Stephan T. Grilli and Zhimin Hu Malcolm L. Spaulding
Associate Professor Postdoctoral Res. Associate Professor and Chair
Department of Ocean Engng.
niversity of Rhode Island
Narragansett, RI 02882, USA
Abstract :
This work is part of a research project, funded by the U.S.
Coast Guard (Oil Pollution Research Grant Program}, U.S. Department
of Transportation, Grants No. DTRS57-94-G-00076 (FY94) and DTRS57-95-G-00065
(FY95).}, aimed at developing a hydrodynamic model of {\em oil containment}
by booms. The main goal of the project is to use the model to analyze oil
containment failure mechanisms causing substantial loss of oil under the
boom. Due to its more catastrophic nature, the failure mode referred to
as critical accumulation is the main object of the study.
An extensive literature review was conducted for interfacial instabilities between two fluids and for oil containment failure problems. Based on this review, a hierarchy of modeling strategies was proposed. The Phase I model was developed, implemented, and tested as part of this project. Other models are being developed as continuations of this project.
The Phase I model uses piecewise-constant vortex sheets (VS) to represent the oil-water interface in a contained oil slick. Biot-Savart's law is used to calculate flow velocities induced by vorticity distributions in the VSs. An evolution equation is derived for time updating vorticity along VSs, including the effects of inertia, gravity, oil and water density differences, and surface tension at the interface. Higher-order modeling of the VS's geometry is introduced, based on 4th-order sliding polynomials and cubic splines.
The idealized case of a periodic Kelvin-Helmholtz instability is first solved to test and validate the principal numerical algorithms in the model. The pure headwave instability case (i.e., without a boom) is then solved. Model calculations are found to be both stable and accurate. Computational results are qualitatively similar to other published results. Applications of the model to more realistic cases of oil containment by a boom are then presented.