9 FEB; 1984
ÄRC.HIEF.
A Method for Estimating
Sloshing Load.
Many researches Izare been conducted on the sloshing forces of liquid in a ship tank, in the course of the rationálization of crude oil carriers, and the following derclopnent of new type of liquefièd gas carriers, i.e., LPGC, LNGC. As its result, the slosh ing plie-,zomena are being made gradual/v clear Hou e er because of the comnplei-ztj of the phenomena they cannot be solved by theoretical approach alone and most of the studies dependon experimental approach. The data accumulated by experimental approach, how-crer, lack generality and are not applicable to the design of new ships
¡n this report as one of the countermeasures ansut ering the request in the hull design stage authors present the practical design method for estimating flicsloshing loadsacting¡n an actual s/zip on tile basis of past epci imental data and a concept of the mt crac tion of s/os/i ing loads and s/lip hull strength. Further, it introduces the results-of application oftilemethod to Panamax type 60
kDWT Ore-Bulk-Oil carrier.
I. Introduction
A considerable amount of research has so far been made, both at home and abroad, on the sloshing of liquid cargo in the ship tank and the impact load thereby imparted to the tank walls since the start of the rationalization of crude oil carrier hull design and,.later, the development of liquefied gas (LPG and LNG) carrier containment system. Because of its complexity, however, the liquid cargo sloshing
phe-nomenon cannot be dealt with by theoretical method
alone, so the research in most instances depends on experi-ment for necessary data, i.e., by oscillating a liquid-filled ship tank model. MHI also have carried out many such model tests, thereby accumulating useful data for use in the
design of actual ship hulls.
Actually, howevér, the experimental data thus obtained mostly pertain to limited ship types, e.g., LPGC, LNGC etc., and hence are not universally applicable to many other ship types. Meanwhile, when the ordinary oil tankers or ore-bulk-oil carriers to be built are expected to have their holds partially filled with the liquid cargo in service, the problem of sloshing of liquid cargo likewise demands due consideration at their hull design stage.
Accordingly, as an aid in dealing with the problem of sloshing at the hull design stage, the authors herein suggest a practical method for estimating the impact load of slosh-ing liquid which they have devised through a careful study of the experimental data accumulated in the past, and discuss a design concept of interaction between impact load of sloshing liquid and hull strength. Also, by way of exam-ple, the results of application of this proposed method to a Panamax type 60000 tDW ore-bulk-oil carrier are reviewed.
2. Outline of liquid sloshing phenomenon 2.1 Motion of liqüid in a tank
Sloshing is a phenomenon in which liquid with free sur-face inside a tank oscillates in response to linear or angular excitation given to the tank externally. The term "slashing"
Dr. Eng.. Nagasaki Technical Institute, Technical Headquarters **Nag.jsakj Tehnical Institute, Technical Headquarters
Ship Engineering l)ept .,. Shipbuilding & Steel StructUres Headquarters Nagasaki Shipyard & En°gine Works
the Strength of Ship Hulls Against
Lab.
.v. Scheepsbouwkunde
Technische Hogeschool Köichi Hagiwara*
Shigeru Tozawa**
Deift
. Hidetoshi Sueoka*Kunifumi Hashimoto
covers a wide variety of physical phenomena, such as-gravi-. ty waves, hydraulic and hydrodynamic instabilities, spray, liquid/solid impacts, etc. In the marine engineering field, however, the term refers to, customarily, phenomenon in which the relative motion of a tank and liquid in it imparts impact load to the tànk walls or tank internal structural members.
Accordingly, the authors also call the impact pressure created by the- relativé motion of a tank and liquid in it the "slashing pressure", and focus their discussion on that kind of phenomenon. Also, with the sea-going ships carrying liquid cargoes, their cargo tanks to consider in connection with the sloshing problem are square or nearly square with a bottom corner sliced off in shape except the spherical tank of the LNG carrier, so the square cargo tank is selected
as most representative.
Liquid motions, though varied in form as well as in magnitude and area they hit as impact loads, may generally
be classified into three categories as follows. Standing waves
Standing waves generally occur when h/i 0.2, and
impart high impact pressures mainly to the tank top (see Fig. I).
Fig. i Standing wave
249
Travelling waves .
Travelling waves generally occur whenh/i< 0.2. Even when not definable as shallow waves like that, they sometimes are generated depending on the degree of
250
Fig. 2 Travelling wave
Fig. 3 Swirling
sympathy between the tank oscillation period and natu-ral frequency of liquid in the tank, too, and, in such an instance, impart hIgh impact pressures to both side walls and tank top (See Fig. 2).
(3) Swirling
lt is known that even when subjected to forced uni-directional rotary oscillation (pitch or roll), the swirling occurs in the visiiiity of resonance .between the oscilla-tion period and liquid natural frequency. Such a swirling phenomenon, though considered to be dynamic and unstable, takes time to grOw, and hence may be ruled out as hardly taking place in such irregular oscillations as ordinary ship motions. The swirling, therefore, is not essentially as important as (1) and (2), and are dropped out of conideratiòn as such (See Fig. 3).
