Optimal H2 order-one reduction by solving eigenproblems for polynomial equations

A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based search, and hence avoids the usual problems of local minima. We examine mostly the case when the model order is reduced by one, and when the original system has distinct poles. This case exhibits special structure which allows us to provide a complete solution. The problem is converted into linear algebra by exhibiting a finite-dimensional basis for a certain space, and can then be solved by eigenvalue calculations, following the methods developed by Stetter and Moeller. The use of Buchberger's algorithm is avoided by writing the first-order optimality conditions in a special form, from which a Groebner basis is immediately available. Compared with our previous work the method presented here has much smaller time and memory requirements, and can therefore be applied to systems of significantly higher McMillan degree. In addition, some hypotheses which were required in the previous work have been removed. Some examples are included.

Defect and disorder reduction by annealing in hydrogenated tetrahedral amorphous carbon

Hydrogenated tetrahedral amorphous carbon (ta-C:H) is a form of diamond-like carbon with a high sp3 content (>60%), grown here using a plasma beam source. Information on the behaviour of hydrogen upon annealing is obtained from effusion measurements, which show that hydrogen does not effuse significantly at temperatures less than 500 °C in films grown using methane and 700 °C in films grown using acetylene. Raman measurements show no significant structural changes at temperatures up to 300 °C. At higher temperatures, corresponding to the onset of effusion, the Raman spectra show a clustering of the sp2 phase. The density of states of ta-C:H is directly measured using scanning tunnelling spectroscopy. The measured gradients of the conduction and valence band tails increase up to 300 °C, confirming the occurrence of band tail sharpening. Examination of the photoluminescence background in the Raman spectra shows an increase in photoluminescence intensity with decreasing defect density, providing evidence that paramagnetic defects are the dominant non-radiative recombination centres in ta-C:H.

Numerical modelling of lubricated foil rolling

A model of lubricated cold strip rolling (1, 2) is extended to the thin foil regime. The model considers the evolution of asperity geometry and lubricant pressure through the bite, treating the strip using a conventional slab model. The elastic deflections of the rolls are coupled into the problem using an elastic finite element model. Friction between the roll and the asperities on the strip is modelled using the Coulomb and Tresca friction factor approaches. The shear stress in the Coulomb friction model is limited to the shear yield stress of the strip. A novel modification to these standard friction laws is used to mimic slipping friction in the reduction regions and sticking friction in a central neutral zone. The model is able to reproduce the sticking and slipping zones predicted by Fleck et al. (3). The variation of rolling load, lubricant film thickness and asperity contact area with rolling speed is examined, for conditions typical of rolling aluminium foil from a thickness of 50 to 25 μm. T he contact area and hence friction rises as the speed drops, leading to a large increase in rolling load. This increase is considerably more marked using Coulomb friction as compared with the friction factor approach. Forward slip increases markedly as the speed falls and a significant sticking region develops.

Reduction of porosity in RE1Ba2Cu3Oy pseudo crystals

The distribution of porosity in Y1Ba2Cu3Oy (Y-123) pseudo-crystals prepared by hot seeded melt growth of precursor pellet samples pre-sintered at elevated temperatures in air or vacuum has been investigated. The results demonstrate that the porosity within the Y-123 pseudo-crystal matrix could be reduced dramatically by pre-sintering in vacuum, compared with that for precursor pellets processed in air.

The influence of peel angle on the mechanics of peeling flexible adherends with arbitrary load-extension characteristics

The peel test is commonly used to determine the strength of adhesive joints. In its simplest form, a thin flexible strip which has been bonded to a rigid surface is peeled from the substrate at a constant rate and the peeling force which is applied to the debonding surfaces by the tension in the tape is measured. Peeling can be carried out with the peel angle, i.e. the angle made by the peel force with the substrate surface, from any value above about 10° although peeling tests at 90 and 180° are most common. If the tape is sufficiently thin for its bending resistance to be negligibly small then as well as the debonding or decohesion energy associated with the adhesive in and around the point of separation, the relation between the peeling force and the peeling angle is influenced both by the mechanical properties of the tape and any pre-strain locked into the tape during its application to the substrate. The analytic solution for a tape material which can be idealised as elastic perfectly-plastic is well established. Here, we present a more general form of analysis, applicable in principle to any constitutive relation between tape load and tape extension. Non-linearity between load and extension is of increasing significance as the peel angle is decreased: the model presented is consistent with existing equations describing the failure of a lap joint between non-linear materials. The analysis also allows for energy losses within the adhesive layer which themselves may be influenced by both peel rate and peel angle. We have experimentally examined the application of this new analysis to several specific peeling cases including tapes of cellophane, poly-vinyl chloride and PTFE. © 2005 Elsevier Ltd. All rights reserved.

Evaluation of wave drag reduction by flow control

An analytical expression is proposed to estimate the wave drag of an aerofoil equipped with shock control. The analysis extends the conventional approach for a single normal shock wave, based on the knowledge that all types of successful shock control on transonic aerofoils cause bifurcated λ-shock structures. The influence of surface curvature on the λ-shock structure has been taken into account. The extended method has been found to produce fairly good agreement with the results obtained by CFD methods while requiring negligible computational effort. This new formulation is expected to be beneficial in the industrial design process of transonic aerofoils and wings where a large number of computational simulations have to be performed.

