NASA Technical Reports Server (NTRS) 20010016109: Detection, Tracking and Analysis of Turbulent Spots and Other Coherent Structures in Unsteady Transition

NASA/CR— 2000-210694

Detection, Tracking and Analysis of
Turbulent Spots and Other Coherent
Structures in Unsteady Transition

Jacques Lewalle

Syracuse University, Syracuse, New York

December 2000

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NASA/CR— 2000-210694

Detection, Tracking and Analysis of
Turbulent Spots and Other Coherent
Structures in Unsteady Transition

Jacques Lewalle

Syracuse University, Syracuse, New York

Prepared under Contract C-76220-D

National Aeronautics and
Space Administration

Glenn Research Center

December 2000

Acknowledgments

This work was performed by Wavelet Diagnostics Ltd. under NASA GRC Contract C-76220-D,
Dr. David Ashpis, project monitor. Data were provided by Dr. David Halstead,

General Electric Aircraft Engines, Evandale, Ohio.

Trade names or manufacturers' names are used in this report for
identification only. This usage does not constitute an official
endorsement, either expressed or implied, by the National
Aeronautics and Space Administration.

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Detection, tracking and analysis
of turbulent spots and other coherent structures
in unsteady transition

Jacques Lewalle

Department of Mechanical, Aerospace
and Manufacturing Engineering
Syracuse University
Syracuse, NY 13244

Abstract

Transition on turbine blades is an important factor in the determination of eventual
flow separation and engine performance. The phenomenon is strongly affected by un-
steady flow conditions (wake passing). It is likely that some physics of unsteadiness
should be included in advanced models, but it is unclear which properties would best
embody this information. In this paper, we use a GEAE experimental database in
unsteady transition to test some tools of spot identification, tracking and character-
ization. In this preliminary study, we identify some parameters that appear to be
insensitive to wake passing effects, such as convection speed, and others more likely
to require unsteadv modeling. The main findings are that wavelet duration can be
used as a measure of spot size, and that spot energy density is most closely correlated
to the wake passing. The energy density is also correlated to spot size, but spot size
appears unrelated to the phase angle. Recommendations are made for further study.

NAS A/CR— 2000-210694

1

1 Introduction

The purpose of this report is to show to what extent wavelet-based methods can assign
quantitative properties to coherent structures (spots and possibly others) occuring in
turbomachinei \ . Specifically, we study traces collected at the wall in a boundary
layer experiencing unsteady transition in relation with wake passings. The data used
in this report is from experiments performed at General Electric Aircraft Engines
(GEAE) in their low speed research turbine facility. The experiment is documented
in Halstead [5] and Haltead et al. [6], where the experimental configuration and data
acquisition are described in detail. The data include free stream hot wire and surface
hot film measurements in a two stage turbine.

In the companion report [11], we focussed on the hot wire records taken upstream
of the first and the second turbine nozzles. In this report, we follow up with an
analysis of the hot film traces collected on the second stage nozzle. Under the effect
of wake passing from the first turbine stage, unsteady transition occurs [5, 6], This
part of the study is devoted to the characterization of recognizable events (turbulent
spots and other phenomena) associated with the wake-induced transition.

The motivation for this analysis comes from the need to model wake-induced
transition and unsteady separation that may occur in low-pressure turbines. The
GEAE data [6] show vividly the dependence of spot formation on wake passing, the
subsequent delay in further spot formation in the becalmed region, the effect of these
phenomena on separation, and the need for unsteady model predictions that take spot
dynamics into account. The explicit goal of this preliminary study was to evaluate
which spot properties can be quantified based on hot film data, and which seem to
be affected by unsteadiness. Whether positive or negative, the outcome would be
of interest, insensitivity to unsteadiness would make conventional transition models
satisfactory, while some effect of unsteadiness may have to be included to improve
model predictions. The fact that the current data was not collected specifically for
this purpose set certain limitations on expected results, but allowed for the evaluation
of methods and software, and some preliminary conclusions are drawn.

