Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 11.7.1 - Large Eddy Simulation of the Breakup of a Kerosene Jet in Crossflow
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00294
 Material Information
Title: 11.7.1 - Large Eddy Simulation of the Breakup of a Kerosene Jet in Crossflow Collision, Agglomeration and Breakup
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Spyrou, N.
Choi, D.
Sadiki, A.
Janicka, J.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: breakup
interface capturing
jet in crossflow
 Notes
Abstract: This paper presents numerical simulation results of the breakup of a turbulent liquid jet injected into a turbulent gaseous crossflow. Three calculations are performed in order to separate effects from a variation of the liquid Weber number Weliq and a grid resolution variation. The numerical method for this investigation employs a surface capturing model based on the volume fraction as indicator function but without an explicit reconstruction of the phase interface in the framework of the finite volume method. To ensure a sharp phase interface resolution an additional convective term is introduced into the transport equation for the volume fraction suitable to avoid numerical smearing of the phase interface. Starting from a base case a second calculation on the same grid is performed withWeliq being the only varied parameter. A third calculation resembles the base case but with a refined mesh by a factor of two in terms of total grid cell amount.
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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Bibliographic ID: UF00102023
Volume ID: VID00294
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1171-Spyrou-ICMF2010.pdf

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


Large Eddy Simulation of the Breakup of a Kerosene Jet in Crossflow


N. Spyrou*, D. Choi*, A. Sadiki* and J. Janicka*

Institute for Energy and Powerplant Technology, TU Darmstadt, Petersenstr. 30, 64287 Darmstadt, Germany
spyrou@ekt.tu-darmstadt.de, choi@ekt.tu-darmstadt.de, sadiki@ekt.tu-darmstadt.de and janicka@ekt.tu-darmstadt.de
Keywords: Breakup, Interface Capturing, Jet in Crossflow




Abstract

This paper presents numerical simulation results of the breakup of a turbulent liquid jet injected into a turbulent
gaseous crossflow. Three calculations are performed in order to separate effects from a variation of the liquid
Weber number Weliq and a grid resolution variation. The numerical method for this investigation employs a surface
capturing model based on the volume fraction as indicator function but without an explicit reconstruction of the phase
interface in the framework of the finite volume method. To ensure a sharp phase interface resolution an additional
convective term is introduced into the transport equation for the volume fraction suitable to avoid numerical smearing
of the phase interface. Starting from a base case a second calculation on the same grid is performed with Wei;, being
the only varied parameter. A third calculation resembles the base case but with a refined mesh by a factor of two in
terms of total grid cell amount.


Introduction

Typical applications where a liquid jet is injected into
a gaseous crossflow are gas turbines. They are of im-
portance in e.g. lean premixed prevaporized (LPP) com-
bustion and in afterburners for gas turbines and also in
ramjets. Since combustion quality, i.e. efficiency and
pollutant formation is directly related to fuel atomiza-
tion, strong efforts are being made to control the struc-
ture of the generated fuel spray in terms of achieving the
desired spray angle, spray penetration and droplet size
distribution.
Several experimental studies subjected to liquid jets
in crossflow (LJCF) have been carried out, delivering in-
formation about penetration of the liquid jet, penetration
of the resulting spray and phenomenological breakup
modes depending on dimensionless groups, see [1]-[6].
For nonturbulent liquid jets Wu et al. (1997) observed
that two different breakup modes can be identified being
termed "surface breakup" and "column breakup". Col-
umn breakup is characterized by growing waves gener-
ated on the liquids surface on the windward side which
leads to the formation of bag-like structures that sep-
arate from the liquid column. In the surface breakup
mode fine structures are stripped by shear from the
liquid columns surface. In laminar jets the breakup
modes occurr separately and Wu et al. (1997) generated
a breakup map distinguishing between column and sur-
face breakup mode in dependence of the momentum flux


