Search results for: tidal stream turbines.

Authors: Christos Meletis, Paul Bougas, George Economakos , Paraskevas Kalivas, Kiamal Pekmestzi

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In this paper, we propose a new architecture for the implementation of the N-point Fast Fourier Transform (FFT), based on the Radix-2 Decimation in Frequency algorithm. This architecture is based on a pipeline circuit that can process a stream of samples and produce two FFT transform samples every clock cycle. Compared to existing implementations the architecture proposed achieves double processing speed using the same circuit complexity.

Keywords: Digital signal processing, systolic circuits, FFTalgorithm.

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Authors: Abdurrahim Bolukbasi, Hassan Athari, Dogan Ciloglu

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The modeling lung respiratory system that has complex anatomy and biophysics presents several challenges including tissue-driven flow patterns and wall motion. Also, the pulmonary lung system because of that they stretch and recoil with each breath, has not static walls and structures. The direct relationship between air flow and tissue motion in the lung structures naturally prefers an FSI simulation technique. Therefore, in order to toward the realistic simulation of pulmonary breathing mechanics the development of a coupled FSI computational model is an important step. A simple but physiologically relevant three-dimensional deep long geometry is designed and fluid-structure interaction (FSI) coupling technique is utilized for simulating the deformation of the lung parenchyma tissue that produces airflow fields. The real understanding of respiratory tissue system as a complex phenomenon have been investigated with respect to respiratory patterns, fluid dynamics and tissue viscoelasticity and tidal breathing period. 

Keywords: Lung deformation and mechanics, tissue mechanics, viscoelasticity, fluid-structure interactions, ANSYS.

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Authors: Abubakar Rashid, Muhammad Saad, Faheem Ahmed

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This paper provides a comprehensive study pertaining to diagnosis of intermittent high vibrations on an industrial gas turbine using detailed vibrations analysis, followed by its rectification. Engro Polymer & Chemicals Limited, a Chlor-Vinyl complex located in Pakistan has a captive combined cycle power plant having two 28 MW gas turbines (make Hitachi) & one 15 MW steam turbine. In 2018, the organization faced an issue of high vibrations on one of the gas turbines. These high vibration peaks appeared intermittently on both compressor’s drive end (DE) & turbine’s non-drive end (NDE) bearing. The amplitude of high vibration peaks was between 150-170% on the DE bearing & 200-300% on the NDE bearing from baseline values. In one of these episodes, the gas turbine got tripped on “High Vibrations Trip” logic actuated at 155µm. Limited instrumentation is available on the machine, which is monitored with GE Bently Nevada 3300 system having two proximity probes installed at Turbine NDE, Compressor DE &at Generator DE & NDE bearings. Machine’s transient ramp-up & steady state data was collected using ADRE SXP & DSPI 408. Since only 01 key phasor is installed at Turbine high speed shaft, a derived drive key phasor was configured in ADRE to obtain low speed shaft rpm required for data analysis. By analyzing the Bode plots, Shaft center line plot, Polar plot & orbit plots; rubbing was evident on Turbine’s NDE along with increased bearing clearance of Turbine’s NDE radial bearing. The subject bearing was then inspected & heavy deposition of carbonized coke was found on the labyrinth seals of bearing housing with clear rubbing marks on shaft & housing covering at 20-25 degrees on the inner radius of labyrinth seals. The collected coke sample was tested in laboratory & found to be the residue of lube oil in the bearing housing. After detailed inspection & cleaning of shaft journal area & bearing housing, new radial bearing was installed. Before assembling the bearing housing, cleaning of bearing cooling & sealing air lines was also carried out as inadequate flow of cooling & sealing air can accelerate coke formation in bearing housing. The machine was then taken back online & data was collected again using ADRE SXP & DSPI 408 for health analysis. The vibrations were found in acceptable zone as per ISO standard 7919-3 while all other parameters were also within vendor defined range. As a learning from subject case, revised operating & maintenance regime has also been proposed to enhance machine’s reliability.

Keywords: ADRE, bearing, gas turbine, GE Bently Nevada, Hitachi, vibration.

