Search results for: numerical representation

Authors: A. Khodabakhshi, A. Mortazavi

Abstract:

Accurate determination of rock mass deformation modulus, as an important design parameter, is one of the most controversial issues in most engineering projects. A 3D numerical model of standard plate load test (PLT) using the FLAC3D code was carried to investigate the mechanism governing the test process. Five objectives were the focus of this study. The first goal was to employ 3D modeling in the interpretation of PLT conducted at the Bazoft dam site, Iran. The second objective was to investigate the effect of displacements measuring depth from the loading plates on the calculated moduli. The magnitude of rock mass deformation modulus calculated from PLT depends on anchor depth, and in practice, this may be a cause of error in the selection of realistic deformation modulus for the rock mass. The third goal of the study was to investigate the effect of testing plate diameter on the calculated modulus. Moreover, a comparison of the calculated modulus from ISRM formula, numerical modeling and calculated modulus from the actual PLT carried out at right abutment of the Bazoft dam site was another objective of the study. Finally, the effect of plastic strains on the calculated moduli in each of the loading-unloading cycles for three loading plates was investigated. The geometry, material properties, and boundary conditions on the constructed 3D model were selected based on the in-situ conditions of PLT at Bazoft dam site. A good agreement was achieved between numerical model results and the field tests results.

Keywords: Deformation modulus, numerical model, plate loading test, rock mass.

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Authors: M. D. Kokate, T. R. Sontakke, P. W. Wani

Abstract:

This paper deals with an adaptive multiuser detector for direct sequence code division multiple-access (DS-CDMA) systems. A modified receiver, precombinig LMMSE is considered under time varying channel environment. Detector updating is performed with two criterions, mean square estimation (MSE) and MOE optimization technique. The adaptive implementation issues of these two schemes are quite different. MSE criterion updates the filter weights by minimizing error between data vector and adaptive vector. MOE criterion together with canonical representation of the detector results in a constrained optimization problem. Even though the canonical representation is very complicated under time varying channels, it is analyzed with assumption of average power profile of multipath replicas of user of interest. The performance of both schemes is studied for practical SNR conditions. Results show that for poor SNR, MSE precombining LMMSE is better than the blind precombining LMMSE but for greater SNR, MOE scheme outperforms with better result.

Keywords: LMMSE, MOE, MUD.

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Authors: Chien-Hung Chen, Yan-Chun Hsing, Yung-Chun Chang

Abstract:

The Internet has grown into a powerful medium for information dispersion and social interaction that leads to a rapid growth of social media which allows users to easily post their emotions and perspectives regarding certain topics online. Our research aims at using natural language processing and text mining techniques to explore the public emotions expressed on Twitter by analyzing the sentiment behind tweets. In this paper, we propose a composite kernel method that integrates tree kernel with the linear kernel to simultaneously exploit both the tree representation and the distributed emotion keyword representation to analyze the syntactic and content information in tweets. The experiment results demonstrate that our method can effectively detect public emotion of tweets while outperforming the other compared methods.

Keywords: Public emotion recognition, natural language processing, composite kernel, sentiment analysis, text mining.

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Authors: Mohammed Benbrahim, Adil Daoudi, Khalid Benjelloun, Aomar Ibenbrahim

Abstract:

The automatic discrimination of seismic signals is an important practical goal for earth-science observatories due to the large amount of information that they receive continuously. An essential discrimination task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, two classes of seismic signals recorded routinely in geophysical laboratory of the National Center for Scientific and Technical Research in Morocco are considered. They correspond to signals associated to local earthquakes and chemical explosions. The approach adopted for the development of an automatic discrimination system is a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "modified Mexican hat wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis.

Keywords: Seismic signals, Wavelets, Dimensionality reduction, Artificial neural networks, Classification.

