The effect of bow flare on deck wetness

.EHOORT BL]

f3RlEn d.a.

___-van

Synopsis

ThE EFFECT OF BOW FLARE ON DECK WETNESS by

Ir.J.J. Blok, Netherlands Ship Model Basin Ir.H.Vermeer, Netherlands Directorate General

Lab. y. Schee

wkOed Maritime Affairs

Technische 1-logeschool

Deift

-2-ARCHIEF

This paper gives a presentation of model test results showing the effect of a systematic variation of bow flare on the amount of water shipped over the bow The tests have been carried out with a self-propelled, unrestrained model of

a bulk carrier in regular head waves covering a range of wavelengths and wave-heights; the model speed was kept the same for all experiments. The experimental data are compared with the predicted estimates determined by means of a simplified mathematical model which has been developed along the lines of linear ship motion

theory. The information obtained in this manner supplemented by the results of

previous studies afford the possibility to draw some. conclusions on various

as-pects of this phenomenon. In the discussion on the subject the influence of the parameters governing the process of shipping of water over the bow will be

high-lighted and topics of a general nature such as the feasibility of mode.l testing, the accuracy of the mathematical prediction instrunent and the associated

statis-tical properties in irregular seas will be touched upon. Introduction

Shipping of water may pose a problem for the o?erational performance of a number of ship types. There exists for instance a great variety of workships where due to their task assignment the exposed deck should form a stable and

safe,and therefore dry7working platform. The intact stability of the vEssel might also be endangered due to water trapped on deck such as is the case with

a deckwell on smaller fishing vessels or a deckcargo cf pipes on supply vessels. A more general problem is the watertight integrity of the exposed deck, the

closing appliances and the superstructure, This becois prominent for ships having a forward superstructure such as heavy-load vessels and more in particular the lash barge carriers.

In an attempt to produce a prediction method for the amount of water that may be shipped over the bow a simplified mathematical madel has been developed.

In order to acquire sorne notion of its accuracy initial calculations have been

carried out on the basis of data obtained by two prious series of model tests.

The results of this comparison have been reported iir reference

C1J.

The experimental data of the first series of model tests supplemented by the

corresponding calculated data are presented in Figtne 1. The model in question was a bulk carrier with vertical sides and a full romded form of bow'. All the measurements have been carried out at a speed of approximately 17 knot.s in

regular head waves. The experimental data of the second series of model tests complemented by the corresponding calculated data are presented in Figure 2.

The model in question was the same bulk carrier with vertical sides, however, with a fairly sharp wedged form of bow. All the measurements have been carried out at a speed of approximately 12 knots in regular head waves.

It should be noted that shipping of green water may only occur if the relative mot: exceeds the freeboard. Both parameters are strongly influenced by swell-up

phenomena. The relative motion is affected by the dynamic swell-up caused by the vertical oscillation of the ship in waves. The freeboard is affected

by the static swell-up, primarily the ship's own wave system, resulting in a

correction of the geometrical freeboard giving a-reducedeffectiYe fr&eboard F.T1-effective freeboard in the second series of tests is determined from the mean value of the relative motion in waves, which procedure is t preferred. Ii'.

addition to this method (Fe1) an alternative method (Fe2) bas been applied & the first series of tests, where the effective freeboard is determined fror.n the bow wave instill water, thereby producing less accurate results.

It is observed that the agreement between the experimental data and the cal-culated data in the second series of tests is relatively better than in the first series of tests. This may probably be attributed to diffraction phenomena which are not explicitly included in the mathematical model and

which were more present on the full bow of:series 1 than on the wedge shaped bow

of series 2.

The mathematical model takes into account the ship's speed, which is of major importance, the orbital velocity in the wave, the surga motion and the effect of flare. The results of model experiments and corresponding calculations presented in the present paper aim at a more thorough investigation of the effect of the surge motion and the effect of a systematic variation of bow flare on the quantity of water shipped over the bow. This third series of tests has been carried out using the same model as in the previous test programmes,

provided with three different bow forms. The results of t:hese model experiments

have been reported in reference C2J.

From a small scale literature survey rlJ a limited amount of information on the subject in general could be gathered. Specific inforiition on shipping of water in terms of volumes however is very scarce. In this context it is

inte-resting to note reference

C3J

which gives an account of a series of moiel experiments with the same aim as the present stud. Im the referenced paper

the author proposed a semi-empirical formula for the estilrmtion of the volume

of water shipped over the bow per oscillation in the early stage of deck wetness for the vessel with forward speed in head waves. This apprximation will also be applied in the present study for the purpose of a comparison.

