Measurement of Velocity and Vorticity Fields in the Wake of an Airfoil in Periodic Pitching Motion

29 Pages·2003·1.74 MB·English

https://ntrs.nasa.gov/search.jsp?R=19880003620 2018-12-26T04:50:46+00:00Z
i
1 , NASA
1
Technical
I
Paper
1
2780
I 987
Measurement of Velocity
J
and Vorticity Fields in
the Wake of an Airfoil in
Periodic Pitching Motion
Earl R. Booth, Jr.
Langley Research Center
Hampton, Virginia
National Aeronautics
and Space Administration
Scientific and Technical
Information Division
Abstract to a 2-D BVI study. In addition, some data were
1 obtained with a specially designed vorticity probe,
The velocity field created by the wake of an air-
which yielded greater spatial resolution than the
foil undergoing a prescribed pitching motion was
conventional cross-wire method.
sampled by using hot-wire anemometry. Data analy-
sis methods concerning resolution of velocity compo- Symbols
t nents from cross-wire data, computation of vorticity I
The coordinate system used in this study is pre-
1 from velocity time history data, and calculation of
vortex circulation from vorticity field data are dis- sented in figure 1.
cussed. These data analysis methods are applied to a A constant
flow field relevant to a two-dimensional blade-vortex
calibration constant
interaction study. A1
Velocity time history data were differentiated to B constant
yield vorticity field data, which were used to char-
B1 calibration constant
acterize the wake of the pitching airfoil. Measure-
ments of vortex strength in sinusoidal and non- c chord length of vortex generator, 6.0 in.
sinusoidal wakes show vortices in the sinusoidal wake d hot-wire diameter
have stronger circulation and more concentrated vor-
E hot-wire bridge voltage, V
ticity distributions than the tailored nonsinusoidal
wake. Also, the tailored nonsinusoidal wake exhib- f frequency of airfoil oscillation, Hz
ited separation of positive vortices of the order of
i hot-wire current, A
five times the chord length of the vortex generator,
while vortices of the opposite sign were effectively k reduced frequency, 7r f c/U,
suppressed. In addition, some data are presented
m integer
which were obtained with a specially designed vor-
ticity probe, which yielded greater spatial resolution n calibration constant
than the conventional cross-wire method. Q heat lost from hot wire to flow
R resistance, R
Introduction
S reciprocal of sample rate, sec
Blade-vortex interaction (BVI) is the source of a
major component of helicopter noise. To study the t time, sec
fundamental physics of BVI, a research program de- U total velocity in the z-direction, U, + u,
signed to explore two-dimensional blade-vortex in-
ft/sec
teraction (2-D BVI) was initiated at NASA Langley
u,
Research Center. The key to simulation of 2-D BVI is free-stream velocity, ft/sec
the generation of two-dimensional vortex flow fields. U perturbation velocity in the z-direction,
The method of generation chosen was oscillation of ft/sec
an airfoil in pitch such that the vorticity shed from
the airfoil into the wake organized into sufficiently V perturbation velocity in the y-direction,
ft/sec
concentrated transverse vortices. The method of vor-
tex generation has been reported along with an an- velocity normal to hot wire, ft/sec
Vn
alytical method for determining the resulting wake
velocity normal to wire 1 and wire 2,
structure (ref. l),b ut the actual flow field had not Vl, 02
respectively
been measured directly, a serious shortcoming. This
study was designed to make flow field measurements X downstream direction
in the vortex flow field to complement the 2-D BVI
data (refs. 1, 2, and 3). An additional objective of Y direction perpendicular to the free-
stream velocity vector
this investigation was to evaluate a prototype vortic-
ity probe in a research environment. z direction normal to x-y plane
The velocity field created by the wake of an
airfoil angle of attack, deg
airfoil undergoing a prescribed pitching motion was Q
r
sampled by using hot-wire anemometry. The velocity circulation of vortex, ft2/sec
data were differentiated to yield vorticity field data.
