S. A. Kinnas;

S. A. Kinnas

Massachusetts Institute of Technology

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W. B Coney

W. B Coney

Massachusetts Institute of Technology

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Paper presented at the SNAME Propellers '88 Symposium, Virginia Beach, Virginia, USA, September 1988.

Paper Number:
SNAME-PSS-1988-01

Published:
September 20 1988

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

On the Optimum Ducted Propeller Loading

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.

The preliminary ducted propeller loading has been

selected to minimize the absorbed power for a given

thrust of the propulsor. The optimum ducted propeller

loading has usually been determined from momentum

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

ducted propeller loading by representing the propeller

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

that area have been published by Morgan[UJ, Caster[ J

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 fs_{0 }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)

an_{0 }

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