamics model in the cavern and the heat conduction model of the cavern wall medium to obtain the coupling model of air thermodynamics in the cavern and heat conduction of the cavern wall medium.

[0036] Preferably, the process of simulating and calculating the changes in temperature and pressure in the cavern during the processes of "air filling - gas storage - gas release - gas storage" includes:

[0037] Use the finite difference method to solve the air thermodynamics model in the cavern, and use the isogeometric analysis method to solve the heat conduction model of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the processes of "air filling - gas storage - gas release - gas storage".

[0038] Preferably, the process of establishing the phase field model for the thermo - mechanical coupling fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock includes:

[0039] Based on the phase-field model for fatigue failure analysis under thermo-mechanical coupling of steel and rock-like materials, combined with the additional interface phase-field model, a phase-field model for fatigue failure analysis of steel seal layer-concrete lining-surrounding rock under thermo-mechanical coupling is established to simulate the internal fractures of the seal layer, lining and surrounding rock, as well as the interface fractures between the seal layer-lining-surrounding rock.

[0040] Preferably, an isogeometric fourth-order phase-field method calculation model for fatigue failure analysis of the segmented steel seal layer is constructed. The process of numerically simulating the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel seal layer on its fatigue failure includes:

[0041] Based on the established phase-field model for fatigue failure analysis of the steel seal layer-concrete lining-surrounding rock, the weak form of the control equation is obtained. The isogeometric analysis based on TH-NURBS is used to discretize the field variables, and the discrete control equation is derived.

[0042] The Nitsche method with variational consistency characteristics is used to impose the coupling constraints between two-phase field models.

[0043] Based on the Nitsche method, the multi-patch isogeometric analysis control equations for the displacement field, phase field, and temperature field are respectively derived. The coefficient value of the stabilization term is estimated through local eigenvalues, and then the influence of the coefficient value of the stabilization term on the results is calculated. Finally, the values of the coefficient of the stabilization term in the multi-patch isogeometric analysis control equations for the displacement field, phase field, and temperature field are respectively determined.

[0044] The steel seal layer adopts a segmented design, and the blocks are welded together during construction. The welding methods include two-pass welds and three-pass welds. The multi-patch modeling method is adopted, with each block regarded as one or more patches, and each weld as a patch, to establish the isogeometric phase-field method model and calculation method for the segmented steel seal layer.

[0045] Adopt the adaptive analysis, global-local technique and loop skipping algorithm acceleration scheme.

[0046] The initial stress / strain state of the weld is determined by welding process modeling, and then the fatigue analysis of the seal layer is carried out.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] (1) The present invention realizes the integration of the design and analysis of the steel seal layer, can obtain excellent layout methods and welding methods for the steel seal layer, and has high design efficiency;

[0049] (2) The isogeometric phase field method adopted by the present invention has geometric accuracy, high-order continuity, high precision, no mesh generation process in the traditional sense, simple mesh refinement, and can uniformly simulate complex fracture processes such as crack initiation, propagation, branching, and coalescence. It does not require fracture criteria and does not require special technical treatment for the incompatible meshes after local refinement, avoiding many difficulties brought by the existence and propagation of cracks, and can effectively simulate and reproduce the failure process of "alternating temperature and pressure load - material property degradation - fatigue damage accumulation - sealing performance failure" of the sealing layer;

[0050] (3) The present invention adopts a high-order phase field model, which can reduce the element size requirements related to the length scale, has higher regularity in describing cracks, and thus improves the convergence speed and accuracy of numerical approximation;

[0051] (4) The present invention uses isogeometric analysis to solve the phase field model, and its high-order continuity can well solve the problem that the high-order phase field model requires a shape function with at least C1 continuity.

