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which must be addressed. By using systematic verification analysis, numerical uncertainties can be made relatively small. However, improvement in numerics is required, particularly, efficiency and accuracy. Modeling uncertainties are daunting and their estimation requires EFD validation data which, unfortunately, is very difficult to obtain. For single-phase flow, modeling uncertainty is due to geometry, turbulence, wave-breaking, and free-surface boundary conditions. In contrast, there are many areas of concern for two-phase flow. The accumulation of bubbles in the boundary layer suggests that other possible mechanisms of interfacial momentum and mass transfer may be important in this region, such as bubble-bubble collision and interfacial pressure, Einstein forces, dissolution, and breakup. Some of these models will require incorporation of an approach to handle polydisperse bubble populations: a formidable computational challenge.

To accurately predict bubbly-wake signatures, much future work remains. For the near-field RANS, farther improvements in both numerics and models will be made in conjunction with work on more complex single-phase flows, e.g., unsteady flow. Also, capability to resolve appendages, calculate sinkage and trim, and employ more sophisticated propeller-hull interaction methods must be incorporated. The lack of strong thermal-hydrodynamic interaction suggests that a variety of common and in-situ temperature profiles be studied. In certain environments, salinity fields may need to be included in the transport and density calculations. Finally, work on two-fluid modeling will focus on extending the method for nonzero Fr, development of a coupled multigroup scheme to calculate bubble-size distribution, including bubble breakup and dissolution, and inclusion of propulsor effects on the bubble size distribution.

ACKNOWLEDGMENTS

This research was sponsored by Office of Naval Research Grants N00014 –93–1–0052 (Iowa), N00014–96-AF00002 (NSWC CSS), and N00014–91-J-1271 (RPI) under the administration of Dr. E.P. Rood. The computations were performed on the Naval Oceanographic Office, NASA Numerical Aerodynamic Simulation Program, and San Diego Supercomputer Center supercomputers. The assistance of Dr. Rood and Ms. Margo Frommeyer is especially acknowledged.

REFERENCES

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10. Lopez de Bertodano, M., “Turbulent Bubbly Two-Phase Flow in a Triangular Duct,” Ph.D. Thesis, Rensselaer Polytechnic Insitute, Troy, NY, 1992.

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