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and propeller-hull interaction. While most applications of the algorithm have been to generic hull forms such as the Wigley hull and to research forms such as the Series 60, accurate simulation of the flow around these hulls suggest that it is capable of general application and represents a good starting point for complex forms such as combatants with transom sterns and bulbous bows.

At full scale, this flow is not uniformly single phase. Air bubbles from boundary-layer entrainment, propeller ventilation and/or cavitation, and breaking waves serve to inject bubbles into the flow. In most regions the void fraction is small and does not influence the flow, but in others it can become large enough to play a significant role on flow dynamics. Even though the degree of complexity of the problem increases considerably when the bubbles are taken into account, two phase flow modeling of (3,4,5) can be used to determine the spatial distribution of moderately high concentration (i.e., alpha less than 10%), monodisperse air bubble populations and the associated fluid coupling in turbulent flows. While the mechanisms and degree of air entrainment at the free surface remain unresolved, considerable insight can be achieved by introducing air void at likely injection locations and calculating its evolution.

More or less simultaneously, considerable effort has been devoted toward developing computational models of surface ship wakes. The effort has been motivated by a desire to estimate micro-bubble populations in the far wake as well as predict the radar scattering characteristics of the free surface. The work in (6,7,8) detail application of far-wake modeling to micro-bubble evolution. In general, the strategy has been to model the hydrodynamic and relevant scalar fields via a parabolic subset of the RANS equations. Scalar fields such as temperature, micro-bubble populations, salinity and surface contaminants have been included because of their influence on the flow field and because they are of interest in their own right.

The ability to predict the near and far fields of naval surface ships requires that these models be extended to include realistic hull geometries and operating environments and coupled together. The work presented in this paper discusses some of the extensions necessary to use these tools to simulate the flow fields associated with naval combatants operating in commonly encountered conditions. They are illustrated via a set of simulations on a U.S. Navy FF-1052 (figure 1). This ship represents most of the geometric complexities found in modern combatant forms; a transom stern and bulbous bow. The near-and far-field flow is computed for both the unpropelled and propelled hull operating in a thermally-stratified environment. The transport of a monodisperse microbubble population introduced in the near-bow region is also computed for the unpropelled hull at zero Froude number.

This paper is arranged in the following manner. The problem formulation is described in section 2. In section 3 the computational methods are briefly discussed. The conditions and grids are presented in section 4 and the uncertainty analysis in section 5. Results for both the FF-1052 near and far field are presented in section 6. Finally, concluding remarks and discussion of future work are provided in section 7.


To predict surface-ship bubbly wakes, separate, but coupled, CFD methods are used for the near and far fields. Formulation of the problem is based upon coupling the RANS method (1), which has been extended for combatant geometries (9) [i.e., multi-block to handle transom stern and propeller-hull interaction using (2)] and thermal stratification, and an Eulerian two-fluid ensemble-averaged model (4) for the near field and a parabolic method (6) for the far field with its initial data plane (IDP) prescribed by the near-field solution. It should also be noted that (9) provides detailed documentation, user instructions, and discussion of and implementation recommendations for uncertainty analysis. Figure 2 provides a schematic of the relationship between near-and far-field domains.

Near Field

The unsteady three-dimensional continuity and RANS equations for a gas-liquid two-phase flow are written for each phase separately and derived assuming: negligible bubble inertia (i.e., ρg « ρ); small void fraction and void-fraction gradients; spherical bubbles; and constant liquid density. Using Cartesian tensor notation and in non-dimensional form, the liquid-phase equations are



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