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Authors: H. Bevrani, A. G. Tikdari, T. Hiyama

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Optimal load shedding (LS) design as an emergency plan is one of the main control challenges posed by emerging new uncertainties and numerous distributed generators including renewable energy sources in a modern power system. This paper presents an overview of the key issues and new challenges on optimal LS synthesis concerning the integration of wind turbine units into the power systems. Following a brief survey on the existing LS methods, the impact of power fluctuation produced by wind powers on system frequency and voltage performance is presented. The most LS schemas proposed so far used voltage or frequency parameter via under-frequency or under-voltage LS schemes. Here, the necessity of considering both voltage and frequency indices to achieve a more effective and comprehensive LS strategy is emphasized. Then it is clarified that this problem will be more dominated in the presence of wind turbines.

Keywords: Load shedding, emergency control, voltage, frequency, wind turbine.

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Authors: H. Kiani, S. Moradi, B. Soltani Soulgani, S. Mousavian

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Desalting/dehydration plants (DDP) are often installed in crude oil production units in order to remove water-soluble salts from an oil stream. In order to optimize this process, desalting unit should be modeled. In this research, artificial neural network is used to model efficiency of desalting unit as a function of input parameter. The result of this research shows that the mentioned model has good agreement with experimental data.

Keywords: Desalting unit, Crude oil, Neural Networks, Simulation, Recovery, Separation.

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Authors: Yusuf Yasa, Erkan Mese

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This paper investigates the thermal issue of permanent magnet synchronous generator which is frequently used in direct drive gearless small-scale wind turbine applications. Permanent Magnet Synchronous Generator (PMSG) is designed with 2.5 kW continuous and 6 kW peak power. Then considering generator geometry, mechanical design of wind turbine is performed. Thermal analysis and optimization is carried out considering all wind turbine components to reach realistic results. This issue is extremely important in research and development (R&D) process for wind turbine applications.

Keywords: Direct drive, gearless wind turbine, permanent magnet synchronous generator (PMSG), small-scale wind turbine, thermal management.

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Authors: Sebastien Harasse, Laurent Bonnaud, Michel Desvignes

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Counting people from a video stream in a noisy environment is a challenging task. This project aims at developing a counting system for transport vehicles, integrated in a video surveillance product. This article presents a method for the detection and tracking of multiple faces in a video by using a model of first and second order local moments. An iterative process is used to estimate the position and shape of multiple faces in images, and to track them. the trajectories are then processed to count people entering and leaving the vehicle.

Keywords: face detection, tracking, counting, local statistics

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Authors: U. Bawa

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Macro invertebrates have been used to monitor organic pollution in rivers and streams. Several biotic indices based on macro invertebrates have been developed over the years including the Biological Monitoring Working Party (BMWP). A new biotic index, the Gammarus:Asellus ratio has been recently proposed as an index of organic pollution. This study tested the validity of the Gammarus:Asellus ratio as an index of organic pollution, by examining the relationship between the Gammarus:Asellus ratio and physical chemical parameters, and other biotic indices such as BMWP and, Average Score Per Taxon (ASPT) from lakes and streams at Markeaton Park, Allestree Park and Kedleston Hall, Derbyshire. Macro invertebrates were sampled using the standard five minute kick sampling techniques physical and chemical environmental variables were obtained based on standard sampling techniques. Eighteen sites were sampled, six sites from Markeaton Park (three sites across the stream and three sites across the lake). Six sites each were also sampled from Allestree Park and Kedleston Hall lakes. The Gammarus:Asellus ratio showed an opposite significant positive correlations with parameters indicative of organic pollution such as the level of nitrates, phosphates, and calcium and also revealed a negatively significant correlations with other biotic indices (BMWP/ASPT). The BMWP score correlated positively significantly with some water quality parameters such as dissolved oxygen and flow rate, but revealed no correlations with other chemical environmental variables. The BMWP score was significantly higher in the stream than the lake in Markeaton Park, also The ASPT scores appear to be significantly higher in the upper Lakes than the middle and lower lakes. This study has further strengthened the use of BMWP/ASPT score as an index of organic pollution. But additional application is required to validate the use of Gammarus:Asellus as a rapid bio monitoring tool.

