Near-Boom Oil-Slick Instability Criterion in Viscous Flows and the Influence of Free-Surface Boundary Conditions
Author:
Sundararaghavan H.1, Ertekin R. C.1
Affiliation:
1. Department of Ocean Engineering, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 2540 Dole Street, Holmes Hall 402, Honolulu, HI 96822-2333
Abstract
Booms are often used to contain oil spills prior to various oil removal techniques. Under certain conditions, the oil droplets can leave the oil slick and enter the water. A simple balance of hydrodynamic forces on a droplet results in an instability criterion which determines whether the droplet will be swept past the boom or not. For viscous flows, it is shown here that the instability criterion consists of a term proportional to the pressure gradient along the boom, as in the potential-flow case, and a term that is inversely proportional to the Reynolds number, although the magnitude of this new term is found to be very small. The solution of viscous flow past an oil boom is obtained using the fractional-step method in a curvilinear coordinate system and the instability criterion is estimated. The influence of the approximate free-surface conditions, such as the rigid-lid no-slip, rigid-lid free-slip, and the exact free-surface condition, the instability criterion is also investigated. The different approximations of free-surface conditions are shown to influence the pressure distributions, thus resulting in different neutral stability curves.
Publisher
ASME International
Subject
Geochemistry and Petrology,Mechanical Engineering,Energy Engineering and Power Technology,Fuel Technology,Renewable Energy, Sustainability and the Environment
Reference12 articles.
1. Ananthakrishnan, P., 1991, “Surface Waves Generated by a Translating Two-dimensional Body: Effects of Viscosity,” Ph.D. dissertation, University of California, Berkeley, CA. 2. Chorin A. J. , 1968, “Numerical Solution of the Navier-Stokes Equations,” Mathematics of Computation, Vol. 22, No. 104, pp. 745–762. 3. Ertekin, R. C., and Sundararaghavan, H., 1994, “Potential and Viscous Flows Past an Oil Boom: The Instability Problem,” Proceedings, 13th International Conference of Offshore Mechanics and Arctic Engineering, ASME, Vol. I, pp. 189–197. 4. Ertekin R. C. , and SundararaghavanH., 1995, “The Calculation of the Instability Criterion for a Uniform Viscous Flow Past an Oil Boom,” ASME Journal of Offshore Mechanics and Arctic Engineering, Vol. 117, pp. 24–29. 5. Fletcher, C. A. J., 1991, Computational Techniques for Fluid Dynamics, 2nd Edition, Vol. II, Springer-Verlag, Berlin, Germany.
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