Fluctuating load perceived by the downstream turbine in a farm

Abstract

This paper presents computations of a four tidal turbine array, with a row of three upstream devices and a downstream turbine. The studied configuration is based on the layout initially proposed in the framework of the NEPTHYD project. The simulations were carried out with a three-dimensional unsteady Lagrangian Vor-tex software. A synthetic eddy method is used to take into account the ambient turbulence encountered in tidal energetic sites. The loads perceived by the turbines are estimated with a lifting line approach, recently added in the software. To study the interaction between the upstream and downstream turbines, numerical velocity maps, wake lines, unsteady velocity variations obtained with numerical probes as well as fluctuations of power and thrust coefficients are presented.

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Fluctuating load perceived by the downstream turbine
in a farm
Myriam Slama, Grégory Pinon, Yasmine Ben Belkacem, Camille Choma Bex,
Michael Togneri, Iestyn Evans
To cite this version:
Myriam Slama, Grégory Pinon, Yasmine Ben Belkacem, Camille Choma Bex, Michael Togneri, et al..
Fluctuating load perceived by the downstream turbine in a farm. 14th European Wave and Tidal
Energy Conference, Sep 2021, Plymouth, United Kingdom. �hal-03372956�

1
Fluctuating load perceived by the downstream
turbine in a farm
M. Slama, G. Pinon, Y. Ben Belkacem, C. Choma Bex, M. Togneri, I. Evans
Abstract—This paper presents computations of a four
tidal turbine array, with a row of three upstream devices
and a downstream turbine. The studied configuration is
based on the layout initially proposed in the framework
of the NEPTHYD project. The simulations were carried
out with a three-dimensional unsteady Lagrangian Vor-
tex software. A synthetic eddy method is used to take
into account the ambient turbulence encountered in tidal
energetic sites. The loads perceived by the turbines are
estimated with a lifting line approach, recently added
in the software. To study the interaction between the
upstream and downstream turbines, numerical velocity
maps, wake lines, unsteady velocity variations obtained
with numerical probes as well as fluctuations of power
and thrust coefficients are presented.
Index Terms—Numerical computations; synthetic eddy
method; tidal energy converters; turbulence; vortex method.
I. INTRODUCTION
THE Atlantic Area interreg project named MON-
ITOR proposed to study, via a multi-model ap-
proach, tidal turbine blade reliability. Several work-
packages were design to carry out this study, such as
the laboratory testing one, the numerical one or even
the at-sea testing one based on full scale tidal proto-
types. This 3 years project will end in late Autumn
2021; it is now time to review and summarise the work
performed so far. The objective of the current paper is
to present one of the topic treated in the numerical
work-package.
In that respect, a 4 tidal turbine array representative
of a commercial farm is considered for the present
work (see Fig. 1). This turbine array is the NEPTHYD
project formerly awarded to Alstom/General Electric
- Engie for their project to the French 2013 call for
tender [1]. Unfortunately, this project was stopped a
couple of years ago due to the fact that General Electric
The ID number of this paper is 2227 of the conference track
THM (Tidal Hydrodynamic Modelling). This work was supported
in part by the European Regional Development Fund through the
Interreg Atlantic Area Programme, via the MONITOR project. This
work was also supported in part by the ERDF and the Normandy
Regional Council via programs such as NEPTUNE, SEMARIN and
DIADEMAR. CCB acknowledges the financial support of IFREMER
for the funding of her Ph.D. grants. YBB acknowledges the financial
support of Labex EMC3 programme Graduate School - Material
and Energy Science. Some authors of this work are also co-financed
by the European Regional Development Fund through the Interreg
FCE (France Channel England), via the TIGER project. The present
work was performed on computing resources provided by CRIANN
(Normandy, France).
M. Slama, Y. Ben Belkacem and G. Pinon are with Normandie Univ,
UNIHAVRE, UMR 6294 CNRS, LOMC 76600 Le Havre, France (e-
mail: gregory.pinon@univ-lehavre.fr).
M. Togneri and I. Evans are with Energy & Environment Research
Group, Swansea University, Bay Campus, Swansea SA1 8EN, UK.