Keywords: Asellus, Biotic index, Gammarus, Organic pollution, Macro invertebrate.

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Authors: Mostafa A. Elshahed, Magdy M. Elmarsfawy, Hussain M. Zain Eldain

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In this paper, a Dynamic Economic Dispatch (DED) model is developed for the system consisting of both thermal generators and wind turbines. The inclusion of a significant amount of wind energy into power systems has resulted in additional constraints on DED to accommodate the intermittent nature of the output. The probability of stochastic wind power based on the Weibull probability density function is included in the model as a constraint; A Here-and-Now Approach. The Environmental Protection Agency-s hourly emission target, which gives the maximum emission during the day, is used as a constraint to reduce the atmospheric pollution. A 69-bus test system with non-smooth cost function is used to illustrate the effectiveness of the proposed model compared with static economic dispatch model with including the wind power.

Keywords: Dynamic Economic Dispatch, StochasticOptimization, Weibull Distribution, Wind Power

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Authors: Vitaliy Tayanov

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In this paper we present the algorithm which allows us to have an object tracking close to real time in Full HD videos. The frame rate (FR) of a video stream is considered to be between 5 and 30 frames per second. The real time track building will be achieved if the algorithm can follow 5 or more frames per second. The principle idea is to use fast algorithms when doing preprocessing to obtain the key points and track them after. The procedure of matching points during assignment is hardly dependent on the number of points. Because of this we have to limit pointed number of points using the most informative of them.

Keywords: video tracking, real-time, Hungarian algorithm, Full HD video.

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Authors: V. Karri, W. K. Yap, J. Titchen

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A renewable energy system discussed in this paper is a stand-alone wind-hydrogen system for a remote island in Australia. The analysis of an existing wind-diesel power system was performed. Simulation technique was used to model the power system currently employed on the island, and simulated different configurations of additional hydrogen energy system. This study aims to determine the suitable hydrogen integrated configuration to setting up the prototype system for the island, which helps to reduce the diesel consumption on the island. A set of configurations for the hydrogen system and associated parameters that consists of wind turbines, electrolysers, hydrogen internal combustion engines, and storage tanks has been purposed. The simulation analyses various configurations that perfectly balances the system to meet the demand on the island.

Keywords: Hydrogen power systems, hydrogen internal combustion engine, modeling and simulation of hydrogen power systems.

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Authors: Anmin Zhao, Weiyong Yingı , Haitao Zhang, Hongfang Ma, Dingye Fang

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The Ni/α-Al2O3 catalysts with different amounts of La as promoter from 0 to 4 wt % were prepared, characterized and their catalytic activity was investigated in syngas methanation reaction. Effects of reaction temperature and lanthanum loading on carbon oxides conversion and methane selectivity were also studied. Adding certain amount of lanthanum to 10Ni /α-Al2O3 catalysts can decrease the average NiO crystallite diameter which leads to higher activity and stability while excessive addition would cause deactivation quickly. Stability on stream towards deactivation was observed up to 800 min at 500 °C, 0.1MPa and 600000 mL·g-1·h-1.

Keywords: Methanation; Nickel catalysts; Syngas methanation

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Authors: Hicham Serhoud, Djilani Benattous

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In this paper present a sensorless maximum wind power extraction for variable speed constant frequency (VSCF) wind power generation systems with a doubly-fed induction generators (DFIG), to ensure stability and to impose the ideal feedback control solution despite of model uncertainties , using the principles of an active and reactive power controller (DPC) a robust sliding mode power control has been proposed to guarantees fast response times and precise control actions for control the active and reactive power independently. The simulation results in MATLAB/Simulink platform confirmed the good dynamic performance of power control approach for DFIGbased variable speed wind turbines.

Keywords: Doubly fed induction generator , sliding modecontrol, maximal wind energy capture, MRAS estimator

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Authors: Basudev Ghosh, Sailendranath Paul, Sreyasi Banerjee

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Using quantum hydrodynamical (QHD) model the linear dispersion relation for the electron plasma waves propagating in a cylindrical waveguide filled with a dense plasma containing streaming electron, hole and stationary charged dust particles has been derived. It is shown that the effect of finite boundary and stream velocity of electrons and holes make some of the possible modes of propagation linearly unstable. The growth rate of this instability is shown to depend significantly on different plasma parameters.

