Search results for: FVM (Finite Volume Method)

Authors: Zhi Zhang, Liling Cao, Seyedbabak Momenzadeh, Lisa Davey

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Reinforced concrete (RC) flat slab-column systems are commonly used in residential or office buildings, as the flat slab provides efficient clearance resulting in more stories at a given height than regular reinforced concrete beam-slab system. Punching shear of slab-column joints is a critical component of two-way reinforced concrete flat slab design. The unbalanced moment at the joint is transferred via slab moment and shear forces. ACI 318 provides an equation to evaluate the punching shear under the design load. It is important to note that the design code considers gravity and environmental load when considering the design load combinations, while it does not consider the effect from differential foundation settlement, which may be a governing load condition for the slab design. This paper describes how prestressed reinforced concrete slab punching shear is evaluated based on ACI 318 provisions and finite element analysis. A prestressed reinforced concrete slab under differential settlements is studied using the finite element modeling methodology. The punching shear check equation is explained. The methodology to extract data for punching shear check from the finite element model is described and correlated with the corresponding code provisions. The study indicates that the finite element analysis results should be carefully reviewed and processed in order to perform accurate punching shear evaluation. Conclusions are made based on the case studies to help engineers understand the punching shear behavior in prestressed and non-prestressed reinforced concrete slabs.

Keywords: differential settlement, finite element model, prestressed reinforced concrete slab, punching shear

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Authors: Yuanhao Gao, Ping Lin, Kees Weijer

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An optimal control system model is proposed for the cell flow in the process of chick embryo gastrulation in this paper. The target is to determine the cellular interaction forces which are hard to measure. This paper will take an approach to investigate the forces with the idea of the inverse problem. By choosing the forces as the control variable and regarding the cell flow as Stokes fluid, an objective functional will be established to match the numerical result of cell velocity with the experimental data. So that the forces could be determined by minimizing the objective functional. The Lagrange multiplier method is utilized to derive the state and adjoint equations consisting the optimal control system, which specifies the first-order necessary conditions. Finite element method is used to discretize and approximate equations. A conjugate gradient algorithm is given for solving the minimum solution of the system and determine the forces.

Keywords: optimal control model, Stokes equation, conjugate gradient method, finite element method, chick embryo gastrulation

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Authors: P. M. Keshtiban, M. Zadshakoyan

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One of the important factors that alter different process and geometrical parameters on metal forming processes is friction between contacting surfaces. Some important factors that effected directly by friction are: stress, strain, required load, wear of surfaces and then geometrical parameters. In order to control friction effects permanent lubrication is necessary. In this article, the friction coefficient is elicited by the most effective method, ring compression tests. The tests were done by both finite element method and practical tests. Different friction curves that extracted by finite element simulations and has good conformity with published results, used for obtaining final friction coefficient. In this study Mos2 is used as the lubricant and Al5754 alloy used as the specimens material.

Keywords: experiment, FEM, friction coefficient, ring compression

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Authors: Gabriel Wosiak, Dyovani Coelho, Evaldo B. Carneiro-Neto, Ernesto C. Pereira, Mauro C. Lopes

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In this work, the theoretical and experimental effects of induced charging currents on fast-scan cyclic voltammetry (FSCV) are investigated. Induced charging currents arise from the effect of ohmic drop in electrochemical systems, which depends on the presence of an uncompensated resistance. They cause the capacitive contribution to the total current to be different from the capacitive current measured in the absence of electroactive species. The paper shows that the induced charging current is relevant when the capacitive current magnitude is close to the total current, even for systems with low time constant. In these situations, the conventional background subtraction method may be inaccurate. A method is developed that separates the faradaic and capacitive currents by using a combination of voltametric experimental data and finite element simulation, by the obtention of a potential-dependent capacitance. The method was tested in a standard electrochemical cell with Platinum ultramicroelectrodes, in different experimental conditions as well in previously reported data in literature. The proposed method allows the real capacitive current to be separated even in situations where the conventional background subtraction method is clearly inappropriate.