Fig. 1: Four tidal turbine array configuration based on
the NEPTHYD project configuration and reproduced
from information given in [1].
decided to stop all tidal energy development at the
time. However, this project is very interesting because
first, it represents a real array configuration representa-
tive of a pre-commercial farm and second because the
fourth turbine is positioned downstream of the 3 oth-
ers during flood. Therefore, wake generated induced
turbulence can then be estimated and compared to
recent ambient measurement experimentally observed
in-situ owing to several French research projects such
as THYMOTE [2], [3] or HYD2M, for instance.
In a paper published recently [4], the numerical
assessment of the ambient and wake generated turbu-
lence level in this pre-commercial farm was studied.
In case of a small tidal angular asymmetry, the wake
of an upstream turbine can interact with the down-
stream one and therefore enhance the fluctuating load
perceived by the downstream device. The Lagrangian
software Dorothy was used with the latest features
developed to take into account the ambient turbulence,
such as the Synthetic Eddy Method proposed by Jar-
rin et al. [5] and recently adapted to the Lagrangian
vortex framework [6]. For the present work, a lifting
line method was added in the software to compute
the torque and thrust for each turbine. A comparison
between the fluctuating load perceived by an upstream
turbine, only subjected to ambient turbulence, and the
downstream turbine, subjected to a combined ambi-
ent+wake generated turbulence will be presented.
12227-
Proceedings of the 11th European Wave and Tidal Energy Conference 5-9th Sept 2021, Plymouth, UK
ISSN 2309-1983 Copyright © European Wave and Tidal Energy Conference 2021
European Wave and Tidal Energy Conference 2021, 5-9 Sept. 2021, Plymouth

2
II. NUMERICAL METHOD
A Lagrangian Vortex particle method is used in the
Vortex Blob formulation. The Vortex method is an
unsteady Lagrangian method, based on a discretisation
of the flow into vorticity carrying particles [7], [8].
The governing equations for an unsteady and incom-
pressible flow are the Navier-Stokes equations in their
velocity/vorticity (u,ω)formulation:
∇·u= 0,(1)
Dω
Dt = (ω·∇)u+ν∆ω,(2)
where uis the velocity field, ω=∇∧uis the vorticity
field and νis the kinematic viscosity. A first adaptation
of this numerical method to the tidal energy sector
is presented in [9] using a panel integral method to
represent the turbine blades.
For the present work, a lifting line will be preferred
as a representation of the blades in order to have a
better evaluation of the turbine torque and thrust force
together with a more rapid calculation cost. The rotor
blades are represented by several blade elements, for
which the local relative velocity Vrel and angle of attack
αare estimated at each time step (see Fig. 2). The loads
are obtained using tabulated values for the lift and
drag coefficients CLand CD(see [10] for more details).
Fig. 2: Cross-sectional blade element.
Particles are emitted at the root and tip of each blade
element. Their vorticity is estimated with a lifting line
representation which is similar to the work of Murray
et al. [11] for instance. The bound vortex attached to
a blade element is related to the lift coefficient at any
time t:
ΓB(r, t) = 1
2cVrelCL(3)
where ris the spanwise dimension and cis the local
chord. The trailing and spanwise vorticity shed in the
wake, denoted by ΓTand ΓSrespectively, are related
to spanwise and temporal variations of ΓB:
ΓTr−dr
2, t=ΓB(r, t)−ΓB(r−dr, t)(4)
ΓS(r, t)=ΓB(r, t −dt)−ΓB(r, t)(5)
where dtis the time step and dris the distance between
two consecutive blade element centres.
Fig. 3: Four tidal turbine array configuration based on
the NEPTHYD project configuration and reproduced
from information given in [1]. (a) Configuration with
an incoming flow yawed with an angle α. (b) Similar
representation but for which the flow is represented
horizontally.
