Search

Computational fluid dynamics (CFD) was first introduced in the ventilation industry in the 1970s. CFD has been increasingly used since then, as testified by the number of peer-reviewed articles, which was less than 10 per year in the 1990s, and which is now 60 to 70 per year.This article discusses the principle behind CFD, the development in numerical schemes, turbulence models and the importance of the increased computer size since the 1970s.Special attention is given to the selection of the correct governing equations, to the understanding of low turbulent flow, to the selection of turbulence models, and to addressing situations with more steady-state solutions.The article finishes with a number of different case studies such as design of air supply openings, smoke management in buildings, cross-infection risks from the exhalation of particles and calculation of people moving in a room. The use of benchmark tests is also addressed.

The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT). The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model). The second model was consisting of Functionally Graded Material (FGM) as a coated layer and metal substrate (FGC model). From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials. The Authors, published by EDP Sciences, 2018. Scopus

In this paper, we introduce a space fractional negative binomial (SFNB) process by subordinating the space fractional Poisson process to a gamma subordinator. Its one-dimensional distributions are derived in terms of generalized Wright functions and their governing equations are obtained. It is a L\'evy process and the corresponding L\'evy measure is given. Extensions to the case of distributed order SFNB process, where the fractional index follows a two-point distribution, is analyzed in detail. The connections of the SFNB process to a space fractional Polya-type process is also pointed out. Moreover, we define and study a multivariate version of the SFNB obtained by subordinating a $d$-dimensional space-fractional Poisson process by a common independent gamma subordinator. Some applications of the SFNB process to the studies of population's growth and epidemiology are pointed out. Finally, we discuss an algorithm for the simulation of the SFNB process., Comment: 25 pages, 4 figures

Date of Conference: 27-31 August 2017 Conference Name: ASME 2017 15th International Conference on Nanochannels, Microchannels, and Minichannels, ICNMM 2017 The purpose of this study is presenting an active micromixer, which is based on AC electro-osmotic flow driven on 3D micro wires. In order to solve governing equations of AC electroosmosis, a commercial software COMSOL Multiphysics® is implemented. Different wire configurations with various imposed electric fields and flow rates are tested for evaluating mixing efficiencies. The analyses show that mixing performance is significantly improved by number of the wires as well as wire orientation. It is also revealed that the degree of mixing can also be controlled by the tuning of the applied voltage for a given flow rate.

Analysis of natural convection in porous right angled triangular enclosures with a concave/ convex hypotenuse has been carried out using the Bejan's heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case. Copyright � Taylor & Francis Group, LLC.

In this study a set of twelve linearized disturbance dynamic equations in canonical form is derived systematically and in a comprehensive manner based on the first order shear deformation theory to study the buckling and vibration analysis of helical coil springs made of isotropic linear materials. Those complete equations comprise the axial and shear deformation effects together with rotatory inertia effects. The special case of these equations corresponds also to the equations for straight and circular rods. The main differences among the existing formulations based on the same approach are discussed briefly. The resulting equations are used for numerical buckling and free vibration analyses to show its soundness. © Springer Science+Business Media B.V. 2011. Acknowledgements The material covered in this paper is based upon work was supported by the research grant 106M307 from Technical Research Council of Turkey (TUBITAK).

The Transmission Line loudspeaker is an audio loudspeaker enclosure topology devoted to extending the low frequency range near the loudspeaker frequency resonance. A few models based on physical properties of damped pipes have been proposed to characterize the Transmission Line loudspeaker systems. Unfortunately, Thiele/Small parameters, which are usually employed in enclosure designs, are not useful as parameters of design for these loudspeakers. In this paper, a comprehensive numerical formulation of a Transmission Line loudspeaker is presented, which is based in a finite difference approach of the governing equations, including the effects of the absorbing material allocated inside the pipe. The influence of the main empirical parameters is tested on the proposed model, which is also compared to a real prototype for validation purposes. © 2011 Elsevier Ltd. All rights reserved., Authors want sincerely thank to Daniel Garcia for his valuable collaboration performing simulations. Authors are also very grateful to Dr. Viciana for her thoughtful and critical comments about this work. This work has been supported by Spanish Ministry of Science and Technology (MCYT) under Project Ref. TEC2009-14414-C03-01 and FEDER funds.

