Search results for: Finite Volume Method

Authors: N. Targui, H. Kahalerras

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The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy-Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: double pipe heat exchanger, nanofluids, nanoparticles, porous baffles

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Authors: M. Amoura, M. Benmoussa, N. Zeraibi

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The flow and heat transfer is an important phenomenon in engineering systems due to its wide application in electronic cooling, heat exchangers, double pane windows etc.. The enhancement of heat transfer in these systems is an essential topic from an energy saving perspective. Lower heat transfer performance when conventional fluids, such as water, engine oil and ethylene glycol are used hinders improvements in performance and causes a consequent reduction in the size of such systems. The use of solid particles as an additive suspended into the base fluid is a technique for heat transfer enhancement. Therefore, the heat transfer enhancement in a horizontal circular tube that is maintained at a constant temperature under laminar regime has been investigated numerically. A computational code applied to the problem by use of the finite volume method was developed. Nanofluid was made by dispersion of Al2O3 nanoparticles in pure water and ethylene glycol. Results illustrate that the suspended nanoparticles increase the heat transfer with an increase in the nanoparticles volume fraction and for a considered range of Reynolds numbers. On the other hand, the heat transfer is very sensitive to the base fluid.

Keywords: Al2O3 nanoparticles, circular tube, heat transfert enhancement, numerical simulation

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Authors: M. Zareh, H. Mohammadi, B. Naser

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Atherosclerotic plaque rupture is the main trigger of heart attack and brain stroke which are the leading cause of death in developed countries. Better understanding of rupture-prone plaque can help clinicians detect vulnerable plaques- rupture prone or instable plaques- and apply immediate medical treatment to prevent these life-threatening cardiovascular events. Therefore, there are plenty of studies addressing disclosure of vulnerable plaques properties. Necrotic core and fibrous tissue are two major tissues constituting atherosclerotic plaque; using histopathological and numerical approaches, many studies have demonstrated that plaque rupture is strongly associated with a large necrotic core and a thin fibrous cap, two morphological characteristic which can be acquired by two-dimensional imaging of atherosclerotic plaque present in coronary and carotid arteries. Plaque rupture is widely considered as a mechanical failure inside plaque tissue; this failure occurs when the stress within plaque excesses the strength of tissue material; hence, finite element method, a strong numerical approach, has been extensively applied to estimate stress distribution within plaques with different compositions which is then used for assessment of various vulnerability characteristics including plaque morphology, material properties and blood pressure. This study aims to evaluate significance of three-dimensional morphology on vulnerability degree of atherosclerotic plaque. To reach this end, different two-dimensional geometrical models of atherosclerotic plaques are considered based on available data and named Main 2D Models (M2M). Then, for each of these M2Ms, two three-dimensional idealistic models are created. These two 3D models represent two possible three-dimensional morphologies which might exist for a plaque with similar 2D morphology to one of M2Ms. Finite element method is employed to estimate stress, von-Mises stress, within each 3D models. Results indicate that for each M2Ms stress can significantly varies due to possible 3D morphological changes in that plaque. Also, our results show that an atherosclerotic plaque with thick cap may experience rupture if it has a critical 3D morphology. This study highlights the effect of 3D geometry of plaque on its instability degree and suggests that 3D morphology of plaque might be necessary to more effectively and accurately assess atherosclerotic plaque vulnerability.

Keywords: atherosclerotic plaque, plaque rupture, finite element method, 3D model

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Authors: Lei Li, Ming M. Chai, Xiao X. Lu, Jia W. Wang

