Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 15.5.3 - Relations between preferential sampling and turbophoresis of inertial particles
ALL VOLUMES CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00102023/00382
 Material Information
Title: 15.5.3 - Relations between preferential sampling and turbophoresis of inertial particles Particle-Laden Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Sardina, G.
Picano, F.
Gualtieri, P.
Casciola, C.M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: particle-laden gas
turbophoresis
turbulent pipe flow
DNS
 Notes
Abstract: In wall flows turbophoresis amounts to a large accumulation of inertial particle close to the wall. This complex phenomenon, although deeply studied, has not been sufficiently understood. In this paper we want to stress the role of particle preferential sampling of certain fluid events in the turbophoretic mechanism. In order to investigate both the transient and the asymptotic equilibrium states a spatial evolving DNS of particle laden turbulent pipe flow has been run. Particles with relaxation time comparable to buffer layer characteristic flow turbulent time scales have been found as the most accumulating ones. From the data, it emerges that different inertia exhibit comparable level of wall accumulation although at very different developing lengths. In the equilibrium asymptotic region, a balance between the turbophoretic drift and the particle preferential sampling of fluid events occurs since the mean particle flux in the wall normal direction vanishes. The transient phase is characterized by particle dispersion, which is influenced by both turbophoretic drift and the preferential sampling. Increasing the particle inertia the relevance of the latter phenomenon decreases.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00382
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1553-Sardina-ICMF2010.pdf

Full Text



7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Relations between preferential sampling and turbophoresis of inertial particles


G. SardinaT F. PicanoT P. GualtieriT and C.M. Casciola*

Dipartimento di Meccanica e Aeronautica Sapienza Universith di Roma via Eudossiana 18, 00184 Roma, Italy

gaetano.sardina ~uniromal1.it
Keywords: Particle-laden gas, turbophoresis, turbulent pipe flow, DNS




Abstract

In wall flows turbophoresis amounts to a large accumulation of inertial particle close to the wall. This complex
phenomenon, although deeply studied, has not been sufficiently understood. In this paper we want to stress the role
of particle preferential sampling of certain fluid events in the turbophoretic mechanism. In order to investigate both
the transient and the asymptotic equilibrium states a spatial evolving DNS of particle laden turbulent pipe flow has
been run. Particles with relaxation time comparable to buffer layer characteristic flow turbulent time scales have been
found as the most accumulating ones. From the data, it emerges that different inertia exhibit comparable level of wall
accumulation although at very different developing lengths. In the equilibrium asymptotic region, a balance between
the turbophoretic drift and the particle preferential sampling of fluid events occurs since the mean particle flux in
the wall normal direction vanishes. The transient phase is characterized by particle dispersion, which is influenced
by both turbophoretic drift and the preferential sampling. Increasing the particle inertia the relevance of the latter
phenomenon decreases.


Introduction


The carrier phase obeys to the incompressible Navier-
Stokes equations,


Particle laden wall flows have been investigated in sev-
eral configurations both through experimental and nu-
merical approaches Balachandar & Eaton (2010); Sol-
dati & Marchioli (2009); Young & Leeming (1997).
Main feature of these multiphase flows is the so-called
turbophoresis, a curious phenomenology consisting of
a substantial particle concentration increase at the wall.
The classical numerical approach used to address this
process, is based on time evolving simulations where
the flow is evolved in time up to the eventual steady
state for particle distributions. This approach can not
provide information on the transient dynamics and the
interrelated features which block the turbophoretic drift
leading to the asymptotic equilibrium conditions. In this
context, the preferential localization of particles induc-
ing the preferential sampling of certain fluid events is
shown to be crucial.
A new spatial evolving configuration was considered
to follow the particle dynamics through the developing
region up to the asymptotic far-field, more details in Pi-
cano, Sardina & Casciola (2009). Aim of present work
is to expand on the role of preferential sampling of spe-
cific fluid events as key feature of the whole accumula-
tion process.


+u
8= xy


1l 8p 8 Ui
+vi~djz


where p and v are density and kinematic viscosity of the
fluid, respectively, with as the fluid velocity. As usual
the control parameter of the flow is the Reynolds num-
ber, Re UbRIV, where R is the pipe radius and Ub
the bulk velocity across the section. It is useful to in-
troduce the friction Reynolds number Re, U,R/V,
where U, Jr is the friction velocity, based on
the shear stress at the wall 7,. The simulation we dis-
cuss concerns a fully turbulent flow with Re 3000
corresponding to Re, = 200.
Assuming small and diluted particles with density
much larger than the fluid, the particle feedback on the
fluid and inter-particle collisions can be neglected (one-
way coupling). The viscous Stokes drag remains as
the only force acting on a particle Armenio & Fiorotto
(2001). The dynamics of each particle is described by a


Methodology







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


.. +

S..


