A two-phase model based on unified formulation for continuum mechanics applied to sediment transport in geophysical flows: Application to sedimentation, consolidation and erosion. Study case- the Gironde Estuary (France)
K.D. NguyenLaboratory Saint-Venant for Hydraulics, Université PARIS-EST, 78400 CHATOU , FRANCE
Thanks to my co-workers
Sylvain Guillou(1993-present)- University of Caen
Damien Pham-Van-Bang (2008-present), Lab Saint-Venant, Université Paris-Est
Nataly Barbry (Ph.D., 1996-2000, University of Caen)
Julien Chauchat (Ph.D., 2003-2007, Post-Doc, 2008 in University of Caen)
Duc Hau Nguyen (Ph.D. 2008-2011, University of Caen)
Miguel Uh-Zapata, Post-Doc, 2011-present)
Shafuil Islam (Ph.D., 2012-present, Université Paris-Est)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 2
CONTEXT
Requirement from a lot of applications of sediment transport modelling: Turbidity maximum in estuaries, Dredging operation, silting and scouring process, ....
Scientific Challenges: Physical challenges: Rheology of
sediments, very dense flows, fluid-bed interaction, liquid-like and solid-like of solid fraction, and turbulence ..
Numerical challenges & parallelisation (MPI-CPU, CUDA-GPU)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
FORMATION OF TURBIDITY MAXIMUM IN ESTUARIES
3
PROCESSING OF SEDIMENT TRANSPORT
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 4
Fictive bed concept
Extr
a m
od
el
CONTENTSREMARKS ON THE SIGNLE- and TWO-PHASE MODELS
TWO-PHASE MODELLING
Description
CFD Techniques for Advection and Poisson ‘s Equation
Test-cases:
• Sedimentation-Consolidation-
• Dredged sediment release in open sea water
• Water & Sediment Interfaces: Kelvin-Helmholtz instabilities
Vertical Erosion Test: Unified formulation for continuum mechanics
Gironde Application
DISCUSSION & CONCLUSIONS
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 5
REMARKS ON SINGLE- AND TWO-PHASE MODEL
Single-phase Models“Passive scalar” hypothesisNo fluid-particles
interactions. Fluid-bed interaction by empiric formulas for deposit and erosion fluxes
Fictive-bed conceptionExtra models for
consolidation of solid particles
Two-phase ModelsNo “passive scalar”
hypothesisFluid-particles interaction.
Fluid-bed interaction by the models
No fictive-bed conceptionConsolidation process
included in the models
Unphysical description for very dense flows (?) -Small computing costAcceptable to engineering problems
All interactions consideredCorrect physical descriptionHigh computing cost
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 6
OBJECTIVES of THIS WORK
To develop a two-phase model that is able to simulate the main processes of sediment transport in estuarine and coastal zones, such as suspension, sedimentation, consolidation and erosion. (The computing domain should cover from non-erodible beds
to free water surfaces).
To propose efficient CFD and HPC techniques, which provide the high accuracy and the reduction of computing cost.
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 7
DESCRIPTION FOR TWO-PHASE MODEL
Two-phase (fluid & solid particles) model with unified formulation for continuum mechanics (Navier-Stokes and Navier Equations)
Non hydrostatic pressure
k-ε turbulence model (Kf, f, Ks and Ksf) , K-Ω and LES (in progress)
Adaptative Eulerian mesh in Z and unstructured in (x,y)
Projection method + Finite volume method
2-D Vertical Version completed (parallelised by MPI-CPU, CUDA-GPU)
3-D version development in progress (Summer 2014)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 8
GOVERNING EQUATIONS
- Averaged equations
Effective Stress for solid phase
- Closure Laws
Transfer laws
2
4
1
'-
sffffi
pifisi
kkkikkik
uupp
Hpp
MpM
( ( ) )
'
' '
si fi f
Tf f f f
s D vm L F B
f s
u u
M F F F F F
M M
. 0
k kk k k
Bu B
t
. .
k k kk k k k k k k k k k k
uu u p I g M
t
ss
gel
ssees withpp
max50~
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 9
For
Constitutive laws
Viscous Stresses
Particles Pressure
1. . .
