The waves inside count too!

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The waves inside

count too!

Right: An example of the 'linear' type ofliquid motion, showing the wave breaking on impact with the sides and roof

of the tank.

Opposite: A typical 'non-linear' situation, showing the development ola hydraulic jump or bore. Both pictureswere

taken during the tests performed at the Technische Hoge-school, Delft.

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F 5/g,iLycs

'l'ue accurate estimation at the design stage of pressures on ship structures has assumed

para-mount importance in recent years. As ships have increased in size and sophistication, so the cost of practical trials has soared and the potential rcsults of structural collapse during service have become still mure appalling. Naturally, as the overall length and beam of oil and chemical tankers, and

bulk and gas carriers become larger, the volume

of their tanks increases also. This in turn leads to a

potential increase in _{pesstirc on the walls of those} tanks. 'I'he need to gauge and allow for the maximum possible pressure as early _{as possible has therefore} become an urgent priority fbr structural analysts.

A further recent trend has aggravated the problem of pressures on tank walls, namely the increased desire of shipo\vners to _{ll their tanks to arbitrary} and unrestricted levels. _{Lloyd's Register's Hull} Structures Development Unit _{has, for example,} received many more_{requests in the past few years}

regarding arbitrary tank fillings in bulk carriers, liquefied gas carriers and chemical tankers.

Pre-viouslv, it had been sufficient in most cases to

estimate pressures for a restricted level of filling. Now, the resultant vall pressures must be calcu-lated for any possible filling.

Both these factorsthe greater size of ships and

their tanks and the increased demand for arbitrary

tank fillingslcd Lloyd's Register to carry out a series of investigations as part of its long-term

research programme concerning ship structures and their behaviour and responses in an ocean

environment. The results of the first investigation in

this fielddealing with the problem of liquid

motions in a smooth-sided rectangular tankhave led to the development of a computer program, LR 321. This program enables the designer to

predict pressures which can be used at the design

stage to avoid the possibility of damage to tank

valls (lue to the sloshing of the liquid.

Both model experiments and theoretical

calcu-lations were carried out simultaneously on this subject. Comparisons made between the results

of both showed a good degree of agreement.

The findings referred to an ideal liquid, that is an

incompressible one without viscosity, while the

tank was assumed to oscillate with a simple, regular harmonic motion, as well as being subjected to a vertical acceleration.

The first experiments conducted by the Society in fact resulted from requests receivc(l to investi-gate damage found in transverse and longitudinal bulkheads of several bulk carriers. The damage-mainly consisting of plating set in between

still'-enershad plainly been caused by ballast water

motion in partially filled holds. Having calculated the equivalent static head, or pressure on the walls caused solely by the weight of liquid when still, which would have been required to cause the collapse of the plate panels concerned, the Society then initiated a series of model experiments. These were designed

to determine the dynamic heada function of the weight and velocity of the liquidwhich resulted

from filling the holds at various levels and using a number of oscillation angles.

The investigations were complicated by the fact that liquid motion in tanks can be divided into two entirely different types. The first is the 'linear' or standing wave type, which causes relatively small pressures since it is vertical rather than horizontal in nature. The second, 'non-linear' type is predomi-nain when the level of filling is relatively low and when angles of roll or pitch arc severe. lt involves the building up of a hydraulic jump or bore which moves at speed and slams with great force against the tank walls. lt is understandably the latter type of motion which causes the most damage to

bulk-heads. Unfortunately it has also been by far the

more difficult to estimate at the design stage. Two plastie models were designed and construc-ted at the Society's research laboratory in Crawley,

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Sussex, to study these liquid motions. All the tests

were perfirmed at the Technische Hoge.-schooi,

Deift, Holland, where the authorities kindly

permit-ted Lloyd's Register to use their oscillating rig

and electronic equipment. The models represented an actual tank and were built to the scales of 1/20 and 1/32 respectively. Twelve housings were fitted

at the tank side and two housings at the tank top

in order lo have the four available pressure

trans-ducers pltigged into the required positions. The

transducers were

of the

piezo-electrical type,

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Experiment 2

Theory_____

which induce a charge when the pressure is changed. The charge is then amplified aoci recorded using a

UV recorder. The very high natural frequency

of these pressure transducers made any resonance phenomenon between the transducer and the liquid extremely unlikely.

