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Full-scale, 3D, time-dependent aerodynamics and fluid–structure interaction (FSI) simu-lations of a Darrieus-type vertical-axis wind turbine (VAWT) are presented. A structural model of the Windspire VAWT (Windspire energy, http://www.windspireenergy.com/) is developed, which makes use of the recently proposed rotation-free Kirchhoff–Love shell and beam/cable formulations. A moving-domain finite-element-based ALE-VMS (arbi-trary Lagrangian–Eulerian-variational-multiscale) formulation is employed for the aero-dynamics in combination with the sliding-interface formulation to handle the VAWT mechanical components in relative motion. The sliding-interface formulation is aug-mented to handle nonstationary cylindrical sliding interfaces, which are needed for the FSI modeling of VAWTs. The computational results presented show good agreement with the field-test data. Additionally, several scenarios are considered to investigate the tran-sient VAWT response and the issues related to self-starting. [DOI: 10.1115/1.4027466]
Content may be subject to copyright.
Y. Bazilevs
Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
e-mail: yuri@ucsd.edu
A. Korobenko
Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
X. Deng
Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
J. Yan
Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
M. Kinzel
Department of Aerospace Engineering,
Division of Engineering and Applied Science,
California Institute of Technology,
Pasadena, CA 91125
J. O. Dabiri
Department of Aerospace Engineering,
Division of Engineering and Applied Science,
California Institute of Technology,
Pasadena, CA 91125
Fluid–Structure Interaction
Modeling of Vertical-Axis
Wind Turbines
Full-scale, 3D, time-dependent aerodynamics and fluid–structure interaction (FSI) simu-
lations of a Darrieus-type vertical-axis wind turbine (VAWT) are presented. A structural
model of the Windspire VAWT (Windspire energy, http://www.windspireenergy.com/)is
developed, which makes use of the recently proposed rotation-free Kirchhoff–Love shell
and beam/cable formulations. A moving-domain finite-element-based ALE-VMS (arbi-
trary Lagrangian–Eulerian-variational-multiscale) formulation is employed for the aero-
dynamics in combination with the sliding-interface formulation to handle the VAWT
mechanical components in relative motion. The sliding-interface formulation is aug-
mented to handle nonstationary cylindrical sliding interfaces, which are needed for the
FSI modeling of VAWTs. The computational results presented show good agreement with
the field-test data. Additionally, several scenarios are considered to investigate the tran-
sient VAWT response and the issues related to self-starting. [DOI: 10.1115/1.4027466]
1 Introduction
In recent years, the wind-energy industry has been moving in
two main directions: off shore, where energy can be harvested
from stronger and more sustained winds, and urban areas, which
are closer to the direct consumer. In the offshore environments,
large-size horizontal-axis wind turbines (HAWTs) are at the lead-
ing edge. They are equipped with complicated pitch and yaw con-
trol mechanisms to keep the turbine in operation for wind
velocities of variable magnitude and direction, such as wind gusts.
The existing HAWT designs are currently more efficient for
large-scale power production compared with the VAWT designs.
However, smaller-size VAWTs are more suitable for urban envi-
ronments and are currently employed for small-scale wind-energy
generation. Nevertheless, wind-energy technologies are maturing,
and several studies were recently initiated that involve placing
VAWTs off shore [2,3].
There are two main configurations of VAWTs, employing the
Savonius or Darrieus rotor types [4]. The Darrieus configuration
is a lift-driven turbine. It is more efficient than the Savonius con-
figuration, which is a drag-type design. Recently, VAWTs resur-
faced as a good source of small-scale electric power for urban
areas. The main reason for this is their compact design. The gener-
ator and drive train components are located close to the ground,
which allows for easier installation, maintenance, and repair.
Another advantage of VAWTs is that they are omidirectional (i.e.,
they do not have to be oriented into the main wind direction),
which obviates the need to include expensive yaw control
mechanisms in their design. However, this brings up issues related
to self-starting. The ability of VAWTs to self-start depends on the
wind conditions as well as on airfoil designs employed [5]. Stud-
ies in Refs. [6,7] reported that a three-bladed H-type Darrieus
rotor using a symmetric airfoil is able to self-start. In Ref. [8], the
author showed that significant atmospheric wind transients are
required to complete the self-starting process for a fixed-blade
Darieus turbine when it is initially positioned in a dead-band
region defined as the region with the tip-speed-ratio values that
result in negative net energy produced per cycle. Self-starting
remains an open issue for VAWTs, and an additional starting sys-
tem is often required for successful operation.
Due to increased recent emphasis on renewable energy, and, in
particular, wind energy, aerodynamics modeling and simulation
of HAWTs in 3D have become a popular research activity [917].
FSI modeling of HAWTs is less developed, although, recently,
several studies were reported showing validation at full-scale
against field-test data for medium-size turbines [18], and demon-
strating feasibility for application to larger-size offshore wind-
turbine designs [10,19]. However, 3D aerodynamics modeling of
VAWTs is lagging behind. The majority of the computations for
VAWTs are reported in 2D [2022], while a recent 3D simulation
in Ref. [23] employed a quasi-static representation of the air flow
instead of solving the time-dependent problem. A detailed 3D
aerodynamics analysis of a VAWT used for laboratory testing was
recently performed by some of the authors of the present paper in
Ref. [24]. The studies included full 3D aerodynamic simulations,
validated using experimental data, and a simulation of two side-
by-site counter-rotating turbines.
