Energy 175 (2019) 278e291
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Steady wind performance of a 5 kW three-bladed H-rotor Darrieus
Vertical Axis Wind Turbine (VAWT) with cambered tubercle leading
edge (TLE) blades
~ o a, Louis Angelo M. Danao a, b, *
Ian Carlo M. Lositan
a
b
Energy Engineering Graduate Program, University of the Philippines Diliman, Quezon City, 1101, Philippines
Department of Mechanical Engineering, University of the Philippines Diliman, Quezon City, 1101, Philippines
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 9 November 2018
Received in revised form
18 February 2019
Accepted 6 March 2019
Available online 11 March 2019
The performance of a 5 kW three-bladed H-rotor Darrieus Vertical Axis Wind Turbine with cambered
Tubercle Leading Edge NACA 0025 blades was established using computational fluid dynamics. 3D
models and simulations of the VAWT were realized using CAD and CAE software, after which postprocessing analyses provided understanding of the VAWT and blade flow physics. Results showed the
TLE to be detrimental to flow and performance of a cambered VAWT. Using torque, lift and drag data, the
cambered TLE VAWT was shown to deviate significantly against the cambered VAWT over one complete
converged rotation. Cambered TLE VAWT blades encounter reduced lift forces and increased drag forces
leading to lowered and eventual reversal of torque values. The z-vorticity and Q-criterion visualizations
further supported the numerical results with the post-processed images showing vortices the size of the
blade chord generated at blade wakes of the cambered TLE. The vortices emanate from the flow separation at the blade crests creeping in at the blade trailing edge at 75 azimuth and reaching halfway
through the blade chord length at 106 azimuth. Spanwise separation was observed to be restricted at
blade crests. The resulting flow degradation translated to the poor performance of the wind turbine.
© 2019 Elsevier Ltd. All rights reserved.
Keywords:
TLE
Camber
VAWT
CFD
1. Introduction
Wind turbine performance, and therefore power generation,
rely heavily on aerodynamics. Airfoils aerodynamically designed
for aircraft have only been adopted as wind turbine blades [1].
Disregarding structural considerations, which presents additional
design variables, blade design alone greatly impacts turbine flow
behavior across a wind stream. Force-velocity analyses of a vertical
axis wind turbine (VAWT) blade across a wind flow as shown in
Fig. 1 generally depicts VAWT performance to be improved by
increasing the lift force FL, decreasing the drag force FD while
optimizing the angle of attack (AOA) a. The turbine blade rotating at
a speed u about an axis of radius R has blade velocity Vb, the
product of u and R, summing up vectorially to a resultant velocity Vr
with the local wind velocity V, which emanates from the freestream
wind velocity U. The blade tangential and normal forces FT and FN,
* Corresponding author. Energy Engineering Graduate Program, University of the
Philippines Diliman, Quezon City, 1101, Philippines.
E-mail address: louisdanao@coe.upd.edu.ph (L.A.M. Danao).
https://doi.org/10.1016/j.energy.2019.03.033
0360-5442/© 2019 Elsevier Ltd. All rights reserved.
respectively, decompose into the forces FL and FD via the resultant
force FR. Overall turbine configuration is likewise a factor to turbine
performance. For the case of rotor solidity, higher solidity VAWTs or
those with three blades perform better than two-bladed counterparts over most of the operating range [2].
The use of motion controls to further improve wind turbine
performance is also a practice. Leading edge slats and flaps are
widely used active controls in airfoils effectively increasing
cambering and improving the flight or flow of the airfoil by
improving lift characteristics [3]. Motion control can also be passive, meaning built-in stationary modifications or immovable parts
attached to a body surface influencing flow dynamics. Cambering
and tubercle leading edge (TLE) are two such passive motion controls [4]. Cambering in airfoils is the modification of its crosssectional symmetry. Whereas a symmetrical airfoil has its top
and bottom cross-sectional profile symmetrical with respect to an
axial or horizontal plane cutting across its centroid, a cambered
airfoil introduces convexity to the profile, so the top and bottom
halves of the airfoil are asymmetric. The TLE, oftentimes referred to
as leading edge serrations, are undulations on the leading edge
formed by the wavelike impression of the protraction and
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retraction of the airfoil profile from end to end of the blade length.
TLE is a biomimetic structure based on the tubercles on humpback
whale (Megaptera novaeangliae) flippers [5].
Cambering has been shown to enhance lift [4,6], improve lift-todrag ratios, delay stall [6], and increase rotor performance [4,6e8]
by increasing torque and thrust values [6,8] of H-rotor Darrieus
VAWTs. Meanwhile, TLE effects vary with VAWT design and operational conditions. Wang and Zhuang [9] effectively applied TLE in a
low tip speed ratio (TSR) setting two-bladed H-rotor Darrieus
VAWT, conducting a parametric computational fluid dynamics
(CFD) study on TLE dimensions of wavelength and amplitude, and
Reynolds number. TLE was shown to generally improve the baseline
VAWT design at lower TSRs, favoring lower wind speeds. At 3 m/s,
0.061 or a 50.1% increase in coefficient of performance (CP) was
noted in the TLE VAWT against the baseline, with increases
lowering non-linearly as wind speeds increase. Flow physics
further revealed the suppression of flow separation and increased
torque in the TLE VAWT due to counter-rotating vortex pairs in the
TLE serrations. Conversely, the results of Bai et al. [10] for a low TSR
three-bladed H-rotor Darrieus VAWT present the TLE to be detrimental to performance in that the thrusts of the VAWT blades with
TLE decreased significantly.
The combined effects of both cambering and TLE have only been
documented in standalone airfoils [11]. TLE and cambering advances post-stall recovery and enhances lift to improve airfoil
aerodynamic performance. Separately, each have been shown
extensively to better airfoil performance.
To improve the lift at a certain angle of attack, a greater camber
is advised [3]. The effective use of camber improves the lift coefficient of airfoils, be they the systematic, serial NACA family of airfoils
or any other airfoil [12].
In airfoils, TLE increases lift and stall angle, reduces drag to delay
separation, and minimizes tip stall to restrict spanwise flow [4].
Hansen [3], along with Wang and Zhuang [9] and Bai et al. [10] for
VAWTs, concluded that keeping the TLE amplitude-to-wavelength
ratio, A/W, low resulted to the best airfoil and VAWT performances, respectively. In other studies, TLE in airfoils were shown to
increase the maximum lift by 4.8%, lift-to-drag ratio by 17.6%, and
decrease induced drag by 10.9% [13], and observed to positively
influence laminar separation or bubble formation near the leading
edge, dynamic stall and tonal noise [14].
279
Fig. 1. Force-velocity analyses of turbine blade across a wind flow.
With limited available research on VAWTs and particularly the
influence of TLE to its performance, this CFD study investigated the
steady wind performance of a 5 kW three-bladed H-rotor Darrieus
VAWT with TLE and cambering as passive motion controls on the
NACA 0025 blades. VAWT research stalled in the 1990s in favor of
the more commercially viable horizontal axis wind turbine (HAWT)
and is only currently gaining momentum. The United States is into
offshore VAWT research having exemplified large scale Darrieus
VAWTs to perform well against similar capacity HAWT equivalents
[15].
