Mixing and dissipation in particle-driven gravity currents

Abstract

Results are presented from a high-resolution computational study of particle-driven gravity currents in a plane channel. The investigation was conducted in order to obtain better insight into the energy budget and the mixing behaviour of such flows. Twoand three-dimensional simulations are discussed, and the effects of different factors influencing the flow are examined in detail. Among these are the aspect ratio of the initial suspension reservoir, the settling speed of the particles, and the initial level of turbulence in the suspension. While most of the study is concerned with the lockexchange configuration, where the initial height of the suspension layer is equal to the height of the channel, part of the analysis is also done for a deeply submerged case. Here, the suspension layer is only one-tenth of the full channel height. Concerning the energy budget, a careful analysis is undertaken of dissipative losses in the flow. Dissipative losses arising from the macroscopic fluid motion are distinguished from those due to the microscopic flow around each sedimenting particle. It is found that over a large range of settling velocities and suspension reservoir aspect ratios, sedimentation accounts for roughly half of all dissipative losses. The analysis of the mixing behaviour of the flow concentrates on the mixing between interstitial and ambient fluid, which are taken to be of identical density. The former is assumed to carry a passive contaminant, whose dispersion with time is analysed qualitatively and quantitatively by means of Lagrangian markers. The simulations show the mixing between interstitial and ambient fluid to be more intense for larger values of the particle settling velocity. Finally, the question is addressed of whether or not initial turbulence in the suspension may exert a significant effect on the flow evolution. To this end, results from three simulations with widely different levels of initial kinetic energy are compared. While the initial turbulence level strongly affects the mixing within the current, it has only a small influence on the front velocity and the overall sedimentation rate.

Lock-exchange flows in sloping channels

“…They are related by the Schmidt number 13) which represents the ratio of kinematic viscosity and molecular diffusivity. Test calculations showed the effect of variations in Sc to be very small, so that we took Sc = 1 for all cases; see also Necker et al (2005). A detailed discussion of the above governing equations is given in Birman et al (2005) and will not be repeated here.…”

“…When the driving force is provided by particle loading rather than compositional variations, a host of new phenomena arise, as discussed in the investigations by Bonnecaze, Huppert & Lister (1993), Bonnecaze & Lister (1999) and Necker et al (2002Necker et al ( , 2005. Such particle-driven flows frequently occur over sloping bottoms, e.g.…”

High-fidelity simulations of the lobe-and-cleft structures and the deposition map in particle-driven gravity currents

“…There has been an intensive effort to study those structures, with many experimental investigations, 3,7,[12][13][14][15] theoretical approaches, 16,17 and more recently with numerical investigations based on Direct Numerical Simulations (DNS). [18][19][20][21][22][23][24] Experiments 3,7,12 investigating a) s.laizet@imperial.ac.uk lobe-and-cleft patterns have typically imaged the gravity current from below, allowing the growth, merging, and bifurcation of the structures to be tracked. This analysis identified the origin of the instability as the unstable stratification generated as ambient fluid is overrun by the current head, subject to a frictional surface.…”

Suspension-Driven gravity surges on horizontal surfaces: Effect of the initial shape

“…Implicit in Eq. (11) , is the assumption that the time scale of the particles is much smaller than the time flow timescales and thus the particle faithfully follows the local fluid velocity except for the vertical drift due to gravitational settling [1,23] . The settling velocity v s corresponds to the balance between the Stokes drag force, acting on a single spherical particle assuming a small particle Reynolds number, and the buoyancy force.…”

“…This is common practice in these types of flows [23] . Furthermore, Bonometti & Balachandar [6] and Necker et al [23] demonstrate that the effect of the Schmidt number on the flow in the range of Re numbers considered here is not important as long as it is of order 1. We therefore do not expect our results to be sensitive to the precise value of Schmidt number.…”