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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Abstract: The adjoint method has been used as a successful tool to
obtain sensitivity gradients in aerodynamic design and optimisation
for many years. This work presents an alternative approach to the
continuous adjoint formulation that enables one to compute gradients
of a given measure of merit with respect to control parameters other
than those pertaining to geometry. The procedure is then applied to
the steady 2–D compressible Euler and incompressible Navier–Stokes
flow equations. Finally, the results are compared with sensitivities
obtained by finite differences and theoretical values for validation.
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.
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.
Abstract: A theoretical study of a humidification
dehumidification solar desalination unit has been carried out to
increase understanding the effect of weather conditions on the unit
productivity. A humidification-dehumidification (HD) solar
desalination unit has been designed to provide fresh water for
population in remote arid areas. It consists of solar water collector
and air collector; to provide the hot water and air to the desalination
chamber. The desalination chamber is divided into humidification
and dehumidification towers. The circulation of air between the two
towers is maintained by the forced convection. A mathematical
model has been formulated, in which the thermodynamic relations
were used to study the flow, heat and mass transfer inside the
humidifier and dehumidifier. The present technique is performed in
order to increase the unit performance. Heat and mass balance has
been done and a set of governing equations has been solved using the
finite difference technique. The unit productivity has been calculated
along the working day during the summer and winter sessions and
has compared with the available experimental results. The average
accumulative productivity of the system in winter has been ranged
between 2.5 to 4 (kg/m2)/day, while the average summer productivity
has been found between 8 to 12 (kg/m2)/day.