The hot film records consisted of a collection of 400 samples of 700 data points
each (the first 512 of which are used in our analysis) at 24 chord wise locations on
the suction surface of the second stage vane. The amplitude of the signals is a mea-
sure of pseudo- wall-shear-stress (PWSS), which can be interpreted as the footprint
of velocity fluctuations in the boundary layer. The relation between maps of the
instantaneous velocity field and the wall heat transfer was established by Van Atta
Helland [13], and can also provide a high- frequency-response non-intrusive access
to the transitioning boundary layers in high speed flows [8, 2],

Preprocessing of the GEAE data yielded an ensemble average at each station,
which provides smooth data to measure the phase relative to the first stage blade

NAS A/CR— 2000-2 1 0694

passing; and fluctuations around this ensemble mean, from which we endeavored to
extract individual events. The availability of simultaneous traces at 24 chordwise
stations along the vane provides an opportunity to document the evolution of spot
size, time scales, energy levels, convection speed, etc., as a function of phase relative to
the wake passing. The motivation for this focus is to determine which spot properties
are affected by the variations in freestream conditions. The answer to this question
would affect the demands on computational models of transition on turbine blades.

This report is in three parts. Section 2 will focus on spot detection and tracking
along the chord. This work differs from conventional methods by the identification
and matching of possible events in the time- frequency domain, which allows for the
superposition of events of different sizes. In Section 3, event properties and their
evolution are mapped. The results are discussed in Section 4, where suggestions are
made for future work.

2 Spot detection and tracking

Turbulent spots and their distinguishing characteristics are well documented, e.g.
[13]. However, their appearance is strongly affected by the unsteady mean flow, the
ambient turbulence, and the frequency resolution of the hot-film sensors. Throughout
this report, ‘spot’ is used as a generic term for an energetic turbulent event that can
be followed from station to station. From the physics of the flow, it is clear that some
of these events are indeed associated with spots. The frequency resolution of the
data does not allow us to determine unambiguously if the event’s internal structure
is consistent with a spot or not, and it is possible that some events are fluctuations
in PWSS other than spots. Further study based on higher frequency resolution data
may lead to refinements in this regard.

In this work, spot detection is a three-step process. In the first step, candidate
events are located in each trace separately, as explained in Subsection 2.1. Visual
inspection of the traces and wavelet maps showed that the properties of small spots
superposed on energetic large-scale events were modified by these dominant events,
and the successful removal of the large events in the time-frequency domain, described
in Subsection 2.2, yielded more accurate event properties. If events can be tracked
reliably at several chordwise locations, they are retained as ‘coherent structures’ or
‘spots’, whereas untrackable events are discarded. The tracking algorithm is described
in Subsection 2.3. In Section 3, the analysis of spot properties and their evolution is
based on the remainder of the collection.

NAS A/CR— 2000-2 10694

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0 15

Figure 1: Trace of pseudo-wall-shear-stress (PWSS) at the beginning of transition
(station 12 of the GEAE data), and Mexican hat wavelet transform.

2.1 Event detection

Traditional methods of spot detection (Hedley & KcfFer [7]; Lewalle, Ashpis A Sohn
[10]) are based on the presence of smaller scale turbulence in the spot than outside.
Because of the frequency resolution of the hot film sensors, such algorithms could not
be used with this data. Instead, we relied on the increased PWSS associated with the
turbulent transport in each spot. We recorded as candidate event any point at which
the PWSS is maximum 1 . Such maxima are readily observable on the traces (see Fig.

1, top.)

A description of recognizable events should include their time of occurence, mag-
nitude and scale, shape, internal structure and eventually dynamics. The first three
of these factors point to wavelet analysis [3, 4, 9, 10], and we focussed on the charac-
terization of the events in the time-frequency domain [4, 9]. Wavelets have imposed
themselves as a rigorous tool for time- frequency analysis, with solid mathematical

Alternative criteria, based e.g. on local curvature of the traces, were attempted but were not
sufficiently sensitive to large events and excessively sensitive to noise.

