GB2113311A - A wave powered prime mover - Google Patents

Abstract

Essentially the prime mover comprises a pair of rafts 1 and 2 pivoting about a pivot shaft 3 supported on a semi-submersible bridle structure 5 which retains the pivot shaft 3 in position substantially fixed relative to the mean wave water level. The bridle structure comprises a mast 10 projecting from a damping plate 8 which damps out vertical movement. The pivotal movement of the rafts 1 and 2 about the shaft 3 is converted to usable energy by means of pumps 20 and 21 which pump sea water to a header tank on shore through a conduit 27. Connecting rods 22 and 23 of the pumps 20 and 21 are connected to the mast 5 of the semi-submersible bridle structure. In another embodiment, Fig. 3 (not shown), both pumps are mounted on the raft 1. <IMAGE>

Description

SPECIFICATION A wave powered primer mover The present invention relates to a wave powered prime mover.

According to the invention there is provided a wave powered prime mover comprising at least one wave engaging float pivotal about a pivot axis, means to retain the pivot axis substantially fixed relative to the mean wave water level, and means to convert the pivotal movement of the float into usable energy. Preferably, the pivot axis is defined by a pivot shaft.

Preferably, the retaining means is provided by a semi-submersible bridle structure comprising a submersible base member and a mast projecting upwardly from the base member to support the pivot shaft.

Advantageously, the base member is a damping plate to damp out vertical movement of the bridle structure.

In one embodiment of the invention a flexible mooring member is provided to moor the retaining means to the sea bed.

Preferably, a pair of floats are provided on opposing sides of the retaining means.

Advantageously, the floats pivot on a common pivot axis.

In one embodiment of the invention in use, the free end of the leading float is moored to a mooring buoy by a flexible mooring member.

In a further embodiment of the invention the means to convert the pivotal movement of each float is provided by a water pump mounted on a float and operable by a linkage assembly.

Advantageously, the water pump delivers sea water to a header tank.

The invention will be more clearly understood from the following description of some preferred embodiments thereof given by way of example only with reference to the accompanying drawings in which: Figure 1 is a partly diagrammatic elevational view of a wave powered prime mover according to the invention, Figure 2 is a sectional side view on the line ll-il of the prime mover of Fig. 1, Figure 3 is a partly diagrammatic elevational view of a wave powered prime mover according to another embodiment of the invention, Figure 4 is a diagrammatic representation of the prime mover of Fig. 1 illustrating the notation used in the experiment, Figure 5 is a graph illustrating a plot of the magnification factor as a function of the frequency ratio and wavelength-to-raft length ratio, Figure 6 is a diagram illustrating the energy efficiency as a function of the frequency ratio, and Figure 7 is a graph showing a plot of power efficiency as a function of frequency ratio.

Referring to the drawings and initially to Figs. 1 and 2 thereof there is illustrated a wave powered prime mover according to the invention. The wave powered prime mover comprises a pair of wave engaging floats, in this case steel rafts 1 and 2 which are pivotly mounted on a pivot shaft 3 which defines a pivot axis 4. The pivot shaft 3 is supported on a semi-submersible bridle structure 5. The rafts 1 and 2 are free to pivot about the shaft 3 under the action of passing waves 7. The semi-submersible bridle structure 5 comprises a base member formed by a damping plate 8 of reinforced steel plate and a mast 10 extending from the plate 8. The mast 10 is formed by a pair of hollow steel tubular uprights 11 joined by a cross member 1 2 also of steel. The pivot shaft 3 extends between the uprights 11.The bridle structure 5 under the action of the damping plate 8 which damps out vertical movement substantially retains the pivot shaft 3 in a fixed position relative to the mean wave water level illustrated by the broken line 1 4 in Fig. 1. The uprights 11 being tubular act as ballast tanks and sea water may be pumped in and out of the uprights as desired to alter the trim and the level of the bridle. The means for doing this is not shown but such means should be well known to those skilled in the art.

