2D simulation of fluid-structure interaction using finite element method

This paper deals with pressure-based finite element analysis of fluid–structure systems considering the coupled fluid and structural dynamics. The present method uses two-dimensional fluid elements and structural line elements for the numerical simulation of the problem. The equations of motion of the fluid, considered inviscid and compressible, are expressed in terms of the pressure variable alone. The solution of the coupled system is accomplished by solving the two systems separately with the interaction effects at the fluid–solid interface enforced by an iterative scheme. Non-divergent pressure and displacement are obtained simultaneously through iterations. The Galerkin weighted residual method-based FE formulation and the iterative solution procedure are explained in detail followed by some numerical examples. Numerical results are compared with the existing solutions to validate the code for sloshing with fluid–structure coupling.     

Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid–structure interaction by differential quadrature method

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier–Stokes (N–S) equations by firstly taking fluid–structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.     

Hydraulic fracturing modeling using the enriched numerical manifold method

Recent attempts to solve rock mechanics problems using the numerical manifold method (NMM) have been regarded as fruitful. In this paper, a coupled hydro-mechanical (HM) model is incorporated into the enriched NMM to simulate fluid driven fracturing in rocks. In this HM model, a “cubic law” is employed to model fluid flow through fractures. Several benchmark problems are investigated to verify the coupled HM model. The simulation results agree well with the analytical and experimental results, indicating that the coupled HM model is able to simulate the hydraulic fracturing process reliably and correctly.     

Numerical simulation of fluid-structure interaction problems by a coupled SPH-FEM approach

In scientific computing there is a great interest in numerical simulation of fluid-structure interaction (FSI) problems. Within this work a numerical approach to simulate fluid-structure interactions between elastic structures and weakly incompressible fluids is developed. For the fluid part and the solid part the Smoothed Particle Hydrodynamics method (SPH) and the Finite Element Method (FEM) are used, respectively. To transfer the resulting reaction forces from the fluid particles onto the structure's surface two methods are implemented, investigated and compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short shots and industrial case studies: Understanding fluid flow and solidification in high pressure die casting

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three dimensional fluid flow with significant free surface fragmentation and splashing. A simulation method that has proved particularly suited to modelling HPDC is Smoothed Particle Hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling more accurate prediction of fluid flows involving complex free surface motion. Three practical industrial case studies of SPH simulated HPDC flows are presented; aluminium casting of a differential cover (automotive), an electronic housing and zinc casting of a door lock plate. These show significant detail in the fragmented fluid free surfaces and allow us to understand the predisposition to create defects such as porosity in the castings. The validation of flow predictions coupled with heat transfer and solidification is an important area for such modelling. One powerful approach is to use short shots, where insufficient metal is used in the casting or the casting shot is halted part way through, to leave the die cavity only partially filled. The frozen partial castings capture significant detail about the order of fill and the flow structures occurring during different stages of filling. Validation can occur by matching experimental and simulated short shots. Here we explore the effect of die temperature, metal super-heat and volume fill on the short shots for the casting of a simple coaster. The bulk features of the final solid castings are found to be in good agreement with the predictions, but the fine details appear to depend on surface behaviour of the solidifying metals. This potentially has significant implications for modelling HPDC.     

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.     

Modeling and simulation of injection molding process of polymer melt by a robust SPH method

In the present study, the injection molding process of polymer melt based on the generalized Newtonian fluid model is investigated by a robust smoothed particle hydrodynamics (SPH) method. The numerical method is proposed by introducing a Rusanov flux into the continuity equation to improve the prediction of the pressure distribution and employing a corrected kernel gradient to improve the computational accuracy. In addition, a robust treatment of solid boundary is presented and verified by the spin-down problem. The merits of the robust SPH method are firstly illustrated by 2D dam breaking flow. Then the numerical method is extended to deal with the flow phenomena related to injection molding process of polymer melt. A number of numerical examples including 2D injection moldings of a thin plate mold, a circular disc with core, a ring-shaped channel, and a S-shaped cavity, and 3D injection moldings of a Z-shaped cavity and a four-legged fork are conducted. The numerical results are in agreement with the experiments, which demonstrate that the SPH method proposed here is capable of handling with injection molding process of polymer melt in a robust manner. Moreover, the robust SPH method allows to recover the fluctuations-free pressure and velocity fields which in most cases cannot be easily obtained by the traditional SPH method.     

