A finite element method with a hybrid lagrange line for fluid mechanics problems involving large free surface motion

In this paper, free surface flow problems involving large free surface motion are analysed using finite element techniques. In solving these problems a spatially fixed Eulerian mesh is employed, in conjunction with a moving Lagrangian free surface line. The coupling, between the equations valid on the free surface and the equations valid on the fluid domain, is carried out using hybrid finite element techniques. Physical problems involving solitary wave propagation, sloshing dynamics and porous media flow are analysed to demonstrate the developed technique.     

The enriched space–time finite element method (EST) for simultaneous solution of fluid–structure interaction

The paper introduces a weighted residual‐based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple‐flow‐immersed solid objects. The fluid flow is described by the incompressible Navier–Stokes equations. The current configuration of the thin structure of linear elastic material with non‐linear kinematics is mapped to the flow using the zero iso‐contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space–time finite element discretization of the domain. Interfacial constraints of the multi‐field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid–structure systems. Embedding a thin structure into a flow results in non‐smooth fields for the fluid. Based on the concept of the extended finite element method, the space–time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space–time (EST) method. Numerical examples of fluid–structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of the particle collision behavior in spiral jet milling

Collision behaviors of particles in spiral jet milling were analyzed by using a simulation. The motion of the particles was tracked by the discrete element method (DEM), and the air flow was represented by the computational fluid dynamics (CFD). The DEM was coupled with the CFD by a one-way coupling method. The simulated air flow was validated by comparing the fluid velocity field with the measured one in a model experiment. Furthermore, the air flow and particle behaviors in a spiral jet mill used commercially were analyzed by using the simulation. As a result, the particles with a region balancing between centrifugal and radial drag forces could be mainly ground by the high-speed collisions between the particles circulating near the top and bottom walls of the grinding chamber.     

Flexible discretization technique for DEM-CFD simulations including thin walls

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) method is regarded as a standard approach for a simulation of a gas-solid mixture system. In the DEM-CFD method, the local volume average technique is employed, and hence the fluid motion is calculated based on the void fraction. Although the accuracy of the DEM-CFD method has been improved through lots of studies, inflexibility may become a problem due to the local volume average technique. Specifically, calculations of a gas-solid flow involving thin walls is substantially impossible even by the improved DEM-CFD method. This is because the thin wall cannot be represented when its thickness becomes as large as one grid size due to usage of the local volume average technique. In order to solve this problem, a flexible discretization technique is newly proposed, where the signed distance function and the immersed boundary method are introduced into the dual grid model. In this technique, two kinds of grids are used to calculate the void fraction and the fluid flow. Thus, this technique makes it possible to simulate a gas-solid flow involving a thin wall. Verification and validation tests are performed to show the adequacy of this technique. Through this study, the proposed technique is illustrated to reproduce the exact solution and experimental results in the gas-solid flow involving the thin wall. Consequently, the proposed technique is shown to yield reasonable results in gas-solid flows involving the thin walls.     

爆破漏斗形成过程的DDA模拟分析

对于块体等非连续介质在外力作用下运动或破坏规律的模拟,有限元(FEM)和离散元(DEM)法有一定的局限性,而非连续变形分析方法(DDA)更适用。本研究中,利用二维DDA对有、无节理面强度两种情况下一半无限域内球形药包爆炸时爆破漏斗的形成过程进行了动态模拟,并对模拟结果进行了分析和比较。结果表明,用DDA法模拟被节理分割的岩体在爆炸载荷作用下块体的运动规律具有独特的优越性,但它还不能模拟爆炸近区的特征。     

On the computation of steady‐state compressible flows using a discontinuous Galerkin method

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.     

