THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS
601 Pavonia Avenue, Jersey City, NJ 07306
Paper to be presented at the Propellers '88 Symposium,
Virginia Beach, Virginia, September 20-21, 1988
No.1
S. A. Kinnas, Associate Member and W.B. Coney, Student Member, Massachusetts Institute of
Technology, Cambridge, MA
All of the previous methods however, have assumed
that the interactions between the duct and the propeller
were axisymmetric.
It is only recently that the non-axisymmetric flow in
ducted propeller has been adressed by solving for the
flow around the duct induced by the non-axisymmetric
flow field due to the propeller. VanHouten[15) and Feng
and Dong[5) have published works in that area.
Abstract
A
numerical approach to determine the optimum circ~•
18
lation distibution of a propeller inside a given duct
presented. The propeller blades are modelled by lifting
lines. The duct is represented in non-linear theory by
a
using a potential based panel method.
The propeller lifting lines are approximated by a fi•
nite number of vortex horseshoes. The strengths of the
horseshoes are determined by using a numerical non•
linear optimization technique to maximize the pro~ulsor
efficiency. The non-axisymmetric duct/propeller inter•
actions are included within the design procedure.
Results are presented for propellers designed to op-
Very recently, Kerwin, Kinnas et al.[9) have devel•
oped
a method for the analysis of ducted propellers in
which the flow on the duct is analyzed by using a poten•
tial based panel method and the flow on the propeller is
analyzed by using a lifting surface method. In that work
a
strong angular variation of the circulation around a
duct, and of the pressure distributions on the surface
of a duct working with a propeller, has been presented.
They conclude that the circumferential variation of the
duct-propeller interaction is important and should be
·
· 'd f two different
erate at various thrust coe c1ents ms1 e 0
ducts and at several advance ratios.
ffi
included in the analysis of the flow of
peller.
a ducted pro•
1
Introduction
Ducted propellers have been an alternative form of
propulsion during the last sixty years with aplications
ranging from supertankers to remote operating :ehicles
and fishing vessels. Their purpose has been either to
increase efficiency or to reduce the cavitation of the
propulsor as well as to protect the propeller from dam•
age.
The analysis of the flow around a ducted prope!ler
has evolved together with the evolution of numerical
methods for the analysis of the flow around propellers
The design of ducted propellers until recently, has
been achieved by a "trial and error" procedure. In de•
tail, for specified advance coefficient, thrust coefficient
and duct thrust/propeller thrust ratio, a preliminary
design is determined. That design is then conseque•
tively modified and verified by using any of the previ•
ously cited analysis methods, until the design objectives
are met.
selected to minimize the absorbed power for a given
thrust of the propulsor. The optimum ducted propeller
theory. This procedure, however, does not allow for
finite number of blades and for detailed duct geome•
try. Sparenberg [18J and [19J determined the optimum
and ducts.
The first generation of analysis methods _represe~ted
the duct in linear theory by distributing rmg vortices
and sources on
a approximate mean surface. _T~e p~o•
peller was represented by using actuator disc, hftmg h~e
or lifting surface theories. Some representative works m
3
with lifting lines and the duct with
a concentrated ring
and Dyne[6].
vortex of varying strength circumferentially.
The next generation of analysis methods represented
In the present work a new approach is developed
in order to determine the optimum circulation distribu•
tion of a propeller operating inside a given duct. The
propeller is replaced with lifting lines, which are then
approximated by a finite number of vortex horseshoes.
the duct in non-linear theory by distributing surf~e
vorticity on the duct, and represented the propeller with
actuator disc or lifting line theory. Ryan and Glover[l7),
Gibson and Lewis[7) and Falcao de Cam~os[~) ar~ some
of the investigators who have made contr1but1ons m that
area.
1-1
C
.
a.r theory by using
.
ented m non-\"me
h
The duct is repres
h d The strengths of t e
. \ based pane\ met o .
d"
a potent1a
d
th the prope\\er \oa mg
,
lifting \ine horseshoes, an
us . e the propu\sive
.
Ct
·
d such as to max1mi1.
.
d
a.re then etermme
.
.
\
non-linear opt1-
.
ffi . y by usma a numenca
0
device e c1enc
mintion techniClue.
t d design approach are
X
T
he advantages of the presen e
_
__.. ___
threefo\d.
-- ----
----·
t· \ way to deter-
h
1t offers a. systematic mat ema ica
.
mine the optimum ducted prope\\er \oadmg.
The duct is represented in non-\inear theory
within the design procedure
.
T~e non-a.,dsymmetric duct-prope\\er interactions
are considered within the design process.
Figure 1: Geometry of the Duct
An
th
a
lysis of the Flow Around
2
e
Duc
t
plane ca be seen in Figure 2. The \ifting \ine is lo~ate~
at :t = n:tu
a
nd the corresponding prope\\er radius 1s
to the adius of the duct at :tu, as shown
The geometry of the duct as shown in Figure l is defined
by the fo\\owing parameters:
defined equa
\
r
in Figure 2.
The perturbation potentia\, </lo
found by applyin Green's theorem on the duct surface:
,
on the duct can be
The chord\ength, c, which is defined as the nose•
tail distance of the duct section.
g
The radius, R.n, at the nose of the duct.
o
l
2rr4>o(P) = f fs0 l<l>o(Q) ono R(P; Q)
The ang\e, a, of the duct section with respect to
the axis of the duct.
o</>olQ)
an0
1
\dS
R
(P; Q)
The section of the duct, defined as the cut of th
duct with the meridional planes.
e
a
1
+ JJsw 6.</lo(Q) anQ R(P; Q)dS
The camber distribution, J(:z:), and thickness dis•
tribution, t(:z:). of the duct section, defined in the
same way as for a hydrofoil section. Positive cam•
ber points inside the duct.
+
47r
,j,LL(P).
(2)
P corresponds to any point on the duct
s
urface
So.
The ducts to be considered in this paper are ax•
Q corresponds to any point on Sv and the duct
isymmetric. A brief discussion about the treatment of
non-axisymmetric ducts can be found in Section 7.
The flow around the duct is assumed to be inviscid,
incompressible and irrotational. lf the incoming veloc•
ity field is given by Um, then the velocity flowfield, q,
around the duct can be expressed in terms of the per•
turbation velocity potential, ,J,, defined as fol\ows:
wake surface Sw.
R( P; Q) is the distanc
e
between the points P and
Q
and actually corresponds to the infinite fluid
domain Green's function.
cl>LL is the potential on the duct due to the pro•
peller lifting lines.
• t:.¢0 is the jump of the potential in the wake of