A coupled NMM-SPH method for fluid-structure interaction problems

The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.     

数值流形方法的变分原理与应用

针对线弹性体静力问题,根据数值流形方法的特点及相应的位移模式,得到了面向物理覆盖的数值流形方法的变分原理,详细推导了基于变分原理的数值流形方法的理论计算公式,建立了数值流形方法的控制方程。作为实际应用,给出了相应的数值算例,结果表明,求解精度和效益令人满意。     

A high-order numerical manifold method with continuous stress/strain field

Recent attempts to solve solid mechanical problems using the numerical manifold method (NMM) are very fruitful. In the present work, a high-order numerical manifold method (HONMM) which is able to obtain continuous stress/strain field is proposed. By employing the same discretized model as the traditional NMM (TNMM), the proposed HONMM can yield much better accuracy without increasing the number of degrees of freedom (DOFs), and obtain continuous stress/strain field without recourse any stress smoothing operation in the post-processing stage. In addition, the “linear dependence” (LD) issue does not exist in the HONMM, and traditional equation solvers can be employed to solve the simultaneous algebraic equations. A number of numerical examples including four linear elastic continuous problems and five cracked problems are solved with the proposed method. The results show that the proposed HONMM performs much better than the TNMM.     

Hydraulic fracturing with a simplified fluid model and XFEM

In hydraulic fracturing, the pressure exerted by the fracking fluid onto the surrounding solid, is typically obtained from solving the Reynolds equation. This is not always robust and leads to a complex behaviour at the crack front (toughness or viscous regimes). In the presented work, the Reynolds equation is replaced by a simplified fluid model, where pre-defined pressure distributions are assumed which lead to a simpler and robust coupled problem. The surface integration of the fluid pressure onto the surrounding solid is outlined without any limitations on the distributions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A modified numerical manifold method for simulation of finite deformation problem

With many people contributing to its modifications and advancements, the numerical manifold method (NMM) is now recognized as an efficient tool to solve the continuum–discontinuum coupling problem in geotechnical engineering. However, false solutions have been found when modeling finite deformation problems using the original NMM. Based on the finite deformation theory, a modified version of NMM is derived from the weak form of conservation of momentum and the corresponding traction boundary condition. By taking the dual cover system as the displacement approximation, the governing equations of the modified NMM are formulated. A comparison of the governing equations of the original NMM and modified NMM illustrates the reason that the original NMM is not suitable for simulation of finite deformation problems. Three numerical examples are investigated to verify the capability of proposed method to predict static and dynamic finite deformation response. Numerical results show that the modified NMM eliminates the errors caused by large rotation and large strain, and obtains a good agreement with analytical solutions and the finite element method.     

Modeling 2D transient heat conduction problems by the numerical manifold method on Wachspress polygonal elements

Due to the use of dual cover systems, i.e., the mathematical cover and the physical cover, the numerical manifold method (NMM) is able to solve physical problems with boundary-inconsistent meshes. Meanwhile, n-gons (n>4) are very impressive, due to their greater flexibility in discretization, less sensitivity to volumetric and shear locking, and better suitability for complex microstructures simulation. In this paper, the NMM, combined with Wachspress-type hexagonal elements, is developed to solve 2D transient heat conduction problems. Based on the governing equations, the NMM temperature approximation and the modified variational principle, the NMM discrete formulations are deduced. The solution strategy to time-dependent global equations and the spatial integration scheme are presented. The advantages of the proposed approach in both discretization and accuracy are demonstrated through several typical examples with increasing complexity. The extension of polygonal elements in unsteady thermal analysis within the NMM is realized.     