6 flow direction angle, deg
The vorticity data were used to characterize the wake
of the pitching airfoil for two conditions relevant P viscosity, slug/ft-sec
P density, slug/ft3 conditionally sampled by using the flow velocity data
to arm the system and the time reference encoder sig-
w component of vorticity vector in the z-
nal to trigger the A/D unit, which then sampled the
direction, l/sec
hot-wire bridge voltage at a given sample rate for
a specified length of time. To provide data records
Experimental Methodology
covering more than one oscillation period, the sam-
pling rate for the sinusoidal wake was 10000 sam-
Experimental Setup
ples/sec covering a time of 0.15 sec. Similarly, for
The experiment was performed in the Langley the tailored wake, the sampling rate was 5000 sam-
Aircraft Noise Reduction Laboratory using the Quiet ples/sec and the record length was 0.30 sec. Both
Flow Facility as a low-speed, low-turbulence wind conditions yielded a data record 1500 points long.
tunnel. A two-dimensional test section was formed Two types of hot-wire probes were employed in
by installing two side plates to the edges of a 1.0- the current study. Most of the data were obtained
by 1.5-ft nozzle, which was itself mounted to the with a commercially produced cross-wire probe.
4-ft-diameter low-speed duct of the facility. The Some data were obtained with a prototype vorticity
laboratory is described in more detail in reference 4. probe.
An oscillating airfoil device was installed between
the side plates downstream of the nozzle exit plane. Cross-wire probe. Several commercially obtained
A 6-in. chord, NACA 0012 airfoil model was driven in cross-wire probes were used to survey the flow field
pitch about the quarter-chord station in pitch sched- in the wake downstream of the oscillating airfoil.
ules determined by a motor-cam-transmission assem- The probes were Dantec 55P51 probes described
bly. The pitch schedules, determined by inserting in reference 5. The cross-wire probe was used to
the proper cam, consisted of a sinusoidal oscillation measure velocity and flow direction in the x-y plane
and a tailored oscillation, both with a 10" amplitude. as functions of spatial position and time. A sketch of
The tailored-oscillation pitch schedule consisted of the probe and a photograph of the probe in the test
a sinusoidal-like sweep from minimum incidence to section are presented as figure 2.
maximum incidence for the first 20 percent of the
Vorticity probe. As covered in the data analysis
cycle, with a linear return sweep making up the re-
section below, the data obtained with the cross-
maining 80 percent of the cycle. Oscillation rate was
wire probe were used to compute the vorticity field
set by motor speed, which was continuously variable.
that characterizes the wake. However, this method
The two wakes of interest in this study were pro-
required time-synchronized velocity time histories
duced by oscillating the airfoil sinusoidally at 30 Hz,
at two closely spaced points to perform the data
referred to henceforth as the sinusoidal wake, and by
reduction; thus spatial resolution of the vorticity
oscillating the airfoil by the tailored pitch schedule
calculation is determined by both the sample rate
at 6 Hz, referred to as the tailored wake. An opti-
and the spatial distance between data points. A
cal encoder in the motor system provided the time
more complicated probe, designed to improve spatial
reference signal for conditional sampling.
resolution of the vorticity measurement as well as
Velocity in the two-dimensional test section was
to eliminate the need for correlation between data
monitored with a Pitot-static probe at the nozzle exit
samples from two points, was employed to measure
plane. Since the wake produced by the oscillating air-
the tailored wake. Data obtained with the vorticity
foil is a function of reduced frequency IC, the desired
probe are compared with data from the cross-wire
test velocity was determined by the oscillation rate
probe. A full description of the vorticity probe is
and was 20 ft/sec, as measured at the nozzle exit.
contained in reference 6; a sketch of the probe and
This flow rate actually produced a mean velocity of
a photograph of the probe in the test section are
15 ft/sec at the flow survey station. Because of the
presented as figure 3.
low test velocity and the open circuit wind-tunnel fa-
cility, variation in outside wind conditions produced
Description of Experimental Process
significant variation of test section velocity. As a re-
sult, data were taken conditional to both the flow
Two basic types of flow survey were accomplished
velocity and the time reference signal.
in the experiment. First, data were obtained at a
given x, y location in various z planes to determine
Description of Hot-wire Probes
to what extent the wake produced by the oscillat-
Data were acquired with a constant temperature ing airfoil was two-dimensional. Second, data were
hot-wire anemometer connected directly to a four- obtained at a given 2,z location at a series of y sta-
channel analog-to-digital A/D unit. The data were tions to yield the velocity field crossing the survey
2
r
line as a function of time. The hot-wire probe was changes in calibration coefficients. As a result, the
i
I traversed mechanically across a selected survey line calibration process was performed daily to minimize
at the z/c = 1.0 station. Data were obtained for error in velocity data.
