Results of model sloshing experiments for two bulk-carrier shaped tanks due to rolling

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REF:. DEVELOPMENT UNIT REPORT No.50

TITLE: RESULTS OF MODEL SLOSHING EXPERIMENTS FOR TWO BULK-CARRIER SHAPED TANKS DUE

TO ROLLING

AUTHOR: C.A. Blixell, Civ.Ing., C.Eng., MRINA

DEPARTMENT: Development Unit, Hull Structures

PRINCIPAL: R.A. Goodman, B.Sc., Ph.D., C.Eng.

TANK MODELS ₂ RESULTS ₄ CONCLUSIONS ₇ FURTHER RESEARCH 8 ACKNOWLEDGEMENTS 9 REFERENCES _lo

1. INTRODUCTION

LLOYD'S REGISTER OF SHIPPING

71,

Fenchurch Street, London, E.C.3

RESULTS OF MODEL SLOSHING EXPERIMENTS FOR TWO BULK-CARRIER SHAPED TANKS DUE

TO ROLLING

1.1 This report contains the results from model experiments on the pressures caused by liquid sloshing due to rolling of the ship in partially filled bulk-carrier shaped tanks, representing different ballast conditions.

1.2 The aim of this investigation is to obtain pressures exp-erimentally and to compare these with calculated pressures

for a rectangular tank in order to establish a calculation procedure based on the rectangular tank case with factors to obtain results for shaped tanks.

1.3 Two tank models representing typical designs have been utilized for the tests: one with lower hopper tanks and vertical sides and the other with lower hopper tanks, vertical sides and saddle tanks.

1.4 These model tests are a continuation of earlier performed tests for rectangular tanks and part of Lloyd's Register long-term research program on pressures caused by liquid motions in tanks.

This Certificate is issued upon the terms of the Rules and Regulations of the Society, which provide

that:-"The Committees of the Society use their best endeavours to ensure that the functions of the Society are properly executed, but it is to be

understood that neither the Society nor any Member of any of its Committees nor any of its Officers, Servants or Surveyors is under any circumstances whatever to be held responsible or liable for any inaccuracy in any report or certificate issued by the Society or its Surveyors, or in any entry in the Register Book or other publication of the Society, or for any act or omission, default or negligence of any of its Committees or any Member thereof, or of the Surveyors, or other Officers, Servants or Agents of the Society".

inertial forces.

2.3 The tanks are made of Perspex and manufactured by the Society's Research Laboratory at Crawley.

2.4 The pressures have been recorded by 4 piezo-electric transducers, which have a very short response time and are able to measure impact pressures with good accuracy.

2.5. In the tests the filling ratio has varied from 10% to 90% sof the tank depth, the amplitude of oscillation has been 100 and 150 and the range of periods of

oscillation from well under, to well above the natural period with a concentration of data collection around and at the natural period.

2. TANK MODELS

2.1 The two tank models utilized for the experiments are shown in Figs. i and 2.

CD

o

co

Fig i Tank i 250

The numbers i - 13 refer to transducer positions

Q CD co Fig 2 Q 12 13 2 760 680

9 H--

---p600 i

f520

R-

---490

óf---

_f360

5

---

₂₈₀ 4 ₂₄₀ 1 (ÛO 20 80 14

- 1 760

- 680 600

9--- ---4

I ₅₇₀ 8 - 360 280 -- ₂₀₀

-j 160

-- 120

-- 80

j

40 1 000 290 Tank 2 300

Tic numbers -- 15 refer to transducer Dositions

i

o

3. RESULTS

3.1. The results are represented graphically in Figs. 3-48.

3.2 The recorded maximum pressures show some scatter during the period of measurement, usually 15-30 cycles, espec-ially for irirnact pressures which might indicate that there is a satistical distribution of maximum pressures. However, in this report, the largest recorded pressure during the neriod of measurement have been represented. Figs. 3-14 show tyDical results for the total pressure, i.e. the sum of dynamic and static pressure components, measured in head of fresh water as a function of the teriod of oscillation.

3.3 The maximum recorded pressure for each combination of

filling, amplitude and transducer position for the two tanks has then been plotted in Figs. 15-48.

3.4 As a comparison the pressures for a rectangular tank under

identical conditions have been calculated using program LR321, Ref. (I). These results are also shown in Figs.

15-48 except for very low degrees of filling when the calculation method is not applicable.

3.5 The evaluation does not take into account if the pressure is of the sinusoidal linear or the impact non-linear type.

In general, however, for fillings up to 25% of the tank depth the non-linear type is predominant and for higher

fillings the linear type.

3.6 From the results it can also be seen that the non-linear

pressure varies considerable over the lower hopper tank side and the explanation for this is that this area acts in the same way as a beach and the bore breaks over this region creating local areas of high pressures.

