Convected level set method for the numerical simulation of fluid buckling

‘Fluid buckling’ is a phenomenon characterized mainly by the existence of fluid toroidal oscillations during flow. It appears when a high viscosity fluid flows vertically against a flat surface and may occur in industrial applications, as in injection molding of a propergol in complex‐shaped cavities. These coiling or folding oscillations appear during the mold filling stage, leading to air entrapment. To understand and to model this free surface flow problem, a convected level set method is proposed. First, a sinus filter is applied to the distance function to get a smooth truncation far from the interface. Second, the reinitialization is embedded in the transport equation model, avoiding it as a separate step during calculation. In order to validate the method, numerical results are presented on classical interface capturing benchmarks. Finally, results are shown on two‐dimensional and three‐dimensional viscous jet buckling problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Lattice Boltzmann method for the simulation of viscoelastic fluid flows

The simulation of viscoelastic fluids is a challenging task from the theoretical and numerical points of view. This class of fluids has been extensively studied with the help of classical numerical methods. In this paper we propose a new approach based on the lattice Boltzmann method in order to simulate linear and non-linear viscoelastic fluids and in particular those described by the Oldroyd-B and FENE-P constitutive equations. We study the accuracy and stability of our model on three different benchmarks: the 3D Taylor–Green vortex decay, the simplified 2D four-rolls mill, and the 2D Poiseuille flow. To our knowledge, the methodology described in this work is a first attempt for the simulation of non-trivial flows of viscoelastic fluids using the lattice Boltzmann method to discretize the constitutive and conservation equations.     

Numerical simulation of unsteady multidimensional free surface motions by level set method

This paper presents a numerical method that couples the incompressible Navier–Stokes equations with the level set method in a curvilinear co‐ordinate system for study of free surface flows. The finite volume method is used to discretize the governing equations on a non‐staggered grid with a four‐step fractional step method. The free surface flow problem is converted into a two‐phase flow system on a fixed grid in which the free surface is implicitly captured by the zero level set. We compare different numerical schemes for advection of the level set function in a generalized curvilinear format, including the third order quadratic upwind interpolation for convective kinematics (QUICK) scheme, and the second and third order essentially non‐oscillatory (ENO) schemes. The level set equations of evolution and reinitialization are validated with benchmark cases, e.g. a stationary circle, a rotating slotted disk and stretching of a circular fluid element. The coupled system is then applied to a travelling solitary wave, and two‐ and three‐dimensional dam breaking problems. Some interesting free surface phenomena are revealed by the computational results, such as, the large free surface vortices, air entrapment and splashing of the water surge front. The computational results are in excellent agreement with theoretical predictions and experimental data, where they are available. Copyright © 2003 John Wiley & Sons, Ltd.     

基于ALE方法的3D充填流动模拟

基于任意拉格朗日-欧拉方法发展了三维充填流动的数值模拟方案.该方案采用ALE方法准确地追踪移动自由面的位置并避免了网格扭曲;基于移动最小二乘曲面拟合方法提出了移动自由面上网格节点重定位方法,将充填流动的网格更新过程简化为自由面附近的局部网格重划分过程,并通过分级多面体三角剖分实现,减小了网格划分的计算量,实现了实时网格生成.给出的数值算例结果表明了该数值模型对三维充填流动模拟的有效性.     

Numerical simulation of mold filling in foam reaction injection molding

A numerical simulation of reaction injection molding (RIM) of polymeric foam is developed, using a finite volume method (FVM). In this study we predict mold filling with a variable‐density fluid that fills a mold by self‐expansion. We deal with two‐dimensional, isothermal cases. With the assumptions of ideal mixing and rapid bubble nucleation, the foam is modelled as a continuum with a time‐dependent density. The continuum is assumed to be a Newtonian fluid. We develop a pressure‐based FVM for unstructured meshes that includes the SIMPLE algorithm with treatment of fluid compressibility. Cell‐based, co‐located storage is used for all physical variables. To treat the moving interface, an explicit high‐resolution interface capturing method is used. Foam flow in a slit is investigated, and the numerical calculations are in good agreement with an approximate analytic solution. For fountain flow in a rectangular cavity, the shape of the flow front is flatter and the traces of the particles are more complicated for an expanding foam than for a constant‐density fluid. An example of mold filling by an expanding foam demonstrates the geometric flexibility of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

Application of a level set method for simulation of droplet collisions

A level set technique for interface tracking is presented, both for the continuum surface force formulation and the ghost fluid method approach. A projection method is used to solve incompressible Navier–Stokes equations that are coupled to a transport equation for the level set function, defined as the algebraic distance to interface. Results are presented for head-on droplet collisions in coalescence and reflexive regimes with a 2D axi-symmetric code, and for an off-center droplet collision in a separation regime for a large impact parameter with 3D code. Simulations provided realistic and various droplet collision behaviors and they correspond to experimental observations.     

