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Near-wake flow simulation of a vertical axis turbine using an actuator line model

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In the present work, the near‐wake generated for a vertical axis wind turbine (VAWT) was simulated using an actuator line model (ALM) in order to validate and evaluate its accuracy. The sensitivity of the model to the variation of the spatial and temporal discretization was studied and showed a bigger response to the variation in the mesh size as compared with the temporal discretization. The large eddy simulation (LES) approach was used to predict the turbulence effects. The performance of Smagorinsky, dynamic k‐equation, and dynamic Lagrangian turbulence models was tested, showing very little relevant differences between them. Generally, predicted results agree well with experimental data for velocity and vorticity fields in representative sections. The presented ALM was able to characterize the main phenomena involved in the flow pattern using a relatively low computational cost without stability concerns, identified the general wake structure (qualitatively and quantitatively), and the contribution from the blade tips and motion on it. Additionally, the effects of the tower and struts were investigated with respect to the overall structure of the wake, showing no significant modification. Similarities and discrepancies between numerical and experimental results are discussed. The obtained results from the various simulations carried out here can be used as a practical reference guideline for choosing parameters in VAWTs simulations using the ALM.
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Received: 3 April 2018 Revised: 12 July 2018 Accepted: 31 August 2018
DOI: 10.1002/we.2277
RESEARCH ARTICLE
Near-wake flow simulation of a vertical axis turbine using an
actuator line model
Victor Mendoza1Peter Bachant2Carlos Ferreira3Anders Goude1
1Department of Engineering Sciences, Division
of Electricity, U ppsala University, Uppsala,
Sweden
2WindESCo Inc., Boston, Massachuse tts
3TU Delft, Delft University W ind Energy
Research Institute, Delft, The Netherlands
Corres pon den ce
Victor Mendoza, Department of Engineering
Scienc es, Division of Elec tricity, Upp sala
University, Uppsala 751 21, Sweden.
Email: victor.mendoza@angstrom.uu.se
Abstract
In the present work, the near-wake generated for a vertical axis wind turbine (VAWT) was
simulated using an actuator line model (ALM) in order to validate and evaluate its accuracy.
The sensitivity of the model to the variation of the spatial and temporal discretization was
studied and showed a bigger response to the variation in the mesh size as compared with
the temporal discretization. The large eddy simulation (LES) approach was used to predict
the turbulence effects. The performance of Smagorinsky, dynamic k-equation, and dynamic
Lagrangianturbulence models was tested, showing very little relevantdifferences between them.
Generally, p redicted results agree well with expe rime ntal data for velocity and v orticity fields
in representative sections. The presented ALM was able to characterize the main phenomena
involved in the flow pattern using a relatively low computational cost without stability concerns,
identified the general wake structure (qualitatively and quantitatively), and the contribution from
the blade tips and motion on it. Additionally, the effec ts of the tower and struts were investigated
with respect to the overall structure of the wake, showing no significant modification. Similarities
and discrepancies between numerical and experimental results are discussed. The obtained
results from th e variou s sim ulations carried out here c an be use d as a practical refe rence
guideline for choosing parameters in VAWTs simulations using the ALM.
KEYWORDS
actuator line model, dynamic stall model, near wake simulation, vawt, vertical axis wind turbine
1INTRODUCTION
The current trend of the wind energy industry aims for large scale turbines in offshore farms1-3bringing a renewed interest in VAWTs,
since they have several advantages over the conventional HAWTs, and their implementation can potentially mitigate the new challenges that
the offshore environmen t presents. 4-6Th e om ni- directionality of VAW Ts allows th em to wo rk with winds f rom any direction, re sulting in a
simpler mechanical design with fewer moving parts, which excludes the yawing, and often the pitching system. This is a relevant advantage
since a significant amount of failures encountered in HAWTs occur in their yawing mechanism,7-9and it is highly appreciated in an offshore
facility where operation and maintenance have a relatively large contribution in the total energy production cost. Another advantage of the
VAWTs is the fact that the generator can be placed at sea level, reducing the complexity of the installation and maintenance. Additionally, this
characteristic improves the stability of the structure and, moreover, it would reduce the dimension and cost of the base. The concerns abo ut
the size and weight of the generator are minimized, favoring the installation of heavy direct drive generators with permanent magnets. 10 All
these features of VAWTs show higher potentials for scalability, taking into account the operational inconveniences in HAWTs produced by
the yawing system and the generator location. Both European and North American research programs are studying the feasibility of floating
large VAWT.11,12
VAWT operation is characterized by complex and unsteady three-dimensional fluid dynamics, which presents considerable challenges for both
description through measurements and numericalmodeling.13 Moreover, VAWTs are inherently exposed to cyclic variation in the angle of attack,
giving cyclic blade forces which can produce material fatigue damage. As the energy conversion process in VAWTs is based on the variation of the
blade's circulation along its rotation, the produced wake differs significantly to the one created by HAWTs: The near wake structure is strongly
Wind Energy. 2018;1–18. wileyonlinelibrary.com/journal/we © 2018 John Wiley & Sons, Ltd. 1
2MENDOZA ET AL.
dominated by the effects of the vortices produced on the blade tips (end effects) and the angle of attack variations, these create recovery levels
because of the vertical flow transport which is larger than the one produced by the turbulent fluctuation. 14 This characteristic is not present in
HAWTs.
As the interest for designing and analysis of VAW T facilities is increasing, there will remain a need for reliable numerical models to characterize
the VAWTs flow dynamics, thereby correctly predicting the wake recovery and allowing for the precise evaluation of the most efficient turbine
array layouts.
