Search results for: Euler Deconvolution

Authors: T. M. Ismail, M. A. El-Salam

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A mathematical model study was carried out to investigate gasification of biomass fuels using high-temperature air and steam as a gasifying agent using high-temperature air up to 1000°C. In this study, a 2D computational fluid dynamics model was developed to study the gasification process in an updraft gasifier, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using a Euler−Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k−ε turbulence model was used in the gas phase, and the particle phase was modeled using the kinetic theory of granular flow. The results show that the present model giving a promising way in its capability and sensitivity for the parameter effects that influence the gasification process.

Keywords: computational fluid dynamics, gasification, biomass fuel, fixed bed gasifier

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Z. Ž. Lazarević, D. L. Sekulić, V. N. Ivanovski, N. Ž. Romčević

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NiFe2O4 (nickel ferrite), ZnFe2O4 (zinc ferrite) and Ni0.5Zn0.5Fe2O4 (nickel-zinc ferrite) were prepared by mechanochemical route in a planetary ball mill starting from mixture of the appropriate quantities of the Ni(OH)2/Fe(OH)3, Zn(OH)2/Fe(OH)3 and Ni(OH)2/Zn(OH)2/Fe(OH)3 hydroxide powders. In order to monitor the progress of chemical reaction and confirm phase formation, powder samples obtained after 25 h, 18 h and 10 h of milling were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM), IR, Raman and Mössbauer spectroscopy. It is shown that the soft mechanochemical method, i.e. mechanochemical activation of hydroxides, produces high quality single phase ferrite samples in much more efficient way. From the IR spectroscopy of single phase samples it is obvious that energy of modes depends on the ratio of cations. It is obvious that all samples have more than 5 Raman active modes predicted by group theory in the normal spinel structure. Deconvolution of measured spectra allows one to conclude that all complex bands in the spectra are made of individual peaks with the intensities that vary from spectrum to spectrum. The deconvolution of Raman spectra allows to separate contributions of different cations to a particular type of vibration and to estimate the degree of inversion.

Keywords: ferrites, Raman spectroscopy, IR spectroscopy, Mössbauer measurements

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Authors: Falek Kamel

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Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.

Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory

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Authors: Gholamreza Koochaki

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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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Authors: Hamioud Saida, Khalfallah Salah

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In this study, a spectral element method is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion, which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation

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Authors: Raphael Naryongo, Philip Ngare, Anthony Waititu

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This paper deals with numerical simulation of Wishart processes for a single asset risky pricing model whose volatility is described by Wishart affine diffusion processes. The multi-factor specification of volatility will make the model more flexible enough to fit the stock market data for short or long maturities for better returns. The Wishart process is a stochastic process which is a positive semi-definite matrix-valued generalization of the square root process. The aim of the study is to model the log asset stock returns under the double Wishart stochastic volatility model. The solution of the log-asset return dynamics for Bi-Wishart processes will be obtained through Euler-Maruyama discretization schemes. The numerical results on the asset returns are compared to the existing models returns such as Heston stochastic volatility model and double Heston stochastic volatility model

Keywords: euler schemes, log-asset return, infinitesimal generator, wishart diffusion affine processes

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Authors: Utkan Caliskan

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Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach.

Keywords: cell centered finite volume method, compressible Euler equations, OpenFOAM mesh format, OpenMP

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Yuan Li, Yitao Han, Zhao Zhu

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In this paper, the effect of blasting loads on steel-concrete composite bridges has been investigated considering the slope reflection effect. Reasonable values of girder size, plate thickness, stiffening rib, and other design parameters were selected according to design specifications. Modified RHT (Riedel-Hiermaier-Thoma) was used as constitutive relation in analyses. In order to simulate the slope reflection effect, the slope of the bridge was precisely built in the model. Different blasting conditions, including top, middle, and bottom explosions, were simulated. The multi-Euler domain method based on fully coupled Lagrange and Euler models was adopted for the structural analysis of the explosion process using commercial software AUTODYN. The obtained results showed that explosion overpressure was increased by 3006, 879, and 449kPa, corresponding to explosions occurring at the top, middle, and bottom of the slope, respectively. At the same time, due to energy accumulation and transmission dissipation caused by slope reflection, the corresponding yield lengths of steel beams were increased by 8, 0, and 5m, respectively.

