Search results for: Crossed rectangular hole array

Authors: Hong-Wen Hsieh, Shun-Tung Yen

Abstract:

We theoretically demonstrate modulation of light polarization by a crossed rectangular hole array with asymmetric arm lengths. There are two waveguide modes that can modulate the x- and y- polarized incident waves independently. A specific structure is proposed to convert a left-hand incident wave to a right-hand outgoing wave by transmission.

Keywords: Crossed rectangular hole array, extraordinary optical transmission, polarization modulation.

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Authors: Jheng-Cheng Chen, Chia-Jui Lai, Chang-Hsiung Tsai,

Abstract:

The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.

Keywords: Interconnection network, Hamiltonian, crossed cubes, prescribed edge.

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Authors: Petarpa Boonserm, Tritos Ngampitipan, Matt Visser

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A “clean” black hole is a black hole in vacuum such as the Schwarzschild black hole. However in real physical systems, there are matter fields around a black hole. Such a black hole is called a “dirty black hole”. In this paper, the effect of matter fields on the black hole and the greybody factor is investigated. The results show that matter fields make a black hole smaller. They can increase the potential energy to a black hole to obstruct Hawking radiation to propagate. This causes the greybody factor of a dirty black hole to be less than that of a clean black hole.

Keywords: A dirty black hole, Greybody factor, Hawking radiation, Matter fields.

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Authors: Se Kyung Oh, Ary Bachtiar Krishna Putra, Soo Whan Ahn

Abstract:

A numerical study on the turbulent flow and heat transfer characteristics in the rectangular channel with different types of baffles is carried out. The inclined baffles have the width of 19.8 cm, the square diamond type hole having one side length of 2.55 cm, and the inclination angle of 5o. Reynolds number is varied between 23,000 and 57,000. The SST turbulence model is applied in the calculation. The validity of the numerical results is examined by the experimental data. The numerical results of the flow field depict that the flow patterns around the different baffle type are entirely different and these significantly affect the local heat transfer characteristics. The heat transfer and friction factor characteristics are significantly affected by the perforation density of the baffle plate. It is found that the heat transfer enhancement of baffle type II (3 hole baffle) has the best values.

Keywords: Turbulent flow, rectangular channel, inclined baffle, heat transfer, friction factor.

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Authors: Nitin Kumar Jain

Abstract:

The distributions of stresses and deflection in rectangular isotropic and orthotropic plates with central circular hole under transverse static loading have been studied using finite element method. The aim of author is to analyze the effect of D/A ratio (where D is hole diameter and A is plate width) upon stress concentration factor (SCF) and deflection in isotropic and orthotropic plates under transverse static loading. The D/A ratio is varied from 0.01 to 0.9. The analysis is done for plates of isotropic and two different orthotropic materials. The results are obtained for three different boundary conditions. The variations of SCF and deflection with respect to D/A ratio are presented in graphical form and discussed. The finite element formulation is carried out in the analysis section of the ANSYS package.

Keywords: Finite Element Method, SCF, Deflection, Plate, Boundary conditions

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Authors: M. Tajdari, A. R. Nezamabadi, M. Naeemi, P. Pirali

Abstract:

Mechanical buckling analysis of rectangular plates with central circular cutout is performed in this paper. The finiteelement method is used to study the effects of plate-support conditions, aspect ratio, and hole size on the mechanical buckling strength of the perforated plates subjected to linearly varying loading. Results show that increasing the hole size does not necessarily reduce the mechanical buckling strength of the perforated plates. It is also concluded that the clamped boundary condition increases the mechanical buckling strength of the perforated plates more than the simply-supported boundary condition and the free boundary conditions enhance the mechanical buckling strength of the perforated plates more effectively than the fixed boundary conditions. Furthermore, for the bending cases, the critical buckling load of perforated plates with free edges is less than perforated plates with fixed edges.

Keywords: Buckling, Perforated plates, Boundary condition, Rectangular plates

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Authors: Ali Mutlu, Berrin Mutlu

Abstract:

In this paper we use the definition of CW basis of a free simplicial algebra. Using the free simplicial algebra, it is shown to construct free or totally free 2−crossed modules on suitable construction data with given a CW−basis of the free simplicial algebra. We give applications free crossed squares, free squared complexes and free 2−crossed complexes by using of 1(one) skeleton resolution of a step by step construction of the free simplicial algebra with a given CW−basis.

Keywords: Free crossed square, Free 2−crossed modules, Free simplicial algebra, Free square complexes, Free 2−crossed complexes CW−basis, 1−skeleton. A. M. S.Classification:[2000] 18D35, 18G30, 18G50, 18G55, 55Q05, 55Q20.