Several models have been tested for the prediction of the important three-dimensional effects in the VAWT wake. For example, fully
resolved body-fitted grid simulations using Reynolds-averaged Navier-Stokes (RANS) turbulence models have shown a satisfactory performance
to characterize the average performance and near-wake structure of the VAWT. However, accuracy depends on the turbulence model.15-19
Nevertheless, these geometrically fully resolved models have large computational costs since they have to solve the governing equations in local
highly refined grid regions close to the blade boundary layers. This fact restricts the implementation of the model for a solution in a large scale
facility (wind farms, fo r example), due to its nonviable calculation time. Another approach is to simulate the blades by using the so-called actuator
line technique, which is an unsteady method that uses an external force model to solve the loads on the blade elements location and apply them
as a body force term into the momentum equation; hence, it excludes the need of solving the boundary layer flow. This fact dramatically reduces
the computational expenses and makes it feasible to run studies of the wake of VAWT and VAWT wind farms.20-23
The present work studies the resulting wake of an H-shaped VAWT using an actuator line model (ALM), identifying the most relevant
aerodynamic phenomena involved. First, the mathematical description of the model is presented together with the description of the studied
VAWT. Then, the obtained results are presented for the spatial and temporal sensitivity in order to evaluate the response of the model to the
variation of the mesh and time discretization, and its influence on the accuracy of the results. Different turbulence models were tested for
analyzing their performance, and therefore, to define the reliability of each one. Additionally, a study of the operational turbine without the struts
and without the tower was carried out for quantifying the contribution of these turbine components on the general wake structure. Simulated
velocity and vorticity fields of representative sections are used for the flow analysis and they were also compared against measurements from a
VAWT performing in the Open Jet Facility (OJF) of the Delft University of Technology, obtaining a good agreement, and for which experimental
activity and results are reported in Tescione et al.24 All the obtained results from the different tests mentioned above can be used as a practical
reference guideline for choosing parameters in VAWTs simulations using the ALM. The model presents stability and accuracy, which makes it a
potential suitable tool in the design of VAWTs for the prediction of the w ake structure.
2METHODOLOGY
The blade force equations were solved using an ALM (a blade element method) coupled to a dynamic stall model (DSM)25;theformersamples
the flow velocity from the Navier-Stokes solver and therefore calculates the angle of attack and relative velocity for each blade element. The
DSM is used to calculate dynamic blade force coefficients, which the ALM uses to impart the body forces back into the flow solver as a body
force term in the momentum equation. A large eddy simulation (LES) model was then used for predicting turbulence effects.
In the present study, the focus was on wake modeling rather than loading or power prediction. For this work, the turbinesFoam library,
developed by Bachant et al26-28 was used for the implementation of the ALM using the OpenFOAM open-source CFD framework. In
previous work, the model had been validated against wind tunnel data for force coefficients in a pitching blade, with reasonable agreement.25
The employed ALM and DSM are described in detail in Bachant et al27 and Dyachuk,29 re spectively, and only a brief descrip tion is
given here.
2.1 Actuator line model
Based on the classical blade element theory, the ALM is a three-dimensional and undsteady aerodynamic model developed by Sørensen and
Shen,30 and it is used to study the flow around wind turbines. In the ALM, turbine blades are divided into n-blade elements that behave
aerodynamically as two-dimensional airfoil profiles. The forces are determined through a dynamic stall model commonly based on empirical data.
The original governing Navier-Stokes equations are filtered for using the LES approach and based on an incompressible fluid case:
ui
xi
=0,(1)
ui
t+
ui
uj
xj
=−
1
p
xi
+2
ui
xjxj
fi
ij
xj
,(2)
where
uiand
pcorresp on d to th e veloc ity and press ure grid- filtered va lue s, re spective ly, is the kinematic viscosity, fithe acting body (blade)
forces and ij is the subgrid scale (SGS) stress defined as ij =
uiuj
ui
uj.
MENDOZA ET AL. 3
The sectional drag and lift coefficients considered in this work are taken from the technical report of Sheldahl and Klimas,31 which is a
well-known database containing the values for a wide range of Reynolds numbers, and these values are used as an input into the DSM. The
coefficients are linearly interpolated from a table, per the local angle of attack; then, combining with the blade element approach the body forces
acting on the blades are determined. A diagram of a cross-sectional airfoil element at radius r in the plane perpendicular to the turbine axis is
depicted in Figure 1. The relative flow velocity Vrel and the angle of attack are obtained for each blade through the geometric relation between
the blade velocity Vblade and the local incident flow velocity Vin which is commonly lower than the asymptotic velocity V:
Vrel =
Vin
It is common to consider the inflow velocity which is placed in the same location of the element. However, in the present work, this is
obtained through the averaged value from defined numbers of local velocity samples in the region around the element, which are symmetrically
To consider the dynamic stall phenomenon and its effect on the drag and lift curves, the Leishman-Beddoes DSM Model32 with the
modifications of Sheng et al33 and Dyachuk29 was employed.
Once the angle of attack and relative velocity are obtained, the blade element lift and drag forces per length unit of spanwise are calculated as
follows:
fL=1
2cCLVrel 2,(4)
fD=1
2cCDVrel 2,(5)
where CLand CDare the lift and drag coefficients, respectively. Both are function of the Reynolds number and the angle of attack. The lift force
is orthogonal to the relative velocity
Vrel and the central axis, while the drag force is parallel to the relative velocity
Vrel .Thechordlengthis
represented by c. An overview of the ALM implementation coupled with the DSM is illustrated in Figure 2
The same procedure is used to obtain the forces from the shaft and blade support arms of the turbine. Once all these forces are calculated for
the actuator lines, they are added as a source of body force per unit of density (under the assumption of incompressibility) in the equation for
the conservation of momentum (Equation 2).
FIGURE 1 Illustration of velocity vectors and forces acting at the cross-section airfoil element [Colour figure can be viewed at
wileyonlinelibrary.com]
FIGURE 2 Flow chart of the actuator line model (ALM) combined with the dynamic stall model (DSM) for every time-step [Colour figure can be
viewed at wileyonlinelibrary.com]
4MENDOZA ET AL.