Using models like the two-equation eddy-viscosity k-u shear
stress transport (SST) turbulence model, CFD applies time- or
Reynolds-averaging to numerically solve the mass conservation
and momentum equations in three dimensions e the Navier-Stokes
equations e as a function or not of time. This study used the k-u SST
turbulence model because it provides detailed and accurate information in near-wall regions while allowing freestream independence in the farfield [16]. It has been shown to ably predict airfoil
experimental behavior [17], and correctly duplicate VAWT experimental results with 2D and 3D models [2,18].
Besides appropriateness of turbulence model, its agreement
with the CFD VAWT model is needed, to which mesh studies are
pursued for validation and optimization. To match VAWT model
meshes to the corresponding turbulence models, yþ is used as blade
near-mesh quality indicator [18]. With their mesh convergence
study, Zadeh et al. [19] correlated mesh quality with convergence:
Nomenclature
FL
FD
a
u
R
Vb
Vr
V
U
FT
FN
FR
CP
A/W
yþ
c
z
A
W
lift force
drag force
angle of attack
rotational velocity
rotor radius
blade velocity
resultant velocity
wind velocity
freestream wind velocity
tangential force
normal force
resultant force
coefficient of performance
amplitude to wavelength ratio
dimensionless wall distance
blade chord length
blade length along the z-direction
amplitude
wavelength
N
N
rad/s
M
m/s
m/s
m/s
m/s
N
N
N
dimensionless
dimensionless
e
M
M
M
m
L
Ds
u*
y
v
Re
l
Dt
q
N
TB
r
A
Cm
Cl
Cd
CL
CD
PW
characteristic length
first cell height
friction velocity at the nearest wall
distance to the nearest wall
kinematic viscosity
Reynolds number
tip speed ratio
time step
azimuth angle
number of blades
net blade torque
density
area
coefficient of moment
lift coefficient
drag coefficient
corrected lift coefficient
corrected drag coefficient
wind power
m
m
m/s
m
m2/s
dimensionless
dimensionless
s
e
Nm
kg/m3
m2
dimensionless
dimensionless
dimensionless
dimensionless
dimensionless
W
280
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the finer the mesh, the more accurate the solutions and refined the
flow visualizations were.
2. Methodology
2.1. Study framework
Computer-aided design (CAD) and computer-aided engineering
(CAE) software were used to make the VAWT models, run transient
numerical simulations on the models to quantify wind flow parameters needed to compute CP values and other derived quantities, conduct further analyses such as lift and drag characterization,
and post-processing for the comparative performance analyses
between the baseline NACA 1425 (cambered) airfoil VAWT and that
with TLE (cambered TLE). CFD requires proper discretization e
geometry modeling of the design VAWTs and meshing of the fluid
environment e of the domain, solver settings and calculation, and
post-processing.
The VAWT geometry and domain boundaries were constructed
to their actual sizes for use in meshing the fluid environment. The
need to properly discretize the mesh and set its boundary conditions required model validation against baseline experimental and
CFD results of performance curves of similar 5 kW capacity threebladed H-rotor Darrieus NACA XX25 VAWTs from literature [6,20]
in lieu of actual experimental validation. Both the baseline results
have discretized 2D domains. Thus, a transitional 2D model was
first constructed and validated prior the actual CFD studies in 3D.
Starting off with the 2D model, parametric studies on the yþ,
blade node density and time step were performed to optimize
simulation settings. The yþ study resolved the boundary layer requirements of near-wall cells, particularly the cell meshes surrounding and nearby blade surfaces. The node density study
determined a suitable if not optimal cell size distribution near the
critical areas of flow, which are the cells near and adjacent to the
leading and trailing edges of the blades. The time step study optimized the temporal distribution of the wind flow across the VAWT.
It is necessary to set the appropriate node density and time step in
the simulations to fully capture the wind flow regime across the
blades without missing out on key flow phenomena while
computationally offloading the solver.
Performance analyses involved examining the torque results
and determining the CP of the two VAWT models, lift and drag
characterization of the flow, and flow visualizations. These gave
detailed insights into the flow behavior of the VAWT with its
cambered TLE blades.
Solver ANSYS® Fluent® 18 was used for all simulations. A 64-bit
desktop computer with four physical cores, eight threads operating
up to 3.4 GHz frequency, and with 16 Gb DDR4 RAM was used for
the study.
Fig. 2. (a) Isometric and (bed) orthographic views of the cambered TLE blade
geometry.
extruded along the z and ez directions by 0.3 m each so the full test
wing span measured 0.6 m. Each 3D cambered blade was treated as
an infinitesimally small portion of a continuously long blade since
the geometry ends were to be set as symmetric boundary conditions in the mesh. To come up with the TLE surface on the leading
edge, the airfoil profile was lofted along the path of the sinusoidal
wave given by (1) situated along the 0.6 m length span in the z-axis
such that the chord ends on the leading edges of the lofted airfoil
profile coincided with the wave. Equation (1) is a generally
accepted definition of TLE in NACA and VAWT airfoils [3,10].
LðzÞ ¼ A cosð2pz=WÞ
(1)
TLE amplitude was set to 0.02 m and wavelength 0.2 m to keep
the A/W ratio low at 0.1 or the amplitude at 10% of the wavelength.
The wavelength is 4/3 of the chord. The 3D cambered TLE geometry
was likewise treated as an infinitesimal blade unit with both of its
ends terminating in the sinusoidal wave crests. Fig. 2 shows the
isometric and orthographic views of the 3D cambered TLE model
where the resulting modified blade has three tubercles on the
airfoil leading edge. Fig. 3 shows a comparative perspective of the
3D (a) cambered and (c) cambered TLE blades where Fig. 3b shows
the former containing the latter to highlight their geometric
differences.
The computational domain was discretized into the rotor and
stationary farfield sub-grids compliant with the sliding mesh
technique. The rotor sub-grid is a 4.2m-diameter cylinder containing the VAWT geometry with the center hub centered at the
origin of the x-y-z Cartesian coordinate system. This was so as a
significant extension of the fluid around the VAWT rotates with it in
fully developed flows. The rotor sub-grid is contained in a cylindrical opening in the farfield sub-grid, which is dimensioned 30 m
in width and 40 m in length, with the shorter sides to the left and
2.2. VAWT CFD model
The wind turbine designed is a 3.0m-diameter three-bladed Hrotor Darrieus VAWT with airfoil blades having chord lengths of
c ¼ 0.15 m. The baseline cambered airfoil used is NACA 1425 or
NACA 0025 with 1.5% camber. Assumed aerodynamic center of the
airfoil is 0.0375 m from its leading edge along the airfoil chord line.
Pitch angle was set to zero with no provision for pitching
throughout the azimuthal rotation. The geometry foregoes struts
and other blade support structures for faster numerical computations by neglecting drag and blockage effects. Only the center hub
or post, about which the blades rotate, remain in the geometry as it
poses wake effects to a blade downwind.
