Vertical-Axis Tidal-Current Generators and the Pentland Firth

SPECIAL ISSUE PAPER 181 Vertical-axis tidal-current generators and the Pentland Firth S H Salter and J R M Taylor School of Engineering and Electronics, University of Edinburgh, Edinburgh, UK

The manuscript was received on 1 March 2006 and was accepted after revision for publication on 13 November 2006.

DOI: 10.1243/09576509JPE295

Abstract: This paper extends ideas presented to the World Renewable Energy Conference [1, 2]. One idea involves the impedance of flow channels and its relevance to the maximum tidal- stream resource. Estimates of the inertial and damping terms of the impedance of the Pentland Firth suggest a much higher resource size than studies based purely on the kinetic flux, because adding extra turbines will have less effect on flow velocities than in a low impedance channel. This very large resource has pushed the design of the turbine towards the stream velocities, depth, and seabed geology of this site. A second idea is an algorithm to control the pitch of close-packed vertical-axis generators to give an evenly distributed head. Finally, there are sug- gestions for a seabed attachment aimed specifically for conditions in the Pentland Firth and intended to allow rapid installation of a self-propelled tidal-stream generator.

Keywords: vertical-axis turbine, tidal stream, marine-current generator, channel impedance, low-head hydro, variable pitch, Betz momentum theory, Darrieus, troposkien, tri-link, inﬂatable

1 BACKGOUND perform the function of a geometrically tolerant bearing providing axial and radial location. The The earliest field work on Darrieus-type underwater blade pitch was controlled only by the choice of a turbines was reported by Fraenkel [3]. It involved torque limit which allowed blades to adjust their testing models of fixed pitch vertical-axis rotors and own pitch-angle above a chosen level of pitch confirmed the performance in water to be compar- torque so as to prevent stall. Mooring was by tension able to results obtained with fixed-pitch vertical legs which passed through the centre of pressure of axis wind turbines. the rotor to avoid inducing pitching torque. How- Pitch variation was an essential feature of the Edin- ever, tank tests showed that tension legs would burgh vertical-axis tidal-current generator which was suffer unacceptable snatch loads following any slack- first described at the 1998 European wave energy ening, even in quite small waves. conference at Patras [4] and is shown in Fig. 1. The design had several layers of short blades with variable pitch. The layers were separated by elliptical 2 CHANNEL IMPEDANCE AND THE PENTLAND section rings and cross-braced by streamlined wires FIRTH which gave torsional and shear rigidity. Power take- off was above the surface and out at the rim, An important question for all tidal projects is the housed in a floating torus. It used a quad ring-cam, extent to which the introduction of generating variable-displacement, high-pressure oil pump to plant will reduce the flow. This can be thought of give the correct torque to convert from a variable in terms of the ‘impedance’ of the flow, a concept input speed to the constant speed required by syn- which is familiar to electrical engineers but less so chronous generators. The cam rollers could also to mechanical, marine, and civil engineers even though there are many instances where it can be Corresponding author: School of Engineering and Electronics, useful. One anthropomorphic way to think of impe- University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JL, dance is as the determination needed for a current UK. email: [email protected] to overcome obstacles placed in its path. One of the

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 182 S H Salter and J R M Taylor

two is

L C f (3) Z Cp

If this ratio is unity, the power already being lost as bed friction will be equal to that of one bank of rotors filling the entire cross-section and the current status is on the edge of the change from a low to a high impedance channel. Note that aeronautical engineers and turbine designers use half for drag Fig. 1 An artist’s impression by Carn Gibson of the and power equations but oceanographers do not, first ideas for the Edinburgh vertical axis turbine and so care is needed in collecting values of friction coefficients. A friction value of 0.017, has been measured at the extremes would be a source of constant current Menai Strait by Campbell et al. [5]. If this is used in a which has to flow and which will create whatever very simplified model of the Pentland Firth with a head (or voltage) is needed to overcome all resist- channel length L of 23 000 m, a depth Z of 70 m, ances placed in its path. This is the tendency with and a turbine performance coefficient of 0.4, the long, shallow, rough flow channels where many LCf/ZCp ratio is 14 and so a channel of these dimen- banks of turbines might be installed in series up to sions is clearly a high impedance source. If the chan- some limit at which the increased upstream head nel width was 10 000 m, the seabed dissipation at a would cause flooding. Less desirable would be the flow velocity of 3 m/s would be 53 GW. Friction other extreme of a low impedance source where the would be setting the flow velocity and many banks flow could be stopped by an obstruction or easily of turbines would reduce it only a little. Perhaps find an alternative passage. one third of 53 GW could be captured giving an aver- In electrical engineering, the impedance of a age output well above previous estimates [6]. source would be the ratio of the open-circuit voltage The Pentland Firth has an irregular coast line, pits divided by the short-circuit current. In a non-linear going to below 100 m, shallows known as the Merry device, like a zener diode, the local impedance Men of Mey which generate eddies at the surface, a could be obtained from the local slope of the cur- 308 bend and two islands – Stroma and Swona – rent/voltage curve. For turbines a resistive impe- which must suffer large drag forces. The Menai fric- dance can be calculated from the turbine power tion coefficient of 0.017 is only four times more divided by the square of flowrate through the turbine than that of a highly polished wing of a fighter air- flow window or from the square of a water head craft at zero angle of incidence. divided by the power being generated. The effects The velocities of tidal streams have been studied of side channels could be calculated, just as in elec- by Bryden et al. [7], who has shown that they are trical network theory for series and parallel resistors. more complicated, turbulent, and variable than Ratios of turbine power to bottom friction power might be suggested by a first look at Admiralty tide are of particular interest. Consider a very simple tables. Work must be done to measure direction case of steady flow in a channel of length L, width and velocity texture. There is also a need to measure W, depth Z, and bottom friction coefficient Cf, impedance values in all flow channels and their side having a current velocity U of fluid density r comple- branches before making an accurate assessment of tely filled with rotors having a performance coeffi- the tidal stream resource. cient of Cp. The power at present being wasted by bed friction is 3 MEASURING IMPEDANCE

1 The driving function of the tides depends on the Pf ¼ r W L U 3 C (1) 2 f skewness, non-circularity, and precession of the orbits of the moon round the earth and their com- The power from a single full rotor bank would be bined orbit round the sun. Further complications are that large masses of water attract one another 1 by detectable amounts and that any non-linearity Pr ¼ r W Z U3 C (2) 2 p caused by propagation in shallow water will make every component generate frequencies which are By cancelling common terms, the ratio of the the sum and difference between its frequency and

