Propeller excitation and response of 230.000 TDW tankers

FRAN

-STATENS SKEPPSPROVNINGSANSTALT

(PUBLICATIONS OF THE SWEDISH STATESHIPBUILDING EXPERÌMENTAL TANK)

Nr 70 GÖTEBORG' 1972

PROPELLER EXCITATION and RESPONSE

of 230 000 TDW TANKERS

BY

STOCKHOLM

PRINTED IN SWEDEN BY

In cooperation betwéen U d d e y a 11 a y a r y e t A B (U V),

the Swedish State Shipbuilding Experimental

Tank (SSPA) and Det norske Ventas (DnV) a

com-prehensive investigation concerning propulsion, cavitation and vibra tion has been carried out on two 230,000 TDW tanker ships. The results with reference to propulsion, propeller cavitation and erosion

have been repOrted at the 1972 Spring Meeting of the R o y.a i

Institution of Naval Architects [4].

In the present report the results concerning vibration are reported Full scale measurements of propeller mduced pressure fluctuations at different positions on the stern, static, and dynamic thrust and torque in the shaft, as well as vibratory response in different parts of the structure have been carried out.

In model scale the experiments of primary interest in this connection are the measurements of propeller induced pressure fluctuations in the stern, carried out under cavitatmg and non cavitatmg conditions, the transducers being placed in the same positions as in full scale. These tests were parried out in the new cavitation tunnel at SSPA, allowing the use of the same ship model, for the cavitation tests as for the tests in the towing tank.

The results of the full scale and model experiments for different ship-propeller-configurations (five- and six-bladed propellers, hull with and without stern fins) have been analysed and compared.

Included in the comparison are results of theoretical calculations of the extent of cavitation over the propeller blades, different kinds of shaft vibrations and propeller induced hull pressure fluctuations from cavitating propellers.

The ships included in t present investigations are the first two m a series of tankers of about 230,000 tons deadweight, which are

to be delivered from ljddevallavarvet AB (UY) withm

the next few years The first ship, T/T 'Thorshammer", was delivered in December 1969, bemg equipped with a five bladed propeller

The model tests m the towmg tank indicated very good propulsive pérfbrmànce, 'which was confirmed by the résults of thè speed trials with the firt sh1p.

At the trials with this ship extensive measurements Of vibratory résponse and pressure fluctuations ön the hull near' the sterÍì-pbst were èarried out by D e t n o r s ke V e r i t a s (D n V) togethér with recordings Of different kiñds of shaft vibrations [I]. 'The results of these measurements indicated that'the levels of the pressure flúctua-tions registered by some of the transduers were very high; in addition

a loud pattering noise could b heard in the aft part of the ship.

The vibration levels recorded were, however, not annoying.

At the döcking of thé ship, shortlr after the trials, erosÏon was detectéd on four of five blades. The blâdes were modified but after one voyage tO the Persian Gull and back, erosion was again observed. The high lève! of the pressure f1utuatibns was attributed to 'signi-ficant development of various forms of unstable cavitation and it was felt that there was a risk that the structure of the stern might be 'damaged. A proposal was niadè to fit' the ship with streamline fins on the afterbody above the propeller' aid after etensive model

testing of different alternatives in the towing tank the ship was

fitted with fins, as shôwn in Fig. 1, and new full sèale measurements

of vibrations and pressure flctüatións were carried out [2]. The

results of these measurements were promising. The pressurê fluCtua-tions, as well as the noise and vibration levels, were lower. Further the service reports confirmed the results of the model tests, indicating no increase of the power consumption. The problem of erosion of the propeller blades was, however, not solved, although some im-provement could be noticed.

The main modification applied to the second ship was that fins (somewhat different from those of the first ship, see Fig. 1) were fitted during construction. In addition, a six-bladed propeller was fitted, having a radial load distribution different from the original five-bladed design.

Successful trials were carried out with this ship [3]. Further, the new propeller has so far worked without any trouble.

AQ = developed blade area ratio

CL = dL/+pc db V2=lift coefficient

= (ppo)/+p V2=pressure coefficient e = blade chord

D = propeller diametór dL lift of profile

J

= VA/nD=advance ratio for propeller

= 2pIpD2n2=non-dimensional coefficient for blade frequency amplilude

= T/pD¼2=thrust coefficient

ka correctjon factor for ideal angle of incidence, due to lifting

surface effect

- correction factor for angle of incidence, due to thickness effect

n = number of revolutions

P

propeller pitóh

p = static pressure

p0 = static pressure in undisturbed flow

cavitation pressure

Pv = vapor pressure

r

= radius of propeller blade section

T

=thrust

t = maximum thickness of profile

V = inflow velocity to blade section

VA = advance vèlocity of propeller V5 = ship speed

w = local wake

WT = effectIve wake from thrust identity

x = non-dimensional chordwise coordinate, measured from leading edge

z = number of blades = air content p = denóity of water

a = (Ppv)/p V42=cavitation number for propeller

When the project work was completed it was felt that, if compie-'mentary model tests and full scale measurements could be carried out with the second ship, an opportunity had arisen to obtain unique material showmg the influence of different modifications on the model as well as on the tüll scale, whereby investigations concerning the correlation factors for propulsion, vibratory resp9nse and cavitation coüld be made.

Accordingly a research program was established, which was carried out in close cooperation between U d d e y a Il a y a r y e t, S S P A

and DnV.

Together with the investigations carried out on the first, ship the full scale program included:

Speed trials with measurements of propeller thrust and thrust variations (second ship only)

Photographing of cavitation patterns at different propellerloadings and angular blade positions (second ship only).

Inspection of the propellers with regard to cavitation erosion. Meaurement of propeller induced hull pressure variations. Meäsurement of hull vibratiòns.

Corresponding model experiments were carried out, including studies of propeller cavitation behind complete ship models. In addition the model investigations included measurements of wake patterns and static pressure with and without propeller 'in the towing tank as well as in the cavitation tunnèl, speóial streamline tests and tests with a ducted propeller.

The present report will deal primarily with items 4 and 5 above. The 'results of the measurements under items 1-3 above were sum marized in [4).

The main dimensions. of the ships are: Length between perpéhthcular

Breadth

Draught, fully laded coñdition Draught, ballast condition, fore Diaùght, ballast conditioñ, aft Displacement

Deadweight Block coefficient

Capacity of cargo oil tanks Clean water ballast CT No 3

L= 1020'O"'

BM ==157'lÓ"

T=

TF=

260,850 long tons 228,250 long tons =0.844 10,124,300 cft 836,900 cit

Class Det norske Ventas +1.A.1. "Tankskip for bijelast, F, EO." Main engine, Generäl Electric steam türbiñe, 32,420 SHP (metric) at 85rpm

Model scale 1:43.5

The different ship and propellér coigaions 'testéd are

sum-marized in Table I. TABLE = 310.89 m

= 48.lOm

20.44 m 10.7 rn 13.0 m

Model No 1800-B ("Thorshammer") ha2 a slightly different fm (smalier) than 1600-C ("Norse Ki"). Model 1600-B was not tested.

Refers to the full scale propeller. The corresponding value for the model propeller

was 2% lówer, i.e. P/DmodelO.723.

Nozzle propeller. Dimenalons of nozzle, Dmax= 10.0 m. ¿=4.13 m.

Ship _Propeller

D AD/AO P/D

Name Model No., Fins ModelNo Z m % 0.7 J?

Thorsharnmer 16OOA 1600-B') Without With P1378. 5, 5 8.80 0.58 0.7382)

Norse King 1600-C With P1493 6 8.50 0.64 0.795

The two conventional propellers were designed using the vortex theory in accordance with the standard procedure used for merchant ship propellers at SSPA. Different radial circulation distributions were used for the two propellers, resulting in different radial camber and pitch distributions.

On the first ship tests were carried out at two different occasions; at the delivéry trials and at trials arranged after the ship had been fitted with stern fins. On the second ship tests were carried out at the delivery trials and immediately after, the tests on this ship in-òluding photographing of cavitation patterns on the propeller blades The equipment for taking these photographs is indicated in Fig. 1. It is further described in [4].