3.7 The impact type oressure also occurs independent of filling,

for tank 1, Fig. 1, and positions 5, 9, 10, 11 for tank 2. Fig. 2. The duration of an impact is measured to be approximately 0.02 seconds.

3.8 The reason for pressure concentration in the corners is probably due to the fact that the tank boundaries have to deviate the liquid flow from one direction to another in this region.

3.9 A comparison between measured and calculated square tank pressures, shown in Figs. 15-48, indicates the following for the two

tanks:-Tank 1, 100 Rolling Amplitude

Non-linear motions, filling 25% of depth.

The measured pressures are, except for 15% filling, lower than the calculated. This depends mainly on that a

hydraulic jumo or bore, clearly seen in a rectangular tank, is not fully developed when lower hopper tanks are fitted.

Linear motions, filling > 25% of depth.

The influence of the shape is much less pronounced for higher fillings except in the corner between the hopper

tank and the vertical bulkhead where a peak value of about two times the calculated has been measured.

Tank 1, 15 Rolling Amplitude

Non-linear motions, filling - 25% of depth.

Measured pressures lower than calculated.

Linear motions, filling > 25% of depth.

Measured pressures slightly higher than calculated, mainly depending on secondary effects, i.e. a high impact pressure

transducers. The impact pressure in the top corner is underestimated by the theoretical calculation by a factor of, say, 2-3. This is especially important for independent tanks.

Tank 2, 10° ol1inq Amrlitude

Non-linear motions, filling 25% of depth.

Measured pressures lower than calculated.

Linear motions, filling > 25% of depth.

Measured pressures slightly higher than calculated mainly depending on secondary effects.

Tank 2, 15° Rolling Amrlitude

Non-linear motions, filling 4 25% of depth.

Corner effects very pronounced, but otherwise measured pressure much lower than calculated.

Linear motions filling > 25% of depth.

Measured nressures for positions l-5 slightly higher than calculated, mainly due to corner and secondary effects. The measured pressures against the lower part of the saddle

tanks are 2-4 times calculated values.

3.10 A comparison between calculated and measured natural periods for both tanks is shown in Fig. 49. For lower degrees of filling un to 25% of depth, the measured natural period is shorter than that calculated but for higher fillings the period is longer.

-7-4. CONCLUSIONS

4.1 The aim of this research namely to investigate the

feasibility of introducing a calculation procedure based on the rectangular tank case with correction factors to obtain results for shared tanks has been largely achieved and results are satisfactory when applied to tanks similar to those tested.

4.2 When using a rectangular tank approach for a bulk-carrier shaped tank of similar type to those tested with partial filling the following should be considered.

For fillings 25% of depth or 20% of tank breadth. The effect of the hydraulic jump or bore is less

pronounced when hopper tanks are fitted and the theore-tically calculated pressure against the flat areas

is higher than the actual measured. A pressure reduction of 25% is feasible.

For fillings > 25% of depth or > 20% of tank breadth. The measured pressure against the flat areas agrees

fairly well with those calculated and hence no correction is required.

Special consideration should be given to corners in the tank as high impact pressures occur in these regions.

Paragraphs l-3 are shown graphically in Figs. 50-51 with experimentally obtained correction factors.

The statement "Tank of similar type" is defined in Fig. 52.

5. FURTHER RESEARCH

5.1 The present investigation is not to be seen as final on the subject, but has indicated some areas requiring

further research; these are as follows.

Study of the response of structures subject to impact loads.

Model exneriments on tanks under combined pitch and roll motions. C.A Blixell, Surveyor to Lloyd's Register of Shipping. R.A. Goodman, Principal Surveyor to

-9-6. ACKNOWLEDGEMENTS

The author wishes to thank Prof. J. Gerritsma and his staff for help and useful discussions, and the Society would like to expresss their appreciation to the

Shipbuilding Laboratory Deift for errnission to use their equipment.

1. C.A. BLIXELL,

Calculations of Wall Pressures in a Smooth Rectangular Tank due to Movement of Liquids.

R.&.T.A..S. Report No. 5108, Lloyd's Register of Shipping, 1972.

100f

r

U -o o 0o Fig 3 !00 E () o 50 o a o. e e S Period(sec) 2

MEASURED TOTAL PRESSURE

e

i Perod(sec) ₂

5 M[!\SURED TOTAL PRESSURE

Tank number i FHNn9 15% Amplitude 10 Postion 5 Tcnk number 1 Filling 30% Amplitude 10° Pc;ition 6 150 100 o C-5 0 o 150 o O

Fig 4 MEASURED TOTAL PRESSURE

Fig 6 e e o e e e PerTod(sec) 2 a 00 o o Period(sec) 2 MEASURED TOTAL PRESSURE

Tank number

Filling

.L\rnpltude 10! Posito 5. Tank nu;r;i:erl1 FilHng 50% Amplitude 10 Positi 12 -4 g 150f

i

S e S a a e a o o e _e e e n a

:

Period(sec) 2 3 MEASURED TOTAL PIESSURE

o

(J)

I

-' _f

.PrIoc(se:) ¿

MEASURED TOTAL PRESSURE Fg 10 100 c. e CC C C C 50

r

O O Period(sec) 2 3

Fig 8 MEASURED FOTAL PRESSURE

C ' e' C

. *.