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 183 all the others. A useful listing of the components, level and velocity components for points at each periods, and relative phases of 18 components for end of the Pentland Firth (R. Protor, 2006, personal Delaware Bay is given in reference [8]. communication). The slope of the water surface Thevenin’s theorem says that an electrical network could be calculated from the difference in head pre- of any complexity can be reduced to a single voltage dictions. The eastward (conventionally known as U) source in series with a single impedance driving the component of velocity was almost the same at each load under study. The drive voltage would be what- end. The phase relationship of head to velocity was ever voltage would be present if the load under of particular interest. There are two ways to get an study were absent. Its analogy in water flows is the estimate. The easiest and crudest, suitable for engin- head difference that would be developed if a dam eers in a hurry, is to look at the times of zero cross- were built across the channel entry. The impedance ings and assume that the records are well-behaved in series with that head would be the total series/par- sine waves. A square wave is generated using a allel combination of the other channels in the logic statement that gives a value one if the head is absence of the channel under study. positive and the velocity is negative or if the head is A measure of the impedance between two points negative and the velocity positive. The mark–space in a channel could be calculated from measurements ratio of the square wave will give a measure of of the head difference at the points and the mean of phase. For the main length of the Pentland Firth their current velocities. The acoustic Doppler current between 588440N38180W and 588420N3890W the profiler method [9] is excellent for measuring vel- zero crossing method gives a lag between head and ocity and direction through the entire water column. velocity of 638. Satellite measurements can give accurate measure- A more respectable phase calculation, suitable for ments of changes of the mean level of large oceans mathematicians, uses Fourier transforms. These but this requires many transits, and advice from D.T carry all the information about each separate com- Pugh (2006; personal communication) is that they ponent of the spectrum. For each frequency the would not give enough coverage over the Pentland transform produces a real and imaginary number Firth for the required resolution. His suggestion is to indicating the amplitude and phase of that com- measure changes of head through the tidal cycle ponent relative to a notional cosine wave of the using bottom-mounted pressure transducers at a same frequency with 08 referred to the beginning of number of points along a channel over a period of a the record. few months, together with simultaneous velocity The ratio of the imaginary to the real amplitude at measurements at the same points. Recently devel- each frequency gives the tangent of the phase angle oped instruments combine both pressure and acous- between the signal and the notional cosine wave. tic Doppler velocity measurements [10]. Repeating this for both head and velocity records Before deciding on a programme of field measure- gives the inertial and resistive parts of the channel ments it is worth trying to make an approximate esti- impedance between the observation points. The mate. The simplest analysis would reduce a complex technique can give spillage over into adjacent fre- network of channels to three impedances. The first is quencies, and so it can be useful to integrate over a the impedance, which sets the flow induced by the short section of the frequency spectrum. Between astronomical forcing function from the Atlantic. the map coordinates given above, the phase lag This would be in parallel with the impedance of the between the head and the velocity of the strong M2 parallel paths through and north of the Orkneys frequency as measured by this technique was 468. which can allow water to bypass the Pentland Firth. This is shown in the Lissajous plot of slope against It is known from reference [11] that there are quite the U component of velocity in Fig. 2. large phase differences between tidal levels at the Based on the electrical analogy, this implies that, nearest observing stations at Kinlochbervie and despite the short channel-propagation time, flow- Wick, so at least some of these impedances must rates are defined by the ‘inertia’ of the water in the have complex terms analogous to inductance and Pentland Firth just as much by bed friction or the capacitance. Finally, there is the impedance of the entry orifice. The installation of quite large numbers Pentland Firth itself. The celerity of a long shallow of turbines in several close-packed banks will change water wave over a 70 m bed would be 26 m/s so it the phase of the velocity but not initially to the same would take ,15 min to travel along the full length. extent as its magnitude, so there is a second reason to This seems very short compared with the 12.42 h expect a higher resource than would be indicated M2 tidal period and so it might be thought that the purely from the present kinetic flux. reactive terms ought not to be dominant. By dividing the differences between each sample The Proudman Laboratory has developed numeri- in the Proudman velocity data by the time interval cal tidal prediction software known as POL and between them the acceleration of the flow can be cal- kindly supplied their time-series prediction of water culated. The difference in head between two

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 184 S H Salter and J R M Taylor

Fig. 3 A comparison of the Fourier transforms of real Fig. 2 A Lissajous plot of slope against easterly observations of current velocities showing odd velocity at the ends of the Pentland Firth harmonic components (suggesting truncation of the higher velocities) with a spectrum of numerical data plotted negatively. The positions along the channel gives us the force that frequency scaling is adjusted to put the would have to be exerted by some very large, imagin- 12.42 h M2 component at unity ary piston to produce the flow. Mass can be calculated when force and acceleration are known. For the Proudman Pentland data this mass, 2.7 1013 kg, is and east into the North Sea should be known. These about double what would have been calculated from will add to the channel impedance and so reduce the length, depth, and width. The reason for the increase effects of high turbine numbers even further. It is safe is that any reduction in width or depth will need a to expect that the increase of the northerly leakage higher local acceleration which will add to the impedance due to turbine installations in the Burra requirement for the driving force and also the local and Eynhallow Sounds, where the first painful full- kinetic energy. scale lessons will be learned, will improve the econ- Inertia behaves in a linear fashion with flow accel- omics of the Pentland Firth and vice versa. eration being proportional to driving slope. However, A useful numerical experiment would be to build a the flowrates in both short orifice-controlled and ‘dam’ across the west entry to the Pentland Firth and long friction-controlled channels will depend on record the new tidal head and the change in velo- the square root of the driving head difference. This cities in the bypass channel round the north of the would selectively reduce the higher velocities, dis- Orkneys and in the channels between the islands. torting the wave form and producing odd-order har- This work would indicate the best positions for the monics which could be detected by Fourier analysis deployment of a pattern of combined pressure of the velocity signal, giving spikes above the fre- sensors and acoustic Doppler velocity sensors, quencies of the major components. Figure 3 shows which would finally allow us to estimate accurately the spectrum of an acoustic Doppler velocity the Pentland Firth resource. Although numerical measurement collected by A. Owen (2006, personal models are very powerful, it is unfortunate that so communication) at Burra Sound opposite an inverted few real velocity measurements from the Pentland version of the Proudman Pentland velocity signal. Firth are available in the public domain. The peak measured velocity at Burra was 3 m/s, while for the modelled Pentland Firth data it was only 2.2 m/s but the spectra have been normalized 4 COMPARISONS BETWEEN VERTICAL AND to have equal areas. The frequency axis has been HORIZONTAL GEOMETRY set so that the strong 12.42 h M2 period is at unity. Clearly there are strong odd-order harmonics in the Although the horizontal-axis configuration is now real measurement but none in the numerical one. universal for wind turbines, the vertical-axis con- This rudimentary analysis tells us only what is hap- figuration with rim-drive, faired rings between pening between the observing points but more about blade banks and cross-bracing [2] shown in Fig. 1 the impedances looking west into the Atlantic Ocean may have some advantages for tidal streams and

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 185 marine currents, especially in high impedance chan- self-propelled vessels like tugs equipped with nels. The arguments are as follows. Voith-Schneider propellers [12]. The most common objection to the vertical-axis con- 1. The rectangular flow window of the vertical-axis figuration with fixed-pitch has been that the vel- rotor, particularly one where the rotor depth of ocities of blades moving upstream are higher than individual machines can be tailored with those of blades moving downstream. This leads to additional layers of blades, can fill a large fraction uneven power production across the flow window of a channel cross-section. An evenly distributed with a risk of stall for part of the rotation and insuffi- pressure across close-packed contra-rotating cient lift for another part. However, with a sophisti- rotors will give lower wake turbulence. It will cated pitch-control this problem can be entirely reduce the leakage between rotors and so may overcome. It could be argued that the velocity allow improvements in the performance coeffi- compromises are less than those arising from the cient above the Betz limit for a rotor in an open difference between hub and tip velocities in a field. horizontal-axis machine. 2. The vertical axis allows a large diameter rotor, Wind turbine designers like high tip-speed ratios which would be stable in pitch and roll and (five or more) because the requirement for torque which could be used in either deep-or shallow- in the blade roots, shaft, and gearing is inversely water and allow power ratings of tens of proportional to it. Torque, especially in gears, is megawatts. expensive. The limits to high tip-speed ratios are 3. By keeping velocity high, the full diameter rim- set by increased noise and, above some critical drive reduces power-conversion forces. speed, by a sharp rise in the damage from impacts 4. For a given foil velocity, a larger diameter will with rain drops. The torque argument would also have a longer rotation period and so will suffer apply to rotors working in water. However, the fewer fatigue cycles and will make lower torque droplet erosion effect is replaced by the much demands on the pitch-drive system needed for more serious effect of cavitation. Even by we choos- accelerating the inertia of the blades and the ing foil sections with low pressure-coefficients given added inertia of the water around them. by large radii of curvature at the nose, tip-speed 5. Rotors can generate from flows from any direc- ratios will be 2.5 or less in the highest current tion, even in turbulent flows, which vary round velocities. the rotor circumference and through the depth of the channel. Banks of separate short blades would allow operation with the right pitch angle in deep water with a large velocity-shear. 5 A PITCH CONTROL ALGORITHM 6. In the event of an electrical fault on land, gener- FOR CLOSE-PACKED ROTORS ation can be stopped instantly with no actuator power by releasing all the foils to head into the The Betz theory [13] for optimal performance of local flow direction. wind turbines in an open flow field requires that 7. In the highest spring tides and unforeseen the momentum of the flow through a rotor should surges, pitch angles can be reduced to shed be reduced by two thirds of the upstream value by power and avoid upstream flooding. its passage through the rotor. Strictly this should 8. The rings that support blades at both ends apply to all points across the swept disc. However, reduce bending moments by a factor of four rela- as there is a strong reduction in blade velocity tive to cantilevered blades, and thus ease the task towards the hub of horizontal-axis machines, a com- of the bearings needed for variable-pitch. promise has to be reached with respect to higher 9. The bottom ring can reduce tip vortices and give chords and increased pitch angles near the hub. flow augmentation equivalent to longer blades. The same momentum requirements will apply to 10. The rings can house pitch actuators and the vertical-axis wind turbines except that the compro- bottom ring can contain airbags, which can be mise is in the change of relative velocity across the inflated to lift the entire structure clear of the window. water for inspection or for the removal of With vertical-axis marine-current turbines which biofouling. operate at the surface, the situation is slightly differ- 11. Generation plant can be easily accessible in the ent because water cannot flow over the machine. If dry and can even be inspected during operation. they are part of a close-packed array, water will not 12. Blades can have a constant cross-section, giving be able to flow easily round the sides. If they cheap tooling and perhaps extrusion. occupy a fairly large fraction of the water depth 13. With internal fuel tanks, Diesel power and then it will not be easy for the water to flow beneath. fast pitch-variation, rotors can become agile, This means that the performance coefficient of large