2.1.1 Force distribution
The applied forces in the ALM must to be distributed smoothly on several mesh cells in o rder to avoid instability produced by high gradients.
A three-dimensional Gaussian kernel is employed for this purpose projecting the source force terms around the element location. This gives a
smoothing function which is multiplied by the computed force on the element location and then imparted on a cell with a distance
rfrom the
actuator line element quarter chord position:
=1
332exp
r
2.
The smoothing width parameter is chosen by the maximum value from three different contributions related to the 25% of the chord length, the
mesh size, and the momentum thickness due to drag force, and it is expressed as follows:
=max c
4,43
Vcell,cCD
2,
where Vcell is the cell volume. M ore d etails about force projec tio n are in B achant et al.27
2.2 Dynamic stall model
The DSM used is able to calculate the unsteady effects for the lift, pitching moment and drag, resulting in the physical description of the
aerodynamics. The presented results in this work correspond for an operating turbine with a tip speed ratio (TSR) of =4.5. Thus, dynamic stall
effects can be neglected while the DSM is implemented regardless of change in conditions. In previous work,25 the model has been tested in
different stall conditions (low, medium and deep), showing good agreement with experimental data.
3SIMULATION PARAMETERS: VALIDATION CASE
An H-shaped VAWT model was studied. Experimental studies for this have been performed in the Open Jet Facility (OJF) of Delft University
of Technology, and it is available in Tescione et al.24 Phase-locked measurements were acquired at the turbine mid span plane and seven
representative vertical planes in order to study the resulting wake. The turbine consists of two rotor blades extruded from a NACA0018 aluminum
airfoil profile of 1 m of height (H), a rotor diameter (D)of1m,andachordlengthof0.06m(c), and it is operatin g un der a free stream in let v elocity
of 9.3 m/s (
V). The blades have a constant rotational speed (Ω) of 800 rpm within a local Reynolds numbers of Re 2.1×105. The attachment
pointisplacedatadistanceof0.4cfrom the leading edge. Two aerodynamically profiled struts NACA0018, with a chord of 0.023 m, make the
connection between the blades and the turbine tower and they are installed at a distance of 0.2 m from the blade tips. The domain consists on a
13.7D×6.6D×8.2Dtest section and an octagonal jet in the inlet with a cross-section of 2.85D×2.85Dand a contraction ratio of 3:1 as it is
depicted in Figures 3 and 5.
A Cartesian coordinate system has been used with the origin placed at the center of the turbine at the equatorial blade plane, such that the x-axis
is pointing positively in the downwind direction. A positive angular rotation in counter-clockwise direction is seen from the top of the turbine.
Figure 3 shows the drawing of the used turbine and the schematic of the blade motion on a VAWT.
The whole turbine geometry has been considered in the numerical analysis including blades, struts, and the central shaft. The used domain of
the study cases has the same geometry as the experimental campaign at the OJF.24 No-slip velocity conditions were considered at the walls.
FIGURE 3 OJF, test turbine, and setup in Tescione et al24 (left), 3D drawing of the simulated VAWT for this study with dimensions in millimeter
(center) and schematic of the blade motion (right) [Colour figure can be viewed at wileyonlinelibrary.com]
MENDOZA ET AL. 5
FIGURE 4 Instantaneous normalized streamwise velocity in the horizontal (left) and vertical (right) middle plane [Colour figure can be viewed at
wileyonlinelibrary.com]
4RESULTS AND DISCUSSION
In this section, obtained velocity and vorticity fields for representative sections are analyzed in order to study the evolution of the wake behind
the operational VAWT. These results have been compared againstthe experimental data. A large eddy simulation (LES) modelwas used to predict
the turbulence effects.
Figure 4 depicts the obtained instantaneous streamwise velocity fields for the whole domain in the horizontal and vertical plane, respectively.
The jet flow at the inlet and its expansion is clearly identified as well as the blockage produced by the operating turbine. The general structure of
the wake is characterized by a vertical shrinking and a horizontal expansion as the flow moves downstream until it breaks to start the recovery
process, the region w here the wake breaks can be identified. The length of the chamber is not large enough to produce the full recovery of the
wake. Stagnation (recirculation) areas are produced around the inlet jet.
4.1 Verification
4.1.1 Spatial sensitivity
A test of the response of the model to the variation in the mesh size has been carried out. Several domain discretizations were tested using
different (maximum) mesh resolutions of D/ 40, D/ 80, D/96, and D/112 cells, corresponding to domains with 1.5×106,8.39×106, 13.5×106,and
FIGURE 5 xzview of the chamber domain, the operational VAWT turbine with the finest refinement region within the blue box (left), a
detailed zoom at the entrance of the chamber (right), and a vertical section showing the different refinement levels of the mesh topology
(bottom) [Colour figure can be viewed at wileyonlinelibrary.com]
6MENDOZA ET AL.
21.1×106mesh cells, respectively. All the discretized domains have the same mesh topology: a uniform hexahedral distribution of cells with local
refinement level of n=4(the cell of reference is divided equally in 23n=4096 sub-cells) in the region close to the rotor of the turbine and
which is gradually surrounded by zones with lower refinements levels, in order to capture the wake details where it is produced. This topology
was kept constant and globally refined: The mesh has been proportionally scaled in all the coordinates. The finest refinement region covers
0.9Dand 3.3Dfrom the central shaft to the negative x-direction (upwind) and x-direction (downwind). It equally covers 0.9Dfrom the origin in
both horizontal y-directions perpendicular to the incoming flow and 0.8Dfrom the equatorial blade section in both vertical z-directions. Figure 5
shows the whole computational domain with its dimensions and details of the employed mesh topology.
