7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Sensitivity Analysis of Spray Dispersion and Mixing for Varying Fuel Properties
Holger Grosshans, RobertZoltan Szasz and Laszlo Fuchs
Division of Fluid Mechanics, Lund University, Sweden
holger.grosshans @energy.lth.se, robertzoltan.szasz@energy.lth.se and laszlo.fuchs@energy.lth.se
Keywords: Spray, viscosity, surface tension, density, Large Eddy Simulation, Spray, Gas Turbine Burner
Abstract
A swirl stabilized gas turbine burner has been simulated in order to assess the effects of fuel physical properties on
spray dispersion and fuelair mixing.
The properties under consideration include fuel surface tension, fuel viscosity and fuel density. Surface tension is
varied in a range from 0.O1N/m to 0.08N/m, viscosity from 103 k to 10 6 and fuel density in a range from
21 11 to 11 .i'i. Large eddy simulation is used for the gaseous phase and Lagrangian particle tracking for the
liquid phase. Momentum, energy and mass exchange between the two phases are realized by twoway coupling.
Bag and stripping breakup regimes are modeled for secondary droplet breakup, using the ReitzDiwakar and the
Tayloranalogy breakup models, respectively a model for evaporation is included. A Weibull distribution with a
Sauter mean diameter of 60pm is chosen for the droplet diameters at injection. The results show high sensitivity
of the spray structure to variations of surface tension, fuel viscosity and fuel density. These properties stabilize the
droplets, hence lower surface tension, smaller fuel viscosity or higher fuel density lead to faster breakup. For all three
cases the breakup creates smaller droplets and increases the overall surface area which leads to faster evaporation and
mixing. The breakup also increases the relative importance of the aerodynamic forces acting on the smaller droplet
whereas the relative importance of inertia decreases. Thereby the spray is more influenced by the turbulent structures
of the gaseous phase and the droplet dispersion is increased.
Nomenclature
Roman symbols
C drag force coefficient ()
D molecular diffusivity (m2s 1)
Di injector nozzle diameter (m)
Dp droplet diameter (m)
F force (N)
g gravitational constant (ms 2)
h specific enthalpy (m2s 2)
L characteristic length scale (m)
m mass (kg)
p pressure (Nm 2)
R specific gas constant (Jkg 1K 1)
Q heat flux (Js m 2)
T temperature (K)
t time (s)
U characteristic velocity scale (ms 1)
u flow field velocity (ms 1)
v droplet velocity (ms 1)
x spatial coordinate (m)
Z mixture fraction ()
Greek symbols
a heat diffusivity (m2 s 1)
v viscosity (n2s 1)
p density (kgm 3)
a surface tension (Nm 1)
T response time (s 1)
0 phase volume fraction ()
Superscripts
c continuous phase
d droplet
f fuel
9 gas
p parcel
Abbreviations
DNS Direct Numerical Simulation
FDM Finite Difference Method
LES Large Eddy Simulation
PDF Probability Density Function
SGS Sub Grid Scale
SMD Sauter Mean Diameter
WENO Weighted Essentially NonOscillatory
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Nondimensional Numbers
Pr Prandtl number
Re Reynolds number
Sc Schmidt number
St Stokes number
We Weber number
Introduction
Major issues related to utilization of gas turbines for
power production include fuel flexibility and emissions.
These factors are influenced largely by the processes that
are closely related to the injection of liquid fuel and its
mixing with air. Hence the mixing of fuel and air for
varying fuel properties is studied in the following. The
physical parameters that are considered include fuel den
sity, its viscosity and surface tension. The goal is to
model the liquid fuel until it evaporates as well as its
mixing with air. The modeled gas turbine (depicted in
Fig. 1) is a swirl stabilized combustor and a study of the
flow field has been done in Salewski et al. (2007).
The study of the structure of sprays is an active re
search field. It is difficult to measure in experiments,
since the region is optically dense. Details of the
breakup in the dense parts of the spray and the dominat
ing breakup mechanisms are not completely understood.
