Search results for: finite volume method
32670 Mathematical Modeling of Elastically Creeping State of Arbitrarily Orientated Cavities in the Transversally Isotropic Massif
Authors: N. Azhikhanov, T. Turimbetov, Zh. Masanov, N. Zhunisov
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It can be determined in preference between representative mechanical and mathematical model of elasticcreeping deformation of transversally isotropic array with doubly periodic system of tilted slots, and offer of the finite elements calculation scheme, and inspection of the states of two diagonal arbitrary profile cavities of deep inception, and in setting up the tense and dislocation fields distribution nature in computing processes.
Keywords: Mathematical model, tunnel, transversally isotropic, finite elements.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 159232669 Static Response of Homogeneous Clay Stratum to Imposed Structural Loads
Authors: Aaron Aboshio
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Numerical study of the static response of homogeneous clay stratum considering a wide range of cohesion and subject to foundation loads is presented. The linear elastic–perfectly plastic constitutive relation with the von Mises yield criterion were utilised to develop a numerically cost effective finite element model for the soil while imposing a rigid body constrain to the foundation footing. From the analyses carried out, estimate of the bearing capacity factor, Nc as well as the ultimate load-carrying capacities of these soils, effect of cohesion on foundation settlements, stress fields and failure propagation were obtained. These are consistent with other findings in the literature and hence can be a useful guide in design of safe foundations in clay soils for buildings and other structure.Keywords: Bearing capacity factors, finite element method, safe bearing pressure, structure-soil interaction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 199632668 Application of the Central-Difference with Half- Sweep Gauss-Seidel Method for Solving First Order Linear Fredholm Integro-Differential Equations
Authors: E. Aruchunan, J. Sulaiman
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The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method.Keywords: Integro-differential equations, Linear fredholm equations, Finite difference, Quadrature formulas, Half-Sweep iteration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 181332667 Numerical Optimization of Trapezoidal Microchannel Heat Sinks
Authors: Yue-Tzu Yang, Shu-Ching Liao
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This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm2 ≦q"≦ 40W/cm2. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.
Keywords: Microchannel heat sinks, Conjugate heat transfer, Optimization, Genetic algorithm method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 215832666 Behavior of the Masonry Infill in Structures Subjected to the Horizontal Loads
Authors: Nawel Mezigheche, Abdelhacine Gouasmia, Allaeddine Athmani, Mouloud Merzoud
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Masonry infill walls are inevitable in the selfsupporting structures, but their contribution in the resistance to earthquake loads is generally neglected in the structural analyses. The principal aim of this work through a numerical study of masonry infill walls behavior in structures subjected to horizontal load is to propose by finite elements numerical modeling, a more reliable approach, faster and close to reality. In this study, 3D Finite Element Analysis was developed to study the behavior of masonry infill walls in structures subjected to horizontal load; the finite element software being used was ABAQUS, it is observed that more rigidity of the masonry filling is significant, more the structure is rigid, we can so conclude that the filling brings an additional rigidity to the structure not to be neglected; it is also observed that when the framework is subjected to horizontal loads, the framework separates from the filling on the level of the tended diagonal.Keywords: Finite element, Masonry infill walls, Rigidity of the masonry, Tended diagonal.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 211732665 Large Amplitude Free Vibration of a Very Sag Marine Cable
Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart
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This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.
Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 82532664 A Comparative Study between Displacement and Strain Based Formulated Finite Elements Applied to the Analysis of Thin Shell Structures
Authors: Djamal Hamadi, Oussama Temami, Abdallah Zatar, Sifeddine Abderrahmani
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The analysis and design of thin shell structures is a topic of interest in a variety of engineering applications. In structural mechanics problems the analyst seeks to determine the distribution of stresses throughout the structure to be designed. It is also necessary to calculate the displacements of certain points of the structure to ensure that specified allowable values are not exceeded. In this paper a comparative study between displacement and strain based finite elements applied to the analysis of some thin shell structures is presented. The results obtained from some examples show the efficiency and the performance of the strain based approach compared to the well known displacement formulation.
