Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 141

Search results for: finite difference

141 Analysis of One Dimensional Advection Diffusion Model Using Finite Difference Method

Authors: Vijay Kumar Kukreja, Ravneet Kaur

Abstract:

In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 37
140 MHD Natural Convection Flow of Tangent Hyperbolic Nanofluid Past a Vertical Permeable Cone

Authors: A. Mahdy

Abstract:

In this paper, a non-similraity analysis has been presented to exhibit the two-dimensional boundary layer flow of magnetohydrodynamic (MHD) natural convection of tangent hyperbolic nanofluid nearby a vertical permeable cone in the presence of variable wall temperature impact. The mutated boundary layer nonlinear governing equations are solved numerically by the an efficient implicit finite difference procedure. For both nanofluid effective viscosity and nanofluid thermal conductivity, a number of experimental relations have been recognized. For characterizing the nanofluid, the compatible nanoparticle volume fraction model has been used. Nusselt number and skin friction coefficient are calculated for some values of Weissenberg number W, surface temperature exponent n, magnetic field parameter Mg, power law index m and Prandtl number Pr as functions of suction parameter. The rate of heat transfer from a vertical permeable cone in a regular fluid is less than that in nanofluids. A best convection has been presented by Copper nanoparticle among all the used nanoparticles.

Keywords: Tangent hyperbolic nanofluid, finite difference, non-similarity, isothermal cone.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 73
139 Electromagnetic Wave Propagation Equations in 2D by Finite Difference Method

Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 99
138 A Numerical Study of Seismic Response of Shallow Square Tunnels in Two-Layered Ground

Authors: Mahmoud Hassanlourad, Mehran Naghizadehrokni, Vahid Molaei

Abstract:

In this study, the seismic behavior of a shallow tunnel with square cross section is investigated in a two layered and elastic heterogeneous environment using numerical method. To do so, FLAC finite difference software was used. Behavioral model of the ground and tunnel structure was assumed linear elastic. Dynamic load was applied to the model for 0.2 seconds from the bottom in form of a square pulse with maximum acceleration of 1 m/s2. The interface between the two layers was considered at three different levels of crest, middle, and bottom of the tunnel. The stiffness of the two upper and lower layers was considered to be varied from 10 MPa to 1000 MPa. Deformation of cross section of the tunnel due to dynamic load propagation, as well as the values of axial force and bending moment created in the tunnel structure, were examined in the three states mentioned above. The results of analyses show that heterogeneity of the environment, its stratification, and positioning of the interface of the two layers with respect to tunnel height and the stiffness ratio of the two layers have significant effects on the value of bending moment, axial force, and distortion of tunnel cross-section.

Keywords: Dynamic analysis, shallow-buried tunnel, two-layered ground.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 218
137 Numerical Evaluation of Lateral Bearing Capacity of Piles in Cement-Treated Soils

Authors: Reza Ziaie Moayed, Saeideh Mohammadi

Abstract:

Soft soil is used in many of civil engineering projects like coastal, marine and road projects. Because of low shear strength and stiffness of soft soils, large settlement and low bearing capacity will occur under superstructure loads. This will make the civil engineering activities more difficult and costlier. In the case of soft soils, improvement is a suitable method to increase the shear strength and stiffness for engineering purposes. In recent years, the artificial cementation of soil by cement and lime has been extensively used for soft soil improvement. Cement stabilization is a well-established technique for improving soft soils. Artificial cementation increases the shear strength and hardness of the natural soils. On the other hand, in soft soils, the use of piles to transfer loads to the depths of ground is usual. By using cement treated soil around the piles, high bearing capacity and low settlement in piles can be achieved. In the present study, lateral bearing capacity of short piles in cemented soils is investigated by numerical approach. For this purpose, three dimensional (3D) finite difference software, FLAC 3D is used. Cement treated soil has a strain hardening-softening behavior, because of breaking of bonds between cement agent and soil particle. To simulate such behavior, strain hardening-softening soil constitutive model is used for cement treated soft soil. Additionally, conventional elastic-plastic Mohr Coulomb constitutive model and linear elastic model are used for stress-strain behavior of natural soils and pile. To determine the parameters of constitutive models and also for verification of numerical model, the results of available triaxial laboratory tests on and insitu loading of piles in cement treated soft soil are used. Different parameters are considered in parametric study to determine the effective parameters on the bearing of the piles on cemented treated soils. In the present paper, the effect of various length and height of the artificial cemented area, different diameter and length of the pile and the properties of the materials are studied. Also, the effect of choosing a constitutive model for cemented treated soils in the bearing capacity of the pile is investigated.

