Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.6.4 - Heat transfers in a droplet-laden turbulent jet
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Title: 10.6.4 - Heat transfers in a droplet-laden turbulent jet Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Meftah, H.
Reveillon, J.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: DNS
heat transfer
turbulence
droplets dispersion
 Notes
Abstract: Direct numerical simulations of two-phase flows have been carried out to study the temperature distribution in a dispersing spray. The configuration is a turbulent laden jet surrounded by a preheated coflow. Droplets are embedded in the main stream that is mixed with hot gases because of the development of the turbulent structures. Heat transfers between the droplets ans the surrounding atmosphere are studied with a specific focus on the temperature distribution in the liquid phase. It is demonstrated that, contrary to some existing assumption, this distribution does not have a Gaussian shape but follows the Nukiyama-Tanasawa law.
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: VID00268
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Resource Identifier: 1064-Meftah-ICMF2010.pdf

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


Heat transfers in a droplet-laden turbulent jet


H. Meftah and J. Reveillon

CORIA, INSA, Avenue de l'Universit6, 76800 Saint Etienne du Rouvray, France.
hmeftah@gmail.com
Keywords: DNS, heat transfer, turbulence, droplets dispersion.




Abstract

Direct numerical simulations of two-phase flows have been carried out to study the temperature distribution in a
dispersing spray. The configuration is a turbulent laden jet surrounded by a preheated coflow. Droplets are embedded
in the main stream that is mixed with hot gases because of the development of the turbulent structures. Heat transfers
between the droplets ans the surrounding atmosphere are studied with a specific focus on the temperature distribution
in the liquid phase. It is demonstrated that, contrary to some existing assumption, this distribution does not have a
Gaussian shape but follows the Nukiyama-Tanasawa law.


Introduction

During the last decades, combustion chamber modeling
has been extensively developed thanks to progresses
made in various domains. Indeed, most of the physical
phenomena present in engines or furnaces are know well
known, from the liquid fuel injection, down to the com-
bustion process and gas exhaust. However, to optimise
the environmental and economical outputs the consid-
ered systems, models' accuracy needs to be unceasingly
improved. Numerous physical phenomena are interact-
ing within the chamber but, its bottom performances de-
pend directly from the combustion phenomena, which
determine the burnt gases temperature and the pollutants
level.
Because a liquid fuel is generally injected in the
chamber, combustion occurs once liquid droplets have
been dispersed and evaporated. More and more combus-
tion models are taking into account the presence of an
evaporating dispersed phase prior to combustion. How-
ever, they focus mainly on the momentum and mass ex-
changes between the carrier phase and the spray. Indeed
it is a key point that determines the topology of the vapor
of fuel and consequently, the combustion regimes and
the model performance. But because of the actual opti-
mization level of combustion processes, a slight change
of the physical parameters inside the chamber may lead
to a significant modification of the combustion regime.
Thus, all possible interactions between the spray, the
turbulent carrier phase and combustion have to be ac-
counted for. However, heat transfers between the liq-
uid and the gas phases is often neglected. Indeed, the


decrease of temperature of the carrier phase due to the
liquid evaporation is weak compared to the energy pro-
vided by chemical reactions. However, before combus-
tion delivers its energy, the ignition process needs to be
captured and it depends on the amount of energy of the
fresh gases. A local decrease of temperature could pre-
vent ignition or, at least, delay it. From the spray point
of view, the analysis of the liquid temperature evolution
is still and open problem though it is a major issue if
one want to capture correctly the evaporation rate that
produces the local topology of the vapor, which will de-
termine the combustion processes.
At the experimental level, few studies (Letty et al.
(2007); Castanet et al. (2003)) dedicated to the mea-
surement of the temperature distribution within spray
or droplets exist since the techniques are still under de-
velopments. On the other hand, some numerical works
have been carried out but it remains a very open subject.
Jaberi (1998) studied the statistical behavior of fluid
temperature and particles in homogeneous isotropic tur-
bulence with a direct numerical simulation. He showed
that the effects of initial conditions on the fluid statistics
and particles are very important. Shotorban et al. (2003)
are carried out anisothermal duct simulations and stud-
ied the change of temperature variances of the fluid and
particles depending the rate of loading particles and the
relation between relaxation time dynamic and thermal
of particles. Sato et al. (1998) have studied the effects of
the presence of a temperature gradient on the Lagrangian
statistics of particles in homogeneous isotropic turbu-
lence. They found that the imposed temperature gradient
affects the autocorrelation coefficient of fluid tempera-







