Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.5.3 - Orientation, distribution and deposition of elongated, inertial fibers in turbulent channel flow
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 Material Information
Title: 5.5.3 - Orientation, distribution and deposition of elongated, inertial fibers in turbulent channel flow Particle-Laden Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Marchioli, C.
Dearing, S.
Soldati, A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: Eulerian-Lagrangian simulations
fiber-laden gas
DNS
dispersion
orientation
 Notes
Abstract: In this paper we investigate the dispersion of rigid elongated fibers in turbulent channel flow at shear Reynolds number Re = 150. Direct Numerical Simulation (DNS) and Lagrangian tracking are employed assuming one-way coupling between the two phases. Fibers are treated as prolate ellipsoidal particles which move according to inertia and hydrodynamic drag and rotate according to hydrodynamic torques. The orientational behavior of fibers is examined together with their preferential distribution, near-wall accumulation, and wall deposition: all these phenomena are interpreted in connection with turbulence dynamics near the wall. A wide range of fiber classes, characterized by different elongation (quantified by the fiber aspect ratio, ) and different inertia (quantified by a suitably defined fiber response time, p) is considered. Results confirm that in the vicinity of the wall fibers tend to align with the mean streamwise flow direction. However this alignment is not stable, especially for fibers with higher inertia, and is maintained for relatively short times before fibers are set into rotation in the vertical plane. Furthermore fiber orientational and translational behavior are observed to influence the process of fiber accumulation at the wall: compared to spherical particles, elongation has little or no effect on segregation, yet it affects the wallward drift velocity of fibers in such a way that longer fibers tend to deposit at higher rates.
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
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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30- June 4, 2010


Orientation, distribution and deposition
of elongated, inertial fibers in turbulent channel flow


C. Marchioli* t S.S. Dearing*and A. Soldati*

Department of Energy Technologies, University of Udine, Udine, 33100, Italy
t Centro Interdipartimentale di Fluidodinamica e Idraulica, University of Udine, Udine, 33100, Italy
marchioli@uniud.it, stella.dearing@uniud.it and soldati@uniud.it
Keywords: Eulerian-Lagrangian simulations, fiber-laden gas, DNS, dispersion, orientation




Abstract

In this paper we investigate the dispersion of rigid elongated fibers in turbulent channel flow at shear Reynolds number
Re, = 150. Direct Numerical Simulation (DNS) and Lagrangian tracking are employed assuming one-way coupling
between the two phases. Fibers are treated as prolate ellipsoidal particles which move according to inertia and
hydrodynamic drag and rotate according to hydrodynamic torques. The orientational behavior of fibers is examined
together with their preferential distribution, near-wall accumulation, and wall deposition: all these phenomena are
interpreted in connection with turbulence dynamics near the wall. A wide range of fiber classes, characterized by
different elongation (quantified by the fiber aspect ratio, A) and different inertia (quantified by a suitably defined
fiber response time, Tp) is considered. Results confirm that in the vicinity of the wall fibers tend to align with the
mean streamwise flow direction. However this alignment is not stable, especially for fibers with higher inertia, and
is maintained for relatively short times before fibers are set into rotation in the vertical plane. Furthermore fiber
orientational and translational behavior are observed to influence the process of fiber accumulation at the wall:
compared to spherical particles, elongation has little or no effect on segregation, yet it affects the wallward drift
velocity of fibers in such a way that longer fibers tend to deposit at higher rates.


Introduction


Roman symbols
a Fiber semi-minor axis (pm)
K Resistance tensor (-)
m Fiber mass (kg)
Re, shear Reynolds number (-)
Reb bulk Reynolds number (-)
S Fiber-to-fluid density (-)
t time (s)
u/v Fluid/Fiber velocity (ms 1)
Greek symbols
A fiber aspect ratio (-)
T fiber response time (s)
p fluid dynamic viscosity (Pa s)
p density (kg m-3)
Subscripts
p Fibers
Superscripts
+ Wall units


