Numerical modelling and validation of Marangoni and surface tension phenomena using the finite volume method

Surface tension induced flow is implemented into a numerical modelling framework and validated for a number of test cases. Finite volume unstructured mesh techniques are used to discretize the mass, momentum and energy conservation equations in three dimensions. An explicit approach is used to include the effect of surface tension forces on the flow profile and final shape of a liquid domain. Validation of this approach is made against both analytical and experimental data. Finally, the method is used to model the wetting balance test for solder alloy material, where model predictions are used to gain a greater insight into this process. Copyright © 2000 John Wiley & Sons, Ltd.

Magnetic modelling and magneto-hydro-dynamic simulations of an aluminium production electrolytic cell

A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto-hydro-dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

Turbulence modelling and its effects on electronic systems

This paper presents simulated computational fluid dynamics (CFD) results for comparison against experimental data. The performance of four turbulence models has been assessed for electronic application areas considering both fluid flow and heat transfer phenomenon. CFD is vast becoming a powerful and almost essential tool for design, development and optimization in engineering problems. However turbulence models remain to be the key problem issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the performance of the turbulence model employed together with the wall functions implemented. To be able to resolve the abrupt changes in the turbulent energy and other parameters near the wall a particularly fine mesh is necessary which unfortunately increases the computer storage capacity requirements. The objective of turbulence modelling is to enhance computational procdures of sufficient acccuracy and generality for engineers to anticipate the Reynolds stresses and the scalar transport terms.

Turbulence modelling and its impact on CFD predictions for cooling of electronic components

This paper will discuss Computational Fluid Dynamics (CFD) results from an investigation into the accuracy of several turbulence models to predict air cooling for electronic packages and systems. Also new transitional turbulence models will be proposed with emphasis on hybrid techniques that use the k-ε model at an appropriate distance away from the wall and suitable models, with wall functions, near wall regions. A major proportion of heat emitted from electronic packages can be extracted by air cooling. This flow of air throughout an electronic system and the heat extracted is highly dependent on the nature of turbulence present in the flow. The use of CFD for such investigations is fast becoming a powerful and almost essential tool for the design, development and optimization of engineering applications. However turbulence models remain a key issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the turbulence model employed together with the wall functions implemented. In order to resolve the abrupt fluctuations experienced by the turbulent energy and other parameters located at near wall regions and shear layers a particularly fine computational mesh is necessary which inevitably increases the computer storage and run-time requirements. The PHYSICA Finite Volume code was used for this investigation. With the exception of the k-ε and k-ω models which are available as standard within PHYSICA, all other turbulence models mentioned were implemented via the source code by the authors. The LVEL, LVEL CAP, Wolfshtein, k-ε, k-ω, SST and kε/kl models are described and compared with experimental data.

A modelling and experimental analysis of the no-flow underfill process for flip-chip assembly

In the flip-chip assembly process, no-flow underfill materials have a particular advantage over traditional underfills as the application and curing of this type of underfill can be undertaken before and during the reflow process - adding high volume throughput. Adopting a no-flow underfill process may result in underfill entrapment between solder and fluid, voiding in the underfill, a possible delamination between underfill and surrounding surfaces. The magnitude of these phenomena may adversely affect the reliability of the assembly in terms of solder joint thermal fatigue. This paper presents both an experimental and mdeling analysis investigating the reliabity of a flip-chip component and how the magnitude of underfill entrapment may affect thermal-mechanical fatigue life.

Microwave modelling and validation in food thawing applications

Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

Modelling and prototyping the conceptual design of 3D CMM micro-probe

This paper details the prototyping of a novel three axial micro probe based on utilisation of piezoelectric sensors and actuators for true three dimensional metrology and measurements at micro- and nanometre scale. Computational mechanics is used first to model and simulate the performance of the conceptual design of the micro-probe. Piezoelectric analysis is conducted to understand performance of three different materials - silicon, glassy carbon, and nickel - and the effect of load parameters (amplitude, frequency, phase angle) on the magnitude of vibrations. Simulations are also used to compare several design options for layout of the lead zirconium titanate (PZT) sensors and to identify the most feasible from fabrication point of view design. The material options for the realisation of the device have been also tested. Direct laser machining was selected as the primary means of production. It is found that a Yb MOPA based fiber laser was capable of providing the necessary precision on glassy carbon (GC), although machining trials on Si and Ni were less successful due to residual thermal effects.To provide the active and sensing elements on the flexures of the probe, PZT thick films are developed and deposited at low temperatures (Lt720 degC) allowing a high quality functional ceramic to be directly integrated with selected materials. Characterisation of the materials has shown that the film has a homogenous and small pore microstructure.

Time-dependent modelling and experimental validation of the metal/flux interface in a continuous casting mould

A finite volume computer model of the continuous casting process for steel flat products has been developed. In this first stage, the model concentrates on the hydrodynamic aspects of the process and in particular the dynamic behavior of the metal/slag interface. The model was validated against experimental measurements obtained in a water model apparatus.