As can be seen in Fig. 1, the waves move in the direction of the arrow A and the prime mover is moored by a mooring buoy 1 5 which is connected by a mooring rope 1 6 to the bow of the leading raft 1. An anchor 1 6 anchors the buoy 1 5.

Means to convert the relative pivotal movement of the rafts 1 and 2 into useful energy is provided by a pair of piston type water pumps 20 and 21 mounted on the rafts 1 and 2 respectively. The pumps 20 and 21 are connected to the upright 11 by means of their connecting rods 22 and 23 and accordingly are actuated by the pivotal movement of the rafts 1 and 2. The pumps 20 and 21 pump the sea water to a header tank (not shown) on shore. The sea water is delivered to the pumps through inlet pipes 25 and 26 projecting through the bottom of each raft 1 and 2. A flexible delivery conduit connected to the outlets of each pump 20 and 21 delivers sea water from the pumps to the header tank. The conduit 27 extends down the mast 10 and along the sea bed. The fact that the conduit 27 is flexible accommodates the rising and falling of the prime mover due to tidal variations.

In use, the wave powered prime mover is towed to the desired site and moored in position by the buoy 1 5. The passing waves cause the rafts 1 and 2 to pivot about the shaft 3, thereby actuating the pumps 20 and 21. Sea water is delivered by the pumps 20 and 21 to the header storage tank (not shown). The water in the storage header tank may then be used to power any suitable apparatus, for example, water turbines to drive an electrical generator and the like. In fact, it is envisaged that the prime mover would be ideally suited to store water in the header tank for the generation of peak electricity.

Referring now to Fig. 3, there is illustrated a wave powered prime mover according to another embodiment of the invention. This prime mover is substantially similar to that just described with the exception that the linkage assembly for the pump is different. In this embodiment of the invention two pumps 40 and 41 are mounted in the raft 1, and the linkage assembly 42 is connected between the pumps 40 and 41 and a mast 45 rigidly mounted on the deck of the raft 2. Accordingly, the pumps 40 and 41 in this embodiment of the invention are actuated by the relative pivotal movement between the rafts 1 and 2. The linkage mechanism comprises a main link 46 pivotally connecting the mast 45 with an upstanding link 48.

The link 48 is pivotal on the deck of the raft 1 and is pivotally connected by means of links 49 and 50 to actuate levers 51 and 52 of the pumps 40 and 41. Accordingly, as the rafts 1 and 2 pivot relative to each other the linkage assembly 42 acutates the pumps 40 and 41. It can clearly be seen from Fig. 3 that while one pump is on a suction stroke, the other will be pumping to a header tank (not shown). Pipes 56 and 57 in the base of the raft 1 connect the pumps 40 and 41 to the sea while the flexible delivery conduit 27 delivers sea water from the pumps to the storage header tank (not shown) on the shore.

The mast 10 of the semi-submersible bridle in this embodiment of the invention is also formed by hollow vertical steel tubes which support the pivot shaft 3, and act as ballast tanks.

The leading raft 1 is moored by a mooring rope 60 to a buoy (not shown).

Having described the wave powered prime mover in detail, results of experiments carried out on a scale model and the theoretical analysis behind the results will now be described.

Experimental Results Experimentals were carried out on the prime mover illustrated in Figs. 1 and 2. The rafts 1 and 2 were of equal length each being 2.4 metres. The experiments were carried out in a tank 4.88 metres deep and 7.92 metres wide. Regular waves generated by a wave generator were used in the experiment.

Theoretical analysis Referring to Fig. 4 for notation, the component rafts of the wave powered prime mover obey the following equations: Raft No. 1:(1r+Ai)Oi+BaiOi + Bb1(#1 - #2) + C1#1 = M,ocos(t + 8) (1) Raft No. 2: (1y2 + A2)fl2 + A2)6 2 + Ba2t12 + Bb2(92 - 0i) + C282 = M20cos(cot+ & (2) where I, = mass moment of inertia about the pivot shaft A= added-mass moment of inertia about the pivot shaft Ba = radiation plus linear viscous damping coefficient of the raft Bb = equivlent linear damping coefficient due to the energy conversion C= hydrostatic restoring moment Mo = wave-induced pitching moment amplitude 8 = pitching displacement X = circular wave frequency (27rf = 27r/T), where f is the wave frequency in Hz and T is the wave period in seconds 8= phase difference between the wave and the wave-induced moment.