Keywords: Displacement formulation, Finite elements, Strain based approach, Shell structures.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 263532663 Mathematical Modeling of the AMCs Cross-Contamination Removal in the FOUPs: Finite Element Formulation and Application in FOUP’s Decontamination
Authors: N. Santatriniaina, J. Deseure, T.Q. Nguyen, H. Fontaine, C. Beitia, L. Rakotomanana
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Nowadays, with the increasing of the wafer's size and the decreasing of critical size of integrated circuit manufacturing in modern high-tech, microelectronics industry needs a maximum attention to challenge the contamination control. The move to 300 [mm] is accompanied by the use of Front Opening Unified Pods for wafer and his storage. In these pods an airborne cross contamination may occur between wafers and the pods. A predictive approach using modeling and computational methods is very powerful method to understand and qualify the AMCs cross contamination processes. This work investigates the required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs. Numerical optimization and finite element formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. The least square distance between the model (analytical 1D solution) and the experimental data are minimized. The behavior of the AMCs intransient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. The methodology is applied, first using the optimization methods with analytical solution to define physical constants, and second using finite element method including adsorption kinetic and the switch of Dirichlet to Neumann condition.
Keywords: AMCs, FOUP, cross-contamination, adsorption, diffusion, numerical analysis, wafers, Dirichlet to Neumann, finite elements methods, Fick’s law, optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 317232662 Contact Stress Analysis of Spur Gear Teeth Pair
Authors: Ali Raad Hassan
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Contact stress analysis between two spur gear teeth was considered in different contact positions, representing a pair of mating gears during rotation. A programme has been developed to plot a pair of teeth in contact. This programme was run for each 3° of pinion rotation from the first location of contact to the last location of contact to produce 10 cases. Each case was represented a sequence position of contact between these two teeth. The programme gives graphic results for the profiles of these teeth in each position and location of contact during rotation. Finite element models were made for these cases and stress analysis was done. The results were presented and finite element analysis results were compared with theoretical calculations, wherever available.Keywords: Contact stress, Spur gear, Contact ratio, Finite elements
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1212932661 Optimal Policy for a Deteriorating Inventory Model with Finite Replenishment Rate and with Price Dependant Demand Rate and Cycle Length Dependant Price
Authors: Hamed Sabahno
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In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.Keywords: Deteriorating items, Dynamic programming, Finitereplenishment rate, Inventory control, Operation Research.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 140232660 Dynamic Meshing for Material Point Method Computations
Authors: Wookuen Shin, Gregory R. Miller, Pedro Arduino, Peter Mackenzie-Helnwein
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This paper presents strategies for dynamically creating, managing and removing mesh cells during computations in the context of the Material Point Method (MPM). The dynamic meshing approach has been developed to help address problems involving motion of a finite size body in unbounded domains in which the extent of material travel and deformation is unknown a priori, such as in the case of landslides and debris flows. The key idea is to efficiently instantiate and search only cells that contain material points, thereby avoiding unneeded storage and computation. Mechanisms for doing this efficiently are presented, and example problems are used to demonstrate the effectiveness of dynamic mesh management relative to alternative approaches.
Keywords: Numerical Analysis, Material Point Method, Large Deformations, Moving Boundaries.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 214632659 Evaluation of Settlement of Coastal Embankments Using Finite Elements Method
Authors: Sina Fadaie, Seyed Abolhassan Naeini
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Coastal embankments play an important role in coastal structures by reducing the effect of the wave forces and controlling the movement of sediments. Many coastal areas are underlain by weak and compressible soils. Estimation of during construction settlement of coastal embankments is highly important in design and safety control of embankments and appurtenant structures. Accordingly, selecting and establishing of an appropriate model with a reasonable level of complication is one of the challenges for engineers. Although there are advanced models in the literature regarding design of embankments, there is not enough information on the prediction of their associated settlement, particularly in coastal areas having considerable soft soils. Marine engineering study in Iran is important due to the existence of two important coastal areas located in the northern and southern parts of the country. In the present study, the validity of Terzaghi’s consolidation theory has been investigated. In addition, the settlement of these coastal embankments during construction is predicted by using special methods in PLAXIS software by the help of appropriate boundary conditions and soil layers. The results indicate that, for the existing soil condition at the site, some parameters are important to be considered in analysis. Consequently, a model is introduced to estimate the settlement of the embankments in such geotechnical conditions.
