Aalborg Universitet

A Three Dimensional Sea Facility for Deep and Shallow Water Waves

Burcharth, Hans F.; Nielsen, Søren R.K.; Schaarup-Jensen, Kjeld

Published in:Proceedings of the Fifth International Symposium on Offshore Mechanics and Arctic Engineering

Publication date:1986

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Link to publication from Aalborg University

Citation for published version (APA):Burcharth, H. F., Nielsen, S. R. K., & Schaarup-Jensen, K. (1986). A Three Dimensional Sea Facility for Deepand Shallow Water Waves. In J. S. Chung (Ed.), Proceedings of the Fifth International Symposium on OffshoreMechanics and Arctic Engineering (Vol. 1). American Society of Mechanical Engineers.

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A THREE DIMENSIONAL SEA FACILITY FOR DEEP AND SHALLOW WATER WAVES

H. F. Burcharth S.R.K. Nielsen K. Schaarup-Jensen October 1985

A THREE DIMENSIONAL SEA FACILITY FOR DEEP AND SHALLOW WATER WAVES

H. F. Burcharth S. R. K. Nielsen K. Schaarup-Jensen October 1985

Presented at the OMAE Symposium, Tokyo, 1986.

A THREE DIMENSIONAL SEA FACILITY FOR DEEP AND SHALLOW WATER WAVES

ABSTRACT

by

H. F. Burcharth, Professor of marine civil engineering S. R. K. Nielsen, Assoc. Prof.

K. Schaarup-Jensen, Assoc. Prof.

University of Aalborg Department of Civil Engineering

Sohngaardsholmsvej 57 DK-9000 Aalborg, Denmark

The paper describes a low-cost wave tank for the testing of structures in short crested seas and current. The paddle system is of the snake type and used for the generation of both deep ~nd shallow water waves. The quality of the waves and scale problems related to small scale tests are discussed. Some results from testing of circular cylinders in 3-dimensional waves are presented.

INTRODUCTION

Wave tank model testing of marin~ structures is still in many cases a very important part of the design process. The two main problems are to obtain a realistic reproduction of t he sea and to avoid or control the scale effects. It is well documented that both fixed and floating structures respond differently to long and short crested seas (2 -D and 3-D waves), Huntington et al. 1976, Kirkegaard et al. 1980, Thunbo Christensen et al. 1984. Therefore it is of great importance for a wide range of tests that models are run in 3-D waves at least for a period long enough to clarify the correlation between response of the various structures in 2-D and 3-D waves. Since a lot of work needs to be done it is of importance to initiate and to discuss the design and construction of 3 -D wave tanks.

3-D wave tanks are expensive as they involve multi paddle systems, and because the total costs are more or less proportional to the volume of the tank (a large tank of say 35 m x 25 m x 4 m is very expensive). For this reason there is a need for the development of designs which in costs can be handled not only by few commercial laboratories but also by universities.

The lower limit for the dimensions of a tank is determined by three main factors:

a) Scale effects related to reproduction of forces. b) Size of test area (dependent of type of tests). c) Size, weight and sensitivity of devises for the recording of forces,

movements etc.

Thus the size of the facility described in this paper is a compromise between these factors and the costs.

OBJECTIVES OF THE DESIGN

The wave tank is a university facility meant for both teaching and research related to marine civil engineering structures in deep and shallow water. It was regarded essential that resources for run­ning the facility in terms of costs and time were kept small.

2.

Moreover testing of space requiring floating structures, such as two tankers in tandem moored to a buoy, was given low priority compared to testing of fixed structures and floating structures with more restricted horizontal movements.

The facility should be able to reproduce both deep water and shallow water waves with the fol­lowing typical characteristics: Spectral peak periods in the range 0.9 - 1.3 sec, significant wave heights up to app. 0.20 m. This compares to model length scale in the range 1:30 - 1: 100 for ty­pical coastal structures and offshore structure in moderate water depths.

Any realistic 2-dimensional and 3-dimensional power spectrum should be reproducible .

DESCRIPTION OF THE WAVE TANK

The dimensions of the steel bar reinforced concrete tank are 15.7 x 8 .5 x 1.5 meter. A 1.5 meter deep section of 4.5 x 2.1 meter with windows for under water inspection of models allows water depths up to app. 3.0 meter, figure 1.

E /PADDLE SYSTEM N

c:i

\ V r--r--

V 1---r--

V 1--- WAVE ABSORBER ~ r--1---r--r--

\ r-- 1-DEEP SECT ION

r-- I 1--- !

--.....

