PTV for the Characterization of Turbulent
Channel Flow: Comparison of Experimental and
Simulation Approaches
M. Moroni1, J. Nogueira2, M. Miozzi1, G.P. Romano1, A. Cenedese1, P.A. Rodriguez2, A. Lecuona2
1
2
University of Rome “La Sapienza”, Via Eudossiana 18, Roma, Italy
Carlos III University of Madrid, C/ Madrid 126 28903 - Getafe (Madrid), Spain
Abstract
The presence of a large number of different software codes for image analysis, including several variants for the image interrogation, suggests the need for testing
the suitability and accuracy of the developed algorithms. One of the possible approaches is testing these systems with experiments of well-known flow properties.
Otherwise, tests can be performed by analyzing synthetically generated images.
The advantage of the latter approach is that there is no need to set-up an experiment and the flow field is known in detail. On the other hand, there are obvious
doubts on how close a synthetic image can describe the reality. This paper provides some insight on the relation between results on real and synthetic images
both in a turbulent channel flow. A classical Particle Tracking Velocimetry (PTV)
algorithm will be presented as well as the advanced PTV using Feature Tracking.
1 Introduction
Over the past few decades particle imaging based techniques have been used to
develop whole-field velocity measurements. Today it is common to distinguish
between two methods of image interrogation, depending on the number density:
- Particle Tracking Velocimetry (PTV) for low image density (Lewis et al., 1987;
Kobayashi et al., 1989; Cenedese et al., 1997, among others);
- Particle Image Velocimetry (PIV) for medium image density (Adrian, 1991;
Westerweel, 1998; Nogueira et al., 2001, among others).
Particle Tracking Velocimetry is less extensively used and, compared to PIV,
allows a larger spatial resolution and an increased velocity dynamic range. Another of its big advantages is that, with the proper experimental set-up, it is a fully
three-dimensional technique through which long trajectories can be reconstructed.
It is therefore especially suited to a Lagrangian study of fluid motion, a feature
that the other techniques do not have (Virant and Dracos, 1997).
The flow in the vicinity of a smooth wall (inner region) has, due to effects of
viscous stresses and the anisotropy imposed by the wall, a distinctly different
character than in the outer region (Alfredsson and Johansson, 1984). Turbulent
280 Session 5
flows, even in the presence of walls, are classically described, in a Eulerian
framework, by the mean velocity, the turbulent intensities and the Reynolds stress
profiles.
Few works deal with the motion of particles in turbulent flow fields in the Lagrangian framework (Shlien and Corrsin, 1974). On the other hand, direct numerical simulation (DNS) of turbulent flows allows one to extract Lagrangian data by
particle tracking, and thus to thoroughly investigate the Lagrangian statistics properties of such flows (Yeung and Pope, 1989; Squires and Eaton, 1991).
The present paper describes some results on the relation between PTV results
on real and synthetic images both in a turbulent channel flow, focusing on the
measurement of turbulent flow statistics. This flow has two basic characteristics:
statistical results are well-known from direct numerical simulation (DNS) at low
Reynolds numbers and large velocity gradients are present close to the wall. The
latter property makes it particularly difficult for the analysis by image interrogation methods.
The specific problems we are addressing are: (i) the problem of instantaneous
and square averaged velocity fluctuations, (ii) the sensitivity of the results to the
algorithm and to the image analysis “parameters”, (iii) the computation of the
variables to derive non-dimensional results, and (iv) the relation between quantities describing turbulence in the Eulerian and Lagrangian frameworks.
The turbulence statistics investigated are: mean velocity in the axial and normal
directions, the root mean square (rms) of both velocity components (turbulent intensities) and relative Reynolds stress in the Eulerian framework; the translient
matrix and time scales in the Lagrangian framework (Stull, 1984 ).
2 The classical PTV Algorithm
Particle Tracking Velocimetry (PTV) allows tracking the paths of individual particles in space.
