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MODELIZATION AND SIMULATION OF THE FLUID
DYNAMICS OF THE FUEL IN SUNKEN TANKERS AND
OF THE DISPERSION OF THE FUEL SPILL
Francesc Xavier GRAU, Leonardo VALENCIA, Alexandre
FABREGAT, Jordi PALLARES,
Ildefonso CUESTA
ECoMMFiT research group
University Rovira i Virgili
Department of Mechanical Engineering
Avinguda dels Països Catalans, 26
43007

Tarragona. Spain
URL:
http://ecommfit.urv.es
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Introduction
Simulation of the fluid dynamics of the fuel in sunken
tankers
–
Macroscopic model
–
Numerical simulation
Conclusions
Simulation of the fluid dynamics of fuel spills
Current work
OUTLINE
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This
presentation
describes
the
main
results
obtained
by
the
Fluid
Mechanics
Group
of
Tarragona
ECoMMFiT
within
the
project
VEM
2003

2004
:
"Modelization
and
simu

lation
of
the
fluid
dynamics
of
fuel
within
a
sunken
tanker
and
the
subsequent
oil
slick“
This
project
covers
the
development
of
CFD
codes
for
the
simulation
of
both
flow/heat
transfer
processes
:
–
of
the
oil
in
a
sunken
tanker
and
–
the
dispersion
of
oil
spills
.
INTRODUCTION
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The
research
group
developed
two
domestic
codes
for
the
simulation
of
:
–
fluid
flow
and
heat/mass
transfer
3
DINAMICS
–
for
the
simulation
of
oil
spills
SIMOIL
These
codes
needed
specific
improvements
and
optimization
of
the
numerical
methods,
as
well
as
the
extension
of
their
simulation
capabilities
through
the
implementation
of
different
models
INTRODUCTION
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Physical overview
Natural convection
vertical boundary

layer
Unstable density
stratification
Stable density
stratification
Lateral tank
H=19 m L
l
=9.6 m
Central tank
H=19 m L
c
=15.2 m
(only half is shown)
g
Highly unsteady
flow
O(Ra
H
) = 10
13
10
4
< Pr < 8 10
6
L
c
/2=7.6 m
At t=0...
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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The macroscopic model
T
l
T
c
q
l t
q
c t
q
l w
q
l e
q
c w
q
l b
q
c b
T
t
Hypothesis
•
The core of the tanks are
perfectly mixed (T
l
and T
c
)
•
Correlations for natural
convection on vertical and
horizontal flat plates are
used
•
Unsteady conduction heat
transfer through the bottom
walls
y
x
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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T
l
q
l w
q
l e
T
t
Top wall
East wall
Bottom wall
West wall
q
c w
q
l b
q
c b
q
l t
q
c t
T
c
Lateral tank
Central tank
Top wall
Bottom wall
West & east walls
•
Energy balance in the lateral tank
•
Energy balance in the central tank
•
Energy balance on the mid

wall
y
x
The macroscopic model
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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Time evolution of the volume

averaged temperatures
The macroscopic model
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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•
Continuity
•
Momentum
•
Thermal energy
Mathematical model
•
Hypothesis: 2D model, Boussinesq fluid except for the
temperature

dependent viscosity
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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Boundary conditions
•
No slip condition at the isothermal walls: u
i
=0, T
w
=2.6ºC
•
Symmetry condition: (
启
砩
x=17.2m
=0, (
瘯
砩
x=17.2m
=0,
u
x=17.2m
=0
Initial conditions
•
T(x,y)=50ºC
•
u
i
=0
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
Mathematical model
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Computational code:
3DINAMICS
•
Finite volume
•
2nd order accuracy
•
QUICK discretization for the convective fluxes
•
Centered scheme for the diffusive fluxes
•
ADI method for time