The aerodynamics and FSI computational challenges in
VAWTs are different than in HAWTs due to the differences in
their aerodynamic and structural design. Because the rotation axis
Manuscript received March 25, 2014; final manuscript received April 14, 2014;
accepted manuscript posted April 22, 2014; published online May 7, 2014. Assoc.
Editor: Kenji Takizawa.
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is orthogonal to the wind direction, the wind-turbine blades expe-
rience rapid and large variations in the angle of attack resulting in
an air flow that is constantly switching from being fully attached
to being fully separated. This, in turn, leads to high-frequency and
high-amplitude variations in the aerodynamic torque acting on the
rotor, requiring finer mesh resolution and smaller time-step size
for accurate simulation [24]. VAWT blades are typically long and
slender by design. The ratio of cord length to blade height is very
low, requiring finer mesh resolution also in the blade height direc-
tion in order to avoid using high-aspect-ratio surface elements,
and to better capture turbulent fluctuations in the boundary layer.
When the FSI analysis of VAWTs is performed, the simulation
complexity is further increased. The flexibility in VAWTs does
not come from the blades, which are practically rigid (although
blades deform at high rotational speeds), but rather from the tower
itself, and its connection to the rotor and ground. As a result, the
main FSI challenge is to be able to simulate a spinning rotor that
is mounted on a flexible tower.
In the present paper, we focus on the following developments.
We propose a set of techniques that, for the first time, enable FSI
simulations of VAWTs in 3D and at full-scale. We first develop a
3D structural model of a Windspire VAWT [1], which makes use
of the recently proposed rotation-free Kirchhoff–Love shell and
beam/cable formulations, and their coupling. The model allows
for the rotor to spin freely and for the tower and blades to undergo
elastic deformations. We validate the aerodynamics of the Wind-
spire design using the field data reported in Refs. [2527]. For the
FSI computations, to accommodate the spinning rotor and deflect-
ing tower and blades, the FSI formulation from Ref. [19]is
enhanced to allow the cylindrical sliding interface to also move in
space. Finally, with these new techniques, we perform preliminary
FSI computations in an effort to better understand the self-starting
issues.
The paper is outlined as follows. In Sec. 2, we introduce the
FSI formulation and present the governing equations of aerody-
namics and structural mechanics. We also briefly describe the
discretization techniques employed and the aforementioned
enhancement of the sliding-interface formulation. In Sec. 3,we
show the aerodynamic and FSI computations of the Windspire
VAWT and discuss start-up issues. In Sec. 4, we draw conclusions
and discuss possible future research directions.
2 Methods for Modeling and Simulation of VAWTs
2.1 Governing Equations at the Continuum Level. To per-
form the VAWT simulations, we adopt the FSI framework devel-
oped in Ref. [28]. The wind turbine aerodynamics is governed by
the Navier–Stokes equations of incompressible flows. The
incompressible-flow assumption is valid for the present applica-
tion because the Mach number is low (0:1). The Navier–Stokes
equations are posed on a moving spatial domain and are written in
the ALE frame [29] as follows:
q1
@u
@t^
x
þðu^
uÞ$uf1

$r1¼0(1)
$u¼0(2)
where q1is the fluid density, f1is the external force per unit mass,
uand ^
uare velocities of the fluid and fluid mechanics domain,
respectively. The stress tensor r1is defined as
r1u;pðÞ¼pIþ2leuðÞ (3)
where pis the pressure, Iis the identity tensor, lis the dynamic
viscosity, and euðÞis the strain-rate tensor given by
euðÞ¼
1
2$uþ$uT
 (4)
In Eq. (1),j^
xdenotes the time derivative taken with respect to a
fixed referential domain spatial coordinates ^
x. The spatial deriva-
tives in the above equations are taken with respect to the spatial
coordinates xof the current configuration.
The governing equations of structural mechanics written in the
Lagrangian frame [30] consist of the local balance of linear
momentum, and are given by
q2
d2y
dt2f2

$r2¼0(5)
where q2is the structural density, f2is the body force per unit
mass, r2is the structural Cauchy stress, and yis the unknown
structural displacement vector.
At the fluid–structure interface, compatibility of the kinematics
and tractions is enforced, namely
udy
dt¼0(6)
r1n1þr2n2¼0(7)
where n1and n2are the unit outward normal vectors to the fluid
and structural mechanics domain at their interface. Note that
n1¼n2.
The above equations constitute the basic formulation of the FSI
problem at the continuous level. In what follows, we discuss the
discretization of the above system that is applicable to VAWT
modeling. For a variety of discretization options, FSI coupling
strategies, and applications to a large class of problems in engi-
neering, the reader is referred to the recent book on computational
FSI [31].
2.2 Discretization and Special FSI Techniques for
VAWTs. The aerodynamics formulation makes use of the FEM-
based ALE-VMS approach [29,32,33] augmented with weakly
enforced boundary conditions [3436]. The former acts as a turbu-
lence model, while the latter relaxes the mesh size requirements in
the boundary layer without sacrificing the solution accuracy. ALE-
VMS was successfully employed for the aerodynamics simulation
of HAWTs and VAWTs in Refs. [9,16,24,37,38], and fluid–
structure interaction simulation of HAWTs in Refs. [10,18,19,28].
The structural mechanics of VAWTs are modeled using a com-
bination of the recently proposed displacement-based Kirchhoff–
Love shell [10,18,39] and beam/cable [40] formulations. Both are
discretized using NURBS-based isogeometric analysis (IGA)
[41,42].