Figure 6 reveals the variation on the obtained results for the streamwise velocities varying the size of the mesh discretization for diff erent
sections of the domain. All curves have good agreement with the experimental results; there is not a considerable improvement in the accuracy
by increasing the mesh resolution. However, it is observed that the curves are more irregular in shape when using a bigger mesh size because the
model is able to capture more details from the wake with the finer discretization.
Figure 7 shows the angle of attack and normal force response during one revolution for simulated values, varying the number of mesh points
of the domain. There is a small difference in the results for the values of azimuthal angle close to 90. Th ere is an ev ide nt trend to a c on vergence
with the increasing of the mesh resolution for the obtained results of the angle of attack.
FIGURE 6 Comparison of the spanwise (top) and vertical (bottom) profiles of the normalized mean streamwise velocity at different downstream
sections xD, for domain meshes with D/80, D/96 and D/ 112 cells [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 7 The angle of attack (top) and normal force (bottom) response for domain meshes with D/80, D/ 96, and D/112 cells [Colour figure
can be viewed at wileyonlinelibrary.com]
MENDOZA ET AL. 7
FIGURE 8 Contours of normalized out of plane vorticity for the horizontal plane using different discretization of the domain [Colour figure can
be viewed at wileyonlinelibrary.com]
FIGURE 9 Comparison of the spanwise (top) and vertical (bottom) profiles of the normalized mean streamwise velocity at different downstream
sections xD, for maximum Courant numbers equal to 0.25, 0.5, and 0.95 [Colour figure can be viewed at wileyonlinelibrary.com]
Figure 8 depicts the vorticity field for two dif ferent discretized meshes. The larger mesh resolution produced better simulation of the vortices
created by the blades, which are essential for identifying and representing the far wake recovery (in open sites, for example).
4.1.2 Temporal sensitivity
Another concern for validating the model is the temporal sensitivity verification. Different maximum Courant numbers (Co)valueswerechosen
for a varying temporal discretization test: Co =0.25, 0.50 and 0.95. In this study, a mesh with D80 cells was used. The variation of the obtained
angle of attack is evaluated for one revolution using the different Co. The maximum Courant number limit is given by Courant-Friedrichs-Lewy
(CFL) condition, necessary for the convergence: Its value should be lower than unity. On the other hand, small time-step discretization could carry
numerical instabilities due to the fluctuation of the flow fields resolving the transient term
t.ForthecaseusingCo =0.25, the time discretization
is such that the blades do not move more than one grid cell per time-step in the mesh region with local refinement. When the streamwise velocity
profile s fro m Fig ure 9 are compared w ith Figure 6, th e results were more s ensitive for varying the mesh size than the time- step discretization.
Previou s wo rks carried out by Bacha nt27 and Mendoza25 showed the same characteristic. There is no relevant difference on the obtained fields
between the case with Co =0.25 and 0.5, results start to differ for Co =0.95, and therefore, the latter is not a recommended value to work
with since it could affect the accuracy on the results.
Regarding the blade response during one revolution, Figure 10 reveals that there is a small change in the value of the angle of attack for
the azimuthal angles close to 90, which is the same behavior as was shown in the spatial sensitivity study (Figure 7). Nonetheless, the change
is less sensitive for the temporal discretization test. In the second half of the revolution (between 180and 360), there is a more pronounced
variation between the different results, specifically in the case using Co =0.95. This can be produced by the influence of the change in temporal
8MENDOZA ET AL.
FIGURE 10 The angle of attack (top) and normal force (bottom) response for maximum Courant numbers equal to 0.25, 0.50, and 0.95 [Colour
figure can be viewed at wileyonlinelibrary. com]
FIGURE 11 Comparison of the spanwise (top) and vertical (bottom) profiles of the normalized mean streamwise velocity at different
downstream sections xD, for Smagorinsky, dynamic k-equation, and dynamic Lagrangian turbulence models [Colour figure can be viewed at
wileyonlinelibrary.com]
discretization ove r the resulting f low fro m the first half o f the revolution within the rotor. T hese curve s have be en obtaine d using th e values from
the last revolution of the different cases.
4.1.3 Turbulence model comparison
Thre e dif fe rent turbulence models have bee n tested in order to evalu ate their performanc e and acc uracy: S magorinsky, 34 dynamic k-equation,35
and dynamic Lagrangian.36 In the latter model, the Smagorinsky constant Csis dynamically computed based on the information provided by the
resolved scales of motion with a Lagrangian-concept averaging procedure, while in the standard Smagorinsky model, Csis a chosen value which
for this study is equal to 0.17.
The comparison of the obtained velocity profiles in Figure 11 shows a small difference between the individual models and good agreement
with experiments for all of them.
It is shown in Figure 11 that for the dynamic Lagrangian case, the results slightly differ from the other turbulence model. However, this
variation is not relevant and it cannot be considered either as an improvement or diminishment in terms of the accuracy.
MENDOZA ET AL. 9
FIGURE 12 The angle of attac k (top) and normal force (bottom) respo ns e fo r one revolution using dif fe rent turbulence mod els [Colou r figure
can be viewed at wileyonlinelibrary.com]
FIGURE 13 Comparison of the spanwise profiles of the normalized absolute velocity fluctuations at different downstream sections xD,for
Smagorinsky, dynamic k-equation, and dynamic Lagrangian turbulence models [Colour figure can be viewed at wileyonlinelibrary.com]
Figure 12 shows a similar pattern in the variation of the angle of attack and normal force using any of the models, there are no considerable
differences. Therefore, the variation in the resulting velocity field (Figure 11) is dominated by the effect of the turbulence models and not by the
force prediction.
