Search results for: Maxwell equations

Authors: Shyh Ming Chern

Abstract:

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

Procedia PDF Downloads 535

Authors: Abdulatif Abdusalam, Mohamed Shaban

Abstract:

In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

Procedia PDF Downloads 317

Authors: Pius W. Molo Chin

Abstract:

Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

Procedia PDF Downloads 215

Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: exponentially shrinking sheet, magnetic field, mixed convection, suction

Procedia PDF Downloads 330

Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

Procedia PDF Downloads 363

Authors: S. Levitsky, R. Bergman

Abstract:

Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.

Keywords: elastic tube, sound propagation, temperature effect, viscoelastic liquid

Procedia PDF Downloads 420

Authors: Alex Fedoseyev

Abstract:

This study investigates a generalized hydrodynamic equation (GHE) simplified model for the simulation of turbulent flow over a two-dimensional backward-facing step (BFS) at Reynolds number Re=132000. The GHE were derived from the generalized Boltzmann equation (GBE). GBE was obtained by first principles from the chain of Bogolubov kinetic equations and considers particles of finite dimensions. The GHE has additional terms, temporal and spatial fluctuations, compared to the Navier-Stokes equations (NSE). These terms have a timescale multiplier τ, and the GHE becomes the NSE when $\tau$ is zero. The nondimensional τ is a product of the Reynolds number and the squared length scale ratio, τ=Re*(l/L)², where l is the apparent Kolmogorov length scale, and L is a hydrodynamic length scale. The BFS flow modeling results obtained by 2D calculations cannot match the experimental data for Re>450. One or two additional equations are required for the turbulence model to be added to the NSE, which typically has two to five parameters to be tuned for specific problems. It is shown that the GHE does not require an additional turbulence model, whereas the turbulent velocity results are in good agreement with the experimental results. A review of several studies on the simulation of flow over the BFS from 1980 to 2023 is provided. Most of these studies used different turbulence models when Re>1000. In this study, the 2D turbulent flow over a BFS with height H=L/3 (where L is the channel height) at Reynolds number Re=132000 was investigated using numerical solutions of the GHE (by a finite-element method) and compared to the solutions from the Navier-Stokes equations, k–ε turbulence model, and experimental results. The comparison included the velocity profiles at X/L=5.33 (near the end of the recirculation zone, available from the experiment), recirculation zone length, and velocity flow field. The mean velocity of NSE was obtained by averaging the solution over the number of time steps. The solution with a standard k −ε model shows a velocity profile at X/L=5.33, which has no backward flow. A standard k−ε model underpredicts the experimental recirculation zone length X/L=7.0∓0.5 by a substantial amount of 20-25%, and a more sophisticated turbulence model is needed for this problem. The obtained data confirm that the GHE results are in good agreement with the experimental results for turbulent flow over two-dimensional BFS. A turbulence model was not required in this case. The computations were stable. The solution time for the GHE is the same or less than that for the NSE and significantly less than that for the NSE with the turbulence model. The proposed approach was limited to 2D and only one Reynolds number. Further work will extend this approach to 3D flow and a higher Re.

Keywords: backward-facing step, comparison with experimental data, generalized hydrodynamic equations, separation, reattachment, turbulent flow

Procedia PDF Downloads 61

Authors: Huei Chu Weng, Chien-Hung Liu

Abstract:

This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases.

Keywords: microfluidics, forced convection, gas rarefaction, second-order boundary conditions

Procedia PDF Downloads 450

Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

Abstract:

Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

Procedia PDF Downloads 462

Authors: Madhu Aneja, Sapna Sharma

Abstract:

The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: bioconvection, finite element method, gyrotactic micro-organisms, inclined stretching sheet, nanofluid

Procedia PDF Downloads 189

Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

Abstract:

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

Procedia PDF Downloads 129

Authors: Jyh-Cherng Gu, Ming-Ta Yang, Dai-Ling Tsai

Abstract:

Both sparse lashing and dense lashing are applied to secure overhead XLPE (cross-linked polyethylene) covered power lines on ceramic insulators or HDPE polymer insulators. The distribution of electric field in and among the lashing wires, the XLPE power lines and insulators in normal clean condition and when conducting materials such as salt, metal particles, dust, smoke or acidic smog are present is studied in this paper. The ANSYS Maxwell commercial software is used in this study for electric field analysis. Although the simulation analysis is performed assuming ideal conditions due to the constraints of the simulation software, the result may not be the same as in real situation but still be of sufficient practical values.

Keywords: electric field intensity, insulator, XLPE covered aerial line, empty

Procedia PDF Downloads 263

Authors: Krzysztof Pomorski

Abstract:

In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

Procedia PDF Downloads 145

Authors: Damir Latypov

Abstract:

A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

Procedia PDF Downloads 154

Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

Abstract:

In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

Procedia PDF Downloads 308

Authors: David Rafetseder, Walter Bauer, Florian Poltschak, Wolfgang Amrhein

Abstract:

A flat double-stator linear induction machine (DSLIM) with a short squirrel-cage mover is designed for high thrust force at moderate speed < 5m/s. The performance and motor parameters are determined on the basis of a 2D time-transient simulation with the finite element (FE) software Maxwell 2015. Design guidelines and transformation rules for space vector theory of the LIM are presented. Resulting thrust calculated by flux and current vectors is compared with the FE results showing good coherence and reduced noise. The parameters of the equivalent circuit model are obtained.

