On the hydrodynamic characteristics of ducted propeller in uniform and non-uniform flow

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HØVIK OUTSIDE OSLO, MARCH 20. - 25. 1977

"ON THE HYDRODYNAMIC CHARACTERISTIC OF DUCTED

PROPELLER IN UNIFORM AND NON-UNIFORM FLOW"

By

H. Okamoto and K. Nozawa Kawasaki Heavy Industries, Ltd.

- Kobe Works -, Japan

F

lío

,

3 SEP. 184

ARCHEi

SYMPOSIUM ON

PAPER 20/4 - SESSION 2

¿4')

Lab.

_{y. Scheepsbouwkunde}

Teclin;sche Hogsclioo1

Oeift

On the Hydrodynamic Characteristics of 1)ucted Propel 1er In Uniform and Non-lJniform Il ow

by Ii. ()kamoto* and K. Noz;lw;.'*

Summary:

A theory is described for the calculation of the hydrodynamic characteristics of the ducted propeller (hereinafter called "D.P. :) in uniform and

non-unIform flows. Some calculations about the hydrodynamic characteristic.'; and velocity fields are presented and agreement with experimental results is shown to be good.

Furthermore, the interaction of the D.P. and the body of revolution or rudder is investigated.

As a result, it is cleared that the D.P. characteristics are affected by nominai wake (especially radial wake) and induced wake due to interaction of the D.F. and hull or rudder, and these characteristics are much different

from the D.P. characteristics in a uniform flow and that this discrepancy is considerably larger than in the case of the conventional propeller

(hereinafter called "C.P.'T).

In conclusion, it is shown that the above-mentioned nominal wake and induced wake must be fully considered in the D.F. design and analysis of self-propulsion test.

1.

Introduction:

[n the ami lys is of seh-propiilsioii test of l).F.-equipped ships.

The

method

using

the open propeller characteristics has been

conventionally adopted as well as in the case of C.P.-equipped ship.

lin comparison of these propulsion factors,

the following problems may be pointed out:

[11

[2].

There is a considerable amount of difference between each

propulsion factor in D.P.-equipped and C.P.-equipped ships.

Individual components of the D.F. ch,aracteristics, Ktn, Ktp, Kq,

etc. obtaiiie

by

the analysis of self-propulsion test for

a D.P.-equipped ship have mitch difference from these of the

open characteristics.

In connection with (2) above, the impeller thrust ratio for

total thrust

t'

has increased more than

Z'

which is to be

expected by the D.P. open characteristics, and this tendency will

make decrease in the efficiency.

These matters show that the inflow velocity distribution, i.e. the

nominal wake of the hull and induced wake due to the interaction of

the D.F. and hull or rudder will largely give Influence upon the D.F.

and that

characteristicsT7fore, by Investigating the following twu pit11s('.

D.P. characteristics in the non-uniform flow, and

D.F. characteristics due to interaction with the hull or the rudder,

the above-mentioned problems should be cleared and as a result of it,

method

an analysis of self-propulsion test appropriate to D.P.-equipped ships

will be established.

The calculating method referred to in this paper will be applied as one process of such analysis method.

lt is described here that wake distribution will largely influence the D.P. characteristics, by calculating these

condition

characteristics in each of uniform flow, axisyimrietrical flow and non-uniform flow. Furthermore, as the D.P.-hull interaction, it is shown that the D.P. characteristics

will be largely affected by the nominal and índuced wakes but the C.P. characteristics will be hardly affected.

And it is shown in the end here that

in the D.P.-rudder interaction, the induced wake of the rudder makes the nozzle thrust decrease and makes the impeller thrust and torque increase and therefore these characteristics becomes different from the D.F. open characteristics.

2. Calculation of Ducted Propeller Performance:

2-1 General Flow Chart:

The General Flow Chart of the D.P. calculation is shown in Fig. 1, being briefly composed of four blocks, ,

(3

,

(3 ,

and

(3.

The function is outlined as follows:

Q:

Inputs of D.P. Geometory and Wake Distribution, Fourier Analysis.

The part that separates the axisyrnmetrical nozzle component in the axisymmetrical flow and the non-axisymmetrical nozzle component in the non-uniform flow, and delivers them to (3

Axisymmetrical Ducted Propeller Calculation in Axisymmetrical Flow:

The part that satisfies the boundary conditions of the impeller and nozzle with the iterative method, and calculates the flow fields around D.P., pressure distribution and D.P. characteristics.

Non-axisymmetricalDucted Propeller Calculation in Non-Uniform

Flow:

The part that calculates the non-uniform vortex distribution of the impeller due to non-uniform flow components, induced velocities to the nozzle position thereof, and the lifting surface of the non-axisymmetrical nozzle, etc. As a part of this calculation, the result

f above is applied.

The part that outputs each induced velocity, pressure, and characteristics calculated in and above.

As for the D.P. characteristics due to the D.P.-hull interaction and D.P.-rudder interaction, these calculations are simplified as an

axisymmetrical problem and ignored the viscous effect because of these complexity. The thrust deduction was also calculated on the same assumption. But it is not deeply discussed here on account of limited space.

2-2 Calculation of Ducted Propeller:

(1) Ducted Propeller Characteristics in Axisymrnetrical Flow: For quantitative calculation of the performance of the D.P., it is desirable to apply the lifting surface theory as well as

But, calculation of the characteristics of the D.P. requires great calculation compared with the C.P. because mutual influence of the nozzle and the impel 1er is entangled iii the non-1 i tìe;1 r i

ypt'

So calculating method of the D.P. characteristics was shown under

following assumption in this paper.

The nozzle lifting surface is dealt with as a cylinder, and the camber and thickness are replaced by the vortex and source distribution.

The impeller is r.placed in the lifting line of finite number of blades, and only steady components of the induced velocity is to affect the nozzle.

Water viscosity is ignored, but the local drag coefficient is induced only when calculating forces of the nozzle and the impeller.

On the above-mentioned assumption, the characteristics and the velocity field of the D.P. can be calculat:ed through the following four iterative process. i.e.

