Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Effect of Injection Mode of Nozzle on Mixing Characteristics
of Evaporating Spray with Crossflow
Huijuan Sun, Haibin Zhang, Li Liu and Bofeng Bai
Xi'an Jiaotong University, State Key Laboratory of Multiphase Flow in Power Engineering
No.28, Xianning West Road, Xi'an, 710049, China
bfbai@mail.xjtu.edu.cn
Keywords: mixing characteristics, evaporating spray, crossflow, injection mode
Abstract
A numerical investigation on evaporating spray with a turbulent air crossflow was presented to understand the mixing
characteristics of the water vapor and the crossflow. The numerical simulation was conducted upon a horizontal tube. Four
pressure swirl nozzles, which were evenly mounted in the same cross section of the tube, were used to inject spray droplets
into the air crossflow. Twoway coupling between the continuous phase and dispersed phase was considered. Different nozzle
injection modes were investigated in an attempt to discover the desired injection mode that leads to optimum mixing effect and
maximum temperature drop along the tube. A new formulation of degree of mixedness was proposed to assess the mixing
effect of the evaporating spray and the crossflow. The results show that under the condition of axial injection mode, the flow
structure, average temperature distribution and degree of mixedness demonstrate similar variation tendency with the
evaporation of droplets and development of mixing along the crossflow. Counterrotating vortex pairs appear due to the
disturbance of spray droplets and promote the mixing performance to some extent. A small tangential injection angle, 5,
provides optimal mixing effect as a result of large vortex instead of counterrotating vortex pairs in the cross section of the
tube. Moreover, unbiased injection mode results in considerable temperature drop along the tube.
Introduction
Water spray is traditionally applied in the fields of fire
extinguishment, humidifying, cooling, food processing, etc.
In recent years, water spray finds its new promising
application in underwater propulsion system, in particular,
water ramjet system. In the mixing chamber of water ramjet,
the water is injected by the nozzles to the main crossflow
discharged from the combustion chamber. The spray
evaporates in the influence of the crossflow at high
temperature and then the vapor mixes with the crossflow.
On one hand, water spray can assist to decrease the
temperature of the fuel gas from the combustion chamber;
on the other hand, the addition of water spray contributes to
the increase of the working substance of the nozzle at the
end of the water ramjet. A large temperature drop and good
mixing effects play an important role on the thrust of the
water ramjet. Therefore, it is necessary to investigate the
mixing characteristics under the influence of different
factors in order to discover the role and mechanism.
Since the mixing process is dominant in water ramjet, the
present study concentrates on the mixing characteristics of
evaporating spray droplets and crossflow. Generally, the
objective is to obtain a homogeneous mixture of the
injectant and mainstream (Liscinsky et al., 1996). Many
researches have been reported regarding the mixing process
in gas turbine combustor, solid and liquid rocket motor, etc.
Evaluation and enhancement of the performance of the
mixing section for the combustor concept,
Richburn/Quickmix/Leanburn (RQL), has been the
subject of many experimental and numerical studies of
crossflow mixing (Holdeman 1993; Liscinsky et al., 1994;
Holdeman et al., 1997; Everson et al., 1998; Leong et al.,
2000). In the gas turbine combustor, Holdeman (1993)
proposed that the most important design parameters were
jettomainstream momentumflux ratio and orifice
spacingtoduct height ratio. In other researches, the
arrangement method of orifices is usually the hot research
subject because it significantly influences the distribution of
jet flow and mainstream. However, the studies on the
mixing process in water ramjet are much less than in the
above motors. In this type of motor, the water jet is usually
sprayed into droplets by the centrifugal nozzles and then the
droplets are heated into vapour by the hot crossflow. The
factors influencing the temperature drop and the mixing
characteristics include the ratio of mass flow of spray and
crossflow, the initial temperature of the spray and the
crossflow, the spray angle, the initial diameter of the spray
droplets, the velocity difference between the spray droplets
and the crossflow, the number of the nozzle and the nozzle
injection mode, etc.
The heat and mass transfer between the spray and main
stream is the classical research subject in multiphase flow.
Kachhwaha et al. (1997) developed a simple and efficient
numerical model for estimation of heat and mass transfer
between water spray droplets and an air stream in horizontal
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
parallel flow and counter flow configuration. Barata et al.
(2005) evaluated and improved an Eulerian/Lagrangian
approach to account for turbulent dispersion, evaporation
and coupling between both processes in spray systems. It
was extended to the case of an array of evaporating droplets
through a crossflow and the result was found to be strongly
dependent on the evaporation models used. Wang et al.