N AS A/CR— 2000-210694

4

A A

\i v A

N A\,

0.0010

0.0020

0.0030

0.0010

0.0020 0.0030

Elapsed time (s)

/\

(A i

0.0040

0.0050

0.0040

0 0050

0.10

Figure 2: Local maxima of energy density isolate the 1 events' to be studied. The same
sample as on Fig . 1 is shown.

underpinnings for the wavelet transform, its inverse (with or without filtering), and
the generalization of power spectral density to intermittent signals. Contour lines of
the wavelet coefficients, multiplied by the square root of scale (\/k) to enhance domi-
nant events at all scales, are shown on Fig. 1, bottom. The square of the coefficients
measure the energy density per octave according to Parseval’s theorem [3]. A good
correspondence between the local maxima of this energy map and local maxima of
the signal can be observed on Fig. 2. (For the algorithm of extrema identification,
see Lewalle, Ashpis & Sohn [10]). The location of the local maximum of energy in
the wavelet domain provides the time of occurence and scale of of the event, while
the peak energy level is a local measure of the magnitude.

A correction to this idea was required due to an observation related to the im-
perfect time/frequency localization of the events (a manifestation of Heisenberg s
uncertainty principle in the wavelet plane). With the Mexican hat wavelet, temporal
localization is favored [9], resulting in fairly long spectral tails for each bump as seen
on Fig. 1. In the case when the small events (0.1 ms duration and less) overlaps in

NAS A/CR— 2000-2 1 0694

5

time with a large scale event (which is associated with a wake passing as a matter of
course), the coefficients associated with the peak of the weaker event are superposed
on the tail of the stronger event. This affects both the peak frequency and the mag-
nitude of the smaller event, an undesirable contamination from the viewpoint of our
analysis. Thus, we turned to intermittent filtering to improve the accuracy.

2.2 Removal of large events

Iri a first attempt, a conventional high-pass filtering was attempted to remove the
large scale events. In the Fourier domain, this strategy failed because the wake-passing
events are not sinusoidal, even though they are nearly periodic. The higher-frequency
corrections that account for their average shape turned out to interfere more with
the desired event characterization than the original peaks. In the wavelet domain,
frequency filtering obviously leaves unchanged the higher- frequency contamination.
What is needed is a method to remove the dominant bumps and their higher-frequency
tails.

Let us call t the time variable on the experimental traces, and u(t) the signal; k
is the wavelet number [10] playing a role similar to the frequency of Fourier analysis,
and g-i is the Mexican hat wavelet function

*•<*) - <»

The large event removal algorithm devised in this study is based on the inverse wavelet
transform formula:

u(t) = f k 1/2 f — t)) u 2 (k, t) dr dn (2)

JO J — oo

Integrations by parts and the definition of the Gaussian bell curve

9o(t) = e- <2/2 (3)

give

«(*) = Io° K ~* S-o o 5 o(k(* - r)) £iU 2 (k, t) dr dn
= /* o dr j„ x *g 0 (K(t - t)) J^u 2 (k, t)]

~ E, a t g 0 (Ki(t - Ti)) (4)

This equation shows that the signal can be decomposed into a superposition of Gaus-
sian bell-shaped curves go(n(t — r)) over the continuum of times and scales. The
dominant contributions to the signal will be those associated with the times and

NAS A/CR— 2000-2 1 0694

6

scales where k~* J^U 2 (/c, r) is largest. It has been shown (Lewalle, unpublished) that
a multipole expansion around the extrema gives a discretized Gaussian bump as the
leading term.

