Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.1.4 - Mixing induced by a random dispersion at high particulate Reynolds number
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 Material Information
Title: 10.1.4 - Mixing induced by a random dispersion at high particulate Reynolds number Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Besnaci, C.
Roig, V.
Risso, F.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: dispersed two-phase flows
mixing
planar laser induced fluorescence
 Notes
Abstract: Dispersed-two phase flows are often used in industrial applications in order to enhance mixing. The objective of this work is to understand the mixing mechanisms induced by the motion of the dispersed phase. Some of them, such as entrainment by the wake and vortex trapping (White & Nepf (2003)), occur in the vicinity of the dispersed particles and are thus difficult to address practically. However, a previous work has shown that the flow through a random array of fixed spheres is a realistic model of a swarm of rising bubbles (Amoura (2008)). Here, this flow is used to investigate the mixing of a scalar at high Schmidt number. Two hundred spheres of diameter d=2 cm, fixed by stems, are randomly distributed in a section of a square hydraulic channel of 22 cm side and 80 cm long, resulting in a volume fraction of 2%. Fluorescein is injected at a single point within the array. Two-dimensional concentration fields are measured by means of laser induced fluorescence (PLIF) in planes perpendicular to the flow direction. Various tests are done by varying the bulk liquid velocity U in the channel and the distance from the injection. At low Reynolds number, the mixing essentially results from successive interactions with spheres, which make more and more thin and complex sheets. When the dye goes past a sphere, the concentrated region is rapidly distorted by the potential flow that develops upstream. Due to the wake, the concentration field does not recover downstream the state it has before the interaction with the sphere. At large Re, the flow becomes unstable, fluctuations develop all over the channel and turbulent diffusion plays a major role. By varying both Re and the measurement planes, we analyze the relative importance of these two mechanisms.
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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Volume ID: VID00244
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Holding Location: University of Florida
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Resource Identifier: 1014-Besnaci-ICMF2010.pdf

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


Mixing induced by a random dispersion at high particulate Reynolds number


C. Besnaci*, V Roig* and F. Risso*

Institute de M6canique des Fluides de Toulouse, Universit6 de Toulouse (INP, UPS) and CNRS, Toulouse, France
Cedric.Besnaci@imft.fr, Veronique.Roig@imft.fr and Frederic.Risso@imft.fr
Keywords: Dispersed two-phase flows, Mixing, Planar Laser Induced Fluorescence




Abstract

Dispersed-two phase flows are often used in industrial applications in order to enhance mixing. The objective of this
work is to understand the mixing mechanisms induced by the motion of the dispersed phase. Some of them, such as
entrainment by the wake and vortex trapping (White & Nepf (2003)), occur in the vicinity of the dispersed particles
and are thus difficult to address practically. However, a previous work has shown that the flow through a random
array of fixed spheres is a realistic model of a swarm of rising bubbles (Amoura (2008)). Here, this flow is used
to investigate the mixing of a scalar at high Schmidt number. Two hundred spheres of diameter d=2 cm, fixed by
stems, are randomly distributed in a section of a square hydraulic channel of 22 cm side and 80 cm long, resulting in
a volume fraction of 2%. Fluorescein is injected at a single point within the array. Two-dimensional concentration
fields are measured by means of laser induced fluorescence (PLIF) in planes perpendicular to the flow direction.
Various tests are done by varying the bulk liquid velocity U in the channel and the distance from the injection. At
low Reynolds number, the mixing essentially results from successive interactions with spheres, which make more and
more thin and complex sheets. When the dye goes past a sphere, the concentrated region is rapidly distorted by the
potential flow that develops upstream. Due to the wake, the concentration field does not recover downstream the state
it has before the interaction with the sphere. At large Re, the flow becomes unstable, fluctuations develop all over the
channel and turbulent diffusion plays a major role. By varying both Re and the measurement planes, we analyze the
relative importance of these two mechanisms.