Suspensions of tiny elongated particles in turbulent
flows are commonly encountered in several industrial
and environmental applications. Examples include pulp
production and paper making, where controlling the
theological behavior and the orientation distribution of
fibers is crucial to optimize production operations. In
these processes, in particular, anisotropic fiber orien-
tation induced by the carrier flow strongly influences
the mechanical properties of manufactured paper. Elon-
gated fibers also represent an interesting (and more fea-
sible) alternative to the use of flexible polymers for re-
ducing pressure drops in fluid transport systems: even
though fibers yield lower drag reductions, they are more
resistant to shear degradation and can be easily sepa-
rated from the conveyed fluid at the end of the pipeline
(Paschkewitz et al., 2005). Despite its practical im-
portance, however, the problem of elongated particles
dispersed in turbulent wall-bounded flows has become
a topic for research only in recent years. Fiber dis-


Nomenclature











person in internal flows has been investigated through
experiments (Parsheh et al., 2005; Paschkewitz et al.,
2005), and modelled using Fokker-Planck type equa-
tions (Krochack et al., 2009; Gillissen et al., 2007;
Parsheh et al., 2005; Paschkewitz et al., 2005; Paschke-
witz et al., 2004). Yet, a limited number of phenomeno-
logical studies based on accurate numerical simulations
is available. As a result, differently from the case of
spherical particles, current knowledge of the mecha-
nisms that are responsible for fibers-turbulence interac-
tion is not satisfactory, and a deeper understanding of the
physical problem is required (Paschkewitz et al., 2004).
Among numerical Eulerian-Lagrangian works, the first
Direct Numerical Simulation (DNS) of ellipsoidal par-
ticle transport and deposition in channel flow was per-
formed by Zhang et al. (2001); followed by the comple-
mentary DNS of Mortensen et al. (2008). These studies
showed that ellipsoidal particles, similarly to spherical
particles, accumulate in the viscous sublayer and pref-
erentially concentrate in regions of low-speed fluid ve-
locity. Being "non isotropic", however, these elongated
particles tend to align themselves with the mean flow di-
rection, particularly very near the wall where their lateral
tilting is suppressed.
In this paper, we investigate further on the problem by
looking at the dynamical behavior of ellipsoidal parti-
cles, mimicking the dispersion of elongated rigid fibers,
in a fully developed channel flow at moderate Reynolds
number. The focus is on the combined influence of
the particle aspect ratio and the particle response time
on particle distribution, orientation, translation and ro-
tation. Our objective is to highlight the circumstances
in which fibers behavior significantly deviates from that
of spherical particles, in an effort to infer valuable con-
clusions significant to real situations including dilute air
flows with velocity of a few meters per second in ducts
with hydraulic diameters of a few centimeters, dilute wa-
ter flows in microchannels, or fibrous aerosols transport
in zero-gravity conditions.


Problem Formulation and Governing Equations

The Eulerian fluid dynamics is governed by the conti-
nuity and Navier-Stokes equations written for incom-
pressible, isothermal and Newtonian fluid. A pseudo-
spectral flow solver is employed to solve such equations
at a shear Reynolds number Re, 150, based on the
shear velocity and the channel half height (correspond-
ing to a bulk Reynolds number, Reb 2250). The flow
solver is based on the Fourier-Galerkin method in the
streamwise (x) and spanwise (y) directions, whereas a
Chebyshev-collocation method in the wall-normal di-
rection (z). Time integration of fluid uses a second-
order Adams-Bashforth scheme for the non-linear terms