To generate the three-dimensional (3D) cambered geometry,
the two-dimensional (2D) airfoil shape resting on the x-y plane was
Fig. 3. Perspective views of the (a) cambered TLE blade, (b) overlain blades and (c)
straight cambered blade.
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right of the rotor, and the lengths up and below equidistant to the
rotor. The farfield sub-grid extends up, below and left of the rotor
15 m or five rotor diameters away from the center hub, and to the
right, 25 m away. This configuration allowed for the treatment of
the wind flow across the rotor as an unobstructed stream emerging
from the leftmost end of the farfield and exiting its farthest right.
For the 3D geometry, both the rotor and farfield sub-grids are 0.2
rotor diameter or 0.6 m thick. Fig. 4 shows the dimensioned 2D
geometry.
The rotor and farfield sub-grid domains each necessitated a
unique discretization and thus were meshed separately and
differently. The farfield domain is coarse and fully unstructured
with its domain ends divided into nodes of 1 m spacing while the
circular hole housing the rotor sub-grid is dimensioned to be less
than the blade chord c ¼ 0.15 m or around 0.11 m. All unstructured
mesh cells were generated automatically with the Advancing Front
Ortho algorithm and anisotropic tetrahedral extrusion inherent to
the meshing software. The 2D farfield mesh was generated growing
cells from the circular hole to the domain ends. While fully unstructured, its mesh remained quadrilateral-dominant (quaddominant) with a boundary decay of 0.95 and cell growth of 1.1.
Having a quad-dominant 2D farfield mesh translates to an equivalent 3D mesh largely populated by tetrahedral cells (tets). The 3D
mesh remained a hybrid mesh of tets, prisms, pyramids and hexahedral cells (hexes). The objective of creating quad-dominant and,
consequently, tetrahedral-dominant (tet-dominant) meshes is
reducing the cell population since two or more triangular cells
usually make up a quadrilateral (quad) and reducing the cell population saves on computational time. The 3D farfield volume mesh
also has a cell growth of 1.1 and boundary decay of 0.95. This volume mesh grows out from the 3D domain interior to the seven (7)
surface mesh extents of the farfield e the velocity inlet and pressure outlet surfaces to the left and right, respectively, of the rotor
sub-grid; the wall surfaces up and below the rotor sub-grid; the
two surfaces of symmetry adjacent and perpendicular to the two
walls, and velocity inlet and pressure outlet surfaces; and the circular interface centered at (0, 0, 0) of the x-y-z Cartesian coordinate
system. All surface nodes of the 3D surface planes were discretized
according to the spacings specified for the 2D mesh.
Comprised of inner structured and outer unstructured cells, the
rotor sub-grid involved more detailed meshing. Starting with the
2D domain, three structured mesh control circles or O-grids were
created before growing the cells from the bounds of these control
circles to the extents of the rotor sub-grid as an unstructured mesh.
ANSYS® requires a minimum of 10 structured cell layers normal to a
wall to fully capture shear flow layers [16]. This general
Fig. 4. The dimensioned 2D model geometry.
281
requirement for wall boundary layer simulations holds true for the
k-u SST turbulence model and the VAWT blades experiencing
viscous shear forces were treated accordingly so. This was done by
conducting a yþ study on the rotor sub-grid. The mechanism of
creating O-grid structured meshes involves building layer upon
layer of cells from the wall boundary until the preferred cell layer
thickness, and the cell height of the first cell layer adjacent to the
blade, hereafter referred to as the first cell height Ds, was identified
with the yþ study. The O-grid cell layer thickness also varied
depending on the expansion of the cells based on the yþ.
The yþ defined by (2) is a dimensionless parameter for wallbounded flows that qualifies the mesh ability to model the flow.
It is model-specific and for the k-u SST turbulence model, the
acceptable yþ ranges are 0.1e1, 1 to 5 and 30 to 300 where higher
values yield longer first cell heights and, therefore, coarser meshes.
yþ ¼ ðu*yÞ=v
(2)
þ
A wide range of y values were used in the study. Particularly,
representative yþ values of 0.1, 1 and 30, with the first as baseline,
were used to compute for the Ds values needed in meshing the
control circles of the rotor sub-grid. The yþ study required checking
yþ values of the first cell layer cells after full steady wind simulation
to see if values were within the or out of range. yþ values out of
range mean unacceptable results, disqualifying the mesh. Meshing
of the remaining portion of the rotor sub-grid and farfield domains
proceeded as previously detailed to come up with the 2D VAWT
model prior further simulations. Establishing the correct yþ value
resolves the viscous sublayers of all three VAWT blades, thus
allowing for provisions to coarsen the mesh, which should save
meshing and computational time.
Cell growth and boundary decay from the control circles and
post to the extents of the rotor sub-grid are 1.1 and 0.3, respectively.
These settings ensured the cells grew out from the domain interior
slower than those in the farfield so more cells populated the
domain and complied with the target cell size and skewness.
Average cell size in the rotor sub-grid needed to be less than the
chord length of c ¼ 0.15 m. For cell skewness, the acceptable
average for the mesh is 0.6.
Coming up with the 3D rotor sub-grid mesh involved initially
creating surface meshes on the VAWT geometries e the blades and
post e and then growing the volume mesh from these surface
meshes to those at the extents of the rotor sub-grid. To fully resolve
the boundary layer of each blade in the volume mesh, the same
optimal yþ setting resulting from the 2D domain yþ parametric
study was sought. To attain this yþ setting in 3D, the cells surrounding the blades up to 90 layers were fully structured hexes.
Beyond the 90th hex-cell layer, cells grew out to the extents of the
rotor sub-grid as a fully unstructured mesh of tets and pyramids.
Cell growth and boundary decay in the entire rotor sub-grid followed that of the 2D domain. As to the rotor sub-grid dimensions,
those of the 2D were maintained. Thus, the fluid rotor sub-grid is
cylindrical or an extrusion of the 2D circular domain to a depth of
0.6 m with its cylindrical center at (0, 0, 0) of the x-y-z Cartesian
coordinate system. The optimal node density of the 2D blades were
also imposed on the 3D blades.
In total, 10 surface meshes were created for the rotor sub-grid.
Each blade has one each for its upper and lower cambers. The
post has one. The rest of the surfaces are for the cylindrical ends of
the rotor sub-grid e the rotor interface sliding with the farfield
interface and the two symmetrical circular surfaces. These two
symmetrical circular surfaces have their inside mesh terminate
with the outlines of the post and three blades. The 3D domain is
represented by Fig. 5 where the vertical dimension is blown-up 42
times that of the x and y axes to emphasize the rotor sub-grid
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282
Fig. 5. Dimensions and surface boundary conditions of the 3D domain.
containing the blades.
