PERGAMON
Progress in Energy and Combustion Science 27 (2001) 483±521
www.elsevier.com/locate/pecs
Effervescent atomization
S.D. Sovani a, P.E. Sojka a,*, A.H. Lefebvre b
a
Maurice J. Zucrow Laboratories (formerly Thermal Sciences and Propulsion Center), School of Mechanical Engineering, Purdue University,
West Lafayette, IN 47907-1003, USA
b
Cran®eld Institute of Technology, and Purdue University, West Lafayette, IN 47907-1003, USA
Received 5 May 1999; accepted 5 November 2000
Abstract
Effervescent atomization is a method of twin-¯uid atomization that involves bubbling a small amount of gas into the liquid
before it is ejected from the atomizer. The technique of bubbling gas directly into the liquid stream inside the atomizer body is
essentially different from other methods of twin-¯uid atomization (either internal or external mixing) and leads to signi®cant
improvements in performance in terms of smaller drop sizes and/or lower injection pressures. Furthermore, the amount of
atomizing gas required is considerably less than what is employed in all other twin-¯uid atomization techniques.
Effervescent atomization has been used successfully in a number of applications since its inception over ten years ago. It has
been well studied during this period, and the published literature includes experimental and analytical investigations of both
atomizer performance and the fundamental mechanisms involved in the atomization process. The literature also includes
application-oriented studies that report the development of effervescent atomizers for gas turbine combustors, consumer
products, furnaces and boilers, internal combustion (IC) engines, and incinerators. Through these studies a fair appreciation
of the capabilities of the technique has been achieved. Continuing work is aimed at exploring the use of effervescent atomization in new areas, as well as acquiring a better understanding of current applications. More in-depth studies are also in progress
on the various basic mechanisms that contribute to the overall atomization process.
The purpose of this article is threefold. First, to summarize the results obtained from investigations of effervescent atomizer
performance embracing wide variations in atomizer design, liquid properties, and operating conditions. Second, to review
current theories on the basic mechanisms involved in the atomization process and to discuss the scope for future research. Third,
to provide an overview of current applications and to suggest possible areas for future practical applications, including ®re
suppression, paint sprays, agricultural sprays, and fuel injection for liquid-rockets and spark-ignition IC engines. q 2001
Published by Elsevier Science Ltd.
Keywords: Effervescent; Twin-¯uid; Atomization; Spray
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Description of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Studies on fundamentals of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1. Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1. Drop size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.1. In¯uence of injection pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.2. In¯uence of atomizing gas-to-liquid ratio . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.3. In¯uence of liquid type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.4. In¯uence of liquid physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
* Corresponding author. Tel.: 11-765-494-1536; fax: 11-765-494-0530.
E-mail address: sojka@ecn.purdue.edu (P.E. Sojka).
0360-1285/01/$ - see front matter q 2001 Published by Elsevier Science Ltd.
PII: S 0360-128 5(00)00029-0
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3.1.1.5. In¯uence of atomizer internal geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.6. In¯uence of ambient density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.7. In¯uence of atomizing gas molecular weight . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1.8. In¯uence of space and time coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2. Drop velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3. Patternation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4. Spray cone angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5. Spray momentum rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.6. Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Fluid mechanics of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1. Internal ¯ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2. External ¯ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Applications of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1. Gas turbine combustors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. IC engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Furnaces and boilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Incineration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5. Consumer products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Scope for future study and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1. Experimental studies on basic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1. Atomized liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2. Transient spray behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3. Fluid mechanics of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Modeling of the effervescent atomization process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Most airblast and air-assist atomizers are of the externalmixing type in which the bulk liquid is ®rst transformed into
a jet or sheet before being exposed to atomizing gas ¯owing
at high velocity. Where internal mixing is employed, the
impact between the high-velocity atomizing gas and the
liquid takes place within the atomizer body. The effervescent atomizer falls into the category of `internal-mixing'
but, in marked contrast to all other types of twin-¯uid
atomizers, the atomizing gas is injected into the liquid at
very low velocity to form a bubbly two-phase mixture
upstream of the discharge ori®ce. Owing to its relatively
low density, the gas occupies a signi®cant proportion of the
total cross-sectional ¯ow area. This improves atomization by
reducing the characteristic liquid dimensions within the
discharge ori®ce. The atomization process is further enhanced
by the rapid expansion of bubbles at the nozzle exit that
shatters the issuing liquid stream into ligaments and drops.
Since its inception over 10 years ago [1], effervescent
atomization has been a topic of increasing interest and
research, as illustrated in Fig. 1. This is attributed to its
signi®cant advantages over other atomization methods in
certain applications.
