Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 62

Search results for: Marco T. C. Faria

62 Finite Element Analysis of Oil-Lubricated Elliptical Journal Bearings

Authors: Marco T. C. Faria

Abstract:

Fixed-geometry hydrodynamic journal bearings are one of the best supporting systems for several applications of rotating machinery. Cylindrical journal bearings present excellent loadcarrying capacity and low manufacturing costs, but they are subjected to the oil-film instability at high speeds. An attempt of overcoming this instability problem has been the development of non-circular journal bearings. This work deals with an analysis of oil-lubricated elliptical journal bearings using the finite element method. Steadystate and dynamic performance characteristics of elliptical bearings are rendered by zeroth- and first-order lubrication equations obtained through a linearized perturbation method applied on the classical Reynolds equation. Four-node isoparametric rectangular finite elements are employed to model the bearing thin film flow. Curves of elliptical bearing load capacity and dynamic force coefficients are rendered at several operating conditions. The results presented in this work demonstrate the influence of the bearing ellipticity on its performance at different loading conditions.

Keywords: Elliptical journal bearings, non-circular journal bearings, hydrodynamic bearings, finite element method.

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61 Solitons and Universes with Acceleration Driven by Bulk Particles

Authors: A. C. Amaro de Faria Jr, A. M. Canone

Abstract:

Considering a scenario where our universe is taken as a 3d domain wall embedded in a 5d dimensional Minkowski space-time, we explore the existence of a richer class of solitonic solutions and their consequences for accelerating universes driven by collisions of bulk particle excitations with the walls. In particular it is shown that some of these solutions should play a fundamental role at the beginning of the expansion process. We present some of these solutions in cosmological scenarios that can be applied to models that describe the inflationary period of the Universe.

Keywords: Solitons, topological defects, Branes, kinks, accelerating universes in Brane scenarios.

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60 Stability Analysis of a Tricore

Authors: C. M. De Marco Muscat-Fenech, A.M. Grech La Rosa

Abstract:

The application of stability theory has led to detailed studies of different types of vessels; however, the shortage of information relating to multihull vessels demanded further investigation. This study shows that the position of the hulls has a very influential effect on both the transverse and longitudinal stability of the tricore. HSC stability code is applied for the optimisation of the hull configurations. Such optimization criteria would undoubtedly aid the performance of the vessel for both commercial or leisure purposes

Keywords: Stability, Multihull, Tricore

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59 Resistance Analysis for a Trimaran

Authors: C. M. De Marco Muscat-Fenech, A. M. Grech La Rosa

Abstract:

Although a lot of importance has been given to resistance analysis for various vessel types, explicit guidelines applied to multihull vessels have not been clearly defined.  The purpose of this investigation is to highlight the importance of the vessel’s layout in terms of three axes, the transverse (separation), the longitudinal (stagger) and the vertical (draught) with respect to resistance analysis. When a vessel has the potential to experience less resistance at a particular range of speeds a vast selection of opportunities are made available for both the commercial and leisure market.

Keywords: Multihull, Reistance, Trimaran.

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58 Radiation Effects in the PVDF/Graphene Oxide Nanocomposites

Authors: Juliana V. Pereira, Adriana S. M. Batista, Jefferson P. Nascimento, Clascídia A. Furtado, Luiz O. Faria

Abstract:

Exposure to ionizing radiation has been found to induce changes in poly(vinylidene fluoride) (PVDF) homopolymers. The high dose gamma irradiation process induces the formation of C=C and C=O bonds in its [CH2-CF2]n main chain. The irradiation also provokes crosslinking and chain scission. All these radio-induced defects lead to changes in the PVDF crystalline structure. As a consequence, it is common to observe a decrease in the melting temperature (TM) and melting latent heat (LM) and some changes in its ferroelectric features. We have investigated the possibility of preparing nanocomposites of PVDF with graphene oxide (GO) through the radio-induction of molecular bonds. In this work, we discuss how the gamma radiation interacts with the nanocomposite crystalline structure.

Keywords: Gamma irradiation, grapheme oxide, nanocomposites, PVDF.

