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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, 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]
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Y. Bazilevs
Department of Structural Engineering,
University of California–San Diego,
La Jolla, CA 92093
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,
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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C2014 by ASME
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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
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:
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
 (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
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
where n1and n2are the unit outward normal vectors to the fluid
and structural mechanics domain at their interface. Note that
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)
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
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
ratio Density
Part t/r(mm) E(GPa) q(kg/m
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
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
/rad, while for 6.0 m/s wind
we find that closs ¼0:23 kg m
/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.
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
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... These methods show significant advantages when being deployed to flow problems with moving interfaces and boundaries. Several recent validations and applications include environmental flows [38][39][40][41], wind energy [28,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60], tidal energy [58,[61][62][63][64][65], cavitation flows [66,67], supersonic flows [68], bio-mechanics [69][70][71][72][73][74], gas turbine [75][76][77], and transportation engineering [23,[78][79][80][81][82]. ...
Full-text available
This paper presents a predictive computational framework for surrogate modeling of pressure field and optimization of pressure sensor placement for wind engineering applications. Firstly, a machine learning-derived surrogate model, trained by high-fidelity simulation data using finite element-based CFD and informed by a turbulence model, is developed to construct the full-field pressure from scattered sensor measurements in near real-time. Then, the surrogate pressure model is embedded in another neural network (NN) for optimizing pressure sensor placement. The goal of the NN-based optimizer is to learn the best layout of a fixed number of pressure sensors over the structural surface to deliver the most accurate full-field pressure prediction for various inflow wind conditions. We deploy the model to a representative low-rise building subjected to different wind conditions. The performance of the proposed framework is assessed by comparing the predicted results with finite element-based CFD simulation results. The framework shows excellent accuracy and efficiency, which could be potentially integrated with structural health monitoring to enable digital twins of civil structures.
... These methods show significant advantages when being deployed to flow problems with moving interfaces and boundaries. Several recent validations and applications include environmental flows [68][69][70][71], wind energy [59,[72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90], tidal energy [88,[91][92][93][94][95], cavitation flows [96,97], supersonic flows [98], bio-mechanics [99][100][101][102][103][104], gas turbine [105][106][107], and transportation engineering [108][109][110][111][112][113]. ...
Full-text available
We present a new computational framework to simulate the multi-phase convective conjugate heat transfer (CHT) problems emanating from realistic manufacturing processes. The paper aims to address the challenges of boundary-fitted and immersed boundary approaches, which cannot simultaneously achieve fluid-solid interface accuracy and geometry-flexibility in simulating this class of multi-physics systems. The method development is built on a stabilized Arbitrary Lagrangian-Eulerian (ALE)-based finite element thermal multi-phase formulation, which is discretized by overlapping one boundary-fitted mesh and non-boundary-fitted mesh with a quasi-direct coupling approach via Schwarz alternating method. The framework utilizes a volume-of-fluid (VoF)-based multi-phase flow model coupled with a thermodynamics model with phase transitions to capture the conjugate heat transfer between the solid and multi-phase flows and the multi-stage boiling and condensation phenomena. The quasi-direct coupling approach allows the exact and automatic enforcement of temperature and heat-flux compatibility at the fluid-solid interface with large property discontinuities. From the perspective of method development, the proposed framework fully exploits boundary-fitted approach’s strength in resolving fluid-solid interface and boundary layers and immersed boundary approach’s geometry flexibility in handling moving objects while circumventing each individual’s limitations. From the perspective of industry applications, such as water quenching processes, the resulting model can enable accurate temperature prediction directly from process parameters without invoking the conventional empirical heat transfer coefficient (HTC)-based approach that requires intensive calibration. We present the mathematical formulation and numerical implementation in detail and demonstrate the claimed features of the proposed framework through a set of benchmark problems and real-world water quenching processes. The accuracy of the proposed framework is carefully assessed by comparing the prediction with other computational results and experimental measurements.
... The interaction of this flow with an energy extracting machine, such as a wind turbine, is complex and thus not easily predictable. Some of these effects can be modelled (Bazilevs et al., 2014) but in complex flow fields the power typically is still estimated based on local velocities and not measured directly (Ge, Gayme, & Meneveau, 2021). ...