Introduction

Although bubbly flows are used in many industrial reac-
tors, the mixing of a dissolved component in the liquid
phase is far from being understood. The objective of
this work is to characterize the mixing mechanisms of
a solute in the generic case of a homogeneous swarm
of particles moving relative to fluid at high particulate
Reynolds numbers Re = Ud/v and high Schmidt num-
bers Sc v/D (where U is relative velocity, d the parti-
cle diameter, v the kinematic viscosity and D the molec-
ular diffusivity). In such a flow, the molecules of the
solute successively cross various regions where the mix-
ing mechanisms are different: direct interactions with
inclusions, such as captures and releases by recirculating
wakes; dispersion by velocity fluctuations either within
individual wakes or in the interstitial flow between the
particles. Varying the volume fraction a, it is expected
that the predominant mechanism will change.
There are few studies about mixing in bubbly flows.
In a pioneer experimental investigation, Mareuge &
Lance (1995) considered low gas volume fraction


(0.:' and showed that the bubble-induced agitation
causes an efficient mixing, which is deeply anisotropic.
Abbas et al. (2009) focused on the role of hydrody-
namic interactions by varying the gas volume fraction
up to 1:-'. in a uniform flow. Time-averaged distribu-
tions of the concentrationwere measured and interpreted
by means of an equivalent diffusivity introduced in a
random-averaged transport equation. The mixing was
shown to be a steep non-monotonic function of a and
could not be reproduced by models assuming potential
flow (Mareuge & Lance (1995), Eames & Bush (1999)).
It is now known that high-Reynolds-number bubble-
induced agitation involves vorticity production and wake
interactions (Risso & Ellingsen (2002), Roig & Lame
de Tournemine (2007), Risso et al. (2008)), the proper-
ties of which have been characterized in Riboux et al
(2010a). Moreover, large eddies simulations (Riboux
(2007), Riboux et al (2010b)) have shown that the flow
through a random array of fixed bubbles was a good
model of the agitation within a swarm of rising bub-
bles. This gave us the idea of designing an experimental
setup that consists of a uniform flow through a random







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


array of fixed spheres, which has been shown to repro-
duce well the bubble-induced agitation (Amoura (2008),
Risso et al. (2010)). Thanks to the fact that measure-
ments were done in a frame where the spheres are fixed,
two different contributions to the agitation have been
distinguished: (i) the spatial heterogeneities associated
to the random distribution of the spheres and (ii) the time
fluctuations caused by hydrodynamics instabilities of the
flow. This decomposition is essential in order to disen-
tangle the various physical mechanisms responsible for
the mixing. A similar decomposition was introduced by
White & Nepf (2003), Tanino & Nepf (2008) and Tanino
& Nepf (2009) for the mixing in the flow through a ran-
dom array of cylinders (which is a model of canopy) and
allowed them to interpret the measured effective diffu-
sivity.
Here, we report an experimental investigation of the
mixing in the same random array of spheres as Risso
et al. (2010). The flow regime is very different from
that of Tanino & Nepf (2008) and Tanino & Nepf (2009)
for three reasons: we used spheres instead of cylinders,
we considered much lower volume fractions and much
larger Reynolds numbers.

Experimental setup and measurement method

Flow configuration
A schematic of the setup is shown in Fig. 1. Two hun-
dred rigid spheres of diameters d=20 mm are randomly
distributed within a section of a square channel of side
1=220 mm and length L=800 mm. The spheres are fixed
by means of horizontal stainless steel rods of 2 mm di-
ameter mounted in tension between two opposite chan-
nel walls. The minimal distance between the rods is
5 cm and the resulting volume fraction of spheres is
a=0.02. A uniform flow of water is supplied at the top of
the test section. The bulk velocity (U) is varied from 5
to 50 mm/s in order to vary the sphere Reynolds number
Re=(U)d/v from 100 to 1000. Fluorescein is injected
from a circular nozzle of diameter / . = 2mm located
on the channel axis at various distances, z =11, 21 and
31 cm, upstream of the measurement section. The in-
jection velocity is the same as the bulk water velocity
through the channel. Figures 2 and 3 show side views of
the fluorescein behaviors for two contrasted regimes of
scalar transport corresponding respectively to Reynolds
numbers Re = 100 and Re = 600. Fluorescein has
a very low molecular diffusivity and the corresponding
Schmidt number is thus very large (Sc z2000). It is a
fluorescent dye, the concentration of which is measured
by means of Planar Laser Induced Fluorescence (PLIF)
in a horizontal (x, y) plane located 10 cm downstream
of the array of spheres.
PLIF method for concentration measurements


Figure 1: Flow configuration


Figure 2: Side view of an injection of fluorescein in the
array at Re = 100


Planar Laser Induced Fluorescence (PLIF) is a mod-
em technique for measuring two-dimensional fields of
concentration of a fluorescent dye (Koochesfahani and
Dimotakis (1985), Crimaldi (2008)). Here, a 2 mm-
thick laser sheet is generated by a 2*200mJ Argon-ion
laser (532 nm) equipped with a cylindrical lens. Fluo-
rescein molecules that cross the laser sheet emit a light,
the intensity of which is an increasing function of the in-
cident light they have absorbed. The fluoresced light is