Keywords: Cement-treated soils, pile, lateral capacity, FLAC 3D.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 279
136 Numerical Modelling of Crack Initiation around a Wellbore Due to Explosion

Authors: Meysam Lak, Mohammad Fatehi Marji, Alireza Yarahamdi Bafghi, Abolfazl Abdollahipour

Abstract:

A wellbore is a hole that is drilled to aid in the exploration and recovery of natural resources including oil and gas. Occasionally, in order to increase productivity index and porosity of the wellbore and reservoir, the well stimulation methods have been used. Hydraulic fracturing is one of these methods. Moreover, several explosions at the end of the well can stimulate the reservoir and create fractures around it. In this study, crack initiation in rock around the wellbore has been numerically modeled due to explosion. One, two, three, and four pairs of explosion have been set at the end of the wellbore on its wall. After each stage of the explosion, results have been presented and discussed. Results show that this method can initiate and probably propagate several fractures around the wellbore.

Keywords: Crack initiation, explosion, finite difference modelling, well productivity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 393
135 Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: Biomagnetic fluid, FHD, nonlinear stretching sheet, slip parameter.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 430
134 A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity

Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 495
133 3D Numerical Analysis of Stone Columns Reinforced with Horizontal and Vertical Geosynthetic Materials

Authors: R. Ziaie Moayed, A. Khalili

Abstract:

Improvement and reinforcement of soils with poor strength and engineering properties for constructing low height structures or structures such as liquid storage tanks, bridge columns, and heavy structures have necessitated applying particular techniques. Stone columns are among the well-known methods applied in such soils. This method provides an economically justified way for improving engineering properties of soft clay and loose sandy soils. Stone column implementation in these soils increases their bearing capacity and reduces the settlement of foundation build on them. In the present study, the finite difference based FLAC3D software was used to investigate the performance and effect of soil reinforcement through stone columns without lining and those with geosynthetic lining with different levels of stiffness in horizontal and vertical modes in clayey soils. The results showed that soil improvement using stone columns with lining in vertical and horizontal modes results in improvement of bearing capacity and foundation settlement.

Keywords: Bearing capacity, FLAC3D, geosynthetic, settlement, stone column.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 533
132 Unsteady Natural Convection Heat and Mass Transfer of Non-Newtonian Casson Fluid along a Vertical Wavy Surface

Authors: A. Mahdy, Sameh E. Ahmed

Abstract:

Detailed numerical calculations are illustrated in our investigation for unsteady natural convection heat and mass transfer of non-Newtonian Casson fluid along a vertical wavy surface. The surface of the plate is kept at a constant temperature and uniform concentration. To transform the complex wavy surface to a flat plate, a simple coordinate transformation is employed. The resulting partial differential equations are solved using the fully implicit finite difference method with SUR procedure. Flow and heat transfer characteristics are investigated for a wide range of values of the Casson parameter, the dimensionless time parameter, the buoyancy ratio and the amplitude-wavelength parameter. It is found that, the variations of the Casson parameter have significant effects on the fluid motion, heat and mass transfer. Also, the maximum and minimum values of the local Nusselt and Sherwood numbers increase by increase either the Casson parameter or the buoyancy ratio.

Keywords: Casson fluid, wavy surface, mass transfer, transient analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 472
131 Two-Dimensional Observation of Oil Displacement by Water in a Petroleum Reservoir through Numerical Simulation and Application to a Petroleum Reservoir

Authors: Ahmad Fahim Nasiry, Shigeo Honma

Abstract:

We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 667
130 Tsunami Inundation Modeling in a Boundary Fitted Curvilinear Grid Model Using the Method of Lines Technique

Authors: M. Ashaque Meah, M. Shah Noor, M Asif Arefin, Md. Fazlul Karim

Abstract:

A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4th order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.