Keywords: Consolidation, coastal embankments, settlement, numerical methods, finite elements method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 78732658 FEM Analysis of Occluded Ear Simulator with Narrow Slit Pathway
Authors: M. Sasajima, T. Yamaguchi, M. Watanabe, Y. Koike
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This paper discusses the propagation of sound waves in air, specifically in narrow rectangular pathways of an occluded-ear simulator for acoustic measurements. In narrow pathways, both the speed of sound and the phase of the sound waves are affected by the damping of the air viscosity. Herein, we propose a new finite-element method (FEM) that considers the effects of the air viscosity. The method was developed as an extension of existing FEMs for porous, sound-absorbing materials. The results of a numerical calculation for a three-dimensional ear-simulator model using the proposed FEM were validated by comparing with theoretical lumped-parameter modeling analysis and standard values.Keywords: Ear simulator, FEM, simulation, viscosity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 209732657 Analysis of a TBM Tunneling Effect on Surface Subsidence: A Case Study from Tehran, Iran
Authors: A. R. Salimi, M. Esmaeili, B. Salehi
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The development and extension of large cities induced a need for shallow tunnel in soft ground of building areas. Estimation of ground settlement caused by the tunnel excavation is important engineering point. In this paper, prediction of surface subsidence caused by tunneling in one section of seventh line of Tehran subway is considered. On the basis of studied geotechnical conditions of the region, tunnel with the length of 26.9km has been excavated applying a mechanized method using an EPB-TBM with a diameter of 9.14m. In this regard, settlement is estimated utilizing both analytical and numerical finite element method. The numerical method shows that the value of settlement in this section is 5cm. Besides, the analytical consequences (Bobet and Loganathan-Polous) are 5.29 and 12.36cm, respectively. According to results of this study, due tosaturation of this section, there are good agreement between Bobet and numerical methods. Therefore, tunneling processes in this section needs a special consolidation measurement and support system before the passage of tunnel boring machine.Keywords: TBM, Subsidence, Numerical Method, Analytical Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 540932656 Ultimate Load Capacity of the Cable Tower of Liede Bridge
Authors: Weifeng Wang, Xilong Chen, Xianwei Zeng
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The cable tower of Liede Bridge is a double-column curved-lever arched-beam portal framed structure. Being novel and unique in structure, its cable tower differs in complexity from traditional ones. This paper analyzes the ultimate load capacity of cable tower by adopting the finite element calculations and model tests which indicate that constitutive relations applied here give a better simulation of actual failure process of prestressed reinforced concrete. In vertical load, horizontal load and overloading tests, the stepped loading of the tower model is of linear relationship, and the test data has good repeatability. All suggests that the cable tower has good bearing capacity, rational design and high emergency capacity.
Keywords: Cable tower of Liede Bridge, ultimate load capacity, model test, nonlinear finite element method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 211532655 Performance Prediction of a SANDIA 17-m Vertical Axis Wind Turbine Using Improved Double Multiple Streamtube
Authors: Abolfazl Hosseinkhani, Sepehr Sanaye
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Different approaches have been used to predict the performance of the vertical axis wind turbines (VAWT), such as experimental, computational fluid dynamics (CFD), and analytical methods. Analytical methods, such as momentum models that use streamtubes, have low computational cost and sufficient accuracy. The double multiple streamtube (DMST) is one of the most commonly used of momentum models, which divide the rotor plane of VAWT into upwind and downwind. In fact, results from the DMST method have shown some discrepancy compared with experiment results; that is because the Darrieus turbine is a complex and aerodynamically unsteady configuration. In this study, analytical-experimental-based corrections, including dynamic stall, streamtube expansion, and finite blade length correction are used to improve the DMST method. Results indicated that using these corrections for a SANDIA 17-m VAWT will lead to improving the results of DMST.