The FSI modeling employed here makes use of nonmatching
discretization of the interface between the fluid and structure sub-
domains. Nonmatching discretizations at the fluid–structure inter-
face require the use of interpolation or projection of kinematic
and traction data between the nonmatching surface meshes (see,
for example, Refs. [28,31,32,4352]), which is what we do here.
To handle the rotor motion in the aerodynamics problem, the
sliding-interface approach is employed. The sliding-interface for-
mulation was developed in Ref. [53] to handle flows about objects
in relative motion, and used in the computation of HAWTs in Ref.
[16], including FSI coupling [19], and VAWTs in Ref. [24]. We
note that in application of the FEM to flows with moving mechan-
ical components, alternatively to the sliding-interface approach,
the Shear–Slip Mesh Update Method [5456] and its more general
versions [57,58] may also be used to handle objects in relative
motion. A recently developed set of space-time (ST) methods can
serve as a third alternative in dealing with objects in relative
motion. The components of this set include the ST/NURBS mesh
update method [17,59,60], ST interface tracking with topology
change [61], and ST computation technique with continuous
representation in time [62].
To accommodate the spinning motion of the rotor superposed
on the global elastic deformation of the VAWT, and to maintain a
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moving-mesh discretization with good boundary-layer resolution
critical for aerodynamics accuracy, the sliding-interface technique
is “upgraded” to handle more complex structural motions. While
at the fluid–structure interface the fluid mechanics mesh follows
the rotor motion, the outer boundary of the cylindrical domain
that encloses the rotor is only allowed to move as a rigid object.
The rigid-body motion part is extracted from the rotor structural
mechanics solution (see, e.g., Ref. [63]) and is applied directly to
the outer boundary of the cylindrical domain enclosing the rotor.
The inner boundary of the domain that encloses the cylindrical
subdomain also moves as a rigid object. It follows the motion of
the cylindrical subdomain, but with the spinning component of the
motion removed. The fluid mechanics mesh motion in the interior
of the two subdomains is governed by the equations of elasto-
statics with Jacobian-based stiffening [43,57,6467] to preserve
the aerodynamic mesh quality.
3 Computational Results
The computations presented in this section are performed for a
1.2 kW Windspire design [1], a three-bladed Darrieus VAWT.
The total height of the VAWT tower is 9.0 m and the rotor height
is 6.0 m. The rotor uses the DU06W200 airfoil profile with the
chord length of 0.127 m, and is of the Giromill type with straight
vertical blade sections attached to the main shaft with horizontal
struts (see Fig. 1). The blades and struts are made of aluminum,
and the tower is made of steel. The material parameters and
masses of the main structural components are given in Tables 1
and 2.
The VAWT blades and part of the tower that spins with the
rotor are modeled using Kirchhoff–Love shells, while the struts
and main shaft are modeled as beams. The struts are connected to
the blades, tower shell, and main shaft, which gives a relatively
simple VAWT structural model that can represent the 3D mechan-
ics of a spinning, flexible rotor mounted on a flexible tower. See
Figs. 1(b)and 1(c)for more details of the VAWT geometry
description. The density of the tower shell is set to be very small
(see Table 1) so that most of tower mass is distributed evenly
along the beam. Quadratic NURBS are employed for both the
beam and shell discretizations. The total number of beam ele-
ments is 116, and total number of shell elements is 7029. We note
that all the aerodynamically important surfaces that are “seen” by
the fluid mechanics discretization are modeled using shells.
The aerodynamics and FSI simulations are carried out at realis-
tic operating conditions reported in the field-test experiments con-
ducted by the National Renewable Energy Laboratory [25] and
Caltech Field Laboratory for Optimized Wind Energy [26,27]. For
all cases, the air density and viscosity are set to 1.23 kg/m
3
and
1:78 105kg/ms, respectively.
The outer aerodynamics computational domain has the dimen-
sions of 50 m, 20 m, and 30 m in the streamwise, vertical, and
spanwise directions, respectively, and is shown in Fig. 2. The
VAWT centerline is located 15 m from the inflow and side boun-
daries. The radius and height of the inner cylindrical domain that
encloses the rotor are 1.6 m and 7 m, respectively.
At the inflow, a uniform wind velocity profile is prescribed. On
the top, bottom, and side surfaces of the outer domain no-
penetration boundary conditions are prescribed, while zero
traction boundary conditions are set at the outflow.
The aerodynamics mesh has about 8 M elements, which are lin-
ear triangular prisms in the blade boundary layers, and linear tetra-
hedra elsewhere. The boundary-layer mesh is constructed using
18 layers of elements, with the size of the first element in the
Fig. 1 Windspire VAWT structural model with dimensions
included: (a) full model using isogeometric NURBS-based
rotation-free shells and beams; (b) model cross section 1 show-
ing attachment of the struts to the blades and tower shell; (c)
model cross section 2 showing attachment of the struts and
tower shell
Table 1 Geometric and material properties of the main VAWT
structural components
Thickness/
radius
Young’s
modulus
Poisson’s
ratio Density
Part t/r(mm) E(GPa) q(kg/m
3
)
Blades 2/NA 70 0.35 2700
Strut 12.7/NA 70 0.35 2700
Tower shell 5/44.45 210 0.33 78
Tower beam NA/41.08 210 NA 5120.9
Table 2 Masses of the main VAWT structural components
Part Mass (kg)
Blades 26.3
Strut 14.1
Tower 243.4
Total 283.8
Fig. 2 The VAWT aerodynamics computational domain in the
reference configuration, including the inner cylindrical region,
outer region, and sliding interface that is now allowed to move
in space as a rigid object
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wall-normal direction of 0.0003 m, and growth ratio of 1.1. A 2D
slice of the mesh near the rotor is shown in Fig. 3, while Fig. 4
shows the zoom on the boundary-layer mesh near one of the
blades. The mesh design employed in this simulation is based on a
refinement study performed for a Darrieus-type experimental tur-
bine in Ref. [24].