[0052] (5) The present invention adopts isogeometric analysis based on TH-NURBS splines, which can adopt multi-scale computational meshes, improve accuracy and save computational effort. In addition, the TH-NURBS spline basis functions are linearly independent and can accurately describe any complex geometry;

[0053] (6) The present invention takes into account the welding method of the steel sealing layer;

[0054] (7) The present invention adopts a variety of acceleration schemes to significantly improve the computational efficiency;

[0055] (8) The present invention gives an optimal layout method and welding method for the steel sealing layer, guiding the design and construction of the steel sealing layer. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0057] Figure 1 It is a schematic flow chart of a design method for a steel sealing layer of an underground artificial cavern for compressed air energy storage based on the isogeometric phase field method according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0058] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0059] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0060] Embodiment 1

[0061] As Figure 1 shown, the embodiment of the present invention provides a design method for the steel sealing layer of an underground artificial cavern for compressed air energy storage based on the isogeometric phase field method, including the following steps:

[0062] S1. Establish a coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium;

[0063] S2. Solve the changes in temperature and pressure in the cavern during the "charging - gas storage - discharging - gas storage" process;

[0064] S3. Establish a phase field model for thermo - mechanical fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock;

[0065] S4. Establish an isogeometric fourth - order phase field method calculation model for fatigue failure analysis of the segmented steel sealing layer;

[0066] S5. Numerically simulate the effects of the segmented layout method, welding method, welding defects, welding residual stress, etc. of the steel sealing layer on the fatigue failure of the steel sealing layer;

[0067] S6. Statistically analyze the numerical simulation results, count the relationship between the fatigue life and the sealing layer layout method and welding method, and summarize the optimal steel sealing layer layout method and welding method.

[0068] As a preferred technical solution of the present invention, the specific content of S1 is as follows:

[0069] S11. Based on the theory of mixed and forced convection heat transfer, correct the convective heat transfer coefficient between the cavern wall and the compressed air, so that the heat transfer process between the air inside the cavern and the cavern wall medium in the thermodynamic model established by Kushnir et al. is more in line with the actual situation;

[0070] S12. According to the heat conduction theory, establish the heat conduction equations in the steel sealing layer, concrete lining, and surrounding rock respectively. To simplify the problem, the influence of damage cracking of the cavern wall medium on the thermal conductivity of the medium is not considered;

[0071] S13. Combine the air thermodynamic model in the combined chamber and the heat conduction model of the chamber wall medium to obtain a coupled model of air thermodynamics and chamber wall medium heat conduction in the chamber, which can consider the heat conduction of the chamber wall caused by the change of air temperature in the chamber during operation and the influence of the heat conduction of the chamber wall on the change of air temperature in the chamber.

[0072] As a preferred technical solution of the present invention, the S2 is specifically as follows:

[0073] S21. To save the calculation amount, the finite difference method is used to solve the thermodynamic model in the chamber, and the isogeometric analysis method is used to solve the heat conduction model of the chamber wall medium, and the changes of temperature and pressure in the chamber during the process of "inflation - gas storage - deflation - gas storage" are simulated and calculated;

[0074] S22. Explore the influence of different calculation methods of the compression factor (such as: BB equation, DAK equation, BWRS equation, Berthelot equation, etc.) and different convective heat transfer models between the chamber wall and the compressed air on the changes of air temperature and pressure in the chamber. According to the comparison between the simulation results and the operation monitoring data of the existing power stations, determine the appropriate calculation method of the compression factor and the convective heat transfer model between the chamber wall and the compressed air;

[0075] The change of air temperature in the chamber will cause the heat conduction of the chamber wall, and the heat conduction of the chamber wall will in turn affect the change of air temperature in the chamber. By solving the coupled model of air thermodynamics and chamber wall medium heat conduction (transient heat conduction) in the chamber, the temperature and pressure in the chamber at the thermal equilibrium state are used as the loads for the fatigue failure analysis of the sealing layer.

[0076] As a preferred technical solution of the present invention, the S3 is specifically as follows:

[0077] S31. The fatigue failure analysis of the steel sealing layer is considered as low - cycle fatigue considering elastoplasticity. For the thermo - mechanical coupling fracture problem, the total potential energy of the system = elastic strain energy + plastic strain energy + plastic dissipation energy + fracture energy + thermal energy - external work;

[0078] S32. Only the elastic strain energy in the tensile state drives crack propagation. The elastic strain energy density is decomposed into the elastic strain energy density in the compressive state and the elastic strain energy density in the tensile state by using the decomposition method of the spherical strain tensor and the deviatoric strain tensor;

[0079] S33. The Von Mises yield criterion is adopted, and isotropic linear hardening is considered. The plastic strain energy density and the plastic dissipation energy density Δ p can be expressed by the yield strength σ y , the equivalent plastic strain α and the hardening modulus H, that is

[0080]

[0081] Δ p = σ y α.

