Modelling the fluid dynamics and coupled phenomena in arc weld pools

A 3D model of melt pool created by a moving arc type heat sources has been developed. The model solves the equations of turbulent fluid flow, heat transfer and electromagnetic field to demonstrate the flow behaviour phase-change in the pool. The coupled effects of buoyancy, capillary (Marangoni) and electromagnetic (Lorentz) forces are included within an unstructured finite volume mesh environment. The movement of the welding arc along the workpiece is accomplished via a moving co-ordinator system. Additionally a method enabling movement of the weld pool surface by fluid convection is presented whereby the mesh in the liquid region is allowed to move through a free surface. The surface grid lines move to restore equilibrium at the end of each computational time step and interior grid points then adjust following the solution of a Laplace equation.

Viscoelastic flow through a planar contraction using a semi-Lagrangian finite volume method

A semi-Lagrangian finite volume scheme for solving viscoelastic flow problems is presented. A staggered grid arrangement is used in which the dependent variables are located at different mesh points in the computational domain. The convection terms in the momentum and constitutive equations are treated using a semi-Lagrangian approach in which particles on a regular grid are traced backwards over a single time-step. The method is applied to the 4 : 1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions. The development of vortex behaviour with increasing values of We is analyzed.

Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Feature-oriented grid topology design for aerospace configurations

The last few years have seen a substantial increase in the geometric complexity for 3D flow simulation. In this paper we describe the challenges in generating computation grids for 3D aerospace configuations and demonstrate the progress made to eventually achieve a push button technology for CAD to visualized flow. Special emphasis is given to the interfacing from the grid generator to the flow solver by semi-automatic generation of boundary conditions during the grid generation process. In this regard, once a grid has been generated, push button technology of most commercial flow solvers has been achieved. This will be demonstrated by the ad hoc simulation for the Hopper configuration.

A coarse grid extraction of sound signals for computational aeroacoustics

Sound waves are propagating pressure fluctuations, which are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes equations do not resolve the acoustic fluctuations. This paper discusses a defect correction method for this type of multi-scale problems in aeroacoustics. Numerical examples in one dimensional and two dimensional are used to illustrate the concept. Copyright (C) 2002 John Wiley & Sons, Ltd.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

High electric current density-induced interfacial reactions in micro ball grid array (μBGA) solder joints

The effect of a high electric current density on the interfacial reactions of micro ball grid array solder joints was studied at room temperature and at 150 °C. Four types of phenomena were reported. Along with electromigration-induced interfacial intermetallic compound (IMC) formation, dissolution at the Cu under bump metallization (UBM)/bond pad was also noticed. With a detailed investigation, it was found that the narrow and thin metallization at the component side produced “Joule heating” due to its higher resistance, which in turn was responsible for the rapid dissolution of the Cu UBM/bond pad near to the Cu trace. During an “electromigration test” of a solder joint, the heat generation due to Joule heating and the heat dissipation from the package should be considered carefully. When the heat dissipation fails to compete with the Joule heating, the solder joint melts and molten solder accelerates the interfacial reactions in the solder joint. The presence of a liquid phase was demonstrated from microstructural evidence of solder joints after different current stressing (ranging from 0.3 to 2 A) as well as an in situ observation. Electromigration-induced liquid state diffusion of Cu was found to be responsible for the higher growth rate of the IMC on the anode side.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Multiple reflow study of ball grid array (BGA) solder joints on Au/Ni metallization

This paper evaluates the shearing behavior of ball grid array (BGA) solder joints on Au/Ni/Cu pads of FR4 substrates after multiple reflow soldering. A new Pb-free solder, Sn–3Ag–0.5Cu–8In (SACI), has been compared with Sn–3Ag–0.5Cu (SAC) and Sn–37Pb (SP) solders, in terms of fracture surfaces, shearing forces and microstructures. Three failure modes, ball cut, a combination of solder shear and solder/pad bond separation, and pad lift, are assessed for the different solders and reflow cycles. It is found that the shearing forces of the SP and SAC solder joints tend to increase slightly with an increase in the number of reflow cycles due to diffusion-induced solid solution strengthening of the bulk solder and augmentation of the shearing area. However, the shearing forces of the SACI solder joints decrease slightly after four cycles of reflow, which is ascribed to the thermal degradation of both the solder/intermetallic compound (IMC) and IMC/Ni interfaces. The SACI solder joints yield the highest strengths, whereas the SP solder joints give the smallest values, irrespective of the number of reflow cycles. Thickening of the interfacial IMC layer and coarsening of the dispersing IMC particles within the bulk solders were also observed. Nevertheless, the variation of shearing forces and IMC thickness with different numbers of reflow cycles was not so significant since the Ni under layer acted as an effective diffusion barrier. In addition, the initially-formed IMC layer retarded the further extensive dissolution of the pad material and its interaction with the solder

Shear strength analysis of ball grid array (BGA) solder interfaces

Ball shear test is the most common test method used to assess the reliability of bond strength for ball grid array (BGA) packages. In this work, a combined experimental and numerical study was carried out to realize of BGA solder interface strength. Solder mask defined bond pads on the BGA substrate were used for BGA ball bonding. Different bond pad metallizations and solder alloys were used. Solid state aging at 150degC up to 1000 h has been carried out to change the interfacial microstructure. Cross-sectional studies of the solder-to-bond pad interfaces was conducted by scanning electron microscopy (SEM) equipped with an energy dispersive X-ray (EDX) analyzer to investigate the interfacial reaction phenomena. Ball shear tests have been carried out to obtain the mechanical strength of the solder joints and to correlate shear behaviour with the interfacial reaction products. An attempt has been taken to realize experimental findings by Finite Element Analysis (FEA). It was found that intermetallic compound (IMC) formation at the solder interface plays an important role in the BGA solder bond strength. By changing the morphology and the microchemistry of IMCs, the fracture propagation path could be changed and hence, reliability could be improved

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.

Grid effects

Zaha Hadid's Kartal Pendik Masterplan (2006) for a new city centre on the east bank of Istanbul proposes the redevelopment of an abandoned industrial site located in a crucial infrastructural node between Europe and Asia as a connecting system between the neighbouring areas of Kartal in the west and Pendik in the east. The project is organised on what its architects call a soft grid, a flexible and adaptable grid that allows it to articulate connections and differences of form, density and use within the same spatial structure [1]. Its final overall design constitutes only one of the many possible configurations that the project may take in response to the demands of the different areas included in the masterplan, and is produced from a script that is able to generate both built volumes and open spaces, skyscrapers as well as parks. The soft grid in fact produces a ‘becoming’ rather than a finite and definitive form: its surface space does not look like a grid, but is derived from a grid operation which is best explained by the project presentation in video animation. The grid here is a process of ‘gridding’, enacted according to ancient choreographed linear movements of measuring, defining, adjusting, reconnecting spaces through an articulated surface rather than superimposed on an ignored given like an indifferent colonising carpet.