Simulation of a MW rotor equipped with vortex generators using

Simulation of a MW rotor equipped with vortex
generators using CFD and an actuator shape model
Niels Troldborg∗, Frederik Zahle
∗
Niels N. Sørensen†,
Technical University of Denmark, Wind Energy Department, 4000 Roskilde, Denmark
This article presents a comparison of CFD simulations of the DTU 10 MW reference
wind turbine with and without vortex generators installed on the inboard part of the
blades. The vortex generators are modelled by introducing body forces determined using
a modified version of the so-called BAY model. The vortex generator model is validated
by applying it for modelling an array of VGs on an airfoil section compared to both wind
tunnel measurements and fully gridded CFD.
I.
Introduction
A vortex generator (VG) is an aerodynamic device originally introduced by Taylor,26 which is now
widely used by the aircraft and wind turbine industry for passive flow control.9, 10, 24, 25 It is a small winglet
attached at an angle to the oncoming flow on the suction side of the wing/blade, which generates longitudinal
vortices and thereby causes local mixing of the flow, re-energizing the boundary layer and consequently
delays/prevents flow separation. Therefore, VGs can be used to improve the effectiveness of wings/blades
at high angles of attack. From an engineering point of view, there is a strong need for knowledge on how to
incorporate VGs into the design process at an early stage, in order to choose the size, shape, position and
inclination angles of the VGs. In the design codes used by wind industry today, the influence of equipping an
airfoil section with VGs is incorporated through its modified lift, drag and moment polars. The usual way
to obtain the polars are through wind tunnel experiments, which can be costly and also difficult to perform
at the high Reynolds numbers needed today and for the relatively thick airfoils sections typically used on
modern wind turbine blades.
Alternatively, one can use Navier-Stokes based CFD methods to compute the effect of the VGs.23 However,
due to the large range of scales present for a wing equipped with VGs, it is computationally very costly to
directly simulate a full wind turbine blade equipped with a large number of VGs. To overcome this difficulty
Bender et al.3 developed the so-called BAY model in which the VG is modelled by adding body forces in the
momentum equations thereby removing the need of a mesh around the individual VG. The applied forces
are determined from the Prandtl lifting theory and are normal to the local flow direction, parallel to the
surface and simulates the side force induced by the VG.
The model has been validated and calibrated against both measurements and fully gridded CFD for a variety
of flow cases.1, 3–5, 9 Through these studies the BAY model has proven capable of capturing the effect of the
VG with far fewer grid points than fully resolved (FR) CFD.
In the present work we use CFD and a modified version of the BAY model to simulate the DTU 10 MW
reference wind turbine2 equipped with a span-wise array of VGs on the inner part of the blades and compare
its aerodynamic performance to its baseline design without VGs. As part of the work we initially validate
the modified BAY model by applying it for modelling an array of VGs attached on a FFA-W3-301 airfoil
section and compare it to both wind tunnel measurements and fully gridded CFD.
∗ Senior
Scientist, DTU Wind Energy, 4000 Roskilde, Denmark
DTU Wind Energy, 4000 Roskilde, Denmark
† Professor,
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II.
Actuator VG model
In the present work the VGs are modelled using an actuator VG model, which is based on the BAY
model3 and the actuator shape model.18 The basic idea behind the model is to let the VG be represented by
a lift force which depends on the local flow conditions and the VG shape and is determined using an analogy
to thin aerofoil theory, see Figure 1. In the original formulation of Bender et al.,3 the force applied to a cell,
Figure 1. Sketch of VG with definition of terms in the BAY model
which is intersected by the VG, depends on the ratio of the volume of the cell to the total volume of all cells
that are intersected by the VG.
Here we use a formulation of the model, which is similar to that of Jirásek,5 where the force applied to a
given computational cell, i, is proportional to the area of the intersection between the VG and the cell, i.e.
Li = CV G ρAi |U|2 αeL
(1)
where
eL
=
α ≈
U×b
|U|
cos α sin α =
U·tU·n
|U| |U|
and Ai is the area of the intersection between cell i and the VG and CV G is a calibration coefficient. If
CV G is set to a very high value the flow will be aligned with the VG (α → 0) and consequently Li will be
independent of CV G . Initial studies showed that for CV G > 1, the simulation results were rather insensitive
to CV G and therefore we use CV G = 4 throughout this article.
The forces on the VGs are applied into the computational domain by using the actuator shape model18 and
a modified Rhie-Chow algorithm17 to avoid odd/even pressure decoupling.
III.