C

C

Peri od(sec) 2

MEASURED TOTAL PRLSSURE

Tank nunbe 2

FINg 20%

Amp t Pcsition 2 --i 150 100 ç: u o 50 Tank number i FWing 20% Amplitude 10° Position 1 o ) o

i ob E L) -o 3

i

150 I u 1' sa Q u o

Fig 13

Pciod (sec)

e Tank No 2 Filling 40%

Ampltude

15° Position 4 2 ₃ (i -o o Ci)

i:

50

00

o e e e e

se

e e e e o

Fi-g 14 _{Period (sec)}

2 ₃ 2 -f 1501

_T

TonkNo

2 1 FiIUricj 40% Amplitude 15° Po.!,jön

1

loo Hg Period (sec) 150 Tank No 1 2 Filling _50% AmpiitLde i5 e _{Position U} 100 u. Tank No I i n g Ampi ¡ tude Position 2 1 25% 10° 4 o -3 o

I

50 e e

s.

u e e e e

0

e Period (sec) Fig 11

Fig 15 17 Measured Caculated LR32l

9

fs

o

1,0 0,5 Mcx head m 7 -5 Centre cf oscillatior-,

Taiki

Filling 20 10 _{Amplitude 10°}

Cnte cf i

oscillation.

Nl

Still water level '

r

»

__J

1,0 0,5 Mix head m 1,5 1,0

t7

F7c 13 o Mea:,ured O Calculated LR 321 U4

t_

2 head m StiJJ \2t 0,5 Max t

H,5

1,0 Fig 16

-9

Centre of oscillation

\.2 Still water eíe1î

8

-- 7

L6

5 0,5 Max head m

j

Tank i Filling 25% Amplitude 10

Critre of

oscillaton

3_

N j

Stil[vaïr1evT

I

/

---.

Teak No i FilUng 30% Amplitude 100 Measured Calculated LR 321 Measured

o Calculated L32i

12 13 10

9 stm

_{water level} 5 4

Still water levei

3

ÇÌre

oScillation 3 Centre of

oscillation '

Measured Calculated LR 321 Measured o Calculated LR 32 12 6 5 4 13'

i

Still water leveij

,10.

9

8

7.

6

7 _{Stilt water levcl}

3 _Centre oscillation Tank No 1. Filling 90%' Amplitude 10° Centre of osci F latÏon -1,0 Max 0,5 Fg 19 head m 6 8

TnkNo1

7 _Fifting7O%' Amplitude 10° 1,5 _1,0! n. ¿ 0,5 Mcx head m -1 C _{Tank No 1} Filling 50% Amplitude ìO 8 1,5 _{1,0 0,5 Max} head m Fig 20 1,5 _{0,5 ox.}

hcd m

'0

Fig 22

12 Measured OCaTculated 1R 321

L

1,0

C,5Ñ1am

Fig 23 LL I t 1,0 _{O,5Max head m} flg 25 5 13

11

---9 8 7 6 5 4 2 Centre of osci Motion Stfll water levej

_/

i I 1,5 1,0 g 24 Tank i Fflhing 20% Amplitude 15

Cenr' of

osciliation' 3

-Still water level'.

o Measured OCa Iculated LR 321 0,5Max head m 0,5Max head ni

9

L8

- 7 6 Centre of o3cilIatiofl N 2 StIM water 12 13

j

Tank i

FilÌig 25%

lo

_{Amolitude 1}. 9 8 7 5 4 3St,H water level

j

___p.

Cenrc o

03Cl ilat

t-9

1,5 1,0 Fia 26

I

L Fig29

--8

L6

5 4. L 0,5 Max head m 6

. _

Hwciterlevel 3

-I

Centre of I lotion

/1

Centre of I oscillation

5.

