Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators

The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.

Topology of toroidal helical fields in non-circular cross-sectional tokamaks

The ordinary differential magnetic field line equations are solved numerically; the tokamak magnetic structure is studied on Hefei Tokamak-7 Upgrade (HT-7U) when the equilibrium field with a monotonic q-profile is perturbed by a helical magnetic field. We find that a single mode (m, n) helical perturbation can cause the formation of islands on rational surfaces with q = m/n and q = (m +/- 1, +/- 2, +/- 3,...)/n due to the toroidicity and plasma shape (i.e. elongation and triangularity), while there are many undestroyed magnetic surfaces called Kolmogorov-Arnold-Moser (KAM) barriers on irrational surfaces. The islands on the same rational surface do not have the same size. When the ratio between the perturbing magnetic field B-r(r) and the toroidal magnetic field amplitude B(phi)0 is large enough, the magnetic island chains on different rational surfaces will overlap and chaotic orbits appear in the overlapping area, and the magnetic field becomes stochastic. It is remarkable that the stochastic layer appears first in the plasma edge region.

Photoelectron angular distributions of molecules in bichromatic laser fields of circular polarization

Photoelectron angular distributions (PADs) from above-threshold ionization of O-2 and N-2 molecules irradiated by a bichromatic laser field of circular polarization are Studied. The bichromatic laser field is specially modulated such that it can be used to mimic a sequence of one-cycle laser pulses. The PADs are greatly affected by the molecular alignment, the symmetry of the initial electronic distribution, and the carrier-envelope phase of the laser pulses. Generally, the PADs do not show any symmetry, and become symmetric about an axis only when the symmetric axis of laser field coincides with the symmetric axis of molecules. This study shows that the few-cycle laser pulses call be used to steer the photoelectrons and perform the selective ionization of molecules. (C) 2008 Elsevier B.V. All rights reserved.

Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Wave-front analysis method of circular aperture sampling for collimation testing

A new type of wave-front analysis method for the collimation testing of laser beams is proposed. A concept of wave-front height is defined, and, on this basis, the wave-front analysis method of circular aperture sampling is introduced. The wave-front height of the tested noncollimated wave can be estimated from the distance between two identical fiducial diffraction planes of the sampled wave, and then the divergence is determined. The design is detailed, and the experiment is demonstrated. The principle and experiment results of the method are presented. Owing to the simplicity of the method and its low cost, it is a promising method for checking the collimation of a laser beam with a large divergence. © 2005 Optical Society of America.

On the added mass of sphere in a circular cylinder considering real fluid effects

An experimental method combined with boundary layer theory is given for evaluating the added mass of a sphere moving along the axis of a circular cylinder filled with water or oil. The real fluid effects are separated from ideal fluid effects.

The experimental method consists essentially of a magnetic steel sphere propelled from rest by an electromagnetic coil in which the current is accurately controlled so that it only supplies force for a short time interval which is within the laminar flow regime of the fluid. The motion of the sphere as a function of time is recorded on single frame photographs using a short-arc multiple flash lamp with accurately controlled time intervals between flashes.

A concept of the effect of boundary layer displacement on the fluid flow around a sphere is introduced to evaluate the real fluid effects on the added mass. Surprisingly accurate agreement between experiment and theory is achieved.

Analytic expression of the diffraction of a circular aperture

Recurring to the characteristic of Bessel function, we give the analytic expression or the Fresnel diffraction by a circular aperture, thus the diffractions on the propagation axis and along the boundary of the geometrical shadow are discussed conveniently. Since it is difficult to embody intuitively the physical meaning from this series expression of the Fresnel diffraction, after weighing the diffractions on the axis and along the boundary of the geometrical shadow, we propose a simple approximate expression of the circular diffraction, which is equivalent to the rigorous solution in the further propagation distance. It is important for the measurement of the parameter or the beam, such as the quantitative analysis of the relationship of the wave error and the divergence of the beam, In this paper, the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is discussed too. (c) 2005 Elsevier GrnbH. All rights reserved.

Numerical simulation of wavefronts diffracted by apertures with circular symmetry

The numerical simulation of the wavefronts diffracted by apertures with circular symmetry is realized by a numerical method. It is based on the angular spectrum of plane waves, which ignored the vector nature of light. The on-axial irradiance distributions of plane wavefront and Gauss wavefront diffracted by the circular aperture have been calculated along the propagation direction. Comparisons of the simulation results with the analytical results and the experimental results tell us that it is a feasible method to calculate the diffraction of apertures. (c) 2006 Published by Elsevier GmbH.

Finite element analysis on a circular wedge prism with 400 mm diameter

The paper comprehensively analyzes the distortions of a circular wedge prism with 400 mm diameter in a scanner by method of optical-mechanical-thermal integrating analysis. The structure and intensity of the prism assembly is verified and checked, and the surface deformations of the prism under gravity load, as well as the thermo-elastic distortions of the prism, are analyzed in detail and evaluated, which is finally contrasted with the measured values of Zygo Mark interferometer. The results show: the maximal distortion of the prism assembly is 10 nm magnitude and the maximal stress is 0.441 Mpa, which has much tolerance to the precision requirement of structure and the admissible stress of material; the influence of heat effect on the surface deformations of prism is proved to be far greater than the influence of gravity load, so some strict temperature-controlled measures are to be considered when the scanner is used. (c) 2006 Elsevier GmbH. All rights reserved.