Mathematical analysis of maximum power generated by photovoltaic systems and fitting curves for standard test conditions

The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

A novel methodology for simulating contact-line behavior in capillary-driven flows

<p>Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.</p> <p>Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities. </p> <p>To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.</p> <p>All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.</p>

Análise comparativa entre simuladores de linha de fluxo e diferenças finitas para um reservatório de petróleo submetido a injeção de água

Water injection is the most widely used method for supplementary recovery in many oil fields due to various reasons, like the fact that water is an effective displacing agent of low viscosity oils, the water injection projects are relatively simple to establish and the water availability at a relatively low cost. For design of water injection projects is necessary to do reservoir studies in order to define the various parameters needed to increase the effectiveness of the method. For this kind of study can be used several mathematical models classified into two general categories: analytical or numerical. The present work aims to do a comparative analysis between the results presented by flow lines simulator and conventional finite differences simulator; both types of simulators are based on numerical methods designed to model light oil reservoirs subjected to water injection. Therefore, it was defined two reservoir models: the first one was a heterogeneous model whose petrophysical properties vary along the reservoir and the other one was created using average petrophysical properties obtained from the first model. Comparisons were done considering that the results of these two models were always in the same operational conditions. Then some rock and fluid parameters have been changed in both models and again the results were compared. From the factorial design, that was done to study the sensitivity analysis of reservoir parameters, a few cases were chosen to study the role of water injection rate and the vertical position of wells perforations in production forecast. It was observed that the results from the two simulators are quite similar in most of the cases; differences were found only in those cases where there was an increase in gas solubility ratio of the model. Thus, it was concluded that in flow simulation of reservoirs analogous of those now studied, mainly when the gas solubility ratio is low, the conventional finite differences simulator may be replaced by flow lines simulator the production forecast is compatible but the computational processing time is lower.

Development of Physics-based Models and Design Optimization of Power Electronic Conversion Systems

The main objective for physics based modeling of the power converter components is to design the whole converter with respect to physical and operational constraints. Therefore, all the elements and components of the energy conversion system are modeled numerically and combined together to achieve the whole system behavioral model. Previously proposed high frequency (HF) models of power converters are based on circuit models that are only related to the parasitic inner parameters of the power devices and the connections between the components. This dissertation aims to obtain appropriate physics-based models for power conversion systems, which not only can represent the steady state behavior of the components, but also can predict their high frequency characteristics. The developed physics-based model would represent the physical device with a high level of accuracy in predicting its operating condition. The proposed physics-based model enables us to accurately develop components such as; effective EMI filters, switching algorithms and circuit topologies [7]. One of the applications of the developed modeling technique is design of new sets of topologies for high-frequency, high efficiency converters for variable speed drives. The main advantage of the modeling method, presented in this dissertation, is the practical design of an inverter for high power applications with the ability to overcome the blocking voltage limitations of available power semiconductor devices. Another advantage is selection of the best matching topology with inherent reduction of switching losses which can be utilized to improve the overall efficiency. The physics-based modeling approach, in this dissertation, makes it possible to design any power electronic conversion system to meet electromagnetic standards and design constraints. This includes physical characteristics such as; decreasing the size and weight of the package, optimized interactions with the neighboring components and higher power density. In addition, the electromagnetic behaviors and signatures can be evaluated including the study of conducted and radiated EMI interactions in addition to the design of attenuation measures and enclosures.

The Influence of Healed Intrablock Rockmass Structure on the Behaviour of Deep Excavations in Complex Rockmasses

Conventional rockmass characterization and analysis methods for geotechnical assessment in mining, civil tunnelling, and other excavations consider only the intact rock properties and the discrete fractures that are present and form blocks within rockmasses. Field logging and classification protocols are based on historically useful but highly simplified design techniques, including direct empirical design and empirical strength assessment for simplified ground reaction and support analysis. As modern underground excavations go deeper and enter into more high stress environments with complex excavation geometries and associated stress paths, healed structures within initially intact rock blocks such as sedimentary nodule boundaries and hydrothermal veins, veinlets and stockwork (termed intrablock structure) are having an increasing influence on rockmass behaviour and should be included in modern geotechnical design. Due to the reliance on geotechnical classification methods which predate computer aided analysis, these complexities are ignored in conventional design. Given the comparatively complex, sophisticated and powerful numerical simulation and analysis techniques now practically available to the geotechnical engineer, this research is driven by the need for enhanced characterization of intrablock structure for application to numerical methods. Intrablock structure governs stress-driven behaviour at depth, gravity driven disintegration for large shallow spans, and controls ultimate fragmentation. This research addresses the characterization of intrablock structure and the understanding of its behaviour at laboratory testing and excavation scales, and presents new methodologies and tools to incorporate intrablock structure into geotechnical design practice. A new field characterization tool, the Composite Geological Strength Index, is used for outcrop or excavation face evaluation and provides direct input to continuum numerical models with implicit rockmass structure. A brittle overbreak estimation tool for complex rockmasses is developed using field observations. New methods to evaluate geometrical and mechanical properties of intrablock structure are developed. Finally, laboratory direct shear testing protocols for interblock structure are critically evaluated and extended to intrablock structure for the purpose of determining input parameters for numerical models with explicit structure.