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


(which are calculated in a pseudo-spectral way with
de-aliasing in the periodic directions) and an implicit
Crank-Nicolson scheme for the viscous terms (Marchi-
oli and Soldati, 2002). The size of the computational
domain is 47h x 27h x 2h in x, y and z, respectively;
computations are carried out using 128 x 128 x 129 grid
points. Periodic boundary conditions are applied in x
and y, no-slip conditions are enforced at both walls. The
grid resolution is uniform in the homogeneous directions
x and y, whereas a grid refinement (providing a mini-
mum non-dimensional grid spacing of 0.045 wall units)
is applied near the walls in the non-homogeneous direc-
tion, z. The non-dimensional step size for time integra-
tion is 0.045 in wall units. Regarding the Lagrangian
particle dynamics, the dispersed phase is treated in the
same way as in Gallily and Cohen (1979), Zhang et al.
(2001) and Mortensen et al. (2008). The translational
equation of motion of an individual particle is given by
the linear momentum equation:
dv F
m (1)
dt m
where v is the particle velocity, F is the total hydro-
dynamic drag force acting on the particle and m
(4/3)aa3App is the particle mass (a and A are the semi-
minor axis and the aspect ratio of the ellipsoid, whereas
pp is the density of the particle). The expression for
F used in our simulations was first derived by Bren-
ner (1963) for an ellipsoid under creeping flow condi-
tions: F = pK(u v), where p is the fluid dynamic
viscosity, K is the resistance tensor (whose components
depend on the orientation of the fiber through the well-
known Euler parameters) and u is the fluid velocity at
particle position, obtained using a one-sided interpola-
tion scheme based on sixth-order Lagrangian polynomi-
als. The above particle equation of motion is advanced
in time by means of a fourth-order Runge-Kutta scheme
using the same step size as that of the fluid. The total
tracking time in wall units was t+ 1056 (note that the
superscript + is used in this paper to represent variables
in non-dimensional form). The relevant parameters to
be specified for time integration are a, A and the particle
response time, defined following Zhang et al. (2001):

+ 2(a+)2S Aln(A+ A -1)
9 =A 1 (2)

where S is the particle-to-fluid density ratio. In this
study, we have selected a+ 0.36, A 1.001 (spher-
ical particles), 3, 10, 50, and t+ = 1, 5, 30, 100, thus
extending the database of Mortensen et al. (2008) to 16
cases in the (A, p7,)-space. To ensure converged statis-
tics, swarms of N 200, 000 fibers are tracked for each
fiber category, assuming dilute flow conditions and one-
way coupling between the phases. Further details on the













numerical methodology can be found in Fantoni et al.
(2010).



Results and Discussion


Fig. 1 shows the instantaneous distribution of the 7,
30 particles with A 50. Similar distributions are ob-
served for the other particle categories, but they are not
shown in this paper for sake of brevity. It is apparent that
particles cluster into groups leaving regions empty of
particles (Fig. la) and that particles are aligned with the
mean flow direction. We remark here that the regions de-
pleted of particles have the same location for all the par-
ticle categories investigated: this means that, regardless
of the strong mathematical coupling between rotational
and translational equations due to the dependency of the
resistance tensor on the orientation, particle distributions
are practically unaffected by the aspect ratio and depend
only on the response time. This is the case for many
translational velocity statistics, as already observed by
Mortensen et al. (2008). Also acceleration statistics are
little affected by fiber elongation, as shown by Figs. 2,
3, 4, and 5. Fig. 2 shows the dimensionless stream-
wise component of the mean fiber acceleration, a+, for
all cases in the (A, T7,)-space. Regardless of the aspect
ratio, all fibers are characterized by uniform streamwise
acceleration as long as they remain confined in the cen-
ter of the channel. Strong deceleration is observed when
fibers approach the wall. The strength of such decelera-
tion decreases for increasing response time, whereas no
significant effect can be attributed to elongation.


a) 300
250
200
z+ 150
100
50
0


b) Wuu
250
200
z+ 150
100
50
0


300 600


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


Fig. 3 shows the dimensionless wall-normal compo-
nent of the mean fiber acceleration, a+. Fibers with
small response time (T7 = 1 and 5) are characterized
by negative acceleration in the center of the channel and


(a) c+=1
=1 001
a 1=3
S,=10
- =50


0 20 40 60 80 100 120 140






(b) z+=5
S=1 001
0 1=3
=10
- =50



0 20 40 60 80 100 120 140


I ,-u 14.- l-**-* *


(c) +=30
1=1 001
- ?=3
1-=10
X =50


2 0 20 40 60 80 100 120 140
900 001

0


-0 03


300 600


g -0 04
900
-0 05


(6) T=100
- =1 001
X ,=3
X=10
X =50


Figure 1: Instantaneous fiber distribution at the end of
the simulation (T7 = 30, A 50). Panels: (a) cross-
sectional view (mean flow directed towards the reader;
0 < x+ < 200); (b) lateral view (mean flow directed
from left to right; 600 < y+ < 750).


