Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing ‘mathematical’ crack in an infinite plate and the respective Stress Intensity Factors

This is the first part of a short three-paper series, aiming to revisit some classical concepts of Linear Elastic Fracture Mechanics. The motive of this first paper is to highlight some controversial issues, related to the un­natu­ral overlapping of the lips of a ‘mathematical’ crack in an in­fin­­­ite plate load­ed by specific combinations of principal stresses at in­finity (predicted by the clas­si­c­al solu­tion of the respective first fundamental problem), and the closely as­so­ciated issue of negative mode-I Stress Intensity Factor. The problem is con­­­front­ed by superimposing to the first funda­mental problem of Lin­ear Elastic Frac­ture Mechanics for an in­fin­ite cracked plate (with stress-free crack lips) an ‘in­­verse’ mixed fund­amental problem. This superposition provides naturally ac­­­­­­­­ceptable stress and displacement fields, prohibiting overlapping of the lips (by means of contact stresses generated along the crack lips, which force the over­lapped lips back to naturally accepted position) and, also, non-negative mode-I Stress Intensity Factors. The solu­tions of this first paper form the basis for the next two papers of the series, dealing with the respective prob­lems in fi­­n­ite do­­mains (recall, for example, the cracked Brazil­ian disc con­fig­u­ra­tion) weak­­ened by artificial notches (rather than ‘math­e­mat­ical’ cracks), by far more interesting for practical engineer­ing ap­pli­­ca­tions

Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length

General formulae for double initial and caustic curves (reflected and transmitted) are obtained in the case of smooth contact of two cylindrical elastic bodies of arbitrary radii. Namely, based on the method of reflected and transmitted caustics, the conditions for the development of double initial and contact caustic curves are established as functions of six independent para­meters, while easy-to-use closed-form expressions are given for obtaining the contact length. An experimental protocol is then implemented in the case a thin cylindrical transparent disc is compressed between the jaws of the Inter­na­tional Society for Rock Mechanics suggested device for the execution of the Brazilian-disc test. The experimental method of caustics can provide the con­tact length quite accurately, even in the case of double curves which seem that are not always a consequence of a wide contact region

Hybrid PV and solar-thermal systems for domestic heat and power provision in the UK: Techno-economic considerations

A techno-economic analysis is undertaken to assess hybrid PV/solar-thermal (PVT) systems for distributed electricity and hot-water provision in a typical house in London, UK. In earlier work (Herrando et al., 2014), a system model based on a PVT collector with water as the cooling medium (PVT/w) was used to estimate average year-long system performance. The results showed that for low solar irradiance levels and low ambient temperatures, such as those associated with the UK climate, a higher coverage of total household energy demands and higher CO2 emission savings can be achieved by the complete coverage of the solar collector with PV and a relatively low collector cooling flow-rate. Such a PVT/w system demonstrated an annual electricity generation of 2.3 MW h, or a 51% coverage of the household’s electrical demand (compared to an equivalent PV-only value of 49%), plus a significant annual water heating potential of to 1.0 MW h, or a 36% coverage of the hot-water demand. In addition, this system allowed for a reduction in CO2 emissions amounting to 16.0 tonnes over a life-time of 20 years due to the reduction in electrical power drawn from the grid and gas taken from the mains for water heating, and a 14-tonne corresponding displacement of primary fossil-fuel consumption. Both the emissions and fossil-fuel consumption reductions are significantly larger (by 36% and 18%, respectively) than those achieved by an equivalent PV-only system with the same peak rating/installed capacity. The present paper proceeds further, by considering the economic aspects of PVT technology, based on which invaluable policy-related conclusions can be drawn concerning the incentives that would need to be in place to accelerate the widespread uptake of such systems. It is found that, with an electricity-only Feed-In Tariff (FIT) support rate at 43.3 p/kW h over 20 years, the system cost estimates of optimised PVT/w systems have an 11.2-year discounted payback period (PV-only: 6.8 years). The role and impact of heat-based incentives is also studied. The implementation of a domestic Renewable Heat Incentive (RHI) at a rate of 8.5 p/kW h in quarterly payments leads to a payback reduction of about 1 year. If this incentive is given as a one-off voucher at the beginning of the system’s lifetime, the payback is reduced by about 2 years. With a RHI rate of 20 p/kW h (about half of the FIT rate) PVT technology would have approximately the same payback as PV. It is concluded that, if primary energy (currently dominated by fossil fuels) and CO2 emission minimisation are important goals of national energy policy, PVT systems offer a significantly improved proposition over equivalent PV-only systems, but at an elevated cost. This is in need of careful reflection when developing relevant policy and considering technology incentivation. Currently, although heat outweighs electricity consumption by a factor of about 4 (by energy unit) in the UK domestic sector, the support landscape has strongly favoured electrical microgeneration, being inclined in favour of PV technology, which has been experiencing a well-documented exponential growth over recent decades

Implementation of the Finite Difference Time Domain algorithm for the analysis of terahertz waves

