Search results for: method of the boundary integrated equations

Authors: Sung-Chul Hwang, Di Ren, Sang-Moon Yoon, Jong-Chun Park, Abbas Khayyer, Hitoshi Gotoh

Abstract:

This paper presents a fully Lagrangian coupled Fluid-Structure Interaction (FSI) solver for simulations of fluid-structure interactions, which is based on the Moving Particle Semi-implicit (MPS) method to solve the governing equations corresponding to incompressible flows as well as elastic structures. The developed solver is verified by reproducing the high velocity impact loads of deformable thin wedges with three different materials such as mild steel, aluminium and tin during water entry. The present simulation results for aluminium are compared with analytical solution derived from the hydrodynamic Wagner model and linear Wan’s theory. And also, the impact pressure and strain on the water entry wedge with three different materials, such as mild steel, aluminium and tin, are simulated and the effects of hydro-elasticity are discussed.

Keywords: Fluid-structure interaction (FSI), Moving Particle Semi-implicit (MPS) method, Elastic structure, Incompressible fluid Wedge slamming impact.

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

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A numerical study of flow in a horizontally channel partially filled with a porous screen with non-uniform inlet has been performed by lattice Boltzmann method (LBM). The flow in porous layer has been simulated by the Brinkman-Forchheimer model. Numerical solutions have been obtained for variable porosity models and the effects of Darcy number and porosity have been studied in detail. It is found that the flow stabilization is reliant on the Darcy number. Also the results show that the stabilization of flow field and heat transfer is depended to Darcy number. Distribution of stream field becomes more stable by decreasing Darcy number. Results illustrate that the effect of variable porosity is significant just in the region of the solid boundary. In addition, difference between constant and variable porosity models is decreased by decreasing the Darcy number.

Keywords: Lattice Boltzmann Method, Porous Media, Variable Porosity, Flow Stabilization

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Authors: O. Bendermel, C. Seladji, M. Khaouani

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In this work, we made anumerical study of the thermal and dynamic behavior of air in a horizontal channel with electronic components.The influenceto use baffles on the profiles of velocity and temperature is discussed.The finite volume method and the algorithm Simple are used for solving the equations of conservation of mass, momentum and energy.The results found show that baffles improve heat transfer between the cooling air and electronic components. The velocity will increase from 3 times per rapport of the initial velocity.

Keywords: Electronic components, baffles, cooling.

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Authors: A. Khelassi, R. Bendib

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The paper considers the effect of feed plate location on the interactions in a seven plate binary distillation column. The mathematical model of the distillation column is deduced based on the equations of mass and energy balances for each stage, detailed model for both reboiler and condenser, and heat transfer equations. The Dynamic Relative Magnitude Criterion, DRMC is used to assess the interactions in different feed plate locations for a seven plate (Benzene-Toluene) binary distillation column ( the feed plate is originally at stage 4). The results show that whenever we go far from the optimum feed plate position, the level of interaction augments.

Keywords: Distillation column, assessment of interactions, feedplate location, DRMC.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

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Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: Mohammed Sabri Ali Akresh

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The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM.

Keywords: Harmonic equations, coordinate system, projections, algorithms and parallels.

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Authors: Soon-ok Myong, B.G. Nurzhanov

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This paper applies an anthropological approach to illuminate the dynamic cultural geography of Kazakhstani Korean ethnicity focusing on its turning point, the historic “Seoul Olympic Games in 1988." The Korean ethnic group was easily considered as a harmonious and homogeneous community by outsiders, but there existed deep-seated conflicts and hostilities within the ethnic group. The majority-s oppositional dichotomy of superiority and inferiority toward the minority was continuously reorganized and reinforced by difference in experience, memory and sentiment. However, such a chronic exclusive boundary was collapsed following the patriotism ignited by the Olympics held in their mother country. This paper explores the fluidity of subject by formation of the boundary in which constructed cultural differences are continuously essentialized and reproduced, and by dissolution of cultural barrier in certain contexts.