The main steps to follow when a PTV investigation is developed through classical algorithms are: (a) seeding the flowing fluid with small highly reflecting particles while maintaining a low particle density; (b) illuminating as uniformly as
possible the flow field with a light sheet; (c) acquiring images of the particles located in this volume with an imaging rate that determines the time resolution of
the method; (d) eventually pre-processing the images to eliminate background
noise; (e) determining the particle image coordinates in each frame with sub-pixel
accuracy and (f) tracking particle centroids frame by frame. Details on the algorithms we used can be found in Udrea et al., 2000.
Since there is no theoretical limitation to the length of the trajectories that can be
recognized, tracking of single exposed images allows evaluating the Lagrangian
statistics of turbulence and in particular the Lagrangian time scales. On the other
hand, interpolating the sparse velocity vectors on regular grids, Eulerian velocity
can be detected as well.
Turbulence and PTV 281
3 Advanced PTV using Feature Tracking
The feature tracking technique, derived from the Kanade-Lukas-Tomasi tracker
(Lucas and Kanade, 1981; Tomasi and Kanade, 1991; Shi and Tomasi, 1994), can
be considered as an extension of the classical PTV technique. As a matter of fact,
instead of reconstructing trajectories through evaluating the position of tracer particle centroids within each frame, trajectories are reconstructed by analyzing the
evolution, frame by frame, of the displacements and the deformations of windows
surrounding selected features. Such windows may contain a portion of the tracer
particle, the whole particle or more than one particle. Gradient fronts can be
tracked as well.
The Feature Tracking (FT) algorithm is a Particle Image Velocimetry method
based on distance measure (SSD, Sum of Squared Differences) minimization
problem. This algorithm can be classified as a local (tracking), differential, optical
flow method: the general hypothesis concerns the Brightness Constancy Constrain, an acceptable condition for a fluid dynamic experimental set-up in when
lighting conditions don’t change (or at least their change is very small) during image acquisition. The method defines the matching measure between fixed-sized
feature windows in two consecutive frames: the displacement (velocity) is defined
as the one that minimize SSD.
Before tracking features, they have to be extracted. The feature extraction algorithm is defined in such a way that the optimal solution of the tracking algorithm
is achieved. It is not necessary to provide the algorithm with non-objective parameters (to be provided to classical PTV routines). Rather than defining a subjective, a priori, notion of a good window, this definition is based on the method
used for tracking itself: “a good window is one that can be tracked well”. With this
approach, one knows that a window is omitted only if it is not good enough for the
purpose; it follows that the selection criterion is optimal by construction.
More details on the technique can be found in Miozzi, 2003 and Cenedese et
al., 2003.
4 The Synthetic Image Generator
The synthetic images generated for this work follow traditionally accepted conceptions (Westerweel et al. 1997, Fincham and Speeding 1997, Nogueira et al.
1999, among others). The most recent milestone in this path is the SIG (synthetic
image generator) developed within Europiv2, whose details are described elsewhere in this book.
The particular characteristics concerning the images used in this work were designed to match the experimental images to which they compare; this is described
in detail below. The value of the effective mean distance between particles in the
images depends on the range of light intensity that is considered. The illumination
of the particles corresponds to a laser light-sheet with a Gaussian profile. A particle located in the center of the light sheet produces a maximum gray level of 1020.
This value goes down to 1020·e-8= 0.34 at two light-sheet widths (commonly the e-
282 Session 5
2
positions in the Gaussian profile define the laser light-sheet width). Considering
all the particles within the light sheet, the mean distance between particle images
is δ=15 pixels i.e. 4/(πδ2)~5.5·10-3 ppp (particles per pixel area). The particles have
equal possibility of being in any position in respect to the laser sheet. Consequently, the mean distance between particles for any other intensity range can be
easily calculated.
IN
y
z
x
in fra red L A S E R
h ig h s pe e d
vid e o ca m e ra
m irro r
OUT
PC
Fig. 1. Experimental set-up.
The range of gray-levels depicted in the image is from 0 to 255. This means
that gray levels above this value are considered as saturation and depicted in the
255 level. The shape of the particles is Gaussian as well. It is integrated with unity
fill factor over each pixel surface (Westerweel, 1998). The e-2 diameter of the
Gaussian particle images is d=4 pixels ± a random value within 0 and 1.4 pixels.
