18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Volumetric distribution and velocity of inertial particles
in a turbulent channel flow
Filippo Coletti1,*, Mostafa Toloui2, Kee Onn Fong1, Andras Nemes1, Lucia Baker1
1: Department of Aerospace Engineering & Mechanics, University of Minnesota, Minneapolis (MN), USA
2: Department of Mechanical Engineering, University of Minnesota, Minneapolis (MN), USA
* Correspondent author: fcoletti@umn.edu
Keywords: particle-laden flow, turbulence, turbophoresis, two-way coupling, particle tracking velocimetry, digital in-line holography
ABSTRACT
The segregation of inertial particles in specific regions of a turbulent fluid flow is a well known phenomenon, but
experimental observations of its three-dimensional nature have lacking. Here we are concerned with the transport of
small inertial particles in a vertically oriented turbulent channel flow. The working fluid is air laden with sizeselected glass particles. We focus on a regime in which both preferential concentration/turbophoresis as well as twoway coupling are expected to be substantial. We measure statistics of particle and fluid using two-dimensional
imaging, and we reconstruct volumetric distributions of the inertial particles using digital in-line holography. The
inertial particles are found to accumulate near the wall, but in a much less extreme fashion than what simulations
indicate. The particles have a flatter velocity profile and higher velocity fluctuations compared to the fluid. Using
Voronoi analysis we find evidence of strong particle clustering especially in the near-wall regions, indicating that the
preferential concentration is driven by the near-wall turbulence structures.
1. Introduction
Particle imaging techniques are widely used to characterized single-phase velocity fields, and in
recent years their capabilities in capturing large ensembles of tracer particles in 2 and 3
dimensions have greatly improved. However the latest advances, especially in volumetric
imaging, have not been exploited to reconstruct the motions of inertial particles immersed in the
fluid. The latter is a problem of utmost significance which recently has been studied mostly by
numerical simulations. Notably, the clustering of inertial particles in specific regions of a
turbulent flow is a well known phenomenon with far reaching consequences, but experimental
observations of its three-dimensional nature are lacking.
Here we are concerned with the transport of small inertial particles in wall-bounded
turbulence, in particular in the case in which the working fluid is a gas. In this situation the
particle-to-fluid density ratio is high, and even micron-sized particles have significant inertia. It
is well known that inertial particles in turbulence experience preferential concentration or
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
clustering, i.e. collection in high-strain, low-vorticity regions (Maxey 1987, Squires and Eaton
1991). This mechanism is most effective when particles have sufficient inertia to depart from
fluid streamlines, but not enough to take ballistic trajectories, and is primarily dictated by the
Stokes number St = τ /τ , the relative strength of the aerodynamic response time of the particle τ
p
f
p
to a fluid timescale τ . The latter is typically taken to be either the Kolmogorov time scale or the
f
viscous time in wall units. In wall-bounded turbulence, clustering typically occurs on scales
associated with streaks and coherent structures in the inner wall region (Rouson and Eaton
2001), and the collective interaction with such structures results in so-called turbophoresis, i.e. a
significant drift towards the wall (Marchioli and Soldati 2002). This is typically most effective for
St = 10 - 100.
+
Inertial particles in wall-bounded turbulent air flows are relevant to a wealth of industrial,
environmental, and biological settings, from dust ingestion in aircraft engines to ocean see spray
and aerosol drug delivery. In all these examples, a crucial feature is that mass, momentum, and
energy of the gas phase and particle phase are comparable, so that the understanding and
solution of the strongly coupled dynamics is indispensable for an accurate prediction of even
first-order statistics. This is because, given sufficiently high concentrations, particles can modify
turbulence through dynamic coupling between phases (two-way coupling). At even higher
volume fractions (typically above 10 , still well in the dilute regime) inter-particle collisions
-4
become significant (Elghobashi 1994). This is especially true in the context of preferential
concentration and turbophoresis, where both intermittent and mean concentration distributions
can be locally very high (Sardina et al. 2012). In turn, inter-particle collisions have a strong effect
on the concentration distribution, increasing the wall-normal transport and reducing the near
wall-concentration of particles (Vreman 2007).