Speed, Number of Revs and Sea State

Most of the tests were carried out in connection with the speed trials but not at the runs on the measured mile. The speeds for the tests reported here were recorded with the log of the ship, which is not a very accurate method. Accurate registration of the number of revs was, however, carried out in connection with all measurements by using a photoelectric cell, mounted on the shaft. Most of the results in this paper are therefore related to number of revs instead of speed.

In Table II the sea state during various tests is presented.

TABLE lI. Soa state during trials.

Loading Wind

Ship Fins Z Condition Beaufort Sea

Thorshammer No 5 Loaded

Thorshainmer No 5 Ballast

Thorshamnier Yes 5 Loaded 2 2

Thorshammer Yes 5 Ballast 2-3 2-3

Norse Kiñg Yes 6 Loaded 6 4

Vibratory Response in the Structure of the Ship

Vibratory response was registered at about 20 points in the structure (wing tank), engine room and deck .houê with the use of velocity transducers manufactured by CEC. The positions of those trans-ducers, which were fitted at least at two of the trials, are shown in Fig. I. The fins, when installed, were fitted with accelerometers, positioned in the vicinity of the pressure transducers, see Table III.

Ncvigation deck

Upper Deck and 2nd opdeck

D2D3

III

25 6I 62

Wing tank No.5 SB

pr.sur, transduc.rs

Fig. L eneral arrangement and positions of vibration pickups.

TABLE III. Poitions of pressíre transdûàers in full scale

. From aft end of stern post at the height considered.

Not working at fully loaded condition.

-') Fin, bottom

4):Fin top.

-P'ìessu,e Fluctuations iii the Alerbody

Measurements of the pressure fluctuations were carried out at different points in the afterbody using semi=conductor strain gauge transducers (ElDEVCO); see Fig. 2 and Table III, having a mem-brane diameter of 8 mm.

The circuits included low pass filters (32 Hz). Acçelerometers were fitted to the hull close to the transducers, in order th rècord the

in-fluence of the hull vibrations on 'the propeller induced pressure

field, [27]. .

Height

above Distance from _Corresp.

Trans baào'' entr' transd.

Ship' Fins diicer. lino 'lino - AP -'' Side Woiking módel rn Thors- No 1 9.12 -0.8 1.21) _SB 2) hammer 2 9.12 -0.5 0.91) _SB 2) 3 9.12 -0.3 0.6') SB Yes 4 9.12 -0.5 0.91) _{P Yes} 5 10.12 -0.55 0.9') SB 2) 6 10.12 -0.55 0.9') P No Thors- Ys 1 - .11.10') -3.5 _{10.0 SB Yes} hammer 2 13.104) 1.5 5.7 SB Yes 3 11.10') 1.5 5.7 SB Yes 4 11.10') -0.2 3.75 ' 'SB Yes 5 9.12 -0.3 0.6') SB Yes 6 10.12 -0.55 0.91) SB No

Norse Yes 1 11.10') -0.5 3.3 SB Yes

King - 2 11.10') 0 3.3 CL Yes . 3 ' 11.10') -0.5 3.3 P Yes 4 11.10') -0.5 4.2 SB Yes 5 11.10') 0 4.2 CL Yes 6 11.10') -0.5 4.2 P Yos 7 9.85 0.3 0.5') SB Yes

Model tests

QFull Scote'Thorshammer 5 bI without fins with

E

'Norse King 6 bI with fins

Fig. 2. Positions of transducers for measuring pressure fluctuations on tho model and full scale ship. For exact positions of transducers iii full scale, see Table III. In model

Propeller Cavitation

The equipment used for. observation of propeller cavitation is described in [4].

NoiseLeveUin the Afterbody

A tape-recorder Tandberg TB1 1P wads positioned in the aft part of

the main engme room and m locations adjacent to the propeller

(the emergency exit channel).

Thrust, Thrust Väriations and Shalt Response -

-fhrust, Thrust Variations and Shaft Resp:onse were measured by strain gauges (Hottmger) on the thrust bearmg fundament and shaft and thé signals telemetered to a digital voltmeter (thrust) and a UY-recorder (thrust variations). AlsO this circuit included a low pass filter.

Further, axial shaft resonances were recorded by a spring trans-ducer, working against the flange coupling between propeller and intermediate shaft.

Vibratory Response in the Structure of the Ship

The results of the measurements of the vibration levels at different points in the deck house and in wing tank No 5 SB are shown in Figs 3 and 4. The levels are given as amplitudes. In Fig. 3 some levels, indicating the degree of unpleasantness, are marked for comparison. They were calculated from the ISSC criteria, based Ou accèleration, by using the formula

y = a/(2irf) where

y = vibration amplitude a = acceleratiOn, vertical

f = frequency of vibration

The results from the measurements in the wing tank indicate weak resonance at certain shaft speeds. The results of Fig. are the largest values measured over the speed range.

The diagrams of Figs 3 and 4 show that the vibration amplitudes in the aòcomodation spaces were of reasonable magnitude. On the first ship without fins the amplitudes measured in the wing tank. were, however, considerable due to resonance at certain shaft speeds (in general not the normal service speed). Unfortunately no measure-ments were carried out in the wing tank on this ship, when fitted with fins. From the results of the measurements in the deckhouse at the different occasions it can, however, be concluded that the introduction of fins reduced the vibration level considerably, but that the replacement of the five-bladed propeller with a six-bladed one caused no further reduction of the vibration level; (In this

con-nection it should be remarked that the structures of the hull and

deckhouse are identical for the two ships, apart from the fact that the second ship was fitted with bilge keels).

--o- First shipThorshommer" 5bt. without fins

,.Q...-. sa u s, st _with n

AmpI. Sr1 ship;Norse King"6b[.

mm 0.20 0.15 QiO 0.05 o Meas, point

Dl D2 03

01 02 D3 Dl. 05 06

Direct, of vibr. V L

Ir

V L

Ir

V V

V

Fig. 3. Vibration levels in deck house. For positions of pickups, see Fig. 1. Numbers indicate approximate number of revs per min.

_stiht1yjncomf. 85 85

\

\

I Ballast

_ce_

i

\

Q i

i

1 Fully

Looded-\

_I'

85

----

-i---85 Q _75k /\85

\

85 I

/

weak I

I,

I /

I

/ 0\ 85

80 /

L/ 85i

\ 85

I I I

2

Ampi mm

Meas

---°--Fjrst Ship'Thorshammer"5 bt.without fins

u Second ShipNorse King"6b[ with fins

62

Fig. 4. Vibration levels in wing tank No 5, SB. For positions of pickups,_{see Fig. 1.} Numbers indicate approximate number of revs per min.

U.0 OE5 0.4 0.3 02 -65 _BALLAST It 81. FULLY LOADED

It

/

I 78cf I \ I ¡ t / I i i \

I

¡t

I 62 I I i i I / t 1 68 p I

tse

,\

j i 7%

J\N61W

f

V62 84 8

/

O Doint V2 V2 VL Vi VS Vs v vi Vc vi v v

Pressure Fluctuations on the Huit

The resu1ts of the measurements of the pressure fluctuatiOns at different points in the stern are given in Figs 5-6. n Fig. 5 the two versions of the first ship are compared at fully loaded and ballast conditions The results shown were obtamed with transducers Nos 3 and 5 respectively, approximately corresponding to measurmg pomt  in model tests. The diagram shows fäired mean values of the peak to peak va1iies 2p, obtained in the way shown in Fig.. 7, normalised as

K

2p

" _pD¼2

These results show the beneficial influence of the fins and it is further evident that the ampÏitudes in ballast condition are larger than in fully loaded condition.

In Fig. 6 the two ship configurations having five-bladed (first ship) and six-bladed (second ship) propellers are compared, both

5-btaded propeller with fins without fins Kp Q3 30 50 70 90 Numbér of revs/mm

Fig. 5. Pressure fluctuations in full scale. "Thorshammer" (first ship) wlth and without

fins. Transducers 3 and 5 respectively (measuring point A, see Table III and Fig. 2).

