In recent years, the flow analysis by means of computational fluid dynamics (CFD) has become a useful design and optimization tool. Unfortunately, despite advances in the computational power, numerical simulations are still very time consuming. Thus, empirical correlation models keep their importance as a tool for early stages of axial compressor design and for prediction of basic performance parameters. These correlations were developed based on experimental data obtained from 2D measurements performed on cases of classical airfoils such as the NACA 65-series or C.4 profiles. There is insufficient amount of experimental data for other families of airfoils, but CFD simulations can be used instead and their results correlated using artificial neural networks (ANN), as described in this work. Unlike the classical deep learning approach using perceptrons, this work presents neural networks employing higher order neural units.
{"title":"Compressor cascade correlations modelling at design points using artificial neural networks","authors":"Patrik Kovář, Jiří Fürst","doi":"10.24132/acm.2023.828","DOIUrl":"https://doi.org/10.24132/acm.2023.828","url":null,"abstract":"In recent years, the flow analysis by means of computational fluid dynamics (CFD) has become a useful design and optimization tool. Unfortunately, despite advances in the computational power, numerical simulations are still very time consuming. Thus, empirical correlation models keep their importance as a tool for early stages of axial compressor design and for prediction of basic performance parameters. These correlations were developed based on experimental data obtained from 2D measurements performed on cases of classical airfoils such as the NACA 65-series or C.4 profiles. There is insufficient amount of experimental data for other families of airfoils, but CFD simulations can be used instead and their results correlated using artificial neural networks (ANN), as described in this work. Unlike the classical deep learning approach using perceptrons, this work presents neural networks employing higher order neural units.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138992674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work deals with estimations of errors, which are a consequence of a finite spatial discretisation that appears while solving differential equation numerically. More precisely, it deals with the estimation of errors that occur while computing compressible inviscid fluid flow over 2D airfoil cascades. This flow is described by the 2D Euler equations that are solved by the finite volume method in their conservative form. Numerical computations are performed on structured meshes consisting of four blocks, so the number of cells in the mesh can be easily adjusted. In this work, two estimation methods are used. Firstly, the grid convergence index is used to estimate the amount of cells needed to obtain certain accuracy of the solution. Secondly, the Richardson extrapolation is used to approximate the exact solution from a series of solutions obtained with meshes of different sizes. This analysis is performed on a well-known compressor cascade, which is composed of NACA 65 series airfoils. The obtained results should lead to a reasonable choice of the number of elements in a computational mesh based on the required accuracy of the solution and therefore also to computational time reduction while performing airfoil cascade computations. The results indicate that even for very precision demanding applications, 100 000 is a sufficient number of cells in a mesh.
{"title":"Mesh convergence error estimations for compressible inviscid fluid flow over airfoil cascades using multiblock structured mesh","authors":"Adam Tater, J. Holman","doi":"10.24132/acm.2023.827","DOIUrl":"https://doi.org/10.24132/acm.2023.827","url":null,"abstract":"This work deals with estimations of errors, which are a consequence of a finite spatial discretisation that appears while solving differential equation numerically. More precisely, it deals with the estimation of errors that occur while computing compressible inviscid fluid flow over 2D airfoil cascades. This flow is described by the 2D Euler equations that are solved by the finite volume method in their conservative form. Numerical computations are performed on structured meshes consisting of four blocks, so the number of cells in the mesh can be easily adjusted. In this work, two estimation methods are used. Firstly, the grid convergence index is used to estimate the amount of cells needed to obtain certain accuracy of the solution. Secondly, the Richardson extrapolation is used to approximate the exact solution from a series of solutions obtained with meshes of different sizes. This analysis is performed on a well-known compressor cascade, which is composed of NACA 65 series airfoils. The obtained results should lead to a reasonable choice of the number of elements in a computational mesh based on the required accuracy of the solution and therefore also to computational time reduction while performing airfoil cascade computations. The results indicate that even for very precision demanding applications, 100 000 is a sufficient number of cells in a mesh.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69073993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, the authors analyze laminated composite panels supported on an elastic foundation considering the effects of transverse normal strain. A 2-parameter, i.e., Winkler and Pasternak foundation model is assumed to represent the interaction between the panels and the foundation. The theory presented here takes into account the effects of transverse shear and normal strains. The theory plots realistic distributions of the transverse shear stress through the plate thickness and satisfies the shear-free conditions at the extreme surfaces of the panel. The differential equations of the present model are obtained from the principle of virtual work. The laminated composite panel resting on the elastic foundation is analyzed for simply supported boundary conditions. For the verification purpose, the presented problems are also solved using the Reddy's model, Mindlin's model, and the classical model. Good agreement is observed between the numerical results obtained using the present model and the other models.