integration
•
Coupling V

P: conjugate gradient method for the
iterative solution of the Poisson
equation
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
Mathematical model
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•
Numerical method: 3DINAMICS
•
Tested successfully in the Validation Exercise
“Natural convection in an air filled cubical cavity with different inclinations”
CHT’01 Advances in Computational Heat Transfer II. May 2001. Palm Cove.
Queensland. Australia
10
4
Ra
8
0º
㤰9
Heated from
below
Heated from
the side
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
Mathematical model
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•
Numerical grids
Nx=81, Ny=64
Nx=141, Ny=146
•
Grid spacing
Horizontal
x

direction
Vertical
y

direction
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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•
Results
Time evolution of the volume

averaged temperatures
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
Results
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•
Results
Fine grid: 5 days
only half of
the vectors
are shown
in each
direction
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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•
Results
Coarse grid: 42 days
Numerical Simulation
SIMULATION OF THE FLUID DYNAMICS
OF THE FUEL IN SUNKEN TANKERS
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CONCLUSIONS
•
The heat transfer process is governed by the
interaction
between the natural convection
vertical boundary

layers
along the lateral walls and the unstable stratification at the
top walls
•
The macroscopic model gives
reasonable time

evolution
of the volume

averaged
temperatures
when
temperature

dependence viscosity corrections are
introduced in the conventional correlations
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•
Maximum differences between
predictions of the
macroscopic model
and the fine

grid numerical
simulation are about
10%
(t<5 days)
•
The high Prandtl number and the strong temperature

dependent viscosity require
grid spacings of the order
of millimeters near the walls
•
According to the macroscopic estimation
after 500 days
the temperature of the fuel is about 3ºC
in both
tanks
CONCLUSIONS
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OF THE FUEL IN SUNKEN TANKERS
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SIMOIL:
computational code for the
numerical simulation of the evolution of oil
spills
SIMOIL
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Oil is a complex mixture of
many chemical compounds.
Composition of crude oil may
differ depending of the zone of
the extraction
Following the main
components:
•
Hydrocarbons
•
Asphalts
•
Paraffins
Physical properties of oil
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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DEGRADATION OF AN OIL SPILL
Spreading
Advection
Evaporation
Dispersion
Dissolution
Emulsification
Photo

oxidation
Sedimentation
Biodegradation
Physical properties of oil
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OF FUEL SPILLS
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Oil spill increases surface extension
gravity
inertia
Friction, viscosity
Surface tension
spreading
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
In this work, a constant oil velocity profile has been
assumed in the vertical direction, and the problem
has been reduced to a
two

dimensional
one, with the
thickness of the slick as the unique unknown.
All the fluids involved, air, sea water and crude oil,
have been assumed to be
newtonian
and
nonmiscible
, with
constant physical properties
.
While
spreading
is
dominated
by
gravity
and
viscous
forces
:
in
a
gravity

viscosity
dominated
flow
regime,
the
displacement
of
the
oil
slick
is
mainly
due
to
the
combined
effect
of
wind
and
sea
currents
.
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A
global
convection
velocity
is
calculated
at
each
computational
point
and
time
step
by
adding
to
the
actual
sea
motion
the
local
induced
sea
current
.
This
induced
velocity
is
assumed
to
be
produced
by
known
permanent
currents
and/or
tidal
flows,
in
which
case
the
period
and
amplitude
of
tides
are
taken
into
account
.
ADVECTION
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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The
evaporation
process
can
produce
losses
up
to
60
%
of
the
original
spill
.
The
model
developed
by
Mackay
et
al
.
(
1980
)
has
been
adopted
in
this
work
.
This
model
is
based
on
the
concept
of
evaporative
exposure
as
a
function
of
elapsed
time,
oil
slick
surface
and
a
mass
transfer
coefficient,
which
varies
with
wind
velocity
EVAPORATION
K
h
=
0•00l5
W
0.78
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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A
single
governing
equation
for
the
evolution
of
the
oil
thickness
h
in
isothermic
systems
can
be
obtained
by
combining
the
continuity
and
the
momentum
conservation
equations
.
Under
a
gravity