ratio and the crossflow Weber number. However if the
liquid jet is turbulent the breakup modes occur not in a
separated manner but both mechanisms exist in parallel,
see Lee et al. (2007) and Sallam et al. (2004). Besides
the visualization of breakup mechanisms experimental
investigations also provide several correlations, e.g. for
the near field penetration of the liquid jet, jet trajectory
and Sauter mean diameter of the droplets. The experi-
mental investigations by Becker and Hassa (2002) and
Bellofiore (2006) are two among the few that focused
on the breakup at elevated air pressure. From their ex-
perimental data they provided correlations for the near
field penetration and for the trajectory of the liquid jet.
Yet, aiming at predictive models for LJCF the under-
standing of the primary breakup process is not sufficient
to deliver such models. Several mechanisms that lead
to breakup might occur simultaneous in the close prox-
imity of the jet's surface, a region where the optical ac-
cess is not suited for traditional experimental techniques.
The use of detailed numerical simulations can provide
additional information of the processes at the phase in-
terface of the jet. Experimental correlations are suited
and helpful to verify simulation results and the reliabil-
ity of numerical methods up to a certain point. From
there on the numerics have to break new ground and de-
tailed simulations of the phase interface dynamics are
necessary to advance the understanding of the precur-
sors of primary breakup. Herrmann (2009) and Pai et al.
(2008) carried out detailed simulations of turbulent liq-











uid jets in subsonic crossflows at ambient air pressure.
Both their numerical methods were based on a level set
approach with enhanced resolution of the phase inter-
face resulting in promising results. For the conditions
chosen in their study the numerical predictions by Pai et
al. (2008) showed that the crossflow Weber number has
little impact on the size of the disturbances on the wind-
ward side of the liquid jet and that the smallest liquid
length scales seem to be controlled by the liquid Weber
number. Herrmann (2009) transferred small scale drops
into a Lagrangian point particle description and provided
drop size distributions.

Governing equations and interface capturing
approach

Single field formulation

The investigated flow is mathematically modelled by
the Navier Stokes equations for incompressible fluids in-
cluding the force due to surface tension at the phase in-
terface. The continuity and momentum equations read


V U =0,


OpU
Op + V (pUU)
at


-Vp+V-T+pg+f,, (2)


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


a volumetric force. For constant surface tension a the
CSF model states


f, = aKVY,


where K is the curvature of the interface, expressed by

K -V .) (7)

Turbulence

To derive the Large Eddy Simulation (LES) formu-
lation of the governing equations a filtering procedure
must be applied to equations (1), (2) and (3) which corre-
sponds to volume averaging of the phase weighted prop-
erties. After filtering due to the nonlinearity of the con-
vective term in the momentum equation (2) the unknown
subgrid scale (SGS) stress tensor rTsg arises which has
the form:
sg. = UU UU, (8)
with the filter operation denoted by the overbar. To
close the unknown SGS stress tensor it is approximated
through the eddy viscosity assumption:


sgs ksgs


/Pss [Vu(VU()T
p


with p, U, p and g being the density, velocity, pressure
and gravitational vector, respectively. T represents the
viscous stress tensor which reduces for incompressible
flows to T =p iVU + (VU)T] and f, accounts for
the force due to surface tension at the phase interface.
Since the two phase flow is described by a single-field
representation with one set of equations for both phases
an indicator function is needed to account for the phase
present on a certain location at a certain time. Following
the Volume of Fluid (VOF) approach the indicator func-
tion is defined as the volume fraction 7, whose evolution
in time and space is described by an advection equation:

S+ V (Uy) 0. (3)

Based on the distribution of the liquid volume fraction
the physical properties of the two phase mixture are cal-
culated as weighted averages:

P = Pl + P (1 ') (4)