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Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

Abstract:

These days, the field of tissue engineering is getting serious attention due to its usefulness. Bone tissue engineering helps to address and sort-out the critical sized and non-healing orthopedic problems by the creation of manmade bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature “parametric sweep”, with which we will be able to predict the oxygen, glucose and cell density dynamics, more accurately. We will fix these problems by modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes and by transient analysis.

Keywords: Bone tissue engineering, Transient Analysis, Scaffolds, fabrication techniques.

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Sreeyuth Lal, Yohei Sato, Bojan Niceno

Abstract:

With the long-term objective of Critical Heat Flux (CHF) prediction, a Direct Numerical Simulation (DNS) framework for simulation of subcooled and saturated nucleate pool boiling is developed. One case of saturated, and three cases of subcooled boiling at different subcooling levels are simulated. Grid refinement study is also reported. Both boiling and condensation phenomena can be computed simultaneously in the proposed numerical framework. Computed bubble detachment diameters of the saturated nucleate pool boiling cases agree well with the experiment. The flow structures around the growing bubble are presented and the accompanying physics is described. The relation between heat flux evolution from the heated wall and the bubble growth is studied, along with investigations of temperature distribution and flow field evolutions.

Keywords: CFD, interface tracking method, phase change model, subcooled nucleate pool boiling.

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Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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Authors: Masoud Madadelahi, Amir Shamloo, Seyedeh Sara Salehi

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Previously, some materials like solid metals and their alloys have been used as implants in human’s body. In order to amend fixation of these artificial hard human tissues, some porous structures have been introduced. In this way, tissues in vicinity of the porous structure can be attached more easily to the inserted implant. In particular, the porous bone scaffolds are useful since they can deliver important biomolecules like growth factors and proteins. This study focuses on the properties of the degradable porous hard tissues using a three-dimensional numerical Finite Element Method (FEM). The most important studied properties of these structures are diffusivity flux and concentration of different species like glucose, oxygen, and lactate. The process of cells migration into the scaffold is considered as a diffusion process, and related parameters are studied for different values of production/consumption rates.

Keywords: Bone scaffolds, diffusivity, numerical simulation, tissue engineering.

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Authors: O. Z. Jasim

Abstract:

An accuracy digital map must satisfy the users for two main requirements, first, map must be visually readable and second, all the map elements must be in a good representation. These two requirements hold especially true for map generalization which aims at simplifying the representation of cartographic data. Different scales of maps are very important for any decision in any maps with different scales such as master plan and all the infrastructures maps in civil engineering. Cartographer cannot project the data onto a piece of paper, but he has to worry about its readability. The map layout of any geodatabase is very important, this layout is help to read, analyze or extract information from the map. There are many principles and guidelines of generalization that can be find in the cartographic literature. A manual reduction method for generalization depends on experience of map maker and therefore produces incompatible results. Digital generalization, rooted from conventional cartography, has become an increasing concern in both Geographic Information System (GIS) and mapping fields. This project is intended to review the state of the art of the new technology and help to understand the needs and plans for the implementation of digital generalization capability as well as increase the knowledge of production topographic maps.

Keywords: Cartography, digital generalization, mapping, GIS.

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Authors: F. Ekoue, A. Fouache d'Halloy, D. Gigon, G Plantamp, E. Zajdman

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This work focuses on analysis of classical heat transfer equation regularized with Maxwell-Cattaneo transfer law. Computer simulations are performed in MATLAB environment. Numerical experiments are first developed on classical Fourier equation, then Maxwell-Cattaneo law is considered. Corresponding equation is regularized with a balancing diffusion term to stabilize discretizing scheme with adjusted time and space numerical steps. Several cases including a convective term in model equations are discussed, and results are given. It is shown that limiting conditions on regularizing parameters have to be satisfied in convective case for Maxwell-Cattaneo regularization to give physically acceptable solutions. In all valid cases, uniform convergence to solution of initial heat equation with Fourier law is observed, even in nonlinear case.

