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

ρAdCU2

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

Dω

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

2ρAdU2

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