Tests with an oscillating plunger type model wavemaker

ARCHIEF

tab. y.

Scheepsbouwkunde

Technische Hogeschool

FINLAND INSTITUTE OF TECHNOLOY

SHIPBUILDING LABORATORY

Report No. i

*

TESTS WITH AN OSCILLATING PLUNGER

TYPE MODEL WAVEMAKER

by

V. Kostilainen and J-E. Jansson

TESTS WITH AN OSCILLATING PLUNGER TYPE

MODEL WAVEMAKER

by

V. Kostilainen*) and 1.-E. Jansson°0)

Introduction

Early in 1965, the development of a wavemaker

model was started at Finland Institute of

Tech-nology. The aim of the program was to obtain

design information for wavemakers to be designed and installed in the Shipbuilding Laboratory of the Institute. After considering various types of wave-makers, it was decided that the most suitable type

for this particular installation would be a simple oscillating plunger similar to that developed at

Stevens Inslitute of Technology [1] from the

sug-gestion of Prof. B. Korvin-Kroukovsky. Since

com-parative tests with different types of plungers and beaches have

already been made [2],

[3], it

was decided to investigate the form and

dimen-sions of the waves generated by one selected

plun-ger type and the corresponding power

require-ments. The size of the seakeeping and

manoeuvre-ing basin of the Finland Institute of Technology

according to present designs will be 40 m X 40 m X 3 m. A two-dimensional model wavemaker in

scale 1 : 2 was built and installed in the narrow

20 m X 1.5 m X 1.7 m tank of the Hydraulic

Laboratory of the same Institute.

General Considerations

According to the

operation plan the

fuilsize

wavemaker should be capable of generating

re-gular waves from 1.5 m long by 0.1 m height up to 15 m long by 0.6 m height. The celerity of the wave is given by

c- - gL tanh 27rh

2r L

(1)

The depth to the bottom of the tank will be 3 m,

thus it is not possible to generate long deep water waves. If the accuracy limit of 1 percent in wave

celerity is chosen as the transition limit, then waves

0) _{Scientific Officer.}

0*) _{Professor, Department of Naval Architecture, Finland} Institute of Technology.

1-up to 8.2 m in length can be considered as deep

water waves.

Since the model scale was 1 : 2, then the model

wavemaker should be capable of generating the

waves (0.75-7.50) m long by (0.05-0.30) m

height. Thus the required frequency range of the model wavemaker is abt. (0.4-1.5) 1/s.

The Construction of Model Wavemaker and Wave

Damper

To avoid the phenomenon of cross waves men-tioned in [2] the plunger was designed to have the

form of a 15 degrees wedge at the point. The wedge

was widened towards the higher waterlines, where the wedge angle is abt. 25 degrees. A comparison

of the full scale plunger form with the double

5330

Fig. 1. Plunger forms.

FIT

20

3370 5L90

wedge of the Admiralty Experiment Works, Haslar,

is made in Fig. 1. The inside surface of the curved

wedge is unrolled flat for comparison. The plunger was made of polystyrene plastic foam covered with resin-impregnated glass fabric.

The layout of the model wavemaker is shown in

Fig. 2. The lever of the plunger, crank and con-necting rod were aluminium. A steel torque

tube was placed below the waterline and was

sup-ported from the sides of the tank by water

lubri-cated bearings. The combined flywheel-variable

stroke eccentric was driven by a 5 kW geared A.C.

balance motor. The revolutions of the motor were

controlled by an adjustable transformer-silicum

rectifier unit. The entire installation is shown in

Fig. 3.

The grating type wave damper was selected

based on NSMB test results [4]. The grating

con-Fig. 8. Model wavemaker.

2-sists of laths 70 mm X 70 mm with a spacing of 120

mm. The inclination of the plane ground plate was i 5.

Test Program

The model wavemaker was run with the eccen-tricity e varied from 10 mm to 70 mm in steps of 10 mm. The frequency was varied in steps of abt.

0.05 1/s from 0.7 1/s to 1.7 1/s for small eccentricity

and frcm 0.38 1/s to 0.80 i/s for large eccentricity.

Fig. 4. Some typical waveform recordings.

,ç\ \\ \_\". ,'"

F (w]

10

50

The oscillating double amplitudes of the plunger

corresponding the eccentricities of (10-70) mm are

0.025 .... 0.175 radians. The wave form was

re-corded using a Leica-camera equipped with a

polarizing filter. The period was measured by tak-ing the total time of 10 oscillations. As a balance

motor was used, the input power was also obtained.

An example of wave form recordings is presented

in Fig. 4.

Tests Results

The results of the wavemaker model tests are

presented in Figures 5 through 8. The values of input power are plotted against the values of the

L H2

quantity _T

in Fig. 5. L

is the wave

p

length, H

wave height and T

the period.

