ALBERT

Description: This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segre-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration. © 1994, Cambridge University Press. All rights reserved.

Description: An analytical expression for the fringe shift in the N-wave is derived from the improved linearized theory for a slender supersonic projectile. From this expression an approximate mapping function is found which gives a simple test for N-wave flow. The validity of the fringe-shift expression is quantitatively confirmed by measuring an interferogram of the flow around a sphere. N-wave flow is shown to exist around a small sphere for r greater than about 70 diameters. Measurements of the shock waves from a sphere and a cone-cylinder show that the shocks assume their asymptotic positions for r 〉 14 diameters for the sphere, and r 〉 7 diameters for the cone-cylinder.

Description: A magnetic field is shown to be asymptotically (t→∞) decaying in a flow of finite conductivity with v = Cr, where C = Cξ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers. © 1984, Cambridge University Press. All rights reserved.

Description: A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleigh quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain. © 1994, Cambridge University Press. All rights reserved.

Description: This paper reports the result of direct simulations of fluid-particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier-Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active draf-ting-kissing-tumbling scenario are realized at increasing Reynolds numbers. The nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published. © 1994, Cambridge University Press. All rights reserved.

Description: Oscillations of a tank at a near-resonant frequency have been shown to produce a response which changes from a ‘hard-spring’ to a ‘soft-spring’ response as the depth passes through a critical value. This paper investigates the transition region and it is shown, using a symbolic manipulator, that in fact the large-amplitude response is that of a soft spring on either side of this critical depth. © 1994, Cambridge University Press. All rights reserved.

Description: Low-density flow of molecular hydrogen from a small nozzle is studied using numerical and experimental techniques. The conditions in the nozzle indicate that nonequilibrium effects will significantly influence the flow. Therefore, the numerical analysis is undertaken using a Monte Carlo approach. The experimental studies employ spontaneous Raman scattering. Comparisons of the measured data and computed results are made for total number density, rotational temperature, and for the number density of the first rotational level. The numerical results are found to be quite sensitive to the rotational relaxation rate, and a strong degree of thermal nonequilibrium is observed at the exit plane of the nozzle. Comparisons between experiment and analysis permit estimation of the rotational relaxation rate for hydrogen. Investigations are also conducted for expansion of the supersonic jet into a finite back pressure. The interaction of the plume with the chamber background gas is found to form shock waves in both the simulations and experiments. This phenomenon is investigated further by increasing the background pressure. Direct comparison of the simulation results and experimental measurements is very favourable. © 1994, Cambridge University Press. All rights reserved.

Description: Potential flows of incompressible fluids admit a pressure (Bernoulli) equation when the divergence of the stress is a gradient as in inviscid fluids, viscous fluids, linear viscoelastic fluids and second-order fluids. We show that in potential flow without boundary layers the equation balancing drag and acceleration is the same for all these fluids, independent of the viscosity or any viscoelastic parameter, and that the drag is zero when the flow is steady. But, if the potential flow is viewed as an approximation to the actual flow field, the unsteady drag on bubbles in a viscous (and possibly in a viscoelastic) fluid may be approximated by evaluating the dissipation integral of the approximating potential flow because the neglected dissipation in the vorticity layer at the traction-free boundary of the bubble gets smaller as the Reynolds number is increased. Using the potential flow approximation, the actual drag D on a spherical gas bubble of radius a rising with velocity U(t) in a linear viscoelastic liquid of density p and shear modules G(s) is estimated to be and, in a second-order fluid, where ±1 〈 0 is the coefficient of the first normal stress and p is the viscosity of the fluid. Because oq is negative, we see from this formula that the unsteady normal stresses oppose inertia; that is, oppose the acceleration reaction. When U(t) is slowly varying, the two formulae coincide. For steady flow, we obtain the approximate drag D — 12Π±µ U for both viscous and viscoelastic fluids. In the case where the dynamic contribution of the interior flow of the bubble cannot be ignored as in the case of liquid bubbles, the dissipation method gives an estimation of the rate of total kinetic energy of the flows instead of the drag. When the dynamic effect of the interior flow is negligible but the density is important, this formula for the rate of total kinetic energy leads to D = (p±—p)VBg.ex-p±VBU where p± is the density of the fluid (or air) inside the bubble and VB is the volume of the bubble. Classical theorems of vorticity for potential flow of ideal fluids hold equally for second-order fluid. The drag and lift on two-dimensional bodies of arbitrary cross-section in a potential flow of second-order and linear viscoelastic fluids are the same as in potential flow of an inviscid fluid but the moment M in a linear viscoelastic fluid is given by where MT is the inviscid moment and I(t) is the circulation, and in a second-order fluid. When r(t) is slowly varying, the two formulae for M coincide. For steady flow, they reduce to which is also the expression for M in both steady and unsteady potential flow of a viscous fluid. Moreover, when there is no stream, this moment reduces to the actual moment M = liif on a rotating rod. Potential flows of models of a viscoelastic fluid like Maxwell’s are studied. These models do not admit potential flows unless the curl of the divergence of the extra stress vanishes. This leads to an over-determined system of equations for the components of the stress. Special potential flow solutions like uniform flow and simple extension satisfy these extra conditions automatically but other special solutions like the potential vortex can satisfy the equations for some models and not for others. © 1994, Cambridge University Press

Description: The final effort of the CLIMAP project was a study of the last interglaciation, a time of minimum ice volume some 122,000 yr ago coincident with the Substage 5e oxygen isotopic minimum. Based on detailed oxygen isotope analyses and biotic census counts in 52 cores across the world ocean, last interglacial sea-surface temperatures (SST) were compared with those today. There are small SST departures in the mid-latitude North Atlantic (warmer) and the Gulf of Mexico (cooler). The eastern boundary currents of the South Atlantic and Pacific oceans are marked by large SST anomalies in individual cores, but their interpretations are precluded by no-analog problems and by discordancies among estimates from different biotic groups. In general, the last interglacial ocean was not significantly different from the modern ocean. The relative sequencing of ice decay versus oceanic warming on the Stage 6/5 oxygen isotopic transition and of ice growth versus oceanic cooling on the Stage 5e/5d transition was also studied. In most of the Southern Hemisphere, the oceanic response marked by the biotic census counts preceded (led) the global ice-volume response marked by the oxygen-isotope signal by several thousand years. The reverse pattern is evident in the North Atlantic Ocean and the Gulf of Mexico, where the oceanic response lagged that of global ice volume by several thousand years. As a result, the very warm temperatures associated with the last interglaciation were regionally diachronous by several thousand years. These regional lead-lag relationships agree with those observed on other transitions and in long-term phase relationships; they cannot be explained simply as artifacts of bioturbational translations of the original signals.

Description: Euromech Colloquium 173 was held at Delphi from 13–16 September 1983. Thirty-six participants from eleven countries were present. Papers were presented on: (1) various approaches to calculating and computing air flow in rough terrain in the presence of changes in surface roughness, elevation and temperatures, including methods for interpolating, subject to certain physical constraints, the wind field from measurements at various fixed stations; (2) measurement and satellite photography of air flow in rough terrain near isolated mountains, near coastlines, over mountains, and over mountains near coastlines; (3) the applications of these studies to air-pollution dispersion and the exploitation of wind energy in rough terrain. The discussions led to agreement about how best to use and relate the various techniques for calculating air flows, the role of new techniques in remote sensing for improving understanding of flow in rough terrain, the factors determining air-pollution concentration that need particular study, and the special kinds of information about turbulence needed for estimating wind energy in rough terrain. © 1984, Cambridge University Press. All rights reserved.