Search results for: Critical trajectory method

Authors: M. Bayareh, S. Mortazavi

Abstract:

The migration of a deformable drop in simple shear flow at finite Reynolds numbers is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objectives of this study are to examine the effectiveness of the present approach to predict the migration of a drop in a shear flow and to investigate the behavior of the drop migration with different drop sizes and non-unity viscosity ratios. It is shown that the drop deformation depends strongly on the capillary number, so that; the proper non-dimensional number for the interfacial tension is the capillary number. The rate of migration increased with increasing the drop radius. In other words, the required time for drop migration to the centreline decreases. As the viscosity ratio increases, the drop rotates more slowly and the lubrication force becomes stronger. The increased lubrication force makes it easier for the drop to migrate to the centre of the channel. The migration velocity of the drop vanishes as the drop reaches the centreline under viscosity ratio of one and non-unity viscosity ratios. To validate the present calculations, some typical results are compared with available experimental and theoretical data.

Keywords: drop migration, shear flow, front-tracking method, finite difference method.

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Authors: Zongyan Li, Matt Best

Abstract:

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: Correlation analysis, F-ratio, Levenberg-Marquardt, MSE, NARX, neural network, optimisation.

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Authors: R. Saini, R. Lal

Abstract:

The effect of non-homogeneity on the free transverse vibration of thin rectangular plates of bilinearly varying thickness has been analyzed using generalized differential quadrature (GDQ) method. The non-homogeneity of the plate material is assumed to arise due to linear variations in Young’s modulus and density of the plate material with the in-plane coordinates x and y. Numerical results have been computed for fully clamped and fully simply supported boundary conditions. The solution procedure by means of GDQ method has been implemented in a MATLAB code. The effect of various plate parameters has been investigated for the first three modes of vibration. A comparison of results with those available in literature has been presented.

Keywords: Bilinear thickness, generalized differential quadrature (GDQ), non-homogeneous, Rectangular.

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Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

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Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla

Abstract:

The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.

Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs

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Authors: Jawad H AlKhateeb, Jianmin Jiang, Jinchang Ren, Stan S Ipson

Abstract:

Efficient preprocessing is very essential for automatic recognition of handwritten documents. In this paper, techniques on segmenting words in handwritten Arabic text are presented. Firstly, connected components (ccs) are extracted, and distances among different components are analyzed. The statistical distribution of this distance is then obtained to determine an optimal threshold for words segmentation. Meanwhile, an improved projection based method is also employed for baseline detection. The proposed method has been successfully tested on IFN/ENIT database consisting of 26459 Arabic words handwritten by 411 different writers, and the results were promising and very encouraging in more accurate detection of the baseline and segmentation of words for further recognition.

Keywords: Arabic OCR, off-line recognition, Baseline estimation, Word segmentation.

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Authors: Randa Boukhris Trabelsi, Alima Damak Masmoudi, Dorra Sellami Masmoudi

Abstract:

Nowadays, hand vein recognition has attracted more attentions in identification biometrics systems. Generally, hand vein image is acquired with low contrast and irregular illumination. Accordingly, if you have a good preprocessing of hand vein image, we can easy extracted the feature extraction even with simple binarization. In this paper, a proposed approach is processed to improve the quality of hand vein image. First, a brief survey on existing methods of enhancement is investigated. Then a Radon Like features method is applied to preprocessing hand vein image. Finally, experiments results show that the proposed method give the better effective and reliable in improving hand vein images.

Keywords: Hand Vein, Enhancement, Contrast, RLF, SDME

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Authors: Ravi Shah, V. L. Manekar, R. A. Christian, N. J. Mistry

Abstract:

There are two types of drought as conceptual drought and operational drought. The three parameters as the beginning, the end and the degree of severity of the drought can be identifying in operational drought by average precipitation in the whole region. One of the methods classified to measure drought is Reconnaissance Drought Index (RDI). Evapotranspiration is calculated using Penman-Monteith method by analyzing thirty nine years prolong climatic data. The evapotranspiration is then utilized in RDI to classify normalized and standardized RDI. These RDI classifications led to what kind of drought faced in Bhavnagar region on 12 month time scale basis. The comparison between actual drought conditions and RDI method used to find out drought are also illustrated. It can be concluded that the index results of drought in a particular year are same in both methods but having different index values where as severity remain same.

