Modeling and Simulation of Oil Dispersion under Breaking Waves
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Oil dispersion under a deep-water plunging breaker of a height 0.15 m was studied by coupling the Lagrangian particle tracking code (NEMO3D) with the population balance model (VDROP). The wave hydrodynamics obtained in Part I (Cui et al. in Environ Fluid Mech 2020 (in press)) was used as input. It was observed that droplet inertia and major forces on droplets significantly impacted the transport of oil droplets under wave conditions, and neglecting it caused less entrainment into the water column and horizontal spread of the oil plume. For droplets less than 400 microns, the droplet size distribution (DSD) tended to follow a power-law distribution with an exponent close to − 2.3, which was consistent with earlier experimental observations by Delvigne and Sweeney (Oil Chem Pollut 4(4):281– 310, 1988). The distribution of large-size droplets evolved with time and showed agreement with a power-law distribution having an exponent of − 9.7 about 20 s after the passage of the wave train. Reducing the interfacial tension enhanced droplet breakup and increased the exponent of power-law distribution to − 6.1 for droplets smaller than 400 microns. It was also found that neglecting the vertical gradient of eddy diffusivity led to the accumulation of oil droplets in low eddy diffusivity regions at the bottom part of the wave breaker. The investigation herein could be used to obtain design values for breakers that could be used in oil spill models to predict the oil droplet size distribution.
Published papers for details:
Cui, F., Daskiran, C., King, T., Robinson, B., Lee, K., Katz, J. and Boufadel, M.C., 2020. Modeling oil dispersion under breaking waves. Part I: wave hydrodynamics. Environmental Fluid Mechanics, 20(6), pp.1527-1551.
Cui, F., Zhao, L., Daskiran, C., King, T., Lee, K., Katz, J. and Boufadel, M.C., 2020. Modeling oil dispersion under breaking waves. Part II: Coupling Lagrangian particle tracking with population balance model. Environmental Fluid Mechanics, 20(6), pp.1553-1578.
Cui, F., Boufadel, M.C., Geng, X., Gao, F., Zhao, L., King, T., and Lee, K., 2018. Oil droplets transport under a deep‐water plunging breaker: Impact of droplet inertia. Journal of Geophysical Research: Oceans 123 (12), 9082-9100
Figure 1. Wave profle acquired using 2.1×2.1 mm grid resolution (the blue contour) and 1.2×1.2 mm grid resolution (the black dashed line) at t*=−0.01
Figure 2. Numerical results against snapshots of wave profiles from the experiment at various times. The interval indicates 10 cm in both numerical simulation and experimental results
Figure 3. Non-dimensionalized velocity predicted by simulation and observed in the experiment at x*=0.60 and z*=−0.026 (5 cm below the MWL of 0.6 m): a horizontal velocity, positive values imply forward, and b vertical velocity, positive values imply upward.
Figure 4. Distribution of oil droplets at various times for Case A, Case B, and Case C. The black dots indicate oil droplets with different diameters. The overall behaviors of oil plumes are similar, but the number of oil droplets in the water column is distinct for different cases. Note that a different vertical scale is used for results at t=25.00 s
Figure 5. Droplet size distribution averaged within every 5 s at depths larger than 8 cm in the whole domain: (a) Kb = 0.25 and Sigma = 2.0e − 2 N/m, (b) Kb = 1.0 and Sigma = 2.0e − 2 N/m), and (c) Kb = 1.0 and Sigma = 2.0e − 3 N/m. Note different scales of the y-axis.
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