Computational Investigations of Air Entrainment, Hysteresis, and Loading for Large-Scale, Buoyant Cavities Michael P. Kinzel, Jules W. Lindau, Joel Peltier, Frank Zajaczkowski, Thomas Mallison, and Robert F. Kunz The Pennsylvania State University, Applied Research Laboratory, State College, PA {mpk176, jwl10, ljp8, fxz101, tmm142, rfk102}@only.arl.psu.edu Roger Arndt and Martin Wosnik The University of Minnesota, St. Anthony Falls Laboratory, Minneapolis, MN arndt00@umn.edu Abstract A complete physical model of ventilated supercavitation is not well established. Efforts documented display the ability, with a finite volume, locally homogeneous approach, to simulate supercavitating flows and obtain good agreement with experiments. Several modeling requirements appear critical, especially in physical hysteretic conditions or configurations. The hysteresis presented is due to obstruction of the flow with a solid object. The modeling approach taken correctly captures a full hysteresis loop and the corresponding dimensionless ventilation rate to cavity pressure (C Q - ) relationship. This correspondence supports the suggestion that the main mechanism of cavity gas entrainment is via shear layers attached to the cavity walls. With such validated solutions, additional insight into the flow within the cavity is gained. Nomenclature C 1 , C 2 turbulence model constants C Q dimensionless ventilation rate [q/(U 0 Dc 2 )] (q is volume flow rate) C prod, C dest mass transfer model parameter L c , D c cavity length and max. diameter Fr Froude Number [U O /(Dg) 1/2 ] k, turbulence model eddy viscosity and dissipation rate L t turbulent length scale P turbulence model production term k , turbulence model Schmidt Numbers for k and k gas volume fractions p preconditioning matrix m , m ,t mixture molecular, and eddy viscosity , k mixture and isolated liquid, gas, and vapor densities cavitation index [(p -p c )/(0.5 U 2 )] 1. Introduction Supercavitation is a concept for high speed watercraft that in short, reduces the overall vehicle drag coefficient by reducing the viscous component of drag. This viscous drag component is reduced by enveloping the vehicle in a less dense and less viscous medium, normally air or water vapor, which has roughly one-hundredth the molecular viscosity and one-thousandth of the density. Compared to design procedures for other vehicles, such as aircraft, rotorcraft, ships, and submarines, the hydrodynamic design procedure for supercavitating vehicles is not well understood. Traditional analysis methods are described by semi- empirical relations (Semenenko, 2001). For a fully enveloped configuration, such empirical relations can fairly well predict ventilation rate to cavity pressure (C Q - ) relationships, cavity profiles, cavity elevation due to lift and buoyancy, and the idealized vehicle drag. These methods are extremely fast, accurate, and are considered to be standardized design-level analysis methods. Other methods, including those based on potential flow (Kirschner, et al., 2001 and Young and Kinnas, 2003), can predict the cavity shape with fewer constraints than the empirical methods. These methods rely heavily on cavity closure models which remain a research topic. Furthermore, interactions with propulsors, hysteretic behavior, and other inviscid, viscous, and any unsteady interactions require further modeling efforts. Two methods that may be straightforwardly applied to such cases include water tunnel experiments and a multiphase, finite-volume computational fluid dynamics (CFD) approach with modeled turbulence. Physical experiments HPCMP USERS GROUP CONFERENCE 2007 (HPCMP-UGC 2007) 0-7695-3088-5/07 $25.00 © 2007