..
*:


Lagrangian formulation, Maxey & Riley (1983),

(2)
di V, (3


where v; denotes the particle velocity and 7,
P, d /(Pvl8) is the particle response time (Stokes time),
with di, the particle diameter. So the so-called Stokes
number, ratio of ri, and the characteristic time scale of
the carrier fluid, represents the only parameter influenc-
ing the particle dynamics in a given flow field. For
wall-bounded flows the characteristic fluid time is con-
veniently taken as the viscous time scale (v/U, ), leading
to define the viscous Stokes number St+ = U,/v.
Concerning wall-particle interaction, we assume here a
pure elastic rebound when the particle surface hits the
wall.
The fluid solver is based on the discretization of the
equations (1) in cylindrical coordinates with a conser-
vative second order finite difference scheme on a stag-
gered grid. The simulation evolves in time by an ex-
plicit third order low-storage Runge-Kutta scheme. The
primary pipe element, see below for a complete descrip-
tion of the geometry, has the length L, = 2i7R and is
discretized by a uniform grid of 128 x 80 x 128 nodes in
the axial z, radial r and azimuthal 9 directions, respec-
tively.
The particle positions and velocities evolve with the
same time scheme used for the fluid ((2)-(3)) and the
fluid velocity u is interpolated at the particle position by
linear-quadratic Lagrange polynomials. The simulation
involves seven different populations of particles (St
0.1, 0.5, 1, 5, 10, 50, 100) which are injected at fixed rate
near the axis at the inlet section. The particle dynamics
is followed through in a very long domain (~ 200R)
consisting of 32 replications of the primary periodic pipe
flow element (see Picano, Sardina & Casciola 2009, for
details).
In order to provide a qualitative view of the simula-
tion, figure 1 shows an instantaneous visualization of
the particle near field just beyond the injection point
(only 1/8 of the whole axial extension of the domain
is drawn). The particles injected at the axis, cross the
first pipe element (colors correspond to isolevels of ax-
ial fluid velocity) and disperse through the domain. The
wall accumulation process is already operating at the
furthest station displayed in the figure, z/R ~ 25.

Results

For a quantitative analysis of the dispersion and accu-
mulation, the mean concentrations in the classical four
regions characteristic of wall bounded flows, namely


Figure 1: Instantaneous particle configuration (St+ =
10 population) in the early stages after the injection.
Contours represent the instantaneous axial fluid veloc-
ity field in the primary pipe element


wake, log, buffer and viscous regions, respectively, are
plotted in figure 2. The data are normalized by the con-
centration achieved by the lightest particles (almost La-
grangian tracers) in the wake region of the far-field.
Lightest particles St+ 0.5, 1. undergo dispersion
until reaching a quasi-uniform distribution across the
section beyond z/R ~ 50. Despite the small Stokes
number a slight amount of wall accumulation still ex-
ists as shown by the concentration in the viscous region.
Along the transient a progressive filling of the four re-
gions is observed, from the wake down to the wall.
A completely different mechanism is ap.nemhll'll act-
ing on particles with Stt 5., 10., which are found
to achieve huge wall accumulations, middle panels. For
these particles, the buffer layer concentration (blue sym-















wake --
3000 log -
buffer












e-06t

0 50 100 150 2E
zlR

wake --
3000~ log
buffer


VISOU C -

100~


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010




wake --
log
buffer -- *; -


te-UD
0 50 100 150 200
lR

wake --
10000~ log
buffer











le-04


le-06
0 50 100 150 200


O 50 100
z/R


150 200


wake -
log
buffer
V15cous


le-04


le-04 ~


le-06
0 50 100
z/R


150 200


wake -
log
buffer
v15COUS


100DD


le-04i


le-06
0 50 100 150 200


Figure 2: Mean particle concentration vs axial distance z/R in every region characteristic of wall bounded flows. Top
left plot Stt 0.5, top right Stt 1 ., middle left Stt 5., middle right Stt 10., bottom left Stt 50. and
bottom right Stt 100.


bols) in the developing region, 15 < z/R < 25, is the
lowest across the section, i.e. below the values found ei-
ther in the log and viscous layers. This behavior particles
tend to be expelled from the buffer layer, keeping the lo-
cal concentration to a minimum. The effect is strongest
at St+ 10, consistently with a rough estimate of the
resonance condition in the buffer layer, St(- . r fer)

1, based on the the typical buffer time scale ,.". ,fer/v,
yielding resonance for St+ 5 + 50. Heavier parti-


cles, Stt = 50., 100., initially show a definite trend to-
wards homogenization with the same progressive filling
of the cross section described for the lightest particles
St+ .5. Further downstream, z/R > 30, turbophore-
sis takes over leading to particle segregation in the vis-
cous sublayer.


