Two fluid approach to high speed impact interaction amongst solid structures

The issues surrounding collision of projectiles with structures has gained a high profile since the events of 11th September 2001. In such collision problems, the projectile penetrates the stucture so that tracking the interface between one material and another becomes very complex, especially if the projectile is essentially a vessel containing a fluid, e.g. fuel load. The subsequent combustion, heat transfer and melting and re-solidification process in the structure render this a very challenging computational modelling problem. The conventional approaches to the analysis of collision processes involves a Lagrangian-Lagrangian contact driven methodology. This approach suffers from a number of disadvantages in its implementation, most of which are associated with the challenges of the contact analysis component of the calculations. This paper describes a 'two fluid' approach to high speed impact between solid structures, where the objective is to overcome the problems of penetration and re-meshing. The work has been carried out using the finite volume, unstructured mesh multi-physics code PHYSICA+, where the three dimensional fluid flow, free surface, heat transfer, combustion, melting and re-solidification algorithms are approximated using cell-centred finite volume, unstructured mesh techniques on a collocated mesh. The basic procedure is illustrated for two cases of Newtonian and non-Newtonian flow to test various of its component capabilities in the analysis of problems of industrial interest.

A mixed Eulerian-Lagrangian approach for metal extrusion

In this paper a mixed Eulerian-Lagrangian approach for the modelling metal extrusion processes is presented. The approach involves the solution of non-Newtonian fluid flow equations in an Eulerian context, using a free-surface algorithm to track the behaviour of the workpiece and its extrusion. The solid mechanics equations associated with the tools are solved in Lagangrian context. Thermal interactions between the workpiece are modelled and a fluid-structure interaction technique is employed to model the effect of the fluid traction load imposed by the workpiece on the tools. Two extrusion test cases are investigated and the results obtained show the potential of the model with regard to representing the physics of the process and the simulation time.

A cell-centred finite volume method for modelling viscoelastic flow

An unstructured cell-centred finite volume method for modelling viscoelastic flow is presented. The method is applied to the flow through a planar channel and the 4:1 planar contraction for creeping flow of an Oldroyd-B fluid. The results are presented for a range of Weissenberg numbers. In the case of the planar channel results are compared with analytical solutions. For the 4:1 planar contraction benchmark problem the convection terms in the constitutive equations are approximated using both first and second order differencing schemes to compare the techniques and the effect of mesh refinement on the solution is investigated. This is the first time that a fully unstructured, cell-centredfinitevolume technique has been used to model the Oldroyd-B fluid for the test cases presented in this paper.

Parametrical modeling and design optimization of blood plasma separation device with microchannel mechanism

This paper presents an analysis of biofluid behavior in a T-shaped microchannel device and a design optimization for improved biofluid performance in terms of particle liquid separation. The biofluid is modeled with single phase shear rate non-Newtonian flow with blood property. The separation of red blood cell from plasma is evident based on biofluid distribution in the microchannels against various relevant effects and findings, including Zweifach-Fung bifurcation law, Fahraeus effect, Fahraeus-Lindqvist effect and cell free phenomenon. The modeling with the initial device shows that this T-microchannel device can separate red blood cell from plasma but the separation efficiency among different bifurcations varies largely. In accordance with the imbalanced performance, a design optimization is conducted. This includes implementing a series of simulations to investigate the effect of the lengths of the main and branch channels to biofluid behavior and searching an improved design with optimal separation performance. It is found that changing relative lengths of branch channels is effective to both uniformity of flow rate ratio among bifurcations and reduction of difference of the flow velocities between the branch channels, whereas extending the length of the main channel from bifurcation region is only effective for uniformity of flow rate ratio.

Effect of fluid dynamics and device mechanism on biofluid behaviour in microchannel systems: modelling biofluids in a microchannel biochip separator

Biofluid behaviour in microchannel systems is investigated in this paper through the modelling of a microfluidic biochip developed for the separation of blood plasma. Based on particular assumptions, the effects of some mechanical features of the microchannels on behaviour of the biofluid are explored. These include microchannel, constriction, bending channel, bifurcation as well as channel length ratio between the main and side channels. The key characteristics and effects of the microfluidic dynamics are discussed in terms of separation efficiency of the red blood cells with respect to the rest of the medium. The effects include the Fahraeus and Fahraeus-Lindqvist effects, the Zweifach-Fung bifurcation law, the cell-free layer phenomenon. The characteristics of the microfluid dynamics include the properties of the laminar flow as well as particle lateral or spinning trajectories. In this paper the fluid is modelled as a single-phase flow assuming either Newtonian or Non-Newtonian behaviours to investigate the effect of the viscosity on flow and separation efficiency. It is found that, for a flow rate controlled Newtonian flow system, viscosity and outlet pressure have little effect on velocity distribution. When the fluid is assumed to be Non-Newtonian more fluid is separated than observed in the Newtonian case, leading to reduction of the flow rate ratio between the main and side channels as well as the system pressure as a whole.