The aim of this report is to present results related to the application of the Finite Difference Time Domain (FDTD) method for the study of various devices at terahertz frequencies. The FDTD method has emerged as one of the most widely used numerical analysis methods used for electromagnetic simulations. The FDTD method can be used to solve numerous types of problems ranging from modelling the behaviour of microwave circuits, waveguides, and photonics to simulating terahertz devices and plasmas. In this study the FDTD approach is derived from first principles (finite differences) and explicit equations are shown based on Maxwell's equations. Furthermore, absorbing boundary conditions (ABCs) are discussed for the FDTD method. The algorithm is tested against a range of problems to ensure its validity and accuracy. The FDTD method is then applied for the numerical analysis of a range of devices at terahertz frequencies. The numerical results obtained from the application of the FDTD method to examine a microstrip circuit with filter loading and a Multi-mode Interference (MMI) coupler at terahertz frequencies are discussed in detail. Moreover, the results of the application of the FDTD method for the calculation of the dispersion characteristics of plasmonic waveguides are also presented. Finally, a summary of the work carried out is presented and an outline is given for future research which can be carried out by using the FDTD method for the study of terahertz frequency devices

A UK-based assessment of hybrid PV and solar-thermal systems for domestic heating and power: System performance

AbstractThe goal of this paper is to assess the suitability of hybrid PVT systems for the provision of electricity and hot water (space heating is not considered) in the UK domestic sector, with particular focus on a typical terraced house in London. A model is developed to estimate the performance of such a system. The model allows various design parameters of the PVT unit to be varied, so that their influence in the overall system performance can be studied. Two key parameters, specifically the covering factor of the solar collector with PV and the collector flow-rate, are considered. The emissions of the PVT system are compared with those incurred by a household that utilises a conventional energy provision arrangement. The results show that for the case of the UK (low solar irradiance and low ambient temperatures) a complete coverage of the solar collector with PV together with a low collector flow-rate are beneficial in allowing the system to achieve a high coverage of the total annual energy (heat and power) demand, while maximising the CO2 emissions savings. It is found that with a completely covered collector and a flow-rate of 20L/h, 51% of the total electricity demand and 36% of the total hot water demand over a year can be covered by a hybrid PVT system. The electricity demand coverage value is slightly higher than the PV-only system equivalent (49%). In addition, our emissions assessment indicates that a PVT system can save up to 16.0tonnes of CO2 over a lifetime of 20years, which is significantly (36%) higher than the 11.8tonnes of CO2 saved with a PV-only system. All investigated PVT configurations outperformed the PV-only system in terms of emissions. Therefore, it is concluded that hybrid PVT systems offer a notably improved proposition over PV-only systems

Distributed heat conversion technologies based on organic fluid cycles for a high-efficiency and sustainable energy future

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.This paper presents and discusses the emergence of two distinct classes of energy conversion systems based on thermodynamic vapour-phase heat engine cycles undergone by organic working fluids, namely organic Rankine cycles (ORCs) and two-phase thermofluidic oscillators (TFOs). Each type of system has its own distinctive characteristics, advantages and limitations. ORCs are a more well-established and mature technology, are more efficient, especially with higher temperature heat sources and at larger scales, whereas TFOs have the potential to be more cost-competitive, in particular at lower temperatures and at smaller scales. Specifically, ORC systems are particularly well-suited to the conversion of low- to mediumgrade heat (i.e. hot temperatures up to about 300 – 400 °C) to mechanical or electrical work, and at an output power scale from a few kW up to 10s of MW. Thermal efficiencies in excess of 25% are achievable at the higher temperatures, and efforts are currently in progress to develop improved ORC systems by focussing on advanced architectures, working fluid selection, heat exchangers and expansion machines. Correspondingly, TFO systems are a more recent development aimed at the affordable conversion of low-grade heat (i.e. hot temperatures from 20 – 30 °C above ambient, up to about 100 – 200 °C) to hydraulic work for fluid pumping and/or pressurisation. Ultimately, TFOs could emerge at scales of up to a few hundred W and with a thermal efficiency of the order of a few % points. The two energy conversion systems are complementary, and together have a great potential to be used for distributed power generation and improved energy efficiency, leading to primary energy (i.e. fuel) use and emission minimisation. Relevant applications and fields of use include the recovery of waste heat and conversion to useful work including mechanical, hydraulic or electrical energy, or the effective utilisation of renewable energy sources such as geothermal, biomass/biogas and solar energy.dc201

Simultaneous capacitive probe and planar laser-induced fluorescence measurements in downwards gas-liquid annular flow

Various experimental techniques are available to analyse two-phase flows. The measurement concept and the applicability can however vary greatly. Prime examples from the opposite spectrum are planar laser-induced measurements (PLIF) versus capacitive probes. PLIF is an optical technique, it is non-intrusive but optical access is necessary. PLIF based measurements are known for their high temporal and spatial resolution but require a costly set-up. In contrast, the capacitive probe is another non-intrusive technique but doesn’t require optical access. It is fairly easy to set up, robust, and is cheap to construct. To rigorously compare both techniques, simultaneous PLIF and capacitive probe measurements are made in this work. As the void fraction is one of the key parameters to classify flow regimes, both techniques are compared on the determination of the void fraction. This is done for a limited set of six annular flows. The experiments were performed in a downward annular-flow facility with demineralized water - air as working medium. The first results indicate that both techniques give similar volume averaged void fractions. The mean absolute percentage error and the maximum relative error between both techniques are 0.30% and 0.54%, respectively. The PLIF measurements confirm however to have a better spatial resolution