Overall three different behaviors can be distinguished.
Light particles are more or less convected with the fluid
and show modest accumulation. Particles with interme-























































.~1 0 -U

50
-0.005
20 80 140 200


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010



0.1
0.01 0.01 Vq
0.00 0.05 .0

-0.005 -0.005

20 80 140 200 I 20 80 140 200




-0.05-



-0.1
50 100 150 200 0 50 100 150 200
zlR zlR


50 100 150 200 0 50 100
zlR zlR


0 50 100
2/R


0

0.0
2DD


-0.0

-0.

-0.1
150 200


50 100
zlR


150 200


Figure 3: Particle mean radial velocity V,, fluid mean radial velocity
velocity drift V, -7, ap vs z/R in the buffer layer region 5 < y
Stt 1 ., middle left Stt 5., middle right Stt 10., bottom left St



diate inertia are strongly coupled to the turbulent fluc-
tuations in the buffer layer, to end up with a substantial v
wall segregation and wall concentrations of the order of
hundred times the wake concentration. The heaviest par- where vr
ticles still manifest a certain level of segregation, which is the mear
is reached, however, further downstream. and a,, is
dial directic
The mechanism of particle accumulation can be spot- ties toward
ted by addressing the wall normal component of the en- V, -7, a
semble average of equation (2) towards the


sampled by particles Uf and turbophoretic
< 20. Top left plot Stt 0.5, top right
50. and bottom right Stt 100.





r(r, z) = 1|. (r, z) 7parp(r, z), (4)

Sis the mean particle radial velocity, -.I.|
n fluid radial velocity sampled by particles
the mean acceleration of particles in the ra-
on (hereafter positive values denote veloci-
s the wall). The turbophoretic drift velocity

r (r, z) promotes the motion of the particles
:wall. In the quasi-Lagrangian limit, parti-







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


cles with small 7,, the turbophoretic velocity can be es-
timated in terms of fluid acceleration. Since the particle
and fluid accelerations are almost identical in this case,
it follows


~(, )~-f()dr t 5

Hence the maximum fluid acceleration occurring close
to the wall in the buffer-layer region, produces a strong
turbophoretic drift V, directed towards the wall. The ar-
guments presented here hold for small relaxation time
and provide a linear dependence of the turbophoretic
drift on 7,. In the general case, the particle acceleration
differs from that of the fluid leading to a more complex
dependence (see Young & Leeming 1997, for a collec-
tion of experimental results). The three different behav-
iors discussed previously concerning the axial variation
of the particle concentrations, figure 2, can be explained
by looking at figure 3. There the three terms of (4),
namely the average particle radial velocity 17, v,,
the average fluid radial velocity sampled by particles
LT; -- ...| and the turbophoretic drift Vt --q,<,1,, are
reported as a function of the axial coordinate z/R in the
buffer layer. More precisely in the figure 1 is plotted
in red, -LT, in blue and -VT in green (note the change
of sign introduced for better readability). The accumu-
lation process progressively changes from the injection
section to the fully developed region as shown by the
different terms locally dominating the balance (4).
For the smallest particles, Stt 0.5 + 1 top pan-
els, in the near field at z/R ~ 15, the mean particle
velocity is essentially given by the mean fluid velocity
sampled by the particles, T, Uf Particles, injected at
z/R 0 on the axis, initially tend to sample more fre-
quently fluid motions from the bulk of the pipe towards
the near wall region. In this region, z/R < 25, the tur-
bophoretic velocity V, does not play any relevant role
and the mean particle velocity is dominated by turbu-
lent dispersion. The dynamics changes in the developed
region where the axially-homogeneous equilibrium dis-
tribution is achieved and the mean particle velocity nec-
essarily vanishes. Here, downstream of z/R ~ 50 + 60,
the small turbophoretic drift, directed towards the wall,
is balanced by the mean fluid velocity sampled by the
particles which is directed in the opposite direction. We
see how crucial is the preferential sampling of outward
fluid velocity events in establishing the equilibrium con-
ditions. The low level of wall accumulation found in this
case, is somehow associated to the small intensity of 15
induced by the modest 7,.
The dynamics is different for intermediate particles,
Stt 5 + 10, middle panels of figure 3. The devel-
oping stage is here characterized by a combined effect
of the preferential sampling of fluid velocity and the tur-