Calculation of given impeller alone

Calculation of the average velocity field of the impeller Calculation of the nozzle characteristics in the velocity

field of (ii) above

Calculation of the nozzle induced velocity at the impeller position

Outline of this calculating method is shown as follows but in detail, references of the authors' [3] can be referred.

Many theories on the propeller lifting line theory with lifting

surface correction have been issued and lifting surface correction method basing upon the Lerbs's method [4] is applied here. Its outline is shown as follows. The coordinate system is given as Fig. 2.

If the non-dimensional value of the circulation distribution

r

in the radial direction of the impeller is set to

L4

TfWs

r

₍₁₎

where, Dp is the propeller diameter, and

_¿J.

is the ship's speed. Now, the following (r.r') are transformed to (

f

% ) which are

concerned with the following equation.

7(ui-7)_

whe re

R

By giving P, ₉ and free vortex pitch angle , the

induction factor , are obtained. From both the Fourier

9 sin coefficient of and the function

(9)

obtained from the Fourier cosine coefficient i, of _{z ,}

following simultaneous equations for of the impeilur willi givuil shape can be obtained.

71ii O 1dÇ

j3. -ßd :i

¿ M

(3)

- 7rTh9,7

(4)

tJ

f - ¿Op (so) +

_{+ ZUd/t5}

74

(5)

where,

fl

: number of impeller revolution _Q : chord length

d CL

lift slope zero lift angle

axisymmetrical wake : impeller induced velocities

¿lid

nozzle induced velocity (3d : nozzle induced inflow angle

By solving these simultaneous equations by the iterative method,

=tanf3.

are obtained. In detail, the lifting surface correction

[51 about the pitch angle and camber is applied to Eq. (3) above.

Next, induced velocities of the impeller to the nozzle position must he calculated. As stated in 2-1 above, an assumption that only steady components of impeller induced velocities influence the nozzle is equivalent to an assumption that the impeller has infinite number of blades. Under this assumption, calculation of its induced velocities become very simple and equations can be shown in the following.

Ua

2

-

_!

_{('Á(e4.j(f',)d.5-_L I'L.X (ì;}

Lia. -

2)4

f

=

__L

U-'('A)J

-Ç- T (q; ,)p)d

(Ja.

27

i

Va

J

Suffix b and f each shows the induced velocities by the bound vortex and free vortex, and

and Wbecome zero.

Moreover,

T, Xf, 1

and are shown by the elliptic integrals, available for easy calculation by means of,a computer [3].

_Tp

is the non-dimensional circulation distribution with infinite number of blades, being in the relationship of

27T(5°0)

With this, the impeller induced velocities at the nozzle position are

obtained.

Next, the boundary condition for nozzle lifting surface is shown.

As shown in 2-1 above, on the assumption that the thin wing approximation would be applicable to the nozzle, the boundary condition will be enough

for being satisfied with the nozzle camber, and the condition that the flow follows the given camber will result in the following equation.

1L

Wz

-

=O(fl

(7)

(la

Dr. Hanaoka [6] has deduced is obtained as follows.

«) f'

_{sr (-}

_(w(-j'i)c'-

L

f'

T'(Ii) d'

27t

_ç-ç

271

where,

S?flX 4-(iii)

and

5(iz) ;

induction factors of the

annular lifting surface, W

;

Where, and are based ori impeller induced velocities

and

nominal inflow velocities, besicles nozzle induced velocities.

And

ris the nozzle camber and

is its tangent

Now, the induced velocities

Lia ' Lia

of the nozzle circulation

distribution

are represented as follows, using the complete

elliptic integrals; provided that the coordinate system is taken to the middle of the nozzle length and that etc. re non-dimensionized variables by the half length of the nozzle and,

7

is by the inflow velocity _Ua..

It' Lia

-

-:-f_1;i

{(

E(i)

(k()E())J'

_

'1' {

E(k_

_{2(fc(k)-E())1'}

Ua - 71J"

ç)Z(79j')2J%

_i-E

(8)

By setting up

'-*7'

by substituting Eq. (8) into Eq. (7), and by taking into consideration of the singularity of kernal function

the integral equation of annular lifting surface

In addition, as for the nozzle thickness, by using the non-dimensional source density i which can be obtained by the thin wing approximation

is used, its induced velocities can also be shown in the elliptic integrals.

In the D.P. calculation,

j,

(3

_ß

, and can be obtained

which satisfy the boundary conditions of both impeller and nozzle by carrying out the iteration of (i) through (iv).

If reasonable quantities are obtained, the total velocities in the nozzle surface can be easily calculated from Eq. (10) and the pressure

distribution is obtained by Eq. (11). Furthermore, the D.P. characteristics such as nozzle thrust Ktn, impeller thrust Ktp, torque Kq, coefficient

etc. can be obtained by applying the Kutta-Joukowski Force and drag coefficient derived from local viscosity coefficient Cd.

= +

wl

+

W'z

Va

(Ja

2

Ut,, r

+

₊

UJpr

Va

U2

iLl,

a

r

PPc0

L-P'

f

¿j2 -

i

-(L2 i

L. (Ja

LIc»J

(2) Ducted Propeller Characteristics in Non-Uniform Flow:

This calculation become considerably complicated because of its circumferential non-uniformity compared with the axisymmetrical flow calculation stated in (1) above. Therefore, the calculation is made here on the following assumption:

a. The impeller circulation distribution is approximated with the distribution

tp(Dof

infintte number of blades.

Accordingly, the calculated induced velocity is non-uniform but steady.

Free vortex pitch

_2Jt

being obtained in axisymmetrical calculation (1) is used.

The free vortex generating from the nozzle vortex distribution extends parallel to the axis, infinitely backward.

lic!

Now, the outward normal vector

4 (X,r,9)

ori the nozzle camber and the total velocity vector are given, and these

axisymmetrical components _{4 ,} and the non-axisymmetrical components are separated and shown as in Eq. (14).

(4 cosfl9 + Bs1»)

(13)

The non-uniform inflow is assumed to he potential flow.

