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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 

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 


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. 

Available from 

NASA Center for Aerospace Information 
7121 Standard Drive 
Hanover, MD 21076 
Price Code: A03 

National Technical Information Service 
5285 Port Royal Road 
Springfield, VA 22100 
Price Code: A03 

Available electronically at http: // 

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 


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 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 


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 


A A 

\i v A 

N A\, 





0.0020 0.0030 

Elapsed time (s) 


(A i 




0 0050 


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 


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 

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) 


«(*) = 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 


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 


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 


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 

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 


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 


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 


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 


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 


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 
















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 


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 

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 


(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 



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NAS A/CR— 2000-2 1 0694 



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December 2000 


Final Contractor Report 


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


Jacques Lewalle 

WU-5 23-26-33-00 


Syracuse University 

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


E- 12622 


National Aeronautics and Space Administration 
Washington, DC 20546-0001 


NASA CR— 2000-210694 


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


Unclassified - Unlimited 

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

Available electronically at 

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. 


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








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