Particle settling from constant-flux surface gravity currents and a near-stationary particle-bearing layer

2021 ◽  
Vol 6 (6) ◽  
Author(s):  
Bruce R. Sutherland ◽  
Brianna Mueller ◽  
Brendan Sjerve ◽  
David Deepwell
Keyword(s):  
Gravity Currents ◽  
Surface Gravity ◽  
Particle Settling ◽  
Flux Surface ◽  
Constant Flux ◽  
Bearing Layer

The effects of capillary forces on the axisymmetric propagation of two-phase, constant-flux gravity currents in porous media

2013 ◽  
Vol 25 (3) ◽  
pp. 036602 ◽  
Author(s):  
Madeleine J. Golding ◽  
Herbert E. Huppert ◽  
Jerome A. Neufeld
Keyword(s):  
Porous Media ◽  
Capillary Forces ◽  
Gravity Currents ◽  
Two Phase ◽  
Constant Flux ◽  
Phase Constant

Compressible particle-driven gravity currents

2001 ◽  
Vol 445 ◽  
pp. 305-325 ◽  
Author(s):  
MARY-LOUISE E. TIMMERMANS ◽  
JOHN R. LISTER ◽  
HERBERT E. HUPPERT
Keyword(s):  
Large Scale ◽  
Numerical Solutions ◽  
Volcanic Eruptions ◽  
Gravity Currents ◽  
Scale Height ◽  
Pyroclastic Flows ◽  
Water Model ◽  
Model Approximation ◽  
Particle Settling ◽  
Density Scale

Large-scale particle-driven gravity currents occur in the atmosphere, often in the form of pyroclastic flows that result from explosive volcanic eruptions. The behaviour of these gravity currents is analysed here and it is shown that compressibility can be important in flow of such particle-laden gases because the presence of particles greatly reduces the density scale height, so that variations in density due to compressibility are significant over the thickness of the flow. A shallow-water model of the flow is developed, which incorporates the contribution of particles to the density and thermodynamics of the flow. Analytical similarity solutions and numerical solutions of the model equations are derived. The gas–particle mixture decompresses upon gravitational collapse and such flows have faster propagation speeds than incompressible currents of the same dimensions. Once a compressible current has spread sufficiently that its thickness is less than the density scale height it can be treated as incompressible. A simple ‘box-model’ approximation is developed to determine the effects of particle settling. The major effect is that a small amount of particle settling increases the density scale height of the particle-laden mixture and leads to a more rapid decompression of the current.

The effect of confining impermeable boundaries on gravity currents in a porous medium

2010 ◽  
Vol 649 ◽  
pp. 1-17 ◽  
Author(s):  
MADELEINE J. GOLDING ◽  
HERBERT E. HUPPERT
Keyword(s):  
Free Surface ◽  
Gravity Current ◽  
Mass Conservation ◽  
Propagation Rate ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Constant Flux ◽  
Channel Shape ◽  
Dimensional Gravity ◽  
Uniform Cross Section

The effect of confining boundaries on gravity currents in porous media is investigated theoretically and experimentally. Similarity solutions are derived for currents when the volume increases as tα in horizontal channels of uniform cross-section with boundary height b satisfying b ~ a|y/a|n, where y is the cross-channel coordinate and a is a length scale of the channel width. Experiments were carried out in V-shaped and semicircular channels for the case of gravity currents with constant volume (α=0) and constant flux (α=1). These showed generally good agreement with the theory.Typically, we find that the propagation of the current is well described by L ~ tc for some scalar c. We study the dependence of c on the time exponent of the volume of fluid in the current, α, and the geometry of the channel, parameterized by n. For all channel shapes, there exists a critical value of α, αc = 1/2, above which increasing n causes an increase in c and below which increasing n causes a decrease in c, where increasing n corresponds to opening up the channel boundary to the horizontal. The current height increases or decreases with respect to time depending on whether α is greater or less than αc. It is this fact, along with global mass conservation, which explains why varying the channel shape n affects the propagation rate c in different ways depending on α.We also consider channels inclined at an angle θ to the horizontal. When the slope of the channel is much greater than the slope of the free surface of the current, the component of gravity parallel to the slope dominates, causing the current to move with a constant velocity, Vf say, regardless of channel shape n and flux parameter α, in agreement with results for a two-dimensional gravity current obtained by Huppert & Woods (1995) and some initially axisymmetric gravity currents presented by Vella & Huppert (2006). If the effect of the component of gravity perpendicular to the channel may not be neglected, i.e. if the slopes of the channel and free surface of the current are comparable, we find that, in a frame moving with speed Vf, the form of the governing equation for the height of a current in an equivalent horizontal channel is recovered. We calculate that the height of a constant flux gravity current down an inclined channel will tend to a fixed depth, which is determined by the channel shape, n, and the physical properties of the fluid and rock. Experimental and numerical results for inclined V-shaped channels agree very well with this theory.

The dynamics of sedimenting surface gravity currents

1999 ◽  
Vol 392 ◽  
pp. 27-44 ◽  
Author(s):  
T. MAXWORTHY
Keyword(s):  
Interstitial Fluid ◽  
Lower Layer ◽  
Gravity Current ◽  
Gravity Currents ◽  
Surface Gravity ◽  
Physical Situation ◽  
Total Density ◽  
Heavy Particles ◽  
Two Fluids ◽  
Series Of Experiments

We have performed a series of experiments on the dynamics of sedimenting, surface gravity currents. The physical situation concerns a current, with total density ρC, evolving at the surface of a fluid of greater density, ρA. In turn ρC is made up of interstitial fluid of density ρI and heavy particles with a concentration by weight c and a density ρP. Only the case of the release of a constant volume of particles and interstitial fluid has been considered in detail. It has been found that the sedimentation of the particles, plus some of the interstitial fluid, through the interface between the two fluids has a profound effect upon the motion of the current. When the rejected mixture of particles and upper- and lower-layer fluids reaches the bottom of the experimental tank it generates a secondary gravity current which in turn interacts with the primary current to further modify its behaviour. Using simple models we have been able to rationalize the observations and reveal the dynamical balances which appear to be important. A subsidiary experiment and analysis on the flux characteristics of the interface have been performed in order to further clarify the important effects of the particle motion through that region.