bophoretic velocity Vt, which are both directed towards
the wall. For Stt 10 particles, right middle panel,
the turbophoretic drift is the leading term in the whole
axial span of the domain. This comparatively strong tur-
bophoretic effect is presumably the reason for the min-
imum concentration achieved by these particles in the
buffer layer of the developing region, see figure 2. As
always at equilibrium, here z/R > 80, preferential sam-
pling of outward fluid motions exactly balances the tur-
bophoretic drift Vt.
Concerning heavy particles, Stt 50 + 100 bottom
panels, the dynamics in the developing region, 10 <
z/R < 20, is dominated by the turbophoretic drift Vt
with negligible influence of preferential sampling which
eventually becomes effective in the far field, z/R > 50,
where 177 is bound to balance Vt Fully developed con-
ditions are achieved further downstream than in the other
cases (z/R ~ 180 for St+ 50 and at z/R > 200 for
the other ones).
Preferential sampling is realized as an anomalous spa-
tial concentration of particles in correspondence of co-
herent structures where the fluid departs slowly from the
wall. This effect is graphically shown in figure 4 where
the sign of the instantaneous particle-sampled fluid ve-
locity is represented as a colored circle (blue departing,
red approaching) in the buffer layer of both the develop-
ing region (25 < z/R < 35, top panel) and the far-field
(190 < z/R < 200, bottom panel). In the far-field,
the axially elongated particle aggregates which prefer-
entially sample departing fluid motion are clearly con-
nected with the classical low-speed streaks which are
known to be associated with wall departing fluid velocity
fluctuations. Such localization effect is absent in the de-
veloping region where particles are not segregated into
well defined patterns and show no net preferential sam-
pling effect.

Conclusions

A detailed analysis of particle preferential sampling has
been discussed in relation with wall accumulation us-
ing data from a direct numerical simulation of a particle
laden turbulent pipe flow at Re v = 200. The simulation
concerns the spatial evolution of particle populations
along the axial coordinate. After the initial injection,
near the axis, particles are subjected to both dispersion
and turbophoretic drift which are both directed towards
the wall in the near field region. These two different
mechanism contribute in different proportions to wall
migration depending on particle inertia. The lightest
particles are dominated by the dispersion while migra-
tion of heaviest particles is controlled by turbophoretic
drift. After the developing phase, inertial particles be-
gin to accumulate in the near wall region with the in-















.









I, I: t *,


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


state. Particles tend to be preferentially localized in
stream-wise elongated aggregates which are well corre-
lated with the classical low-speed streaks populating the
near wall region. We stress that such coherent state is
established only in the asymptotic state, whereas more
random spatial distribution characterizes the first devel-
oping stages of the accumulation process. we feel that
the above considerations may have a certain relevance
for the closure theories for panticle laden flow.

References

Balachandar S. and Eaton J.K., Turbulence Dispersed
Multiphase Flow, Annual Review of Fluid Mechanics
,2010

Young J. and Leeming A., A theory of particle deposi-
tion in turbulent pipe flow, Journal of Fluid Mechanics,
Vol. 340, pp. 129-159, 1997

Soldati A., Marchioli C., Physics and modeling of tur-
bulent particle deposition and entrainment: Review of a
systematic study, Int. J. of Multiphase Flow, Vol. 35, pp.
827, 2009

Picano F., Sardina G. and Casciola C.M., Spatial devel-
opment of panticle-laden turbulent pipe flow, Physics of
Fluids, Vol. 21, 2009

Armenio V. and Fiorotto V., The importance of the
forces acting on particles in turbulent flows, Physics of
Fluids, Vol. 13, 2001

Maxey M.R. and Riley J.J., Equation of motion for a
small rigid sphere in a nonuniform flow, Physics of Flu-
ids, Vol. 26, 1983


34





N 30





26


-4 -2 0


2 4


Figure 4: Instantaneous snapshot of particles with
Stt 10 in the buffer layer. Developing region, top
panel; developed asymptotic region, bottom panel. Red
and blue circles denote particles sampling approaching
and departing fluid velocity, respectively.


termediate particles St+ = 10, 50 reaching maximum
levels of wall concentration even hundred times larger
than the average value. Particles keep on accumulat-
ing until an axially independent statistical equilibrium
is reached sufficiently far from the injection point. The
equilibrium in the asymptotic region, is characterized
by the balance between turbophoretic drift and average
particle-sampled fluid velocity. The occurrence of an
outwards average panticle-sampled fluid velocity corre-
sponds to the preferential sampling of slow fluid depart-
ing motions. The competition between turbophoretic
drift and preferential sampling eventually drives the wall
normal panticle flux to zero establishing the equilibrium




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - Version 2.9.7 - mvs