No influence f the non-uniformity upon the nozzle thickness is taken into account in particular.

Now, the outline of the calculation is shown as follows.

inØ

of

the General Flow Chart, Fourier expansion in the circumferential direction is made for the nozzle camber and the non-uniform flow, and coefficients of Eq. (12) and Eq. (13) come to be known.

r'(z,e)

a0(1)+(a.cosn9+bsmn9)

_{(1 2)}

1, i

Ix (

,9) =

c.&s P19

Sin ne)

)fl. r.)

=

Pl(z,r) + rIfr7((,V.t9)

U(7r.)

&.Y) +1('J)

(14)

At first, it is considered about the boundary condition which should be satisfied on the nozzle surface.

As for the normal velocity of the nozzle, by separating an independent item and a dependent item to Q and by setting each item to zero, Eq. (15) and (16) are obtained, on condition that

_eIfr7.Q1

is negligible

amount,

?Lin =0

L11L

-17Z=O

(16)

Eq. (15) is corresponding to the axisymmetrical calculation dealt with in Flow Chart and Eq. (16) is corresponding to the non-axisymmetrical D.F. calculation in the non-uniform flow dealt with in

In Eq. (16), leaving only the non-uniform nozzle induced velocities

(11Jz

and

11Jp ),

and all of the remains are transformed to the right side, Eq. (17) is obtained.

LW,x flx +

fly

_[(+lz).

+1y+AWr)flr

+ Ux

+Üflr +

(17)

The content of the right side of Eq. (17) is as follows:

Liz, Uy, Us

: Total velocity components obtained by

axisymmetrical calculation

, : Non-uniforni components of inflow velocity

Eq. (19) are obtained.

N

ßflz

Lfl9=

and non-uniform component

I

X

(E

cosfl& -f.

¡flSMfl9)

,1 I e-

&

(E

cas fl9

s;ow)

CI

In addition,

_/

_flz,

_fly.

etc. are only depending

on ,

obtained by the axisymmetrical calculation

).

Next, the non-uniform components of the impeller induced velocities

and

can be calculated in the following manner:

i.e.

the vortex distribution ',,9)of the impeller

is supposed to be

given in Eq. (20) as a sum of the

axisymmetrical component

_'Tpo

(19)

¿flz,4flr,6)7

t

_{Axisymmetrical and non-axisymnietrical}

components of outward normal vector on the

nozzle camber

The

non-dimensional vortex distribution of

the

nozzle is put as Eq. (18).

A A N A

1 (;')

=

Ao') -F21 (Ah.cosfl6 B')smt)

(18)

Now, the non-uniform indued velocities and

_LU1,U

of the nozzle

in Eq. (17) can be represented by the integration along the nozzle length, including M(')in Eq. (18), and they will result io the shape of the Fourier series by picking up of the coefficients of

CoSflG

and

SMfl9

On the other hand, considering the right side of Eq. (17), the non-uniform inflow velocity components are given by the Fourier series shown iñ Eq. (13), and the non-axisymmetrical outward normal vector components are obtained from Eq. (12) and coefficients of

M

(21)

mI

and can, if this , i.e.

[Tr4 [j

, and the free

vortex pitch are given, be obtained as Fourier series same as Eq. (13)

by applying the Riot Savort's law. This Fourier series are comparatively complicated and indicated as a multiple integration including elliptic integrai, modified Bessel function, modified Struve function, whose concrete shape are referred to the reference [3].

Next, as for the relationship between and the non-uniform flow velocity in Eq. (13), it is thought reasonable that, strictly

speaking, an unsteady calculation [7] is made to obtain the circulation distribution of the impeller.

But, it is difficult to apply directly this method to the D.P. case from

view point of calculating amount, for Which the fol lowing method is apl led. The steady prope 11er lifting surface cal co I atino is made, as quas i-steady problem, for the advance ratio

J()

based on the axial velocity at each blade position and the non-dimensional circulation distribution

is obtained.

í7Js;?19'

=

Zoô+

7()

(20)

Among them,

7po

has been already obtained in the axisymmetrical calculation as in Eq. (21). On the other hand, , as in the

It was found from this calculation that the shape of G for different J

is of near similarity, having peak value ar =

0.7 and that only

the peak value changes as

J

does. Therefore, by using the

relationship

between peak and

_{J which}

is

calculated beforehand,

Ç-

peak for the

non-uniform component AlJ i.e.49. is obtained,

arid furthermore

Fourier coefficients are obtained from

obtained therefrom, as

[Tm1

'

[Im]

. L1J9.

is considered to be an apparent difference of the impeller revolution number, but Is ignored.

With the above, the

non-uniform components of the impeller induced

velocitíes,U)pz and

lIJpr are obtained as the Fourier series same as

in Eq. (13). The coefficients obtained here, are written as

,z ,r

Both sides of Eq. (17) are all represented in the

Fourier series as

such,

and accordingly, if each coefficient of

C0Sfl0 ,

S»Ifl&

is equally positioned,

Eq.

(23) cari

he obtained as integral

equations for the nozzle distributions

Eq. (18).

r,

p.

i

F&ri3C4*'

cos-type

J-I

Ç

3d=-

5Lc)

J -1 --

!

/711

E]

'r1

5n() -[(B+bfl (6

r*fl

U91+v1J

Provided that, the coordinate system

is transferred to the

nozzle

center and

,

are non-dimensionized

by the half length of the nozzle The disturbance function

Cn) ,

and

5")

are composed of the above-mentioned Fourier coefficients.

sin-type

This is the kernel function which is obtained by applying the Blot Savart 's law from both the non-un i form bound vortex on the nozzle cylinder and the non-uniform free vortex which extends infinitely backward starting therfrom, and the shape of

becomes corresponding to the induction factor of the non-axisymmetrical nozzle lifting surface in a non-uniform flow. This

is composed of _1X3 and

_[R]

obtained by the bound vortex and

[Rj

by the free vortex, each being represented by the elliptic integral, which will be referred to a reference [3].

A

If An and Bn are obtained, the non-uniform components of nozzle induced velocities can be calculated [3] of Fig. i shows the iteration process between impeller Nozzle for the above-mentioned calculation.