Keywords: Vertical axis wind turbine, analytical, double multiple streamtube, streamtube expansion model, dynamic stall model, finite blade length correction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 58432654 FEA for Teeth Preparations Marginal Geometry
Authors: L. Sandu, F. Topalâ, S. Porojan
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Knowledge of factors, which influence stress and its distribution, is of key importance to the successful production of durable restorations. One of this is the marginal geometry. The objective of this study was to evaluate, by finite element analysis (FEA), the influence of different marginal designs on the stress distribution in teeth prepared for cast metal crowns. Five margin designs were taken into consideration: shoulderless, chamfer, shoulder, sloped shoulder and shoulder with bevel. For each kind of preparation three dimensional finite element analyses were initiated. Maximal equivalent stresses were calculated and stress patterns were represented in order to compare the marginal designs. Within the limitation of this study, the shoulder and beveled shoulder margin preparations of the teeth are preferred for cast metal crowns from biomechanical point of view.Keywords: finite element, marginal geometry, metal crown
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 205932653 Study on Ultrasonic Vibration Effects on Grinding Process of Alumina Ceramic (Al2O3)
Authors: Javad Akbari, Hassan Borzoie, Mohammad Hossein Mamduhi
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Nowadays, engineering ceramics have significant applications in different industries such as; automotive, aerospace, electrical, electronics and even martial industries due to their attractive physical and mechanical properties like very high hardness and strength at elevated temperatures, chemical stability, low friction and high wear resistance. However, these interesting properties plus low heat conductivity make their machining processes too hard, costly and time consuming. Many attempts have been made in order to make the grinding process of engineering ceramics easier and many scientists have tried to find proper techniques to economize ceramics' machining processes. This paper proposes a new diamond plunge grinding technique using ultrasonic vibration for grinding Alumina ceramic (Al2O3). For this purpose, a set of laboratory equipments have been designed and simulated using Finite Element Method (FEM) and constructed in order to be used in various measurements. The results obtained have been compared with the conventional plunge grinding process without ultrasonic vibration and indicated that the surface roughness and fracture strength improved and the grinding forces decreased.Keywords: Engineering ceramic, Finite Element Method, Plunge grinding, Ultrasonic vibration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 238832652 Estimation of Natural Convection Heat Transfer from Plate-Fin Heat Sinks in a Closed Enclosure
Authors: Han-Taw Chen, Chung-Hou Lai, Tzu-Hsiang Lin, Ge-Jang He
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This study applies the inverse method and three- dimensional CFD commercial software in conjunction with the experimental temperature data to investigate the heat transfer and fluid flow characteristics of the plate-fin heat sink in a closed rectangular enclosure for various values of fin height. The inverse method with the finite difference method and the experimental temperature data is applied to determine the heat transfer coefficient. The k-ε turbulence model is used to obtain the heat transfer and fluid flow characteristics within the fins. To validate the accuracy of the results obtained, the comparison of the average heat transfer coefficient is made. The calculated temperature at selected measurement locations on the plate-fin is also compared with experimental data.
Keywords: Inverse method, FLUENT, k-ε model, Heat transfer characteristics, Plate-fin heat sink.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 383532651 Implicit Eulerian Fluid-Structure Interaction Method for the Modeling of Highly Deformable Elastic Membranes
Authors: Aymen Laadhari, Gábor Székely
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This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, 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 presented method. We show that stability is maintained for significantly larger time steps.Keywords: Fluid-membrane interaction, stretching, Eulerian, finite element method, Newton, implicit.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 128532650 Experimental Study on Flexural Strength of Reinforced Geopolymer Concrete Beams
Authors: Khoa Tan Nguyen, Tuan Anh Le, Kihak Lee
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This paper presents the flexural response of Reinforced Geopolymer Concrete (RGPC) beams. A commercial finite element (FE) software ABAQUS has been used to perform a structural behavior of RGPC beams. Using parameters such: stress, strain, Young’s modulus, and Poisson’s ratio obtained from experimental results, a beam model has been simulated in ABAQUS. The results from experimental tests and ABAQUS simulation were compared. Due to friction forces at the supports and loading rollers; slip occurring, the actual deflection of RGPC beam from experimental test results were slightly different from the results of ABAQUS. And there is good agreement between the crack patterns of fly ash-based geopolymer concrete generated by FE analysis using ABAQUS, and those in experimental data.