y/c values from -0.5 to 0.5 in increments of 0.033~. The calibration was based on King's Law. This
These data were used to compute the vorticity field approach assumes that, although the hot wire actu-
as a function of y/c and time. The bulk of the data ally can exchange heat with the test medium through
reported here is from the second type of flow survey. radiation, conduction, and convection, the heat lost
because of conduction and radiation is negligible. In
Data Analysis the steady state, the amount of heat Q lost from the
hot wire to the flow (through convection) is
Data analysis involved three main processes: en-
semble averaging of the hot-wire bridge voltage sig-
nals, conversion of hot-wire bridge voltage time his- Q = i2R (1)
tories into velocity time histories, and calculation of This equation can be expressed in terms of non-
vorticity from the velocity time histories. dimensional Nusselt number Nu and Reynolds num-
ber Re as
Ensemble Averaging of Hot-wire Signals
+
NU = A B&
The raw data were in the form of bridge voltage
from the hot-wire anemometer at a time referenced where A and B are found from calibration (ref. 8).
to airfoil oscillation for a series of data points. Since Since Nu is proportional to the square of the bridge
this was a real flow, some variation due to turbulence, voltage, this equation can be expressed as
variation of test section velocity, and other factors
combined to make each data sample unique and only (3)
partially representative of the flow for which mea- To allow another degree of freedom in the curve
surement was desired. As a result, it was necessary fit, the power to which the Reynolds number is raised
to average the conditionally sampled data to produce is expressed as l/n, with the understanding that n
a data sample representing an average flow. This should be close to 2. Thus, the Reynolds number can
process, known as ensemble averaging, is described be expressed as a function of bridge voltage by the
in reference 7 along with methods to estimate the relation
uncertainty in the data.
Unaveraged time history data were collected and
examined to determine what percentage of the hot- (4)
wire signal was random and to compute the number
The data were thus converted from bridge voltage
of averages needed for a given uncertainty level. The
to Reynolds number by the above relation. Velocity
time history data were then averaged and compared
was obtained from the Reynolds number by using the
with independent averaged data to confirm data
relation
repeatability. It was determined that 20 data records
could be averaged into a data record with good
repeatability characteristics. The repeatability of the (5)
data is vital to perform the vorticity calculation, as
with measured density for p, standard values for p,
differentiation magnifies the randomness present in
and the hot-wire diameter for d.
sampled data, particularly the cross-wire data, where
At this point, the data were in the form of ve-
independent samples are cross differentiated.
locity normal to the hot wire as a function of time.
To convert from this coordinate system to the exper-
Resolution Into Velocity Data
imental frame of reference, a further calibration was
Hot-wire bridge voltage data were converted into performed. At a constant velocity, the hot wire was
velocity data by using calibration coefficients ob- rotated from an angle of 6' = -90" to 6' = 90" in 2" in-
tained during calibration runs. A probe was removed crements, where the probe was aligned with the flow
from the experimental apparatus and placed in a at 6' = 0'. The ratio of the normal velocities from
variable-speed flow. The output bridge voltage was wires 1 and 2 was used as a calibration curve for flow
then curve fitted to Reynolds number based on the direction. This curve exhibits a maxima near 6' = 45"
wire diameter. Parameters describing the resulting and a minima near 6' = -45", so the curve between
curve were used as calibration coefficients. Although these extrema was used to compute flow direction. In
day-to-day changes in the calibration coefficients are addition, a flow magnitude correction was computed
small, indicated velocity is very sensitive to small based on the square root of the sum of the squares
3
of VI and v2 divided by the t,rue velocity. With these distance the probe appears to have moved, from the
two curves, the velocity data were converted from v1 vortex’s perspective, -U,At. Thus, in the vortex-
and v2 to U and v as functions of time. The constant fixed reference system
mean velocity, 15 ft/sec, was subtracted from U as
I
the free-stream velocity to yield u.