Keywords: Drought, Drought index, Reconnaissance Drought Index (RDI), Precipitation.

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Authors: C. Ardil

Abstract:

The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.

Keywords: stealth fighter aircraft selection, fuzzy uncertainty theory (FUT), fuzzy entropic decision (FED), fuzzy linguistic variables, triangular fuzzy numbers, multiple criteria decision making analysis, MCDMA, TOPSIS, WSM, WPM

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Authors: Milica Stojanovic, Natasa Petkovic, Petar Mitkovic

Abstract:

This paper develops a critical perspective on using culture and creativity as tools for urban regeneration. Following a brief assessment of the evolution of cultural policy in recent decades and different urban regeneration scheme, the concepts of creativity and creative cities are discussed. This is followed by an attempt to clarify the relationship between the concepts of creativity and culture. A more detailed critique of cultural and creative initiatives in Serbian cities is then undertaken. These attempts show that the potential for development of urban regeneration driven by culture and creativity exist. But, these initiatives failed to produce adequate results because they did not take root as a comprehensive urban regeneration strategy, therefore, recommendations for further development are offered.

Keywords: creativity, culture, Serbia, urban regeneration

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Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo

Abstract:

In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.

Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.

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Authors: P. Zamani, S. Mohajerzadeh, R. Masoudinejad, Kh. Farhangdoost

Abstract:

Riveting process is one of the important ways to keep fastening the lap joints in aircraft structures. Failure of aircraft lap joints directly depends on the stress field in the joint. An important application of riveting process is in the construction of aircraft fuselage structures. In this paper, a 3D finite element method is carried out in order to optimize residual stress field in a riveted lap joint and also to estimate its fatigue life. In continue, a number of experiments are designed and analyzed using design of experiments (DOE). Then, Taguchi method is used to select an optimized case between different levels of each factor. Besides that, the factor which affects the most on residual stress field is investigated. Such optimized case provides the maximum residual stress field. Fatigue life of the optimized joint is estimated by Paris-Erdogan law. Stress intensity factors (SIFs) are calculated using both finite element analysis and experimental formula. In addition, the effect of residual stress field, geometry and secondary bending are considered in SIF calculation. A good agreement is found between results of such methods. Comparison between optimized fatigue life and fatigue life of other joints has shown an improvement in the joint’s life.

Keywords: Fatigue life, Residual stress, Riveting process, Stress intensity factor, Taguchi method.

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

The Maximum entropy principle in spectral analysis was used as an estimator of Direction of Arrival (DoA) of electromagnetic or acoustic sources impinging on an array of sensors, indeed the maximum entropy operator is very efficient when the signals of the radiating sources are ergodic and complex zero mean random processes which is the case for cosmic sources. In this paper, we present basic review of the maximum entropy method (MEM) which consists of rank one operator but not a projector, and we elaborate a new operator which is full rank and sum of all possible projectors. Two dimensional Simulation results based on Monte Carlo trials prove the resolution power of the new operator where the MEM presents some erroneous fluctuations.

Keywords: Maximum entropy, Cosmic source, Localization, operator, projector, azimuth, elevation, DoA, circular array.

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Authors: Kee-Young Kwahk

Abstract:

Previous studies have indicated that one of the most critical failure reasons of enterprise systems is the lack of knowledge sharing and utilization across organizations. As a consequence, many information systems researchers have paid attention to examining the effect of absorptive capacity closely associated with knowledge sharing and transferring on IS usage performance. A lack of communications and interactions due to a lack of organizational citizenship behavior might lead to weak absorptive capacity and thus negatively influence knowledge sharing across organizations. In this study, a theoretical model which delves into the relationship between usage performance of enterprise systems and its determinants was established.

Keywords: Usage performance of information systems, Social exchanges, Enterprise systems.