Keywords: Geopolymer concrete beam, finite element method, stress strain relation, modulus elasticity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 248632649 Numerical Investigation of Baffle Effect on the Flow in a Rectangular Primary Sedimentation Tank
Authors: M. Shahrokhi, F. Rostami, M.A. Md Said, S. Syafalni
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It is essential to have a uniform and calm flow field for a settling tank to have high performance. In general, the recirculation zones always occurred in sedimentation tanks. The presence of these regions may have different effects. The nonuniformity of the velocity field, the short-circuiting at the surface and the motion of the jet at the bed of the tank that occurs because of the recirculation in the sedimentation layer, are affected by the geometry of the tank. There are some ways to decrease the size of these dead zones, which would increase the performance. One of the ways is to use a suitable baffle configuration. In this study, the presence of baffle with different position has been investigated by a finite volume method, with VOF (Volume of Fluid) model. Besides, the k-ε turbulence model is used in the numerical calculations. The results indicate that the best position of the baffle is obtained when the volume of the recirculation region is minimized or is divided to smaller part and the flow field trend to be uniform in the settling zone.Keywords: Sedimentation tanks, Baffle, Numerical Modeling, VOF, Circulation Zone
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 272632648 Numerical Investigation of Embankment Settlement Improved by Method of Preloading by Vertical Drains
Authors: Seyed Abolhasan Naeini, Saeideh Mohammadi
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Time dependent settlement due to loading on soft saturated soils produces many problems such as high consolidation settlements and low consolidation rates. Also, long term consolidation settlement of soft soil underlying the embankment leads to unpredicted settlements and cracks on soil surface. Preloading method is an effective improvement method to solve this problem. Using vertical drains in preloading method is an effective method for improving soft soils. Applying deep soil mixing method on soft soils is another effective method for improving soft soils. There are little studies on using two methods of preloading and deep soil mixing simultaneously. In this paper, the concurrent effect of preloading with deep soil mixing by vertical drains is investigated through a finite element code, Plaxis2D. The influence of parameters such as deep soil mixing columns spacing, existence of vertical drains and distance between them, on settlement and stability factor of safety of embankment embedded on soft soil is investigated in this research.
Keywords: Preloading, soft soil, vertical drains, deep soil mixing, consolidation settlement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 71732647 Rational Points on Elliptic Curves 2 3 3y = x + a inF , where p 5(mod 6) is Prime
Authors: Gokhan Soydan, Musa Demirci, Nazli Yildiz Ikikardes, Ismail Naci Cangul
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In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.
Keywords: Elliptic curves over finite fields, rational points.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 224932646 Finite Element Modelling of a 3D Woven Composite for Automotive Applications
Authors: Ahmad R. Zamani, Luigi Sanguigno, Angelo R. Maligno
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A 3D woven composite, designed for automotive applications, is studied using Abaqus Finite Element (FE) software suite. Python scripts were developed to build FE models of the woven composite in Complete Abaqus Environment (CAE). They can read TexGen or WiseTex files and automatically generate consistent meshes of the fabric and the matrix. A user menu is provided to help define parameters for the FE models, such as type and size of the elements in fabric and matrix as well as the type of matrix-fabric interaction. Node-to-node constraints were imposed to guarantee periodicity of the deformed shapes at the boundaries of the representative volume element of the composite. Tensile loads in three axes and biaxial loads in x-y directions have been applied at different Fibre Volume Fractions (FVFs). A simple damage model was implemented via an Abaqus user material (UMAT) subroutine. Existing tools for homogenization were also used, including voxel mesh generation from TexGen as well as Abaqus Micromechanics plugin. Linear relations between homogenised elastic properties and the FVFs are given. The FE models of composite exhibited balanced behaviour with respect to warp and weft directions in terms of both stiffness and strength.