-0 06
0 20 40 60 80 100 120 140
z

Figure 2: Mean streamwise acceleration, a+, along the
wall-normal direction, z+. Panels: (a) T7 = 1; (b)
T 5; (c) T+ 30; (d) Tp 100.













by strong wallward acceleration as they approach the
wall. Acceleration is much smaller for fibers with re-
sponse time T+= 30 and becomes everywhere negligi-
ble for the T+ 100 fibers.


(a) T+=1
S=1001

x =10
X 6=50


0005


-0005
0
0015 -


001


+ 0 005


0


-0005
0015


+N 0005


0


-0005
0015


001


0+ 0005


20 40 60 80 100 120 140


(b) T =5
X =1001
S =3
x=10
X =50


0 20 40 60 80 100 120 140


(c) t=30
x=1001
X=3
S =10
e x=50


0 20 40 60 80 100 120 140


(d)c= 100
S=1001
X=3
S x=10
X =50


-0 005 601
0 20 40 60 80 100 120 140


Figure 3: Mean wall-normal acceleration, a+, along the
wall-normal direction, z+. Panels: (a) T7 = 1; (b)
T 5; (c) T 30; (d) T 100.
P I P P -


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


Again, the effect of the response time in determining
the rate of change of fiber momentum is clear, whereas
elongational effects are negligible. We remind here that
the different fiber classes considered in this study are ob-
tained varying two parameters (the aspect ratio and the
density of the fiber) while keeping the response time of
each class constant. This means that: i) for a given value
of the aspect ratio (namely for a given volume of the el-
lipsoid), the mass of a fiber increases with its response
time due to an increase of the fiber density; ii) for a given
value of the response time, the mass of a fiber increases
with its elongation so longer fibers have higher inertia
(even if their density is lower). These observations may
help to explain the trends observed in Figs. 2 and 3.

To conclude the analysis on fiber acceleration, in Fig.
4 and in Fig. 5 we show the streamwise and the wall-
normal components of the root mean square of fiber ac-
celeration, respectively. Considerations similar to those
drawn for the mean accelerations can be made. The
main effect is due to an increase of fiber inertia asso-
ciated to higher fiber density, which acts to damp accel-
eration fluctuations in both directions. Elongational ef-
fects are only noticed for the intermediate T 5 fibers
in the region where the intensity of acceleration fluctu-
ations reaches a maximum (Figs. 4b and 5b). The ac-
celeration statistics just discussed are presented here for
the first time (to the best of our knowledge) and com-
plement the discussion on translational dynamics made
in Fantoni et al. (2010) since they further confirm the
substantial non sensitivity of translational statistics to
elongation. One important exception, however, is given
by the particle wall-normal velocity, w'. Besides being
strongly dependent on the particle response time, this
quantity is also significantly influenced by A as shown
in Fig. 6 for the T7 = 30 particles case (again, similar
curves are obtained for the other particle categories, but
they are not shown here for brevity). Note that the pro-
files in this figure were smoothed out by time-averaging
over the last 200 wall time units of the simulation. Such
time-averaging procedure was adopted for ease of com-
parison and for visualization purposes only: the pro-
files considered refer to a statistically-developing con-
dition for the particle concentration and, thus, wp' is a
time-dependent quantity which asymptotically tends to
zero as the steady-state condition is approached. In the
case shown, the aspect ratio produces a slight increase
of w' for the A 3 fibers followed by a monotonic de-
crease as A increases. In the buffer layer (z+ < 30),
reduction of wall-normal velocity becomes significant
only for A 50. Similar trends are observed for the
T= 100 particles (not shown), whereas for the smaller
T 5 (also not shown) we observe a non monotonic
variation of w' leading to a maximum increase for A 3
and a subsequent decrease for A = 10 and A = 50. This















complex dependency of w' on both 7T and A produces
remarkable changes in the rate at which particles travel
towards the wall and, in turn, modify the build-up of par-
ticles in the near-wall region, as shown by the instan-
taneous concentration profiles (computed as volumetric
particle number density) of Fig. 7.



