1. [1/38] 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

2. [2/38]  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

3. [3/38]  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

4. [4/38]  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

5. [5/38] 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

6. [6/38] The macroscopic model TlTl TcTc q l t q c t q l w q l e q c w q l b q c b TtTt 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

7. [7/38] TlTl q l w q l e TtTt Top wall East wall Bottom wall West wall q c w q l b q c b q l t q c t TcTc Lateral tankCentral 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

8. [8/38] Time evolution of the volume-averaged temperatures The macroscopic model SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

9. [9/38] 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

10. [10/38] Boundary conditions No slip condition at the isothermal walls: u i =0, T w =2.6ºC Symmetry condition: (  T/  x) x=17.2m =0, (  v/  x) 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

11. [11/38] 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

12. [12/38] 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  10 8 0º    90º Heated from below Heated from the side Numerical Simulation SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS Mathematical model

13. [13/38] 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

14. [14/38] Results Time evolution of the volume-averaged temperatures Numerical Simulation SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS Results

15. [15/38] 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

16. [16/38] Results Coarse grid: 42 days Numerical Simulation SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

17. [17/38] 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

18. [18/38] 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 SIMULATION OF THE FLUID DYNAMICS OF THE FUEL IN SUNKEN TANKERS

19. [19/38] SIMOIL: computational code for the numerical simulation of the evolution of oil spills SIMOIL SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

20. [20/38]  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

21. [21/38] DEGRADATION OF AN OIL SPILL  Spreading  Advection  Evaporation  Dispersion  Dissolution  Emulsification  Photo-oxidation  Sedimentation  Biodegradation Physical properties of oil SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

22. [22/38] Oil spill increases surface extension  gravity  inertia  Friction, viscosity  Surface tension spreading SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

23. [23/38] 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.

24. [24/38]  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

25. [25/38]  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 = 000l5 W 0.78 Mathematical model SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

26. [26/38]  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

27. [27/38]  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,  Mathematical model SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

28. [28/38] Physical domain Computational grid Mathematical model SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

29. [29/38]  The original equation is shown in generalized coordinates () DISCRETIZATION Mathematical model SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

30. [30/38]  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

31. [31/38]  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

32. [32/38] 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

33. [33/38]  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

34. [34/38] 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

35. [35/38] 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

36. [36/38]  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

37. [37/38] Mathematical model SIMULATION OF THE FLUID DYNAMICS OF FUEL SPILLS

38. [38/38] 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