Keywords: steel-concrete composite bridge, explosion damage, slope reflection, blasting loads, RHT

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Authors: Liliana Patricia Olivo Arias

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The present study focused on the hydrodynamic study in a three-phase fluidized bed reactor and the influence of important aspects, such as volume fractions (Hold up), velocity magnitude of gas, liquid and solid phases (hydrogen, gasoil, and gamma alumina), interactions of phases, through of drag models with the k-epsilon turbulence model. For this purpose was employed a Euler-Euler model and also considers the system is constituted of three phases, gaseous, liquid and solid, characterized by its physical and thermal properties, the transport processes that are developed within the transient regime. The proposed model of the three-phase fluidized bed reactor was solved numerically using the ANSYS-Fluent software with different mesh refinements on bed expansion zone in order to observe the influence of the hydrodynamic parameters and convergence criteria. With this model and the numerical simulations obtained for its resolution, it was possible to predict the results of the volume fractions (Hold ups) and the velocity magnitude for an unsteady system from the initial and boundaries conditions were established.

Keywords: three-phase fluidized bed system, CFD simulation, mesh dependency study, hydrodynamic study

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Mojtaba Ghodsi, Hamidreza Ziaifar, Morteza Mohammadzaheri, Payam Soltani

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This article presents an analytical model to estimate the harvested power from a Magnetostrictive cantilevered beam with tip excitation. Furthermore, the effects of internal and external damping on harvested power are investigated. The magnetostrictive material in this harvester is Galfenol. In comparison to other popular smart materials like Terfenol-D, Galfenol has higher strength and machinability. In this article, first, a mechanical model of the Euler-Bernoulli beam is employed to calculate the deflection of the harvester. Then, the magneto-mechanical equation of Galfenol is combined with Faraday's law to calculate the generated voltage of the Magnetostrictive cantilevered beam harvester. Finally, the beam model is incorporated in the aforementioned combination. The results show that a 30×8.5×1 mm Galfenol cantilever beam harvester with 80 turn pickup coil can generate up to 3.7 mV and 9 mW. Furthermore, sensitivity analysis made by Response Surface Method (RSM) shows that the harvested power is only sensitive to the internal damping coefficient.

Keywords: internal damping coefficient, external damping coefficient, euler-bernoulli, energy harvester, galfenol, magnetostrictive, response surface method

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Authors: G. Judakova, M. Bause

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The ability to model and simulate numerically natural gas flow in pipelines has become of high importance for the design of pipeline systems. The understanding of the formation of hydrate particles and their dynamical behavior is of particular interest, since these processes govern the operation properties of the systems and are responsible for system failures by clogging of the pipelines under certain conditions. Mathematically, natural gas flow can be described by multiphase flow models. Using the two-fluid modeling approach, the gas phase is modeled by the compressible Euler equations and the particle phase is modeled by the pressureless Euler equations. The numerical simulation of compressible multiphase flows is an important research topic. It is well known that for nonlinear fluxes, even for smooth initial data, discontinuities in the solution are likely to occur in finite time. They are called shock waves or contact discontinuities. For hyperbolic and singularly perturbed parabolic equations the standard application of the Galerkin finite element method (FEM) leads to spurious oscillations (e.g. Gibb's phenomenon). In our approach, we use stabilized FEM, the streamline upwind Petrov-Galerkin (SUPG) method, where artificial diffusion acting only in the direction of the streamlines and using a special treatment of the boundary conditions in inviscid convective terms, is added. Numerical experiments show that the numerical solution obtained and stabilized by SUPG captures discontinuities or steep gradients of the exact solution in layers. However, within this layer the approximate solution may still exhibit overshoots or undershoots. To suitably reduce these artifacts we add a discontinuity capturing or shock capturing term. The performance properties of our numerical scheme are illustrated for two-phase flow problem.