Thus, a first order approximation of the wake-passing bump consists of the Gaus-
sian bell at the time and scale of each bump. The event removal algorithm is therefore
summarized as follows:

1. Identify the location and scale of the wake-passing events from the large-scale
maxima of the energy map Fig. 2;

2. Calculate the magnitude of the Gaussian model so that its energy peak coincides
with the wake passing energy signature;

3. Construct the model Gaussian bump with these parameters;

4. Subtract the model bump from the signal and from its wavelet transform.

A more extensive discussion of the Gaussian model for wake passing events will be
found in Section 4. The result of the procedure is shown on Figs. 3 and 4. One-by-
one mapping of the original maxima of the raw signal (the candidate events) w r as found
to be satisfactory; hardly any original events were lost in the procedure, thanks to the
scale separation, and new events introduced as a result of the subtraction of model
Gaussians were not included in the list. In other words, the events analyzed below
were always identified on the original traces, without exception. The map of wavelet
coeffficients (Fig. 3) shows that the tail of the bumps has effectively been removed,
and the modified energy peaks (compare Figs. 2 and 4) are deemed to provide a valid
correction to the contaminated parameters obtained previously. Events were retained
if we could match the local maximum of the raw trace to a local energy peak in the
filtered energy map.

2.3 Spot tracking

Up to this point, the list of events and their properties are calculated for each trace
independently. The last step in the procedure consists in matching them at successive
stations. The occurence of ‘similar’ events with some time delay on the next trace is
the basis for a match. The time delay is first estimated from the peak of the cross
correlation function for the tw T o traces [1]; The events are paired up based on a posit ive
convection speed and the ‘best’ overall matching of time, scale and magnitude. Since
a given event can find a suitable match only in very small region of the time- frequency
domain at the next station, the automated pairing procedure was relatively easy even
if time-consuming. All unmatched events were deleted from the list of candidates.
The result is shown on Fig. 5.

NASA/CR— 2000-2 1 0694

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Figure 5: One sample of simultaneous traces (horizontal solid lines) from the beginning
of transition (station 10) to the trailing edge ( station 24). Events are traced from
station to station. Ensemble mean is shown in dashed lines. Abscissa shows 512
successive samples, ordinate is PWSS in arbitrary units.

NAS A/CR— 2000-2 10694

9

On Fig. 5, the stations are labeled from 10 (beginning of transition) to 24 (trailing
edge) in the streamwise direction, following the notations of Halstead et, al. [6]. The
four major ‘events’ at station 10 are interpreted as the wake passings. The excerpt
used for illustrations on Figs. 1 to 4 appears at station 12. The gradual increase in
the number of smaller scale events is consistent with the development of turbulence
along the blade surface. Convection of the events along the blade surface is reflected
in the slope of their trajectories on the plot.

Some of the details, however, are not quite right. For example, between traces
14 and 15 at t = 400 units, the algorithm chooses a fairly slanted trajectory (low
convection velocity) as a better match than the obvious rise leading up to the peak.
This is caused by the lack of shape characterization (pattern recognition) in our
algorithm, and possibly by the next-trace matching as opposed to a multiple trace
matching. Improvements in this regard will be discussed in Section 4.

3 Spot properties and their evolution

The events analyzed below were extracted from the Halstead data [6], using the first
512 points from each record. The events, presumably spots, can be followed between
successive traces and can be assigned some quantitative properties. Not all properties
are equally accurate, as pointed out for each item in the list:

1. Time of occurence: some arbitrariness in selecting a maximum (on time traces)
or peak of wavelet transform; alternatives include a center-of-mass or other
weighted local moment of the signal.

2. Phase angle relative to the wake passing at each location; this is based on
ensemble averages traces, and is accurate.

3. Chord value: as provided.

4. Dominant frequency: the scale corresponding to the peak value of wavelet spec-
tral energy density. This could be affected by the grazing 2 overlap of the (as-
sumed) arrowhead shape of a spot on each sensor.

5. Energy 7 density: here also, grazing overlap would affect the measured energy
content.

6. Age: we only know when the structure starts showing on the traces, it could
preexist and have grazing contact with the sensor.

2 By grazing, we mean that the center of the spot, being aligned randomly relative to the center
and edges of the sensor can result in partial overlap.

