Dynamic fluid–structure interaction using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

Modelling the Performance of Flexible Substrates for Lead-Free Applications

In this paper, the performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track. Secondly, an ACF flip chip was taken as a typical lead-free application of the flex substrate. The reflow effect on the reliability of ACF interconnections was analyzed. Higher stress was identified along the interface between the conductive particle and the metallization, and the interfacial stress increases with the reflow peak temperature and the coefficient of thermal expansion (CTE) of the adhesive. The moisture effect on the reliability of ACF joints were studied using a macro-micro modeling technique, the predominantly tensile stress found at the interface between the conductive particle and metallization could reduce the contact area and even cause the electrical failure. Modeling results are consistent with the findings in the experimental work

Analyzing the performance of flexible substrates for lead-free applications

The performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track and the thickness of the flex. Secondly, an anisotropic conductive film (ACF) flip chip was taken as a typical lead-free application of the flex substrate and the moisture effect on the reliability of ACF joints were studied using a 3D macro-micro modeling technique. It is found that the time to be saturated of an ACF flip chip is much dependent on the moisture diffusion rate in the polyimide substrate. The majority moisture diffuses into the ACF layer from the substrate side rather than the periphery of the ACF. The moisture induced stress was predicted and the predominant tensile stress was found at the interface between the conductive particle and metallization which could reduce the contact area and even cause the electrical failure

The study of flow and temperature fields in conducting droplets suspended in a DC/AC combination field

Electromagnetic Levitation (EML) is a valuable method for measuring the thermo-physical properties of metals - surface tensions, viscosity, thermal/electrical conductivity, specific heat, hemispherical emissivity, etc. – beyond their melting temperature. In EML, a small amount of the test specimen is melted by Joule heating in a suspended AC coil. Once in liquid state, a small perturbation causes the liquid envelope to oscillate and the frequency of oscillation is then used to compute its surface tension by the well know Rayleigh formula. Similarly, the rate at which the oscillation is dampened relates to the viscosity. To measure thermal conductivity, a sinusoidally varying laser source may be used to heat the polar axis of the droplet and the temperature response measured at the polar opposite – the resulting phase shift yields thermal conductivity. All these theoretical methods assume that convective effects due to flow within the droplet are negligible compared to conduction, and similarly that the flow conditions are laminar; a situation that can only be realised under microgravity conditions. Hence the EML experiment is the method favoured for Spacelab experiments (viz. TEMPUS). Under terrestrial conditions, the full gravity force has to be countered by a much larger induced magnetic field. The magnetic field generates strong flow within the droplet, which for droplets of practical size becomes irrotational and turbulent. At the same time the droplet oscillation envelope is no longer ellipsoidal. Both these conditions invalidate simple theoretical models and prevent widespread EML use in terrestrial laboratories. The authors have shown in earlier publications that it is possible to suppress most of the turbulent convection generated in the droplet skin layer, through use of a static magnetic field. Using a pseudo-spectral discretisation method it is possible compute very accurately the dynamic variation in the suspended fluid envelope and simultaneously compute the time-varying electromagnetic, flow and thermal fields. The use of a DC field as a dampening agent was also demonstrated in cold crucible melting, where suppression of turbulence was achieved in a much larger liquid metal volume and led to increased superheat in the melt and reduction of heat losses to the water-cooled walls. In this paper, the authors describe the pseudo-spectral technique as applied to EML to compute the combined effects of AC and DC fields, accounting for all the flow-induced forces acting on the liquid volume (Lorentz, Maragoni, surface tension, gravity) and show example simulations.

Reliability analysis for power electronics modules

This paper discusses the reliability of power electronics modules. The approach taken combines numerical modeling techniques with experimentation and accelerated testing to identify failure modes and mechanisms for the power module structure and most importantly the root cause of a potential failure. The paper details results for two types of failure (i) wire bond fatigue and (ii) substrate delamination. Finite element method modeling techniques have been used to predict the stress distribution within the module structures. A response surface optimisation approach has been employed to enable the optimal design and parameter sensitivity to be determined. The response surface is used by a Monte Carlo method to determine the effects of uncertainty in the design.

Predicting the reliability of power electronic modules

This paper discusses the reliability of an IGBT power electronics module. This work is part of a major UK funded initiative into the design, packaging and reliability of power electronic modules. The predictive methodology combines numerical modeling techniques with experimentation and accelerated testing to identify failure modes and mechanisms for these type of power electronic module structures. The paper details results for solder joint failure substrate solder. Finite element method modeling techniques have been used to predict the stress and strain distribution within the module structures. Together with accelerated life testing, these results have provided a failure model for these joints which has been used to predict reliability of a rail traction application

Investigation of precision grinding process for production of silicon diaphragms

The application of precision grinding for the formation of a silicon diaphragm is investigated. The test structures involved 2-6 mm diam diaphragms with thicknesses in the range of 25-150 //m. When grinding is performed without supporting the diaphragm, bending occurs due to nonuniform removal of the silicon material over the diaphragm region. The magnitude of bending depends on the µNal thickness of the diaphragm. The results demonstrate that the use of a porous silicon support can significantly reduce the amount of bending, by a factor of up to 300 in the case of 50 m thick diaphragms. The use of silicon on insulator (SOI) technology can also suppress or eliminate bending although this may be a less economical process. Stress measurements in the diaphragms were performed using x-ray and Raman spectroscopies. The results show stress of the order of 1 X107-! X108 Pa in unsupported and supported by porous silicon diaphragms while SOI technology provides stress-free diaphragms. Results obtained from finite element method analysis to determine deterioration in the performance of a 6 mm diaphragm due to bending are presented. These results show a 10% reduction in performance for a 75 µm thick diaphragm with bending amplitude of 30 fim, but negligible reduction if the bending is reduced to