(2007) simulated the humidifying process involving
twophase flow of air and water droplets in the counterflow
spray saturator for humid air turbine cycle. Moukalled et al.
(2008) tested three numerical techniques based on a full
multiphase approach, a multisizegroup (MUSIG) approach
and a heterogeneous MUSIG (HMUSIG) approach for the
prediction of mixing and evaporation of liquid droplets
injected into a stream of air at all speeds. Different from
above researches, this work try to provide a new perspective
to investigate the spray and crossflow system.
In our recent experiment (Bai et al., 2009), the injection
mode of the nozzles was considered as one important factor
affecting the mixing effect in the turbulent mixing of
nonevaporating spray droplets and crossflow. The present
work will focus on the influence of nozzle injection modes
on the mixing characteristics of evaporating spray and
crossflow. Moreover, a new formulation of degree of
mixedness will be proposed to quantitatively evaluate the
mixing effect. Consequently, the optimum arrangement of
the nozzles will be obtained to provide theoretical basis for
the performance optimization of the water ramjet system.
Nomenclature
BM mass transfer number
BT heat transfer number
CD drag coefficient
c, specific heat (Jkg1 'K'1)
Dg binary diffusion coefficient (m2s1)
D, droplet diameter (m)
e restitution coefficient
F momentum source (N)
g gravitational constant (ms2)
L latent heat (Jkg ')
m mass (kg)
ri rate of evaporation of droplet (kgs')
1mp mass flow rate of droplet (kgs'1)
M mass momentum (kgs'1)
n number of regions in the cross section
Nu Nusselt number
Pr Prandtl number
Q Energy source (Js1)
Re Reynolds number
S source term
Sc Schmidt number
Sh Sherwood number
t time (s)
T temperature (K)
u velocity (ms 1)
normal velocity of droplet after rebound from the
Va" wall (ms')
tangential velocity of droplet after rebound from
vat the wall (ms 1)
normal velocity of droplet before rebound from
vbn the wall (ms 1)
Vbt tangential velocity of droplet before rebound
from the wall (ms 1)
dependent value of region i
average value
Greek letters
0 1, v,H, C, k and
zp velocity relaxation time (s)
p density (kgm3)
p dynamic viscosity (Pas)
A heat conductivity (Wm1 K1)
r degree of mixedness
F diffusion coefficient (kgm 's1)
0, injection angle of droplet from the wall
A difference
a axial injection angle of nozzle ()
# tangential injection angle of nozzle ()
Subscripts
0 initial state
g gas
L water
p droplet
Mathematical Models
Regarding the simulation of gasdroplets twophase flow
in the tube, the crossflow is treated as continuous phase,
transport equations of which are solved using the Eulerian
approach. The spray droplets are treated as dispersed phase,
transport equations of which are solved using the
Lagrangian approach.
Gas phase equations
The gas flow equations consist of the conservation for
mass, momentum, energy and concentration for one
continuous phase. The realizable ks model is applied to
characterize the turbulence effect. All the governing
equations can be unified as
a a a +
(pu )= c (F )+S, +SF (1)
In equation (1), 0 represents the dependent variable, 1, v, H,
C, k and e.
The gas phase equations are solved numerically using a
controlvolume technique embodied in the SIMPLE
algorithm.
Dispersed phase equations
The formation of the liquid film, the breakup process of
sheet and the generation of droplets aren't taken into
account while the hollow cone spray shape and the Sauter
diameter of the droplets are concerned. The pressureswirl
spray model, named as the linearized instability sheet
atomization (LISA) model of Schmidt et al.(1999), is
applied to add droplets into the crossflow. The atomization
process involves breakup, collision, and coalescence of
droplets. The well known TAB breakup model (O'Rourke et
al., 1987) is used, which is suitable for predicting the
secondary breakup regime in the jet process with low We
number. O'Rourke statistical particle method (O'Rourke
1989), for which parcels of droplets are tracked
Paper No
Paper No
simultaneously in threedimensional space and with time, is
used to simulate the collision and coalescence process of
droplets.
The droplet trajectories are calculated in Lagrangian
framework. The forces acting on the droplets generally
include aerodynamic drag, gravitation, added mass, gas
phase pressure gradient, Basset history integral, Saffman
and Magnus lift force. The Basset force acting on the
particles in the turbulent flow can be ignored. The Saffman
and Magnus lift force can also be neglected in the case of
small velocity gradient in the main flow (Liu et al., 1996).
