Kristen Thyng
September 02, 2013
1.2k

# Tidal current turbine power capture and impact in an idealized channel simulation

Poster presented at the European Wave and Tidal Energy Conference (EWTEC) in 2013.

## Kristen Thyng

September 02, 2013

## Transcript

1. Tidal current turbine power capture
and impact in an idealised channel
simulation
Kristen M. Thyngα and Thomas Rocβ
αOceanography, Texas A&M University; βDepartment of Marine Energy, IT Power Ltd.
[email protected], [email protected]
Introduction
• Turbines have been modeled in an ocean modelling code,
ROMS, without many of the restrictions that such models
typically have
• Want to evaluate power capture by two array layouts
• Want to understand the effects of turbines on a represen-
tative ﬂow system
Numerical Model
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
Turbine Model
Force term in momentum equations, representing the tur-
bine in a grid cell:
F = −
1
2
d
,
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):
Dk
Dt
=

∂z
KM
σk
∂k
∂z
+ Ps + PB − ε + Pk

Dt
=

∂z
KM
σω
∂ω
∂z
+
ω
k
(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
U3
d
∆x
− Cd
Udk
∆x
; Pω = Cω
P2
s
ε
,
∆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:
Plocal =
1
T
10
N
n
t
dN,t
(U∞N,t
− UdN,t
) × ∆t.
N: turbine index, U∞N
(UdN,t
): u-velocity component of un-
perturbed (perturbed) ﬂow at Nth turbine location (for a
given time index t).
Global approach:
Available
Power
=
n
t i,j,k
1
2
ρ v∞t,i,j,k
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.
Remaining
Power
=
n
t i,j,k
1
2
ρ vt,i,j,k
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
coloring same:
( 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.
Conclusions
• 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
system downstream.
• The path of a large lee headland eddy is slightly altered,
and all effects have potentially signiﬁcant impacts for a
real system.
EWTEC 10th European Wave and Tidal Energy Conference Tenth European Wave and Tidal Energy Conference 2013, 2-5 September 2013, Aalborg, Denmark