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# Conditional averages of large scale motions through synchronous PIV and surface shear stress measurements

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## Abstract and Figures

Synchronous stereo particle image velocimetry (PIV) and fluctuating wall shear stress measurements were performed in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Multiple, discrete PIV planes allow for a reconstruction of the wall shear stress-streamwise velocity cross correlation in a volume around the sensor. The velocity field is averaged on imposed conditions of the wall shear stress to identify large scale motions during these conditions. A simple condition based on large scale dynamics is introduced to identify periodic patterns of the velocity field associated with wall-distance scaling. This study represents a novel application of microelectromechanical systems floating element wall shear stress sensor types simultaneously with PIV, and addresses experimental procedures to prevent degradation and signal corruption caused by both seeded flow and laser radiation.
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13th International Symposium on Particle Image Velocimetry – ISPIV 2019
Munich, Germany, July 22-24, 2019
Conditional averages of large scale motions through
synchronous PIV and surface shear stress
measurements
Rommel J. Pabon1, Lawrence Ukeiley1, David Mills2, Mark Sheplak1,2
1University of Florida, Mechanical and Aerospace Engineering, Gainesville, FL USA
2Interdisciplinary Consulting Corp, Gainesville, FL, USA
ukeiley@uﬂ.edu
Abstract
Synchronous stereo particle image velocimetry (PIV) and ﬂuctuating wall shear stress measurements were
performed in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Multiple, dis-
crete PIV planes allow for a reconstruction of the wall shear stress-streamwise velocity cross correlation in
a volume around the sensor. The velocity ﬁeld is averaged on imposed conditions of the wall shear stress
to identify large scale motions during these conditions. A simple condition based on large scale dynamics
is introduced to identify periodic patterns of the velocity ﬁeld associated with wall-distance scaling. This
study represents a novel application of microelectromechanical systems ﬂoating element wall shear stress
sensor types simultaneously with PIV, and addresses experimental procedures to prevent degradation and
signal corruption caused by both seeded ﬂow and laser radiation.
1 Introduction
With recent advances in microelectromechanical systems (MEMS) manufacturing, a variety of sensor types
have been introduced into the ﬂuid experimentalist’s toolbox that help facilitate the understanding of ﬂow
structures. These not only assist in detailed studies paired with simulations for validation purposes, but are
required for very large Reynolds number experiments where traditional apparatus fail to resolve required
scales. Therefore, the need for time resolved, accurate measurement of the ﬂuctuating wall shear stress,
τ0
w, is expected to increase as ﬂow Reynolds numbers increase. MEMS ﬂush mounted wall shear stress
sensors enable a direct, non intrusive sensing method that captures relevant ﬂow scales without imposing
restrictive assumptions on the ﬂow (Naughton and Sheplak (2002)). These sensors are expected to play an
important role in revealing the organized motions in the velocity ﬁeld that have the greatest impact in the wall
shear stress. However, their ability to withstand the experimental conditions of particle image velocimetry
(PIV) has still not been studied. This includes the undesirable sensitivity to incident ﬂuence and associated
electromagnetic interference with generating the laser pulse as well as damping or damage when a ﬂoating
element sensor is exposed to a seeded environment.
The importance of wall measurements in this work is to capture energetic motions through the use
of conditional sampling and averaging. These techniques have identiﬁed phenomena critical to the life
cycle of turbulence in a turbulent boundary layer, and are still used to propose structures that involve the
coherent alignment of smaller structures (Kovasznay et al. (1970); Wallace et al. (1972); Zhou et al. (1999)).
Blackwelder and Kovasznay (1972) introduced the variable interval time average (VITA) as a detection
criteria for turbulence in a localized spatio-temporal region. The VITA of a ﬂuctuating quantity q0(t)can be
deﬁned as
VITA(q0) = ˆq(t,T) = 1
TZt+T/2
tT/2
q0(s)ds,(1)
which serves as a local averaging technique with arbitrary averaging time T, which should be of the order
of the relevant ﬂow time scale. In addition, Blackwelder and Kaplan (1976) added a measure of the local
turbulent energy by applying the VITA to the square of the velocity, called the VARVITA of the signal,
VARVITA(q0) = c
var(t,T) =
b
u2(t,T)[b
u(t,T)]2.(2)
where detection criteria can be deﬁned as a threshold when the VARVITA exceeds a chosen constant multi-
plier of the global variance. These techniques, and others such as number of zero crossings, are principally
statistics based, and do not use dynamics in previous measurements, for example, as condition. Dynamic
changes in the shear stress can be introduced to monitor bursting-sweeping incidents or large scale changes
of shear direction. However, the high turbulence of the wall shear stress occludes information directly from
differential measurements as being a result of high turbulence events. Therefore, a technique to isolate scales
of interest needs to be introduced. In this work, a variety of conditional sampling techniques will be applied
to identify aspects of large scale motions utilizing the synchronous measurement of velocity through PIV
and ﬂuctuating wall shear stress through MEMS ﬂoating element wall shear stress sensors.
