Measurement of exciting forces in short waves

Measurement of exciting forces in short

waves

G . M O E Y E S

Ship Hydromeciianics Laboratory Delfl Universiiy of Teclinology Meiielweg 2

Delfl-2208, The Netherlands

Delfl Progr. Rep., 2 (1976) pp. 87-107.

77((' distribution and magnitude of nave e.wiiing forces iuis been measured on a .segmented tanker model. Wave length ratios ranged from 0.1 lo 1.5 nhile .speed covered values from below to far above .service speed. Linearity of llie measured forces is investigated. From a comparison of measured forces with calculations by strip theory il could he concluded tliat this theory does not give useful predictions in mires sliorier tiian about half the model length.

1 Introduction

The recent development of dimensions and construction of ships has sometimes resulted in such elastic properties that continious resonance phenomenae in one of the elastic modes may occur.

This phenomenon is called springing. It has been observed at Great Lakes bulkcarriers and very large tankers (two-node vertical mode) and long container and other open-deck ships (one-node torsional mode).

Though springing stresses have generally low amplitudes, their frequency is so high that fatigue problems may occur. Therefore springing is avoided in practice by changing course, decreasing speed or additional ballasting.

Each of these measures troubles nonnal operation and may involve extra costs, so better understanding and predictability of springing is necessary.

From several mentioned causes the continious excitation by short waves is the most widely accepted. In that case the frequency of encounter approximates the natural frequency of the lowest order elastic mode.

Based on this concept Goodman' and Van Gunsteren^ developed a method of analysis, starting from sectional hydrodynamic forces calculated with the ordinary strip theory^. This strip theory can be considered as a lowest order approximation ofthe slender-body theory with the assumption that wave length has the order of magnitude of the ship's (small) beam"*.

Despite this restrictive assumption the strip theory is considered, after extensive experi-mental checks, as a very practical tool for prediction of exciting forces and ship motions in waves with lengths of the same order of magnitude as the ship length.

It is intuitively felt by many investigators that specific three-dimensional effects which are not included in ordinary strip methods, will play a growing role when wave length decreases, thus contradicting one of the basic theoretical assumptions.

slender body theories like Faltinsen's' are used, although this theory neither describes principal three-dimensional effects at bow and stern.

To provide basic data for springing analysis and to investigate the validity of existing theories, measurements of magnitude and distribution of exciting forces in very short waves have been carried out in the Delft Ship Hydromechanics Laboratory. M i n i m u m wave length-ship length ratio's of about 1/10 are considered.

Due to the towing tank arrangement the investigation had to be restricted to head waves. To provide practical application possibilities o f the measured data a very large crude carrier, which is rather sensitive to springing in head waves, is chosen to be modelled. The body plan of the ship is shown in Fig. 1. When linearity is assumed the wave exciting forces may be measured on a restrained model, consisting of sections separately fixed to a stiff beam.

2 Experimental set-up 2.7 IVave generation

Because the existing pneumatic wave generator in the towing tank is not able to generate the required very short wave, a special wave-generator had to be constructed. This one consists of a plunjer with a plain back and an exponentially curved front side, to be oscillated parallel to the non-vertical back side. Waves with a minimum length of about 0.3 m could be obtained in a part o f t h e tank which was sufficiently long for doing measurements.

Wave steepness and wave retardation along the tank walls turned out to be major factors in the quality of short wave generation. The driving mechanism of the plunjer was sufficiently accurate (steady) in period and amplitude. To avoid transverse standing waves a curtain consisting of thin deep vertical plates was fixed just in front of the wave-maker.

According to later experience this curtain could be omitted.

2.2 Model set-up

The number o f model sections and the model size have been set, considering: - minimum wave length ratios X/L of less than 1/10 are required.

- practical wave generation possibilities

- ratio o f section length to minimum wave length (because forces harmonically varying over length may be integrated to zero on a whole section).

longitudinal cut:

Fig. 2. General model set-up.

- maximum signal magnitude for sufficiently accurate signal analysis - tank dimensions

- model shop manufacturing facilities The number of sections is selected as 24.

The separation distance between sections is fixed to 3 mm after preliminary tests with regard to force transfer between successive sections, both static and dynamic.

