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 Cf
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 = ?
68 mm
bob
Pentland bed stills. P Hayes. Fisheries Research Aberdeen 2006-8
Friction coefficients for Fshear = 0.5 ρ U2 Cf
Source
Campbell, Simpson and Allen
Estuarine Coastal and Shelf Science vol 46 1998.
George K. Hydrographic Journal October 2005
Abbot and von Doenhoff.
Dover 1959.
CF for ½ ρU2
Menai strait
(0.0086 ± 0.0002) x 2 = 0.0172
Positions along Menai strait
0.006, 0.008, 0.013, 0.015, 0.018, 0.02
One side of a NACA 0006 fighter wing at 0 deg
incidence. Rey No 6E6.
Polished 0.0025
Standard 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 current
0.0052 ± 0.0004
Vitale ASCE Journal of Waterway,Port, Coastal
and ocean Division August 1979.
Bagnold. Proc. Roy. Soc. December 1946.
Average wave friction from many sites
0.094, 0.1, 0.106, 0.116,0.166, 0.28
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
3
 2.75   0.55


 3.35 
3
 2.75   0.58


 3.3 
NASA
EWTEC Patras 1998
Edinburgh vertical-axis, variable pitch with rim power take off.
Downstream force on a 140 diameter rotor as a fraction of ideal
1.2
1.2
1
0.8
fds i4
FDSi4
0.6
0.4
0.2
0
0
 70  60  50  40  30  20  10
 DR
2
0
Xi
10
20
30
40
50
60
DR
2
70
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 . . . . . . . . . . . . .
S.Salter@ed.ac.uk
www.see.ed.ac.uk/~shs