On the design of the propulsion systems with Z-drives for hydrofoil ships

Pełen tekst


15 SE 172


bhotheek van de

OnderafdeUn. -:.sbouw .ncie

nische Hogeschoo,



DATUM: j OKt. 1973



The Ninth Symposium on Naval Hydrodynamics


by A.A.Rousetsky



y. Scheepsbouwkund

Technische Hogeschool


The propeller powered through an inclined shaft is the. most extensively employed propulsion system forhydrofoil ships. Such propulsion systems distinguished by simple design are used

for most hydrofoil ships now in operation. However, this system

has some disadvantages. The oncoming flow obliquity due to the

propeller shaft inclination resultà in the periodic change of

the incident angles of the propeller elementé, th amplitude

being increased with the decrease in the relative radius. The

variation of the incident angles prevents fròm designing the optimum propeller, from the point of view of propulsion quali-ties, and forces the designers to make. a certain compromise, while choosing the propeller elements, to avoid the intensive

erosIon damages on the prdpeller blades. The methód of

de8ign-Ing the propellers adapted to the oblique flow is described in

papers [i],


The experience obtained in calculating such propellers shows that with the oblïque flow angles exceeding l4°-15° the design of the ship propeller displaying satisfactöry erosion

characteristics has failed. At the same time the improvement

of the hydrofoil ship seakeeping qualities requires the increase in clearance between the ship bottom and free surface and this


is why the propulsion system known as "Z" drive came into use

on seagoing hydrofoil ships. There are different variants for

"Z" drives distinguished by the arrangement of ship propellers: (a) single propeller "Z" drive with one propeller at the forward end or at the after end of the propulsion pod and (b) twin pro-peller "Z" drive where one propro-peller is at the forward end of

the propulsion pod an4 the other is at its after end. The

dis-advantages of the latter "Z" drive are due to the forward peller effect upon the flow around "Z" drive and the after

pro-peller operation. This effect can result in intensive erosion

damages on Z-drive elements situated in the forward propeller

wake. As a consequence such type of the propeller arrangement is used only for "Z" drive intended for high power transmission where the decrease in dimensions of the gear assembly and

pro-pulsion pod is required. Prom the point of view of providing

the uniform velocity field in the propeller disk, (a)-variant with a propeller at the forward end of the propulsion pod is

preferable; however, the propulsion efficiency of this "Z" drive is somewhat below the efficiency of "Z" drive with a propeller

at the after end of the propulsion pod. Besides there is a

danger of erosion damage on "Z" drivò hull. Thus at present "Z"



a single after propeller is considered to be the most attractive; a number of hydrofoil ships are equipped with such

"Z'! drives.

The desii of propeller "Z" drive propulsion system involves a series of problems which can. be divided into two groups: the first group deals with choosing the geometry of the propulsion pod and strut; the second group deals with


designing ship propellers adapted to the velocity field generat-ed by "Z" drive hull.

Generally the propulsion pod-and-Strut croas sections are predetermined taking into account the arrangement of the gear

assembly and bearings of the vertical shaft. Since the increase

in the wetted surface is unfavourable, from the point of view of resistance, the problem is reduced to the choice of minimum length-to-diameter ratio providing the absence of cavitation on these elements.

As the calculations and experiments show, length-to-diameter ratio providing the minimum resistance lies in the range of 4-5; in this case no cavitation occurs on the propulsion pod up to

cavitation numbers 0.2-0.3. Circular-arc cross sections for the

propulsion pod are preferable. provided that there are no struc-tural impedimenta.

To preclude cavitation on the strut its maximum relative thic1iesa in the first approximation may be determined according to the following empirical formula:

max - 2,5 (1)

where 5 is the cavitation number.

This formula holds fOr thé profiles with a fairly uxique pressure distribution. Specifically, NACÂ-l6 and Mandel profiles


with these

requirements. At the place of the strut-free surface intersection the strut profile usually has the form of a symmetric segment developing smoothly into the parent profile of


part immersed. The moat critical element of "Z" drive is


parti-cularly in its bow part,.the cavitation


is possible. The radius of the fillet at the place of junction is chosen so

that the thickne 88-Chord ratio should not exceed the value


It is obvious that with the proper choice of "Z" drive forma the cavitation can be avoided only in a comparatively narrow range of inci4ent angles. The critical cavitation number versus the angle of incidence is shown in Pig.l.