Keywords: Maxwell-Cattaneo heat transfers equations, fourierlaw, heat conduction, numerical solution.

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Authors: Ricardo Mestre

Abstract:

The soundscape stands out as an agglomeration of sounds available in the world, associated with different contexts and origins, being a theme studied by various areas of knowledge, seeking to guide their benefits and their consequences, contributing to the welfare of society and other ecosystems. With the objective for a greater recognition of sound reality, through the selection and differentiation of sounds, the soundscape studies focus on the contribution for a better tuning of the world and to the balance and well-being of humanity. Sound environment, produced and created in various ways, can provide various sources of information, contributing to the orientation of the human being, alerting and manipulating him during his daily journey, like small notifications received on a cell phone or other device with these features. In this way, it becomes possible to give sound its due importance in relation to the processes of individual representation, in manners of social, professional and emotional life. Ensuring an individual representation means providing the human being with new tools for the long process of reflection by recognizing his environment, the sounds that represent him, and his perspective on his respective function in it. In order to provide more information about the importance of the sound environment inherent to the individual reality, one introduces the term sound instance, in order to refer to the whole sound field existing in the individual's life, which is divided into four distinct subfields, but essential to the process of individual representation, called sound matrix, sound cycles, sound traces and sound interference. Alongside volunteers we were able to create six representations of sound instances, based on the individual perception of his/her life, focusing on the present, past and future. With this investigation it was possible to determine that sound instance has a tool for self-recognition, considering the statements of opinion about the experience from the volunteers, reflecting about the three time lines, based on memories, thoughts and wishes.

Keywords: Sound instance, soundscape, sound art, self-recognition.

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Authors: A. Bendarma, T. Jankowiak, A. Rusinek, T. Lodygowski, M. Klósak, S. Bouslikhane

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The analysis of the mechanical characteristics and dynamic behavior of aluminum alloy sheet due to perforation tests based on the experimental tests coupled with the numerical simulation is presented. The impact problems (penetration and perforation) of the metallic plates have been of interest for a long time. Experimental, analytical as well as numerical studies have been carried out to analyze in details the perforation process. Based on these approaches, the ballistic properties of the material have been studied. The initial and residual velocities laser sensor is used during experiments to obtain the ballistic curve and the ballistic limit. The energy balance is also reported together with the energy absorbed by the aluminum including the ballistic curve and ballistic limit. The high speed camera helps to estimate the failure time and to calculate the impact force. A wide range of initial impact velocities from 40 up to 180 m/s has been covered during the tests. The mass of the conical nose shaped projectile is 28 g, its diameter is 12 mm, and the thickness of the aluminum sheet is equal to 1.0 mm. The ABAQUS/Explicit finite element code has been used to simulate the perforation processes. The comparison of the ballistic curve was obtained numerically and was verified experimentally, and the failure patterns are presented using the optimal mesh densities which provide the stability of the results. A good agreement of the numerical and experimental results is observed.

Keywords: Aluminum alloy, ballistic behavior, failure criterion, numerical simulation.

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Authors: Shoeib Mahjoub, Ali Mahtabroshan

Abstract:

The steady incompressible flow has been solved in cylindrical coordinates in both vapour region and wick structure. The governing equations in vapour region are continuity, Navier-Stokes and energy equations. These equations have been solved using SIMPLE algorithm. For study of parameters variation on heat pipe operation, a benchmark has been chosen and the effect of changing one parameter has been analyzed when the others have been fixed.

Keywords: Vapour region, conventional heat pipe, numerical simulation.

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Authors: Aymen Laadhari

Abstract:

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: Finite element method, Newton method, level set, Navier-Stokes, inextensible membrane, liquid drop.

