Are Nearly all Tidal Stream
Turbines Designs Wrong
for the Pentland Firth?
Stephen Salter
Institute for Energy Systems
University of Edinburgh
S.Salter@ed.ac.uk
www.see.ed.ac.uk/~shs
No names, no pack drill.
EWTEC Patras 1998
Edinburgh vertical-axis, variable-pitch with rim power take off.
. . . just like wind turbines but under water.
Pmax 
1
2
3 16
 AU 
27
Frederick Lanchester 1868-1946 Albert Betz 1885-1968
BUT for a turbine in a duct:
Pmax   gAUH
Open flow field
Duct
1
3 16
Pow   AU 
2
27
Pow   gAH U
3
.296 U
gH U
No names, no pack drill.
Ross McAdam
1.4
B=0.59
1.2
B=0.47
1
CP at peak
Betz Limit
0.8
0.6
0.4
0.2
0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Froude number
0.14
0.16
0.18
0.20
McAdam RA, Houlsby GT, Oldfield MLG.
Experimental measurements of the hydrodynamic
performance and structural loading of the transverse horizontal
axis water turbine: part 1.
Renewable Energy vol. 59 pp. 105-114. 2013
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
EWTEC Patras 1998
Edinburgh vertical-axis, variable-pitch with rim power take off.
Cam circumference
628 m
Cam rise
120 mm
Cam wavelength
970 mm
Lobe number
653 x 4
2612
Bogie length
600 mm
Coach number
60
Stations per coach
16
Rollers per station
8
Roller number
Roller force
Cycles per rotation
Power
60 x 16 x 8
= 7680
10 E5 N
2612 x 7680 = 20 million
No tip-to-hub velocity reduction
No squeezing torque through a bearing.
On-line shirt-sleeve access at the surface.
Thousands of force lines.
Contact-free gutter seal.
Lots of space.
GOOGLE IMAGES
MoD order the stretcher bearers to be at the same end ?
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Ratio of head increase to flow-rate reduction.
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Ratio of head increase to flow-rate reduction.
m. sec sec
Z
 2
3
m
m
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Ratio of head increase to flow-rate reduction.
m. sec sec
Z
 2
3
m
m
sec 1
Z 2.
m rho. g
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Ratio of head increase to flow-rate reduction.
m. sec sec
Z
 2
3
m
m
sec 1
Z 2.
m rho. g
DeltaH
Z
2
Power
Flow Impedance
The determination of the water to flow despite the
introduction of obstacles.
Ratio of head increase to flow-rate reduction.
m. sec sec
Z
 2
3
m
m
sec 1
Z 2.
m rho. g
DeltaH
Z
2
Power
Tidal turbine array optimisation using the adjoint approach.
S.W.Funke P.E.Farrell M.D.Piggott
Renewable Energy 2013
Tidal turbine array optimisation using the adjoint approach.
S.W.Funke P.E.Farrell M.D.Piggott
Renewable Energy 2013
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
Baston and Harris
Abbot I H and von Doenhoff AE
Theory of Wing Sections
NACA 64-006
Friction coefficients for Fshear = 0.5 ρ U2 Cf
6.165 TW x 0.04 = 247 GW
Are Nearly all Tidal Stream
Turbines Designs Wrong
for the Pentland Firth?
Stephen Salter
Institute for Energy Systems
University of Edinburgh
S.Salter@ed.ac.uk
www.see.ed.ac.uk/~shs