[0082] S34. The crack surface density function of the fourth-order fracture phase field method is d is the phase field, l0 is the length scale parameter describing the crack band width, is the phase field gradient field, Δ is the Laplace operator. Based on the crack surface density function, the fracture energy can be calculated;

[0083] S35. The thermal energy density can be expressed as (c is the heat capacity, θ0 and θ are the reference temperature and temperature), and the thermal energy can be obtained by performing a volume integral within the computational domain.

[0084] S36. The elastic strain energy degradation function g1(d), plastic strain energy degradation function g2(d,α), plastic dissipation energy degradation function g3(d,α), and yield surface degradation function g4(d,α) are introduced. α is the equivalent plastic strain. The degradation functions are multiplied by the elastic strain energy, plastic strain energy, plastic dissipation energy, and yield strength to obtain the damage-weakened elastic strain energy, plastic strain energy, plastic dissipation energy, and yield strength. Select g1(d) = s[(1 - d) 3 -(1 - d) 2 +3(1 - d) 2 -2(1 - d) 3 , where s is a positive number close to 0. To simplify the problem, select g2(d,α) = g3(d,α) = g4(d,α) = s[(1 - d) 3h(α) -(1 - d) 2h(α) +3(1 - d) 2h(α) -2(1 - d) 3h(α) , and determine the reasonable form of h(α) based on experimental data;

[0085] S37. To consider the effects of plasticity and fatigue on the fracture process, a degradation function related to the equivalent plastic strain and fatigue history variable is used to weaken the fracture toughness, where: is the fatigue degradation function( is the cumulative fatigue history variable), and f2(α) is the fracture toughness degradation function for elastoplastic fracture. The asymptotic fatigue degradation function proposed by Alessi et al. is used Plasticity is irreversible, so the degradation function decreases monotonically with the increase of the equivalent plastic strain. The fracture toughness degradation function for ductile fracture proposed by Yin and Kaliske is used, that is

[0086]

[0087] where, α cfis the plastic threshold for triggering the degradation mechanism, and a and b are the softening parameters that define the profile of the degradation function.

[0088] S38. Damage also weakens the thermal conductivity of the material. The true thermal conductivity k after damage is given by k = [(1 - k s )g1(d)+k s k0, where k0 is the thermal conductivity of the intact material and k s is a small stability parameter;

[0089] S39. According to the F - M variational principle, the basic equations and boundary conditions that the displacement field and the phase field should satisfy are derived. To avoid crack self - healing, a history variable H is introduced following the approach of Miehe. To analyze mixed - mode fracture problems, based on the F - criterion, is used to replace H I and H II in the phase - field evolution equation. H I and H II are the history variables for mode I and mode II respectively. Similar to the tensile - compressive decomposition of the elastic strain energy density, H

[0090] S310. A phase - field model for thermo - mechanical coupled fatigue failure analysis of rock - like materials is established, similar to the phase - field model for thermo - mechanical coupled fatigue failure analysis of steel. Since rock - like materials and steel have different properties, there are differences in the construction of their phase - field models, which are mainly reflected in: (1) Rock - like materials follow the Mohr - Coulomb yield criterion. (2) The fracture modes of rock - like materials include tensile fracture, compression - shear fracture, and tensile - shear fracture. The differences in the fracture energy release rate G cI for mode I, G cII for mode II, and G cs for compression - shear fracture are large, and the internal friction angle and cohesion have an impact on fracture. (3) Rock - like materials exhibit strain softening;

[0091] The coupled control equations of the phase - field model for thermo - mechanical coupled fatigue failure analysis of rock - like materials are

[0092]

[0093] where b is the body force, σ is the Cauchy stress tensor, k is the stability parameter, usually taking a value of 1×10 -9 . ρ is the mass density, c is the specific heat capacity of the material, is the rate of change of the temperature field, γ is the heat source of the temperature field, and J is the heat flux of the temperature field. and Denotes the critical energy release rate weakened by the fatigue effect, the fatigue degradation function Denotes the weakening of the material in the fatigue damage area, in the form of

[0094]

[0095] where Denotes a cumulative fatigue history state variable, α T Is the fatigue limit threshold of the material.