NAS A/CR— 2000-2 1 0694

10

Dominant frequency (kHz)

Figure 6: Relation between spot size (time interval between leading and trailing edge,
as estimated from wavelet maps) and dominant frequency. Different symbols identify
successive stations (see Fig. 1 caption).

7. Convection speed: by associating spot centers at successive chord locations, we
can obtain their convection speeds from the time lag from sensor to sensor. This
depends on correct times of occurence as well as trace-to-trace matching.

8. Leading and trailing edge locations: somewhat arbitrary, we look for change of
sign in the wavelet map at the dominant frequency. Frequency resolution of the
data does not allow a precise determination except for a few ‘nice’ spots.

9. Size: time difference between leading and trailing edge, it may be biased to low
values because of grazing incidence on the sensor. It should be related to the
frequency through the covnection speed.

10. Leading and traling edge convection speeds are easy to obtain from the above,
with the same uncertainties.

NAS A/CR— 2000-210694

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1 10 100
Size (ms)

Figure 7: Scatter plot of phase (relative to wake passing) versus spot size at successive
stations. Symbols: + traces 8 and 9; * traces 10 and 11; ■ traces 12 and 13; o traces
14 and 15; n traces 16 and 17; A traces 18 and 19; x traces 20 and 21; filled V
traces 22 - 24 -

Fig. 6 shows the relation between the spot size, as measured by the time interval
between leading and trailing edge for each spot, and the frequency, measured by the
peak frequency on the energy maps. The inverse proportionality (slope -1 on the log-
log plot) appears to hold best for the largest spots, while the shorter ones exhibit a
slope closer to -2. The lack of linearity is presumably associated with the inaccuracies
associated with spots that cover only a few data points. Higher frequency resolution
of the data might improve the results. The overall one-to-one relation between size
and frequency over all stations is encouraging.

Fig. 7 shows that spot size seems independent of phase relative to wake passing.
Furthermore, no pattern emerges that would relate spot size to chordwise location.
This conflicts with the expectation of spot growth in the streamwise direction. A
similar lack of trend was observed when spot dominant frequency was substituted for
size. Two interpretations are possible. First, the accuracy of the size and frequency

NAS A/CR— 2000-2 10694

12

Dominant frequency (kHz)

Figure 8: Scatter plot of energy density vs. frequency. Symbols as for Fig. 7.

parameters could be at fault, because of confounding effects of grazing overlap of the
spot on the sensors, and/or because of frequency resolution effects. Alternatively,
it is possible that crowding of spots in the rapidly evolving flow interferes with the
determination of size.

Size, however, is not a meaningless parameter, as seen from Fig. 8. The scatter
plot of energy density versus frequency reveals a few trends that might merit further
scrutiny. For example, at the top of the plot, the most energetic events occur over a
relatively small range of scales. Spots of median energy level occur over the widest
range of scales, while the weakest spots are the smallest ones as well, and are associ-
ated with the earliest events. Since the energy' measure is a density , this observation
is not trivial. Further study might indicate if grazing incidence of spots on the sensors
accounts for this correlation, or if a physical connection exists.

A different section through our parameter space is given by the plot of energy
as function of phase relative to wake passing on Fig. 9. We see the most energetic
events occuring in phase opposition to wake passings, and at the early stations in the
transition process. This points to the largest spot energy densities being associated

NASA/CR— 2000-2 10694

13

0.0 0.2 0.4 0.6 0.8 1.0

Energy density (orb. units)

Figure 9: Energy density as a function of phase relative to the wake passing. The
strongest events are seen to be at a relative phase of approximately .5, i.e. to be
located preferably between wakes. Also, these events occur in the transition. Symbols
as for Fig. 7.

NAS A/CR— 2000-2 1 0694

14

Leading edge speed (arb. units)

Figure 10: Scatter plot of leading edge speed and energy density along the blade.
Symbols as for Fig. 7.

with natural, as opposed to wake-induced, transition. It is worth noting that grazing
incidence does not overcome this trend, and that spot crowding (or lack thereof)
seems to affect the energy density or its measurement.