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 186 S H Salter and J R M Taylor marine current systems should be able to exceed the edge of the foil by a small angle whose tangent Betz limit. However, as this will not be the case for is the ratio of lift to drag. Away from stall this the very first installations it is useful to consider the angle will be very small, ,18. Betz design criterion. 5. If the angle between this resultant force and the Starting with the assumption that the momentum upstream direction is known, the magnitude of objective has been achieved and that the water vel- the hydrodynamic force that would have the ocity through the entire rotor window is two thirds right upstream component from blades in that of the distant upstream value, the water must experi- slit can be calculated. ence a force that will reduce its momentum to one- 6. The cross-stream component of the force can be third of the original value while it is passing through calculated, which will allow the calculation of the rotor. The volume of water must be conserved the change of direction of the flow through an iso- while it is within the swept volume of the rotor. lated machine or the change of head between According to the Bernoulli equation there will be an rotors in a close-packed array of contra-rotating abrupt loss of head going through both the upstream turbines where the direction changes are and downstream arcs of the rotor followed by a slow prevented. recovery along the wake. 7. There will not always be blades in a slit, but the For this analysis, the stream tubes used by Strick- fraction of time that any blade axis will be in a land [14] are replaced for the troposkien blades of given slit can be calculated. Therefore, the blade the Darrieus ‘egg-beater’ wind turbines with vertical forces can be calculated by dividing the slit force stream ‘slits’. These are drawn in Fig. 4, where the slit by the fraction of occupancy. boundaries are defined by points at equal angles 8. By knowing the blade chord and the resultant round the circumference of the rotor. This implies velocity on a blade in any slit the Reynolds that the time taken for a blade axis to pass through number for that slit can be calculated and the a slit is constant (An analysis using slits of equal appropriate lift and drag coefficients looked up. width is also possible). It is assumed that the For known lift and drag, a given choice of blade reduction in flow velocity starts some appreciable chord and knowledge of the magnitude of the distance upstream, that the velocity through the resultant water velocity at any slit, we can rotor is two thirds of the upstream velocity, and calculate the angle of incidence that a blade in that the reduction to one third is complete at some a slit should have to the resultant local velocity. long distance downstream. For isolated turbines the additional angle needed to allow for flow divergence can be added. The variation of pitch angle through a 6 OPTIMUM PITCH-ANGLE CALCULATION rotation cycle for one design case of a close- STEPS packed machine is shown in Fig. 5(b). To avoid excessive angular acceleration of the blade 1. The width of each slit and the ideal flow velocity inertia, this includes a compromise that loses are known: therefore the mass flow through it is about 1 per cent of the blade’s power. Note that also known. It may help to think of the water as the position of maximum pitch angle comes a long train moving through the rotor window. slightly later than the angle to the upstream 2. The tangential velocity of the blades will have direction. been chosen with cavitation in mind. For each 9. The useful component of the force driving the tur- slit, the direction and magnitude of the resultant bine and the drag on the foil rings and cross-wires velocity that would be seen by an observer riding can be calculated. Knowing the useful force and on a blade are known. the blade speed we can calculate the efficiency, 3. In each slit the component of force acting on the the output power, and the torque which would water in the upstream direction should produce have to be provided by the power conversion the desired two thirds reduction in momentum mechanism. The contribution to the power of for that mass flow. With close-packed rotors in one blade through a full rotation is shown in high impedance channels, we can choose the Fig. 5(c). force that will give the same chosen head across the rotor diameter. This is plotted in Fig. 5(a). For Fig. 5, the lift and drag coefficients of a NACA 4. This force must be a component of the hydrodyn- 0018 foil were taken from Hanley Innovations Multi- amic forces on the blades moving through the slit Element software [15]. A 140 m diameter rotor would and, if the blades are not stalled, it will be nearly have 20 blades per bank with 2.3 m chord and 11 m perpendicular to the direction of the resultant vel- span and a tip-speed ratio of 2.5. The open-stream ocity on the blades. More accurately, it will be velocity of 3 m/s would generate 11.3 MW per bank. inclined from that direction towards the trailing Reynolds number would be 7.6 million.

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 187

Fig. 4 The geometry of a vertical-axis rotor rotating anti-clockwise seen from above with flow from the top of the page. For a tip-speed ratio of two the chord dimension for this number of blades has been exaggerated by a factor of two for clarity. The directions of the apparent flow at each blade are fixed by the down-stream velocity and the tangential velocity of the rotor. Blade and current velocity vectors (shown with arrows) and their resultant (shown bold) are in the true proportion. Momentum forces on the blades needed for the velocity reduction will be proportional to the width of each slit and are shown with a T-bar. The corresponding hydrodynamic lift forces are drawn with small circle ends. The blade pitch-angles needed to give the correct lift forces are drawn accurately for this chord and tip-speed

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 188 S H Salter and J R M Taylor

Fig. 5 (a) Flapwise blade force in kilo Newton to give the required change in momentum plotted against blade rotation; (b) The ideal pitch angle in degrees and a compromise (dashed) to avoid excess acceleration plotted against blade rotation; (c) Useful and wasteful (dashed) forces in kilo Newton against blade rotation; and (d) Power into or out of the pitch actuation system of one blade in kilowatt with the mean value dashed

7 RESULTS figure. The drag from the diagonal ties (shown in These steps have been implemented as a Mathcad Fig. 6) with streamlined fairings would reduce it by worksheet, which allows easy variation of all design about 1 per cent and the skin drag of unfouled variables with instant calculations of the optimum rings by a further 2.5 per cent. The drag loss of the pitch angles, forces, torques, cavitation pressure, effi- lower ring is likely to be less than that from the tip ciency, and power. It gives structural weights for any vortex, which it suppresses. In combination these choice of working stress and total cost based on give an estimated performance coefficient of 0.51. generic material prices. This coefficient should apply across a wide range of The mean drag power from the rotor blades solidities, flow velocites, and tip-speed ratios, reduces output by 4.5 per cent of the ideal Betz provided that the appropriate pitch control is used.