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Authors: Y. Parish, F. Najaei Abadi

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This paper presents a numerical analysis of the seismic behaviour of earth dams. Analysis is conducted for the solid phase. It may correspond to the response of the dam before water filling. Analysis is conducted for a simple case which concerns the elastic response of the dam. Numerical analyses are conducted using the FLAC3D program. The behaviour of the Shell and core of the dam and the foundation behaviour is assumed to be elastic. Result shows the influence of the variation of the shear modulus of the core and shell on the seismic amplification of the dam. It can be observed that the variation of the shearing modulus of the core leads to a moderate increase in the dynamic amplification and the increase in the shell shearing modulus leads to a significant increase in the dynamic amplification.

Keywords: Numerical, earth dam, seismic, dynamic, core, FLAC3D.

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

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The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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Authors: Rajeev, N. K. Raigar

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In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Madiha Khan, Sidrah Ramzan, Seemab Khan, Shahzad Hassan, Kamran Saeed

Abstract:

Measuring semantic similarity between texts is calculating semantic relatedness between texts using various techniques. Our web application (Measuring Relatedness of Concepts-MRC) allows user to input two text corpuses and get semantic similarity percentage between both using WordNet. Our application goes through five stages for the computation of semantic relatedness. Those stages are: Preprocessing (extracts keywords from content), Feature Extraction (classification of words into Parts-of-Speech), Synonyms Extraction (retrieves synonyms against each keyword), Measuring Similarity (using keywords and synonyms, similarity is measured) and Visualization (graphical representation of similarity measure). Hence the user can measure similarity on basis of features as well. The end result is a percentage score and the word(s) which form the basis of similarity between both texts with use of different tools on same platform. In future work we look forward for a Web as a live corpus application that provides a simpler and user friendly tool to compare documents and extract useful information.

Keywords: GraphViz representation, semantic relatedness, similarity measurement, WordNet similarity.

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Authors: H. Golchoobian, S. Saedodin, M. H. Taheri, A. Sarafraz

Abstract:

In this paper, natural convection in an attic is numerically investigated. The geometry of the problem is considered to be a triangular enclosure. ANSYS Fluent software is used for modeling and numerical solution. This study is for steady state. Four right-angled triangles with height to base ratios of 2, 1, 0.5 and 0.25 are considered. The behavior of various parameters related to its performance, including temperature distribution and velocity vectors are evaluated, and graphs for the Nusselt number have been drawn. Also, in this study, the effect of geometric shape of enclosure with different height-to-base ratios has been evaluated for three types of boundary conditions of winter, summer day and one another state. It can be concluded that as the bottom side temperature and ratio of base to height of the enclosure increases, the convective effects become more prominent and circulation happened.

Keywords: Enclosure, natural convection, numerical solution, Nusselt number, triangular.

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Authors: A. Kojah, A. Nacaroğlu

Abstract:

Single phase transmission lines are used to transfer data or energy between two users. Transient conditions such as switching operations and short circuit faults cause the generation of the fluctuation on the waveform to be transmitted. Spatial voltage distribution on the single phase transmission line may change owing to the position and duration of the short circuit fault in the system. In this paper, the state space representation of the single phase transmission line for short circuit fault and for various types of terminations is given. Since the transmission line is modeled in time domain using distributed parametric elements, the mathematical representation of the event is given in state space (time domain) differential equation form. It also makes easy to solve the problem because of the time and space dependent characteristics of the voltage variations on the distributed parametrically modeled transmission line.

Keywords: Energy transmission, transient effects, transmission line, transient voltage, RLC short circuit, single phase.

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Authors: Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini

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A dynamic stall-corrected Blade Element-Momentum algorithm based on a hybrid polar is validated through the comparison with Sandia experimental measurements on a 5-m diameter wind turbine of Troposkien shape. Different dynamic stall models are evaluated. The numerical predictions obtained using the extended aerodynamic coefficients provided by both Sheldal and Klimas and Raciti Castelli et al. are compared to experimental data, determining the potential of the hybrid database for the numerical prediction of vertical-axis wind turbine performances.