Flow solver - EllipSys3D
The VG model has been implemented in the Navier-Stokes flow solver EllipSys3D developed by Michelsen13, 14
and Sørensen.19 This code solves the incompressible finite volume Reynolds-Averaged Navier-Stokes (RANS)
equations in general curvilinear coordinates in a collocated grid arrangement to facilitate complex mesh geometries. In all simulations, the EllipSys3D code is used in steady state mode, running local time stepping
towards a steady state solution. Furthermore, the coupled momentum and pressure-correction equations are
solved using the SIMPLE16 algorithm while the convective terms are discretized using the QUICK8 scheme.
IV.
Validation of the VG model
The modified BAY model is validated by applying it for modelling an array of VGs attached to the suction
side of a FFA-W3-301 airfoil section and compare it to wind tunnel measurements27 and fully gridded CFD.23
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IV.A.
Vortex generator set-up
In the considered configuration the VGs are shaped as delta wings with h = 0.01c, l = 0.038c and with their
leading edge at x = 0.2c, where c denotes the chord of the airfoil. The VGs are positioned in pairs in a
counter rotating configuration with β = ±15.5o, ∆1 = 0.04c and ∆2 = 0.05c, see Figure 2.
Figure 2. Left: Top-down view of the airfoil equipped with an array of VGs. The coloured region indicates the symmetry unit used
in the computations and the incoming flow is from down. Right: A sketch defining the characteristic dimensions of the VG setup
IV.B.
Simulation set-up
The simulation set-up is as in the fully gridded simulations by Sørensen et al.:23 The Reynolds number based
on airfoil chord is Re = 3 · 106 , the turbulence in the boundary layer is modelled using the k − ω SST11
model and laminar/turbulent transition is modelled with the γ −Reθ correlation based transition model.12, 22
IV.C.
Computational meshes
The grids used for the simulations has an O-mesh structure with a radius of approximately 16c. In order
to limit the computational requirements of the fully gridded CFD simulations, only one of the two vanes in
a VG unit was simulated exploiting the geometrical symmetry of a VG unit (see Figure 2). This grid has
Nc = 448 grid cells in the chord-wise direction, Nn = 128 normal to the airfoil and Ns = 64 in the span-wise
direction.
In order to establish the overall requirements for the grid when using the modified BAY model, a grid
sensitivity study was carried out. The study mainly focused on the sensitivity of the model to span-wise
resolution. This was achieved by increasing the span, Ls , of the simulated aerofoil section and hence also
the number of VGs, NV G . The tested grid configurations are listed in Table 1, where G0 represents the grid
used for the fully gridded simulation.
Grid
Nc
Nn
Ns
Ls /c
NV G
G0
G1
G2
G3
G4
448
256
256
256
256
128
128
128
128
128
64
32
32
32
32
0.045
0.045
0.090
0.180
0.360
1
1
2
4
8
Table 1. Grid configurations used for the sensitivity study
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IV.D.
Results
Figure 3 compares the lift and drag curves obtained using the BAY model on different grids with the fully
resolved results. As seen the BAY model predicts the lift quite accurately on all grids. On grid G4 the drag
3.5
0.05
Clean (exp)
VG (exp)
Clean (G0)
VG (FR,G0)
VG (BAY,G1)
VG (BAY,G2)
VG (BAY,G3)
VG (BAY,G4)
2.5
CL
2
1.5
0.04
0.03
CD
3
VG (exp)
Clean (G0)
VG (FR,G0)
VG (BAY,G1)
VG (BAY,G2)
VG (BAY,G3)
VG (BAY,G4)
0.02
1
0.01
0.5
0
0
5
10
15
20
0
0
25
5
aoa
10
15
20
25
aoa
Figure 3. Comparison of lift and drag curves for the FFA-W3-301 aerofoil with VGs obtained on different grids.
is seen to be slightly over predicted at high angles of attack, when compared to the predictions on the other
grids. The simulated drag is seen to be underestimated on all grids in comparison with the measurements,
which is most likely a consequence of not simulating the bed that the VGs are installed on in the experiment.
V.
Simulation of the DTU 10 MW turbine
In this section we simulate the DTU 10 MW wind turbine both with and without an array of VGs
installed on the inboard part of the blades and compare the aerodynamic performance.
V.A.
The DTU 10 MW Reference Wind Turbine
The DTU 10 MW reference wind turbine is a fully open source research turbine design, which includes fully
documented geometry, aeroelastic and structural models as well as 3D CFD rotor meshes. The rotor has a
radius of 89.166 m and uses the publicly available FFA-W3 airfoil series along the entire blade.
V.B.
Vortex generator set-up
The VG configuration is as as shown in Figure 2, where β = ±16o, h = 0.01cmax, l = 0.04cmax, ∆1 =
0.045cmax and ∆2 = 0.055cmax, where cmax = 6.2 m is the max chord of the blade.
The leading edge of the VGs are positioned along a line starting at a chord-wise position of 0.50c at a
span-wise position of r = 5 m and ends at 0.21c at r = 30 m, where c denotes the local chord length. This
yields a total of 40 VG pairs on each blade.