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The mixing process of two liquid layers in a cylindrical container includes the upper liquid with higher density rushing into the lower liquid with lighter density, the lower liquid rising into the upper liquid, meanwhile the two liquid layers having interactions with each other, forming vortices, spreading or dispersing in others, entraining or mixing with others. It is a complex process constituted of flow instability, turbulent mixing and other multiscale physical phenomena and having a fast evolution velocity. In order to explore the mechanism of the process and make further investigations, some experiments about the interfacial instability and mixing behavior between two liquid layers bounded in different volumes are carried out, applying the planar laser induced fluorescence (PLIF) and the high speed camera (HSC) techniques. According to the results, the evolution of interfacial instability between immiscible liquid develops faster than theoretical rate given by the Rayleigh-Taylor Instability (RTI) theory. It is reasonable to conjecture that some mechanisms except the RTI play key roles in the mixture process of two liquid layers. From the results, it is shown that the invading velocity of the upper liquid into the lower liquid does not depend on the upper liquid's volume (height). Comparing to the cases that the upper and lower containers are of identical diameter, in the case that the lower liquid volume increases to larger geometric space, the upper liquid spreads and expands into the lower liquid more quickly during the evolution of interfacial instability, indicating that the container wall has important influence on the mixing process. In the experiments of miscible liquid layers’ mixing, the diffusion time and pattern of the liquid interfacial mixing also does not depend on the upper liquid's volumes, and when the lower liquid volume increases to larger geometric space, the action of the bounded wall on the liquid falling and rising flow will decrease, and the liquid interfacial mixing effects will also attenuate. Therefore, it is also concluded that the volume weight of upper heavier liquid is not the reason of the fast interfacial instability evolution between the two liquid layers and the bounded wall action is limited to the unstable and mixing flow. The numerical simulations of the immiscible liquid layers’ interfacial instability flow using the VOF method show the typical flow pattern agree with the experiments. However the calculated instability development is much slower than the experimental measurement. The numerical simulation of the miscible liquids’ mixing, which applying Fick’s diffusion law to the components’ transport equation, shows a much faster mixing rate than the experiments on the liquids’ interface at the initial stage. It can be presumed that the interfacial tension plays an important role in the interfacial instability between the two liquid layers bounded in finite volume.

Keywords: interfacial instability and mixing, two liquid layers, Planar Laser Induced Fluorescence (PLIF), High Speed Camera (HSC), interfacial energy and tension, Cahn-Hilliard Navier-Stokes (CHNS) equations

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Authors: Arber Sejdiji, Jan Schmitz-Huebsch, Christian Mittelstedt

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Due to its use in a broad range of temperatures, the prediction of elastic properties of fiber composite materials under thermal load is significant. Especially the transversal stiffness dominates the potential of use for fiber-reinforced composites (FRC). A numerical study on the influence of thermal stress on transversal stiffness of fiber-reinforced composites is presented. In the numerical study, a representative volume element (RVE) is used to estimate the elastic properties of a unidirectional ply with finite element method (FEM). For the investigation, periodic boundary conditions are applied to the RVE. Firstly, the elastic properties under pure mechanical load are derived numerically and compared to results, which are obtained by analytical methods. Thereupon thermo-mechanical load is implemented into the model to investigate the influence of temperature change with low temperature as a key aspect. Regarding low temperatures, the transversal stiffness increases intensely, especially when thermal stress is dominant over mechanical stress. This paper outlines the employed numerical methods as well as the derived results.

Keywords: elastic properties, micromechanics, thermal stress, representative volume element

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Shubham Jaiswal

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In this study, the numerical solution of two-dimensional solute transport system in a homogeneous porous medium of finite-length is obtained. The considered transport system have the terms accounting for advection, dispersion and first-order decay with first-type boundary conditions. Initially, the aquifer is considered solute free and a constant input-concentration is considered at inlet boundary. The solution is describing the solute concentration in rectangular inflow-region of the homogeneous porous media. The numerical solution is derived using a powerful method viz., spectral collocation method. The numerical computation and graphical presentations exhibit that the method is effective and reliable during solution of the physical model with complicated boundary conditions even in the presence of reaction term.