Keywords: 3D woven composite, meso-scale finite element modelling, homogenisation of elastic material properties, Abaqus Python scripting.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 92132645 Turbulent Forced Convection Flow in a Channel over Periodic Grooves Using Nanofluids
Authors: Farshid Fathinia, Mohammad Parsazadeh, Amirhossein Heshmati
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Turbulent forced convection flow in a 2-dimensional channel over periodic grooves is numerically investigated. Finite volume method is used to study the effect of turbulence model. The range of Reynolds number varied from 10000 to 30000 for the ribheight to channel-height ratio (B/H) of 2. The downstream wall is heated by a uniform heat flux while the upstream wall is insulated. The investigation is analyzed with different types of nanoparticles such as SiO2, Al2O3, and ZnO, with water as a base fluid are used. The volume fraction is varied from 1% to 4% and the nanoparticle diameter is utilized between 20nm to 50nm. The results revealed 114% heat transfer enhancement compared to the water in a grooved channel by using SiO2 nanoparticle with volume fraction and nanoparticle diameter of 4% and 20nm respectively.
Keywords: Forced convection, Periodic grooves, Nanofluids, Turbulent model, Heat transfer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 206232644 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach
Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam
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Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 177232643 An Identification Method of Geological Boundary Using Elastic Waves
Authors: Masamitsu Chikaraishi, Mutsuto Kawahara
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This paper focuses on a technique for identifying the geological boundary of the ground strata in front of a tunnel excavation site using the first order adjoint method based on the optimal control theory. The geological boundary is defined as the boundary which is different layers of elastic modulus. At tunnel excavations, it is important to presume the ground situation ahead of the cutting face beforehand. Excavating into weak strata or fault fracture zones may cause extension of the construction work and human suffering. A theory for determining the geological boundary of the ground in a numerical manner is investigated, employing excavating blasts and its vibration waves as the observation references. According to the optimal control theory, the performance function described by the square sum of the residuals between computed and observed velocities is minimized. The boundary layer is determined by minimizing the performance function. The elastic analysis governed by the Navier equation is carried out, assuming the ground as an elastic body with linear viscous damping. To identify the boundary, the gradient of the performance function with respect to the geological boundary can be calculated using the adjoint equation. The weighed gradient method is effectively applied to the minimization algorithm. To solve the governing and adjoint equations, the Galerkin finite element method and the average acceleration method are employed for the spatial and temporal discretizations, respectively. Based on the method presented in this paper, the different boundary of three strata can be identified. For the numerical studies, the Suemune tunnel excavation site is employed. At first, the blasting force is identified in order to perform the accuracy improvement of analysis. We identify the geological boundary after the estimation of blasting force. With this identification procedure, the numerical analysis results which almost correspond with the observation data were provided.
Keywords: Parameter identification, finite element method, average acceleration method, first order adjoint equation method, weighted gradient method, geological boundary, navier equation, optimal control theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 158232642 CFD Simulation of Fixed Bed Reactor in Fischer-Tropsch Synthesis of GTL Technology
Authors: Sh. Shahhosseini, S. Alinia, M. Irani
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In this paper 2D Simulation of catalytic Fixed Bed Reactor in Fischer-Tropsch Synthesis of GTL technology has been performed utilizing computational fluid dynamics (CFD). Synthesis gas (a mixture of carbon monoxide and hydrogen) has been used as feedstock. The reactor was modeled and the model equations were solved employing finite volume method. The model was validated against the experimental data reported in literature. The comparison showed a good agreement between simulation results and the experimental data. In addition, the model was applied to predict the concentration contours of the reactants and products along the length of reactor.
Keywords: GTL, Fischer–Tropsch synthesis, Fixed Bed Reactor, CFD simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 292032641 Heat and Mass Transfer of an Oscillating Flow in a Porous Channel with Chemical Reaction
Authors: Z. Neffah, H. Kahalerras
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A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.Keywords: Chemical reaction, heat transfer, mass transfer, oscillating flow, porous channel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2010