Keywords: two-phase flow, gas-particle mixture, inviscid two-fluid model, euler equation, finite element method, streamline upwind petrov-galerkin, shock capturing

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Authors: Mohamed Abdalla Saleem, Hana Ellafi

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The study area is located in the eastern part of the Sirt Basin, in the Sarir-Hameimat arm of the basin, south of Amal High. The area covers the northern part of the Hamemat Trough and the Rakb High. All of these tectonic elements are part of the major and common tectonics that were created when the old Sirt Arch collapsed, and most of them are trending NW-SE. This study has been conducted to investigate the subsurface structures and the sedimentology characterization of the area and attempt to define its development tectonically and stratigraphically. About 7600 land gravity measurements, 22500 gridded magnetic data, and petrographic core data from some wells were used to investigate the subsurface structural features both vertically and laterally. A third-order separation of the regional trends from the original Bouguer gravity data has been chosen. The residual gravity map reveals a significant number of high anomalies distributed in the area, separated by a group of thick sediment centers. The reduction to the pole magnetic map also shows nearly the same major trends and anomalies in the area. Applying the further interpretation filters reveals that these high anomalies are sourced from different depth levels; some are deep-rooted, and others are intruded igneous bodies within the sediment layers. The petrographic sedimentology study for some wells in the area confirmed the presence of these igneous bodies and defined their composition as most likely to be gabbro hosted by marine shale layers. Depth investigation of these anomalies by the average depth spectrum shows that the average basement depth is about 7.7 km, while the top of the intrusions is about 2.65 km, and some near-surface magnetic sources are about 1.86 km. The depth values of the magnetic anomalies and their location were estimated specifically using the 3D Euler deconvolution technique. The obtained results suggest that the maximum depth of the sources is about 4938m. The total horizontal gradient of the magnetic data shows that the trends are mostly extending NW-SE, others are NE-SW, and a third group has an N-S extension. This variety in trend direction shows that the area experienced different tectonic regimes throughout its geological history.

Keywords: sirt basin, tectonics, gravity, magnetic

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Authors: Mahrooz Abed, Amir R. Masoodi

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Many structural lateral systems are used in tall buildings such as rigid frames, braced frames, shear walls, tubular structures and core structures. Some efficient structures for drift control and base moment reduction in tall buildings is outrigger and belt truss systems. When adopting outrigger beams in building design, their location should be in an optimum position for an economical design. A range of different strategies has been employed to identify the optimum locations of these outrigger beams under wind load. However, there is an absence of scientific research or case studies dealing with optimum outrigger location using buckling analysis. In this paper, one outrigger system is considered at the middle of height of structure. The optimum location of outrigger will be found based on the buckling load limitation. The core of structure is modeled by a clamped tapered beam. The exact stiffness matrix of tapered beam is formulated based on the Euler-Bernoulli theory. Finally, based on the buckling load of structure, the optimal location of outrigger will be found.

Keywords: tall buildings, outrigger system, buckling load, second-order effects, Euler-Bernoulli beam theory

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Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

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In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations

Keywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow

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Authors: Guozhen Li, Philip Hall, Nick Miles, Tao Wu, Jie Dong

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This paper presents a Euler-Lagrange model of the water-particles multiphase flows in a Vorsyl separator where particles with different densities are separated. A series of particles with their densities ranging from 760 kg/m³ to 1380 kg/m³ were fed into the Vorsyl separator with water by means of tangential inlet. The simulation showed that the feed materials acquired centrifugal force which allows most portion of the particles with a density less than water to move to the center of the separator, enter the vortex finder and leave the separator through the bottom outlet. While the particles heavier than water move to the wall, reach the throat area and leave the separator through the side outlet. The particles were thus separated and particles collected at the bottom outlet are pure and clean. The influence of particle density on separation efficiency was investigated which demonstrated a positive correlation of the separation efficiency with increasing density difference between medium liquid and the particle. In addition, the influence of the split ratio on the performance was studied which showed that the separation efficiency of the Vorsyl separator can be improved by the increase of split ratio. The simulation also suggested that the Vorsyl separator may not function when the feeding velocity is smaller than a certain critical feeding in velocity. In addition, an increasing feeding velocity gives rise to increased pressure drop, however does not necessarily increase the separation efficiency.