Extension of SPH to simulate non-isothermal free surface flows during the injection molding process

This article presents an extension of smoothed particle hydrodynamics (SPH) to non-isothermal free surface flows during the injection molding process. Specifically, we use the method presented by Xu and Yu, Appl. Math. Model. 48 (2017) pp. 384–409, in which the corrected kernel gradient is implemented to increase the computational accuracy and the Rusanov flux is introduced into the continuity equation to alleviate large and random pressure oscillations. To model non-isothermal free surface flows, a working SPH discretization of the temperature equation is derived. An enhanced treatment of the wall boundary is further developed, which can model arbitrary-shaped mold walls. The proposed SPH method is first validated by solving non-isothermal Couette flow and non-isothermal injection molding of a circular disc with a core and comparing the SPH results with those obtained by other numerical methods or experiments. We then extend the numerical method to non-isothermal injection molding of F-shaped and N-shaped cavities. The convergence of the method is examined with several different particle sizes. The effects of the operating conditions (e.g., injection temperature, temperature of the mold wall, and injection velocity) on the flow behavior are analyzed. All the results illustrate that the present SPH method is a powerful computational tool for simulations of non-isothermal free surface flows during the injection molding process.     

Three dimensional modelling of lava flow using Smoothed Particle Hydrodynamics

The paper describes the use of the grid-free Smoothed Particle Hydrodynamics (SPH) method to investigate lava flow from volcanic eruptions using real three dimensional topography in the form of Digital Terrain Models (DTM). Heat transfer resulting from conduction and radiation and solidification of the lava modelled via a variable viscosity are coupled to the fluid flow solution. Simulations show that the run-out distance and the nature of the lava flow are affected significantly by the lava viscosity and that this is dependent on the scale of the volcanic eruption, with solidification effects strongest on the smallest scale. SPH appears to be a highly effective technique for predicting lava flow with very good representations of the fluid free surface, close interaction with the complex topography, easy inclusion of the thermal and solidification effects leading to very plausible flow predictions. The pile-up of the lava at the front as it solidifies and the subsequent deceleration of the flow are easily modelled by SPH.     

三维PTT黏弹性液滴撞击固壁面问题的改进SPH模拟

基于光滑粒子动力学(smoothed particle hydrodynamics, SPH)方法,对三维Phan-Thien Tanner(PTT)黏弹性液滴撞击固壁面问题进行了数值模拟.为了有效地防止粒子穿透固壁,且缩减三维数值模拟所消耗的计算时间,提出了一种适合三维数值模拟的改进固壁边界处理方法.为了消除张力不稳定性问题,采用一种简化的人工应力技术.应用改进SPH方法对三维PTT黏弹性液滴撞击固壁面问题进行了数值模拟,精细地捕捉了液滴在不同时刻的自由面,讨论了PTT黏弹性液滴不同于Newton(牛顿)液滴的流动特征,分析了PTT拉伸参数对液滴宽度、高度和弹性收缩比等的影响.模拟结果表明,改进SPH方法能够有效而准确地描述三维PTT黏弹性液滴撞击固壁面问题的复杂流变特性和自由面变化特征.     

On the numerical modelling of initiation of sediment transport using Smoothed Particle Hydrodynamics

Mobilization of solid particles at the interface between a porous and a free flow domain is a relevant subject in many fields of mechanical, civil and environmental engineering. One example is the initiation of sediment transport as it appears in river beds. To approximate this initiation state, various theoretical models exist. Common approaches use two-domain formulations as in [1] or one-domain formulations as in [6]. The named approaches were compared with Direct Numerical Simulations (DNS) using Smoothed Particle Hydrodynamics (SPH) in [3]. The results of these simulations showed that the theoretical models often underestimate the occurring velocities at the interface and therefore critical velocities to initialize the motion of single grains can be lower than predicted by theoretical approaches. In our numerical simulations, we study creeping flow in a free flow domain coupled to flow in a porous media applying various porous structures. To investigate velocities and shear stresses at the interface more intensively we then compare our numerical results to data from experiments that were performed on equivalent microstructures. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D SPH flow predictions and validation for high pressure die casting of automotive components

The geometric complexity and high fluid speeds involved in high pressure die casting (HPDC) combine to give strongly three-dimensional fluid flow with significant free surface fragmentation and splashing. A Lagrangian simulation technique that is particularly well suited to modelling HPDC is smoothed particle hydrodynamics (SPH). Materials are approximated by particles that are free to move around rather than by fixed grids, enabling the accurate prediction of fluid flows involving complex free surface motion.     

