6

Ship propulsion

We will limit ourselves here to ships equipped with propellers. Waterjets as alternative propulsive systems for fast ships, or ships operating on extremely shallow water are discussed by Merz (1993) and Kruppa (1994).

6.1 Interaction between ship and propeller

Any propulsion system interacts with the ship hull. The flow field is changed by the (usually upstream located) hull. The propulsion system changes, in turn, the flow field at the ship hull. These effects and the open-water efficiency of the propeller determine the propulsive efficiency D:

D D H 0 R D RT Vs PD

H D hull efficiency

0 D open-water propeller efficiencyR D relative rotative efficiency

PD D delivered power at propeller RT D total calm-water resistance Vs D ship speed

D 0.6±0.7 for cargo shipsD 0.4±0.6 for tugs

Danckwardt gives the following estimate (Henschke, 1965):

D D 0:836 0:000165 n r1=6

n is the propeller rpm and r [m3] the displacement volume. All ships checked were within 10% of this estimate; half of the ships within 2.5%.

Keller (1973) gives:

p

D D 0:885 0:00012 n Lpp

HSVA gave, for twin-screw ships in 1957:

		Vs	3
	D D 0:69 12 000 0:041		0:02
		n DP

180

Ship propulsion 181

Ship speed Vs in [kn], propeller diameter DP in [m], 0:016 Vs=.n DP/ 0:04.

The installed power PB has to overcome in addition efficiency losses due to shafts and bearings:

PB D S PD

The shaft efficiency S is typically 0.98±0.985.

The hull efficiency H combines the influence of hull±propeller interaction:

1 t

H D

1 w

Thrust deduction fraction t and wake fraction w are discussed in more detail below.

For small ships with rake of keel, Helm (1980) gives an empirical formula:

0:895

0:0065 L

0:005

B

0:033

C

0:2

C

0:01

lcb

H D

r1=3

T

P C

M C

lcb is here the longitudinal centre of buoyancy taken from Lpp=2 in [%Lpp]. The basis for this formula covers 3:5 L=r1=3 5:5, 0:53 CP 0:71,

2:25 B=T 4:50, 0:60 CM 0:89, rake of keel 40%T, DP D 0:75T. T is taken amidships.

Thrust deduction

The thrust T measured in a propulsion test is higher than the resistance RT measured in a resistance test (without propeller). So the propeller induces an additional resistance:

1.The propeller increases the flow velocities in the aftbody of the ship which increases frictional resistance.

2.The propeller decreases the pressure in the aftbody, thus increasing the inviscid resistance.

The second mechanism dominates for usual propeller arrangements. The thrust deduction fraction t couples thrust and resistance:

t	D	T RT	or T.1		t/	D	R
		T					T

t is usually assumed to be the same for model and ship, although the friction component introduces a certain scale effect. Empirical formulae for t are:

For single-screw ships:

t D 0:5 CP 0:12; Heckscher for cargo ships

t D 0:77 CP 0:30; Heckscher for trawlers

t D 0:5 CB 0:15; Danckwardt for cargo ships

t D w .1:57 2:3 CB=CWP C 1:5 CB/; SSPA for cargo ships

tD 0:001979 L=.B.1 CP// C 1:0585 B=L 0:00524 0:1418D2=.BT/; Holtrop and Mennen (1978)

182 Ship Design for Efficiency and Economy

For twin-screw ships:

t D 0:5 CP 0:18; Heckscher for cargo ships

t D 0:52 CB 0:18; Danckwardt for cargo ships

t D w .1:67 2:3 CB=CWP C 1:5 CB/; SSPA for cargo ships p

t D 0:325 CB 0:1885 DP= B T; Holtrop and Mennen (1978)

Alte and Baur (1986) give an empirical coupling between t and the wake fraction w:

.1 t/ D .1 w/0:4±0:8

In general, in the early design stage it cannot be determined which t will give the best hull efficiency H. t can be estimated only roughly in the design stage and all of the above formulae have a much larger uncertainty margin than those for w given below. t thus represents the largest uncertainty factor in the power prognosis.

Wake

The wake is usually decomposed into three components:

Friction wake

Due to viscosity, the flow velocity relative to the ship hull is slowed down in the boundary layer, leading, in regions of high curvature (especially in the aftbody) to flow separation.

Potential wake

In an ideal fluid without viscosity and free surface, the flow velocity at the stern resembles the flow velocity at the bow, featuring lower velocities with a stagnation point.

Wave wake

The steady wave system of the ship changes locally the flow as a result of the orbital velocity under the waves. A wave crest above the propeller increases the wake fraction, a wave trough decreases it.

For the usual single-screw ships, the frictional wake dominates. Wave wake is only significant for Fn > 0:3 (Alte and Baur, 1986).

The measured wake fraction in model tests is larger than in full scale as boundary layer and flow separation are relatively larger in model scale. Correction formulae try to consider this overprediction, but the influence of separation can only be estimated and this often introduces a significant error margin. The errors in predicting the required power remain nevertheless small, as the energy loss due to the wake is partially recovered by the propeller. However, the errors in predicting the wake propagate completely when computing optimal propeller rpm and pitch.

Model tests feature relatively thicker boundary layers and stronger separation than full-scale ships. Consequently the model wake is more pronounced than the full-scale wake. However, this hardly affects the power prognosis, as part of the greater energy losses in the model are regained by the propeller. Errors in correcting the wake for full scale affect mostly the rpm or pitch of the

Ship propulsion 183

propeller. Proposals to modify the shape of the model to partially correct for the differences of model and full-scale boundary layers (Schneekluth, 1994) have not been implemented.

The propeller action accelerates the flow field, again by typically 5±20%. The wake distribution is either measured by laser-doppler velocimetry or computed by CFD (see Section 2.11). While CFD is not yet capable of reproducing the wake with sufficient accuracy, the integral of the wake over the propeller plane, the wake fraction w, is predicted well. In the early design stage, the following empirical formulae may help to estimate the wake fraction:

For single-screw ships, Schneekluth (1988) gives, for cargo ships with stern bulb:

w D 0:5 CP	1:6		16
	1 C DP=T		10 C L=B

Other formulae for single-screw ships are:

w D

0:75 CB 0:24; Kruger¨ (1976)

w D

0:7 CP 0:18; Heckscher for cargo ships

w D

0:77 CP 0:28; Heckscher for trawlers

w D

0:25 C 2:5.CB 0:6/2;

Troost for cargo ships

w D

0:5 CB; Troost for coastal feeders

w D CB=3 C 0:01; Caldwell for tugs with 0:47 CB 0:56

w D

0:165 CB .r1=3=DP/ 0:1 .Fn 0:2/; Papmehl

w

3

B E

1

1:5

D C ."Cr/

; Telfer for cargo ships

D 1 .CP=CWP/2 L T

B

" is the skew angle in radians, r is the rake angle in radians, E is height of the shaft centre over keel.

For twin-screw ships:

w D 0:81 CB 0:34; Kruger¨ (1976) for cargo ships

w D 0:7 CP 0:3; Heckscher for cargo ships

w D CB=3 0:03; Caldwell for tugs with 0:47 CB 0:56

Holtrop and Mennen (1978) and Holtrop (1984) give further more complicated formulae for w for single-screw and twin-screw ships, which can be integrated in a power prognosis program.

All the above formulae consider only a few main parameters, but the shape of the ship, especially the aftbody, influences the wake considerably. Other important parameters are propeller diameter and propeller clearance, which are unfortunately usually not explicitly represented in the above formulae. For bulk carriers with CB 0:85, w < 0:3 have been obtained by form optimization. The above formulae can thus predict too high w values for full ships.