V.C.
Simulation set-up
The rotor simulations used the steady state moving mesh option in EllipSys3D21 and assumed a fully
developed turbulent boundary layer on the blade surface using the k − ω SST11 turbulence model.
V.D.
Computational mesh
The 3D mesh was made on the rotor configured with no prebend, no coning and no spinner and nacelle. The
surface mesh was generated using an automated procedure that uses an in-house set of Python scripts. The
rotor surface mesh consisted of 256 cells in the chord-wise direction and 480 cells in the span-wise direction
with a 64×64 cells tip cap on each blade tip. In the region of the blades where VGs are installed the cell
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length in the span-wise direction is 0.0775 m, corresponding to 8 cells per VG pair in agreement with the
requirements found in section IV.D. Figure 4 shows the rotor surface mesh including the VGs.
The volume mesh was of the O-O type and was generated using the hyperbolic mesh generator HypGrid.20
Figure 4. Left) Surface mesh for the DTU 10MW RWT rotor; Right) Close view of surface mesh at the inboard section with VGs
To obtain a y+ of less than 2 the height of the first cell in the boundary layer was set to 2 × 10−6 m. The
volume mesh was grown away from the surface using 128 cells in the normal direction to form a sphere with
a radius of approximately 1800 m, corresponding to 20 rotor radii.
V.E.
Flow characteristics
In order to illustrate the overall effect of the VGs, Figures 5 and 6 show the surface restricted streamlines
on the blade without and with VGs at a free-stream velocity of 10 m/s. Also included in the plots are the
contours of the tangential component of the vorticity at a cross section through the blade axis. The counter
rotating vortices induced by the VGs are clearly seen from the vorticity contours and the streamlines reveal
that these vortices effectively prevent flow separation causing the flow to be rather two-dimensional here.
The individual vortices generated by the inboard part of the VG row are not visible in the vorticity contours,
which is probably because the VGs here are fully submerged in the boundary layer. As a consequence this
part of the VGs are unable to prevent separation and therefore there is a strong radial flow here as is also
seen on the blade without VGs.
Figure 5. Surface restricted streamlines and tangential vorticity at the inboard part of the clean blade
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Figure 6. Surface restricted streamlines and tangential vorticity at the inboard part of the blade with VGs
V.F.
Rotor performance
Figure 7 compares the normal and tangential forces along the span of the blade with and without VGs at
wind speeds of 6 m/s, 10 m/s and 12 m/s. The VGs cause and increase in both tangential and normal forces
at the inboard part of the blade. Interestingly, the VGs not only affect the inboard region of the blade loads.
For the 6 m/s and 10 m/s cases, the VGs cause a slight reduction in both the tangential and normal forces
on the outer part of the blade compared to the corresponding cases without VGs. At these wind speeds
the rotor is designed to extract maximum energy from the wind and therefore the increased loading near
the VGs may increase the axial induction so that the blade operates at lower efficiency. A similar reduction
in the outboard part of the blade was found by Johansen et al.6 when they redesigned a rotor to extract
more power from the root region. In the 12 m/s case the blade with VGs has higher loads than the clean
blade along almost the entire blade span. The reason that the VGs increase the loads at 12 m/s is that the
blade is pitched at this wind speed to reduce loads and hence the clean blade operates further away from
its optimum. Figure 8 compares the thrust and power curves of the turbine with and without VGs. Below
9000
8000
1400
without VGs
with VGs
1200
12 m/s
7000
1000
10 m/s
6000
F [N/m]
12 m/s
5000
4000
400
3000
6 m/s
10 m/s
200
2000
0
1000
0
0
600
t
Fn [N/m]
800
without VGs
with VGs
6 m/s
20
40
60
80
100
−200
0
20
r [m]
40
60
80
r [m]
Figure 7. Normal and tangential forces along the blade with and without VGs at three different wind speeds.
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100
the rated wind speed of 12 m/s the VGs only marginally increase power and thrust, which is because the
increase in loading near the VGs is accompanied by a decrease in loading on the outboard span of the blades
as shown in Figure 7. The power increase due to the VGs is only 0.25%, 0.51% and 0.41% at wind speeds
of 6 m/s, 10 m/s and 12 m/s, respectively.
From 12 m/s and above the blades are pitched in order to keep the electrical power around 10 M W and
here the VGs therefore increase both thrust and power more significantly. Figures 7 and 8 show that even
1400
12000
without VGs
with VGs
1300
without VGs
with VGs
10000
1200
Mech. power [kW]
Thrust [kN]
1100
1000
900
800
8000
6000
4000
700
2000
600
500
6
8
10
12
14
V [m/s]
16
18
20
0
6
8
10
12
14
V [m/s]
16
18
20
Figure 8. Normal and tangential forces along the blade with and without VGs at three different wind speeds.
though VGs may improve the aerodynamic behaviour locally one the blade one cannot simply attach VGs
on an existing blade design and expect correspondingly higher power since the VGs have a global effect on
the rotor loads. Thus, ideally the layout (shape, spacing, size and position) of the VGs should be integrated
in the design process.