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57 Dynamics In Production Processes

Authors: Marco Kennemann, Steffen C. Eickemeyer, Peter Nyhuis

Abstract:

An increasingly dynamic and complex environment poses huge challenges to production enterprises, especially with regards to logistics. The Logistic Operating Curve Theory, developed at the Institute of Production Systems and Logistics (IFA) of the Leibniz University of Hanover, is a recognized approach to describing logistic interactions, nevertheless, it reaches its limits when it comes to the dynamic aspects. In order to facilitate a timely and optimal Logistic Positioning a method is developed for quickly and reliably identifying dynamic processing states.

Keywords: Dynamics, Logistic Operating Curves, Production Logistics, Production Planning and Control

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56 A Numerical Study of the Interaction between Residual Stress Profiles Induced by Quasi-Static Plastification

Authors: G. F. Guimarães, A. R. de Faria, R. R. Rego, A. L. R. D’Oliveira

Abstract:

One of the most relevant phenomena in manufacturing is the residual stress state development through the manufacturing chain. In most cases, the residual stresses have their origin in the heterogenous plastification produced by the processes. Although a few manufacturing processes have been successfully approached by numerical modeling, there is still lack of understanding on how these processes' interactions will affect the final stress state. The objective of this work is to analyze the effect of the grinding procedure on the residual stress state generated by a quasi-static indentation. The model consists in a simplified approach of shot peening, modeling four cases with variations in indenter size and force. This model was validated through topography, measured by optical 3D focus-variation. The indentation model configured with two loads was then exposed to two grinding procedures and the result was analyzed. It was observed that the grinding procedure will have a significant effect on the stress state.

Keywords: plasticity, residual stress, finite element method, manufacturing

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55 A Retrospective of High-Lift Device Technology

Authors: Andrea Dal Monte, Marco Raciti Castelli, Ernesto Benini

Abstract:

The present paper deals with the most adopted technical solutions for the enhancement of the lift force of a wing. In fact, during several flight conditions (such as take off and landing), the lift force needs to be dramatically enhanced. Both trailing edge devices (such as flaps) and leading edge ones (such as slats) are described. Finally, the most advanced aerodynamic solutions to avoid the separation of the boundary layer from aircraft wings at high angles of attack are reviewed.

Keywords: High lift devices, Trailing Edge devices, Leading Edge devices, Boundary Layer Control devices

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54 Experimental Tests of a Vertical-Axis Wind Turbine with Twisted Blades

Authors: Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

Abstract:

An experimental campaign of measurements for a Darrieus vertical-axis wind turbine (VAWT) is presented for open field conditions. The turbine is characterized by a twisted bladed design, each blade being placed at a fixed distance from the rotational shaft. The experimental setup to perform the acquisitions is described. The results are lower than expected, due to the high influence of the wind shear.

Keywords: Vertical-axis wind turbine, Darrieus wind turbine, twisted blades, experimental measurements, wind shear.

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53 The Synthetic T2 Quality Control Chart and its Multi-Objective Optimization

Authors: Francisco Aparisi, Marco A. de Luna

Abstract:

In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.

Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.

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52 Dynamically Monitoring Production Methods for Identifying Structural Changes relevant to Logistics

Authors: Marco Kennemann, Steffen C. Eickemeyer, Peter Nyhuis

Abstract:

Due to the growing dynamic and complexity within the market environment production enterprises in particular are faced with new logistic challenges. Moreover, it is here in this dynamic environment that the Logistic Operating Curve Theory also reaches its limits as a method for describing the correlations between the logistic objectives. In order to convert this theory into a method for dynamically monitoring productions this paper will introduce methods for reliably and quickly identifying structural changes relevant to logistics.