Also, during meshing, most importantly of the rotor sub-grid,
careful consideration leaned towards the following mesh characteristics: cell size, cell skewness and cell population. As stated, the
average cell size in the rotor domain was kept to less than
c ¼ 0.15 m and cell skewness to z0.6. Cell population was kept in
check as reaching six (6) million cells crashed the solver. Both cell
size and cell skewness conditions promote convergence of results
and therefore computational time advantages.
Gravitational effects, having a negligible influence on the VAWT
operation, was disregarded in the 3D VAWT model.
2.3. Steady wind simulation
The steady wind simulations were transient, pressure-based.
Rotor sub-grid rotation was set to a constant rotational velocity
based on the TSR setting. With freestream wind velocity at the left
end of the farfield domain constant at U ¼ 5 m/s, the rotational
velocity is Vr ¼ 13.33 m/s at the peak TSR l ¼ 4. The right end of the
farfield domain served as pressure outlet while the upper and
lower bounds were set to stationary no-slip wall zones.
To accomplish the sliding mesh setup, the rotor sub-grid
boundary and the circular hole of the farfield domain were interfaced with each other, both interfaces sliding past each other during
rotor rotation to allow flow continuity from the farfield domain
cells to and through the rotor sub-grid. For the 3D domain, the
upper and lower depths with the blade ends were treated as
symmetrical surfaces and set as symmetry zones.
k-u SST turbulence model was used for the transient steady
wind simulations and solve the pressure-based RANS equations.
This model is fit for the low Reynolds number values of the flow
under study averaged to be Re ¼ 4.96 104 at the peak TSR of l ¼ 4.
Default settings of the k-u SST turbulence model were used, with
the Production Limiter option toggled on for turbulence energy
correction in the u equation. Gradient evaluation method was Least
Squares Cell-Based. Pressure, momentum, turbulence kinetic energy and specific dissipation rate interpolating schemes as well as
the transient component were all of second order. Pressure and
velocity were also coupled.
Benchmark validation of both the 2D and 3D models required
the recreation of performance curves by simulating the VAWT over
a TSR range. For the 2D model, TSR range was one (1) to six (6)
taken at one (1) unit increments with half increments between the
TSR values of three (3) and five (5). The 3D model TSR range was
from 3.5 to five (5) at half increments. Each simulation required 10
complete rotor revolutions for the solution and residuals to
converge. Residual convergence was set to 1 106.
The 2D node density study resolved how dense and aggregated
cells should be, more specifically those adjacent to the blade walls
and those running through the leading and trailing edges. Node
density spacing at the leading and trailing edges were set to
0.0002 m. Constraining the cells in the leading and trailing edges
provides better resolution of the area, which are of high curvatures
and angles. Adjustments to this node spacing were done accordingly in response to cell aspect ratio values. The following blade
node densities were considered in the node density study: 100, 210
and 300. Node density of 210 was set as baseline.
The 2D time step study involved the determination of the best
fitted time increment to model the actual fluctuation of the fluid
flow across the domain. To simplify the resolution of the transient
model simulation with respect to the azimuth angle rotation, it was
deemed best to assume a certain degree of rotation as equivalent to
one (1) time step. Three azimuth angle rotations were considered:
2 , 1 and 0.5 . The equivalent time step Dt was computed using (3).
Dt ¼ ð2pqÞ=ð360uÞ
(3)
To select the appropriate time step, the torque results of the fully
converged simulation rotations of all azimuth angle options were
compared. Azimuth angle q ¼ 1 was set as the baseline setting
from which the two azimuth angles were compared to.
2.4. Performance analyses and post-processing
To analyze the performance of the VAWT, it was necessary to
plot the CP values at different TSRs. To compute the mean CP for one
full rotation, the instantaneous coefficient of performance (Cp)
values for the last rotation were averaged. The instantaneous Cp for
each torque value was determined using (4). CP values were then
plotted against the TSR to come up with the performance curve and
relate the performances of the VAWT models.
Cp ¼ ð2N uTB Þ
.
rAV 3
(4)
The net blade torque TB is the sum of the individual blade torques Tb at a time step instance. Individual blade torques were
computed using (5) given the coefficient of moment (Cm) values
monitored individually for the blades throughout the simulation.
The torque results plotted against the time step is the torque chart.
Tb ¼ 0:5rV 2 ARCm
(5)
Lift and drag characterization, along with flow visualizations
from post-processing of the 3D results provided a parametric and
visual understanding of the flow physics of the VAWT. In this regard, the coefficients of lift Cl and drag Cd were also monitored
during the simulations. The monitored values were then corrected
and transformed based on the geometric angle of attack and blade
azimuthal position using Equations (6) and (7). Flow physics offer
detailed representations of the fluid vortices and flow fields in
relation to the numerical results of the study.
.
0:6cV 2r
(6)
.
CD ¼ ½Cd cosðq aÞ þ Cl sinðq aÞ 0:6cV 2r
(7)
CL ¼ ½Cd sinðq aÞ Cl cosðq aÞ
3. Results and discussion
3.1. 2D model validation
The net blade torque measurements of the 2D model validation
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283
Fig. 6. TB values for the 10 rotations of the 2D baseline mesh.
Fig. 8. Individual Tb for the last VAWT rotation.
for convergence at the peak TSR l ¼ 4 with one time step set to
q ¼ 1 are presented in Fig. 6. The torque chart showing all 10 rotations depict cyclical convergence visually noticeable at the
beginning of the fifth rotation.
Fig. 7 supplements this with the overlain net torque curves per
rotation for all 10 rotations showing indistinguishable differences
of the curves from the seventh rotation onwards indicating cyclical
convergence. On average, the cycle-averaged torque during the
ninth rotation varies by 5.0% with that of the last rotation. Besides
cyclical convergence, numerical convergence was also achieved
with all conserved variables falling below the minimum of
1.0 106, indicating acceptability of the results and the CFD
model. The coefficient of performance is CP ¼ 0.32, which is well
within the tolerated range for Darrieus VAWTs [21]. The value is 6%
lower than the results of Bausas and Danao [5] for a similar setup
but is still higher compared to the CP value for their symmetrical
airfoil VAWT. The CP value obtained was averaged for the last VAWT
rotation harnessing from the available wind power of
WP ¼ 229.7 W.
In Fig. 8, breakdown of the net blade torque into the individual
blade torques of the three blades for the 10th or last rotation show
the individual blade torques to be mostly positive throughout the
converged range signifying the positive net performance earlier
noted with the CP and TB values. Here and in succeeding charts with
individual blade references, blade 1 denotes the VAWT blade
initially at azimuth q ¼ 0 or upwind at the start of the rotation,
blade 2 at azimuth q ¼ 120 and blade 3 at azimuth q ¼ 240 . The
same individual blade torque values when overlain by adjusting the
two lagging blades by 120 and 240 accordingly as shown in Fig. 9
show the cyclic nature of steady wind dynamics occurring in one
rotation: all three blades experience the same phenomena at every
azimuthal position.
Besides convergence, the mesh needed checking of yþ values of
blade-adjacent cells. Set to yþ ¼ 0.1 during meshing, monitored yþ
values for the baseline mesh needed to be always within the
acceptable range of 0e1. Fig. 10 is a scatterplot of the last yþ values
of near-wall or blade-adjacent cells for all three blades where all
630 cells for all blades have yþ values within the required range.