Balise

/

///

Fully loaded 02 0.1

0.3 02 0.1 6 bladed propeller 5-bluded propeller 30' 50 70 90 Number of revs/mm

Fig. 6. Pressure flùctuations in full scale. First and second ship (5- and 6-bladed pro-peller) with fins. Transducers 4 arid 2 respectively (measuring point D, see Table III

and Fig. 2). KvaIues based on diameter of 6-bladed propeller.

being fitted with fins. The results were obtained for the transducers 4 and 2 respectively, which were placed at the bottom of the fin, on the starboard side, close to the centerline of the ship. The positions were slightly different for the two ships, as is shown in Table III and Fig. 2. The difference is, however, small enough to allow direct

comparison of the results.

The positions correspond approximately to measuring point D in

model scale. The diagram shows that the pressure fluctuations

measured on the two, ships are very similar, in spite of the fact that the first ship was equipped with a five-bladed and the second with a sixbladed propeller. [n fully loaded condition the six-bladed pro-peller caused somewhat larger amplitudes than the five-bladed.

(The fact that only the second ship was fitted with bilge keels is not considered when making this comparison).

A. sample record, obtained at the full scale measurements, is shown in Fig. 8.

0.6 -2 o--x o. C4 w Q-E w u, u) w 0.4 Q3 0.2 0.1 Number of re's/min

Fig. 7. Pressure fluctuations in full scale. "Norse King" (with fins, 6-bladed propeller). Measuring point D. Ballast condition.

/1

1/

/

/

Mean

/

Mox/

/

/

//

_/

/

50 70

o

h

RECORD FROM SHIP MEASUREMENTS, CELL 2 (0)

ENERGY SPECTRUM E 'n o, l/T "NORSE KING'S BALLAST RPM 85.h VS 17.8 knots

Fig. 8. Pressure fluctuations i full scale. Sample of energy spectrum.

S Iwl Amp 1J2SIw)maA)

6

Propeller Cavitation

Some of the photographs taken during the trials with "Norse King" were reproduced and discussed in [4] In the present report some sketch-es based on thsketch-ese photographs are given in Figs 14 and 17 together with the results of the measurements of the pressure fluctuations and the corresponding cavitation patterns, obtained at the model tests. Noise Level in the Afterbody

The nOise level in the afterbody of "Thorshammer" is of a transient type, varying directly as the vibratory response in the structure of the ship and the recorded pressure fluctuations. This observation is valid for the ship with and without fins installed.

The noise level onboard "Norse King" is stable (mainly pulses of short duration, occurence frequency equal tè blade frequency) in the higher speed range (70-85 RPM).

Mean Thrust, Thrust Fluctudtions and Shaft Response

Recordings of mean thrust are presented in [1], [3] and [4]. In Fig. 9 results of calculations of the natural frequency in the axial mode for the two ships are shown, assuming different values of the thrust bearing stiffness. As shown in the Figure, the measured natural frequencies for the two cases correspond to almost the same value of the thrust bearing stiffness, indicating that recorded reso-nances of shaft vibration in the axial mode are predicted with fairly good accuracy by a method now in use at D n V [5]. The vibratory output from the shaft through the thrust bearings is of moderate magnitude for all ship-propeller configurations.

Propeller Blade Erosion

The results of erosion studies in full scale and model scale were given in [4] and will not be discussed in the present report. It should, however, be noted that the eroded areas were similar in model and full scale. Regarding the relative merits of the different configura-tions, the full scale, as well as the model tests, showed that the area

of erosion was not reduced essentially by the introduction of fins on the first ship, but was eliminated by fitting the second ship with a six-bladed propeller of new design.. On the propeller of the first

ship the erosion was, however, less rapid after the introduction

500

300

NATURAL FREQUENCIES,.AXIAL VIBRATIONS

+- T/TTHORSHAMMERÇALCULATED THRUST VARIATION 0F 10th AND 15th ORDER:± Z2met.toñs

O

0 T/T"NORSE KING CALCULATED

THRUST VARIATION 0F 6th ORDER :t2omet.tOflS

¿SURED

NOR KIG( b BL.) NATURAL FREÜUENCIE5

I2.ORDER THORSHAÑMERI 73 RPM bBt..I IO. ORDER 52.5 RPM 4SSUMED STIFFNESS RANGE AT CALCULATION 6. ORDER PROP. RPM 85 EXCITATION FREQUENCY I I. 5. ,. 05 2 3

THRUST BEARING STIFFNESS IKT( kplcm)

Fig. 9. Axial mode of shaft vibration. Natural frequency of actual vibrations.

1100 C E >-o z w o w 900 u--J

I

z 700

Cavitatión Tùnnéi

-The cavitation tests were carried out iñ the new, large cavitation tunnel of SSPA. This tunnel, see [6] and Fig. 10, is powered by álOOG Hp mòt6r and has two interchangeable tet sectións,one being circular, as the re _{aining part of the circuit. The other test section,} vhich is of interest in-this connection, is of rectangular shape with

a breadth of 2.6 th, a heih:of 1.5 m and a length of about 10 m.

The section is covered by a'reçess in which the ship model is placed. This model is the one used in th towing tank for the self propulsion tests and it is normally made of päraffin wax.

The vertical position of the model is adjusted in such a way that the waterline, corresponding to the level of the free water surface in the towing tank, is flush with the top oî the test section. individu-ally cut wooden plates are then fitted to simulate the free surface, and the test section and the recess are filled completely with water. Up to now flat plates have been used and no' attempts have been

made to simulate the wave system around the hull. The maximum water speed is 6.8 rn/sec. An electric motor and a strain gauge dyna-mometer for measuring thrust and torque for the propeller are placed in a watertight cylinder in the model.

Measurement of Pressure Fluctuations on the Hull

For the measurements of the prèssûre f11 'euatiois differential transducers were used, being of the strain gauge type, manufactured by Statham. The maximum range for the, transducers, used at .the tests m the cavitation tunnel is + 25 psi, the natural frequency being

about. 9 kHz. The diameter of the membrane is 1/4" (635 mm)

One end of the transducer was connected to the atmospheric pressure. The signals were amplified and registered on an oscillographic recorder, two channels being used for each transducer. One channel was used for the original signals, on the other a filtered signal was registered,' the filter being tuned on the blade frequency. The natural frequency öf. the galvanometers was i 50 Hz (original signais) and 400. Hz. (filtered signals). For obtaining higher harmonics a frequency analyser (manufacturer Brüel and Kjr, type 2107) was used. The range 63-2000 Hz was used, the total sweeping time being 6 min for this range. The band width is about 6% of the frequency registered.

No accelerometer was fitted to the model during the tests as, at earlier measurements of a similar kind, carried out at SSPA, only low levels of the accelerometer signals were obtaine.d.

The first condition to be fúlfilled in order to obtain reasOnable

results with regard to cavitation patterns, 'erosion patterns and

pressure fluctuations is to accomplish a realistic wake distribution behind the ship model in the cavitation tunnel. This problem was thoroughly discussed in [4] and it will oniy be stated here that the agréement between the wake distributions in the towing tank and cavitation tunnel was very good, in 'particular in fully loaded condi-tion, as is evideñt frim Fig. 11. Thus it has been dernonstiated at these tests that a representative wake distribution can be realised without incorporating a free water surface. The comparison was ma-de by using ordinary PRANDTL-tUbes. Recently, when using five-hole spherical pitot tubes on another, similar project, the same degree of agreement was obtained also for the tangential velocities and flow angles.

For these kinds of tests it is further required to define the loading cases for the propeller. In the present investigation two combinations of advance ratio J and cavitation number a were tested, one corres-ponding to the values of J and effective wake w, obtained from the propulsión tests in the towing tank, the other corresponding to the predicted full scale values of J and WTS. The prediction method used for obtaining the latter values was discussed in [4].

The desired combination of J and a was realised in the tunnel by using thrust identity with the open water tests.

Most of the tests in the tunnel were carried out at a water speed of V=4 rn/s and an air content ratio of o/c O.4, but in some cases these parameters were varied.