4t2) - v(t1) (9)
vortex fixed = lim
Calculation of Vorticity and Circulation ax ~ t - 0 -U,At
The main purpose of this flow survey was to This is the appropriate derivative for vorticity cal-
determine the circulation of the vortices in the wake culation, and the appropriate length scale for resolu-
of an oscillating airfoil. In a two-dimensional flow, tion of the vorticity measurement is some multiple of
only one component of vorticity is present. The U,At.
purpose of this section is to explain how vorticity at A space-centered first approximation of the vor-
a point is computed with the velocity time histories ticity is given by
and how these vorticity data are used to calculate
the circulation of vortices in the airfoil wake. +
In the experiment, velocity time history data of v(y, t - ms) - v(y, t ms)
4 Y ,t ) =
the form 2msU,
u = U(Y,t)
(6)
v = V(Y,t)
were obtained for a series of points spatially sepa-
rated by a constant Ay. Obviously then, Ay is one where m is chosen so that
length scale defining spatial resolution of the veloc-
ity measurement. In two-dimensional flow, vorticity m = Integer - (11)
is given by [S%l
so that the two length scales are approximately
av au
u=--- (7) equal. For the data from the tailored oscilla-
ax ay tion, s = 0.0002 sec/point, U, = 15 ft/sec, and
Ay = 0.20/12 ft. Thus, m = 6 for this case.
Evaluation of au/ay is straightforward; however,
An implication of this method is that vorticity
evaluation of av/ax requires a bit of manipulation.
cannot be computed for the first six data points or
Consider a two-dimensional vortex traveling
the last six data points of the data record. In this
through the test section at a velocity U,. Fixed
case, this is not a major concern, since the data
inside the test section is a cross-wire probe measur-
record length exceeds one oscillation period. Also,
ing the velocity sum of U, and perturbation veloc-
this method is valid only if the data are sampled at
ities induced by the vortex, u and v. As the vortex
a rate greater than U,/Ay.
approaches the probe at time ti, the probe measures
The above method applies to the cross-wire data.
velocities U,+u(tl) and v(t1). Some small At later,
+ The vorticity probe uses four hot-wire elements: two
at t2, the probe measures velocities U, u(t2) and
crossed wires and two parallel wires normal to the
v(t2). In a probe-fixed coordinate system, then
flow direction. Thus, the Ay used for the vorticity
probe is the distance between the parallel wires,
hence the length scale for the measurement is much
less. As a result, a smaller sample area is considered
in the vorticity calculation with m (from eq. (11))
Unfortunately, this is not the dv/dx appropriate equal to one. Thus, vorticity is measured with
for calculation of vorticity in the vortex. Measuring greater spatial resolution.
vorticity distribution in a vortex, as opposed to With the present data, there are particularly
measuring vorticity flux at the probe, requires a large concentrations of vorticity indicative of the
vortex-fixed coordinate system. Consider, in such a major vortex filaments in the wake. The purpose
reference frame, that the cross-wire probe appears to of this investigation was to determine the strength of
fly through the vortex at a velocity -Urn. At time tl, these vortex filaments.
+
the probe measures U, u(t1) and v(t1) as before. Once the vorticity is known for a given range of
Similarly, at time t2, the probe measures U,+u(t2) y/c and time, it is possible to integrate the vorticity
and 4 2 ) . This time, however, the length scale is the over an “area” to compute the circulation acting in
4
that area. The method used is described in refer- Figure 4(c) contains the velocity survey from the
ence 9. By using the relation below, the vorticity is centerline to the front side plate. Of interest is the
integrated over a surface to produce the circulation. fact that a delayed velocity variation is not as ev-
ident in the data nearest the side plate, although
the smearing of the velocity time history in a sec-
r=-//w.ndS (12)
ondary minima occurring around 0.21 sec grows pro-
gressively worse as the side plate is approached. One
where S is the surface over which the integration
possible explanation for the lack of the delay fea-
takes place, in this case the z-y plane. The double
1 ture could be that the survey was not performed as
integral was rewritten as a double summation, the
close to the side plate as for the previous case be-
differential area was computed by using the sampling
cause of interference between the side plate and the
rate, free-stream velocity, and distance between sur-
probe mount. Note that the data for the z/c = 0.500
vey points, and a relatively simple computer routine
station were obtained on a different day from the re-
was written to perform the integration.
mainder of the data in the figure, and the 0.5 ft/sec
difference in the mean velocity data is probably rep-
Results
resentative of typical day-to-day repeatability of the
data. Figure 4(d), containing the velocity normal to
The data will be discussed in three parts: assess-
the other wire in the probe, shows little variation
ment of flow two-dimensionality, results from the si-
with z-station.
nusoidal wake, and results from the tailored wake.