Keywords: Dynamics, Logistic Operating Curves, Production Logistics, Production Planning and Control

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51 Numerical Analysis of the Influence of Tip Devices on the Power Coefficient of a VAWT

Authors: Federico Amato, Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

Abstract:

The aerodynamic performances of vertical axis wind turbines are highly affected by tip vortexes. In the present work, different tip devices are considered and simulated against a baseline rotor configuration, with the aim of identifying the best tip architecture. Three different configurations are tested: winglets, an elliptic termination and an aerodynamic bulkhead. A comparative analysis on the most promising architectures is conducted, focusing also on blade torque evolution during a full revolution of the rotor blade. The most promising technology is concluded to be a well designed winglet.

Keywords: Darrieus Wind Turbine, Tip Devices, Tip Vortexes, Winglet, Elliptic Termination, Aerodynamic Bulkhead

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50 Effect of Gamma Irradiation on the Crystalline Structure of Poly(Vinylidene Fluoride)

Authors: Adriana Souza M. Batista, Cláubia Pereira, Luiz O. Faria

Abstract:

The irradiation of polymeric materials has received much attention because it can produce diverse changes in chemical structure and physical properties. Thus, studying the chemical and structural changes of polymers is important in practice to achieve optimal conditions for the modification of polymers. The effect of gamma irradiation on the crystalline structure of poly(vinylidene fluoride) (PVDF) has been investigated using differential scanning calorimetry (DSC) and X-ray diffraction techniques (XRD). Gamma irradiation was carried out in atmosphere air with doses between 100 kGy at 3,000 kGy with a Co-60 source. In the melting thermogram of the samples irradiated can be seen a bimodal melting endotherm is detected with two melting temperature. The lower melting temperature is attributed to melting of crystals originally present and the higher melting peak due to melting of crystals reorganized upon heat treatment. These results are consistent with those obtained by XRD technique showing increasing crystallinity with increasing irradiation dose, although the melting latent heat is decreasing.

Keywords: Differential scanning calorimetry, gamma irradiation, PVDF, X-ray diffraction technique.

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49 Microclimate Variations in Rio de Janeiro Related to Massive Public Transportation

Authors: Marco E. O. Jardim, Frederico A. M. Souza, Valeria M. Bastos, Myrian C. A. Costa, Nelson F. F. Ebecken

Abstract:

Urban public transportation in Rio de Janeiro is based on bus lines, powered by diesel, and four limited metro lines that support only some neighborhoods. This work presents an infrastructure built to better understand microclimate variations related to massive urban transportation in some specific areas of the city. The use of sensor nodes with small analytics capacity provides environmental information to population or public services. The analyses of data collected from a few small sensors positioned near some heavy traffic streets show the harmful impact due to poor bus route plan.

Keywords: Big data, IoT, public transportation, public health system.

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48 Design and Social Innovation: A Systemic Approach

Authors: Marco Ogê Muniz, Luiz Fernando Gonçalves De Figueiredo

Abstract:

Design, as an area of knowledge, is subject to changes that affect it through different approaches, both theoretical and practical; its include matters related with responsibility, environment, social worries, and things alike. Commensurately, such contemporary aspects open room for social initiatives. This scenario begins to be looked at, especially in creative communities. Such proposal for a systemic approach of design is seen as a way to involve the stakeholders in the processes of investigation and of social innovation, which can decisively contribute for the development of traditional local communities. As a theoretical basis for the research, this paper outlines some especial features of design and social innovation, in their particular and in their complementary aspects, as well as in the way they relate with each other.

Keywords: Responsible design, social innovation, creative community, systemic approach, network.

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47 Characterization of Gamma Irradiated PVDF and PVDF/Graphene Oxide Composites by Spectroscopic Techniques

Authors: Juliana V. Pereira, Adriana S. M. Batista, Jefferson P. Nascimento, Clascídia A. Furtado, Luiz O. Faria

Abstract:

The combination of the properties of graphene oxide (OG) and PVDF homopolymer makes their combined composite materials as multifunctional systems with great potential. Knowledge of the molecular structure is essential for better use. In this work, the degradation of PVDF polymer exposed to gamma irradiation in oxygen atmosphere in high dose rate has been studied and compared to degradation of PVDF/OG composites. The samples were irradiated with a Co-60 source at constant dose rate, with doses ranging from 100 kGy to 1,000 kGy. In FTIR data shown that the formation of oxidation products was at the both samples with formation of carbonyl and hydroxyl groups amongst the most prevalent products in the pure PVDF samples. In the other hand, the composites samples exhibit less presence of degradation products with predominant formation of carbonyl groups, these results also seen in the UV-Vis analysis. The results show that the samples of composites may have greater resistance to the irradiation process, since they have less degradation products than pure PVDF samples seen by spectroscopic techniques.

