# MODELIZATION AND SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS AND OF THE DISPERSION OF THE FUEL SPILL

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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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

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

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: (

x=17.2m
=0, (

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

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

SIMULATION OF THE FLUID DYNAMICS

OF THE FUEL IN SUNKEN TANKERS

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Maximum differences between
predictions of the
macroscopic model

and the fine
-
grid numerical
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

SIMULATION OF THE FLUID DYNAMICS

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

Evaporation

Dispersion

Dissolution

Emulsification

Photo
-
oxidation

Sedimentation

Physical properties of oil

SIMULATION OF THE FLUID DYNAMICS

OF FUEL SPILLS

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Oil spill increases surface extension

gravity

inertia

Friction, viscosity

Surface tension

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

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

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
.

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

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
)

IC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

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,

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