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


Figure 1: Sketch of the planarjet configuration.


ture and the temperature fluctuations of particles is well
correlated with the particle velocity in the direction of
the imposed temperature gradient.
However, there is a great unknown in the Eulerian dis-
persion models of particles concerning the shape and in-
tensity of the temperature distribution within the liquid
jet. And once the distributions is known we need to be
able to develop accurate models for complex applica-
tions resolved in large eddy simulation (LES) solvers.
Eulerian modeling of two-phase flows requires knowl-
edge of the distribution laws of size, velocity and tem-
perature drops. However, if the size dispersion (Laurent
and Massot (2001)) and velocity (Simonin et al. (2002);
Reveillon et al. (2' 1 4)) are well known, it is not the case
as gar as the temperature distribution is concerned. The
objective of this work is to carry out direct numerical
simulations to characterize the temperature distribution
in a spray of vaporizing droplets. In the following we
present the planar turbulent jet configuration that have
been used for this study. The mathematical formulation
of two-phase flows including heat transfer and coupling
between the carrier phase and the dispersed phase is de-
tailed in the paper of Reveillon (2007). The result sec-
tion presents the temperature distributions that have been
observed thanks to the simulations. An analytical law is
proposed in order to fit these distributions, and later to
model them in the framework of large eddy simulation.


Configuration

The proposed configuration consists in a sheared planar
jet defined in a previous study by Bouali et al. (2010).
Figure 1 represents a sketch of the 2D system. The
jet emerges from a nozzle of width b 3mm with a
maximum axial velocity uo 10m/s. Data are nor-
malized by the length b and the velocity uo. The com-
putational domain is 6b height and 12b length. At the
edge of the injector, as shown in figure 1, velocity fol-
lows a hyperbolic tangent profile defined by the relation:
r uo(p+(l p) +uc) with +tani h (b- 2
where 0 = 0.1 allows to define the maximum velocity


SDNS: direct
interaction of the
droplets with all the
turbulent scales of the
flow.


SLES: the droplets
interact with the
filtered DNS field.


Figure 2: Sketch of the interaction between spray fami-
lies and the DNS and LES fields.


gradient. ucc is the velocity of the preheated coflow and
is equal to 15% of the axial velocity (uo). Its tempera-
ture is equal to 600 K while the main jet temperature is
300 K. The turbulence is injected using the method de-
scribed by Klein et al. (2003) with a velocity root mean
square urms equal to 2.5% of the injection profile.


A-priori analysis

The purpose of this section is to study the spray disper-
sion by analyzing the distribution of size and tempera-
ture of droplets in both LES and DNS frameworks. To
carry out this objective, we have considered two fami-
lies of spray. A first family (SDNS) that interacts di-
rectly with the DNS fields (velocity, temperature, etc.)
and a second family (SLES) that interacts with the fil-
tered DNS fields as sketched in figure 2. This second
family would correspond to the dispersion of droplets in
a LES computation without any subgrid model to correct
the velocity and temperature dispersion. By comparing
the dispersion results of SDNS and SLES we will put
forward the impact of the subgrid scales on dispersing
sprays.
Control volumes (CV) have been disposed in our
computational domain to collect statistics on both fami-
lies.The location of the CV in the computational domain
are shown in figure 3.
As mentioned in the introduction, the Eulerian spray
modeling requires knowledge of the dispersion laws for
the diameter, the velocity and the temperature of the
droplets. Many studies have been conducted concerning
droplets size distribution and velocity distribution and
several empirical forms of presumed distribution exist.
The most common are described in detail in the papers
of Babinsky and Sojka (2002); Simonin et al. (2002);
Reveillon et al. (2i 1 4) and references therein but, to be
complete, some results are given in this paper. The last
unknown information that is necessary to close spray























Figure 3: Vapor mixture fraction and droplets, the color
of which represent the liquid temperature.
The eighth boxes are the analysis control vol-
umes.


models is the temperature distribution. In the follow-
ing we present the analysis performed with the statistics
collected in the various volume controls. Both size and
temperature distributions have been studied.