Keywords: capacitive current, fast-scan cyclic voltammetry, finite-element method, electroanalysis

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: N. Guo, C. Xu, Z. C. Yang

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In order to ensure the high reliability of an aircraft, the accurate structural dynamics analysis has become an indispensable part in the design of an aircraft structure. Therefore, the structural finite element model which can be used to accurately calculate the structural dynamics and their transfer relations is the prerequisite in structural dynamic design. A dynamic finite element model updating method is presented to correct the uncertain parameters of the finite element model of a structure using measured modal parameters. The coordinate modal assurance criterion is used to evaluate the correlation level at each coordinate over the experimental and the analytical mode shapes. Then, the weighted summation of the natural frequency residual and the coordinate modal assurance criterion residual is used as the objective function. Moreover, the hybrid pattern search (HPS) optimization technique, which synthesizes the advantages of pattern search (PS) optimization technique and genetic algorithm (GA), is introduced to solve the dynamic FE model updating problem. A numerical simulation and a model updating experiment for GARTEUR aircraft model are performed to validate the feasibility and effectiveness of the present dynamic model updating method, respectively. The updated results show that the proposed method can be successfully used to modify the incorrect parameters with good robustness.

Keywords: model updating, modal parameter, coordinate modal assurance criterion, hybrid genetic/pattern search

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Authors: Mohamed Gaith, Zaid Haddadin, Abdulah Wahbe, Mahmoud Hamam, Mahmoud Qunees, Mohammad Al Khatib, Mohammad Bsaileh, Abd Al-Aziz Jaber, Ahmad Aqra’a

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The crack is one of the most common types of failure in pipelines that convey fluid, and early detection of the crack may assist to avoid the piping system from experiencing catastrophic damage, which would otherwise be fatal. The influence of flow velocity and the presence of a crack on the performance of a tapered simply supported pipe containing moving fluid is explored using the finite element approach in this study. ANSYS software is used to simulate the pipe as Bernoulli's beam theory. In this paper, the fluctuation of natural frequencies and matching mode shapes for various scenarios owing to changes in fluid speed and the presence of damage is discussed in detail.

Keywords: damage detection, finite element, tapered pipe, vibration characteristics

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: Yang Zhong, Meijie Xu

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The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: Khatir Omar, Fekih Sidi Mohamed, Sahli Abderahmene, Benkhettou Abdelkader, Boudjemaa Ismail

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Advancements in technology have revolutionized healthcare, with notable impacts on auditory health. This study introduces an approach aimed at optimizing materials for middle ear prostheses to enhance auditory performance. We have developed a finite element (FE) model of the ear incorporating a pure titanium TORP prosthesis, validated against experimental data. Subsequently, we applied the Functionally Graded Materials (FGM) methodology, utilizing linear, exponential, and logarithmic degradation functions to modify prosthesis materials. Biocompatible materials suitable for auditory prostheses, including Stainless Steel, titanium, and Hydroxyapatite, were investigated. The findings indicate that combinations such as Stainless Steel with titanium and Hydroxyapatite offer improved outcomes compared to pure titanium and Hydroxyapatite ceramic in terms of both displacement and stress. Additionally, personalized prostheses tailored to individual patient needs are feasible, underscoring the potential for further advancements in auditory healthcare.

Keywords: middle ear, prosthesis, ossicles, FGM, vibration analysis, finite-element method

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Authors: Farid Saeidi, Serkan Dag

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In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, Variable Fiber Spacing, Thermoelasticity, T-stress, Finite Element Method, Fibrous Composite.

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Authors: Ehsan Yari

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In this paper, a numerical study of sheet cavitation has been performed on DTMB4119 and E779A marine propellers with the boundary element method. In propeller design, various parameters of geometry and fluid are incorporated. So a program is needed to solve the flow taking the whole parameters changing into account. The capability of analyzing the wetted and cavitation flow around propellers in steady, unsteady, uniform, and non-uniform conditions while decreasing computational time compared to numerical finite volume methods with acceptable precision are the characteristic features of the present method. Moreover, modifying the position of the detachment point and its corresponding potential value has been considered. Numerical results have been validated with experimental data, showing a good conformation.

