Transient waves for ship floating structure testing

ELSEVIER

Applied Ocean Research 16 (1994) 71-85

© 1994 Elsevier Science Limited Printed in Great Britain. All rights reserved 0141-1187/94/$07.00

Transient waves for ship and floating

structure testing

G. J . Grigoropoulos," N. S. Florios^ & T. A. Loukakis"

"Department of Naval Architecture and Marine Engineering, National Teclmical University of Alliens, 9 Iroon Polyteclmeiou str., Zografou 15780, Greece ''Marine Tedmology Development Co., 16 II Merarchias str., Pireaiis 18535, Greece

The dynamic behaviour of ships and other floating structures can be determined experimentally using regular, random or transient waves for system excitation. Testing using transient waves is much less time consuming and greatly reduces tank wall interference phenomena. However, for reasons probably connected with the convenience, familiarity and ease of the testing procedure, transient wave testing is not yet used for routine experiments. A new, easy to apply technique for the generation of transient wave packets is proposed. The method has been successfully tried on ship models in a towing tank, moving or stationary, with very good results. In addition, the new method allows for the accurate determination of the concentration point of the waves.

1 I N T R O D U C T I O N

The essential advantage o f testing ship or floating structure models i n transient waves is the drastic reduction of the required time and hence the cost o f the experiments, when compared to regular or random wave testing. I n this case, in order to establish the response function of a body, a single pass of a transient wave packet past the body is adequate. I n comparison, numerous regular wave tests are necessary and testing f o r a long time i n random waves is required i n order to obtain statistically valid results.

Additional advantages of transient wave testing are: • avoidance o f excitation contamination f r o m beach

and/or wavemaker reflected waves; • reduction of tank wall interference; • repeatability of testing conditions.

Finally, a new type of testing is possible using transient waves, which can be programmed to concen-trate at some point near or on the structure under investigation, which can thus be loaded i n an extreme manner.

On the other hand the use of transient waves introduces some experimental problems. I n this respect care should be taken to keep the ratio o f wave amplitude to wavelength small enough to avoid premature (i.e. before the concentration point) wave breaking and other non-linearities. The occurrence of premature wave breaking leads to deformation of the energy spectrum due to energy dissipation. I n addition, the wave amplitude should also be kept high enough to avoid

measurement inaccuracies. W i t h i n this range one could try several amphtudes of the transient wave train to check for the presence o f important non-linearities i n the specific experiment.

Furthermore, some difficulties arise during the recording of transient waves because much information is contained i n a short record length. A relatively high sampling rate is used to compensate for the short duration of the experimental time history, which is easy w i t h modern data acquisition instrumentation. H o w -ever, the aforementioned short duration limits the accuracy of the analysis when using Fourier transform techniques and hence, use of other methods (e.g. maximum entropy or autoregressive methods) can be considered.

The transient wave technique was introduced by Davis and Zarnick,' who used an electrically produced signal containing a range of linearly varying frequencies. The RAOs (response amplitude operators) of a ship were determined using F F T for the analysis. N o wave concentration was possible with this method.

A t the same time. Smith and Cummins^ proposed the use of impulse excitation o f ship models for the estimation of the hydrodynamic coefficients. Later, Kerwin and Narita^ applied a step excitation on a model allowed only to pitch and estimated its added mass and damping coefficients by numerical approxima-tion of the convoluapproxima-tion integral which expresses the response of a linear system to a step input. Freakes and Keay"* used the same technique to estimate the respective coefficients for heave. They also investigated the effect o f shaffow water on these motion parameters.

72 _{G. J. Grigoropoulos, N. S. Florios, T. A. Loukakis}

The problem o f wave concentration was successfully treated by Takezawa et al.^"'' Their method required the concentration of the waveform at a point where all components arrive simuhaneously. Starting with the desired wave spectrum and the zero phase angle requirement at the concentration point, the correspond-ing electrical signal spectrum was computed uscorrespond-ing the theoretical transfer function of the signal-wave system. F r o m this spectrum, the excitation signal was obtained using inverse Fourier transform. The method was successfully used to test ship models. However, probably due to the use of the theoretical phase transfer function and the deep water phase relation-ship, deviations f r o m the predicted f o r m of the wave-f o r m at the concentration point and o wave-f the position owave-f this point have been reported. Mansard and Funke^'^ specified the desired waveform at the concentration point, obtained its spectrum using Fourier transform and, following a procedure similar to Takezawa, computed the excitation electrical signal. They reported better waveform characteristics and some deviation f o r the position of the concentration point.