Mathematical model

The amount of water shipped per oscillation can be determined from

inte-gration of the local positive flux (see Figure 3) over the length x of thE exposed deck. The total result can be represented as follow:

L k '1.2.

VFI113

_{J(.._i)_}

_j-cc0J

c L' f.2

L4/

r2

cV2

I ±

_{- (I-}

Q-

-z-.

_"-'C.

jI

¿

-xF

-

E /y1z3 / - .'-ccc' _-

(i- ')

Q-=

dx

-2-(I)

in which V1, represents the contribution as a result of the ship's speed, V2 the contribution as a result of the orbital velocity in the wave, V3 the

contribution due to the surge speed and V4 the cd"tribution from the

flare. A possible contribution as a result of the pressure height, associated with the instantaneous waterlevel above the deck has been ignored.

The slope of the waterline of the exposed deck, defined by , and the flare

in the transverse direction and the longitudinal direction, defined by respectively _b and , are explained in Figure 3.

The alternative expression for the amount of water per cycle of oscillation for a vessel with forward speed is according to Tasaki:

(6)

with the restriction that S ¡Fe 11, which indicates that the approxima-tion formula is valid only or the initial stage of shipping of water, in which the relative motion is only just exceeding the freeboard.

Computation of shipping of water quantities in irregular waves poses a rther complicated problem from the mathematical point of üew because the V-response is in a strongly non-linear way dependent on wave height. Reference

CiJ

gives

some procedures to calculate the average volume of shipped water per time unit in an irregular seaway. However these procedures need further evaluation and validation which is outside the scope of this paper.

Model experiments

In order to validate the mathematical uodel with respect to the influs.ice

of bow flare on the amount of water shipped over the bow, a systematic series of experiments was carried out, reported in C2J

Three model bow shapes were designed that wOErid all f i. to the same bulkcarier aftbody used for the foregoing two series of model experiments. The bow

shapes featured a systematic variation of f lire as shovn in Figure 4. The link between the forms was the lateral angle that the section at station 20 made with the vertical at the ie'cel of the frecastle ffeck. The respective angles were 15, 30 and 45 degrees and the rest of the flare shape was made in proportion. It should be noted that the uaderwater sull forms 'were kept the same so as to obtain the sane ship motiQns for all three variants. A ria-tion in flare angle, retaining the saine finemess of the waterlíns, resul

accordingly into a correspondìng variation OEf the stew angle.

The amount of water that would couie on board constituted the most, important.

quantity and for its measurentent the "catch-tank" approach was taken. For this purpose the forecastle deck was made open leaving only the ship's si intact to the level of the forecastle deck, and a collecting tmk was bui1t into the model so that any water that would come on deck would be trapped in the tank. A couple of high discharge punps in the aftbody of the model pumped the water to a measuring vessel on the carriage to avoid that the iodel would sink deeper and alter trim and inertia properties.

The experiments were all done in the seakeeping basin, measuring 100 x 24. x 2,5 m

in length, width and waterdepth, on a self-propelled, self-steered model..

For the validation of the mathematical model one speed (12 knots) and regular waves from ahead would suffice. Besides the amount of water, records were also made of the relative motion at various stations along tht bow. Because

the computational model determines the amount of water from t1ìe relative

motion which in turn comes from the basic ship motions, the '.7alidation of the

relative motion was also a necessity. In addition to the routine measurement of the wave elevation in front of the model the longitudinal horizontal ship motion - surge - was measured as it might play an important role in the

analytical model.

pr

-4-Shipping of water can only take place if and where a relative motion exceeds

the local freeboard height. The transfer function of relative motion acts as a sharply peaked filter, like its main component of pitching. Expressed in terms of wave length, water would only be shipped if the wave length to shiplength ratio would be within the 1.0 to 1.4 range. Apart fr the wave

length dependency the influence of wave amplitude was also quite dramatic.

Obviously, shipping of water is a threshold crossing problem and a siight increase in relative motion would manifold the amount of shipping water, which is clearly shown in Figure 5.