A numerical model is developed for studying the transport of bacterial facilitated contaminants in a coupled fracture-matrix system. The contaminants and bacteria are assumed to sorb onto the fracture surface, the contaminants are assumed to diffuse into the rock-matrix. Bacteria are assumed not to diffuse into the rock-matrix. The sorption of the contaminants onto the mobile and immobile bacteria within the fracture is assumed to be linear. The governing equations describing the bacterial transport and contaminant transport along the fracture as well as rock-matrix are coupled with each other. The coupled non-linear equations are solved numerically with fully implicit finite difference method. Constant concentration is assumed at the inlet of the fracture for both contaminants and bacteria. A varying grid is adopted at the fracture and rock-matrix interface to capture the flux transfer to ensure fluid mass transfer. Sensitivity analysis is performed to investigate the effects of various bacterial transport properties on the contaminant concentration in the fracture-matrix coupled system. Results suggest that for the contaminant and bacterial transport parameters that have been analysed, the bacterial concentration increases nearer to the fracture inlet due to consumption of contaminant substrate and consequently the contaminant concentration drastically reduces at the in the vicinity of fracture inlet. When the bacterial cells completely decay, the dead bacterial cells release the contaminants into the aqueous phase resulting in instantaneous increase in the contaminant concentration further away from the fracture inlet. For low matrix porosity and high half fracture aperture, bacterial concentration is consistent for a large portion of the fracture. There is significant bacterial concentration throughout the length of the fracture when the sorption coefficient of bacteria on the fracture wall surface is very low. When specific growth rate of bacteria is very high, an exponential growth pattern is observed nearer to the fracture inlet. � 2011 Elsevier B.V.

Analysis of thermoacoustic instability is performed in a horizontal Rijke tube with an electrical resistance heater as the heat source. The analysis starts with the governing equations for the ∞uid ∞ow. The governing equations become stifi and are di‐cult to solve by CFD, as the Mach number of the steady ∞ow and the thickness of the heat source (compared to the acoustic wavelength) are small. Therefore asymptotic analysis is performed in the limit of small Mach number and compact heat source to eliminate the above stifiness problem. The unknown variables are expanded in powers of Mach number. Two systems of governing equations are obtained: one for the acoustic fleld and the other for the unsteady ∞ow fleld in the hydrodynamic zone around the heater. The coupling between the acoustic fleld and the unsteady heat release rate from the heater appears naturally from asymptotic analysis. Further, a non-trivial additional term appears in the momentum equation of the hydrodynamic zone, which has serious consequences on the stability of the system. This additional term is the pseudo-acceleration term, which appears due to the change in the frame of reference from an inertial frame to an accelerating frame of reference, performed in the hydrodynamic zone during the asymptotic analysis. The presence of pseudo-acceleration term is generic, when there are two length scales involved in the problem. Subcritical transition to instability is simulated in the present paper and is related to the hysteresis in the asymptotic state of the system with the heater power, observed in Rijke tube experiments. The global asymptotic stability of the system with the system parameters is investigated using bifurcation diagram. Present numerical simulations conflrm the importance of the pseudo-acceleration term. Bifurcation diagrams obtained from the simulations with and without pseudo-acceleration term are completely difierent. The transition to instability occurs via difierent types of bifurcations in the above two cases. Simulations performed with the response function for the unsteady heat release rate are compared with the simulation with pseudo-acceleration term. Numerical simulations are performed using the Galerkin technique for the acoustic zone and CFD for the hydrodynamic zone. Acoustic streaming is shown to happen during limit cycle and its efiect on the unsteady heat release rate is discussed.

Heatline approach has been implemented to visualize heat transfer and to study efficient thermal mixing of laminar natural convective flow in a square cavity with distributed heat sources. Four different cases, depending upon the location of the heat sources on the walls of the cavity, are studied. Wide range of fluids ( Pr = 0.015 – 1000 ) have been studied over a range of Rayleigh numbers ( Ra = 10 3 – 10 5 ) . Governing equations and Poisson-type of equations for streamfunction and heatfunction have been solved using penalty finite element method. Heatlines and streamlines are found to be adequate to visualize and understand heat energy distribution and thermal mixing occurring inside a cavity. Various qualitative and quantitative features on variations of local and average Nusselt numbers for test cases are adequately explained based on heatlines. The efficacy of distributed heating over conventional bottom heating for optimal thermal mixing is established via correlating with heatlines and cup-mixing temperature. The distributed heat sources are found to play major role for processing of molten materials and gaseous substances. Overall, it is shown that heatlines give suitable guidelines to assemble discrete heat sources and the heatline analysis on heat flow management with distributed heat sources is reported for the first time in this work.