Clauss and Bergman'" have implemented the use of Gaussian wave packets f o r determining the transfer functions of floating structures. Several wave packets are necessary to cover the entire frequency range of interest. The theoretical transfer function of the facility was used. Several successful applications of the method have been reported.

Finally, Kjeldsen et a/.""'^ have developed a technique for producing 2-D and 3-D 'freak waves' and Johnson et al}^ have developed a waveform containing equally spaced components i n the frequency of encounter domain f o r use with ship models.

2 T H E O R E T I C A L B A C K G R O U N D

Consider a ship sailing through waves and suppose that the ship behaves as a linear dynamic system, an assumption that works satisfactorily f o r engineering purposes. The response of the ship to a sinusoidal wave history x{t) of a particular frequency w will asymp-totically approach a steady state sinusoidal response of the same frequency w. The ratio of the output amplitude to the input amplitude ( R A O ) and the phase diff'erence between output and input f o r all frequencies defines the frequency response o f the system and is represented by the complex transfer function G{juj).

When a ship sailing i n calm water encounters a transient wave history x{t) o f sufficient duration relative to the frequencies of interest and the length o f t h e vessel, then some response y{t) w i l l be measured. I t is well known that the transient signal x{t) can be decomposed, according to Fourier theory, into a continuous distribution of infinitesimal sinusoidal components and the Fourier transform X{ju)) of x{t) is given by the

complex quantity

X{iu;)= r x{t)Q^j^'At (2.1)

J - o o

which represents the amplitude and the phase of the components at frequency w.

Considering further that the response y{t) is the summation of the response to each o f the input frequencies, the frequency response o f the system throughout the complete range o f interest G{j<jo) can be estimated by a single transient test w i t h input and output Fourier transforms X{j(jS) and Y{juj), respec-tively, using the relationship

G{jw) = r ( ; a ; ) / Z ( » (2.2)

As has been pointed out by Davis and Zarnick,' a more accurate description o f the phenomena involved i n transient wave testing would be a configuration where the wave height and the ship response are both viewed as responses, Hi{juj) and HiUui) respectively, to some undefined initial excitation, the mechanism which produces the waves. However, since wave height and ship motion are completely related in the sense that they respond to a single cause, i t is proper to consider that ship motion can be related to wave height by the frequency relation

G ( » = H2{M/Hi {joj) = Y{jui)lX{jw) (2.3) where G{ju)) is the ratio of the frequency responses o f

two physical systems.

Furthermore, in order to establish the phase transfer function of the ship responses, the input x{t) is arbitrarily defined as the instantaneous amplitude o f the undisturbed wave surface which would pass through the centre o f gravity o f the model.

Thus, the problem o f defining the frequency response of a ffoating or sailing structure by a single run reduces to the generation of a transient wave history x{t) w i t h energy content i n the desired frequency range and the recording of the time histories yi{t) of the responses when the floating body encounters the wave train.

Seakeeping tests are usually performed i n long, narrow towing tanks, where waves generated by the towed model and oncoming waves diffracted by the model are reflected again on the tank side walls, contaminating the oncoming waves. This phenomenon, which is apparent especially at the stern region o f the model when towed at low speeds, results i n erroneous measurements o f the response function when testing i n regular waves, and i n particular f o r the lower frequen-cies which propagate at higher speeds. I n order to reduce the tank wall interference effects, an experiment of relatively short duration is advisable. The method proposed in the present paper provides a better prediction of the concentration point, which results i n an improved control o f the length of the time history along its route and consequently o f the time history encountered by the model.

Transient waves for ship and floating structure testing 73

Transient wave methods are based i n general on a unidirectional wave group of finite duration consisting, in the context of Unear theory, of an infinite number o f infinitesimal sine wave components. I f this wave group is observed at two points at a distance x along the direction of propagation in shallow water, each wave component with frequency w has an apparent phase lag'^

Ao/x

g tanh (/c/j)

(2.4)

where ^ = 2 / [ l + 2/c/z/sinh {llcli)], /c = wave number, and h = tank depth.