Throughout the last converged rotation, these cells had yþ values
oscillating within the acceptable range, signifying the mesh to
successfully model the k-u SST turbulence model and therefore the
VAWT as well.
The baseline 2D mesh shown in Fig. 11 has 54,000 cells in the
mixed-cell rotor sub-grid and 8634 in the fully unstructured farfield sub-grid. Maximum cell edge length in the rotor sub-grid is
0.13601856 m or 0.9c.cC, observed particularly in the unstructured
Fig. 7. Overlain TB chart per rotation of 2D baseline mesh.
Fig. 9. Overlain individual Tb over the last 0 e360 VAWT rotation.
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Fig. 10. Blade yþ values for the last instance of the baseline mesh.
3.1.1. Parametric studies
Simulation runs for the yþ values of 1 and 30 yielded torque
curves departing from the baseline yþ value of 0.1. The same
simulation procedure of 10 complete VAWT rotations at the peak
TSR and time step setting of one time step equivalent to q ¼ 1 was
used. The torque curve of yþ ¼ 1 coincided with that of the baseline
but remained asymptotic and underperforming throughout the
rotation, varying even by 2.1Nm utmost against the baseline at
some point upwind. On average, its torque differed against the
baseline by 21.1%. Those of yþ value of 30 varied by 89.6% on
average against the baseline. Furthermore, both test meshes have
blade-adjacent cell yþ values at the last converged rotation outside
the range limits. The mesh with yþ ¼ 30 has blade-adjacent cell yþ
values below the minimum acceptable of yþ ¼ 30, and the yþ ¼ 1
has values exceeding the maximum of yþ ¼ 5 although numbering
only a few cells in the upwind leeward portion of the flow. As a
result of this yþ study, the baseline mesh was deemed appropriate
for the VAWT model of the study.
3.1.1.1. Node density study. The node density study resulted with
the baseline and 300-node density meshes having torque curves
overlapping e differing by 0.92% on average e throughout the
converged duration of the last two VAWT rotations. Meanwhile, the
100-node density mesh underperformed cyclically compared to the
two, with a mean difference of 6.29% against the baseline. Given the
similarity of results of the baseline and 300-node density meshes
meant the lower density baseline mesh behaved much the same
way with the other, and therefore was adequate to stand in for the
higher density 300-node density mesh.
3.1.1.2. Time step study. For the time step study, the baseline mesh
was run full 10 VAWT rotations using the time step settings of 0.5
and 2 . Using (3), Dt and no. of time steps were 0.000654498s and
1,800, respectively, for q ¼ 0.5 , and 0.002617994s and 7,200,
respectively, for q ¼ 2 . The resulting torque curves showed the
baseline time step and time step setting of q ¼ 0.5 to vary only by
0.0871% suggesting their similarity and therefore interchangeability. Increasing the time step to q ¼ 2 , on the other hand, yielded
an offset torque curve intersecting the baseline every 120 and
differing against it by 12.0% on average, which clearly depicted
deviation between the two. The baseline time step setting, therefore, was useable in place of the lower time step for having similar
converged results in half the computational time. The former runs
twice faster than the latter since at the peak TSR, the baseline mesh
required 3600 time steps and the latter twice this for the same
simulated time duration.
Fig. 11. Baseline 2D mesh showing the rotor and farfield sub-grids, and an O-grid
around an airfoil.
mesh outside the O-grid meshes around the blades. Inside the Ogrids grown to 90 cell layers at 1.1 cell growth, cell dimensions are
in millimeter scales considering the blades have 210 nodes around
each that are spaced 0.0002 m at the trailing and leading edges,
and the first cell height Ds ¼ 5.5,602,360,537 106. Maximum cell
skewness is 0.81149165 at the rotor sub-grid but the averages are
0.22091140 and 0.04304509 for the farfield and rotor sub-grids,
respectively. Also presented are zoom-ins of the rotor sub-grid
and an O-grid where the mesh structure is shown for appreciation of the cell layers, cell growth and other cell properties.
3.1.2. 2D model performance curve validation
Using the baseline mesh as the optimal 2D VAWT model,
simulation runs were performed for the specified TSR settings of
the VAWT to arrive at the CP values over the identified operating
range. Comparing the resulting performance curve of the 2D model
validated its adaptability towards transitioning to the 3D model.
The 2D model performance curve for the TSR test range of l ¼ 1 to
l ¼ 6 is shown in Fig. 12 along with the reference performance
curves where visual comparison of that of the 2D model against the
reference curves show its general agreement to all. While the same
trend can be observed for these performance curves, the output
performance curve of the 2D model specifically conforms to the
CFD results of Bausas and Danao [5] throughout the TSR range
tested. Outside the peak TSR, VAWT performance similarly drops
profoundly to zero at TSR values l ¼ 2 and l ¼ 6. The 2D model was
then apt for adoption into the 3D model serving as basis for the
meshing and simulation procedures.
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Fig. 12. Performance curve results.
3.2. 3D model validation
With the aim of reducing cell count in the 3D model against the
2D, adjustment to its discretization was done accordingly. Nearwall cells around the blades needed compliance to yþ settings
while mesh away from the blades towards the farfield allowed for
compromise. From 2D to 3D, the average cell size inside the rotor
sub-grid was preserved at less than c ¼ 0.15 m. Cell skewness in all
sub-domains was set to 0.6 like that of the 2D model. The farfield
sub-grid mesh, set with a boundary decay of 0.95 and cell growth of
1.1, is coarse and fully unstructured but still tet-dominant. The rotor
sub-grid mesh is mixed-cell in nature. Meshes around the blades up
to 90 cell layers are structured O-type meshes with Ds set to
yþ ¼ 0.1, after which the meshes grow outwards unstructured with
boundary decay of 0.3 and cell growth of 1.1. A cut-up along the x-y
plane of the 3D mesh in Fig. 13 shows the cross-sectional cell distribution in that plane. This is a cross-sectional plane midway of the
volumetric 3D mesh comparable to the planar 2D mesh in Fig. 11.
Fig. 14a moreover shows a perspective view of the same crosssection zoomed-in on the blade and nearby cell structures.
Table 1 details parametric details of the 2D and 3D meshes for
additional feature-for-feature contrast and comparison. While the
maximum skewness of the 3D cambered mesh reached
0.90178168 at a setting of 0.6, this value for some cells of the farfield
sub-grid is insignificant to the performance results as will be
attested to by the succeeding mesh validation. The average of the
parameter at 0.54546740 is also acceptable.