A three dimensional, steady state, non-isothermal, single phase model was developed and simulations were carried out in order to find the effect of cathode channel dimensions (width, depth and height) on the performance of an air-breathing fuel cell. The model was solved using commercial CFD package Fluent (version 6.3). Separate user defined functions were written to solve the electrochemical equations and the water transport through the membrane along with the other governing equations. Analyses were carried out for three different channel widths (2, 4 and 6�mm), for three different channel depths (2, 6 and 10�mm) and for three different cell heights (15, 30 and 45�mm). Cell characteristics like current distribution, species distribution, oxygen mass transfer coefficient, cell temperature, cathode channel velocities and net water transport coefficients are reported. The results show that the cell performance improves with increase in cathode channel width, channel depth and with decrease in cell height. Maximum power density obtained was 240�mW/cm2 for a channel width of 4�mm and channel depth of 6�mm. When the channel depth was 2�mm the performance was limited mainly due to the resistance offered by the channel for the buoyancy induced flow. For channel depths higher than 2�mm, the diffusion resistance of the porous GDL also contributed significantly to limit the performance to low current densities. At low current densities the fuel cell is prone to flooding whereas at high current densities ohmic overpotential due to dehydration of the membrane significantly contributes to the overall voltage loss. � 2009 Elsevier Masson SAS. All rights reserved.

This paper presents domain form of the interaction integrals based on three independent formulations for computation of the stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials. Conservation integrals of J-type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields. Each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of the interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of the numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of two examples. � 2008 Elsevier Ltd. All rights reserved.

A three-dimensional numerical study has been carried out for laminar flow of air past an inline arrangement of circular tubes built-in with a rectangular channel in the presence of vortex generators. The governing equations of momentum and energy are solved with the help of a developed computational code based on finite-volume technique. Computed flow and temperature field results are analyzed with an aim to find an optimum location of vortex generators resulting in the maximum enhancement of heat transfer causing a minimum increase in pressure drop. To find the optimized location of vortex generators, the effect of variation of the Reynolds number on flow and heat transfer has also been studied.

International audience; A method to obtain the state matrix of an arbitrary linear homogeneous medium excited by a plane wave is proposed. The approach is based on projections on the eigenspace of the governing equations matrix. It is an alternative to manually obtaining a linearly independent set of equations by combining the governing equations. The resulting matrix has been validated against previously published derivations for an anisotropic poroelastic medium.

Natural convection in a fluid saturated porous medium has been numerically investigated using a generalized non-Darcy approach. The governing equations are solved by using Finite Volume approach. First order upwind scheme is employed for convective formulation and SIMPLE algorithm for pressure velocity coupling. Numerical results are presented to study the influence of parameters such as Rayleigh number (106 ?Ra ?108), Darcy number (10-5 ? Da ? 10-2), porosity (0.4 ? ? ? 0.9) and Prandtl number (0.01 ? Pr ? 10) on the flow behavior and heat transfer. By combining the method of matched asymptotic expansions with computational fluid dynamics (CFD), so called asymptotic computational fluid dynamics (ACFD) technique has been employed to generate correlation for average Nusselt number. The technique is found to be an attractive option for generating correlation and also in the analysis of natural convection in porous medium over a fairly wide range of parameters with fewer simulations for numerical solutions. � 2007 Springer-Verlag.

International audience; Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Heat transfer in electronic systems is studied by simulating flow in a two pass channel with the divider representing a circuit board. Bypass holes are introduced on the circuit board to obtain detailed physical insights of the reversed flows in the second pass and thereby improve the cooling effect. The time-dependent governing equations are solved using an in-house code based on Streamline upwind/Petrov-Galerkin finite element method for Reynolds number ranging from 100 to 900. It is observed that stagnant zones are formed in the return path along the upper heated wall due to the formation of primary recirculation region on the divider plate. These stagnant zones are convected downstream by introducing bypass slots thereby enhancing the convective cooling. A parametric study on the location and number of bypass slots reveals that for a particular combination, the flow becomes unsteady thereby the heat transfer is increased. The presence of multiple slot jets also reduces the overall pressure drop required to drive the flow and heat transfer is very high at the point of impingement between the slots.

