Walter
P.
Wolfe
Engineering Sciences Center
Sandia National Laboratories
Albuquerque,
NM
871 85-0836
Stuart
S.
Ochs
Aerospace Engineering Department
Iowa
State University
Ames,
IA
5001
1
CFD Calculations
of
S809
Aerodynamic Characteristics'
Steady-state, two-dimensional CFD calculations were made
for
the
,5809
laminar-$ow, wind-turbine airfoil using the commercial code CFD-ACE.
Comparisons
of
the computed pressure and aerodynamic coeflcients were
made with wind tunnel data from the Delft University
1.8
m
x
1.25
m low-
turbulence wind tunnel. This work highlights
two
areas
in
CFD that require
further investigation and development in order
to
enable accurate numerical
simulations
of
flow about current generation wind-turbine aigoils: transi-
tion prediction and turbulence modeling. The results
show
that the laminar-
to-turbulent transition point must be modeled correctly to get accurate simu-
lations
for
attached $ow. Calculations also show that the standard turbu-
lence model used in most commercial CFD codes, the
k-E
model,
is
not
appropriate at angles
of
attack with $ow separation.
Introduction
In the design of a commercially viable wind turbine, it is
critical that the design team have an accurate assessment
of
the aerodynamic characteristics of the airfoils that are being
considered. Errors in the aerodynamic coefficients will result
in errors in the turbine's performance estimates and economic
projections. The most desirable situation is to have accurate
experimental data sets for the correct airfoils throughout the
design space. However, such data sets are not always avail-
able and
the
designer must rely on calculations.
In
1995,
we began a limited investigation into
the
appli-
cability of commercially available computational fluid
dynamics
(CFD) codes for calculating the aerodynamic char-
acteristics of horizontal-axis wind-turbine airfoils. Because
of
the
limited resources available, we had to limit our study to
one
CFD
code and one airfoil section. In the following, we
present the results to date from this study.
Airfoil
Section
For
this
study, we chose an airfoil whose aerodynamic
characteristics are representative of horizontal-axis wind-tur-
bine (HAWT) airfoils,
the
S809.
The
S809
is a
21%
thick,
laminar-flow airfoil designed specifically for HAWT applica-
tions (Somers,
1989).
A
sketch of the airfoil is shown in Fig-
ure 1.
A
600
mm-chord model of the
S809
was tested in
the
1.8
m
x
1.25
m, low-turbulence wind tunnel at the Delft Uni-
versity
of
Technology. The results of these tests are reported
This work was supported by the United States Department
of
Energy under Contract
DE-AC04-94AL85000.
0.20
r-----l
0.10
e
0.00
x
-0.10
-0.20
I
I I
I
-I
0.00
0.20
0.40
0.60
0.80
1
.00
X/C
Figure
1.
S809
Airfoil Profile
by Somers
(1989)
and
are
used in
this
work for comparison
with the numerical results. Another similarly sized model of
the
S809
was tested at Ohio State University. Our compari-
sons of the two experimental data sets showed that the results
are
essentially identical. In this paper, we do not show error
bars on the experimental data since the original wind-tunnel
data report does not provide error estimates.
The experimental data show that at positive angles of
attack below approximately
5",
the flow remains laminar over
the forward half
of
the airfoil. It then undergoes laminar sep-
aration followed by a turbulent reattachment.
As
the angle of
attack is increased further, the upper-surface transition point
moves forward and the airfoil begins to experience small
amounts of turbulent trailing-edge separation. At approxi-
mately
9",
the last
5%
to
10%
of the upper surface is sepa-
rated. The upper-surface transition point has moved forward
1
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DISCLAIMER
This
report
was prepared as an account of work sponsored by
an
agency
of
the
United States Government. Neither the United States Government nor any agency
thereof, nor any of their employees, makes any warranty, express
or
implied, or
assumes any legal liability
or
responsibility for the accuracy, completeness,
or
use-
fulness
of
any information, apparatus, product, or process disclosed,
or
represents
that its
use
would
not
infringe privately owned rights. Reference herein to
any
spe-
cific commercial
product,
process.
or
service
by trade name, trademark, manufac-
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does
not necessarily constitute or imply its endorsement, mom-
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favoring by the United States Government
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The views and opinions of authors expressed herein do not necessarily state or
reflect those of the United States Government
or
any agency thereof.
to approximately the leading edge. As the angle of attack is
increased to 15", the separated region moves forward to about
the midchord. With further increases in angle of attack, the
separation moves rapidly forward to
the
vicinity of the lead-
ing edge,
so
that at about
20",
most of the upper surface is
stalled.
The S809 profile was developed using the Eppler design
code (Eppler and Somers, 1980a, 1980b). Consequently, the
surface profile is defined by a table of coordinates rather than
by an analytical expression. To obtain the fine resolution
needed for our numerical simulations, we interpolated
between the defining surface coordinates using a cubic
spline.
CF'D Code
Since we could examine only one code, we wanted a
code with capabilities that were more or less representative of
most commercial CFD codes. We looked for the capability to
calculate incompressible, laminarhrbulent, 2-D/3-D, steady/
unsteady flows, and to run on desk-top workstations. For our
calculations, we used a
SUN
SPARC-10. Resource con-
straints forced
us
to look at codes that were currently licensed
for Sandia's computing facilities. We made no effort to find
the "best" CFD code for wind turbine applications.