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 189

Fig. 6 Plan view (top) and elevation (below) of ﬂoating 45 MW vertical-axis tidal-current generator with ring-cam high-pressure oil power-take-off

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 190 S H Salter and J R M Taylor

It was reassuring to note that, if all the drag coeffi- channel value. Rotors may also have to be removed cients are set to zero, the MathCad model predicts a from time to time, with effects on the pitch-control performance coefficient very close to the 16/27 figure strategy of those on either side of the gap. All these of a perfect Betz rotor. Halving the value of the drag considerations point to the need for retrospective coefficient improves the performance coefficient by modifications of the pitch-control algorithms. 3 per cent. The addition of a blade pitch-error of 18 reduces the performance coefficient by ,0.2 per 7.1 Pitch actuation cent indicating a wide plateau of good operation. At an open stream flow of 3 m/s the prediction for Advanced algorithms for pitch control require a suit- the head difference across the turbine is 0.4 m. Close- able pitch actuator. If the foil bearings are placed for- packed units filling most of the flow window in high ward of the centre of pressure there will be a pitching impedance channels will behave more like turbines moment tending to bring the blade noses in to the in ducts and so the Betz limit will not be applicable. resultant velocity. For more than half the rotation With more blades or larger chords the performance period the required movement of the foil is in the coefficient should reach about 0.75. same sense as the hydrodynamic torque on it, so There is a wide range of equally good choices of blade pitch movement will be generating rather blade number, blade chord, and tip-speed ratio than absorbing power. Figure 5(d) shows the instan- with just two design boundaries. The first boundary taneous power to or from one blade actuator through is that the angle of incidence is never above the one cycle of rotation together with the mean output. stall angle at any point of the rotation. If stall were The power output could be increased by moving the to arise then the chord or number of blades would blade pitch axis nearer to the nose. have to be increased so as to allow a smaller angle The energy produced can be recycled to return a foil of incidence for the same force. Therefore the to its optimum position during the rest of the cycle. It number and chord should be chosen such that would be possible to use a combination of switching the stall angle in not exceeded. Higher numbers valves, cross-connections, and pressure accumulators make for a good structural truss. Higher chords give to achieve the required control. However, an extre- blades that have good beam strength and so can be mely versatile system, which can apply any comput- lighter than slender blades. It might be helpful to able control strategy, can be implemented by digital keep foil chords low enough for transport in sea poppet-valve machines, [16, 17]. The block diagram containers. in Fig. 7 shows a three-bank machine controlling The second design boundary requires that no point two rams and a link to a common accumulator. A on any blade ever experiences a negative pressure three-bank poppet valve machine for this power coefficient high enough to induce cavitation. Pressure rating would easily fit in the rotor rings. coefficients depend on the curvature of the foil at Digital hydraulic machines have two electromag- the nose, its angle of incidence and the magnitude netically controlled poppet valves on each chamber. of the resultant velocity. Fortunately the highest vel- Radial geometry allows them to share a common ocities are associated with small angles of incidence. shaft, which in this case might be started by an elec- Cavitation can be reduced somewhat by modified tric motor/generator. No magnet can ever overcome nose curvature, lower tip-speed ratios, or the use of the force of hydraulic pressure on a poppet valve but larger chords, which need smaller angles of incidence valves can be moved at times when there is no to produce the required forces. For this set of design pressure difference across them. The correct timing choices the worst cavitation pressure was 73 kilo Pas- of valve operation allows individual chambers to be cals on a blade at 24.58 from the cross-current diam- idle, to pump or to motor. The unit can change eter into the up-current sector. between these modes in one half revolution of the In the case of an isolated rotor there will be the extra shaft, much faster than any swash-plate machine. complication that the upstream foils will induce a At angles of a few degrees either side of the 0 and change of flow direction, giving a diverging fanlike 180 positions, both rams will be allowed to act as flow. However, the effect of this will be to change unloaded pumps, sending oil freely to the low- the angles of incidence to the down-stream blades pressure tank, and the blade will head directly into by a predictable amount and so will be easy to correct. the local current. After a few degrees the hydrodyn- A likely installation scenario is that a rotor would be amic pitch moment will rise and bank 1 of the first installed and operated as an isolated machine machine will act as a motor, giving way reluctantly and later joined by close neighbours, which will coun- to a rising pressure from ram A with the level of reluc- ter the diverging flow. Rotors at the end of a row will tance set by a computer. Meanwhile bank 2 can send experience increased flow velocities but these will oil back to the cylinder of ram B at very low pressure. be reduced when there are enough banks built in The required energy balance can be maintained by series to give an impedance which approaches the using bank 3 to pump oil to the high-pressure

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 191

Fig. 7 Block diagram of the pitch-control system with a multi-bank poppet-valve machine

accumulator, thus storing most of the energy gener- with spherical end-bearings can be used. These ated by the blade movement. At some angle beyond are shown in plan and elevation in Fig. 6. This will the upstream direction the blade will reach its maxi- give the rotor freedom to heave, pitch, and roll mum pitch angle and it will be necessary to move it but will prevent surge, sway, and yaw. Good tidal- back against the pitching moment, which by this stream sites, which are open at both ends, are likely time is fortunately reducing. This will be done by to be swept clear down to solid rock or very drawing power from the high-pressure accumulator large boulders. However, closed estuaries such as to drive bank 3 as a motor while bank 1 pumps oil Morecambe Bay will have thick layers of mobile back to ram A and ram B sends oil back to the low- sediment. An even more difficult seabed would be pressure tank. loose sediment containing large boulders or rock The electrical machines are needed to perform as outcrops and the worst would be loose sand contain- motors only for the initial start. They can be a mix ing obstructions like abandoned trawling gear or of DC brushless and AC induction types. Once the mines. In two wars Britain and Germany deployed system is running they can be used to generate 600 000 mines. Only 180 000 have so far been power for control logic, instrumentation, communi- accounted for. Many will have been put near cations, hydrostatic bearings, compressors for inflat- Scapa Flow, close to promising tidal-stream sites. ing air bags which can lift the rotor clear of the A thorough survey with seabed-penetrating radar is water, dolphin repulsion, anti-fouling, or cathodic indicated. protection. The direct connection of the two rams For the easiest case of good rock the preferred to the low-pressure tank can be used as a fail-safe choice, shown in Figs 6 and 8, is a set of three conical panic measure. fabrications pulled down into a conical crater by In this condition the blades will move to align with post-tensioned steel strands protected from cor- the local flow whatever its direction, and there will be rosion by alkaline grout. The size of the cone is set no lift and very low drag. This is useful for towing to by the strength of the rock. For the Pentland Firth site and for installation. It also provides a way to dis- the seabed rock is red sandstone with a bending connect the power input that is faster, cheaper, and strength in the plane of the strata of 37 MPa. With a more reliable than any braking system and that maximum stress of 10 MPa and the pre-stress would be needed following any loss of the network factor of 0.4, the diameter of a 608 cone for a connection. 60 MW rotor would be 4 m. Cones can be made of Cor-ten (a corrosion-resistant but easily weldable steel) with an anti-fouling treatment. 7.2 The seabed attachment The conical holes in the rock would be produced The seabed attachment affects the entire design of by equipment mounted on a Bryden Sea Snail [18], tidal stream turbines and is highly dependent on a novel seabed vehicle, which gains its down-thrust local geology. For a vertical-axis rotor, a system from the water flow and has proved to be much known as a tri-link which consists of three rigid legs more effective than clump anchors. The snail