Finally, the ambient turbulence in the upstream flow
is accounted for by modifying the upstream velocity
which is rewritten via the use of a Reynolds decompo-
sition:
u∞(x, t) = u∞(x) + u′(x, t),(6)
where u∞is the mean velocity of the flow and u′
its fluctuating part. This velocity fluctuating part u′is
represented by a Synthetic Eddy Method (SEM). The
representation of this fluctuating velocity u′is inspired
from the work of Jarrin et al. [5] using a source and
sink approximation of the turbulent structures. The
fluctuating velocity u′could then be represented as:
u′(x) = 1
√N
N

k=1
ckfλ(x−xk
λ),(7)
where fλis a shape function and ckis the intensity
of a single turbulent structure kof centre point xk
and Nthe total number of turbulent structures. Much
more numerical details are given in the recent work of
Choma Bex et al. [6].
III. NUMERICAL PARAMETERS
The schematic representation of Fig. 3 shows the
turbines layout and spacing within the computation
domain. An inclination of the incoming velocity vector
is indicated in Fig. 3(a) with an angle α. Such a con-
figuration with a yaw angle in the incident upstream
velocity is tested in the present work as interactions
will be highly enhanced between the middle upstream
device and the downstream one as observed in Slama et
al. [4]. Of course, as these turbines were supposed to
be equipped with a yaw adaptation device, all the
four turbines would reorient to align perfectly with the
incoming flow. To facilitate the flow representation for
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SLAMA et al.: FLUCTUATING LOAD PERCEIVED BY THE DOWNSTREAM TURBINE IN A FARM 3
the following simulations presented in Section IV, the
configuration of Fig. 3(b) is used. In this configuration,
the turbines are yawed by an angle α= 10◦so that the
velocity vector always aligns with the x-axis. As the
bathymetry cannot be taken into account in this study,
the four turbines are set to the same vertical position.
The tidal turbine used for this study has a diame-
ter Dof 18 m. The blade characteristics and profiles
correspond to the open-geometry turbine of IFREMER
(French Research Institute for Exploitation of Sea).
More details about IFREMER’s turbine can be found
in [4]. For the presented simulations, the rotor blades
are modelled by a lifting line for which each blade is
represented by 30 elements. Each blade element then
has a length dr = 0.3 m discretizing the blade along
the whole radius. The local value of the Reynolds
number is taken into account for the polar curves
used to evaluate the local lift and drag coefficients.
The incoming upstream velocity was set to U∞= 3.2
m/s and the TSR (tip speed ratio) was set to 4.1,
which corresponds to the optimal rotational speed of
the devices. Further discretization and time parameters
are considered, the inter-particle spacing is set to dh =
0.648 m with a smoothing parameter of δ= 1.5dh, a
time step of dt = 0.0479 s and the whole simulation
time was set to t= 200 s.
In order to account for the ambient turbulence, an
isotropic turbulence with an intensity of I∞= 10% is
used, leading to 11339 turbulent structures to be con-
sidered following considerations mentioned in previ-
ous works [4], [6]. The size of each structure is λ= 4.5 m
and its standard deviation is σ(λ)= 75%. Moreover, a
study space is defined where the turbulent structures
will be placed, owing to the SEM contribution. The
sizes of this space are Lx= 10D, Ly= 12D and Lz
= 6D respectively along the flow axis, in width and
vertically along the water depth.
IV. RES ULT S
Unless mentioned, all the following results are
averaged over a time from t= 102 s to t= 182 s
(representing 168 instantaneous velocity fields) in
order to be fully converged. Moreover, for the sake
of comparison, a computation was also performed
without any ambient turbulence.
1) Velocity wake maps and wake lines:
Fig. 4 presents the computed velocity wake maps
for the tested configuration. For the case considered
without ambient turbulence I∞= 0%, an important
interaction is observed between the middle upstream
device and the downstream turbine. Besides, the wakes
extension is very long and exceeds the 10D length
presented in this figure. The account for ambient tur-
bulence has modified the flow pattern when compared
to the case without ambient turbulence. The wakes are
shorter and other interaction phenomena are encoun-
tered mainly between the upper and middle upstream
turbines wake and the downstream turbine. The results
obtained for several configurations in [4] show that the
value of the ambient turbulence intensity really has an
Fig. 4: Time-averaged velocity wake maps, I∞=0% and
I∞=10%.
important influence on the wake shape. This is further
confirmed with these lifting lines computations and
very similar observations can be drawn.