Keywords: Darrieus wind turbine, Blade Element-Momentum Theory, extended airfoil database, hybrid database, Sandia 5-m wind turbine.

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Authors: Isaac K. E. Ampomah, Seong-Bae Park, Sang-Jo Lee

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Over the past decade, there have been promising developments in Natural Language Processing (NLP) with several investigations of approaches focusing on Recognizing Textual Entailment (RTE). These models include models based on lexical similarities, models based on formal reasoning, and most recently deep neural models. In this paper, we present a sentence encoding model that exploits the sentence-to-sentence relation information for RTE. In terms of sentence modeling, Convolutional neural network (CNN) and recurrent neural networks (RNNs) adopt different approaches. RNNs are known to be well suited for sequence modeling, whilst CNN is suited for the extraction of n-gram features through the filters and can learn ranges of relations via the pooling mechanism. We combine the strength of RNN and CNN as stated above to present a unified model for the RTE task. Our model basically combines relation vectors computed from the phrasal representation of each sentence and final encoded sentence representations. Firstly, we pass each sentence through a convolutional layer to extract a sequence of higher-level phrase representation for each sentence from which the first relation vector is computed. Secondly, the phrasal representation of each sentence from the convolutional layer is fed into a Bidirectional Long Short Term Memory (Bi-LSTM) to obtain the final sentence representations from which a second relation vector is computed. The relations vectors are combined and then used in then used in the same fashion as attention mechanism over the Bi-LSTM outputs to yield the final sentence representations for the classification. Experiment on the Stanford Natural Language Inference (SNLI) corpus suggests that this is a promising technique for RTE.

Keywords: Deep neural models, natural language inference, recognizing textual entailment, sentence-to-sentence relation.

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Authors: V. Přivřelová

Abstract:

Well-designed composite steel and concrete structures highlight the good material properties and lower the deficiencies of steel and concrete, in particular they make use of high tensile strength of steel and high stiffness of concrete. The most common composite steel and concrete structure is a simply supported beam, which concrete slab transferring the slab load to a beam is connected to the steel cross-section. The aim of this paper is to find the most adequate numerical model of a simply supported composite beam with the cross-sectional and material parameters based on the results of a processed parametric study and numerical analysis. The paper also evaluates the suitability of using compact concrete with the lightweight aggregates for composite steel and concrete beams. The most adequate numerical model will be used in the resent future to compare the results of laboratory tests.

Keywords: Composite beams, high-performance concrete, highstrength steel, lightweight concrete slab, modeling.

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Authors: Manish K Rathod, Jyotirmay Banerjee

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The storage of thermal energy as a latent heat of phase change material (PCM) has created considerable interest among researchers in recent times. Here, an attempt is made to carry out numerical investigations to analyze the performance of latent heat storage units (LHSU) employing phase change material. The mathematical model developed is based on an enthalpy formulation. Freezing time of PCM packed in three different shaped containers viz. rectangular, cylindrical and cylindrical shell is compared. The model is validated with the results available in the literature. Results show that for the same mass of PCM and surface area of heat transfer, cylindrical shell container takes the least time for freezing the PCM and this geometric effect is more pronounced with an increase in the thickness of the shell than that of length of the shell.

Keywords: Enthalpy Formulation, Latent heat storage unit(LHSU), Numerical Model, Phase change material (PCM)

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Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

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This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: Finite-discrete element method, dry stone masonry structures, static load, dynamic load.

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Authors: M. Fakharian, M. I. Khodakarami

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In this paper, a new trend for improvement in semianalytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific subparametric elements. Mapping functions are uses as a class of higherorder Lagrange polynomials, special shape functions, Gauss-Lobatto- Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.

Keywords: 2D Elastodynamic Problems, Lagrange Polynomials, G-L-Lquadrature, Decoupled SBFEM.

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

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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: Rabah Haoui

Abstract:

This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.

Keywords: Supersonic flow, viscous flow, finite volume, cone body

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