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 192 S H Salter and J R M Taylor would be fitted with a rock drill which can be but its cost can be written off over many hundreds inclined at 608 to the horizontal and also rotated of installations. about the vertical axis. This would produce a ring When a leg is in compression the typical maximum of inclined holes which would nearly meet at the force of about 20 MN from a 45 MW rotor will go centre. These would be filled with explosives. A ring safely straight down into the rock and increase the of low energy propellant will produce a bubble cur- compressive stress at the cone-to-rock interface. tain to contain the effects of the blast. A similar When a leg is in tension the hold-down force must method can clear debris from the crater. exceed the vertical component of the leg tension The outer surface of the lower cone slope would which could reach 14 MN. The system has the be fitted with stiffeners in the form of lengths of same features as a post-tensioned concrete structure angle iron. They will initially be filled with clay and the upward force is supplied by a reduction of and will later form passages for post-tensioning the compressive stress between cone and rock. This tendons. Across the cone would be a conical contact has much less elasticity than the long ten- socket, set at an angle to be perpendicular to the dons and so the tendon stress remains constant mooring leg. The weight of steel would be about and fatigue is avoided. Furthermore, all tendons 12 tonnes. A float on the top of the cone would will have been fully tested during the post-tensioning give it enough buoyancy to allow placement with process before the turbine is installed. an inflatable vessel. The float would be released, The lower end of each leg, shown in Fig. 8, will be and concrete weighing about 20 tonnes would be fitted to the cylinder of a large hydraulic ram. The pumped inside the cone and in the rough spaces rod of the ram will be fitted to the outer of a between the cone and the surrounding blast-crater plain spherical bearing such as the SKF GEC 1250 in the rock. The total weight will keep the cone FSA [19]. This has a dynamic rating of 35.5 MN and additional tooling in place. and a static rating of 52 MN. It can take rotation Drilling holes and placement of post-tensioning of 38 either side of centre. The pressure in the tendons can be done with a robot-like machine ram will be an accurate measure of the force on which can sit on the upper cone and be indexed the leg. If oil from each side of the ram piston is about its vertical axis. A ring of 45 holes will be drilled fed to the appropriate side of the bearing it can through the clay in the angle-iron stiffeners and then partly offset the contact force without going all a further 20 m into the bed rock. Eight lengths of the way to the higher leakages of a full hydrostatic 50 mm diameter, 3 m drill tube will be held in a rotat- bearing. The small exit flow from the bearing ing can like the chamber of a revolver. It would be must be scavenged and returned to the system. sequentially fed downward at 308 from the vertical The inner of the plain bearing will carry a female and returned to the can when the hole has reached cone with a 458 half angle which turns into a much full depth. A design for this machine will be pre- more acute angle, probably 2.58. The choice of this sented in a future paper. angle is important because it will form the contact A plastic hose on the indexing head will be fed with a male cone permanently placed on the down to the bottom of the holes and grout pumped seabed. The axes of the cones will lie perpendicular into the bottom three-quarters of the depth of to the direction of the leg. The female cone will con- each hole. The rest of the hole and the passages tain a set of reinforced-textile air-bags made of a through the cone will be filled with a non-setting material similar to that used for fire hoses. These alkaline, hydrophobic, conformable paste, perhaps will act as cushions when inflated but will vent air based on lithium grease, with a density above that and slowly collapse as the cones approach one of sea water. The non-adhesion of the top quarter another. The outer end of the female cone will be of the tendon above the grout level is desirable to bell-mouthed. store elastic energy and to maintain a constant tension to avoid fatigue. 7.3 Installation The tendons would be 15 mm diameter, seven- strand wire. This can safely be wrapped round and Conventional marine installation uses tugs and tow- paid out from a 3.5 m diameter drum, but this wire lines. An inelastic cable connecting two objects, diameter is rather small for a rock drill hole. Three which are far enough apart to be in waves of opposite strands will be passed into each of the 45 holes phase can experience a tension, which is the relative drilled to 50 mm diameter. The odd number means separating acceleration (possibly twice the accelera- that the holes will miss each other. The final tool tion of the water in a wave) times the mass plus on the indexing head will crop the strands, place a added hydrodynamic mass of the lighter object. triplex collet over their ends, pull them to the work- Even higher tensions can result if a cable is allowed ing tension and finally fit a protective cap. This com- to go slack and then retighten after the build-up of plex tool will require advanced robotic techniques, kinetic energy. An elastic cable can store energy,

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 193

Fig. 8 Composite views of the sea-bed connection showing cones, post-tensioning tendons, 33 KV loops with exo-skeleton and breakable contacts which will be half the square of the peak tension jobs and when they have no work. Until the oil has times the spring rate of the rope. If the cable gone, the marine renewables cannot compete with should ever break it will release this stored energy the charter prices of oil ﬁrms. A single installation in a frighteningly short space of time. cycle can be a large fraction of initial capital cost Cables can apply only tension and in only one and early devices may need many cycles of removal direction. They are slow to make changes in that and reinstallation. direction. To connect or disconnect heavy cables at A better system would place the tug and the struc- sea requires intelligent communication and the con- ture being towed close enough to be in the same trol of large forces and heavy objects at both ends of wave phase and arrange that their phase and ampli- the cable, but vessels in distress often have no power tude responses to wave spectra are similar. This to move heavy objects and sometimes not even a would produce a large reduction in the forces crew. The only attractive things about a cable are between them. The driver vessel should be able to that the tug can be at a safe distance from a danger- apply force in any direction through a short connect- ous client vessel which is burning or about to explode ing link and change it quickly. The system should and that the cable can be coiled for compact stow- allow instant connection and disconnection with age. Everything else about towing cables is bad. intelligence at only one place and no need for hand- Conventional tugs must be able to make trans- ling heavy weights. ocean crossings lasting many days in any weather The drag of a hydrofoil at zero angle of incidence is and must provide acceptable living conditions for about one fortieth of the drag of a circular cylinder quite large crews. This makes hire expensive, typi- which would just ﬁt inside it. If the rotor foils are cally tens of thousands of pounds a day for an unpre- free to point into the direction of the local water vel- dictable number of days. Furthermore, availability ocity, turbines will be quite easy to tow. However, and hire costs vary widely depending on weather, with fuel and a Diesel engine on board, a pair of ver- demands of other work, and the location of the tug. tical-axis rotors could act like ocean-going vessels The vessels have to be paid for as they move between with an astonishing bollard pull and extreme agility