ORC cogeneration systems in waste-heat recovery applications

The performance of organic Rankine cycle (ORC) systems operating in combined heat and power (CHP) mode is investigated. The ORC-CHP systems recover heat from selected industrial waste-heat fluid streams with temperatures in the range 150°C-330°C. An electrical power output is provided by the expanding working fluid in the ORC turbine, while a thermal output is provided by the cooling water exiting the ORC condenser and also by a second heat-exchanger that recovers additional thermal energy from the heat-source stream downstream of the evaporator. The electrical and thermal energy outputs emerge as competing objectives, with the latter favoured at higher hot-water outlet temperatures and vice versa. Pentane, hexane and R245fa result in ORC-CHP systems with the highest exergy efficiencies over the range of waste-heat temperatures considered in this work. When maximizing the exergy efficiency, the second heat-exchanger is effective (and advantageous) only in cases with lower heat-source temperatures (< 250°C) and high heat-delivery/demand temperatures (> 60°C) giving a fuel energy savings ratio (FESR) of over 40%. When maximizing the FESR, this heat exchanger is essential to the system, satisfying 100% of the heat demand in all cases, achieving FESRs between 46% and 86%

Solar-thermal and hybrid photovoltaic-thermal systems for renewable heating

Grantham Briefing Papers analyse climate change and environmental research linked to work at Imperial College London, setting it in the context of national and international policy and the future research agenda. This paper and other Grantham publications are available from: www.imperial.ac.uk/grantham/publicationsThis paper looks at the barriers and opportunities for the mass deployment of solar-thermal technologies and offers a vision for the future of solar-thermal systems. HEADLINES: -Heat constitutes about half of total global energy demand. Solar heat offers key advantages over other renewable sources for meeting this demand through distributed, integrated systems. -Solar heat is a mature sustainable energy technology capable of mass deployment. There is significant scope for increasing the installed solar heat capacity in Europe. -Only a few European countries are close to reaching the EU target of 1 m2 of solar-thermal installations per person. -One key challenge for the further development of the solar-thermal market arises from issues related to the intermittency of the solar resource, and the requirement for storage and/or backup systems. The former increases investment costs and limits adaptability. -An analysis of EU countries with good market development, suggests that obligation schemes are the best policy option for maximising installations. These do not present a direct cost to the public budget, and determine the growth of the local industry in the long term. -Solar-thermal collectors can be combined with photovoltaic (PV) modules to produce hybrid PV-thermal (PV-T) collectors. These can deliver both heat and electricity simultaneously from the same installed area and at a higher overall efficiency compared to individual solar-thermal and PV panels installed separately. --Hybrid PV-T technology provides a particularly promising solution when roof space is limited or when heat and electricity are required at the same time.Preprin

Systematic testing of hybrid PV-thermal (PVT) solar collectors in steady-state and dynamic outdoor conditions

Hybrid photovoltaic-thermal (PVT) collectors have been proposed for the combined generation of electricity and heat from the same area. In order to predict accurately the electrical and thermal energy generation from hybrid PVT systems, it is necessary that both the steady-state and dynamic performance of the collectors is considered. This work focuses on the performance characterisation of non-concentrating PVT collectors under outdoor conditions. A novel aspect concerns the application of existing methods, adapted from relevant international standards for flat plate and evacuated tube solar-thermal collectors, to PVT collectors for which there is no formally established testing methodology at present. Three different types of PVT collector are tested, with a focus on the design parameters that affect their electrical and thermal performance during operation. Among other results, we show that a PVT collector suffers a 10% decrease in thermal efficiency when the electricity conversion is close to the maximum power point compared to open-circuit mode, and that a poor thermal contact between the PV laminate and the copper absorber can lead to a significant deterioration in thermal performance. The addition of a glass cover improves the thermal efficiency, but causes electrical performance losses that vary with the glass transmittance and the solar incidence angle. The reduction in electrical efficiency at large incidence angles is more significant than that due to elevated temperatures representative of water-heating applications. Dynamic performance is characterised by imposing a step change in irradiance in order to quantify the collector time constant and effective heat capacity. This paper demonstrates that PVT collectors are characterised by a slow thermal response in comparison to ordinary flat plate solar-thermal collectors, due to the additional thermal mass of the PV layer. A time constant of 8¿min is measured for a commercial PVT module, compared to 2¿min for a flat plate solar-thermal collector. It is also concluded that the use of a lumped, first-order dynamic model to represent the thermal mass of the PVT collector is not appropriate under certain irradiation regimes and may lead to inaccurate predictions of the system performance. This paper outlines a procedure for the testing and characterisation of solar collectors, provides valuable steady-state and dynamic performance characterisation data for various PVT collector designs, and also provides a framework for the application of this data in a system model to provide annual performance predictions in a range of geographical settings.Peer ReviewedPostprint (author's final draft