015


0(a) "'+=1
o01 X=l 001
0X=3
f I X=10


005


0
0
015


20 40 60 80 100 120 140


(c) t =30

01 X =1001
01
< X=3



0 05


u -
0
015


005


20 40 60 80 100 120 140


(d) t =100
S=1 001
X=3
S=10
X =50


0 20 40 60 80 100 120 140
z+


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



From a quantitative viewpoint, the most evident
changes occur very near the wall (within a few wall units
from it): each profile develops a peak of concentration
which is located at different positions depending on the
aspect ratio. The peak value also changes, according to
the variations of w discussed above.




008

007 (a) T+=1





001001
003 ----3

002 X60

001

0
0 20 40 60 80 100 120 140
006 z

05 0 a (b) t=5

00 4 *6


U o (c) t+=30

004 =1001
0 04
X=3

003 e = U=50

002

001

0
0 20 40 60 80 100 120 140
006


(d) t =100
S=1001
X= 1 001
X ==3
S=10
X 6=50


003

002 r


0 20 40 60 80 100 120 140
z


Figure 4: Root mean square of streamwise fiber acceler-
ation, RMS(a ), along the wall-normal direction, z+.


Figure 5: Root mean square of wall-normal fiber accel-
eration, RMS(a ), in the wall-normal direction, z+.








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


Outside the viscous sublayer, variations are less evi-
dent and, again, the elongation of the particle does not
seem to play an important role. To investigate further
the role of A and 7t, we analyzed the orientation statis-
tics. Orientations statistics have been shown previously
by Zhang et al. (2001) and by Mortensen et al. (2008),
who used the absolute value of mean direction cosines to
represent mean fiber orientations. As shown in Fantoni
et al. (2010), our results match very well those shown
by Mortensen et al. (2008) for fibers with 7, 5
and 7T = 30. Hence, here we show the same quan-
tities for the other two values of the response time we
considered, namely T7 = 1 in Fig. 8 (fast fibers) and
T7 = 100 in Fig. 9 (slow fibers). Results indicate
that fast fibers, which are characterized by relatively
low densities (ranging from ppl=x=ool 45.14 kg/m3
to pplX=so 9.80 kg/m3) are more aligned in the
streamwise direction than slow fibers, which are charac-
terized by higher densities (ranging from pp = 1.ool
4514 kg/m3 to pplA=so = 980 kg/m3).


0.04


0.03


0.02


0.01


0 20 40 60 80
Z


100 120 140


2


//
0/


(a) ~p'= 1
=1 001
S=3
=- 10
S=50
U~s

"Usieg


o (b) ,p=5
20 =1 001
X=3
X= 10
X=50
15
O

S10

5


3
1 10
30


251 =1 001
=3
20 d =10

0 15

10

5

0
1 10

IU(di)p 100


U-


0 5







0


- =1 001
S=3
-- =10
S=50


sII


Figure 6: Mean wall-normal translational velocity, wp,
for the = 30 fibers. Panel (b) shows a close-up view
of the profiles in the near-wall region (log-lin plot).


Figure 7: Wall-normal fiber concentration profiles
(taken at t+ 1056). Panels: (a) + 1, (b) T+ 5,
(c) 7 30, (d) T+ 100.


- =1.001
SX=3 (b)
_ --- =10
X=50



,"


S


-V
J~U

^U














Also, mean direction cosines confirm that: i) prefer-
ential orientation of fast fibers in the streamwise direc-
tion increases significantly and monotonically with as-
pect ratio (see Fig. 8a), whereas the orientation of slow
fibers does not change much with elongation (see Fig.
9a); ii) slow fibers are less oriented in the spanwise di-
rection than fast fibers (as demonstrated by Figs. 8b
and 9b) since spanwise fluctuations are relatively weak
and their capability of altering the alignment of a fiber
is reduced as fiber inertia increases; ii-bis) this trend in-
creases monotonically with elongation; iii) fast fibers are


06


05


04

08

07

06

Sns5


0 20 40 60 80 100 120


X=1 001
Xo =3
SX =10
B X=50


E- n a fln-1 L n


04

03


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



less oriented toward the wall than slow fibers. In an ef-
fort to go beyond these observations, we also focused
on the orientation time for each particle category. The
orientation time is the overall time spent by the particles
in a given position of alignment with respect to the mean
flow. To perform this calculation, we proceeded for each
particle category in the following way: I) The alignment
of each particle was classified by subdividing the abso-
lute value of the direction cosines, Icos(0) |, which de-
termine the orientation of the particle with respect to the
Cartesian axes, into 10 equally-spaced bins (e.g. first bin




S=1 001
0 8 =3
)=10
X=50
07


06

5* .E*...E...........

