Direct Numerical Simulation of Particle Settling in Model Estuaries

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Direct Numerical Simulationof Particle Settling
in Model Estuaries

• R. Henniger(1), L. Kleiser(1), E. Meiburg(2)
• (1) Institute of Fluid Dynamics, ETH Zurich
• (2) Department of Mechanical Engineering, UCSB

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Outline

• Introduction / motivation
• Computational setup
• flow configuration
• governing equations and physical parameters
• simulation code
• Results
• freshwater / saltwater mixing
• particle settling
• Conclusions and outlook

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Introduction

• Estuary mouth
• light fresh-water
• heavy salt-water
• Suspended particles
• e.g. sediment or pollutants
• transport out to the ocean
• particles settle and deposit
• Other influences
• temperature profile
• Coriolis effect, tide,
• Focus of the present study basic investigation
  of
• freshwater / saltwater mixing
• particle transport, particle settling and
  particle deposition

Magdalena River (Colombia)
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Freshwater / saltwater mixing

• Typically hypopycnal inflow
• (Super-)critical?
• Convective mixing, enhanced by
• turbulence in river
• Kelvin-Helmholtz or Holmboe waves

salty
salt wedge
freshwater
salty
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Particle load

• hypopycnal
• hyperpycnal

freshwater particles
salty
freshwater particles
salty
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Particle transport

• Surface plume
• (Enhanced) particle settling
• flocculation?
• turbulence enhanced settling?
• Bottom propagating turbidity
• current

(1)
(2)
(3)
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Example Yellow River
(from http//www.grid.unep.ch/activities/global_ch
ange/atlas/images/YellowRiver.jpg)
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Motivation

• Particle transport mechanisms
• surface freshwater current
• particle settling
• undersea gravity currents
• Consequences
• spillage of ocean bed /
• continental shelf
• environmental pollution
• disruption of infrastructure
• State of research
• many quantitative field observations
• few laboratory experiments
• little evidence about mechanisms
• Focus of the present study basic investigation
  of
• freshwater / saltwater mixing
• particle transport, particle settling and
  particle deposition

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Model estuary configuration
salt sponge
convective outflow
inflow
symmetry planes
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Governing equations, non-dimensional

• Incompressible Navier-Stokes and concentration
  transport equations (in Boussinesq regime)
• Reynolds number
• Schmidt number
• Richardson number
• Particle settling velocity

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Physical parameters
reality laboratory simulation
Re 105-107 103-104 1500
Scsal 500-3000 500-3000 1
Scpart gt Scsal gt Scsal 2
Risal 0.5-1 0.5-1 0.5
Ripart lt 0.05 lt 0.05 0.05
-us/U lt 10-2 lt 10-2 0.01-0.02
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Newly developed simulation code (summary)

• Incompressible flows active scalars
• Discretization
• compact finite differences in space
• explicit or semi-implicit time integration
• Massively parallel platform
• 3D domain decomposition (gt95 parallel
  efficiency)
• sustained 16 peak performance on Cray XT
• scalability tested to up to 8000 cores and 17
  billion grid points
• Validation
• convergence orders in time and space
• convergence properties of iterative solvers
• temporal and spatial growth of eigenmodes
• channel flow
• shear layer flows with passive scalar
• transitional and turbulent channel flow (vs. P.
  Schlatter)
• particle-driven gravity current (vs. F. Necker)
• parallel scaling properties

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Resultsfreshwater / saltwater mixing
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Freshwater current
salt sponge
internal waves
Kelvin-Helmholtz waves
csal 0.75
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Group velocity of internal waves
(measured with potential energy at y 0)
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Streamlines on water surface
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Sub-/supercritical flow

• kinetic vs. buoyant forces
• measured with bulk Richardson number

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Interface stability

• shear stress vs. density difference
• measured with gradient Richardson number

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Resultsparticle settling
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Particle settling

• Three different settling velocities us/U
  -0.02, -0.015, -0.01
• Qualitative agreement with laboratory
  experiments?
• Maxworthy (JFM, 1999)
• Parsons et al. (Sedimentology, 2001)
• McCool Parsons (Cont. Shelf Res., 2004)
• Open questions
• extent of particle plume?
• particle settling modes (transient, steady
  state)?
• effective settling velocity?
• deposit profile?

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Particle plume
us/U -0.02, cpart 0.1
x1
x1
x2
t 300
t 400
x1
x1
x2
t 450
t 600
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Convective particle settling
us/U -0.02
x1 26
x2 5
t 300
x3
x1
x2
t 350
x3
x1
x2
t 400
x3
x1
x2
t 600
x3
x1
x2
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Particle mass
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Potential energy of particles
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Effective particle settling velocity
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Particle Deposit
us/U -0.020, t 710
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Particle Deposit
us/U -0.015, t 920
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Particle Deposit
us/U -0.010, t 1040
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Conclusions

• Definition of simulation setup
• parameters
• inflow
• boundary conditions
• sponge zones, etc.
• Results Basic effects compare well with
  laboratory experiments
• freshwater-brine mixing
• finger convection
• enhanced convective particle settling
• Results obtained at moderate Re and Sc,
  accessible to DNS

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Outlook

• Further increase of Re and Sc with LES in the
  future
• Implemented LES models
• ADM-RT model (filter model)
• (HPF) Smagorinsky
• (upwinding)
• Validation of LES to be completed
• Further option more complex domains e.g. by
• orthogonal curvilinear grids
• immersed boundary method
• (immersed interface method)

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Appendix