Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 154

Search results for: DQ axis with Fourier

154 A Performance Study of Fixed, Single-Axis and Dual-Axis Photovoltaic Systems in Kuwait

Authors: A. Al-Rashidi, A. El-Hamalawi

Abstract:

In this paper, a performance study was conducted to investigate single and dual-axis PV systems to generate electricity in five different sites in Kuwait. Relevant data were obtained by using two sources for validation purposes. A commercial software, PVsyst, was used to analyse the data, such as metrological data and other input parameters, and compute the performance parameters such as capacity factor (CF) and final yield (YF). The results indicated that single and dual-axis PV systems would be very beneficial to electricity generation in Kuwait as an alternative source to conventional power plants, especially with the increased demand over time. The ranges were also found to be competitive in comparison to leading countries using similar systems. A significant increase in CF and YF values around 24% and 28.8% was achieved related to the use of single and dual systems, respectively.

Keywords: Single-axis and dual-axis photovoltaic systems, capacity factor, final yield, renewable energy, Kuwait.

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153 Efficient Web-Learning Collision Detection Tool on Five-Axis Machine

Authors: Chia-Jung Chen, Rong-Shine Lin, Rong-Guey Chang

Abstract:

As networking has become popular, Web-learning tends to be a trend while designing a tool. Moreover, five-axis machining has been widely used in industry recently; however, it has potential axial table colliding problems. Thus this paper aims at proposing an efficient web-learning collision detection tool on five-axis machining. However, collision detection consumes heavy resource that few devices can support, thus this research uses a systematic approach based on web knowledge to detect collision. The methodologies include the kinematics analyses for five-axis motions, separating axis method for collision detection, and computer simulation for verification. The machine structure is modeled as STL format in CAD software. The input to the detection system is the g-code part program, which describes the tool motions to produce the part surface. This research produced a simulation program with C programming language and demonstrated a five-axis machining example with collision detection on web site. The system simulates the five-axis CNC motion for tool trajectory and detects for any collisions according to the input g-codes and also supports high-performance web service benefiting from C. The result shows that our method improves 4.5 time of computational efficiency, comparing to the conventional detection method.

Keywords: Collision detection, Five-axis machining, Separating axis.

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152 Adjustment and Compensation Techniques for the Rotary Axes of Five-axis CNC Machine Tools

Authors: Tung-Hui Hsu, Wen-Yuh Jywe

Abstract:

Five-axis computer numerical control (CNC) machine tools (three linear and two rotary axes) are ideally suited to the fabrication of complex work pieces, such as dies, turbo blades, and cams. The locations of the axis average line and centerline of the rotary axes strongly influence the performance of these machines; however, techniques to compensate for eccentric error in the rotary axes remain weak. This paper proposes optical (Non-Bar) techniques capable of calibrating five-axis CNC machine tools and compensating for eccentric error in the rotary axes. This approach employs the measurement path in ISO/CD 10791-6 to determine the eccentric error in two rotary axes, for which compensatory measures can be implemented. Experimental results demonstrate that the proposed techniques can improve the performance of various five-axis CNC machine tools by more than 90%. Finally, a result of the cutting test using a B-type five-axis CNC machine tool confirmed to the usefulness of this proposed compensation technique.

Keywords: Calibration, compensation, rotary axis, five-axis computer numerical control (CNC) machine tools, eccentric error, optical calibration system, ISO/CD 10791-6

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151 Soil Properties after Plowing with Vertical and Horizontal Axis Rotavator

Authors: M. Azadbakht, B. Azadbakht, R. Janzade Galogah, A. Kiapei, H. Jafari

Abstract:

In this research, performance of rotavator with horizontal rotary axis and vertical rotary axis has been evaluated and compared. The mean weight diameter (MWD), cross-sectional area disturbed and cone index of soil investigated. Factorial experiments based on a randomized complete block with 18 treatments, three different velocities 2.2, 3.5, 6.1 km/h; three different depth of 5, 10, 15cm and with two rotary plows horizontal axis and vertical axis with three replications were used. Result showed that maximum MWD in 6.1 km/h and 15cm of depth were 55.6 and 52.5mm for horizontal axis rotavator, respectively. The minimum MWD in 2.2 km/h and 5cm of depth for vertical axis rotavator were 34.9 and 35.1mm, respectively. The values of cone index 1861.1 and 2339.5 kPa for vertical axis rotavator and horizontal axis rotavator were obtained, respectively, also the values of cross-sectional area disturbed 687 and 497.2cm2 for vertical axis rotavator and horizontal axis rotavator were obtained, respectively.