In combination, these results show that spots with the largest energy density tend
to occur in the absence of wake-induced disturbances, and they tend to be of moderate
size. The bypass transition associated with wake passing and the downstream growth
(and crowding) of spots as the transition process nears completion, do not favor large
energy densities.

Other combinations of parameters showed no significant trends. They are worth
reporting, since an absence of trend would allow for simpler models to be used. For
example, on Fig. 10, the leading edge speed is plotted against the energy density.
Similar results were obtained with spot center convection speed. The considerable
scatter in speeds was already visible on Fig. 2.3. In contrast, Fig. 11 shows a wider
range of scales for the slow-moving spots, and a narrow band of (small) spot sizes for
the large speeds. This indicates that a lack of trends on other plots is not due to the

NAS A/CR— 2000-2 1 0694

15

N

>>

U

c

0

13

er

0

c

r—i,

c

E

o

Q

0.00 0.10 0.20 0.30 0.40

Leading edge speed (arb. units)

Figure 11: Scatter plot of leading edge speed and frequency along the blade. Symbols
as for Fig. 7.

NAS A/CR— 2000-210694

16

0.00 0.10 0.20 0.30 0.40

Leading edge speed (arb. units)

Figure 12: Scatter plot of leading edge speed and phase relative to wake passing along
the blade. Symbols as for Fig. 7.

speed being a bad statistic. So, the observation on Fig. 12 that spot speed is not
strongly phase dependent is potentially useful for modeling purposes.

4 Discussion

The GEAE database on unsteady transition was used in the evaluation of spot char-
acterization. This study aimed at the evaluation of techniques for measuring spot
properties, at preliminary assessment of which properties appear sensitive or insensi-
tive to wake-induced or natural transition, and at recommendations for further data
collection aimed specifically at the collection of data for modeling spot properties in
turbomachinery.

The main findings are that four spot properties of modeling interest have been
quantified: frequency, energy, convection speed and phase. The correlation between
energy density and phase (Fig. 9) maybe counter-intuitive, since the most energetic
events occur between wakes. Although this observation is subject to interpretation

NASA/CR— 2000-210694

17

(below), its confirmation would affect modeling requirements in unsteady transition.
The energy density is also correlated to spot size (Fig. 8), but size and phase do not
seem to be correlated (Fig. 7). When convection speed is concerned, no correlations
were apparent .

The measurement of spot properties is conditioned by the naturally unpredictable
location of spots relative to the sensors. A systematic documentation of the effect of
grazing or head-on overlap of individual spots and sensors would provide a measure of
the magnitude of this effect. Given this uncertainty, we were able to assign a number
of quantitative properties to the events. The representation of individual traces in
the time-frequency domain enabled us to isolate individual events, and to remove
the effect of large-scale energetic neighbors from the measured properties. The most
significant improvement s would result from improved event tracking, resulting in more
reliable convection speeds. Current tracking is based on matching an event in a given
trace with the best possible candidate at the following station. Visual examination
shows that, while the algorithm is generally satisfactory, it might benefit from two-
directional matching over more than two stations.

While improved algorithms (above) and dedicated data collection (below) would
yield better quantitative results, a preliminary assessment is possible about the effect
of wake passing on spot properties. A lack of effect makes the modeler’s job easier, and
this seems to be case for spot convection speed. However, some caution is necessary
because convection speed is affected by both the tracking algorithm and the frequency
resolution of the data. Also preliminary, but with consequences on modeling needs,
is the variability in energy density and spot size with phase and chordwise location.
These effects seems weakly correlated, in spite of the confounding effect of grazing spot
incidence. Both effects could be related to spot crowding as the transition progresses.

The database used in this project is extremely rich in information, and was not
assembled to study the details of spot motion. Higher frequency resolution would
have several beneficial consequences: insight into the internal structure of events,
with the possible distinction of spots and other disturbances, and improved location
of the spots leading edges, would directly improve the current results. Also, the use of
multiple miniature sensor arrays would provide useful information about the relative
location of spots and sensors, and ensuing distortions of the spot’s footprint.

