Are Nearly all Tidal Stream Turbines Designs Wrong?

Stephen Salter

Institute for Energy Systems

University of Edinburgh

S.Salter@ed.ac.uk

www.see.ed.ac.uk/~shs

Cells are 1 minute of arc lat. 1.5 minutes long = 2.617 km2.

Power = 6.165 TW x CfCourtesy Proudman Labs

Peak spring Pentland sea-bed friction

= 6.165 TeraWatt x Cf

But what is Cf ?

From Black and Veatch 2011.

Using values for the Pentland Firth U = 3m/s, ρ = 1025 kg/m3, channel length = 23 km,

channel width = 10 km

in combination with a more appropriate bed friction coefficient CD = 0.0015 energy dissipated due to bed friction averaged over a tidal cycle calculated is 4.05 GW.

Laminaria Hyperborea (kelp) are found along the

edges of the Pentland Firth at depths up to 30 m.

Length can reach 3.5 metres.

Cf = ?

Pentland bed stills. P Hayes. Fisheries Research Aberdeen 2006-8

68 mm bob

Friction coefficients for Fshear = 0.5 ρ U2 Cf

Source CF for ½ ρU2

Campbell, Simpson and Allen Estuarine Coastal and Shelf Science vol 46 1998.

Menai strait(0.0086 ± 0.0002) x 2 = 0.0172

George K. Hydrographic Journal October 2005 Positions along Menai strait0.006, 0.008, 0.013, 0.015, 0.018, 0.02

Abbot and von Doenhoff.Dover 1959.

One side of a NACA 0006 fighter wing at 0 deg incidence. Rey No 6E6.

Polished 0.0025Standard roughness 0.0045

Bricker, Inagaki and Monismith. ASCE Journal of Hydraulic Engineering June 2005.

Combinations of waves and currents with results depending on ratio of current at one metre above

bed to maximum orbital wave velocity.San Franciso Bay. Silt and fine sand.

0.004 (low waves) to 0.08

Rippeth, Williams and Simpson. Journal of Physical Oceanography vol 32, 2002.

Menai Strait with ADCP and mean depth current0.0052 ± 0.0004

Vitale ASCE Journal of Waterway,Port, Coastal and ocean Division August 1979.

Average wave friction from many sites 0.094, 0.1, 0.106, 0.116,0.166, 0.28

Bagnold. Proc. Roy. Soc. December 1946. Waves with sand ripples0.05, 0.144, 0.16, 0.18,

6.165 TeraWatt x 0.04

= 247 GWX 0.38 = 93.7 GW

at peak spring

O’Doherty DM. Mason-Jones Morris, O’DohertyT, Bryne, Pricket, Grosvenor.

Interaction of marine turbines in close proximity.

EWTEC 2011

2.75

3.35

3

0.55

2.75

3.3

3

0.58

NASA

Edinburgh vertical-axis, variable pitch with rim power take off.

EWTEC Patras 1998

70 60 50 40 30 20 10 0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1

1.2Downstream force on a 140 diameter rotor as a fraction of ideal

1.2

0

fdsi 4

FDSi 4

DR

2

DR2

Xi

R.A. McAdam , G.T. Houlsby , M.L.G. OldfieldStructural and Hydrodynamic Model Testing of the Transverse Horizontal Axis Water Turbine

EWTEC 2011

Speed up x 30Range up x 6000

Payload up x 20,000Cost down ÷ 100

Something for the simpletons

Variable pitch advantagesEasy tow to installation site with 2.5% drag of circular members

Agile self propulsion

Instant disconnection of delivered power

Relief of bending stress in rings

Avoidance of cavitation

Double performance at lower tip speed ratios for 1.5% extra cost

Online conversion from open flow field to close packed

Survivor repulsion

Sibling assistance

Reactive loading to tune Pentland Firth to M2

Potential for delayed generation

Degreeslag

Phase by zero crossings 63.4

Phase by real and imaginary M2 spectral FFT peaks of slope and velocity

58.1

Phase by voltage induced by the earth’s magnetic field 68

Problems for horizontal-axis axial-flow rotors

Lower efficiency near the hub. Low packing-fraction means poor use of resource. Longer power cables. Higher bending moments at the blade roots. Coincidence of shear and bending stress. Vortex shedding at blade tips. Tower leverage. Hydrodynamic wake pollution. Sensitivity to flow direction change. Volume constraint for pitch mechanism. Betz limit. Bearing leverage. Bending moments limit power rating. Hydrostatic pressure variation. Submerged power-conversion mechanism. Lack of space for power conversion. Submerged main bearings. Less power smoothing. More expense for tapered and twisted hydrofoils. No bridge option. Need for high rubbing seal velocity . . . . . . . . . . . . .

S.Salter@ed.ac.uk

www.see.ed.ac.uk/~shs