Keywords: Horizontal rotary axis, vertical rotary axis, rotavator, MWD, cone index, cross-sectional area.

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150 Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain

Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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149 On Fourier Type Integral Transform for a Class of Generalized Quotients

Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

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148 Quality Factor Variation with Transform Order in Fractional Fourier Domain

Authors: Sukrit Shankar, Chetana Shanta Patsa, K. Pardha Saradhi, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform.

Keywords: Fractional Fourier Transform, Quality Factor, Fractional Fourier span, transient signals.

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147 Deriving Generic Transformation Matrices for Multi-Axis Milling Machine

Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

Abstract:

This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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146 Numerical Evaluation of the Aerodynamic Efficiency of the Stevens and Jolly Vertical- Axis Windmill (1895)

Authors: M. Raciti Castelli, E. Benini

Abstract:

This paper presents a numerical investigation of the unsteady flow around an American 19th century vertical-axis windmill: the Stevens & Jolly rotor, patented on April 16, 1895. The computational approach used is based on solving the complete transient Reynolds-Averaged Navier-Stokes (t-RANS) equations: a full campaign of numerical simulation has been performed using the k-ω SST turbulence model. Flow field characteristics have been investigated for several values of tip speed ratio and for a constant unperturbed free-stream wind velocity of 6 m/s, enabling the study of some unsteady flow phenomena in the rotor wake. Finally, the global power generated from the windmill has been determined for each simulated angular velocity, allowing the calculation of the rotor power-curve.

Keywords: CFD, vertical-axis rotor, windmill.

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145 Adaptive Fourier Decomposition Based Signal Instantaneous Frequency Computation Approach

Authors: Liming Zhang

Abstract:

There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents an adaptive Fourier decomposition and (α-counting) based instantaneous frequency computation approach. The adaptive Fourier decomposition is a recently proposed new signal decomposition approach. The instantaneous frequency can be computed through the so called mono-components decomposed by it. Due to the fast energy convergency, the highest frequency of the signal will be discarded by the adaptive Fourier decomposition, which represents the noise of the signal in most of the situation. A new instantaneous frequency definition for a large class of so-called simple waves is also proposed in this paper. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. The α-counting instantaneous frequency can be used to compute the highest frequency for a signal. Combination of these two approaches one can obtain the IFs of the whole signal. An experiment is demonstrated the computation procedure with promising results.

Keywords: Adaptive Fourier decomposition, Fourier series, signal processing, instantaneous frequency

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144 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function

Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients.

Keywords: Fractional Fourier Transform, Perturbation, Fractional Fourier span, amplitude, phase, transform order, filterbanks.

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143 Kinematic Parameter-Independent Modeling and Measuring of Three-Axis Machine Tools

Authors: Yung-Yuan Hsu

Abstract:

The primary objective of this paper was to construct a “kinematic parameter-independent modeling of three-axis machine tools for geometric error measurement" technique. Improving the accuracy of the geometric error for three-axis machine tools is one of the machine tools- core techniques. This paper first applied the traditional method of HTM to deduce the geometric error model for three-axis machine tools. This geometric error model was related to the three-axis kinematic parameters where the overall errors was relative to the machine reference coordinate system. Given that the measurement of the linear axis in this model should be on the ideal motion axis, there were practical difficulties. Through a measurement method consolidating translational errors and rotational errors in the geometric error model, we simplified the three-axis geometric error model to a kinematic parameter-independent model. Finally, based on the new measurement method corresponding to this error model, we established a truly practical and more accurate error measuring technique for three-axis machine tools.

Keywords: Three-axis machine tool, Geometric error, HTM, Error measuring

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142 Numerical Investigation of the Optimal Spatial Domain Discretization for the 2-D Analysis of a Darrieus Vertical-Axis Water Turbine

Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

The optimal grid spacing and turbulence model for the 2D numerical analysis of a vertical-axis water turbine (VAWaterT) operating in a 2 m/s freestream current has been investigated. The results of five different spatial domain discretizations and two turbulence models (k-ω SST and k-ε RNG) have been compared, in order to gain the optimal y+ parameter distribution along the blade walls during a full rotor revolution. The resulting optimal mesh has appeared to be quite similar to that obtained for the numerical analysis of a vertical-axis wind turbine.