[0096] S311. The elastic strain energy density is decomposed into the elastic strain energy density in the compression state and the elastic strain energy density in the tensile state by the spectral decomposition method. Based on this decomposition, the strain energy density (energy driving force) of the tensile crack and the strain energy density of the tensile-shear crack can be directly constructed. Based on the over-shear stress and the Mohr-Coulomb yield criterion, the strain energy density of the compression-shear crack can be calculated, which is related to the Lame constant, the internal friction angle, the cohesion and the principal strain, and the influence of the intermediate principal stress is considered;

[0097] S312. Denote the historical variables of the energy driving forces of the tensile crack, the tensile-shear crack and the compression-shear crack as H t , H ts and H cs respectively, and let G cs =k1G cII , where k1 is a coefficient. Based on the F criterion, use to replace in the phase field evolution equation. This can avoid crack self-healing;

[0098] S313. The surrounding rock is generally inhomogeneous, and the interface fracture of inhomogeneous materials needs to be considered. The additional interface phase field model is used to deal with the interface fracture problem. The interface failures between the sealing layer and the concrete lining, and between the concrete lining and the surrounding rock can be simulated by the additional interface phase field model. The historical field method proposed by Borden et al. is used to simulate the interface defects or the initial defects in the surrounding rock, which is the most convenient and flexible in the isogeometric analysis method;

[0099] The additional interface phase field model uses a scalar β in the range of [0,1] to characterize the interface, and disperses the material properties on the interface into the surrounding matrix to form an equivalent field with a continuous distribution of material properties. β = 1 represents the interface, and β = 0 represents the matrix. The material parameter that varies continuously on the interface is

[0100] Θ s (β)=Θ i [1-(1-β) 2 +Θ m (1-β) 2 ;

[0101] Among them, Θs is the equivalent material parameter, and Θi and Θm are the material parameters of the interface and the matrix, respectively.

[0102] The historical strain field record is used to calculate the maximum strain energy experienced by the grid integration points or midpoints during the loading process. The historical field method is to artificially delimit a region with extremely large initial strain energy as the initial defect in the interface defect or surrounding rock, which can very conveniently locate the initial defect at any position in the calculation domain without the need for complex defect modeling.

[0103] S314. Based on the phase field model for fatigue failure analysis under thermo-mechanical coupling of steel and rock-like materials, combined with the additional interface phase field model, a phase field model for fatigue failure analysis of steel seal layer - concrete lining - surrounding rock under thermo-mechanical coupling is established, which can simulate the internal fractures of the seal layer, lining and surrounding rock, as well as the interface fractures of the seal layer - lining - surrounding rock.

[0104] As a preferred technical solution of the present invention, the specific content of S4 is as follows:

[0105] S41. Based on the established phase field model for fatigue failure analysis of steel seal layer - concrete lining - surrounding rock, write the integral form (weak form) of the governing equation, and its expression is:

[0106]

[0107] Among them,

[0108] The isogeometric analysis based on TH-NURBS is used to discretize the field variables, and the discrete governing equation for solving the field variables is derived, that is

[0109] K u U = F u

[0110]

[0111] And

[0112]

[0113] Among them, R u and R φ are the basis function matrices of the displacement field and the phase field respectively, and B u and B φ are the gradient matrices of the basis function matrices of the displacement field and the phase field respectively.

[0114] S42. For a complex calculation domain, it is necessary to use multiple patches for description. Each patch can be discretized arbitrarily. The Nitsche method with variational consistency characteristics is used to apply the coupling constraints so that the field variables at the interface between the two patches remain continuous;

[0115] S43. For the thermo-mechanical coupling problem, based on the Nitsche method, the multi-patch isogeometric analysis solution equations for the displacement field, phase field, and temperature field are derived respectively. The preliminary stabilization term coefficient value is estimated by calculating the local eigenvalue, and the influence of different values on the results is studied by numerical experiments near the preliminary stabilization term coefficient value. Finally, the reasonable values of the stabilization term coefficients in the multi-patch isogeometric analysis control equations for the displacement field, phase field, and temperature field are determined respectively;

[0116] The weak forms of the multi-patch isogeometric analysis solution control equations for the displacement field \(u\), phase field \(\varphi\), and temperature field \(\theta\) are respectively (taking the computational domain divided into two subdomains as an example):

[0117]