From the data presented, one may conclude that
the wake produced by the pitching airfoil is indeed
Flow Two-Dimensionality
two-dimensional for a large portion of the test section
Ideally, a two-dimensional flow field is invariant in span.
one dimension, in this case the z-direction. Of course,
Survey of Sinusoidal Wake
a real flow may be influenced by such factors as
boundary layer effects and vortex filament twisting. Initially, in the two-dimensional blade-vortex
An attempt to assess the invariance of the velocity study, the wake produced by oscillating the airfoil si-
field in the z-direction was made by sampling the nusoidally at 30 cycles/sec was used as the test flow.
velocity at a fixed z,y point in various z-planes. In this section, the wake produced by those condi-
The data, in the form of velocity time histories, tions will be examined.
are presented in figure 4. The data presented were
obtained at z/c = 1.0, y/c = 0.333 with the tailored Velocity fierd. The velocity field produced by
wake as the incident flow. the sinusoidal oscillation case is presented in fig-
In figure 4(a), the velocity normal to wire 1 is ure 5. In figure 5(a), the u velocity component is
presented for several stations between the centerline shown to be periodic, with a period of approximately
of the test section and the back side plate. It is 0.033 sec, which corresponds to an oscillation fre-
immediately evident that the velocity time histories quency of 30 Hz and (at a free-stream velocity of
at all stations are very similar. The two large velocity 15 ft/sec) a spatial separation of IC. Another item
variations occurring at the start of the data record of note is that the amplitude of the u velocity com-
and around 0.17 sec are the result of a vortex passage. ponent reaches a maximum very near the center of
Notice that, with the exception of the data taken the flow field. Figure 5(b) displays similar trends for
at z/c = -0.917 (0.5 in. away from the rear side the v velocity field. Another interesting feature in
plate), the amplitude and timing of the velocity the ZI component data is that the shape of the ve-
variation are invariant with z-station. This indicates locity time history curves changes at approximately
that the flow is two-dimensional from the centerline the center of the test section to a near mirror image;
to within an inch of the side plate. Delay of the this indicates that the flow features in one-half of the
velocity variation because of the vortex passage at flow are nearly opposite and equal to what is hap-
the z/c = -0.917 station indicates that the boundary pening in the other half of the flow. Actually, this is
layer on the side plate is tending to bend the end a consequence of the fact that the sinusoidal oscilla-
of the vortex structure as it drags against the solid tion produces a train of vortices of alternating sign
surface in the boundary layer. Figure 4(b), which and nearly equal magnitude.
depicts the velocity normal to the other wire in the Examination of the velocity field for a single cycle
cross-wire probe, shows a similar trend, although the is useful to gain a more thorough understanding
delay caused by the side plate boundary layer is not of the flow field. In figure 6, velocity data for
as evident. each component are displayed for a single cycle. In
5
figure 6(a), there are two main velocity “ridges,” one velocity between the vortex filaments is nearly uni-
at the beginning of the data record that is partially form for the u velocity component. This indicates
repeated at the end of the record and one centered that the vortices in the wake are spaced far enough
about t = 0.022. These ridges are indicative of vortex to be considered isolated. Spatially, the distance be-
filaments whose cores are located at the point where tween the vortices is on the order of 5.1~.
the magnitude of the velocity changes sign. The In order to compare the velocity field with calcu-
fact that the vortex at the beginning of the record lations as in the sinusoidal case, the velocity field
has a negative u region in the lower half of the flow associated with the vortex between t = 0.16 and
while the other vortex has a negative u region in the 0.19 sec is presented in figure 9. A noticeable dif-
top half of the flow indicates that they are positive ference is that the velocities for this case are much
and negative vortices, respectively. Notice also that smaller, in fact, on the order of one-half of the ve-
the y/c coordinate of the vortex cores is different, locities of the sinusoidal case. This implies that the
thus the vortex train consists of staggered vortices of circulation of the vortex produced is less than that
opposite signs. The vortex filaments cause the step- produced by the sinusoidal wake.
type change in the component shown in figure 6(b).