Efficient simulation of nonlinear viscoelastic fluid flows

This paper presents a new and efficient method for computing the flow of a non-Newtonian fluid. The approach is based on two independent concepts:Time-dependent simulation of viscoelastic flow: A new decoupled algorithm, presented in P. Saramito, Simulation numérique d'ecoulements de fluides viscoélastiques par éléments finis incompressibles et une méthode de directions alternées; applications, Thèse de l'Institut National Polytechnique de Grenoble, 1990 and P. Saramito, Numerical simulation of viscoelastic fluid flows using incompressible finite element method and a θ-method, Math. Modelling Num. Anal., 35 (1994) 1–35, enables us to split the major difficulties of this problem, and to solve it more efficiently. Moreover, this scheme is of order two in time, and can be used to obtain stationary flows in an efficient way.Conservative finite element method: this method combines the incompressible Raviart Thomas element, the discontinuous Lesaint-Raviart element, and a finite volume element method. It satisfies exactly the mass conservation law, and leads to an optimal size for the nonlinear system in terms of the total degree of freedom versus the mesh size.We apply our numerical procedure to the Phan-Thien-Tanner model with a classical benchmark: the four to one abrupt contraction. The numerical solutions exhibit good behavior, especially near the singularity, in the vicinity of the re-entrant corner. The numerical experiments present the main features of such flows: vortex development and overshooting of the velocity profile along the axis of symmetry in the entry region.     

Simulation of fiber reinforced composite materials mold filling process and mechanical properties analysis

A dynamic simulation of fiber reinforced composite materials mold filling process with double inlets is presented based on the gas–solid–liquid model proposed by Yang et al. [B.X. Yang, J. Ouyang, J. Tao, C.T. Liu, Modeling and simulation of fiber reinforced polymer mold filling process by level set method, CMES – Computer Modeling in Engineering and Sciences 63 (3) (2010) 191–222]. Numerical results show that the fibers far away from the melt interface are in skin-core-skin structure, while those near the interface are almost parallel to the arc of the interface. When the two streams of melts meet, the weld line will be formed, where the orientation of fibers is perpendicular to the flow direction. The orientation of fibers of the numerical result shows well agreement with the experimental results. Finally, the mechanical properties of fiber reinforced composite materials are analyzed. The composite materials with skin-core-skin structure are regarded as laminated orthogonal plywood and the elastic modulus, the shear modulus and Poisson’s ratio are predicted under different slenderness ratios and fiber volume fractions.     

A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves

A coupled level set and volume-of-fluid (CLSVOF) method is implemented for the numerical simulations of interfacial flows in ship hydrodynamics. The interface is reconstructed via a piecewise linear interface construction scheme and is advected using a Lagrangian method with a second-order Runge–Kutta scheme for time integration. The level set function is re-distanced based on the reconstructed interface with an efficient re-distance algorithm. This level set re-distance algorithm significantly simplifies the complicated geometric procedure and is especially efficient for three-dimensional (3D) cases. The CLSVOF scheme is incorporated into CFDShip-Iowa version 6, a sharp interface Cartesian grid solver for two-phase incompressible flows with the interface represented by the level set method and the interface jump conditions handled using a ghost fluid methodology. The performance of the CLSVOF method is first evaluated through the numerical benchmark tests with prescribed velocity fields, which shows superior mass conservation property over the level set method. With combination of the flow solver, a gas bubble rising in a viscous liquid and a water drop impact onto a deep water pool are modeled. The computed results are compared with the available numerical and experimental results, and good agreement is obtained. Wave breaking of a steep Stokes wave is also modeled and the results are very close to the available numerical results. Finally, plunging wave breaking over a submerged bump is simulated. The overall wave breaking process and major events are identified from the wave profiles of the simulations, which are qualitatively validated by the complementary experimental data. The flow structures are also compared with the experimental data, and similar flow trends have been observed.     

A finite-element/finite-difference simulation of the injection-molding filling process

A detailed formulation is presented for simulating the injection-molding filling of thin cavities of arbitrary planar geometry. The modelling is in terms of generalized Hele-Shaw flow for an inelastic, non-Newtonian fluid under non-isothermal conditions. A hybrid numerical scheme is employed in which the planar coordinates are described in terms of finite elements and the gapwise and time derivatives are expressed in terms of finite differences.The simulation is applied to the filling of a two-gated plate mold having an intentionally unbalanced runner system. Good agreement is obtained with experimental results in terms of short-shot sequences, weldline formation and pressure traces at prescribed points in the cavity.     

