Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in induction crucible models is known to be unstable, turbulent and difficult to predict in the regime of medium frequencies when the electromagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference velocity probe in a cylindrical container filled with eutectic melt In-Ga-Sn. The parallel numerical simulation of the long time scale development of the turbulent average flow is presented. The numerical flow model uses an implicit pseudo-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The results compare reasonably to the experiment and demonstrate the time development of the turbulent flow field and the turbulence energy.

A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena

High-integrity castings require sophisticated design and manufacturing procedures to ensure they are essentially macrodefect free. Unfortunately, an important class of such defects—macroporosity, misruns, and pipe shrinkage—are all functions of the interactions of free surface flow, heat transfer, and solidication in complex geometries. Because these defects arise as an interaction of the preceding continuum phenomena, genuinely predictive models of these defects must represent these interactions explicitly. This work describes an attempt to model the formation of macrodefects explicitly as a function of the interacting continuum phenomena in arbitrarily complex three-dimensional geometries. The computational approach exploits a compatible set of finite volume procedures extended to unstructured meshes. The implementation of the model is described together with its testing and a measure of validation. The model demonstrates the potential to predict reliably shrinkage macroporosity, misruns, and pipe shrinkage directly as a result of interactions among free-surface fluid flow, heat transfer, and solidification.

Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in inducation crucible models is known to be higly unstable and turbutlen in the regim e of medium frequecies when the elctronmagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference veolocity probe in a cylindirical container filled with eutecti mlt In-Ga-SN. The parallel numerical simulation of the long time scale development of the turbulen average flow is presented. The numerical lfow model uses a pseud-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The result compare reasonably to the experiment and demonstrate the time development of the turbulent flow field.

The application of free-surface techniques to metal forming processes

In this paper the use of free-surface techniques, within the framework of a finite volume methodology, are investigated for the simulation of metal forming processes. In such processes, for example extrusion and forging, a workpiece is subjected to large scale deformation to create the product's shape. The use of Eulerian free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remmeshing. Two free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remesingh. Two free-surface techniques are compared by modelling a typical example of this type of process - non-Newtonian extrusion of an aluminium workpiece through a conical die.

Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Computational modeling of mold filling and related free-surface flows in shape casting: an overview of the challenges involved

Accurate representation of the coupled effects between turbulent fluid flow with a free surface, heat transfer, solidification, and mold deformation has been shown to be necessary for the realistic prediction of several defects in castings and also for determining the final crystalline structure. A core component of the computational modeling of casting processes involves mold filling, which is the most computationally intensive aspect of casting simulation at the continuum level. Considering the complex geometries involved in shape casting, the evolution of the free surface, gas entrapment, and the entrainment of oxide layers into the casting make this a very challenging task in every respect. Despite well over 30 years of effort in developing algorithms, this is by no means a closed subject. In this article, we will review the full range of computational methods used, from unstructured finite-element (FE) and finite-volume (FV) methods through fully structured and block-structured approaches utilizing the cut-cell family of techniques to capture the geometric complexity inherent in shape casting. This discussion will include the challenges of generating rapid solutions on high-performance parallel cluster technology and how mold filling links in with the full spectrum of physics involved in shape casting. Finally, some indications as to novel techniques emerging now that can address genuinely arbitrarily complex geometries are briefly outlined and their advantages and disadvantages are discussed.

Stochastic analysis of free surface flow through earth dams

This research investigated the unconfined flow through dams. The hydraulic conductivity was modeled as spatially random field following lognormal distribution. Results showed that the seepage flow produced from the stochastic solution was smaller than its deterministic value. In addition, the free surface was observed to exit at a point lower than that obtained from the deterministic solution. When the hydraulic conductivity was strongly correlated in the horizontal direction than the vertical direction, the flow through the dam has markedly increased. It is suggested that it may not be necessary to construct a core in dams made from soils that exhibit high degree of variability.

A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

Relaxation of surface tension in the free-surface boundary layers of simple Lennard-Jones liquids

In this paper we use molecular dynamics to answer a classical question: how does the surface tension on a liquid/gas interface appear? After defining surface tension from the first principles and performing several consistency checks, we perform a dynamic experiment with a single simple liquid nanodroplet. At time zero, we remove all molecules of the interfacial layer of molecules, creating a fresh bare interface with the bulk arrangement of molecules. After that the system evolves towards equilibrium, and the expected surface tension is re-established. We found that the system relaxation consists of three distinct stages. First, the mechanical balance is quickly re-established. During this process the notion of surface tension is meaningless. In the second stage, the surface tension equilibrates, and the density profile broadens to a value which we call “intrinsic” interfacial width. During the third stage, the density profile continues to broaden due to capillary wave excitations, which does not however affect the surface tension.We have observed this scenario for monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at different temperatures, monitoring a wide range of physical observables.

Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,