Modeling the structural breakdown of solder paste using the structural kinetic model

Solder paste is the most important strategic bonding material used in the assembly of surface mount devices in electronic industries. It is known to exhibit a thixotropic behavior, which is recognized by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterization of this time-dependent rheological behavior of solder pastes is crucial for establishing the relationships between the pastes structure and flow behavior; and for correlating the physical parameters with paste printing performance. In this article, we present a novel method which has been developed for characterizing the time-dependent and non-Newtonian rheological behavior of solder pastes and flux mediums as a function of shear rates. We also present results of the study of the rheology of the solder pastes and flux mediums using the structural kinetic modeling approach, which postulates that the network structure of solder pastes breaks down irreversibly under shear, leading to time and shear-dependent changes in the flow properties. Our results show that for the solder pastes used in the study, the rate and extent of thixotropy was generally found to increase with increasing shear rate. The technique demonstrated in this study has wide utility for R&D personnel involved in new paste formulation, for implementing quality control procedures used in solder-paste manufacture and packaging; and for qualifying new flip-chip assembly lines.

Modelling the time-dependent behaviour of solder pastes used in the electronics assembly applications

Solder paste is the most widely used bonding material in the assembly of surface mount devices in electronic industries. It generally has a flocculated structure (show aggregation of solder particles), and hence are known to exhibit a thixotropic behavior. This is recognized by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this timedependent rheological behaviour of solder pastes is crucial for establishing the relationships between the pastes’ structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a novel method which has been developed for characterising the timedependent and non-Newtonian rheological behaviour of solder pastes as a function of shear rates. The objective of the study reported in this paper is to investigate the thixotropic build-up behaviour of solder pastes. The stretched exponential model(SEM) has been used to model the structural changes during the build-up process and to correlate model parameters with the paste printing process.

Modelling of the time-dependent flow behaviour of lead-free solder pastes used for flip-chip assembly applications

The market for solder paste materials in the electronic manufacturing and assembly sector is very large and consists of material and equipment suppliers and end users. These materials are used to bond electronic components (such as flip-chip, CSP and BGA) to printed circuit boards (PCB's) across a range of dimensions where the solder interconnects can be in the order of 0.05mm to 5mm in size. The non-Newtonian flow properties exhibited by solder pastes during its manufacture and printing/deposition phases have been of practical concern to surface mount engineers and researchers for many years. The printing of paste materials through very small-sized stencil apertures is known to lead to increased stencil clogging and incomplete transfer of paste to the substrate pads. At these very narrow aperture sizes the paste rheology and particle-wall interactions become crucial for consistent paste withdrawal. These non-Newtonian effects must be understood so that the new paste formulations can be optimised for consistent printing. The focus of the study reported in this paper is the characterisation of the rheological properties of solder pastes and flux mediums, and the evaluation of the effect of these properties on the pastes' printing performance at the flip-chip assembly application level. Solder pastes are known to exhibit a thixotropic behaviour, which is recognised by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this time-dependent theological behaviour of solder pastes is crucial for establishing the relationships between the pastes' structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a number of methods which have been developed for characterising the time-dependent and non-Newtonian rheological behaviour of solder pastes and flux mediums as a function of shear rates. We also present results of the study of the rheology of the solder pastes and flux mediums using the structural kinetic modelling approach, which postulates that the network structure of solder pastes breaks down irreversibly under shear, leading to time and shear dependent changes in the flow properties. Our results show that for the solder pastes used in the study, the rate and extent of thixotropy was generally found to increase with increasing shear rate. The technique demonstrated in this study has wide utility for R&D personnel involved in new paste formulation, for implementing quality control procedures used in solder paste manufacture and packaging; and for qualifying new flip-chip assembly lines

Preparation of o/w emulsions stabilized by solid particles and their characterization by oscillatory rheology