20 15 P [w] 10 D LwH _[ms/s]

Fig. 5. Measured input power values.

01 0.02 0.03 2 0,04 0.05

i,tk [m's]

Fig. 6. Input power of the model wavemaker, correlation

lines.

3-0.09

..SOmm

--

l*tIIuIfl1.!WIIV0TI!

-.... KIXAI. INPUT PWER, FLAP

--TYPE WAVEMAI<ER

-IXAI. INPUT PWER, FLAP TYPE WAVEMAI<ER __

-

__

--

ENERGY7RANSENERGY7RANS BY SINE WAVES/.BY SINE WAVES/.

20

15

0.05 QOS 0.07 0.08 0.09

0.01 0.02 0.03 0.0/.

Energy transferred by a sine wave during 1 second

is

Pi-jBwpg WTW

i

LH2

p

(2)

where B is the width of the wave. According to

Ref. [5] the ideal mean input power of a flap type

wavemaker is: 2

i.

P11 =

B _pg

T

Correlation lines for input power were computed

separately for each eccentricity, and they are pre-sented in Fig. 6 together with the graphs of equa-tions (2) and (3). The equation of the correlation

line of all the tests is

L H

P [W] = 57 + 1194

w w

(4)

where L [m], H [m] and Tp [s]. No-load

L [m:I 250 200 150 H [mm] 100 5G Q

input of this particular wavemaker is thus approx-imately 57 W. In dimensionless form we get the

following approximate formula for the input power

of an oscillating plunger type wavemaker:

2

LH

P = Po + 0.0828 Bpg

T (5)

w w

p

where Po is no-load input power of the system; po is to be approximated on the basis of the size of the installation, the type of the linkage used,

and the gear ratio.

4-The relationship between the wave length and

the period is presented in Fig. 7. Test data

cor-responding to deep water waves (L < 2h)

eoin-cide relatively well with the parabola L

₌

gT

/2r.

The measured wave heights are plotted against the wave lengths in Fig. 8.

In examining the relationship between wave dimensions and eccentricity of the wavemaker mechanism the following approach was made. If

it is supposed that the amount of the water

dis-placed from still water level is equal to the «dis-placement-amplitude'> of the plunger, then using

the notation of Fig. 9 there can be written

A=A1+A2

(6)

In Fig. 9 a is the double amplitude angle of the plunger. For sine-waves

i

A1 + A2 = - H L

thus

Fig. 9. Dispacement-amp1itude approach of wavemaking.

1

/1

J2h

o.lO,rn,, o 20mm £ 30mo, a 40mm 50n,n, V 6Oro,n ?Omm e 7e V L L V L 40a a e V A 3o S o, o

7

s aa 1:0 Los

-a

V è V L 3 4 5 6 8 L[m]

Fig. 8. Measured wave heights as a function of wave length.

0 05 10 15 20 25 30

T [s]

H [mm] 250 200 150 100

However this formula gives too small wave

dimensions compared with the test results. Using the method of leasit squares the following general

formula was obtained from the measured wave

dimensions:

L H = 4.70 A

(9)

For this model wavemaker A [ma] 0.627 a

[rad] = 1.68 e [m]. Fig. 10 presents the graphs

of (9) for tested eccentricity values e = 10. .. 70

mm of the model wavemaker. If Figures 8 and

10 are compared, it is observable that the correl-ation of the measured values with the graph is in general satisfactory. However for some values of

eccentricity formula (9) gives too small wave height

when the wave length is small and too large wave height when the wave length is large.

Nomenclature

A= Area in general

B=« Width of the wave

e = Wave celerity

e = Eccentricity

h= Water depth

Hw= Wave height

-5-Fig. 10. Wave heights for different eccentricities as functions

of wave length according to formula (9).

L = Wave length

P = Power in general

Tp Length of a period

a = Double amplitude angle of the

oscillating plunger type wavemaker

p Density

REFERENCES

E. Nurnata, P. Spens, A. L. Muley: «New Facilities at Stevens for Research on Seakeeping Qualities of Ships.» Stevens Institute of Technology. ETT Report

No. 677. 1957.

A. J. Vosper: «Facilities and Ship-Model Instrument-ation at the Admiralty Experiment Works, Haslar.» Symposium on the Towing Tank Facilities. Zagreb 1960.

R. N. Newton: «New Facilities at Admiralty Experi-ment Works, Haslar.» TINA 1962.

W. P. A. van Lammeren, G. Vossers: «The

Seakeep-ing Laboratory of the Netherlands Ship Model Basin.»

NSMB Publication No. 140. 1957.

K. Taniguchi, J. Shibata: «Wavemaker of Mitsubishi

Nagasaki Experimental Tank.» Symposium on the

Towing Tank Facilities. Zagreb 1960.

o 2 3

L [m]