A Porous Media Model to Describe the Behaviour of Brain Tissue

The human brain is a very sensitive organ. Even small changes in the cranium cavity can cause life–threatening effects. In case of medical intervention, biomechanics can assist the therapy decisions by simulating the physical behaviour of brain tissue, e.g., the coupled interaction of the fluid motion and the deformation of the brain tissue. In the context of the Theory of Porous Media (TPM), a convenient model of the brain is introduced, which is able to simulate essential mechanical effects in the porous structure of the brain material. The fluid–saturated brain can be treated as an immiscible binary mixture of constituents. In this macroscopic biphasic model, the mixture consists of a solid phase (brain tissue) and a fluid phase (interstitial fluid or blood plasma). Both constituents are assumed to be materially incompressible. The resulting set of coupled partial differential equations is then spatially discretised using mixed finite elements with a backward Euler time integration. Numerical examples are presented illustrating the fundamental effects on the brain tissue under heart–rate dependent pulsative pressure variations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

考虑流固耦合效应的重力坝水力劈裂模拟

裂缝的高压水力劈裂是混凝土高坝安全评估的重要部分,研究其过程中的流固耦合作用是准确预测在各种情况下裂纹扩展路径和危险程度的关键.该文利用扩展有限元法在模拟裂纹扩展方面的优势,对大坝的裂纹进行水力劈裂模拟研究.裂纹中的水压分布模型采用Brühwiler和Saouma水力劈裂试验的成果,体现了水压和裂纹宽度的耦合关系,给出了扩展有限元在裂纹面上施加水压力荷载的实施方法,对一典型重力坝裂纹的水力劈裂进行了数值模拟分析.研究结果表明:采用扩展有限元法模拟水力劈裂,克服了常规有限元法存在的缺点,裂纹扩展时不用重新划分网格,裂纹的实时宽度可以由加强节点的附加自由度得到,裂纹面上水压的施加也变得简单易行.当考虑裂纹内的流固耦合效应时,裂纹的扩展路径相比不考虑耦合效应时的扩展路径(均布全水头水压),扩展角变大,扩展距离变短.     

Phase-Field Modeling of Hydraulic Fracture

Hydraulically driven fracture has gained more and more research activity in the last few years, especially due to the growing interest of the petroleum industry. Key challenge for a powerful simulation of this scenario is an effective modeling and numerical implementation of the behavior of the solid skeleton and the fluid phase, the mechanical coupling between the two phases as well as the incorporation of the fracture process. Existing models for hydraulic fracturing can be found for example in [1], where the crack path is predetermined, or in [2] who use a phase field fracture model in an elastic framework, however without incorporating the fluid flow. In this work we propose a new compact model structure for the Biot-type fluid transport in porous media at finite strains based on only two constitutive functions, that is the free energy function ψ and a dissipation potential ϕ that includes the incorporation of an additional Poiseuille-type fluid flow in cracks. This formulation is coupled to a phase field approach for fracture and is fully variational in nature, as shown in [3]. In contrast to formulations with a sharp-crack discontinuity, the proposed regularized approach has the main advantage of a straight-forward modeling of complex crack patterns including branching. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

非线性数值流形方法的变分原理与应用

针对非线性力学问题,根据数值流形方法的特点及相应的位移模式,得到了面向物理覆盖的非线性数值流形方法的变分原理,详细推导了基于变分原理的非线性数值流形方法的理论计算公式,建立了非线性数值流形方法的理论体系和控制方程。作为实际应用,给出了相应的数值算例,结果表明,求解精度和效益令人满意。     

二维稳态热传导问题的正六边形流形元研究

发展了用于分析二维稳态热传导问题的多边形数值流形方法（numerical manifold method,NMM）.根据热传导问题的控制方程、边界条件以及多边形NMM的温度近似函数,采用修正变分原理导出了多边形NMM求解稳态热传导问题的总体方程,给出了多边形单元上的域积分策略.考虑到NMM中数学覆盖系统可不与物理域边界一致以及规则单元的精度优势,采用Wachspress正六边形数学单元对两个典型热传导问题进行了仿真,计算结果与参考解能较好地吻合,表明多边形NMM可以很好地模拟平面稳态热传导问题.     