The effervescent atomization technique was developed in
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the late 1980s by Lefebvre and co-workers [1±4]. Although
the term `effervescent atomization' was used colloquially
right from the outset, it did not appear in any publication
until Buckner et al. [5,6] in 1990. Prior to that the technique
was described more formally as `aerated liquid atomization'
by Lefebvre and co-workers [1±4].
One incentive to the development of effervescent atomization was the drawbacks associated with ¯ash atomization
and dissolved gas atomization [7±9]. Flash atomization
depends on the rapid evaporation (¯ashing) of a small
portion of the liquid. Dissolved gas atomization relies on a
dissolved gas coming out of solution to form bubbles. As a
result, these techniques apply only to a limited range of
liquids that are either highly volatile or which can hold a
signi®cant quantity of dissolved gas.
To avoid the practical problems associated with ¯ash
atomization and dissolved gas atomization, Lefebvre and
co-workers [1±3] introduced the technique of effervescent
atomization whereby a gas is bubbled into the bulk liquid
through an aerator to form a bubbly two-phase mixture
upstream of the ®nal discharge ori®ce. This method of
atomization is not restricted to volatile liquids or liquids
that can hold a substantial amount of dissolved gas. Neither
is the choice of gas restricted to those that can dissolve
readily into the liquid. Furthermore, the bubble formation
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Nomenclature
Roman symbols
A
Area, m 2
ALR
Same as GLR when atomizing gas is air
d
Diameter, m
D
Drop diameter in Rosin±Rammler function, m
E
Entrainment number, dimensionless
f
Non-dimensional ¯ow behavior index, dimensionless
GLR
Gas-to-liquid ratio: ratio of mass ¯owrate of
atomizing gas through the atomizer to that of
liquid, dimensionless
K
Consistency index, kg/m-s n
L
length, m
m_
Mass ¯ow-rate, kg/s
_
M
Momentum rate, N
p
Pressure, Pa
pG
Injection pressure, Pa
q
Exponent in Rosin±Rammler function
representing drop size distribution width,
dimensionless
Q
Variable in the Rosin±Rammler function
representing the fraction of total volume
contained in drops of diameter less than D,
dimensionless
SMD
Sauter mean diameter, m
process does not involve mass diffusion of dissolved gas to
the nucleation sites, as in dissolved gas atomization, or
energy diffusion necessary for evaporation, as in ¯ash
atomization. These inherently slow processes necessitate
the use of expansion chambers in ¯ashing and dissolved
gas systems, limitations not found in effervescent atomizers.
During the past decade, many detailed experimental
studies have been carried out to determine the performance
and spray characteristics of effervescent atomizers over
wide ranges of operating conditions. The results of these
experiments indicate that effervescent atomizers exhibit
the following advantages over conventional pressure, rotary,
and twin-¯uid atomizers:
² Good atomization can be achieved at injection pressures
that are several times lower than those required by other
types of atomizers [1,3,4,10].
² For any given injection pressure, smaller drop sizes are
obtained than those produced by more conventional
methods of atomization [1,3,4,10].
² Gas ¯ow-rates are much smaller than those employed in
most other forms of twin-¯uid atomization [1,3,4,10].
² Exit ori®ce diameters are larger than those of other
atomizer types having a comparable ¯ow rate. This
alleviates clogging problems and facilitates atomizer
fabrication [2,5,10,11].
SR
v
V
x
X
485
Inter-phase velocity slip ratio, dimensionless
Volume, m 3
Velocity, m/s
Distance, m
Constant in Rosin±Rammler function, m
Greek symbols
a
Void fraction, dimensionless
DpG
Pressure drop across discharge ori®ce, Pa
e
A model coef®cient, dimensionless
g
Deformation rate, s 21
m
Viscosity, kg/m-s
r
Density, kg/m 3
s
Surface tension, kg/s 2
t
Shear stress, Pa
ty
Yield shear stress, Pa
Subscripts
a
Ambient gas
e
Entrained gas
g
Atomizing gas
h
Aerator holes
j
Jet
l
Ligament
L
Liquid
o
Atomizer discharge ori®ce
x
Conditions at atomizer exit plane
² In combustion applications, effervescent atomizerproduced sprays are conducive to lower pollutant
emissions due to the presence of air (atomizing gas) in
the spray core [1].
Fig. 1. Publications on effervescent atomization over last 12 years
(data consolidated from the list of references).
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Fig. 2. A typical effervescent atomizer.
² Mean drop size is relatively insensitive to liquid viscosity. This means that a single atomizer can handle a variety
of liquids without compromising performance [12±17].