Current work attempts to study the heatline patterns during natural convection for different types of Dirichlet heatfunction boundary conditions. The enclosures with various shapes (square, curved, trapezoidal, tilted square and parallelogrammic) are considered with various thermal boundary conditions such as (a) case 1: hot left wall, cold right wall and adiabatic horizontal walls, (b) case 2: hot bottom wall, cold left and right walls and adiabatic top wall and (c) case 3: hot bottom wall with other cold walls. Traditionally, the reference of heatfunction ( Π = 0 ) is assumed at the adiabatic wall and the implementation of reference ( Π = 0 ) may be non-trivial for the case with zero or multiple adiabatic wall(s). Various heatfunction boundary conditions have been formulated based on locations of Π = 0 for systems with more than one adiabatic walls (case 1) or no adiabatic wall (case 3). As test problems, Π = 0 is considered at the junctions of isothermal walls (cases 2 and 3) or on the isothermal wall (case 3). The governing equations are solved via the Galerkin finite element method at various Rayleigh numbers ( 10 3 and 10 5 ) and Prandtl numbers ( Pr = 0.015 and 7.2). The magnitudes of the heatfunctions change drastically with the location of the datum of Π ( Π = 0 ) whereas, the heat flow patterns remain same irrespective of the heatfunction boundary conditions. The gradients of heatfunctions or the heat flux along the active walls (hot/cold) are invariant of the choice of the reference ( Π = 0 ). The local and average Nusselt numbers are also independent of the choice of Π = 0 and the Nusselt numbers are found to be identical with heatfunction gradients obtained with various locations of Π = 0 . Current work may be useful for heat flow visualization in various thermal systems involving complex thermal boundary conditions.

The Cell Method (CM) is a computational tool that maintains critical multi-dimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This paper highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modelling heterogeneous materials.

In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrödinger equation (NLSE) extended by R. Smith (1976). This extended NLSE accounts for the effects of current gradient on the nonlinear dynamics of the ocean surface near blocking point. Using a split-step scheme we show that the extended NLSE of Smith is unstable against random chaotic perturbation in the current profile. Therefore the monochromatic wave field with unit amplitude turns into a chaotic sea state with many peaks. By comparing the numerical and analytical results, we show that rogue waves due to perturbations in the current profile are in the form of rational rogue wave solutions of the NLSE. We also discuss the effects of magnitude of the chaotic current profile perturbations on the statistics of the rogue wave generation at the ocean surface. The extension term in Smith's extended NLSE causes phase shifts and it does not change the total energy level of the wave field. Using the methodology adopted in this study, the dynamics of rogue wave occurrence on the ocean surface due to blocking effect of currents can be studied. This enhances the safety of the offshore operations and ocean travel. Publisher's Version

Computational fluid dynamics (CFD) was first introduced in the ventilation industry in the 1970s. CFD has been increasingly used since then, as testified by the number of peer-reviewed articles, which was less than 10 per year in the 1990s, and which is now 60 to 70 per year.This article discusses the principle behind CFD, the development in numerical schemes and computer size since the 1970s. Special attention is given to the selection of the correct governing equations, to the understanding of low turbulent flow, to the selection of turbulence models, and to addressing situations with more steady-state solutions.The article finishes with a number of different case studies such as flow in occupied spaces, smoke management in buildings, cross-infection risks from the exhalation of particles and calculation of people moving in a room. The use of benchmark tests is also addressed.

A numerical model is developed for analyzing the effect of time varying fracture skin thickness on contaminant transport mechanism in the fractured porous media. Recent investigations by researchers in subsurface media have brought out the importance of fracture-skin formation and its effect of contaminant transport in fracture-matrix coupled system. Implicit finite difference numerical technique has been used to solve the coupled non-linear governing equations for the triple continuum model consisting of fracture, fracture-skin and the rock-matrix. A varying grid is adopted at the fracture and fracture-skin interface to capture the mass transfer at the interface. The fracture-skin thickness is assumed to increase with time and the effect of time varying fracture skin thickness on the contaminant transport mechanism is analyzed. Results suggest that the mass transfer from the fracture to the fracture-skin is high when the fracture-skin thickness is small. The contaminant concentration for both constant as well as time varying fracture-skin thickness remains the same during the initial simulation time and varies as time progresses. The time varying fracture-skin thickness has a significant effect on the contaminant concentration at larger simulation periods. The effect of time varying fracture-skin thickness on contaminant concentration reduces with increment in the initial fracture-skin thickness. � 2014 Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg.