{"title":"Higher order computational model considering the effects of transverse normal strain and 2-parameter elastic foundation for the bending of laminated panels","authors":"A. S. Sayyad, Shailesh Palekar, B. M. Shinde","doi":"10.24132/acm.2023.808","DOIUrl":"https://doi.org/10.24132/acm.2023.808","url":null,"abstract":"In this study, the authors analyze laminated composite panels supported on an elastic foundation considering the effects of transverse normal strain. A 2-parameter, i.e., Winkler and Pasternak foundation model is assumed to represent the interaction between the panels and the foundation. The theory presented here takes into account the effects of transverse shear and normal strains. The theory plots realistic distributions of the transverse shear stress through the plate thickness and satisfies the shear-free conditions at the extreme surfaces of the panel. The differential equations of the present model are obtained from the principle of virtual work. The laminated composite panel resting on the elastic foundation is analyzed for simply supported boundary conditions. For the verification purpose, the presented problems are also solved using the Reddy's model, Mindlin's model, and the classical model. Good agreement is observed between the numerical results obtained using the present model and the other models.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69074348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Bouisfi, Achraf Bouisfi, M. El Bouhali, Hamza Oarriche, Khalid Lamzoud, Mohamed Chaoul
{"title":"Geometry effect of irrigation storage basin on particles removal efficiency: A computational fluid dynamics study","authors":"F. Bouisfi, Achraf Bouisfi, M. El Bouhali, Hamza Oarriche, Khalid Lamzoud, Mohamed Chaoul","doi":"10.24132/acm.2023.800","DOIUrl":"https://doi.org/10.24132/acm.2023.800","url":null,"abstract":"","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90337509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.
{"title":"Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability","authors":"C. Nwaigwe, J. Oahimire, A. Weli","doi":"10.24132/acm.2023.767","DOIUrl":"https://doi.org/10.24132/acm.2023.767","url":null,"abstract":"This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69074230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The onset and spread of flutter in a turbine blade cascade are numerically studied. Due to the application of the reduced-cascade model consisting of simple elements (springs, rigid bodies, linear dampers) and aeroelastic forces introduced by the analytical Van der Pol model, it is useful to study the dangerous states of vibration of such complicated turbine parts. This study examines aeroelastic instabilities of a 10-blade cascade at running excitation that arise due to wakes flowing from the stator blades to the rotating blades. Unlike our previous work, it brings a new definition of the Van der Pol model of self-excitation that is controlled by relative inter-blade motion of neighbouring blades.