² Flow velocities in the discharge ori®ces of effervescent
atomizers are much lower than those encountered in
conventional atomizers because two-phase ¯ows choke
at signi®cantly lower velocities than single-phase ¯ows.
This reduces ori®ce erosion when handling liquids with
solid suspensions [18,19].
² The device is simple, rugged, and reliable. It requires
little or no maintenance and can be operated at low cost
[10].
The main drawback of effervescent atomization, which it
shares with many other forms of twin-¯uid atomization, is
the necessity of having a supply of pressurized gas.
However, since the gas ¯ow-rates needed are small, this
requirement can often be met with relative ease.
2. Description of effervescent atomization
A typical steady-state effervescent atomizer is illustrated
in Fig. 2 [21]. It consists of four main components: liquid
and gas supply ports, a mixing chamber where the gas is
bubbled into the liquid stream, and an exit ori®ce. In the
geometry shown in Fig. 2, liquid is supplied to the atomizer
through a port at the top and ¯ows down inside a perforated
central tube to the exit ori®ce. The gas Ð referred to as
`atomizing gas' Ð is supplied to an annular chamber
surrounding the perforated central tube. The gas supply
pressure is slightly higher than that of the liquid. Being at
Fig. 3. Pressure jump at the nozzle exit for two-phase ¯ows at
relatively low injection pressures.
a higher pressure, the gas ¯ows through the perforations in
the central tube into the liquid stream, and forms bubbles.
The internal cavity of the central tube serves as the mixing
section. The bubbly two-phase mixture formed ¯ows downward and is ejected through the exit ori®ce.
A typical effervescent atomizer is approximately 100 mm
long with a diameter of 50 mm, though individual designs
could measure considerably different. Mixing chamber
diameters have ranged from about 5±25 mm in different
designs with typical exit ori®ce sizes lying between 0.1
and 2.5 mm.
The ef®ciency of effervescent atomizers (in terms of energy
needed for atomization) is found to be substantially higher than
the ef®ciencies of pressure, rotary, and most forms of twin¯uid atomizers. This advantage over pressure and rotary atomizers stems in part from the fact that effervescent atomization is
a twin-¯uid technique. Chawla [18] attributes the better atomization performance of twin-¯uid techniques over single-¯uid
techniques to the substantial difference in the speed of sound
between single and two-phase media, as discussed below. In a
gas±liquid two-phase medium the speed of sound is markedly
less than that in either of the individual phases. As an example,
Chawla [18] notes that the minimum speed of sound in an air/
water mixture at standard temperature and pressure is 20±
30 m/s, as compared to 300 and 1500 m/s in the individual
air and water phases, respectively.
Since a two-phase ¯ow through a nozzle chokes at a
signi®cantly lower velocity than that at which a singlephase ¯ow would choke, a two-phase ¯ow will experience
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
487
Fig. 4. Possible ¯ow regimes in the discharge ori®ce.
a steep pressure jump at the nozzle exit, even at relatively
low ¯ow velocities and low injection pressures, as
illustrated in Fig. 3. Since atomization quality is greatly
enhanced by the sudden pressure drop at the nozzle exit, it
is possible to achieve good atomization with two-phase
¯ows even at low ¯ow rates and low injection pressures.
Furthermore, due to its low sonic velocity, a two-phase
¯ow can remain choked while ¯owing through ori®ces
larger than those required for single-phase ¯ows. As a result,
a two-phase ¯ow can provide good atomization even with
exceptionally large exit ori®ces.
The lower sonic velocity of a two-phase mixture and the
consequent pressure jump at the atomizer exit is an advantage that effervescent atomization shares with other internalmixing twin-¯uid atomization techniques. The speci®c
reason for the better performance of effervescent atomizers
over conventional twin-¯uid atomizers lies in the ¯ow structure immediately downstream of the discharge ori®ce. It is
this ¯ow structure that is the distinguishing feature of
effervescent atomization. It is described brie¯y in the
following paragraphs.
The principle of effervescent atomization has been investigated experimentally by Lefebvre and Sojka and their coworkers. Roesler [22] and Roesler and Lefebvre [3,23]
conducted experiments to visualize both the two-phase
¯ow inside an effervescent atomizer as it approaches the
exit ori®ce and the near-nozzle liquid break-up mechanism.
Sojka et al. [12,24,25] also conducted experiments to visualize the two-phase ¯ow issuing from the atomizer exit
ori®ce. These investigations into the internal two-phasephase ¯ow and the near-nozzle spray structure have
provided useful insights into the principles of effervescent
atomization.