Keywords: Vorsyl separator, separation efficiency, CFD, split ratio

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Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

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A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, Nonlocal Strain Gradient Theory, velocity gradient

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Authors: Sara Bilal, Abdi Omar Shuriye, Raihan Othman

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Numerical Methods is a course that can be conducted using workshops and group discussion. This study has been implemented on undergraduate students of level two at the Faculty of Engineering, International Islamic University Malaysia. The Numerical Method course has been delivered to two Sections 1 and 2 with 44 and 22 students in each section, respectively. Systematic steps have been followed to apply the student centered learning approach in teaching Numerical Method course. Initially, the instructor has chosen the topic which was Euler’s Method to solve Ordinary Differential Equations (ODE) to be learned. The students were then divided into groups with five members in each group. Initial instructions have been given to the group members to prepare their subtopics before meeting members from other groups to discuss the subtopics in an expert group inside the classroom. For the time assigned for the classroom discussion, the setting of the classroom was rearranged to accommodate the student centered learning approach. Teacher strength was by monitoring the process of learning inside and outside the class. The students have been assessed during the migrating to the expert groups, recording of a video explanation outside the classroom and during the final examination. Euler’s Method to solve the ODE was set as part of Question 3(b) in the final exam. It is observed that none of the students from both sections obtained a zero grade in Q3(b), compared to Q3(a) and Q3(c). Also, for Section 1(44 students), 29 students obtained the full mark of 7/7, while only 10 obtained 7/7 for Q3(a) and no students obtained 6/6 for Q3(c). Finally, we can recommend that the Numerical Method course be moved toward more student-centered Learning classrooms where the students will be engaged in group discussion rather than having a teacher one man show.

Keywords: teacher centered learning, student centered learning, mathematic, numerical methods

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Authors: V. Kumar, K. Jha

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The present study is done to explore design modifications of the vortex finder, as it has a significant effect on the cyclone separator performance. It is evident that modifications of the vortex finder improve the performance of the cyclone separator significantly. The study conducted strives to improve the overall performance of cyclone separators by utilizing a converging-diverging (CD) vortex finder instead of the traditional uniform diameter vortex finders. The velocity and pressure fields inside a Stairmand cyclone separator with body diameter 0.29m and vortex finder diameter 0.1305m are calculated. The commercial software, Ansys Fluent v14.0 is used to simulate the flow field in a uniform diameter cyclone and six cyclones modified with CD vortex finders. Reynolds stress model is used to simulate the effects of turbulence on the fluid and particulate phases, discrete phase model is used to calculate the particle trajectories. The performance of the modified vortex finders is compared with the traditional vortex finder. The effects of the lengths of the converging and diverging sections, the throat diameter and the end diameters of the convergent divergent section are also studied to achieve enhanced performance. The pressure and velocity fields inside the vortex finder are presented by means of contour plots and velocity vectors and changes in the flow pattern due to variation of the geometrical variables are also analysed. Results indicate that a convergent-divergent vortex finder is capable of decreasing the pressure drop than that achieved through a uniform diameter vortex finder. It is also observed that the end diameters of the CD vortex finder, the throat diameter and the length of the diverging part of the vortex finder have a significant impact on the cyclone separator performance. Increase in the lower diameter of the vortex finder by 66% results in 11.5% decrease in the dimensionless pressure drop (Euler number) with 5.8% decrease in separation efficiency. Whereas 50% decrease in the throat diameter gives 5.9% increase in the Euler number with 10.2% increase in the separation efficiency and increasing the length of the diverging part gives 10.28% increase in the Euler number with 5.74% increase in the separation efficiency. Increasing the upper diameter of the CD vortex finder is seen to produce an adverse effect on the performance as it increases the pressure drop significantly and decreases the separation efficiency. Increase in length of the converging is not seen to affect the performance significantly. From the present study, it is concluded that convergent-divergent vortex finders can be used in place of uniform diameter vortex finders to achieve a better cyclone separator performance.