[0118] where \(\Omega\) m is the \(m\)-th subdomain, \(\Gamma\) is the coupling edge, and are the jump operator and average operator, \(\alpha\) u , \(\alpha\) φ and \(\alpha\) θ are the stabilization parameters to ensure the positive definiteness of the stiffness matrix, \(k\) s is the degraded thermal conductivity. For two-dimensional problems,

[0119] S44. The steel seal layer is designed in a block-by-block manner and welded between blocks during construction. The welding methods include two-pass welds and three-pass welds. Using the multi-patch modeling method, each block is regarded as one or more patches, and each weld is regarded as a patch. The isogeometric analysis is used to discretize the field variables and the Nitsche method is used to couple the patch-patch interface (ensuring the continuity of the field variables at the patch-patch interface) to establish the isogeometric phase field method calculation model of the block-by-block steel seal layer;

[0120] S45. Due to the introduction of the phase field gradient, in order to ensure the calculation accuracy, the spatial discretization near the crack band must have sufficient numerical resolution. In order to significantly improve the calculation efficiency and realize the fatigue failure analysis of the steel seal layer of the compressed air energy storage artificial cavern, acceleration schemes such as adaptive analysis, global-local technique, and cyclic jump algorithm can be adopted, that is

[0121] The first step: Select a suitable refinement index

[0122] The critical phase field at crack nucleation is 0.25. Define a value slightly smaller than 0.25 as the refinement threshold \(d\) c to obtain the crack initiation region. To obtain better refinement effects, an energy index based on the element residual historical strain energy \(Y\) e is supplemented. The energy index \(Y\) e > \(Y\) ec and the phase field index \(d > d\)c Combination can not only determine the crack initiation and damage areas, but also predict the fracture area at the crack tip front in the next step.

[0123] Step 2: Determine the elements to be refined

[0124] When the element size is greater than the preset minimum size, mark the elements where the phase field value at the element nodes is greater than the refinement threshold or the element residual historical strain energy is greater than the critical residual historical strain energy. To ensure a smooth transition of the mesh refinement size, use the critical size of the adaptive element to guide the mesh refinement, and automatically determine the critical size of each element according to the phase field value, that is

[0125]

[0126] According to the phase field value d in and d cr Divide the entire region into an unbroken region, a fractured region, and a transition region. The critical sizes of the elements in the three regions gradually decrease from large to small according to the phase field value, achieving a smooth transition of the mesh size.

[0127] Step 3: Local mesh refinement

[0128] Extract the basis functions of the elements marked in the second step, and subdivide the TH-NURBS basis functions by the structured mesh method to achieve mesh refinement. An element is subdivided into four or eight new sub-elements, thus realizing the adaptive local refinement of the mesh. In addition, adopt the global-local method scheme, solve the fracture problem in the local region and the elastoplastic problem in the global region, thereby further reducing the computational time.

[0129] Step 4: Interpolation mapping and refinement-correction

[0130] Mutually map the displacements, phase fields, and historical variables on the control points of the original mesh and the newly generated mesh. Use the Lagrangian interpolation method for variable projection to approximately assign variables to the control points of the newly generated mesh; use the same projection method to update the displacement and temperature variables on the initial mesh. Then, perform an alternating solution. The meshes used for solving the displacement field and temperature field are the initial coarse meshes, and the phase field solution uses the newly generated locally refined mesh. After the alternating solution, the phase field distribution in the newly refined mesh can be obtained. Check whether there are still coarse elements that meet the refinement criteria. If so, return to Step 3 and repeat the whole process using the current mesh; otherwise, enter the next time step. Within a single time step, repeat this process until all crack regions are completely included in the refined mesh region.

[0131] Step 5: Loop jump algorithm

[0132] The fatigue analysis can use an explicit cyclic jump algorithm to accelerate the solution process. First, calculate the state variables of the system for several cycles, and then extrapolate the state variables of the system after cyclic jumps using these known quantities. For the fatigue cumulative history variable perform extrapolation, and the remaining variables are obtained by solving the system control equations. Let q be the end state of the cycle, that is Perform Perform a second-order Taylor series expansion at cycle N, and we can get

[0133]

[0134] To further improve the calculation speed, the method of adaptive cyclic jump step is used to dynamically adjust the jump step size. ΔN jp is the adaptive jump step size, and its size is determined according to the sensitivity of the crack system to the fatigue history variable during the per-cycle calculation before the jump, that is

[0135] ΔN jp = min(sΔN cw , ΔN min + β(ΔN max - ΔN min ))

[0136] where, ΔN cw is the number of cycles required for per-cycle calculation, ΔN min and ΔN max are the minimum and maximum number of cycles of the jump step size set artificially respectively, s is the sensitivity parameter set artificially, and β is used to reflect the sensitivity of the system to the fatigue history variable. When β is close to 0, it means that the jump step size needs to be reduced. When β is close to 1, it means that the time step size needs to be increased.