Modeling and simulation of relaxation in viscoelastic open cell materials and structures

Open cell materials with cubic anisotropy and structures made thereof are investigated with respect to their linear viscoelastic properties, in particular their relaxation behavior. The study is concerned with the prediction of the effective behavior which results from the isotropic bulk material properties as well as the cellular architecture. Finite Element Method simulations of three-dimensional structures are employed to predict the effective response to a wide range of loading modes in the time domain.For predicting the properties of the cellular materials and structures by the Finite Element Method different modeling strategies are employed. The first approach is a periodic unit cell method modeling an infinite medium by means of periodic boundary conditions. This way the entire effective linear viscoelastic constitutive behavior can be computed. However, it is not possible to capture effects as being attributed to traction free faces and load introduction in specimens or structures. A second approach follows to account for these effects by generating finite sample models to represent situations which occur in experimental testing. Finally, an analytical constitutive material law is developed to model linear viscoelasticity for cubic anisotropy in the time domain. It is implemented into the commercial Finite Element software ABAQUS/Standard and the material parameters are gained from the unit cell investigations. This enables the simulation of structures, parts, and components which consist or contain such cellular materials.     

Modeling and simulation of aerial refueling by finite element method

The aerial refueling hose-and-drogue system is a special case of a generalized aerial cable towed system. The present work investigates the effect of pertinent parameters such as the cable tension, tow point disturbance and vortex wake on the dynamic behavior and stability of the generalized model by using the finite element method with an accurate and computationally efficient three-noded, curved beam element. The analysis results show that the conventional modal and spectrum analysis method is inappropriate for the dynamic stability analysis of the aerial cable towed system. This is because the mechanism of instability due to the tow point disturbance is not the resonance of the aerial cable towed system but the wave propagation downstream along the cable absorbing energy from the airflow when the wave propagation speed is less than the airflow speed. The study also demonstrates that the vortex wake has a significant impact on the dynamics of the aerial cable towed system. The short cable system will orbit with the vortex and the orbiting behavior will diminish as the cable length increases.     

On surface tension modelling using the level set method

The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface‐tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two‐phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching‐off of interfaces, the traditional level set model of surface tension produces an error that results in non‐converging solutions for film‐like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first‐order convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

Gradient augmented reinitialization scheme for the level set method

A hybrid scheme for reinitializing the level set function and its gradient within the frame work of the augmented level set method is presented. It is based on first dividing the domain into an interfacial region (i.e. nodes close to the interface) and its complement. Within the interfacial region, the level set and its gradient are updated explicitly through a modified version of Newton's method (Chopp, 2001, SIAM J. Sci. Comput. 23 230‐244) and is implemented here within the context of Hermite polynomials. In the region away from the interface, the solution pertains to a semi‐Lagrangian implementation of the reinitialization equations, which are solved based on Hermite polynomials and are time marched with a single step and a multipoint scheme. It is shown that for various exercises, the present method predicts the signed distance function and its gradient to 4^th and 3^rd order (in space), respectively with regards to the L₁, L₂, and L _∞ norms, provided the level set field is sufficiently smooth. A range of test cases are also considered from the literature, where the present method is compared with existing methods and shown to be generally more accurate. Moreover, the well‐known issue of volume loss due to reinitialization is addressed successfully with the current implementation, even for objects that are of the size of one grid cell, and whose local radius of curvature falls below the local grid size. For both time marching schemes, it is shown that the L₂ and L _∞ errors decay to negligible levels, are smooth in space, and do not exhibit temporal oscillations. Finally the performance of the hybrid scheme is evaluated by applying it on various kinematic test cases. For solid body rotation problems (zero deformation flow field), the benefit stemming from hybrid reinitialization is marginal. When applied to kinematic cases involving severe deformation, such as the standard vortex flow, the reinitialization strategy helps maintain a smooth level set field, which prevents serious numerical errors from developing.Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison of stabilisation approaches for finite-volume simulation of viscoelastic fluid flow

In this work we compare different stabilisation approaches currently used in the simulation of viscoelastic fluid flow. These approaches are: the both-sides diffusion, the positive definiteness preserving scheme, the log-conformation tensor representation and the symmetry factorisation of the conformation tensor. The evaluation of these approaches is done regarding their implementation complexity, stability, accuracy, efficiency and applicability to complex problems. Their performances are examined for an Oldroyd-B fluid in the test cases of lid-driven cavity, flow past a cylinder and 4:1 contraction flow. We summarise the situations in which the different approaches can be recommended.     

Level set方法在自适应Cartesian网格上的应用

采用基于自适应Cartesian网格的level set方法对多介质流动问题进行数值模拟。采用基于四叉树的方法来生成自适应Cartesian网格。采用有限体积法求解Euler方程,控制面通量的计算采用HLLC（Hartern, Lax, van Leer, Contact）近似黎曼解方法。level set方程也采用有限体积法求解,采用Lax-Friedchs方法计算通量,通过窄带方法来减少计算量,界面的处理采用ghost fluid方法。Runge-Kutta显式时间推进,时间、空间都是二阶精度。对两种不同比热比介质激波管问题进行数值模拟,其结果和精确解吻合;对空气/氦气泡相互作用等问题进行模拟,取得令人满意的结果。