1. . .
1
2
f f ff f fs s
s s sf f ss s
T
k k k
D DB
D DB
D u B u B
ff
fsfs
ffff
2
fss
ffssf
fsss
sdhdhdhdh
1
)/21(
1
)/21(
1
)/2(
1
/1
1
4
9
2
52
)C(
0
B
,
,,
*
21
G )(
10 )(
)( )(
)()()()(
f
f
eG
G
Gp
pppp
f
B
f
sfcollss
fscollsscinssss
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 10
CFD Techniques: Advection terms
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 11
Advection equation
Numerical Scheme: ULSS+LED (Nguyen et al., C&F, 2013)Test-case:The computational domain is [-1; 1] x [-1; 1]x[ -1; 1] The initial condition is an sphere of radius 0.25 withThe velocity field is a solid-body rotation flow field
CFD Techniques: Poisson Equation
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 12
CFD Techniques: Poisson Equation (2/3)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 13
CFD Techniques: Poisson Equation (3/3)Errors & Accuracy
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 14
15
0,0 0,2 0,4 0,60
1
2
3
4
5
6
0 5 10 15 20 25 30 350
1
2
3
4
5
beginning of MRI's records
Vdown
Vup
experiment
simulation
11 profiles (t=2 min)
z (c
m)
solid volume fraction
No consolidation
Vdown
Vup
characteristic lines
t (min)
z (
cm)
Sedimentation of
granular
(cohesionless)
suspension by MRIPham Van Bang et al. 2008
Settling column
tests on cohesive
suspension
(Gironde mud)Villaret et al. 2010
Sedimentation and Consolidation
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 15
Sedimentation and Consolidation of non-cohesive particles
Evolution of the water-sediment interface
Profile de volume fraction of the solid phase
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
(Nguyen et al., Advances in Water Res., 2009, p 1187-1196)
16
Sedimentation and Consolidation of cohesive particles (Kaolin)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
(Chauchat et al., JHR, 2003, 2013.768798 )
17
Comparison of two-phase model results with experiments for initial concentrations αs = 1.2, 2.2 and 5.2%. ime evolution of the mud–clear water interface position (symbols: experiments; lines: model) and (b) solid volume fraction profiles (dashed blue lines :experiments; solid red lines: model)
Dredged Sediment Release in Open Sea
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
(Nguyen et al., Advances in Water Res., 2012)
Fig. 1: Definition sketch: (upper) location of Optical Probes
(OP) for turbidity measurements; (lower) sediment release
(Boutin, 2000).
Isocontour map of the vertical-velocity lag between the fluid and
solid phases (ws-wf= -wsett).
18
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
Comparison between single- and two-phase modelsCase of sediment release in open sea
Two-phaseSingle-phase
19
Dredged sediment release in open sea
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 20
Water-Sediment Interface: Kelvin-Helmholtz Instability (1/3)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
Non-cohesive cohesive
21
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 22
Caulfield and Peltier, JFM 2000
Compartmentalization of the flow into core (dotted rectangle), eyelid (dashed rectangle) and braid regions (dot-dashed rectangle)
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 23
Kelvin-Helmholtz Instability: Solid and Fluid velocity and voticity differences (3/3)
24
A two-phase, soil and liquid, model based on a unified formulation for continuum
mechanics: application to a dredging jet
CETMEF
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 24
25
Overview
Part 1: Experimental investigation (Prof. P. Gondret, FAST)
Part 2: Numerical modelling (NSMP, two-phase model)
2.1 Governing equations
2.2 Specific Treatment for stress analysis of soil
Part 3: Simulation results
3.1 Numerical and physical parameters
3.2 Preliminary results
Conclusions
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 25
26
Part 1 : Experimental investigation
Jet
Fluidization
H=
49
.5cm
Hb
W=20cm
L
D
H
L
S. Badr,
G.