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Authors: Y. Z. Wu, Z. Dong, S. K. You

Abstract:

Global approximation using metamodel for complex mathematical function or computer model over a large variable domain is often needed in sensibility analysis, computer simulation, optimal control, and global design optimization of complex, multiphysics systems. To overcome the limitations of the existing response surface (RS), surrogate or metamodel modeling methods for complex models over large variable domain, a new adaptive and regressive RS modeling method using quadratic functions and local area model improvement schemes is introduced. The method applies an iterative and Latin hypercube sampling based RS update process, divides the entire domain of design variables into multiple cells, identifies rougher cells with large modeling error, and further divides these cells along the roughest dimension direction. A small number of additional sampling points from the original, expensive model are added over the small and isolated rough cells to improve the RS model locally until the model accuracy criteria are satisfied. The method then combines local RS cells to regenerate the global RS model with satisfactory accuracy. An effective RS cells sorting algorithm is also introduced to improve the efficiency of model evaluation. Benchmark tests are presented and use of the new metamodeling method to replace complex hybrid electrical vehicle powertrain performance model in vehicle design optimization and optimal control are discussed.

Keywords: Global approximation, polynomial response surface, domain decomposition, domain combination, multiphysics modeling, hybrid powertrain optimization

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Authors: Asadollah Boshra, Ahmad Seif, Mehran Aghaei

Abstract:

A model of (4, 4) single-walled boron-nitride nanotube as a representative of armchair boron-nitride nanotubes studied. At first the structure optimization performed and then Nuclear Magnetic Resonance parameters (NMR) by Density Functional Theory (DFT) method at 11B and 15N nuclei calculated. Resulted parameters evaluation presents electrostatic environment heterogeneity along the nanotube and especially at the ends but the nuclei in a layer feel the same electrostatic environment. All of calculations carried out using Gaussian 98 Software package.

Keywords: Boron-nitride nanotube, Density Functional Theory, Nuclear Magnetic Resonance (NMR).

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Authors: A.Campanile, M. Mandarino, V. Piscopo

Abstract:

This paper deals with the problem of non-uniform torsion in thin-walled elastic beams with asymmetric cross-section, removing the basic concept of a fixed center of twist, necessary in the Vlasov-s and Benscoter-s theories to obtain a warping stress field equivalent to zero. In this new torsion/flexure theory, despite of the classical ones, the warping function will punctually satisfy the first indefinite equilibrium equation along the beam axis and it wont- be necessary to introduce the classical congruence condition, to take into account the effect of the beam restraints. The solution, based on the Fourier development of the displacement field, is obtained assuming that the applied external torque is constant along the beam axis and on both beam ends the unit twist angle and the warping axial displacement functions are totally restrained. Finally, in order to verify the feasibility of the proposed method and to compare it with the classical theories, two applications are carried out. The first one, relative to an open profile, is necessary to test the numerical method adopted to find the solution; the second one, instead, is relative to a simplified containership section, considered as full restrained in correspondence of two adjacent transverse bulkheads.

Keywords: Non-uniform torsion, Asymmetric cross-section, Fourier series, Helmholtz equation, FE method.

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Authors: Nazar Zaki, Safaai Deris, Hany Alashwal

Abstract:

Detecting protein-protein interactions is a central problem in computational biology and aberrant such interactions may have implicated in a number of neurological disorders. As a result, the prediction of protein-protein interactions has recently received considerable attention from biologist around the globe. Computational tools that are capable of effectively identifying protein-protein interactions are much needed. In this paper, we propose a method to detect protein-protein interaction based on substring similarity measure. Two protein sequences may interact by the mean of the similarities of the substrings they contain. When applied on the currently available protein-protein interaction data for the yeast Saccharomyces cerevisiae, the proposed method delivered reasonable improvement over the existing ones.

Keywords: Protein-Protein Interaction, support vector machine, feature extraction, pairwise alignment, Smith-Waterman score.