Keywords: equivalent circuit model, finite element model, linear induction motor, space vector theory

Procedia PDF Downloads 566

Authors: Elsayed M. A. Elbashbeshy, T. G. Emam, M. S. El-Azab, K. M. Abdelgaber

Abstract:

The effect of thermal radiation on flow, heat and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder embedded in a porous medium with suction/injection is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.

Keywords: laminar flow, boundary layer, stretching horizontal cylinder, thermal radiation, suction/injection, nanofluid

Procedia PDF Downloads 382

Authors: Mounir Belattar

Abstract:

In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

Procedia PDF Downloads 443

Authors: Niloufar Ghoreishi, Ali Nekouzadeh

Abstract:

The stability of the flight during maneuvering and in response to probable perturbations is one of the most essential features of an aircraft that should be analyzed and designed for. In this study, we derived the non-linear governing equations of aircraft dynamics during the climb/descend phase and simulated a model aircraft. The corresponding force and moment dimensionless coefficients of the model and their variations with elevator angle and other relevant aerodynamic parameters were measured experimentally. The short-period mode and phugoid mode response were simulated by solving the governing equations numerically and then compared with the desired stability parameters for the particular level, category, and class of the aircraft model. To meet the target stability, a controller was designed and used. This resulted in significant improvement in the stability parameters of the flight.

Keywords: flight stability, phugoid mode, short period mode, climb phase, damping coefficient

Procedia PDF Downloads 170

Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

Abstract:

This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

Procedia PDF Downloads 198

Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

Procedia PDF Downloads 413

Authors: Emmanuel Ophel Gilbert, Williams Speret

Abstract:

The control for fluid flow behaviours of viscous fluids and heat transfer occurrences within heated mini-channel is considered. Heat transfer and flow characteristics of different viscous liquids, such as engine oil, automatic transmission fluid, one-half ethylene glycol, and deionized water were numerically analyzed. Some mathematical applications such as Fourier series and Laplace Z-Transforms were employed to ascertain the behaviour-wave like structure of these each viscous fluids. The steady, laminar flow and heat transfer equations are reckoned by the aid of numerical simulation technique. Further, this numerical simulation technique is endorsed by using the accessible practical values in comparison with the anticipated local thermal resistances. However, the roughness of this mini-channel that is one of the physical limitations was also predicted in this study. This affects the frictional factor. When an additive such as tetracycline was introduced in the fluid, the heat input was lowered, and this caused pro rata effect on the minor and major frictional losses, mostly at a very minute Reynolds number circa 60-80. At this ascertained lower value of Reynolds numbers, there exists decrease in the viscosity and minute frictional losses as a result of the temperature of these viscous liquids been increased. It is inferred that the three equations and models are identified which supported the numerical simulation via interpolation and integration of the variables extended to the walls of the mini-channel, yields the utmost reliance for engineering and technology calculations for turbulence impacting jets in the near imminent age. Out of reasoning with a true equation that could support this control for the fluid flow, Navier-stokes equations were found to tangential to this finding. Though, other physical factors with respect to these Navier-stokes equations are required to be checkmated to avoid uncertain turbulence of the fluid flow. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme via numerical simulation method that takes into account certain terms in the full Navier-Stokes equations. However, this resulted in dropping out in the approximation of certain assumptions. Concrete questions raised in the main body of the work are sightseen further in the appendices.

Keywords: frictional losses, heat transfer, laminar flow, mini-channel, number simulation, Reynolds number, turbulence, viscous fluids

Procedia PDF Downloads 176

Authors: Yasaman Azarmjoo

Abstract:

Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

Procedia PDF Downloads 93

Authors: Ayesha Sohail, Khadija Maqbool, Anila Asif, Haroon Ahmad

Abstract:

The field of tissue engineering is an active area of research. Bone tissue engineering helps to resolve the clinical problems of critical size and non-healing defects by the creation of man-made bone tissue. We will design and validate an efficient numerical model, which will simulate the effective diffusivity in bone tissue engineering. Our numerical model will be based on the finite element analysis of the diffusion-reaction equations. It will have the ability to optimize the diffusivity, even at multi-scale, with the variation of time. It will also have a special feature, with which we will not only be able to predict the oxygen, glucose and cell density dynamics, more accurately, but will also sort the issues arising due to anisotropy. We will fix these problems with the help of modifying the governing equations, by selecting appropriate spatio-temporal finite element schemes, by adaptive grid refinement strategy and by transient analysis.

