AIAA-87-0111
Vortical Patterns in the
Wake
of
an
Oscillating Airfoil
M.
M.
Koochesfahani, California
Institute of Technology, Pasadena,
CA
AlAA
25th
Aerospace Sciences Meeting
January
12-1
5,
1987lRen0,
Nevada
For pennlssion to copy or republish, contact the American Institute of Aeronautics and
Astronautics
1633
Broadway,
New Yo&, NY
10019
VORTICAL
PAlTERNS
IN
THE
WAKE
OF
AN
OSCILLATING AIRFOIL
1)
M,
M.
Koochesfahani
Caiifornia Institute of Technology
Pasadena. California
Abstract
Sinusoidal oscillation of an airfoil has been
The
vertical
flow
patterns
in
the
of
a
the traditional form of periodic oscillation
NACA
0012
airfoil pitching
@t
small amplitudes are
theoretically, numerically and
studied
in
a
low
speed
water
channel.
It
is
shown
experimentally. In the present work. the effect
that
a
great
deal
of
control,can
be
exercised
on
of both sinusoidal and nonsinusoidal shape of the
the
structure
of
the
wake
by
the
control
of
the
waveform on the vortical patterns in the wake of
a
frequency,
amplitude
and
also
the
shape
of
the
pitching airfoil
is
investigated. Qualitative
waveform.
An
in
features are determined from flow visualization
this
study
has
been
the
existence
of
an
axial
flow
pictures. Laser Doppler velocimetry
is
utilized
along
the
cores
of
the
wake
vortices.
Estimates
to obtain quantitative measurements of the mean
of
the magnitude of the axial flow suggest a
streamwise velocity component. Using the velocity
linear dependence on the oscillation frequency and
profiles, the dependence of the airfoil
drag/thrust on the oscillation amplitude and
rnpli tude
.
frequency
is
determined. The existence of
an
axial flow along the cores of the wake vortices
is
Introduction
pointed out.
Its
origin and dependence on the
oscillation amplitude and frequency are discussed.
The classical unsteady aerodynamic theory of
oscillating airfoils'
**
was developed as a result
Experimental Facility
5
Instrumentation
of interest in aircraft flutter problem. This
theory later found extensive use in These experiments were performed in the Low
biofluiddynamics since the propulsion of certain Speed Water Channel of the Graduate Aeronautical
species of birds, insects and aquatic animals
is
Laboratories of California Institute of Technology
characterized by a heaving and pitching motion of (GALCIT). The airfoil
was
based on the NACA
0012
a high aspect ratio wing or fin3
*4
.
The main wing section with a chord of
C
=
8
cm, a span of
ingredients of the classical analysis are the b
=
39
cm
and
was
pivoted about the 1/4-chord
two-dimensional potential flow along with point. The airfoil
was
fitted with end plates
linearized boundary conditions,
small
perturbation since, due to mechanical linkage requirements, the
velocities and the assumption of a planar vortex span was smaller than the channel width (45 cm).
wake. The effects of non-linear processes such
as
A
shaker coil mechanism in conjunction with a
rolled-up wake patterns have been addressed using closed-loop feedback servosystem drove the airfoil
numerical techniques5
-7
.
to the desired angular position in pitch (see
figure
1).
With this setup, the airfoil angular
1n comparison with the many theoretical and position followed a command
signal
which, for
numerical studies that have been devoted
to the these measurements, originated from a function
subject of oscillating airfoils, there appear to generator (HP3314A). The mean angle of attack.
be
quite few experimental results available. the amplitude
A.
the frequency f
,
and the shape of
Among the available experimental investigations, the oscillation waveform could, in this
way,
be
most have concentrated on measuring the forces on independently controlled.
oscillating wings8
-'
,
while studying the
characteristics of the wake seems to have received
lesser attention.
Bratt's" smoke flow
visualization of the vorticity roll-up in the wake
of a
wing
performing rolling oscillation
is
one of
the earliest works on wake flow patterns and has
9k
been used for verification of the numerical
&toil
-+
Ez.-
rmcFlcr
Oat
n
techniques mentioned above.
pootion
B
C
&tory
Wri&
OiftuUatiol
Tmmduar
*
Present address: Department of Mechanical
Engineering, Michigan State University, East
Lansing,
MI
48824. Member
AIAA.
Fig.
1
Schematic of servosystem for control of
Copyright
O
American Institute of Aeronautics
mad
Astronmutics, Inc.,
1987.
All
rights resewed.
airfoil angular position.