25

o

FULLY WADED

FINS

Fig. 11. Wake patterns in towing tank and cavitation tunnel.

-FACI LIlY WATER SPEED

1OMNG TANK 1.25 M/S

---- CAY TUNNEL:

2 .4

II

_i

ti

.... f1THOUT

- -.-0UT PR01

¿5 90 135 I.° 180 BALLAST WITHOUT FINS o ¿5 90 135 ° 180 W.'. 100-' a. X

50-25 o 100 w.,. 75 a-. .0

25t

o 100 w 'i. 75 'Q-o 5° a_ I.-o T 25 o

Cavitating Flow, Comparison with Theoretical Calculations

In Fig. 12 the first harmonics of the pressüre fluctuations obtained for the model with fins, fitted with the .six'bladed propeller; are shown in fully: loaded, as well as ballast condition. Amplitudes, obtained in the following mnner, are included in the.diagram:

Measurements in the towing tank, model speed 1.2-1.5 meters/see. Amplitudes registered on oscilographic recorder, original signals. These curves give the mean values over the speed range 11-18 knots.

Measurements in the: .cavitationtunnel, water speed 4 meters/sec. J-value=Jtowingtank Amplitudes registered on oscifiographic re-corder, filtered signals. Measuring accuracy about the same as in towing tank.

Theoretical calculations, carried out by SSPA. Wake influence considered. Method of calci ation described in. [7].

Theoretical calculations, carried out by D n V Wake influence considered.. Method of calCulation described in [8-d].

From.the diagram in Fig. 12 it can be concluded that the agreement between the measuremente in cavitation tunnel and towing tank is reasonably good. Also the agreement between calculation and

experi-ment is satisfactory. .

The influence of number of blades and fins on the pressure fluctua tions in non cavitating flow is demonstrated in connection with the results in cavitating flow, see section 12 .

Kp 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 o TMeandispersion of V(U5S (towing tank) V rn/s V-l2-l. rn/s DNV -O---- Cotunne1

- -a- - - Towing tank -. -6---- Cotcutotions,SSPA

BalLast - Fully Loaded

s s

..

-D s

i

i

AN.

i

/ -.- 'S.

/

i

¡

i

_// / /

i

¡ /

i

¡I

si

A s I I s I j ¡ _..A I I j A B C A B C D

Measuring point No.

Fig. 12. Pressure fluctuations in model scale. Non-cavitating flow. _{Model with fins.}

tions in Cavitation Tunnel Under Cavitating

Conditions.

Variation of Test Parameters, Wall Effects

Apart from the wake distribution the two most important test

parameters in the cavitation tunnel are water speed and air content.. Both parameters are known to affect the extent of the cavitation. With regard to the air content cc/c it is plausible that it might affect the damping of the water and thereby the lève! of the pressure fluc-tuations registered by the transducers. Damping of the cavitating soürce is discussed briefly in Appendix C.

In order to investigate this influence, four different combinations of water speed and air content (4 and5 meters/sec, x/o=O.l3 and 0.40) were investigated for one propellerhull configuration

(six-bladed propeller, model without fins). -From the results, some of which are given in Fig. 13, it can be concluded that the influence of these parameters on the amplitudes was considerable for the filtered signals but rather small for the maximum values of the non-filtered signals.

A problem, which should not be neglected in connection with this kind of measurements, is that of wall effect. This has been discussed by Huse in [10], from whom we quote:

"The pressure signal recorded by the pressure transducers may be split into two parts,

the "direct pressure wave" induced by propeller and cavity, propagating directly to the field point (pressure transducer), and

the reflected pressure wave induced by propeller and cavity, propagating to the field point by one or more reflections at the tunnel walls."

02Ò K 0.15 oso 005 o

Fig. 13. Pressure fluctuations in model scale. Influence of water speed and air content. .15 _i 22,24

_»

-V.hm/s OEia -o'/.. S

e-I

=

V5mM ai 13°. ---O 9

Thick tines, no fttermux. amol.

\

N

o.

\

\.

\Thifl 1ines,fitteed vaL, mean ampL

for the combination of test section and propeller size used at his experiments

"wall effects are bf minor lmportancffi m the case of a non cavita ting propeller and also m the cale of cavities of constant volume during the propeller revolution The pressure field due to volume variation, however, is reflected from the tunnel walls in such a way that the reflected amplitüde may possibly be of the same magnitude or even higher thañ.the diiect wave amplitude." In fact, for one - Of the fléld pointé investigate4, the calculations gave reflected amplitudes 4 times larger than those of the direct pressure wave.

It could be expected that, in the- much larger test section used for the experiments reported here, the wall ffects are of less importance

In this paragraph sorne test results will be given, which illústrate

the correlation obtained between the measurements of pressure

fluctuations in the tunnel under cavitating conditions and the corre-sponding full scale results. Analogous problems in connection with cavitation patterns and erosion patterns were discussed in [4].

In [4] it was shown that the erosion patterns as well as the cavita-tion patterns in fully loaded condicavita-tion agreed very well in model and full scale. In ballast condition, however, the extension of the cavita-tion, as observed in the cavitation tunnel, was somewhat smaller than in full scale. Some of these comparisons are shown in Figs 14 and 17 in connection with the comparisons of the pressure fluc-tuations.

Pressure fluctuations, measured in model scale and full scale, are compared in Figs 14-17. In all the diagrams the following kinds of results are given in non-dimensional form:

Model tests, filtered signals, mean values over about 10-20 revs. Model tests, signals obtained without filters, max values during 10-20 revs.

Full scale results, max values obtained as shown in Fig. 7. This kind of curve should correspond to results according to B for the model. (For the case shown in Fig. 16 this kind of value was not available..)

Full scale results, mean values obtained as shown in Fig. 7. In Figs 14, 15 and 17 some values òf the following kind are also shown:

Full scale results, mean values of the first harmonic of blade

fre-quency, obtained from the energy spectrum (with the use of

TJV-recorders, D-Mac curve follower, paper tape and a computer program, estimating the energy spectrum of stationary stochastic processes, see [28]). These results correspond approximately to results of type A frOm the model tests.

01

30 50 70 90

Number of rvs/rnin Fig. 17. Pressure fluctuations and cavitation patterns in model and full scale. "Norse

King" (with fins, 6-bladed propeller). Measuring point B. Ballast condition.

eon FULL SCALE 44r/m 59 r/m 68r/m - 78r1m 85r/m CAVITATION TUNNEL J=0.437 0=45 26 19 12 CAVITATION TUNNEL J=0.379 0= 34 25 16 o model lower J model

---LfuLL scaLe

--

-

,-first hormonic..-A 02 Kp

In Figs 14 and 17 also the cavitation patterns obtained in full

scale and model scale are shown. The full scale patterns were obtained from photographs taken in connection with, the speed trials, the model patterns were sketched directly when observing the cavitation in the tunnel, the position angle for the blade being 200 from upright position fOr the sketches in Fig. 14 and 250 for Fig. 17..

From Figs 14-16 it is evident that, in fully loaded condition, the agreement between the pressure fluctuations in model and full scale is reasonably good. This applies to the non-filtered signals as well as to the few cases where a comparison was made for the filtered signals In ballast condition, however, the amplitudes were lower during the model tests, which seems to be due to' the fact that the extension of the cavitatiOn was smaller on the model propeller in this case. When the propeller was run at a lower J (J and corre-sponding to sell propulsion tests in the towirg tank) the level of the unfiltered signals increased, however, to values reasonably close to those measured in full scale.

0.05

0.04

0.03

002

0.01

Ô--- Ve-lO knots (atm press.)

.-A-. V5-14

--O----V5=16

I t

5.

5 6

Yes No No

Fig. 19. Pressure fluctuations in cavitation tunnel. Different hullpropeller configura.

tions. Measuring point B. Filtered signals, maximum values.

o

NcL of bLades 6

V5- =14 knots

'=16 knots

Fig. 20. Pressure fluctuations 'in cavitation tunnel. Different hullpropeller

con-figurations. Measuring point B. Non-filtered signals, maximum values.