Another group of essential quantities for characterizing the wake structure is the turbulence-related statistics. In Figure 13, the spanwise
profile of the root-mean-square of absolute velocity is shown for different downstream locations. These profiles have two maxima in every
studied section, which are located in the edges of the wake and are produced by the unsteady shed vorticity from the blades.37,38 Numerical
results show a good representation of the profiles in terms of the trend. However, there is a lack in the representation of the fluctuations close
to the center of the wake in the first studied sections (xD=0.75,1.0and 1.25). It can be considered that there is no one better model in terms
of performance, since all of them have good accuracy with no distinguishably difference. Nevertheless, the dynamic k-equation and Lagrangian
models perform better in the profile peaks with some overestimation of them in the further sections. The standard Smagorinsky model predicts
lower velocity fluctuations due to the big value considered for Cs, which produces excessive damping of turbulence fluctuations.
4.2 Model validation
Once the response of the model for varying the mesh size, time discretization, and turbulence approach have been tested, a series of simulations
were carried out using the following configuration: a mesh with a resolution of D/ 80 cells for the spatial discretization, since it fulfills the LES
turbulence and ALM domain resolution requirements. A maximum Courant number of 0.25 in order that the blades move one cell per time-step.
10 MENDOZA ET AL.
The LES Smagorinsky approach has been chosen for the turbulence effect prediction due to its low computational cost, and because this work
focuses on the modeling part of the velocity field rather than the turbulence levels. The obtained results are presented in the following sections,
and these are the average of phase-locked instantaneous velocity and vorticity fields.
4.2.1 Horizontal plane
Velocity and vorticity components are compared between numerical and experimental values. Figures 14, 15, and 16 depict the obtained fields
for Ux,Uy,andz, which represent the streamwise velocity, cross-stream velocity, and out-of-plane vorticity components, respectively. The plots
of the experimental values are placed at the left and the simulated ones at the right side of the figures. The field values have been normalized
using the asymptotic velocity and the chord length in order to facilitate the analysis and comparison. The lateral structure of the wake is identified
and, theref ore, the contribution from the blade pitch motion on it as well.
From Figures 14, 15, and 16, it can be noticed that there is a general good agreement for the wake prediction in the whole studied region,
including the rotor region (0.5xD0.5). A pronounced wake is created by the rotating shaft of the turbine, and this wake is slightly
inclined toward the y-direction. The simulated wake has a lower lateral expansion (in the y- axis direction) compared with the experimental one.
This can be due to the lack of mesh resolution for reproducing a proper shed vorticity from the blades. An asymmetric wake behavior is revealed
FIGURE 14 Normalized streamwise velocity in the horiz ontal middle plane fo r exp erimen tal (left) and nu merical (righ t) results [Co lour figure can
be viewed at wileyonlinelibrary.com]
FIGURE 15 Normalized cro ss-stream ve locity in the horizontal middle plane fo r experimental (left) and numerical (right) results [Colo ur figure
can be viewed at wileyonlinelibrary.com]
FIGURE 16 Normalized out-of-plane vorticity in the horizontal middle plane for experimental (left) and numerical (right) results [Colour figure
can be viewed at wileyonlinelibrary.com]
MENDOZA ET AL. 11
in both experimental and simulated resu lts w ith a larger regio n of v elocity de ficit in the y-direction. This can be produced by tw o different main
contributions: vortex shedding and the momentum transport.39 First, stronger vortex she dding and therefore more sev ere f low separation is
produced where the blades move in the opposite direction of the main flow (y>0). Second, the wake flow is transported to the y-direction due
to the lower pressure produced by the blade wake in this region and the strong angular momentum in the downstream side which drags the wake
flows. Figure 15 shows the lateral velocity field characterized by a flow transportation more pronounced in the y-direction.
A smaller region of higher wake deficit (UxV0.2) is pre sent in th e sim ulated re sults. Fu rther, the numerical streamwise velocities are
larger than the experimental results in the outer region of the wake (UxV=1.1). Vortical structures generated by blades are dissipated along
the main flow direction. Vortices structures were well simulated in the downwind direction after the rotor with more accurate size and location
in the negative y-direction region (yD0). Experimental and numerical results showed a smoothly effect due to their averaging process.24 A
good representation of the inner rotor wake and its interaction with the blade was made by the simulation. There is a uniform flow pattern within
the rotor region and this is disturbed by the blade motion path and previously by the shaft.
ItisshowninFigure16thatthechosenkernelwidthis too big. Comparing experimental and numerical results, a smaller value w ould
produce shed vortical structures that match better the experiments. However, running simulations with such a small is too expensive in terms
of computational cost.
4.2.2 Vertical planes
Figures 17, 18, an d 19 reveal th e normalized streamwise, cross- stream, and vertic al ve loc ity comp on ents, respective ly, f or diffe rent represen tative
sections in the vertical plane (yD=−0.5,0.4,0.2,0,0.2,0.4, and 0.5), allowing us to represent and identify the vertical structure of the
wake in terms of size, position and geometry, and also, the influenc e of the vorticity from the blade tips on it. As in the previous section, results
FIGURE 17 Normalized streamwise velocity at different representative sectio ns in the vertical plane for experimental (left) and numerical (right)
results [Colour figure can be viewed at wileyonlinelibrary.com]
12 MENDOZA ET AL.
FIGURE 18 Normalized cross-stream velocity at different representative sections in the vertical plane for experimental (left) and numerical
(right) results [Colour figure can be viewed at wileyonlinelibrary.com]
are normalized using the asymptotic velocity and the chord length. In general, a good agreement with experimental values could be obtained in
all the regions of every section. A better numerical representation can be noticed at the region close to the rotor, and it loses concordance in the
more distant areas. Vortical structures from the blade tips are well represented, specially in the sections close to the vertical middle plane (y/ D0)
and they are dissipated along the main flow direction (Figure 19). Their position is similar for both results, but the size is underestimated in the
numerical cases as it was for the horizontal plane, giving as a result a smaller expansion of the wake in both vertical and horizontal directions
compared with the experimental data. Therefore, the simulated wake has a lower extension and intensity of the wake deficit. Pronounced effects
by the shaft of the turbine on the wake can be identified in the middle vertical plane (yD=0) for the streamwise velocity component, it is
shown that the flow is strongly decelerated (color blue), starting at the location of the shaft xD=0.