Keywords: Former Soviet Korean's Russianization, inferior/superior dichotomy, Seoul Olympic Games, subject's fluidity.

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Authors: Seyed Abolhasan Naeini, Mohammad Hossein Zade

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This article is an attempt to present a numerically study of the behaviour of an eccentrically loaded circular footing resting on sand to determine ‎its ultimate bearing capacity. A surface circular footing of diameter 12 cm (D) was used as ‎shallow foundation. For this purpose, three dimensional models consist of foundation, and medium sandy soil was modelled by ABAQUS software. Bearing capacity of footing was evaluated and the ‎effects of the load eccentricity on bearing capacity, its settlement, and modulus of subgrade reaction were studied. Three different values of load eccentricity with equal space from inside the core on the core boundary and outside the core boundary, which were respectively e=0.75, 1.5, and 2.25 cm, were considered. The results show that by increasing the load eccentricity, the ultimate load and the ‎modulus of subgrade reaction decreased.

Keywords: Circular foundation, eccentric loading, sand, modulus of subgrade reaction.

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: Hossain Aziz, Rinku Mukherjee

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A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface" boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface" boundary condition Kelvin-s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Keywords: Aerodynamics, Airfoils, Configuration, Unsteady.

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Authors: Eda Gök

Abstract:

Peridynamics is a new modeling concept of non-local interactions for solid structures. The formulations of Peridynamic (PD) theory are based on integral equations rather than differential equations. Through, undefined equations of associated problems are avoided. PD theory might be defined as continuum version of molecular dynamics. The medium is usually modeled with mass particles bonded together. Particles interact with each other directly across finite distances through central forces named as bonds. The main assumption of this theory is that the body is composed of material points which interact with other material points within a finite distance. Although, PD theory developed for discontinuities, it gives good results for structures which have no discontinuities. In this paper, displacement control of the isotropic plate under the effect of tensile and bending loading has been investigated by means of PD theory. A MATLAB code is generated to create PD bonds and corresponding surface correction factors. Using generated MATLAB code the geometry of the specimen is generated, and the code is implemented in Finite Element Software. The results obtained from non-local continuum theory are compared with the Finite Element Analysis results and analytical solution. The results show good agreement.

Keywords: Flexural loading, non-local continuum mechanics, Peridynamic theory, solid structures, tensile loading.

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Authors: Masato Sasaki, Masayoshi Yamamoto

Abstract:

The majority of wireless power transfer (WPT) systems transfer power in a directional manner. This paper describes a discrete exciting voltage control technique for WPT via magnetic resonant coupling with two orthogonal transmitter coils (2D omni-directional WPT system) which can maximize the power transfer efficiency in response to the change of coupling status. The theory allows the equations of the efficiency of the system to be determined at all the rate of the mutual inductance. The calculated results are included to confirm the advantage to one directional WPT system and the validity of the theory and the equations.

Keywords: Wireless power transfer, orthogonal, omni-directional, efficiency.

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Authors: G. Khamooshian

Abstract:

One of the main points of application of the mechanisms of the series and parallel is the subject of managing them. The control of this mechanism and similar mechanisms is one that has always been the intention of the scholars. On the other hand, modeling the behavior of the system is difficult due to the large number of its parameters, and it leads to complex equations that are difficult to solve and eventually difficult to control. In this paper, a six-linkage robot has been presented that could be used in different areas such as medical robots. Using these robots needs a robust control. In this paper, the system equations are first found, and then the system conversion function is written. A new controller has been designed for this robot which could be used in other parallel robots and could be very useful. Parallel robots are so important in robotics because of their stability, so methods for control of them are important and the robust controller, especially in parallel robots, makes a sense.

Keywords: 3-RRS, 6 linkage, parallel robot, control.

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Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

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This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: Non-stationary, BINARMA(1, 1) model, Poisson Innovations, CML

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations.