2.2 Natural period of liquid in tank
Of basic importance to dealing with the sloshing cf liquid cargo in cargo tank is to avoid the resonance between the liquid natural.frequency and ship motiòn. It therefòre follows that the natural frequency of liquid in the tank should be determined as accurately as possible. Generally, an ideal liquid may be ássumed with consideration of only little influence of viscosity when discussing the wave
mo-tion.
Fig. 4 Coordinate system
Take, for example, a two-dimensional rectangular tank of the, type shown in Fig. 4, theñ the lowest ñatural period of liquid in such a tank can be expressed by the following
equation as is generally well-known.
T=27r/iJ__tanh_=2.JJ!!_coth../L
(sec)(Ï)
Fig. 5 compares the results which were calcúlated by the Eq. (1) and obtained by a model test. lt is clear from Fig. 5 that the measured oscillation period at which the pressure response reaches its peak is 10-20% longer than calculated when the liquid in the tank is at the middle or high level but, conversely, shorter than calculated when the liquid is
-1/2 Free surface o
h
1/2
Circular trepuoncy w
Fig. 6 Maximum wave.amplitude
at the low level, probably for the following reasons. The influence of damping ñot taken into accouñt by the theoretical formula (including the damping caused
by the liquid surface hitting the tank top). '
The travelling waves occur when the liquid level is low, the phenomenon of which is different from what is assumed by the theoretical formula.
The influence of the essential characteristic that the oscillation period 'at which ¡he amplitude Of fluid mo-" tion reaches its maximum is slightly longer when mease -ured than estimated by the Eq. (1) assuming waves' to be
small
The item (3) has already been discussed in detail in the literature (1). There however is an instance in which the undulatory equation has three solutions for one frequency when' the nonlinearity of free surface is taken iñto account, so that the maximum amplitude of fluid motion is obtained
as illustrated in Fig. 6. In this figure, w represents the
lowest liquid natural frequency calculated by the Eq. (1). There exists, in the rañge ôf co < w1, three solutions, one of which, however, is physically unstable and nonexistent. lt has also been pointed out that in the limited range of frequencies lower than coi, the situation that may exist varies depending on the manner in which the assumed fre-quency is 'approached (e.g., approached from the high; frequency side). The above phenomenon (3) therefore is expláined here because 'w1 < c" always remains valid.
Mitsubishi Heavy. Industries, L tcL 0.7 0.6 0.5 o o 0.4 o 00 o o Calculation '0.3 o Experiment ° (Pitching amplitudeSi o 0 o 0.2 00 o o 0 1.0 ---2.0 3.0 4.0
The lowest natiial period T' (s)
Fig. 5 The lowest natural periodofthe water
ai o tho o o. E a, E E E
Position 03 P&iod L658s Detail of A B
L25
mn 15mo (g/cm2) 600 500 400 -300 200 o 100 Q-Detail of Position B 4 A. Period 1.685 s 25mo 2 (g,cm)Fig. 7 Examples of slashing pressure
150
-1.0 2.0
200
-
100-TECHNICAL REVIEW. October 1982
-Filling ratio h/D=0.3 Position B 5 Periodj 1.745 s 0.25ms 25 ois Detail of A B 025s -J Position B4 luD = 0.3 Pitching 8 - WaterAir LPG- Propaneglus 3.0 Priod T (s)
Fig. 8 Comparison of pressures obtained by LPG with those by water 0.3)
On the other hand, in a tank having internal structural members, the peak of pressure response usually does not
appears clearly but generally tend to shift to the long
period side. From the above it appears possible to estimate the natural period of liquid in a tank using the Eq. (1) by ällowing margins Of 0.9 T to 1.2 T for every liquid level.
2.3 Characteristics of sioshing pressure
Siñce the sloshing phenomenon is an interdisciplinary subject that reaches into both hydrodynamics and struc-turai meáhanics, there are many related parameters to con-sider. Also, the sloshing phenomenon is so complex that the influences of these parameters defy easy separation. The authors therefore discuss here the basic çharacteristics
of the sloshing pressure. 2.3.1 Similitude law
It is considered that the macroscopic liquid motion, being dictated largely by gravity and inertia, conforms to the Froude's law of similarity. Next, regarding the impact
800 700 , 500 g E 200 o -o o o o Air 100% . le 53% He 93% Air 47% Air 7%
Fig. 9 Water impactpressure versus helium density
pressure, two cases may be considered-; one in which the liqtiid surface directly hits an object and the other in which
- the li4uid surface entraps part of gas and hits an object with
the adiabatically compressed gas in between. In the former - instance, the static pressure and dynamic pressure including impact pressure are in proportion to the ratio of size añd the density of liquid. Examples of time history of sloshing pressure are shown in Fig. 7. It is seen from Fig. 8 indicat-ing the results of the experiment(2) performed usindicat-ing lique-fied propane that the impact pressure decreases approxi-matëly according to the ratio of density as-against the case with water when tested with the liquid level of 30 percent in height in which gas in the upper part of tank is hardly
entrapped. -
-Here, the effects of physical properties of gas above liquid are considered as follows. Although the effects of deformation of- the liquid surface are thought to appear in cases where the impact takes place approximately parallel to the liquid surface, the deformation is considered to be related with the manner in which gas escapes immediately before the impact takes place. - Therefore, there is a possi-bility of the impact pressure being somewhat higher with
elusive gas.