3.2.1. 3D mesh validation
Before model validation, the resulting 3D cambered VAWT mesh
needed mesh validation by comparing blade torque results against
those of the 2D model. Computed individual blade torque results of
the simulation at the peak TSR l ¼ 4 for 10 complete VAWT rotations were shown to converge cyclically. 3D cambered VAWT torque results were lower than that of the 2D model by a factor of 2/3
due to the geometric height of the 3D model at L ¼ 0.6 m. The 2D
model blade depth is taken as unity.
yþ monitoring on blade-adjacent cells have shown that the
mesh sufficiently models fluid flow across the VAWT using the k-u
SST turbulence model. All 4000 hex cells around the three blades in
the last converged rotation have yþ values below 0.6.
3.2.2. 3D model performance curve validation
At the peak TSR l ¼ 4, the performance coefficient was
computed to be CP ¼ 0.30. This value is lower than the 2D model
result, which is expected given the more realistic flow in three
dimensions of the 3D model compared to the 2D. Together with the
CP results from the simulations at the three other TSR values of 3.5,
Fig. 13. 3D mesh of the cambered airfoil VAWT showing the rotor and farfield subgrids, and a zoom-in of the O-grid around an airfoil.
4.5 and 5, the performance curve was plotted as shown in Fig. 12.
While performance deviation also occurs at l ¼ 4.5, values at l ¼ 3.5
and l ¼ 5 were like that of the 2D. Overall, the results are acceptable
given the observable similar trend in the performance curves of
both models.
3.3. Performance analyses of the cambered TLE VAWT
Meshing of the 3D cambered TLE VAWT mesh was procedurally
the same with that of the 3D cambered mesh. To generate a 3D
mesh control circle, a set of O-grid planar meshes along the blade
depth in the z dimension were extruded continuously from trough
to crest, crest to trough, and alternately thereafter until the full
blade length was covered. While procedurally the same with the 3D
cambered mesh, this differed in the creation of five additional
intermediary O-grid meshes to incorporate the TLE surface. The 3D
cambered mesh has a straight leading edge requiring only one Ogrid extruded along the blade depth.
Each 3D mesh control circle of the 3D cambered TLE VAWT
mesh contains 540,000 cells or 180,000 more cells than the 3D
cambered VAWT mesh. Control circle cells are all structured hex
cells, particularly made so in consideration of the yþ requirements
of the k-u SST turbulence model. The perspective view of a control
circle in Fig. 14b gives a visual comparison of the cambered TLE
blade against the cambered blade. Table 2 summarizes the parametric differences of the two 3D meshes.
3.3.1. Cambered versus cambered TLE VAWT performance
The output torque curve for one blade of the cambered TLE
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The cycle-averaged torque of the cambered TLE blade in Fig. 15 is
Tb ¼ 0.24Nm, which is a quarter of the torque generated with the
cambered blade. This value also amounts to a net blade torque of
TB ¼ 0.70Nm. Given an available wind power of PW ¼ 137.8 W, the
TLE modification reduced by 78% to 9.28 W the cambered VAWT
power output of 41.63 W at the peak TSR l ¼ 4 over one full
rotation.
Simulations on the cambered TLE model at the other three TSR
values of l ¼ 3.5, l ¼ 4.5 and l ¼ 5 depict the same trend in
degraded performance as shown in Fig. 12. While the performance
curve shifted its peak to the right, at the higher TSR value of l ¼ 5,
the cycle-averaged torques for all TSR test values do not amount to
more than the cycle-averaged blade torque of Tb ¼ 0.26Nm and the
corresponding net blade torque of TB ¼ 0.79Nm at this new peak
TSR. Detrimental effects of the TLE modification on the performance of the 3D cambered VAWT remained remarkably profound
throughout the TSR test range.
Fig. 14. Zoom-in perspective views of the (a) cambered and (b) cambered TLE blades
showing the structured O-grid volume mesh adjacent and surrounding each blade, and
the surrounding unstructured meshes beyond their control circles.
VAWT simulation is shown in Fig. 15 with that of the equivalent or
coincident blade of the cambered VAWT. This is for a complete 360
rotation; the tenth or last converged rotation. Statistical convergence of results was noted with all equation residuals below the
minimum of 1.0 106. Cyclical convergence of results was also
achieved checking the superimposed individual blade torques and
comparing the last two (2) rotations. yþ values of the 6000 walladjacent cells have also been monitored to be below 0.5, well
within the required range of 0e1, thereby demonstrating successful
modeling of the cambered TLE VAWT with the k-u SST turbulence
model.
3.3.2. Torque analyses
Differences in the performances of the cambered and cambered
TLE VAWTs is visually straightforward in Fig. 15. Both blades follow
the same torque curve path from the start at 1 but depart from each
other at the azimuth angle of q ¼ 55 , therein labeled 2. From 2, the
cambered blade remains trailing linearly towards its peak blade
torque of Tb ¼ 4.57Nm at the azimuth of q ¼ 90 while the TLE blade
had an earlier onset of torque reversal at the azimuth of q ¼ 74 ,
labeled 3. From 3, the torque of the cambered TLE blade dips until
values become negative. This negative trend continues up to the
lowest point of 3.59Nm, labeled 4 in the torque curve, at the azimuth angle q ¼ 106 . The observed progressive declining trend is
linear and the shift in signs of the scalar torque values beginning at
the azimuth angle of q ¼ 74 denotes blade motion reversal from
counterclockwise to clockwise rotation.
After the vertex of the torque curve at 4, moment reversal on the
blade is comparably the reversed linear trend of the previous torque dipping, but instead of a full reversal, the curve experiences a
setback in values in the azimuth angle range of q ¼ 132 and
q ¼ 151. The torque just slightly recovers from then on and between the azimuth angles of q ¼ 180 and q ¼ 360 , labeled 5 to 1,
torque values fluctuate unlike the cambered blade although the
average blade torque Tb over the range of both are the same at
Tb ¼ 0.49Nm.
3.3.3. Lift and drag characterization
Referring again to Fig. 15, during the period labeled 1 to 2 in the
torque curve when both the cambered and cambered TLE blades
have the same torque values, approximately the same lift and drag
forces are experienced by both blades as shown labeled in the plots
of CL and CD against AOA in Fig. 16 and Fig. 17, respectively. The same
points of the torque curve of the cambered TLE blade in Fig. 15 are
therein labeled accordingly in the plots of CL and CD. After point 2,
Table 1
Parametric comparison of the 2D baseline and 3D cambered meshes.
Average Skewness
Maximum Skewness
Maximum Edge Length
Cell population
Farfield
Rotor
Farfield
Rotor
Farfield
Rotor
Rotor
Farfield
Total
Structured
Unstructured
BASELINE/2D MESH
3D CAMBERED MESH
0.22091140
0.04304509
0.68762318
0.81149165
1.3738530
0.13441569
54,000
5865
2769
62,634
0.54546740
0.15526986
0.90178168
0.83047406
1.4051636
0.21503057
1,080,000
586,420
21,253
1,687,673
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Table 2
Parametric comparison of the 3D cambered and cambered TLE VAWT meshes.