In equation (1) and (2) the coupling is due to the energy extraction mechanism which, for the wave powered prime mover is a hydraulic pump.

For this prime mover having two identical rafts equations (1) and (2) can be combined into a single equation of motion.

That is (1,+ A)(e, 02)+Ba(Oi 2) + 2Bb(082) + C(B, - 8) = M,Ocos(t + 6i) - M20cos(a;t + 92) = Mo cos(a;t + 8) (3) where the exciting linear wave is described by H n = -cos(a;t) (4) 2 where H is the wave height.

Before solving equation (3) an explanation of the damping coefficient Bb should be supplied.

This is an "equivalent" linear coefficient used to represent a nonlinear damping. We can assume that the damping due to the energy extraction (caused by the pumps and waterlines) is quadratic so that the actual damping moment can be represented by the expression Mb = ss(&commat; 2)2 = (5) where # = #1 - O2 The average energy removed by the prime mover is

Since the motion of the prime mover is nearly sinusoidal, we can approximately equate the energy obtained by combining equations (5) and (6) to that obtained by combining equation (6) with the linear damping moment, Mb = Bb# (7) The resulting equivalent linear damping coefficient is found to be 8 ss Bb = ##O = bb##O (8) 3 7r where #O is the amplitude of 0. The average power converted by the prime mover is, then,

= Bb##Ȏ/2 4 B = # # O (9) 3 # where the quadratic damping coefficient, ss, is determined experimentally.

Returning to the equation of motion, eq. (3), the coefficients can be approximated by using the "strip theory" as described in "Principles of Naval Architecture" edited by Comstock (1967) published by Society of Naval Architects and Marine Engineers, New York and illustrated in "Ocean Engineering and Wave Mechanics" by McCormick (1973) published by Wiley Interscience, New York. The strip theory is found to have best applicability to marine vehicles in motion. The Application here, then, must be considered to be a rough approximation used for the purpose of illustration since the raft system is not under way. Each raft is assumed to have a box shape with no bow or stern flare, although the rafts of the prime mover of the invention, the subject of the experiment do have bow and stern flare.The coefficients for the theoretical model are the following: L3 Z2 Iy = m(+) (10) 3 2 where Z is the raft height. The raft mass is m = pL W d (11) where p is the mass-density of the sea water, W is the raft width and d is the draft.

A = 0.04rm(L3/d) (12) Ba( < < Bb) = [0] (13) C p g L3 W/3 (14) MO = p g H W(e -kd + L LkL cos(kL) - sin(kL)] (15) k2 where the wave number is k = 2sr/A (16) and, finally, # = 90 With the approximation in equation (1 3) the solution of equation (3) is, then, # = #O cos (#t + # - &gamma;)

where the phase angle between the moment and the motion is

the natural frequency is

and the critical damping coefficient is

Note: The equivalent linear damping coefficient, Bb, defined by equation (8) is a function of both frequency and displacement amplitude. Thus, the magnification factor Zo = #oC/Mo (21) is not obtained directly from equation (17).Instead, we must first combine the amplitude expression of equation (17) with equation (8) and solve for f0. The result is

For low values of (w/w,) the approximation of equation (1 3) does not hold since the quadratic damping is also of zero order. A plot of the magnification factor of equation (21) is discussed later, using the results of the amplitude equation, eq. (22).

If the radiation damping, viscous damping and quadratic damping are all of the same order of magnitude, then the equation from which (Po is obtained is biquadratic. Although closed solutions of this equation can be obtained, the level of complexity of the solution discourages the use of this approach.

The analytical expression for the power conversion efficiency in deep water (where A > h/2) is 1024 ep = Pb/P = ------ (23) 3 pg2H2T4W where, again, the value of ss is experimentally determined, and the deep water wave power expression is pg2H2 T W p = ----------- (24) 327r Results obtained from applying equation (23) to the experimental model are discussed below.