I n the case of deep water, eqn (2.4) is simplified to

= 2u?x/g (2.5)

These expressions are a direct consequence of the solution of the Laplace equation which satisfies the free surface condition. The formulation of the general two-dimensional problem of propagation of transient waves can be found, for example, i n Mei.'^ The problem of determining the ship responses using transient waves has been treated by Davis and Zarnick' and Takezawa* f o r the case of deep water. Omitting the mathematical analysis, which is beyond the scope of the present paper, the wave elevation at a distance x before the concentra-tion point h{x, t) is approximated for a large gt^/Ax by the expression

li{x, t) = {g/7rxf^A{gt/2x) cos {gt^Ax - 7r/4)

(2.6) where A{gt/2x) is the amplitude o f the wave spectrum at the so called 'local' frequency WL = gt/'^x.

According to eqn (2.6), the frequency part of moves in group velocity along the direction of propagation with amplitude {g/TrxY^^A{iJi^) and the amplitude distribution of the spectrum corresponds to the envelope of the time history. Furthermore, the hnear dependence of WL on time gave the base f o r the construction of transient wave groups by hnear sweep of frequency. I t is obvious that i n order to create a wave train which can concentrate at a point x along the tank, we have to generate the higher frequencies first, which travel at lower speeds. This has been achieved by the generation of successive simple harmonic wave compo-nents at discrete frequencies sweeping the frequency band of interest. For each component a single period is produced, while the frequency o f each generated wave period is determined according to the experimental phase lag, measured previously, instead of the corres-ponding theoretical one represented by eqn (2.4).

Although the wave-form described exists only as an electrical signal, the transient waves produced finally have been found experimentally to possess aU the necessary characteristics.

3 M E T H O D

The basic objectives of the new method, i.e. to produce a waveform containing a frequency range appropriate f o r seakeeping tests, which can also be programmed to concentrate at a predetermined point, have been achieved w i t h simple but rehable means.

The electrical signal which excites the wavemaker (Fig. 1) is formed by a succession of wave singlets, i.e. single period sine waves, arranged i n decreasing order o f their frequency. The selected frequencies cover the entire range of interest. The highest frequency/i is selected and the desired concentration point x = Xc is specified. The second frequency f2 is deduced f r o m the requirement that i t reaches the concentration point simultaneously w i t h / i and the procedure is repeated until a frequency near the low end of the frequency range is reached. This is shown schematically in Fig. 1.

Before proceeding with the description of the method, a comment is necessary regarding the wave singlets. I t is well known to the authors that wave singlets do not constitute any material entities i n nature. Furthermore, it is not possible to generate a unique wave singlet i n the tank. However, this term is used i n this paper f o r convenience purposes.

W i t h this clarification i n mind, and f o r the procedure to be successful, the group velocity of the various components should be known. I t is remarkable that previous methods use theoretical relationships f o r the phase transfer function along the flume, the corresponding group velocity and usually those f o r deep water, when the water i n the laboratory is shallow for the longer waves and i t is known that even the shaUow water predictions are not i n adequate agreement with the experiment.*'^ This is shown i n Fig. 2, where i t can be seen that the experimental phase transfer function is smaller for the higher frequencies than the theoretical values and therefore the experimental group velocity is higher than the theoretical predictions.

As a consequence, i n our method only experi-mentally determined transfer functions are used. The transfer functions of interest (phase and amplitude) include:

• the transfer function between the excitation signal and the motion of the paddle of the wavemaker; • the transfer function between the paddle motion

and the generated waves at the position o f the paddle;

• the transfer function between the waves at the position o f the paddle and at the desired concen-tration point.

The first transfer function can be readily measured. The amphtude part of the third transfer function is known to be practicaUy constant and equal to unity, assuming no breaking occurs, a fact which has been

74

CONCENTRATION POINT

G. J. Grigoropoulos, N. S. Florios, T. A. Loulcalcis

WAVEMAKER

BEACH

The wave singlet of frequency f l travels the distance Xc in time t.