Figure 1: Schematic of PIV measurement planes (in green) relative to static sensor location (in red), with
nominal spacing between planes (except for near sensor) of 8 mm (0.3δ)and plane thickness of 3.8 mm.
2 Experimental Methods
2.1 Facility
All experiments were performed in the Engineering Laboratory Design (ELD) 407B circulating wind tunnel
at the University of Florida. The ELD tunnel uses a heat exchanger mounted alongside a ﬂow conditioning
section, along with a set point controller to regulate incoming chilled water ﬂow so that air temperature can
be controlled to within ±1C. Downstream of this section and a 25:4 area contraction, the experimental test
section was mounted with dimensions of 0.61 m ×0.61 m ×2.44 m, and a velocity range up to 90 m/s,
with optical access to the test section interior provided by acrylic windows on all four sides. Further details
of the experimental conﬁguration used for this study can be found in Pabon (2018).
A ﬂat plate model was installed in the test section to create a turbulent boundary layer on the top surface.
The leading edge used the optimized proﬁle of Hanson et al. (2012) to reduce the length of the non-zero
pressure gradient region. An aluminum trailing edge ﬂap is used to control the circulation around the ﬂat
plate by rotation around a supporting hinge, in practice, along with a streamwise row of static pressure taps,
a linear pressure gradient can be imposed on the top surface. For a given run speed, a trailing edge ﬂap angle
is interpolated from a library of previous measurements that results in a zero pressure gradient across the
measurement surface. The measurement windows of the ﬂat plate model allow the shear stress sensor to be
placed 1.41 m from the leading edge, allowing for both upstream and downstream viewing from cameras.
Along with sandpaper roughness for tripping near the leading edge, at a nominal run speed of 25 m/s, Reθ
for the measurement planes was between 4200 and 4400. For further details on the construction, design, and
implementation of the zero pressure gradient condition, the reader is directed to Pabon et al. (2018), where
hot-wire measurements were performed in the same experimental setup.
2.2 Particle Image Velocimetry
Stereo particle image velocimetry was utilized to capture non-time resolved, two-dimensional, three-component
velocity ﬁelds at a series of measurement planes relative to the shear stress sensor. The illumination source
was a Litron Nano L 135-15 Nd:YAG laser outputting 532 nm wavelength light, with a maximum output
and double-pulse repetition rate of 135 mJ and 15 Hz, respectively. A focusing and cylindrical lens optical
setup allowed a light sheet thickness approximately 3.8 mm thick. While on the higher end of recommended
thicknesses (Raffel et al. (2007)), this experimental choice allowed for larger pulse time separations, thus
allowing higher particle displacements in the in-plane directions. Two LaVision Imager sCMOS cameras
with a sensor size of 2560 ×2160 pixels, a maximum frame rate of 50 Hz, and 16-bit digital output were
used with a stereoscopic angle of 68, with the cameras on either spanwise side of the wind tunnel. This
angle helps improve robustness to the out-of-plane velocity gradients and other factors during calibration
LaVision (2016). The cameras were equipped with 200 mm lenses, and for certain positions, polarizing
ﬁlters to reduce the specular reﬂection of the laser plane off of the acrylic plate.
A LaVision type 11 calibration plate was utilized along with external LED lighting to carry out the
stereo calibration procedure, and to focus the image plane as close as possible to the laser plane. A pinhole
model is utilized to ensure approximate agreement between the calculation and the physical setup, as well
as to ensure the edges of the image (areas typically without calibration target spots), especially near the
wall, will be correctly calibrated. For a given plane, a preliminary image set of 200 images is used for the
self-calibration step to improve the calculation of the location of the image plane relative to the laser plane.