Impact of heterogeneously distributed solid particles in the transition zone between porous and free flow domain

We present a direct numerical simulation approach for the simulation of shallow water flow using the particle based meshfree Smoothed Particle Hydrodynamics (SPH) method. Simulations of single phase flow are done to characterize the occurring flow parameters on both macro-scale and pore-scale. More precisely, we examine initiation of motion and sediment transport as appearing at the interface between a free flow and porous flow domain under parallel flow conditions. Therefore we evaluate three theoretical models presenting analytical solutions for this coupled problem. Moreover, we discuss the influence of heterogeneities at the interface on forces on single grains by implementing and testing various microstructures into our numerical model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A meshless numerical approach based on Integrated Radial Basis Functions and level set method for interfacial flows

This paper reports a new meshless Integrated Radial Basis Function Network (IRBFN) approach to the numerical simulation of interfacial flows in which the two-way interaction between a moving interface and the ambient viscous flow is fully investigated. When an interface between two immiscible fluids moves, not only its position and shape but also the flow variables (i.e. velocity field and pressure) change due to the presence of surface tension along the moving interface. The velocity field of the ambient flow, on the other hand, causes the interface to move and deform as a result of momentum transport between the two immiscible fluids on both sides of the interface. Numerical investigations of such a two-way interaction is reported in this paper where the level set method is used in combination with high-order projection schemes in the meshless framework of the IRBFN method. Numerical investigations on the meshless projection schemes are performed with typical benchmark incompressible viscous flow problems for verification purposes. The approach is then demonstrated with the numerical simulation of two bubbles moving, stretching and merging in an incompressible ambient fluid under the action of buoyancy force.     

Modeling Abrasive Wear Caused by Small Solid Particles of Different Sizes

Abrasive wear is one of the mechanisms which cause the decrease of efficiency of hydraulic machines. The working fluid of a hydraulic machine, e.g., a turbine of a hydroelectric power plant, transports small solid particles of different sizes. Those small particles damage the surface of the hydraulic machine when contacting. In contrast to classical approaches in fluid dynamics, here, we present an approach where only mesh-free methods are applied. The Smoothed Particle Hydrodynamics (SPH) method is used for modeling the fluid in this study. The SPH method is a mesh-free method which has its advantages in describing transient fluid flows with free surfaces and large motions. The loading of the fluid consists of small solid particles of different sizes. A coupled approach for describing the loading is used. For the larger abrasive particles the Discrete Element Method and for smaller ones a transport equation is utilized. In doing so it is possible to model a loading of the fluid consisting of small particles of different sizes. The abrasive wear is described with an abrasive wear model. The wear model takes into account different parameters like the size, the velocity of the abrasive particles, and of course material parameters of both the target and the particles. On impact of an abrasive particle, the amount of removed material is stored at the boundary and in doing so the removed material over time is identified. In this work, a representative numerical example is presented. The simulations were performed with the code Pasimodo, developed at the Institute of Engineering and Computational Mechanics. It is the aim of this work to point out that it is possible to model abrasive wear due to abrasive particles with different sizes with a mesh-free approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions

A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.     

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.     

Numerical manifold method for vibration analysis of Kirchhoff's plates of arbitrary geometry

Many rectangular plate elements developed in the history of finite element method (FEM) have displayed excellent numerical properties, yet their applications have been limited due to inability to conform to the arbitrary geometry of plates and shells. Numerical manifold method (NMM), considered to be a generalization of FEM, can easily solve this issue by viewing a mesh made up of rectangular elements as mathematical cover. In this study, ACM element (Adini and Clough element from A. Adini, R.W. Clough, Analysis of plate bending by the finite element method, University of California, 1960), a typical rectangular plate element is first integrated in the framework of NMM. Then, vibration analysis of arbitrary shaped thin plates is conducted employing the tailored NMM. Using the definition of integral of scalar functions on manifolds, we developed a mathematically rigorous mass lumping scheme for creating a symmetric and positive definite lumped mass matrix that is easy to inverse. A series of numerical experiments have been studied and analyzed, including free and forced vibration of thin plates with various shapes, validating the proposed mass lumping scheme can supersede the consistent mass formulation in those cases.     

A study of truly incompressible and weakly compressible Smoothed Particle Hydrodynamics methods to model incompressible flows with free surfaces

The Smoothed Particle Hydrodynamics (SPH) method is a meshless discretization method for solving, e.g., the Navier-Stokes equations. By now, it is used for hydraulic problems as well as for solid bodies. In general, there are two distinguishable approaches for incompressible fluid flows. One is called weakly compressible SPH (WCSPH) and the other is called truly incompressible SPH (ISPH). The main difference between these two approaches is the way of pressure evaluation. In WCSPH, a state equation is used, while in ISPH the pressure Poisson equation is solved. Each approach has its advantages as well as its disadvantages, for example the complexity of the numerical algorithm for WCSPH is smaller than for ISPH, but the pressure field is more accurate for ISPH. In this work, two representative examples are studied. The simulations were performed with two different codes, one developed at the Institute of Engineering and Computational Mechanics and one at the Institute of Chemical Process Engineering. It is the aim of this work to show some properties of WCSPH and ISPH as well as to compare two different implementations that, in detail, are very complex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)