Experiment and Results The experimental model of the wave powered prime mover is illustrated in Figs. 1 and 2 and 4. For that model the following values apply: L, = L2 = L = 2.40 m W= 1.20 m d = 7.87 x 10-3 m m = 22.7 kg Z=0.102 m Using these values, the parameters described by equations (10), (11), (13) and (14) are, respectively, Iy = 43.6 N-m-s2/rad A = 5,010 N-m-s2/rad C = 54,200 N-m/rad and

= M20 The prime mover had two identical pumps, each excited by one raft only. This allows for the separate analyses of the results of each component raft.

The damping for each pump is found to vary with frequency and angular displacement of the specific raft. This fact is seen in the results of Fig. 5 where the theoretical and experimental values of the magnification factor, Z0, are shown as functions of the frequency ratio, f/fn. In Fig.

5 results are for the following conditions.

1. undamped linear vibrations, equation (17).

2. critically damped linear vibrations, equation (17).

3. quadratically damped vibrations where Bb = 2BC, at f/fn = 0.8 (p = 10.3 x 107N-m-s2/rad2) in equation (9), 4. experimental values of rafts 1 and 2.

The experimental results of equation (4) show that the leading raft (1) has a maximum energy loss at a frequency ration of 0.8. This, then should correspond to a maximum energy or power production, according to equation (9). The values for raft (2), however, continuously decrease with f/fn with the exception of the value at f/fn = 1.92. It appears that above f/fn = 0.80 the power absorbed by raft 1 is significantly greater than that of raft 2 since 82 is significantly less than O.

The average energy absorbed by each raft, as evidenced by the raft motions, is calculated by using the expression

where 80 is the amplitude of the raft in question, as shown in "Ocean Wave Energy Convertion" by McCormick (1981) published by Wiley Interscience, New York. Values obtained from this expression using the experimental frequencies and displacements result in efficiency values obtained from = = Eb/E

where the deep water wave energy expression is pg2 H2 T2 W (27) 167r These energy efficiency values are presented in Fig. 6.We note that the efficiency values of rafts 1 and 2 are approximately equal for f/fn = 0.8; however, for f/fn > O.8 the efficiency of raft 2 decreases with f/fn, except when f/fn = 1.92. For this frequency ratio value the total system efficiency (EE1 + EE2) is 118%.

Also shown in Fig. 6 are the energy efficiency values as determined from pumping and maintaining a head of water in a 1-inch diameter (0.0254 meter) tube. The head can be increased or decreased by adjusting the length of the level arm. The maximum head obtained is 3.26 m, and is obtained using the level arm configuration sketched in Fig. 7. This maximum head corresponds to an efficiency of 28.0% and a frequency ratio value of 0.77.

The experimental power efficiency values are determined from the expression of equation (9), where the maximum quadratic damping value is ss = 5.1 7 X 105 N - m - s2/rad2. These power efficiency values are presented in Fig. 8 for rafts 1 and 2, the total system efficiency and the efficiency obtained from pump 1 with a constant head of 0.532 meter. The maximum power efficiency obtained by the pump is 8.70% at a frequency ratio of 0.960. Needless to say, by using a more efficient pump, for example a pump with an efficiency of 65% to 70% considerably improved results would be achieved.

Discussion and Conclusions Results of the experimental study of the prime mover are presented in Figs. 5, 6 and 8. In Fig. 5 the magnification factor is presented as a function of the frequency ratio. The data show that the system damping due to the energy extraction is greater than the critical damping at f/fn = 0.8, where Bb/BC, = 1.13 for each raft. Since each raft-pump system in the study is operating independently, we can see that for f/fn > 0.8 the energies absorbed by the two rafts are significantly different, while for f/fns0.8 the energies are approximately equal.For this nonlinear system, therefore, we must assume that the damped natural frequency for each raft is fd-0.8 (28) This frequency, of course, depends on the magnitude of the damping, which, according to equation (9), is indicative of the wave power converted. Also presented in Fig. 5 is the equivalent deep water wavelength-to-raft length ratio. We see that the value of this ratio corresponding to f/fn = 0.8 is A = 3.75 L (29) a value which has no particular significance. We must conclude, therefore, that the frequency ratio is the significant independent dimensionless parameter. The wave steepness is actually implicit in magnification factor; thus, the results in Fig. 5 do include the H/A effects.