Fig. 5 depicts the corresponding wake lines of Fig. 4.
They are taken from the turbines centre of rotation
and are aligned with the turbines axis. Those lines
represent the axial induction in front of each device.
For these configurations, two of the upstream wake
lines are similar and the third upstream wake line
(purple dashed-dotted line) is a little bit modified,
possibly due to the interaction mechanism with
the downstream wakes. A small acceleration is
also observed on the dotted lines upstream of the
downstream turbine, mainly due to the Venturi effect
imposed by the upper and middle upstream turbines.
Similarly, a small acceleration is observed for the
middle turbine line (dashed-dotted line) after the
wake recorvery for the configuration with ambient
turbulence I∞= 10%, most probably due to the bypass
phenomenon too.
In addition, an important velocity deficit is observed
in the case considered without ambient turbulence
I∞= 0%. Finally, the upstream flow conditions are
quickly recovered in the case with ambient turbulence,
that is to say that the account of ambient turbulence
significantly improves the results. As one can see,
32227-

4
0 2.5 5 7.5 10 12.5 15
x/R
1
1.5
2
2.5
3
3.5
u[m/s]
I∞=0%
0 2.5 5 7.5 10 12.5 15
x/R
1
1.5
2
2.5
3
3.5
u[m/s]
I∞=10%
Upstream top
Upstream middle
Upstream bottom
Downstream
Fig. 5: Time-averaged wake lines, I∞=0% and I∞=10%.
some interesting physical phenomena are already
present is these computations.
2) Velocity fluctuation based on the velocity probes:
Similarly to Slama et al. [4] and to better quantify
the previous discussed phenomena, numerical probes
were defined in the computation domain. These probes
are represented by the points denoted from 1 to 6
in each plot of Fig. 4. Probes 1 and 2 are positioned
one diameter upstream of the upper and middle up-
stream turbines respectively. These probes are included
in order to give a reference value, as a matter to
show the incoming flow disrupted only by ambient
turbulence. Probes 4 and 6 are centred one and two
diameters upstream of the downstream turbine respec-
tively, whereas probes 3 and 5 are located in front of the
blade tip of the downstream turbine, still one and two
diameters upstream respectively. The velocity recorded
by each probe for both cases are indicated in Fig. 6.
For the case with I∞=0%, probes 1 and 2 show
the unmodified incoming flow at the given incoming
velocity of U∞= 3.2 m/s only slightly modified by
the turbine axial induction. This can be further con-
firmed from the corresponding mean values presented
in Table I with a velocity slightly lower than 3.1 m/s
and a corresponding σ(u)of 0.024 m/s each. These
values can be identified as unmodified or reference
values. Probes 4 and 6 present the velocity records in
0 50 100 150 200
Time [s]
1
2
3
4
5
Velocity [m/s]
Probe 1
Probe 2
Probe 3
Probe 4
Probe 5
Probe 6
(a)
0 50 100 150 200
Time [s]
1
2
3
4
5
Velocity [m/s]
Probe 1
Probe 2
Probe 3
Probe 4
Probe 5
Probe 6
(b)
Fig. 6: Instantaneous velocity records measured at
the different probe locations for: (a) I∞=0% and (b)
I∞=10%.
TABLE I: Time-average uand the standard deviation
σ(u)of the velocity recorded by the probes at I∞=0%
(left) and I∞=10% (right).
Probes I∞= 0% I∞= 10%
u[m/s] σ(u)[m/s] u[m/s] σ(u)[m/s]
13.084 0.024 3.094 0.373
23.091 0.024 3.107 0.415
32.339 0.277 2.665 0.404
43.246 0.019 3.324 0.368
52.236 0.390 2.668 0.499
63.186 0.018 3.196 0.336
the by-pass depicting a combination of both physical
effects: slightly accelerated flow in the by-pass and a
velocity reduction owing to the downstream turbine
axial induction, this last phenomenon being more and
more important for probe 6 that is closer to the turbine.