Keywords: Bio-heat, Boussinesq, conduction, convection, eye.

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Authors: Azadeh Maroufmashat, Sourena Sattari Khavas, Halle Bakhteeyar

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Multi-energy systems will enhance the system reliability and power quality. This paper presents an integrated approach for the design and operation of distributed energy resources (DER) systems, based on energy hub modeling. A multi-objective optimization model is developed by considering an integrated view of electricity and natural gas network to analyze the optimal design and operating condition of DER systems, by considering two conflicting objectives, namely, minimization of total cost and the minimization of environmental impact which is assessed in terms of CO2 emissions. The mathematical model considers energy demands of the site, local climate data, and utility tariff structure, as well as technical and financial characteristics of the candidate DER technologies. To provide energy demands, energy systems including photovoltaic, and co-generation systems, boiler, central power grid are considered. As an illustrative example, a hotel in Iran demonstrates potential applications of the proposed method. The results prove that increasing the satisfaction degree of environmental objective leads to increased total cost.

Keywords: Multi objective optimization, DER systems, Energy hub, Cost, CO2 emission.

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Authors: Yuzana, Khin Marlar Tun

Abstract:

Personal name matching system is the core of essential task in national citizen database, text and web mining, information retrieval, online library system, e-commerce and record linkage system. It has necessitated to the all embracing research in the vicinity of name matching. Traditional name matching methods are suitable for English and other Latin based language. Asian languages which have no word boundary such as Myanmar language still requires sounds alike matching system in Unicode based application. Hence we proposed matching algorithm to get analogous sounds alike (phonetic) pattern that is convenient for Myanmar character spelling. According to the nature of Myanmar character, we consider for word boundary fragmentation, collation of character. Thus we use pattern conversion algorithm which fabricates words in pattern with fragmented and collated. We create the Myanmar sounds alike phonetic group to help in the phonetic matching. The experimental results show that fragmentation accuracy in 99.32% and processing time in 1.72 ms.

Keywords: natural language processing, name matching, phonetic matching

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

Abstract:

The seismic response of steel shear wall system considering nonlinearity effects using finite element method is investigated in this paper. The non-linear finite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of finite element code. A numerical model based on the finite element method for the seismic analysis of shear wall is presented with developing of finite element code in this research. To develop the finite element code, the standard Galerkin weighted residual formulation is used. Two-dimensional plane stress model and total Lagrangian formulation was carried out to present the shear wall response and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The presented model in this paper can be developed for analysis of civil engineering structures with different material behavior and complicated geometry.

Keywords: Finite element, steel shear wall, nonlinear, earthquake

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Authors: E.Assareh, M.A. Behrang, R. Assareh, N. Hedayat

Abstract:

An integrated Artificial Neural Network- Particle Swarm Optimization (PSO) is presented for analyzing global electricity consumption. To aim this purpose, following steps are done: STEP 1: in the first step, PSO is applied in order to determine world-s oil, natural gas, coal and primary energy demand equations based on socio-economic indicators. World-s population, Gross domestic product (GDP), oil trade movement and natural gas trade movement are used as socio-economic indicators in this study. For each socio-economic indicator, a feed-forward back propagation artificial neural network is trained and projected for future time domain. STEP 2: in the second step, global electricity consumption is projected based on the oil, natural gas, coal and primary energy consumption using PSO. global electricity consumption is forecasted up to year 2040.

Keywords: Particle Swarm Optimization, Artificial NeuralNetworks, Fossil Fuels, Electricity, Forecasting.

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Authors: Stéphanie Pellerin, Bérengére Podvin, Luc Pastur

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In aerovehicles context, the flow around an Ahmed body profile is simulated using the velocity-vorticity formulation of the Navier-Stokes equations, associated to a penalization method for solids and Large Eddy Simulation for turbulence. The study focuses both on the ground influence on the flow and on the dissymetry of the wake, observed for a ground clearance greater than 10% of the body height H. Unsteady and mean flows are presented and analyzed. POD study completes the analysis and gives information on the most energetic structures of the flow.