Keywords: Open boundary condition, moving boundary condition, boundary-fitted curvilinear grids, far field tsunami, Shallow Water Equations, tsunami source, Indonesian tsunami of 2004.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 474
129 Numerical Study of Flapping-Wing Flight of Hummingbird Hawkmoth during Hovering: Longitudinal Dynamics

Authors: Yao Jie, Yeo Khoon Seng

Abstract:

In recent decades, flapping wing aerodynamics has attracted great interest. Understanding the physics of biological flyers such as birds and insects can help improve the performance of micro air vehicles. The present research focuses on the aerodynamics of insect-like flapping wing flight with the approach of numerical computation. Insect model of hawkmoth is adopted in the numerical study with rigid wing assumption currently. The numerical model integrates the computational fluid dynamics of the flow and active control of wing kinematics to achieve stable flight. The computation grid is a hybrid consisting of background Cartesian nodes and clouds of mesh-free grids around immersed boundaries. The generalized finite difference method is used in conjunction with single value decomposition (SVD-GFD) in computational fluid dynamics solver to study the dynamics of a free hovering hummingbird hawkmoth. The longitudinal dynamics of the hovering flight is governed by three control parameters, i.e., wing plane angle, mean positional angle and wing beating frequency. In present work, a PID controller works out the appropriate control parameters with the insect motion as input. The controller is adjusted to acquire desired maneuvering of the insect flight. The numerical scheme in present study is proven to be accurate and stable to simulate the flight of the hummingbird hawkmoth, which has relatively high Reynolds number. The PID controller is responsive to provide feedback to the wing kinematics during the hovering flight. The simulated hovering flight agrees well with the real insect flight. The present numerical study offers a promising route to investigate the free flight aerodynamics of insects, which could overcome some of the limitations of experiments.

Keywords: Aerodynamics, flight control, computational fluid dynamics, flapping-wing flight.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 914
128 A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 871
127 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1049
126 A Comparative Study of High Order Rotated Group Iterative Schemes on Helmholtz Equation

Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 755
125 The Simulation and Experimental Investigation to Study the Strain Distribution Pattern during the Closed Die Forging Process

Authors: D. B. Gohil

Abstract:

Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with the actual material by using the theory of similarity. There are several methods available to resolve the complexity involved in the closed die forging process. Finite Element Method (FEM) and Finite Difference Method (FDM) are relatively difficult as compared to the slab method. The slab method is very popular and very widely used by the people working on shop floor because it is relatively easy to apply and reasonably accurate for most of the common forging load requirement computations.

Keywords: Experimentation, forging, process modeling, strain distribution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 914
124 EHD Effect on the Dynamic Characteristics of a Journal Bearing Lubricated with Couple Stress Fluids

Authors: B. Chetti, W. A. Crosby

Abstract:

This paper presents a numerical analysis for the dynamic performance of a finite journal bearing lubricated with couple stress fluid taking into account the effect of the deformation of the bearing liner. The modified Reynolds equation has been solved by using finite difference technique. The dynamic characteristics in terms of stiffness coefficients, damping coefficients, critical mass and whirl ratio are evaluated for different values of eccentricity ratio and elastic coefficient for a journal bearing lubricated with a couple stress fluids and a Newtonian fluid. The results show that the dynamic characteristics of journal bearings lubricated with couple stress fluids are improved compared to journal bearings lubricated with Newtonian fluids.

Keywords: Circular bearing, elastohydrodynamic, stability, couple stress.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 856
123 Investigation of Flame and Soot Propagation in Non-Air Conditioned Railway Locomotives

Authors: Abhishek Agarwal, Manoj Sarda, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

Abstract:

Propagation of fire through a non-air conditioned railway compartment is studied by virtue of numerical simulations. Simultaneous computational fire dynamics equations, such as Navier-Stokes, lumped species continuity, overall mass and energy conservation, and heat transfer are solved using finite volume based (for radiation) and finite difference based (for all other equations) solver, Fire Dynamics Simulator (FDS). A single coupe with an eight berth occupancy is used to establish the numerical model, followed by the selection of a three coupe system as the fundamental unit of the locomotive compartment. Heat Release Rate Per Unit Area (HRRPUA) of the initial fire is varied to consider a wide range of compartmental fires. Parameters, such as air inlet velocity relative to the locomotive at the windows, the level of interaction with the ambiance and closure of middle berth are studied through a wide range of numerical simulations. Almost all the loss of lives and properties due to fire breakout can be attributed to the direct or indirect exposure to flames or to the inhalation of toxic gases and resultant suffocation due to smoke and soot. Therefore, the temporal stature of fire and smoke are reported for each of the considered cases which can be used in the present or extended form to develop guidelines to be followed in case of a fire breakout.

