ALBERT

Description: A computational study is performed of the transport of a particulate suspension through a corrugated tube using a discrete-element method (DEM). The tube is axisymmetric with a radius that varies sinusoidally along the tube length, which, in the presence of a mean suspension flow, leads to periodic inward and outward acceleration of the advected particles. The oscillations in radial acceleration and straining rate lead to a net radial drift, with mean acceleration measuring about an order of magnitude smaller than the instantaneous radial acceleration, which over time focuses small particles within the tube. The foundations of particle focusing in this flow are examined analytically using lubrication theory, together with a low-Stokes-number approximation for the particle drift. This lubrication-theory solution provides the basic scaling for how the particle drift will vary with wave amplitude and wavelength. Computations are then performed using a finite-volume method for a fluid flow in the tube at higher Reynolds numbers over a range of amplitudes, wavelengths and Reynolds numbers, examining the effect of each of these variables on the averaged radial fluid acceleration. A DEM is used to simulate particle behaviour at finite Stokes numbers, and the results are compared to an asymptotic approximation valid for low Stokes numbers. At low tube Reynolds number (e.g. Re = 10), the drift velocity induced by the tube corrugations focuses the particles onto the tube centreline, in accordance with the low-Stokes-number approximation based on the axial-averaged fluid radial acceleration. At higher tube Reynolds numbers (e.g. Re = 100), the correlation between the particle radial oscillation and the fluid acceleration field leads the outermost particles to drift into a ring at a finite radius from the tube centre, with little net motion of the particles in the innermost part of the tube. At larger Stokes numbers, particles can be dispersed to the outer regions of the tube due to particle outward dispersion from the large instantaneous radial acceleration. The effects of eddy formation within the corrugation crests on particle focusing are also examined. © 2010 Cambridge University Press.

Description: HR8799 is a young (20–160 Myr) A-dwarf main sequence star with a debris disc detected by IRAS (InfraRed Astronomical Satellite). In 2008, it was one of two stars around which exoplanets were directly imaged for the first time. The presence of three Jupiter-mass planets around HR8799 provoked much interest in modelling the dynamical stability of the system. Initial simulations indicated that the observed planetary architecture was unstable on timescales much shorter than the lifetime of the star (~105 yr). Subsequent models suggested that the system could be stable if the planets were locked in a 1:2:4 mutual mean motion resonance (MMR). In this work, we have examined the influence of varying orbital eccentricity and the semi-major axis on the stability of the three-planet system, through dynamical simulations using the MERCURY n-body integrator. We find that, in agreement with previous work on this system, the 1:2:4 MMR is the most stable planetary configuration, and that the system stability is dominated by the interaction between the inner pair of planets. In contrast to previous results, we find that with small eccentricities, the three-planet system can be stable for timescales comparable to the system lifetime and, potentially, much longer.