Keywords: CFD, vertical axis water turbine, NACA 0025, blade y+.

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141 Proposal of a Means for Reducing the Torque Variation on a Vertical-Axis Water Turbine by Increasing the Blade Number

Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

This paper presents a means for reducing the torque variation during the revolution of a vertical-axis water turbine (VAWaterT) by increasing the blade number. For this purpose, twodimensional CFD analyses have been performed on a straight-bladed Darrieus-type rotor. 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, four and five-bladed rotor architectures, characterized by a NACA 0025 airfoil. For each proposed rotor configuration, flow field characteristics are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade number on flow geometric features and dynamic quantities, such as rotor torque and power. Finally, torque and power curves are compared for the three analyzed architectures, achieving a quantification of the effect of blade number on overall rotor performance.

Keywords: Vertical-Axis Water Turbine, rotor solidity, CFD, NACA 0025

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140 Investigation of the Neutral Axis in the Positive Moment Region of Composite Beams

Authors: Su-Young Jeong, Won-Kee Hong, Seon-Chee Park, Gyun-Taek Lim, Eric Kim

Abstract:

Researchers investigate arious strategies to develop composite beams and maximize the structural advantages. This study attempted to conduct experiments and analysis of changes in the neutral axis of positive moments of a Green Beam. Strain compatibility analysis was used, and its efficiency was demonstrated by comparing experimental and analytical values. In the comparison of neutral axis, the difference between experimental and analytical values was found to range from 8.8~26.2%. It was determined that strain compatibility analysis can be useful for predicting the behaviors of composite beams, with the ability to predict the behavior of not only the elastic location of the composite member, but also of the plastic location

Keywords: Composite beam, Strain compatibility, Neutral axis, Green Beam

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139 Mathematical Model and Control Strategy on DQ Frame for Shunt Active Power Filters

Authors: P. Santiprapan, K-L. Areerak, K-N. Areerak

Abstract:

This paper presents the mathematical model and control strategy on DQ frame of shunt active power filter. The structure of the shunt active power filter is the voltage source inverter (VSI). The pulse width modulation (PWM) with PI controller is used in the paper. The concept of DQ frame to apply with the shunt active power filter is described. Moreover, the detail of the PI controller design for two current loops and one voltage loop are fully explained. The DQ axis with Fourier (DQF) method is applied to calculate the reference currents on DQ frame. The simulation results show that the control strategy and the design method presented in the paper can provide the good performance of the shunt active power filter. Moreover, the %THD of the source currents after compensation can follow the IEEE Std.519-1992.

Keywords: shunt active power filter, mathematical model, DQ control strategy, DQ axis with Fourier, pulse width modulation control.

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138 Progressive Strategy of Milling by means of Tool Axis Inclination Angle

Authors: Sadílek M., Čep R.

Abstract:

This work deals with problems of tool axis inclination angles in ball-end milling. Tool axis inclination angle contributes to improvement of functional surface properties (surface integrity - surface roughness, residual stress, micro hardness, etc.), decreasing cutting forces and improving production. By milling with ball-end milling tool, using standard way of cutting, when work piece and cutting tool contain right angle, we have zero cutting speed on edge. At this point cutting tool only pushes material into the work piece. Here we can observe the following undesirable effects - chip contraction, increasing of cutting temperature, increasing vibrations or creation of built-up edge. These effects have negative results – low quality of surface and decreasing of tool life (in the worse case even it is pinching out). These effects can be eliminated with the tilt of cutting tool or tilt of work piece.

Keywords: CAD/CAM system, tool axis inclination angle, ballend milling, surface roughness, cutting forces.

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137 Numerical Analysis of the Performance of the DU91-W2-250 Airfoil for Straight-Bladed Vertical-Axis Wind Turbine Application

Authors: M. Raciti Castelli, G. Grandi, E. Benini

Abstract:

This paper presents a numerical analysis of the performance of a three-bladed Darrieus vertical-axis wind turbine based on the DU91-W2-250 airfoil. A complete campaign of 2-D simulations, performed for several values of tip speed ratio and based on RANS unsteady calculations, has been performed to obtain the rotor torque and power curves. Rotor performances have been compared with the results of a previous work based on the use of the NACA 0021 airfoil. Both the power coefficient and the torque coefficient have been determined as a function of the tip speed ratio. The flow field around rotor blades has also been analyzed. As a final result, the performance of the DU airfoil based rotor appears to be lower than the one based on the NACA 0021 blade section. This behavior could be due to the higher stall characteristics of the NACA profile, being the separation zone at the trailing edge more extended for the DU airfoil.