The energy efficiency, È, is shown as a function of f/fn in Fig. 6. The values for rafts 1 and 2 and, therefore, the total efficiency are shown to have inflection points at f/fnO.8 For f/fn > 0.8 the energy efficiencies of raft 1 and the total mechanical increase, while those for no. 2 decrease (with the exception of f/fn = 1.92). The exception noted corresponds to X/L 0.176, a value which has no significance. The exception, therefore, is attributed to a standing wave resulting from the radiated wave from the raft systems. One can conclude from the data of Fig.

6 that the two-raft systems are equally efficient in energy production for f/fn < 0.8, while raft 1 absorbs most of the energy for f/f, > 0.8. The pump efficiency values shown in Fig. 6 depend on the lever arm configuration. For a given wave condition eE can be increased by adjusting the lever arm to the optimum configuration shown in Fig. 7. An overall peak energy efficiency of 28% is seen at f/fn0.77 Although no amplitudes were measured during the lever arm adjustment, it was noted that the amplitude of the raft did increase as the overall efficiency increased. This indicates impedance-matching is accomplished.

The power efficiency data of Fig. 8 are the most significant. We see that combined efficiency value of 65% is obtained at f/fn0.88 where the efficiency of raft 1 is 59% and that of raft 2 is 6%. The next highest combined efficiency value is approximately 46% where the efficiencies of both rafts are 23% at f/f,u0.77. The measured values of the overall power efficiency of each pump never exceed 8.7%, as shown in Fig. 8. Thus, we can conclude that the pump inefficiency is significant. It must also be noted that the pumps used in the study are commercially available bilge pumps which are not designed for energy production. The pump design for the prototype system is critical to the system performance. For f/fn < 0.8 two pumps are required in the system since the efficiencies of each raft system are equal.For f/fn > 0.8, however, only the leading raft is required since the power produced by the trailing raft is relatively small.

These results may be used to determine the performance of a full scale prototype. By way of example the results are applied to a prototype sixty times larger than the model tested.

The scaling equations as presented in "Ocean Wave Engineering Conversion" by McCormick (1981) are used. These are the following: Length: L,,/Lp = n = 1/16 = 0.0625 Time: Tm/Tp = n112 = 0.25 Energy: Em/Ep = n = 0.0625 Power: Pm/ Pp = n7/2 = 6.10 x 10-5 where the subscript "m" refers to model values and "p" refers to prototype values. Applying these equations to the prototype, we obtain L = 38.4 m (87.8 m overall) W= 19.2 m Z= 1.63 m d=0.126 m Tn = 7.68 sec.

Using the maximum head developed at f/f,-0.77 fry = 28%) in Fig. 6, the maximum prototype head developed from equation (32) is 3.26/n = 52.2 meters while the maximum power produced by the raft motions at f/fn0.88 (ep~65%) indicate a maximum prototype raft power of 16.9/n7/2 = 277 kW.

These prototype values show that the wave powered prime mover according to the invention is particularly suitable for a wave energy excited pump-storage system. With an improved pump design the peak raft motion power can nearly be achieved as the overall power. For f/fn < O.8 a two-raft system is most feasible, while for f/f, > 0.8 only the lead raft is needed. The sea condition of f/fn < 0.8 can be considered to be that corresponding to a swell, whereas f/fn > 0.8 can be considered the range of the wind-generated sea.

It has been found that fixing the pivot shaft relative to the mean wave water level of the waves produce a relatively efficient prime mover. It will be appreciated that a considerable advantage of this is that the prime mover according to the invention may operate with a substantially constant efficiency.

It will also be appreciated that while a particular construction of means to retain the pivot shaft in a fixed vertical position has been described, any other suitable means could be used.