Where particles overlap, the corresponding intensities are added. To account for
the camera thermal noise, each pixel has an additional random value from 0 to 16
added to the gray level. Also the accumulation of particles on the channel walls
was simulated. Based on the observation of the experimental images, the particle
image diameters for the lower wall were allowed to range between 0.5 and 4 pixels. For the upper wall this range was fixed between 0.21 and 0.36 pixels. All this
gave a realistic representation when comparing to the particles in the experimental
images. Nevertheless the background light scattered around these particles and the
borders of the channels were not simulated.
The flow field contained in the synthetic cases corresponds to a channel flow
DNS data provided by the Laboratory for Aero and Hydrodynamics (AHD) of the
Delft University of Technology (Haarlem, 2000). Only one frozen frame of this
DNS was used. Taylor hypothesis allows advancing in time. The Reynolds num-
Turbulence and PTV 283
ber of this flow is, Re= 3300 based on h (the channel half-width) and on U (the
mean velocity at the centerline).
5 Experimental Set-up
Experiments were run in a horizontal water channel of rectangular cross-section (2
cm×22 cm) containing a fully developed turbulent flow (Fig. 1).
A coordinate system is introduced with its origin on the lower channel wall, the
x-axis in the flow direction and the y-axis normal to the bottom of the channel
positive in the upward direction. The corresponding components of the velocity
vector U are u and v.
Two water tanks supply the inlet and the outlet of the channel. Different velocities are achieved changing the height of the inlet vessel. Measurements are
made at about 140 cm downstream of the inlet (x/h = 140, where h= 1 cm). The
water is re-circulated.
The infrared radiation of a laser diode array (maximum power equal to 15 W) is
focused on a region of the (x, y) plane. The thickness of the laser sheet is about 1
mm. Images of the well reflecting tracers (pollen particles with an average size
equal to dp= 40 µm) are recorded using a high-speed video camera (MotionScope® PCI Redlake). The particles are injected into the flow at a point located
1.3 m from the acquisition window.
The camera allows a high frame rate (from 50 to 1000 fps). The number of acquired images as well as their resolution depends on the frame rate. They are
stored directly on the mass memory of the computer (till 100Mbyte per acquisition). For the present set of measurements, the time interval between images, as
well as the temporal resolution, is 1/250 s whereas the space resolution is equal to
480×420 pixels. The dimension of the illuminated area is 2 cm × 2.28 cm.
6 Comments about Synthetic and Real Images and Details
on the Analysis
Fig. 2 displays the negatives of one of the PTV images acquired during the experiments.
There is an evident background light near the walls, mostly close to the upper
one that was not subjected to attenuation during the experiments. This background
light near the walls has not been included in the simulation. Further, the light sheet
was not homogeneous in the axial direction, causing an inhomogeneous tracer
particle density within each experimental image. The simulation parameters have
been adjusted to match the left half of the real image, i.e. the one more illuminated, and a homogeneous seeding was imposed.
284 Session 5
Fig. 2. Negative of a PTV image.
Figs. 3 and 4 present a composition of respectively ten real and ten synthetic
images, each shifted with respect to the following one along the streamwise direction of 24 pixels (about 0.8 times the mean axial velocity at the center of the
channel). The differences that can be observed are:
- there is no light reflection on the upper part of synthetic images;
- due to the light sheet homogeneity, in the synthetic images there is almost double effective seeding density;
- the camera background noise in the synthetic images is random.
Fig. 3. Composition of 10 real images subtracting 24 pixels between consecutive ones.
The experimental data at Re = 2,900 consist of 11 series of 512 images each (Se-
Turbulence and PTV 285
ries1). The synthetic image data consist of 20 series of 101 images generated to be
as similar as possible to images of Series1 (Series2) and 5 series of 401 images
with a mean displacements approximately ¼ of the above (Series3). The synthetic
images of Series3 were analyzed with both the classical algorithm and with the
advanced one. It should be noticed that the frame rate associated to the synthetic
images is larger than 250 fps.