Based on these criteria and constraints, we selected
CFD-ACE for our studies. CFD-ACE is a computational fluid
dynamics code that solves the Favre-averaged Navier-Stokes
equations using the finite-volume approach on a structured,
multi-domain, non-overlapping, non-orthogonal, body-fitted
grid (CFDRC, 1993). The solution algorithms
are
pressure
based. The code can solve laminar and turbulent, incompress-
ible and compressible, 2-D and 3-D, steady and unsteady
flows. Several turbulence models are available, including
Baldwin-Lomax, Launder and Spalding
k-E,
Chien low-Rey-
nolds number
k-E,
RNG'
k-E,
and
k-o.
The default model is
Launder and Spalding
k-E.
During
this
investigation, we
experienced problems with the
k-o
model. CFDRC was able
to duplicate our results and began an effort to identify and fix
the problem. The
k-o
model, therefore, was not available for
this study. CFD-ACE has the capability to handle domain
interfaces where the number of cells in adjacent domains are
ReNormalization
Group
not equal, although each cell in
the
coarser-grid domain must
exactly interface with an integer number of cells in the finer-
grid domain. This capability was used in our simulations
of
mixed laminar/turbulent flow.
Numerical
Results
Our initial CFD simulations used a C-type grid topology
with approximately
300
cells along the airfoil's surface and
24 cells normal to the surface. The normal grid spacing was
stretched
so
that the cell thickness at the surface gave
y+
2
30.
In the streamwise direction, the wake was modeled with 32
cells. The computational domain extended to
10
chord
lengths from
the
body in all directions. Fully turbulent flow
was assumed using
the
default
k-E
turbulence model. All cal-
culations were made at a Reynolds number of 2~10~.
Figures 2 through
4 show comparisons between the cal-
culated and experimental surface pressure distributions for
angles of attack of
O",
1.02", and 5.13', respectively. The
Cp
comparisons for
0"
and
1'
show reasonably good agreement
over
the
entire airfoil surface, except in
the
regions of
the
laminar separation bubbles. The experimental pressure
distri-
butions show the laminar separation bubbles just
aft
of
the
midchord on both the upper and lower surfaces. They are
indicated by the experimental data becoming more-or-less
constant with respect to
dc,
followed by an abrupt increase in
pressure as the flow undergoes turbulent reattachment. Since
the calculations assume fully turbulent
flow,
no separation is
indicated in
the
numerical results. Figure
4
shows that the
pressure comparison for
5"
is
good except over the forward
half of the upper surface. Here
the
calculation is not ade-
quately capturing the suction-side pressure.
Table 1 compares the aerodynamic coefficients for these
same cases. The predicted lift coefficients
are
accurate to
within 10% and the moment coefficients to within 16%. The
predicted drag coefficients are between 50% and 80% higher
than
the
experiment results. This overprediction of drag was
expected since the actual airfoil has laminar
flow
over the for-
ward half.
Before proceeding with calculations at higher angles of
attack, we made a more detailed analysis of the errors in the
calculated pressure on the forward half of the upper surface
for 5" angle of attack. We ran calculations with all of the
available turbulence models and tried several grid refine-
ments, especially around the nose. The results were essen-
-
Nomenclature
c
chord
Cd
drag coefficient
=
dqS
Cl
lift coefficient
=
UqS
C,
moment coefficient about 0.25~
Cp
pressure coefficient
=
(p-pm)/q
d
drag
1
lift
=
dqcS
pitch moment
y
+
dimensionless sublayer distance
pressure from wall
=
uTy/v
freestream reference pressure
a
angle
of
attack
dynamic pressure
=
p
U,/2
freestream velocity
p
density
friction velocity
=
,/*;
Pw
density at wall
axial coordinate from nose
2,
wall shear stress
normal coordinate from meanline
v
kinematic viscosity
2
2
-1.00
-0.50
$0.00
0.50
1
1 .00
0.00
0.20
0.40
0.60
0.80
1.00
X/C
Figure 2. Pressure Distribution for
a
=
O",
Fully Turbulent
Calculation
-1.00
I
I I
I
1
-0.50
"a,,
X/C
Figure 3. Pressure Distribution for
a
=
1.02", Fully Tur-
bulent Calculation
tially the same
as
those shown in Figure 4. To check the
effects of the fully turbulent
flow
assumption, we also ran an
Euler calculation at this angle of attack. The results are
shown in Figure
5. This comparison shows very good agree-
ment over the forward half of both the upper and lower sur-
faces, indicating that the disagreement in Figure
4 is a result
of assuming turbulent flow over the forward half of the
air-
-1.50
I
I
I
I
1.00
0.00
0.20 0.40
0.60
0.80
1
.00
X/C
Figure 4. Pressure Distributions for
a
=
5.13", Fully Tur-
bulent Calculation
1.00
'
I
I
I I
I
0.00
0.20
0.40
0.60
0.80
1.00
X/C
Figure 5. Pressure Distribution for
a
=
5.13", Euler Calcu-
lation
foil. The pressure at the
tail
of the airfoil shows some error
because the effect of the thickening boundary layer is not
captured. We tried running a fully laminar calculation, but
could not get a converged solution. The laminar flow sepa-
rated on both surfaces at approximately the 50% chord posti-
tions, but because there was no turbulence model, it was
unable to transition and reattach as occurs in the actual flow.
Table
1.
Comparisons Between Calculated and Experimental Aerodynamic Coefficients,
Fully Turbulent Calculations
0
0.1324 0.1469 -145 -10 0.0108
0.0070
38
54 -0.0400 -0.0443
43 -10
1.02 0.2494 0.2716 -222
-8
0.0110
0.0072
38
53 -0.0426 -0.0491 65 -13
5.13 0.7123 0.7609
-486 -6
0.0124
0.0070
54 77
-0.0513 -0.0609 96 -16
3