Keywords: Electron Plasma wave, Quantum plasma, Quantum Hydrodynamical model.

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Authors: Jun Liu, Feihang Zhou, Gungyi Wang

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This paper expounds on the direct-driven PMSG wind power system control strategy, and analyses the stability conditions of the system. The direct-driven PMSG wind power system may generate the intense mechanical vibration, when wind speed changes dramatically. This paper proposes a new type of torque control strategy, which increases the system damping effectively, mitigates mechanical vibration of the system, and enhances the stability conditions of the system. The simulation results verify the reliability of the new torque control strategy.

Keywords: Damping, direct-driven PMSG wind power system, mechanical vibration, torque control.

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Authors: Xuguang Leng

Abstract:

The theory of tectonic plate asteroid driver provides that comet and asteroid collisions have ample energy to fracture, move, and deform tectonic plate. The enormous kinetic energy of an asteroid collision is dissipated through the fracture and violent movement of the tectonic plates, and stored in the plate deformations. The stored energy will be released in the future through plate slow movement. The reflection of plate edge upwards upon collision impact causes the plate to sit on top of adjacent plate and creates the subduction plate. Higher probability and higher energy of asteroid collision in the equator area provides the net energy to drive heavier land plates to higher latitudes, offsetting the tidal and self spin forces, creating a more random land plates distribution. The trend of asteroid collisions is less frequency and intensity as loose objects are merging into the planets and Jupiter is taking ever larger shares of collisions. As overall energy input from asteroid collision decreases, plate movement is slowing down and eventually land plates will congregate towards equator area. The current trajectory of plate movements is the cumulative effect of past asteroid collisions, and can be altered, new plates be created, by future collisions.

Keywords: Tectonic plate, Earth, asteroid, comet.

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Authors: Ruili Zhou, Yuesheng Zhu

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In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.

Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM

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Authors: Dehghan Manshadi M., Mirzaei M., Soltani M. R., Ghorbanian K.

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Subsonic wind tunnel experiments were conducted to study the effect of tripped boundary layer on the pressure distribution in the contraction region of the tunnel. Measurements were performed by installing trip strip at two different positions in the concave portion of the contraction. The results show that installation of the trip strips, have significant effects on both turbulence and pressure distribution. The reduction in the free stream turbulence and reduction of the wall static pressure distribution deferred signified with the location of the trip strip.

Keywords: Contraction, pressure distribution, trip strip, turbulence intensity.

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Authors: V. Thamizh Arasan, G. Dhivya

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Traffic Density provides an indication of the level of service being provided to the road users. Hence, there is a need to study the traffic flow characteristics with specific reference to density in detail. When the length and speed of the vehicles in a traffic stream vary significantly, the concept of occupancy, rather than density, is more appropriate to describe traffic concentration. When the concept of occupancy is applied to heterogeneous traffic condition, it is necessary to consider the area of the road space and the area of the vehicles as the bases. Hence, a new concept named, 'area-occupancy' is proposed here. It has been found that the estimated area-occupancy gives consistent values irrespective of change in traffic composition.

Keywords: Density Measurement, Heterogeneity, Occupancy, Traffic Flow.

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Authors: L. Hermanns, M.A. Santoyo, L. E. Quirós, J. Vega, J. M. Gaspar-Escribano, B. Benito

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We study the dynamic response of a wind turbine structure subjected to theoretical seismic motions, taking into account the rotational component of ground shaking. Models are generated for a shallow moderate crustal earthquake in the Madrid Region (Spain). Synthetic translational and rotational time histories are computed using the Discrete Wavenumber Method, assuming a point source and a horizontal layered earth structure. These are used to analyze the dynamic response of a wind turbine, represented by a simple finite element model. Von Mises stress values at different heights of the tower are used to study the dynamical structural response to a set of synthetic ground motion time histories

Keywords: Synthetic seismograms, rotations, wind turbine, dynamic structural response

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Authors: Fulya Zaralı, Harun Resit Yazgan

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Logistics centers represent areas that all national and international logistics and activities related to logistics can be implemented by the various businesses. Logistics centers have a key importance in joining the transport stream and the transport system operations. Therefore, it is important where these centers are positioned to be effective and efficient and to show the expected performance of the centers. In this study, the location selection problem to position the logistics center is discussed. Alternative centers are evaluated according certain criteria. The most appropriate center is identified using the axiomatic design method.

