Power production based on focused swells

Lab.

y.. Scheepsbouwkwuk

Technische Hogeschoo1

Powér production based on focused ocean swells

Deflt

ARCH IEF

By

Jan Helstad, Central Institute för IndUstrial Research, Os/o

Keywords: energy production, power plant, swell, wave energy

Abstract

According to measurements carried out in recent years, the average energy

contained in the waves coming in from the North Atlantic to the coasts of

Europe is between 20 MW/km and 80 MW/km. Approximately half of this. energy is contained in the. ocean swells. As the numbers indicate, ocean swells represent an enormous energy resource. A great deal of effort has been expen-dedby scientists around the world to find some effective way of transforming wave energy into electric power.

However, most of the methods proposed so far to effect this transformation

are so complicated that they are not at present economically competitive with conventiönal energy production methods.

In this article we present a new and effective method for production of

elec-tric power from the energy of ocean swells. Estimates made of the costs of building and running a power plant based on our method indicate that it is probably feasible to produce eleçtric energy at a price that compares

favourably with that produced by conventional methods.

The method has been developed at the. Central Instituteof Industrial

Rese-arch in Oslo, Norway, where theoretical reseRese-arch in the field of wave focusing has been going on since 1971.

1. Basic principles

The relationship between the speed of surface waves on-water and the depth can be expressed as

V=1/gk.Tanh(kh)

where

k-X = wavelength

h=depth

When the depth is less than half the wavelength the

waves will go slower. This explains why waves slow up in shallow waters and why shoals tend to alter the form of the wave fronts.

It occurred to the scientistis at SI that one could use.

this effect to harness ocean swells to produce electric

energy.

¿e-frik

A common feature of the earlier proposals was their aim to extract energy directly from the incoming wave

front. In contrast, our proposal is to concentrate the

wave energy before transforming it into electric power:

It is perhaps worth noting that this idea of energy

concentration represents nothing new in:energy

produc-tion. In fact, it is utilized all the time in hydro.electric power production Instead of building one small power

plant at each little creek up in the mountains, the water

Norwegian Maritime Research

No.4/1980

34

--

-j

Fig. I Wave pattern in an optical lens.

is gathered in huge reservoirs and passed through one

large production plant.

In order to concenträte the wave energy one needed a

focusing lens for waves, to. act in the, same way as an

optical léns focus as light (see Fig. I).

An optical lens has the the property that an incoming plane wave after passage through the lens is transformed into a spherical wave converging towards the focal

point of the lens. The transformation from an incident

plane wave to a converging spherical wave is ordinarily

achieved by sending the light through a lens which

consists of a piece of glass of varying thickness. Inside the glass the wave velocity is less that in the surrounding

air, and since the lens is thicker at the center than at the edges the wave front at the center will be retarded

relative to the wave front at the edges after passage

through the lens.

perfect spherical wave. (See fig. 1.)

lt is apparent from the above considerations that the key property of a lens is its ability to retard some parts of the wave front relative to other parts so as to effect the transformation from an incoming plane wave to an

emerging spherical wave.

By analogy with the optical case two facts become

apparent: Firstly, a lens for water waves should possess the property that an incoming wave having crests parallel to the lens emerges from the lens as a wave with circular crests centeredat and converging towards some desired

focal point. Secondly, the lens must have the ability to

retard some parts of the wave front relative to other

parts.

Fig. 2. Artificial shoal or lens element floating 30 meters

below the surface. Swells will slow up over the

element.

2. Lens for swells

Since the wavelength and hence the speed of water

waves increases with the depth of the water, a possible way of making a lens for water would be to have some

structure

consisting of a number of plates placed

horizontaly and at varying depths below the water

surface. Preliminary design considerations indicate that the typical depth would be around 30 m. (See fig. 2.)

In addition to having the elementary focusing proper. ty, there are several other demands that the lens should meet: It should reflect as little as possible of the energy of the incident wave: it should be designed so as to work

efficiently even if the main wave direction changes by

35

Fig. 3 When passing a

positioned significantly less than a wavelength

below the surface, waves will propagate in a new direction.

Fig. 4 By making a lens of several elements in a pattern

as shown, the wave crests may be broken up,

deviated, re-shaped and re-combined into curved crests which converge into a focal area.