The frequency f2 is calculated by the requirement that the corresponding wave singlet travels the distance Xc in time t - T l .

3.00 m

V X / / / / / / / / / / / / / / A

y / / / / / / / / / / / / / / / / / / / / / / / / / / / ^

Fig. 1. The generated transient wave train at the wave malcer.

verified. The phase part of this transfer function was determined at positions 20, 35, 50 and 65 m along the 90-m long tank, using single frequency wave packets. These wave packets are actually sine waves of finite duration with varying wave amplitude per period in order to identify the same period at the electrical signal and at the wave elevation records. A typical wave packet of this Icind is shown i n Fig. 3. The electrical signal and the wave elevation at the aforementioned four equi-distant points along the tank have been sampled simultaneously, so that the time necessary for the wave packet to travel a given distance is identified and hence the respective phase lag determined.

As can be seen f r o m Fig. 2, i t is a good assumption that the phase difference per unit length propagation of the waves is practically constant along the tank for a constant frequency as is the case f o r the theoretical results. Therefore, a single phase difference per unit length curve has been produced and is shown i n Fig. 4. O n the basis of this curve the sequence of the frequencies of the transient wave packet is determined as follows.

Let fx be the maximum frequency o f interest and XQ the ordinate of the concentration point. The time required f o r the peak o f the first wave singlet to reach

the concentration point is given by

U = 4>\Xc 1

2-Kf, ^ A f , (3.1)

where 0 i is obtained f r o m Fig. 4.

The corresponding time f o r the second wave singlet with frequency ƒ 2 is given by

l / / i (3.2)

From eqn (3.2) and f r o m the experimental curve o f Fig. 4, (f>2 and f i can be determined.

One o f the advantages of this method is that the shape o f the energy spectrum of the transient wave package is independent o f the concentration capabilities o f the method. The only limitation is that no waves with very high slope, resulting i n premature breaking, should be included. F r o m the desired wave spectrum (Fig. 5) and taking into account the amplitude part of the three aforementioned transfer functions, the energy spectrum of the electrical signal can be readily determined (Fig. 6).

For each frequency f = l/T,-, which is included i n the transient electrical signal, the corresponding amplitude

Transient waves for sltip and floating structure testing 75 XI 1100 H 1000 -A 900 REFERENCE POINT: 20 m . o Experimental values

Theoretical for shallow water, c a l c u l a t e d by the formula;

ip = k ' ( 2 n f ) ' * x / g • ( l / l a n h { k h ) ]

A i " ^ ! / [1 + 2 k h / s i n h ( 2 k h ) ] k = wave number

h = flume depth

X = distance along the flume

800 700 4 600 500 -4 400 300 -4 200 4 100 1.7671 Hz 1.2495 Hz 0.6835 Hz 0.6246 Hz 0.5101 Hz 0.4416 Hz 0.3951 Hz 0.3000 Hz 50 65 Distance (m)

Fig. 2. Phase transfer function along the flume. Thus, the energy content ofthe singlet with frequency ĥ is

[fl,-cos (wOf d? = a?/2 (3.3)

80.0 100.0 TIME (see) Fig. 3. Typical single frequency wave packet.

This energy can only be present i n the frequency band [ f - { f i - f i - i ) / 2 , f + {fi+i-fi)/2] o f extent

Sfi = (ƒ.+! - y ; _ i ) / 2 and its magnitude can be expressed

as S { f ) 6 f i , where S { f ) is the spectral density of the signal at frequency f . Thus, the amplitude o f the ith component of the transient signal is given by

«f = [2S{fm"' (3-4) The proposed method f o r producing transient waves

is well suited for a modified F F T analysis. Taking into account that we have only one fuU period per frequency of duration T,- = 1 /ĥ, within the transient wave record of duration TQ, the total energy corresponding to that period is interpreted by the Fourier transform to be distributed over the whole record length at an amplitude fii,r,/ro (Fig. 7). The correct wave amplitude can be found by scahng the spectral density of the resulting spectrum by T^/Tt. The reason f o r this scaling is that f o r each frequency f , instead o f analysing the whole record TQ, we actually analyse only the part o f t h e

76 _{G. J. Grigoropoulos, N. S. Florios, T. A. Loulcakis} 30 -0 25 + 20 15 + 10 Experimental curve

Theoretical for shallow water,calculated by the formula:

= A • (ZTTf)' • x/g • (l/tanhCkh)] where A = 2 / [1 + 2kh/sinh(21(h)] k = wave number h = flume depth x = 1 m 0.5 1.0 1.5

Frequency (Hz)

Fig. 4. Pliase difference per meter for a progressive wave in tfie flume.