Disparity vectors are minimized until average disparity is below 0.3 px for a new triangulated plane as close
as possible to the light sheet center. A Gaussian mean with ﬁlter length of 7 image pairs is subtracted over
the images to eliminate background artifacts from the data. A minor pre-processing step was used after this
to normalize particle intensities and backgrounds, primarily to correct minor differences in the laser intensity
along the plane. The spectral cross correlation step is implemented on interrogation windows of ratio 2:1
(spanwise:wall-normal). Two initial passes are performed to reﬁne the windows with 50% overlap, and the
ﬁnal two passes utilized adaptive windows with one-quarter the initial area, resulting in the ﬁnal vector grid
resolution. Between passes, only vectors with peak-to-peak ratios (PPR) worse than 1.1 are removed, along
with a minor universal outlier detection median ﬁlter (Nogueira et al. (1997); Westerweel et al. (2005)).
High-accuracy mode with B-spline-6 reconstruction is utilized in the ﬁnal pass.
101102103104
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Figure 2: Power spectral density of CSSS at 25 m/s compared to noise ﬂoor (0 m/s) with (on) and without
(off) simultaneous PIV laser ﬁring at a distance of 7 mm. A) CS-A05 sensor with SNR = 4 dB, and B)
CS-D100 sensor with SNR = 33 dB, each at 1 kHz.
The major post-processing steps after vectors are calculated increases the PPR tolerance to 1.25, with
the same tolerance in median ﬁlter, to iteratively ﬁnd preferred peaks. If a grid point failed all these steps,
spatial interpolation was introduced, but there is no smoothing introduced in any pass. Interpolation was
found to occur in approximately 1% of a given snapshot, with 90% of these interpolated points occurring at
or just above the physical wall. Thus, masking the ﬁrst calculated row above the wall drastically cut down
spurious vectors, resulting in the closest wall normal position to the wall being near 320 µm. After the stereo
and self calibration steps, the rms ﬁt error was calculated at 1.02 px, the scale factor was 63 px/mm, and the
vector grid resolution was 254 µm.
Eleven separate measurement planes are utilized, where illumination planes were wall-normal, spanwise
oriented, with a series of such planes at different relative streamwise locations relative to the sensor. This
is seen in a schematic in Fig. 1, spanning a streamwise distance of about 6δand a total of 96000 image
pairs. Most planes were composed of 8000 image pairs, with the ﬁrst plane consisting of 16000 image pairs
to verify statistical convergence. A nominal spacing between planes of 8 mm, approximately 2 laser plane
thicknesses is used, except for directly on top of the sensor, and just downstream. While direct incident laser
radiation was avoided due to data contamination to be discussed in a later section, the experimental setup
did not allow for calibration just downstream of a sensor due to placement of the calibration plate, with the
sensor needing to be mounted during calibration to avoid movement of cameras and windows.
2.3 Capacitive Shear Stress Sensor
Two IC2 DirectShear CS-D100 MEMS ﬂoating element differential capacitive shear stress sensors (CSSS)
were used in this study, identiﬁed as I25-D818 and I25-U818. Their ﬂoating element sizes are 2 mm ×0.4
mm (L+×W+126 ×25), with the major axis aligned in the streamwise direction. They have bandwidths
of 2.5 kHz ( f+0.2), sensitivities of 29 mV/Pa, and height perturbations from manufacturing and assembly
of approximately 25 µm (h+1.), allowing a ﬂushness approximation for the sensor die. They are each
powered by an external sensor control unit with battery operation mode to attenuate power line noise. The
reader is directed to Mills et al. (2018) and Mills et al. (2017) for a comprehensive guide to the manufacturing
processes behind the sensor system, as well as recent developments improving the sensor, electronics, and
control unit for aerodynamic measurements.
While higher bandwidth sensors were considered with the goal of resolving the smallest relevant ﬂow
scales, the current sensors were chosen because they provided sufﬁcient signal sensitivity to overcome re-
sponse to the laser pulse. A comparison between a CS-A05 sensor, with a bandwidth of 5 kHz, and the
CS-D100 used in this study is presented in Fig. 2 when presented with laser radiation at a distance of 7
mm, with the signal-to-noise ratio of the CS-D100 being 33 dB. This was determined to be sufﬁcient to
continue experiments, although reﬂective coating and other electronic changes to avoid such contamination
is suggested for future sensor designs.
101102103
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Figure 3: Power spectral density of CSSS measurements over full range of measurements, verifying laser
degradation over time, A) for I25-D818 sensor, which lasted for all eleven PIV planes, and B) for I25-U818
sensor, which failed for undetermined reasons, most likely due to PIV seeding, after the fourth PIV plane.