Size dispersion

As a first step, we considered an injection of mono-
dispersed droplets. A polydispersion appears very
quickly because of the turbulence mixing as shown by
figure 6 where the droplet diameter distribution is rep-
resented for both families of drops, SDNS and SLES.
In the control volume 1 (CV1), the distribution is a sin-
gle delta peak due to the injection of mono-dispersed
droplets. Along the jet axis, close to the injector (CV3),
the initial Dirac form of the distribution widens a little
but decreases abruptly to 0 since evaporation just started
for both spray families SDNS and SLES. It is possible to
observe a slightly larger dispersion of the LES droplets
diameter. Further along the jet axis, in volume CV6, the
jet undergoes strong instabilities and the droplets beat
around the control volume. A wide diameter distribu-
tion is observed with a slight growth towards the large
droplets diameters that are prevalents before a sudden
decreases. Another set of analysis has been carried out
on the jet border, in the areas were the turbulent struc-
tures are developing and the mixing between cold and
warm gases occur. It is possible to observe significant
differences between SDNS and SLES sprays. Close to
the injector, in volume CV2 (Fig. 6), the diameter dis-
tribution is much more wide than in the core of the jet.
More importantly, a significant difference may be ob-
served between LES and DNS distributions. As we are
still close to the injector, the injection diameter still pre-
vails in CV2 as far as SDNS droplets are concerned. On
the other hand, SLES are already smaller and the max-
imum population of droplets have a diameter equal to


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


SI r. of the injection size. Both distributions present in-
termediary values of the diameter because the evapora-
tion takes place very quickly in the mixing zone. But, if
there is less droplets with a large diameter in the SLES
spray compared to the SDNS one, there is much more
droplet with intermediary diameters (between ". and
- .'. of the injection diameter). This due to a general-
ized evaporation of the droplets because of the LES tem-
perature field, the gradient of which being much more
smooth than the DNS temperature field in the shear layer
area. Droplets that should be embedded in cold gases in
DNS simulations are then surrounded by slightly pre-
heated gases due to the filtering of the temperature pro-
files. Thus, they are evaporating with an intermediary
mass rate, which leads to a wider population of medium
size droplets. Away from the injector, control volumes
CV4 and CV5 have been positioned on the jet border
where the largest vortices are generated by the sheared
flow. CV4 is mostly situated in the jet core and a dis-
tribution similar to the one observed in CV2 may be
observed. However, CV5 is in the path of the vor-
tices issued from the jet destabilization. Droplets are
engulfed in the turbulent structures that passe periodi-
cally over the control volume. A rather homogeneous
diameter distribution may be observed except for a peak
at i r of the injection diameter as far as SDNS is con-
cerned. This peak is much less pronounced in the LES
configuration, indeed the impact of the filtering on the
turbulent structures leads to a more homogeneous en-
vironment for the droplets. All these shapes are non-
conventional but one must not forget that the droplets
were initial mono-dispersed. Therefore only the turbu-
lent mixing and the evaporation process are controlling
the distribution shape and not a usual atomization pro-
cess.
In a second step we injected a poly-dispersed distri-
bution of the droplets in the computational domain. The
diameter distribution follows a Log-Normal law (Babin-
sky and Sojka (2'" i I12,, which may be written:


=(a) 1 exp In( 2 / In(LN )2])
v ln(Lw)a 2 a \
(1)
where aLN is a dimensionless parameter that character-
izes the deviation to the mean characteristic diameter a.
This type of distribution is equivalent to a Gaussian dis-
tribution whose variable is the logarithm of the diameter.
The effective distribution of the droplets' diameter at the
injector has been plotted in figure 4.
Contrary to what we observed in the case of a mono-
dispersed spray, where diameter distributions take sev-
eral different shapes, the poly-dispersed spray distribu-
tion keeps its original Log-Normal shape in all the con-
trol volume of the configuration (Fig. 7), which quite





























Figure 4: Distribution of the droplet's diameter in the
injector for the poly-dispersed configuration.


reassuring from the modeling point of view. Moreover,
the SDNS and SLES distribution shapes are very close
to each others. From this point of view, no special clo-
sure seems necessary, at least in the physical conditions
used in this simulation.


Temperature dispersion

In this section, we discuss the dispersion of the temper-
ature of the droplets. This is an original analysis that
has never been addressed before from a DNS or a LES
point of view. Using the same "control volume" anal-
ysis we discussed in the previous section, we can first
observe CV1 for both mono- and polydispersed sprays
(Fig. 8 and 9). All the droplets are at their injection tem-
perature: 300 K although a slight part of them has been
heated in the DNS configuration, monodispersed spray.
The energy transfer between the gas and liquid phases
determines the heating rate of the liquid. In the DNS
case, since the temperature gradient are strong close to
the injector, as soon as a droplet crosses some hot gases
area, its temperature rises very quickly. On the other
hand, gradient smoothing induced by LES filter leads
to weaker heat transfers. Further away from the injec-
tor, either in the jet core (CV3, CV4) or at the border
(CV5), the droplets' temperature of SLES rises more
quickly than the one of SDNS. This is due to the tur-
bulent mixing that induce, from a LES point of view, a
higher global gas temperature 'seen' by the droplets.
In the case of a monodispersed spray, it is possible
to observe in volume CV3 (jet axis) that few droplets
are still at 300 K while the main peak of the distribu-
tion is around 315K. There is few differences between
SDNS and SLES temperature profiles though it is possi-


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


ble to observed a slight rise of SLES droplets tempera-
ture. Similarly, further down the jet axis in volume CV6,
temperature distributions of SDNS and SLES remain
very close. But it is possible to notice a non-gaussian
shape for the distribution. The lowest temperatures are
prevalent and then a slow decrease to the saturation tem-
perature may be observed. A more dramatic difference
may be observed on thejet border where the temperature
gradients are the strongest.
In volume CV2, we can observe a larger distribution
of the temperature of the SDNS droplets, with a distribu-
tion of temperature roughly between 310 K and 335 K.
Again, as we already observed for volumes CV1, CV3
and CV6, there is a non-symmetrical decrease of the
temperature distribution for the warmer drops, ie, from
335K to saturation level, which is equal to 360K. Still
in volume CV2, we focus now on the SLES spray. A re-
markable result is a complete modification of the shape
of the distribution of the droplet temperature. Indeed,
from a LES point of view a Gaussian distribution is ob-
served in the area where strong temperature gradients
may be found. A similar observation may be done in
volume CV5. The general shapes have been extracted
in figure 10. It means that the subgrid fluctuations of
the carrier phase temperature mays have a strong in-
fluence on the heat transfers between the gaseous and
carrier phases. Indeed, the diminution of the strong
variations of temperature seen by the droplets tends to
smooth the temperature distribution. A next step will be
to determine if this difference between SLES and SDNS
temperature has a strong impact on the spray evapora-
tion and on the resulting vapor mass fraction field. It
will be done in future works. As a first step, we pro-
pose an analytical expression for the SDNS temperature
distribution shape. As far as the size and velocity of
droplets are concerned, the corresponding distributions
have been widely studied Laurent and Massot (2001);
Simonin et al. (2002); Reveillon et al. (21 4), however
there is no information concerning the distribution of
temperature. In the absence of detailed experimental
data on the temperature distribution, it was proposed to
choose a Gaussian function for the temperature distri-
bution but the results presented above shows that it is
not correct from the DNS point of view. After testing
several analytical shapes, it appears that the Nukiyama
Tanasawa law (Nukiyama and Tanasawa (1939)) present
strong similarities with the shape of the temperature dis-
tribution that we encountered in our analysis for SDNS
drops. This shape is sometime utilized for droplet size
distributions. We propose to adapt it to presume the dis-
tribution of temperature. It is written :