Model dimensions, which are given in Table I, are set to such high values that blockage effects of about 2 % in speed occur. It is assumed that its influences on the investigated dynamic phenomenae are of negligeable importance compared to the advantages of higher signal amplitudes and the possibility to measure in longer shortest waves, which can better be generated.

During preliminary tests the signal-noise rafio turned out to be unsatisfactory due to local vibrafions and coupling between vertical and other vibrafion modes, so in the final design much attention was paid to this.

Therefore transverse symmetry has rigorously been maintained in secfion and dynamo-meter construction.

Sections consist of a wooden frame (see Fig. 2) modelled with foam and Araldite. The sections are by means of dynamometers connected to a beam at the carriage (Fig. 2). The stiffness of the beam is determined so that its natural vertical two-node vibration mode does not interfere with natural and excited vibrafions of the carriage, which were measured in advance.

2.3 Dynamometers

The dynamometers had to combine high sensitivity with a high natural frequency. Besides, symmetry should be maintained because of reasons menfioned in the preceding paragraph. After preliminary tests a bending type dynamometer with semi-conducfive strain gages is selected. Semi-conductive strain gages are used to increase sensitivity

semi-conductive strain gages.

M O D E L

Fig. 3. Dynamometer.

and because only dynamic effects would be considered. Besides, protection to and partial compensation of temperature changes was possible. The dynamometer (Fig. 3) consists of:

- a stiff tubular housing

- a wheel with four spokes as measuring section - a central axis with membrane as guiding mechanism

A sensitivity of abt. 1000 /jstrain/kg force was obtained. Linearity was sufficient in a very wide range, e.g. when loading stepwise fiom 0 to 40 kgf the tangent to the load-strain curve changed abt. 1 %.

The natural frequency o f t h e dynamometer with section mass plus virtual mass in water is calculated as 155 cps.

As calculated the yield stress will be exceeded with a load of 640 kgf on the total dynamo-meter.

An alternative dynamometer with a pull-push measurement element would have good sensitivity and stiffness properties but suffered to a high risk of buckling.

2.4 Signal analysis

The wave is recorded with a conductive wave probe abt. 1.07 m in front of the model. At this distance interference effects between the incoming wave system and the oscillat-ing or stationary wave system of the ship could not be detected.

The wave signal was visualised with a UV-recorder and analysed manually.

In order to obtain the first harmonic in the noisy force signal a Fourier-analysis on a base of the encountered wave signal was carried out with the aid of analogue instru-mentation, (see Fig. 4).

The main part is the phase-measurement system which is normally in use in the Delft Ship Hydromechanics Laboratory during planar mofion tests*.

In-phase and quadrature components of the measured signal are determined by sine and cosine mulfiplication with synchro-resolvers and integration over a prescribed number of periods.

In this case no oscillator mofion could be used to drive the resolvers, so their turning motion is generated synchronous to the recorded encountered wave signal by means of a phase-locked loop servo system^.

Significant data are printed with a data-log system.

Because of capacity restricfions only eight force signals could be analysed at a time.

2.5 Test-program

The model has been tested in full load and heavy ballast condifion. However, contrary

strain gage meters resotvers integrators print - out

servo-motor quadrature component in-ptiase component 1 . mutti- integrator pticator

•

Table I. Particulars of ship and model full ship hall. full model ball. length between pp. 310.0 m 4.65 m breadth moulded 47.16 0.707 m depth moulded 24.50 m 0.368 m 0.184 m draught 18.87 m 1'2.27 m 0.283 m 0.184 m displacement 235000 m^ 151100 m^ 0.793 m 3 0.510 m ' bloclc coefficient 0,852 0.842 0.852 0.842 prismatic coefficient 0.855 0.855 LCB/Lpp in percent + 3.1 + 3.1

to practice the ballast condition is fixed to an even keel condition in order to ease th theoretical calculations with which experiments should be compared. Characteristics of both tested conditions are given in Table I .

The investigated wave length ratios and Froude numbers are given in Table IF The speed range has been extended far above the service speed, corresponding to Fn = 0.15,

to demonstrate speed effects. Some wave length-speed combinations could not be tested because of equipment limitations, others provided partly inaccurate results due to wall influence.

During one run only eight sectional forces could be measured, so each condition was repeated several times. These eight sections were distributed over the total model length and contained at least one section from the preceding series for reproduction purposes (instrumentation checks).