Keywords: CFD, vertical axis wind turbine, DU91-W2-250, NACA 0021

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136 An Evaluation Method for Two-Dimensional Position Errors and Assembly Errors of a Rotational Table on a 4 Axis Machine Tool

Authors: Jooho Hwang, Chang-Kyu Song, Chun-Hong Park

Abstract:

This paper describes a method to measure and compensate a 4 axes ultra-precision machine tool that generates micro patterns on the large surfaces. The grooving machine is usually used for making a micro mold for many electrical parts such as a light guide plate for LCD and fuel cells. The ultra precision machine tool has three linear axes and one rotational table. Shaping is usually used to generate micro patterns. In the case of 50 μm pitch and 25 μm height pyramid pattern machining with a 90° wedge angle bite, one of linear axis is used for long stroke motion for high cutting speed and other linear axis are used for feeding. The triangular patterns can be generated with many times of long stroke of one axis. Then 90° rotation of work piece is needed to make pyramid patterns with superposition of machined two triangular patterns. To make a two dimensional positioning error, straightness of two axes in out of plane, squareness between the each axis are important. Positioning errors, straightness and squarness were measured by laser interferometer system. Those were compensated and confirmed by ISO230-6. One of difficult problem to measure the error motions is squareness or parallelism of axis between the rotational table and linear axis. It was investigated by simultaneous moving of rotary table and XY axes. This compensation method is introduced in this paper.

Keywords: Ultra-precision machine tool, muti-axis errors, squraness, positioning errors.

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135 Numerical Analysis of the Performance of a Shrouded Vertical-Axis Water Turbine based on the NACA 0025 Blade Profile

Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

This paper presents a numerical analysis of the performance of a five-bladed Darrieus vertical-axis water turbine, based on the NACA 0025 blade profile, for both bare and shrouded configurations. A complete campaign of 2-D simulations, performed for several values of tip speed ratio and based on RANS unsteady calculations, has been performed to obtain the rotor torque and power curves. Also the effect of a NACA-shaped central hydrofoil has been investigated, with the aim of evaluating the impact of a solid blockage on the performance of the shrouded rotor configuration. The beneficial effect of the shroud on rotor overall performances has clearly been evidenced, while the adoption of the central hydrofoil has proved to be detrimental, being the resulting flow slow down (due to the presence of the obstacle) much higher with respect to the flow acceleration (due to the solid blockage effect).

Keywords: CFD, vertical axis water turbine, shroud, NACA 0025

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134 Evaluation of A 50MW Two-Axis Tracking Photovoltaic Power Plant for AL-Jagbob, Libya: Energetic, Economic, and Environmental Impact Analysis

Authors: Y. Aldali, F. Ahwide

Abstract:

This paper investigates the application of large scale (LS-PV) two-axis tracking photovoltaic power plant in Al-Jagbob, Libya. A 50MW PV-grid connected (two-axis tracking) power plant design in Al-Jagbob, Libya has been carried out presently. A hetero-junction with intrinsic thin layer (HIT) type PV module has been selected and modeled. A Microsoft Excel-VBA program has been constructed to compute slope radiation, dew-point, sky temperature, and then cell temperature, maximum power output and module efficiency for this system, for tracking system. The results for energy production show that the total energy output is 128.5 GWh/year. The average module efficiency is 16.6%. The electricity generation capacity factor (CF) and solar capacity factor (SCF) were found to be 29.3% and 70.4% respectively. A 50MW two axis tracking power plant with a total energy output of 128.5 GWh/year would reduce CO2 pollution by 85,581 tonnes of each year. The payback time for the proposed LS-PV photovoltaic power plant was found to be 4 years.

Keywords: Large PV power plant, solar energy, environmental impact, Dual-axis tracking system.

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133 MRI Reconstruction Using Discrete Fourier Transform: A tutorial

Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

Abstract:

The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.

Keywords: Discrete Fourier Transform (DFT), K-space Data, Magnetic Resonance (MR), Spin, Windows.