P(T) = d(T Tmi,)P exp(-b(T Tmi,)q) (2)

where Tm,n represents the minimum temperature of the







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


0 02 ---------------------------

0016 q=0










a


Figure 5: Typical shapes of Nukiyama-Tanasawa law
with p = 2. a in pm.


droplets. b, p and q are adjustable parameters and d a
normalization constant. The width of the distribution
and location of the peak is controlled by b, p and q. An
illustration of the influence of these parameters is shown
in figure 5.
As shown in figure 10 where non-symmetrical ana-
lytical functions matching the temperature distribution
have been plotted thanks to the Nukiyama Tanasawa law,
it is clear that it is able to reproduce in a large part the
shape of the distribution of the temperature of SDNS
spray.

Conclusion

The preliminary work presented in this paper focuses on
the study of heat transfer between a two-phase sheared
jet and preheated coflow. It is an important topic that
has not yet been really addressed. We have studied the
dispersion of spray by presenting analysis of distribution
of the droplets' size and temperature of two sprays. The
first one undergoes all the turbulent fluctuations of ve-
locity and temperature of the turbulent flow thanks to the
DNS field while the second set of particles are only able
to see the large scale fluctuations through an a-priori fil-
tering. Two main conclusions may be drawn : first, the
temperature distributions are not similar from DNS and
LES point of views. A non symetrical shape is observed
for the distribution of the SDNS sprays while a Gaus-
sian distribution matches the SLES spray. Second, the
Nukiyama-Tanasawa law, usually used for size distribu-
tion, may be adapted to match the droplet temperature
distribution.








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


35

30

25

20

15

10

5

0
0 02 04 06 08 1
CV1


- .nn fl aflll


0 02 04 06
CV3


15




05

0 02 04 06
CV5


08 1


CV4


15




05


0 02 04
CV6


08 1


02 04 06 08 1 0 02 04 06 08
CV7 CV8

Figure 6: Distribution of droplet diameters for mono-disperse injection. Black: DNS, White: LES.


02 04 06 08
CV2








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


CV2


02 04 06 08
CV3


02 04
CV4


CV5


CV6


CV7 CV8

Figure 7: Distribution of droplet diameters for polydisperse injection. Black: DNS, White: LES.


CV1


06 08







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


S60 280 300 320 340 360 380 400
CV1


5-ill .
260 280 300 320 340 360 380 400 420
CV3


260 280 300 320 340 360 380 400 420
CV2
14

12

10

8

6

4



60 280 300 320 340 360 380 400 420
CV4


4

2L

60 280 300 320 340 360 380 400
CV5


CV6


M0 300 320 340 360 380 400 420 260 280 300 320 340 360 380 400 420
CV7 CV8

Figure 8: Distribution of droplet temperature for mono-disperse injection. Black: DNS, White: LES.








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


12,


'60 280 300 320 340 360 380 400
CV1


260 280 300 320 340 360 380 400 420
CV3


2


60 280 300 320 340 360 380 400
CV5


4L




60 280 300 320 340 360 380 400 420
CV2


60 280 300 320 340 360 380 400 420
CV4


CV6


CV7


CV8


Figure 9: Distribution of droplet temperature for polydisperse injection. Black: DNS, White: LES.








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


260 280 300 320 340 360 380 400 420

CV2 cas mono-disperse


260 280 300 320 340 360 380 400 420

CV5 cas mono-disperse


01 __ In nimnim3-., 01 1 minnl iinii ni niM- -----
260 280 300 320 340 360 380 400 420 260 280 300 320 340 360 380 400 420

CV2 cas poly-disperse CV5 cas poly-disperse

Figure 10: Comparison between the distribution of temperature drops and presumed distribution at the edge of the jet.
Black: DNS, White: LES. Red: Nukiyama-Tanasawa, green: Gaussian.











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