There are a number of experimental imaging techniques
for the visualization of spray structures and breakups,
e.g. Faeth et al. (1995) or Zhijun et al. (2006). How
ever most of these techniques are limited to the dilute
spray region, due to multiple scattering effects intro
duced in the measurement when imaging the dense spray
region, and to identifying rather large droplets or more
global parameters of the spray. Modern experimental
techniques as SLIPI (see Berrocal et al. (2009)) can re
duce this noise arising from multiple scattered photons
and resolve droplets of a minimum diameter of about
20pm (see Linne et al. (2009)). To receive a higher
resolution numerical simulations need to be performed.
This is done e.g. in Lee et al. (2002), where the macro
scopic structure of the spray, that means spray develop
ment, spray penetration and the Sauter Mean Diameter
of the droplets depending on axial and radial distance of
the nozzle, were studied.
The first aim of the present paper is, to give a more de
tailed view on the three dimensional structure of a fuel
spray. To analyze this, an Eulerian approach has been
chosen to model the gaseous phase and a Lagrangian
approach to model the liquid phase. Monitoring points
have been introduced in the domain at several axial and
radial positions at which the droplet diameter distribu
tion is monitored.
15. 1.
droplet radius
3.e07 3.e05 6.e05
50.
9.e05 0.0001
Figure 1: Snapshot of the droplet distribution, the axial
velocity of the gas and the geometry of the burner
The second objective is to analyze the spray structure
for varying fuel properties. The effect of different fuel
types on spray shape and penetration length has already
been analyzed by simulations in Pogorevc et al. (2007),
where diesel, biodiesel and a blend of both has been
used. The aim of the present paper is to vary only a sin
gle parameter such as fuel surface tension, fuel viscos
ity or fuel densities, while keeping the others constant.
Thereby the impact of individual physical properties on
the spray dispersion can be assessed.
Governing Equations and Numerical Methods
Continuous Phase
The continuous gaseous phase is described in Eulerian
framework by the continuity, momentum, energy and
mixture fraction transport equation for Newtonian fluids
with constant diffusivities. The nondimensional equa
tions are given in eq. (1 4). Low Mach number flow
is assumed, which means that the density is function of
the temperature only. Thereby acoustic effects are ne
glected. The continuous phase volume fraction 0c is as
sumed to be unity.
I
op 9puj
+ ms (1)
at axj
Opui 0 .. ... p 1 82ui
+ a+ 5 + F,,i (2)
at 0xj axi Re x 2 i (
aph apuj h 1 2h .
at 0j RePr ax2 + Qs (3)
apZ 1pujZ 1 02Z
at + x ReSc ax (4)+
Ths, Fi, Qs and Z, are source terms for mass, mo
mentum, energy and mixture fraction, which account for
the coupling from the liquid to the gaseous phase. The
nondimensional numbers in the above equations, which
are the Reynolds number Re, the Schmidt number Sc
and the Prandtl number Pr, are defined in eq. (5 7).
The gas density is not varying due to pressure
changes, but due to temperature changes. Hence, the
system of equations is closed by the equation of state for
incompressible flows
po pRT, (8)
where po is the constant reference pressure. The gov
erning equations are discretized by the FDM. The con
vective terms are approximated by an up to fifthorder
WENO scheme, the diffusive and pressure terms by
forthorder central differences and the time derivatives
by a second order upwind scheme.
The large scale structures in the flow field are sim
ulated by a LargeEddySimulation (LES), where the
computational grid acts as a lowpass filter. From filter
ing the governing equations new terms appear, the resid
ual stresses. The additional (the socalled SubGrid
Scale, SGS) terms of the equations have to be closed
by a turbulence model. The SGS terms can be shown to
be proportional to the square of the filter size. As the
filter size is reduced through grid refinement, the con
tribution of the SGS terms diminishes. When the SGS
terms become small, the LES becomes Direct Numerical
Simulation (DNS). Thus, for fine enough grids one may
approximate the SGS terms by neglecting them. How
ever, the SGS terms have also a function of dissipating
energy that are transferred by the energy cascade. The
dissipation must be provided either by an explicit or an
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
implicit model. By not including explicit dissipation,
the overall dissipative properties of the methods are re
duced. One may also argue that once there is a clear sep
aration of scales between the dissipative and the integral
scales, the exact form of the dissipation is not important
since the energy transfer from large to small scale is (at
least on average) viscosity independent for high enough
Reynolds numbers (Kolmogorov hypothesis). These ar
guments are the physical basis of the socalled 'implicit'
SGS modeling (Pope (2000)), where no explicit SGS
expression is used. It has to be emphasized that one may
rely on such a model only if the resolution is fine enough
to allow a clear separation of scales of the integral and
the dissipative scales. This is reasonable if large parts
of the turbulence energy spectrum are resolved, i.e. the
computational grid is fine enough. In this case the grid
is chosen to be approximately 4 times finer than the size
of Taylor microscale eddies.
