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The 9th Symposium on River, Coastal and Estuarine Morphodynamics,
RCEM 2015
EFFECTS OF HYDROKINETIC ENERGY TURBINE ARRAYS ON
SEDIMENT TRANSPORT AT SÃO MARCOS BAY, BRAZIL
E. González-Gorbeña1*; G. Wilson Jr.2*; P. C. C. Rosman3*; R. Y. Qassim4*
* Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia – COPPE, da Universidade Federal do
Rio de Janeiro – UFRJ, BRAZIL. 1 eduardogg@oceanica.ufrj.br; 2 gwj@gmail.com; 3 pccrosman@ufrj.br;
4 qassim@peno.coppe.ufrj.br
1. Introduction
At the present time, the role of renewable energy in
Brazil is significant as hydropower and other renewable
energies, mainly biomass, contribute with 70.7% and
9.6%, respectively, towards the total offer for electric
energy, as compared to the corresponding figures of
14.8% and 5.6% regarding worldwide averages (MME,
2014). Nevertheless, there is already an increasing role
which is played by wind energy, and a promising
potential for tidal current energy.
2. Objectives
This paper is concerned with the assessment of the tidal
current resource in São Marcos Bay, located on the
north-eastern coast of Brazil in the state of Maranhão
(Figure 1), and possesses a highly promising potential
for the generation of electricity through the conversion
of tidal current energy. Also, the impact of in-stream
Hydrokinetic Energy Turbine (HET) arrays would have
on the bay’s morphology is studied.
Figure 1. Baía de São Marcos and region of study.
3. Methodology and results
Three potential zones for tidal power exploitation have
been identified, Figure 2, employing SisBaHiA® finite
element hydro-sedimentological model (Rosman, 2015)
based on the sediment transport equation of Engelund &
Hansen (1967). Potential zones have surface areas of 1
km² to 5 km², mean spring peak tidal currents in the
range of 2–2.7 m/s and water depths range from 22 m to
40 m.
Figure 2. Hot spots for efficient tidal current power
extraction in São Marcos Bay. Zoom region shows
bathymetry contours.
An analytical power model applied for each zone
defines HET array characteristics and demonstrates an
annually potential output in the range of 34-49 GWh.
The analytical power model has, for simplification, a fix
lateral spacing between HETs set in 3 rotor diameters
and considers cut-in and cut-off velocities. Table 1
summarizes HET arrays characteristics for each zone.
Zone
Diameter
DR of
rotor (m)
∆x
(m)
No of
HETs
per
row
No
of
rows
Generated
Power
(GWh/ano)
A
20
400
16
3
49.0
B
15
450
25
3
41.0
C
20
400
14
3
34.0
Table 1. HET array characteristics for each zone.
An additional stress term, Equation (2), has been added
to the model momentum equations, Equation (1), in
order to include HET operation as a momentum sink,
taking into account thrust coefficient.
2* 3* 4*
1*
ˆˆ
ˆ
11 ˆˆ
ii
jji
S F T
ij i i i i
i
uu
ug
t x x
Ha
Hx
(1)
where z = (x, y, t) stands for the free surface elevation,
z = – h (x, y, t) for the bottom bathymetry, and ûi, for the
depth averaged velocity in the i-th direction. In models
with fixed bathymetry, h is time–independent. Here
H = ζ + h stands for the local water column height, âi,
represents the Coriolis acceleration term, 1* are depth
averaged turbulent shear stresses, 2* and 3* stands for
shear stresses in the i-th direction and at the free surface
and at the bottom, respectively. Finally, 4* stands for the
turbine stress term added in order to account for the
head losses due to the influence of TEC. The turbine
stress term is expressed as:
22
0.5
1ˆ ˆ ˆ
2
T
i T i
C u v u
(2)
CT represents the thrust coefficient, which is related to
the power coefficient, CP, through the linear momentum
actuator disk theory in an open channel developed by
Houlsby et al., (2008), and based on the work of
Rankine (1865) and Froude (1889). If AT is the swept
area of a TEC, AI is the area of influence of each
computational node, and NT is the number of turbines
per computational node, then,
. /
P T I
N A A
(3)
which represents the total swept area per computational
node, is known as nodal blockage. Then the power
available for a TEC is:
3
0.5 PT
P C A U
(4)
Six scenarios with full-scale HET arrays are modelled to
study hydrodynamic influences between arrays, as well
as morphological effects. During simulations a constant
thrust coefficient of 0.54 (Fraenkel 2009) is maintained.
The hydrosedimentological scenarios include, initially, a
simulation without HET arrays to adjust bathymetry of
possible data uncertainties to an equilibrium condition,
afterward individual simulations of each array, followed
by pairs of arrays. Even though, the sediment transport
model accepts differentiating granulometry and erosion
limit at each calculating node of the domain, it was
adopted a uniform granulometry consisting of five types
of sediments distributed in an erodible layer of up to
5 m. Results for the hydrodynamic interference study
indicate gains and losses in power output up to 16.7 %
and 10.7 % respectively, see Table 2. Morphological
effects are studied in the proximities of the promising
zones. Results, interpreted in a qualitative manner,
indicate the formation of sand banks with heights lower
than 0.75 m and regions experiencing levels of erosion
of the same order.
Zone
Percent of power density gain (+) or loss (-)
due to array interference for HET arrays
A
B
C
A-B
A-C
B-C
A
---
3.2
-5.4
---
---
-10.7
B
-2.5
---
9.5
---
-10.4
---
C
-4.1
16.7
---
13.2
---
---
Table 2. Percent of power density gain (+) or loss (-)
due to array interference.
4. Conclusions
The study concludes that there are large amounts of tidal
energy available at São Marcos Bay Future that can be
transformed to electricity using HETs. Nevertheless, it
has been confirmed that HET arrays influenced erosion
and deposition rates of regions up to a distance of
15 km. Future work is directed towards layout
optimisation to maximise electric energy generation
(Gorbeña et al., 2015), minimising adverse effects in
sediment dynamics.
Acknowledgments
The corresponding author wishes to acknowledge the
postdoctoral fellowship provided by the following
funding agency from Brazil: Conselho Nacional de
Desenvolvimento Científico e Tecnológico (CNPq).
References
Engelund, F., Hansen, E. (1967), A monograph on
sediment transport in alluvial streams. Teknisk Forlag,
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Fraenkel, P. (2009), SeaGen: progress with the world’s
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