Furthermore, the forces except drag and volume forces are
negligible when the gas/particle density ratio is smaller than
103 (Crowe et al., 1996). Therefore, aerodynamic drag and
gravitation are considered to be nonnegligible. The droplets
are assumed to be spherical. The motion of the droplets is
described by
dup
dt (u up) / rp + g
2 4 ,D2
S 24pLD
S18/CDRep
P Pglug uplD
CD 24 (1+0.15Re0687) (Re<1000)
CD =0.44 (Rep1000)
The turbulence effect is simulated using the stochastic
droplet tracking method, in which the instantaneous velocity
of gas phase is decomposed into a mean and fluctuating
component
u = u + u (6)
where, u is determined through solving gas phase equations
and u'is sampled randomly from a Gaussian probability
distribution of gas phase velocity.
The momentum change of a droplet as it passes through
each control volume is computed as
18CDPg
F Z= (ug up,)rpAt (7)
24pp D
This momentum exchange appears as a momentum sink in
the continuous phase momentum balance.
The rate of vaporization is given by
h = 27cgDgDpSh ln(1 +B,) (8)
1,1
rh= 2I DpNu ln(1+BT) (9)
pg
Sh= 2+0.6Rel/2Sc'/3 (10)
Nu = 2 + 0.6Re/2Pr1/3 (11)
Assuming that Le=l, the heat transfer rate is equal to the
mass transfer rate, so equations (8) and (9) are equivalent.
The droplet's temperature is obtained via the heat balance
of the convective and latent heat transfer
dT 6 /x L mc t
S x (T T)Nu +T (7)
dt Dpc, L cp,g
The mass exchange as a source of mass in the continuity
equation and also a source of species for water vapor of the
continuous phase is computed as
M = p ,,0 (8)
mp,O
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The heat exchange as a enthalpy sink for the continuous
phase enthalpy equation is described as
Q =pcppAT + (L., cpdT)]rhp, (9)
mp,o mp,o f,
As regard to the interaction of droplet and wall, the
rebound model (Bai et al., 1995) is applied. The normal (van)
and tangential (vat) velocity of droplets after rebound are as
calculated as
an = evbn (10)
5vb,
vat = (11)
7
e = 0.993 1.760, +1.560,2 0.490,3 (12)
Simulation Conditions
'Ihe~~~~~~~~~~ sipiidgoer tutr ftemxn hme
The simplified geometry structure of the mixing chamber
(2) and the computational domain are shown in Fig.l. The
simulation is conducted in a horizontal tube with a length of
(3) 500mm and inner diameter of 95mm. Four pressure swirl
nozzles are mounted on the same cross section of the tube
with a 100mm distance from the inlet. The hollow cone
(4) spray is injected by the swirl nozzles into the tube and then
the spray droplets evaporate in the hot crossflow. The
symbols in Fig.1, a and /, denote the axial and tangential
injection angle of the nozzle respectively.
air 100
crossflow ^a
Sweater spray
z x
mixture
^^
r
Fig. 1: Schematic structure and coordinate system.
The work conditions for different cases are shown in
Table 1.
Table 1
Computing conditions
Crossflow
Material
Inlet temperature
Inlet velocity
Pressure
Air
600K
30m/s
101325Pa
Spray
Droplet material Water
Mass flow rate per nozzle 0.02kg/s
Initial Sauter diameter 150160gm
Spray angle 800
Initial temperature 300K
a 600, 800, 900, 1000, 1200
8# 00, 50, 100, 200
* When a 600, 800, 900, 1000 and 1200, 3=00.
# When/ =00, 50, 100 and 200, a=900.
a=900 and P=0 represent the same condition, that is,
unbiased injection mode.
Results and Discussion
Paper No
Validation with the experiment
Since few data in the previous studies can be found
related to the present research, the present numerical
algorithm and computed results are validated by comparing
the simulated results with the experiment results conducted
by the authors. The experiment was carried out in a
rectangular duct with cross section size of 95x95mm. The
crossflow material was air with inlet temperature of 673K
and inlet velocity of 30m/s. One nozzle instead of four
nozzles was used. The spray material was acetone with mass
flow rate of 0.001kg/s, initial temperature of 284K, initial
Sauter diameter of 48gm, and spray angle of 800. Figure 2
shows the temperature drop in half of the cross sections
along the duct. The two sub figures illustrate that the
simulation results agree well with the experiment ones.
Based on the validation, we can further proceed with the
simulation.
40
20
X=200mm X=300mm X=40mm X=500mm
(b)
Fig. 2: Temperature drops in half of cross sections: (a),
experimental results, and (b), simulation results.