K I

.§ - -':..:... ' <0

~I " I---

~I ~

\ i ~ /

I--- 4.5m

j ~ .....___ r BRI DGE ON RAILS T ------ r~EMOVABLE SKOT - ENTRANCE FOR TRUCK) -

E N

0 15 7m

f . ~ -~ - ~ ~

~ -~I . ~ 7LT 1~~ ""-~~ - =--

j_ ":J ~Jl 11 11 + ~REMOVABLE FALSE FLOOR

·.·•·• · .. :_.· .·.

BASEMENT l ~WINDOWS _5J E

-- FROM PUMP "' TO PUMP

Figure 1. Wave tank.

~

I

1 e 1 6 m

= ~ v-

•·• ...

-

Il l

+ J>.

+

j ![

I I I

I

' E

~ I ' r--

3.

A removable false floor of steel panels, strong enough to carry a 1.5 t lifting capacity truck covers

the deep section.

Since the total volume of the tank is only 220 m 3 it can be filled directly from the public tap water system through a 50 mm pipe in less than 6 hours. For this reason no attempt was made to include an otherwise needed comparatively costly reservoir with pump and filter systems.

The level of the wave absorber can be adjusted according to the water level.

THE PADDLE SYSTEM

The paddle system is of the snake-front type with translatory movements. It can be moved up and down and in connection with changeable water level both deep water and shallow water waves can be generated at various scales, fig. 2 .

MAX STROKE 2.Sm

a)

WAVE-----;;<~---+-+---"

ABSORBER

b)

· Figure 2. Principle of generation of a) deep waves and b) shallow water waves.

The discontinuity of waterparticle movements at the bottom of the flap in the case of deep water wave generation disturbes the particle path close to the generator. However, within a distance of one wave length from the generator, the orbital movements are adjusted to the theoretically correct paths.

The paddle consists of nine elements hinged with vertical axes to ten hydraulic pistons, thus allowing both a horizontal translation and a rotation of the individual elements. Two small non­rotating elements form the ends of the paddle front at the tank walls, fig. 3 .

~-------------------------p----,~·

// PISTONS N01' SHOWN

/ / - wOODEN Pt.AT£ ( 21mm) ~-~S~~~~'tEGSSCv~;~~)R . ~'8mm

- STAINLESS STEELPLATE I ( 1 Smm) ~PIVOT ON ROTAT ING

/ r~JI8mm SLI DE ROD / CYLINDER (STAINLESS STEEL) , - RUBBER SEALING

-f ---

POL'fETHVLENE SLIDE BEARING( 35mm)-

I - CONTOUR OF' , PA.OOLE - PUSrlC ART

Principle of flap system.

of

E "' 0

' • E

"' 0

Flap system.

Flap connection seen from rear.

Figure 3. The paddle system.

4.

The height of the flaps are 1.0 m and the width selfadjustable between 0.9 m and 1.08 m. The max width compares to situations where the positions of neighbour pistons are maximum and minimum, which compares to 0.60 m difference in stroke.

The fairly large stroke of 0.60 m makes it possible to compensate for the parasitic 2' order long waves, Bowers 1977, Ottesen Hansen et al. 1980.

The flap width was determined as a compromise between costs and quality of waves. The costs decrease with increasing width, but at the same time the quality of the generated waves decreases due to spurious waves, as discussed later.

The flaps are driven by hydraulic pistons giving a force of 2.7 kN by a working oil pressure of 80 bar and a piston speed of 0.60 m/sec corresponding to a flow of 2 x 10-4 m3 /sec.

The position feed back system for the flaps are controlled by MOOG valves and inductive posi­tion transducers with linear response. The oil pumps giving 160 bar is driven by a 50 Hp electric motor. Hydraulic pistons were chosen instead of step motors because fairly big forces are needed to drive the relatively wide, but few flaps.

On the rear side of the flaps wave absorbers are installed to prevent serious splashing, fig. 2.

5.

WAVE ABSORPTION

The wave damping is provided by a spending beach of perforated, corrugated glasfibre panels, which can be positioned at various levels matching the water table position, fig. 1 and fig. 4.

I {. I.

Overall view of wave absorber.

Detail of glasfibre panel.

Figure 4. Wave absorber.

Wave absorption takes place only along the end side of the basin because the two side walls are used for reflection of waves in the case of directional seas. In this way, a larger test area can be obtained, cf. figure 6.

When generating regular long crested waves with relatively high frequency cross waves can occur due to the lack of wave absorbers along the two walls. However, these cross waves can be nearly eliminated by mounting small perforated steel panels at right angle on the front of the flaps.

6.