Using a finite-volume nodal-based code, we introduce a new consistent numerical scheme for approximating the seepage velocity in variable-density flow in porous media. It has been known from previous works that the lack of consistency in the numerical approximation for the seepage velocity can severely compromise the accuracy of numerical solutions of salt-transport in porous media. This paper provides a detailed description of the code needed for the new consistent velocity approximation, including numerical approximations and algorithm implementations. The new scheme is tested against two challenging benchmark cases in the field: the hydrostatic test and the salt-pool problem. Results obtained with the newly proposed consistent scheme show the best agreement with the benchmark experiments achieved so far. When an inconsistent approximation is used instead, the accuracy of the numerical results is greatly degraded. The current work confirms that using a consistent velocity approximation is essential for maintaining accuracy in numerical simulations of variable-density flow, especially in cases with high salt mass fraction, when the system of governing equations is strongly coupled. © 2013 Elsevier B.V. 507 33 51 33-51

Transient and laminar natural convection in a square cavity has been investigated using smoothed particle hydrodynamics (SPH) technique as a discretisation tool on uniform Eulerian grids. Although SPH is a mesh-free Lagrangian method and always applied to discretise Lagrangian form of governing equations, in this study, Eulerian form of governing equations are discretised using SPH operators. This approach is thought to be the upper limit of accuracy of Lagrangian SPH computations by preventing density error accumulation and particle disordering. In the present method, incompressibility is strictly enforced by employing SPH pressure projection method in order to obtain a divergence-free velocity field as in incompressible SPH (ISPH) method. Natural convection in a square cavity is simulated for Rayleigh numbers, Ra, between 103 and 106. Effect of Ra on the flow field and heat transfer characteristics is investigated and the method is validated by data available in the literature. Results obtained from ISPH method on Eulerian grids are in excellent agreement with data available in the literature. © 2013 Copyright Taylor and Francis Group, LLC.

The interaction of managed ice covers with a wide structure is examined. Numerical simulations are used to simulate the modes of ice cover deformation and forces on the structure. The objective of the present work is to validate the performance of the numerical model using historical data recorded during operations of the Kulluk in the Beaufort Sea during the 1980s and early 1990s. This paper is the last part of an investigation aimed at developing an approach for modeling managed ice interaction with wide moored structures. Previous papers examined the role of the mooring system (Sayed and Barker, 2011) and the effects of ice cover confinement and managed floes sizes (Sayed et al., 2012). The focus of the present paper is on providing quantitative comparison between predicted ice force statistics and observations. The numerical model is based on solving equations describing the conservation of mass and linear momentum together with a plastic yield criterion that describes ice properties. The managed ice cover consists of a heterogeneous ensemble of relatively small floes. The floes are assigned varied thickness values in order to reflect field conditions. The simulations address a class of interaction scenarios corresponding to confined managed ice. As the ice cover is driven within confined boundaries, pressure conditions arise. These conditions are of interest to designers since forces are considerably higher than those corresponding to unconfined ice covers. The solution of the governing equations simulate the evolution of the distributions of ice thickness, concentration (or coverage) and stresses. The resulting ice forces, including peak values, averages and rise-time of forces, are compared to field measurements. The influence of ice thickness and velocity on expected ice forces is also examined., OTC Arctic Technology Conference, December 3-5, 2012, Houston, Texas, USA

The differential quadrature method (DQM) and the Boubaker Polynomials Expansion Scheme (BPES) are applied in order to compute the eigenvalues of some regular fourth-order Sturm-Liouville problems. Generally, these problems include fourth-order ordinary differential equations together with four boundary conditions which are specified at two boundary points. These problems concern mainly applied-physics models like the steady-state Euler-Bernoulli beam equation and mechanicals non-linear systems identification. The approach of directly substituting the boundary conditions into the discrete governing equations is used in order to implement these boundary conditions within DQM calculations. It is demonstrated through numerical examples that accurate results for the first kth eigenvalues of the problem, where k= 1,. 2,. 3,. .... , can be obtained by using minimally 2(k+. 4) mesh points in the computational domain. The results of this work are then compared with some relevant studies. © 2011 Elsevier Inc.

Retinopathy is a surgical process in which maladies of the human eye are treated by laser irradiation. A two-dimensional numerical model of the human eye geometry has been developed to investigate transient thermal effects due to laser radiation. In particular, the influence of choroidal pigmentation and that of choroidal blood convection-parameterized as a function of choroidal blood perfusion-are investigated in detail. The Pennes bio-heat transfer equation is invoked as the governing equation, and finite volume formulation is employed in the numerical method. For a 500- ?m diameter spot size, laser power of 0.2W, and 100% absorption of laser radiation in the retinal pigmented epithelium (RPE) region, the peak RPE temperature is observed to be 103�C at 100ms of the transient simulation of the laser surgical period. Because of the participation of pigmented layer of choroid in laser absorption, peak temperature is reduced to 94�C after 100ms of the laser surgery period. The effect of choroidal blood perfusion on retinal cooling is found to be negligible during transient simulation of retinopathy. A truncated three-dimensional model incorporating multiple laser irradiation of spots is also developed to observe the spatial effect of choroidal blood perfusion and choroidal pigmentation. For a circular array of seven uniformly distributed spots of identical diameter and laser power of 0.2W, transient temperature evolution using simultaneous and sequential mode of laser surgical process is presented with analysis. � 2012 John Wiley & Sons, Ltd.

