Migration in an oscillatory flow of a laminar suspension measured by laser anemometry

Oscillatory flow occurs in a wide range of areas of engineering importance. Two-way lateral migration of particles was observed in the flow of a steady, laminar, dilute, neutrally-buoyant suspension of rigid particles in a tube. The equilibrium particle-position was dependent on the dimensionless Womersley parameter. Experiments were performed in which the Womersley parameter was varied between 1.12 and 8.0. For low values of the parameter, two-way radial migration was observed as in steady, laminar flow. For higher values of the parameter, two equilibrium positions were observed, together with three particle free layers across the radius of the tube.     

Stability of noisy nonlinear auto-parametric systems

The purpose of this work is to examine the stationary motion and stability properties of stationary motion of two degree-of-freedom noisy auto-parametric systems We shall use analytical techniques to extend the existing results to examine such multi-dimensional nonlinear systems with noise, and in particular additive white noise. We obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of the so-called single-mode stationary motion. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ɛ and dissipation ɛ² the exponent grows in proportion with ɛ^2/3.     

Wavefront sensing for single view three-component three-dimensional flow velocimetry

We present the application of wavefront sensing to particle image velocimetry for three-component (3C), three-dimensional (3D) flow measurement from a single view. The technique is based upon measuring the wavefront scattered by a tracer particle and from that wavefront the 3D tracer location can be determined. Hence, from a temporally resolved sequence of 3D particle locations the velocity vector field is obtained. Two approaches to capture the data required to measure the wavefronts are described: multi-planar imaging using a distorted diffraction grating and an anamorphic technique. Both techniques are optically efficient, robust and compatible with coherent and incoherent scattering from flow tracers. The depth (range) resolution and repeatability have been quantified experimentally using a single mode fiber source representing a tracer particle. The anamorphic approach is shown to have the greatest measurement range and hence was selected for the first proof of principle experiments using this technique for 3D particle imaging velocimetry (PIV) on a sparsely seeded gas phase flow.     

Bifurcation of coisotropic invariant tori under locally Hamiltonian perturbations of integrable systems and nondegenerate deformation of symplectic structure

We study the bifurcation problem for a Cantor set of coisotropic invariant tori in the case where a Liouville-integrable Hamiltonian system undergoes locally Hamiltonian perturbations and, simultaneously, a deformation of the symplectic structure of the phase space. We consider a new case where the deformed symplectic structure generates a nondegenerate matrix of the Poisson brackets of action variables. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 221–232, April–June, 2006.     

Symmetry, Optima and Bifurcations in Structural Design

Motivated by optimization problems in structural engineering, we study the critical points of symmetric, ‘reflected', one-parameter family of potentials U(p, x) = max (f(p,x), f(p, −x)), yielding modest generalizations of classical bifurcations, predicted by elementary catastrophe theory. One such generalization is the ‘five-branch pitchfork’, where the symmetric optimum persists beyond the critical parameter value. Our theory may help to explain why symmetrical structures are often optimal.     

On the instability of microjets

The instability of an axisymmetric viscous liquid jet in a gas or in a vacuum is examined using the interface formation theory. This model allows for variable surface tension at constant temperature, generalising the classical continuum formulation by using irreversible thermodynamics. Steady-state solutions are determined and found to be unstable to a travelling wave that propagates down the liquid jet, causing the jet to break-up into drops. The linear instability results are compared to those of the classical formulation. These are especially found to differ when the jets are on the micron scale. This will give rise to significantly revised predictions in some parameter ranges for the break-up length and droplet sizes produced by microjets. Comparisons with molecular dynamics simulations are also presented, with encouraging results. Finally, the dependence of the results on the initial conditions is discussed. PACS 68.03.Cd     

Numerical analysis of free vibrations of a beam with oscillators

The problem of free vibrations of a beam with free ends of variable cross section and mass, from which point masses (oscillators) are suspended by bars, is considered. It is shown that parametric resonances can occur in this oscillating system. Numerical examples showing the efficiency of the calculation method proposed are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 135–144, July–August, 2006.     

Area rule for the wake behind a three-dimensional body

In three-dimensional flows, the local characteristics of the medium in the wake behind a supersonic body at Reynolds numbers Re 5·10⁴ depend in a complicated manner on the coordinates. However, in a number of cases it is important to know only the parameters of the medium averaged over the transverse section of the wake. For example, for the diagnostics of the plasma of the wake behind a body by means of microwave resonators the electron density averaged over the section is used [1]. The chemiluminescent radia tion of the wake is also obtained in an averaged form [2]. It is therefore worthwhile obtaining the average characteristics of the medium without detailed study of the local parameters. In the present paper, a rule is established that makes it possible to use the results obtained for the far viscous wake behind an axisymmetric body in the case of the wake behind a three-dimensional body that is nearly axisymmetric, the flow conditions being similar. The three-dimensional wake is considered to the distances until it degenerates into an axisymmetric wake.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 148–150, May–June, 1980.We thank G. Yu. Stepanov and É. Z. Apshtein for helpful advice in a discussion of the results.