A FEM-BEM approach for Fluid-Structure Interaction

In an earlier attempt to solve problems of Fluid-Structure Interaction (FSI), a high-order finite element code, which can be applied to solve problems of Computational Structural Dynamics (CSD) has been coupled to a Lattice Boltzmann (LB) fluid solver. In order to extend this approach to maritime applications and to increase the computational efficiency, the CSD solver is coupled to a fluid solver based on the Boundary Element Method (BEM). In this way, the computational effort for the discretisation of the fluid is significantly reduced. In this paper the proposed coupling scheme is discussed and compared to a FSI scheme where the BEM is replaced by a method based on the Reynolds-averaged Navier-Stokes equations (RANSE). Special emphasis is placed on the question of how to exchange the data between the different discretisation schemes and the development of a stable and efficient coupling scheme for FSI simulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.     

Numerical analysis for the multi-phase flow of pulverized coal injection inside blast furnace tuyere

The pulverized coal injection (PCI) system was modified from single lance injection into double lance injection at No. 3 Blast Furnace of CSC. It is beneficial to reduce the cost of coke. However, the injected coal was found very close to the inner wall of the tuyere during the operation, such as to cause the possibility of erosion for the tuyere. In this study a three-dimensional mathematical model has been developed based on a computational fluid dynamics software PHOENICS to simulate the fluid flow phenomena inside blast furnace tuyere. The model was capable of handling steady-state, three-dimensional multi-phase flow of pulverized coal injection. The model was applied to simulate the flow patterns of the injection coal inside the tuyere with two kinds of lance design for the PCI system. The distribution of injection coal was simulated such as to estimate the possibility of erosion for the tuyere. The calculated results agreed with the operating experience of CSC plant and the optimum design of double lance was suggested. The model was also applied to simulate the oxygen concentration distribution with these different oxygen enrichments for the coal/oxygen lance system. The calculated results agreed with the experimental measurement. These test results demonstrate that the model is both reasonably reliable and efficient.     

Weakly coupled analysis of a blade in multiphase mixing vessel

Two or more physical systems frequently interact with each other, where the independent solution of one system is impossible without a simultaneous solution of the others. An obvious coupled system is that of a dynamic fluid-structure interaction. [8] In this paper a computational analysis of the fluid-structure interaction in a mixing vessel is presented. In mixing vessels the fluid can have a significant influence on the deformation of blades during mixing, depending on speed of mixing blades and fluid viscosity. For this purpose a computational weakly coupled analysis has been performed to determine the multiphase fluid influences on the mixing vessel structure. The multiphase fluid field in the mixing vessel was first analyzed with the computational fluid dynamics (CFD) code CFX. The results in the form of pressure were then applied to the blade model, which was the analysed with the structural code MSC.visualNastran forWindows, which is based on the finite element method (FEM). (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and numerical simulation of two-phase flows using Fourier pseudospectral and front-tracking methods: The proposition of a new method

In the present work, an extension of the Fourier Pseudospectral Method coupled with the Immersed Boudary Method for non-periodic problems (IMERSPEC) applied to numerical simulation of two-phase flow was developed. The proposed method was originally developed for single-phase, incompressible flow. Here, the method is extended to two-phase flows using the front-tracking method (IMERSPEC-FT) to model fluid-fluid interfaces. The proposed method was verified and validated through results involving spurious currents, mass conservation and numerical experiments analysis for rising bubbles. IMERSPEC-FT is shown to be a promising scheme for the two-phase computational fluid dynamics (CFD).     

Numerical Simulation of Heat Loads in a Cryogenic H2/O2 Rocket Combustion Chamber

A Finite Element solver for a coupled simulation of fluid and structure in an axisymmetric domain is presented. The method employs an explicit solution of the flow and structure variables. The computational domain of the fluid is discretised by unstructured triangles and rectangles while the sturcture domain is discretised by unstructured triangles only. For the purpose of code validation the solution of in total three test cases are shown. One test case deals with the structure only while the other two simulate heat transfer problems with a defined temperature distribution along a boundary wall and coupled conditions. Finally the code is used to simulate the heat load in a cryogenic H₂/O₂ rocket combustion chamber.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.