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 194 S H Salter and J R M Taylor in any direction. A single rotor could do quite well if inhibitor. Pressure can then be reduced to the level fitted with some torque reaction. An installation at the surface allowing the 7 bar water pressure to vessel using very large inflated tubes, GPS-linked hold the cone closed against the full leg force with 3608 variable-pitch vector-thrusters and, a quick-dis- no reliance on friction at the 2.58 cone contact. connect magnetic coupling has been described [20]. Drying air will be circulated to leave conditions suit- Each can produce a thrust of 200 kN so a group of able for high-voltage connections. four could install a large rotor, even without assist- The proposed transmission voltage is 33 kV, so ance from the rotor itself. 60 MW will need 1049 A per phase or, say, 1200 for Before the installation, one inflatable vessel will a reasonable power factor. The turbine side of the arrive at the site, where there will be three marker connection will consist of three coaxial conductors buoys with lines running down to caps protecting insulated with 18 mm of Teflon leading to three the male cones on the seabed. The buoys will be 50 mm thick 200 mm diameter discs with rims captured and their lines will be made fast to the machined to 22 mm curvature leaving a 6 mm vessel. The lines will contain air hoses leading to cylindrical track. This gives a potential contact area the inside of the caps so that they can be released of 3700 mm2. If an even contact pressure can be by compressed air. Device arrival will be timed for achieved the current density at the contact face will just after the seabed cone-caps have been removed. be 0.3 A per square millimetre. All this will be The turbine will be accurately positioned over its potted into a 200 mm probe, housed in a tube designated site with help from a carrier-phase differ- attached to the top of the female cone. ential GPS navigation system. Analysis of records The seabed side of the connection consists of three from acoustic Doppler instruments shows that sev- hollow annular shells with a wall thickness of eral sites never have completely slack water but 1.5 mm, with a slightly elliptical section having a rotors can ‘hover’ accurately enough for the lower minor diameter of about 100 mm and an inner ends to make connection with the seabed attach- major diameter which is 0.1 mm clear of the inner ment points. probe assembly. The three shells will be housed When the rotor has reached approximately the cor- within the male cone. A sealing piston-plug with O- rect position and the support vessels have rotated it rings will block the entry to each side of the electrical to the correct azimuth angle, the legs can be lowered contact but can slide towards the seabed side once by partial filling with water. Three winches will con- conditions are dry. Pressure will be applied to the trol the lowering of each leg. One winch will take the probe in the female cone and will advance it, pushing main weight of the leg. The other two can pull the leg away the piston-plug which was sealing the male outwards or inwards. The third degree of freedom cone. When the discs of the turbine side are aligned needed for full positioning control can come from with the seabed rings, oil pressure will be applied the ram at the lower end of each leg. The end bearing to the inside of the elliptical section annuli. This will be fitted with acoustic sensors to give the final, will distort them to the circular shape and make a high-precision position relative to datum points on uniform high-pressure contact. The complicated the male cone. The rams can allow some inaccuracy shape of the elliptical section annulus can be made in the positioning of the seabed attachment. They from electroformed nickel. This has a rather high can provide controlled yielding to wave loads. They electrical resistivity but plating with 0.2 mm of can even generate a moderate amount of wave copper will reduce the dissipation in the annulus to power from long period swell. less than 20 W at 600 A. Force from the leg will pass to the seabed through When a turbine has to be removed, air will be the contact between male and female cones looking pumped into the mooring legs to give them some like a rather over-designed butterfly net (see Fig. 8). small positive buoyancy and a tension will be applied During the final approach, air will be released from by winches on the power torus. Hydraulic pressure the annular cushion bags of the female cone. The applied to the underside of the probe piston will initial force collapsing the cushion bags can come pull it back into its housing dragging the male cone from the weight of the leg. After the 2.58 cones are piston-plug after it and leaving both entries sealed. in contact, the space between them will still be full High pressure air will be injected into the space of sea-water containing sediment and animal life. between the cones to supply a large force to break This can be cleared with a flow of filtered sea water the contact. It is important that all three legs and then air, both at pressures set below that which disconnect simultaneously. The Morse tapers used would separate the cone contact. This will be for large twist drills have half-angles of about 1.58 followed by flushing with fresh water to remove salt but, interestingly, are not all quite the same angle. residue, air to remove most of the fresh water, ethyl They need a sharp tap to break contact. Such a tap alcohol to remove the last of the water, and a spray could be provided by an air cylinder driving a of biocompatible, electrically insulating corrosion hammer head.

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 195

It should be ensured that the cone contact does with a wall thick enough to take all the foil forces in not corrode while a turbine is absent. It can be pro- shear, as well as vertical forces due to heave tected by lowering a cap in the form of a similar acceleration. female cone. This can be done by three of the inflat- Blades are separated by faired rings which are able vessels described above. braced diagonally by sloped cross-ties like some Electrical cables and hydraulic hoses which are designs of gasometer. This braced structure is forced to bend are a notorious source of poor strong in torsion and shear and so there is no pro- reliability. The problems are invariably found at the blem about passing torque from the lowest blade ends where bending is concentrated. The problem set up to the power torus. The vertical component can be reduced if the cables and hoses are formed of the diagonal wires will induce compression in into loops of a generous diameter by an ‘exo- the vertical spars but they are short enough not to skeleton’ which forces the cable to enter the loop buckle. However, the cross-ties give no strength in along a defined tangent and spreads the necessary the radial direction. This must come from the separ- bending evenly over the full circumferential length ating rings, which will suffer the most critical stresses of the loop. Figure 8 top right shows such a mechan- in the structure. For large rotor diameters the ring ism at the ends of the rams. Four metres of ram travel can be split into inner and outer parts, separated will need a change of about 158 in 2.25 turns of the by diagonal webs to increase the section moment outer loops and 308 spread over 4.5 turns of the (see Fig. 6). centre loop. If the loops are 2 m in diameter these All torsion and shear forces pass to the ring-cam changes in curvature would produce less than 1000 in the power torus. The cam is made as a necklace microstrain at the outer sheath of a 50 mm cable. of post-tensioned cam sections with junctions This would be low enough for a steel pipe and so placed at the cam troughs. The pump must oper- there should be an infinite fatigue life. ate as a bearing as well as a power conversion The rod of the ram can be protected by a rubber mechanism. The critical stress is the Hertzian con- ‘Belofram’ ‘rolling seal’, which works like a stocking tact stress between rollers and cam. At full working partly turned inside out. This is contained by a can pressure this will be 750 MPa, well below values at the end of the ram rod which runs back over the used in smaller pumps and railways. Many hun- cylinder body. This rod-can will carry a bearing to dreds of contact lines are used in parallel. Any allow the ram end to rotate independently of the faulty lobes or rollers can be identified by a exo-skeleton linkage so that rolling of the rotor will change in the rolling noise signature and can not be transferred to the seabed attachment. Three then be disabled by software. The torque is trans- helical loops between the legs and the ram end will ferred by roller forces on the cam slopes, and goes allow the 33 kV cables and control hoses to tolerate from the roller through hydrostatic oil films that this rotation. are pressurized by the piston. The radial piston forces are taken by bulkhead frames into the body of the power torus. The tangential forces go 7.4 Structural forces through swinging struts. Torque presented by the A close analysis of the complete force path through a ring-cam will be of the order of 108 N/m. structure is an important part of the design process. The circular shape of the power torus is maintained The dominant hydrodynamic flap-wise force on the by tension spokes like those of a bicycle wheel or of blades will have its largest component radial to the the London Eye. The upstream arc of the power rotor, either inwards or outwards, and will be com- torus will be in compression like the stones of an bined with the smaller, useful tangential component. arch and will induce radial outward forces along the The flap-wise forces will produce reversing bending diameter perpendicular to the flow direction just as moments in each blade but, because of the support an arch induces in its abutments. These forces will at both ends and the short length, these are not be resisted by spokes. The downstream arc will be serious. The forces at each blade end will pass in tension which can be taken by spokes and by a through pitch bearings to vertical spars running hoop tension member which pulls the arch elements from top to bottom of the rotor. At an open stream together. Up to this point the forces have been well current velocity of 4 m/s, 7 m blades with a 2 m distributed though many short parallel paths but chord would experience a peak bearing load of a now they must be collected round the circumference little over 200 kN – well within the infinite fatigue and concentrated at the three points where the post- life of SKF spherical roller bearings. A hydrostatic tensioned concrete mooring legs are connected bearing pressurized by filtered sea water with pads through plain bearings. Post-tensioned concrete is that can tilt through 28 is also possible. excellent for taking both tension and compressions There is plenty of room inside an 18 per cent thick- without fatigue. The slope of the legs produces an ness foil section for a 300 mm diameter tubular spar unwelcome vertical component, upward on one leg

