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Particle-driven gravity currents

Particle-driven gravity currents. Herbert Huppert Andrew Hogg. Examples of particle-driven gravity currents. Pyroclastic flow. Water injection dredging. Turbidity current. Outline of lecture. Particle-driven gravity currents

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Particle-driven gravity currents

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  1. Particle-driven gravity currents Herbert Huppert Andrew Hogg

  2. Examples of particle-driven gravity currents Pyroclastic flow Water injection dredging Turbidity current

  3. Outline of lecture • Particle-driven gravity currents • Particle-driven gravity currents in the presence of a uniform flow • Reversing buoyancy • Bidisperse gravity currents

  4. Laboratory experiment

  5. Experimental results • Experiments conducted in long flume with silicon carbide particles suspended in water • Results from 16 experiments.(Data from Bonnecazeet al. 1993.) • Vary particle size, initial concentration and initial volume of release. xN(t)

  6. Gravity currents Evolution equations for height (h), velocity (u) and volume fraction of particles (). • The flows are shallow (h<<xN) and so the pressure is hydrostatic • Conservation of fluid mass • The motion is driven by pressure gradients (drag negligible) u(x,t) h(x,t) xN(t)

  7. Governing equations • Particle transport: Particles are suspended in the fluid, transported horizontally and settle to the underlying boundary. • It is assumed that the particle volume fraction is approximately vertically uniform and settle out at the base of the flowing layer (Hazen’s Law) and that the flows do not erode deposited particle from base • Front condition: • Global volume: Particles are lost from the flow through settling

  8. Box model • Initial conditions: L=0, f=f0at t=0 • The maximum distance runout by the current is when f(t)=0: the runout length (L) Shallow layer model Box model h(t) L(t) How to find the runout length:

  9. Prediction of time evolution • The volume fraction of particles in suspension • The rate at which the current expands

  10. Deposit • The deposit is formed by particles progressively settling out of suspension. • The shape of the deposit can be determined from the box model:h(x): mass per unit area

  11. h X Y L=X+Y Particle-driven currents in a uniform flow U Conservation of mass: Evolution of particles: Downstream: Upstream: Solve in terms of the length of the current (L=X+Y) and the position of the centroid(Z=X-Y) as functions of time.

  12. Length and centroid • The runout length and time scales are given by L/L Length Centroid t/t Dimensionless strength of flow (L) z/L t/L

  13. 0.6 0.5 0.4 0.3 0.2 0.1 0 2 . 5 h 2 I n c r e a s i n g 1 . 5 L 1 0 . 5 Flow 0 - - 1 . 5 - 1 0 . 5 0 0 . 5 Distribution of deposit • The asymmetry of the deposit depends on the relative strength of the flow, measured by magnitude of L • The particle driven flow is able to propagate upstream for a distance, d+, which is given by d L + m  m 23 m m 37 m m 53 d+/ L = f () Function fully determined by box-model Theory 0 0.5 1 1.5 L

  14. Reversing buoyancy • Particle are suspended in a fluid that is less dense than the surroundings – but the presence of the particles make the overall density in excess of the surroundings.r= ri+(rs-ri)f0 and r>ra • Particle sedimentation progressively reduces the density of the gravity current. • Eventually the gravity current is less dense than the surroundings and lofts.

  15. Reversing buoyancy runout • The lift off distance Lo relative to the runout length Lis then just a function of g • Experiments were conducted using particles suspended in water and alcohol moving through water. These gravity currents loft after sufficient particles have sedimented from them.

  16. Bidisperse currents • What happens when the suspension is composed of two different species of particles with different settling velocities? • The velocity of the current is not linearly proportional to the volume fractions and so the effects are not additive. • Separate evolution of the volume fraction of each species • The total volume fraction F=f1+f2 determines the excess density and drives the motion. • How well is the runout represented by treating the suspension as effectively monodisperse with settling velocity given by the initial average (ws1f+ws2(1-f)) and with the combined initial volume fraction (F0)? At t=0 f1=fF0 f2=(1-f)F0

  17. Bidisperse currents: runout lengths The runoutlength for ws2/ws1=1/4:L=L when f1=f2=0. Relative to a current with average settling velocity Relative to a current of only coarse particles Enhancement of Runout length L /Lc Enhancement of Runout length L /La 100% coarse 100% fine 100% fine 100% coarse Fraction of coarse particles Fraction of coarse particles

  18. Bidisperse currents: Temporal evolution • Length of current L(t) for ws2/ws1=1/4 L(t)/La Final runout 100% coarse 100% fine Fraction of coarse particles

  19. Bidisperse currents: deposit h(t) The depth of the deposit and its composition for ws2/ws1=1/7 L(t) f(t) 100% fine ws Surface of deposit Vertical and longitudinal grading of deposit Depth within deposit z/[F0A/La] 100% coarse Distance from release x/La

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