As boundary conditions at the inlet, Dirichlet con
dition is applied, i.e. fixed values are given, and at the
outlet zerogradient condition is applied to the velocity
components and scalars. At the walls noslip condition
is applied for the velocity components and zerogradient
condition is applied to the scalars.
Dispersed Phase
The dispersed phase is described by the stochastic par
cel method, the droplet probability distribution function
distribution function is given by eq. (9).
f(, j, r, T, y, y)dY, dv, dr, dT, dy, dl
The droplet distribution function gives the number of
droplets which are present between Y and 7 + dL, of a
speed between v and v + dv, of a radius between r and
r + dr, of a temperature between T and T+ dT and with
distortion parameters between y and y + dy and y and
y + dy. The complete number of droplets are discretized
in parcels of which each represents the corresponding
number of droplets f. Each parcel is tracked individually
in Lagrangian framework.
Only aerodynamic forces are taken into account for
the momentum exchange between gaseous and liquid
phase. The acceleration of a spherical, isolated, rigid
droplet can be expressed as:
d v 3p, Cdl
dt 4PdD,
SI(S it)
For the drag force coefficient the following relations
are used :
24 1
Cd = (1+ /3)
Re 0.424 6
(,1, 0.424
for Rep < 1000 (11)
for Rep > 1000 (12)
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
U
10. 5. 20. 35. 50.
The liquid is already injected as dispersed droplets,
hence no atomization model is used. The droplet diam
eters at injection satisfy a RosinRammler distribution.
The SMD of the droplets at injection is 60/m. The in
jector nozzle has a diameter of D, = 0.0005m, the fol
lowing results are normalized with this value. The sec
ondary breakup is modeled according to Caraeni et al.
(2000): As long as the droplets contain more than 95%
of the initially injected mass, break up is modeled by the
Wave Breakup Model according to Reitz et al. (1986).
If the droplet has less than 95% of the injected mass it is
modeled by the Taylor Analogy Breakup Model accord
ing to O'Rourke et al. (1978).
The evaporation of liquid mass is taken into ac
count by an evaporation model, which assumes single
component spherical droplets with uniform properties as
described in Amsden et al. (1989).
Problem SetUp
The domain has in xdirection a size of 230 Di. In
radial direction it has a size of 44 Di from the cen
treaxis. The injection nozzle is located on the centreaxis
at x 15Di. In order to analyze spray dispersion, in
total 154 monitoring points have been introduced in the
domain, see Fig. 2. At five axial positions (20D, 40D,
60D, 80D and 100D), there is one monitoring point in
the center and up to nine points (depending on domain
size in the relevant plane) in each radial direction. As
it is shown for two example monitoring points in Fig.
3, the average results are axisymmetric to the combustor
centreline, hence in the following only the results for the
monitoring points in positive ydirection from the cen
treaxis are presented, the results for the other three di
rections are identical.
The results in this monitoring points are presented as
Probability Distribution Functions (PDFs). The PDF
gives the relative probability of a droplet occurring at
this point in space to be of a certain radius. If the PDF is
integrated over the droplet radiuses, the resulting area is
per definition 1.
Results
The aim of this work is to study the effect of fuel
dependent properties on spray dispersion and mixing.
Therefore the cases given in Table 1 are simulated and
the results are compared to each other.
x(D)
U
I 10.
6.
I2.
1.
5.
S '
o7 n
z (D)
Figure 2: Average axial velocity of the gas for Case 1,
geometry of the burner and monitoring points. Cut at
z=0 (top) and at x=60D (bottom)
Gaseous Phase
The average axial velocity of the gas for Case 1 and
the geometry of the combustor is shown in Fig. 2. To
the left the inlets of the gas can be seen: Radial channels
that create the swirl of the flow and axial channels close
to the center which support the atomization of the spray.
The gas is accelerated due to the momentum of the air at
the inlets, the injected spray and centrifugal forces and
reaches its peak values when flowing along the walls.