Keywords: Fire dynamics, flame propagation, locomotive fire, soot flow pattern.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 744
122 Numerical Simulations of Fire in Typical Air Conditioned Railway Coach

Authors: Manoj Sarda, Abhishek Agarwal, Juhi Kaushik, Vatsal Sanjay, Arup Kumar Das

Abstract:

Railways in India remain primary mode of transport having one of the largest networks in the world and catering to billions of transits yearly. Catastrophic economic damage and loss to life is encountered over the past few decades due to fire to locomotives. Study of fire dynamics and fire propagation plays an important role in evacuation planning and reducing losses. Simulation based study of propagation of fire and soot inside an air conditioned coach of Indian locomotive is done in this paper. Finite difference based solver, Fire Dynamic Simulator (FDS) version 6 has been used for analysis. A single air conditioned 3 tier coupe closed to ambient surroundings by glass windows having occupancy for 8 people is the basic unit of the domain. A system of three such coupes combined is taken to be fundamental unit for the entire study to resemble effect to an entire coach. Analysis of flame and soot contours and concentrations is done corresponding to variations in heat release rate per unit volume (HRRPUA) of fire source, variations in conditioned air velocity being circulated inside coupes by vents and an alternate fire initiation and propagation mechanism via ducts. Quantitative results of fractional area in top and front view of the three coupes under fire and smoke are obtained using MATLAB (IMT). Present simulations and its findings will be useful for organizations like Commission of Railway Safety and others in designing and implementing safety and evacuation measures.

Keywords: Air-conditioned coaches, fire propagation, flame contour, soot flow, train fire.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 890
121 Increase of Energy Efficiency by Means of Application of Active Bearings

Authors: Alexander Babin, Leonid Savin

Abstract:

In the present paper, increasing of energy efficiency of a thrust hybrid bearing with a central feeding chamber is considered. The mathematical model was developed to determine the pressure distribution and the reaction forces, based on the Reynolds equation and static characteristics’ equations. The boundary problem of pressure distribution calculation was solved using the method of finite differences. For various types of lubricants, geometry and operational characteristics, axial gaps can be determined, where the minimal friction coefficient is provided. The next part of the study considers the application of servovalves in order to maintain the desired position of the rotor. The report features the calculation results and the analysis of the influence of the operational and geometric parameters on the energy efficiency of mechatronic fluid-film bearings.

Keywords: Active bearings, energy efficiency, mathematical model, mechatronics, thrust multipad bearing.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 817
120 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 771
119 Numerical Analysis and Influence of the Parameters on Slope Stability

Authors: Fahim Kahlouche, Alaoua Bouaicha, Sihem ChaƮbeddra, Sid-Ali Rafa, Abdelhamid Benouali

Abstract:

A designing of a structure requires its realization on rough or sloping ground. Besides the problem of the stability of the landslide, the behavior of the foundations that are bearing the structure is influenced by the destabilizing effect of the ground’s slope. This article focuses on the analysis of the slope stability exposed to loading by introducing the different factors influencing the slope’s behavior on the one hand, and on the influence of this slope on the foundation’s behavior on the other hand. This study is about the elastoplastic modelization using FLAC 2D. This software is based on the finite difference method, which is one of the older methods of numeric resolution of differential equations system with initial and boundary conditions. It was developed for the geotechnical simulation calculation. The aim of this simulation is to demonstrate the notable effect of shear modulus « G », cohesion « C », inclination angle (edge) « β », and distance between the foundation and the head of the slope on the stability of the slope as well as the stability of the foundation. In our simulation, the slope is constituted by homogenous ground. The foundation is considered as rigid/hard; therefore, the loading is made by the application of the vertical strengths on the nodes which represent the contact between the foundation and the ground. 

Keywords: Slope, shallow foundation, numeric method, FLAC 2D.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 760
118 A Semi-Implicit Phase Field Model for Droplet Evolution

Authors: M. H. Kazemi, D. Salac

Abstract:

A semi-implicit phase field method for droplet evolution is proposed. Using the phase field Cahn-Hilliard equation, we are able to track the interface in multiphase flow. The idea of a semi-implicit finite difference scheme is reviewed and employed to solve two nonlinear equations, including the Navier-Stokes and the Cahn-Hilliard equations. The use of a semi-implicit method allows us to have larger time steps compared to explicit schemes. The governing equations are coupled and then solved by a GMRES solver (generalized minimal residual method) using modified Gram-Schmidt orthogonalization. To show the validity of the method, we apply the method to the simulation of a rising droplet, a leaky dielectric drop and the coalescence of drops. The numerical solutions to the phase field model match well with existing solutions over a defined range of variables.