Keywords: two-dimensional solute transport system, spectral collocation method, Chebyshev polynomials, Chebyshev differentiation matrix

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Authors: Güneş Aydın, Razi Kalantari Osgouei, Murat Emre Öztürk, Ahmad Partovi Meran, Ekrem Tüfekçi

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Advanced lightweight laminated composite shells are increasingly being used in all types of modern structures, for enhancing their structural efficiency and performance. Such thin-walled structures are susceptible to buckling when subjected to various loading. This paper focuses on the buckling of cylindrical shells under axial compression and torsional loads. Effects of fiber orientation on the maximum buckling load of carbon fiber reinforced polymer (CFRP) shells are optimized. Optimum fiber angles have been calculated analytically by using MATLAB program. Numerical models have been carried out by using Finite Element Method program ABAQUS. Results from analytical and numerical analyses are also compared.

Keywords: buckling, composite, cylindrical shell, finite element, compression, torsion, MATLAB, optimization

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Authors: M. Naji, A. R. Khalim, M. Naji

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Integral Abutment Bridges (IAB) are defined as simple or multiple span bridges in which the bridge deck is cast monolithically with the abutment walls. This kind of bridges are becoming very popular due to different aspects such as good response under seismic loading, low initial costs, elimination of bearings and less maintenance. However, the main issue related to the analysis of this type of structures is dealing with soil-structure interaction of the abutment walls and the supporting piles. A two-dimensional, non-linear finite element (FE) model of an integral abutment bridge has been developed to study the effect of lateral time history displacement loading on the soil system.

Keywords: integral abutment bridge, soil structure interaction, finite element modeling, soil-pile interaction

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Authors: Said Algarni

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The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

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Authors: Masoud Mahdavi

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The structure is made using different members and combining them with each other. These members are basically based on technical and engineering principles and are combined in different ways and have their own unique effects on the building. Trusses are one of the most common and important members of the structure, accounting for a large percentage of the power transmission structure in the building. Different types of trusses are based on structural needs and evaluating and making complete comparisons between them is one of the most important engineering analyses. In the present study, four types of trusses have been studied; 1) Hawe truss, 2) Pratt truss, 3) k truss, and 4) warren truss, under cyclic loading for 80 seconds. The trusses are modeled in 3d using st₃₇ steel. The results showed that Hawe trusses had higher values ​​than all other trusses (k, Pratt and Warren) in all the studied indicators. Indicators examined in the study include; 1) von Mises stresses, 2) displacement, 3) support force, 4) velocity, 5) acceleration, 6) capacity (hysteresis curve) and 7) energy diagram. Pratt truss in indicators; Mises stress, displacement, energy have the least amount compared to other trusses. K truss in indicators; support force, speed and acceleration are the lowest compared to other trusses.

Keywords: hawe truss, pratt truss, K truss, warren truss, cyclic loading, finite element method

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Authors: Hannah F. Opayinka, Adedayo A. Adepoju

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This study is an extension of a prior study on the modification of the existing m-out-of-n (moon) bootstrap method for heavy-tailed distributions in which modified m-out-of-n (mmoon) was proposed as an alternative method to the existing moon technique. In this study, both moon and mmoon techniques were applied to two real income datasets which followed Lognormal and Pareto distributions respectively with finite variances. The performances of these two techniques were compared using Standard Error (SE) and Root Mean Square Error (RMSE). The findings showed that mmoon outperformed moon bootstrap in terms of smaller SEs and RMSEs for all the sample sizes considered in the two datasets.

Keywords: Bootstrap, income data, lognormal distribution, Pareto distribution

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Authors: Reza Mohammadi, Mahdieh Sahebi

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

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Vimal Jasoliya, Purnank Bhatt, Mit Shah

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The Injection Moulding is one of the principle methods of conversions of plastics into various end products using a very wide range of plastics materials from commodity plastics to specialty engineering plastics. Injection Moulding Machines are rated as per the tonnage force applied. The work present includes Design & Finite Element Analysis of a structure component of injection moulding machine i.e. clamp cylinder. The work of the project is to upgrade the 1300T clamp cylinder to 1500T clamp cylinder for injection moulding machine. The design of existing clamp cylinder of 1300T is checked. Finite Element analysis is carried out for 1300T clamp cylinder in ANSYS Workbench, and the stress values are compared with acceptance criteria and theoretical calculation. The relation between the clamp cylinder diameter and the tonnage capacity has been derived and verified for 1300T clamp cylinder. The same correlation is used to find out the thickness for 1500T clamp cylinder. The detailed design of 1500T cylinder is carried out based on calculated thickness.

