A cavitating blade design technique (CAVOPT-3D)
was developed recently [28, 29].
The method consists of a non-linear optimization algorithm
which under given certain design conditions and constraints,
produces the most efficient cavitating propeller design. Design conditions
required by CAVOPT-3D include; advance coefficient ( 
), the wake inflow,
cavitation number ( 
),
Froude number ( 
), number of blades (NBLADE), hub radius ( 
),
and thrust coefficient ( 
). This method also provides the user with
the option of imposing constraints on the propeller design. The cavity area
constraints, CAMAX and FAMAX, limit the amount of back and face cavity
area respectively. The skew constraint, SKMAX, limits the maximum skew angle
at the tip of the blade. VVMAX limits the values of the cavity volume
velocity harmonics, which are directly related to the magnitude of
the hull pressure harmonics. The quantities used in CAVOPT-3D are
are determined
via quadratic expansions of the results from THPUF-3A in terms
of the blade parameters. CAVOPT-3D usually takes several
hours on a DEC Alpha to reach a ``convergent'' blade geometry.
The following study uses CAVOPT-3D to
produce cavitating propeller geometries with combined forward and
backward skew. This is accomplished by allowing for a quadratic
expression for skew rather than a linear expression. The description
of the skew consists of the skew at the tip of the blade, as well as a new
parameter, RFOR, which defines the radius at which the forward skew
reaches a maximum value.
For this study, the following design conditions were used:
, 
, 
, NBLADE = 3,
, 
. These are the same conditions as given
in [28]. The wake inflow is the same to that shown in Fig.
5.
Three cases were run for these design conditions, each with
different imposed constraints. A summary of the imposed constraints
are given at the top of Figure 11. Run 1 imposes no constraints
and no skew. The resulting blade geometry has excessive amounts of
cavitation. Run 2 imposes maximum quadratic skew of 
(RFOR=0.4)
and a maximum
cavity to blade area ratio equal to 
. Run 3 imposes the same constraints
as Run 2 and, in addition, imposes a limit on the cavity volume velocity
to a 
lower value of that from Run 2. Notice that the resulting geometry
slightly violates the constraint on CVV (CVV>VVMAX). Also notice the
smaller cavity volume of Run 3 to that of Run 2 (at all blade angles).
As expected Run 3 is more loaded at the hub and less loaded at the tip
in order to have the cavity volume reduced at the tip while maintaining the
same thrust.
Figure 11: Results from CAVOPT-3D. The constraints for each
of the three runs are shown at the top part, and the resulting geometries are shown
at the bottom part, together with the resulting cavity patterns at a blade angle
of 
.