Degree ofmixedness
The influences of injection modes of nozzles on mixing
characteristics of evaporating spray with crossflow are
assessed by two main parameters, the degree of mixedness
and the temperature drop. The quantitative index for
mixing, degree of mixedness, is proposed as
Sn min X X + max X, X
= = Y (13)
n,1 XX +max X,X
1l<
In equation (13), X is the parameter of interest, which
can be temperature and mass fraction of one of the species
in continuous flow, et al. The cross section is divided into n
small regions, and X, means the value of region i. X is
the average value. The degree of mixedness is bounded
between 0 and 1. The higher value indicates the more
desirable mixing effect.
In this work, temperature is used to calculate the degree
of mixedness.
Effect of axial injection mode ofnozzles on mixing
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 3, 4, 5, and 6 show the temperature distribution,
flow structure and mixing effect with different axial
injection angles including 600, 800, 900, 1000 and 1200. It
can be observed from Fig.3 that axial injection mode does
not show distinct superiority in bringing about large
temperature drop. Instead, unbiased injection (900) can
cause considerable temperature drop. The degree of
mixedness reflects the uniformity of temperature in the
cross section. It undergoes similar variation tendency
under different axial injection angles. In nearnozzle region
(e.g. x=120mm in Fig.5), though the temperature in the
cross section seems high, the temperature distribution is
relatively even. Therefore, the degree of mixedness
reaches a relatively high value in a short distance.
However, with the evaporation of droplets and the increase
of mixing distance, the degree of mixedness will suffer
some degree of decrease. It is due to the increase of the
temperature difference in the cross section (e.g. x=500mm
in Fig.5). As Fig.4 shows, the degrees of mixedness at the
outlet of the tube under different axial injection angles
approximate to each other. Moreover, the flow structures
under different conditions are similar, too. It is obvious in
Fig.6 that counterrotating vortex pairs (CVPs) appear in
the cross section. The CVP was regarded as the main
reason influencing the mixing effect in the cold state
experiment without considering the evaporation of droplets
(Bai et al., 2009). The CVPs also occur in the mixing with
the evaporation of spray droplets and improve the mixing
of different components to some extent. However, with the
increase of a, the penetration depth of the spray to the
crossflow decreases, leading to weak disturbance. When
a=1200, the CVPs tend to fade compared to other
conditions (see Fig.6 (j)).
600
c =600
580 o U=80
u'=90o
560 ,,vc=100o
540 1 ou=1200
&520
S500
480 
0.1 0.2 0.3 0.4 0.5
x[m]
Fig. 3: Average temperature in the cross sections under
different axial injection angles of the nozzles.
S0.75
Gd
S0.70
0.65
0.60
Fig. 4: Degree of mixedness in the cross sections under
different axial injection angles of the nozzles.
Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
004
004 0, 004 00004 ,
002 50 002 0
6 5 5 t 5
(a)a=60,x.120mm (b) a=60, x500mm (a) a=60, x=120mm (b) a=60, x500mm
S02 002 5 002 0 02 I
0 04 004 0 04 0 04
.I . . . . .\.. L . LI I L' L 'o .. L L I I
0 04 002 0 0 02 004 004 002 0 0 02 004 004 002 0 002 004 004 002 0 0 02 004
z(m) z(m) z(m) z(m)
(a) a=60, x=120mm (b) a=600, x=500mm (a) a=600, x=120mm (b) a=60, x=500mm
004 004 'A2 \ 0/
=542 /
009
004 002 0 002 004 004 0 02 0 002 004 004 002 0 0 2 004 4 2 0 002 004
0 04 0 02 0 0 02 0 04 0 04 0 02 0 0 02 0 04 0 04 0 02 0 0 02 0 04 0 04 0 02 0 '0 02 0 04
z(m) z(m) z(m) z(m)
(c) a=800, x=120mm (d) a=800, x=500mm (c) a=800, x=120mm (d) a=800, x=500mm
004n 004 510 0004 50 04 
00o 51 0a o
002 590002 0002 "
0020
500
0 02 02 5 40 \ 02
0 5 I 0
002 002 5 0 02
0 04 0 04 0 040 0 04 04I
I. I .. I 1 0' 1 1 1. I I L
004 0 02 0 0 02 0 04 0 04 002 0 002 0 04 004 002 0 002 004 004 002 0 0 02 0 04
z(m) z(m) z(m) z(m)
(e) a=900, x=120mm (f) a=900, x=500mm (e) a=900, x120mm (f) a=900, x500mm
004
004 004
0 5904 0 004 538 544 004 0 0
002 00 02 0 = ,
Ec 555 50 0 o o
5 0 55 >som d i 0 \in
~6565 5
0 02 0 02  )002 0 
004 04 540 0 04 0 04
004 002 0n) 002 004 004 002 0 002 004 004 002 0 002 004 004 002 0 002 004
z(i) Z(M) (M) Wm)
S) a=1000, x=120mm (h) a=1000, x=500mm () a=1000, x120mm (h) a=1000, x500mm
004 004 '5 00 04
S002 \
002 002 002
578 1 43
002 U UZ 5 002 0 02
0 04 0 04 0 04 0 04
004 002 0 002 004 004 002 0 002 004 004 002 0 002 004 004 002 0 002 004
z(7) z(m) (i) Z(m)
(i) a=1200, x=120mm (j) a=1200, x=500mm (i) a=1200, x=120mm (j) a=1200, x=500mm
Fig. 5: Temperature distribution in the cross sections under Fig. 6: Velocity vector in the cross sections under different
different axial injection angles of the nozzles, axial injection angles of the nozzles.