In conclusion, this study points to future work related to spot characterization
in turbomachinery flows. Feasible improvements to the data acquisition and the
processing algorithms would lead to a more reliable and quantitative evaluation of
modeling expectations in these complex flows.

NASA/CR— 2000-2 10694

18

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LS 1998-06, F.A.E. Breugelmans Ed.), Parts I, II and III.

[10] J. Lewalle, D.E. Ashpis and K.-H. Sohn (1997), ‘Demonstration of wavelet
techniques in the spectral analysis of bypass transition data’, NASA TP-3555.

[11] J. Lewalle, D.E. Ashpis, D.E. Halstead and D.C. Wisler, (2000), ‘The estima-
tion of integral time scales in unsteady flows.’, NASA TM-2000-209452.

[12] Y. Meyer (1993), ‘Wavelets: algorithms and applications’, S.I.A.M.

[13] CAV. Van Atta and K.N. Helland (1980), ‘Exploratory temperature tagging
measurements of turbulent spots in a heated laminar boundary layer’, J. Fluid
Mech. 100 , 243-255.

NAS A/CR— 2000-2 1 0694

19

REPORT DOCUMENTATION PAGE

Form Approved
OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,
gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this
collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports 1215 Jefferson
Davis Highway. Suite 1204. Arlington. VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington DC 20503

1 . AGENCY USE ONLY (Leave blank)

4. TITLE AND SUBTITLE

2. REPORT DATE

December 2000

3. REPORT TYPE AND DATES COVERED

Final Contractor Report

5. FUNDING NUMBERS

Detection, Tracking and Analysis of Turbulent Spots and Other Coherent
Structures in Unsteady Transition

6. AUTHOR(S)

Jacques Lewalle

WU-5 23-26-33-00
C-76220-D

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Syracuse University

Department of Mechanical, Aerospace and Manufacturing Engineering
Syracuse, New York 13244

8. PERFORMING ORGANIZATION
REPORT NUMBER

E- 12622

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration
Washington, DC 20546-0001

10. SPONSORING/MONITORING
AGENCY REPORT NUMBER

NASA CR— 2000-210694

11. SUPPLEMENTARY NOTES

Project Manager, David Ashpis, Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center,
organization code 5820, 216-433-8317.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Categories: 34, 02, and 07 Distribution: Nonstandard

Available electronically at http://gltrs.grc.nasa.gov/GLTRS

This publication is available from the NASA Center for AeroSpace Information, 301-621-0390.

13. ABSTRACT (Maximum 200 words)

Transition on turbine blades is an important factor in the determination of eventual flow separation and engine perfor-
mance. The phenomenon is strongly affected by unsteady flow conditions (wake passing). It is likely that some physics of
unsteadiness should be included in advanced models, but it is unclear which properties would best embody this informa-
tion. In this paper, we use a GEAE experimental database in unsteady transition to test some tools of spot identification,
tracking and characterization. In this preliminary study, we identify some parameters that appear to be insensitive to wake
passing effects, such as convection speed, and others more likely to require unsteady modeling. The main findings are that
wavelet duration can be used as a measure of spot size, and that spot energy density is most closely correlated to the wake
passing. The energy density is also correlated to spot size, but spot size appears unrelated to the phase angle. Recommen-
dations are made for further study.

14. SUBJECT TERMS

Turbulence; Transition; Turbomachinery; Unsteady flows; Boundary layers;
Turbulent spots; Wavelets; Wakes; Freestream turbulence; Coherent structures

17. SECURITY CLASSIFICATION
OF REPORT

18. SECURITY CLASSIFICATION
OF THIS PAGE

19. SECURITY CLASSIFICATION
OF ABSTRACT

20. LIMITATION OF ABSTRACT

Unclassified

Unclassified

Unclassified

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18
298-102