The CS-D100 was not rated for use in a seeded environment as would be required for PIV, and prelimi-
nary experiments suggested that long-term sensor degradation was possible. A procedure was implemented
to minimize the opportunities for seed to become trapped under the ﬂoating element and between the comb
ﬁngers. First, the CSSS were removed with the tunnel still running at low speeds (<5 m/s), to prevent the
density difference from allowing the seed to deposit on the top surface of the ﬂat plate, and thus the sensor.
For future work, a similar experiment is recommended to use the measurement surface on the bottom side
of the plate, so that seed is less likely to settle on the die head. In addition, during removal, a tunnel window
was opened to allow entrainment of unseeded air in the room and further minimize number density in the test
section. Second, the sensor was physically transported to a separate room without seed present for storage.
Finally, sensor checks before and after runs were implemented to track and verify sensor functionality. How-
ever, sensor degradation was not totally avoided, and the second sensor, I25-U818, failed after the fourth
plane. A comparison of the power spectral density between the two sensors is presented in Fig. 3, with a
degradation around the resonant peak visible between planes for the -U818 sensor, but not for the -D818
sensor. This degradation did not affect the measurements, due to the low-pass ﬁlter removing the sensor
response past the bandpass frequency, as well as the magnitude response of the sensor at each plane being
very consistent in the passband. The degradation near the resonant peak suggests seed related damping, and
ﬁnally failure, and after microscopic investigation, the ﬂoating element is seen to be clamped to one set of
sensor electrodes. The fact that each sensor was given the same treatment implies a substantial risk to CSSS
use in seeded ﬂow unless changes are made to the sensor design. After the failure of the -U818 sensor,
experiments were repeated using only the -D818 sensor, with an increased number of required planes to
capture the desired streamwise ﬁeld of view. The compound reconstruction of the PIV planes onto a single,
artiﬁcial ‘global’ sensor is seen in Fig. 1, where the planes relative to each sensor used are displayed. The
sensors were mounted 38.1 mm apart (1.75δ), differences in energy due to downstream distance (i.e. Reθ
of 4250 vs 4300) were considered negligible for the reconstruction.
3 Results and Discussions
The wall shear stress is captured synchronously with the velocity, but at different sampling speeds, 10.8
kHz and 12 Hz, respectively, each triggered to begin on the ﬁrst laser pulse. The wall shear stress signal is
low pass ﬁltered at its +3 dB cutoff bandwidth of 2.5 kHz. Since temporal information pre- and post- laser
pulse is required, the data from the ﬁrst and last laser pulse and resulting wall shear stress information is
(a)
-10 -5 0 5 10
tU/δ
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Rτu,DS
0.014
0.036
0.058
0.113
0.278
y/δ
(b)
Figure 4: Rτuvs. non-dimensional time delay for select wall normal positions along the spanwise centerline
for PIV planes with streamwise location xp/δ=a) -1.82, and b) 3.95.
3.1 Cross correlation
Typically, the temporal cross correlation coefﬁcient between wall shear stress and streamwise velocity, Rτu,
would be calculated in spectral space for the popularity and efﬁciency of FFT algorithms, but this is not
possible in the current study with the PIV sampling rate being much lower than the wall shear stress sam-
pling rate. Instead, an average over a certain temporal separation window is performed, assuming that an
instantaneous PIV sample retains its value between each sample for necessity of the averaging process. The
window used is approximately tU/δ=20 to allow a return to zero correlation at extreme time lags for the
extremes of the PIV planes. The result is displayed in Fig. 4 for the most upstream and downstream plane,
respectively, with respect to the sensor located at xp=0. Convection of the correlation is observed, as well
as a decorrelation with distance from the sensor. The approximate noise value (rms of the correlation at
‘extreme’ time lags) of Rτuis approximately 0.02. The primary source of noise is ﬁrst, the cross correlation
procedure which reduces the number of averages compared to spectral methods, for example, and second,
the sPIV algorithm itself. However, the relatively high correlation coefﬁcient values (0.5), compared fa-
vorably to previous HWA experimental values (Pabon et al. (2018)), suggesting estimation methods using
PIV based on correlations are achievable.
Figure 5: Volumetric reconstruction of isosurfaces of Rτu(t=0)calculated in each PIV data plane, Rτu=0.1
in red and Rτu=0.1 in blue.
At each measurement plane, Rτu(δt=0), the zero time lag cross correlation, is presented in Fig. 5, using
a volumetric reconstruction, interpolating between planes, and an isosurface threshold of Rτu>±0.1 for
red and blue surfaces, respectively. The principal positively correlated region is approximately 4δ×0.5δ×
0.5δ, with smaller negatively correlated regions ﬂanking on either side. While the data could be averaged
along the z-axis to improve the statistical representation, the resulting asymmetries qualitatively show limits
of the experimental setup in terms of noise, error, or any actual asymmetries present.
