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
05/05/2009 R. Henniger, L. Kleiser, E. Meiburg
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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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
Introduction
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Magdalena River (Colombia)
05/05/2009 R. Henniger, L. Kleiser, E. Meiburg
Freshwater / saltwater mixing
Typically hypopycnal inflow
(Super-)critical?
Convective mixing, enhanced by turbulence in river Kelvin-Helmholtz or Holmboe waves
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salty
freshwater
salt wedge
salty
05/05/2009 R. Henniger, L. Kleiser, E. Meiburg
Particle load
hypopycnal:
hyperpycnal:
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salty
salty
freshwater + particles
freshwater + particles
05/05/2009 R. Henniger, L. Kleiser, E. Meiburg
Particle transport
(1) Surface plume
(2) (Enhanced) particle settling flocculation? turbulence enhanced settling?
(3) Bottom propagating turbidity
current
(1)
(2)
(3)
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Model estuary configuration
symmetry planes
inflow
convective outflow
salt sponge
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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:
266664H100G10H20G200H3G3D1D2D30377775¢266664u1u2u3p377775=266664b1b2b30377775()·HGD0̧¢·up̧=·f0̧
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Physical parameters
reality laboratory simulation
Re 105-107 103-104 1500
Scsal500-3000 500-3000 1
Scpart > Scsal > Scsal2
Risal0.5-1 0.5-1 0.5
Ripart< 0.05 < 0.05 0.05
-us/U < 10-2 < 10-2 0.01-0.02 particle plume extent
extent
turbulence
turbulence
“sharpness” of interfaces
interfaces
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particle load
loading
sub-/supercritical flow
inertial forces
05/05/2009 R. Henniger, L. Kleiser, E. Meiburg
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 (>95% 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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Results:
freshwater / saltwater mixing
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Freshwater currentsalt sponge
internal waves
Kelvin-Helmholtz waves
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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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Results:
particle 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
t = 300 t = 400
t = 450 t = 600
us/U = -0.02, cpart = 0.1
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x1 x1
x1 x1
x2
x2
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Convective particle settling
t = 300
t = 350
t = 400
t = 600
us/U = -0.02
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x1 = 26x2 = 5
x1
x1
x1
x1
x2
x2
x2
x2
x3
x3
x3
x3
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Particle mass
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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
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