Keywords: clamp cylinder, fatigue analysis, finite element analysis, injection moulding machines

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Authors: Afef Dridi, Salah Mezlini

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Since experimental devices cannot calculate stress and deformation of complex structures. The Finite Element Method FEM has been widely used in several fields of research. One of these fields is orthodontics. The advantage of using such a method is the use of an accurate and non invasive method that allows us to have a sufficient data about the physiological reactions can happening in soft tissues. Most of researches done in this field were interested in the study of stresses and deformations induced by orthodontic apparatus in soft tissues (alveolar tissues). Only few studies were interested in the distribution of stress and strain in the orthodontic brackets. These studies, although they tried to be as close as possible to real conditions, their models did not reproduce the clinical cases. For this reason, the model generated by our research is the closest one to reality. In this study, a numerical model was developed to explore the stress and strain distribution under the application of real conditions. A comparison between different material properties was also done.

Keywords: visco-hyperelasticity, FEM, orthodontic treatment, inverse method

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Authors: Yongmin You

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Electric machines for office automation device such as printer and scanner have been required the low noise and vibration performance. Many researches about the low noise and vibration of polygon mirror scanner motor have been also progressed. The noise and vibration of polygon mirror scanner motor can be classified by aerodynamic, structural and electromagnetic. Electromagnetic noise and vibration can be occurred by high cogging torque and nonsinusoidal back EMF. To improve the cogging torque and back EMF characteristic, we apply unequal air-gap. To analyze characteristic of a polygon mirror scanner motor, two dimensional finite element method is used. To minimize the cogging torque of a polygon mirror motor, Kriging based on latin hypercube sampling (LHS) is utilized. Compared to the initial model, the torque ripple of the optimized unequal air-gap model was reduced by 23.4 % while maintaining the back EMF and average torque. To verify the optimal design results, the experiment was performed. We measured the vibration in motors at 23,600 rpm which is the rated velocity. The radial and axial gravitational acceleration of the optimal model were declined more than seven times and three times, respectively. From these results, a shape optimized unequal polygon mirror scanner motor has shown the usefulness of an improvement in the torque ripple and electromagnetic vibration characteristic.

Keywords: polygon mirror scanner motor, optimal design, finite element method, vibration

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Authors: Azzedine Abdedou, Khedidja Bouhadef

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The present study is an analysis of the forced convection heat transfer in porous channel with an oriented jet at the inlet with uniform velocity and temperature distributions. The upper wall is insulated when the bottom one is kept at constant temperature higher than that of the fluid at the entrance. The dynamic field is analysed by the Brinkman-Forchheimer extended Darcy model and the thermal field is traduced by the energy one equation model. The numerical solution of the governing equations is obtained by using the finite volume method. The results mainly concern the effect of Reynolds number, jet angle and thermal conductivity ratio on the flow structure and local and average Nusselt numbers evolutions.

Keywords: forced convection, porous media, oriented confined jet, fluid mechanics

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Authors: Adjal Yassine, Semmani Amar

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During the last decades, The risk of collision has been increased, especially in high maritime traffic. As the consequence, the demand is required for safety at sea and environmental protection. For this purpose, the consequences prediction of ship collisions is recommended in order to minimize structural failure. additionally, at the design stage of the ship, damage generated during the collision event must be taken into consideration. This structural failure, in some cases, can develop into the progressive collapse of other structural elements and generate catastrophic consequences. The present study investigates the progressive collapse of ships damaged by collisions using the Non -linear finite element method. The failure criteria are taken into account. The impacted area has a refined mesh in order to have more reliable results. Finally, a parametric study was conducted in this study to highlight the effect of the ship's speed, as well as the different impacted areas of double-bottom ships.