3.2 Conditional Averages
To describe an average picture of the velocity ﬁeld during intense events of the wall shear stress, conditional
averaging is applied. This procedure presents a qualitative view of the ﬂow ﬁeld on average during desired
wall shear stress events. This allows a comparison of the effect of threshold level as well as symmetry of
threshold during locally positive vs negative shear events around the global mean. Conditions described in
Pabon et al. (2018) are used here, to calculate the mean streamwise velocity conditioned on positive shear
ﬂuctuation,
e
Uh, and on negative shear ﬂuctuation,
e
Ul, such that
e
Uh(x,y,z) = hu(x,y,z,t)|τ0
w(x=y=z=0,t)>0i,(3)
e
Ul(x,y,z) = hu(z,y,z,t)|τ0
w(x=y=z=0,t)<0i,(4)
Fig. 6 shows isosurfaces of the difference between these conditionally averaged ﬂow ﬁelds and the global
mean velocity ﬁeld, U+
h(x,y,z) = (
e
UhU(x,y,z))/uτand U+
l(x,y,z) = (
e
UhU(x,y,z))/uτ, respectively.
The red and blue isosurfaces represent U+=0.1 and -0.1, respectively. Comparison between the positive
(a) (b)
Figure 6: Volumetric reconstruction using interpolation between each PIV data plane of a) U+
h(x,y,z)
(conditioned on τ(t=0)>0), and b) U+
l(x,y,z)(conditioned on τ(t=0)<0.
and negative conditions shows that the ﬂanking oppositely-signed regions to the central correlated region
is slightly upstream about δfor the negative shear condition compared to the positive. They also appear to
be larger, and extend further away from the wall. Each conditional average has striking similarity to the
cross correlation volume of Fig. 5, with opposite sign for the negative condition. Once again, the slight
asymmetries in the spanwise direction for each condition supports the high quality of the experiments.
With recent works investigating the impact of wall-attached structures on the boundary layer, such as
through the self-similarity of the linear coherence spectrum (Baars et al. (2017); Pabon et al. (2018); Baidya
et al. (2019)), a conditional sampling scheme was developed to identify the pattern these structures create.
From previous work in the current setup using hot-wire anemometry in Pabon et al. (2018), an approximate
linear relation region in the coherence spectrum has been identiﬁed within 2 <λ/δ<10, where λ=
U/fsince only temporal measurements are taken. To isolate velocity dynamics in this region, a bandpass
ﬁlter is applied to the wall shear stress with these limits. Conditions on this ﬁltered mean subtracted wall
shear stress signal, ˜
τ0, are further divided into four regions: I) locally high positive shear stress with low
gradient magnitude, II) locally high negative shear stress with low gradient magnitude, III) locally high
positive gradient with low magnitude of shear, and IV) locally high negative gradient with low magnitude
of shear stress. The time gradient of the bandpassed signal is calculated using a ﬁrst-order backward ﬁnite
difference, for simplicity as well as being for future real time control applications, calculated as
e
τ0
w(tk) =
e
τ0
w(tk)
e
τ0
w(tk1). A representation of these regions can be seen in a simple schematic in Fig. 7. These
differential level VITA conditions, henceforth referred to as DIFFLEVITA, are
DIFFLEVITA I=VITA(
e
τ0
w)>CIσe
τ∩ |VITA(
e
τ0
w)|<DIσe
τ(5)
DIFFLEVITA II =VITA(
e
τ0
w)<CI I σe
τ∩ |VITA(
e
τ0
w)|<DII σe
τ(6)
DIFFLEVITA III =VITA(
e
τ0
w)>CIIIσe
τ∩ |VITA(
e
τ0
w)|<DIIIσe
τ(7)
DIFFLEVITA IV =VITA(
e
τ0
w)<CIV σe
τ∩ |VITA(
e
τ0
w)|<DIV σe
τ(8)
and the coefﬁcients Cand Dare threshold coefﬁcients for the signal magintude and differential signal mag-
nitude, respectively. The additional threshold value for each signal increases arbitrariness for a one-to-one
comparison, but even for the classic VARVITA condition, there is no threshold value at which the result is
independent of threshold Morrison et al. (1989). As such, only qualitative conclusions at best can be taken,
and no large weight can be placed on actual magnitudes from the conditional analysis. The resulting thresh-
olds, to be rooted in a physical phenomenon related to the wall-attached and relevant scales, are chosen such
that the total number of samples retained for each condition is 9% of the total, half the traditional bursting
frequency (Corino and Brodkey (1969)). In addition, the thresholds were desired to be symmetric between
the positive and negative conditions, such that the ﬁnal threshold values were CI=CII =CIII =CIV =0.75
and DI=DII =DIII =DIV =0.5.