Fig. 9 shows the results of the water impact test, in which the density of gas was varied. In this test, a pressure gage is fitted to the bottom of a cylinder 170 mm in dia-meter and this cylinder was dropped from a height of 0.2-1.5 m to the water surface. The density of gas was varied by mixing different amounts of helium gas with air, to He 53%Air 47% which is nearly methane and to meh lighter He 93%Air 7%. lt is seen from Fig. 9 that the lighter the gas, or the higher the density of helium gas, the higher the
pressure and especially its maximum pressure. Fig. IO
shows the results of a test performed in the same manner as the test of Fig. 8 with the liquid level raised to 96%, which appears to suggest that the impact pressure is
con-Drop height 1m
Relative angle 8 = 0
Mean
252
150
'I
2.0 ---3.0
Period T (s)
Fig. 10 Comparison of pressures obtained by LPG with those
- by water (hID = 0.96)
siderably low influenced by high density of propane gas. Thus, it can be seen that the entrapment and the properties of gas greatly influence the impact pressure.
There were instances in which experiments were per-formed for LNG and LPG, with the space above the liquid made nearly vacuum to keep the liquid boiling. It however is not considered appropriate because in such tests the effects of gas above the liquia cannot be correctly evälu-ated. It. is considered that such motion of gas should be taken into account just as carefully when the pressure is reduced to simulate the cushion effects of gas above the liquid. The effects of viscosity of liquid are not considered to be very significant because, generally, the liquid surface hits the tank top Or because the damping effects of non-linear motion are greater.
2.3.2 Effects of loaded area(3)('2)
The effects ofloaded area, though seemingly infrequent-ly mentioned in general discussions, should be said very important. The authors are discussing this problem in detail
in Chapter 4. -
-2.3.3 Scattering of
pressure-The impact pressure is a phenomenon which is in essence highly unpredictable and full of scatters. It nevertheless is very important to practical design in what probability dis-i tribution to approximate the frequency of its occurrence. Fig. 11 shows examples of- experimental resúlts regarding the regular and irregular motions as plotted on Wëibul probability paper, in which data on the two kinds of mo-tion are indicated side by side to observe the form of
dis-tribution.
-Take as a high-pressure region, for example, the slope in approximately the upper 1/3, then it is seen that most of the plottings of regular motion, including those not iñdi cated here, indicate a slope between the Rayleigh and exponential distribut-ions, or seemingly èloser to Rayleigh distribution. The plottings of the irregular- motion on the other hand are distributed very closely approximating the exponential distribution. All this suggests that With the
-o 2e a T top 99.9 90 80 60 40 20 o s Rayleigh distribution Exponential distribution O Regular motiön Irregular motion Pressure
-Fig. 11 Scattering of sloshing pressure
Bottom
0 - 100 200 300
- Pressure (g/èm°)
Fig. 12 Distribt.tion of sloshingpressure
Pitching 94 % fHing
0---
0.96 tjuin0 0--0_80 II --a---050 n ---a--030 n 3--o.10 /,irregular motion the emergent fÈequency of occurrence of
-impact pressure in the high-pressure region can be expressed by the exponential distribution.
2.3.4 Effects of liquid level in tank
-Fig. 12 shows the magnitude of sloshing pressure pro-
-duced by liquid at each different level in the tank of bulk-carrier type of ship. It can be seen that the travelling waves occurs with low liquid levels and that high sloshing pres-
-sures are imparted to the bulkhead near the liquid surface
at rest.
-3. Method of estimating sloshing pressure
3.1 - Basic concept - - -
-The loads which are applied to the hull structural mem-bers by sloshing may be divided into three as follows.
The load acting upon both bùlkhead and top of the
tank without internal structural members -
-The load acting upon both bulkhead and top of the tank with internal structural members
The load acting upon such tank internal structural members as the horizontal girder, deck transverse,
swash-bulkhead, etc. -
-Of the above three, it is the tank without internal struc-tural members that poses the most serious sioshing pro-blem. The sloshing problem associated with the tank of this type has been the subject of continued experimental stùd-ies, and in each instance the results of the model tank test have been obtained for many conditions iñ the form of
-frequency characteristic of sloshing pressure (called
"pres--sure response function"). -
-Examples of the pressure response fünction are shown.
in Fig. 13 and Fig. I4(). The sloshing pressure and its
-short-term distribution in the tank without internal
struc-Position03
\
Pitching8 h/fl =096 Water-Air LPG-Propane gas E 10 o ¿I o.
o0.15
o O
TECHNICAL REVIEW October 1982
tûral members are estimated using both pressure response function derived from the existing data and ship motion determined by calculation (ordina;y strip method) applying linear superposition theory which is used in short-term estimation of ship motion.