Keywords: Ahmed body, bi-stability, LES, near wake.

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Authors: Young-Kyun Kim, Tae-Gu Lee, Jin-Huek Hur, Sung-Jae Moon, Jae-Heon Lee

Abstract:

In this paper, three dimensional flow characteristic was presented by a revision of an impeller of an axial turbo fan for improving the airflow rate and the static pressure. TO consider an incompressible steady three-dimensional flow, the RANS equations are used as the governing equations, and the standard k-ε turbulence model is chosen. The pitch angles of 44°, 54°, 59°, and 64° are implemented for the numerical model. The numerical results show that airflow rates of each pitch angle are 1,175 CMH, 1,270 CMH, 1,340 CMH, and 800 CMH, respectively. The difference of the static pressure at impeller inlet and outlet are 120 Pa, 214 Pa, 242 Pa, and 60 Pa according to respective pitch angles. It means that the 59° of the impeller pitch angle is optimal to improve the airflow rate and the static pressure.

Keywords: Axial turbo fan, Impeller, Blade, Pitch angle.

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Authors: Igor Nedelkovski, Ilios Vilos, Tale Geramitcioski

Abstract:

Computational simulation of steam flow and heat transfer in power plant condensers on the basis of the threedimensional mathematical model for the flow through porous media is presented. In order to solve the mathematical model of steam flow and heat transfer in power plant condensers, the Streamline Upwind Petrov-Galerkin finite element method is applied. By comparison of the results of simulation with experimental results about an experimental condenser, it is confirmed that SUPG finite element method can be successfully applied for solving the three-dimensional mathematical model of steam flow and heat transfer in power plant condensers.

Keywords: Navier-Stokes, FEM, condensers, steam.

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Authors: Rajendra K. Ray, H. V. R. Mittal

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A numerical study is made of laminar, unsteady flow behind a rotationally oscillating circular cylinder using a recently developed higher order compact (HOC) scheme. The stream function vorticity formulation of Navier-Stokes (N-S) equations in cylindrical polar coordinates are considered as the governing equations. The temporal behaviour of vortex formation and relevant streamline patterns of the flow are scrutinized over broad ranges of two externally specified parameters namely dimensionless forced oscillating frequency Sf and dimensionless peak rotation rate αm for the Reynolds-s number Re = 200. Excellent agreements are found both qualitatively and quantitatively with the existing experimental and standard numerical results.

Keywords: HOC, Navier-Stokes, non-uniform polar grids, rotationally oscillating cylinder.

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Authors: Alireza Osareh, Bita Shadgar

Abstract:

Segmenting the lungs in medical images is a challenging and important task for many applications. In particular, automatic segmentation of lung cavities from multiple magnetic resonance (MR) images is very useful for oncological applications such as radiotherapy treatment planning. However, distinguishing of the lung areas is not trivial due to largely changing lung shapes, low contrast and poorly defined boundaries. In this paper, we address lung segmentation problem from pulmonary magnetic resonance images and propose an automated method based on a robust regionaided geometric snake with a modified diffused region force into the standard geometric model definition. The extra region force gives the snake a global complementary view of the lung boundary information within the image which along with the local gradient flow, helps detect fuzzy boundaries. The proposed method has been successful in segmenting the lungs in every slice of 30 magnetic resonance images with 80 consecutive slices in each image. We present results by comparing our automatic method to manually segmented lung cavities provided by an expert radiologist and with those of previous works, showing encouraging results and high robustness of our approach.

Keywords: Active contours, breast cancer, fuzzy c-means segmentation, treatment planning.