Keywords: scaffolds, porosity, diffusion, transient analysis

Procedia PDF Downloads 541

Authors: Davide Forcellini, James Marshal Kelly

Abstract:

Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

Procedia PDF Downloads 435

Authors: I. Kruashvili, I. Inashvili, K. Bziava, M. Lomishvili

Abstract:

Seepage capillary anomalies in the active layer of soil, related to the soil water movement, often cause variation of soil hydrophysical properties and become one of the main objectives of the hydroecology. It is necessary to mention that all existing equations for computing the seepage flow particularly from soil channels, through dams, bulkheads, and foundations of hydraulic engineering structures are preferable based on the linear seepage law. Regarding the existing beliefs, anomalous seepage is based on postulates according to which the fluid in free volume is characterized by resistance against shear deformation and is presented in the form of initial gradient. According to the above-mentioned information, we have determined: Equation to calculate seepage coefficient when the velocity of transition flow is equal to seepage flow velocity; by means of power function, equations for the calculation of average and maximum velocities of seepage flow have been derived; taking into consideration the fluid continuity condition, average velocity for calculation of average velocity in capillary tube has been received.

Keywords: seepage, soil, velocity, water

Procedia PDF Downloads 462

Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: operational matrix of differentiation, similarity transformation, shifted second kind chebyshev wavelets, stefan problem

Procedia PDF Downloads 402

Authors: Sudip Sudhir Godbole

Abstract:

In transmission line surface potential gradient is a critical design parameter for planning overhead line, as it determines the level of corona loss (CL), radio interference (RI) and audible noise (AN).With increase of transmission line voltage level bulk power transfer is possible, using bundle conductor configuration used, it is more complex to find accurate surface stress in bundle configuration. The majority of existing models for surface gradient calculations are based on analytical methods which restrict their application in simulating complex surface geometry. This paper proposes a novel technique which utilizes both analytical and numerical procedure to predict the surface gradient. One of 400 kV transmission line configurations has been selected as an example to compare the results for different methods. The different strand shapes are a key variable in determining.

Keywords: surface gradient, Maxwell potential coefficient method, market and Mengele’s method, successive images method, charge simulation method, finite element method

Procedia PDF Downloads 538

Authors: Mohammad R. Jalali

Abstract:

Movement of liquid with a free surface in a container is known as slosh. For instance, slosh occurs when water in a closed tank is set in motion by a free surface displacement, or when liquid natural gas in a container is vibrated by an external driving force, such as an earthquake or movement induced by transport. Slosh is also derived from resonant switching of a natural basin. During sloshing, different types of motion are produced by energy exchange between the liquid and its container. In present study, a numerical model is developed to simulate the nonlinear even harmonic oscillations of free surface sloshing of an initial disturbance to the free surface of a liquid in a closed square basin. The response of the liquid free surface is affected by amplitude and motion frequencies of its container; therefore, sloshing involves complex fluid-structure interactions. In the present study, nonlinear interaction of free surface sloshing of an initial Gaussian hump with its uneven container is predicted numerically. For this purpose, Green-Naghdi (GN) equations are applied as governing equation of fluid field to produce nonlinear second-order and higher-order wave interactions. These equations reduce the dimensions from three to two, yielding equations that can be solved efficiently. The GN approach assumes a particular flow kinematic structure in the vertical direction for shallow and deep-water problems. The fluid velocity profile is finite sum of coefficients depending on space and time multiplied by a weighting function. It should be noted that in GN theory, the flow is rotational. In this study, GN numerical simulations of initial Gaussian hump are compared with Fourier series semi-analytical solutions of the linearized shallow water equations. The comparison reveals that satisfactory agreement exists between the numerical simulation and the analytical solution of the overall free surface sloshing patterns. The resonant free surface motions driven by an initial Gaussian disturbance are obtained by Fast Fourier Transform (FFT) of the free surface elevation time history components. Numerically predicted velocity vectors and magnitude contours for the free surface patterns indicate that interaction of Gaussian hump with its container has localized effect. The result of this sloshing is applicable to the design of stable liquefied oil containers in tankers and offshore platforms.

Keywords: fluid-structure interactions, free surface sloshing, Gaussian hump, Green-Naghdi equations, numerical predictions

Procedia PDF Downloads 398

Authors: Hassan Parandvar, Mehrdad Farid

Abstract:

In this paper, a finite element modeling is presented for large amplitude vibration of functionally graded material (FGM) plates subjected to combined random pressure and thermal load. The material properties of the plates are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The material properties depend on the temperature whose distribution along the thickness can be expressed explicitly. The von Karman large deflection strain displacement and extended Hamilton's principle are used to obtain the governing system of equations of motion in structural node degrees of freedom (DOF) using finite element method. Three-node triangular Mindlin plate element with shear correction factor is used. The nonlinear equations of motion in structural degrees of freedom are reduced by using modal reduction method. The reduced equations of motion are solved numerically by 4th order Runge-Kutta scheme. In this study, the random pressure is generated using Monte Carlo method. The modeling is verified and the nonlinear dynamic response of FGM plates is studied for various values of volume fraction and sound pressure level under different thermal loads. Snap-through type behavior of FGM plates is studied too.

Keywords: nonlinear vibration, finite element method, functionally graded material (FGM) plates, snap-through, random vibration, thermal effect

Procedia PDF Downloads 262