?J
Vorticity fieZd. In figure 10, the vorticity field as-
Vorticity field. In figure 7, the vorticity com- sociated with the tailored wake is presented. Exam-
puted for the velocity field in figure 5 is presented. ination of the positive vorticity data in figure lO(a)
Because of the plotting method used, only the pos- shows no significant accumulations of vorticity. The
itive vorticity (associated with the negative vortex) vorticity with negative sign, associated with the pos-
is shown in figure 7(a), while the negative vorticity itive vortex, is shown in figure 10(b). Notice that the
(associated with the positive vortex) is shown in fig- vorticity is concentrated into two well-defined ridges,
ure 7(b). Notice that the positive vorticity shown in as was the velocity field.
figure 7(a) tends to be centered in the positive y/c In figure 11, a slice of data from t = 0.16
region while the negative vorticity is centered in the to 0.19 sec is shown. In this figure, it is evident
lower half of the flow. It is also evident that the vor- that the vorticity is concentrated into two main lobes.
ticity concentrations are staggered in time (and thus Flow visualization of the vortex in figure 12 confirms
the 2-direction) and are nearly equal in absolute am- that this is a single vortex, so the distribution of vor-
plitude. Integration of the vorticity regions yields ticity for this vortex is different from the vortices in
a magnitude of 8.41 ft2/sec for the positive vortex the sinusoidal wake. At any rate, the integration of
and 7.44 ft2/sec for the negative vortex. From these the vorticity results in a circulation of 3.59 ft2/sec for
observations, the sinusoidal wake might be consid- the large lobe and 1.71 ft2/sec for the smaller vortic-
ered almost symmetric, although such was shown not ity lobe. It is interesting to note that these circula-
to be the case in a previous study (ref. 2) where the tions are significantly smaller than the amplitude of
trajectory of the vortex train was examined. circulation associated with the sinusoidal wake. Even
if the two vorticity lobes are the remains of a sin-
Survey of Tailored Pitch Schedule Wake gle vortex, the sum of circulations for the two lobes,
5.30 ft2/sec, is still smaller than the circulation of
The standard incident flow field for most of the the positive vortex of the sinusoidal wake.
two-dimensional blade vortex interaction study was
Comparison with vorticity probe data. The tailored
the tailored wake. Basically, the concept behind the
wake was also surveyed with the specially designed
tailored wake was to produce a single isolated vortex
vorticity probe, which unfortunately did not survive
per cycle. In this section, the degree to which this
goal was attained and the strength of the resulting the test. As a result, a partial survey of the wake
vortices in the wake will be examined. from y/c = -0.466 to y/c = -0.033 exists. Although
not as valuable as a complete survey, it is a large
Velocity fieZd. In figure 8 the velocity field as- enough segment of the wake to compare with the
sociated with the tailored wake is shown for almost data obtained with the conventional cross wire.
two cycles. The u velocity field in figure 8(a) shows The vorticity field measured by the probe is pre-
a nearly uniform shift in velocity from the upper to sented in figure 13. As compared with figure 10, the
the lower halves of the flow field. The portions of data appear noisier, or more choppy. This is a di-
the wake associated with the vortex are the ridges rect result of at least two factors: the smaller micro-
in the velocity map centered about t = 0.01 sec and circulation domain used to compute the vorticity,
t = 0.18 sec. In figure 8(b) the ?J velocity field dis- and the prototype nature of the probe. First, the
plays the characteristic step change in sign associated smaller microcirculation domain, resulting from the
with a vortex flow field. Notice particularly that the use of the parallel wires as “direct” measurement of
6
the du/dy term, is less numerically stable. In equa- of the circulation of the negative vortex is 7.44 ft2/sec
tion (lo), the magnitudes of the denominator terms and that of the positive vortex is 8.41 ft2/sec.
decrease by an order of magnitude, therefore, a given The velocity field produced by the tailored wake
error in the numerator terms is magnified by that shows that the vortex filaments are not as strong
order of magnitude. A second reason for the noisier as for the sinusoidal wake and are separated by
data is the prototype nature of the probe, being itself about 5. IC. Although prominent positive vortices are
a research project instead of a commercial product. present in the tailored wake, no strong negative vor-
A commercially designed and manufactured vorticity tex is evident. The positive vortex feature appears in
probe probably would exhibit cleaner output data as the vorticity data as two distinct vorticity accumu-
well as being a bit more rugged. lations, although flow visualization data show only a
Two interesting features of the data in figure 13 single vortex feature. The circulation of the vortex
are that the magnitudes of the negative vorticity is 5.30 ft2/sec.