Ojo 0.05

-/

/

./

//

-

7.

,.

/

-knots

/

No.ofbtades6 - 5 5 6 Fiñs Yes No No

d) 1.0

''

X OB OB 1.0 X OB Os

Tip vortex,attached to the btadecontinuous lip vortex following the blade, often intermittent

H

,1

/

Model with finsa 6.- bladed propeller

S-'

Model with fins, 5- bladed propeller

/

Model without fins, 5-bLaded propeller

Model without fins 6-bladed propeller

Fig. 23. Tests in cavitation tunnel. Radial extension of cavitation in different blade positions. Different hullpropeller configurations. Fully loaded condition, 16 knots.

I

nns'

_NJ

_N

I S--,

360 270 180 90 O

Position ungle degrees,from upright

1.0

X

OB

The amplification of the signals, caused by cavitation, is appreciably higher for the six-bladed than for the five-bladed propeller. The same tendency, although less pronounced, was found at systematic tests

carried out at W a g e n i n g en,

using a dummy model [11]. The maximum amplifaction factors found at the present tests were 4 (filtered signals) añd 17 (max non-filtered/filtered without cavitation). Apart from being observed from the non-filtered signals, the diffe-rence between the five- and the six-bladed propeller can be seen in the diagrams obtained from the frequency analyser, see Fig. 21. It is evident that the content of higher harmonics is larger for the five-bladed than for the sixfive-bladed propeller. Results of comparisons of higher harmonics have not been included here as, in several cases, it was difficult to detemine the amplitudes with reasonable accuracy.

From the diagrams in Figs 22 and 23 it is evident that the maxi-mum extent of cavitation in different blade positions is rather similar for the different hullpropeller configurations.

The main difference between the cavitation patterns for the five-and sixbladed propellers seems to be that, for the five-bladed pro-peller, the extension of the cavitation was more fluctuating with time than for the six-bladed. This may be one explanation of the fact that the high pressure pulses from the five-bladed propeller were of such a short duration that they were not manifested on the registrations of the filtered signals. It should also be mentioned that rather small band widths were used when filtering the signals.

The extension of the cavitation was rather similar, whether the model was fitted with fins or not. In spite of this a beneficial influence of the fins could be noted on the amplitudes of the pressure fluctua-tions.

A type of cavitation, which is regarded as important in connection with fluctuating pressures on the hull, is the so called propellerhull-vortex cavitation [10]. This type of cavitation was observed fre-quently during the tests, but to about the same extent for the two propellers. This kind of cavitation was probably present during the full scale trials with the first ship, see [12], but could not be observed on the second ship, when making visual observations in connection with the photographing of cavitation.

to reproduce the experimental results in behind condition for the relatively few experimental results available. In Fig. 24 is shown how both the lifting line and lifting surface technique may work poorly, when interaction between propeller and hull wake field is not con-sidered. The propeller model in question works behind a 220,000 TDW tanker. Clearly, our method of approach, which includes inter-action corrections. based on simple continuity of flow, reproduces the experiments "within experimental accuracy" [16].

Local advance ratios, as may be experienced in the tip region of. the blade when passing a wake peak, will lead to a significantlynon-linear CLcC relationship This effect has been approximated by use of results of experiments for low aspect ratio wings described in [17] and [18].

To decrease the risk for a "happy coincidence to occur" we have performed other comparisons with experiments. Thus in Fig. 25 results from a one-blade dynamometer test are compared with

cal-culated values, obtained by using our approach; the calculations being based on the nominal wake field and the detailed propeller

MEASURED ANO CALCULATED KT PER BLADE

Z .h AE FA0 0.585 010 K PER BLADE 0.05 CALCULATED 90 l0 - 270- Çlp 350

CD It2 pvD 4 - 0.6 -0. £ -0.2 02 p - p0

CHORDWISE PRESSURE DISTRIBUTION J oO.I088 EXP. SV HØI8YSEEQ.FIU2I I /CALCLJLATED.009

i.:

.

00 02 0.4 06 0,0 1.0

RADIUS 07H CHORD FRACTION

Fig. 26. Chordwise pressure distribution of a propeller blade section. Experiments and calculations.

geometry. As far as we understand, thé praòticai implications of the observations given above, aré thé f011owing:

The wake survey should b,e performed in the propeller plane of the towed modelfrom the shaft CL to at least. 1.3 x R

(R=pro-peller radius). . . .

It is important to include both the axial añd tangential wake

field in the analysis.

It is possibly neeséary to extend the lifting surface theory to

include non-linearity and effects of interactioh with nearby

boundaries. . .

The reséarch nOw initiated wi1 coñtinue in tbe Ì972-1974 period.

Calculation of Radial, and Chordwise Pressuré Distributions

The corresponding .detailed, pressure, distributions

are found,

applying a method presented in [14] and [19] and brièfly outlined in Appendix A. n Figs 26 and 27 detailed pressure distributions cal-culated in accordance with the said appendix are shown to correlate well with HørBY's experiments (see [14], Fig. 21, J=O.1068).

SPANWISE PRESSURE DISTRIBUTION AT 1/4-CHORD

05 07 09 tIR

Fig. 27. Spanwise pressure distribution of propeller blade. Experiments and calculations.

CalcuLation oJ Cavity Formation

For the ships considered in this report, the pressure distributions for the propeller blades in upwards vertical position (#= 0) and cor-responding extent of cavitation are given as follows:

Fig. 28 illustrates the calculated extent o. cavitation on the full scale propeller mounted onboard T/T "Thorshammer" with observed erosion on the blades included. (In [4] it is concluded that model and full scale erösion patterns are similar). Figs 29 and 30 show the corresponding calculated pressure distributions. Fig. 31 gives the observed and calculated extent of. cavitation in fülly loaded and ballast condition onboard T/T "Norse King", in the latter case for RPM= 66, V= 12.5 knots. More interesting are the theoretical/full scale correlation and the theoretical/model correlation presented in Fig. 32. (The corresponding pressure distributions are given in Figs 33 and 34). Assuming no scale effect on the cavitation tunnel wake field, we observe that the calculated difference in radial variation of the dynamic pressure rIative to the static pressure is actually ex-perienced by visual cavitation observations. Some difficulties reported with eíact simulatión of velocity, number of revs and tunnel pressure may also expinin some of the discrepencies between model and full scale observations. J06 U PRESSURE SIDE

I

SUCTION SIDE J IEICP.HOIBV - CALCULATED, Doy SUCTION SIDE CALCULATEDDnV PRESSURE SIDE 0.25 0.7 0. 5 0.3 0. 1 0.0 0.1 0. 3

Fig. 28. "Thorähammer" without fins (5-bladed ptepeller). Estimated extension of propeller cavitation. Blade position upright. Ballast condition.

Vl8.l knots, N=86 r/m.

OBSERVED FULL SCALE

EROSIO N

0.5 nR 1.0

Fig. 29. "Thorshammei" without fins (5-bladed propeller). Calculated radiai distribu. tion of minimun local pressure and cavitation pressure. Loading case, see Fig. 28.

Cp

-0.5

0.5 _x/c 1.0

Fig. 30. "Thorshainrner" without fins (5-bladed propeiler) Calculated chordwise

pressure distribution at 0.8 R. Loading case, sei Fig. 28.

OBSERVED EXTENT 0F CAVITATION, FULL SCALE

-0

ESTIMATED

-

-.

Cp

Fig. 31. "Norse King" (6-bladed propeller). Estimated and observed extension of, cavitation. Blade position upriglit.

FULLY LOADED BALLAST

N8L,S i/rn N66.0 i/rn

OBSERVED EXTENT OF CAVITATION ESTIMATED

FULL SCALE MODEL

Fig. 32. "Norse Kiùg" (6-bladed propeller). Estirnatel and obsérved extensión of

cavitation. Ballast condition. Blade position upright. V= 17.8 knots, N=85.4 r/m.