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Authors: Shao-Tzu Huang, Chen-Chien Hsu, Wei-Yen Wang

Abstract:

Matching high dimensional features between images is computationally expensive for exhaustive search approaches in computer vision. Although the dimension of the feature can be degraded by simplifying the prior knowledge of homography, matching accuracy may degrade as a tradeoff. In this paper, we present a feature matching method based on k-means algorithm that reduces the matching cost and matches the features between images instead of using a simplified geometric assumption. Experimental results show that the proposed method outperforms the previous linear exhaustive search approaches in terms of the inlier ratio of matched pairs.

Keywords: Feature matching, k-means clustering, scale invariant feature transform, linear exhaustive search.

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Authors: Emiliano Matta

Abstract:

Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.

Keywords: Amplitude-independent damping, Homogeneous friction, Pendulum nonlinear dynamics, Structural control, Vibration resonant absorbers.

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Authors: Li Hongwei

Abstract:

In this paper, a predator-prey model with time delay and habitat complexity is investigated. By analyzing the characteristic equations, the local stability of each feasible equilibria of the system is discussed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By choosing the sum of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as  crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.

Keywords: Predator-prey system, delay, habitat complexity, HOPF bifurcation.

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Authors: K. Abbaspoursani, M. Allahyari, M. Rahmani

Abstract:

Thermal conductivity is an important characteristic of a nanofluid in laminar flow heat transfer. This paper presents an improved model for the prediction of the effective thermal conductivity of nanofluids based on dimensionless groups. The model expresses the thermal conductivity of a nanofluid as a function of the thermal conductivity of the solid and liquid, their volume fractions and particle size. The proposed model includes a parameter which accounts for the interfacial shell, brownian motion, and aggregation of particle. The validation of the model is verified by applying the results obtained by the experiments of Tio2-water and Al2o3-water nanofluids.

Keywords: Critical particle size, nanofluid, model, and thermal conductivity.

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Authors: J. Mirzaei, H. Kazemi Kargar

Abstract:

This paper presents a new approach for setting frequency relays based on the dynamic of power system. A simplified model of the power system based on the load-frequency control loop will be developed to be used instead of the complete model of the power system. The effects of the equipments and their responses on the frequency variations of the power plant will be investigated and then a method for adaptive settings of frequency relays will be explained. The proposed method will be investigated by analyzing a simplified model of a power plant by MATLAB software.

Keywords: Adaptive Settings, Frequency Relay (FR), PowerSystem Dynamics, SFR model.

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Authors: Sebastian B. Mendes

Abstract:

The presence of a vertical edge-crack within a web plate subjected to pure bending induces local compressive stresses about the crack which may cause tension buckling. Approximate theoretical expressions were derived for the critical far-field tensile stress and bending moment capacity of an edge-cracked web plate associated with tension buckling. These expressions were validated with finite element analyses and used to investigate the possibility of tension buckling in web-cracked trial girders. It was found that tension buckling is an unlikely occurrence unless the web is relatively thin or the crack is very long.

Keywords: Fatigue crack, tension buckling, Rayleigh-Ritz, structural stability.

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Authors: Taiyo Matsumura, Kota Funabashi, Nobumichi Sakai, Takashi Ono

Abstract:

The purpose of this research is to construct a watching system that monitors human activity in a room and detects abnormalities at an early stage to prevent unattended deaths of people living alone. In this article, we propose a method whereby highly urgent abnormal conditions of a person are determined by changes in the concentration of CO₂ generated from activity and respiration in a room. We also discussed the effects the amount of activity has on the determination. The results showed that this discrimination method is not dependent on the amount of activity and is effective in judging highly urgent abnormal conditions.

Keywords: Abnormal conditions, multiple sensors, people living alone, respiratory arrest, unattended death, watching system.

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Authors: H. Özkan

Abstract:

In this study, a new and fast algorithm for Ascending Aorta (AscA) and Descending Aorta (DesA) segmentation is presented using Computed Tomography Angiography images. This process is quite important especially at the detection of aortic plaques, aneurysms, calcification or stenosis. The applied method has been carried out at four steps. At first step, lung segmentation is achieved. At the second one, Mediastinum Region (MR) is detected to use in the segmentation. At the third one, images have been applied optimal threshold and components which are outside of the MR were removed. Lastly, identifying and segmentation of AscA and DesA have been carried out. The performance of the applied method is found quite well for radiologists and it gives enough results to the surgeries medically.