In this work, we extended the application of "the modified reductive perturbation method" to long water waves and obtained the governing equations as the KdV hierarchy. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameter c(1) so as to remove the possible secularities that might occur. The present method is seen to be fairly simple as compared to the renormalization method [Kodama, Y., & Taniuti, T. (1977). Higher order approximation in reductive perturbation method 1. Weakly dispersive system. Journal of Physics Society of Japan, 45, 298-310] and the multiple scale expansion method [Kraenkel, R. A., Manna, M. A., & Pereira, J. G. (1995). The Korteweg-deVries hierarchy and long water waves. Journal of Mathematics Physics, 36, 307-320]. Publisher's Version Author Post Print

[EN] Solution of governing equations for one-dimensional compressible unsteady flow has been performed traditionally using a homogenously distributed spatial mesh. In the resulting node structure, the internal nodes are solved by applying a shock capturing finite difference numerical method whereas the solution of the end nodes, which define the boundary conditions of the pipe, is undertaken by means of the Method of Characteristics. Besides the independent solution of every method, the coupling between the information obtained by the method of characteristics and the finite difference method is key in order to reach a good accuracy in gas dynamics modeling. The classical spatial mesh could provide numerical problems leading the boundary to generate lack of mass, momentum and energy conservation because of the interpolation methodology usually applied to draw the characteristics and path lines from its departure point at calculation time to the end of the pipe during the next time-step. To deal with this undesirable behavior, in this work a modification of the traditional grid including an extra node close to the boundary is proposed in order to explore its ability to provide numerical results with higher conservation fulfillment. © 2010 Elsevier Ltd.

Natural frequencies and modes of a floating crane with a suspended load are studied. Both the floating crane and the suspended load are modeled as rigid bodies with six degrees of freedom. The suspended load is considered to be partially immersed in the sea water. A wire rope for load suspension is assumed to be non-extensible and without bending stiffness. Linearized governing equations for a coupled dynamic response are derived based on the multibody system dynamics with small displacements assumption. An added mass for the floating crane as well as the partially immersed load is determined using traditional potential theory and tree-dimensional boundary element method (in a frequency domain). Mapping from the frequency to the time domain is necessary to determine the correct added mass value for calculating above described natural frequencies and modes. A damping of the overall system can be calculated as some small portion of a critical damping. A numerical example is based on the floating crane during positioning of precast concrete piles. These piles are main part of foundations for over sea bridges.Copyright © 2011 by ASME

In this study free vibration analysis of a Timoshenko column with a tip mass having rotary inertia is carried out by both exact solution and differential transform method (DTM). The support of the system is modeled by an elastic spring against rotation. Fixity factor is used to define the relative stiffness of the elastic connection and the column. The governing equation of the column is solved by the separation of variables method including the rotatory inertia to get the exact solution. The same problem is also solved by DTM algorithm and the results are compared with the ones of exact solution. The comparison tables are presented in numerical analysis to show that a very good agreement is observed for DTM. (C) 2011 Elsevier Ltd. All rights reserved.

Present work is the development of a finite difference scheme based on Richardson extrapolation technique. It gives an exponential compact higher order scheme (ECHOS) for two-dimensional linear convection-diffusion equations (CDE). It uses a compact nine point stencil, over which the governing equations are discretized for both fine and coarse grids. The resulting algebraic systems are solved using a line iterative approach with alternate direction implicit (ADI) procedure. Combining the solutions over fine and coarse grids, initially a sixth order solution over coarse grid points is obtained. The resultant solution is then extended to finer grid by interpolation derived from the difference operator. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be monotone. The higher order accuracy and better rate of convergence of the developed algorithm have been demonstrated by solving numerous model problems. � 2011 Published by Elsevier B.V. on behalf of IMACS.