Effect of ;,,, i,. ,,,1 injection mode ofnozzles on mixing
Figure 7, 8, 9, and 10 show the temperature distribution,
flow structure and mixing effect under different tangential
injection angles including 50, 100, 200. Actually, the
tangential injection angle of 00 occurs at the same
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
condition as the axial injection angle of 900 does in this
study, that is, they refer to the unbiased injection. Similar
to the axial injection mode, as Fig.7 shows, the unbiased
injection (0) provide substantial temperature drop.
Although the tangential injection angle of 50 and 100 could
not bring about satisfying temperature drop, they provide
good mixing effect (see Fig.8). It can be observed from
Fig.9 (b) that the temperature is slightly different from
region to region in the outlet cross section (x=500mm).The
flow structures in Fig. 10 for the tangential injection angles
of 50 and 100 are different from that for the tangential
injection angles of 00 and 200. Large vortex appears in the
cross section for the former two cases, and as a result the
large vortex is in favour of mixing. It can be deduced that
the slightly tangential injection is beneficial to obtain
optimal mixing.
0.1 0.2 0.3 0.4 0.5
x[m]
Fig. 7: Average temperature in the cross sections under
different tangential injection angles of the nozzles.
0 04
004 002 0 002 004 004 002 0 002 004
z(m) z(m)
(e) P=200, x=120mm (f) =200, x=500mm
Fig. 9: Temperature distribution in the cross sections under
different tangential injection angles of the nozzles.
0 04
r .*x 004
i ' .
0 04 0 02 0 0 02 0 04
z(m)
(a) P=50, x=120mm
0 04
002
002
0o0
Fig. 8: Degree of mixedness in the cross sections under
different tangential injection angles of the nozzles.
(a)/ =50, x=120mm
004 002 0 002 004
z(m)
(b) 8=5, x=500mm
004 002 0 002 004
(c) z(m)x20
(c) f=10,x=120mm
0 0
0 0
0 0:
I i . i
0 04 0 02 0 0 02 004
z(m)
(b) P=50, x=500mm
(d) f=100, x=500mm
4 
'i '
2 '* *; ,
L. I I...T I .. I. I I. I 1' I
004 002 0 002 004 004 002 0 002 004
z(m) z(m)
(e) P=200, x=120mm (f) f=200, x=500mm
Fig. 10: Velocity vector in the cross sections under
different tangential injection angles of the nozzles.
Conclusions
The axial injection angles of nozzles involving 600, 800,
Paper No
O009
Paper No
900, 1000 and 1200, the tangential injection angles of
nozzles involving 50, 100 and 200 and unbiased nozzle
injection were investigated in order to discover favourable
injection modes that optimize mixing effect and maximize
temperature drop as well. The unbiased injection provide
large average temperature drop. However, the slightly
tangential injection brings about optimal mixing effect. The
average temperature and degree of mixedness in the cross
section show similar variation tendency under different axial
injection angles. The counterrotating vortex pairs occur due
to the disturbance of spray droplets and promote the mixing
performance to some extent. Large vortex appears when the
tangential injection angles are 50 and 100, and consequently
the optimal mixing effect is obtained due to the onset of
large vortex.
The crossflow velocity in this paper is the same value
under different nozzle injection modes. Since the relative
velocity between the spray droplets and crossflow greatly
influences the droplets evaporation, we speculate that the
nozzle injection modes will exert different influences on the
mixing performance at different crossflow velocity. It will
be further investigated in the followup research.
Acknowledgements
The present work was financially supported by the
National Nature Science Foundation of China for Creative
Research Groups under the Contract No. 50821604.
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