Details connected with determination of type and extent of cavita-tion are described in [19] and briefly outlined in Appendix B. Applying symmetrical hysteresis effect, (although non-symmetrical in the tip region) and assuming that time dependent factors, sùch as inertia

and duration of transient pressure, do not influence the onset of

cavitation, a simple "maximum bubble radims" concept has been used to establish the extent of cavitation. Fiïrther, it has been assumed that the degree of turbulence of the inlet flow is so large that no laminar separation occurs. Also when ignoring effects of sudden changes of angle of incidence and several other effects, we find that,

for several cases considered, the quality of the results obtained,

when operating in behind condition, is satisfactory fOr engineering purposes [19].

The thiòkness of the sheet of cavities at 0.95 nR is found by esti mating the height of the tip vortex, as described in [18]. The radial thickness distribution is then found by linear interpolation, as the radial inception point is already determined The method is briefly outlined in Appendix B.

Cp

0.5

-Cp

Fig.. 33. "Norse King" (6-bladed propeUer). Calculated radial distribution of mmum

local pressure and cavitation pressure. Loading case, see Fig. 32.

0.5. x/c 1.0

Fig. 34. "Norse King" (6-bladed propeller) Calculated chordwise pressure distribution

Calculation of Pressure Fluctuations on the Hull

Fiiially, in this section we will illustrate how. simple mathematical models may be used in this case to approximate the complicated transfer function, giving rise to a fluctuating hull pressure field, during the formation of unstable cavities

The acceleration potential caused by the cavity formation may be found by solution of the VOLTERRA integral equation, if the formation be accurately represented at any tirne during growth and collapse. The vapour/liquid mixture representing a pulsating s*olume cannot

be said to constitute a surface of

shape. Consequently, an ideal mathematical model of moderate complexity should be em-ployed, together with empirical corrections found by experiments.

The mathematical model now in usé at D n V [20] is described in some detail in Appendlix Ç. The cavitation patternsobserved onboard T/T. "Norse King", simulated as shown in Figs 35 and 36, have been used, to obtain the results, presented in Fig. 37. Clearly, the calculated values for blade frequency pressures on the hull closely resemble full scale values recorded. Also twice blade frequency components, as calculated, correspond approximately with values recorded, see Fig. 38.

T H IC K NESS

(mm)

FULL SCALE OBSERVATIONS

A O.95R

O

X 0.8 R D

- THEORY

Fig.. 35."Norse King" (6-bladed propeller). Estimated extension and maximum

thickness of cavitation at different blade positiòns Full scade, badlast condition. 18.1 knots, N=86 r/m.

300

50

0.9R 0.95R

320 340

FULL- SCALE OBSERVATIONS

A 0 0.9 R -X - 0.8R THEORY EXTENT x/C 1.0 20 A 40 o 40 Ô.95R 60 60

Fig. 36. "Norse King" (6-Naded propeller) Estimated exten2ion and maximum

Lthico of cavitation at different blade positions Full scale, fully loaded condition. 16.1 knots, N=84 rim.

NON CAY. 0.01B1 NON CAV. 0.01933 CELL 5 BALLAST Cp.0.O - CpI.0.osi. - p. NON CAY. 0.021 LOADED UPCP.0.052

jTALCP00

NON CAY. 0.022

Fig 37. "Norso King" (6-b1ded propeller). Prossuro fluctuations in full scale.

BALLAST MEASURED Cp0,O38 NON CAV. 0.00309 BALLAST 1EASURED Cp.0.O3 THEORET!C ÇP O.03 CAy. 0.0294 CAy. 0.0 34 LOA D E D MEAS cp CAy. 0.0033 CAy. 0.0172 CELL 5 NON CAy. 0.00223 LOA D E D MEASURED cp 0.o!._: THEORETIÇAL Cp O.0165 CAy. 0.00228 CAy. 0.0143

Fig. 38. "Norse King" (6-bladed propeller). Préssure fliíctiiiltids iñ fill! sòale.

The most important conclusions to be drawn from the results of the present investigation can be summarised as follows:

From the vibration measurements in full scale it can be concluded that the introduction of afterbody fins lowered the level of the blade frequency hull vibrations. No further improvement seems to have been achieved by replacing the original five-bladed propeller on the first ship by a six-bladed propeller of different design on the second ship. For all configurations the amplitudes were some-what larger in ballast than in fully loaded condition.

The conclusions drawn above were confirmed in general by the results of the measurements of hull pressure fluctuations in diffe-rent points of the stern, made simultaneously with the vibration measurements. In fully loaded condition the amplitudes of the pressure fluctuations were, however, larger for the six-bladed than for the five-bladed propeller over most of the speed range, the vibration levels being about the same, as mentioned above. Under non-cavitating conditions reasonable agreement was ob-tained between cavitation tunnel, towing tank and theoretical calculations for the amplitudes of the blade frequency harmonic of the pressure fluctuations. The pressure fluctuations obtained were similar for the different hullpropeller configurations. The amplitudes of the pressure fluctuations in full scale and those

obtained in the cavitation tunnel under cavitating conditions

showed reasonably good agreement. This applies to the maximum peak to peak values, as well as the first harmonic for the fully loaded condition. In the ballast condition the amplitudes were smaller in model scale.

When judging the relative merits of the five- and six-bladed propellers from the vibration point of view on the basis of pressure fluctuations, measured in the cavitation tunnel under cavitating conditions, the results have to be analysed very carefully. Thus,

in the present case, a relation between the different hullpropeller configurations, agreeing with the tendency of the full scale experi-ences, was obtained only when the maximum peak to peak_values were used for comparison. Apparently, _{the pressure signals} recorded for the five-bladed propeller, were of pulse nature with rather unstable phase shifting. Consequently they did not afféct the levels of the filtered signals, obtained in non-cavitating flow. In the cases considered the, amplification _{of the amplitudes of} the pressure fluctuations, caused by cavitation, was larger for the six-bladed than the five-bladed propeller. Results reported in

[il] show thesame tendency.

The type and extension df the cavitation, _{as observed On the full} scale ship (six-bladed propeller) and in the cavitation tunnel, are reasonably similar for the fully loaded condition. In the ballast condition, however, cavitation is more extensive on the ship than on the model propeller.

The observed type and extent of cavitation _{were confirmed with} reasonable accuracy by the calculations illustrated in the present paper.

The pressure impulses of both blade and twice blade frequency, recorded onboard the ship, correlated well with those calculated with the use of the method developed for the caiculatiön of pressure fluctuations from cavitating propellers.

The investigation was cárried oüt in close cooperation. between the initiator,

Uddevallavarvet AB,

the

Swedish

State Shipbuilding Experimental Tank and

D e t n o r s k e V e r i t a s. The work has bee

sponsored partly

by the Swedish Board. for Technical

Develop-m e n t and partly by the shipyarft and the shiowner

companies involved, i.e. A/S T h o r D a h I, Sandefjord and Od d G o d

a-ger and Co, Oslo.

The authors would like to express their sincere thanks to all those members of the staffs of the above-mentioned establishments and companies, ,who have taken part in the investigations and ontributed to the analysis of the material.

NESS, L M.: "TJT Thorshamrner, Uddevallavarvets b.nr 226,

Vibrasjonsmh-linger", DnV Report No 70-31-O, Oslo, May 1970 (in Norwegian).

JØRGENSEN, 0: "T/T Thorshammer, tJddevallavarvets b nr 226", Dn.V Report

No 70-46-O, Oslo, April 1970 (in Norwegian).

JORGENSEN, 0: "T/T Norse King, Tfddevallavarvets b nr 234", DnV Report No 71-20-O, Oslo, Febr 1971 (in Norwegian).

LrNDGREN, H, JomessoN, C-A and SIMoNssoN, E: "Propulsion and Cavitation

Investigation on 230,000 tons dwt TankersFull Scale and Model

Experi-ments", The Royal Institution of Naval Architects, Spring Meetings 1972, Paper No 8.

"Computer program NV517: Holzer Tabulation of Axiàl Vibration in Straight

Marine Shaft Systems".'