The effectiveness of the wave absorber was studied by analysis of reflected long crested regular and irregular waves. The analysis is based on the method of Goda and Suzuki, 1976, using simul­taneous recordings from two wave gauges arranged in line of wave orthogonals. The results are presented in table 1 for monocromatic wavelets. The results correspond to an irregular 2 -dimen­sional seastate (JONSWAP-spectrum). As seen the wave absorber is less effective at very short and very long waves with highest efficiency at T - 1.0 s.

Table 1. Measured reflection coefficients for waves. 0. 77 m water depth.

Period of Wave height Reflection REFLECTION COEFFICIENT

regular waves coefficient ( IRREGULAR SEASTATE)

(sec) (cm) 0.44

0.467 2.3 0.310 0.34

0.653 4.5 0.127 0.22

0.959 4.8 0.048

1.42 6.7 0.065 0.1 2

1.89 4.8 0.126 FREQUENCY

2.27 3.8 0.346 0.00

0.25 0.50 1.00 1.50 2.00 2. 25 Hz

The effectiveness of the wave absorber can be improved by adding another set of perforated pa­nels on top of the corrugated panels. Actual the high reflection coefficients measured at the high frequency range are due to reflections on the relatively high vertical sides of the ribbles of the glasfibre panels.

At the moment there is no system installed to eliminate reflected waves by on -line adjusting of the paddle movements.

SCALE EFFECTS

A typical model scale for testing of for example oil rigs in the tank will be 1:100. This is half the size of many of such models which typically have been in scale 1:50. It is therefore of interest to analyze and compare scale effects in models of various sizes. The following discussion is based on fixed structures only.

Because wave impact on structures generally involves viscous forces a viscous scale effect will be present in a Froude model. This effect is small and some times negligible when inertia forces dominate drag forces. A typical example is overall wave forces on gravity structures. Such prob­lems can be studied successfully even in very small models as demonstrated in figure 5, which shows results from a 1:267 scale model study, Burcharth, Brorsen 1978.

The hydrodynamic gain factor determined from regular and irregular waves compares well to the gain factor theoretically determined from the Froude-Krylov force theory, which again is gener­ally confirmed in model tests of much larger scales.

However, wave impact on many structures involves significant viscous effects. Model testing of for example jackets in large waves will be in the drag-inertia regime even for relatively large models. It is, however, not obvious that a 1:50 model provides more realistic results than a 1 :100 model. If Morisons equation is taken for valid we find large variations of the coefficients CM and C0 with the Reynolds' number, the Keulegan-Carpenter number and the relative roughness para­meters. These variations show both positive and negative trends in the typical model scale range of these parameters. As an example take a 5 m diameter smooth vertical cylinder at level -20 m

4

I I Cl RCULAR LEGS.

Dl AMETER Sm

80 x 80 m BOTTOM TANK

;(.;!v, 'v , (<.

HYDRODYNAMIC GAl N FACTOR

IHC l)j N cm'' I

y~j

t 90'1, conl odence onterval ( 1 = 1 Hzl

EXPERIMENTS

SWL

'NI·A

30 m

18 m

3 m

- 31 m

-SI m

DETERMINISTIC CALCULAT ION BASED ON THE FROUDE -KRV ­LOV FORCE

o (a,(l))'/2 RAT IO OF FORCE AND WAVE a. ( l l AMPLITUDE

.,,s. ,( f)j

0 s, ctJ

RAT IO OF SPECTRAL OENSITIES OF FORCE AND SURFACE ELE­VAT ION

RATIO CROSS-SPECTRAL DEN­SITY AND SPEC TRAL DENSITY OF SU RFACE ELEVATION.

" 1 90'1, coni odence onterval ( 1 = 2 Hz )

• 0 +-+--+-+--1---+-+-+--+---+---1----+..,. I sec'' 0 05 10 IS 20 25 30

Figure 5. Hydrodynamic gain factor for overall horizontal forces in 2-D waves determined from a 1:267 model.

exposed to a wave of 30 m height and 20 sec period in 100 m water depth. In prototype CD and CM can be estimated to 1.45 and 1.3 respectively. In a 1:50 model the coefficients will be 0.9 and 1.4 and in a 1:100 model1.9 and 0.95 respectively, Sarpkaya 1976 a and b. If Morisons for­mula is used to calculate the maximum forces in the models and these forces are transferred to prototype forces by the Froudian model law, the 1:50 model will underestimate the force by app. 40% and the 1:100 model will overestimate the force by app. 10%. The same exercise per­formed with a 2 m diameter smooth cylinder shows a completely different tendency as both models overestimate the force significantly, but the 1: 100 model by 25% more than the 1 :50

model (this last case compares to the commonly found opinion on viscous scale effects). The confusing picture holds also for rough cylinders. Moreover, the very large scatter in CD and CM

found in the literature and also confirmed by several small scale experiments at the University of Aalborg should be kept in mind and so should the pronounced influence of estimation method on the values of CD and CM .