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132 Comparison of Stationary and Two-Axis Tracking System of 50MW Photovoltaic Power Plant in Al-Kufra, Libya: Landscape Impact and Performance

Authors: Yasser Aldali

Abstract:

The scope of this paper is to evaluate and compare the potential of LS-PV(Large Scale Photovoltaic Power Plant) power generation systems in the southern region of Libya at Al-Kufra for both stationary and tracking systems. A Microsoft Excel-VBA program has been developed to compute slope radiation, dew-point, sky temperature, and then cell temperature, maximum power output and module efficiency of the system for stationary system and for tracking system. The results for energy production show that the total energy output is 114GWh/year for stationary system and 148GWh/year for tracking system. The average module efficiency for the stationary system is 16.6% and 16.2% for the tracking system.

The values of electricity generation capacity factor (CF) and solar capacity factor (SCF) for stationary system were found to be 26% and 62.5% respectively and 34% and 82% for tracking system. The GCR (Ground Cover Ratio) for a stationary system is 0.7, which corresponds to a tilt angle of 24°. The GCR for tracking system was found to be 0.12. The estimated ground area needed to build a 50MW PV plant amounts to approx. 0.55km2 for a stationary PV field constituted by HIT PV arrays and approx. 91MW/ km2. In case of a tracker PV field, the required ground area amounts approx.2.4km2 and approx. 20.5MW/ km2.

Keywords: Large PV power plant, solar energy, environmental impact, Dual-axis tracking system, stationary system.

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131 Evaluation of Wind Potential for the Lagoon of Venice (Italy) and Estimation of the Annual Energy Output for two Candidate Horizontal- Axis Low-Wind Turbines

Authors: M. Raciti Castelli, L. M. Moglia, E. Benini

Abstract:

This paper presents an evaluation of the wind potential in the area of the Lagoon of Venice (Italy). A full anemometric campaign of 2 year measurements, performed by the "Osservatorio Bioclimatologico dell'Ospedale al Mare di Venezia" has been analyzed to obtain the Weibull wind speed distribution and the main wind directions. The annual energy outputs of two candidate horizontal-axis wind turbines (“Aventa AV-7 LoWind" and “Gaia Wind 133-11kW") have been estimated on the basis of the computed Weibull wind distribution, registering a better performance of the former turbine, due to a higher ratio between rotor swept area and rated power of the electric generator, determining a lower cut-in wind speed.

Keywords: Wind potential, Annual Energy Output (AEO), Weibull distribution, Horizontal-Axis Wind Turbine (HAWT).

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130 A Low-Area Fully-Reconfigurable Hardware Design of Fast Fourier Transform System for 3GPP-LTE Standard

Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou

Abstract:

This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm2 and dissipates 233.5 mW at maximal operating frequency of 250 MHz.

Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.

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129 An Efficient Hamiltonian for Discrete Fractional Fourier Transform

Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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128 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators

Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

Abstract:

Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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127 Numerical Investigation of Non Fourier Heat Conduction in a Semi-infinite Body due to a Moving Concentrated Heat Source Composed with Radiational Boundary Condition

Authors: M. Akbari, S. Sadodin

Abstract:

In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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126 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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125 Cubic Splines and Fourier Series Approach to Study Temperature Variation in Dermal Layers of Elliptical Shaped Human Limbs

Authors: Mamta Agrawal, Neeru Adlakha, K.R. Pardasani

Abstract:

An attempt has been made to develop a seminumerical model to study temperature variations in dermal layers of human limbs. The model has been developed for two dimensional steady state case. The human limb has been assumed to have elliptical cross section. The dermal region has been divided into three natural layers namely epidermis, dermis and subdermal tissues. The model incorporates the effect of important physiological parameters like blood mass flow rate, metabolic heat generation, and thermal conductivity of the tissues. The outer surface of the limb is exposed to the environment and it is assumed that heat loss takes place at the outer surface by conduction, convection, radiation, and evaporation. The temperature of inner core of the limb also varies at the lower atmospheric temperature. Appropriate boundary conditions have been framed based on the physical conditions of the problem. Cubic splines approach has been employed along radial direction and Fourier series along angular direction to obtain the solution. The numerical results have been computed for different values of eccentricity resembling with the elliptic cross section of the human limbs. The numerical results have been used to obtain the temperature profile and to study the relationships among the various physiological parameters.

Keywords: Blood Mass Flow Rate, Metabolic Heat Generation, Fourier Series, Cubic splines and Thermal Conductivity.

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