Here we investigate a regime in which both preferential concentratiom (and its
macroscopic consequence: turbuophoresis) as well as two-way coupling are simultaneously at
play. Very few experimental studies are available that considered two-way coupling. In Tab. 1 we
list the main studies that have looked at two-way coupling in what is arguably the most
fundamental configuration of wall-bounded gas-particle flows, i.e. the fully developed particleladen turbulent channel flows (with air as working fluid). Of these, the studies of Kulick et al.
(1994) and Paris (2000), although designed to have a smooth wall, turned out to have effectively
rough walls. Moreover, most of these studies had particles of very large Stokes numbers, for
which preferential concentration/turbophoresis is not expected. The study of Li et al. (2012)
represents an exception, but the volume fraction was so small that the two-way coupling was
probably marginal. Moreover, all previous studies have characterized particle transport uing
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
point-wise (e.g. LDV) or at most 2D (PIV) measurement techniques. In the present study we use
a combination of 2D PIV/PTV and 3D PTV based on Digital In-line Holography (DIH-PTV) to
quantitatively characterize the instantaneous and mean fields of particle concentration and
velocity.
Reτ
St+
d+
ΦV
Kulick et al. (1994) – rough wall
650
1500 –2000
2.5 – 5
4·10-5 – 10-4
Paris (2000) – rough wall
650
1500–2000
2.5 – 5
4·10-5 – 10-4
Kussin & Sommerfeld (2002)
700 – 1300
400 – 2000
2 – 40
4·10-4 – 4 ·10-3
Benson et al. (2005)
650
1500
5
6·10-5
Li et al. (2012)
430
100
1.7
2.5·10-7 – 5 ·10-6
Present study
300
100
1
5·10-5
Tab. 1 Summary of previous and present studies focused on the fully developed particle-laden
turbulent channel flows, with air as working fluid.
2. Experimental facility and measurement techniques
Experiments are conducted in an installation consisting of a 2.5 m long channel flow with a 0.24
m by 0.03 m cross-section (Fig. 1). The channel is vertically oriented, so that gravitational
accumulation on the walls does not affect the particle-turbulence interaction. A centrifugal
blower drives air downward to a bulk velocity U
bulk
= 5 m/s, resulting in a friction Reynolds
number of Re = 300. The air mass flow rate is continuously monitored through a Venturi meter.
τ
Before the air enters the channel, size-selected glass beads (density of 2.5 g/cc, 50±6 µm in
diameter, see Fig. 2) are issued into the flow through a precision screw-feeder (VibraScrew). A
flow conditioning section (consisting of four screens and three honeycombs) disperses the
particles uniformly at the channel inlet. The particle Stokes number in wall units is St = 100 (St =
+
η
10 based on the Kolmogorov time scale). The main measurement station consists of a 0.3 m long,
fully transparent Plexiglas section that follows a 2 m long development section. This ensures that
the flow is fully developed and the particles have reached terminal velocity in the measurement
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
section. The particles exhausted from the channel are collected in a settling chamber, allowing
long run times needed to achieve well-converged statistics, without particles being ingested into
the blower. The smooth aluminum walls which make up most of the channel length are provided
with static discharge wires and are grounded to structural supports. This prevents the particles
from accumulating upon impaction and building up unwanted roughness, an effect which has
affected past experiments (Benson et al. 2005). Moreover, the Froude number, defined as the ratio
of the bulk flow velocity over the gravitational settling velocity of the particles, is large (Fr =
U /τ g = 30), gravitational effects can be considered negligible (Sardina et al. 2012).
bulk
p
Fig. 1: Left: schematic of the considered flow configuration. Right: laboratory installation to
study particle-laden turbulent channel flow.
Fig. 2: Left: schematic of the considered flow configuration. Right: laboratory installation to
study particle-laden turbulent channel flow.