All computations are carried out in a parallel computing envi-
ronment. The mesh is partitioned into subdomains using METIS
[68], and each subdomain is assigned to a compute core. The
parallel implementation of the methodology may be found in
Ref. [37]. The time-step is set to 1:0105s for the aerodynam-
ics computation and 2:0105s for the FSI analysis.
3.1 Aerodynamics Simulation of the Windspire VAWT.
We first performed two pure aerodynamic simulations of the
Windspire VAWT, one using the wind speed of 8.0 m/s and rotor
speed of 32.7 rad/s, and another using the wind speed of 6.0 m/s
and rotor speed of 20.6 rad/s. The time history of the aerodynamic
torque for both cases is plotted in Fig. 5together with the experi-
mental values reported from field-test experiments [2527]. After
the rotor undergoes a full revolution, a nearly periodic solution is
attained in both cases. For 8.0 m/s wind, the predicted average tor-
que is 18.9 Nm, while its experimentally reported value is about
12.7 Nm. For 6.0 m/s wind, the predicted average torque is 9.5
Nm, while its experimentally reported value is about 4.8 Nm.
In both cases, the experimental value of the aerodynamic torque
is derived from the average power produced by the turbine at the
target rotor speed. The difference in the predicted and experimen-
tally reported aerodynamic torque is likely due to the mechanical
and electrical losses in the system, which are not reported. To esti-
mate those, we perform the following analysis. For simplicity, we
assume that the torque loss is proportional to the rotational speed
of the turbine, that is
Tloss ¼closs
_
h(8)
Here, Tloss is taken as the difference between the predicted and
reported torque values, _
his the rotation speed, and closs is the
“loss” constant that characterizes the turbine. The data for the
8.0 m/s wind give closs ¼0:19 kg m
2
/rad, while for 6.0 m/s wind
we find that closs ¼0:23 kg m
2
/rad. The two values are reasonably
close, which suggests that the torque overestimation is consistent
with the loss model. In fact, this technique of combining experi-
mental measurements and advanced computation may be
employed to approximately estimate losses in wind turbines.
3.2 FSI Simulations of the Windspire VAWT. In this sec-
tion, we perform a preliminary investigation of the start-up issues
in VAWTs using the FSI methodology described earlier and the
structural model of the Windspire design. We fix the inflow wind
speed at 11.4 m/s, and consider three initial rotor speeds: 0 rad/s,
4 rad/s, and 12 rad/s. Of interest is the transient response of the
system. In particular, we will focus on how the rotor angular
speed responds to the prescribed initial conditions, and what is the
range of the tower tip displacement during the VAWT operation.
The starting configuration of the VAWT is shown in Fig. 3.
Blade 1 is placed parallel to the flow with the airfoil leading edge
facing the wind. Blades 2 and 3 are placed at an angle to the flow
Fig. 3 A 2D cross section of the computational mesh along the
rotor axis. The view is from the top of the turbine, and the
blades are numbered counterclockwise, which is the expected
direction of rotation. The sliding interface may be seen along a
circular curve where the mesh appears to be nonconforming.
Fig. 4 A 2D cross section of the blade boundary-layer mesh
consisting of triangular prisms
Fig. 5 Time history of the aerodynamic torque for the pure aerodynamics simulations. (a) 8.0 m/s wind with experimental data
from Ref. [25] and (b) 6.0 m/s wind with experimental data from Refs. [26,27].
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with the trailing edge facing the wind. (Blade numbering is shown
in the figure.)
The time history of rotor speed is shown in Figs. 68. For the
0 rad/s case, the rotor speed begins to increase suggesting this con-
figuration is favorable for self-starting. For the 4 rad/s case, the
rotor speed has a nearly linear acceleration region followed by a
plateau region. In Ref. [7], the plateau region is defined as the re-
gime when the turbine operates at nearly constant (i.e., steady-
state like) rotational speed. From the angular position of the
blades in Fig. 7, it is evident that the plateau region occurs approx-
imately every 120 deg when one of the blades is in a stalled posi-
tion. It lasts until the blade clears the stalled region, and the lift
forces are sufficiently high for the rotational speed to start
increasing again. As the rotational speed increases, the angular ve-
locity is starting to exhibit local unsteady behavior in the plateau
region. While the overall growth of the angular velocity for the
4 rad/s case is promising for the VAWT to self-start, the situation
is different for the 12 rad/s case (see Fig. 8). Here, the rotor speed
has little dependence on the angular position and stays nearly con-
stant, close to its initial value. It is not likely that the rotor speed
will reach to the operational levels in these conditions without an
applied external torque, or a sudden change in wind speed, which
is consistent with the findings of Ref. [8].
Figure 9shows, for a full turbine, a snapshot of vorticity col-
ored by flow speed for the 4 rad/s case. Figure 10 zooms on the
rotor and shows several flow vorticity snapshots during the rota-
tion cycle. The figures indicate the complexity of the underlying
flow phenomena and the associated computational challenges.