Full-text available
The placement of a scaled-down Savonius (drag) vertical-axis wind turbine on model buildings is analysed experimentally by the use of turbine performance and flow field measurements in a wind tunnel. The set-up consists of two surface mounted cubes aligned in the flow direction. The turbine is tested at six different streamwise positions – three on each cube. Velocity field measurements are performed with particle image velocimetry along the centreline of the cubes with and without the turbine. The performance at each position is evaluated based on measurements of the produced torque and the rotational speed of the turbine. It is demonstrated that the common practice of estimating wind resources based on the urban flow field without the turbine present is insufficient. The turbine has a substantial influence on the flow field and thus also on the available power. The performance is found to be optimal in the front and centre of the first building with a significant drop-off to the back. This trend is reversed for the downstream building. Holistically, for more generic geometries and varying wind directions, the results suggest the central position on a building is a good compromise.
... FSI model becomes the preliminary effort for a better understanding of H-Darrieus WT for components elastic deformations and self-starting issues of the turbine (Bazilevs et al. 2014). The transient response of this system at inflow wind speed was 11.4 m/s and considers three initial rotor speeds: 0 rad/s, 4 rad/s, and 12 rad/s. ...
Full-text available
The wind is one of the most promising green energy resources that replenishes itselves in less than a human lifetime without depleting the planet’s resources. According to the disposition of the blade concerning the shaft, wind turbine can be classified as horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT). In contrast to VAWT, HAWT covers most commercial installations around the globe. However, VAWTs became a promising alternative for areas far away from grid-connected electricity, they have certain drawbacks associated with aerodynamic performance. The present work overviews the magnitude of factors affecting the aerodynamics of typical VAWT, i.e H-Darrieus VAWT and enhancement options associated with cutting edge performance. Additionally, the accuracy of the turbine performance predicting tools through computational investigation and optimization was also assessed. Therefore, the review covered the factors that altered the turbine performance and viable enhancement options studied in the existing literature. Finally, FSI simulation was tics of materials commonly used for turbine blade manufacturing. It was determined that the computational tools employed significantly influence the accuracy of the model, and proper model selection and more experimental validations are compulsory. It was determined that the computational tools employed significantly influence the accuracy of the model, and proper model selection and more experimental validations are compulsory.
... This flag-wind interaction is a general example of fluidstructure interaction problems [1,2]. It has several applications such as energy harvesting [3,4], wind turbines [5], naval ships [6], etc. In addition, the FIM is being used to remove the heat from the hot elements with the most recent developments by increasing the convective heat transfer [7][8][9]. ...
The paper presents the comparative study of the vortex-induced cooling of a heated channel for the four different cross-sections of the rigid cylinder, i.e., circular, square, semi-circular, and triangular, with or without the rigid/flexible splitter plate at the Reynolds number (based on the hydraulic diameter) of 200. The study presents a comprehensive analysis of the flow and thermal performance for all the cases. For flexible plate cases, a partitioned approach is invoked to solve the coupled fluid-structure-convection problem. The simulations show the reduction in the thermal boundary layer thickness at the locations of the vortices resulting in the improved Nusselt number. Further, the thin plate's flow-induced motion significantly increases the vorticity field inside the channel, resulting in improved mixing and cooling. It is observed that the plate-motion amplitude is maximum when the plate is attached to the cylinder with the triangular cross-section. The power requirement analysis shows that the flexible plate reduces the power required to pump the channel's cold fluid. Thus, based on the observations of the present study, the authors recommend using the flexible plate attached to the cylinder for improved convective cooling.
In this paper, the issue of pitch control in a vertical axis wind turbine was tackled. Programming the Actuator Cylinder model in MATLAB, a theoretical optimum pitch solution was found and then a classic four-bar mechanism was adapted to that theoretical solution to achieve a simple and elegant control of the pitch in the turbine. A simulation using the mechanism worked to find the optimum pitch cycles, where it was found that the mechanism would, in fact, increase the efficiency of the VAWT, by at least 11% and in the best case, over 35%. Another aspect that is studied is the possibility of self�start of the turbine by only changing the pitch on the blades. This analysis, however, proved that a further individual pitch control must be used to surpass the cogging torque. All analyses conducted were done for a specific wind turbine that is 2 m2 in the swept area.