In the first part of the combustor where its diameter in
creases downstream a recirculation zone can be seen and
the gas in the center is accelerated back in the direction
of the inlet. After the recirculation zone the gas is flow
ing towards the outlet on the right, increasing its speed
due to the reduction of the combustor diameter. It can
be observed, that the average flow field is axisymmetric.
The effects of the varying fuel properties on the gaseous
phase will be presented in the following subsections to
gether with the results for the dispersed phase.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
_ = 0.01 N/m, x=40D, y=+/20D, z=+/20D
vf = 1E5 m2/s, x=40D, y=+/20D, z=+/20D
Surface E kkinetic
7WDP 2 D PPdUrel
We pD.., 12
(rf
2 4 6 8
droplet radius (pm)
Figure 3: PDFs of droplet diameter for 4 symmetrical
points in Case 1 and 4 symmetrical points in Case 6
Table 1: Summary fuel properties used in computations.
Case No. Tf Vf pf
1 0.01 2.85 10 6 700
2 0.02 2.85 10 6 700
3 0.04 2.85 10 6 700
4 0.08 2.85 10 6 700
5 0.02 1.00 10 6 700
6 0.02 1.00. 105 700
7 0.02 1.00 104 700
8 0.02 1.00 103 700
9 0.02 2.85 10 6 200
10 0.02 2.85 10 6 400
11 0.02 2.85 10 6 800
12 0.02 2.85 10 6 1600
Variation of Surface Tension
The droplet diameter probability density function
for varying fuel surface tensions is shown for selected
monitoring points in Fig. 4 to 5. It can generally be seen
that the smaller the surface tension is the smaller are the
droplets in the domain. The surface tension of the fuel
is acting against the aerodynamic forces, which deform
the droplet and support the droplet breakup. Taking into
account only aerodynamic forces acting on the droplet
one can assume, that short before breakup occurs
the kinetic energy of the droplet is of the same order
than the surface tension energy. With this assumption
the expression for the Weber number We, which is
defined as the ratio between inertia and surface tension
forces, can be deduced and a value for the stability
limit of the droplet can be estimated (see eq. (13) (15)).
Hence, the droplet gets unstable when reaching a We
ber number of around 12. The higher the surface tension,
the lower the Weber number. This relation is also used
in the numerical breakup models.
The effect of spray dispersion due to turbulent eddies
can be seen e.g. for Case 4 at downstream location x
40D in Fig. 6. The fraction of big droplets is the highest
for radial position y 12D above the centreline and is
getting smaller at the outside of the domain. The peak
value is about 25pm and is decreasing in radial direction
to a peak value of about 4pm at y = 24D. The reason is
the Stokes number dependency of the spray dispersion.
The Stokes number is defined as the ratio between the
particle response time and flow time scale:
t d
If the particle response time is much larger than one,
the particle is hardly disturbed by the gas flow, if it is
much smaller than one it is highly disturbed and follows
the flow. For a spherical droplet the response time scale
is defined as:
pdD2
Td p (17)
pc18V'
Hence, the bigger the droplet diameter, the larger the
Stokes number and the less the droplet will follow the
flow. If the spray would not be disturbed by the gas flow
at all, the droplets would pass at downstream position
x 40D the monitoring point at y 12D. Hence, the
largest droplets still pass this point as they are disturbed
the least from the flow. Smaller droplets will be more
dispersed from the flow, hence the PDFs show less large
droplets and more small droplets for outer monitoring
points.
The same observation can also be made for down
stream position x 60D, where the most large droplets
are at y 20D, and for downstream position x 80D
(see Fig. 5), where the most large droplets are at y
28D.