For the execution of the tests this meant a great emphasis to be laid upon the accuracy of ship speed, incident wave properties and the measurements. A considerable effort was expended on trial runs to determine the"window of

relevant parameterst' to be adopted for the full measurement runs.As it turned

out all three bow forms could be tested in regular waves of almost the same he without the amount of caught water becoming unmeasurable (either too mich or

too little). In view of the great difference in bow form this is not just an bvious result. Measurements of relative motions were harmonically analyzed to extract the mean value and to determine the first order transfer function. Presentation of results from model experiments and computations

The results of the experiments and the computations can be compara to one another at various levels i.e. motions, relative motions and the amount of water trapped in the 'catch-tank'. The latter is of course the most siiificant

for the present study and constitutes the main result. Figure 5 shows tie comparison for the three bowforms and for the three di±Ierent wave heigats. It appears at a glance that a comparatively small change in wave height alters the amount of water dramatically. The data obtained f r the model experiments are shown as fully drawn lines, the data obtained from tie present computation method are also shown. Some of the data coincide quite well, others show

considerable discrepancies. As a side-step the method 0± Tasaki

C3J

has also

been applied to the present bow forms. Although the Tasaki formula had been derived from experiments on a different hull form it wculd be interesting to

investigate the generality of Tasaki's method. The data thus obtained are also shown in the same diagrams and although some of the computation poiiits concur with the experimental measurements, the correlatixn with the experiments is generally not as good as for the present more comprehensive computational

method..

Discussion and corciusions

In addition to the effective relative vertical motion, the effective freeboard and the frequency of encounter the phenomenon of shipping of water is affected by ship speed, the surge motion, the orbital wave motion and the Ship's flare. Calculations and model experiments have shown that ship speed

governs the process of shipping water to a great extent and that in fact the oth parameters metioned are of lesser importance.

Obviously wave height and frequency of encounter (or conversely wave Lcngtl') are of paramount importance, as Figure 5 shows at a glance.

The surge motion contributed only 1 percent to the amount of shipped water and from a practical point of view this parameter may be disregarded in deck wetness calculations at normal ship speeds.

The orbital wave motion contributed, depending on the wave height, approximately 20 percent to the amount of shipped water and may consequently not be ignored in the lower ship speed regime.

Systematic calculations with the outlined mathematical model showed that the amount of water can be reduced by _{a percentage as much} as 15 percent for a transverse flare angle of 45 degrees.

So, an empirical relation can be derived to show that the percentual reduction in amount of water is equal to one third of the transverse

flare angle in degrees.

However, the model experiments have shown that the increase _{of flare} did not substantially reduce the amount of water that came on deck and it is evident that the favourable effect of flare is cancelled _{by a substantial}

increase of the width of the exposed deck near the ship's _{bow. Tasaki} reported the same tendencies i.e. increasing quantities of shipped _water

close to resonance conditions for excessive flare and _{a constant rate or} minor decrease of quantities of shipped water close to the limiting _values of the range of wavelength to shiplength ratios where shipping of _water

occurs. For illustration Tasaki's results are reproduced in Figure 6.

Generally speaking it can be observed that Tasaki has used the domina-ting effect of ship speed on shipping of water and presented _{an approximate} formula for shipping of water quantities which is only applicable for _{a low rate} of shipping of water and the ship having a moderate speed.

So, contrary to expectations bow flare does not have a dramatic influence on the amount of green water, that is taken over the bow. Yet in the less severe seaways where spray is more of a problem bow flare is important to keep the deck dry.

Considerations on future work

A mathematical prediction of the quantity of shipped water as a secondary effect possesses the inherent property of being a rough approximation because the phenomenon is very sensitive to fluctuations both in the effective free-board and the effective relative motion. Instead of extending the mathemati-cal model to oblique waves it is more effective to apply this prediction in-strument for the particular case of longitudinal waves in compaiative studies of this phenomenon. Therefore future investigations should concentrate on the development of an improved method for the estimate of the effect of swell-up on both freeboard and relative motion, see e.g. reference

_{E 41..}

Additionally an empirical correction factor, defined by ship form parameters, may be eva-luated compensating for the discrepancy between experimental data and the corresponding computations due to e.g. diffraction phenomena.