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Authors: Basharat Ali Haider, Naveed Durrani, Nadeem Aizud, Salimuddin Zahir

Abstract:

The aerodynamic stall control of a baseline 13-percent thick NASA GA(W)-2 airfoil using a synthetic jet actuator (SJA) is presented in this paper. Unsteady Reynolds-averaged Navier-Stokes equations are solved on a hybrid grid using a commercial software to simulate the effects of a synthetic jet actuator located at 13% of the chord from the leading edge at a Reynolds number Re = 2.1x106 and incidence angles from 16 to 22 degrees. The experimental data for the pressure distribution at Re = 3x106 and aerodynamic coefficients at Re = 2.1x106 (angle of attack varied from -16 to 22 degrees) without SJA is compared with the computational fluid dynamic (CFD) simulation as a baseline validation. A good agreement of the CFD simulations is obtained for aerodynamic coefficients and pressure distribution. A working SJA has been integrated with the baseline airfoil and initial focus is on the aerodynamic stall control at angles of attack from 16 to 22 degrees. The results show a noticeable improvement in the aerodynamic performance with increase in lift and decrease in drag at these post stall regimes.

Keywords: Active flow control, Aerodynamic stall, Airfoilperformance, Synthetic jet actuator.

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Authors: H. Ajabi Naeeni, M. Haghpanahi

Abstract:

Dynamic shear test on simulated phantom can be used to validate magnetic resonance elastography (MRE) measurements. Phantom gel has been usually utilized for the cell culture of cartilage and soft tissue and also been used for mechanical property characterization using imaging systems. The viscoelastic property of the phantom would be important for dynamic experiments and analyses. In this study, An axisymmetric FE model is presented for determining the dynamic shear behaviour of brain simulated phantom using ABAQUS. The main objective of this study was to investigate the effect of excitation frequencies and boundary conditions on shear modulus and shear viscosity in viscoelastic media.

Keywords: Viscoelastic, MR Elastography, Finite Element, Brain.

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Authors: S. Boorboor, S. A. H. Feghhi, H. Jafari

Abstract:

The ionizing radiations cause different kinds of damages in electronic components. MOSFETs, most common transistors in today’s digital and analog circuits, are severely sensitive to TID damage. In this work, the threshold voltage shift of CD4007 device, which is an integrated circuit including P-channel and N-channel MOS transistors, was investigated for low dose gamma irradiation under different gate bias voltages. We used linear extrapolation method to extract threshold voltage from I_D-V_G characteristic curve. The results showed that the threshold voltage shift was approximately 27.5 mV/Gy for N-channel and 3.5 mV/Gy for P-channel transistors at the gate bias of |9 V| after irradiation by Co-60 gamma ray source. Although the sensitivity of the devices under test were strongly dependent to biasing condition and transistor type, the threshold voltage shifted linearly versus accumulated dose in all cases. The overall results show that the application of CD4007 as an electronic buffer in a radiation therapy system is limited by TID damage. However, this integrated circuit can be used as a cheap and sensitive radiation dosimeter for accumulated dose measurement in radiation therapy systems.

Keywords: Threshold voltage shift, MOS transistor, linear extrapolation, gamma irradiation.

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Authors: Mehtap Dursun, Zeynep Şener

Abstract:

Supplier selection is considered as one of the most critical issues encountered by operations and purchasing managers to sharpen the company’s competitive advantage. In this paper, a novel fuzzy multi-criteria group decision making approach integrating quality function deployment (QFD) and decision making trial and evaluation laboratory (DEMATEL) method is proposed for supplier selection. The proposed methodology enables to consider the impacts of inner dependence among supplier assessment criteria. A house of quality (HOQ) which translates purchased product features into supplier assessment criteria is built using the weights obtained by DEMATEL approach to determine the desired levels of supplier assessment criteria. Supplier alternatives are ranked by a distance-based method.

Keywords: DEMATEL, Group decision making, QFD, Supplier selection.

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Authors: M. Karami Khorramabadi, P. Khazaeinejad

Abstract:

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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