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
For 2D measurements, an Nd:Yag (50 mJ/pulse) laser is used to illuminate a wall-normal
2D plane (Fig. 3, top), synchronzied to a 4 Mpxl CCD camera. The particle-laden air flow is
seeded with DEHS oil atomized by a Laskin nozzle into droplets of 1-2 µm. The small size of the
oil tracers ensures they can be readily discerned from the inertial particles (Fig. 3, bottom), which
is accomplished automatically via an image processing algorithm based on size and intensityand
inspired by Khalitov and Longmire (2002). Therefore, using the same sets of images, Particle
Image Velocimetry (PIV) can be applied to the tracer particles to measure the air flow field, while
Particle Tracking Velocimetry (PTV) is applied to find position and trajectories of the inertial
particles. The latter is performed using the relaxation method proposed aby Baek & Lee (1996).
Fig. 3: Top: 2D PIV system measuring on wall-normal plane. Bottom: example of acquired image
with tracers and inertial particles (left), which can be easily distinguished based on size and
intensity, as apparent from the zoomed in view (right).
For 3D reconstruction of the inertial particles position and velocity, we use an advanced
DIH-PTV method recently proposed by Toloui and Hong (2015). A typical setup consists of a
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
single camera with an imaging lens, a laser source, and other collimating optics (Fig. 4). The
camera records the light interference from the forward scattering of tracer particles and unscattered portion of the laser into holograms. The holograms are then digitally reconstructed into
3D optical fields, from which the 3D tracer positions are extracted. Tracking algorithms are
subsequently applied to determine tracer displacements and 3D velocity fields. DIH-PTV suffers
from major limitations including poor longitudinal resolution, human intervention (i.e.
requirement for manually determined tuning parameters during tracer field reconstruction and
extraction), limited tracer concentration, and expensive computations. The method of Toloui and
Hong (205) consists of multiple steps involving 3D deconvolution, automatic signal-to-noise
ratio enhancement and thresholding, and inverse iterative particle extraction. The entire method
is implemented using GPU-based algorithm to increase the computational speed significantly,
and it was validated for standard velocimetry (i.e. measureing motions of fluid tracers) against
laminar flow in a microchannel as well as synthetic tracer flow fields generated using a DNS
turbulent channel flow database. Here the method is applied for the first time to inertial particles
in a turbulent flow.
Fig. 4: Principle of in-line digital holographic PtV (Figure credit: Jiarong Hong, University of
Minnesota).
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 5: Left: DIH-PTV optical setup. Right: reconstructed 3D of particle distribution
The DIH-PTV optical setup is shown in Fig. 5 (left), and consists of a He-Ne continuous laser
(633 nm) and a HX high speed camera mounting a 105 Nikkor lens and recording at 22 kHz
during 2.9 s. The camera acquires 5 by 5 mm holograms, from which 5 by 5 by 30 mm
2
3
instantaneous volumes are reconstructed (Fig. 5, right). In order to reconstruct a more extended
volume in streamwise direction, we exploit the temporal resolution of the particles: we assume
that the particles, which have significant inertia, advect in a quasi-frozen manner according to
the measured wall-normal velocity profile. By converting time to space (similarly to applying
Taylor hypothesis) we reconstruct a streamwise extended volume of 400 by 50 by 30 mm (in
3
streamwise, spanwise, and wall-normal directions, respectively).
3. Results
Figure 6 shows the wall-normal profile of particle concentration as measured by 2D imaging.
This is calculated from the estimate of the illuminated volume, which is in turn based on an
estimate of the laser sheet thickness. As expected, the concentration is much larger in the nearwall region due to turbophoresis. However, the near-wall segregation is much less extreme
compared to found by point-particle DNS, both in one-way coupling (Sardina et al. 2012) and in
two-way coupling (Zhao et al. 2013). This is likely due to the fact that the locally high
concentration causes particle-particle collision (as well as particle-wall collisions), which
modulate the tendency of the particles to accumulate near the wall. We notice that the average
concentration calculated
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 6: Wall-normal profile of particle concentration as measured by 2D imaging.
