Francesc Xavier GRAU, Leonardo VALENCIA, Alexandre FABREGAT, Jordi PALLARES, Ildefonso CUESTA

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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 groupUniversity Rovira i VirgiliDepartment of Mechanical EngineeringAvinguda dels Països Catalans, 2643007-Tarragona. SpainURL: 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 VEM2003-2004:"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

3DINAMICS

– 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 convectionvertical boundary-layer

Unstable densitystratification

Stable densitystratification

Lateral tankH=19 m Ll=9.6 m

Central tankH=19 m Lc=15.2 m(only half is shown)

g

Highly unsteadyflow

O(RaH) = 1013

104< Pr < 8 106

Lc/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

Tl Tc

ql t qc t

ql w ql e qc w

ql b qc b

Tt

Hypothesis

• The core of the tanks

are perfectly mixed (Tl

and Tc)

• Correlations for natural convection on vertical and horizontal flat plates are used• Unsteady conduction heat transfer through the bottom walls

y

x


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Tl

ql w ql e

Tt

)TT(h)TT(h tccwtlle

)TT(hA

)TT(hA

t/)TT(kA

)TT(hAdt

dTCpM

tllele

wllwlw

wllb

wlltltl

l

Top wall

East wall

Bottom wallWest wall

qc w

ql b qc b

ql t qc t

Tc

Lateral tank Central tank

)TT(hA2

t/)TT(kA

)TT(hAdt

dTCpM

tccwcw

wclb

wcctctc

c

Top wallBottom wallWest & east walls

• Energy balance in the lateral tank

• Energy balance in the central tank

• Energy balance on the mid-wally

x

The macroscopic modelSIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

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days

T(º

C)

10-1 100 101 102 103

0

5

10

15

20

25

30

35

40

45

50

55

ConductionConvection (Lateral Tank)Convection (Central Tank)Convection (/w)0.21 (Lateral Tank)Convection (/w)0.21 (Central Tank)T=2.6ºC

Time evolution of the volume-averaged temperatures

The macroscopic modelSIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

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• Continuity

• Momentum

• Thermal energy

Mathematical model

0x

u

i

i

jj

2

j

j

xx

T

x

Tu

t

T

)TT(gx

u

x

u)T(

xx

p1

x

uu

t

uo2

i

j

j

i

jjoj

iji

• Hypothesis: 2D model, Boussinesq fluid except for the temperature-dependent viscosity

Numerical SimulationSIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

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Boundary conditions

• No slip condition at the isothermal walls: ui=0, Tw=2.6ºC

• Symmetry condition: (T/x)x=17.2m=0, (v/x)x=17.2m=0,

ux=17.2m=0

Initial conditions

• T(x,y)=50ºC

• ui=0


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


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

104 Ra 108

0º 90ºHeated from

belowHeated from

the side


Mathematical model

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• Numerical grids

X

Y

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170123456789

10111213141516171819

X

Y

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 170123456789

10111213141516171819

Nx=81, Ny=64

Nx=141, Ny=146Y

Y

10-3 10-2 10-1 1000123456789

10111213141516171819

Coarse GridFine Grid

Frame 001 10 Feb 2003 Internally created data set

X

X

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1710-3

10-2

10-1

100

Coarse gridFine Grid

Frame 001 10 Feb 2003 Internally created data setFrame 001 10 Feb 2003 Internally created data set

X

X

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1710-3

10-2

10-1

100

Coarse gridFine Grid

Frame 001 10 Feb 2003 Internally created data set

Y

Y

10-3 10-2 10-1 1000123456789

10111213141516171819

Coarse GridFine Grid

Frame 001 10 Feb 2003 Internally created data setFrame 001 10 Feb 2003 Internally created data set

• Grid spacingHorizontal x-direction

Verticaly-direction


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• Results Time evolution of the volume-averaged temperatures

Days Tl Tc Tl Tc Tl Tc1 47 49 48 48 49 493 42 47 45 45 46 47

10 31 40 36 38 - -100 8 13 - - - -500 3 4 - - - -

Coarse grid Fine gridNumerical simulationMacroscopic

model

days

T(º

C)

10-1 100 101 102 103

0

5

10

15

20

25

30

35

40

45

50

55

ConductionConvection (/w)0.21 (Lateral Tank)Convection (/w)0.21 (Central Tank)2D Simulation Fine Grid (Lateral Tank)2D Simulation Fine Grid (Central Tank)2D Simulation Coarse Grid (Lateral Tank)2D Simulation Coarse Grid (Central Tank)T=2.6ºC


Results

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• ResultsFine grid: 5 days

only half ofthe vectors are shownin each direction


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• ResultsCoarse grid: 42 days


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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

CONCLUSIONSSIMULATION 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

SIMOILSIMULATION 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

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

Product Specific gravity

Gasoline 0.74 - 0.73

J et Fuel 0.75 - 0.80

Kerosene 0.80 - 0.88

Fuel Oil #2 (Diesel) 0.88

Lube Oil 0.87

Kuwait Light Crude Oil 0.83

Fuel oil #6 (Bunker) 0.96 - 0.97

Nort Slope Crude Oil 0.89

San Argo Crude Oil 0.99

Residual asphaltene -

Physical properties of oilSIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

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DEGRADATION OF AN OIL SPILLDEGRADATION OF AN OIL SPILL

SpreadingAdvectionEvaporationDispersionDissolutionEmulsificationPhoto-

oxidationSedimentationBiodegradatio

n

Physical properties of oilSIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

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Oil spill increases surface extensiongravityinertiaFriction, viscositySurface tension

spreadingSIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

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Mathematical modelSIMULATION 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.

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


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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

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

Kh = 0•00l5 W0.78


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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

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

0hCA)hdiv(th 32


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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,

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,


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Physical domain

Computational grid


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The original equation is shown in generalized coordinates ()

The original equation is shown in generalized coordinates ()

DISCRETIZATION

yyxxh32

2y

2

x

2

2

32

y

2

x

2

2h32

CJh

J1Jh

J1

th AA


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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.

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


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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 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


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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.

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


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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

tidesThe 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.

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

tidesThe 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


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As a result a set of pictures for the time evolution of the slick is obtained

As a result a set of pictures for the time evolution of the slick is obtained


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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

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


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Domain: Tarragona coast (35 km)Wind: (5 m/s, -1 m/s)Quantity spilled: A total 80000 m3 of crude oil continuously spilled in

24 hOil density: 870 kg/ m3

Sea density: 1030 kg/ m3

Domain: Tarragona coast (35 km)Wind: (5 m/s, -1 m/s)Quantity spilled: A total 80000 m3 of crude oil continuously spilled in

24 hOil density: 870 kg/ m3

Sea density: 1030 kg/ m3

NUMERICAL EXEMPLE – INPUT DATA


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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

Documents

Francesc Xavier GRAU, Leonardo VALENCIA, Alexandre FABREGAT, Jordi PALLARES, Ildefonso CUESTA