Keywords: cavitation, BEM, DTMB4119, E779A

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Authors: Kuen-Ming Shu, Jyun-Wei Chen

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Encapsulated O-rings are specifically designed to address the problem of sealing the most hostile chemicals and extreme temperature applications. Ultrasonic vibration hot embossing and ultrasonic welding techniques provide a fast and reliable method to fabricate encapsulated O-ring. This paper performs the design and analysis method of the acoustic horns with double extrusion to process tube double side flange simultaneously. The paper deals with study through Finite Element Method (FEM) of ultrasonic stepped horn used to process a capsulated O-ring, the theoretical dimensions of horns, and their natural frequencies and amplitudes are obtained through the simulations of COMOSOL software. Furthermore, real horns were fabricated, tested and verified to proof the practical utility of these horns.

Keywords: encapsulated O-rings, ultrasonic vibration hot embossing, flange making, acoustic horn, finite element analysis

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Authors: Mohamed A. Alsharif, Peter A. Wallace, Donald M. Hepburn, Chengke Zhou

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Worldwide, most PILC MV underground cables in use are approaching the end of their design life; hence, failures are likely to increase. This paper studies the electric field and potential distributions within the PILC insulted cable containing common void-defect. The finite element model of the performance of the belted PILC MV underground cable is presented. The variation of the electric field stress within the cable using the Finite Element Method (FEM) is concentrated. The effects of the void-defect within the insulation are given. Outcomes will lead to deeper understanding of the modeling of Paper Insulated Lead Covered (PILC) and electric field response of belted PILC insulted cable containing void defect.

Keywords: MV PILC cables, finite element model/COMSOL multiphysics, electric field stress, partial discharge degradation

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Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah

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A new numerical algorithm is developed to solve coupled convection-radiation heat transfer in a two dimensional enclosure. Radiative heat transfer in participating medium has been carried out using the control volume finite element method (CVFEM). The radiative transfer equations (RTE) are formulated for absorbing, emitting and scattering medium. The density, velocity and temperature fields are calculated using the two double population lattice Boltzmann equation (LBE). In order to test the efficiency of the developed method the Rayleigh Benard convection with and without radiative heat transfer is analyzed. The obtained results are validated against available works in literature and the proposed method is found to be efficient, accurate and numerically stable.

Keywords: participating media, LBM, CVFEM- radiation coupled with convection

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: Safwan Kanan, Jonathan Dewsbury, Gregory Lane-Serff

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A salinity gradient solar pond is a free energy source system for collecting, converting and storing solar energy as heat. In this paper, the principles of solar pond are explained. A mathematical model is developed to describe and simulate heat and mass transfer behavior of salinity gradient solar pond. Matlab codes are programmed to solve the one dimensional finite difference method for heat and mass transfer equations. Temperature profiles and concentration distributions are calculated. The numerical results are validated with experimental data and the results are found to be in good agreement.

Keywords: finite difference method, salt-gradient solar-pond, solar energy, transient heat and mass transfer

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Authors: Maria Neagu

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

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

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Authors: Sari Elkahina, Zergoug Mourad, Benachenhou Kamel

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The main purpose of this paper is to perform a computations comparison of stress intensity factor 'SIF' evaluation in case of cracked thin plate with Aluminum alloy 7075-T6 and 2024-T3 used in aeronautics structure under uniaxial loading. This evaluation is based on finite element method with a virtual power principle through two techniques: the extrapolation and G−θ. The first one consists to extrapolate the nodal displacements near the cracked tip using a refined triangular mesh with T3 and T6 special elements, while the second, consists of determining the energy release rate G through G−θ method by potential energy derivation which corresponds numerically to the elastic solution post-processing of a cracked solid by a contour integration computation via Gauss points. The SIF obtained results from extrapolation and G−θ methods will be compared to an analytical solution in a particular case. To illustrate the influence of the meshing kind and the size of integration contour position simulations are presented and analyzed.