Keywords: Gamma irradiation, PVDF, PVDF/OG composites, spectroscopic techniques.

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46 Enabling Integration across Heterogeneous Care Networks

Authors: Federico Cabitza, Marco P. Locatelli, Marcello Sarini, Carla Simone

Abstract:

The paper shows how the CASMAS modeling language, and its associated pervasive computing architecture, can be used to facilitate continuity of care by providing members of patientcentered communities of care with a support to cooperation and knowledge sharing through the usage of electronic documents and digital devices. We consider a scenario of clearly fragmented care to show how proper mechanisms can be defined to facilitate a better integration of practices and information across heterogeneous care networks. The scenario is declined in terms of architectural components and cooperation-oriented mechanisms that make the support reactive to the evolution of the context where these communities operate.

Keywords: Pervasive Computing, Communities of Care, HeterogeneousCare Networks, Multi-Agent System.

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45 Two Spatial Experiments based on Computational Geometry

Authors: Marco Hemmerling

Abstract:

The paper outlines the relevance of computational geometry within the design and production process of architecture. Based on two case studies, the digital chain - from the initial formfinding to the final realization of spatial concepts - is discussed in relation to geometric principles. The association with the fascinating complexity that can be found in nature and its underlying geometry was the starting point for both projects presented in the paper. The translation of abstract geometric principles into a three-dimensional digital design model – realized in Rhinoceros – was followed by a process of transformation and optimization of the initial shape that integrated aesthetic, spatial and structural qualities as well as aspects of material properties and conditions of production.

Keywords: Architecture, Computer Aided Architectural Design, 3D-Modeling, Rapid Prototyping, CAD/CAM.

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44 The Problem of Using the Calculation of the Critical Path to Solver Instances of the Job Shop Scheduling Problem

Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

Abstract:

A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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43 A Retrospective of Wind Turbine Architectural Integration in the Built Environment

Authors: Stefano Degrassi, Marco Raciti Castelli, Ernesto Benini

Abstract:

Since the European renewable energy directives set the target for 22.1% of electricity generation to be supplied by 2010 [1], there has been increased interest in using green technologies also within the urban enviroment. The most commonly considered installations are solar thermal and solar photovoltaics. Nevertheless, as observed by Bahaj et al. [2], small scale turbines can reduce the built enviroment related CO2 emissions. Thus, in the last few years, an increasing number of manufacturers have developed small wind turbines specifically designed for the built enviroment. The present work focuses on the integration into architectural systems of such installations and presents a survey of successful case studies.

Keywords: Wind turbines, architectural integration, wind resources, urban areas, built enviroment, renewable technologies.

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42 Gesture Recognition by Data Fusion of Time-of-Flight and Color Cameras

Authors: Piercarlo Dondi, Luca Lombardi, Marco Porta

Abstract:

In the last years numerous applications of Human- Computer Interaction have exploited the capabilities of Time-of- Flight cameras for achieving more and more comfortable and precise interactions. In particular, gesture recognition is one of the most active fields. This work presents a new method for interacting with a virtual object in a 3D space. Our approach is based on the fusion of depth data, supplied by a ToF camera, with color information, supplied by a HD webcam. The hand detection procedure does not require any learning phase and is able to concurrently manage gestures of two hands. The system is robust to the presence in the scene of other objects or people, thanks to the use of the Kalman filter for maintaining the tracking of the hands.

Keywords: Gesture recognition, human-computer interaction, Time-of-Flight camera.