The estimation
is based on the assumption that the
sloshing pressure is in proportion. to the amplitude of oscil-lation and yet corresponds to each osciloscil-lation. This assump-tion, however, is not necessarily a prerequisite condiassump-tion, and it is just as acceptable to take into account, instead, the nonlinearity, such as the saturation of pressure at high amplitudes of motion.
The pressure acting upon bulkhead and top of the tank with intethal structural members can be determined based on the results of calculation for the tank having no internal structural members and multiplying thereto the damping effects of each internal structural member. The internal structural membets include the following.
Swash bulkhead
Bottom transverse
Deck transverse Side frame
-.(e) Horizontal girder (f) Pipe tower (Experiment) Response function of sloshing prssure of model tank Response.fundtion of sloshing pressure of actual strip Similitude law (Froudes law) Assumption of
-1
RayleighdistributionSpectrum of sloshing- pressure
Thê1xtrithkI bf sloshing pr ssure (Pitch and roll motion)
(Catcülation)
Frequency response of
stripmotión inreqular
waves
Wave spectrum
(ISSC)
Up to here the estime value is left out of consideration
Assumption of
exponential
distribution
The loads acting upon the internal structural members listed in (3), may, appropriately, be expressed by semi-empirical formula based on individual experimental data.
Moreover, for the design pressure to be selected, the
correc-tiòñ factor to be used for actual - ship should be obtained
through comparison with actual data.
-Consequently, it is indispensable, in developing a for-mula for estimating the load acting on each internal struc-tural member, that an enormous volume of experimental data be available as supporting data. At the present time, however, the research has not reached the level yet where
all the data required are available.
-3.2 Tank without internal structural mèmbers
-The- sloshing pressure in the tank without internal struc-turàl members may he determined in the following manner
(See Fig. 15).
(1) The pressure response function will be selected for the tañk in question from the existing model tank test data. Modifications will be made to the data òñ the taísk shape, etc., as required at this stage- to suit thô tank in question completely.. -For this purpose, Mitsubishi has systematically maintáined experimental data files for rectangular tanks, bulk-carrier-type tanks and other tanks. Also, it is assumed that the data for actual ship
application can be converted in accordance with
Froude's law and that scatters in pressure take place in
conformance with Rayleigh distribution.
-(2)- The short-term distribution of pressure will be esti-mated by calculating the ship motion and then applying the linear superposition theory from the calculated ship. motion and pressure response function determined in (I) above. In other words, the standard deviation of sloshing pressure can be obtained by the following
equa-tion. - - -a. A° o A £ A e A A A o A A
Aia
A L O a D .D GsA8.
RolUng 12 -. o : Filling ratio 98% Filling ratio 96% o Fining ratio 94% Filling ratio 92%besign value of sloshing pressure
Fig. 15 Flow chart of estimation
Ì
OElO A - o Filling ratio 90%Doe 1.0 1.5 2.0. 2.5 3.0
Period (s)
254
R2=
Hwof"f
2 {Cf(wr)J2
4(w.z_r).j_J }dT.d
(2)R: standard deviatiön of sloshing pressure
Jiw power spectrum of waves
response function of ship motion
o.
pressure response fünctionz: angle between ship's course and mean wave direction
r: angle between mean wave direction and
direction of each component wave
(3) Sea wave requires to be defined in relation with (2). The information on sea waves is rarely given in wave height and wave period but in Beaufort scale in the najority of instances. The Beaufort scale howeveris for indicating the force of wind and essentially not a para-meter for sea waves. It therefore is not an easy task to define sea waves especially when performingthe short term estimation of ship motion, wave loads, etc. The authors define the sea waves as shown in Tablei on the basis, of Roll's c'.ata(5), and adopt. the wave spectrum proposed by issc(6).
Table i Relation between seawaves and Beaufort scale
The largest expectation will be determined based on the value of standard deviation obtained in (2) and
assuming the pressure to conform with the exponential distributioñ. If the highest mean value of I O is em-ployed hére as the largest expectation, the estimated
pressure is given as below.
Pj=(1+lnN).R.k (3)
where "k" is the correction factor for estimating the pressure, which is determined taking into account vari-ous effects déscribed in Section 2.2.
Applying the above-mentioned methods for each of ship motion components of pitch, surge, roll and sway, finalÏy the sioshing pressure will be obtained by the fol
lowing equation.