7 Properties of the Flow in the Eulerian Framework
The particle tracking procedure developed yields a considerable number of
reconstructed trajectories. Therefore, a rather small number of repetitions of the
experiment under identical conditions allows one to acquire in a short time a
sufficiently large number of data for statistical analysis. The application of the
PTV procedure yields to two velocity components randomly distributed inside the
observation window.
Fig. 4. Composition of 10 synthetic images subtracting 24 pixels between consecutive ones.
The analysis of those data must take into account the inhomogeneity of the flow
along the y direction. The hypotheses of ergodicity and stationarity allow Eulerian
quantities such as the mean velocity (u+ and v+) and turbulent intensities (u′+ and
v′+) in both the streamwise and normal directions, as well as the Reynolds stress,
to be determined. Further, assuming homogeneity in thin horizontal slices of the
flow, profiles of the quantities of interest can be computed through averaging over
these slices in both time and space. The thickness of these slices is about 0.33 mm,
giving a total of 60 slices.
286 Session 5
The number of velocity vectors N found in each slice varies with depth. Series1
is characterised by a larger number of velocity samples per each depth. We believe
that being the number of samples always larger than 600, reliable statistics can be
computed.
2
Y/d
1.8
1.6
u+ - Exp
v+ - Exp
u+ - Synthetic
v+ - Synthetic
u+ - Kim
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-20
-15
-10
-5
0
u+
5
Fig. 5. Mean velocity as a function of depth for Series1 and Series 2.
2
1.8
1.6
1.4
u'+ - Exp
v'+ - Exp
u'+ - Synthetic
v'+ - Synthetic
u'+ - Kim
v'+ - Kim
1.2
Y/d 1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
u'+, v'+
Fig. 6. Turbulent intensities as a function of depth for Series 1 and Series 2.
The empirical formula by Djenidi et al. (1997) has been used to compute the
friction velocity suitable for having non-dimensional velocity (Cenedese et al.,
2003).
Details on the procedures applied to interpolate the sparse velocity vectors on
regular grids and to compute the friction velocity with empirical formula can be
found in Moroni et al. (2003).
Turbulence and PTV 287
Fig. 5 shows the mean velocity profiles as a function of depth for Series1 and
Series2, whereas Figs. 6 and 7 display the corresponding turbulent intensities and
Reynolds stress, always as a function of depth. Experimental profiles are
compared to DNS data (Kim et al., 1983). The agreement of the mean velocity
profiles is good for both the Series. We underline that an improved match among
experimental curves and the numerical profile is obtained by changing of a given
percentage the friction velocity. This procedure is applied to the data with the
intent to stress the difficulties in determining the “right” friction velocity, mostly
when empirical formulas are employed.
2
(u'v')+ - Exp
(u'v')+ - Synthetic
(u'v')+ - Kim
Y/d
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-4
-3
-2
-1
0
1
2
(u'v')+
Fig. 7. Reynolds stress as a function of depth for Series1 and Series 2.
2
Y/d
1.8
1.6
1.4
1.2
1
u+ - PTV Advanced
v+ - PTV Advanced
u+ - PTV Standard
v+ - PTV Standard
u+ - Kim
0.8
0.6
0.4
0.2
-2.00E+01
-1.50E+01
-1.00E+01
-5.00E+00
0
0.00E+00
u+ 5.00E+00
Fig. 8. Mean velocity as a function of depth for Series3 and PTV algorithm.
The match among turbulent intensities and Reynolds stress from the
experiments and the DNS data is rather good for the experimental data. It is quite
surprising the mismatch between turbulent intensities, but mostly the Reynolds
288 Session 5
stress, of simulated images and the DNS data. This can be due to the smaller
number of samples available for averaging the quantities of interest in the case of
Series2. Further, being the mean particle displacement of approximately 30 pixels,
a quite large number of wrong velocity vectors are reconstructed. In both cases the
turbulent intensities are overestimated around the centreline of the channel. Instead of applying a post-processing algorithm suitable for filtering away “wrong”
velocity vectors, the particle tracking algorithms were applied to new synthetic
images with a mean displacements approximately ¼ of the original ones.