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Authors: T.F.Lai, Wan Nor Liza Mahadi, Norhayati Soin

Abstract:

This paper present a circular patch microstrip array antenna operate in KU-band (10.9GHz – 17.25GHz). The proposed circular patch array antenna will be in light weight, flexible, slim and compact unit compare with current antenna used in KU-band. The paper also presents the detail steps of designing the circular patch microstrip array antenna. An Advance Design System (ADS) software is used to compute the gain, power, radiation pattern, and S11 of the antenna. The proposed Circular patch microstrip array antenna basically is a phased array consisting of 'n' elements (circular patch antennas) arranged in a rectangular grid. The size of each element is determined by the operating frequency. The incident wave from satellite arrives at the plane of the antenna with equal phase across the surface of the array. Each 'n' element receives a small amount of power in phase with the others. There are feed network connects each element to the microstrip lines with an equal length, thus the signals reaching the circular patches are all combined in phase and the voltages add up. The significant difference of the circular patch array antenna is not come in the phase across the surface but in the magnitude distribution.

Keywords: Circular patch microstrip array antenna, gain, radiation pattern, S-Parameter.

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Authors: Hari Singh, Abhishek Kamboj, Sudhir Kumar

Abstract:

This investigation proposes a grey-based Taguchi method to solve the multi-response problems. The grey-based Taguchi method is based on the Taguchi’s design of experimental method, and adopts grey relational analysis (GRA) to transfer multi-response problems into single-response problems. In this investigation, an attempt has been made to optimize the drilling process parameters considering weighted output response characteristics using grey relational analysis. The output response characteristics considered are surface roughness, burr height and hole diameter error under the experimental conditions of cutting speed, feed rate, step angle, and cutting environment. The drilling experiments were conducted using L27 orthogonal array. A combination of orthogonal array, design of experiments and grey relational analysis was used to ascertain best possible drilling process parameters that give minimum surface roughness, burr height and hole diameter error. The results reveal that combination of Taguchi design of experiment and grey relational analysis improves surface quality of drilled hole. 

Keywords: Metal matrix composite, Drilling, Optimization, step drill, Surface roughness, burr height, hole diameter error.

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Authors: Hassan M. Elkamchouchi, Samy H. Darwish, Yasser H. Elkamchouchi, M. E. Morsy

Abstract:

Methodology is suggested to design a linear rectangular microstrip array antenna based on Yagi antenna theory. The antenna with different directors' lengths as parasitic elements were designed, simulated, and analyzed using HFSS. The calculus and results illustrate the effectiveness of using specific parasitic elements to improve the directivity and gain for microstrip array antenna. The results have shown that the suggested methodology has the potential to be applied for improving the antenna performance. Maximum radiation intensity (Umax) of the order of 0.47w/st was recorded, directivity of 6.58dB, and gain better than 6.07dB are readily achievable for the antenna that working.

Keywords: Directivity, director, gain improvement, microstrip antenna.

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Authors: Naser Ojaroudi Parchin, Atta Ullah, Haleh Jahanbakhsh Basherlou, Raed A. Abd-Alhameed, Peter S. Excell

Abstract:

A design of beam-steerable antenna array for the future cellular communication (5G) is presented. The proposed design contains eight elements of compact end-fire antennas arranged on the top edge of smartphone printed circuit board (PCB). Configuration of the antenna element consists of the conductive patterns on the top and bottom copper foil layers and a substrate layer with a via-hole. The simulated results including input-impedance and also fundamental radiation properties have been presented and discussed. The impedance bandwidth (S₁₁ ≤ -10 dB) of the antenna spans from 17.5 to 21 GHz (more than 3 GHz bandwidth) with a resonance at 19 GHz. The antenna exhibits end-fire (directional) radiation beams with wide-angle scanning property and could be used for the future 5G beam-forming. Furthermore, the characteristics of the array design in the vicinity of user-hand are studied.

Keywords: Beam-steering, end-fire radiation mode, mobile-phone antenna, phased array.

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Authors: S. Pradittara, M. Uthansakul, P. Uthansakul

Abstract:

A concept of switched beam antennas consisting of 2×2 rectangular array spaced by λ/4 accompanied with a null locating has been proposed in the previous work. In this letter, the performance evaluations of its prototype are presented. The benefits of using proposed system have been clearly measured in term of signal quality, throughput and delays. Also, the impact of position shift which mesh router is not located on the expected beam direction has also been investigated.

Keywords: Antenna array, Beamforming, Null steering, WMNs.