Modelling and optimization of a pneumatic microfeeder system

This paper presents modelling and design optimization of a microfeeder which, as part of a microassembly system, is used for contactless object delivery. The microfeeder consists of an array of microactuators which are controlled by electrostatic actuation and used for maneuvering outcoming air jet for object hovering and delibery. The airflow behaviour in the microactuator is analysed by means of fluid mechanics and Computational Fluid Dynamics (CFD) simulation from three aspects, theoretical analysis, initial design assessment, and design modifications. The focus is put on the basic types of the microfeeder structure and the effects of structural details to the systematic performance. The structural pattern of the microactuator for forming airflow nozzle is identified and two design plans are proposed as basic structure patterns of pneumatic microactuators. The optimized design numerically shows the ability of delivering objects. This paper analyses the flow distribution pattern in microactuators and points out a way for effective design of pneumatic microfeeder systems. The optimization strategy provided by the present paper has close relevance to the design and manufacture of pneumatic microfeeder systems.

Electrostatic modelling and measurement of airborne particles concentration

Granular air-borne particles generally carry very small amounts of electric charge as a consequence of charging by the triboelectric effect. The presence of such particles induces charge of opposite polarity on a stationary conducting electrode. The amount of charge carried by the particles and the trajectories of the particles have significant random components and the signals produced are of very low level. The signal processing is further complicated by the random variation in the concentration of particles, i.e. the solid/gas ratio. This paper compares the results obtained from the electrostatic modelling of such sensors with those obtained from experiments.

Molecular dynamics simulation of observed c(4x4) and c(4x3) C60 alignments on the Si(100) reconstructed surface.

We have implemented a large-scale classical molecular dynamics simulation at constant temperature to provide a theoretical insight into the results of a recently performed experiment on the monolayer and multi-layer formations of molecular films on the Si(100) reconstructed dimerized surface. Our simulation has successfully reproduced all of the morphologies observed on the monolayer film by this experiment. We have obtained the formation of both c(4 4) and c(4 3) structures of the molecules and have also obtained phase transitions of the former into the latter.

Likelihood, entropy and species diversity; some comparisons in a Sumatran forest

In attempts to conserve the species diversity of trees in tropical forests, monitoring of diversity in inventories is essential. For effective monitoring it is crucial to be able to make meaningful comparisons between different regions, or comparisons of the diversity of a region at different times. Many species diversity measures have been defined, including the well-known abundance and entropy measures. All such measures share a number of problems in their effective practical use. However, probably the most problematic is that they cannot be used to meaningfully assess changes, since thay are only concerned with the number of species or the proportions of the population/sample which they constitute. A natural (though simplistic) model of a species frequency distribution is the multinomial distribution. It is shown that the likelihood analysis of samples from such a distribution are closely related to a number of entropy-type measures of diversity. Hence a comparison of the species distribution on two plots, using the multinomial model and likelihood methods, leads to generalised cross-entropy as the LRT test statistic of the null that the species distributions are the same. Data from 30 contiguous plots in a forest in Sumatra are analysed using these methods. Significance tests between all pairs of plots yield extremely low p-values, indicating strongly that it ought to been "Obvious" that the observed species distributions are different on different plots. In terms of how different the plots are, and how these differences vary over the whole study site, a display of the degrees of freedom of the test, (equivalent to the number of shared species) seems to be the most revealing indicator, as well as the simplest.

Forward and inverse transport of particulate matter and gaseous pollutants affecting the region bordering the English Channel

The ATTMA "Aerosol Transport in the Trans-Manche Atmosphere" project investigates the transportation and dispersion of air pollutants across the English Channel, in collaboration with local authorities and other Universities in Southern England and Northern France. The research is concerned with both forward and inverse (receptor based) tracking. Two alternative dispersion simulation methods are used: (a) Lagrangian Particle Dispersion (LPD) models, (b) Eulerian Finite Volume type models. This paper is concerned with part (a), the simulations based on LPD models. Two widely applied LPD models are used and compared. Since in many observed episodes the source of pollution is traced outside the region of interest, long range, trans-continental transport is also investigated.

Approximation Algorithms for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications

We consider a knapsack problem to minimize a symmetric quadratic function. We demonstrate that this symmetric quadratic knapsack problem is relevant to two problems of single machine scheduling: the problem of minimizing the weighted sum of the completion times with a single machine non-availability interval under the non-resumable scenario; and the problem of minimizing the total weighted earliness and tardiness with respect to a common small due date. We develop a polynomial-time approximation algorithm that delivers a constant worst-case performance ratio for a special form of the symmetric quadratic knapsack problem. We adapt that algorithm to our scheduling problems and achieve a better performance. For the problems under consideration no fixed-ratio approximation algorithms have been previously known.

Numerical Modelling for Electronic Packaging - Future Requirements

The fabrication, assembly and testing of electronic packaging can involve complex interactions between physical phenomena such as temperature, fluid flow, electromagnetics, and stress. Numerical modelling and optimisation tools are key computer-aided-engineering technologies that aid design engineers. This paper discusses these technologies and there future developments.