peaks are much greater than those in figure 10 and The vorticity data measured with a prototype
that the negative vorticity peaks in figure 13 are ac- vorticity probe exhibit more numerical noise, which
companied by adjoining positive vorticity peaks that has been ascribed to the smaller measurement do-
are not at all evident in figure 10. A possible ex- main and the prototype nature of the probe. The
planation of this may be that the increase in spa- vorticity probe data reveal details in the vorticity
tial resolution inherent in the vorticity probe is de- field not evident in the cross-wire data because of
tecting real flow features that were smeared over by the greater spatial resolution of the probe. Magni-
the conventional probe. A method of testing this tude differences in the vorticity data are the result of
hypothesis is to compute the circulation over a se- the smaller measurement volume used by the probe.
lected area in both data sets and compare the results. Integration of vorticity over an area in both data sets
The region selected is bounded by t = 0.15 sec, t = produced similar values of circulation.
0.21 sec, y/c = -0.466, and y/c = -0.033. The
resulting values of circulation are 0.272 ft2/sec for NASA Langley Research Center
the vorticity probe as compared with 0.340 ft2/sec Hampton, Virginia 23665-5225
November 5, 1987
for the cross wire. Since these values are similar,
the additional vorticity features are probably due to
References
the spatial resolution of the vorticity probe. Further
development of the vorticity probe is therefore war- 1. Booth, Earl R., Jr.; and Yu, James C.: New Technique
ranted for measurements where the additional reso- for Experimental Generation of Two-Dimensional Blade-
lution of the probe is required. Vortex Interaction at Low Reynolds Numbers. NASA
TP-2551, 1986.
Summary of Results 2. Booth, E. R., Jr.; and Yu, J. C.: Two-Dimensional
Blade-Vortex Flow Visualization Investigation. AIAA
The velocity field produced by an airfoil oscillat- J., vol. 24, no. 9, Sept. 1986, pp. 1468-1473.
ing about its quarter-chord has been surveyed by 3. Booth, Earl R., Jr.: Surface Pressure Measurement Dur-
ing Low Speed Two-Dimensional Blade-Vortex Inter-
using hot-wire anemometry. The velocity field was
action. AIAA-861856, July 1986.
used to calculate the vorticity in the wake, which
4. Hubbard, Harvey H.; and Manning, James C.: Aero-
was used to calculate the circulation of the coherent
acoustic Research Facilities at NASA Langley Research
vortex filaments embedded in the wake. These data Center-Description and Operational Characteristics.
were examined to characterize the vortex wake for NASA TM-84585, 1983.
two conditions relevant to a two-dimensional blade- 5. DISA Probe Catalog. Publ. No. 2201 E, Dantec Elec-
vortex investigation. tronics Inc., Mar. 1982.
Examination of velocity time histories taken at 6. Foss, John F.; Klewicki, Casey L.; and Disimile, Peter
several spanwise locations verifies that the velocity J.: Transverse Vorticity Measurements Using an Array of
field is two-dimensional for a large portion of the span Four Hot- Wire Probes. NASA CR-178098, 1986.
7. Hardin, Jay C.: Introduction to Time Series Analysis.
of the test section.
NASA RP-1145, 1986.
Data from the sinusoidal wake reveal that the
8. Liepmann, H. W.; and Roshko, A.: Elements of Gas-
wake is composed of staggered vortices of opposite
dynamics. John Wiley & Sons, Inc., c.1957.
sign and nearly equal amplitude. The spacing of
9. Kuethe, Arnold M.; and Chow, Chuen-Yen: Foundations
adjacent vortices of like sign is on the order of IC (the of Aerodynamics: Bases of Aerodynamic Design, Third
chord length of the vortex generator). The amplitude ed. John Wiley & Sons, c.1976.
7
fY Positive T y/C = 0.5
U, vortex
I
n
t
Survey line
x/c= 1.0
1
Oscillating airfoil
y/C = - 0.5
Negative
vortex
Figure 1. Sketch of coordinate system used in the experiment.
9