As a conclusion of this rather incomplete analysis it can be said that very little is known about scale effects quantitatively and very little can be said before much more reliable values of CD and CM are obtained or a better alternative theory is developed. On this basis it cannot be stated that a 1 : 50 model of a fixed structure is significantly better than a 1: 100 model in terms of scale effects.

7.

8 .

QUALITY OF WAVES AND SIZE OF TEST AREA

The quality of the waves and also the costs increase with decreasing width of the paddles . In this case a width of app. 0.9 meter was chosen because a wave quality analysis based on estimation of the spurious waves, Sand 1979, showed that such a width gives reasonable reproduction of waves within a test area of reasonable size for testing of fixed structures, cf. table 2 and figure 6.

Table 2 .

A L/'Q'.

0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

a)

b)

Analysis of spurious waves. Maximum angle of propagation fJmax (in degrees) as a fun c-tion of L /Q (model wave length/flap width) and A (amplitude of main wave height/am-plitude of max spurious wave height).

1.00

7 .18 14.48 22.0 30.0 38.7 48.6 61.0 90.0 90.0

1.25 1.50 1.75

6.78 6.45 6.18 13.65 12.99 12.43 20.7 19.7 18.8 28.2 26.7 25 .5 36.2 34.2 32.6 45.1 42.4 40.2 55.7 51.9 48.9 70.8 64.0 59.4 90.0 90.0 75.6

A =>0 172 . L =0.90m A => 3 34. L = 1. 80 m A =>2 1. 69 ,L=3.60m A ~56.03 , L=5.40m

2.00

5.94 11.95 18.1 24.5 31.2 38.4 46.5 55.9 68.7

c)

2.50

5.56 11.17 16.9 22.8 29.0 35.5 42.7 50.8 60.7

10·l m 2s SPECTRAL DEN SITY

WAVE PADDLE FRONT

WAVE PADDLE FRONT

>. ;> 2, L=0.90m A ~K66, L =1.80m

A ;> 74.9 , Ld.60m A'> 181. 9, L = 5.40m

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0 0.2 0.4

3.00

5.25 10.55 15.9 21.5 27.2 33.3 39.8 47.1 55.4

0 .6

E 0

"' M

" ...

4 .00 5.00

4.78 4.43 9.59 8.89

14.5 13.4 19.5 18.0 24.6 22.7 30.0 27.6 35.7 32.7 41.8 38.2 48.6 44.1

- JONSWAP SPECTRU M

(fp = 0 625Hz , H,=0. 13m)

E g -" ...J

E 0

"' 0

" ...

FREQUENCY

0.8 1.0 1.2 1.4 Hz

Figure 6. Examples of size and quality of test areas as a function of wavelength L.

a) Max angle of propagation less than 45°. b) Max angle of propagation less than 24.5° . c) Position of frequencies on surface elevation spectrum.

9.

Table 2 shows the maximum angle of propagation as a function of L/Q, within which the ampli­tude of the main wave is greater than A. times the maximum spurious wave amplitude. L is the model wave length and Q = 0.90 m is the flap width.

Figure 6a and 6b show examples of the quality of the reproduced waves for a test area defined by max angle of propagation equal to 45° and 24.5° respectively. As seen, the quality of the gene­rated waves are highly increased at the lower frequencies (increasing A.-values). The test area should be reduced by 1 wavelength from the paddle front, within which the transients in the Biesel solution are supposed to die out.

a)

IQ·3m2s SPECTRAL DE NS ITY

3.5

3.0

2.5

2.0

8 0 0

- JONSWAP SPECTRUM b) (fo = 0.625 Hz , Hs = 0.13m)

o MEASUREMENTS

SPREADING FUN~TION

71.9

1.5

1.0

0 0 :~59~~~~~~~~~~t 00

·359

0.5

FREQUENCY

- 180 0 '----'---"-----'----=.::..::..::-+

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Hz 0 30 0 63 0 93 I 25 Hz

Figure 7. Specified and recorded wave spectra in 2D and 3D waves. a) Autospectral density of surface elevation (model scale). b) Spreading function H(f, 8 }, histogram and target distribution.

Although the use of waves reflected from the side walls gives a larger test area, it is recommended to have a longer paddle front of e.g. 13 m instead of the 9 m front which was determined by the size of the room available.

