A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

Nebular gas drag and co-orbital system dynamics

Aims. We study trajectories of planetesimals whose orbits decay due to gas drag in a primordial solar nebula and are perturbed by the gravity of the secondary body on an eccentric orbit whose mass ratio takes values from mu(2) = 10(-7) to mu(2) = 10(-3) increasing ten times at each step. Each planetesimal ultimately suffers one of the three possible fates: (1) trapping in a mean motion resonance with the secondary body; (2) collision with the secondary body and consequent increase of its mass; or (3) diffusion after crossing the orbit of the secondary body.Methods. We take the Burlirsh-Stoer numerical algorithm in order to integrate the Newtonian equations of the planar, elliptical restricted three-body problem with the secondary body and the planetesimal orbiting the primary. It is assumed that there is no interaction among planetesimals, and also that the gas does not affect the orbit of the secondary body.Results. The results show that the optimal value of the gas drag constant k for the 1: 1 resonance is between 0.9 and 1.25, representing a meter size planetesimal for each AU of orbital radius. In this study, the conditions of the gas drag are such that in theory, L4 no longer exists in the circular case for a critical value of k that defines a limit size of the planetesimal, but for a secondary body with an eccentricity larger than 0.05 when mu(2) = 10(-6), it reappears. The decrease of the cutoff collision radius increase the difusions but does not affect the distribution of trapping. The contribution to the mass accretion of the secondary body is over 40% with a collision radius 0.05R(Hill) and less than 15% with 0.005R(Hill) for mu(2) = 10(-7). The trappings no longer occur when the drag constant k reachs 30. That means that the size limit of planetesimal trapping is 0.2 m per AU of orbital radius. In most cases, this accretion occurs for a weak gas drag and small secondary eccentricity. The diffusions represent most of the simulations showing that gas drag is an efficient process in scattering planetesimals and that the trapping of planetesimals in the 1: 1 resonance is a less probable fate. These results depend on the specific drag force chosen.

Finite element analysis of warpage in laminated aluminium alloy plates for machining of primary aeronautic parts

The aim of this paper consists in presenting a method of simulating the warpage in 7xxx series aluminium alloy plates. To perform this simulation finite element software MSC.Patran and MSC.Marc were used. Another result of this analysis will be the influence on material residual stresses induced on the raw material during the rolling process upon the warpage of primary aeronautic parts, fabricated through machining (milling) at Embraer. The method used to determinate the aluminium plate residual stress was Layer Removal Test. The numerical algorithm Modified Flavenot Method was used to convert layer removal and beam deflection in stress level. With such information about the level and profile of residual stresses become possible, during the step that anticipate the manufacturing to incorporate these values in the finite-element approach for modelling warpage parts. Based on that warpage parameter surely the products are manufactured with low relative vulnerability propitiating competitiveness and price. © 2007 American Institute of Physics.

Análise da execução de um algoritmo numérico cbs para simulação de escoamento utilizando elementos finitos

This work intends to analyze the application and execution time of a numerical algorithm that simulates incompressible and isothermal flows. It was used the explicit scheme of the Characteristic Based Split (CBS) algorithm and the Artificial Compressibility (AC) scheme for coupling pressure-velocity equations. The discretization was done with the finite element method using a bilinear elements grid. The free software GNU-Octave was used for implementation and execution of routines. The results were analyzed using the classic lid-driven cavity problem. This work shows results for tests with several Reynolds' number. The results for these tests show a good agreement when compared with previous ones obtained from bibliography. The code runtime's analysis shows yet that the matrix's assembly is the part of greater consumption time in the implementation.

Nebular gas drag and planetary accretion with eccentric high-mass planets

Aims.We investigate the dynamics of pebbles immersed in a gas disk interacting with a planet on an eccentric orbit. The model has a prescribed gap in the disk around the location of the planetary orbit, as is expected for a giant planet with a mass in the range of 0.1-1 Jupiter masses. The pebbles with sizes in the range of 1 cm to 3 m are placed in a ring outside of the giant planet orbit at distances between 10 and 30 planetary Hill radii. The process of the accumulation of pebbles closer to the gap edge, its possible implication for the planetary accretion, and the importance of the mass and the eccentricity of the planet in this process are the motivations behind the present contribution. Methods. We used the Bulirsch-Stoer numerical algorithm, which is computationally consistent for close approaches, to integrate the Newtonian equations of the planar (2D), elliptical restricted three-body problem. The angular velocity of the gas disk was determined by the appropriate balance between the gravity, centrifugal, and pressure forces, such that it is sub-Keplerian in regions with a negative radial pressure gradient and super-Keplerian where the radial pressure gradient is positive. Results. The results show that there are no trappings in the 1:1 resonance around the L 4 and L5 Lagrangian points for very low planetary eccentricities (e2 < 0.07). The trappings in exterior resonances, in the majority of cases, are because the angular velocity of the disk is super-Keplerian in the gap disk outside of the planetary orbit and because the inward drift is stopped. Furthermore, the semi-major axis location of such trappings depends on the gas pressure profile of the gap (depth) and is a = 1.2 for a planet of 1 MJ. A planet on an eccentric orbit interacts with the pebble layer formed by these resonances. Collisions occur and become important for planetary eccentricity near the present value of Jupiter (e 2 = 0.05). The maximum rate of the collisions onto a planet of 0.1 MJ occurs when the pebble size is 37.5 cm ≤ s < 75 cm; for a planet with the mass of Jupiter, it is15 cm ≤ s < 30 cm. The accretion stops when the pebble size is less than 2 cm and the gas drag dominates the motion. © 2013 ESO.