Note the presence of quasi-2D vortex tubes that are created due to
massive flow separation, and that quickly disintegrate and turn
into fine-grained 3D turbulence further downstream. For more dis-
cussion on the aerodynamics phenomena involved in VAWTs the
reader is referred to Ref. [24].
Figure 11 shows the turbine current configuration at two time
instances during the cycle for the 4 rad/s case. The displacement is
mostly in the direction of the wind, however, lateral tower dis-
placements are also observed as a result of the rotor spinning
motion. The displacement amplitude is around 0.10–0.12 m,
which is also the case for the 0 rad/s and 12 rad/s cases.
Fig. 6 Time history of the rotor speed starting from 0 rad/s
Fig. 8 Time history of the rotor speed starting from 12 rad/s
Fig. 7 Time history of the rotor speed starting from 4 rad/s
Fig. 9 Vorticity isosurfaces at a time instant colored by veloc-
ity magnitude for the 4 rad/s case
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4 Conclusions and Future Work
In this paper, dynamic FSI modeling of VAWTs in 3D and at
full-scale was reported for the first time. A structural model of a
Windspire wind turbine design was constructed and discretized
using the recently proposed isogeometric rotation-free shell and
beam formulations. This approach presents a good combination of
accuracy due to the structural geometry representation using
smooth, higher-order functions, and efficiency due to the fact that
only displacement degrees of freedom are employed in the formu-
lation. The ALE-VMS technique for aerodynamics modeling was
augmented with an improved version of the sliding-interface for-
mulation, which allows the interface to move in space as a rigid
object and accommodate the global turbine deflections in addition
to the rotor spinning motion. The pure aerodynamics computation
produced good agreement with the field-test data for the Wind-
spire turbine, and the FSI simulations were performed to investi-
gate turbine start-up issues.
From the FSI computations, we see that for given wind condi-
tions, the rotor naturally accelerates at lower values of angular
speed. However, as the angular speed grows, the rotor may en-
counter a dead-band region. That is, the turbine self-starts, but
then it is trapped in a lower rotational speed than is required for
optimal performance, and some additional input (e.g., a wind gust
or applied external torque) is required to get the rotor to accelerate
further. There may be multiple dead-band regions that the turbine
needs to overcome, with external forcing applied before it reaches
the target rotational speed. In the future, to address some of these
issues, we plan to couple our FSI formulation with an appropriate
control strategy (see, e.g., Ref. [69]) to simulate more realistic
VAWT operation scenarios.
Acknowledgment
This work was supported through the NSF CAREER Award
No. 1055091. The computational resources of the Texas
Fig. 10 Vorticity isosurfaces of vorticity colored by velocity magnitude for the 4rad/s case. Zoom on the rotor. From left to
right: vorticity at 1.12 s, 1.24 s, 1.40 s, and 1.50 s.
Fig. 11 Turbine current configuration at two time instances for the 4 rad/s case.
The tower centerline in the reference configuration is shown using the dashed line
to illustrate the range of turbine motion during the cycle. The range of the tower tip
displacement during the cycle is about 0.10–0.12 m.
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Advanced Computing Center (TACC) [70] were employed for the
simulations reported in this work. This support is gratefully
acknowledged.
References
[1] “Windspire Vertical Wind Turbine,” 2014, Ark Alloy, LLC, Reedsburg, WI,
http://www.windspireenergy.com/
[2] Vita, L., Paulsen, U. S., and Pedersen, T. F., 2010, “A Novel Floating Offshore
Wind Turbine Concept: New Developments,” European Wind Energy Confer-
ence & Exhibition (EWEC 2010), Warsaw, Poland, April 20–23.
[3] Vita, L., Paulse n, U. S., Madsen, H. A., Nielsen, H. P., Berthelsen, P. A., and
Cartsensen, S., 2012, “Design and Aero-Elastic Simulation of a 5 MW Floating
Vertical Axis Wind Turbine,” ASME Paper No. OMAE2012-83470.
[4] Hau, E., 2006, Wind Turbines: Fundamentals, Technologies, Application, Eco-
nomics, 2nd ed., Springer, Berlin.
[5] Kirke , B., and Lazauskas, L., 1991, “Enhancing the Performance of a Vertical
Axis Wind Turbine Using a Simple Variable Pitch System,” Wind Eng., 15(4),
pp. 187–195.
[6] Dominy, R., Lunt, P., Bickerdyke, A., and Dominy, J., 2007, “Self-Starting
Capability of a Darrieus Turbine,” Proc. Inst. Mech. Eng., Part A,221(1),
pp. 111–120.
[7] Hill, N., Dominy, R., Ingram, G., and Dominy, J., 2009, “Darrieus Turbines:
The Physics of Self-Starting,” Proc. Inst. Mech. Eng., Part A,223(1),
pp. 21–29.
[8] Baker, J. R., 1983, “Features to Aid or Enable Self Starting of Fixed Pitch Low
Solidity Vertical Axis Wind Turbines,” J. Wind Eng. Ind. Aerodyn.,15(1–3),
pp. 369–380.
[9] Bazilevs, Y., Hsu, M.-C., Akkerman, I., Wright, S., Takizawa, K., Henicke, B.,
Spielman, T., and Tezduyar, T. E., 2011, “3D Simulation of Wind Turbine
Rotors at Full Scale. Part I: Geometry Modeling and Aerodynamics,” Int. J.
Numer. Methods Fluids,65(1–3), pp. 207–235.