基于流固耦合的重载飞艇副气囊形态分析与试验研究

为了研究非饱和副气囊在重载飞艇升降和巡航过程的形态变化,建立了缩尺比例氦气囊模型。基于向量式有限元(vector form of intrinsic finite element,VFIFE)对副气囊膜结构进行结构动力学分析,并考虑几何大变形和边界非线性;基于有限元法对氦气域和空气域进行流体动力学分析,分别采用自编MATLAB程序和ANSYS软件流体模块独立求解控制方程之后,通过映射网格在CSD(computational structural dynamics)/CFD(computational fluid dynamics)之间进行数据传递并迭代,以实现双向流固耦合。开展了氦气囊的缩尺比例模型试验,对囊体在泄气过程中得到的位移测量值与数值模拟结果进行对比。结果表明,氦气囊在不同充盈度下的形态变化与双向流固耦合数值分析结果一致,证明了该研究提出的数值模拟方法可有效用于副气囊随氦气充盈度变化导致的非稳定形态变化规律的研究。     

Porosity Distribution in Monodisperse and Polydisperse Fixed Beds and Its Impact on the Fluid Flow

This work is devoted to the numerical study of the porosity distribution and gas flow within randomly packed fixed beds comprising polydisperse spherical particles with Rosin–Rammler particle size distribution in a cylindrical container. The fixed bed is numerically generated using gravity-forced sedimentation modeled utilizing the discrete element method. The radial porosity distribution of monodisperse fixed beds was validated against published experimental data and good agreement was achieved. The diameter ratio of smallest to largest particle was varied from 1:2 to 1:5 and then 1:10. The simulation revealed overall porosities of 0.38 for the monodisperse bed and 0.345 and 0.33 for polydisperse beds with ratios of 1:2 and 1:10, respectively. In the second part, the fluid flow within the generated fixed beds was examined using a numerical solution to the incompressible Navier–Stokes equations in the Brinkman–Forcheimer formulation. An analysis of the results showed that in the case of a monodisperse fixed bed and low Reynolds numbers (Re) the pressure drop predicted numerically is close to the values calculated using Ergun's relation. The increase inRe leads to the deviation between the numerical and analytical predictions. This effect is because of channeling due to the sinusoidal distribution of the void fraction close to the wall.     

A two‐scale approach for fluid flow in fractured porous media

A two‐scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid‐saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two‐scale approach and integrated over time. By exploiting the partition‐of‐unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non‐linear due to the non‐linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.     

Lower‐dimensional interface elements with local enrichment: application to coupled hydro‐mechanical problems in discretely fractured porous media

In this study, we develop lower‐dimensional interface elements to represent preexisting fractures in rock material, focusing on finite element analysis of coupled hydro‐mechanical problems in discrete fractures–porous media systems. The method adopts local enrichment approximations for a discontinuous displacement and a fracture relative displacement function. Multiple and intersected fractures can be treated with the new scheme. Moreover, the method requires less mesh dependencies for accurate finiteelement approximations compared with the conventional interface element method. In particular, for coupled problems, the method allows for the use of a single mesh for both mechanical and other related processes such as flow and transport. For verification purposes, several numerical examples are examined in detail. Application to a coupled hydro‐mechanical problem is demonstrated with fluid injection into a single fracture. The numerical examples prove that the proposed method produces results in strong agreement with reference solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach

Finite deformation contact of flexible solids embedded in fluid flows occurs in a wide range of engineering scenarios. We propose a novel three-dimensional finite element approach in order to tackle this problem class. The proposed method consists of a dual mortar contact formulation, which is algorithmically integrated into an eXtended finite element method (XFEM) fluid–structure interaction approach. The combined XFEM fluid–structure-contact interaction method (FSCI) allows to compute contact of arbitrarily moving and deforming structures embedded in an arbitrary flow field. In this paper, the fluid is described by instationary incompressible Navier–Stokes equations. An exact fluid–structure interface representation permits to capture flow patterns around contacting structures very accurately as well as to simulate dry contact between structures. No restrictions arise for the structural and the contact formulation. We derive a linearized monolithic system of equations, which contains the fluid formulation, the structural formulation, the contact formulation as well as the coupling conditions at the fluid–structure interface. The linearized system may be solved either by partitioned or by monolithic fluid–structure coupling algorithms. Two numerical examples are presented to illustrate the capability of the proposed fluid–structure-contact interaction approach.     