Keywords: Logistic center, axiomatic design, facility location, information systems.

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Authors: A. M. Tahsini

Abstract:

Supersonic hydrogen-air cylindrical mixing layer is numerically analyzed to investigate the effect of inlet swirl on ignition time delay in scramjets. Combustion is treated using detail chemical kinetics. One-equation turbulence model of Spalart and Allmaras is chosen to study the problem and advection upstream splitting method is used as computational scheme. The results show that swirling both fuel and oxidizer streams may drastically decrease the ignition distance in supersonic combustion, unlike using the swirl just in fuel stream which has no helpful effect.

Keywords: Ignition delay, Supersonic combustion, Swirl, Numerical simulation, Turbulence.

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Authors: Jesús M. Martín, Francisco Corona, Dolores Hidalgo

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Landfills present long-term threats to soil, air, groundwater and surface water due to the formation of greenhouse gases (methane gas and carbon dioxide) and leachate from decomposing garbage. The composition of leachate differs from site to site and also within the landfill. The leachates alter with time (from weeks to years) since the landfilled waste is biologically highly active and their composition varies. Mainly, the composition of the leachate depends on factors such as characteristics of the waste, the moisture content, climatic conditions, degree of compaction and the age of the landfill. Therefore, the leachate composition cannot be generalized and the traditional treatment models should be adapted in each case. Although leachate composition is highly variable, what different leachates have in common is hazardous constituents and their potential eco-toxicological effects on human health and on terrestrial ecosystems. Since leachate has distinct compositions, each landfill or dumping site would represent a different type of risk on its environment. Nevertheless, leachates consist always of high organic concentration, conductivity, heavy metals and ammonia nitrogen. Leachate could affect the current and future quality of water bodies due to uncontrolled infiltrations. Therefore, control and treatment of leachate is one of the biggest issues in urban solid waste treatment plants and landfills design and management. This work presents a treatment model that will be carried out "in-situ" using a cost-effective novel technology that combines solar evaporation/condensation plus forward osmosis. The plant is powered by renewable energies (solar energy, biomass and residual heat), which will minimize the carbon footprint of the process. The final effluent quality is very high, allowing reuse (preferred) or discharge into watercourses. In the particular case of this work, the final effluents will be reused for cleaning and gardening purposes. A minority semi-solid residual stream is also generated in the process. Due to its special composition (rich in metals and inorganic elements), this stream will be valorized in ceramic industries to improve the final products characteristics.

Keywords: Forward osmosis, landfills, leachate valorization, solar evaporation.

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Authors: Muhammad Naveed, Richard Stechow, Sebastian Bolz, Katharina Hobusch, Sabine Weiß

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Solid particle erosion has been identified as a critical wear phenomenon which takes place during operation of aeroengines in dusty environment. The present work discusses the erosion behavior of Ti-44.5Al-6.25Nb-0.8Mo-0.1B alloy (TNB-V4) which finds its application in low pressure gas turbines and can be used for high pressure compressors too. Prior to the erosion tests, the alloy was heat treated to improve the mechanical properties. Afterwards, specimens were eroded at impact angles of 30° and 90° at room and high temperatures (100 °C-400 °C). Volume loss and erosion behavior are studied through gravimetric analysis, whereas erosion mechanisms are characterized through scanning electron microscopy. The results indicate a clear difference in the erosion mechanism for different impact angles. The influence of the test temperature on the erosion behavior of the alloy is also discussed in the present contribution.

Keywords: Solid particle erosion, gamma TiAl, TNB-V4, high temperature erosion.

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Authors: Sharul S. Dol, U. Azimov, Robert J. Martinuzzi

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Turbulence studies were made in the wake of a rotating circular cylinder in a uniform free stream. The interest was to examine the turbulence properties at the suppression of periodicity in vortex formation process. An experimental study of the turbulent near wake of a rotating circular cylinder was made at a Reynolds number of 9000 for velocity ratios, λ between 0 and 2.7. Hot-wire anemometry and particle image velocimetry results indicate that the rotation of the cylinder causes significant changes in the vortical activities. The turbulence quantities are getting smaller as λ increases due to suppression of coherent vortex structures.