In such manner, the results of Steps and are summed up in to obtain the total velocity field, and the pressure is obtained from Bernoulli's law, and forces is obtained from Kutta Joukwski's law. With the above, the calculating method of hydrodynamíc characteristics of the D.P. have been briefly shown.

3. Performance of Ducted Propeller:

3-1 Ducted Propeller Characteristics in Uniform Flow:

By applying the calculating method shown in (2), the D.P. and the C.P. characteristics and velocity fields were calculated. Table i shows the particulars of the D.P. No. 1, No. 2 and the

3

:ìLL

(J.

(1) Characteristics of Ducted Propeller:

Comparison between the calculated and measured characteristics for the D.P. No. I and the

C.P. is shown in

iTigs. 3 and 4.

Among them, Fig. 3 shows the characteristics of the impeller alone (without nozzles) (hereinafter called "C.P."), Fig. 4 shows the characteristics in case of the D.F.

As for the C.P. case, the comparison between the calculated

value and the experimental one shows that thrust coefficient

Kt is in good accordance, torque coefficient Kq is a little high in the calculated ne and accordingly the efficiency 'p shows

a little high in the experimental one. On the other hand, in the characteristics of the D.P., the calculated value of the

nozzle

thrust Ktn is a little low, but impeller thrust Ktp and torque Kq are almost in accordance with the experimental one. Lt is not clear why the calculated value of the nozzle thrust became lower as such. As stated in the calculation assumption in 2. above, however, it may be thought as one of the cause that finite number of blades and the width of the blade of the impeller have not been taken into consideration. But, so far as the D.F. characteristics can be calculated in such extent of accuracy, it would be sufficiently applied to comparison between performance of the D.P.s with various

geome tory.

(2) Velocity Field around Ducted Propeller:

About both D.P. No. i and the impeller alone (C.P.) each flow diagram is shown in Fig. 5 and Fig. 6, as comparison between

calculated and measured results when operating with J 0.4 (V = 1.0 m/s,N = 15 rps; uniform flow).

From these figures, detailed comparison between the I).P. and the C.P. cari be be made as follows.

Comparatively good accordance in the calculation and the experiments ís found in both propellers, and it is cleared that not only macroscopical characteristícs but also microscopical flow field can be sufficiently estimated by this calculating method shown in 2.

II From the flow pattern around the tip of the impeller of the D.P.,

the flow begins to contract from = x/R = -1.3 (forward of the impeller), and after then, flows into the impeller with inclination of about 200. But, the flow behind the impeller is almost parallel to the shaft with influence of the nozzle and no contract is almost found.

III In case of the C.P., the flow begins to contract from = -0.6 or -0.7 and then, strongly contracts at the impeller with an inclination of about 100 and comes again gradually to a parallei flow in a symmetric shape with respect to the impeller. The ratio of contraction of the

backward flow becomes about 0.85. Therefore, the measured fiow field of 0.9 < nR < 1.0, behind the impeller, is

just coming to the tendency without free vortex.

IV As a comparison of the flow pattern between the D.P. and the C.P., considering each propeller load, it can be found that in case of the D.P.,,the axial velocity in front. of the impeller is larger

and contraction is also stronger in spite of the l).P. load

being low as compared with the C.P. case. This is because the nozzle projects forward the impeller and the inward

to the above flow contraction.

V From such results, it is expected that the D.P. wilt hnve stronger interaction with the hull and therefore the 1).P.

characteristics will be strongly influenced by deformation of inflow velocity due to this interaction. And the thrust deduction fraction t also will become larger than the C.P. case.

3-2 Ducted Propeller Characteristics in Axisymmetrica Flow:

The wake distribution around the propeller position is generally non-uniform to some extent.

As an example of this, the nominal wake distribution of VLCC model ship of Cb = 0.82 is shown in Fig. 7. This indicates the axial wake

distribution and the circumferential distribution of the radial wake. The inward radial velocity is indicated as negative. According to this,

flow

-it is understood that around nR = 1.0 comes to be about

iJ./iJ =

-having an inward velocity.

- o,o

That such "Converging Flow" will increase the nozzle thrust and result in decrease of the impeller load can be easily expected from the result of 3-1 above.

The D.P. characteristics in the axisymmetrical flow with axial and radial wake, are quantitatively discussed here.

Fig. 8 shows a sketch explaining the working condition of the nozzle in the uniform and axisymmetrical flows,. (i) shows the case ofuniform flow and (ii) shows the case of the axisymmetrical flow. The circum-ferentially averaged flow field of the shiphehind wake of a VLCC shown in Fig. 7 is also similar to the case (ii).

Now, how the flow diagram of the nozzle in cases of (i) and (ii) each will change is shown in the lower column.

In the uniform flow, the inflow velocity of the nozzle based on the impeller induced velocities

_{IJJjz and ttlpr}

and the uniform flow V are set as W (i) flow angle _¿3('g . But, in the rixisymmetrical flow,

UJ.

in the radial direction andttJHZin the axial direction are added the flow velocity willchange to W* (ii) flow angle 'z provided

that, for simplification in this sketch, tlìe impeller induced velocities

c7

in both conditions of (fl and (ii) are equal.

As easily expected from this sketch, IL is understood that increase in both W* and makes the nozzle thrust increase on condition that the nozzle will not occur flow separation and that Whr is effective for increase in both W* and , but Whx makes W* increase and

decrease and accordingly the nozzle thrust will not change so much.

Now, Fig. 9 shows the calculated characteristics of the uniform flow (a) of D.P. No. 2 together with the measured value with the number of

propeller revolution changed as 10, 15 and 20 rps. In addition, shown therein is the calculation (b) where only 1J(rwas considered as the

axisymmetrical flow and the calculation (c) where both and

_lJj.

were considered. _1J and

tir

are the axisymmetrical velocities obtained

from Fig. 7. From the result of these (a), (b) and (c), the following matter has come to be clear.