Full-text available
We are introducing the Carrier-Domain Method (CDM) for high-resolution computation of time-periodic long-wake flows, with cost-effectives that makes the computations practical. The CDM is closely related to the Multidomain Method, which was introduced 24 years ago, originally intended also for cost-effective computation of long-wake flows and later extended in scope to cover additional classes of flow problems. In the CDM, the computational domain moves in the free-stream direction, with a velocity that preserves the outflow nature of the downstream computational boundary. As the computational domain is moving, the velocity at the inflow plane is extracted from the velocity computed earlier when the plane’s current position was covered by the moving domain. The inflow data needed at an instant is extracted from one or more instants going back in time as many periods. Computing the long-wake flow with a high-resolution moving mesh that has a reasonable length would certainly be far more cost-effective than computing it with a fixed mesh that covers the entire length of the wake. We are also introducing a CDM version where the computational domain moves in a discrete fashion rather than a continuous fashion. To demonstrate how the CDM works, we compute, with the version where the computational domain moves in a continuous fashion, the 2D flow past a circular cylinder at Reynolds number 100. At this Reynolds number, the flow has an easily discernible vortex shedding frequency and widely published lift and drag coefficients and Strouhal number. The wake flow is computed up to 350 diameters downstream of the cylinder, far enough to see the secondary vortex street. The computations are performed with the Space–Time Variational Multiscale method and isogeometric discretization; the basis functions are quadratic NURBS in space and linear in time. The results show the power of the CDM in high-resolution computation of time-periodic long-wake flows.
Full-text available
We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.
With the increased need for alternative energy sources, wind energy has become a hotly debated topic. Improving the performance of a wind turbine has been a significant focus of study, with several new technologies and designs developed. The aerodynamic performance and structural integrity of a wind turbine are the major variables that demonstrate the turbine's utility. The performance metrics, such as the Power Coefficient and Tip Speed Ratio, indicate the amount of mechanical power that the turbine can create. These parameters are amenable to numerical, computational, and practical estimation. The study presents numerical approaches for estimating the aforementioned parameters, such as the Blade Element Momentum Theory, Actuator Disc Approach, and Single-stream Tube Theory. Similarly, the fundamentals of computational fluid mechanics (CFD) have been covered under computational techniques. The turbine's structural integrity can be investigated using Finite Element Structural Analysis or a Fluid Structural Interaction Study. Wind tunnel testing and other practical approaches have also been considered. Each approach produces different findings, and the accuracy of the numerical and computational methods may be evaluated by comparing their output to the experimental output.
Technical Report
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Fixed pitch Darrieus wind turbines lack the necessary starting torque for stand-alone applications such as positive displacement pumps. Variable pitch 'Gyromills' or 'cycloturbines' in which blades pitch according to a preset schedule of fixed amplitude fail to achieve the desired combination of high starting torque and high efficiency at operating speed, while those with variable amplitude become very complex and expensive. These problems may be overcome by means of a simple and inexpensive variable pitch system in which blade pitch is 'self-acting', i.e. pitch amplitude is governed by a combination of aerodynamic forces on the blade and inertial forces on a stabilising mechanism. The performance of a turbine using this stabilised self-acting variable pitch system has been modelled using an extended double multiple stream tube approach adapted to variable pitch systems. Modelling predicts both a high starting torque and a peak performance significantly superior to that of fixed pitch machines.
Full-text available
We discuss the stabilized finite element computation of unsteady incompressible flows, with emphasis on the space-time formulations, iterative solution techniques and implementations on the massively parallel architectures such as the Connection Machines. The stabilization technique employed in this paper is the Galerkin/least-squares (GLS) method. The Deformable-Spatial-Domain/Stabilized-Space-Time (DSD/SST) formulation was developed for computation of unsteady viscous incompressible flows which involve moving boundaries and interfaces. In this approach, the stabilized finite element formulations of the governing equations are written over the space-time domain of the problem, and therefore the deformation of the spatial domain with respect to time is taken into account automatically. This approach gives us the capability to solve a large class of problems with free surfaces, moving interfaces, and fluid-structure and fluid-particle interactions. In the DSD/SST approach the frequency of remeshing is minimized to minimize the projection errors involved in remeshing and also to increase the parallelization potential of the computations. We present a new mesh moving scheme that minimizes the need for remeshing; in this scheme the motion of the mesh is governed by the modified equations of linear homogeneous elasticity. The implicit equation systems arising from the finite element discretizations are solved iteratively by using the GMRES search technique with the clustered element-by-element, diagonal and nodal-block-diagonal preconditioners. Formulations with diagonal and nodal-block-diagonal preconditioners have been implemented on the Connection Machines CM-200 and CM-5. We also describe a new mixed preconditioning method we developed recently, and discuss the extension of this method to totally unstructured meshes. This mixed preconditioning method is similar, in philosophy, to multi-grid methods, but does not need any intermediate grid levels, and therefore is applicable to unstructured meshes and is simple to implement. The application problems considered include various free-surface flows and simple fluid-structure interaction problems such as vortex-induced oscillations of a cylinder and flow past a pitching airfoil.