This is also evidenced by the corresponding data in
Table I, also showing a very low velocity fluctuation
for this I∞=0%-case. On the contrary, for probes 3
and 5, increased values of the standard deviation of
the velocity (σ(u)) are recorded, the higher value the
closer to the turbine. This means that, locally for the
tip of the downstream blade, high velocity fluctuations
characterised by σ(u)= 0.277 m/s and 0.390 m/s are
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SLAMA et al.: FLUCTUATING LOAD PERCEIVED BY THE DOWNSTREAM TURBINE IN A FARM 5
recorded, levels quasi equivalent to I∞=10% ambient
turbulence (see right hand-side of Table I for probes 1
and 2). This is mainly explained by the fact that these
two probes are in the mixing layer of the middle
upstream turbine wake, and the velocity fluctuation
increases as the wake develops. Conversely, the corre-
sponding averaged velocity values (u) are decreasing
as the wake evolves, with values such as 2.339 m/s
and 2.236 m/s respectively.
For the I∞=10% ambient turbulence case, many
oscillations are observed on Fig. 6(b), potentially due
to the passing of the turbulent structures. It is hardly
impossible to observe tendencies from these time
series, maybe except the slightly smaller values for
probes 3 and 5. Therefore, the physical interpretations
can only be done from either the time-average u
and the standard deviation σ(u)of the velocity and
presented on the right hand-side of Table I. From the
presented values for u, very similar interpretations
than for their I∞=0% counterparts can be done. Very
similar tendencies are observed, maybe except for
probes 3 and 5, where the averaged velocity values
are slightly higher owing to the fact that the wake is
shorter, as depicted also in Fig. 4. This shorter wake
is one of the interesting feature of the higher ambient
turbulence. On the contrary, the standard deviations
are all quite high, with values comprised between
0.370 ≤σ(u)≤0.415 representing the ambient
turbulence level, clearly identified for probes 1 and 2.
Probes 4 and 6 show slightly lower values, possibly
due to the by-pass effect and also identified for the
I∞=0%-configuration. The standard deviation of the
velocity σ(u)is in the ambient range for probe 3 but a
reasonably higher value is observed for probe 5 with
approximately +25% increase. This is most probably
due to the combined effect of the ambient turbulence
level and also the wake generated turbulence, this
probe 5 being located in the mixing layer of the wake,
as evidenced in Fig. 4(b). These observations are very
similar to those already found in the previous study
of Slama et al. [4] showing consistency in the results.
However, the main advantage of using a lifting line
resides in the possibility of assessing associated torque
and thrust fluctuations, as is going to be presented in
the following sub-section.
3) Turbine performance evaluation:
To evaluate the turbine performances, power and
thrust coefficients are used and are respectively defined
by:
CP=Q×ωx
1
2ρSU 3
∞
,(8)
CT=Fx
1
2ρSU 2
∞
,(9)
where Qis the rotor torque, Fxis the rotor thrust,
ωxis the angular velocity in the x-direction and ρis
the fluid density. Fig. 7 shows the normalised power
coefficients (C∗
P) obtained both for I∞= 0% and I∞
= 10% and for the middle upstream turbine and the
0 50 100 150 200
Time [s]
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
CP
∗
I∞=0%
0 50 100 150 200
Time [s]
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
CP
∗
I∞=10%
Upstream middle Downstream
Fig. 7: Power coefficient, I∞=0% and I∞=10%
downstream one. Fig. 8 shows the exact equivalent
but for the thrust coefficients (C∗
T). All the presented
performance coefficients (CPand CT) were normalised
(identified by ∗) by being divided by a reference value
which is:
•the averaged CPvalue over a time of 102s to 200s
at I∞=0% for the power coefficients.
•the corresponding averaged CTvalue over the
same duration and also for I∞=0% for the thrust
coefficients.
The obtained values for the normalised averaged
power and thrust coefficients and their corresponding
standard deviations are presented in Table II.
TABLE II: Normalised averaged power C∗
Pand thrust
C∗
Tcoefficients and their corresponding standard de-
viations σ(·)for the middle upstream turbine and the
downstream one at I∞=0%andI∞= 10 %.
I∞I∞= 0% I∞= 10%
upstr. downstr. upstr. downstr.