I n each condition the wave system along fore- and afterbody was photographed to get Table II. Tested wave lengths and speeds

IIL F„ 0.10 0.15 0.20 0.25 o.so

0.065 B F noi tested due to instrumentatie»

0.075 B restrictions \— 0.075 B B restrictions 0.085 B F B F 0.094 B B B B 0.120 B F B F B F B 0.160 B F B F B F B B 0.215 B F B F B F B B 0.280 B F B F B F B B 0.375 B F B F B F B B 0.550 B F B F B F B B 0.750 B F B F B F 0 B 1.00 B F B F B F B n 1.25 B B F B F B B 1.50 B B F B F B B B = ballast F = full load

information on the amphtude variation of the incoming wave, propagating along the hull.

To check the linearity o f the measured forces wave height was varied for wave length ratios/l/L = 0.120,0.215 and 0.75 and Froude numbers Fn = 0.15 and 0.25. According to these tests (see also paragraph 3.1) the wave amplitude was restricted to values with which the best possible linear results could be expected.

3 Results and discussion 3.1 Linearity

Figures 5, 6 and 7 show section force amplitudes versus wave amplitude for different wave lengths and speeds.

In longer waves (A/L = 0.75) (Fig. 5) slight non-linearities may be observed at sections near bow and stern for wave amplitudes above 2 | to 3 cm (wave steepness £,J?.. above 1/120). A t midbody sections, where the section form is more vertical near the waterline.

300 200 150 lio 80 300 200 150 100 80

kg .2 0 Fn = .15 F n j . 2 5 .2 0 1 l / l 1 ~ y section 24 ( 1 f ^ / 1 1 SP / bowlig) ' 1 ,2 0 ƒ s.23 / 0 / ® .4 .2 0 s.20 .5

i

/

Fig. 6. Force ampliludes in waves witli IjL = 0.215.

the force is linear dependent upon wave amplitude within the investigated range. This conclusion is equally valid for service speed, at Froude number 0.15, and the higher speed, with its excessive wave formation.

I n intermediate to short waves (Fig. 6) non-linearities are significant, even for some wall-sided midbody sections. A t the low service speed it may be concluded that linear results are obtained with wave amplitude values under \ \ to 2 cm (wave steepness below abt. 1/60).

It is remarkable that also the wall-sided sections 9, 13 and 17 seem to be susceptible to non-linearities. These are apparently due to non-linearities in the wave propagation alongside the model.

A t high speed (Fn = 0.25) no real linear range seems to exist i f the origin is taken as a point o f t h e line. However, i f this condition is abandoned the experiments are close to a line, except when the wave amplitude exceeds about 1^ cm (wave steepness abt.

.2 .1 0 Fn = .15 Fn=,25 .2 .1 0 l l l l section lU (bow) .2 .1 0

/

7

•

•

7

Fig. 7. Force amplitudes in waves wit ft X/L = 0.12.

1/70). The phenomenon that the extrapolated experimental points do not pass through the origin might be caused by a disturbed wave propagation due to wave breaking at the bow and wave formation by clefts between sections (see Fig. 8). Both become more serious al higher speeds.

I n very short waves (Fig. 7) the experiments are less accurate because of the small m.agnitudes of forces and wave amplitudes. Though definite conclusions are therefore difficult to draw, it may be observed that a wave amplitude of abt. 1 cm (wave steepness

1/60) is a limit of the linear range at service speed (Fn = 0.15). A t higher speeds it may be wondered whether the tendencies observed in intermediate waves (see Fig. 6) are continued in short waves.

As a general conclusion it may be said that linearity exists in waves with amplitudes lower than abt. ly cm for realistic speed conditions.

A t higher speeds linearity becomes doubtful, especially for sections in entrance and run and in shorter waves.

Fig. 8. Forebodv of tested tani<er F„ = 0.25

X/L = 0.16

(section numbering on plwtograpli is reversed lo numbering in any otlier figure or table of tliis report). 3.2 Longitudinal force distribution

The measured sectional forces are given as amplitude and phase in Figs. 9 through 19, each for a particular wave length and the whole range of speeds. Amplitudes have been divided by wave amplitude and section length to make them better comparable to each other and to calculations.