Quality factor assessment of subwavelength resonant cavities at FIR frequencies

Subwavelength resonators at FIR are presented and studied. The structures consist of 1D cavities formed between a metallized (silver) surface and a metamaterial surface comprising a periodic array of silver patches on a silver-backed silicon substrate. The concept derives from recent discoveries of artificial magnetic conductors (AMC). By studying the currents excited on the metamaterial surface by a normally incident plane wave, the nature of the emerging resonant phenomena and the physical mechanism underlying the AMC operation are investigated. Full wave simulations, based on finite element method and time-domain transmission line modelling technique, have been carried out to demonstrate the effective AMC boundary condition and prove the possibilities for subwavelength cavities. The quality factor of the resonant cavities is assessed as a function of the cavity profile. It is demonstrated that the quality factor drops to about 1/8 of the half-wavelength value for lambda/8 resonant cavity.

Simple control of the polarisation in uniform hybrid waveguide-planar leaky-wave antennas

A simple and original mechanism to control the polarisation of uniform hybrid waveguide-planar leaky-wave antennas is proposed. The operation is based on introducing simple modifications of the planar dimensions of the structure cross-section, which is shown to control the horizontal and vertical components of the radiated fields. The proposed antenna dispenses with the need for periodic elements, commonly used in flexible polarised leaky-wave antennas, and therefore significantly reduces the design complexity. Parametric curves have been obtained to assist in the simple and efficient design of the proposed antenna. The novel mechanism is illustrated by means of several antenna prototypes operating at 5.7 GHz, producing linear, elliptical and circular polarisations. Commercial three-dimensional Finite Element Method has been used for the simulations, and the results are validated with experimental testing.[br].

Correction of dielectric losses in practical leaky-wave antenna designs

In this paper, the leaky-mode theory is applied to take into account for the dielectric losses in millimetre waveband inhomogeneous leaky-wave antennas. A practical dielectric-filled cosine-tapered periodic leaky-wave antenna working in the 45GHz band is studied, showing how the desired sidelobes level and directivity are spoilt due to the effect of the losses. An iterative procedure is used to correct the negative effects of the losses in the radiation patterns of the leaky-wave structure. It is also shown the practical limits of the proposed correction approach. The leaky-mode theory is applied for the first time to compensate the losses in a practical leaky-wave antenna in hybrid waveguide printed circuit technology. This leaky-mode theory is validated with full-wave three-dimensional finite element method simulations of the designed antenna.

Analysis of compressive membrane action in concrete slabs

This paper summarises the results obtained from non-linear finite-element analysis (NLFEA) of a series of reinforced-concrete one-way slabs with various boundary conditions representative of a bridge deck slab strip in which compressive membrane action governs the structural behaviour. The application of NLFEA for the optimum analysis and design of in-plane restrained concrete slabs is explored. An accurate material model and various equation solution methods were assessed to find a suitable finite-element method for the analysis of concrete slabs in which arching action occurs. Finally, the results from the NLFEA are compared and validated with those from various experimental test data. Significantly, the numerical analysis was able to model the arching action that occurred as a result of external in-plane restraint at the supports and which enhanced the ultimate strength of the slab. The NLFEA gave excellent predictions for the ultimate load-carrying capacity and far more accurate predictions than those obtained using standard flexural or elastic theory.

Saturated-unsaturated flow through leaky dams

This research investigated seepage flow through leaky dams using the well known finite-element method. Different areas, locations, and hydraulic conductivities of leaks were examined. An area of leak, equal to 4.4% of the core area, increased the seepage flow through the dam to be about 9.5 times the seepage flow through tight (nonleaky) core. This happened for a dam having a downstream horizontal drainage filter. When the drainage filter did not exist, the increase of flow because of the same area of leak was about seven times the flow through a tight core. When the leak existed at the centerline of the core in the out-of-plane direction, its impact was slightly greater than when it existed at the edge of the core. Moreover, as the location of the leak moved up vertically, its impact was observed to be less. It was also observed that when the leak existed in curtain wall driven into underneath the dam, its impact was not significant compared with the case when it existed in the core.

Three-Dimensional Analysis of Seepage below and around Hydraulic Structures

This paper investigates the problem of seepage under the floor of hydraulic structures considering the compartment of flow that seeps through the surrounding banks of the canal. A computer program, utilizing a finite-element method and capable of handling three-dimensional (3D) saturated–unsaturated flow problems, was used. Different ratios of canal width/differential head applied on the structure were studied. The results produced from the two-dimensional (2D) analysis were observed to deviate largely from that obtained from 3D analysis of the same problem, despite the fact that the porous medium was isotropic and homogeneous. For example, the exit gradient obtained from 3D analysis was as high as 2.5 times its value obtained from 2D analysis. Uplift force acting upwards on the structure has also increased by about 46% compared with its value obtained from the 2D solution. When the canal width/ differential head ratio was 10 or higher, the 3D results were comparable to the 2D results. It is recommended to construct a core of low permeability soil in the banks of canal to reduce the seepage losses, uplift force, and exit gradient.