Keywords: collsion, strucural failure, ship, finite element analysis

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Authors: M. A. Fiidow, Ahmad M. Alenezi

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In this work, we study the inner derivations of diassociative algebras in dimension two and three, an algorithmic approach is adopted for the computation of inner derivation, using some results from the derivation of finite dimensional diassociative algebras. Some basic properties of inner derivation of finite dimensional diassociative algebras are also provided.

Keywords: diassociative algebras, inner derivations, derivations, left and right operator

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Authors: Ishak Hashim, Ammar Alsabery

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

Keywords: conjugate free convection, square cavity, nanofluid, spatial temperature

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Authors: Jakub Zembrzuski, Bartosz Sobczyk, Mikołaj MIśkiewicz

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Besides designing new constructions, engineers all over the world must face another problem – maintenance, repairs, and assessment of the technical condition of existing bridges. To solve more complex issues, it is necessary to be familiar with the theory of finite element method and to have access to the software that provides sufficient tools which to enable create of sometimes significantly advanced numerical models. The paper includes a brief assessment of the technical condition, a description of the in situ non-destructive testing carried out and the FEM models created for global and local analysis. In situ testing was performed using strain gauges and displacement sensors. Numerical models were created using various software and numerical modeling techniques. Particularly noteworthy is the method of modeling riveted joints of the crossbeam of the viaduct. It is a simplified method that consists of the use of only basic numerical tools such as beam and shell finite elements, constraints, and simplified boundary conditions (fixed support and symmetry). The results of the numerical analyses were presented and discussed. It is clearly explained why the structure did not fail, despite the fact that the weld of the deck plate completely failed. A further research problem that was solved was to determine the cause of the rapid increase in values on the stress diagram in the cross-section of the transverse section. The problems were solved using the solely mentioned, simplified method of modeling riveted joints, which demonstrates that it is possible to solve such problems without access to sophisticated software that enables to performance of the advanced nonlinear analysis. Moreover, the obtained results are of great importance in the field of assessing the operation of bridge structures with an orthotropic plate.

Keywords: bridge, diagnostics, FEM simulations, failure, NDT, in situ testing

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Authors: A. Poukens, I. Sluyts, A. Krings, J. Swartenbroekx, D. Geeroms, J. Poukens

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Introduction and Objectives: It has been known for many years that with the administration of intravenous medication, a rather significant part of the planned to be administered infusion solution, the residual volume ( the volume that remains in the IV line and or infusion bag), does not reach the patient and is wasted. This could possibly result in under dosage and diminished therapeutic effect. Despite the important impact on the patient, the reduction of residual volume lacks attention. An optimized and clearly stated protocol concerning the reduction of residual volume in an IV line is necessary for each hospital. As described in my Master’s thesis, acquiring the degree of Master in Hospital Pharmacy, administration of intravenous medication can be optimized by reduction of the residual volume. Herewith effectiveness, user-friendliness, cost efficiency and safety were taken into account. Material and Methods: By usage of a literature study and an online questionnaire sent out to all Flemish hospitals and hospitals in the Netherlands (province Limburg), current flush methods could be mapped out. In laboratory research, possible flush methods aiming to reduce the residual volume were measured. Furthermore, a self-developed experimental method to reduce the residual volume was added to the study. The current flush methods and the self-developed experimental method were compared to each other based on cost efficiency, user-friendliness and safety. Results: There is a major difference between the Flemish and the hospitals in the Netherlands (Province Limburg) concerning the approach and method of flushing IV lines after administration of intravenous medication. The residual volumes were measured and laboratory research showed that if flushing was done minimally 1-time equivalent to the residual volume, 95 percent of glucose would be flushed through. Based on the comparison, it became clear that flushing by use of a pre-filled syringe would be the most cost-efficient, user-friendly and safest method. According to laboratory research, the self-developed experimental method is feasible and has the advantage that the remaining fraction of the medication can be administered to the patient in unchanged concentration without dilution. Furthermore, this technique can be applied regardless of the level of the residual volume. Conclusion and Recommendations: It is recommendable to revise the current infusion systems and flushing methods in most hospitals. Aside from education of the hospital staff and alignment on a uniform substantiated protocol, an optimized and clear policy on the reduction of residual volume is necessary for each hospital. It is recommended to flush all IV lines with rinsing fluid with at least the equivalent volume of the residual volume. Further laboratory and clinical research for the self-developed experimental method are needed before this method can be implemented clinically in a broader setting.