EDSThAND, H: "Kavitationslaboratoriet vid Statens Skeppsprovningsanstalt (The Cavitation Laboratory at SSPA)", Swedish Stale Shipbuilding

Experi-mental Tank Circular No 26, Göteborg 1970 (in Swedish).

[71 Josrusso, C-A: "Pressure Fluctuations Around a Marine Propeller. Results of Calculations and Comparison with Experiment", Swedish State Shipbuilding

Experimental Tank Publ. No 69, Göteborg 1971.

HUBE, E: "The Magnitude and Distribution of Propeller-Induced Surface Forces on a Single-Screw Ship Model", Norwegian Ship Model Experiment Tank Pubi No 100, Trondheim 1968

RAESTAD, A E: "Computer Program NV 538: The Free Stream Pressure Field Induced by the Propeller", DuV Report No 70-22-M, Oslo 1970.

HUSE, E: "Pressure Fluctuations on the Hull Induced by Cavitating Propellers",

Norwegian Ship Model Experiment Tank Publ No 111, Trondheim, March 1972.

VAN Oosssu, P and VAN DER Kooy, J: "Vibratory Hull Forces Induced by

Cavitating Propellers", The Royal Institution of Naval Architects, Spring

Meetings 1972, Paper No 9.

SØNTVEDT, T: Propeller Induced Excitation Forces", DnV Publ No 74, Oslo, Jan.

1971.

SØNTVEDT, T: "Theoretical Calculations of Hydrodynamic Loading on the Marine

Propeller Part I. Open Water Performance. Progress Report No 2", DnV

Report No 71-64-M, Oslo 1971.

Horny, O W: "Three-Dimensional Effects in Propeller Theory", Norwegian Ship

Model Experiment Tank, Publ No 105, Trondheim, May 1970.

KUIPER, G: "Unsteady Lifting Surface Theory", Design and Economical Con-siderations on Shipbuilding and Shipping, Rep of the Post Graduate Course, May 1969, pp 125-149, (Royal Institution of Engineers), Wageningen,

RSsT&n, A E: "Estimation of a Marine Propeller's Induced Effects on the Hull Wake Field", DnV Report No 72-3-M, Oslo 1972.

Kücnsiviw, D: "A Simple Method for Calculating the Span and Chordwise

Loading on Straight and Swept Wings of any Given Aspect Ratio at

Sub-sonic Speed", Aeronautical Research Council, R and M No 2935, London 1956. KÜCHEaIANN, D and KETTLE, D F: "The Effect of Endplates on Swept Wings", Royal Aircraft Establishment, Farnborough, Report No Aero 2429, June 1951.

Hoiiu, K: "Type and Extent of Cavitation on Hydrofoils and Marine Propeller

Blades", DnV Report No 72.2-M, Oslo 1972.

HOLDEN, K and SØNTVEDT, T: "Propeller Cavitation as a Source to Vibration", DnV Report No 72-,5-M, Oslo 1972.

SCHOLTZ, N: "Strömungsuntersuchungen an Schaufelgittern", VDI-Forschungs-heft 442, Düsseldorf 1954.

ScmIcHrrNo, H: "Berechnung der Reibungslosen inkompressiblen Strömung für.

ein vorgegebenes Schaufelgitter", VDI-Forschungsheft 447, Düsseldorf 1955. Poi.io, D and WORDSWORTH, J: "A Comparison of Two Methods for Predicting

the Potential Flow arund Arbitrary Airfoilsin Cascade", Aeronautical

Rese-arch Council, C P No 618, London 1963.

MoRGre, W B, Smovic, V and DHry, S: "Propeller Lifting Surface

Correc-tions", Trans Society of Naval Architects and Marine Engineers, Vol 76 (1968).

STRASBERO, M: "The Influence of Air-Filled Nuclei on Cavitation Inception", David Taylor Model Basin Rep 1078, Washington D C 1957.

JOHNSSON, C-A: "On Theoretical Predictions of Characteristics and Cavitation Properties of Propellers", SSPA Publ No 64, Göteborg 1968.

HUSH, E: "Hull Vibration and Measurements of Propeller-Induced Pressure Fluctuations", Proc 12th mt Towing Tank Conference, Rome, Sept 1969.

DENOOTJ, F E: "Auto-Correlation Functions and Energy Spectrum of Stationary Stochastic Processes", DnV Report No 69-37-S, Oslo 1969.

WEBER, J: "The Calculation of the Pressure Distribution over the Surface of Two-Dimensional and Swept Wings with Symmetrical Aerofoil Sections",

5

Chordw*se Pressure Thstributzon Method of Calculatzon

From [14] and [19] we have for the contributions to the mduced velocities:

L Velocity distribution due to blade thickness

distribution

Ju, (x, z) UNO S(2)(x)

(Sw

_{(x)-T /(}

S(7)(X))

(Q)

S7(x)

-S7(x) 1"1

+

Sx).+S5 (x)

2 V òos (Ï -jL ) Q

S'(x) =

1 Çi:; dz(x') dx' )0 dx'

xx'

S(2)(x) = dx (5) (x) dx

z =profile thichiess ordinates cathber

datÑ

UNO = U0 cos cos Q Q = effective skew anglé

r

= correctiòn factor due to blade thickness taper

I-IT and ¡(Q) =factors taking account of the effect of the centre sectión and the tip region

U0 =resultant inflow velocity==(wr ± Vr)±VA2 ±VR2

Angle of incidénce

JUa(X,Z) i

f 1x\

f

U0

=±S(7)()

kl+(Í)Q

Ugo =Uo Sifl COSy

fi dz(x') f 2z(') dx'

IT J0

dx'.:

1.(1.2x');xx'

y

=akeange

n

=2{i+(ao0r)2}h/4

for a0, see p 67

Mean Line Camber

4u(x,z)

yb(x)

,.LTtanQ

dz(x'

U0 = 2 UNO

1±r2 tan2 Q

dx

+

i

+

1±,LT2tan2Q 1

0=1--

arccos 2ir

4. Thickness of the other blades

The cascade effects are obtained as shown by O.HØIBY [14], SCHOLZ

[21], SCHLICHTrNG [22] and POLLARD and WORDSWORTH [23]. u.(x) k2 Ç1 dz(x')

R(ç6, s, x )dx . (4)

UNO

u=chordwise induced velocity

D ir r'

s =

Z chord

r' =O.825r+O.lO5

sJ0

dx'

(1_x\0

_{1-fl dz(x')(}

z _J

_j0

dx'

\i-P-2r

tan2 Q-1

tan2 Q--i

(2)

e

_dx' X.. X' (3)

dCL/27T

k2---dac R_:

(x_x'.\

.

(xx')/8+n

cos 2 k s J

,i ((xx)/s)±n+2 fl2. c0S2#((x_x')/8)2

= pitch angle

& Bound voiticés ori Other blades

u(x)

] .11

= ky-

J u',, I'(p, Z)dp

NO No

.b

u,,=ehordwise induced velocity r'(p, Z)=circulation

cos4i(r).

I'

47r{(1r(r) Oli(p)q!)2 +r2 ± p2-2rpcos (ç O+&k) }312

2(k-1)

=

, k=2, Z; u',,=chordwise induced velocity: due to

a bound vortex of unit strength at (8k p'

The angle of incidence is found from the following expressions:

dCL 0L

dx -

.

CL

I i

i

r1 V(x)

- +(2n-1) (ßIß)--CL( - -

JI

-

dx .

()

a a

where CL, ß..and_fi are obtained from lifting line calculations

cos,LTQ 2n

a =a0

.- ..

---' nno.

1irn(cot irncOtirn)

¡ Q

flo=i+!zTj

I

a0=O.9( 1+0.8I. 2,r

_CI.

V(x) 1

Ç V'(x)

.1'(p,Z) dp

UNO UNO _J'b1c2

V (x)=induced velocity nOrmal to the chord uñe V'(x)=

rcos &(r)

sin (ç6O+8k)+(P(r)O--/J(p)ç6) cos(4O±8k) sin',(r)

4ir{(i/i(r)Oi/i(p)#)2 +r2 +p2---2rP COS ( O±Sk)}212.