[0137] S46. Idealize the welding process as a thermo-mechanical problem, assuming that the considered thermo-mechanical problem is weakly coupled. Temperature changes will cause volume deformation, while solid deformation does not affect the thermal process. Through thermo-mechanical coupling analysis, numerically simulate the welding process to obtain the initial stress / strain state (residual stress, plastic strain distribution) of the weld, and then perform fatigue analysis on the sealing layer.

[0138] The isogeometric phase field method combines the advantages of isogeometric analysis and fracture phase field method, that is: geometric accuracy, high-order continuity, high precision, no traditional mesh generation process, simple mesh refinement, uniformly simulate complex fracture processes such as crack initiation, propagation, bifurcation and coalescence, and no additional fracture criterion is required, and it can effectively simulate and reproduce the failure process of the sealing layer of the underground artificial cavern for compressed air energy storage "alternating temperature and pressure load - material property degradation - fatigue damage accumulation - sealing performance failure".

[0139] Example Two

[0140] The present invention also provides a design system for the steel sealing layer of an underground artificial cavern for compressed air energy storage based on the isogeometric phase field method. The system is used to implement the aforementioned method, and the system includes: a thermal module, an analysis module, a calculation module, and a statistics module;

[0141] The thermal module is used to establish a coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the processes of "charging - gas storage - discharging - gas storage";

[0142] The analysis module is used to establish a phase field model for the thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock, and realize the fracture analysis inside the sealing layer, lining, and surrounding rock and the interfacial fracture analysis of the sealing layer - lining - surrounding rock;

[0143] The calculation module is used to construct an isogeometric fourth - order phase field method calculation model for the fatigue failure analysis of the segmented steel sealing layer under the framework of isogeometric analysis, in combination with the Nitsche method, and numerically simulate the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel sealing layer on its fatigue failure;

[0144] The statistics module is used to conduct statistical analysis on the numerical simulation results to determine the layout method and welding method of the steel sealing layer.

[0145] In this embodiment, the process of establishing the coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium includes:

[0146] Improve the convective heat transfer model between the cavern wall and compressed air, correct the convective heat transfer coefficient, and improve the Kushnir model to establish the air thermodynamics model in the cavern;

[0147] According to the heat conduction theory, establish the heat conduction models of the cavern wall media in the steel sealing layer, concrete lining, and surrounding rock respectively;

[0148] Combine the air thermodynamics model in the cavern and the heat conduction model of the cavern wall medium to obtain the coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium.

[0149] In this embodiment, the process of simulating and calculating the changes in temperature and pressure in the cavern during the processes of "charging - gas storage - discharging - gas storage" includes:

[0150] Use the finite difference method to solve the air thermodynamics model in the cavern, and use the isogeometric analysis method to solve the heat conduction model of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the processes of "charging - gas storage - discharging - gas storage".

[0151] In this embodiment, the process of establishing the phase field model for the thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock includes:

[0152] Based on the phase field model for fatigue failure analysis under thermo-mechanical coupling of steel and rock-like materials, combined with the additional interface phase field model, a phase field model for fatigue failure analysis of steel seal layer - concrete lining - surrounding rock under thermo-mechanical coupling is established to simulate the internal fractures of the seal layer, lining and surrounding rock, as well as the interface fractures between the seal layer - lining - surrounding rock.

[0153] In this embodiment, an isogeometric fourth-order phase field method calculation model for fatigue failure analysis of the segmented steel seal layer is constructed. The process of numerically simulating the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel seal layer on its fatigue failure includes:

[0154] Based on the established phase field model for fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock, the weak form of the governing equation is obtained. The isogeometric analysis based on TH-NURBS is used to discretize the field variables, and the discrete governing equation is derived.

[0155] The Nitsche method with variational consistency characteristics is used to impose the coupling constraints between two-phase field models.