Fi g28

I,

Fig 30 0,5 Max head rn ,5Mcx head m 6

L-L41

9

r--7

Stiil water level

-6

43

--lank 1 FiHTnj 5C°' Amplitude ì5 13 Ctre of ,__â:' oscl!alion

j

12 Tank2 Filling 10% Amplitude iO

t

/I

Centre of I oscillati on Still wate, level o Mea.ured O Calculated LR 321

G-li

t°

r-9

L8

rT7 Tank 1

Fflinj 30%

Amplitude 151 Measured O Calculated LR 321 -- 1 '1

r-'°

-9

-8

-7

213

G Measured

_i

-.--1 1 Tank i Filling 70% Measured OCalculated LR 321 c

-10

Amplitude 151 C Calculated LR 321

12\i3

ç

12\13

J, Fig 31

i

,1, Fig 33 3,5Max head m 0, 5 Mcx head m 7 1Centr' of 6 oscillation 5

3 Still water ievejj

*1

ii

Tk2

IO. Filling 25% Amplitude 101 Centre of 6 oscillation

5 StilI wafer leve!

4 3

5

Fig 32

'5

Fig 34

L

L 5 Max head m Measured o CIculated LR 32L

¡

6

0,5Maxheodm

7

f.

Centre of:__ i oscillation

t;U water level

3 2 11 10

fl

H

12 Tank 2 FiUing 30% Amplitude Centre cf

osci1latin

water Iev _J

J

13 Measured O Calculated LR 321

Fig 35. Measured O Calculated LR 321 I

/

1,5 1,0 0,5 Max head m Measured t Calculated LR 321

î

/

L L__ 1,0 0,5 Max Fig 37 head m

9

10

9 Still wafer level

8 4 6 5 4 Tank No 2 Filling 40% AmpI luce 10° Centre of

cscillatioiJ

Still water level

_I

T

k

I 3 12 12 13 3 Centre of 1 7 OSCH ation Tank No 2 Filling 60 Amplitude 100 3 Measured O Calculated LR 321

J-1,5 1,0 Fig 36 1,5 Fig 38 1,0 Measured O Calculated LR 321 0,5 Max head n-i 0,5 Max. head m i

Tank N 2

10 FiHing 50% Amplitude 10°

3 _{Still water level}

7 Centre of 0sc lotion 10

L:

2 13

listill

Ievel Centr e of oscillation Tank No 2 Ftlting 70% AmoUtude 10° 3

Fg41

Mecsured

j O Calculated LR 321

1,0

Fillng 10%

Amplitude 15° 7 - Çentre of_L

osd'lation

O,5Mpx head m

Stflwat

1 level Tank 2 FilUng 20% Amplitude 15 Centre of 'oscllaflon

$11

L&I

li

1,5 1 1,5

Fg42

.MeasLred. -O Calculated LR 321f

0,

0,5 tMax head ni:

8

7

1,0

,5Maxheadm

FHhing 15% J :Ampfltude 150 -Centre of

oscllaton;

Sifil íofer 2 _level Tank 2 j

FitUn25%

Amplitude 15°l 7 Centre

of4

6

_dllI3tior

5H11

_'2

Iev 4 J I, Fig 39 1,0 _{0,5Mox head m,}

Fig 43 Fig 45 Measured -O Calculated IR 321 1,0. Meusured O Calculated IR 321 0, 5tMox head m 5

7

Max ea. m

13 .12 Tank 2 10 Filling 30% osci Ilation 6' _{Stfll water level} 12 Tank 2

-lOi

Filling 50% Amplitude 14° 8

_{SHlÏcter level}

6 2 13 Centre of toscillation Meosured O Calculated LR 321 Fig 44 Measured O Calculated LR 32F 0,5Max head m

7 Still water level

6

Tank 2 5 Filling4O% Amplitude 15 8 7

6

11 3 2 12

'3.

ç

Centre of oscillation 13 O Stfll water level Centre of, osci I laton 2 Tank 2 FilUng6O% Ampfltude 15°1

J

1,5 1,0 0,5 Max head m Fig 46

1,5 Fi 1471 0,5 Mcx head r 1 FilITng7O%

-8

Arnplitude 150 7 Centre of, 1oscil laHon 1,5 1,0

0,Maxadrn

ig 48 ..

,,,

j . Filling 30% ,Amplitude 151 1--6 Centre .

of scfllaton

['N2.

N1

Ftg 49

__FifITng Iy'o 9

and omparsion measured periods

bfween

values of natural

Tuiated

x Tank i

_io:

+ Tank i 15 t Tank 2 150:

.oTcrk210

o

'01

+ L X

;Thoretc

¿O 0. _{80 90;} 10

':20

_{30 5} 2,4: 2,3 2,2 2, 1

2,0

1,9 1,8

Impact pressure

N Non-impact pressure

Correction factors for tank type i i.e. multiply rectangular tank

pressure by the factor to obtain the tank type i p essure

Fig 50

-j

I Impact pressure

N =Non impact pres-ure Correction factors for tank type 2

i.e. multiply rectangular tank

pressure by the factor to obtain

the tank type 2 pressure

Fig 51

a'

Definition of tanks of simular type

A tank is of simular type ¡f

cxb

Fig 52

Area Non-linear _regionLinear

A

o,750)

i;o (N)

1,2(l)

2,0(l)