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 196 S H Salter and J R M Taylor and down on a second, which has to be resisted by a magnitude and direction of the torque supplied by change in the water plane area of the power torus the hydraulic motor and this torque is set by the pro- requiring a small tilt. duct of pressure and the enabled fraction of the At the bottom of the leg the forces go through motor cylinders. hydraulic rams which give a chance for accurate The pressure in the gas -accumulator depends only force measurement by a pressure transducer, on the history of inflows and outflows. A digital through another plain-bearing universal joint, poppet-valve machine can change from being a full- through the cones of the seabed attachment and torque motor to idling to being a full-torque pump into the pre-compressed rock of the Pentland Firth. in half a revolution – only 20 ms for a motor driving For such long legs (about 0.8 of the rotor diameter), a four-pole electrical machine on a 50 Hz network. buckling is more of a consideration than direct Subject to not exceeding the upper pressure limit stress. One leg will be in tension and one in com- and suffering from a reduced power rating at low pression with a change at the next tidal phase. Buck- pressures, the instantaneous electrical output (or ling will be complicated by any out-of-straightness of input back from the network) can be left entirely to a leg and by bending moments on the leg caused by the choice of the plant owner. Only batteries feeding the current. It would be interesting to see if slip form- switching-mode four-quadrant DC to AC converters ing can give a small deliberate curvature so that can approach the frequency and phase response. whichever leg is in compression is straightened by The present networks are regulated by large central the current force. plant and suffer problems at the distant periphery. Digital hydraulics and storage can make peripheral plant a valuable asset for grid stability. 7.5 Controls During normal operation, the rotor speed will be Digital hydraulics allows extremely flexible control of the main control-parameter, with the product of the torque from variable-displacement pumps, accumulator pressure and enabled poppet-valve together with true synchronous generation. Initially, fraction being set to be directly proportional to it. A the requirement should be that, within the cavitation reduction in accumulator pressure, resulting per- limit, the speed of the rotor should be directly pro- haps from a short-term network demand, will proportional to the mean current speed. As power will duce an increase in the enabled fraction to keep rise with the cube of current speed it follows that the pump torque correct. Any change in current torque should rise with its square. speed will produce a corresponding change in rotor The torque in Newton metres of an hydraulic velocity, leading to a square-law change in the pump is the product of the pressure in Pascals required torque and so the correct match of tip- to which it is delivering times its displacement speed ratio. Pressure relief valves can protect the per revolution in cubic metres divided by 2p.A accumulator for a short time, about three times the digital pump can have this displacement reduced oil-tank circulation period. from the maximum value by the selection of the If rotor speed is following current speed, the blade fraction of the number of inlet valves which are pitch-angle variations round the circumference will allowed to close at bottom-dead-centre of the be the same for all current speeds. If they are piston strokes. Well-designed valve passages and chosen to put blades at the centre of the best operat- high pressure allow the losses of a disabled ing plateau, then local changes of velocity and direc- chamber to be very low – of the order of one- tion in turbulent flow will have little effect. However, thousandth of the energy delivered by an operat- they can be sensed by the pressures in the rams con- ing chamber. trolling pitch-angle, and perhaps in the pockets of This freedom allows the inclusion of a pressure hydrostatic pitch bearings, so another control vari- accumulator to store useful amounts of energy able is available. between the slow pump and the fast hydraulic For a cold start-up from zero rotor speed, all the motor(s) that drive the generator(s). Even a few blades will be heading freely into the current with seconds of storage will allow the system to ride out their control rams retracted into the S-shaped electrical network transients. Gas accumulators can guide tracks shown in Fig. 7. Blades on the ‘with hold several minutes of output – more than current’ side will be pointing in the wrong direction. enough time for the next fastest plant to respond. However, the pitch-control rams on a blade at 308 The rotation speed of the hydraulic motor and the into the ‘against current’ sector can be advanced to synchronous generator are locked to the frequency engage in the sockets of the blade cross-arm and of the network. The generator can export or import can change the pitch angle to produce torque to energy from that network according to the phase of start the rotor. Each foil can be engaged in turn as its armature relative to its rotating magnetic field. it enters the sector and pitched to increase rotor This angle, and the real output current, is set by the torque until the working speed is reached.

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 197

7.6 Design drivers economics of the later installations will be less favour- able so that a reduction by one third seems more Rotor diameter can be varied widely to suit local likely. During the early phases, turbines at the end geography, with different sizes made up from identi- of a partially completed line will experience higher cal modules with a slight angle adjustment at the velocities than at present because of the blockage of junctions. Large diameters will improve stability in neighbours. There may be a need for as much as a roll and pitch. They will tend to average out the three-to-one velocity range. Self-propelled turbines forces and displacements of shorter waves and give can be easily disconnected and moved to other sites. lower angular acceleration for pitch adjustments Two rows of close-packed turbines feeding power and a smaller number of fatigue cycles. Transformers to a common electrical bus with a wide gap to the switch-gear and power cables will have power ratings next pair of rows will allow machines to be installed of tens of megawatts but will be needed in smaller and removed at any time with no obstruction to numbers. However, the internal tri-link leg mooring cross-firth traffic. If the planform of the twin rows requires rotor diameters to be about twice the installations resembles two mated capital Es a high water depth and increasing diameter will increase blockage can be achieved. The presently large bending moments in the intermediate rings. amount of through-firth traffic would have to Rotor depth is also set by local soundings. The follow a tortuous slalom path with a channel width lowest part of the water column is likely to be turbulent of only a few kilometres. This would not be popular. because of bottom friction and the upper part because Perhaps all vessels above a certain size will have to go of waves. In a good site like the Pentland Firth, the north of the Orkneys. seabed will have quite large rolling boulders. This While the first units to be deployed will float at the suggests that we should not use more than about surface and enjoy the benefits of stability in heave, 70 per cent of the depth – typically 50 m. While the pitch and roll plus protected shirtsleeve access for mean velocities through the channel will eventually inspection, there may be future attractions in work- be reduced by about one third, the velocity below ing below the surface. The extra pressure would the rotor can be close to present values. reduce cavitation. There would be no visual intru- The space needed by a ring-cam power take-off is sion. It might be safe for small vessels to move so small that the minor diameter of the power torus directly over rotors. There is a very fast reduction in can be chosen for the comfort of tall engineers. The wave forces for quite small depths below the surface. same design can suit any installation but larger sec- However, the loss of stability in heave, pitch, and roll tions can be used to house generators, Diesel would need a different mooring design. engines, cam grinding machines, transformers, and Short blades, supported at both ends, will have local strengthening for the mooring leg attachments. quite low bending moments compared with the can- A diameter of more than 3.5 m would cause pro- tilevered blades of horizontal-axis machines. Short blems for movement by road and would also add blades allow different choices for pitch at different wave loading. depths. Because of fears of fatigue in underwater The minor diameter of the torus will also set the welds it was tempting to choose a maximum span upper limit for buoyancy and the hydrostatic buoy- set by the available 7 m length of steel plate. How- ancy stiffness needed to overcome the vertical com- ever, the higher bending moments of the large rings ponent of mooring leg forces. Because the changing of the Pentland Firth need higher section-moduli buoyancy force due to waves is 1808 out of phase for the separating rings and so the span has been with the wave inertial forces on the submerged inter- increased to 11 m, comfortably inside the length of mediate rings there will be one wave period for which an ISO container. If steel is used there will be two the two can be in balance and so no heave response. welds, each 2 m in from the end. The minor diameter will also set the maximum head Rotation speed should be as high as possible, sub- difference that can be tolerated by the non-contact- ject to the limit imposed by cavitation which may be ing gutter seals. approached but not exceeded. Higher blade speed Power rating and rated current velocity are closely means lower torque for a given power and, at the linked and set almost all the structural loads. How- speeds of marine current plant, the cost of the ever, there is a wide range of velocities in different power take-off will be directly proportional to parts of the Pentland Firth, with especially high torque. A tip-speed ratio of 2.5 is likely for a maxi- values to either side of islands. To maximize the mum velocity of 3 m/s in the Pentland Firth. total resource would require that final current vel- Blade chord and blade number together contribute ocities are reduced to just over half their present to solidity. There is possible confusion about the values, with heads across turbines of a completed definition of solidity for vertical-axis machines. One row substantially higher. However, it could take definition could be the ratio of blade area to circum- many years to install this many turbines and the ferential swept area. This would have a value of 0.16.