1
Tb.e effect of nonsinusoidal osciilation 1s
demonstrated
In
terns of
a
symmetry
parameter.
S.
&xch
1s
rile
percentage of
a
period (in 'one cycle)
reqiilred to reach the maximum amplitude starting
from
the
minxmum
amplitude.
When
S=50!:
the
waveform
1s
sinusoidal where=
a value of
S
larger
(smaller) than
50%
corresponds to a slower
(faster) rate of pitch-up than pitch-down. See
figure
2
for
sample waveform shapes.
The wake flow
was
vlsuallzed using
food-coloring issued from small injection tubes
Imbedded in the airfoil t$ailing edge and was
subsequently recorded on photographic film by a
35
cam
camera. The streamwise component of the
velocity vector was measured by a single-channel.
frequency-shifted laser Doppler velocimeter
(LDV)
In the dual scatter mode. The Doppler burst was
processed by a
Track+ng Phase-Locked Loop
(in-house design by P.E.
Dimotakis) whose output
frequency
was
measured by a Real Time Clock card
interfaced to a PDP-11/73 computer.
Results
11
Discussion
For the results reported here, the
free-stream velocity was
approximately
U,
-
15 cmlsec, resulting
in
a chord Reynolds
number of
12,000 and a reduced frequency of
k
=
2nfC/2U,
=
1.67 (f/Hz).
The
mean angle of
attack was set to zero so that the angle of attack
of the airfoil varied between
-A
&
A, A
being the
amplitude of pitch waveform.
The sequence of pictures in figure
3
shows
the dependence of the wake structure on the
oscillation
frequency for a sinusozdal
(S=50%)
pltch waveform. The flow is from right to left
and the downstream distance visible on the
photographs corresponds to approximately
3.75
chord lengths. It
can
be
seen
that. at
low
frequencies, a smoothly undulating wake is formed
which carries the
Karman vortices shed by the
natural wake.
At
higher values of the frequency,
the wake displays characteristic vortex patterns
similar to those observed
by
Bratt" and Thomas
&
h%iffeni2. Numerical calculations of Katz
&
WeihsL3 have suggested a value for the critical
reduced frequency, k
9
2.
above which the wake
rolls up into vortex structures.
Even though this
value agrees with the data of figure
3,
caution
should
be
exercised
in
this comparison. We have
generally observed that the frequency for vortex
roll-up decreases as the oscillation amplitude
Increases. One would expect a similar behavior to
exist in numerical
calculations. Therefore, the
use of a universal critical reduced frequency does
not seem to have much significance.
d-L/-f'J''--
s
=
--*
33r
S
I
50%
5
=
65%
Flg.
2
Examples of pitch waveforms
Upper trace
:
airfoll angular position
Lower trace
:
command
signal.
(a)
A
=
4
deg., f
=
0.5
Hz
(b)
A
=
4
deg., f
=
1.85
Hz
(c)
A
=
2
deg., f
=
4.0
Hz
id)
A
=
2
deg.,
f
=
5.0
Hz
(e)
A
=
2
oeg.,
f
=
6.0
Hz
Fig.
3
Wake of a
NACA
0012
airfckl pitching
sinusoidally about 114-chord point. Flow is from
right to left.
.5
1.
B
1.5
u/u*
Fig.
4
Mean velocity profile at
X/C
=
1
for the
case in figure 3(b).
Figure 3(b) shows a special case where two
vortices of the
same
sign are shed on each
half-cycle of the oscillation. The mean velocity
profile for this case. figure 4, shows that this
vortex pattern corresponds to a double-wake
structure. The pattern remained stable
(i.e.
fixed pattern) all the way to the farthest
downstream distance
(X/C
*
30) at which the wake
was observed.
A
similar stable configuration
could not be sustained at low amplitudes
(e.g.
less than
2
degrees).
At
higher amplitudes.
it
was possible to generate a stable pattern
consisting of three same-sign vortices shed per
half-cycle of the oscillation.
Fig.
5
Mean velocity profiles in the wake of a
sinusoidally pitching
NACA
0012 airfoil
(X/C
=
1).
the alternating vortices are positioned exactly on
a
straight line
as
seen in figure 3(c). The
vortex pattern showed no tendency to deviate from
this alignment
as
it
moved downstream.
As
a
result of this, the mean velocity profile,
U,
measured at X/C
=
3
(not show here)
was
also
approximately uniform at the free-stream value
much the same way
as
at
X/C
=
1
(see figure
5).
Note that this implies that the gradients of
U
in
both streamwise and transverse directions are
nearly zero for this special case.