Average Skewness
Maximum Skewness
Maximum Edge Length
Cell population
Farfield
Rotor
Farfield
Rotor
Farfield
Rotor
Rotor
Structured
Unstructured
Farfield
Total
Fig. 15. Individual blade torque curve comparison of cambered and TLE blades over
one VAWT rotation at the peak TSR l ¼ 4.
when the blade torque of the cambered TLE blade begins departing
from the baseline, is when the lift coefficient also begins decreasing
and the drag coefficient increasing. Arriving at point 3, the rate of
change of drag coefficient increases and more so after this. The lift
coefficient drops from its 0.80 peak at the azimuth angle of q ¼ 90
to 0.16, 11 after point 4. The cambered blade lift coefficient peaks
higher at 0.87 and 6 after that of the cambered TLE blade peak.
From 3 up to the lowest point in the torque curve at 4, the cambered
TLE blade encounters progressive linear decline in torque due to
drag forces overturning the positive torque component on the
Fig. 16. Lift coefficient against the angle-of-attack plot at TSR l ¼ 4 for the 3D
cambered and cambered TLE VAWTs.
3D CAMBERED MESH
CAMBERED TLE MESH
0.54546740
0.15526986
0.90178168
0.83047406
1.4051636
0.21503057
1,080,000
586,420
21,253
1,687,673
0.54546740
0.15984145
0.90178168
0.86451892
1.4051636
0.24140802
1,620,000
554,642
21,253
2,195,895
Fig. 17. Drag coefficient against the angle-of-attack plot at TSR l ¼ 4 for the 3D
cambered and cambered TLE VAWTs.
blade. The inversely increasing behavior of the drag coefficient and
torque peaks approximately at the maximum negative torque. The
drag coefficient curve of the cambered TLE blade is observed to
peak 5 before the lowest blade torque at 4. Its lift coefficient improves after 4 and continues decreasing to 14.47, past point 5 at
the azimuth angle q ¼ 256 or 76 after 4. The cambered blade only
drops slightly in lift coefficient and, despite the same decreasing
trend starting at the equivalent of point 4 of the cambered TLE
blade, maintains a large gap in magnitude with the cambered TLE
blade lift coefficient up to point 5. Overall, from points 1 to 5, the
only noted differences in the lift coefficient of the two blades are
the advanced peaking and lower peak value for the cambered TLE
blade with the deviation beginning at point 2.
Disparity in the torque reaction to notably abrupt lift and drag
changes, such as the 6 earlier onset of torque reduction on the TLE
blade against an increasing lift and decreasing drag, is attributable
to hysteresis and blade force interactions. From these, it is imminent that lowering the lift and increasing drag reversed the net
moments on both blades, with effects markedly intensified with
the cambered TLE blade.
After 5, lift coefficient of the cambered TLE blade recovers with
the torque so that between points 5 to 1 through Figs. 15e17, the
averages for the blade torque, lift coefficient and drag coefficient
are Tb ¼ 0.49Nm, CL ¼ 0.34 and CD ¼ 0.035, respectively. Except for
its drag coefficient averaged at 0.015, the cambered blade has the
same average lift coefficient with the cambered TLE blade over the
same period as the torque. These make the azimuthal period between points 1 and 5 having marked significant differences in
torque, lift and drag of interest in the proceeding flow visualizations. The Q-criterion and z-vorticity image renderings of the flow
visualizations detail the invisible wind dynamics of crucial
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moments of the flow to support the torque, lift and drag observations herein presented.
Figs. 16 and 17 also show the static airfoil plots of lift and drag
coefficients for a pitching NACA 1425 airfoil where the lift coefficient plot shows the static airfoil to stall earlier than the VAWT
blade equivalents but at a higher peak. Drag values of the static
airfoil are also lower throughout the AOA range and these have all
been due to the more complicated wind dynamics of a VAWT blade.
3.3.4. Flow visualizations
Looking into the vorticity profile of the fluid space surrounding
the blades gave insights into the phenomena happening for azimuths of interest over the VAWT rotation. In Fig. 18, a combined
plot of the Q-criterion and z-vorticity detail flow turbulence in the
3D and 2D domains, respectively. A single-value Q-criterion was
rendered to visualize blade wake turbulence in 3D. The 2D zvorticity plot is inserted midway of the domain along the z-axis,
cutting across the blades and post at z ¼ 0. Fig. 18 compares the
vorticity profiles of the (a) cambered and (b) cambered TLE blades,
which show striking contrast of wind flow at blade wakes of blades
at the azimuth angle of q ¼ 105 , approximately point 4 or q ¼ 106
in the torque, lift and drag plots, which was noted with the lowest
torque value for the cambered TLE blade. At the specified azimuth,
the cambered blade vorticity profile shows streamlined flow
instead of vortex generation at the blade wake as observed with the
cambered TLE blade. Behind the cambered TLE blade are explicitly
massive vortices the size of the chord emanating from just before
its trailing edge. Besides experiencing the maximum negative torque, it is also this time that the cambered TLE blade approximately
experiences the peak drag coefficient. This vortex profile of the
cambered TLE blade proliferates until the azimuth angle of q ¼ 180
or point 5, therewith the large vortices have fully disintegrated, and
flow has again become streamlined like that of the cambered blade.
Thus, at the same Q-criterion vortical scale, the TLE blade has been
shown to generate vortices severely increasing the flow-induced
drag and consequently.
Reducing the blade torque.
There is remarkable similarity of blade wakes in both blade
types between q ¼ 345 and q ¼ 225 . This is the result of both
blades having the same net torque and lift coefficient values between q ¼ 180 to q ¼ 360 or points 5 to 1. Besides generating blade
wake vortices, the TLE modification affects vortex shedding as
depicted by the altered vortex street in the z-vorticity profile. The
altered vortex shedding likewise poses blade torque reduction effects as evidenced by the reduced cambered TLE torque blade at the
azimuth angle q ¼ 269 .
Zoom-ins into the z-vorticity profile at blade level in Fig. 19
illustrate the blade and fluid interactions that cannot be given
focus in Fig. 18. For instance, at the azimuth angle of q ¼ 0 , attached
flow can be observed among all three blades and that the flow fields
along the blade leading edges of both crest and trough of the
cambered TLE blade are more apparent than that of the cambered
blade. The same flow field grows more at the azimuth angle of
q ¼ 55 , at which flow separation from the trailing edge slightly
creeps into the airfoil pressure side of the TLE trough location and
the phenomenon progresses towards the azimuth angle of q ¼ 75 .
At the TLE crests, over the range between these last two azimuth
angles, blade vorticities are markedly the same with that of the
cambered blade. It is therefore suggestive that the torque reduction
observed with the TLE blade between the azimuthal period q ¼ 55
and q ¼ 75 is due to the TLE surface on the leading edge of blade
inducing flow separation.
From q ¼ 75 to q ¼ 105 , when the TLE blade torque moves to its
maximum negative value, the creeping flow separation at the TLE
trough location fully develops. And while at the TLE crest location
turbulence is observed, flow in this location remains attached.
Distinctly, the turbulence observed at the TLE trough location is
massive enough to be as long as the blade chord length. Given flow
remains attached at the TLE crest, turbulence in this part is the
spillover of the turbulence formed at the trough section. Fluid flow
between two crests was contained e spanwise restriction of flow e
and generated turbulence that led to the wake vortices and
detachment of flow from the blades.