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41 Application of the Data Distribution Service for Flexible Manufacturing Automation

Authors: Marco Ryll, Svetan Ratchev

Abstract:

This paper discusses the applicability of the Data Distribution Service (DDS) for the development of automated and modular manufacturing systems which require a flexible and robust communication infrastructure. DDS is an emergent standard for datacentric publish/subscribe middleware systems that provides an infrastructure for platform-independent many-to-many communication. It particularly addresses the needs of real-time systems that require deterministic data transfer, have low memory footprints and high robustness requirements. After an overview of the standard, several aspects of DDS are related to current challenges for the development of modern manufacturing systems with distributed architectures. Finally, an example application is presented based on a modular active fixturing system to illustrate the described aspects.

Keywords: Flexible Manufacturing, Publish/Subscribe, Plug & Produce.

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40 Preliminary Studies of MWCNT/PVDF Polymer Composites

Authors: Esther Lorrayne M. Pereira, Adriana Souza M. Batista, Fabíola A. S. Ribeiro, Adelina P. Santos, Clascídia A. Furtado, Luiz O. Faria

Abstract:

The combination of multi–walled carbon nanotubes (MWCNTs) with polymers offers an attractive route to reinforce the macromolecular compounds as well as the introduction of new properties based on morphological modifications or electronic interactions between the two constituents. As they are only a few nanometers in dimension, it offers ultra-large interfacial area per volume between the nano-element and polymer matrix. Nevertheless, the use of MWCNTs as a rough material in different applications has been largely limited by their poor processability, insolubility, and infusibility. Studies concerning the nanofiller reinforced polymer composites are justified in an attempt to overcome these limitations. This work presents one preliminary study of MWCNTs dispersion into the PVDF homopolymer. For preparation, the composite components were diluted in n,n-dimethylacetamide (DMAc) with mechanical agitation assistance. After complete dilution, followed by slow evaporation of the solvent at 60°C, the samples were dried. Films of about 80 μm were obtained. FTIR and UV-Vis spectroscopic techniques were used to characterize the nanocomposites. The appearance of absorption bands in the FTIR spectra of nanofilled samples, when compared to the spectrum of pristine PVDF samples, are discussed and compared with the UV-Vis measurements.

Keywords: Composites materials, FTIR, MWNTs, PVDF, UVVis.

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39 Numerical Evaluation of the Contribution of Inertial and Aerodynamic Forces on VAWT Blade Loading

Authors: Marco Raciti Castelli, Stefano De Betta, Ernesto Benini

Abstract:

A two-dimensional numerical simulation of the contribution of both inertial and aerodynamic forces on the blade loads of a Vertical-Axis Wind Turbine (VAWT) is presented. After describing the computational model and the relative validation procedure, a complete campaign of simulations - based on full RANS unsteady calculations - is proposed for a three-bladed rotor architecture characterized by a NACA 0021 airfoil. For each analyzed angular velocity, the combined effect of pressure and viscous forces acting on every rotor blade are compared to the corresponding centrifugal forces, due to the revolution of the turbine, thus achieving a preliminary estimation of the correlation between overall rotor efficiency and structural blade loads.

Keywords: CFD, VAWT, NACA 0021, aerodynamic forces, inertial loadings.

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38 Unit Testing with Déjà-Vu Objects

Authors: Sharareh Afsharian, Andrea Bei, Marco Bianchi

Abstract:

In this paper we introduce a new unit test technique called déjà-vu object. Déjà-vu objects replace real objects used by classes under test, allowing the execution of isolated unit tests. A déjà-vu object is able to observe and record the behaviour of a real object during real sessions, and to replace it during unit tests, returning previously recorded results. Consequently déjà-vu object technique can be useful when a bottom-up development and testing strategy is adopted. In this case déjà-vu objects can increase test portability and test source code readability. At the same time they can reduce the time spent by programmers to develop test code and the risk of incompatibility during the switching between déjà-vu and production code.

Keywords: Bottom-up testing approach, integration test, testportability, unit test.