In comparison of (b) . which is the D.P. characteristics in the

axisymmetrical wake whose distribution is shown in the upper column of Fig. 9, and (a) which is the characteristics in the uniform flow, it is found as for (h) that the impeller load increases, i .c. Ktp and Kq increase aL the i ¡me the nnzz I e lii rus

Ktn decreases, resulting in decrease in the total efficiency

II The (c) , i. e. if the rad i al velocity

tjr

having i nward componen t

at the nozzle position is added to the condition el (b), Kto increases against the characteristics of (b), Ktp and Kq decrease and increases.

III As shown from the above I and II, axial wake distribution increasing outward from the center reduces the nozzle thrust, but inward radial wake makes it increase. These results are

in good accordanc' with tendency shown ín Fig. 8.

IV In this connection, the D.P. characteristics is considered to be largely subjected to the stern shape that has a strong relationship with the wake distribution.

With the above, it has become clear that, by calculating the charac-teristics of the D.P. in the uniform and axisymmetrical flows, the D.P. characteristics is largely deformed by especially the radial wake Vr, which has less meaning in the C.P. case, and these characteristics become different from the characteristics in the uniform flow.

3-3 Ducted Propel 1er Characteristics in Oblique Flow:

There are many re ferences aboti L the C.1 . cliarac ter Ist I cs i n tut' obi Ique

flow, for example, by De Santis [8] and etc. and it is concluded that remarkable changes in the characteristics have hardly been admitted to the extent of the oblique angle 5°. On the other hand, few full

investigations have been made about the D.P., besides only publication by Dyne [9]. The oblique flow is one of basic patterns of the

characteristics in the oblique flow. And so here, the characteristics in the oblique flow with angle of 0°, 5° and 10° about each of the D.F. No. 2 and the C.P. No. i were experimentally investigated for a comparison with the calculation.

The experiments was carried out in a circulating tank by using the open propeller dynamometer having been used, and so oniy thrust and torque were measured but the transverse force was not measured. Kq, Ktp,

Ktn obtained from torque and thrust of the impeller and nozzle thrust are shown in Figs. 10 and 11, with the advance ratio

i

V.cos«

considering the oblique flow angle . Fig. 10 shows the

characte-ristics of the D.F. case.

If the oblique flow angle is changed to 0°, 5°, and 10°, the nózzle thrust Ktn increases in this order. On the contrary, the impeller thrust Ktp decreases, resulting in some increase in the

total thrust Ktt.

The torque Kq reduces as well as in the impeller thrust.

Accordingly, increase in the oblique flow angle increases total efficiency at least in this experimental range.

Fig. 11 shows the oblique characteristics of the C.P. with this,

Increase in the ob lique f].ow angle reduces Kt and Kq a little, but these difference are smaller compared with those of the D.P. case.

The above results at J = 0.4 are shown in Table 2. According to this,

:

l01jM

The ratio of increase of the D.P. efficiency is about 1.9 Z in the oblique angle of 10°, but there is little difference

in the C.P.

Shown in the right side of Table 2 is the calculation result, being calcu lated in the same condition of the experiments. With this, the followings are known.

According to the calculation, the oblique characteristics of each componeot, Ktn. etc. are in qualitative accordance with

the experimental value; above all, Ktn has a good quantitative accordance.

The ratio of increase of the D.P. efficiency is 1.4 Z.

7. The nozzle thrust increases by about 7.6 , nearly equal to the

experimental value.

But, each difference in the thrust and torque of the impeller is considerably small compared with the each experimental value.

Like the above, the total efficiency or the nozzle thrust by the

calculation showed a good accordance with the experiments, hut the difference in the impeller thrust and torque became fairly extremely small compared with the experimental values. For this reason, it may be assumed that, change in the impeller characteristics obtained by

the experiments wi il be based on the viscous wake of the iiozz le in the oblique flow which has not been theoretically considered in this

cal cul ation.

Now, to investigate whether the above-mentioned increase of thìe nozzle thrust is reasonable or not, resistance of the nozzle alone in the oblique flow was measured. And, it was found that the

resistance decreases according to increase of the oblique angles as = 0°, 5°, and loo.

And furthermore, pure thrust values of the nozzle were approximately obtained by deducting the resistance at = 00 _{from the resistance}

at ' 5° and 10° respectively in order to make comparison with

calculated nozzle thrusts, and good accordance was obtained.

And it became clear that this values is nearly equal to the change in the nozzle thrust of Fig. 10 and so increase in the

nozzle thrust corresponds to increase in the axial component of the nozzle lift due to the oblique flow.

4. Interaction of Ducted Propeller and Body of RevoLution or Rudder:

As stated in the intrQduction, it is much important for

the D.P. design to make clear of the characteristics of the shipbehind D.P. and to establish analysis method of selfpropulsion tests on the

D.P. installed ships. For this purpose, in parallel with the theoretical and experimental investigations mentioned above, various propeller load test

by using

the body of revolution and VLCC model have been taken, and the influence of rudder and its clearance upon D.P. characteristics, wake and thrust deduction fraction were investigated. From the results

obtained at presen t, as an example, the D. P. characteris t ('S dUO to

the in terac t I on between the I).1' . and a body ol rovo I ut I ou nr n rudde r is shown here.

-4-1 lot e ra c tion o i ßodv o i Revo I uti on and )ii c t cd I rope i i or

An in vest i gaL ion i n t lic re i a t i on slìi p wit h t h o C. i' . was made iìow

the I). P. characteristics helìi od body of revol

ut

ion differs froni these in the uniform flow. The body of revolution is a wooden model of 1,000 mm in length with max. dia. of 290.9 mm. Its rough profile

is shown in the upper part of Fig. 13. The body of revolution is of 68° in its fore ending angle, and of 109 mm in radious of

curvature, being fairly of a blunt aft end shape. As for propellers, the D.P. No. 2 and the C.P. No. i were used as shown in Fig. 1.

The propeller diameter, Dp, is each 180 and 197.3 nmi, being considerably big propeller diameter compared with the dimensions of the body 01 revolution.