(a)


20 40 60


80 100 120 140


S=1 001
X =3
SX:=10
X :=50


100 120 140


0 20 40 60 80 100 120 140
07 a--

-- X=1 001


- m~mS-*OgOgg~g*SU6@O!.~


0 20 40 60 80


100 120 140


(c)

0 20 40 60 80 100 120 140


Figure 8: Absolute values of mean direction cosines for
the + 1 fibers. Panels: (a) cos(0x)|, (b) cos(0)|,,
(c) cos(O)|,


Figure 9: Absolute values of mean direction cosines for
the + 100 fibers. Panels: (a) Icos(O)1), (b) Icos(Oy)|,
(c) cos(O;)1,


02
0 20
06


40 60 80


S = I 11 I

* = :1,
X h=50


---ar


8


06 I











in the range [0,0.1], second bin in the range [0.1,0.2],
etc.). Particles are tagged as aligned with a given di-
rection, xi, if they fall in the bin where Icos(0i)| is in
the range [0.9,1]. II) The orientation of each fiber and
the corresponding bin are determined every time step
over a long period of time (T 200 at the end of
the simulation); a time-counter is then updated to com-
pute the overall time, t+(i,j, k), spent by the i-th fiber
of the j-th category in the k-th bin. III) The mean time
per bin is computed as t+(j, k) (1/N)Eit (i, j, k)
where i 1,..., N and then its percentage value is ob-
tained dividing by T+. Such procedure was applied fo-
cusing on two specific regions of the flow: a core region
across the channel centerline (140 < z+ < 160) and
a near-wall region (z+ < 10 from the wall). In Fig.
10 we show the results obtained in the near-wall region
for |cos(0O)| as a function of the different aspect ratios.
All cases in the (A, p7,)-space are shown. For complete-
ness, an inset has been added in each panel to show re-
sults obtained in the channel centerline. In this region,
there is almost no mean shear and turbulence is nearly
homogeneous and isotropic so preferential fiber orienta-
tion is never observed. Only for + 1 and T+ = 5
fibers, whose specific density is 0(10 102), a slight
increase of'. i when cos(0x)| E [0.9, 1] occurs. Inthe
near-wall region, the most probable fiber orientation is
in the streamwise direction, as demonstrated by Zhang
et al. (2001) and by Mortensen et al. (2008). How-
ever, Fig. 10 indicates that fibers are aligned with the
mean flow at most .I' of the time in the most favorable
case [Tp 5, A 50, Fig. 10(b)]; orientation fre-
quencies otherwise decrease, either because the aspect
ratio decreases (for instance, i+ falls to about :II' for
the Tp = 5 fibers with A 3) or because the inertia de-
creases (for instance, + falls to about :II' also for the
Tp = 30 fibers with A = 50, irrespectively of the aspect
ratio). Considering also the results for the spanwise and
wall-normal direction cosines, not shown here for sake
of brevity but reported in Fantoni et al. (2010), these
percentages indicate that the position of near-wall align-
ment imposed by the streamwise fluctuations of the flow,
though statistically probable, is quite "unstable" and can
not be maintained for very long times. In other words,
it can not be maintained for very long times before the
wall-normal fluid velocity gradient induces a nearly pla-
nar rotation of the initially-aligned particles around the
spanwise direction. Such observables are important to
interpret, from a physical viewpoint, the combined effect
of particle shape and inertia on macroscopic phenomena
like particle wall accumulation and particle segregation,
which depend on the nature of particle dynamics in con-
nection with turbulence dynamics (Marchioli and Sol-
dati, 2002). Note that, since the direction cosines are
non-linear functions, equally-spaced bins for Icos(0)|