Por designing the propeller to be mounted on "Z" drive the knowledge of the hull-propeller interaction factors is necessax The distinguishing feature of the propulsion system in question

is the large value of Did ratio where D is the propeller

dia-meter, d ja the pod diameter. In these conditions the decisive

role in the 'formation of the nomina]. wake in way of propeller

belongs to a potential component. Replacing the propulsion pod

with a system of singularities makes it possible to calculate

in the first approximation the value of nominal wake. It is of

interest to note that in the range of diameter relation

(1.5 .< <2.0) under discussion the wake value is practically

independent of this relation. This is supported by the data in

Pig.2 where the values of the nomina]. wake are plotted against

the pod length-to-diameter ratio at different

-s-A8 13

known, "Z" drive propellers operate at comparatively

small load factor values


ranging from 0.3 to 0.6. It make.a

possible in practical calculations to consider the effective wake to be equal to the nominal one. To proceed from the

assump-tion that the wake. is potential, the thrust deduction factor can




where p- propeller advance ratio,

- apparent advance ratio, p - propeller thrust,

- gain in resistance of "Z" drive due to the presence of propeller.

The tests with various types of "Z" drives showed that the wake value was independent of the propeller loading. This gives grounds to consider that the wake value will neither be influ-enced by the propeller loading changes due to cavitation.




where Wp

is the nominal potential wake factor.

The thrust deduction factors calculated by formula (2) hold, strictly speaking, for the perfect fluid only, however, the er-rors due to this assumption are essential but at very small load

factors. The interaction factors can be refined through the

tests in a cavitation tunnel. During the tests "Z" drive

resist-ance and propeller performresist-ance curves are recorded. Apart from

the refinement of the interaction factors, the tests make it

possible to reveal the propeller cavitation effect upon the value

of these factors. When analysing these experimental result8

the wake and thruSt deduction factors may be determined by the following formulae:


Therefore the wake value obtained by the comparison of the

pro-peller performance curves for eubcavitating regimes may be used.

in further calculations. Por the agreement of the propeller

performanoe curves in open water and downstream of "Z" drive under cavitation, use is made of the correction factors taking into account the effects of the flow nonuniformity and pressure

change in the propeller disk upon the propeller thrust and.


The dependence of the thrust deductión factor upon the

pro-peller loading and cavitation nuniber for the propulsion system

with the pod length-todiaineter ratio .-- = 5 and = 1.5 is

shown in Pig.3. As is Been, with the development of cavitation

the thrust deduction factor decreases. This result is ïn

quálitative agreement with the conclusions of the paper [3].

By way of comparison the thrust deduction factor calculated by Eq.(2) is plotted on the saine curve against propeller loading

in the absence of cavitation. The value k40mfoi' the propulsion

system under study amounts to 0.045. The agreement of t-values

in the range of moderate and high. loads is considered to be,

quite satisfactory.

The propeller mounted on "Z" drive operates in a rada1ly

nonuniform axial flow. Besides this the propeller oncoming

flow exhibits circumferential nonuniformii,y due to the strut effect and sometimes due to the foils adjacent to the pod. Por

the purpose of adapting the propeller to the wake the results of the experimental investigation of the velocity field are

used. The typical results of the measurements for "Z" drive

with length-to-diameter ratio = 5 are given in Pig.4 (a)


factors obtained

by integrating

the diagrams

of velocity

dis-tributions are in good agreement with the theoretical data and also with the desii wake factor defined in terms of propeller characteristics.

In màking calculations use is made of the wake values averaged over the circumference; however, after the propeller desii is finished it is necessary to verify the possibility of cvitatiòn inception on the face of propeller blade in the

positions corresponding to the minimum wake values. The most

effective method of verification Is the visual observation during the tests in a cavitation tunnel.

In choosing the optimum,values of the propeller diameter and the number of revolutions for the propulsion systems with "Z" drives it should be taken into account that the increase in,

the number of revolutions makes it possible to decrease the

dimensions of the reduction gear and consequently the propulsion pod dimensions and, as a result, to decrease "Z" drive

resist-ance. In this case the number of revolutions may increase in

comparison with the optimum number specific for an isolated



.A.Titoff, A.A.Rouaetsky, and E.P.Georgievskaya, "Principles of cavitating propeller desii and development on this basis of screw propellers with better resistance to erosion for hydrofoil vessels "Raketa" and "Meteor", Seventh Symposium on Naval Hydrodynamics, 1968, Rome.


2 E.P.Geoxgievskaya, "Propeller cavitation ero8ion and methods

of protection" (in Russian), Sudostroenie, 1970.

3 V.P.Bavin, I.J.Miniovich, "Experimental investigation of.

interaction between hull and cavitating propeller", 10th ITTC, 1963, London.







Critica]. cavitation number versus incident



L 0ß3 Q,O2 ao'i o 10 20


Nominal wake factor versus pod

length-to-diameter ratio.

wP 0,05



Thruat deduction factor of the propeller aituated. at the after part of the propuleion pod.

-- - calculation by formula (2)




-Q -%O 'II



















1,0 V.. vo 0,9 0,6 0,4 0,5 0,6 0,7 0,8

(a) along the radius

- - in the atrxt plae


' 12

-Jt .

4 2


(b) along the circumference at the relative radius


Pig.4. Results of measuring the velocity field in way of


- -


1,0 V vo 1,0 0,9 3,7





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