Proteção Diferencial de Transformadores Usando a Transformada Wavelet

Pós-graduação em Engenharia Elétrica - FEIS

About the Use of the HdHr Algorithm Group in Integrating the Movement Equation with Nonlinear Terms

This work summarizes the HdHr group of Hermitian integration algorithms for dynamic structural analysis applications. It proposes a procedure for their use when nonlinear terms are present in the equilibrium equation. The simple pendulum problem is solved as a first example and the numerical results are discussed. Directions to be pursued in future research are also mentioned. Copyright (C) 2009 H.M. Bottura and A. C. Rigitano.

Numerical simulation of magnetic field enhanced plasma immersion ion implantation

The behavior of plasma and sheath characteristics under the action of an applied magnetic field is important in many applications including plasma probes and material processing. Plasma immersion ion implantation (PIII) has been developed as a fast and efficient surface modification technique of complex shaped three-dimensional objects. The PIII process relies on the acceleration of ions across a high-voltage plasma sheath that develops around the target. Recent studies have shown that the sheath dynamics is significantly affected by an external magnetic field. In this work we describe a two-dimensional computer simulation of magnetic field enhanced plasma immersion implantation system. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded cylindrical vacuum chamber filled with uniform nitrogen plasma. An axial magnetic field is created by a solenoid installed inside the cylindrical target. The computer code employs the Monte Carlo method for collision of electrons and neutrals in the plasma and a particle-in-cell (PIC) algorithm for simulating the movement of charged particles in the electromagnetic field. Secondary electron emission from the target subjected to ion bombardment is also included. It is found that a high-density plasma region is formed around the cylindrical target due to the intense background gas ionization by the magnetized electrons drifting in the crossed ExB fields. An increase of implantation current density in front of high density plasma region is observed. (C) 2007 Elsevier B.V. All rights reserved.

A common Tabu search algorithm for the global optimization of engineering problems

A novel common Tabu algorithm for global optimizations of engineering problems is presented. The robustness and efficiency of the presented method are evaluated by using standard mathematical functions and hy solving a practical engineering problem. The numerical results show that the proposed method is (i) superior to the conventional Tabu search algorithm in robustness, and (ii) superior to the simulated annealing algorithm in efficiency. (C) 2001 Elsevier B.V. B.V. All rights reserved.

A SIMPLE NUMERICAL-METHOD FOR HYDROSTATIC INCOMPRESSIBLE MODELS WITH RIGID LIDS

A simple and easily implemented method is developed to keep the vertical velocity equal to zero at the bottom and top of hydrostatic incompressible numerical models. The pressure is computed at the top by correcting its value given in the previous time step so that the vertical integral of the horizontal divergence is zero at each column. Numerical experiments that exhibit small time variations of pressure at the top are able to simplify the algorithm and save computer time. Numerical simulations illustrate the method effectiveness for a horizontal deformation-induced frontogenesis.

An improved tabu-based vector optimal algorithm for design optimizations of electromagnetic devices

This paper introduces an improved tabu-based vector optimal algorithm for multiobjective optimal designs of electromagnetic devices. The improvements include a division of the entire search process, a new method for fitness assignment, a novel scheme for the generation and selection of neighborhood solutions, and so forth. Numerical results on a mathematical function and an engineering multiobjective design problem demonstrate that the proposed method can produce virtually the exact Pareto front, in both parameter and objective spaces, even though the iteration number used by it is only about 70% of that required by its ancestor.

Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.

Modified Chebyshev algorithm: some applications

Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points of the interval of orthogonality. The other application involves the generation of real Szego polynomials.

A combined wavelet-element free Galerkin method for numerical calculations of electromagnetic fields

A combined wavelet-element free Galerkin (EFG) method is proposed for solving electromagnetic EM) field problems. The bridging scales are used to preserve the consistency and linear independence properties of the entire bases. A detailed description of the development of the discrete model and its numerical implementations is given to facilitate the reader to. understand the proposed algorithm. A numerical example to validate the proposed method is also reported.