Keywords: Rotating circular cylinder, Reynolds stress, vortex.

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Authors: Naresh Yadav, I.A. Khan, Sandeep Grover

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This paper presents a methodology for operational and economic characteristics based evaluation and selection of a power plant using Graph theoretic approach. A universal evaluation index on the basis of Operational and economics characteristics of a plant is proposed which evaluates and ranks the various types of power plants. The index thus obtained from the pool of operational characteristics of the power plant attributes Digraph. The Digraph is developed considering Operational and economics attributes of the power plants and their relative importance for their smooth operation, installation and commissioning and prioritizing their selection. The sensitivity analysis of the attributes towards the objective has also been carried out in order to study the impact of attributes over the desired outcome i.e. the universal operational-economics index of the power plant.

Keywords: Power plant evaluation, Digraph methods, Matrixmethod, operational characteristics of Power plant, Gas turbines

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Authors: S. A. Ahmadi, S. Sharif, R. Jamshidi

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In this article, the flow behavior around a NACA 0012 airfoil which is oscillating with different Reynolds numbers and in various amplitudes has been investigated numerically. Numerical simulations have been performed with ANSYS software. First, the 2- D geometry has been studied in different Reynolds numbers and angles of attack with various numerical methods in its static condition. This analysis was to choose the best turbulent model and comparing the grids to have the optimum one for dynamic simulations. Because the analysis was to study the blades of wind turbines, the Reynolds numbers were not arbitrary. They were in the range of 9.71e5 to 22.65e5. The angle of attack was in the range of -41.81° to 41.81°. By choosing the forward wind speed as the independent parameter, the others like Reynolds and the amplitude of the oscillation would be known automatically. The results show that the SST turbulent model is the best choice that leads the least numerical error with respect the experimental ones. Also, a dynamic stall phenomenon is more probable at lower wind speeds in which the lift force is less.

Keywords: Dynamic stall, Numerical simulation, Wind turbine, Turbulent Model

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Authors: M. A. Abd-Allah, Mahmoud N. Ali, A. Said

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Lightning protection systems (LPS) for wind power generation is becoming an important public issue. A serious damage of blades, accidents where low-voltage and control circuit breakdowns are frequently occur in many wind farms. A grounding system is one of the most important components required for appropriate LPSs in wind turbines WTs. Proper design of a wind turbine grounding system is demanding and several factors for the proper and effective implementation must taken into account. In this paper proposed procedure of proper design of grounding systems for a wind turbine was introduced. This procedure depends on measuring of ground current of simulated wind farm under lightning taking into consideration the soil ionization. The procedure also includes the Ground Potential Rise (GPR) and the voltage distributions at ground surface level and Touch potential. In particular, the contribution of mitigating techniques, such as rings, rods and the proposed design were investigated.

Keywords: WTs, LPS, GPR, Grounding System, Mitigating techniques.

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Authors: Andrei Ursachi, Dorin Bordeasu

Abstract:

The Smart Grid Simulator is a computer software based on advance algorithms which has as the main purpose to lower the energy bill in the most optimized price efficient way as possible for private households, companies or energy providers. It combines the energy provided by a number of solar modules and wind turbines with the consumption of one household or a cluster of nearby households and information regarding weather conditions and energy prices in order to predict the amount of energy that can be produced by renewable energy sources and the amount of energy that will be bought from the distributor for the following day. The user of the system will not only be able to minimize his expenditures on energy factures, but also he will be informed about his hourly consumption, electricity prices fluctuation and money spent for energy bought as well as how much money he saved each day and since he installed the system. The paper outlines the algorithm that supports the Smart Grid Simulator idea and presents preliminary test results that supports the discussion and implementation of the system.

Keywords: Applied Science, Renewable energy sources, Smart Grid, Sustainable energy.

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Authors: Tayeb Lardjane, Rabah Messaci

Abstract:

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

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