[10] Bazilevs, Y., Hsu, M.-C., Kiendl, J., W
uchner, R., and Bletzinger, K.-U., 2011,
“3D Simulation of Wind Turbine Rotors at Full Scale. Part II: Fluid–Structure
Interaction Modeling With Composite Blades,” Int. J. Numer. Methods Fluids,
65(1–3), pp. 236–253.
[11] Chow, R., and van Dam, C. P., 2012, “Verification of Computational Simula-
tions of the NREL 5 MW Rotor With a Focus on Inboard Flow Separation,”
Wind Energy,15(8), pp. 967–981.
[12] Bechmann, A., Sørensen, N. N., and Zahle, F., 2011, “CFD Simulations of the
MEXICO Rotor,” Wind Energy,14(5), pp. 677–689.
[13] Takizawa, K., Henicke, B., Tezduyar, T. E., Hsu, M.-C., and Bazilevs, Y.,
2011, “Stabilized Space–Time Computation of Wind-Turbine Rotor Aero-
dynamics,” Comput. Mech.,48(3), pp. 333–344.
[14] Takizawa, K., Henicke, B., Montes, D., Tezduyar, T. E., Hsu, M.-C., and Bazilevs,
Y., 2011, “Numerical-Performance Studies for the Stabilized Space–Time Compu-
tation of Wind-Turbine Rotor Aerodynamics,Comput. Mech.,48(6),
pp. 647–657.
[15] Sørensen, N. N., and Schreck, S., 2012, “Computation of the National Renew-
able Energy Laboratory Phase-VI Rotor in Pitch Motion During Standstill,”
Wind Energy,15(3), pp. 425–442.
[16] Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2013, “Finite Element Simulation
of Wind Turbine Aerodynamics: Validation Study Using NREL Phase VI
Experiment,” Wind Energy,17(3), pp. 461–481.
[17] Takizawa, K., Tezduyar, T. E., McIntyre, S., Kostov, N., Kolesar, R., and
Habluetzel, C., 2014, “Space–Time VMS Computation of Wind-Turbine Rotor
and Tower Aerodynamics,” Comput. Mech.,53(1), pp. 1–15.
[18] Korobenko, A., Hsu, M., Akkerman, I., Tippmann, J., and Bazilevs, Y., 2013,
“Structural Mechanics Modeling and FSI Simulation of Wind Turbines,” Math.
Models Methods Appl. Sci.,23(2), pp. 249–272.
[19] Hsu, M.-C., and Bazilevs, Y., 2012, “Fluid–Stru cture Interaction Modeling of
Wind Turbines: Simulating the Full Machine,” Comput. Mech.,50(6),
pp. 821–833.
[20] Stein, P., Hsu, M.-C., Bazilevs, Y., and Beucke, K., 2012, “Operator- and
Template-Based Modeling of Solid Geometry for Isogeometric Analysis With
Application to Vertical Axis Wind Turbine Simulation,” Comput. Methods
Appl. Mech. Eng.,213–216, pp. 71–83.
[21] Scheurich, F., Fletcher, T., and Brown, R., 2011, “Simulating the Aerodynamic
Performance and Wake Dynamics of a Vertical-Axis Wind Turbine,” Wind
Energy,14(2), pp. 159–177.
[22] Scheurich, F., and Brown, R., 2012, “Modelling the Aerodynamics of Vertical-
Axis Wind Turbines in Unsteady Wind Conditions”. Wind Energy.,16(1), pp.
91–107.
[23] McLaren, K., Tullis, S., and Ziada, S., 2012 , “Computational Fluid Dynamics
Simulation of the Aerodynamics of a High Solidity, Small-Scale Vertical Axis
Wind Turbine,” Wind Energy,15(3), pp. 349–361.
[24] Korobenko, A., Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2013,
“Aerodynamic Simulation of Vertical-Axis Wind Turbines,” ASME J. Appl.
Mech.,81(2), p. 021011.
[25] Huskey, A., Bowen, A., and Jager, D., 2009, “Wind Turbine Generator System
Power Performance Test Report for the Mariah Windspire 1-kW Wind
Turbine,” National Renewable Energy Laboratory, Golden, CO, Technical
Report No. NREL/TP-500-46192.
[26] Dabiri, J. O., 2011, “Potential Order-of-Magnitude Enhancement of Wind Farm
Power Density Via Counter-Rotating Vertical-Axis Wind Turbine Arrays,” J.
Renewable Sustainable Energy,3(4), p. 043104.
[27] “Biological Propulsion Laboratory at CALTECH (Wind Energy Research),”
2012, California Institute of Technology, Pasadena, CA, http://dabiri.
caltech.edu/research/wind-energy.html
[28] Bazilevs, Y., Hsu, M.-C., and Scott, M. A., 2012, “Isogeometric Fluid–
Structure Interaction Analysis With Emphasis on Non-Matching Discretiza-
tions, and With Application to Wind Turbines,” Comput. Methods Appl. Mech.
Eng.,249–252, pp. 28–41.
[29] Hughes, T. J. R., Liu, W. K., and Zimmermann, T. K., 1981,
“Lagrangian–Eulerian Finite Element Formulation for Incompressible Viscous
Flows,” Comput. Methods Appl. Mech. Eng.,29(3), pp. 329–349.
[30] Belytschko, T., Liu, W. K., and Moran, B., 2000, Nonlinear Finite Elements for
Continua and Structures, Wiley, New York.
[31] Bazilevs, Y., Takizawa, K., and Tezduyar, T. E., 2013, Computatio nal Fluid–
Structure Interaction: Methods and Applications, Wiley, New York.