V '(z) = induced velocity ñormal to the chord line, due to a vortex of unit strength

f'Vc(x)

c =ßß +

- dx JO '-'NO V(x) k2 Ç dz(x') UNO 8

_J°

dx'

V(x)=induced velocity nórmal to the chord line due to thickness of the other blades

12(x_x'\

z

- ir

8

_/

n=1 ((xx')/s)4+n4+2n2 cos2ç6((x__x')/.$)2

dCLIdCL.---P+o)/

oc=effective angle of incidence, corrected for lifting surface effects

i3=i2

k .+k

_D

where k,, and k are found fróm lifting surface theory [24]. From [14] we quote:

"For a swept wing WEBER [29] has shown that a flow parallel to the span must be added, sò that the total pressure distribution is given as:

Gp(x)=l_(U) cös2ocsin2Q

VL(x)= Uo +4u(x) +Ju,,(x) +zIu(x) +u(z) +u(x) I(ç6, s, z') dx'

f2

T1

Cavity Formation, Method of Calcukition

1. Extent of Cavitation

When the detailed blade pressure distribution ils known, the amount of. cavitation may be determined, see [25, 26].

T2 (1)

p

where

z1 .= the point at which the local pressure falls below the cavitation

pressurç Pcac, .Pvapor

x2 =the point at which the local pressure has increased and reached the cavitation pressure

T=the time when Piocai Pcau p =local pressure

dp=p00p

T2 and z3 are found by an iteratiòn process z1 +x3=extent of cavitation

For symmetrical hysteresis k is equal to unity. In the tip región the hysteresis will be non-symmetrical and the factor k.is below unity. The radial distribution of.k is found from propeller cavitation tests

2. Thickness

The diameter of the tip vortex obtained when separation takes place at the tip may be determined by the expression:

h x

CT

'

b 2 (2)

where

h ==diameter of the tip vortex b

=

Blade length

=pitch

fi .=advance aiïgle.

CT=blade section length.at 0.95 R C

=

mean blade section length A =aspect ratio

o =anglè of incidence for separation at tip (relative to_fi). Based

on experiments in [17] a=8° in' this report The pressure in the centre of the vortex:

p(l'F)2

PCPO _8n(h/2)2 (3)

m =pressure at the radial section close to the boundary of the

vortex.

av

=

dr free vortex strength 1' =bound circuintion

Two cases A and B must be considered:

A.

pi0

The maximum cavitation thickness will be equal to the tip vortex diameter. The radial thickness distribution is found from observed shapes of thickness along the radius terminating at the radial incep-tiOn point (calculated or observed).

B. Po>Pcao>pc

The diameter of the cavitating tip vortex is found from the pressure

distribution across the tip vortex radius assuming symmetrical

l'ressure Fluctuations on the ¡full, Method of Calculation

The velocity potential caused by a pulsating cavity may be found by solution of the VOLTERRA equation if the cavity formation be accu-rately represented at any time during growth and collapse. The vapour! liquid mixture representing a pulsating volume cannot be said to

constitute a surface of known shape. Çonsequently, an- ideal mathe-matical model of moderate complexity shoûld be employed together with empirical functions found by experiments.

The net velocity potential at any field point (x1, y1, Z» caused by the small volume source Jr Jx Jr:

U X

Urr

Uar

4=-j

JtJx+-- .JxJr+_ã-

JxJr

+

JrJr+-JxJr

(1)

where: d = distance between volume source and field point

Jr

- thicirness of volume

Jx

= length of volume-along helix

Jr

= length of volume along radius

t

=time

-r = velocity of advance of volume source

-- The first part of the right hand side of the equation is due to the

motion of cavities and derivatives of r, x and r with respect to tine are zero. The last part is due to volume variation of cavities.

For unsteady, irrptational flow the fluctuating pressure p field at a fiel4 point:

s = solid boundary factor [IO]

U=veloçity at the fièld point, negligible at the hull surface Assuming U,.= U,,=O and combining Eqs. (1) and (2):

47rp

=

JxJr+

sp

=Angular position of volume source 2irrn/cos ß

where

ß=geometric pitch angle

We assume that the cavity formation at time t displaces a volume

of liquid bound by the helicoidal blade surf ace and the plane P

parallel to the shaft (z0-axis) (Fig. 39).

In accordance .vith Fig. 40 the thickness distribution in the z-direction:

T(x, r, t)=r(r, t) . ¡(z) (6)

Admittingly, the proposed distribution has been designed to suit mathematical interpretation of the extremely complex "shape" of the vapour/liquid formation.

i

2&rx

x

l2x

1 r

i

2r

+

__]rr+[_(_)_

+

lJXJT+

2 rr

2

xar

(3)

d2=(x1x0)2 ±(f Yo)2 +(zz)2

(4)

where x0, Yo' z0=coordinate. of volume source

2ir rn

atd

where: n =RPS

(5)

ELEMENT OF CAVITY

Fig. 39. Geometry of cavity, assumed at calculations.

The chordwise extent of the volume at any time when periodicity may be assumed a valid assumption:

I4rr2nmt

X _{X0 +} Xm sin _{+ 0m}

m=1

LPiPo

where OmPll2e angle

n =RPS

m = harmonic order

= angular position for collapse of cavitation 0=anguIar position for inception of cavitation

FIELD

POINT

CR PROFILE.

xi

CAVITY

PROFILE

TYPE 1 : TURBULENT SEPARATION

FORMING CLOUD ON EQUIVALENT PROFILE CP. CAV. Le. S T.e. CAVITY VOLUME TURBULENT SEPARATION FRoM PROPELLER CAVITY PROFILE Xt xi CR PROFILE CR CAy. POINT OF TURBULENT SEPARATION FROM PROFILE + CAVITY PROFILE xt CAVITY PROFILE CAVITY VOLUME

TYPE 2: TURBULENT SEPARATION

DOWNSTREAM OF EQUIVALENT PROFILE

Dividing Eq. (3) by n2D2 and making use of derived quantities in given eqs.: pn':D2

=

[s:: s: I1dx dr

+5

±

rxin, -1

+ I

(J3+J5)dx+.i,,

I (8) J where Xgmaz =max. length of cavity along radius

V V

=max. thickness of cavity along radius z = number of propeller blades -. If we assume:that 1=1 in Eq. (6)., V - . V

i

. Il/Kz=uzfIeT+e_r±d_ V VV V (9) V I2IK=e±+ V V (10)

13/K=et+

V (11) V

J4/X=(u+)

,V V V (f2) V

u/'it

2 d V (13)

I6/K=rx

(14)

The expressions for some, of the variables in the above equatipns

are finally listed: V

I 4ir2n \2

=

- V J m2rmSino (15) V

\9to/ m=1

I \2 V V V

-

I J m2xmsinc (16)

\9r-9o/.m=i

V V whereV:

2i()m

V +°m WrWo

A = aspect ratio of the cavitating body k =reduced frequency

s

4 ,,.2 D2

Appendix A Appendix B Appendix C

t

Contents Synopsis -. : Introduction

...4

List of Symbols

...

6

Scope of the Present Investigation ...7

Ship and Model Configurations Tested ...8

Full Sóale Tests. Test Equipment and Test Cónditions 10 FuJi Scale Tests. Results 15

Model Tests. Test Arrangements and Façilities ...24

Test Conditions in the Cavitation Tunnel 26

Results of Model Tests.. Pressure Fluctuations in

Non-Cavitating Flow. Comparison with Theoretical Calculations 28 Results of Model Tests. Measurement' of Préssure Fluctua-tions in Cavitation Tunnel under Cavitating CondiFluctua-tions. Variation of Test Parameters. Wall Effects 30

Results of Model Tests. Comparison with Full Scale ...33

Results of Model Tests. Comparison between Different Pro-peller-Hull Configurations 38 Cavitation Patterns and Pressure Fluctuations. Theoretical Calculations and Comparison with Experiments 46 Summary and Conclusions 60 Acknowledgement 62 List of References

...

. 63

65 69