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


correspond to bins of different "size" for 0i, the "align-
ment" bin being wider than the others. We thus expect
that new results computed considering equally-spaced
bins for 0, would lead to the same (probably even more
striking) qualitative conclusion.
To evaluate the applicability of the abovementioned
results to "real world" situations, simulations have been
recently complemented by experimental measurements
of dilute nylon fiber suspension in turbulent pipe flow.
Experiments were performed in a 10 cm pipe at much
higher Reynolds numbers (Re, > 1700) using Particle
Imaging Velocimetry and in-house phase-discrimination
optimized for ellipsoids: the reader is referred to Dear-
ing et al. (2010) for a detailed description of the exper-
imental set-up and flow parameters. In spite of remark-
ably different flow conditions, aligned orientation and
preferential distribution of fibers in the near-wall region
are confirmed from a qualitative viewpoint, highlighting
the validity of the one-way coupling assumption for di-
lute conditions. Experimental results also suggest that,
albeit simplified, a lumped-parameter model like the one
adopted here incorporates enough physics to capture ad-
equately the strong coupling between the translational
motion and the rotational motion of the fibers.

Conclusions

In the present work, the dynamics of prolate ellipsoidal
particles dispersed in a turbulent channel flow was ana-
lyzed using DNS and Lagrangian particle tracking. Pro-
late ellipsoids were chosen because they reproduce quite
reasonably the behavior of rigid fibers in a number of
applications of both scientific and engineering interest.
Results obtained for several combination of values sam-
pling the (A, Tp)-space indicate clearly that the rotational
motion of elongated particles affects the turbulence-
induced net flux of particles toward the wall by chang-
ing the mean particle wall-normal velocity. This effect,
which can ultimately be ascribed to the shape of the par-
ticles, adds to that due to their inertia and, compared to
the case of spherical particles, modifies from a quanti-
tative viewpoint the build-up of particles at the wall and
the deposition rates, as demonstrated by the concentra-
tion profiles. One possible explanation for such observ-
able can be found by looking at particle rotational dy-
namics: as shown by the analysis of the near-wall parti-
cle orientation times, the preferred condition of stream-
wise alignment with the mean flow is unstable and can
be maintained for rather short times before particles are
forced to rotate around the spanwise axis by the shear-
induced wall-normal velocity gradient, thus changing
their local spatial distribution. The main future develop-
ment of this work is the inclusion of two-way coupling
effects in the simulations.









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


20 k


0
0
60 r


20 k


60

50 (a) Tp =l

40

30

20

10

0 01 02 03 04 05 06 07 08 09 1
Icos(eOI P




4
*---*~-----*- ~a--Bf-P-^::irg-
[ i *} "


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Icos(ex)1


bU
60

50 (b) tp =5
50
40

30 E
-40
20


- 30 ---
30
0 01 02 03 04 05 06 07 08 09 1
Icos(eOj
- 20 -



-10 I I I I I I ---- -

0-


1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1 60 I I I I


- 0
1 0


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Icos(ex)


Figure 10: Streamwise orientation frequency (percent values) in the near-wall region (z+ < 10). For comparison
purposes, percent values in the center of the channel are also shown in the inset of each panel. Panels: (a) T+ 1; (b)
t+ 5; (c) T+ 30; (d) T+ 100. Symbols: () A 1.001, (o) A 3, (m) A 10, (o) A 50.


60

50 (c) pt =30

40

30

20

10
0
0 01 02 03 04 05 06 07 08 09 1
Icos(eOj



-

-_____-_______________*__________-^'^--------


60

50 (d) Ip=100
50
40

30
40
20

100 --_ 4 -i
30
0 01 02 03 04 05 06 07 08 09 1
Icos(O)l
20



10 rJ
S -
10- ---.---~-.----.----.--^-*-^^^--


I I I I I I I I I


I I I I I


I











Hopefully, through these new simulations it will be
possible to provide a physical explanation to the mech-
anism of fiber-induced turbulent drag reduction, which
has been observed in many experiments.


Acknowledgments

Financial support from CIPE Comitato Interministeriale
per la Programmazione Economica under Grant Carat-
terizzazione ed abbattimento di inquinanti e analisi del
rischio nei process di lavorazione del legno, and from
the Regional Authority of Friuli Venezia Giulia under
Grant Nuove metodologie per la riduzione e la .. ii. ,..
di emissioni di COVe particolato per l industriala di pan-
nelli di particelle efibra di legno are gratefully acknowl-
edged.


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