[32] Takizawa, K., Bazilevs, Y., and Tezduyar, T. E., 2012, “Space–Time and ALE-
VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interac-
tion Modeling,” Arch. Comput. Methods Eng.,19(2), pp. 171–225.
[33] Bazilevs, Y., Hsu, M.-C., Takizawa, K., and Tezduyar, T. E., 2012, “ALE-
VMS and ST-VMS Methods for Computer Modeling of Wind-Turbine Rotor
Aerodynamics and Fluid–Structure Interaction,” Math. Models Methods Appl.
Sci.,22(Supp 02), p. 1230002.
[34] Bazilevs, Y., and Hughes, T. J. R., 2007, “Weak Imposition of Dirichlet Bound-
ary Conditions in Fluid Mechanics,” Comput. Fluids,36(1), pp. 12–26.
[35] Bazilevs, Y., Michler, C., Calo, V. M., and Hughes, T. J. R., 2007, “Weak
Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows,” Comput.
Methods Appl. Mech. Eng.,196(49–52), pp. 4853–4862.
[36] Bazilevs, Y., Michler, C., Calo, V. M., and Hughes, T. J. R., 2010,
“Isogeometric Variational Multiscale Modeling of Wall-Bounded Turbulent
Flows With Weakly Enforced Boundary Conditions on Unstretched Meshes,”
Comput. Methods Appl. Mech. Eng.,199(13–16), pp. 780–790.
[37] Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2011 , “High-Performance Comput-
ing of Wind Turbine Aerodynamics Using Isogeometric Analysis,” Comput.
Fluids,49(1), pp. 93–100.
[38] Hsu, M.-C., Akkerman, I., and Bazilevs, Y., 2012, “Wind Turbine Aerodynam-
ics Using ALE–VMS: Validation and the Role of Weakly Enforced Boundary
Conditions,” Comput. Mech.,50(4), pp. 499–511.
[39] Kiendl, J., Bletzinger, K.-U., Linhard, J., and W
uchner, R., 2009, “Isogeometric
Shell Analysis With Kirchhoff–Love Elements,” Comput. Methods Appl.
Mech. Eng.,198(49–52), pp. 3902–3914.
[40] Raknes, S., Deng, X., Bazilevs, Y., Benson, D., Mathisen, K., and Kvamsdal,
T., 2013, “Isogeometric Rotation-Free Bending-Stabilized Cables: Statics, Dy-
namics, Bending Strips and Coupling With Shells,” Comput. Methods Appl.
Mech. Eng.,263, pp. 127–143.
[41] Hughes, T. J. R., Cottrell, J. A., and Bazilevs, Y., 2005, “Isogeometric Analysis:
CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement,”
Comput. Methods Appl. Mech. Eng.,194(39–41), pp. 4135–4195.
[42] Cottrell, J. A., Hughes, T. J. R., and Bazilevs, Y., 2009, Isogeometric Analysis:
Toward Integration of CAD and FEA, Wiley, Chichester, UK.
[43] Tezduyar, T. E., and Sathe, S., 2007, “Modeling of Fluid–Structure Interactions
With the Space–Time Finite Elements: Solution Techniques,” Int. J. Numer.
Methods Fluids,54(6–8), pp. 855–900.
[44] Tezduyar, T. E., Sathe, S., Pausewang, J., Schwaab, M., Christopher, J., and
Crabtree, J., 2008, “Interface Projection Techniques for Fluid–Structure Interac-
tion Modeling With Moving-Mesh Methods,” Comput. Mech.,43(1), pp.
39–49.
[45] Tezduyar, T. E., Schwaab, M., and Sathe, S., 2009, “Sequentially-Coupled Ar-
terial Fluid–Structure Interaction (SCAFSI) Technique,” Comput. Methods
Appl. Mech. Eng.,198(45–46), pp. 3524–3533.
[46] Takizawa, K., Christopher, J., Tezduyar, T. E., and Sathe, S., 2010,
“Space–Time Finite Element Computation of Arterial Fluid–Structure Interac-
tions With Patient-Specific Data,” Int. J. Numerical Methods Biomed. Eng.,
26(1), pp. 101–116.
[47] Tezduyar, T. E., Takizawa, K., Moorman, C., Wright, S., and Christo pher, J.,
2010, “Multiscale Sequentially-Coupled Arterial FSI Technique,” Comput.
Mech.,46(1), pp. 17–29.
[48] Tezduyar, T. E., Takizawa, K., Moorman, C., Wright, S., and Christo pher, J.,
2010, “Space–Time Finite Element Computation of Complex Fluid–Structure
Interactions,” Int. J. Numer. Methods Fluids,64(10–12), pp. 1201–1218.
[49] Takizawa, K., Moorman, C., Wright, S., Purdue , J., McPhail, T., Chen, P. R.,
Warren, J., and Tezduyar, T. E., 2011, “Patient-Specific Arterial Fluid–
Structure Interaction Modeling of Cerebral Aneurysms,” Int. J. Numer. Meth-
ods Fluids,65(1–3), pp. 308–323.
[50] Takizawa, K., and Tezduyar, T. E., 2011, “Multiscale Space–Time Fluid–
Structure Interaction Techniques,” Comput. Mech.,48(3), pp. 247–267.