P- P' + g (1 ) (5)
where the subscripts g and I denote the physical property
related to the gas and liquid phase, respectively. The sur-
face tension force f, can be approximated by the con-
tinuum surface force (CSF) model by Brackbill et al.
(1992), which represents the surface tension effects as


where k,,, and p,s, are the SGS turbulent kinetic en-
ergy and SGS viscosity. I corresponds to the Kronecker
Delta 6ij. To determine ksg, and Pss the one equa-
tion transport model for ksg, by Yoshizawa and Horiuti
(1985) is used:


at + V (kyU) (10)
V [(v + v-98) V-sys] v Sc ,

where e = AC, (k,,)2 is the dissipation of k,,,,
v/gs ACk (k,) )2 with A being the SGS length
scale and S being the filtered rate of strain tensor
S = (VU+ (VU)T). The model constants are
Ck =0.07 and C, = 1.05

This LES formulation corresponds to a single phase
formulation, since the filtering of the equations (1),
(2) and (3) produces additional terms arising from
the surface tension and the transport of the volume
fraction which are neglected in this study. Due to the
grid refinement in the regions near the phase inter-
face it is assumed that the SGS contribution of these
terms is small and can be neglected. In addition the
effects of the neglected terms are oppositional and will
tend to attenuate each other [16], de Villiers et al. (2004).







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


Artificial compression term


Typical VOF methods solve equation (3) either in a
geometrical manner where the interface is reconstructed
or in an interface compression manner, in which case
special discretization techniques like e.g. Ubbink (1997)
or Muzaferija et al. (1998) are utilized. In the present
study a modified approach similar to the one proposed
in Rusche (2002) is used with an advanced model for-
mulation by OpenCFD Ltd. (2007). Reconstruction of
the interphase is not performed and instead of using spe-
cial compressive discretization techniques an additional
convective term is introduced into equation (3):


+ V (U) + V [U, (1 ) 0. (11)

The third term on the lhs is designated artificial com-
pression term containing the compression velocity Ur
which is computed in a way, suitable to avoid smear-
ing of the phase interface. Because of the multiplication
with 7 (1 ) this term acts only in the close proxim-
ity of the phase interface and vanishes in regions away
from it. Introducing the compression term into the ad-
vection equation for the volume fraction is numerically
motivated, hence shifting the challenging task to avoid
smearing of the interface by compressive discretization
techniques to the formulation of the compressive veloc-
ity Ur thus enabling the use of standard differencing
techniques for the volume fraction. The proposed re-
lationship by OpenCFD Ltd. (2007) for the compressive
velocity formulates Ur at the cell faces, based on the
maximum velocity magnitude at the interface region and
its direction:


Ur, n hmin [C max ) (12)


where the subscript f denotes values identified at cell
faces. In equation (12) y, Sf, C_ and nf are the
face volume flux, cell face area vector, compression co-
efficient and face unit normal flux respectively. The face
unit normal flux is defined by:

(nfV= Sf, (13)
(V7)1 +

with 6, being a stabilization factor. The intensity of the
interface compression is controlled by the constant C,
so that the influence of the compression term can be dis-
carded, act in a conservative or enhanced manner by set-
ting the constant to zero, unity or greater than one, re-
spectively. In the present study C, was set to unity.


9d




lid




_______________8d


V+1.56 d


Figure 1: Geometry of the computational domain


Numerical investigation

Test case description

The numerical investigation focuses on the injection
of a kerosene jet into a crossing airflow at elevated air
pressure and the subsequent breakup of the liquid jet.
Figure 1 shows the relevant geometrical information
of the computational domain. The liquid jet is injected
along the z-axis through a plain jet nozzle mounted flush
with the bottom wall of the duct. For a detailed descrip-
tion of the experimental setup the reader is referred to
Becker and Hassa (2002). The liquid jet in crossflow
(LJCF) is parametrized by five independent dimension-
less groups:

Liquid Weber number


Weliq l- U (14)
0r


* Crossflow Weber number

p U, d
Wecf =

* Liquid Reynolds number

Ub,id
Reliq = ,
Vl
* Crossflow Reynolds number

Reqf Ub,gDh
Recn r
V
* Density ratio


Pi
S-
P9


>


z
L*tX







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


Here d stands for the nozzle diameter, Dh is a charac-
teristic length scale of the crossflow (e.g. the hydraulic
diameter of the duct from the experimental investigation
Becker and Hassa (2002)) and the velocities Ub,l and
Ub,g are bulk values along the z-axis and x-axis, respec-
Wei,
tively. In addition the momentum flux ratio q -= W
and the Ohnesorge number Oh can be
V Rliq
expressed by the already mentioned dimensionless
numbers.