[0156] Based on the Nitsche method, the multi-patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field are respectively derived; the coefficient value of the stabilization term is estimated through local eigenvalues, then the influence of the coefficient value of the stabilization term on the results is calculated, and finally the values of the coefficient of the stabilization term in the multi-patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field are respectively determined.

[0157] The steel seal layer adopts a segmented design, and the blocks are welded to each other during construction. The welding methods include two-pass welds and three-pass welds. The multi-patch modeling method is adopted, with each block regarded as one or more patches, and each weld as a patch, to establish the isogeometric phase field method model and calculation method for the segmented steel seal layer.

[0158] Adaptive analysis, global-local technique, and loop skipping algorithm acceleration schemes are adopted.

[0159] The initial stress / strain state of the weld is determined through welding process modeling, and then the fatigue analysis of the seal layer is carried out.

[0160] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention should fall within the protection scope determined by the claims of the present invention.

Claims

1. A design method for the steel sealing layer of an underground artificial chamber for compressed air energy storage based on the isogeometric phase field method, characterized in that The method includes: Establish a coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the "air filling - gas storage - gas release - gas storage" process; Establish a phase - field model for thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock, and realize the fracture analysis inside the sealing layer, lining, and surrounding rock, as well as the interface fracture analysis of the sealing layer - lining - surrounding rock; Under the framework of isogeometric analysis, combined with the Nitsche method, construct an isogeometric fourth - order phase - field method calculation model for fatigue failure analysis of the segmented steel sealing layer, and numerically simulate the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel sealing layer on its fatigue failure; Conduct statistical analysis on the numerical simulation results to determine the layout method and welding method of the steel sealing layer.

2. The method according to claim 1, characterized in that, The method for establishing a coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium includes: Improve the convective heat transfer model between the cavern wall and compressed air, correct the convective heat transfer coefficient, and improve the Kushnir model to establish the air thermodynamics model in the cavern; According to the heat conduction theory, establish the heat conduction models of the cavern wall media in the steel sealing layer, concrete lining, and surrounding rock respectively; Combine the air thermodynamics model in the cavern and the heat conduction model of the cavern wall medium to obtain a coupled model of air thermodynamics in the cavern and heat conduction of the cavern wall medium.

3. The method according to claim 1, characterized in that, The method for simulating and calculating the changes in temperature and pressure in the cavern during the "air filling - gas storage - gas release - gas storage" process includes: Use the finite - difference method to solve the air thermodynamics model in the cavern, use the isogeometric analysis method to solve the heat conduction model of the cavern wall medium, and simulate and calculate the changes in temperature and pressure in the cavern during the "air filling - gas storage - gas release - gas storage" process.

4. The method according to claim 1, wherein The method for establishing a phase - field model for thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock includes: Based on the phase - field model for fatigue failure analysis under thermo - mechanical coupling of steel and rock - like materials, combined with the additional interface phase - field model, establish a phase - field model for thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock, and simulate the internal fractures of the sealing layer, lining, and surrounding rock, as well as the interface fractures of the sealing layer - lining - surrounding rock.

5. The method according to claim 1, characterized in that, The method for constructing an isogeometric fourth - order phase - field method calculation model for fatigue failure analysis of the segmented steel sealing layer and numerically simulating the influence of the segmented layout method, welding method, welding defects, and welding residual stress of the steel sealing layer on its fatigue failure includes: Based on the established phase - field model for thermo - mechanical coupled fatigue failure analysis of the steel sealing layer - concrete lining - surrounding rock, obtain the weak form of the governing equation, use the isogeometric analysis method based on TH - NURBS to discretize the field variables, and derive the discrete governing equation; Use the Nitsche method with variational consistency characteristics to impose the coupling constraints between two phase - field models; Based on the Nitsche method, respectively derive the multi - patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field; estimate the stabilizing term coefficient value through local eigenvalues, then calculate the influence of the stabilizing term coefficient value on the results, and finally determine the values of the stabilizing term coefficients in the multi - patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field respectively; The steel seal layer adopts a block design. During construction, the blocks are welded together. The welding methods include two-pass welds and three-pass welds. The multi-sheet modeling method is used, with each block regarded as one or more sheets, and each weld seam regarded as a sheet, to establish the isogeometric phase-field method model and calculation method for the block-type steel seal layer; Adopt the adaptive analysis, global-local technology and cyclic jump algorithm acceleration scheme; Determine the initial stress / strain state of the weld seam through welding process modeling, and then conduct fatigue analysis of the seal layer.