[51] Tezduyar, T. E., Takizawa, K., Brummer, T., and Chen, P. R., 2011,
“Space–Time Fluid–Structure Interaction Modeling of Patient-Specific Cerebral
Aneurysms,” Int. J. Numer. Methods Biomed. Eng.,27(11), pp. 1665–1710.
[52] Takizawa, K., and Tezduyar, T. E., 2012, “Space–Time Fluid–Structure Inter-
action Methods,” Math. Models Methods Appl. Sci.,22(Supp 02), p. 1230001.
[53] Bazilevs, Y., and Hughes, T. J. R., 2008, “NURBS-Based Isogeometric Analy-
sis for the Computation of Flows About Rotating Components,” Comput.
Mech.,43(1), pp. 143–150.
[54] Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., Kalro, V., and Litke, M.,
1996, “Flow Simulation and High Performance Computing,” Comput. Mech.,
18(6), pp. 397–412.
[55] Behr, M., and Tezduyar, T., 1999, “The Shear-Slip Mesh Update Method,”
Comput. Methods Appl. Mech. Eng.,174(3–4), pp. 261–274.
Journal of Applied Mechanics AUGUST 2014, Vol. 81 / 081006-7
Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 06/19/2014 Terms of Use: http://asme.org/terms
[56] Behr, M., and Tezduyar, T., 2001, “Shear-Slip Mesh Update in 3D Computation
of Complex Flow Problems With Rotating Mechanical Components,” Comput.
Methods Appl. Mech. Eng.,190(24–25), pp. 3189–3200.
[57] Tezduyar, T. E., 2001, “Finite Element Methods for Flow Problems With Moving
Boundaries and Interfaces,” Arch. Comput. Methods Eng.,8(2), pp. 83–130.
[58] Tezduyar, T. E., 2007, “Finite Elements in Fluids: Special Methods and
Enhanced Solution Techniques,” Comput. Fluids,36(2), pp. 207–223.
[59] Takizawa, K., Tezduyar, T. E., and Kostov, N., 2014, “Sequentially-Coupled
Space-Time FSI Analysis of Bio-Inspired Flapping-Wing Aerodynamics of an
MAV,” Comput. Mech., February (published online).
[60] Takizawa, K., 2014, “Computational Engineering Analysis With the New-
Generation Space-Time Methods,” Comput. Mech., March (published online).
[61] Takizawa, K., Tezduyar, T. E., Buscher, A., and Asada, S., 2014, “Space-Time
Interface-Tracking With Topology Change (ST-TC),” Comput. Mech., October
(published online).
[62] Takizawa, K., and Tezduyar, T. E., 2014, “Space–Time Computation Techni-
ques With Continuous Representation in Time (ST-C),” Comput. Mech.,53(1),
pp. 91–99.
[63] Takizawa, K., Tezduyar, T. E., Boben, J., Kostov, N., Boswell, C., and Buscher,
A., 2013, “Fluid–Structure Interaction Modeling of Clusters of Spacecraft Para-
chutes With Modified Geometric Porosity,” Comput. Mech.,52(6), pp. 1351–1364.
[64] Tezduyar, T. E., Behr, M., Mittal, S., and Johnson, A. A., 1992, “Computation
of Unsteady Incompressible Flows With the Finite Element Methods—Space–
Time Formulations, Iterative Strategies and Massively Parallel
Implementations,” New Methods in Transient Analysis, PVP-Vol. 246/AMD-
Vol. 143, ASME, pp. 7–24.
[65] Tezduyar, T., Aliabadi, S., Behr, M., Johnson, A., and Mittal, S., 1993, “Parallel
Finite-Element Computation of 3D Flows,” Computer,26(10), pp. 27–36.
[66] Johnson, A. A., and Tezduyar, T. E., 1994 , “Mesh Update Strategies in Parallel
Finite Element Computations of Flow Problems With Moving Boundaries and
Interfaces,” Comput. Methods Appl. Mech. Eng.,119(1–2), pp. 73–94.
[67] Stei n, K., Tezduyar, T., and Benney, R., 2003, “Mesh Moving Techniques for
Fluid–Structure Interactions With Large Displacements,” ASME J. Appl.
Mech.,70(1), pp. 58–63.
[68] Karypis, G., and Kumar, V., 1999, “A Fast and High Quality Multilevel
Scheme for Partitioning Irregular Graphs,” SIAM J. Sci. Comput.,20(1),
pp. 359–392.
[69] Bazilevs, Y., Hsu, M. C., and Bement, M. T., 2013, “Adjoint-Based Control of
Fluid–Structure Interaction for Computational Steering Applications,” Proc.
Comput. Sci.,18, pp. 1989–1998.
[70] Texas Advanced Computing Center (TACC) 2013, University of Texas, Austin,
TX, http://www.tacc.utexas.edu
081006-8 / Vol. 81, AUGUST 2014 Transactions of the ASME
Downloaded From: http://appliedmechanics.asmedigitalcollection.asme.org/ on 06/19/2014 Terms of Use: http://asme.org/terms
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Book
Wind Turbines addresses all those professionally involved in research, development, manufacture and operation of wind turbines. It provides a cross-disciplinary overview of modern wind turbine technology and an orientation in the associated technical, economic and environmental fields. It is based on the author's experience gained over decades designing wind energy converters with a major industrial manufacturer and, more recently, in technical consulting and in the planning of large wind park installations, with special attention to economics. The second edition accounts for the emerging concerns over increasing numbers of installed wind turbines. In particular, an important new chapter has been added which deals with offshore wind utilisation. All advanced chapters have been extensively revised and in some cases considerably extended.
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