Operating conditions and computational mesh

Three calculations (cases A, B and C) were performed
in the present study. The characteristic parameters of the
LJCF are summarized in Table 1 and the information of
the computational grids is summarized in Table 2.
The comparison AB focuses on the effect of the liq-
uid Weber number Weliq on the breakup process. All
other independent dimensionless numbers and the com-
putational grid are the same in both cases A and B. The
altering of Weliq in case B is reached through increas-
ing the liquid bulk velocity Ub,i. To maintain the value
for the liquid Reynolds number Reliq the viscosity of the
liquid vi is adjusted in case B.
Comparison AC focuses on the effect of the grid res-
olution along the z-axis to the breakup process. All
dimensionless groups in cases A and C are identical.
While the computational grid for case A resolved the
phase interface regions downstream of the nozzle with
cells of size (15 x 15 x 30)pm the grid cells in compu-
tation C were of size (15 x 15 x 15)pim.
To save computational costs the mesh provides
the mentioned grid spacing only in a bounding box
surrounding the evolving jet. This is achieved through
local grid refinement in the interesting regions. Figure
2 shows a clipped part of the mesh in order to illustrate
the refined grid. The dimensions of the refined region
are -1d ... 5.5d x -2.8d... 2.8d x 0d... 6.7d.


Table 1: Summary of operating conditions
Variable Case A Case B Case C Units
Weliq 2782.0 4204.0 2782.0
Wecf 695.0 695.0 695.0
Reliq 3000.0 3000.0 3000.0
Ref 1.1e6 1.1e6 1.1e6
/ 66.0 66.0 66.0
q 4.0 6.0 4.0
d 4.5e-4 4.5e-4 4.5e-4 m
a 0.022 0.022 0.022 N/m
Ub,l 13.1 16.1 13.1 m/s
Ub,g 53.1 53.1 53.1 m/s
Pi 795.0 795.0 795.0 kg/m3
pg 12.05 12.05 12.05 kg/m3
vi 1.96e-6 2.41e-6 1.96e-6 r2/s
vi 1.5e-6 1.5e-6 1.5e-6 m2/s


Table 2: Summary of mesh parameters
Parameters case A case B case C
Axmin d/30 d/30 d/30
Aymin d/30 d/30 d/30
Azmin d/15 d/15 d/30
cell count 5.55e6 5.55e6 10.12e6


computational inlet and slip boundary conditions were
assigned to the upper and both lateral patches. To pro-
vide a transient turbulent inlet condition into the duct the
inflow generator by Klein et al. (2003) was used produc-
ing a time series of fluctuations correlated in space and
time. By superposing the mean velocity profile and the
time series of the fluctuations a data base for transient
turbulent inlet conditions was used for the present inves-
tigation. In a similar fashion the inflow conditions for
the nozzle were generated.


Setup details


The employed crossflow duct in the experimental in-
vestigation by Becker and Hassa (2002) had a cross sec-
tion of 25mm by 40mm. To investigate the LJCF numer-
ically only a subregion is modeled. Therefore a num-
ber of precalculations were performed to provide proper
inlet conditions for the air and jet flow. For the air-
flow a Reynolds Averaged Navier Stokes calculation of
the whole experimental duct were performed to obtain
a mean velocity profile providing the correct air mass
flow through the duct. According to the cross section of
the duct for the computational domain the correspond-
ing part of the mean velocity profile was mapped to the


Figure 2: Refined mesh


11 x







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


Figure 3: Temporal evolution of total liquid mass in the
computational domain during the averaging
process