Fig. 8 shows the mean velocity profiles as a function of depth for Series3. The
synthetic images are analysed employing both the classical tracking algorithm and
the advanced one. Figs. 9 and 10 display the corresponding turbulent intensities
and Reynolds stress as a function of depth for Series3. The number of samples as a
function of the depth is much smaller than in Series1 and Series2, but the smaller
time lag between frame helps in getting more reliable statistics, through a more
accurate velocity field reconstruction.
2
1.5
u'+ -PTV
Y/d
v'+ -PTV
1
u'+ -FT
v'+ -FT
0.5
0
-1.0
0.0
1.0
2.0
3.0
u'+,v'+,(u'v')+
4.0
Fig. 9. Turbulent intensities as a function of depth for Series3 and PTV algorithm.
Decreasing the time lags between frames, both the turbulent intensities and the
Reynolds stress are very close to the numerical result. The small number of samples available for computing statistics justifies data scatter. In half of the channel
both the turbulent intensities, but mostly the Reynolds stress, are overestimated.
The opposite behaviour occurs in the other half. This occurs when both PTV algorithms are used to analyse data.
8 Properties of the Flow in the Lagrangian Framework
Long particle trajectories are needed to perform a Lagrangian analysis. The reliability of classical PTV algorithms is very high especially when the particle density is low. The precision these trajectories are determined with depends solely on
Turbulence and PTV 289
the precision the particle coordinates are gathered.
Each tracer particle moves along a trajectory, X=X(t,x0,t0), where X=x0 when t=
t0. The fundamental kinematical equation states that:
dX
= V(t , x 0 , t 0 )
dt
(1)
where V(t,x0,t0) is the particles Lagrangian velocity.
V(t,x0,t0) may be regarded as a random space function depending on time, t, and
indirectly on space, x0. V(t,x0,t0) can be decomposed as
V (t , x 0 , t 0 ) =< V(t , x 0 , t 0 ) > + v (t , x 0 , t 0 )
(2)
where <V(t,x0,t0)> is the expected value (in time) of the velocity, while v(t,x0,t0)
is the zero-mean velocity fluctuation.
2
1.5
Y/d
(u'v')+ -PTV
1
(u'v')+ -FT
0.5
0
-1.5
-1.0
-0.5
0.0
0.5 u'+,v'+,(u'v')+
1.0
Fig. 10. Reynolds stress as a function of depth for Series3 and PTV algorithm.
The covariance of the velocity components can be computed as well. If
Vi(t,x0,t0) and Vj(t,x0,t0) are the components of velocity in the i and j directions, the
normalized velocity covariance can be written as
ρ ij (τ ) =
< vi (t0 , x 0 , t0 )v j (t0 + τ , x 0 , t0 ) >
[< v (t , x , t )
i
0
0
2
0
> < v j (t0 + τ , x 0 , t0 ) 2 >
]
12
(3)
It should be noted the dependence of ρij on τ, instead of τ and t0, resulting from
the assumption of steady flow.
The time, Tij, during which the velocities are correlated, can be computed as
∞
Tij =∫ ρ ij (τ )dτ
0
(4)
290 Session 5
The horizontal discretization used for the Eulerian analysis is kept for calculating the Lagrangian features of the flow. The initial location of a particle is assigned to the corresponding slice and the mean Lagrangian velocity and its variance in each direction is computed as a function of travel time and initial vertical
position. The steady flow assumption allows the initial position of a particle to be
arbitrarily chosen along a trajectory.
An interesting way of describing the displacement features of tracer particles,
when horizontal homogeneity occurs, is through the translient turbulence theory
proposed by Stull (1984), mostly applied to study the turbulent convective phenomenon.