Keywords: intravenous medication, infusion therapy, IV flushing, residual volume

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Authors: Ahmed Mozamel, Kemal Yildizli

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Due to mechanical energy losses and a competitive of minimizing these losses and increases the machine efficiency, the need for contactless gearing system has raised. In this work, one stage of mechanical planetary gear transmission system integrated with one stage of magnetic planetary gear system is designed as a two-stage hybrid gearbox system. The permanent magnets internal energy in the form of the magnetic field is used to create meshing between contactless magnetic rotors in order to provide self-system protection against overloading and decrease the mechanical loss of the transmission system by eliminating the friction losses. Classical methods, such as analytical, tabular method and the theory of elasticity are used to calculate the planetary gear design parameters. The finite element method (ANSYS Maxwell) is used to predict the behaviors of a magnetic gearing system. The concentric magnetic gearing system has been modeled and analyzed by using 2D finite element method (ANSYS Maxwell). In addition to that, design and manufacturing processes of prototype components (a planetary gear, concentric magnetic gear, shafts and the bearings selection) of a gearbox system are investigated. The output force, the output moment, the output power and efficiency of the hybrid gearbox system are experimentally evaluated. The viability of applying a magnetic force to transmit mechanical power through a non-contact gearing system is presented. The experimental test results show that the system is capable to operate continuously within the range of speed from 400 rpm to 3000 rpm with the reduction ratio of 2:1 and maximum efficiency of 91%.

Keywords: hybrid gearbox, mechanical gearboxes, magnetic gears, magnetic torque

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Authors: Loubna Tani, Nabih Elouzzani

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Crosstalk among interconnects and printed-circuit board (PCB) traces is a major limiting factor of signal quality in high-speed digital and communication equipments especially when fast data buses are involved. Such a bus is considered as a planar multiconductor transmission line. This paper will demonstrate how the finite difference time domain (FDTD) method provides an exact solution of the transmission-line equations to analyze the near end and the far end crosstalk. In addition, this study makes it possible to analyze the rise time effect on the near and far end voltages of the victim conductor. The paper also discusses a statistical analysis, based upon a set of several simulations. Such analysis leads to a better understanding of the phenomenon and yields useful information.

Keywords: multiconductor transmission line, crosstalk, finite difference time domain (FDTD), printed-circuit board (PCB), rise time, statistical analysis

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Authors: Chollawat Pookpienlert, Jintana Sanwong

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An element a of a semigroup S is called left (right) regular if there exists x in S such that a=xa² (a=a²x) and said to be intra-regular if there exist u,v in such that a=ua²v. Let T(X) be the semigroup of all full transformations on a set X under the composition of maps. For a fixed nonempty subset Y of X, let Fix(X,Y)={α ™ T(X) : yα=y for all y ™ Y}, where yα is the image of y under α. Then Fix(X,Y) is a semigroup of full transformations on X which fix all elements in Y. Here, we characterize left regular, right regular and intra-regular elements of Fix(X,Y) which characterizations are shown as follows: For α ™ Fix(X,Y), (i) α is left regular if and only if Xα\Y = Xα²\Y, (ii) α is right regular if and only if πα = πα², (iii) α is intra-regular if and only if | Xα\Y | = | Xα²\Y | such that Xα = {xα : x ™ X} and πα = {xα⁻¹ : x ™ Xα} in which xα⁻¹ = {a ™ X : aα=x}. Moreover, those regularities are equivalent if Xα\Y is a finite set. In addition, we count the number of those elements of Fix(X,Y) when X is a finite set. Finally, we determine the maximal congruence ρ on Fix(X,Y) when X is finite and Y is a nonempty proper subset of X. If we let | X \Y | = n, then we obtain that ρ = (Fixn x Fixn) ∪ (H ε x H ε) where Fixn = {α ™ Fix(X,Y) : | Xα\Y | < n} and H ε is the group of units of Fix(X,Y). Furthermore, we show that the maximal congruence is unique.