Sn(f) (mm^*sec)

Transient waves for sliip and floating stntctive testing 11

Ss(f) (volt^*sec)

f{Hz)

Fig. 6. Electrical signal energy spectrum. record containing frequency f of duration T,-. I n

addition, tlie effective bandwidth of the spectral analysis fQ = l/To can always be arranged to be less than the minimum frequency spacing of the generated wave frequencies, so that at most one generated frequency is included i n each filter. Thus, the only approximation employed is that the central frequency of its filter, containing the generated frequency, is used to scale the window instead o f the actual frequency o f the generated frequency. The linearity of the Fourier transform permits this modification of the F F T analysis.

To estimate the phase transfer functions of the ship responses, the standard F F T analysis can be applied, keeping i n mind that both the input transient wave history x{t) and the response y{t) should be referenced to the L C G of the model.

TOTAL RECORD LENGTH: TO WAVE SINGLET PERIOD: T l

A ' T l / T O

Fig. 7. Wave amplitude correction of wave singlet Ti for the modified FFT.

A n y analysis method used in time histories of small duration, such as the extrapolation method proposed by Schmiechen and Lang'^ or the maximum entropy method,'^ can also be used.

4 A P P L I C A T I O N S

The experimental apphcation of the present method f o r producing transient waves validates the basic assump-tion that each wave singlet within the wave train will propagate as determined by the corresponding indivi-dual experiments. As a result, well concentrated wave-forms were measured, very close to the predicted concentration point. Usually the waves were concen-trated, i.e. the maximum wave height was observed just prior to breaking, at a point less than 5% after the predicted one. The deviation, which is probably due to non-linear phenomena, difficulties i n measuring and imperfect experimental determination of the phase differences o f the singlets, does not interfere w i t h the objective of conducting seakeeping experiments in transient waves.

A n example of the concentrated waveform o f a transient wave train consisting of 76 wave singlets, which occurred at a position 68 m f r o m the wave maker, instead of the predicted 65 m , is shown i n Fig. 8.

The RAOs of three ship models, with vastly varying hull forms, have been determined using the transient wave technique. As discussed earlier, the respective phase angles could also be estimated by the F F T method. However, ony the more useful RAOs are presented i n order to demonstrate the apphcability o f the method and the innovation it introduces.

Models o f a container ship (S7-175), a traditional double-ended fishing boat (of the 'trehandiri' type) and a car/passenger ferry have been tested at various Froude numbers. The main particulars of the models are shown in Table 1.

78 _{G. J. Grigoropoulos, N. S. Florios, T. A. Loukalcis}

model proposed by I T T C for comparative testing by the towing tanks, results are presented at rest and at the Froude nos 0'200 and 0-275 prescribed by I T T C (Figs 9-14). These results compare very well with the corresponding regular wave results. Discrepancies of the order of 5-10% are within acceptable limits, considering the fact that regular wave results f r o m different tanks f o r this model, as presented i n Ref. 19, differ by up to 20% f r o m each other. Differences o f a few percent i n the measured RAOs f r o m regular wave experiments i n the same tank and for subsequent runs are also known to be a usual phenomenon.

I n Figs 15-20 the experimental results for heave, pitch and relative motion for the model o f the fishing boat have been plotted against the respective analytical results using strip theory.^" The results based on the proposed method for transient wave testing are i n good agreement w i t h the regular wave results while numerical estimations are more conservative.