If we subdivide the analyzed volume into M horizontal layers of equal thickness ∆y we can identify with the index i1 the i1-th layer, centered at a depth y=
(i1-0.5)∆y. Stull defined ci1i2 as the fraction of fluid being transported by turbulence from a source layer i1 into a destination layer i2 during a time interval ∆t.
ci1i2 can so be interpreted as the probability that a particles being at a time t and
depth i1∆y can be found after the time interval ∆t at a depth i2∆y. The squared
matrix c(∆t) of all such elements is called a translient matrix (Stull, 1993).
Translient matrix is usually displayed as a contour plot of the element values. This
kind of representation allows an immediate visual description of particles transition probability as a function of the source and destination depths. The absolute
value of the generic matrix element represents the fluid quantity involved in the
mixing process while its relative location characterizes the mixing features.
Figs. 11 and 12 display the translient matrices at two ∆t, where the starting time
is always time zero. The analyzed volume is subdivided into 60 horizontal layers.
The horizontal axis displays the source layer (depth), the vertical axis displays the
destination layer (depth).
For small time increments, the translient matrices present values different than
zero only along the secondary diagonal. This is due to the mostly horizontal displacement of tracer particles for small travel times. Increasing the time increment,
symmetric diffusion around the secondary diagonal of the matrices occurs. The
upper and lower parts of the diagonal, representing the behavior of particles moving near the wall, present a value of the translient matrix equal to one (or slightly
smaller). We conclude the particles are traveling with trajectories that are mostly
horizontal. The analysis of the matrices for large time increments does not suggest
any net flux of particles along a given direction.
As far as it concerns Lagrangian integral scales, the number of samples as a
function of the travel time along the trajectory and for different starting position
along the vertical direction drops as the time increases, making unreliable statistics
for long travel times.
Also the time lag between frames is a crucial parameter for computing Lagrangian statistics. Anyway, also using data of Series3, characterized by the larger
time resolution, we could only draw qualitative conclusions. We find that going
toward the centerline of the channel, the Lagrangian integral scale increases, being
larger the area behind the correlation coefficient. This result agrees with both Romano (1995) and Virant and Dracos (1997).
Turbulence and PTV 291
The behavior highlighted for the velocity correlation coefficient in the streamwise direction occurs also for the direction normal to the flow.
Fig. 11. Translient matrix at time ∆t= 0.001 s.
Fig. 12. Translient matrix at time ∆t= 0.058 s .
Acknowledgement
The group of the University of Rome “La Sapienza” dedicates the present
work to the memory of Dr. Ivan Antonini.
This work has been performed under the EUROPIV 2 project: EUROPIV 2 (A
Joint Program to Improve PIV Performance for Industry and Research) is a col-
292 Session 5
laboration between LML URA CNRS 1441, Dassault Aviation, DASA, ITAP,
CIRA, DLR, ISL, NLR, ONERA, DNW and the universities of Delft, Madrid,
Oldenburg, Rome, Rouen (CORIA URA CNRS 230), St Etienne (TSI URA
CNRS 842) and Zaragoza. The project is managed by LML URA CNRS 1441
and is funded by the CEC under the IMT initiative (contract no: GRD1-199910835).
This work has been also partially funded by the Spanish Minitry of Science and
Technology grant DPI2002-02453.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Adrian R.J., 1991. Particle imaging techniques for experimental fluid mechanics. Ann. Rev. Fluid Mech. 23, 261-304.
Alfredsson P.H. and Johansson A.V., 1984. Time scales in turbulent channel
flow. Phys. Fluid 27(8), 1974-1981.
Cenedese A., Moroni M. and Viotti P., 1997. Velocity field in a porous medium by means of Stereoscopic Particle Image Velocimetry. 7th Int. Conf.
Laser Anemometry Advances and Applications, 8-12 Sept, Karlsruhe.
Cenedese A., Miozzi M., Moroni M. and Romano G.P., 2003. Velocimetry
methods comparisons in a fully developed turbulent channel. In preparation.
Djenidi L., Dubief Y. and Antonia R.A., 1997. Advantages of using a power
law in a low Rθ turbulent boundary layer. Exp. in Fluids 22: pp 348-350.