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


Experimental measures
5000 -Linear regression
4000
03000
2000
1000

Co1 2
Concentration mol/L


Figure 3: Side view of an injection of fluorescein in the
array at Re 600


recorded by means of a digital camera and, since it has
a smaller wavelength, it is separated from the incident
light by means of a high-pass optical filter with a cut-off
wavelength of 540 nm. In the present configuration, a
mirror that makes an angle of 45 degrees relative to the
vertical direction is set within the channel at a distance
z=40 cm downstream of the test section. It makes possi-
ble to image the horizontal laser sheet by means of a 12-
bit PCO SENSICAM digital camera with 1040x 1376
pixels2. The measurement windows is 140 by 185 mm
with a resolution of 0.135mm given by the pixel size.
For each run, 500 to 1000 images have been recorded at
2 or 8 Hz in order to ensure observation duration of at
least one minute. The shutter speed was 1/3000s, which
is enough to avoid any motion blur. A crucial point is
to use the full range of grey levels of the camera to cap-
ture the largest possible range of fluctuation. This can
be achieved by adjusting either the optical aperture of
the camera or the initial concentration C,,j of the water-
fluoresecin solution that is injected. The latter was ad-
justed for each flow regime in order to get a range of con-
centration within the measurement plane that makes the
best compromise between the camera sensitivity, which
requires the maximum of energy, and the fluorescence
phenomenon, which needs a concentration less than 6.5
10 5mol/L to remain in the linear regime. Depending
on the actual range of concentration, the f-stop was then
varied from 4 to 1.2. It is worth noting that even if the
wavelength of the laser source does not correspond to
the peak of adsorption of the fluorescein, this operating
mode is well adapted to the present investigation.
The images need then to be converted into values of
concentration. This requires the determination of the
calibration that relates concentration to grey levels. The


Figure 4: Calibration curve


calibration has been done, in the absence of any flow,
inside the channel which has been filled with homoge-
nous fluorescein solutions of known concentrations. The
raw image Io,cH (Z, y) corresponding to a given homo-
geneous concentration CH appears to be non homoge-
neous for two reasons: (1) the light intensity decreases
in the transversal direction due to the Gaussian shape of
the laser beam; (2) the amount of light that is absorbed
by the fluorescein is not negligible over distances of the
order of the measurement window. However, we can
neglect this phenomena if the light path is less than 15
mm. Figure 4 shows the grey-level intensity G of the im-
age minus the camera noise, Io,cH I,, averaged over
the region where the incident light is homogeneous. For
concentration less than 6.5 x 10 5mol/L, the calibration
curve is linear and reads:

(G) kCH. (1)

The determination of a calibration valid for the whole
measurement window requires to account for absorption
and non uniformity of the incident light. Since the for-
mer occurs in the direction of light propagation and latter
in the perpendicular direction, it is possible to deal with
them separately. Let us start with absorption. Figure 5
shows the evolution of the grey level G in the direction
x of light propagation for different transversal positions
y at CH=5.3 x 10 5mol/L. The decrease is linear with
the same slope K -1.8 m 1 whatever y positions and
writes:
G(x)/G(0) = 1 Kx. (2)
The value of K has been obtained for each concentra-
tion and K(CH) is observed to be a decreasing func-
tion. This allows us to estimate the effect of absorption
for the inhomogeneous images obtained when fluores-
cein is injected within the array of spheres. For the most
critical cases (Re=100 and 200), the largest spots of dye
have a size of about 3 cm and a concentration of 5 10 5
mol/L, which leads to an absorption less than i.'. At
higher Reynolds numbers, the dye spots are larger but
have a much lower concentration and generate a smaller
absorption.