Axisymmetric gravity currents of power-law fluids over a rigid horizontal surface

2013 ◽  
Vol 716 ◽  
Author(s):  
Roiy Sayag ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Early Time ◽  
Gravity Currents ◽  
Similarity Solutions ◽  
Constant Volume ◽  
Rheological Parameters ◽  
Late Time ◽  
Constant Flux ◽  
Shear Thinning Fluids ◽  
Power Law Fluids

AbstractWe analyse axisymmetric gravity currents of power-law fluids theoretically and experimentally. We use aqueous suspensions of Xanthan gum in laboratory experiments of constant-volume and constant-flux release to resolve the rheological parameters of the fluid, which we then compare with measurements made using a strain-controlled rheometer. We find that the constant-volume release of highly shear-thinning fluids involves an early-time evolution dominated by inertia, and non-convex free surfaces that make the application of similarity solutions of the late-time viscously dominated evolution inefficient at resolving material properties. In contrast, constant-flux release of the same fluids can be viscously dominated and consistent with the self-similar solution from early in the evolution, which makes it a more useful method for measuring rheological parameters.

Gravity currents of carbon dioxide with residual gas trapping in a two-layered porous medium

2011 ◽  
Vol 673 ◽  
pp. 60-79 ◽  
Author(s):  
TAKASHI GODA ◽  
KOZO SATO
Keyword(s):  
Carbon Dioxide ◽  
Porous Medium ◽  
Layered Medium ◽  
Gravity Currents ◽  
Initial Profile ◽  
Cross Sectional ◽  
Constant Flux ◽  
Gas Trapping ◽  
Dense Fluid ◽  
Residual Gas

In the geological sequestration of carbon dioxide (CO2), residual gas trapping plays an important role in immobilizing CO2. In this study, we investigate the propagation of gravity currents with residual gas trapping in a two-layered porous medium. We first formulate a model for a constant-flux release of a relatively less dense fluid (CO2) from a point source into a porous medium bounded above by a horizontal less-permeable seal. After a constant-flux release ceases, a fraction of the released fluid remains within the porous spaces at the trailing edge because of the capillary forces. This capillary retention is formulated in a model of gravity currents of a finite-volume release in the two-layered medium. In the latter model, the plume shape at the end of the constant-flux release is used as an initial profile. Using these models sequentially, the propagation of both cross-sectional and axisymmetric currents is quantitatively examined.

scholarly journals Axisymmetric particle-driven gravity currents

1995 ◽  
Vol 294 ◽  
pp. 93-121 ◽  
Author(s):  
Roger T. Bonnecaze ◽  
Mark A. Hallworth ◽  
Herbert E. Huppert ◽  
John R. Lister
Keyword(s):  
Transport Equation ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Gravity Current ◽  
Gravity Currents ◽  
Mean Flow ◽  
Constant Flux ◽  
Coupled Equations ◽  
Fixed Volume ◽  
Free Region

Axisymmetric gravity currents that result when a dense suspension intrudes under a lighter ambient fluid are studied theoretically and experimentally. The dynamics of and deposition from currents flowing over a rigid horizontal surface are determined for the release of either a fixed volume or a constant flux of a suspension. The dynamics of the current are assumed to be dominated by inertial and buoyancy forces, while viscous forces are assumed to be negligible. The fluid motion is modelled by the single-layer axisymmetric shallow-water equations, which neglect the effects of the overlying fluid. An advective transport equation models the distribution of particles in the current, and this distribution determines the local buoyancy force in the shallow-water equations. The transport equation is derived on the assumption that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through a viscous sublayer at the bottom of the current. No adjustable parameters are needed to specify the theoretical model. The coupled equations of the model are solved numerically, and it is predicted that after an early stage both constant-volume and constant-flux, particle-driven gravity currents develop an internal bore which separates a supercritical particle-free region upstream from a subcritical particle-rich region downstream near the head of the current. For the fixed-volume release, an earlier bore is also predicted to occur very shortly after the initial collapse of the current. This bore transports suspended particles away from the origin, which results in a maximum in the predicted deposition away from the centre.To test the model several laboratory experiments were performed to determine both the radius of an axisymmetric particle-driven gravity current as a function of time and its deposition pattern for a variety of initial particle concentrations, particle sizes, volumes and flow rates. For the release of a fixed volume and of a constant flux of suspension, the comparisons between the experimental results and the theoretical predictions are fairly good. However, for the current of fixed volume, we did not observe the bore predicted to occur shortly after the collapse of the current or the resulting maximum in deposition downstream of the origin. This is unlike the previous study of Bonnecaze et al. (1993) on two-dimensional currents, in which a strong bore was observed during the slumping phase. The radial extent R of the deposit from a fixed-volume current is accurately predicted by the model, and for currents whose particles settle sufficiently slowly, we find that R = 1.9(g′0V3 / v2s)1/8, where V is the volume of the current, vs is the settling velocity of a particle in the suspension and g’0 is the initial reduced gravity of the suspension.

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