Fincham AM and Spedding GR, 1997. Low-cost, high resolution DPIV for
measurement in turbulent fluid flows. Exp. in Fluids 23: pp 449-462.
Haarlem, B, 2000. The dynamics of particles and droplets in atmospheric turbulence: a numerical study. Ph.D. Thesis, Delft University of Technology.
Kim, J., Moin, P. and Moser, R., 1987. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133-166.
Kobayashi T. Saga T. and Sekimoto K., 1989. Velocity Measurement of Treedimensional Flow Around Rotating Paralell Disks by Digital Image Processing. ASME-FED vol. 85 Flow Visualization, B. Khalighi et al eds. Pp. 29-36.
Lewis, GS. Cantwell, BJ. and Lecuona, A., 1987. The use of particle tracking
to obtain planar velocity measurements in an unsteady laminar diffusion
flame. Paper 87-35. The Combustion Institute 1987 Spring Meeting (Provo,
Utah).
Lucas, B.D. and Kanade T., 1981. An iterative image registration tecnique
with an application to stereo vision. Proceedings of Imaging Understanding
Workshop, pp. 121-130.
Miozzi, M., 2003. Lagrangian High Density Particle Image Velocimetry using
Feature Tracking. Submitted to Measurement Science and Technology.
Moroni M., Gullo G., Romano G.P., Cenedese A., 2003. Lagrangian statistics
in near-wall turbulence. Second Year Annual report within the European
Project EUROPIV 2: A Joint Program to Improve PIV Performance for Industry and Research. Contract n° G4RD-CT-2000-00190.
Turbulence and PTV 293
14. Nogueira J., Lecuona A. and Rodríguez P.A., 1999. Local field correction
PIV: on the increase of accuracy of digital PIV systems. Exp. in Fluids 27: pp
107-116.
15. Nogueira J, Lecuona A and Rodríguez P.A., 2001. Local field correction PIV,
implemented by means of simple algorithms, and multigrid versions. Meas.
Sci. Technol. 12: 1911-1921.
16. Romano G.P., 1995. Analysis of two-point velocity measurements in nearwall flows. Exp Fluid 20, 68-83.
17. Shi, J. and Tomasi, C., 1994. Good features to track. In Proceedings of IEEE
Conference
on
Computer
Vision
and
Pattern
Recognition.
http://vision.stanford.edu/~birch/klt/.
18. Shlien D.J. and Corrsin S., 1974. A measurement of Lagrangian velocity
autocorrelation in approximately isotropic turbulence. J. Fluid Mech. 62, 255271.
19. Squires K.D. and Eaton J.K., 1991. Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence. J. Fluid
Mech. 226, 1-35.
20. Stull, R.B., 1993. Translient Turbulence Theory. Part I: The concept of eddy
mixing across finite distances. J. Atmos. Sci., 1984, 41, 3351-3367.
21. Tomasi, C. and Kanade, T., 1991. Detection and tracking of point features. In
Shape and motion from image streams: a factorisation method. Carnegie
Mellon University Technical Report CMU-CS-91-132.
22. Udrea D.D., Bryanston-Cross P.J., Querzoli G, Moroni M., 2000. Particle
Tracking Velocimetry techniques. Fluid Mechanics and its Application, 279304, Kluwer Academic, The Netherlands.
23. Virant M. and Dracos T., 1997. 3D PTV and its application on Lagrangian
motion. Meas. Sci. Technol. 8, 1539-1552.
24. Westerweel J, Dabiri D and Gharib M., 1997. The effect of a discrete window
offset on the accuracy of cross-correlation analysis of digital PIV recordings.
Exp. in Fluids 23: pp 20-28.
25. Westerweel J., 1998. Effect of sensor geometry on the performance of PIV.
9th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics. Instituto Superior Técnico, Lisbon, Portugal.
26. Yeung P.K. and Pope S.B., 1989. Lagrangian statistics from direct numerical
simulations of isotropic turbulence. J. Fluid Mech. 207, 531-586.