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The primal and adjoint, time-dependent fluid—structure interaction (FSI) formulations are presented. A simple control strategy for FSI problems is formulated based on the information provided by the solution of the adjoint FSI problem. A well-known benchmark FSI problem is computed to demonstrate the effectiveness of the proposed technique. Such control strategies as proposed in this paper are useful for computational steering or so-called Dynamics Data Driven Application System (DDDAS) simulations, in which the computational model is adjusted to include the information coming from the measurement data, and control strategies may be employed to computationally steer the physical system toward desired behavior.
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This paper will present a novel concept of a floating offshore wind turbine. The new concept is intended for vertical-axis wind turbine technology. The main purpose is to increase simplicity and to reduce total costs of an installed offshore wind farm. The concept is intended for deep water and large size turbines.
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Full-scale, 3D, time-dependent aerodynamics modeling and simulation of a Darrieus-type vertical-axis wind turbine (VAWT) is presented. The simulations are performed using a moving-domain finite-element-based ALE-VMS technique augmented with a sliding-interface formulation to handle the rotor-stator interactions present. We simulate a single VAWT using a sequence of meshes with increased resolution to assess the com-putational requirements for this class of problems. The computational results are in good agreement with experimental data. We also perform a computation of two side-by-side counterrotating VAWTs to illustrate how the ALE-VMS technique may be used for the simulation of multiple turbines placed in arrays. [DOI: 10.1115/1.4024415]
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Since its introduction in 1991 for computation of flow problems with moving boundaries and interfaces, the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation has been applied to a diverse set of challenging problems. The classes of problems computed include free-surface and two-fluid flows, fluid–object, fluid–particle and fluid–structure interaction (FSI), and flows with mechanical components in fast, linear or rotational relative motion. The DSD/SST formulation, as a core technology, is being used for some of the most challenging FSI problems, including parachute modeling and arterial FSI. Versions of the DSD/SST formulation introduced in recent years serve as lower-cost alternatives. More recent variational multiscale (VMS) version, which is called DSD/SST-VMST (and also ST-VMS), has brought better computational accuracy and serves as a reliable turbulence model. Special space–time FSI techniques introduced for specific classes of problems, such as parachute modeling and arterial FSI, have increased the scope and accuracy of the FSI modeling in those classes of computations. This paper provides an overview of the core space–time FSI technique, its recent versions, and the special space–time FSI techniques. The paper includes test computations with the DSD/SST-VMST technique.
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This is an overview of the new directions we have taken the space-time (ST) methods in bringing solution and analysis to different classes of computationally challenging engineering problems. The classes of problems we have focused on include bio-inspired flapping-wing aerodynamics, wind-turbine aerodynamics, and cardiovascular fluid mechanics. The new directions for the ST methods include the variational multiscale version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid meshes, ST techniques with continuous representation in time, and ST interface-tracking with topology change. We describe the new directions and present examples of the challenging problems solved.
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We present a sequentially-coupled space-time (ST) computational fluid-structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The structural mechanics computations are based on the Kirchhoff-Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.
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.
Conference Paper
This paper deals with the design of a 5MW floating offshore Vertical Axis Wind Turbine (VAWT). The design is based on a new offshore wind turbine concept (DeepWind concept), consisting of a Darrieus rotor mounted on a spar buoy support structure, which is anchored to the sea bed with mooring lines [1]. The design is carried out in an iterative process, involving the different sub-components and addressing several conflicting constraints. The present design does not aim to be the final optimum solution for this concept. Instead, the goal is to have a baseline model, based on the present technology, which can be improved in the future with new dedicated technological solutions. The rotor uses curved blades, which are designed in order to minimize the gravitational loads and to be produced by the pultrusion process. The floating platform is a slender cylindrical structure rotating along with the rotor, whose stability is achieved by adding ballast at the bottom. The platform is connected to the mooring lines with some rigid arms, which are necessary to absorb the torque transmitted by the rotor. The aero-elastic simulations are carried out with Hawc2, a numerical solver developed at Risø-DTU. The numerical simulations take into account the fully coupled aerodynamic and hydrodynamic loads on the structure, due to wind, waves and currents. The turbine is tested in operative conditions, at different sea states, selected according to the international offshore standards. The research is part of the European project DeepWind (2010–2014), which has been financed by the European Union (FP7-Future Emerging Technologies).