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Authors: Muhammad Saiful Fadhil Reyhan, Yusnita Rahayu, Fadhel Muhammadsyah

Abstract:

This paper proposed a design of 16 elements, 8x2 linear fed patch antenna array with 16 ports, for 28 GHz, mm-wave band 5G for base station. The phased array covers along the azimuth plane to provide the coverage to the users in omnidirectional. The proposed antenna is designed RT Duroid 5880 substrate with the overall size of 85x35.6x0.787 mm³. The array is operating from 27.43 GHz to 28.34 GHz with a 910 MHz impedance bandwidth. The gain of the array is 18.3 dB, while the suppression of the side lobes is -1.0 dB. The main lobe direction of the array is 15 deg. The array shows a high array gain throughout the impedance bandwidth with overall of VSWR is below 1.12. The design will be proposed in single element and 16 elements antenna.

Keywords: 5G antenna, 28 GHz, MIMO, omnidirectional, phased array, base station, broadband.

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Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wavebeam both in elevation and azimuth. In this paper a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Fotios N. Vlachos, Anastasios D. Garetsos, Nikolaos K. Uzunoglu, Efstathios D. Gotsis

Abstract:

A four element prototype phased array surface probe has been designed and constructed to improve clinical human prostate spectroscopic data. The probe consists of two pairs of adjacent rectangular coils with an optimum overlap to reduce the mutual inductance. The two pairs are positioned on the anterior and the posterior pelvic region and two couples of varactors at the input of each coil undertake the procedures of tuning and matching. The probe switches off and on automatically during the consecutive phases of the MR experiment with the use of an analog switch that is triggered by a microcontroller. Experimental tests that were carried out resulted in high levels of tuning accuracy. Also, the switching mechanism functions properly for various applied loads and pulse sequence characteristics, producing only 10 μs of latency.

Keywords: Automatic tuning, prostate imaging, phased array, spectroscopy.

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Authors: Nguyen Thu Huong, Nguyen Quang Bau

Abstract:

The Hall Coefficient (HC) and the Magnetoresistance (MR) have been studied in two-dimensional systems. The HC and the MR in Rectangular Quantum Wire (RQW) subjected to a crossed DC electric field and magnetic field in the presence of a Strong Electromagnetic Wave (EMW) characterized by electric field are studied in this work. Using the quantum kinetic equation for electrons interacting with optical phonons, we obtain the analytic expressions for the HC and the MR with a dependence on magnetic field, EMW frequency, temperatures of systems and the length characteristic parameters of RQW. These expressions are different from those obtained for bulk semiconductors and cylindrical quantum wires. The analytical results are applied to GaAs/GaAs/Al. For this material, MR depends on the ratio of the EMW frequency to the cyclotron frequency. Indeed, MR reaches a minimum at the ratio 5/4, and when this ratio increases, it tends towards a saturation value. The HC can take negative or positive values. Each curve has one maximum and one minimum. When magnetic field increases, the HC is negative, achieves a minimum value and then increases suddenly to a maximum with a positive value. This phenomenon differs from the one observed in cylindrical quantum wire, which does not have maximum and minimum values.

Keywords: Hall coefficient, rectangular quantum wires, electron-optical phonon interaction, quantum kinetic equation.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Yuriy Tasinkevych, Eugene Danicki

Abstract:

Planar systems of electrodes arranged on both sides of dielectric piezoelectric layer are applied in numerous transducers. They are capable of electronic beam-steering of generated wave both in azimuth and elevation. The wave-beam control is achieved by addressable driving of two-dimensional transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The corresponding nontrivial electrostatic problem is formulated and solved numerically.

Keywords: Beamforming, transducer array, BIS-expansion.

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Authors: Ghoname Abdullah, Hidekazu Nishimura

Abstract:

Dust accumulation on the photovoltaic module's surface results in appreciable loss and negatively affects the generated power. Hence, in this paper, the design of a photovoltaic array cleaning system is presented. The cleaning system utilizes one drive motor, two guide rails, and four sweepers during the cleaning process. The cleaning system was experimentally implemented for one month to investigate its efficiency on PV array energy output. The energy capture over a month for PV array cleaned using the proposed cleaning system is compared with that of the energy capture using soiled PV array. The results show a 15% increase in energy generation from PV array with cleaning. From the results, investigating the optimal scheduling of the PV array cleaning could be an interesting research topic.

Keywords: Cleaning system, dust accumulation, PV array, PV module, soiling.

