[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

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

Micromachined 300GHz high Q resonant slot frequency selective surface filter

The design of a low loss quasi-optical beam splitter which is required to provide efficient diplexing of the bands 316.5-325.5 GHz and 349.5-358.5 GHz is presented. To minimise the filter insertion loss, the chosen architecture is a three-layer freestanding array of dipole slot elements. Floquet modal analysis and finite element method computer models are used to establish the geometry of the periodic structure and to predict its spectral response. Two different micromachining approaches have been employed to fabricate close packed arrays of 460 mm long elements in the screens that form the basic building block of the 30mm diameter multilayer frequency selective surface. Comparisons between simulated and measured transmission coefficients for the individual dichroic surfaces are used to determine the accuracy of the computer models and to confirm the suitability of the fabrication methods.

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.

Design of hydraulic structures considering different sheetpile configurations and flow through canal banks

This research investigated seepage under hydraulic structures considering flow through the banks of the canal. A computer model, utilizing the finite element method, was used. Different configurations of sheetpile driven under the floor of the structure were studied. Results showed that the transverse extension of sheetpile, driven at the middle of the floor, into the banks of the canal had very little effect on seepage losses, uplift force, and on the exit gradient at the downstream end of the floor. Likewise, confining the downstream floor with sheetpile from three sides was not found effective. When the downstream floor was confined with sheetpile from all sides, this has significantly reduced the exit gradient. Furthermore, all the different configurations of the sheetpile had insignificant effect on seepage losses. The most effective configuration of the sheetpile was the case when two rows of sheetpiles were driven at the middle and at the downstream end of the floor, with the latter sheetpile extended few meters into the banks of the canal. This case has significantly reduced the exit gradient and caused only slight increase in the uplift force when compared to other sheetpile configurations. The present study suggests that two-dimensional analysis of seepage problems underestimates the exit gradient and uplift force on hydraulic structures.

A virtual inspection framework for precision manufacturing of aerofoil components

The finite element method plays an extremely important role in forging process design as it provides a valid means to quantify forging errors and thereby govern die shape modification to improve the dimensional accuracy of the component. However, this dependency on process simulation could raise significant problems and present a major drawback if the finite element simulation results were inaccurate. This paper presents a novel approach to assess the dimensional accuracy and shape quality of aeroengine blades formed from finite element hot-forging simulation. The proposed virtual inspection system uses conventional algorithms adopted by modern coordinate measurement processes as well as the latest free-form surface evaluation techniques to provide a robust framework for virtual forging error assessment. Established techniques for the physical registration of real components have been adapted to localise virtual models in relation to a nominal Design Coordinate System. Blades are then automatically analysed using a series of intelligent routines to generate measurement data and compute dimensional errors. The results of a comparison study indicate that the virtual inspection results and actual coordinate measurement data are highly comparable, validating the approach as an effective and accurate means to quantify forging error in a virtual environment. Consequently, this provides adequate justification for the implementation of the virtual inspection system in the virtual process design, modelling and validation of forged aeroengine blades in industry.