C∗
P1.0000 1.0610 1.1298 1.1293
σ(C∗
P)0.0013 0.0130 0.1507 0.1759
C∗
T1.0000 1.0306 1.0577 1.0562
σ(C∗
T)0.0008 0.0080 0.0800 0.1025
For the case without ambient turbulence (I∞=0%),
both upstream values for C∗
Pand C∗
Tare very close
to unity (Fig. 7(a) and Fig. 8(a)), also shown on the
52227-

6
0 50 100 150 200
Time [s]
0.6
0.8
1
1.2
1.4
1.6
CT
∗
I∞=0%
0 50 100 150 200
Time [s]
0.6
0.8
1
1.2
1.4
1.6
CT
∗
I∞=10%
Upstream middle Downstream
Fig. 8: Thrust coefficient, I∞=0% and I∞=10%
averaged corresponding values in Table II, with a unity
value. This was expected and their corresponding stan-
dard deviation are also very low (see Table II). For the
downstream turbine, an increase is obtained, both for
the C∗
P(Fig. 7(a)) and C∗
T(Fig. 8(a)) most probably due
to the flow acceleration in the by-pass. This increase
results in an augmentation of approximately +5% in
both C∗
Pand C∗
Twith respect to unity. However, a sig-
nificant increase is already observable on the associated
standard deviations σ(C∗
P)and σ(C∗
T)as one can see
from Table II, although the absolute values keep fairly
low (σ(C∗
P)=0.0130 m/s and σ(C∗
T)=0.0080 m/s). With
these values, one can identify the associated load fluc-
tuations only due to the wake generated turbulence,
without any input from ambient turbulence.
On the contrary, from both Figs. 7(b) and 8(b) for
an ambient turbulence of I∞=10%, the instantaneous
values of C∗
Pand C∗
Tshow very high fluctuating levels.
These increased levels of both σ(C∗
P)and σ(C∗
T)are
both quite noticeable in Table II, for both upstream
and downstream turbine. However, for this precise
configuration with α= 10◦, the combined effect of
wake generated turbulence is quasi hidden with the
ambient turbulence fluctuating levels. Only a very
small increase is observed from both downstream
σ(C∗
P)and σ(C∗
T)quantities in comparison with their
upstream values. For this geometrical configuration
with a yaw angle of α= 10◦, only the tip part of
the downstream turbine is impacted by the wake flow.
Cases with α= 15◦and α= 20◦were tested in
the study of Slama et al. [4] showing more and more
intense interaction as the angle also increases. These
four computations, corresponding to both I∞=0%- or
I∞=10%-configurations for both higher angles, were
not computed for the writing of this paper due to a
lack of time. Hopefully, these results will be presented
during the conference. A similar analysis could there-
fore be performed as presented in Togneri et al. [12]
but taking into account the combined wake generated
turbulence on top of the ambient turbulence level.
V. CONCLUSIONS AND PROSPECTS
The current communication aims at presenting com-
putations of four tidal turbines in an array. The cho-
sen array configuration is the one submitted by the
consortium led by Alstom/General Electric - Engie
for their project to the French 2013 call for tender [1]
before General Electric stopped its tidal activities. It is
therefore really representative of a real pre-commercial
farm.
In these Lagrangian Vortex computations, the re-
cently adapted Jarrin’s formulation of the Synthetic
Eddy Method is used as an ambient turbulence model.
The ambient turbulence intensity used here is in the
range of those presented in the literature from exper-
imental campaigns performed in the Alderney Race,
close to the location where the farm was supposed
to be built. Depending on the upstream velocity yaw
angle and ambient turbulence characteristics of the
upstream tidal current, small to enhanced interaction
can be presented. These interaction mechanisms can
be identified either by the numerical velocity maps,
wake lines or even numerical probes recording the
unsteady velocity. For the downstream turbine, the
perceived velocity can be highly modified by the wake
interactions. With the very recent implementation of
the lifting line, turbine performance evaluation, both
in terms of power and trust coefficient, can also be
assessed numerically. In the present paper, an extensive
comparison was made for two ambient turbulence
level (I∞=0% and 10%) with a yaw angle of α= 10◦.