对涡轮叶片叶栅颤振的发生和扩散进行了数值研究。由于采用了由简单元件(弹簧、刚体、线性阻尼器)和解析范德波模型引入的气动弹性力组成的简化叶栅模型，有助于研究这类复杂涡轮部件的振动危险状态。本文研究了10叶片叶栅在运行激励下的气动弹性不稳定性，这种不稳定性是由静叶到动叶的尾迹流动引起的。与我们之前的工作不同，它带来了由邻近叶片的相对叶片间运动控制的自激Van der Pol模型的新定义。
{"title":"Numerical simulations of aeroelastic instabilities in a turbine-blade cascade by a modified Van der Pol model at running excitation","authors":"Lukáš Pešek, P. Šnábl, C. Prasad, Y. Delanney","doi":"10.24132/acm.2023.792","DOIUrl":"https://doi.org/10.24132/acm.2023.792","url":null,"abstract":"The onset and spread of flutter in a turbine blade cascade are numerically studied. Due to the application of the reduced-cascade model consisting of simple elements (springs, rigid bodies, linear dampers) and aeroelastic forces introduced by the analytical Van der Pol model, it is useful to study the dangerous states of vibration of such complicated turbine parts. This study examines aeroelastic instabilities of a 10-blade cascade at running excitation that arise due to wakes flowing from the stator blades to the rotating blades. Unlike our previous work, it brings a new definition of the Van der Pol model of self-excitation that is controlled by relative inter-blade motion of neighbouring blades.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69074313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a discussion on the properties of the collocation meshfree method, the Updated Lagrangian Taylor-SPH (UL-TSPH), for dynamic problems in solid mechanics. The PDEs are written in mixed form in terms of stress and velocity for the elastodynamics problems. Two sets of particles are used to discretize the partial differential equations, resulting on avoiding the tensile instability inherent to classical SPH formulations. Numerical examples ranging from propagation of a shock wave in an elastic bar to a stationary Mode-I semi-Infinite cracked plate subjected to uniaxial tension are used to assess the performance of the proposed method.
{"title":"Updated Lagrangian Taylor-SPH method for elastic dynamic problems","authors":"H. K. Serroukh, M. Mabssout","doi":"10.24132/acm.2021.697","DOIUrl":"https://doi.org/10.24132/acm.2021.697","url":null,"abstract":"This paper presents a discussion on the properties of the collocation meshfree method, the Updated Lagrangian Taylor-SPH (UL-TSPH), for dynamic problems in solid mechanics. The PDEs are written in mixed form in terms of stress and velocity for the elastodynamics problems. Two sets of particles are used to discretize the partial differential equations, resulting on avoiding the tensile instability inherent to classical SPH formulations. Numerical examples ranging from propagation of a shock wave in an elastic bar to a stationary Mode-I semi-Infinite cracked plate subjected to uniaxial tension are used to assess the performance of the proposed method.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69073548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present study applies the discontinuous Galerkin finite element method to a numerical simulation of a compressible fluid flow through a labyrinth seal. This paper is proposes a curvilinear hexahedral element, which is deformed in such a way that it matches the rotated walls of the labyrinth seal exactly. A numerical study is performed on the staggered labyrinth seal with two teeth on the rotor and one tooth on the stator. For numerical simulation, three computational meshes with different refinement are considered. All of the numerical simulations are performed for both stationary rotor and for rotor rotating at 50 Hz. The obtained numerical results are compared with results computed by the commercial CFD software Ansys Fluent.
{"title":"Curvilinear element of the discontinuous Galerkin method designed to capture the labyrinth seal geometry exactly","authors":"O. Bublík, A. Pecka, J. Vimmr","doi":"10.24132/acm.2022.732","DOIUrl":"https://doi.org/10.24132/acm.2022.732","url":null,"abstract":"The present study applies the discontinuous Galerkin finite element method to a numerical simulation of a compressible fluid flow through a labyrinth seal. This paper is proposes a curvilinear hexahedral element, which is deformed in such a way that it matches the rotated walls of the labyrinth seal exactly. A numerical study is performed on the staggered labyrinth seal with two teeth on the rotor and one tooth on the stator. For numerical simulation, three computational meshes with different refinement are considered. All of the numerical simulations are performed for both stationary rotor and for rotor rotating at 50 Hz. The obtained numerical results are compared with results computed by the commercial CFD software Ansys Fluent.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69073898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.22055/JACM.2021.38411.3228
W. O. Murillo, I. D. P. Arcila, J. A. Palacio-Fernandez
Genetic-algorithm methods are used here for single-objective (SO) and multi-objective (MO) geometrical optimizations of jet pumps used in vacuum distillation of ethanol, an application not deeply studied in scientific literature. These devices are particularly suitable to allow the azeotrope-breaking below the atmospheric pressure at ambient temperature. Based on this, different working pressures (Pp), five non-dimensional geometrical parameters that can influence the jet pump operation, and three performance parameters (drag coefficient, pressure recovery ratio and energy efficiency) are considered in this work. Furthermore, using a central composite, face-centered, enhanced experimental design, 89 simulation experiments are run to obtain Response Surfaces (RS) by genetic aggregation, applying afterwards the SOGA and MOGA optimization methods. Also, Spearman Rank-order correlation matrix is employed as initial screening, finding strongly negative correlation of drag coefficient and efficiency with the working pressure, Pp. Computational Fluid Dynamic (CFD) model is validated with other numerical and experimental works, obtaining satisfactory results. Additionally, the change of the optimized input and output parameters with Pp is studied, along with the behavior of Mach number. It can be concluded that the optimal nozzle parameters evidently influenced by Pp for the SO optimization are: outlet diameter and length of divergent part, conicity of convergent part, and ratio of inlet to throat area. For the MO optimization, changes of optimized geometrical parameters with Pp are negligible. In contrast, performance parameters are importantly influenced by Pp for all optimizations.