V.G.
Airfoil data
Airfoil data has been derived from the rotor simulations using the azimuthal averaging technique (AAT),7, 15
in which the axial and tangential velocities are extracted in the flow field at a given radius at different axial
locations over an annulus, averaged azimuthally and linearly interpolated at the position of the rotor. The
local angle of attack is then determined as:
α = atan
Vt
− (φ + θp )
Vz
(2)
where θp and φ are the blade pitch and local blade twist, r is the local radius, Ω is the rotational speed
([rad/s]) while Vt and Vz are the tangential and axial velocity in the rotor plane.
The airfoil data was computed with the rotor operating at 10 m/s at the design rotational speed of 8.06RP M
by varying the pitch setting across the range [−16o , 16o] with increments of 4o .
Figures 9-11 show the lift and drag curves with and without VGs at the radial positions r = 18 m, 24 m
and 30 m, with corresponding cross section thickness of approximately 57%, 41% and 34%. Note that the
presented airfoil data for the blade without VGs differ somewhat from those presented by Zahle et al.28 The
reason for the deviations is partly a difference in grid resolution and partly that different methods were used
to interpolate the velocities to the rotor plane in the AAT method.
Despite, the high thickness of the considered sections the lift coefficient is seen to become rather high at high
angles of attack due to the well known 3D effects caused by centrifugal forces in the boundary layer and the
span-wise pressure gradients generated by the Coriolis force. At r = 18 m the VGs do not have a clear effect
on neither lift nor drag in the entire range of angles of attack. The same trend was observed for the sections
further inboard on the rotor and is probably because they are fully submerged in the boundary layer.
At r = 24 m and r = 30 m the VGs increase the lift over a wide range of angles of attack but also cause a
more abrupt stall, which eventually causes a lower lift and higher drag at r = 24 m. For low angles of attack
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the drag is increased by the presence of the VGs but is generally reduced at intermediate angles of attack
below stall.
In future work we will compare the presented airfoil data on the rotor with airfoil data on the same sections
in a non-rotating flow and thereby investigate whether 3D effects are less dominant when VGs are present.
3
0.7
without VGs
with VGs
without VGs
with VGs
0.6
2.5
0.5
2
CD
CL
0.4
1.5
0.3
1
0.2
0.5
0
5
0.1
10
15
aoa [o]
20
0
5
25
10
15
aoa [o]
20
25
15
20
Figure 9. Lift and drag polars for the section at r = 18 m where the airfoil thickness is 57%.
2.2
2
0.4
without VGs
with VGs
0.35
without VGs
with VGs
1.8
0.3
1.6
0.25
D
1.2
C
CL
1.4
1
0.2
0.15
0.8
0.1
0.6
0.05
0.4
0.2
0
5
10
aoa [o]
15
20
0
0
5
10
aoa [o]
Figure 10. Lift and drag polars for the section at r = 24 m where the airfoil thickness is 41%.
VI.
Conclusions
A BAY type vortex generator (VG) model has been presented and applied for simulating both the FFAW3-301 airfoil with a row of VGs and for representing a row of VGs on the inboard part of the blade of the
DTU 10 MW reference wind turbine. The simulations on the airfoil showed good agreement with both wind
tunnel measurements and fully gridded CFD and revealed that a span-wise resolution of 8 grid cells per VG
pair is sufficient to accurately capture the effect of the VGs.
The simulations on the DTU 10 MW turbine showed that VGs may effectively delay flow separation and
therefore can improve the aerodynamic characteristics of the inner part of the blade. However, even though
the VGs may improve the local aerodynamic behaviour of the blade they do not necessarily improve significantly the power production of the turbine since they have a global effect on the rotor loads. Thus, the
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2.5
0.2
without VGs
with VGs
0.18
2
without VGs
with VGs
0.16
0.14
1.5
C
D
CL
0.12
1
0.1
0.08
0.06
0.5
0.04
0.02
0
−5
0
5
10
15
20
0
−5
0
aoa [o]
5
10
15
20
o
aoa [ ]
Figure 11. Lift and drag polars for the section at r = 30 m where the airfoil thickness is 34%.
positioning and configuration of the VGs should ideally be an integrated part of the design process.
Acknowledgments
This work has been funded by the Danish Energy Agency under the EUDP programme within the projects
Overcoming critical design challenges of wind turbines and by the EUDP-2011 II project Demonstration of
Partial Pitch 2-Bladed Wind Turbine Performance as well as the EERA AVATAR project.
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