Results and discussion

Any presented results in this study were obtained after
a certain calculation time in order to ensure that a fully
developed state is reached. This is confirmed by Figure
3 where the temporal evolution of the total liquid mass
in the computational domain ranges close to the mean
value.
In Figure 4 the liquid jet trajectory is compared to cor-
relations derived from experimental investigations. For
the comparison correlations are used where the exper-
iments were performed at elevated air pressures. This
was the case for the experimental investigations from
Becker and Hassa (2002) and Bellofiore (2006). Note
that in Figure 4 the images of the liquid jet are not an
instantaneous snapshot but a superposition of multiple
snapshots. The phase interface is depicted as isosurface
of the volume fraction 7 = 0.5. The red and green lines
represent the correlations by Becker and Hassa (2002)
and Bellofiore (2006), respectively. The latter shows
better agreement with the numerical results but it should
be mentioned that the correlation by Bellofiore (2006)
lies inside the range of the standard deviation specified
by Becker and Hassa (2002) for their correlation. The
agreement between simulation and correlation for cases
A and C (q 4) is better than for the case C, where
q 6.
The lateral dispersion of the jet is prescribed by small
droplets which cannot be resolved with the employed
grid. This shall be emphasized by depicting in Figure
5 the lateral dispersion isosurface of 7 = 0.1.
Figure 6 shows for each case A, B and C a time se-
quence from left to right visualizing the development
and amplification of interfacial instabilities on the wind-
ward side of the liquid jet. The arrows highlight initially
small waves climbing up along the liquid surface in the
direction of the jet axis and being amplified by aerody-
namic forces. That process, denoted as column breakup,
results in large bag-like structures that break off and pro-
duce a wide range of droplets not resolvable in their en-
tirety by the computational grid. The presence of the
large scale instabilities in cases A and B is also captured
by the coarse grid. Furthermore, in each case the onset


Figure 4: Liquid jet trajectory based on superposed
snapshots depicted by isosurface of 0.5


of wave amplitude amplification is not located close to
the nozzle exit but rather at a considerable distance to
it. In conjunction with elevated air pressure the effect
of mass shedding close to the nozzle exit by means of
stripping mechanisms on the jets surface increases, thus
producing ligaments and subsequent detached structures
with a wide size distribution that are not resolved by
the employed grids. Further downstream along the jet
axis the observed large scale disturbances develop due
to combined effects by means of loss of mass, flatten-
ing and bending of the liquid column, Bellofiore (2006).
Note that the location of onset of growing wave struc-
tures denoted in the left column in Figure 6 coincides
with noticeable bending of the liquid column.
The instantaneous snapshots do not show a signifi-
cant impact of the liquid Weber number Weiq on the re-


0 5 1 15 20 0
... 1-1


S[-]
time units -]


2C o







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


Figure 5: Lateral dispersion of the jet, case B correla-
tion by Becker and Hassa (2002)


suiting resolvable liquid structures. But as the detached
structures from the liquid column are suspected to have a
wide range of size an ultimate statement about the influ-
ence of Weil, in this study cannot be made until the nu-
merical grid is further refined. As expected the compar-
ison between cases A and C shows that the refined grid
captures finer liquid structures. Nevertheless the coarser
grid captures the behaviour of the liquid column.

Conclusions

The results of the computations have shown that the
present interface capturing approach, coupled with a
LES formalism can be used to investigate LJCF. The jet
trajectory and liquid column behaviour are reproduced
in accordance to experimental data and phenomenologi-
cal descriptions. In a next step further grid refinement is
necessary to isolate effects of characteristic parameters
like e.g. the liquid Weber number.

Acknowledgements

This work is part of the Graduiertenkolleg 1344 at TU-
Darmstadt and financially supported by the DFG.

References

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a Kerosene Jet in Crossflow at Elevated Pressure, Atom-
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[3] Wu P-K., Kirkendall K. A. and Fuller R. P., Breakup
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Figure 6: Side view snapshots at different times (in-
creasing left to right) for cases A, B and C


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


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