Confirmação do modelo da estrutura 3D do vale inferior do Tejo a partir de dados de ruído sísmico ambiente

Ao longo de sua história a região do Vale Inferior do Tejo VIT foi abalada por vários sismos consideravelmente destrutivas, tendo alguns deles produzido significativas deformações nas estruturas marítimas localizadas no litoral a sudoeste do território Português; outros, moderados, foram produzidos por fontes locais, como os de 1344, 1531 e 1909. Nos últimos anos, devido à melhoria dos modelos de estrutura 3D e o desenvolvimento dos métodos numéricos, foram elaborados vários estudos de síntese de movimento forte do solo para a região do Baixo Tejo utilizando o método de diferenças finitas. Para confirmar o modelo de velocidades desta bacia usámos medidas de ruído sísmico, aplicámos um método baseado na razão espectral H/V, e, a partir destas curvas, por inversão, obtivemos um modelo de velocidades para a região estudada. Os resultados revelam uma boa concordância entre o modelo obtido e os dados geofísicos e geológicos recolhidos na mesma área._ ABSTRACT: Along his history the Lower Tagus Valley (LTV) area was shaken by several earthquakes. The largest reported had their origin in the southwestern part of Iberia. Other moderate earthquakes were produced by local sources such as the 1344, 1531 and the 1909. ln the last years, due to 3D structural model improvement and development in numerical methods, several studies have successful obtained strong-ground motion synthesis for the LVT region using finite difference method. To confirm the velocity model of the LTV sedimentary basin obtained by geophysical and geological data, we use broad-band microtremor measurements and application of the horizontal to vertical (H/V) spectral ratio method. We have obtained a velocity model for the studied region by inversion of the H/V curve. The results have good agreement geological and geophysical data.

Models for reliability estimation of HVDC cable systems

The work carried out in this thesis aims at: - studying – in both simulative and experimental methods – the effect of electrical transients (i.e., Voltage Polarity Reversals VPRs, Temporary OverVoltages TOVs, and Superimposed Switching Impulses SSIs) on the aging phenomena in HVDC extruded cable insulations. Dielectric spectroscopy, conductivity measurements, Fourier Transform Infra-Red FTIR spectroscopy, and space charge measurements show variation in the insulating properties of the aged Cross-Linked Polyethylene XLPE specimens compared to non-aged ones. Scission in XLPE bonds and formation of aging chemical bonds is also noticed in aged insulations due to possible oxidation reactions. The aged materials show more ability to accumulate space charges compared to non-aged ones. An increase in both DC electrical conductivity and imaginary permittivity has been also noticed. - The development of life-based geometric design of HVDC cables in a detailed parametric analysis of all parameters that affect the design. Furthermore, the effect of both electrical and thermal transients on the design is also investigated. - The intrinsic thermal instability in HVDC cables and the effect of insulation characteristics on the thermal stability using a temperature and field iterative loop (using numerical methods – Finite Difference Method FDM). The dielectric loss coefficient is also calculated for DC cables and found to be less than that in AC cables. This emphasizes that the intrinsic thermal instability is critical in HVDC cables. - Fitting electrical conductivity models to the experimental measurements using both models found in the literature and modified models to find the best fit by considering the synergistic effect between field and temperature coefficients of electrical conductivity.