For example, it is envisaged that a structure mounted on the seabed may be used. Indeed, it is envisaged that instead of mooring the prime mover to the mooring buoy, the semi-submersible structure could itself have been moored to the seabed, for example, a mooring cable connected to the semisubmersible structure could be anchored to the seabed. Furthermore, it will be appreciated that although the rafts have been described as being pivotal about a pivot shaft, they could be pivotal about any other suitable member. Additionally, although the invention has been described as comprising two rafts, an efficient prime mover could be provided with only one raft without departing from the scope of the invention. Similarly, many more that two rafts could be provided. Additionally, floats other than rafts could be used.

It will also be appreciated that although a particular construction of means for converting the relative pivotal movement of the rafts into useable energy has been described, any other suitable means could have been used. For example, instead of using a piston pump in each raft, many piston pumps could have been provided in each raft. Additionally, diaphragm pumps could have been used, or indeed a combination of diaphragm and piston pumps. Needless to say, it will be apparent to those skilled in the art that other suitable means could be used.

Furthermore, it is envisaged that instead of the pumps being connected directly to the semisubmersible bridle structure, by means of their piston rods, they could be connected through a linkage arrangement to the structure, or adjacent raft. One such linkage assembly is illustrated in Fig. 3, and it will be appreciated by those skilled in the art that other arrangements could be used.

It is also envisaged that in certain cases, the delivery conduit instead of being routed to the seabed through the semi-submersible bridle structure could have been routed to the seabed through the mooring buoy. Indeed, it will be appreciated by those skilled in the art that any suitable rout could be used for the delivery conduit.

While the damping plate of the bridle structure has been described as a steel plate, any suitable plate could be used, for example, it is envisaged that a damping plate of stainless steel or fibreglass could be usd. Indeed, in certain cases the damping plate could contain ballast tanks.

Claims (16)

1. A wave powered prime mover comprising at least one wave engaging float pivotal about a pivot axis, means to retain the pivot axis substantially fixed relative to the mean wave water level, and means to convert the pivotal movement of the float into usable energy.

2. A wave powered prime mover as claimed in Claim 1 in which the pivot axis is defined by a pivot shaft.

3. A wave powered prime mover as claimed in Claim 1 or 2 in which the retaining means is provided by a semi-submersible bridle structure comprising a submersible base member and a mast projecting upwardly from the base member to support the pivot shaft.

4. A wave powered prime mover as claimed in Claim 3 in which the base member is a damping plate to damp out vertical movement of the bridle structure.

5. A wave powered prime mover as claimed in any of the preceding claims in which a flexible mooring member is provided to moor the retainng means to the sea bed.

6. A wave powered prime mover as claimed in any preceding claim in which a pair of floats are provided on opposing sides of the retaining means.

7. A wave powered prime mover as claimed in Claim 6 in which the floats pivot on a common pivot axis.

8. A wave powered prime mover as claimed in Claims 6 or 7 in which in use the free end of the leading float is moored to a mooring buoy by a flexible mooring member.

9. A wave powered prime mover as claimed in any preceding claims in which the means to convert the pivotal movement of each float is provided by a water pump mounted on a float and operable by a linkage assembly.

10. A wave powered prime mover as claimed in Claim 9 in which the water pump delivers sea water to a header tank.

11. A wave powered prime mover as claimed in Claims 9 or 10 in which the linkage assembly is connected between a water pump and the semi-submersible bridle structure.

1 2. A wave powered prime mover as claimed in Claims 9 or 10 in which the linkage assembly is connected between a water pump in one float and the other float.

1 3. A wave powered prime mover as claimed in any of the Claims 9 to 1 2 in which a water pump is provided in each float.

14. A wave powered prime mover as claimed in any of Claims 9 to 1 3 in which a mast is provided in each float and the linkage assembly is connected between a water pump in one float and the mast in the other float.

1 5. A wave powered prime mover as claimed in any preceding claim in which each float is provided by a raft.

16. Wave powered prime movers substantially as described herein with reference to and illustrated in the accompanying drawings.