Keywords: intra-regular, left regular, maximal congruence, right regular, transformation semigroup

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: Komeil Valipourian

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Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method (FDM)

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Artur Tyliszczak, Ewa Szymanek, Maciej Marek

Abstract:

Flow through granular materials is important to a vast array of industries, for instance in construction industry where granular layers are used for bulkheads and isolators, in chemical engineering and catalytic reactors where large surfaces of packed granular beds intensify chemical reactions, or in energy production systems, where granulates are promising materials for heat storage and heat transfer media. Despite the common usage of granulates and extensive research performed in this field, phenomena occurring between granular solid elements or between solids and fluid are still not fully understood. In the present work we analyze the heat exchange process between the flowing medium (gas, liquid) and solid material inside the granular layers. We consider them as a composite of isolated solid elements and inter-granular spaces in which a gas or liquid can flow. The structure of the layer is controlled by shapes of particular granular elements (e.g., spheres, cylinders, cubes, Raschig rings), its spatial distribution or effective characteristic dimension (total volume or surface area). We will analyze to what extent alteration of these parameters influences on flow characteristics (turbulent intensity, mixing efficiency, heat transfer) inside the layer and behind it. Analysis of flow inside granular layers is very complicated because the use of classical experimental techniques (LDA, PIV, fibber probes) inside the layers is practically impossible, whereas the use of probes (e.g. thermocouples, Pitot tubes) requires drilling of holes inside the solid material. Hence, measurements of the flow inside granular layers are usually performed using for instance advanced X-ray tomography. In this respect, theoretical or numerical analyses of flow inside granulates seem crucial. Application of discrete element methods in combination with the classical finite volume/finite difference approaches is problematic as a mesh generation process for complex granular material can be very arduous. A good alternative for simulation of flow in complex domains is an immersed boundary-volume penalization (IB-VP) in which the computational meshes have simple Cartesian structure and impact of solid objects on the fluid is mimicked by source terms added to the Navier-Stokes and energy equations. The present paper focuses on application of the IB-VP method combined with large eddy simulation (LES). The flow solver used in this work is a high-order code (SAILOR), which was used previously in various studies, including laminar/turbulent transition in free flows and also for flows in wavy channels, wavy pipes and over various shape obstacles. In these cases a formal order of approximation turned out to be in between 1 and 2, depending on the test case. The current research concentrates on analyses of the flows in dense granular layers with elements distributed in a deterministic regular manner and validation of the results obtained using LES-IB method and body-fitted approach. The comparisons are very promising and show very good agreement. It is found that the size, number of elements and their distribution have huge impact on the obtained results. Ordering of the granular elements (or lack of it) affects both the pressure drop and efficiency of the heat transfer as it significantly changes mixing process.

Keywords: granular layers, heat transfer, immersed boundary method, numerical simulations

Procedia PDF Downloads 108

Authors: Djamal Hamadi, Oussama Temami, Abdallah Zatar, Sifeddine Abderrahmani

Abstract:

The analysis and design of thin shell structures is a topic of interest in a variety of engineering applications. In structural mechanics problems the analyst seeks to determine the distribution of stresses throughout the structure to be designed. It is also necessary to calculate the displacements of certain points of the structure to ensure that specified allowable values are not exceeded. In this paper a comparative study between displacement and strain based finite elements applied to the analysis of some thin shell structures is presented. The results obtained from some examples show the efficiency and the performance of the strain based approach compared to the well known displacement formulation.

Keywords: displacement formulation, finite elements, strain based approach, shell structures

Procedia PDF Downloads 395