The purpose of this investigation was to examine the preparation and characterisation of hexane-in-water emulsions stabilised by clay particles. These emulsions, called Pickering emulsions, are characterised by the adsorption of solid particles at the oil/water (o/w) interface. The development of an elastic film at the o/w interface following the adsorption of colloidal particles helps to promote emulsion stability. Three different solid materials were used: silica sand, kaolin, and bentonite. Particles were added to the liquid mixtures in the range of 0.5–10 g dm−3. Emulsions were prepared using o/w ratios of 0.1, 0.2, 0.3, and 0.4. The effect of sodium chloride, on the stability of the prepared emulsions, was assessed in the range of 0–0.5 mol dm−3. In addition the use of a cationic surfactant hexadecyl-trimethylammonium bromide (CTAB) as an aid to improving emulsion stability was assessed in the concentration range of 0–0.05% (w/v). Characterisation of emulsion stability was realised through measurements of rheological properties including non-Newtonian viscosity, the elastic modulus, G', the loss modulus, G", and complex modulus, G*. The stability of the emulsions was evaluated immediately after preparation and 4 weeks later. Using the stability criteria, that for highly stable emulsions: G' > G" and both G' and G" are independent of frequency (varpi) it was concluded that highly stable emulsions could be prepared using a bentonite concentration of 2% (or more); an o/w ratio greater than 0.2; a CTAB concentration of 0.01%; and a salt concentration of 0.05 M or less—though salt was required.

Density-viscosity product of small-volume ionic liquid samples using quartz crystal impedance analysis

Quartz crystal impedance analysis has been developed as a technique to assess whether room-temperature ionic liquids are Newtonian fluids and as a small-volume method for determining the values of their viscosity-density product, rho eta. Changes in the impedance spectrum of a 5-MHz fundamental frequency quartz crystal induced by a water-miscible room-temperature ionic liquid, 1-butyl-3-methylimidazolium. trifluoromethylsulfonate ([C(4)mim][OTf]), were measured. From coupled frequency shift and bandwidth changes as the concentration was varied from 0 to 100% ionic liquid, it was determined that this liquid provided a Newtonian response. A second water-immiscible ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide [C(4)mim][NTf2], with concentration varied using methanol, was tested and also found to provide a Newtonian response. In both cases, the values of the square root of the viscosity-density product deduced from the small-volume quartz crystal technique were consistent with those measured using a viscometer and density meter. The third harmonic of the crystal was found to provide the closest agreement between the two measurement methods; the pure ionic liquids had the largest difference of similar to 10%. In addition, 18 pure ionic liquids were tested, and for 11 of these, good-quality frequency shift and bandwidth data were obtained; these 12 all had a Newtonian response. The frequency shift of the third harmonic was found to vary linearly with square root of viscosity-density product of the pure ionic liquids up to a value of root(rho eta) approximate to 18 kg m(-2) s(-1/2), but with a slope 10% smaller than that predicted by the Kanazawa and Gordon equation. It is envisaged that the quartz crystal technique could be used in a high-throughput microfluidic system for characterizing ionic liquids.

On visco-elastic modelling of polyethylene terephthalate behaviour during multiaxial elongations slightly over the glass transition temperature

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature Tg, the stress-strain curve presents a strain softening effect vs strain rate but a strain hardening effect vs strain under conditions of large deformations. The main goal of this work is to propose a viscoelastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained trough a comparison with the experimental uniaxial and biaxial tests. The in?uence of the temperature on the viscous part is also modelled and an evaluation of the adiabatic self heating of the specimen is compared to experimental results.

Determination of the Physical Properties of Room Temperature Ionic Liquids Using a Love Wave Device

In this work, we have shown that a 100 MHz Love wave device can be used to determine whether room temperature ionic liquids (RTILs) are Newtonian fluids and have developed a technique that allows the determination of the density-viscosity product, rho eta of a Newtonian RTIL. In addition, a test for a Newtonian response was established by relating the phase change to insertion loss change. Five concentrations of a water-miscible RTIL and seven pure RTILs were measured. The changes in phase and insertion loss were found to vary linearly with the square root of the density-viscosity product for values up to (rho eta)(1/2) similar to 10 kg m(-2) s(-1/2). The square root of the density-viscosity product was deduced from the changes in either phase or insertion loss using glycerol as a calibration liquid. In both cases, the deduced values of rho eta agree well with those measured using viscosity and density meters. Miniaturization of the device, beyond that achievable with the lower-frequency quartz crystal microbalance approach, to measure smaller volumes is possible. The ability to fabricate Love wave and other surface acoustic wave sensors using planar metallization technologies gives potential for future integration into lab-on-a-chip analytical systems for characterizing ionic liquids.

Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.