Largeeddy simulation of the formation and evolution of sand ripples

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Large-eddy simulation of the formation and
evolution of sand ripples

• Oliver B. Fringer
• Ph.D. Student Yi-Ju Chou
• Environmental Fluid Mechanics Laboratory
• Department of Civil and Environmental Engineering
• Stanford University
• 30 July 2009
• Support ONR Coastal Geosciences Program

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Motivation and background
Sand Ripples Wavelength O(0.1 m) O(1
m) Shallow, mild flow

• Ripples have a significant impact on
• Sediment transport
• Hydraulic roughness
• Acoustic scatteringetc

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Previous work on modeling and simulation of
ripple dynamics

• Linear stability analysis (e.g. Fredsoe, 1974
  Richards, 1980 Colombini, 2004)
• Numerical simulation over static bed forms (e.g.
  Chang and Scotti, 2003 Zedler and Street, 2006)
  
• No models exist that can simulate formation,
  evolution and destruction of sand ripples under
  turbulent flow induced by waves and/or currents.

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Development of model

• Large-eddy simulation code
• Dynamic mesh
• Suspended sediment model
• Bed elevation model

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Hydrodynamics
Large-eddy simulation code of Zang et al. (1993,
1994), Cui Street (2001, 2004)
Density stratification
Subfilter-scale flux

• Code features
• Finite-volume, curvilinear grid
• Momentum QUICK, Scalars SHARP
• Second-order accurate in time and space
• Written in parallel from scratch (Cui and
  Street, 2001,2004)
• Quadratic drag law at bed with roughness grain
  size (Zedler and Street, 2006)

u1,u2
U1
U2
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Sediment transport
Eulerian approach which assumes small volume
fraction (Clt0.01) (Zedler Street, 2001, 2006
Chou Fringer, 2009)
Large-eddy simulation for suspended sediment
Dynamic mixed model (DMM) for LES sub-grid
scale (SGS) flux dynamic Smagorinsky flux
self-similarity model
Compared with the Smagorinsky model, this
requires less modeling due to the
reconstruction of the SGS flux from the resolved
field.
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Bottom boundary condition for suspended sediment
in LES
Traditional approach LES (or RANS) first then
apply bottom BC
Bottom boundary conditions
Need
Since kT can be small at the bed, the
imposedgradient can be quite large, particularly
in LES whenkT?0 near the wall. Can infer
kTnT/PrT with a parabolic eddy-viscosity
(Zedler and Street, 2001,2004 van Rijn 1986)
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Improved bottom boundary condition
New approach (Chou and Fringer, 2008) apply BC
first, then apply LES
Bottom boundary conditions
Need
Requires no assumptions about underlying
turbulence model to determine kT since the
Neumann condition is no longer required if the BC
is applied beforeimplementing the LES
parameterization.
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Dynamic mesh method

• Finite volume dynamic mesh method on generalized
  moving curvilinear meshes (Chou and Fringer,
  2009)
• -- Consistent with continuity (CWC) which
  conserves sediment mass on a moving grid.
• -- Multi-dimensional geometric conservation
  law
• -- Second order accurate in time
  (Adams-Bashforth method)

CWC
Non-CWC
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Bed elevation model
Mass-balance for the evoluation of the bed
h(x,y,t) (e.g. Gessler et al., 1999)
Gravitationally-inducedavalanche flow
Deposition Erosion
Bed-load transport from Meyer-Peter Mueller,
1948 Ignore this term in favor of animplicit
model for the bed load that relies on
sediment-induced stratification
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Sediment pick-up
flow
Instantaneous bed shear stress
Flat-bed critical non-dim. shear stress (Soulsby,
1997)
Effect of bed slope (Whitehouse and Hardisty,
1988)
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Critical elements for successful simulation of
ripples

• Consistent discretization of transport on a
  moving grid ? Prevents large near-bed sediment
  concentrations
• Omission of bed-load transport term ? Causes
  bedforms that are too big and form too quickly
• Inclusion of avalanche flow term ? Adds
  diffusion or smoothing and correct shape of
  vortex ripples
• Modification of pickup function due to sloping
  bed
• Inclusion of sediment-induced stratification ?
  Restricts portion of suspension to act as
  effective bed load
• Resolution of near-bed coherent structures
  ?Enables direct simulation of bedform
  initiation

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Near-bed coherent structures and their role in
bedform initiation
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Simulation domain and parameters
L 0.6 m W 0.12 m H 0.1 m U 0.45 ms-1
ReH 50,000 Periodic BCs in horizontal
Resolution 320 x 64 x 64 d0 0.27
mm Flow-through timescale (Tf) 1.43 s
Sediment module starts after turbulence is fully
developed.
Flow
Domain configuration with 4 x actual grid size
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Characteristics of the simulated turbulent open
channel flow
Spatio-temporally averaged streamwise velocity
profile
1D velocity spectrum
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Turbulence-induced bedform initiation