Pr"../(Ppfc +Psurge)2+(PRou +Psway)2 (4) This is based on the assúmption that in each group clas-sified by the direction of driving foEce, the phenomenon occurs at the same phase (coefficient of correlation 1), and that between the groûps the phenomenon occurs independently (coefficient of correlation, O).
1-lere, the sloshing pressure is assumed to be linear for the wave height
3.3 Tank with internal structûral members
The sloshing in the tank with internal structural mem-bers requires two consideratiOns to be taken into account
o 1.0 05 -Estimated Experiment OID = 0.8 Tunisg factor =0.92 05 1.0 Type of swash bhd.
on
t'right Shd. Effectiveness of swash Bhd. ) without Bhd.
Fig. 16 Example of influence coefficient of swash bulkhead
The influence coefficients also are determined based on the results of model tank experiments. Fig. 16 shows the influence coefficient of swash bulkhead. This, though rear-rangement of the experimental data obtained by SR 74 committee(7), leads to the following equation for the in-fluence coefficient of swash bulkhead.
4(1A)(1--A)2
(6)where
A : opening rate of swash bulkhead, which is defined as
the opening area divided by the sectional area under water surface
As far as can be seen from such a consequence, influence of opening shape can be ignored, and also it has beeñ re-ported that the influence of numbers of swash bulkhead is
almost nil.
Applying the same procedure, the influence coefficient of other structural members can also be determined. How-ever, in the case of, for example, the side tank of oil tanker, in which several deep ring-shaped girders are provided in the
Mitsubishi Heavy Industries, Ltd.
Significant wave hèight Ji(m) 3 3 5 7 9 9 Mean wave period Tw(SeC) 6 7 8 9 10 11
Beautort scale B.S
7 8 9 10 11
as stated earlier, which are(l) one is the damping effects of internal structural members on the sloshing pressurewhich acts directly upon the bulkhead and tank top, and (2) the pressure which acts upon the internal structural membrs themselves.
The former should be' estimated quantatively, because the internal members exert great diminishing effects to the flid motiOn inside the tank. The dampingeffect of each member is to be determined in the form of influence coef-ficient, based oñ the estimated pressure Pf in the tank without internal structûral members as obtained in 3.1. That is, the sloshing pressure acting upon the bulkhead and top of the tank with internal structuralmembers is given by the following equation.
P1=ßP1 (5)
where
Pj : sloshing pressure in tank without internal structural
members
P1: sloshing pressure in tank with internal structural
members
E E 20 40 O ----o--- '
x----P0---.- 3 Séctional area eider wate,
---o---
f; TArea of ope,-ñng &sider weter---0.5 LO
Period T (s)
TECHNICAL REVIEW. October 1982
1-45(51%) o
0.5 1.0 1.5 - 2.0 Period T (s)
Fig. 17 Inflüence of traverse ring
longitudinal direction,
the damping effect of the ring
girders is very large. Fig. 17 shows the results of experiment performed by SR 38 committee, from which the damping effect of the ring girders is shown to be great, too. Con-sequently, even if the sloshing occurs, it, is low in pressure and creates rio problem in terms of structural strength, as a result of which the hydrostatic pressure has only to be considered as external load.
The load acting upon internal structural members them-selves also has been experimentally investigated by SR 74(7) and SR 38(8) committees. Conclusions obtained by these investigations about the relationship between the acting load and oscillation amplitude or period etc., were not necessary concrete because the experiments were all performed using the regular motion.
The horizontal girder, among other internal structural members, requires a particular consideration against the sloshing load. Very high sloshing pressure can be generated depending on the cargo loading condition when liquid inside the hold undergoes large motion. As for this prob-lem, there are a few data obtained by both model test(8)(9) and full scale measurement(10)(11) but have not been sys-tematically sorted out yet because of the complexity of the phenomenon. More of data should be accumulated and many more comparative studies made of the experimental data, under the circumstances it is important that the con-sideration against sloshing be shared by the ship, too, when
taking on liquid cargo.
The sloshing pressure usually does not act upon the swash bulk hèad. Also, with the swash bulkhead, the
hydro-static pressure may be dropped out of consideration be-cause this structural member, with liquid on its both sides, - remains in the state of equilibrium, so that oñly the
swash-ing pressure caused by liquid motion has to be considered.
On the other hand, the members, such as transverse ring and side frame, are subjected to sloshing relatively low in load and hence suffice if they are so dimensioned as to satisfy the requirements of structural integrity. Thus, it is sufficient if hydrostatic pressure differential is considered
as load.
4. Response and strength of structural members
The authors have discussed iñ the Preceding chapters the procedures for estimating the sloshing pressure. Further-more, to determine the design pressure the response of structural members also has to be taken into account. In this chapter, the authors discuss the relationship between the response and strength ofhull structural members which
. must be considered when establishing the design pressure.