Very interesting observations were already made, both
in terms of averaged quantities or for their standard
deviations. With such a numerical tool, assessment
of combined ambient turbulence and wake generated
turbulence influence on a downstream rotor can be
studied. During the conference, more configurations
with other yaw angles and/or possible different ambi-
ent turbulence levels will be presented in order to have
a more comprehensive assessment of such interactions
in a tidal farm.
REFERENCES
[1] Autorit Environnementale, “Projet nepthyd,” Conseil
G´
en´
eral de l’environement et du d´
eveloppement
durable : http://www.cgedd.developpement-
durable.gouv.fr/IMG/pdf/160406 -
Hydroliennes Raz Blanchard - Nepthyd 50 -
delibere cle05849f.pdf, Tech. Rep., last access
62227-

SLAMA et al.: FLUCTUATING LOAD PERCEIVED BY THE DOWNSTREAM TURBINE IN A FARM 7
2021, March the 9th. [Online]. Available:
http://www.cgedd.developpement-durable.gouv.fr/IMG/
pdf/160406 - Hydroliennes Raz Blanchard - Nepthyd 50 -
delibere cle05849f.pdf
[2] M. Thibaut, J.-F. Filipot, C. Maisondieu, G. Damblans, R. Duarte,
E. Droniou, N. Chaplain, and S. Guillou, “A comprehensive
assessment of turbulence at a tidal-stream energy site
influenced by wind-generated ocean waves,” Energy, vol. 191,
p. 116550, 2020. [Online]. Available: http://www.sciencedirect.
com/science/article/pii/S0360544219322455
[3] A. Sentchev, M. Thi ´
ebaut, and S. Guillou, Turbulence characteri-
zation at tidal-stream energy site in Alderney Race, CRC press ed.,
2020.
[4] M. Slama, C. Choma Bex, G. Pinon, M. Togneri, and I. Evans,
“Lagrangian vortex computations of a four tidal turbine array:
an example based on the NEPTHYD layout in the alderney
race,” Energies, vol. 14, no. 13, 2021. [Online]. Available:
https://www.mdpi.com/1996-1073/14/13/3826
[5] N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser,
“A synthetic-eddy-method for generating inflow conditions for
large-eddy simulations,” International Journal of Heat and Fluid
Flow, vol. 27, pp. 585–593, 2006.
[6] C. Choma Bex, C. Carlier, A. Fur, G. Pinon, G. Germain,
and lie Rivoalen, “A stochastic method to account for the
ambient turbulence in lagrangian vortex computations,” Applied
Mathematical Modelling, vol. 88, pp. 38 – 54, 2020. [Online].
Available: http://www.sciencedirect.com/science/article/pii/
S0307904X20302614
[7] C. Rehbach, “Calcul num´
erique d’´
ecoulements tridimension-
nels instationnaires avec nappes tourbillonaires,” La Recherche
A´erospatiale, vol. 5, pp. 289–298, 1977.
[8] R. Lewis, Vortex element methods for fluid dynamic analysis of
engineering systems. Cambridge University Press, 1991.
[9] G. Pinon, P. Mycek, G. Germain, and E. Rivoalen, “Numerical
simulation of the wake of marine current turbines with a
particle method,” Renewable Energy, vol. 46, no. 0, pp. 111 –
126, 2012. [Online]. Available: http://www.sciencedirect.com/
science/article/pii/S0960148112002418
[10] J. N. Sørensen and W. Z. Shen, “Numerical modeling of wind
turbine wakes,” J. Fluids Eng, vol. 124, no. 2, pp. 393–399, May
2002. [Online]. Available: https://doi.org/10.1115/1.1471361
[11] J. Murray and M. Barone, The Development of CACTUS, a
Wind and Marine Turbine Performance Simulation Code. [Online].
Available: https://arc.aiaa.org/doi/abs/10.2514/6.2011-147
[12] M. Togneri, G. Pinon, C. Carlier, C. Choma Bex, and
I. Masters, “Comparison of synthetic turbulence approaches
for blade element momentum theory prediction of tidal turbine
performance and loads,” Renewable Energy, vol. 145, pp. 408 –
418, 2020. [Online]. Available: http://www.sciencedirect.com/
science/article/pii/S0960148119307839
72227-