Norwegian Maritime Research

a relatively large extent from one period to another

(e.g. from one storm to another): it should be designed so as to work efficiently over a certain angular spread

of wave direction around the main direction añd over a certain spread in frequency around the main frequency

If we assume that the amplitudes of the incoming waves are small enough for linear wave theory to be

appropriate, any incoming wave (no matter how

compli-cated) may be split up into a superposition of plane

waves propagating iii various directions and with various frequencies.

The ideal situation, as far as focusing ¡s concerned, would be if the incident wave consisted of only one

single plane wave. The larger the spread in frequencies

and directions, the less the efficiency of the lens will

be. Thus, in order to find out how well a lens will work

in a given geographical area, measurements mùst be

carriéd out to determine the average spread in frequency and direction of the swells at the location in question.

When such measurements have been performed the task can be undertaken of designing the best possible !ens for the area. Thi task is comparable to that of a lens designer in optics. To determine what the shape of the lens structure should be in order to yield

opti-mum performance, we have at our disposal the differen-tial equations of water waves with appropriate boundary conditions. Thus, if we use the concept of a lens made of submerged plates, the shape of the plates, their relative

Norwegian Maritime Research

No.4/1980

positions and their depths are to be determined so as to

satisfy the various demands on the lens to the highest

degree of accuracy.

Chute

Once.. the wave energy is concentrated in a small area n the form of big waves, the next problem is to convert it into electric energy.

A tapping method that would fit well with the

configuration of the Norwegian coastline would be tó construct a large funnel-shaped chute which the waves wôuld enter and be pressed up to a reservoir lying as far as 100 m above sea level. (See fig. 5.) Estimates

based on experinien ts carried out indicate that 70 to 80

per cent of the energy concentrated into the waves at

sea level would be available as potential energy at the

reservoir.

The water flowing down from the reservoir would

power a conventional hydro-électric plant at sea level.

It should be pointed out, however, that in places

whére the landscape does not ascend rapidly from the

coastline, other solutions are possible.

Initial experiments

From 1971, when all this was merely a faint idea, to

1977 when the first experiments took place, the theory was further investigated and calculations of

performan-Fig.5

A power plant based on a focusing lens. The waves focus in an area at right and enter a chute up to a reservoir which may be located 100 meters above sea level.

37

Fig.6

Adjustable model of a funnel-shaped chute. The waves that enter from the left are pressed up by the shape of the chute and spill out at the top as can be seen at the right.

Fig. 7

Focused waves (from the experiments made in 1977). Plane waves are entering from the top of the picture, passing a lens that focuses the wave. The lens is situated below the water surface and cannot be seen in this picture.

Norwegian Maritime Research No. 4/1 980

t

ce, geometzy and some rough fmancial estimates were made.

In 1976 an application was sent to the Royal

Norwe-gian _{Council for Scientific and Industrial Research}

(NTNF) for funds to start experiments at the NHL

(Norwegian Hydrodynamic Laboratory) in 1977. The

application was rewarded with NOK i million.

The experiments at NHL took place in

a tank

The dimensions of the tank made experiments on a

scale of 1:1000 practicable. Both lens and chute were

tested but in separate experiments. The chute was made of plastic sheets that could be adjusted.

The confirm the theory both an amplitude lens and

a phase shifting lens were tested.

The amplitude lens was made of vertical plates

perpendicular to the movement of the waves leaving slits where the waves could pass. The slits would be

-'

i

--,---i

-'r

--'t- :'

point sources for new wave fronts. In the areas where

these fronts were in phase one could observe an amplifi-cation. However, as expected, the amplitude lens had a very low degree of efficiency.

The phase-shifting lens was much more promising. It was made of triangular plates mounted just below

the surface. When exposed to harmonic shaped waves it did focus the energy with an efficiency of over 80%.

For further experiments the tank at NHL was far

too small and one had to look for a testing site where

experiments on a larger scale could be undertaken. Such a site was found in Hakadal, near Oslo.

5. The Hakadal testing ground

The test facilities for wave power are located at Haka-dal immediately north of Oslo (26 miles) in a former sand-pit, which has been levelled out to form a basin.

(See fig. 8.)

t.

- t

t - _- 71

Fig.8

Test facilities for wave lenses in Hakadal. The basin measuring 150 x 100 meters. is equipped with two wave generators and an arrangement for measuring wave height in the focal area and around the lenses. The edges are covered with corrugated aluminium plates and bales of plastic waste for obviate wave reflections.

