Poster presented at the European Wave and Tidal Energy Conference (EWTEC) in 2013.
Tidal current turbine power capture
and impact in an idealised channel
Kristen M. Thyngα and Thomas Rocβ
αOceanography, Texas A&M University; βDepartment of Marine Energy, IT Power Ltd.
[email protected], [email protected]
• Turbines have been modeled in an ocean modelling code,
ROMS, without many of the restrictions that such models
• Want to evaluate power capture by two array layouts
• Want to understand the effects of turbines on a represen-
tative ﬂow system
Figure 1: Simpliﬁed headland domain with overlaid
magniﬁed views of the regular (left) and staggered (right)
array layout. Green dots represent the TCT location.
• Run in ROMS: hydrostatic, 3D, parallelized
• Horizontal resolution of ∆x = 30 m, ∆y = 10 m, 20 vertical
layers in 100 meter depth
• k-ω turbulence closure scheme is used
• West/ east open and north/south no-slip walls
• M2 tide, linear density proﬁle, N=0.01 s−1
• Quadratic bottom friction with CD = 3 × 10−3
Force term in momentum equations, representing the tur-
bine in a grid cell:
F = −
ρ: ﬂuid density, Ad: rotor-disc area of the turbine, Ud: ﬂow
velocity at turbine, C: function of the coefﬁcient, Ct.
Added terms to simulate reduced turbulence length scales
(Pk) and additional production of wake turbulence due to
the turbine’s presence (Pω):
+ Ps + PB − ε + Pk
(c1Ps + c2PB − c3εFwall + Pω) ,
k: turbulent kinetic energy, KM: vertical eddy viscosity,
Ps, PB: shear production, buoyancy production, ε: turbulent
dissipation rate, ω: turbulent frequency, Fwall: wall function.
The added terms to represent the turbine are given by
Pk = Cp
; Pω = Cω
∆x: grid spacing of the porous disc, Cp, Cd, Cω: functions
of ∆x and turbine properties.
Array Layout Effect on Power Capture
Local calculation of power capture of a 10 device farm:
) × ∆t.
N: turbine index, U∞N
): u-velocity component of un-
perturbed (perturbed) ﬂow at Nth turbine location (for a
given time index t).
2 × ∆Vi,j,k × ∆t,
i, j, k: index in x, y, z directions, v∞t,i,j,k
: unperturbed ﬂow
velocity norm, ∆Vi,j,k: control volume of (i, j, k)th cell.
2 × ∆Vi,j,k × ∆t,
vt,i,j,k : ﬂow velocity norm. Power dissipated by the
present of the TCT farm:
Power Capture = Available Power − Remaining Power.
These local and global approaches permit a complemen-
tary investigation of the power extraction induced by the
two-considered TCT farm layouts on the tidal system.
Extraction by array (MW):
Regular Array Staggered Array
Local Calculation 6.008 6.051
Global Calculation 7.5348 6.1845
Array Hydrodynamic Impacts
Difference in max speed and TKE between initial and reg-
ular turbine array case. Positive (red) values: initial case
has larger max values. Negative (grey): turbine array case
has larger values. Line plots to the left (bottom) of the main
plot area show the along- (across-) channel averages, with
( a ) Speed
( b ) Turbulence kinetic energy
Properties shown at hub height. Overlaid arrows
are velocity vectors, overlaid signal shows time po-
sition in tidal cycle (free surface), and inset plot
shows headland tip area, magniﬁed. All snap-
shots are taken at the same time on ebb tide:
( a ) Initial case: speed
( b ) Regular array: speed
( a ) Initial case: vertical vorticity
( b ) Regular array: vertical vorticity
( a ) Initial case: turbulence kinetic energy
( b ) Regular array: turbulent kinetic energy
Mean kinetic power density. The values for the ini-
tial simulation are shown in colored, ﬁlled contours
and corresponding values for the regular array simu-
lation are overlaid in black contours and labeled.
• The global approach leads to a more realistic result.
• Coherent structures found in the speed, vorticity, and tur-
bulent kinetic energy are disrupted near the headland tip
due to the presence of turbines, leading to a weakened
• The path of a large lee headland eddy is slightly altered,
and all effects have potentially signiﬁcant impacts for a
EWTEC 10th European Wave and Tidal Energy Conference Tenth European Wave and Tidal Energy Conference 2013, 2-5 September 2013, Aalborg, Denmark