RECORDING OF SHORT CRESTED SEA

The analysis of the wave is based on simultaneous recording of the surface elevation and two ho­rizontal orthogonal velocities in the same vertical. The velocities are recorded by an ultrasonic current meter (MINILAB, Model SD-11, Sensordata A/S, Norway, sensitivity: 5 mV/ mm/s)

COMPUTER AND SOFTWARE SYSTEMS

A multiprogrammable INTEL iRMX 86 microprocessor with 512 kbyte RAM, equipped with AID and D/ A converters has been designed for the system. In advance computed control signals for each of the 10 wave paddles are stored on a file , which are recorded and converted into ana-

10.

log signals by the microprocessor. Up to 16 simultaneous test signals can be picked up, digetized and analysed continuously during the test. 2 discette stations are available for control signals, test

data, system- and application software.

The application software consists of routines for computing control signals for the wave paddles and analysing programmes. Discrete wave components with separate frequency, direction of pro­pagation, amplitude and phase may be specified. 2D- and 3D-seastates with continuous distribu­tion of frequencies and propagation directions may be calculated with or without implementa­tion of correction for the parasitic 2. order long waves due to incompatible particle velocities at the wave paddles from set-down waves.

The analysing system consists primary of a programme for spectral and directional analysis of a 3-dimensional seastate. Besides the frequency depending reflection from a structure extending across the wave tank (e. g. the wave damping system) can be analysed in irregular 2-dimensional seas. Finally a programme is available for standard spectral and variance analysis of any two input

signals.

COSTS

The costs given below is based on Danish 1984 prices excl. VAT. The salaries to the staff covering the design and testing of the system incl. computer software (app. 50,000 US S) is not included.

Basin Paddle system including hydraulic pump Wave absorbers Bridge Water circulation pump system Computer, printer Recording instruments Installation of power, water, etc.

ACKNOWLEDGEMENTS

Approximately

25,000 us$ 45,000

5,000 6,000 9,000

30,000 15,000 15,000

150,000 us s

The tank described in the paper is the third 3-D tank in Denmark. The first one is a shallow water wave tank with a snake-type wave generator designed in 1978 by The Danish Hydraulic Institute (DHI) and The Institute of Hydrodynamics and Hydraulic Engineering (ISVA), Technical Univer­sity of Denmark. The second is the DHI deep water wave basin, which has been operating since 1983. Experience from these two facilities was utilized and the authors would like to thank DHI, especially Stig E. Sand and Christian Aage, and ISVA for their kind assistance.

REFERENCES

Bowers, E.C., 1977. Harbour resonance due to set-down beneath wave groups. J. Fluid Mech. Vol. 79 part 1 pp 71-92.

Burcharth, H.F., Brorsen, M., 1978. On the design of gravity structures using wave spectra. Lec­tures on offshore engineering, Edited by W.I. Graff and P. Thoft -Christensen. Inst. of Struc­tural Eng. University of Aalborg. Denmark.

11.

Goda, Y., Suzuki, Y., 1976. Estimation of incident and reflected waves in random sea experi­ments. Proc. Conf. Coastal Eng. 1976, Voll, pp 828-845.

Huntington, S.W., Thompson, D.M., 1976. Forces on a large vertical cylinder in multi-directional random waves. Proc. 8th Offshore Tech. Conf., Houston, Texas, paper 2539.

Kirkegaard , J., Sand, S.E., Ottesen Hansen, N.-E., Hvidbjerg, M., 1980. Effects of directional sea in model testing. Proc. Ports '80'. ASCE. Norfolk 1980.

Ottesen Hansen, N.-E., Sand, S.E., Lundgren, H., S0rensen, T., Gravesen, H., 1980. Correct re­production of group-induced long waves. Proc. 17th Coastal Eng. Conf., Sydney, Australia, 1980.

Sand, S.E., 1979. Three-dimensional deterministic structure of ocean waves. Series paper 24. Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark.

Sarpkaya, T., 1976 a. Vortex shedding and resistance in harmonic flow about smooth and rough circular cylinders at high Reynolds numbers. Report No. NPS-59 SL 76021. Naval Postgra­duate School, Monterey, California, U.S.

Sarpkaya, T., 1976 b. In-line and transverse forces on smooth and sand-roughened cylinders in oscillatory flow at high Reynolds numbers. Report No. NPS - 69 SL 76062. Naval Postgra­duate School, Monterey, California, U.S .

Thunbo Christensen, F., Broberg, P.C., Sand, S.E., Tryde, P., 1984. Behaviour of rubble -mound breakwater in directional and uni-directional waves. Coastal Engineering 8 , 1984 pp 265 -278.