6. A steel sealing layer design system for an underground artificial cavern of compressed air energy storage based on the isogeometric phase field method, the system being used to implement the method according to any one of claims 1-5, characterized in that, The system includes: a thermal module, an analysis module, a calculation module and a statistical module; The thermal module is used to establish a coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium, and simulate and calculate the changes in temperature and pressure in the chamber during the processes of "inflation - gas storage - deflation - gas storage"; The analysis module is used to establish a phase-field model for thermo-mechanical coupled fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock, and realize fracture analysis inside the seal layer, lining and surrounding rock, as well as interface fracture analysis of the seal layer - lining - surrounding rock; The calculation module is used to construct an isogeometric fourth-order phase-field method calculation model for fatigue failure analysis of the block-type steel seal layer under the framework of isogeometric analysis, in combination with the Nitsche method, and numerically simulate the influence of the block layout method, welding method, welding defects and welding residual stress of the steel seal layer on the fatigue failure of the steel seal layer; The statistical module is used to conduct statistical analysis on the numerical simulation results to determine the layout method and welding method of the steel seal layer.

7. The system according to claim 6, wherein The process of establishing a coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium includes: Improve the convective heat transfer model between the chamber wall and compressed air, correct the convective heat transfer coefficient, and improve the Kushnir model to establish the air thermodynamics model in the chamber; According to the heat conduction theory, establish the heat conduction models of the chamber wall media in the steel seal layer, concrete lining and surrounding rock respectively; Combine the air thermodynamics model in the chamber and the heat conduction model of the chamber wall medium to obtain the coupled model of air thermodynamics in the chamber and heat conduction of the chamber wall medium.

8. The system according to claim 6, wherein The process of simulating and calculating the changes in temperature and pressure in the chamber during the processes of "inflation - gas storage - deflation - gas storage" includes: Use the finite difference method to solve the air thermodynamics model in the chamber, and use the isogeometric analysis method to solve the heat conduction model of the chamber wall medium, and simulate and calculate the changes in temperature and pressure in the chamber during the processes of "inflation - gas storage - deflation - gas storage".

9. The system according to claim 6, wherein The process of establishing a phase-field model for thermo-mechanical coupled fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock includes: Based on the phase-field model for fatigue failure analysis under thermo-mechanical coupling of steel and rock-like materials, combined with the additional interface phase-field model, establish a phase-field model for thermo-mechanical coupled fatigue failure analysis of the steel seal layer - concrete lining - surrounding rock, and simulate the internal fractures of the seal layer, lining and surrounding rock, as well as the interface fracture of the seal layer - lining - surrounding rock.

10. The system according to claim 6, wherein The process of constructing an isogeometric fourth-order phase-field method calculation model for fatigue failure analysis of the block-type steel seal layer and numerically simulating the influence of the block layout method, welding method, welding defects and welding residual stress of the steel seal layer on the fatigue failure of the steel seal layer includes: Based on the established phase field model for fatigue failure analysis of steel seal layer - concrete lining - surrounding rock, the weak form of the governing equation is obtained. The isogeometric analysis based on TH-NURBS is used to discretize the field variables, and the discrete governing equation is derived. The Nitsche method with variational consistency characteristics is used to impose the coupling constraints between the two-phase field models. Based on the Nitsche method, the multi-patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field are respectively derived. The stabilizing term coefficient value is estimated through local eigenvalues, and then the influence of the stabilizing term coefficient value on the results is calculated. Finally, the values of the stabilizing term coefficients in the multi-patch isogeometric analysis governing equations for the displacement field, phase field, and temperature field are respectively determined. The steel seal layer is designed in a block-by-block manner. During construction, the blocks are welded together. The welding methods include two-pass welds and three-pass welds. The multi-patch modeling method is used, with each block regarded as one or more patches, and each weld as a patch. The isogeometric phase field method model and calculation method for the block-by-block steel seal layer are established. Adaptive analysis, global-local technique, and loop skipping algorithm acceleration schemes are adopted. The initial stress / strain state of the weld is determined through welding process modeling, and then the fatigue analysis of the seal layer is carried out.

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