When comparing the downstream positions with each
other one can see that in downstream direction the PDFs
shift to smaller droplets. This is reasonable and ex
pected, as droplets break up downstream and one large
droplet will form several smaller ones.
x 105
2.5r
f= 001 N/m
f o= 0 02 N/m
_ f= 0 04 N/m
_ o= 0 08 N/m
10 20 30 40 50
droplet radius (pm)
f= 0 01 N/m
f = 0 02 N/m
of= 0 04 N/m
of= 0 08 N/m
5 10 15 20 25
droplet radius (pm)
__ of= 001 N/m
Sf = 0 02 N/m
Of = 0 04 N/m
f = 0 08 N/m
5 10 15 20 25
droplet radius (pm)
__ of= 001 N/m
of= 0 02 N/m
of= 0 04 N/m
of= 0 08 N/m
Figure 4: droplet radius PDF at x=40D, z=centreline,
y=12D (top), y=16D (2nd), y=20D (3rd), y=24D (bot
tom)
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
18x 104 If 001 N/m
16A If= 0 02 N/m
14 = 0 04 N/m
SIf = 0 08 N/m
10 20 30 40 50
droplet radius (pm)
f= 0 01 N/m
f= 0 02 N/m
f= 0 04 N/m
f= 0 08 N/m
10 20 30 40 50
droplet radius (pm)
Of= 0 01 N/m
__ f= 0 02 N/m
__ f= 0 04 N/m
__ f= 0 08 N/m
10 20 30 40 50
droplet radius (pm)
Of= 0 01 N/m
__ f= 0 02 N/m
__ f= 0 04 N/m
__ f= 0 08 N/m
Figure 5: droplet radius PDF at x=80D, z=centreline,
y=20D (top), y=28D (2nd), y=32D (3rd), y=36D (bot
tom)
x 104
8 A
Sf = 0.02 N/m, x=40D, y=12D, z=centreline
Sf = 0.02 N/m, x=40D, y=16D, z=centreline
Sf = 0.02 N/m, x=40D, y=20D, z=centreline
Sf = 0.02 N/m, x=40D, y=24D, z=centreline
10 20 30 40
droplet radius (pm)
Figure 6: PDFs of droplet diameter for Case 4 at differ
ent radial positions
The average mixture fraction of the evaporated fuel
for Cases 1 to 4 is shown in Fig. 7. As discussed above,
lower surface tension leads to a larger amount of small
fuel droplets due to breakup mechanisms, what means
that the overall surface area of the spray is increased.
The higher surface area leads to faster evaporation of the
fuel droplets. Hence, the mixture fraction of evaporated
gas is the higher, the lower the surface tension is.
Variation of Fuel Viscosity
Results for varying fuel viscosities are shown for
downstream position x 40D in Fig. 8. The results are
similar like the results for varying surface tension, as
fuel viscosity also acts as a stabilization mechanism for
the droplet. But compared to surface tension, breakup
is less sensitive to fuel viscosity, as the Weber number
itself is not depending on viscosity. But it acts like a
damping against deformation of the droplet, hence less
bag breakups occur. Therefore fuel viscosity needs to be
varied over a larger interval to see similar effects than
of surface tension variations. The results for viscosity
changes show, as the results for surface tension changes,
the effects of turbulent dispersion depending on the
droplet diameter and the ongoing droplet breakup in
downstream direction.
Variation of Fuel Density
Results for varying fuel densities are shown for down
stream position x 40D in Fig. 9. Increasing fuel
density (and higher inertia and Weber number) implies
higher stability and delayed breakup of droplets. The in
fluence of the fuel density on the Weber number is of the
same order, but acts inversely, to the influence of the sur
face tension. Hence it can be observed that the changes
of the results are of the same order if the fuel density and
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
surface tension are modified by the same factor, respec
tively the inverse factor. The results for density changes
show, as the results for surface tension and viscosity
changes, the effects of turbulent dispersion depending
on the droplet diameter and the ongoing droplet breakup
in downstream direction.
Conclusions
A computational study has been performed to study the
structure of a fuel spray, depending on the fuel properties
surface tension, viscosity and fuel density. The conclu
sions of this study are summarized as followings.
1. The evolution of the fuel spray shows a high sen
sitivity to variations in fuel properties. Lower fuel
surface tension, fuel viscosity and higher fuel den
sity leads to faster breakup and thereby smaller
droplets.
2. Smaller droplets lead to a larger turbulent disper
sion and faster evaporation of the droplets and bet
ter mixing of the evaporated fuel with the ambient
gas.
3. The effect of variations in surface tension and den
sity is shown to be larger than the effects of fuel
viscosity.
Acknowledgments
This work is partially supported by the Center of Com
bustion Science and Technology (CECOST). The com
putational resources are provided by LUNARC comput
ing center at Lund University.
