Are Nearly all Tidal Stream Turbines Designs Wrong? Stephen Salter Institute for Energy Systems University of Edinburgh

Cells are 1 minute of arc lat. 1.5 minutes long = km 2. Power = TW x Cf Courtesy Proudman Labs

Peak spring Pentland sea-bed friction = TeraWatt x Cf But what is Cf ?

From Black and Veatch 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 = 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 mm bob

Friction coefficients for Fshear = 0.5 ρ U 2 Cf

SourceCF for ½ ρU 2 Campbell, Simpson and Allen Estuarine Coastal and Shelf Science vol Menai strait ( ± ) x 2 = George K. Hydrographic Journal October 2005Positions along Menai strait 0.006, 0.008, 0.013, 0.015, 0.018, 0.02 Abbot and von Doenhoff. Dover One side of a NACA 0006 fighter wing at 0 deg incidence. Rey No 6E6. Polished Standard roughness Bricker, Inagaki and Monismith. ASCE Journal of Hydraulic Engineering June 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 (low waves) to 0.08 Rippeth, Williams and Simpson. Journal of Physical Oceanography vol 32, Menai Strait with ADCP and mean depth current ± Vitale ASCE Journal of Waterway,Port, Coastal and ocean Division August 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 ripples 0.05, 0.144, 0.16, 0.18,

6.165 TeraWatt x 0.04 = 247 GW X 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

NASA

Edinburgh vertical-axis, variable pitch with rim power take off. EWTEC Patras 1998

R.A. McAdam, G.T. Houlsby, M.L.G. Oldfield Structural and Hydrodynamic Model Testing of the Transverse Horizontal Axis Water Turbine EWTEC 2011

Speed up x 30 Range up x 6000 Payload up x 20,000 Cost down ÷ 100

Something for the simpletons

Variable pitch advantages Easy 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

Degrees lag 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