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
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