Phases have not been determined with r,,spect to the v/ave at the ship's center of gravity, as is usual, but at the mid-length position of the concerning section. This presentation may physically better be understood.

The distribution of wave exciting forces has also been calculated with the strip theory as developed by Gerritsma et al.^'^. Two versions of this theory exist. I n the newest^ a term

cu dN'

0)^ dx

where N ' is the sectional damping, is included in the expression for the wave force. Besides, in this expression a term coN' is replaced by

N'.

Both changes contribute, in waves with length equal to model length, for abt. 2 % to the force amplitude at the parallel mid-body and for 20-30 % in some regions of entrance and run.

400 400 400P 400 NO A C C U R A T E EXP. WALL I N F L U E N C E A C C . TO ( 9 ) W.I. F '

3

Fig. 9. Sectional wave forces: ballast A/L = 1.50.

In shorter waves, with A/L = 0.375, their influence is already decreased to nearly zero at the mid-body and 10-20 % at the entrance.

In very short waves the influence becomes negligeable.

For comparison with the experiments the newest formulation of the strip theory* is used, because it is mathematically the most pure one.

To allow a direct comparison with experiments the calculated values are also presented as sectional forces, obtained by vectorial integration o f t!.e continious basic distribution (e.g. limit values f o r infinitely short sections) over the finite section length.

In longer waves (Figs. 11 and 12) the agreement in magnitude between experiment and calculation is good, except for higher speeds. I n this case the excessive wave formation

3

Fig. 10. Sectional wave forces: ballast /./L = 1.25.

gives significant deviations between the actual wetted secfion form and the section f o r m which is taken into account in the linear calculation method.

A n important qualitative disagreement between experiment and strip theory is apparent at the parallel mid-body. The ordinary strip theory predicts equal exciting forces in case of equal secfion forms. However, in practice a decreasing force amplitude .will be observed due to three-dimensional effects causing a diminishing wave amplitude along cylinders. The observations can be done both in long waves (Fig. 12) and in short waves (Fig. 16).

These effects have theoretically been described by Grim'' and are included in higher order slender-body theories l i k e ' and'".

3 ^

Fig. ll. Sectional wave forces: ballast XjL = 1.00.

-i-E

In waves with length A/L = 0.55 the quantitative agreement between experiment and strip theory may still be called satisfactory at speeds less than service speed (Fn = 0.15). However, in the next shorter wave v/hich has been tested, A/L = 0.375, the agreement is fully disappeared, not only in the amplitude curve, but also in phase.

So, as a weak conclusion it may be stated that strip theory offers practical predictions o f wave exciting forces at realistic speeds in waves longer than about half the ship length. Unfortunately, no experiments are known to the author which could confirm this con-clusions for other ship types.

A feature which becomes apparent at higher speeds and in shorter waves, is an upwards tendency from fore to aft of the phase curve, combined with an oscillatory behaviour

5

--_

Fig. 12. Sectional wave forces: ballast XjL = 0.75.

of the amplitude curve. The amplitude attains a maximum when the phase passes multiples of 360 degrees. A minimum occurs when the phase is 180 plus multiples o f 360 degrees. The length difference between two successive amplitude maxima is ap-proximately equal to a wave length. According to slender-body and strip theories the exciting force may be described as:

F'Jx) = F^(x) exp {i(ojJ + /cx)) (3.2.1)

where:

5 ^.

Fig. /.?. Sectional wave forces: ballast XjL = 0.55.

F'^f,(x) is the exciting force (complex)

F,,(x) is a complex function, slowly varying with x 0)^ = the frequency of encounter

« = — is the wave number.

With this expression amplitude and phase curves as observed in e.g. waves with A/L = 0.28 and 0.215 at Fn = 0.10 and 0.15 (see Figs. 15 and 16) may be described i f Fj(x) is indeed slowly varying with x.

I f this condition is retained, as demanded by slender-body theory, the exciting force behaviour described before might only be obtained when a force distribution F j j ( x )

5 ^

3

Fig. 14. Sectional wave forces: ballast XjL = 0.375.

is superposed upon distribution (3.2.1), with the f o r m :

f d d W = f a d d W exp(/(co,? + £)) (3.2.2

where: F^^^in) is a complex function, not oscillating in x but neither necessarily slowly varying in x.