Gauthier,
P. Gondret
THESIS’13
Craters and dunes resulting
from a dynamic equilibrium
• Formation of crater by jet induced
erosion
• Eroded grains create a dense
suspension
• Deposition of particles at preferential
locations
• Granular avalanches produced at the
sandpile’s surface
REGIME 1
« Cratère circulaire »
REGIME 2
« Double cratère »
REGIME 3
« Cratères imbriqués »
Porous flow within the
granular bed
Flow conditions at the
bottom boundary (previous
configuration)
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 26
Geometry of craters (vertical submerged jet) as controlled by the Erosion parameter, Ec (U0 mean velocity at the nozzle outlet; b dimension of the nozzle, L distance to the initial bed, d sediment grain size, s density ratio
between solid and liquid). Depending on Ec value, the jet could be either weakly (a, b) or strongly (c,d) deflected:
redrawn from Aderibigbe & Rajaratnam [16]; figures c) and d) from Giez & Souiler [17].
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
Strongly
deflectedWeakly
deflected
0.2 0.35cE 0.35 2.0cE a)
b)
c)
d)
0( / ) ( 1)cE U b L gd s
27
28
Two fluid pathology
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013
S. Badr,
G.
Gauthier,
P. Gondret
THESIS’13
Part 2 : Numerical modelling (NSMP, two-phase model)
28
Part 2 : Numerical modelling (NSMP, two-phase model)
Non-Newtonian,
(concentration)
Momentum
exchange
between
Phases
(drag,lift, vmf)
Governing equations [Nguyen et al (2009)]
. 0k k k kk k k
Du
Dt t
.k k kk k k k k
D uT g M
Dt
Modeling strategy:
An unified formulation for fluid
and solid phase (liquid-like and
solid-like) based on continuum
mechanics (no coupling)
The FLUID and the SOLID
phase are calculated by using
the FV method in the SAME
computational grid
Extension of the two-fluid
approach into a fluid-soil model Deviation in rheological behavior
between granular flow and quasi-static
sandpile
Newtonian or Non-Newtonian
Viscosity for the granular flow
(Liquid-like)
Elasticity and/or Plasticity (friction’s
law) for the sand heap
(Solid-like)
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 29
Implementation in NSMP
C.J. Greenshields
& H.G. Weller :
Int. J. Numer. Meth.
Engng 2005; Vol. 64,
pp1575-1593
Generalised Hooke’s law
2
1
2
SL
ij s
t
T p I µ
D D
.s s ss s s s s
D ug M
DT
t
2 ( )
1
2
LL
ij s s
t
T p I
U U
iiU D
For small strain
0
t
2 dev dt
dev +
ntSL
ij s
t
s SL
T p I
p I U U
(1 )(1 2 )
2(1 )
E
Eµ G
1 ( ) ( )L SL
ss
L
s s sf f TT T
1t
0
where
dev +
: integration coefficient
SL n
n
kk
k
k
w
w U U
w
( ) ( )s f s
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 30
Smooth transition between Liquid-Like and Solid-Like behavior
f(s)
s
s,up=0.555
s,down=0.37
Dense suspension Loose bed
Solid LikeLiquid-Like
s,cri=0.465
=0.5
d=d-=0.05
[Komatsu et al. (2001)]
Liquid-Like
Tra
ns
itio
n z
on
e
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013
f(αs)=f(αs,sh,shc)
Shc – Critical Shields number
31
Parameters
Grid: 251x101 (dz=2 mm,dx=1-2 mm)
Initial conditions
• Granular bed (s=0.55, h=10cm)
• Quiet water (s=0.0) otherwise
Boundary conditions
• impermeable : left, right of domain
and jet outlet
• Impermeable : top of the domain
• Permeable : bottom of the domain
• Poiseuille profile (jet outlet)
Time step dt=2.10-5s
MPI version is used on IBM BlueGene P
GPU-CUDA version is under development
Elastic parameters:
Young Modulus (E) =6MPa
Poisson coefficient () = 0.5
Shear Modulus (G) =2MPa
‘pseudo-viscosity’
(2Gdt)=80Pa.s
‘effective pseudo-viscosity’
=80.10-3 m2/s
Part 3 : Simulation Results
5 points
jet width: 10mm
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 32
33
Fluid – Soil unified model
L=2cm, Maximum velocity =0.5m/s, Average velocity =0.425m/s
• We obtain a dynamic equilibrium of the solutuion.