Figures 18 and 19 are used for an inner wake analysis. The cross-stream flow shows the lateral expansion of the wake with the velocity
components pointing outwards the middle plane: red colored areas in the positive y-direction and blue colored areas in the negative y-direction.
The cross-stream velocity has low values (close to zero) in the upper regions (z-direction) outside of the wake. The overall structure of the wake
is well represented by the simulated values. How ever, there are quantitative discrepancies, these are related to force prediction issues as was
mentioned previously. The magnitude values of lateral and vertical velocities are more pronounced in the rotor region (0.5xD0.5)
where the incoming flow fac es the turbine and is blocked. From the vertical velocity plots, it is noticed that numerical blade tips vo rtices have
an inclination produced by the outer wake flow. On the other hand, experimental results show that the same vortices kept the vertical structure
within the rotor region.
Figure 20 s hows the cro ss-stream vorticity created by the turbine. The vortical structures produced b y the two b lade tips are similar in the
position for both experimental and numerical results, but they differ in the shape. This can be inferred from their magnitude, propagation, and
dissipation within the flow. Vorticity produced in the struts position (zD=0.3) is also observed but with lower intensity for experimental
MENDOZA ET AL. 13
FIGURE 19 Normalized vertical velocity at different representative sections in the vertical plane for experimental (left) and numerical (right)
results [Colour figure can be viewed at wileyonlinelibrary.com]
results. A pronounced vortical structure is generated by the tip of the tower which is clearly identified in the vertical middle plane (yD=0).
A weaker blade tip vorticity representation was made by the simulation in the section yD=−0.5. Again, as in the horizontal plane study, it is
observed an oversized kernel width in the numerical results.
4.3.1 Struts and tower influence
A test of the influence of the struts and tower in the obtained fields was made. Three simulations were carried out: the complete turbine
including all the components, removing only the struts and removing only the tow er. Figure 21 depicts that the results have a good agreement
with experimental values for all cases, w hich shows the main contribution for the wake structure is made by the blades.
The Figure 22 reveals the streamw ise velocity component in different sections perpendicular to the main flow for the studied cases. The
absence of the tower is easily identified in the region close to yD=0. A strong blockage is present where the blade moves in the opposite
direction to the flow (yD0.5) resulting in a wake expansion for this region, which increases in the downwind direction. The obstruction of the
flow by the tower (central axis) is also captured and this keeps centered outside the wake. A considerable asymmetry was observed. The major
blockage effect occurs in the cases with the complete turbine and removing the struts. In general, the blockage profiles have the same shape
(geometry) with some variations within the wake; therefore, the influence of the struts and tow er are not relevant in the overall structure.
The normal forcesin one blade forthe different studied cases are revealed in Figure 23. In allcases, the major concentration of normal forces is
located in the region between the struts and for the azimuthal position between 0and 90, when the blade faces directly in opposite direction to
the incoming flow . For the case without considering the tower, its absence is noticed in the azimuthal blade position around of 270where there
14 MENDOZA ET AL.
FIGURE 20 Normalized cross-stream vorticity at different representative sections in the vertical plane for experimental (left) and numerical
(right) results [Colour figure can be viewed at wileyonlinelibrary.com]
is no region with almost zero value of forces (white color)as in the other cases. There is not a properrepresentation of the strut-blade joint effects
within the results, since it is expected to have a reduction on the normal forces acting over the blades around (and between) the joints region.
Figure 24 reveals the influence of the tower in the streamwise velocity component. A lower blockage and the total lack of the wake produced
by the tower are appreciable in its absence. There is no relevant difference in the size and shape of the wake comparing the cases with and
without tower.
The response to the variation in the pitching angle of the blades was looked at this study. The blades of the operating turbine were pitched 1
from the leading edge towards the inside of the rotor. The test was made using the coarser discretization of the domain. Figure 25 depicts the
streamwise velocity profiles in representative sections. Due to the pitching, the resulting wake has a bigger lateral expansion in the y-direction;
however, these horizontal changes are not relevant in the general structure. Nevertheless, there is a relevant modification in the vertical wake
structure, it has a more pronounced shrinking compared with the test results without pitching blade. Therefore, the model is highly sensitive to
the variation of the sampled angle of attack for the force prediction.
4.4 General discussion
The results of 3D simulations presented herein show good agreement with experimental results.. However, the ALM is a simplified model which
can represents the overall structure of the wake but there are some underestimation in the proper representation of the vorticity created by the
MENDOZA ET AL. 15
FIGURE 21 Comparison of the spanwise profiles of the normalized mean streamwise velocity at different downstream sections xD,considering
the complete turbine, without the struts and without the tower [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 22 Normalized streamwise velocity at diff erent repres entative sections perpend icular to th e flow , considering the co mplete turb ine
(top), without the struts (center) and without the tower (bottom) [Colour figure can be viewed at wileyonlinelibrary.com]
blade tips and the struts, resulting in a less accurate simulated vertical wake expansion. The authors presume this could be caused by the high
sensitivity that the model shows for the force prediction. In general, a numerical underestimation of the flow blockage by the rotor allowed the
incoming flow to dissipate earlier the resulting operation turbine effects.
Considering all the presented results, there is a better model performance in the horizontal representation of the wake in the negative
y-direction zone. The flow within the rotor has been properly reproduced by the model, capturing the flow blockage produced by the tower and
blade motion. Regarding the resulting velocity field, there is no sign of wake recovery until the further studied sections (xD=2), since the
velocity deficit was still considerable. In terms of the blade force distribution, the joint of the struts with the blades was not considered by the
model; therefore, an improvement on the model force predictions is needed.