38

Norwegian Maritime Research No. 4/1 980

The bottom of the

appro-urnately 3 meters. The basin floor is covered with

'atertight asphalt. A rubber foil, which is glued to the asphalt, covers the side.

Vâter is pumped from the

ieaiby .Hakadal river.

To perform the tests, it is essential to be able to

control the waves. This is achieved by means of tun able wave generators giving circular waves. The wave genera-tors can be regarded as. point-sources. By combining the waves from the generators, various wave patterns can be

et up.

To measure the efficiency of the lens, wave sensors are placed close to the lens and in the focal area. The cocal sensors are mounted on a movable frame so that the wave height in a larger area may be recorded. The

readings from the sensors are processed and stored in a ;omputer at the testing site. Further mathematical treat-cnént of the data will take place at SI.

6. Medium-scale experiments

The first lens geometly to be tested was much like the

one that was tried out at NI-IL, made of one row of

triangular aluminium plates. Since the wave generators here were point sources making circular waves the shape of the elements had to be re-designed. The lens is shown during operation in fig. 9.

The amplitude in the focal area (fig. 10) was 5-10

times the amplitude over the lens, giving an increase in

energy density of 25 to 100 times. Efficiency was

approximately 60%.

Ari optical lens which is achromatic and has some

wide-angle properties is usually built of several glasses with varying refractive indices. In an attempt to make a wide-angle wave lens, a lens consisting of two rows of

elements was constructed. (See fig. 1].) It should take

up a change in the angle of the incoming waves of 20°

and a frequency variation of ± 10 % and still focus in the same area. The lens behaved as predicted and one

was also able to maintain the same wave geometry

though an artificial shoal was placed in the focal area.

In 1980 à lens arrangement consisting of plastic

tubes, 40 cm in diameter, was tried. The various

phase-shifting elements were made of tubes as shown in fig. 12. The experiments with this lense were not

comple-ted in 1980 and will continue in 1981.

When theory has been affirmed or adjusted after two

- ---t..

_.

Fig9

The waves coming from a point source at right are deviated over the lens and focused in an area at left (outside

the picture, see Fig. 10). The wave length is appr. 1 meter and the lens elements are about 12cm below the surface. The picture also shows the waves not hitting the lens and those having frequency too high to be affec-ted by the lens.

.39

Norwegian Maririme Research No. 4/1 980

L

-i

V

Norwegian Maritime Research No. 4/1980

40 Fig. 10

Waves in the focal area. The focal area in this picture is just behind the dinghy. The amplitude is here 5 - 10 times the amplitude over the lens and hence the energydensity has increased 25 - 100 times.

years of experiments in Hakadal, planning and

construc-tion of one element on full scale will start in 98I.

The element will be equipped with instruments to

measure the forces to which element and its anchoring

are exposed by the waves. One will also record wave

height and direction on each side of the element to find the efficiency under variable conditions.

The configurations and shapes of the lenses that

have been tested should be regarded as simplified versi-ons of an actual lens arrangement.

A full-scale operating lens might have some resem-blance to, but in detail would probably be much unlike, the test lenses.

Only extensive experiments on a larger scale and de-tailed calculations can give the final answer to what the lens would look like.

L'r

E

r

Fig. 10

Waves in the focal _area. The focal _area in this picture is just behind the dinghy. The amplitude is here 5

-

times the amplitude _over the lens and hence the energydensity has increased 25

-

years of experiments in Hakadal, planning and construc-

tion of one element on full scale will start in f981.

The element will be equipped with instruments to

measure the forces to which element and its anchoring

are exposed by the waves. One will also record wave

height and direction _on each side of the element to find the efficiency under variable conditions.

The configurations and shapes of the lenses that

have been tested should beregarded _as simplified versi-

ons

of

A full-scale operating lens might have _some resem-

blàrce to, but in detail would probably be much unlike,

the test lenses.

Only extensive experiments _{on a} larger scale and de-

tailed calculations _can give the fmal answer to what the

lens would look like.

Norwegian Maritime Research No. 4/1980

b.

Norwegian Maritime Research No. 4/1980

42 Fig. 12.

Lens elements made of tubes. In an effort to find a cheap and modular construction, lens elements made of plastic tubes with a diameter of 40 cm were tested. At present measurements have not been completely