When speaking in terms of source distributions and considering the measured amplitude and phase distributions, the additional forces (3.2.2) are owing to a series of sources at a rather sharply restricted part o f the forebody, with its strength harmonically varying with tirrie but rather homogenious in x.

5 ^

Fig. IS. Sectional wave forces: ballast XjL = 0.28.

(source) is settled near the bow which varies only with time. From this picture the diffracted flow around the fat tanker model may then physically be understood as consuiting o f a purely three-dimensional part (radiation) around the blunt bow trans-ieviing into a weakly two-dimensional part more aftward. Slender-body theories are principally unable to describe this flow, unless they are modified with respect to the singularity ai the bow.

However, it may be wondered how far the observed distribution will be influenced by non-linearities like wavc-breakiiig.

Fn =.10 F„ =.15 -360 F n = 20 2001-20d 200h - 3 6 0 Fn =-25 -360 Fn = 30 -360 F E=l l l l l l l '

Fig. 16. Sectional wave forces: ballast XjL = 0.215.

4 Conclusions

From the preceding paragraphs it can be concluded that:

- A t speeds below service speed the linear dependance of exciting force f r o m wave amplitude is restricted by section form and wave steepness. A significant linear range exists.

- A t higher speeds non-linearities occur in the wave exciting forces, probably due to wave breaking at the bow.

- Strip theory may give good predictions of wave exciting forces in waves longer than about half the ship length at speeds not above service speed.

i ! ! 11 \\\\ ' ' i ! i M l ; ;, V ?00| 200h 200 -360 Fn = 20 .360 Fn =.25 Fn =.30 F

Fig. 17. Sectional wave forces: bal/a.st A/L = 0.160.

between measured and calculated exciting forces in longer waves.

- A t higher speeds and in shorter waves the longitudinal distribution of wave exciting forces shows typical features which might be declared by a singular source near the bow with a related three-dimensional diffraction fiow around the blunt forebody.

5 Acknowledgement

The underlying report must be considered as a reconnaissance of a part o f t h e experi-mental data. A further analysis of IwUast and fulMoad experiments will be reported in the near Future

3

Fig. 18. Sectional wave forces: hallast A/Z, = 0.120.

enthousiastic support o f t h e technical staff o f Delft Ship Hydromechanics Laboratory. The author is greatly indebted to their ingenuity and conscientiousness in solvmg com-plicated problems.

1. R. A. Goodman, 'Ware-excited main hull fibration in large tankers and bulk carriers', Trans. R I N A 1970.

2. F . F . van Gunsteren, 'Springing-wave induced ship vibrations'. Int. Shipb. Progr., Vol. 19, 195 S^Toerritsma and W. Beukelman, 'Analysis of the modified strip theory for the calculation of ship motions and wave bending moments', Int. Shipb. Progr., Vol. 14, 156 (1967).

4. T . F . Ogilvie and E . O . Tuck, 'A rational strip theory of ship motions: part 1', Dept. of Nav. Architecture and Marine Eng., University of Michigan, Rep. 013 (1969).

Fig. 19 Sectional wave forces: hallast XjL = 0.085.

5. O, Faltinsen, 'Wave forces on a restrained ship in head-sea waves', 9th Symp. on Nav.

Hydro-dynamics, (Paris, 1972).

6. H.J. Zunderdorp and D. Buitenhek, 'Oscillator-techniques at the Shipbuilding Laboratory', Deift Shiphydromechanics Laboratory, Rep. J l l (1963).

7. M. Buitenhek and H . Ooms, Phase-loclced loop servo-system. Delft Ship Hydromechanics Lab. (to be published).

8. J Gerriisina, W. Beukelman and C . C . Glansdorp, 'The effects of beam on the hydrodynamic chavarlerislics of ship hulls', 10th ONR Symp. on Naval Hydrodynamics (1974).

9. O. Grim, 'Die Deformation eines legelma.szigen, in Liingsrichtung laufenden Seeganges durch ein fahrendes Schiff, Schiffsteclm., Vol. 9, '16 (1962).

10. H . Mamo and N. Sasaki, 'On the wave pressure acting on the surface of an elongated body fixed in head seas'. Selected papers from The J. Soc. Naval Architects Japan, Vol. 13 (1975).