In this study, the effect of compressibility on the nonlinear buckling of the simply supported polyurethane spherical shells subjected to an apical concentrated load is presented. The problem is strongly nonlinear both physically and geometrically. Since the closed form solution of the corresponding algebraical and differential equations is not possible, numerical methods are used unavoidably. The governing equations of the problem are converted to algebraical difference equations via the finite difference method and the obtained algebraical equations are solved numerically by using the Newton-Raphson method. Several numerical experiments corresponding to the various values of a thickness parameter, a depth parameter and a material constant related with the compressibility of polyurethane are performed and the force-apex deflection curves are drawn. Concluding remarks pertaining to the effect of the variation of the material constant related with the compressibility on the buckling loads and buckling deflections of the simply supported polyurethane spherical shells, subjected to an apical load, with various thicknesses and depths are presented. © 2010 The Author(s).

A numerical model is developed for studying the transport of colloids accompanied by radionuclides in a coupled fracture-skin-matrix system. The radionuclides and the colloids are assumed to decay, sorb onto the fracture surface, as well as diffuse into the fracture-skin and rock-matrix. The sorption of the radionuclides onto the mobile and immobile colloids within the fracture is assumed to be linear. The governing equations describing the radionuclides and colloid transport along the fracture and diffusion into fracture-skin as well as rock-matrix, normal to the fracture axis are coupled with each other. The coupled non-linear equations are solved numerically with fully implicit finite difference method. Constant concentration is assumed at the inlet of the fracture for both colloids and radionuclide. A varying grid is adopted at the fracture and skin interface to capture the flux transfer. Sensitivity analysis is performed to investigate the effect of various colloid properties on the colloid concentration in the fracture-matrix coupled system in the presence of fracture skin. Results suggests that as the colloid velocity increases the diffusion of colloids into the fracture-skin decreases due to the low residence time available for the colloids, resulting in higher colloidal concentration in the fracture. It is observed that as the filtration coefficient increases, the colloidal concentration in the fracture decreases as more colloids are filtered from the aqueous phase. The reverse mechanism occurs in the case of remobilization coefficient. Further, the effect of colloidal dispersion coefficient and diffusion into the fracture-skin on colloid migration was analysed. The concentration profiles for various diffusion coefficients of colloids in the fracture-skin pose an unusual behavior. � 2010 Elsevier B.V.

A simplified heat and fluid flow model has been used to solve the Gas Tungsten Arc (GTA) linear welding problem for austenitic stainless steel. In this study, an equivalent 2-D (two-dimensional) transient heat and fluid flow model has been used to study the effect of controlled boundary conditions with free bottom surface and with bottom insulation. The governing equations have been solved by a finite volume method. The peak temperature, maximum velocity in the weld pool, weld bead width and depth get reduced when the bottom surface of the stainless steel plate is insulated. Copyright � 2010 Inderscience Enterprises Ltd.

Bu çalışma, 12-24 Haziran 2010 tarihleri arasında İstanbul[Türkiye]’da düzenlenen 10. ASME Biennial Conference on Engineering Systems Design and Analysis’da bildiri olarak sunulmuştur. This work presents a computational fluid dynamics simulation to investigate the effects of inlet geometry on the pressure drop and particle collection efficiency of a tangential inlet cyclone. Three-dimensional, steady governing equations for the incompressible, turbulent flow inside a tangential inlet cyclone are solved numerically under certain boundary conditions. The continuous gas flow is predicted by solving Navier-Stokes equations using the differential RSM turbulence model. The second phase is modeled based on a Lagrangian approach. The commercial CFD code Fluent was used for numerical analysis. Computational results compared experimental data available in the literature for validation. Various cyclones, each has different geometrical ratio of inlet section, studied in this paper Detail analyses of the effects of inlet geometry on the flow behavior, pressure drop and collection efficiency were given. ASME, Petroleum Div

In this work, we extended the application of "the modified reductive perturbation method" to long waves in water of variable depth and obtained a set of KdV equations as the governing equations. Seeking a localized travelling wave solution to these evolution equations we determine the scale function c(1)(tau) so as to remove the possible secularities that might occur. We showed that for waves in water of variable depth, the phase function is not linear anymore in the variables x and t. It is further shown that, due to the variable depth of the water, the speed of the propagation is also variable in the x coordinate Publisher's Version Q1 WOS:000274004500031