Keywords: convergent-divergent vortex finder, cyclone separator, discrete phase modeling, Reynolds stress model

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Authors: Mehdi Tajdari, Farzad Mokhtarnejad, Fatemeh Moradi, Mehdi Najafizadeh

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Nowadays, energy absorbing devices have been widely used in all vehicles and moving parts such as railway couches, aircraft, ships and lifts. The aim is to protect these structures from serious damages while subjected to impact loads, or to minimize human injuries while collision is occurred in transportation systems. These energy-absorbing devices can dissipate kinetic energy in a wide variety of ways like friction, facture, plastic bending, crushing, cyclic plastic deformation and metal cutting. On the other hand, various structures may be used as collapsible energy absorbers. Metallic cylindrical tubes have attracted much more attention due to their high stiffness and strength combined with the low weight and ease of manufacturing process. As a matter of fact, favorable crash worthiness characteristics for energy dissipation purposes can be achieved from axial collapse of tubes while they crush progressively in symmetric modes. However, experimental and theoretical results have shown that depending on various parameters such as tube geometry, material properties of tube, boundary and loading conditions, circular tubes buckle in different modes of deformation, namely, diamond and Euler collapsing modes. It is shown that when the tube length is greater than the critical length, the tube deforms in overall Euler buckling mode, which is an inefficient mode of energy absorption and needs to be avoided in crash worthiness applications. This study develops a new method with the aim of improving energy absorption characteristics of long steel circular tubes. Inserting a helical spring into the tubes is proved experimentally to be an efficient solution. In fact when a long tube is subjected to axial compression load, the spring prevents of undesirable Euler or diamond collapsing modes. This is because the spring reinforces the internal wall of tubes and it causes symmetric deformation in tubes. In this research three specimens were prepared and three tests were performed. The dimensions of tubes were selected so that in axial compression load buckling is occurred. In the second and third tests a spring was inserted into tubes and they were subjected to axial compression load in quasi-static and impact loading, respectively. The results showed that in the second and third tests buckling were not happened and the tubes deformed in symmetric modes which are desirable in energy absorption.

Keywords: energy absorption, circular tubes, collapsing deformation, crashworthiness

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Authors: Somya R. Patro, Arnab Banerjee, G. V. Ramana

Abstract:

A flexural beam carrying elastically mounted concentrated masses, such as engines, motors, oscillators, or vibration absorbers, is often encountered in mechanical, civil, and aeronautical engineering domains. To prevent resonance conditions, the designers must predict the natural frequencies of such a constrained beam system. This paper investigates experimental and analytical studies on vibration suppression in a cantilever beam with a tip mass with the help of spring-mass to achieve local resonance conditions. The system consists of a 3D printed polylactic acid (PLA) beam screwed at the base plate of the shaker system. The top of the free end is connected by an accelerometer which also acts as a tip mass. A spring and a mass are attached at the bottom to replicate the mechanism of the spring-mass resonator. The Fast Fourier Transform (FFT) algorithm converts time acceleration plots into frequency amplitude plots from which transmittance is calculated as a function of the excitation frequency. The mathematical formulation is based on the transfer matrix method, and the governing differential equations are based on Euler Bernoulli's beam theory. The experimental results are successfully validated with the analytical results, providing us essential confidence in our proposed methodology. The beam spring-mass system is then converted to an equivalent two-degree of freedom system, from which frequency response function is obtained. The H2 optimization technique is also used to obtain the closed-form expression of optimum spring stiffness, which shows the influence of spring stiffness on the system's natural frequency and vibration response.

Keywords: euler bernoulli beam theory, fast fourier transform, natural frequencies, polylactic acid, transmittance, vibration absorbers

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

Abstract:

Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Gozel Judakova, Markus Bause

Abstract:

We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, twophase flow

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Authors: Ramish, Farhan Khalique Awan

Abstract:

Kinematic redundancy within the manipulators presents extended dexterity and manipulability to the manipulators. Redundant serial robotic manipulators are very popular in industries due to its competencies to keep away from singularities during normal operation and fault tolerance because of failure of one or more joints. Such fault tolerant manipulators are extraordinarily beneficial in applications where human interference for repair and overhaul is both impossible or tough; like in case of robotic arms for space programs, nuclear applications and so on. The design of this sort of fault tolerant serial 3 DoF manipulator is presented in this paper. This work was the extension of the author’s previous work of designing the simple 3R serial manipulator. This work is the realization of the previous design with optimizing the link lengths for incorporating the feature of fault tolerance. Various measures have been followed by the researchers to quantify the fault tolerance of such redundant manipulators. The fault tolerance in this work has been described in terms of the worst-case measure of relative manipulability that is, in fact, a local measure of optimization that works properly for certain configuration of the manipulators. An optimum fault tolerant Jacobian matrix has been determined first based on prescribed null space properties after which the link parameters have been described to meet the given Jacobian matrix. A solid model of the manipulator was then developed to realize the mathematically rigorous design. Further work was executed on determining the dynamic properties of the fault tolerant design and simulations of the movement for various trajectories have been carried out to evaluate the joint torques. The mathematical model of the system was derived via the Euler-Lagrange approach after which the same has been tested using the RoboAnalyzer© software. The results have been quite in agreement. From the CAD model and dynamic simulation data, the manipulator was fabricated in the workshop and Advanced Machining lab of NED University of Engineering and Technology.