{"title":"Geometric Optimization of Jet Pump Used in Vacuum Distillation Applications under Different Operating Conditions using Genetic-algorithm Methods","authors":"W. O. Murillo, I. D. P. Arcila, J. A. Palacio-Fernandez","doi":"10.22055/JACM.2021.38411.3228","DOIUrl":"https://doi.org/10.22055/JACM.2021.38411.3228","url":null,"abstract":"Genetic-algorithm methods are used here for single-objective (SO) and multi-objective (MO) geometrical optimizations of jet pumps used in vacuum distillation of ethanol, an application not deeply studied in scientific literature. These devices are particularly suitable to allow the azeotrope-breaking below the atmospheric pressure at ambient temperature. Based on this, different working pressures (Pp), five non-dimensional geometrical parameters that can influence the jet pump operation, and three performance parameters (drag coefficient, pressure recovery ratio and energy efficiency) are considered in this work. Furthermore, using a central composite, face-centered, enhanced experimental design, 89 simulation experiments are run to obtain Response Surfaces (RS) by genetic aggregation, applying afterwards the SOGA and MOGA optimization methods. Also, Spearman Rank-order correlation matrix is employed as initial screening, finding strongly negative correlation of drag coefficient and efficiency with the working pressure, Pp. Computational Fluid Dynamic (CFD) model is validated with other numerical and experimental works, obtaining satisfactory results. Additionally, the change of the optimized input and output parameters with Pp is studied, along with the behavior of Mach number. It can be concluded that the optimal nozzle parameters evidently influenced by Pp for the SO optimization are: outlet diameter and length of divergent part, conicity of convergent part, and ratio of inlet to throat area. For the MO optimization, changes of optimized geometrical parameters with Pp are negligible. In contrast, performance parameters are importantly influenced by Pp for all optimizations.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68419271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely backward differentiation formulas (BDF) and diagonally implicit Runge-Kutta (DIRK) methods. Special attention is devoted to embedded DIRK methods, which allow the incorporation of time step size adaptation algorithms in order to keep the computational effort as low as possible. The properties of the numerical solution, such as its order of convergence, are investigated by means of suitably chosen test cases for a linear convection-diffusion-reaction equation and the nonlinear system of Navier-Stokes equations. For problems considered in this work, the DIRK methods prove to be superior to high-order BDF methods in terms of both stability and accuracy.
{"title":"Comparison of implicit time-discretization schemes for hybridized discontinuous Galerkin methods","authors":"Tomáš Levý, G. May","doi":"10.24132/acm.2022.786","DOIUrl":"https://doi.org/10.24132/acm.2022.786","url":null,"abstract":"The present study is focused on the application of two families of implicit time-integration schemes for general time-dependent balance laws of convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely backward differentiation formulas (BDF) and diagonally implicit Runge-Kutta (DIRK) methods. Special attention is devoted to embedded DIRK methods, which allow the incorporation of time step size adaptation algorithms in order to keep the computational effort as low as possible. The properties of the numerical solution, such as its order of convergence, are investigated by means of suitably chosen test cases for a linear convection-diffusion-reaction equation and the nonlinear system of Navier-Stokes equations. For problems considered in this work, the DIRK methods prove to be superior to high-order BDF methods in terms of both stability and accuracy.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69074188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：