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: EulerianLagrangian simulations, fiberladen 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 oneway 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, nearwall 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 semiminor axis (pm)
K Resistance tensor ()
m Fiber mass (kg)
Re, shear Reynolds number ()
Reb bulk Reynolds number ()
S Fibertofluid 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 m3)
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 wallbounded 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 FokkerPlanck 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 fibersturbulence interac
tion is not satisfactory, and a deeper understanding of the
physical problem is required (Paschkewitz et al., 2004).
Among numerical EulerianLagrangian 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 lowspeed 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 zerogravity conditions.
Problem Formulation and Governing Equations
The Eulerian fluid dynamics is governed by the conti
nuity and NavierStokes 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 FourierGalerkin method in the
streamwise (x) and spanwise (y) directions, whereas a
Chebyshevcollocation method in the wallnormal di
rection (z). Time integration of fluid uses a second
order AdamsBashforth scheme for the nonlinear terms
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
(which are calculated in a pseudospectral way with
dealiasing in the periodic directions) and an implicit
CrankNicolson 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, noslip 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 nondimensional grid spacing of 0.045 wall units)
is applied near the walls in the nonhomogeneous direc
tion, z. The nondimensional 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 onesided interpola
tion scheme based on sixthorder Lagrangian polynomi
als. The above particle equation of motion is advanced
in time by means of a fourthorder RungeKutta 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 nondimensional 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 particletofluid 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 wallnormal 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
wallnormal 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 wallnormal acceleration, a+, along the
wallnormal 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 wallnormal 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 timeaveraging
over the last 200 wall time units of the simulation. Such
timeaveraging procedure was adopted for ease of com
parison and for visualization purposes only: the pro
files considered refer to a statisticallydeveloping con
dition for the particle concentration and, thus, wp' is a
timedependent quantity which asymptotically tends to
zero as the steadystate 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 wallnormal 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 buildup of par
ticles in the nearwall 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 wallnormal direction, z+.
Figure 5: Root mean square of wallnormal fiber accel
eration, RMS(a ), in the wallnormal 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 wallnormal translational velocity, wp,
for the = 30 fibers. Panel (b) shows a closeup view
of the profiles in the nearwall region (loglin plot).
Figure 7: Wallnormal 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; iibis) 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 fln1 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 equallyspaced 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 timecounter is then updated to com
pute the overall time, t+(i,j, k), spent by the ith fiber
of the jth category in the kth 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 nearwall region (z+ < 10 from the wall). In Fig.
10 we show the results obtained in the nearwall 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
nearwall 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
wallnormal direction cosines, not shown here for sake
of brevity but reported in Fantoni et al. (2010), these
percentages indicate that the position of nearwall 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
wallnormal fluid velocity gradient induces a nearly pla
nar rotation of the initiallyaligned 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
nonlinear functions, equallyspaced 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 equallyspaced
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 inhouse phasediscrimination
optimized for ellipsoids: the reader is referred to Dear
ing et al. (2010) for a detailed description of the exper
imental setup and flow parameters. In spite of remark
ably different flow conditions, aligned orientation and
preferential distribution of fibers in the nearwall region
are confirmed from a qualitative viewpoint, highlighting
the validity of the oneway coupling assumption for di
lute conditions. Experimental results also suggest that,
albeit simplified, a lumpedparameter 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 wallnormal 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 buildup 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 nearwall 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 wallnormal velocity gradient, thus changing
their local spatial distribution. The main future develop
ment of this work is the inclusion of twoway 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
**~* ~aBfP^::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 nearwall 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 fiberinduced 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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