viscosity
regime
the
vectorial
form
of
this
equation
is
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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The governing equation has been solved in a
two

dimensional domain
corresponding to the marine
environment where the oil is spilled.
The discrete computational domain has been
spanned by a
generalized grid coordinate system,
e, h
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Physical domain
Computational grid
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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The
original
equation
is
shown
in
generalized
coordinates
(
e,h
)
IC剅TIZATION
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Previously
equation
has
been
discretized
by
means
of
a
finite
difference
scheme
which
is
first

order
accurate
(upwind)
for
the
convective
terms
and
second

order
accurate
(centred)
for
the
diffusion

like
terms
.
At
each
time
step,
the
set
of
resulting
algebraic
expressions
was
solved
by
using
an
alternating
direction
implicit
(ADI)
method
to
ensure
second

order
accuracy
for
the
time
derivative
approximation
.
DISCRETIZATION
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Initial
h
values
are
needed
to
start
a
simulation
.
Therefore,
the
initial
location,
volume
and
extension
of
the
oil
slick
have
to
be
known
.
The
application
of
convective
boundary
conditions
at
the
sea
side
allows
the
slick
to
cross
the
limits
of
the
domain,
i
.
e
.
to
be
convected
away
from
the
zone
of
calculation
.
On
the
coast
a
convective

diffusive
boundary
condition
has
been
developed
so
that
oil
can
accumulate
and
disperse
on
the
shoreline
.
INITIAL AND BOUNDARY CONDITIONS
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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1.
Generation
of
the
computational
domain
.
To
this
end
the
map
of
the
area
affected
by
the
spill
is
digitized
to
obtain
the
boundary
points
comprising
the
open
sea
and
land,
and
to
generate
the
grid
in
generalized
coordinates
.
2.
Secondly,
the
discrete
space

time
evolution
of
the
oil
slick
,
in
terms
of
oil
thickness,
is
calculated
for
any
given
input
data
.
3.
The
third
step
includes
the
graphical
presentation
of
the
results
obtained
.
COMPUTATIONAL PROCEDURE
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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The
input
information
include
the
definition
of
the
domain
of
calculation

grid
and
land
boundary
definitions
the
characteristics
of
the
oil
spill

initial
location,
density,
amount
of
oil,
continuous
or
discontinuous
discharge,
etc
.
the
environmental
conditions

air
and
water
temperature,
wind
speed
and
direction
the
dynamic
conditions
of
the
sea,
such
as
currents
and
tides
The
graphic
output
displays
the
areas
of
equal
oil
thickness
,
by
means
of
isolines
and
allows
the
direct
evaluation
of
the
position
and
area
affected
by
the
accident
and
eliminates
the
need
for
storing
large
sets
of
numerical
data
.
COMPUTATIONAL PROCEDURE
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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As a result a set of
pictures for the time
evolution of the slick
is obtained
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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SIMOIL
is
implemented
in
a
Linux
cluster
(
beowulf)
of
24
AMD
opteron
248
processors
(
64
bits),
with
3
Terabytes
of
Disk,
linked
with
a
Gigaethernet
in
a
Linux
environment
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Domain
:
Tarragona
coast
(
35
km)
Wind
:
(
5
m/s,

1
m/s)
Quantity
spilled
:
A
total
80000
m
3
of
crude
oil
continuously
spilled
in
24
h
Oil
density
:
870
kg/
m
3
Sea
density
:
1030
kg/
m
3
NUMERICAL EXEMPLE
–
INPUT DATA
Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Mathematical model
SIMULATION OF THE FLUID DYNAMICS
OF FUEL SPILLS
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Current work
3DINAMICS
•
The performance of the actual version code, which
includes the paralelization and the multigrid technique,
has been improved significantly.
•
Currently we are improving the speed

up of the
parallel version
SIMOIL
•
More accurate results for spill spreading in coastal
areas are obtained if the sea circulation is computed by
a shallow water model which is currently being
implemented
•
Implementation of better discretization schemes
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