Generally, from the standpoint of strength design, the pressure is important not only fôr its value but as "pressure multiplied by area". That is, even high pressure causes no damage to the structural member and hence poses no problem in terms of structural strength as far as the area acted upon by that pressure is very small. The panel area surrounded by stiffeners is usually taken as being the
small-est unit- area.
lt is convenient to employ a concept of equivalent static pressure when studying the relationship between the impact pressure and structural strength. The equivalent static pres-sure is defined as static prespres-sure (uríiform prespres-sure) which produces the largest strain equivalent to that which a cer-tain impact pressure produces in the structural member. which is acted upon by pressures widely varying with loca-tion and time. High impact pressure generally is produced when a plane with a slight inclination collides with the liquid surface, and the equivalent static pressure acting upon the panel and stiffener at this moment can be ob-tamed by calculating statically their strain responses that take place every moment when the pressure distribution determined from pressure gage readings is relocated(12).
Fig. 18 and Fig. 19 show the results of a water impact test which Was carried out in order to obtain effective load produced at the. moment when a structural model of ship bottom was dropped to the water surface with three
rela-tive angles of & O, I .43, and 2.86 degrees. The model used
in this test is not necessarily similar in construction to tanks in general use, being made of panels a little thicker than those commonly used in ship tañks to deal with the slam-ming load. The influence of such a structural difference can
be said insignificant. When = O, air is entrapped under the bottom of the model to create uniform pressure
distribu-tion over almost the entire bottom surface.
On the other hand, when the bottom of the model is inclined slightly against the water surface, air is not caught and very high impact pressure, produced at the area of the first contact, travels up along the inclined bottom surface. As a result, the load acting upon each structural member is considerably lower than that corresponding to the peak of
E 40 8 9. h =6t9mm T-60 (69%) o-,20 8 = 9 h 6tmm T-30 (34%) 2.0 0.5 1.0 1.5 Period T (s)
256 300 200 100 (t) 30 20 10 L.W.L
o-'j'
Load acting on bottom trans.Fig. 18 Pressure and responses(at= 1.43°)
o
X I0 Bending strain of longitudinal membm
impact pressure. In Fig. 18 the loads obtained by quasi-static calculation in accordance with the above-mentioned procedure and those measured using strain gages are shown for comparison. It is clear that although both the bottom plate and small member can satisfactorily be dealt with tatica1ly, the primary member must be dealt with dynami-cally because errors in tnagnitude and phase of response may appear when dealt with statically. Fig. 19 compares equivalent static pressures for individual structural
mem-bers.
Thus, it can be seen that without the entrapment of air, the effective load for the structure decreases with the in-crease in load bearing area. Also, in this instance, the equiv-àlent static. pressure can be obtàiñed directly from pressure gage readings if only the pressure-bearing area of the gage used in the model test corresponds to that of the panel of the tank. With the entrapment of air, however, nearly uniform pressure are applied to a considerably wide area, and the -measured pressure directly translates into the equivalent static pressure regardless of the gage surface area.
It is to be. mentioned in this connection that the sloshing pressure estimated by the method explained in Chapter 3 is close to the load on the panel judging from the size of
pres-sure gages used in the experiment.
On the other hand, structural members must be strong enough to withstand these effèctive loads. The plastic collapse load is used in many instances to indicate the strength, commonly for both panel and stiffener, taking
into account their
collapse mechanisms. For example, strength of a panel is obtained as load required for the panel fastened in way of primary and secondary members to form a roof-shaped plastic hinge. As for the primary members, it is necessary to pay attention also to thebuck-ling of panel which composes their girders.
Na.? CH. No.6 C.H. No.5 CH. No.4 CH. No.3 C.H. No.2 CH. t No.1 C.H.
/C.O.T. IC.O.T. /C.0.T. /C.O.T. ¡COI. ¡COI. ,'C.O.T.
Fig. 20 Arrangement of cargo hold and cargo Oil tank
300 200 100 Pressure1 gage Bottom plate P'm,,a 60 kDWT 080 LPPXBM LOX DM LD DraughtdMLD Displacement 4,, Metacentric height GM Ship apeed V,, F,,: Froude number L.W.L.
* Estimated from strain
**Calculated by use of quasistatic method
Structurat part
Fig. 19 Equivalent static pressure for each structural part
5.
Application of proposed method to Panamax type
60000 tDW Ore-Bulk-Oil carrier
By way of example, the results of application of the proposed method to an actual ship are outlined in this chapter. The actual ship referred to is a Panamax type 60
kDWT Ore-Bulk-Oil catrier.
-Principal particulars and loading condition of ship Principal particulars of the ship are shown in Tàble 2, and the cargo hold and cargo oil tank arrangement in Fig. 20. The assumption used in this study was the case of slack loading in full load condition, which was taken as being the most often employed loading condition. The cargo hold assumed to be partially filled is No. 5 -hold, with three liquid levels of hID 0.25, 0.5, and 0.75 -alternately. The sectional vie.w of the hull hold space is shown in Fig. 21.