Fillings of from to per cent to 40 per cent were used for the first set of tests, together with

oscil-lation amplitudes of 7, io and 13 degrees. The pressure on the tank sides was found to be at its

maximum for this particular tank at a filling of 25

Fig. 1. This comparison between measured and

cal-culated pressure heads shows a fairly close agreement between the two. The results refer to a filling of 25 per

cent and a 13 degree amplitude angle of oscillation, the

total head in metres of fresh water (i.e. the height ofa

water pillar) being plotted against the period T of one

oscillation from port to starboard and back to port. The dimensions of the small tank in the figure are in metres, with the arrow signifying the position of the transducer.

The pronounced maximum reading occurs for the

natural period of the liquid.

per cent, when the natural periods for roll and pitch motions of the liquid in the tank coincided with the estimated natural periods of the ship. However, by comparing the full range of pressure readings with the maximum equivalent static head which could be accepted for the existing scantlings, ir could be

seen that the range of fillings to be avoided was

about i per cent to 35 per cent.

From these findings, which referred essentially to a specific case of bulkhead damage, the Society

went on to observe the liquid movement and

T

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0756 130

25%

Head m 22 20 18 16 14 12 lo 8 6 4 2 204 60% 4 314

Static head for still level

Equivalent total head

due to tank motion Static head when liquid hits the roof

100 Vertical acceleration 03g X Vertical acceleration 02g

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Head m 27 24 21 18 15 12 9 6

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1 2 3 4 5 6 7 8 9 10 160 Filling 0/ 100

°

Fig. 2. A clear pattern emerges when pressure head is plotted against a variety of fillings. For

the particulartank under consideration, the

maxi-mum readings occur at relatively low fillings

when non-linear motions become predominant.

At higher levels of fillings the gentler linear

motion takes over. Each of the levels in the small

figure refers to one of the curves in the graph.

This graph is based on calculated values only.

100

p.x

Var. Filling

200

Fig. 3. This diagram indicates the calculated

pressure distribution along a bulkhead of a given tank due to linear movement of liquid. The level of filling is 60 per cent and the angle of oscillation 10 degrees. The diagram enables one to select at any level in the bulkhead and, by reading across horizontally, to discover the static head when the

tank and liquid are horizontal, the static head

when the tank is tilted and the liquid touches the

roof, and the equivalent total head (including

the dynamic component) which results frnm the movement of the tank. The latter is obviously the

most important reading, since it provides an

accurate estimate of the maximum pressure to be allowed for at any given point along tIle bulkhead.

measure the pressures for a complete range of fillings. The findings were then checked against the theoretically calculated non-linear and linear

pressures for equivalent conditions. As a result of

the theoretical and practical investigation it was

possible to develop a computer program which would

be able to perform the pressure calculations for

both types of pressure. Program LR 321 chooses

non-linear maximum pressures for low degrees

of filling and linear maximum pressures for higher degrees of filling, during one cycle of oscillation.

The choice is based on the relation between still

water depth and tank length.

The program requires for its execution data about the tank size, the height of the centre of rotation above the tank bottom, the percentage of filling, the amplitude of the oscillation angle,

the density of the liquid and finally a value of the

vertical acceleration of the tank, which caters for the location of the tank in the ship.

After printing the title of the run and listing the

input data, the program prints the

calculated natural frequency and period. Pressure values are given by the program on the vertical tank side at io equally spaced positions. These pressures are calculated for eight periods at each position based on the natural period of that filling. The positionof

the points on the tank wall is expressed in a y

coordinate where y = o represents the centre of rota-tion specified in the input. Comparisons which have been made between actual damages and calculated

values have shown that in these cases structural

collapse could have been forecast using this method.

The program has in fact already been used

successfully in some practical cases. The Society is therefore continuing its investigations and

extending their range. Tanks of other than

rect-angular shape are being tested to confirm

calcula-tion methods which cater for all tank mocalcula-tions.

Reference:

Blixell, A, Calculations of Wall Pressures in a smooth rectangular tank due to movements of Liquids, RATAS Report No. ro8, 1972. Obtainable from

the Hull Structures Development Unit, Lloyd's

Register of Shipping, 71 Fenchurch Street, London, EC3M 4BS.

Left: Measuring instruments used in the experiments. To the left is a UV recorder, which describes the pressures