References
Amsden A.A., O'Rourke P.J. and Butler T., "KIVAII:
A Computer Program for Chemically Reactive Flows
with Sprays", Tech. Rep. LA11560MS, Los Alamos
National Laboratory, 1989
Berrocal E., Kristensson E., Sedarsky D. and Linne M.,
ICLASS 2009, 2009
Caraeni D., Bergstr6m C. and Fuchs L., Modeling of
Liquid Fuel Injection, Evaporation and Mixing in a Gas
Turbine Burner Using Large Eddy Simulation, Flow,
Turbulence and Combustion, 65:223244, 2000
Faeth G.M., Hsiang L.P. and Wu PK., Structure and
breakup properties of Sprays, Int. J. Multiphase Flow
Vol. 21, pp. 99127, 1995
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Lee C.S., Park S.W., An experimental and numeri
cal study on fuel atomization characteristics of high
pressure diesel injection sprays, Fuel 81, 2002
Linne M.A., Paciaroni M, Berrocal E., Sedarsky D., Bal
listic imaging of liquid breakup processes, Proc. Com
bust. Inst. (2009), doi:10.1016/j.proci.2008.07.040
O'Rourke P.J., Amsden A.A., The TAB Model for Nu
merical Calculation of Spray Breakup, SAE Technical
Paper 872089, 1978
Pogorevc P., Kegl B. and Skerget L., Diesel and
Biodiesel Fuel Spray Simulations, Energy & Fuels 2008,
2007
Pope S.B., Turbulent Flows, Cambridge University
Press, 2000
Reitz R.D. and Diwakar R., Effect of Drop Breakup on
Fuel Sprays, SAE Technical Paper 860469, 1986
Salewski M., Duwig C., Milosavljevic V. and Fuchs L.,
Large Eddy Simulation of Spray Dispersion and Mixing
in a Swirl Stabilized Gas Turbine Burner, AIAA 2007
924, 45th AIAA Aerospace Sciences Meeting and Ex
hibit, 8 11 January 2007, Reno, Nevada
Zhijun Wu, Zhiyong Zhu, Zhen Huang, An experimental
study on the spray structure of oxygenated fuel using
laserbased visualization and particle image velocimetry,
Fuel 85, 2006
10.
I.
Figure 7: average mixture fraction of evaporated fuel
for Case 1 (top), Case 2 (2nd), Case 3 (3rd), Case 4 (bot
tom)
0.05
0,04
S0.05
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
x 105
vf= 1E3 m2/s
v = 1E4 m2/s
Sf= 1E5 m2/s
vf= 1E6 m2/s
2.5
2
E
71.5
u
1
0.5
0.5
10 20 30 40 50
droplet radius (pm)
V_ f = 1E3 m2/s
__ f = 1E4 m2/s
V_ f = 1E5 m2/s
V_ f = 1E6 m2/s
E 1.5
u
LI
1
0.5
10 20 30 40
droplet radius (pm)
SV
SV
V
V
1E3 m2/s
1E4 m2/s
1E5 m2/s
1E6 m2/s
Spf = 200 kg/m3
__ p = 400 kg/m3
__ p = 800 kg/m3
___ = 1600 kg/m3
5 10 15 20 25
droplet radius (pm)
__ p = 200 kg/m3
__ p = 400 kg/m3
p__ = 800 kg/m3
pf= 1600 kg/m3
5 10 15 20 25
droplet radius (pm)
__ p = 200 kg/m3
__ p = 400 kg/m3
__ p = 800 kg/m3
___ = 1600 kg/m3
1.5
LL
o 1
13
5 10 15 20
droplet radius (pm)
SV
SV
SV
V
1E3 m2/s
1E4 m2/s
1E5 m2/s
1E6 m2/s
5 10 15 20 25
droplet radius (pm)
__ p = 200 kg/m3
__ p = 400 kg/m3
__ p = 800 kg/m3
__p_ = 1600 kg/m3
E 1.5
L.
S1
0.5
Figure 8: droplet radius PDF at x=40D, z=centreline,
y=12D (top), y=16D (2nd), y=20D (3rd), y=24D (bot
tom)
Figure 9: droplet radius PDF at x=40D, z=centreline,
y=centreline (top), y=4D (2nd), y=20D (3rd), y=26D
(bottom)
12x 104