Figure 7 shows wall-normal profiles of mean streamwise velocity (left) and rms of the
streamwise fluctuating velocity (right). Profiles relative to both particles and fluid are reported.
The particles are faster than the fluid in the near-wall region (y < 10), while they lag the flow
+
farther away from the wall. This finding, which is consistent with previous studies (e.g. Kulick et
al. 1994) is a consequence of the inertial particles crossing the fluid streamlines: when a particle
moves in wall-normal direction to turbulent motions, it carries its momentum and it finds itself
in a region of larger/smaller fluid velocity. For similar reasons, particles with very different
velocities can find themselves in nearby positions, resulting in higher rms velocity fluctuations.
Fig. 7: Wall-normal profiles of mean streamwise velocity (left) and rms of the streamwise
fluctuating velocity (right).
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 8: Ensemble of inertial particles reconstructed by DIH-PTV and projected in spanwise
direction.
Figure 8 displays the ensemble of the inertial particles position reconstructed by DIH-PTV
(with the aid of the adapted Taylor hypothesis) and projected in spanwise direction. The higher
near-wall concentration is apparent. In order to characterize the clustering of inertial particles,
we use the Voronoi tessellation: each particle is associated to a Voronoi cell, a polyhedron whose
faces are defined by the distance from neighboring particles. This method has been successfully
used to characterize size and shape of particle clusters obtained by 2D imaging and 3D
simulations (Tagawa et al. 2012) of dispersed turbulent flows, and here is applied for the first
time to 3D imaging data. Figure 9 (left) illustrates the approach, and for clarity it shows a
Voronoi diagram obtained from a 2D slice. The clusters, approximated as the ensemble of cells
associated to their particles, are identified analyzing the PDF of the Voronoi cell volumes. The
comparison against the Γ distribution expected for randomly distributed particles (Tagawa et al.
2012) defines a threshold volume, below which Voronoi cells are labeled as cluster cells (Fig. 9,
right). It is found that the Voronoi cell size associated to particles belonging to a cluster have
typical dimensions smaller than ~8η. This is consistent with the notion that preferential
concentration in turbulence is maximized over length scales of order 10η (Aliseda et al. 2002).
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
Fig. 9: Left: Voronoi diagram illustrating a cluster of inertial particles. Right: PDF of the volumes
of the Voronoi cells, normalized by the average cell volume. The wider distribution compared to
a random Poisson process indicate the presence of clusters (small volumes) and areas devoid of
particles (large volumes).
Because the field is not homogeneous in wall-normal direction, we consider separate bins
of the particle ensemble, centered at different distance from the wall (Fig. 10, left). The standard
deviation of the Voronoi cell volume PDF, which is a metric of the level of clustering, is shown in
Fig. 10 (right). Near-wall particles are substantially more clustered than particles at the center of
the channel, which confirms how clustering in wall-bounded turbulence is mainly driven by the
near-wall structures, such as the low-speed streaks and hairpins (Marchioli and Soldati 2002).
Fig. 10: Left: Wall-normal location of the different considered groups of particles, highlighted in
color. Right: standard deviation of the PDF of the Voronoi volumes versus wall-normal distance.
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016
3. Conclusions
We investigate a vertical turbulent channel flow laden with microscopic inertial particles. Unlike
previous studies, we focus on a regime in which both preferential concentration/turbophoresis
as well as two-way coupling are expected to be substantial. We measure statistics of particles and
fluid using 2D PIV/PTV, and we reconstruct 3D distributions of inertial particles using DIH-PTV.
The inertial particles are confirmed to accumulate near the wall, but in a much less extreme
fashion than what point-particle DNS (neglecting particle-particle collision) indicate. The
particles have a flatter velocity profile compared to the fluid, and a much higher rms velocity
fluctuation. Evidence of strong particle clustering is found especially in the near-wall regions,
indicating that the preferential concentration is driven by the near-wall turbulence structures.
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