Shipping of large amounts of green water and the associated dynamic loads that may endanger the watertight integrity of the superstructures and the closing appliances on the exposed deck, is a stochastic phenomenon with the complication of being a typical threshold crossing problem. Studies in the field of impact pressure induced _{by shipping of water and investigations dealing with}

deterioration of the stability characteristics due to water _{on deck should} necessarily be carried out in conjunction with the associated statistical properties of such random events, _{see e.g. reference LT5J. In addition this} requires a sound and fundamental approach of the problem in the probabilistic

sense.

B(x) local half breadth of exposed deck

Fe local effective freeboard wave height (double amplitude)

k wave number

L ship length

r wave amplitude

Se local amplitude of effective relative vertical motion

Se amplitude of effective relative vertical motion at fore perpendicular

Te period of encounter y ship speed

V volume of shipped water per oscillation

x0 surge amplitude

phase difference between wave motion and relative vertical motion phase difference between surge motion and relative vertical motion wave length

wave circle frequency frequency of encounter

VReferences

-6-f iJ

H.Vermeer, Prediction of the amount of shipping water,

Report R 218 of the Netherlands Maritime Institute,

tec.19&.

[2] J.J.Blok, Model tests in waves to investigate shipment of

water over the bow, Report No.04750-1-ZT of the Netherlands Ship Model Basin, Aug.1983.

[33 R.Tasaki, On the shipping water in head waves, Journal of the Society of Naval Architects in Japan, Vol.107, July 1960

(in Japanese, Neth.translation J.Bongenaar).

[43

J.J.Blok and J.Huisman, Relative motions and swell-up for a frigate bow, The Naval Architect, July/Aug.1984.

[53 W.A.Cleary Jr., Load Lines - the lever of safety,

Trans-actions of the Society of Naval Architects and Marine Engineers, Vol.83, 1975.

500 250 o 750 m E c 500 o .1J -'-1 250 o w 1000 750 500 250 o U Calculation (F e2 2Ç =4.25 m a D a

04

05

Lo in s 0.6

500 250 0 750 m c 500 o 4.) -.-1 250 o C) > U C) 4.) 2 =3.95 m

2Ç =4.10

a o

04

O Experiment Calculation

Fig. 2

° 1000 4) o 2Ç_a

=4.25

m 750 500 250 0.5 0.6 w in s

TRPNSVERSE SECTION

tg = B'(x)

TOP VIEW OF EXPOSED WEATH. DECK

Ship speed y

Wave direction

dx

BOW I

BOW II

BOW III

Relative motion wires

Station 15 16 17 57 18 19 20 s s s 4

2TTT

Fig.. 4 17 Buttick

I/11

9Jf

500 1000 s 54 Q-4 .5 Ci) 500 O 1.0 o 1.0 A A BOW I 6.30

2a =

O & V V Y A BOW I 1000 1000 2803g '1227 1.5

15

500 1000 500 1000 500 o

10

= 6.05 m A o 1.0 o 1.0 V A

2a =

6.05 ni

15

1.5 A 2Ç_a = 6.05 m 500 1000 500 O 1000 500 o 1.5 1 0 BOW I 1.0 1.0 1.5

15

1.5 1000 500 o

10

9 e £ w 1.5 A 5.50 ni

.

A t,

.

A 5.50 th t, A A t, 2 = a 5.50 m A 43V63 2 = a 7.00 m

VI

V

BOW III BOW III BOW III BOW III

X IL A/L AIL BOW I 1000 A 500 e o 1.0

_lE

e 9 Measured data A Calculated V Calculated Tasaki 1000 500 A e w £ C o 1.0 1.5

BOW II BOW II BOW II

1000

BOW II

V44

8 > w 6 .1-) o O4CI

Qw

4 m

oc

s o o 50 40 ci) o 4i w . . 30

co

ow

o .2 . 20 4J o 04 o 04 w 10 E E-O 16 Measured Calculated AB C A A

\Ship speed 16 knots \A/L = 1.00; 2 = 4.23 ni a 14\ Wave height 2a = 0.10 ni A 8 9 10 11 Freeboard F in ni

Fig. 6

Fig. 6B - Influence of freeboard on time proportion of deck wetness

and amount of shipping water

X/L = 1.00 1.25 1.50

BowA

O

BowB

O u A

BowC

U A 0.5 1.0 1.5 Model speed in rn/s

Fig. 6A - Amount of shipping water per cycle

p V

= 1905 ni

Ship speed 20 knots

Wind speed 15 rn/s 200 > w .4) o -'-f o 100

ft

.,4 , o 4J o s o