A proper prediction of the angle of attack is essential for a proper model performance. It has been shown that a variation in one degree of
the pitch angle can produce a signif icant difference on the obtained results; moreover, the model is not that sensitive to the variation on the
16 MENDOZA ET AL.
FIGURE 23 3D normalized normal force distribution over the blade considering the complete turbine (left), without the struts (center) and
without the tower (right) [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 24 Normalized streamwise velocity in the horizontal middle plane for numerical results with (left) and without (right) considering the
tower [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 25 Comparison of the spanwise profiles of the normalized mean streamwise velocity at different downstream sections xD, for a domain
mesh with D/80 cells without blade pitching (left) and with a blade pitching of 1(right) [Colour figure can be viewed at wileyonlinelibrary.com]
mesh size, te mp oral disc retization o r turbu len ce m odel. Therefore, all the parameters th at are relate d to th e angle prediction must be correctly
implemented (as the flow curvature effects, blade attachment point, flow velocity sampling, etc).
It should be highlighted that one of the main advantage of the presented model may be the relatively low computational cost compared with a
similar work carried out with a 3D full body resolved model.
MENDOZA ET AL. 17
5CONCLUSIONS
A 3D actuator line model was used to simulate the resulting near wake of an operational VAWT, capturing the most relevant phenomena. This
included the main characteristics of the flow pattern such as the horizontal expansion and vertical shrinking of the wake, velocity deficit regions
(flow deceleration), inner-wake interaction with the blades, and vortical structures creation from blade pitching and tips.
The model was validated against measurements from an operational H-shaped VAWT, for which experimental activity has been performed at
the Open Jet Facility (OJF) of TU Delft, showing good qualitative and quantitative agreement in general.
The model was tested in terms of the spatial and temporal sensitivity. Even using coarse meshes for the discretization of the domain did give
acc urate results , the details of th e flow o f the vortical stru ctures h ow ev er, w ere n ot accoun ted for. The results w ere n ot sign ificantly influenced
by changing the temporal discretization.
Three different turbulence models were used showing similar performance. It could not be claimed which one was the best for the simulations.
For all the studied cases, the model did not show instabilities issues in the whole domain. The main structure of the resulting wake was not
significantly affected by removing either the tower or the struts, which verifies that these parts do not contribute.
All the results obtained from the tested cases show the potential of the applied ALM for VAWTs simulations, which can then be used a
reference practice guideline for choosing the propers parameters. The model showed numerical stability, which makes it a suitable for application
in VAWTs simulations.
ACKNOWLEDGEMENTS
This work was conducted within the STandUP for Energy strategic research framework and is part of STandUP for Wind. The computational
works we re pe rfo rmed on resource s pro vided b y the Swedish Nation al Inf rastruc ture f or Computing (SNIC) at NSC.
ORCID
Victor Mendoza http://orcid.org/0000- 0001- 5006- 9231
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How to cite this article: Mendoza V, Bachant P, Ferreira C, Goude A. Near-wake flow simulation of a vertical axis turbine using an
actuator line model. Wind Energy. 2018;1–18. https:// doi.org/10.1002/ we.2277
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The current trend of the wind energy industry aims for large scale turbines installed in wind farms. This brings a renewed interest in vertical axis wind turbines (VAWTs) since they have several advantages over the traditional Horizontal Axis Wind Tubines (HAWTs) for mitigating the new challenges. However, operating VAWTs are characterized by complex aerodynamics phenomena, presenting considerable challenges for modeling tools. An accurate and reliable simulation tool for predicting the interaction between the obtained wake of an operating VAWT and the flow in atmospheric open sites is fundamental for optimizing the design and location of wind energy facility projects. The present work studies the wake produced by a VAWT and how it is affected by the surface roughness of the terrain, without considering the effects of the ambient turbulence intensity. This study was carried out using an actuator line model (ALM), and it was implemented using the open-source CFD library OpenFOAM to solve the governing equations and to compute the resulting flow fields. An operational H-shaped VAWT model was tested, for which experimental activity has been performed at an open site north of Uppsala-Sweden. Different terrains with similar inflow velocities have been evaluated. Simulated velocity and vorticity of representative sections have been analyzed. Numerical results were validated using normal forces measurements, showing reasonable agreement.
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Large eddy simulation (LES) is coupled with a turbine model to study the structure of the wake behind a vertical-axis wind turbine (VAWT). In the simulations, a tuning-free anisotropic minimum dissipation model is used to parameterise the subfilter stress tensor, while the turbine-induced forces are modelled with an actuator line technique. The LES framework is first validated in the simulation of the wake behind a model straight-bladed VAWT placed in the water channel and then used to study the wake structure downwind of a full-scale VAWT sited in the atmospheric boundary layer. In particular, the self-similarity of the wake is examined, and it is found that the wake velocity deficit can be well characterised by a two-dimensional multivariate Gaussian distribution. By assuming a self-similar Gaussian distribution of the velocity deficit, and applying mass and momentum conservation, an analytical model is developed and tested to predict the maximum velocity deficit downwind of the turbine. Also, a simple parameterisation of VAWTs for LES with very coarse grid resolutions is proposed, in which the turbine is modelled as a rectangular porous plate with the same thrust coefficient. The simulation results show that, after some downwind distance (x/D ≈ 6), both actuator line and rectangular porous plate models have similar predictions for the mean velocity deficit. These results are of particular importance in simulations of large wind farms where, due to the coarse spatial resolution, the flow around individual VAWTs is not resolved.
Code
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Actuator line modeling library for OpenFOAM. Latest source code freely available from https://github.com/turbinesFoam/turbinesFoam.