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37 Coupling Concept of two Parallel Research Codes for Two and Three Dimensional Fluid Structure Interaction Analysis

Authors: Luciano Garelli, Marco Schauer, Jorge D’Elia, Mario A. Storti, Sabine C. Langer

Abstract:

This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM a software developed at Centro de Investigaci´on de M´etodos Computacionales –CIMEC. The structural part of the coupled process is computed by the research code elementary Parallel Solver – (ELPASO) of the Technische Universit¨at Braunschweig, Institut f¨ur Konstruktionstechnik (IK).

Keywords: Computational Fluid Dynamics (CFD), Fluid Structure Interaction (FSI), Finite Element Method (FEM).

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36 Simulation of Low Cycle Fatigue Behaviour of Nickel-Based Alloy at Elevated Temperatures

Authors: Harish Ramesh Babu, Marco Böcker, Mario Raddatz, Sebastian Henkel, Horst Biermann, Uwe Gampe

Abstract:

Thermal power machines are subjected to cyclic loading conditions under elevated temperatures. At these extreme conditions, the durability of the components has a significant influence. The material mechanical behaviour has to be known in detail for a failsafe construction. For this study a nickel-based alloy is considered, the deformation and fatigue behaviour of the material is analysed under cyclic loading. A viscoplastic model is used for calculating the deformation behaviour as well as to simulate the rate-dependent and cyclic plasticity effects. Finally, the cyclic deformation results of the finite element simulations are compared with low cycle fatigue (LCF) experiments.

Keywords: Complex low cycle fatigue, elevated temperatures, IN718, viscoplastic.

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35 Numerical Simulation of the Flow Field around a Vertical Flat Plate of Infinite Extent

Authors: Marco Raciti Castelli, Paolo Cioppa, Ernesto Benini

Abstract:

This paper presents a CFD analysis of the flow field around a thin flat plate of infinite span inclined at 90° to a fluid stream of infinite extent. Numerical predictions have been compared to experimental measurements, in order to assess the potential of the finite volume code of determining the aerodynamic forces acting on a bluff body invested by a fluid stream of infinite extent. Several turbulence models and spatial node distributions have been tested. Flow field characteristics in the neighborhood of the flat plate have been investigated, allowing the development of a preliminary procedure to be used as guidance in selecting the appropriate grid configuration and the corresponding turbulence model for the prediction of the flow field over a two-dimensional vertical flat plate.

Keywords: CFD, vertical flat plate, aerodynamic force

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34 Comparison between Lift and Drag-Driven VAWT Concepts on Low-Wind Site AEO

Authors: Marco Raciti Castelli, Ernesto Benini

Abstract:

This work presents a comparison between the Annual Energy Output (AEO) of two commercial vertical-axis wind turbines (VAWTs) for a low-wind urban site: both a drag-driven and a liftdriven concepts are examined in order to be installed on top of the new Via dei Giustinelli building, Trieste (Italy). The power-curves, taken from the product specification sheets, have been matched to the wind characteristics of the selected installation site. The influence of rotor swept area and rated power on the performance of the two proposed wind turbines have been examined in detail, achieving a correlation between rotor swept area, electrical generator size and wind distribution, to be used as a guideline for the calculation of the AEO.

Keywords: Annual Energy Output, micro-generationtechnology, urban environment, Vertical-Axis Wind Turbine

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33 Collective Oscillations in a Magnetized Plasma Subjected to a Radiation Field

Authors: Daniel Santos, Bruno Ribeiro, Marco Amato, Antonio Fonseca

Abstract:

In this paper we discuss the behaviour of the longitudinal modes of a magnetized non collisional plasma subjected to an external electromagnetic field. We apply a semiclassical formalism, with the electrons being studied in a quantum mechanical viewpoint whereas the electromagnetic field in the classical context. We calculate the dielectric function in order to obtains the modes and found that, unlike the Bernstein modes, the presence of radiation induces oscillations around the cyclotron harmonics, which are smoothed as the energy stored in the radiation field becomes small compared to the thermal energy of the electrons. We analyze the influence of the number of photon involved in the electronic transitions between the Landau levels and how the parameters such as the external fields strength, plasma density and temperature affect the dispersion relation

Keywords: Collective oscillations, External fields, Dispersion relation.

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