Keywords: Ascending aorta (AscA), Descending aorta (DesA), Computed tomography angiography (CTA), Computer aided detection (CAD), Segmentation

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Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

Abstract:

In this paper, we consider a drift flux mixture model of the blood flow. The mixture consists of gas phase which is carbon dioxide and liquid phase which is an aqueous carbon dioxide solution. This model was used to determine the distributions of the mixture velocity, the mixture pressure, and the carbon dioxide pressure. These theoretical data are used to determine a measurement method of mean gas pressure through the determination of radial velocity distribution. This method can be applicable in experimental domain.

Keywords: Mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity.

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Authors: A. Megalingam, M.M.Mayuram

Abstract:

Evaluation of contact pressure, surface and subsurface contact stresses are essential to know the functional response of surface coatings and the contact behavior mainly depends on surface roughness, material property, thickness of layer and the manner of loading. Contact parameter evaluation of real rough surface contacts mostly relies on statistical single asperity contact approaches. In this work, a three dimensional layered solid rough surface in contact with a rigid flat is modeled and analyzed using finite element method. The rough surface of layered solid is generated by FFT approach. The generated rough surface is exported to a finite element method based ANSYS package through which the bottom up solid modeling is employed to create a deformable solid model with a layered solid rough surface on top. The discretization and contact analysis are carried by using the same ANSYS package. The elastic, elastoplastic and plastic deformations are continuous in the present finite element method unlike many other contact models. The Young-s modulus to yield strength ratio of layer is varied in the present work to observe the contact parameters effect while keeping the surface roughness and substrate material properties as constant. The contacting asperities attain elastic, elastoplastic and plastic states with their continuity and asperity interaction phenomena is inherently included. The resultant contact parameters show that neighboring asperity interaction and the Young-s modulus to yield strength ratio of layer influence the bulk deformation consequently affect the interface strength.

Keywords: Asperity interaction, finite element method, rough surface contact, single layered solid

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Authors: Phoevos K. Koukouvinis, John S. Anagnostopoulos, Dimitris E. Papantonis

Abstract:

This work is an attempt to use the standard Smoothed Particle Hydrodynamics methodology for the simulation of the complex unsteady, free-surface flow in a rotating Turgo impulse water turbine. A comparison of two different geometries was conducted. The SPH method due to its mesh-less nature is capable of capturing the flow features appearing in the turbine, without diffusion at the water/air interface. Furthermore results are compared with a commercial CFD package (Fluent®) and the SPH algorithm proves to be capable of providing similar results, in much less time than the mesh based CFD program. A parametric study was also performed regarding the turbine inlet angle.

Keywords: Smoothed Particle Hydrodynamics, Mesh-lessmethods, Impulse turbines, Turgo turbine.

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Authors: Khwaja Naweed Seddiqi, Zabihullah Mahdi, Shigeo Honma

Abstract:

Recently increasing oil production from petroleum reservoirs is one of the most important issues in the global energy sector. So, in this paper, the recovery of oil by the waterflooding technique from petroleum reservoir are considered. To investigate the aforementioned phenomena, the relative permeability of two immiscible fluids in sand is measured in the laboratory based on the steady-state method. Two sorts of oils, kerosene and heavy oil, and water are pumped simultaneously into a vertical sand column with different pumping ratio. From the change in fractional discharge measured at the outlet, a method for determining the relative permeability is developed focusing on the displacement mechanism in sand. Then, displacement mechanism of two immiscible fluids in the sand is investigated under the Buckley-Leveret frontal displacement theory and laboratory experiment. Two sorts of experiments, one is the displacement of pore water by oil, the other is the displacement of pore oil by water, are carried out. It is revealed that the relative permeability curves display tolerably different shape owing to the properties of oils, and produce different amount of residual oils and irreducible water saturation.

Keywords: Petroleum reservoir engineering, relative permeability, two-phase flow, immiscible displacement in porous media, steady-state method, waterflooding.

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