Marine oil spills can cause serious damage to natural resources and to those whose livelihoods depend on these resources. Therefore, it is important to improve techniques and equipment that facilitate spill cleanup [1] . The common response to an oil spill on water is to contain the oil with booms and recover it with skimming devices. However, in some situations, the booms fail to hold the oil and the oil will escape underneath the boom due to hydrodynamic forces. Poor recovery of oil using booms requires significantly higher cleanup costs. Therefore a better understanding of the dynamics of oil slicks is required [2] .

Besides wind and wave effects, there are three failure mechanisms for the oil boom in the current [3] : drainage failure, entrainment failure and critical accumulation failure. In drainage failure, the boom draft is insufficient to contain the oil slick and some oil goes underneath the barrier. Cross and Hoult described the oil slick profile theoretically [4] [5] . In entrainment failure, oil droplets are broken off from the oil and are swept underneath the boom if the buoyancy forces are insufficiently large [6] . Leibovich [6] and Milgram et al. [7] ascribe the entrainment to breaking of Kelvin-Helmholtz water-oil interfacial waves at sufficiently large relative velocity. Many experimental results can be found in the literatures [6] -[9] . For highly viscous oils of kinematic viscosities exceeding 3000 cSt, Delvigne [3] showed a third failure mechanism: critical accumulation (oil creep) for relative velocities exceeding about 0.15 m/s, independently of the boom draft. Johnston [10] indicated that this mode of failure is due to an insufficient circulation within the oil and suggested to use Bingham-plastic model instead of Newtonian model to improve the understanding of this mode of failure.

Although oil boom is widely used, it is far from being fully investigated. For understanding the boom failure mechanism, it is important to investigate the oil slick behavior behind the boom and the details of the flow field near the boom. For the limit of the measurement approach, it is hard to know the details of the flow field in the oil slick. CFD has its advantages to obtain the process of the oil slick propagation and the details of the flow field in the oil slick. Tkalich et al. [11] -[13] developed a multiphase oil spill model to simulate consequences of oil spill in the marine environment. Goodman et al. [14] [15] investigated the boom failure mechanisms using CFD approach. They only qualitatively studied the boom failure but did not give the quantitative details of the oil slick profiles and the velocity field. In this paper, an open source CFD software package, OpenFOAM v2.2.2, has been used to simulate the oil water flow around a boom. The details of the flow field in the oil slick are studied and the thickness of oil slick is investigated quantitatively.

For the purpose of investigating the oil slick behavior behind the boom under a water current, a CFD software, OpenFOAM, is employed to carry out the numerical simulation. In this software, the Reynolds averaged Navier- Stokes equations (RANS equations) are solved numerically and turbulence modelling is adopted. The volume of fluid (VOF) method is used to track the interface between the oil and water. The incompressible RANS momentum equation solved in the software can be written as:

where is the fluid velocity vector, is the external force vector, is the fluid density, p is the pressure, is the dynamic viscosity, is the Reynolds stress and can be approximated by using Boussinesq’s isotropic eddy viscosity hypothesis as follows:

where is the Kronecker delta, k is the turbulent kinetic energy, is an effective viscosity, the sum of the turbulent eddy viscosity and molecular dynamic viscosity:

The turbulent eddy viscosity is calculated using the standard model [16] as follows:

where is a dimensionless constant, represents the dissipation rate of turbulent kinetic energy. The transport equations for the turbulent kinetic energy k and the dissipation rate are given by:

where, , , are the model constants determined experimentally.

The numerical simulation scenarios are chosen as the similar geometry with the real situation of the Singapore sea area. The computational domain is 30 m long and 5 m deep (see Figure 1). The oil boom is placed near the surface and in the middle of the computational domain in length direction. The boom draft D is chosen as 0.5 m or 1 m. The current velocity U range is chosen of 0.1 - 0.5 m/s at interval of 0.1 m/s.

There are four type of oil (listed in Table 1) used in the simulation which include from light to heavy oil and from low to high viscosity oil. The initial oil volume Q is chosen as 1.2 m³ or 3.6 m³ per unit boom length.

A summary of cases are listed in Table 2. For every case label, there are five different current velocities from 0.1 m/s to 0.5 m/s. Therefore, a total of 80 cases of oil slick are carried out in this study.

For the numerical simulation of all the case, the same meshes are adopted with just slight difference between different boom drafts. The total number of cells is about 53,000. The minimum cell size is 0.025 m. The finest cells are placed near the boom and the water surface. Figure 2 shows the meshes used in the simulation.

A series of numerical simulation cases are carried out based on OpenFOAM multiphase solver in order to study the oil slick behavior behind the oil boom. The flow field near the boom is studied. The relationship of the relative thickness of oil slick with the Froude number is analyzed. It is found that there is a linear relationship between the relative oil slick thickness and the Froude number. This means that we can estimate the relative oil slick thickness using Froude number by the fixed linear relationship regardless of boom draft, initial oil volume and oil type.