A new alternative for reduction of secondary flows in low pressure turbines

This paper describes a new flow mechanism for the reduction of secondary flows in Low Pressure Turbines using the benefit of contoured endwalls. The extensive application of contoured endwalls in recent years has provided a deeper understanding of the physical phenomenon that governs the reduction of secondary flows. Based on this understanding, the endwall geometry of a linear cascade of solid-thin profiles typical of Low Pressure Turbines has been redesigned. Experimental data are presented for the validation of this new solution. Based on these data, a reduction of 72% in the SKEH and 20% in the mixed-out endwall losses can be obtained. CFD simulations are also presented to illustrate the effect of the new endwall on the secondary flows. Furthermore, an explanation of the flow mechanism that governs the reduction of the SKEH and the losses is given. Copyright © 2006 by ASME.

Modelling effects of axial load on behaviour of pile groups in laterally-spreading soil

Previous research into the behaviour of piled foundations in laterally-spreading soil deposits has concentrated on pile groups that carry small or negligible axial loads. This paper presents dynamic centrifuge test results for 2 x 2 pile groups with bending and geometric properties similar to real 0.5 m diameter tubular steel and solid circular reinforced-concrete field piles. Axial loads applied represented upper-bounds on typical working loads. The simultaneous scaling of the relevant properties controlling both lateral and axial behaviour allows comparisons to be drawn regarding the particular mechanisms of failure that would dominate for each type of pile. Flexible reinforced-concrete piles which tend to carry lower loads were found to be dominated by lateral effects, while steel piles, which are much stiffer and usually carry greater loads are dominated by settlement considerations. © 2006 Taylor & Francis Group.

Bacterial load in pond water and different organs of a Indian major carp Cirrhinus mrigala Ham.

During the study period (August, 1993 to July,l994) the mean bacterial load in surface water was found to vary from 1.39 xl05 (July'94) to 3.llxl07CFU/ml (September'93), while that of botrom water ranged from l.Olxl06 (May'94) to 5.90xl07CFU/ml (October '93). The mean total number of bacterial load in body slime, liver and kidney was found to vary from 0.58xl03 (July'94) to 2.37xl07CFU/g (March'94),from 0.22xl03(July'94)to 9.64xl06 CFU/g (March'94) from O.l5xl03 (July'94) to 9.36xl06 CFU/g (March'94), respectively. Bacterial load in slime was significantly correlated with bacterial load in liver, bacterial load in slime was significantly correlated with bacterial load in kidney and bacterial load in liver was significantly correlated with bacterial load in kidney.

Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine

A multi-dimensional combustion code implementing the Conditional Moment Closure turbulent combustion model interfaced with a well-established RANS two- phase flow field solver has been employed to study a broad range of operating conditions for a heavy duty direct-injection common-rail Diesel engine. These conditions include different loads (25%, 50%, 75% and full load) and engine speeds (1250 and 1830 RPM) and, with respect to the fuel path, different injection timings and rail pressures. A total of nine cases have been simulated. Excellent agreement with experimental data has been found for the pressure traces and the heat release rates, without adjusting any model constants. The chemical mechanism used contains a detailed NOx sub-mechanism. The predicted emissions agree reasonably well with the experimental data considering the range of operating points and given no adjustments of any rate constants have been employed. In an effort to identify CPU cost reduction potential, various dimensionality reduction strategies have been assessed. Furthermore, the sensitivity of the predictions with respect to resolution in particular relating to the CMC grid has been investigated. Overall, the results suggest that the presented modelling strategy has considerable predictive capability concerning Diesel engine combustion without requiring model constant calibration based on experimental data. This is true particularly for the heat release rates predictions and, to a lesser extent, for NOx emissions where further progress is still necessary. © 2009 SAE International.

Numerical back-analysis of energy pile test at Lambeth College, London

Energy Piles present an efficient solution for long-term carbon emission reduction and sustainable construction. However, they have received only partial acceptance by the industry, because of concerns regarding the impact of cyclic thermal changes on the serviceability of energy pile foundations. This paper investigates the applicability of the hybrid load transfer approach to load-settlement analysis of single piles behavior during thermal energy exchange processes. Back-analysis results in terms of the thermal and mechanical response of energy piles show good agreement with field test results from Lambeth College in London. © ASCE 2011.

Assessing the potential of yield improvements, through process scrap reduction, for energy and CO2 abatement in the steel and aluminium sectors

Targets to cut 2050 CO2 emissions in the steel and aluminium sectors by 50%, whilst demand is expected to double, cannot be met by energy efficiency measures alone, so options that reduce total demand for liquid metal production must also be considered. Such reductions could occur through reduced demand for final goods (for instance by life extension), reduced demand for material use in each product (for instance by lightweight design) or reduced demand for material to make existing products. The last option, improving the yield of manufacturing processes from liquid metal to final product, is attractive in being invisible to the final customer, but has had little attention to date. Accordingly this paper aims to provide an estimate of the potential to make existing products with less liquid metal production. Yield ratios have been measured for five case study products, through a series of detailed factory visits, along each supply chain. The results of these studies, presented on graphs of cumulative energy against yield, demonstrate how the embodied energy in final products may be up to 15 times greater than the energy required to make liquid metal, due to yield losses. A top-down evaluation of the global flows of steel and aluminium showed that 26% of liquid steel and 41% of liquid aluminium produced does not make it into final products, but is diverted as process scrap and recycled. Reducing scrap substitutes production by recycling and could reduce total energy use by 17% and 6% and total CO 2 emissions by 16% and 7% for the steel and aluminium industries respectively, using forming and fabrication energy values from the case studies. The abatement potential of process scrap elimination is similar in magnitude to worldwide implementation of best available standards of energy efficiency and demonstrates how decreasing the recycled content may sometimes result in emission reductions. Evidence from the case studies suggests that whilst most companies are aware of their own yield ratios, few, if any, are fully aware of cumulative losses along their whole supply chain. Addressing yield losses requires this awareness to motivate collaborative approaches to improvement. © 2011 Elsevier B.V. All rights reserved.