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


On the other hand, the non-uniformity of the incident
light is present for injection experiments as well as for
calibration images. It is however possible to obtain a
map Ie(x, y) of the incident light by correcting a cali-
bration image o, cH (x, y) obtained with a homogeneous
calibration from the effect of the absorption:


le(x, y) = ,c ) (3)
(1 K(CH)x)kCH

Figure 6 shows transverse profiles of I1 obtained for
CH1=5.3 x 10 5mol/L, which shows the Gaussian shape
of the laser sheet. If the absorption of calibration im-
age was exactly corrected by eq. 3, we would obtain
a light map I1 independent of CH. Figure 6 also shows
the transverse profiles of the ratio le(CH1 )Ie(CH2) for
CH2=1.3 x 10 5mol/l. We observe that the residualvari-
ations of the profiles are less than 3%, indicating that this
approach is accurate. In the following, we will only con-
sider the reference light map l (x, y) obtained with the
concentration CH2.
Now, it is possible to use the linear calibration law
(1) to convert the grey levels of the images obtained in
injection experiments Io(x, y) into a real concentration
field C(x,y). After subtraction of the background image
lob(x, y) obtained in the absence of fluorescein, we get
the image I = o lob. Then, C(x, y) is obtained as:

I(x, y)
C(x, y) k 1 I(x, y) (4)
I. (x, y)" (4)

The final accuracy on the measurement of C(x, y) is
3%.
l3io


0 7 1
00 Ull t ,5


15 20


Figure 5: Decrease of the fluoresced light G(x)/G(0)
in the direction of light propagation for various transver-
sal positions. (Symbols that are connected by lines show
corrected intensity divided by 1 Kx)



Description of the mechanisms of mixing

Figures 7 to 11 show instantaneous fields of concentra-
tion C(x, y) at a distance z = 31cm downstream of the
dye injection, a distance which ensures that the dye has


-004
-006 O x2cm
+ x5cm
+l10cm
008-
0 2 4 6
y(cm)


10 12


Figure 6: Spatial heterogeneity of the incident light
(I/Ie((0, 0) 1) in the direction y for various posi-
tions x. Symbols that are connected by lines show
(e(CH1)/e(CH2) 1).


interacted with several spheres. Various Reynolds num-
ber have been considered and the concentrations have
been normalized by the corresponding initial concentra-
tion C,,j. The mixing depends strongly on the Reynolds
number. At Re 100, the concentration field is very
heterogeneous, showing tortuous lines with a length of
the order of d (figure 7). When Re increases the pattern
evolves. Up to Re=200, the lines are still the main fea-
tures. Then, they fade and progressively disappear. Con-
currently, small scales appear, indicating that the con-
centration spectrum fills up and tends to become contin-
uous. This globally leads to a larger and larger area in-
vaded by the dye, which corresponds to lower and lower
local concentrations and therefore to a more efficient
mixing.
This evolution with Re sheds light on the mixing
mechanisms. Figure 2 illustrates the interaction of a dye
filament with a sphere at Re=100. When a filament im-
pacts on the stagnation point, it is changed into an ax-
isymmetric sheet; then, it does not turn back into a fila-
ment because of the wake. When the filament is slightly
off-centered relative to the sphere, the dye path is dis-
placed laterally and a sheet is also produced. When the
off-centering is larger than the sphere radius, the fila-
ment is still stretched in the azimuthal direction but not
enough to make a sheet; in this case, an initial straight
and round filament is simply changed into a tortuous fil-
ament with a complex cross section. Interactions with
successive spheres thus allow us to understand the pat-
terns visible in figure 7. At Re=100, the main mixing
mechanism is the stretching of the velocity field in the
vicinity of a sphere. Of course, turbulent fluctuations are
also present. At low Re, their intensity is low and their
action is limited to vary randomly the distance between
the dye and the spheres. However, turbulence becomes
predominant at large Re and generates a turbulent mix-
ing over a broad range of length scales which includes
both (1) small scales that diffuse and distort the large







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


coherent sheets or filaments and (2) large scales that dis-
perse the dye over much larger distances. This is clearly
visible in the side view at Re=600 (fig. 3) as well as in
horizontal concentration fields at high Re (fig. 9 to 11).
At Re >600, the main mechanism is the diffusion by the
bubble-induced turbulence. For intermediate Reynolds
numbers (200< Re <400), the two mixing mechanisms
have comparable magnitudes. These Reynolds numbers
correspond to the range where the flow through the ar-
ray of spheres becomes unstable and starts to generate
strong time fluctuations, which dominate in the horizon-
tal direction (Risso et al. (2010)).


iv"

,tt%


-2 0
x (cm)


2 4 6


Figure 9: C(x, y)/Cinj for Re=400


o-"-


/,
C)% i


4 -2 0
x (cm)


2 4 6


Figure 7: Concentration field C(x, y)/Cinj for Re=100


-4 -2 0
x(cm)


2 4 6


Figure 10: C(x, y)/Ct, for Re=600


-4 -2 0
x (cm)


0025


#11
-3;r~2:


2 4 6


-4 -2 0
x (cm)


2 4 6


Figure 8: C(x, y)/C,,j for Re=200




Quantitative description of the mixing

In order to describe quantitatively the mixing, we de-
cided to introduce averaged quantities. The previous
qualitative discussion suggests to distinguish the hori-
zontal fluctuations of the spot position from the actual
spreading of the concentration. On the one hand, we de-
fine the instantaneous center of mass (xaG, yGi) of the
concentration field and the standard deviation of its ra-


Figure 11: C(x, y)/C nj for Re=1000



dial coordinate


N1
i_1^


N
7)2 +
i=1


ye)2),


(5)
where N = 1000 is the number of PLIF images. On
the other hand, we average the instantaneous concentra-
tion fields C, after they have been centered around (xai,


0


-2


-46
-6


A,














1 N
i=1


The standard deviation aT is reported in figure 12 as
a function of Re. The evolution of TG with Re shows
the same trends for the three considered values of z, in-
dicating that this evolution is the signature of the relative
weights of the two mixing mechanisms. We observe that
it increases sharply as Re increases from 100 to 400 and
then reaches an almost constant value.


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


be quantified by introducing the standard deviation:

f r2C(r)dr
oc= Vf 0C(r)dr (7)
This parameter is plotted as a function of Re in figure
17. Its behavior is similar to that of oTG. Whatever z, it
increases with Re for Re < 400 and then saturates. This
saturation takes place as the velocity fluctuations in the
array become independent of the Reynolds number.


-3 -2 -1 0
x (cm)


2 3


200 400 600 800
Re


z=11cm
-z=21cm
-z=31cm
1000 1200


Figure 12: Evolution of the standard deviation ca with
Re


Figures 13 and 14 show the normalized average con-
centration fields C(x, y)/Cnj for Re=100 and 1000 at
z 31cm. Average concentrations are very different
from instantaneous ones obtained for the same Re (fig.
7 & 11). They follow an almost circular symmetry, in-
dicating a satisfactory statistical convergence. It appears
clearly that the average spot is much larger at Re=1000
and that the mixing is stronger. This can be better ana-
lyzed by considering the radial profiles of concentration
C(r), which are obtained by averaging C(x, y) in the
azimuthal direction. Figures 15 and 16 show the normal-
ized radial profiles C(r)/C(O) for either z= 1 or 3 1cm,
for five Reynolds numbers between 100 and 1000. At
low Reynolds number, the average spot results from the
superimposition of small concentrated regions involv-
ing a very narrow range of length scales which have
different shapes and orientations. At a given instant, the
mixing is therefore small compared to what is seen on
the averaged map. This spreading mechanism of the av-
erage spot is however not efficient and the average con-
centration profiles are very narrow and peaked at the ori-
gin. Increasing Re, a broad range of scales is involved in
the mixing and the main effect of the averaging is simply
to smooth the concentration fields. Average profiles not
only become broader but also display a different shape.
The differences between low and large Re are enhanced
when the distance z is increased. The width of C(r) can


Figure 13:
Re=100


-2




Figure 14:
Re=1000


Mean concentration field C(x, y)/C,,j for


0
x (cm)


Mean concentration field C(x, y)/Cij for


"In ___
2r/d

Figure 15: Radial profile C(r)/C(0) for z =11cm



Conclusion

The evolution of the concentration of a dye in the flow
through an array of fixed spheres has been investigated















I ,...,





2r/d

Figure 16: Radial profile C(r)/C(O) for z =31cm


2

1 5

0 0

05 0z=11cm
-z=21cm
4z=31cm
0 200 400 600 800 1000 1200
Re

Figure 17: Evolution of the r.m.s. value of the variance
of the concentration radial distribution


with the aim of understanding mixing mechanisms in
dispersed two-phase flows. A PLIF method has been op-
timized to measure highly-heterogenous concentration
fields of large size with an good accuracy. Two mix-
ing mechanisms have been observed. The first, which
dominates at moderate Reynolds numbers, is related to
the stretching of the velocity field in the vicinity of the
dispersed phase. The second, which dominates at large
Re, results from the diffusion by the pseudo-turbulence.
The mixing efficiency has been quantified from the av-
erage properties of the concentration field. This shows
a transition in the dominant mixing mechanism around
Re=400, followed by a regime where the mixing tends
to become independent of the Reynolds number.


Acknowledgements

We thank the lab federation FERMaT for its support.


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7th International Conference on Multiphase Flow,
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