The body of revolution, by a vertical strut incorporated with a differential transformer for resistance measurement, is set 350 niui under the water surface of the circulating tank. In addition, considering influence of the free surface, the water surface at the upper part of the body of revolution is covered with a wave depressor of acryl-make.

Open boat was arranged behind the body of revolution, considering the axial clearance of the D.P. and the body.

Under this condition, D.F. and C.P. characteristics and resistance of the body of revolution were measured by changing the number of propeller revolution and velocity.

These measurements took place by changing the clearance between the

body of revolution and propeller in three kinds as = 0, lOO, 150 mm.

In case of the C.P. , sii iftitig each shaft (enter by i = 61) 111m at lOt) mm, measurements in case of extremely non-axisymmetrical flow was added.

Prior to this experiment, the nominal wake distribution at four sections between = 20 [tui to 150 mm backward the body of

revolution was measured with the five-hole pitot tube. It was found from this results that the high wake zone shifts a little upward in the axial wake distribution of any of the sections and that the secondary flow also has a little upward components.

These tendency will be due to wave depressor effect and etc.

By taking a circumferential average to obtain axisymmetrical components in case of Ç = 50 mm, it became clear that axial wake from the center to the propeller tip changes from 1.Tx/ij= 0.2 to 0.8 and inward radial velocity is -0.1 at the nozzle position.

/ a I

The characteristics of interaction of the D.P. or C.P. and the body of revolution are shown in Figs. 12 and 1.3.

';Hl

¡2

dThese

figures shows the torque Kq, thrusts Ktp and nozzle thrust Ktn, ()c1

1j.I)

Fig. 12 reveals the following matters:

Comparing the D.P. characteristics due to the interaction with its open characteristics, there is a tendency that the torque Kq and thrust Ktp of the impeller decreases and the nozzle thrust Kto increases at the same Ktt.

This will result in increase in the D.P. efficiency.

The tendency in i above is strengthened by decrease of the clearance.

These tendency of the change in the characteristics is very similar to the tetidency as a result of the ¿ixisymmetrical flow calculatioi'i of 3-2 of (3) above.

On the other hand, from case of the C.P. of Fig. 13.

There are few changes in the C.P. characteristics due to the interaction and characteristics of each case are close to the open characteristics. And this tendency maintains even in case

the propeller are positioned eccentrically by 60 mm and the flow field where the propel 1er is placed is extremely non-uniform. This proves that most of the change in Kt and Kq generating from the interaction will be due to change in J depending on axiaI mean wake.

From these relationship, it is expected that, in case of the C.P.. the non-uniform wake will not make so much the C.P. characteristics unreasonable change and therefore the effective wake will be

determined in comparatively a good accuracy by means of thrust or torque identity method having been used.

As a result of the above, it become clear that change of the D.P. characteristics due to the interaction with the 'body of revolution is considerably large compared with the C.P. case, and individual components of the characteristics become quite different from those in the uniform flow.

Such change in the D.P. characteristics may be summarized as follows:

Decrease of the clearance generally leads to decrease of the axial

mean wake and increase of the inward radial wake at the nozzle position. This leads to increase of the nozzle thrust and after all, decrease of the impeller load. Furthermore, induced wake due to the D.P.-body

4-2 Interaction of Ducted Propeller with Ruddcr:

Very few studies on the D.P.-rudder interaction have been made compared with the case of the C.P.-rudder interaction, besides experimental studies by English [101. But, in that paper, only influence of the rudder upon total thrust and torque was discussed and influence upon the impeller thrust and the nozzle thrust was not discussed separately. _{So, in order to make clear about the influence} upon each indivisual component of the D.P. and its hydrodynamical. Mechanism quantitatively, experiments

of interaction with the rudder were made here, using D.F. No. 2 and C.P. No. 1 and a consideration was made basing upon the D.P.-rudder interaction by the calculation shown in 2.

These experiments were taken place in a system of (D.F.) + (Rudder) at our water

circulatingtank. The rudder is penetrated by the propeller shaft

projecting forward the open boat, and set with given axial clearance back of the propeller. This rudder is the reaction rudder designed for D.P. No. 2, its profile being of h x h x t = 289 mm x 236 mm x 36.4 mm, t/b = 15.5 %. _{Fig. 14 shows a case of the D.F. The clearance} is set as the distance _{between the generator line (no skewed) of} the impelLer and the fore end of the rudder, being changed in three kinds - 45, 60 and 75 mm. Fig. 15 shows a case of the C.P. , the

clearance being changed to four kinds - 30, 45, 60 and 75 mm. The

clearance in the actual ship correspondsto about 45 _mm.

From Fig. 14, the followings became clear about the D.F. characteristics.

(1) _{ln the characteristics with rudder compared with these without} rudder, the impeller load, Ktp and Kq increases at ihe same

advance ratio, but the nozzle thrust, Ktn, hardly changes or reduces a little. Therefore, the increase in the total thrust, Ktt almost equals to the increase in Ktp. In addition, the impeller thrust to total thrust ratio r = Ktp/Ktt in case of

with rudder increases.

To make more concrete as for the above-mentioned change, a case of the clearance _Q 45 min with J = 0.4 is shown as follows:

The tendency in (i) above abruptly becomes strong as the c learmice decreases. But, each increasing amount of the characteristics is almost constant for change in J under the same clearance.

As explanatory from the tendency in (1) and (2) above, the

individual characteristics, Ktn, Ktp . .. of the D.P. varies in

different ways by fitting the rudder from the characteristics in the uniform flow.

For more concrete indication of the tendency in (3) above, the individual characteristics with rudder at J = 0.4 is plotted on the open characteristics curve, being shown in the same figure. With this,

(i) With rudder (ii) without rudder [(i)-(ii)] /Ktt,Kq(ii)%

Ktn 0.054 0.054 0 0 Ktp 0.234 0.198 +0.036 14.2 Ktt 0.288 0.252 +0.036 14.2 Kq 0.0384 0.0341 +0.0043 12.6 0.4774 0.4704 +0.007 1.5

t

0.8125 0.786

It is difficult to fully explain about remarkable changes in the 1).P. characteristics by the rudder as a change in the axial mean velocity, i.e. J and the influence of both induced velocities _7Jc and by the rudder, upon the D.P. should be taken into consideration.