In this article, natural convection in a porous triangular cavity has been analyzed. Bejan's heatlines concept has been used for visualization of heat transfer. Penalty finite-element method with biquadratic elements is used to solve the nondimensional governing equations for the triangular cavity involving hot inclined walls and cold top wall. The numerical solutions are studied in terms of isotherms, streamlines, heatlines, and local and average Nusselt numbers for a wide range of parameters Da (10-5-10-3), Pr (0.015-1000), and Ra (Ra=103-5�105). For low Darcy number (Da=10-5), the heat transfer occurs due to conduction as the heatlines are smooth and orthogonal to the isotherms. As the Rayleigh number increases, conduction dominant mode changes into convection dominant mode for Da=10-3, and the critical Rayleigh number corresponding to the on-set of convection is obtained. Distribution of heatlines illustrate that most of the heat transport for a low Darcy number (Da=10-5) occurs from the top region of hot inclined walls to the cold top wall, whereas heat transfer is more from the bottom region of hot inclined walls to the cold top wall for a high Darcy number (Da=10-3). Interesting features of streamlines and heatlines are discussed for lower and higher Prandtl numbers. Heat transfer analysis is obtained in terms of local and average Nusselt numbers (Nu l, Nul) and the local and average Nusselt numbers are found to be correlated with heatline patterns within the cavity. Copyright � Taylor & Francis Group, LLC.

This paper describes a method to analyze for the large deflections of curved prismatic cantilever beams with uniform curvature subjected to a follower load at the tip. The large deflection, the deflection dependent follower load and the initial curved geometry are the important features of the beam considered in this work. Shear force formulation proposed by Lee [Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-Linear Mech 2002;37(3)] is used for deriving the governing equations. Using this approach, the resulting two point boundary value problem (TPBVP) can be reduced to an initial value problem (IVP). Fourth order Runge-Kutta method along with one parameter reverse shooting method is applied to the numerical solution to the problem. A novel approach presented in this paper of integrating from the free end to the fixed end of the cantilever beam simply replaces the two parameter shooting with a single parameter shooting yielding several advantages. This solution technique is demonstrated for various types of follower tip loads on curved and straight cantilever beams and is validated with existing solutions in the literature. � 2009 Elsevier Ltd. All rights reserved.

Transient numerical simulation of sequential, multi-spot, retinal laser irradiation resembling an actual surgery is performed. The retinal and adjacent regions are irradiated in a truncated three-dimensional computational domain by a 3 � 3 square array formed by nine uniformly distributed laser spots, each heated with 0.2W power. A finite volume formulation of the bio-heat transfer model is employed as the governing equation to generate the temperature evolution. Within the heating duration of each retinal spot (?100ms), it is essential the temperature of the previously heated adjacent regions quickly reduce well below 60�C, the photocoagulation temperature. For an adjacent spot distance of D?0.6mm, transient heat diffusion to the adjacent region is shown to be sufficient to reduce the retinal temperatures close to 37�C. Irrespective of the distance between two consecutive spots in an array, pulsating the laser power with a frequency determined to maintain the maximum temperature within �10% of 60�C reduces excess heating and prevents long term retinal thermal damage. 2010 04 15. Copyright � Taylor & Francis Group, LLC.

The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse-flux model. Semi-implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.

This paper reports the results of a numerical investigation of the problem of finding the optimum configuration for five discrete heat sources, mounted on a wall of a three-dimensional vertical duct under mixed convection heat transfer, using artificial neural networks (ANN). The objective is to locate the positions for the five heat sources in such a way that the maximum temperature of any of the heat sources in a given configuration is a minimum. The three-dimensional governing equations of mass, momentum and energy equations for the fluid flow and the energy equation for the solid regime have been solved by using FLUENT 6.3 and a database of temperature versus configuration was generated. The temperature database developed from CFD simulations is used to train the neural network. The trained neural network predicts the temperature of the heat sources very accurately and much faster than the CFD software. With the use of this network, an exhaustive search for all possible configurations was done that resulted in a global optimum for the problem. � 2008 Elsevier Masson SAS. All rights reserved.

An analysis of transient, two dimensional, mixed convection and thermal stratification in cylindrical hot water storage tanks is presented. The governing equations together with inflow and outflow boundary conditions are written for laminar mixed convection flow using a finite volume based computational code in the dynamic discharging mode based on Boussinesq approximations and conjugate heat transfer. The equations are solved numerically and the results are obtained for aspect ratios of the tanks ranging from 1 to 4 in the Richardson number range of 105 to 108 using a finite volume based computational code. The dynamic discharging mode is considered using a conjugate heat transfer model. The transient temperature profiles in the bulk fluid reveal reduced mixing at higher Richardson numbers during discharging process. The system performance in the dynamic mode of operation is defined by a Mix Number and discharging efficiency parameter. Mixing at the bottom of the tank due to inflow of low temperature water from the load is found to have significant influence on the storage efficiency. The discharging efficiency decreases with Fourier number due to increased thermal degradation with time. � 2009 Allerton Press, Inc.