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy 198 S H Salter and J R M Taylor

A second definition would be the ratio of blade area 4. Spectral analysis of velocities at some sites shows to the rectangular flow window and would be 0.49. odd-order harmonics of the strong 12.42 h M2 With both variable-pitch blades and variable-speed component which are not present in the vel- rotors there can be quite a wide range of acceptable ocities predicted by combining the astronomical values of solidity. High values will be needed in forcing functions. These harmonics would be high impedance channels, as the first installations produced by the selective reduction of the are joined by later ones and the Betz free-stream higher velocities caused by a square law bottom behaviour is replaced by closed-channel behaviour. friction law. It may be better to have higher solidity and lower 5. Vertical-axis rotors appear to be attractive in high pitch-angle than to risk the stall from higher angles. impedance channels because the rectangular Large numbers of small blades give a smooth flow window can fill a large fraction of the chan- output and lower local stress but are less effective nel cross-section with a wide range of depths as beams. Larger numbers also give benefits of including the 70 m depth found in large parts mass production. The load on a blade will rise with of the Pentland Firth. By filling a large fraction the first power of chord, but its effectiveness as a and using contra-rotating rotors, sharp shearing beam to flapwise bending will rise with at least the velocities in the turbine wakes are avoided. cube. Chord values lower than the dimensions of 6. The performance coefficient of vertical-axis an ISO sea container will be convenient for transport. machines can be as good as for horizontal-axis A value of 2.3 m with 20 blades in one bank of a ones provided that the vertical-axis machines 140 m diameter rotor seems attractive. have independent pitch control. Variable-pitch turbines can gracefully shed loads 7. The pitch angles can be calculated from the lift due to currents above their rated maximum velocity. forces needed to give the required momentum This will improve capacity factor and reduce stress at change in each flow slit. quite a small cost in total annual energy. 8. Pitch-changing of any desired sophistication can The very high power take-off torque needed by be achieved with three banks of a poppet-valve large, slow turbines is easily achieved in a rim-drive machine and will be a net generator of power design. Ring cam hydraulics can also provide a which can be useful on the rotor. Only a small convenient bearing with low losses and high geometri- amount of energy storage is needed on the cal tolerance. A quad ring cam with differentially- rotor for cold starting. controlled pressures in each quadrant can withstand 9. Pairs of vertical-axis rotors can act as powerful the vertical wave loads as well as the downstream and agile tugs which can install and remove force. themselves. A single turbine can be installed with the help of small, inflatable vessels with magnetic coupling and linked GPS navigation. 8 CONCLUSIONS 10. The tri-link mechanism with rigid legs made from post-tensioned concrete with acoustic 1. The impedance of a flow channel and the source end-guidance gives the correct freedoms and driving it are of great importance for calculations constraints. It avoids the bending moments suf- of the maximum size of resource but little is yet fered by rigid towers and the problem of snatch known about actual values. The L . Cf/Z . Cp ratio loads suffered by ropes and cables. Prevention is proposed as an initial indicator of the resistive of buckling is the main design criterion but, impedance. Many potential sites are likely to with special slip-forming, the deliberate slight have quite high ratios, suggesting that resource bending of a leg towards the upstream direction estimates based only on the kinetic flux may be of the leg in compression can reduce problems of low. bending moments induced by current. 2. Seabed pressure measurements of mean sea 11. A combination of cones, spheres, cushion bags, level at points along a flow channel can be com- water ballasting, and vacuum suction can give pared with flowrates at each cross-section to give mechanical and high-voltage electrical connec- impedance information – both phase and ampli- tions and disconnections in times of a few min- tude – for each section and branch. utes but will leave acceptably low seabed 3. The phase lag between the water velocity relative obstruction at the end of life. to the driving head is an indicator of the importance of the inertia of the water mass in the channel. For the Pentland Firth, the 458 phase-shift ACKNOWLEDGEMENTS between driving head and velocity suggest that the inertia of the water is also a strong controlling We are grateful to David Pugh for advice on factor. impedance measurement, Roger Proctor of the

Proc. IMechE Vol. 221 Part A: J. Power and Energy JPE295 # IMechE 2007 Vertical-axis tidal-current generators 199

Proudman Oceanographic Laboratory for numerical 12 Voith Turbo GmbH & Co. Voith Schneider Propellers. predictions of Pentland Firth flow and Alan Owen Voith Turbo GmbH & Co., Crailsheim, Germany, of the Robert Gordon University for observations available from http://www.voithturbo.com/vt_en_pua_ from Burra Sound. marine_vspropeller.htm 13 Betz, A. Die Windmuhlen im Lichte Neurer Forschung. Die Naturwissenchaft, 1927, 15(46). REFERENCES 14 Strickland, J. H. The Darrieus turbine: a performance prediction model using multiple stream tubes. SAND 1 Salter, S. H. Theta-Islands for flow velocity enhance- 75-041, Sandia National Laboratories, Albuquerque, ment for vertical-axis generators at Morecambe Bay. New Mexico, USA, 1975. World Renewable Energy Conference, Aberdeen, 2005. 15 Hanley, P. Available from http://www.hanleyinno- 2 Salter, S. H. Pitch control for vertical-axis, marine- vations.com. current generators. World Renewable Energy Confer- 16 Salter, S. H., Taylor, J. R. M., and Caldwell, N. Power ence, Aberdeen, 2005. Conversion Mechanisms for Wave Energy. Proc. Instn. 3Fraenkel,P.L.and Musgrove,P.J.Tidal and river current Mech. Engrs. Part M: J. Engineering for the Maritime energy systems. International Conference on Future Environment, 2003, 216, 1–27. energy concepts, London 30 January–1 February 1979, 17 Rampen, W. Artemis technical literature. Available pp. 114–117 (IEE, London). from http://www.artemisip.com. 4 Salter, S. H. Proposal for a large, vertical-axis tidal- 18 Owen, A. and Bryden, I. Prototype support structure stream generator with ring-cam hydraulics. Third Euro- for seabed mounted tidal current turbines. Proc. pean Wave Energy Conference, Patras, September 1998. IMechE, Part E: J. Process Mechanical Engineering, 5 Campbell, A. R., Simpson, J. H., and Allen, G. L. The 2005, 219, 173–183. dynamical balance of flow in the Menai Strait. Est. 19 SKF. Plain bearings catalogue. The SKF Group, Sweden, Coast. Shelf Sci., 1998, 46, 449–455. available from http://www.skf.com/portal/skf/home/ 6 Black and Veatch Consulting Ltd. Phase II UK tidal products?lang¼en&maincatalogue¼1&newlink¼3. stream resource. Carbon Trust, London, 2005, avail- 20 Salter, S. H. A Purpose-designed vessel for the installa- able from http://www.carbontrust.co.uk/technology/ tion of wave power devices. Sixth European Wave and technologyaccelerator/tidal_stream2.htm Tidal Conference, Glasgow, 2005. 7 Bryden, I. G., Grinsted, T., and Melville, G. T. Assessing the potential of a simple tidal channel to deliver useful energy. Appl. Ocean Res, 2005, 26(5), 200–206. APPENDIX 8 Dalrymple, R. A. Tidal prediction with harmonic analysis. Centre for Applied Coastal Research, University of Notation Delaware, USA, available from http://www.coastal. udel.edu/faculty/rad/tide.html Cf bottom friction coefficient 9 Brumley, B. H., Cabrera, R. G., Deines, K. L., and Cp turbine performance coefficient Terrat, E. A. Performance of a broadband acoustic L channel length Doppler current profiler. IEEE J. Ocean. Eng., 1991, 16, Pf, Pr bed friction power or rotor power 402–407. U current velocity 10 Nortek AS. Norwaves – a Nortek newsletter, May 1999, W channel width available from http://www.nortek-as.com/news/NL9.pdf Z channel depth 11 National Tidal and Sea Level Facility. Available from http://www.pol.ac.uk/ntslf/ r fluid density

JPE295 # IMechE 2007 Proc. IMechE Vol. 221 Part A: J. Power and Energy