Keywords: fault tolerant, Graham matrix, Jacobian, kinematics, Lagrange-Euler

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Authors: A. Raj Kumar, A. Okunseinde, P. Raghavan, V. Kapila

Abstract:

Stroke is the leading cause of adult disability worldwide. With recent advances in immediate post-stroke care, there is an increasing number of young stroke survivors, under the age of 65 years. While most stroke survivors will regain the ability to walk, they often experience long-term arm and hand motor impairments. Long term upper limb rehabilitation is needed to restore movement and function, and prevent deterioration from complications such as learned non-use and learned bad-use. We have developed a novel virtual coach, a wearable instrumented rehabilitation jacket, to motivate individuals to participate in long-term skill re-learning, that can be personalized to their impairment profile. The jacket can estimate the movements of an individual’s arms using embedded off-the-shelf sensors (e.g., 9-DOF IMU for inertial measurements, flex-sensors for measuring angular orientation of fingers) and a Bluetooth Low Energy (BLE) powered microcontroller (e.g., RFduino) to non-intrusively extract data. The 9-DOF IMU sensors contain 3-axis accelerometer, 3-axis gyroscope, and 3-axis magnetometer to compute the quaternions, which are transmitted to a computer to compute the Euler angles and estimate the angular orientation of the arms. The data are used in a gaming environment to provide visual, and/or haptic feedback for goal-based, augmented-reality training to facilitate re-learning in a cost-effective, evidence-based manner. The full paper will elaborate the technical aspects of communication, interactive gaming environment, and physical aspects of electronics necessary to achieve our stated goal. Moreover, the paper will suggest methods to utilize the proposed system as a cheaper, portable, and versatile system vis-à-vis existing instrumentation to facilitate post-stroke personalized arm rehabilitation.

Keywords: feedback, gaming, Euler angles, rehabilitation, augmented reality

Procedia PDF Downloads 253

Authors: Di Yao, Gunther Prokop, Kay Buttner

Abstract:

Dynamic parameters, including the center of gravity, mass and inertia moments of vehicle, play an essential role in vehicle simulation, collision test and real-time control of vehicle active systems. To identify the important vehicle dynamic parameters, a systematic parameter identification procedure is studied in this work. In the first step of the procedure, a conceptual parallel manipulator (virtual test rig), which possesses three rotational degrees-of-freedom, is firstly proposed. To realize kinematic characteristics of the conceptual parallel manipulator, the kinematic analysis consists of inverse kinematic and singularity architecture is carried out. Based on the Euler's rotation equations for rigid body dynamics, the dynamic model of parallel manipulator and derivation of measurement matrix for parameter identification are presented subsequently. In order to reduce the sensitivity of parameter identification to measurement noise and other unexpected disturbances, a parameter optimization process of searching for optimal exciting trajectory of parallel manipulator is conducted in the following section. For this purpose, the 321-Euler-angles defined by parameterized finite-Fourier-series are primarily used to describe the general exciting trajectory of parallel manipulator. To minimize the condition number of measurement matrix for achieving better parameter identification accuracy, the unknown coefficients of parameterized finite-Fourier-series are estimated by employing an iterative algorithm based on MATLAB®. Meanwhile, the iterative algorithm will ensure the parallel manipulator still keeps in an achievable working status during the execution of optimal exciting trajectory. It is showed that the proposed procedure and methods in this work can effectively identify the vehicle dynamic parameters and could be an important application of parallel manipulator in the fields of parameter identification and test rig development.

Keywords: parameter identification, parallel manipulator, singularity architecture, dynamic modelling, exciting trajectory

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Authors: İbrahim Aktaş, Árpád Baricz

Abstract:

In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

Procedia PDF Downloads 249