The mean velocity profile
U(y) can
be
used to
estimate the mean streamwise force on the airfoil.
With the usual normalization of the force with the
Once the frequency
is
high enough, an
alternating vortex pattern
is
formed such that the
free-stream dynamic head and the airfoil chord.
the force coefficient
is
given by
vortex with a positive (counter-clockwise)
circulation
is
located on top and the one with
negative circulation on the bottom, see
figure
3(d,e). This arrangement
is
opposite that
of a typical Karman vortex street observed in
wakes and. in fact, this pattern corresponds to a
"jet". The mean velocity profiles measured at
X/C
=
1,
shown in figure
5,
also confirm this
behavior. In this figure,
it
can be seen that the
usual wake profile with velocity deficit
(i.e.
an
airfoil
with
drag) can
be
transformed into a wake
with velocity excess (no longer a wake but
actually a jet.
i.e. an airfoil with thrust)
above a certain frequency.
It
should be noted
that the jet-like vortex pattern corresponding to
a
thrust-generating body
is
a well-known
phenomenon and
was
described by Von Karman
&
Burgersx4 for the case of a flat plate in
transverse oscillation.
Figure
5
also shows that there exists
a
condition (A=2 degrees, f=4 Hz) at which the wake
has no momentum deficit or excess
(i.e. an
airfoil with no drag). This condition occurs when
where the contributions due to the fluctuating
quantities and the pressure term have been
neglected.
A
negative value of
CF
corresponds to
drag and a positive value implies thrust.
A
plot
of
CF
versus reduced frequency
is
shown in
figure
6
for two oscillation amplitudes of two and
four degrees. The classical theory1 indicates
that the
inviscid oscillation of
a
flat plate
around the
114-chord point starts producing thrust
at
a
critical reduced frequency of about
k
=
1,
We note, however, that in the present experiment
thrust
is
produced at a higher reduced frequency.
This discrepancy may be expected since here there
is
a substantial viscous drag to bf? overcome,
which does not of course exist in the
inviscid
case. Also, within the linear assumptions of the
theory, the oscillation amplitude doe's not affect
the predicted critical value of k, in disagreement
with the data of figure
6.
Even though one might
(a)
A
=
2
deg., f
=
4.0Hz
K
Fig.
6
Variation of force coefficient with
reduced
freqeuncy.
0
A
=
2
deg.
P
A
=
4
deg.
be tempted to interpret the observed effect of the
amplitude
as
a truly nonlinear effect, other
difficulties
complicate the issue. Before any
comparison
between the present low Reynolds number
case
and inviscid calculations can be attempted,
it
may
be
necessary that the oscillation amplitude
be "reasonably" large compared to, say, the
boundary layer thickness at the airfoil trailing
edge. In support of this,
it
should
be
mentioned
that when the oscillation amplitude was reduced to
one degree. no evidence of thrust was found up to
k
=
11.
Conversely, the amplitude cannot become
"too" large
if
a comparison with a linear theory
is
to
be
sensible.
It
1s
not presently clear at
what amplitude a fair comparison between this
experiment
and invlscid theory should
be
made.
Nonsinusofdal
OsciZZatfon
The shape of the pitch waveform has a strong
effect on the
vortical patterns in the wake
as
demonstrated in figure 7.
At
a
given frequency,
by simply changing the shape of the waveform,
it
is
possible to generate a vat-iety of complex
vortex-vortex interactions. The general
observation
is
that a single strong vortex
is
formed during the fast part of the cycle, whereas
more than one vortex (of the
sane
sign) form on
the slow cycle. For example. in figure
7(a), two
vortlces of the same sign
are
shed during the slow
cycle. The number of vortices shed during the
slow cycle increases with the oscillation
amplitude
as
can be seen in figure 7(b). Note, in
thls figure, how the pairing events are modified
and delayed
as
the waveform shape changes
slightly.
It
is known that the motion of more
than three point vortices
is
sensitive to the
Initial conditions and could result in chaotic
motions
(see
Amf16). The strong dependence of
the wake vortex
pattern on the initial conditions
which
are
observed here may be a related
(b)
A
=
4
deg.,
f
=
3.0
Hz
IC:
P
=
4
deg.,
f
=
3.0
Hz,
S
-
30%
Fig.
7
Wake patterns for nonslnusoidal
osclllatlon waveform.
phenomenon.
Figure 7(c) shows a particularly
interesting case where a single vortex on top goes
through the wake and ends up on
the
bottom
unscathed.