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Authors: Jessada Monthasuwan, Charinsak Saetiaw, Chanchai Thongsopa

Abstract:

This paper presents the development and design of the curved rectangular patch arrays antenna for small missile application. This design uses a 0.1mm flexible copper sheet on the front layer and back layer, and a 1.8mm PVC substrate on a middle layer. The study used a small missile model with 122mm diameter size with speed 1.1 Mach and frequency range on ISM 2.4 GHz. The design of curved antenna can be installation on a cylindrical object like a missile. So, our proposed antenna design will have a small size, lightweight, low cost and simple structure. The antenna was design and analysis by a simulation result from CST microwave studio and confirmed with a measurement result from a prototype antenna. The proposed antenna has a bandwidth covering the frequency range 2.35-2.48 GHz, the return loss below -10 dB and antenna gain 6.5 dB. The proposed antenna can be applied with a small guided missile effectively.

Keywords: Rectangular path arrays, small missile antenna.

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Authors: Min Wang , Shuyuan Yang

Abstract:

The paper presents a method of designing ultrawide band (UWB) pulse array beamformer in the case of nearfield. Firstly the principle of space-time processing of UWB pulse array is discussed. The radical beampattern transform based on spherical coordinates is employed to solve the nearfield beamforming of UWB pulse array. The frequency invariant technology is considered for the frequency dependent beampattern of UWB pulse array. We use a multirate bank scheme of to implement the FI beamformer of UWB pulse array. By using multirate filters in each element channel, it can make the response of the UWB array to avoid distortion in the whole band. The simulation resultes are given to prove the efficiency and feasibility of this method.

Keywords: UWB pulse array, frequency invariant, multiratebank, nearfield beamformer, radical transform

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Authors: J. Mendoza-López, S. Sánchez-Solano, J. L. Huertas-Díaz

Abstract:

An array of piezoelectric micro actuators can be used for radiation of an ultrasonic carrier signal modulated in amplitude with an acoustic signal, which yields audio frequency applications as the air acts as a self-demodulating medium. This application is known as the parametric array. We propose a parametric array with array elements based on existing piezoelectric micro ultrasonic transducer (pMUT) design techniques. In order to reach enough acoustic output power at a desired operating frequency, a proper ratio between number of array elements and array size needs to be used, with an array total area of the order of one cm square. The transducers presented are characterized via impedance, admittance, noise figure, transducer gain and frequency responses.

Keywords: Pizeoelectric, Microspeaker, MEMS, pMUT, Parametric Array

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Authors: Pavan Badami, Vivek Shrivastava, Saravanan V., Nandeesh Hiremath, K. N. Seetharamu

Abstract:

In the present work flow past circular cylinder and cylinder with rectangular and triangular wake splitter is studied to improve aerodynamic parameters. The Comparison of drag coefficient is tabulated for bare cylinder, cylinder with rectangular and triangular wake splitters. Flow past circular cylinder and cylinder with triangular and rectangular wake splitter is performed at Reynoldsnumber 5, 20, 40, 50,80, 100.An incompressible PISO finite volume code employing a non-staggered grid arrangement is used, a second order upwind scheme is used for convective terms. The time discretization is implicit and a Second order Crank-Nicholson scheme is employed. Length of wake splitter in both configurations is taken to be equal to diameter of cylinder. Wake length is found to be less with rectangular wake splitter when compared to bare cylinder and cylinder with triangular wake splitter. Coefficient of drag is found to be less for triangular wake splitter when compared to bare cylinder & cylinder with rectangular wake splitter.

Keywords: Coefficient of drag and pressure, CFDFLUENT, Triangular and rectangular wake splitter, wake length.

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Authors: Sundara Subramanian Karuppasamy, Che Hua Yang

Abstract:

In this work, the laser ultrasound technique has been used for analyzing and imaging the inner defects in metal blocks. To detect the defects in blocks, traditionally the researchers used piezoelectric transducers for the generation and reception of ultrasonic signals. These transducers can be configured into the sparse and phased array. But these two configurations have their drawbacks including the requirement of many transducers, time-consuming calculations, limited bandwidth, and provide confined image resolution. Here, we focus on the non-contact method for generating and receiving the ultrasound to examine the inner defects in aluminum blocks. A Q-switched pulsed laser has been used for the generation and the reception is done by using Laser Doppler Vibrometer (LDV). Based on the Doppler effect, LDV provides a rapid and high spatial resolution way for sensing ultrasonic waves. From the LDV, a series of scanning points are selected which serves as the phased array elements. The side-drilled hole of 10 mm diameter with a depth of 25 mm has been introduced and the defect is interrogated by the linear array of scanning points obtained from the LDV. With the aid of the Synthetic Aperture Focusing Technique (SAFT) algorithm, based on the time-shifting principle the inspected images are generated from the A-scan data acquired from the 1-D linear phased array elements. Thus the defect can be precisely detected with good resolution.