Determination of response function of pressure
-The response function of sloshing pressure was estab-lished for each of pitch and roll, respectively, from the
Table 2 Principal porticulars of ship
Ldngitudinal member
Full toad even keel
218. 00X32. 20 X 19.20rn 12. 19 m 74 191 ton 2.75m -14.7 kn (F=0. 1636) Bottom tr
Cargo hold / Cargò ot tank
/
t I
Fig. 21 Hold section. 0 0.025 0.05 Measured Calculated"j
O.
Ó---
..
-300- P2 Pressure history 200--s.
-
Measured Calculated 100--) o Time XIO-° 400'-i:
Bending strain at bottom plate
200
1.5 - Pitch (pitching amplitude =8) Envelope of reuponse unction
Period T (s)
Fig. 22 Examples of pressure response
results of experiment with a model tank simulating the bulk carrier type hold. The response function of sloshing pressure for the pitching mode is shown in Fig. 22, in which the envelope of measured values is adopted in ordèr to take account tile effects of. difference in loca-tion, etc.
Frequency response of ship motions
The ship motions in waves were calculated by strip method, using hydrodynamic foices given by the two-dimensional linear potential theory. The calculated re-suits are shown in Figs. 23 and 24. In the case of slack loading, the ship motions are affected by the liquid motions in cargo tanks. Accordingly, the coupling effect of the liquid motion was taken into consideration by using G0AI instead of GM. (On account of the effect of the free water surface, the center of gravity G goes up to G0 apparently.)
Selection of sea waves.
The sea waves were selected as shown in table I.
Estimation of sloshing pressure
The standard deviation of sloshing pressure can be obtained using the mear superposition theory based on the- pressure response function determined in (2) and ship motions estimated in (3). Next, the largést
expecta-tion of pressure can be determined by Eq. (3) using the severest conditions from the above-calculated results. Here, the largest expectation is represented by the high-est mean value of lO, which is takeh as being the value which corresponds to the largest expectation of sloshing pressure that occurs on the voyage of an entire day.
Although the pressure due to each of the pitch and roll motions can be evaluated in this manner, in practice it is necessary to add in the effects of horizontal mo-tions, i.e., surge in the longitudinal direçtiòn of ship and sway in the transverse direction. The authors took into account the effects of surge and sway motions as correc-tion factors t the components of pitch and roll. These -correction factors can be determined through compara-tive studiès- of sloshing pressures caused by rotary and TECHNICAL REVIEW. October 1982
NOr-DIMENSIONAL AMPLITUDES IN-REGULAR WAVES PITCHING AT CENTER 0F GRAVITY
PITCH / 61-IO 25%-filling 0.50 ROLLfKHO - El=0.0. FN =0.1636 - * ---.--- EA =30.0V FN =0.1636 - -o-. EA=60.0 FN =0.1636 ---X--- EA=9O.0 PN=D.1636 F\ --a- E.A=120.0 FN=0.1636 A ----C--- EA = 150.0 FN = 0.1636
".
\.
---)-- EA=I80.0 FN=0.1636-v--vx5'.0
i-:
I -EA=60.0 EA=30.0 = 120.0 = i50.0 FN =0.1636 FÑ=0.1636 FN=01636 EN =0.1636 FN =0.1636 f / + ---'i--- EA=90.0 -D-- EA ---C--- EA + i _,;t_ s' - ----_.'
-.a --_..._:=:-*.__ --..''As 0.00 0.50 - 1.00 L50 2.00 -SQRT ¡Z7A- Fig. 24 Results of ship motion (roll)
horizontal motions in the specified sea waves. From the
abovè, the sloshing pressure is estimated as
follows:-longitudinal direction (P1: due to pitch and surge)
P1=36 Ct/rn2)
transverse direction (Pb: due to roll añd swäy)
Pb=47 (t/m2)
(c) tank corners (P: obtained as the root mean square
ofP,andPb)
-P=P,2+P2=6O (t/m2)
With the only No. 5 hold partially filled and other holds empty, the pressure in the tränsverse directiOn is 2.6 times higher because of the difference in response of ship motion in that direction. Needless to say, when needed, pressure should be corrected in consideration of
the effects of various characteristics mentioned in
Chapter -2.
-(6) Vertical distribution of sloshing pressure
-Nothing really conclusive have been said of the verti cal distribution of sloshing pressure. However, judging from the experimental data obtained in the past, the 0.00
0.501.00
1.50 2.005QRT
Fig. 23 Results of ship motion (pitch)
NON-DIMENSIONAL AMPLITUDES IN REGULAR WAVES ROLLIÑG AT CENTER OF GRAVITY
25 % filling 5. 4. 3. 2. 1.
258
upper part of a'tank above the 25% liquid level is to be to require reinforcement for structural members against the above design pressures, whereas for the part below
that liquid level the pressure may be reduced progressive-ly.