Figure 7: Schematic showing representative bandpassed wall shear stress signal, identifying regions that
satisfy DIFFLEVITA conditions I-IV.
(a) (b)
(c) (d)
Figure 8: Volumetric reconstruction using interpolation between each PIV data plane of difference between
conditionally averaged streamwise velocity ﬁeld and mean streamwise velocity ﬁeld given a) DIFFLEVITA
I, b) DIFFLEVITA IV, c) DIFFLEVITA II, and d) DIFFLEVITA III. Note the increased isosurface values of
0.2 and -0.2, respectively,
Isosurfaces of the volumetric reconstruction of each condition is shown in Fig. 8, in the order I,IV ,
II, and III, suggested by the periodic schematic in 7. Each spatial representation presents as a phase of a
periodic structure that convects downstream following the phase pattern, as well as diminishes at distance
to the sensor. Within the ﬁeld of view, streamwise gradients are visible using this conditional average. This
implies that a life-cycle duration of wall attached eddies is captured here at a single point of wall shear
stress, with the conditional procedure selecting structures of streamwise wavelength of approximately 4δ.
These present as inclined structures that follow each other in convection. The older, convected, and oppo-
sitely signed structure is inﬂuencing the lift-up and inclination of the newer one. This highlights potential
wavelengths and structure models to target for future ﬂow control experiments.
4 Conclusions
The use of MEMS ﬂoating element wall shear stress sensors in a turbulent boundary layer with simultaneous
PIV was completed for the ﬁrst time in this study. A suitable experimental procedure is described that
limited the sensor to damage from seed-exposure as well as data corruption from laser radiation. Multiple,
discrete experiments moving the PIV measurement plane allows for a volumetric reconstruction of the cross
correlation, as well as conditional averages on the wall shear stress. High PIV-wall shear stress correlation
values imply correlation based estimation techniques have merit in following the experimental procedures,
with spectral techniques possible, but limited due to the dissimilar sampling rate, with higher capture rate
PIV being suggested. The large number of PIV image pairs used in the study (100,000) helps acquire both
extreme, rare events of interest to turbulence production, as well as ensuring convergence of statistics. A
novel differential and level based conditional sampling scheme is introduced to capture a periodic structure
associated with wall-attached scaling. The investigation of the dynamic component of identiﬁed shear events
in this work is intended to continue and develop drag control methodologies and structure identiﬁcation.
Acknowledgements
This material is based upon work supported by the National Science Foundation Graduate Research Fel-
lowship under Grant No. DGE-1315138. The authors also wish to acknowledge the support of the Florida
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Streamwise velocity and wall-shear stress are acquired simultaneously with a hot-wire and an array of azimuthal/spanwise-spaced skin friction sensors in large-scale pipe and boundary layer flow facilities at high Reynolds numbers. These allow for a correlation analysis on a per-scale basis between the velocity and reference skin friction signals to reveal which velocity-based turbulent motions are stochastically coherent with turbulent skin friction. In the logarithmic region, the wall-attached structures in both the pipe and boundary layers show evidence of self-similarity, and the range of scales over which the self-similarity is observed decreases with an increasing azimuthal/spanwise offset between the velocity and the reference skin friction signals. The present empirical observations support the existence of a self-similar range of wall-attached turbulence, which in turn are used to extend the model of Baars et al. ( J. Fluid Mech. , vol. 823, p. R2) to include the azimuthal/spanwise trends. Furthermore, the region where the self-similarity is observed correspond with the wall height where the mean momentum equation formally admits a self-similar invariant form, and simultaneously where the mean and variance profiles of the streamwise velocity exhibit logarithmic dependence. The experimental observations suggest that the self-similar wall-attached structures follow an aspect ratio of $7:1:1$ in the streamwise, spanwise and wall-normal directions, respectively.
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Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v , and these classified portions were then averaged to obtain their contributions to the Reynolds stress $-\rho\overline{uv}$ . The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign. The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions ( u < 0, v > 0 and u > 0, v < 0) were found to have significantly larger time scales than the negative stress producing motions ( u < 0, v < 0 and u > 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.