Electrokinetic flow and transport in porous media : experimental methods, numerical analysis, and applications

Electrokinetic transport, electrochromatography, electroosmotic flow, electrophoresis, concentration polarization, fixed beds, monoliths, dynamic NMR microscopy, quantitative confocal laser scanning microscopy, mathematical modelling, numerical analysis

KAM: Automatic Planning and Interpretation of Numerical Experiments Using Geometrical Methods

KAM is a computer program that can automatically plan, monitor, and interpret numerical experiments with Hamiltonian systems with two degrees of freedom. The program has recently helped solve an open problem in hydrodynamics. Unlike other approaches to qualitative reasoning about physical system dynamics, KAM embodies a significant amount of knowledge about nonlinear dynamics. KAM's ability to control numerical experiments arises from the fact that it not only produces pictures for us to see, but also looks at (sic---in its mind's eye) the pictures it draws to guide its own actions. KAM is organized in three semantic levels: orbit recognition, phase space searching, and parameter space searching. Within each level spatial properties and relationships that are not explicitly represented in the initial representation are extracted by applying three operations ---(1) aggregation, (2) partition, and (3) classification--- iteratively.

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Two fast radiative transfer methods to improve the temporal sampling of clouds in numerical weather prediction and climate models

The high computational cost of calculating the radiative heating rates in numerical weather prediction (NWP) and climate models requires that calculations are made infrequently, leading to poor sampling of the fast-changing cloud field and a poor representation of the feedback that would occur. This paper presents two related schemes for improving the temporal sampling of the cloud field. Firstly, the ‘split time-stepping’ scheme takes advantage of the independent nature of the monochromatic calculations of the ‘correlated-k’ method to split the calculation into gaseous absorption terms that are highly dependent on changes in cloud (the optically thin terms) and those that are not (optically thick). The small number of optically thin terms can then be calculated more often to capture changes in the grey absorption and scattering associated with cloud droplets and ice crystals. Secondly, the ‘incremental time-stepping’ scheme uses a simple radiative transfer calculation using only one or two monochromatic calculations representing the optically thin part of the atmospheric spectrum. These are found to be sufficient to represent the heating rate increments caused by changes in the cloud field, which can then be added to the last full calculation of the radiation code. We test these schemes in an operational forecast model configuration and find a significant improvement is achieved, for a small computational cost, over the current scheme employed at the Met Office. The ‘incremental time-stepping’ scheme is recommended for operational use, along with a new scheme to correct the surface fluxes for the change in solar zenith angle between radiation calculations.

Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data

In this work, different methods to estimate the value of thin film residual stresses using instrumented indentation data were analyzed. This study considered procedures proposed in the literature, as well as a modification on one of these methods and a new approach based on the effect of residual stress on the value of hardness calculated via the Oliver and Pharr method. The analysis of these methods was centered on an axisymmetric two-dimensional finite element model, which was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. Simulations were conducted varying the level of film residual stress, film strain hardening exponent, film yield strength, and film Poisson's ratio. Different ratios of maximum penetration depth h(max) over film thickness t were also considered, including h/t = 0.04, for which the contribution of the substrate in the mechanical response of the system is not significant. Residual stresses were then calculated following the procedures mentioned above and compared with the values used as input in the numerical simulations. In general, results indicate the difference that each method provides with respect to the input values depends on the conditions studied. The method by Suresh and Giannakopoulos consistently overestimated the values when stresses were compressive. The method provided by Wang et al. has shown less dependence on h/t than the others.

Numerical and Analytical Methods for Laser-Plasma Acceleration Physics

Theories and numerical modeling are fundamental tools for understanding, optimizing and designing present and future laser-plasma accelerators (LPAs). Laser evolution and plasma wave excitation in a LPA driven by a weakly relativistically intense, short-pulse laser propagating in a preformed parabolic plasma channel, is studied analytically in 3D including the effects of pulse steepening and energy depletion. At higher laser intensities, the process of electron self-injection in the nonlinear bubble wake regime is studied by means of fully self-consistent Particle-in-Cell simulations. Considering a non-evolving laser driver propagating with a prescribed velocity, the geometrical properties of the non-evolving bubble wake are studied. For a range of parameters of interest for laser plasma acceleration, The dependence of the threshold for self-injection in the non-evolving wake on laser intensity and wake velocity is characterized. Due to the nonlinear and complex nature of the Physics involved, computationally challenging numerical simulations are required to model laser-plasma accelerators operating at relativistic laser intensities. The numerical and computational optimizations, that combined in the codes INF&RNO and INF&RNO/quasi-static give the possibility to accurately model multi-GeV laser wakefield acceleration stages with present supercomputing architectures, are discussed. The PIC code jasmine, capable of efficiently running laser-plasma simulations on Graphics Processing Units (GPUs) clusters, is presented. GPUs deliver exceptional performance to PIC codes, but the core algorithms had to be redesigned for satisfying the constraints imposed by the intrinsic parallelism of the architecture. The simulation campaigns, run with the code jasmine for modeling the recent LPA experiments with the INFN-FLAME and CNR-ILIL laser systems, are also presented.