• Turbulence structures in the turbulent boundary
  layer
• 1. Vortex structure counter rotating pairs
• 2. Flow convergence and flow divergence
• 3. Sweeps and ejections

w (u3)
(, )
(-, )
Ejection
u (u1)
(-, -)
(, -)
Sweep
Homes et al. 1996
Longitudinal ridges form in convergence zones
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Bed defect model (Best, 1992)
Longitudinal perturbationresults in lateral
vorticity that leads to formation of
hairpinvortex.
Appearance of streamwise ridges
Formation of bed defects
Formation of ripples
J. Best 1992. On the entrainment of sediment and
initiation of bed defects insights from recent
developments within turbulent boundary layer
research. Sedimentology, 29, 797-811.
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Horizontal velocity structures just above the bed
(unidirectional currents)
X1 (m)
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Longitudinal ridges are formed by multiple
sweepsand ejections. Longitudinal perturbations
caused by low-speed streaks and horseshoe
vortices form streamwise ridges. Longitudinal
perturbationslocalize sweeps and burstsand form
bed defects.
Streamwise velocity
X1 (m)
Bed elevation
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Evolution of the bed elevation
Streamwise ridges
Appearance of bed defects
Appearance of ripple marks
Formation of ripples
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U distribution just above the channel bed
Streamwise velocity dominated by near-bed
turbulent structures
Streamwise velocity dominated by the bed forms
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Sediment transport at the channel bed
Sediment transport dominated by near-bed
turbulence structures
Sediment transport dominated by the bottom
topography
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Resolution study (oscillatory flow)
Less vertical resolution
Less horizontalvertical
Less horizontal resolution
Base case
Higher resolution
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Simulations of lab-generated ripples

• Ripple dynamics
• Comparison to laboratory experiment

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Simulation Setup
L 0.6 m W 0.24 m H 0.15 m Uw 0.42
ms-1 Tw 8 s Total time 35 Tf 5 min Uc 0.0
ms-1, 0.08 ms-1, 0.30 ms-1 ReH 40,000-50,000
Periodic BCs in horizontal Resolution 320 x
128 x 96
Lacy. et al., 2007
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Evolution of bed elevation contours in waves and
wave-current flows
D0 0.15 m
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Evolution of bed elevation contours in waves and
wave-current flows
D0 0.15 m
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Bedforms in waves and wave-current flows at t
24T
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C 1 x 10-5 (volume fraction)
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C 1 x 10-5 (volume fraction)
Bed defects, t 3T
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Initial ripple marks, t 7T
C 1 x 10-5 (volume fraction)
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Rolling grain ripples, t 15T
C 1 x 10-5 (volume fraction)
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Vortex ripples, t 34T
C 1 x 10-5 (volume fraction)
C 5 x 10-4 (volume fraction)
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Turbulence structures
t 7T
t 28T
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Comparison to laboratory results
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Waves only
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Waves only
147 sec
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Waves only
168 sec
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Waves only
210 sec
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Waves weak currents
255 sec
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Waves strong currents
252 sec
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Time history of wave-ripple wavelength derived by
FFT
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Summary

• The first 3D CFD-model which simulates the
  formation and evolution of sand ripples
• Model components
• Consistent discretization of transport on a
  moving grid
• Omission of bed-load transport term
• Inclusion of avalanche flow term
• Modification of pickup function due to sloping
  bed
• Inclusion of sediment-induced stratification
• Resolution of near-bed coherent structures
• Simulated bedform evolution
• -- bed defects gt ripple marks gt rolling
  grain ripples gt vortex ripples
• Laboratory comparison shows good agreement for
  ripples under combined wave-current flows
• Laboratory comparison shows underprediction of
  the wavelength during initial stages of ripple
  evolution in the presence of weak currents.

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Acknowledgements

• Jessica Lacy and David Rubin, USGS Santa Cruz
• Financial support ONR Coastal Geosciences
  Program (Program managers Dr. Tom Drake and Dr.
  Nathaniel Plant)
• Computation time Army Research Laboratory (ARL)
  and Maui High Performance Computing Center
  (MHPCC)

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Sediment Transport Modeling
Single-phase Eulerian method (Zedler Street,
2001, 2006 Chou Fringer, 2009)
Single-phase Eulerian method (Zedler Street,
2001, 2006 Chou Fringer, 2009)
Eulerian-Eulerian method (Hsu et al., 2003 Riber
et al., 2009, Chou Fringer, in prep, 2009)
Eulerian-Eulerian method (Hsu et al., 2003 Riber
et al., 2009 Chou Fringer, in prep, 2009 )
Eulerian-Lagrangian method
Eulerian-Lagrangian method
Simple particle tracking (Wang Maxey, 1993
Elghobashi Truesdell, 1992Fevrier et al., 2005
)
Simple particle tracking (Wang Maxey, 1993
Elghobashi Truesdell, 1992Fevrier et al., 2005
)
Discrete particle method (Drake Calantoni,
2001 Schmeeckle Nelson, 2003)
Discrete particle method (Drake Calantoni,
2001 Schmeeckle Nelson, 2003)
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Evolution of the bed elevation
Streamwise ridges
Appearance of bed defects
Appearance of ripple marks
Formation of ripples