Keywords: Laser ultrasonics, linear phased array, nondestructive testing, synthetic aperture focusing technique, ultrasonic imaging.

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Authors: Lalita Gupta, R. P. Singh

Abstract:

Array signal processing involves signal enumeration and source localization. Array signal processing is centered on the ability to fuse temporal and spatial information captured via sampling signals emitted from a number of sources at the sensors of an array in order to carry out a specific estimation task: source characteristics (mainly localization of the sources) and/or array characteristics (mainly array geometry) estimation. Array signal processing is a part of signal processing that uses sensors organized in patterns or arrays, to detect signals and to determine information about them. Beamforming is a general signal processing technique used to control the directionality of the reception or transmission of a signal. Using Beamforming we can direct the majority of signal energy we receive from a group of array. Multiple signal classification (MUSIC) is a highly popular eigenstructure-based estimation method of direction of arrival (DOA) with high resolution. This Paper enumerates the effect of missing sensors in DOA estimation. The accuracy of the MUSIC-based DOA estimation is degraded significantly both by the effects of the missing sensors among the receiving array elements and the unequal channel gain and phase errors of the receiver.

Keywords: Array Signal Processing, Beamforming, ULA, Direction of Arrival, MUSIC

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising operation, this new definition of entropy can be implemented to compare the performance analysis of filtering methods. In the second part, we apply the concept of pure state in quantum formalism to generalize the maximum entropy method for narrowband and farfield source localization problem. Several computer simulation results are illustrated to demonstrate the effectiveness of the proposed techniques.

Keywords: Von Neumann entropy, Filtering, array, DoA, Maximum Entropy Method.

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Authors: A.Hasanpour, M. Farhadi, H.R. Ashorynejad

Abstract:

In this paper a numerical technique is used to predict the metal temperature of a gas turbine vane. The Rising combustor exit temperatures in gas turbine engines necessitate active cooling for the downstream turbine section to avoid thermal failure. This study is performed the solution of external flow, internal convection, and conduction within the metal vane. Also the trade-off between the cooling performances in four different hole shapes and configurations is performed. At first one of the commonly used cooling hole geometry is investigated; cylindrical holes and then two other configurations are simulated. The average temperature magnitude in mid-plan section of each configuration is obtained and finally the lower temperature value is selected such as best arrangement.

Keywords: Forced Convection, Gas Turbine Blade, Hole Configuration

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Authors: Ahmed A.D. Sarhan, Lim Siew Fen, Mum Wai Yip, M. Sayuti

Abstract:

Ti6Al4V alloy is highly used in the automotive and aerospace industry due to its good machining characteristics. Micro EDM drilling is commonly used to drill micro hole on extremely hard material with very high depth to diameter ratio. In this study, the parameters of micro-electrical discharge machining (EDM) in drilling of Ti6Al4V alloy is optimized for higher machining accuracy with less hole-dilation and hole taper ratio. The micro-EDM machining parameters includes, peak current and pulse on time. Fuzzy analysis was developed to evaluate the machining accuracy. The analysis shows that hole-dilation and hole-taper ratio are increased with the increasing of peak current and pulse on time. However, the surface quality deteriorates as the peak current and pulse on time increase. The combination that gives the optimum result for hole dilation is medium peak current and short pulse on time. Meanwhile, the optimum result for hole taper ratio is low peak current and short pulse on time.

Keywords: Micro EDM, Ti-6Al-4V alloy, fuzzy logic based analysis, optimization, machining accuracy.

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Authors: Parveen K. Saini, Mayank Kushwaha

Abstract:

The influence of material property variation on stress concentration factor (SCF) due to the presence of a circular hole in a functionally graded material (FGM) plate is studied in this paper. A numerical method based on complex variable theory of elasticity is used to investigate the problem. To achieve the material property, variation plate is decomposed into a number of rings. In this research work, Young’s modulus is assumed to be varying exponentially and it is found that stress concentration factor can be reduced by increasing Young’s modulus progressively away from the hole.

Keywords: Stress Concentration, Circular Hole, FGM Plate, Bending.

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Authors: Tao Nie, Weiqiang Liu

Abstract:

In order to obtain an accurate result of the heat transfer of the rib in the internal cooling Rectangular channel, using separation of variables, analytical solutions of three dimensional steady-state heat conduction in rectangular ribs are given by solving three dimensional steady-state function of the rectangular ribs. Therefore, we can get solution of three dimensional temperature field in the rib. Based on the solution, we can get how the Bi number affected on heat transfer. Furthermore, comparisons of the analytical and numerical results indicate agreement on temperature field in the rib.

Keywords: variable separation method, analytical solution, rib, heat transfer

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