• Bottom of the crater has nearly the same position than that of
Shields number field .
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013
Above black line F=0 and below F=1 Initial Condition at t=0.5 sec Shields Number Map
33
Evolution of the crater
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 34
0
0,5
1
1,5
2
2,5
3
0 5 10 15 20
h (cm
)
L (cm)
0
2
4
6
8
10
0 5 10 15 20
D (cm
)
L (cm)
Average velocity(m/s)
Discharge(m3/s)
Maximum velocity(m/s)
Jet Reynolds number(-)
0.283 2.94E-5 0.425 1133
0.425 4.42E-5 0.637 1700
0.566 5.89E-5 0.849 2267
0.708 7.36E-5 1.062 2834
0.779 8.10E-5 1.168 3117
0.850 8.84E-5 1.275 3400
Comparison with experimental data
0
0,5
1
1,5
2
2,5
3
0 5 10 15 20
h (cm
)
L (cm)
0
2
4
6
8
10
0 5 10 15 20
D (cm
)
L (cm)
Average velocity(m/s)
Discharge(m3/s)
Maximum velocity(m/s)
Jet Reynolds number(-)
0.283 2.94E-5 0.425 1133
0.425 4.42E-5 0.637 1700
0.566 5.89E-5 0.849 2267
0.708 7.36E-5 1.062 2834
0.779 8.10E-5 1.168 3117
0.850 8.84E-5 1.275 3400
[Giez & Soulier (2011)]
*
*
Numerical results
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 35
Numerical Results
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
y = 0,6083ln(x) + 1,1047R² = 0,719
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3
D/L
Ec
y = 0,8389x - 0,1858R² = 0,9605
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3
H/L
Ec
a) b)
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20
D (cm
)
L (cm)
V=0.283m/s V=0.425m/s V=0.566m/s
V=0.708m/s V=0.779m/s V=0.850m/s
0
0,5
1
1,5
2
2,5
0 1 2 3
D/L
Ec
-0,5
0
0,5
1
1,5
2
0 1 2 3
H/L
Ec
a) b)
Non-dimensional characteristics of crater geometry : a)
crater depth-Ec; b) crater diameter-Ec
Measurements
Calculations
36
37
CONCLUSIONS
Introduction of the proposed unified formulation gives
promising results:
• Solid-like behaviour for solid bed is obtained.
• Stabilised shape of the crater is obtained.
• Quantitatively, the dimensions (H,D) of crater in good
agreement with experimental observation.
Perspectives:
• More studies required on the f-function and its parameters.
• Extension for other configurations (inclined, horizontal jet).
• 3D (massively parallelized ) version, application to
scouring around structures, dike break.
CETMEF
Fluid-Mediated Particle Transport in Geophysical Flows, KITP, October 31, 2013 37
APPLICATION TO THE GIRONDE ESTUARY
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 38
Coupling technique
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
1 confluence zone (node)/3 branches
Continuity and momentum equations
integrated over the jth layer of the
confluence area:
SFFdz
F jj
n
k
n
k
1
3,1
1 11
Equations Φ Fi Fj S
Continuity 0
Momentum
nok ,
kkuB noknok
w,,
nokw , dtBx
w
x
wwup
f
kfs
kskkkk
k
k
dt
z
w
z
wwwp
j
nof
kf
nos
ksnoknokknok
k
k
,
,
,,,
gM kkz
k
1
39
Contour map of turbidity in spring tide from the two-phase model
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013
at LW+2 at HW+2
40
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 41
CONCLUSION
Needing of two-phase approach
- interactions fluid-particles, particles-particles ignored in the single phase model
- interaction fluid-bed only one domain
Good behavior of the models to simulate free
surface and non-hydrostatic flows and different
processes of sediment transport
New generation for modeling sediment transport ?
Fluid-Mediated Particle Transport in Geophysical
Flows, KITP, October 31, 2013 42
THANK YOU FOR YOUR ATTENTION
11th ISRS, Cap-Town, South-Africa, September 2010