基于特征线分离算法的大涡模拟

将基于特征线的分离算法与大涡模拟相结合,推导了不可压流大涡模拟有限元离散方程组,并将该方法应用于三维流场的层流及湍流非定常计算。将不同雷诺数下的三维顶盖驱动空腔流动计算结果与实验数据以及直接数据模拟结果进行对比,吻合较好,验证了方法的可靠性和准确性。     

The coupled radial–axial deformations analysis of flexible pipes conveying fluid

This paper presents large deformation analysis of pipes conveying fluid in which two complicated behaviours are taken into consideration. The first is the coupling between radial and axial deformations of pipe wall, and the other is the interaction between a deformed pipe and transported fluid having the variable internal flow velocity. The coupled radial–axial deformation theory of the pipes and the continuity theory of flow inside the moving deformed pipes are developed to undertake these coupling behaviours. All strong and weak forms of governing equations are obtained by carrying out the virtual work formulation. The hybrid‐finite element method is used to solve the highly non‐linear static problems, which configure the initial large deflection and large strain conditions of the pipes. The state‐space finite element model for use in analyses of non‐linear vibration and system stability is established as well as the suggested numerical solution procedures. The numerical studies of the pipes under circumstances of intense radial loads such as deep‐water risers demonstrate that even a slight change of the radial deformation has a significant effect in increasing non‐linear responses, and reducing stabilities of the pipes. Copyright © 2004 John Wiley & Sons, Ltd.     

Coupling resolved and coarse-grain DEM models

The discrete element method (DEM) is a well-established approach to study granular flows in numerous fields of application; however, the DEM is a computationally demanding method. Thus, simulations of industrial scale systems are hardly feasible on today’s hardware. This situation is typically resolved by limiting the simulation domain or introducing a coarse-grain model. While the former approach does not provide information of the full system, the latter is especially problematic in systems, where geometric restrictions are in the range of particle size, so both are insufficient to adequately describe large-scale processes. To overcome this problem, we propose a novel technique that efficiently combines resolved and coarse-grain DEM models. The method is designed to capture the details of the granular system in spatially confined regions of interest while retaining the benefits of the coarse-grain model where a lower resolution is sufficient. To this end, our method establishes two-way coupling between resolved and coarse-grain parts by volumetric passing of boundary conditions.     

基于双向流固耦合的机载导弹分离动力学研究

导弹与载机之间的安全与稳定分离过程对导弹飞行稳定性和载机安全具有非常重要作用。为了研究大长径比机载导弹弹射分离过程中与载机之间的相互干扰以及导弹在分离过程中相对于载机的运动轨迹,该文分别使用刚体六自由度（6DOF）方法和计算流体力学/计算结构动力学（CFD/CSD）双向流固耦合方法对典型空空导弹发射分离过程进行了数值模拟,刚体6DOF方法基于对流体力学控制方程与外弹道6DOF运动方程的耦合求解,而CFD/CSD双向流固耦合方法基于对流体力学控制方程与结构运动方程的耦合求解。两种方法得到了导弹分离时的整个气动流场及其变化特性,揭示了不同时刻导弹气动系数随时间的变化曲线和导弹弹道参数,比较与分析了两种计算结果的异同,并对导弹结构弹性变形对其分离运动的影响进行了讨论。     

A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.     

Immersed particle method for fluid–structure interaction

A method for treating fluid–structure interaction of fracturing structures under impulsive loads is described. The coupling method is simple and does not require any modifications when the structure fails and allows fluid to flow through openings between crack surfaces. Both the fluid and the structure are treated by meshfree methods. For the structure, a Kirchhoff–Love shell theory is adopted and the cracks are treated by introducing either discrete (cracking particle method) or continuous (partition of unity‐based method) discontinuities into the approximation. Coupling is realized by a master–slave scheme where the structure is slave to the fluid. The method is aimed at problems with high‐pressure and low‐velocity fluids, and is illustrated by the simulation of three problems involving fracturing cylindrical shells coupled with fluids. Copyright © 2009 John Wiley & Sons, Ltd.     

The combined plastic and discrete fracture deformation framework for finite-discrete element methods

The combined finite-discrete element method (FDEM) was originally developed for fracture and fragmentation of brittle materials, more specifically for cementitious and rock-like materials. In this work, a combination of a discrete crack and plastic deformation has been combined and applied to FDEM simulation of fracture. The deformation is described using a FDEM-specific mechanistic approach with plastic deformation being formulated in material embedded coordinate systems leading to multiplicative decomposition and plastic flow, that is, resolved in stretch space; this is combined with the FDEM fracture and fragmentation criteria. The result and main novelty of the present work is a robust framework for simulation of large strain solid deformation combined with a multiplicative decomposition-based model that simultaneously involves elasticity, plasticity, and fracture.