Keywords: Coalescence, leaky dielectric, numerical method, phase field, rising droplet, semi-implicit method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 272
117 Radiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction

Authors: Motahar Reza, Rajni Chahal, Neha Sharma

Abstract:

This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1413
116 Conjugate Free Convection in a Square Cavity Filled with Nanofluid and Heated from Below by Spatial Wall Temperature

Authors: Ishak Hashim, Ammar Alsabery

Abstract:

The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating.

Keywords: Conjugate free convection, nanofluid, spatial temperature.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1055
115 Probabilistic Simulation of Triaxial Undrained Cyclic Behavior of Soils

Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

Abstract:

In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1205
114 Wetting Characterization of High Aspect Ratio Nanostructures by Gigahertz Acoustic Reflectometry

Authors: C. Virgilio, J. Carlier, P. Campistron, M. Toubal, P. Garnier, L. Broussous, V. Thomy, B. Nongaillard

Abstract:

Wetting efficiency of microstructures or nanostructures patterned on Si wafers is a real challenge in integrated circuits manufacturing. In fact, bad or non-uniform wetting during wet processes limits chemical reactions and can lead to non-complete etching or cleaning inside the patterns and device defectivity. This issue is more and more important with the transistors size shrinkage and concerns mainly high aspect ratio structures. Deep Trench Isolation (DTI) structures enabling pixels’ isolation in imaging devices are subject to this phenomenon. While low-frequency acoustic reflectometry principle is a well-known method for Non Destructive Test applications, we have recently shown that it is also well suited for nanostructures wetting characterization in a higher frequency range. In this paper, we present a high-frequency acoustic reflectometry characterization of DTI wetting through a confrontation of both experimental and modeling results. The acoustic method proposed is based on the evaluation of the reflection of a longitudinal acoustic wave generated by a 100 µm diameter ZnO piezoelectric transducer sputtered on the silicon wafer backside using MEMS technologies. The transducers have been fabricated to work at 5 GHz corresponding to a wavelength of 1.7 µm in silicon. The DTI studied structures, manufactured on the wafer frontside, are crossing trenches of 200 nm wide and 4 µm deep (aspect ratio of 20) etched into a Si wafer frontside. In that case, the acoustic signal reflection occurs at the bottom and at the top of the DTI enabling its characterization by monitoring the electrical reflection coefficient of the transducer. A Finite Difference Time Domain (FDTD) model has been developed to predict the behavior of the emitted wave. The model shows that the separation of the reflected echoes (top and bottom of the DTI) from different acoustic modes is possible at 5 Ghz. A good correspondence between experimental and theoretical signals is observed. The model enables the identification of the different acoustic modes. The evaluation of DTI wetting is then performed by focusing on the first reflected echo obtained through the reflection at Si bottom interface, where wetting efficiency is crucial. The reflection coefficient is measured with different water / ethanol mixtures (tunable surface tension) deposited on the wafer frontside. Two cases are studied: with and without PFTS hydrophobic treatment. In the untreated surface case, acoustic reflection coefficient values with water show that liquid imbibition is partial. In the treated surface case, the acoustic reflection is total with water (no liquid in DTI). The impalement of the liquid occurs for a specific surface tension but it is still partial for pure ethanol. DTI bottom shape and local pattern collapse of the trenches can explain these incomplete wetting phenomena. This high-frequency acoustic method sensitivity coupled with a FDTD propagative model thus enables the local determination of the wetting state of a liquid on real structures. Partial wetting states for non-hydrophobic surfaces or low surface tension liquids are then detectable with this method.

Keywords: Wetting, acoustic reflectometry, gigahertz, semiconductor.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 850
113 Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration

Authors: Maria Neagu

Abstract:

This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parameters. These results are verified using the finite differences method applied to the conservation equations.

Keywords: Finite difference method, natural convection, porous medium, scale analysis, thermal stratification.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1247
112 Finite Difference Method of the Seismic Analysis of Earth Dam

Authors: Alaoua Bouaicha, Fahim Kahlouche, Abdelhamid Benouali

Abstract:

Many embankment dams have suffered failures during earthquakes due to the increase of pore water pressure under seismic loading. After analyzing of the behavior of embankment dams under severe earthquakes, major advances have been attained in the understanding of the seismic action on dams. The present study concerns numerical analysis of the seismic response of earth dams. The procedure uses a nonlinear stress-strain relation incorporated into the code FLAC2D based on the finite difference method. This analysis provides the variation of the pore water pressure and horizontal displacement.

Keywords: Earthquake, numerical analysis, FLAC2D, displacement, Embankment Dam, pore water pressure.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1862