Finally, the model o f the car/passenger ferry was chosen for testing using transient waves. Regular wave testing for that model at low speed (Froud no. = 0T35), because o f tank wall effects, did not provide a reliable estimation of the R A O curves. On the contrary the proposed method is not affected by these effects (Figs 23 and 24). Transient wave results are very close to the empirical method of Murdey^' f o r correcting measured response data for interference effects by taking the midpoints between response curve maxima and minima values. Resuhs with the same model are presented also for the model at rest and at a relatively high speed (Froude no. = 0-307) where the two methods are i n excellent agreement (Figs 21, 22, 25 and 26).

Thus, i n almost all cases the results of the proposed method are i n good agreement with the corresponding regular wave results except for the lower Froude numbers, where the regular wave results suffer f r o m tank wall effects.

0.0 0.8 1.6 2.4 3.2 4.0

X/Lwl

Fig. 9. Transient and regular wave determined heave RAO at Froude no. = 0-00. 0.15 0.104 a 0.05 a 0.00 - 0 . 0 5 4 - 0 . 1 0 -0.15H r 0.0 4.0 8.0 12.0 16.0 20.0 TIME ( s e c )

Fig. 8. Waveform at the concentration point.

Table 1. Main particulars of the models tested Main particulars Container Fishing Ferry

ship boat Ferry Length, L^P (m) 2-500 2-364 1-606 Length/breadth, L/B 6-887 3-700 3-454 Breadth/draft, B/T 2-669 3-043 6-838 Block coefficient, Cg 0-572 0-338 0-557 Model scale 1:70 1:10 1:30

I n all cases the model, running at constant speed or at rest, would be excited by the whole length o f the wave train, which would then concentrate and break.

I n Figs 9-26 transient and regular wave determined RAOs for the three hull forms are shown f o r several different speeds.

5 D I S C U S S I O N

Transient waves for ship and floating structure testing 2.0 o 1.5 1 . 0 - 4 0.5 -4 0.0 MODEL: S 7 - 175 1 F n = 0.0 \ T r a n s i e n l Waves / R u n s 1, 2 & 3 i

1

' / '

Fig. 10. Transient and regular wave determined pitch RAO at Froude no.

0.0

\ / L w l

Fig. 11. Transient and regular wave determined heave RAO at Froude no.

2.0 ^ 1.5 4 2 &. o X a. 1.0 4 0.5 0.0 0.0 1 MODEL: S 7 -F n = 0 . 2 0 0 175

1

1

i

80 G. J. Grigoropoulos, N. S. Florios, T. A. Loukakis 2.0 1.5 O 1.0

I

i 1

1 1

1

1 -•

j i

' /

₁

1 i

Fig. 13. Transient and regular wave determined heave RAO at Froude no. = 0-275.

2.0 J5 O a: o 0,0 0,8 1,6 2,4

Fig. 14. Transient and regular wave determined pitch RAO at Froude no. = 0-275.

2,0 1.5 4 5. o 1,0

I

i

i

i

Transient waves for ship and floating structure testing o

I

Fig. 16. Tlieory and model test determined pitch RAO at Froude no. = 0-00.

2.0 1.5 O 1.0 Di > < w 0.5 0.0 1 MODEL; T R E H A N D I R I 1 F n = 0 . 2 3 0 * Regular Waves + T r a n s i e n t Waves

i

l

l

i * i :

Fig. 17. Theory and model test determined heave RAO at Froude no. = 0-230.

o < a: u H 0.0 4 3.2 4.0 X / L w l 0.0 0.8 1.6 2.4

82 G. J. Grigoropoulos, N. S. Florios, T. A. Loukakis 4.0 O Si § 3.0 4 2.0 1.0 0.0 0.0 I MODEL; T R E H A N D I R I F n = 0 . 2 3 0 Strip theory * Regular Waves •f Transient Waves 1 1 MODEL; T R E H A N D I R I F n = 0 . 2 3 0 Strip theory * Regular Waves •f Transient Waves • j 1 1 1 / 1 / 1 / + — [ • ƒ * -• : * 1 _{! !} -0.8 1.6 2.4 3 . 2 4.0 X / L w l

Fig. 19. Tlieory and model test determined RAO of the relative motion at the bow using the wave profile at a distance of 0-8 m away from the ship at Froude no. = 0-230.