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Vertical axis wind turbines (VAWT) can be used to extract renewable energy from wind flows. A simpler design, low cost of maintenance, and the ability to accept flow from all directions perpendicular to the rotor axis are some of the most important advantages over conventional horizontal axis wind turbines (HAWT). However, VAWT encounter complex and unsteady fluid dynamics, which present significant modeling challenges. One of the most relevant phenomena is dynamic stall, which is caused by the unsteady variation of angle of attack throughout the blade rotation, and is the focus of the present study. Dynamic stall is usually used as a passive control for VAWT operating conditions, hence the importance of predicting its effects. In this study, a coupled model is implemented with the open-source CFD toolbox OpenFOAM for solving the Navier-Stokes equations, where an actuator line model and dynamic stall model are used to compute the blade loading and body force. Force coefficients obtained from the model are validated with experimental data of pitching airfoil in similar operating conditions as an H-rotor type VAWT. Numerical results show reasonable agreement with experimental data for pitching motion.
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In a future sustainable energy vision, in which diversified conversion of renewable energies is essential, vertical axis wind turbines (VAWTs) exhibit some potential as a reliable means of wind energy extraction alongside conventional horizontal axis wind turbines (HAWTs). Nevertheless, there is currently a relative shortage of scientific, academic and technical investigations of VAWTs as compared to HAWTs. Having this in mind, in this work, we aim to, for the first time, study the wake of a single VAWT placed in the atmospheric boundary layer using large-eddy simulation (LES). To do this, we use a previously-validated LES framework in which an actuator line model (ALM) is incorporated. First, for a typical three- and straight-bladed 1-MW VAWT design, the variation of the power coefficient with both the chord length of the blades and the tip-speed ratio is analyzed by performing 117 simulations using LES-ALM. The optimum combination of solidity (defined as Nc/R , where N is the number of blades, c is the chord length and R is the rotor radius) and tip-speed ratio is found to be 0.18 and 4.5, respectively. Subsequently, the wake of a VAWT with these optimum specifications is thoroughly examined by showing different relevant mean and turbulence wake flow statistics. It is found that for this case, the maximum velocity deficit at the equator height of the turbine occurs 2.7 rotor diameters downstream of the center of the turbine, and only after that point, the wake starts to recover. Moreover, it is observed that the maximum turbulence intensity (TI) at the equator height of the turbine occurs at a distance of about 3.8 rotor diameters downstream of the turbine. As we move towards the upper and lower edges of the turbine, the maximum TI (at a certain height) increases, and its location moves relatively closer to the turbine. Furthermore, whereas both TI and turbulent momentum flux fields show clear vertical asymmetries (with larger magnitudes at the upper wake edge compared to the ones at the lower edge), only slight lateral asymmetries were observed at the optimum tip-speed ratio for which the simulations were performed.
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To bridge the gap between high and low fidelity numerical modeling tools for vertical-axis (or cross-flow) turbines (VATs or CFTs), an actuator line model (ALM) was developed and validated for both a high and a medium solidity vertical-axis turbine at rotor diameter Reynolds numbers ReD∼106. The ALM is a combination of classical blade element theory and Navier--Stokes based flow models, and in this study both k--ϵ Reynolds-averaged Navier--Stokes (RANS) and Smagorinsky large eddy simulation (LES) turbulence models were tested. The RANS models were able to be run on coarse grids while still providing good convergence behavior in terms of the mean power coefficient, and also approximately four orders of magnitude reduction in computational expense compared with 3-D blade-resolved RANS simulations. Submodels for dynamic stall, end effects, added mass, and flow curvature were implemented, resulting in reasonable performance predictions for the high solidity rotor, more discrepancies for the medium solidity rotor, and overprediction for both cases at high tip speed ratio. The wake results showed that the ALM was able to capture some of the important flow features that contribute to VAT's relatively fast wake recovery---a large improvement over the conventional actuator disk model. The mean flow field was better realized with the LES, which still represented a computational savings of two orders of magnitude compared with 3-D blade-resolved RANS, though vortex breakdown and subsequent turbulence generation appeared to be underpredicted, which necessitates further investigation of optimal subgrid scale modeling.
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The near-wake of a vertical-axis cross-flow turbine (CFT) was modeled numerically via blade-resolved $k$-$\omega$ SST and Spalart-Allmaras RANS models in two and three dimensions. Results for each case are compared with experimental measurements of the turbine shaft power, overall drag, mean velocity, turbulence kinetic energy, and momentum transport terms in the near-wake at one diameter downstream. It was shown that 2-D simulations overpredict turbine loading and do not resolve mean vertical momentum transport, which plays an important role in the near-wake's momentum balance. The 3-D simulations fared better at predicting performance, with the Spalart-Allmaras model predictions being closest to the experiments. The SST model more accurately predicted the turbulence kinetic energy while the Spalart-Allmaras model more closely matched the momentum transport terms in the near-wake. These results show the potential of blade-resolved RANS as a design tool and a way to "interpolate" experimental flow field measurements.
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Wake characteristics have significant effects on the performance design of standalone turbines and the optimal placement of multiple turbines. In the literature to date, little experimentation has been done on the wake of vertical axis wind turbines (VAWTs), and understanding of such wake is far from adequate. In this work, systematic measurements are presented of both the near and mid-range wake of a five-straight-bladed VAWT in a wind tunnel. The blockage ratio of the VAWT was 1.8%, and no correction of the measured data was required. The wake flow fields were measured up to 10 turbine diameters (10D) to the downstream. The wake exhibited high asymmetry in the horizontal direction. In addition, the wake expanded more in the horizontal direction than in the vertical direction. The causes of the asymmetry were analyzed and discussed through the experimental results. An engineering wake model was proposed to characterize the wake edges and the average velocities. The existence of a pair of counter-rotating vortical structures in the wake was detected. Moreover, the integral length scale was found to steadily grow with the downstream distance. This work contributes to the knowledge of the VAWTs׳ wake and the application of VAWTs in wind farm layout design.