Keywords: crack tip, SIF, finite element method, concentration technique, displacement extrapolation, aluminum alloy 7075-T6 and 2024-T3, energy release rate G, G-θ method, Gauss point numerical integration

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Authors: Nasim Abuali Galehdari, Thomas J. Ryan, Ajit D. Kelkar

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In recent years, nanotechnology has played an important role in the design of an efficient radiation shielding polymeric composites. It is well known that, high loading of nanomaterials with radiation absorption properties can enhance the radiation attenuation efficiency of shielding structures. However, due to difficulties in dispersion of nanomaterials into polymer matrices, there has been a limitation in higher loading percentages of nanoparticles in the polymer matrix. Therefore, the objective of the present work is to provide a methodology to fabricate and then to characterize the functionally graded radiation shielding structures, which can provide an efficient radiation absorption property along with good structural integrity. Sandwich structures composed of Ultra High Molecular Weight Polyethylene (UHMWPE) fabric as face sheets and functionally graded epoxy nanocomposite as core material were fabricated. A method to fabricate a functionally graded core panel with controllable gradient dispersion of nanoparticles is discussed. In order to optimize the design of functionally graded sandwich composites and to analyze the stress distribution throughout the sandwich composite thickness, a finite element method was used. The sandwich panels were discretized using 3-Dimensional 8 nodded brick elements. Classical laminate analysis in conjunction with simplified micromechanics equations were used to obtain the properties of the face sheets. The presented finite element model would provide insight into deformation and damage mechanics of the functionally graded sandwich composites from the structural point of view.

Keywords: nanotechnology, functionally graded material, radiation shielding, sandwich composites, finite element method

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Authors: H. Nouri, A. Tabbel, N. Douib, H. Aitsaid, Y. Zebboudj

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This study and the field test comparisons were carried out on the Algerian Derguna-Setif transmission systems. The transmission line of normal voltage 225 kV is 65 km long, transported and uses twin bundle conductors protected with two shield wires of transposed galvanized steel. An iterative finite-element method is used to solve Poisons equation. Two algorithms are proposed for satisfying the current continuity condition and updating the space-charge density. A new approach to the problem of corona discharge in transmission system has been described in this paper. The effect of varying the configurations and wires number is also investigated. The analysis of this steady is important in the design of HVDC transmission lines. The potential and electric field have been calculating in locations singular points of the system.

Keywords: corona discharge, finite element method, electric field, HVDC

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Authors: N. E.Sam, S. R.Singh

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Pipeline infrastructure are a valuable asset to the country that help in transporting fluid and gas from one place to another and contribute in keeping the country functioning both physically and economically. During seismic activity, additional loads are acted on the buried pipelines becoming a salient parameter to be studied in soil pipe interaction. Winkler Beam Theory is a commonly used approach for design of underground buried structures however this theory does not take into account shear and dynamic loading parameters in consideration. Shear can be addressed in Pasternak Theory – an improved model of Winkler Theory. However dynamic loading condition and horizontal displacement is not considered in either method. A comprehensive critical review between Winkler Beam Method, Pasternak Method and Three-Dimensional Method in finite element analysis is to be done in this paper for seismic forces. Study of the influence of depth and displacement of soil in correspondence to stiffness value and influence of horizontal displacement for design of underground structures is considered.

Keywords: finite element, pasternak theory, seismic, soil-structure interaction, three-dimensional theory, winkler theory

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Authors: Boukelkoul Lahcen

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The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: cost, finite state, Markov model, operation and maintenance

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Authors: I. A Tijani, Y. F Wu, C.W. Lim

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Concrete Damaged Plasticity Model (CDPM) is capable of modeling the stress-strain behavior of confined concrete. Nevertheless, the accuracy of the model largely depends on its parameters. To date, most research works mainly focus on the identification and modification of the parameters for fiber reinforced polymer (FRP) confined concrete prior to damage. And, it has been established that the FRP-strengthened concrete behaves differently to FRP-repaired concrete. This paper presents a modified plastic damage model within the context of the CDPM in ABAQUS for modelling of a uniformly FRP-confined repaired concrete under monotonic loading. The proposed model includes infliction damage, elastic stiffness, yield criterion and strain hardening rule. The distinct feature of damaged concrete is elastic stiffness reduction; this is included in the model. Meanwhile, the test results were obtained from a physical testing of repaired concrete. The dilation model is expressed as a function of the lateral stiffness of the FRP-jacket. The finite element predictions are shown to be in close agreement with the obtained test results of the repaired concrete. It was observed from the study that with necessary modifications, finite element method is capable of modeling FRP-repaired concrete structures.