4.0 ^ 3.0 o < O 2.0 i 3 1.0 0.0 MODEL: T R E H A N D I R I F n = 0 . S 3 0 Strip theory * Regular Waves •f Transient Waves MODEL: T R E H A N D I R I F n = 0 . S 3 0 Strip theory * Regular Waves •f Transient Waves Ï * ^ J 1 * 0.0 0.8 1.6 2.4 3.2 4.0 X / L w l

Fig. 20. Theory and model test determined RAO of the relative motion at the bow using the wave profile on the ship's bow at Froude no. = 0-230.

2.0

3.2 4.0 X / L w l

Transient waves for ship and floating structure testing 2.0 83 1.5 1.0

1

g

Fig. 22. Transient and regular wave determined pitch RAO at Froude no. = 0-00.

2.0 1.5 o 1.0 < 0.5 0.0 2.0 1.5 ^1 Ü o 1.0 4 0.5 0.0 MODEL: F E R R Y - B O A T F n = 0 . 1 3 5 Transient Waves + Regular Waves MODEL: F E R R Y - B O A T F n = 0 . 1 3 5 Transient Waves + Regular Waves ^ / + 7+ t 1 1 1 1 r 1 1 1 0 0.8 1.6 2.4 3.2 4 A / L w l

and regular wave determined heave RAO at Froude no

MODEL: F E R R Y - B O A T F n = 0 . 1 3 5 Transient Waves + Regular Waves MODEL: F E R R Y - B O A T F n = 0 . 1 3 5 Transient Waves + Regular Waves + 1 1 1 1 1 1 1 1 I .0 0.8 1.6 2.4 3.2 4 X / L w l

Fig. 25. Transient and regular wave determined heave RAO at Froude no. = 0-307.

Furthermore, in order to investigate the repeatability of the experimental results, the model o f the I T T C container ship has been successively tested using the same transient wave group. The respective experimental heave and pitch R A O curves for the model at rest have been plotted (Figs 9 and 10). As can be concluded f r o m these plots the results compare very well with each other. This is a direct consequence of the described mechanism of wave generation.

Finally, successive testing performed with different transient wave packets, concentrated at various positions along the tank, led to R A O curves which differ by less than 10% f r o m each other.

6 C O N C L U S I O N S

A simply implemented and reliable method, both i n the

production and its analysis, has been devised for seakeeping tests in transient waves.

The use o f experimentally determined phase transfer functions result, i n contrast to earlier methods, i n experimental concentration points very close to the predicted ones.

The arbitrary selection o f the spectral f o r m o f the wave train permits the determination of the RAOs of the floating or running model with a single pass only, in contrast to the Gaussian wave packet methods.^

The accuracy in the prediction of the concentration point allows for the model-wave encounter time to last very briefly and thus tank wall interference effects are diminished.

Finally, i t should be stressed that good transient wave tests are much shorter and hence less expensive than either regular or random wave tests.

2.0 ^ 1-5 J 3 O a: o 1.0 0.5 4 0.0 MODEL: F E R R Y - B O A T F n = 0 . 3 0 7 Transient Waves Regular Waves

1

Transient waves for ship and floating structure testing

85

REFERENCES

1. Davis, M . C. & Zarnick, E. E., Testing sliip models in transient waves. Proc. 5di Symp. on Naval Hydrodynamics, Sept. 1964, Bergen, Norway.

2. Smith, W. E. & Cummins, W. E., Force pulse testing of ship models. Proc. 5tli Symp. on Naval Hydrodynamics, Sept. 1964, Bergen, Norway.

3. Kerwin, J. E. & Narita, H., Determination of ship motion parameters by a step response technique. / . Ship Research, 9(3) (1965).

4. Freakes, W. & Keay, K. L., Effect of shallow water on ship motion parameters in pitch and heave. MIT, Report No. 66-7, Aug. 1966, Cambridge, MA.

5. Takezawa, S. & Takekawa, M . , Advanced experimental techniques for testing ship models in transient waves: Part I . The transient test technique on ship motions in waves.

11th Symp. on Naval Hydrodynamics, London, 1976.

6. Takezawa, S. & Hirayama, T., Advanced experimental techniques for testing ship models in transient waves; Part I I . The controlled transient water waves for using in ship motion tests. 11th Symp. on Naval Hydrodynamics, London, 1976.

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