Vortex motion around a circular cylinder above a plane

The study of vortex flows around solid obstacles is of considerable interest from both a theoretical and practical perspective. One geometry that has attracted renewed attention recently is that of vortex flows past a circular cylinder placed above a plane wall, where a stationary recirculating eddy can form in front of the cylinder, in contradistinction to the usual case (without the plane boundary) for which a vortex pair appears behind the cylinder. Here we analyze the problem of vortex flows past a cylinder near a wall through the lenses of the point-vortex model. By conformally mapping the fluid domain onto an annular region in an auxiliary complex plane, we compute the vortex Hamiltonian analytically in terms of certain special functions related to elliptic theta functions. A detailed analysis of the equilibria of the model is then presented. The location of the equilibrium in front of the cylinder is shown to be in qualitative agreement with the experimental findings. We also show that a topological transition occurs in phase space as the parameters of the systems are variedComment: 17 pages, 8 figure

Four-vortex motion around a circular cylinder

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vortex system, such as the fact that there is no equilibrium for two pairs of vortices of opposite signs on the opposite sides of the cylinder. (It is argued that such equilibria might exist for vortex flows past a cylinder confined in a channel.) In addition, a new family of opposite-signed equilibria on the normal line is reported. The stability analysis for antisymmetric perturbations is also carried out and it shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid

A new data reduction scheme to obtain the mode II fracture properties of Pinus Pinaster wood

In this work a numerical study of the End Notched Flexure (ENF) specimen was performed in order to obtain the mode II critical strain energy released rate (GIIc) of a Pinus pinaster wood in the RL crack propagation system. The analysis included interface finite elements and a progressive damage model based on indirect use of Fracture Mechanics. The difficulties in monitoring the crack length during an experimental ENF test and the inconvenience of performing separate tests in order to obtain the elastic properties are well known. To avoid these problems, a new data reduction scheme based on the equivalent crack concept was proposed and validated. This new data reduction scheme, the Compliance-Based Beam Method (CBBM), does not require crack measurements during ENF tests and additional tests to obtain elastic properties.FCT - POCTI/EME/45573/200

Finite element analysis of the ECT test on mode III interlaminar fracture of carbon-epoxy composite laminates

In this work a parametric study of the Edge Crack Torsion (ECT) specimen was performed in order to maximize the mode III component (GIII) of the strain energy release rate for carbon-epoxy laminates. A three-dimensional finite element analysis of the ECT test was conducted considering a [90/0/(+45/-45)2/(-45/+45)2/0/90]S lay-up. The main objective was to define an adequate geometry to obtain an almost pure mode III at crack front. The geometrical parameters studied were specimen dimensions, distance between pins and size of the initial crack. The numerical results demonstrated that the ratio between the specimen length and the initial crack length had a significant effect on the strain energy release rate distributions. In almost all of the tested configurations, a mode II component occurred near the edges but it did not interfere significantly with the dominant mode III state.FCT - POCTI/EME/45573/200