3.3.5. TLE performance at different TSR settings
At the different TSR values, the torque output of the cambered
Fig. 18. Vorticity plots using z-vorticity slice at z ¼ 0 and Q-criterion iso-surface of the (a) cambered and (b) cambered TLE VAWTs showing the azimuth of q ¼ 105 , the moment
nearest to the lowest torque value of 3.59Nm at q ¼ 106 for the cambered TLE VAWT blade.
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Fig. 19. Vorticity plots of the cambered TLE and cambered blades for selected azimuth angles.
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TLE VAWT changed accordingly. The individual blade torques, and
net blade torques of the cambered TLE VAWT at the different TSR
settings are presented in Figs. 20 and 21, respectively. In the charts,
the shift in peak TSR to l ¼ 5 of the cambered TLE blade has its
individual and net torque blade values assuming the torque curve
profiles like those of the cambered blade at the peak TSR l ¼ 4. On
average, the cambered TLE VAWT net blade torque values are lower
than that of the cambered VAWT blade by 2.33Nm, thus its lower
performance coefficient of CP ¼ 0.10. The shift does not translate to
any performance improvement and suggests increasing the wind
stream velocity at inlet for optimal flow.
4. Conclusion
Using CFD, the performance of a 5 kW three-bladed H-rotor
Darrieus VAWT with cambered TLE NACA 0025 blades was established. 3D VAWT models were generated and simulations ran using
CAD and CAE software. Thereafter, the VAWT and blade flow
physics were discussed in detail using post-processing analyses
integrating flow visualizations with torque analyses, and lift and
drag characterization.
Transient steady wind flow simulations using the k-u SST turbulence model required 10 complete VAWT rotations each to arrive
at converged results. Coefficients of lift, drag, and moment on all
three blades were individually monitored throughout the simulations. Prior the main objective of performance study, the 3D model
was validated against a transitional baseline 2D model, which itself
was validated against reference studies in lieu of experimental
validation. Using the baseline 2D model, optimal wall yþ setting
was found to be yþ ¼ 0.1. Node density and time step parametric
studies yielded a final 2D model with a mesh consisting of a mixedcell rotor sub-grid with fully structured O-grid control circles
around the blades, and a quad-dominant unstructured cell mesh
from beyond the control circles into the farfield sub-grid, running
at a time step equivalent to q ¼ 1. The 3D equivalent is mixed-cell
as well, with unstructured volume meshes around the extruded 2D
O-grid control circles. Performance curves of both the baseline 2D
Fig. 20. Blade torques (Tb) of the cambered TLE VAWT at different TSR settings.
Fig. 21. Blade torques (Tb) of the cambered TLE VAWT at different TSR settings.
and 3D models showed agreement to reference data despite
coarseness of the 3D meshes, which are at least 26 times more
populated than the baseline 2D mesh.
Torque values of coincident blades for each of the cambered and
cambered TLE VAWTs were shown to deviate throughout a full
converged rotation. The cambered TLE blade behaving similarly
with the cambered blade up to 55 azimuth has earlier onset of
torque reversal at 74 azimuth shown to be caused by the changes
in magnitude and vector of lift and drag forces, and suppression of
torque reaching negative values up to 3.59Nm at 106 azimuth
due to reduced lift forces and increased drag forces. The drag force
overturns the blade rotation. Vorticity plots of the Q-criterion
showed the cambered TLE blade at the moment of lowest torque
value at 106 azimuth generating massive vortices the size of the
blade chord from just before the trailing edge against the streamlined flow of the cambered blade at the same instance. Flow separation reached halfway through the blade chord length from the
trailing edge at this point for the cambered TLE blade as shown by
the blade-level z-vorticity plot. While flow separation already
creeps in at the blade trailing edge at 75 azimuth, flow at the TLE
crests remains attached. Turbulence generated at the cambered TLE
blade troughs then become massive enough to spillover to its
crests, giving rise to the vortices and flow detachment, all of which
relate to flow degradation. Lowering the lift and increasing drag
reversed the net moment on the blade, thus the hysteresis loops of
the lift and drag coefficient plots against the AOA. An altered vortex
street across the cambered TLE VAWT past the VAWT post
encountered by the blade further degraded the performance
downwind.
The cycle-averaged blade torque of the cambered TLE VAWT is
0.24Nm, which is a quarter of that of the cambered VAWT. The
reduction is primarily due to the tubercle curvature at the leading
edge causing large negative torque values upwind of the cambered
TLE VAWT. As a passive motion control structure, the TLE designed
for the cambered NACA 0025 three-bladed H-rotor Darrieus VAWT
has been detrimental to flow that translates to poor performance.
The net blade torque over one rotation of the TLE VAWT at the peak
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TSR is only 9.28 W of blade power. For the available wind power of
PW ¼ 137.8 W, the cambered TLE VAWT has a performance coefficient of CP ¼ 0.07 whereas the cambered VAWT has CP ¼ 0.30. Peak
performance of the former also shifted to TSR l ¼ 5 but without
significance.
The detrimental effects of TLE to the VAWT in study is specific to
the VAWT design and operating conditions set and remains
confined to this study. Restated, this study identified specific parameters such as geometric configurations, and flow and running
conditions detrimental to flow and performance of a VAWT with
cambered TLE blades, but in no way does it discredit other researches, more significantly of those TLE application studies on
VAWTs herein presented. This study showed the TLE, designed
based on recommendations from reference studies, to negate the
performance of a three-bladed H-rotor Darrieus VAWT initially
improved with the incorporation of cambering in its NACA 0025
airfoil blades and operating at the TSR range of l ¼ 3.5 to l ¼ 5 with
l ¼ 4 as peak TSR. The VAWT operates at high TSR values accepting
a steady wind stream of U ¼ 5 m/s, which are realistic values for
wind flow conditions yielding acceptable VAWT performance
efficiencies.
The study builds on previous TLE application studies on VAWTs.
It identifies the need for parametric studies including but not
limited to design, configuration and operating conditions of a
VAWT with cambered TLE blades. Pursuit of further parametric
studies is tantamount to the use of computational resources
beyond capacity of the current computing setup and thus should
form a part of a future endeavor. The study also highlights a CFD
performance study procedure replicable on other alternate VAWT
configurations with blade motion control structures. The procedure
further stands out in its use of 2D model results as benchmarks for
the 3D model, optimizing the 3D model from parametric studies on
a 2D model, and investigating the inherent VAWT flow characteristics with vorticity plots of the Q-criterion and z-vorticity integrated with the detailed torque analyses, and lift and drag
characterization.
Acknowledgment
This work was supported in part by the Department of Science
and Technology of the Republic of the Philippines through a
research grant of its Engineering Research and Development for
Technology (ERDT) Program.
Appendix A. Supplementary data
Supplementary data related to this article can be found at
https://doi.org/10.1016/j.energy.2019.03.033.
291
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