Keywords: Concrete, FRP, Damage, Repairing, Plasticity, and Finite element method

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

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Authors: Chin-Kuei Lin, Wen-KO Liang, Yi-Xiang Wang, Shie-Chen Yang

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In this study, experimental methods and finite element numerical simulation are used to investigate the influences of three different types of heat sinks on the output power of a two-cylinder Stirling engine. The Taguchi method is employed to optimize the geometric parameters of the air-cooled heat sink, aiming to optimize the output thermal efficiency. The parameters of the Taguchi method include the materials of the heat sink, and the shape, height, width, and spacing of the heat sink. The L18 orthogonal array is used for experimental design. The experimental results show that the thermal efficiency of the Stirling engine is significantly influenced by the material and geometric parameters of the heat sinks. The heat sinks effectively decrease the temperature at the cold end of the cylinder, increase the temperature difference between the hot and cold ends of the cylinder, and enhance the thermal efficiency of the Stirling engine. The experimental results are in agreement with the numerical simulation analysis. The results of this study will be more helpful for the application of Stirling engines.

Keywords: two cylinder Stirling engine, Taguchi method, heat sink, finite element method

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Authors: Rafik Bouakkaz

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A finite-volume method simulation is used to investigate two dimensional unsteady flow of nanofluids and heat transfer characteristics past a square cylinder inclined with respect to the main flow in the laminar regime. The computations are carried out of nanoparticle volume fractions varying from 0 ≤ ∅ ≤ 5% for an inclination angle in the range 0° ≤ δ ≤ 45° at a Reynolds number of 100. The variation of stream line and isotherm patterns are presented for the above range of conditions. Also, it is noticed that the addition of nanoparticles enhances the heat transfer. Hence, the local Nusselt number is found to increase with increasing value of the concentration of nanoparticles for the fixed value of the inclination angle.

Keywords: copper nanoparticles, heat transfer, square cylinder, inclination angle

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Authors: Jean Marriz M. Manzano, Marc D. Rosales, Magdaleno R. Vasquez Jr., Maria Theresa G. De Leon

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This paper discusses the effects of surface roughness on a cantilever beam vibrational energy harvester. A silicon sample was fabricated using MEMS fabrication processes. When etching silicon using deep reactive ion etching (DRIE) at large etch depths, rougher surfaces are observed as a result of increased response in process pressure, amount of coil power and increased helium backside cooling readings. To account for the effects of surface roughness on the characteristics of the cantilever beam, finite element method (FEM) modeling was performed using actual roughness data from fabricated samples. It was found that when etching about 550um of silicon, root mean square roughness parameter, Sq, varies by 1 to 3 um (at 100um thick) across a 6-inch wafer. Given this Sq variation, FEM simulations predict an 8 to148 Hz shift in the resonant frequency while having no significant effect on the output power. The significant shift in the resonant frequency implies that careful consideration of surface roughness from fabrication processes must be done when designing energy harvesters.

Keywords: deep reactive ion etching, finite element method, microelectromechanical systems, multiphysics analysis, surface roughness, vibrational energy harvester

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Authors: Abdelazim Makki Ibrahim, Esamaldeen Ali

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This study aims at analysing the load settlement behavior and predict the bearing capacity of piled raft foundation a series of finite element models with different foundation configurations and stiffness were established. Numerical modeling is used to study the behavior of the piled raft foundation due to the complexity of piles, raft, and soil interaction and also due to the lack of reliable analytical method that can predict the behavior of the piled raft foundation system. Simple analytical models are developed to predict the average settlement and the load sharing between the piles and the raft in piled raft foundation system. A simple example to demonstrate the applications of these charts is included.

Keywords: finite element, pile-raft foundation, method, PLAXIS software, settlement

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Authors: Mohamed Driouich, Kamal Gueraoui, Mohamed Sammouda

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The main objective of this work is to establish a numerical code for studying the flow of molten polymers in deformable pipes. Using an iterative numerical method based on finite differences, we determine the profiles of the fluid velocity, the temperature and the apparent viscosity of the fluid. The numerical code presented can also be applied to other industrial applications.

Keywords: numerical code, molten polymers, deformable pipes, finite differences

Procedia PDF Downloads 579