From some theoretical calculation about the D.P.-rudder interation, using axisymmetrical calculation method as shown in 2. above, the qualitative tendency in the characteristics change was in good agreement with the above-mentioned results, hut quantitatively these change were about half

thr

experimental values respectively.

According to this calculation result, it became clear that the rudder placed in the D.P. race induces negative axial velocity and outward radial velocity as a circumferential average, and that this reduction of the axial velocity increases each of the characteristics values as decrease of J, and that the outward radial velocity decreases the nozzle

thrust and increases the impeller load as self-explanatory from the D.P. calculations in 3-2 previously.

lt can he understand that mechanism of the change in the l).P. characterist ics in Fig. 14 is good accordance with the above.

Stated next is about the case of the C.P. according to Fig. 15.

In the characteristics with rudder, both [(t and Kq increase compared with the case of without rudder. This tendency strengthens as

the clearance _Q decreases. Changes in case of 45 mm at J = 0.4 are shown as follows.

-From these, it became clear that changing values of the C.P. characteristics are small as compared in case of the D.P.

(6) If the characteristics value with rudder on condition of J = 0.4 is plotted on the opei characteristics curve as well as in (4) above, it became clear that Jq and Jt, torque base and thrust base advance ratio respectively, are nearly equal and, in case of the C.P. , the unreasonable change of the characteristics due tò the rudder is small and so this is mostly based on change of J due to decrease of the axial mean velocity by the rudder.

Furthermore, it is admitted that this tendency is in good agreement with the theoretical calculation. But, quantitatively, as well as

in the case of the D.P., it comes about half the experimental value. These quantitative difference between the measured and calculated values may he accounted for ignoring about non-uniformity of the rudder induced velocities, property of the rudder as a lifting body, and uns teady effect, etc. , hut it is ¡lot discussed here.

With the above, the mechanism of the interac t ion of the D. P. or the C.P. and the body of revolution or the rudder has been cleared quantitatively.

(i) With rudder (ii) Without rudder I (i)-( i 1)1 /Kt ,Kq( ii )Z

Kt 0.221 0.199 0.022 Il.!

Kq 0.0271 0. 02 49 0. 0022 8.8

5. Conclusion:

The ducted propeller characteristics were discussed calculatively and experimentally by means of our analysis of ducted propeller

characteristics in the uniform flow and non-uniform flow. From this, it became clear that the D.F. characteristics will be strongly

affected by the non-uniform flow

_¿/

and i).. which are based on

the nominal wake or induced wake, etc. and these characteristics will become much different from these characteristics in the uniform flow, and

that, on the other hand, there will be no much difference in case of the C.P.

According, it was further found that it will lead to much unreasonableness that the D.P. designing method and the analysis method of self-propulsion test which are based on the D.P. characteristics in the uniform flow, which have been used in case of C.P.-equlpped ships,are directly npplied

to the D.F. case and therefore it will he necessary for the purpose to take consideration of the D.P. characteristics in the Tlaxisymmetrical flow. _{For this, too, it should be necessary to express the D.P.}

characteristics taking account not only of advance ratio Jx of the mean axial velocity base but also of ndvance ratio Jr basing upon the menu radial velocity of the nozzle position. in addition, though no statement is made here, it has been cleared theoretically and experimentally _that the D.P. will increase the thrust deduction fraction t. And so it is necessary to design the ducted propeller in relation with shape of nozzles, stern shape of hulls, rudder arrangement, and rudder thickness

for the purpose of the prevention of reduction of hull efficiency as well as the improvement of propeller efficiency.

Re fereii ces

Minsaas , K. J ., Jacobsen, G. Nt. ¿jiid Okamoto , H . ''rue

Design nl la rgi

Ducted Propel 1ers for Optimum Efficiency and Manocurvahility". Paper No. 11 Part i. Symposium and Ducted Propeller, RINA, 1973. Narita, H., Kunitake, Y. and Yagi, H. "Application and Development of a Large Ducted Propeller for the 280,000 DWT Tankers MS Thorsaga, Annuel Meeting Nov. SNAME, 1974

r

Nozawa, K. and Okamoto, II. "A Method for Calculating the Hydrodyriamic Characteristics of the Nozzle Propeller" JSNA Japan 137 (1975),

139 (1976).

Lerhs, 1l.W. "Moderately Loaded Propellers with a Finite Number of

Blades and Arbitrary Distribution of Circulation, Trans. SNAME 60 (1952) Morgan, W.B., Silovic, V. and Denny, S.B. "Propeller Lifting Surface Corrections", Trans. SNAME 76 (1968)

Hanaoka, T. "Theory of an Annular Lifting Surface" JSNA Japan 85 (1952) Koyama, K. "A Numerical Method for Propeller Lifting Surface in

Non-Uniform Flow and Its Application" JSNA Japan 137 (1975) De Santis, R. "The Effect of Inclination Immersion and Scale on Propellers in Open Water", TINA LXXVII (1934)

Dyne, G. "Systematic Studies of Accerating Ducted Propellers in

Axial and Inclined Flows", Symposium on Ducted Propellers RINA (1973)

English, J.W. "Hull Propeller Interactions" 14th 1.T.T.C. Proceedings Volume 3 (1975)

-mi, I es ;nid Figures

Table 1 Particulars of ducted and conventional propellers Table 2 D.P. performance in an oblique flow (J = 0.4) Fig. I General flow chart of D.P. calculation

Fig. 2 Coordinate system

Fig. 3 Open water characteristics for C.P. (impeller alone of D.P. No. 1) Fig. 4 Open water characteristics for D.P. No. i

Fig. 5 Flow around D.P. No. i (J = 0.4)

Fig. 6 Flow around C.P. (J = 0.4)

Fig. 7 Model wake distribution of typical full tanker

Fig. 8 Flow diagram of nozzle

Fig. 9 D.P. performance is an axisymetrical flow (D.P. No. 2) Fig. 10 D.P. performance is an ob ligue flow (D.P. No. 2) , measured