Scantlings of structural members
The scantlings of such structural members as bulk-head, stiffened panel, and other supporting members which together constitute No.. 5 hold of the ship are designed with sufficient strength to withstand the esti-mated sloshing loads in accordance with the method as stated in Chapter 4 and taking the arrangement of stiff-eners into consideration.
COmparison with existing rule requirernents(13)(14)
The pressures estimated in (6) are compared with the values determined in conformance with the requirements of the existing ship classification rules in Fig. 25, which shows, by way of example, the estimated pressures
act-ing on the bottom of a top side tank located at the
upper tank corner. What assumption to use for responses àf structural members to sloshing pressures affects the corresponding member scantlings, so it should not be júmped to the conclusion that the comparison of cal-culated pressures automatically determines what scant-lings.to employ. As far as can be seen from Fig. 24,the values calculated this time are somewhat higher than those determined in accordance with the rule require-ments but appear to be fairly close.
For the upper part of the tank, the pressure may be reduced gradually as per the rules. The difference be-tween the pressures estimated by the proposed method and in accordance with the inles probably is attributable. to the difference in condition used in model tests which were performed to obtain the basic data. However, it is not necessarily clear just how the rules assume the scat-tering, probability distribution, and other characteristics
of the sloshing pressure. 6. Summary
As stated in the introduction, it is believed that in not a few instances, the sloshing emerges as an important factor in the initial ship hull design stage. To successfully deal with the problem of sloshing, it is necessary not only to continue with the double-pronged research activities of theoretical and experimental studies but also to reconsider how best to make the most of the past experimental data
available. . .
In fact, this was exactly what the authors intended to do and thus have suggested a practical method for estimating the sloshing load and a design concept of ship hull strength against such a sloshing load. Also, the authors have re-viewed the, results of application of the proposed method to a Panamax type 60000 tDW Ore-Bulk-Oil carrier. It goes. without saying that for prevalent and practical applications in the ship hull design, the, proposed method must 'be further refined based on more of experimental data and more' of fundamental studies on the sloshing phenomenon, both of which can only be achieved through persistent and tireless efforts in future. ' .
MHI
----'-NV ', '
---P4K '
Fig. 25 Comparison with existing regulations (traverse direction)
Referenc
(I) Faltinsen Ö.M., A Nonlinear Theory of Sloshing in Rectangu-larTanks, Journal ofShip Research, Vol. 18 No. 4 (1974) '
Hagiwara K. and otheis, On Some Characteristics of Sloshing Force, Journal of the Society of Naval Architects of Japan, Vol. 142 (1977) (in Japanese) ' '
Hagiwara K. and Yuhara T., Study of Wave Impact Load on Ship Bow, Mitsubishi Technical Review, Vol. 12 No. 2 (1975) Nagamoto R. and others, On Sloshing Force of Rectangular Tank Type LNG Carrier, Journal of the Society of Naval Architects ofJapan, Vol. 145 (1979)
Roll H.V., Dimensions of Seawaves as a Function of \Vind Force, SNAME T&R Bulletin No l-19 (1958)
ISSC, Reports of Committee 1, Environmental Conditions, 2nd ISSC (1964)
SR74 Comittee Report, Dynamic Pressure of Cargo Oil due to Pitching and Effectiveness of Swash Bulkhead in Long Tanks, Shipbuilding Research Association of Japan, No.62 (1968) (in Japanese) '
SR38 Committee Report, Investigation of the Structural Strength of Mammoth Tanker, Shipbuilding Research Asso-ciation of Japan, No.33 (1961) (in Japanese)
Yoshiki M., Yamamoto Y., and Hagiwara K., Experiments on Dynamical Pressure in Cargo 011 Tanks due to Ship Motions, Journal of the Society of Naval Architects of Japan, Vol. 109
(1961)(inJapanese) '
HagiwaraK., Measurements of Dynamical Forces by Water in Long Tank of Ship, Journal of the Society of Naval Architects of Japan, Vol. 121 (1967) (in Japanese)
Hagiwara K. and Tani A., Study on Dynamic Pressure Pro-duced in Long Tanks by the Motion of Ship, Mitsubishi Tech-nical Review, Vol. 5 No. 1(1968)
Hagiwara K. and Matsumoto S., On Strength of Forward Bottom Structure against Slamming, Journal of the Society of Naval Architects of Japan, VoL 147 (1980) (in Japanese) Guidance for Survey of Steel Ships, Nippon Kaiji Kyokai (in
Japanese)
Ships' Load and Strength Manual, Det Norske Veritas(1978)
1-ligashimura M. and Shimizu N., Dynamic Pressure Caused by
Sivashing Fluid in Tanks of Orc-Bulk-Oil Carrier, Journal of the Kansai Society of, Naval Architects,, Japan, VoL 141
(197 1) (in Japanese)
Hagiwara K. and Yamamoto Y., A Theory of Sloshing in Cargo Oil Tanks, Journal of the Society of Naval Architects of Japan, Vol. 112 (1962) (in Japanese)