Fig. Il C.P. performance in an oblique flow (C.P. No. 1), measured

Fig. 12 Interaction between D.P. and body of revolution Fig. 13 Interaction between C.P. and body of revolution

Fig. 14 Interaction between D.P. and rudder

Fig. 15 Interaction between C.P. and rudder

' The appropriate place for each Table and Fig. is indicated in

Kind of Propeller

D. P.

C. P. No.

Item

I

2

Number of Blades

5

5

5

Propeller Dia (m)

0.250

0.180

0.1973

Pitch Ratio 0.7R

0.953

0.979

0. 735

Exp.Ared Ratio

0.6467

0.7185

0.60

Boss Ratio

0.1963

0.200

0. 18G

J0.4

74k 2

Experiments

.1

Catculcitions

o(-10°

¿(10°-0°) 4®°°

c(=0°D

c=10°

¿(100_00) ¿/°/

Ktn 0.056

0.059

0.003

+ 5.4

0.0436

0.0L69 p0.0033

+7.56

Ktp 0.194

0.192

-0.002

-1.0

0.2100

0.20997-0.00003 -0.013

o. Ktt 0.260

0.251

+0.001

+0.4

0.2536

0.2569 #0.0033

1.30

Kq 0.0344

0.0339 -0.0005 -1.45

0.035 6

0.03556 -0.00004 -0.105

t

0.4627

0.4714

+0.0087 +18ß

0.4535

0.4599 fO.0064

+1.41

Kt

0.2015

0.2005

-0.0015 -0.74

Q:

-ci Kq 0.0254

0.0252 -0.0002 -0.79

7p 0.5050

0.5053

4-0.0003 +0.06

(I)

4-a)

o

o-E

o

o

o

o

Q)

E

E

(r)

(n

><

Impeller

Calculation 4 Nozzle Induced Velocities Veloci t es, Pressure Geometory of D.F. Operating Cond. Wake Distribution Fourier Expansion

Nozzle and Wake

A Total Induced Veloci ties 4 Pressure on

Nozzle

Surface Performance of

D.F.

Non Axissymetrical

Impeller

Calculotion 1! Nozzle Induced V e I oc i t ¡ es a)

'- -

_o o (f, G) 9- _L)

00

Impeller

Induced V elocities

Impeller

Induced Veloci t ¡ es C 0 L) Nozzle L O Nozzle

OC

Calculation _Calculation

0.6

0.4

0.2

o

---

Calculated

-

Measured

s

,

/

OKq

'-...

Kt

0.

J,

0.3

0.4

0.5

0.6

0.7

0.6

0.5

0.4

0.3

0.2

0.I

o

0

0.1

0.2

0.3

0.4

0.5

0.6

J

[___L_

Cal1culated

Measured

I

ri

d8,'X

i

'AuOi°fl

POfl3I03.---o.'

80

90

t'o

t'o-

8D-

01-___________

-("t

j

/1

-- :: I.

-i____

4J

1.2

Lo

_Q8

_0.6

-0.4

0.2

)

j

-ilijul

J

-//1

!

I

-j

'

L

-Ua s Wx

Colcukited

--_

Mosured

UosI.Om/s

'J \./i L_.

-Q6

-Q4

-0.2

o

0.

0.6

0.8

'j 1.2

X/Rp

800

0.2

- 0.1

900

0 _0.I 0.2 nR ("/) V 1138 D

97

X A + o

80°

270°

0°

90°

1800

r,R

(i) Uniform Flow Case

(ii)

xissymmetrical Flow Case

WHR

Va.

i

I

i

I s -I s

II,

'J, LLJPx

c,smaII

o(iarge

Impeller

Q4

_0.3

_0.2

_0.1

0 02 04 0.6 0.8

1.0 2

o

a.

C

-0.0

01

r/R

X-.

i'-lOKq

tt

2

X

REVOLUTION

_yx(r/R),yr..O.O94

jzO.O

04

in Wake

ccitcu(ated

0.5

_0.4

4-.

Q3

Q2

0.1

0.0

ç;"

lo

RPS

15RPS Measured Open

--2ORPS_

Calculated

-e----04

0.3

0.2

o.'

Oblique Flow Angle

J

IOKq

.2

50

loO

ii

-

.-n=l5rps

.----.----u .

.Ktt

Ktp

-Ktn

--0.4

0.3

0.2

o.'

Oblique Flow

-00

-0---

Angle

---A---

50

loo

t-,

p:

OKq

'

Kt

0.2

0.3

04

J

0.5

0.4

0.3

Q2

O'

0615

₀₂₀

₀₂₅

IOKq

o

Ktp

Ktn

--f

-

.

-f

- -

-u

o:::1---

__ci---__Lr

_ij0

-_-

_{n_p}

-cr

₊

-030

_Ktt

Q35

0.40

Mark

Condition

n/rps

mrn

o

DPAlone

5

Body

+

D.P

15 150 lOO

+

70

Q35

0.30

025

0.20°

0.15

.

Body Qf

Reution

F.P

rps

in mm

0.20

0.25

Kt

_0.30

Mdrk _Condition n e

Io

CRAlone

15 150

0

Body 15

00

0

u

D-

_{+ 5}

₁₀₀₆₀

1-

C.P

₀

₇₀

₀

(mm) Op/P..

--

45

4.0

60

3.0

WITH RUDDER

75

2.4

WITHOUT RUDDER

mm

Deformed J by Rudder. t ;60

ç-,

Q20

0.25

0.30

0.35

0.40

0.45

0.50

j

-_____

-____

--u_.

--

-

10KO

--KIP

-0.4

0.3

o

o

0.2

z

I-0.I

0.4

0.3

o

o

0.2

0.I

O

(mm) Dp/2.

30

6.577

45

4.384

WITH RUDDER

60

3.283

75

2.63 I

-WITHOUT RUDDER

mm

® Deformed J tisi Rudder. L '6

-'10KQ

KT

--0.20

0.25

0.30

035

0.40

0.45

0.50