Roesler and Lefebvre [3,23] observed that the bubbly
two-phase mixture formed in the mixing chamber evolves
as it ¯ows towards the nozzle exit and may be in either a
bubbly or slug ¯ow regime inside the discharge ori®ce, as
illustrated in Fig. 4a±c. With bubbly ¯ow, the bubbles
discharged from the ori®ce are immersed in the liquid jet.
On leaving the ori®ce the bubbles experience a sudden
pressure relaxation and expand rapidly, thereby shattering
the liquid into drops, as shown schematically in Fig. 5.
When the atomizer is operating in the slug ¯ow regime,
the rapidly expanding gas slugs similarly break up the
liquid. This is a key feature of effervescent atomization.
The experiments of Sojka et al. [12,14±16,24,25] showed
a similar mechanism of rapidly expanding bubbles shattering the liquid into drops. These workers also investigated the
regime where the liquid forms an annular sheath within the
discharge ori®ce which subsequently breaks up into thin
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Fig. 6. Schematic representation of the annular ¯ow, near-nozzle
structure observed by Sojka and coworkers [6,24].
2. The rapidly expanding gas phase has a shattering effect
on the liquid ¯ow leaving the nozzle exit greatly
enhancing ®ne atomization.
The relative contributions made by these two factors vary with
operating conditions. Generally, an increase in DpG/pa
increases the contribution made by bubble expansion.
Both these factors are characteristic features of effervescent
atomization that distinguish it from other atomization
techniques.
Fig. 5. Schematic of the atomization mechanism observed by
Roesler and Lefebvre [22,23].
ligaments due to the rapidly expanding gas core (see Figs.
4d and 6). Under the aerodynamic in¯uence of the atomizing and ambient gases the ligaments break up forming fragments that stabilize into drops. Since the liquid occupies
only a small portion of the ori®ce cross-section, the diameter
of each ligament, and hence the size of drops formed, is
considerably smaller than the diameter of the ori®ce.
It is emphasized that the supply pressure of the atomizing
gas in an effervescent atomizer is only slightly higher than
that of the liquid and is just enough to overcome the pressure drop across the holes in the aerator. Thus the relative
velocity between the liquid and the gas is usually negligibly
small. Unlike other forms of twin-¯uid atomization, effervescent atomization does not make use of the kinetic
energy of a gas stream to enhance atomization. Instead it
uses the atomizing gas to perform two separate functions:
1. The gas phase forces the liquid to ¯ow through a small
fraction of the discharge ori®ce cross section, thus
reducing the size of the liquid shreds and ligaments
from which the drops are formed.
3. Studies on fundamentals of effervescent atomization
The spray characteristics of main interest are drop size
and velocity distributions, spray cone angle, patternation
(the radial and circumferential distribution of the liquid
throughout the spray), spray momentum rate, and entrained
gas mass ¯ow-rate. In any atomization process these spray
characteristics are dependent on several parameters
including liquid physical properties, atomizer internal
geometry, and operating conditions. The range of factors
that in¯uence the characteristics of an effervescent atomizer-produced spray are presented in Fig. 7. These are the
independent variables in effervescent atomization. The
dependent variables are the spray characteristics of interest
in most applications.
The independent variables are classi®ed into categories as
indicated by the boxes in Fig. 7. The variables that can be
governed directly are listed as operating parameters. They
include injection pressure drop and atomizing gas/liquid
ratio by mass (GLR). Independent variables associated
with the liquid include liquid physical properties and liquid
type Ð Newtonian/non-Newtonian and single/multicomponent. Aspects of the atomizer internal geometry that
in¯uence the spray characteristics are illustrated in Fig. 8.
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Fig. 7. Dependent and independent variables in effervescent atomization.
They are described below:
² Outside±in/inside±out gas injection: there are two means
of injecting atomizing gas into the liquid inside an effervescent atomizer. The design depicted in Fig. 2 employs
`outside±in' gas injection geometry. In this case the
liquid ¯ows inside a perforated tube and the atomizing
gas is injected into it through holes in the tube wall.
Outside±in designs have been used by many workers,
including Roesler et al. [3,22,23], Buckner et al. [6,13],
Panchagnula and Sojka [19], Satapathy et al. [21],
Whitlow et al. [26,27], and Chen et al. [28±30].
The alternative approach is to use `inside±out' gas injection
geometry whereby the gas ¯ows inside the perforated tube
and bubbles outward into the surrounding liquid. Atomizers
employing this concept are shown in Figs. 8 and 9. Inside±
out designs have been investigated by Wang et al. [1,4],
Lund et al. [14,15], Sutherland et al. [16,17], and Bush et
al. [31,32]. The relative merits of the two different methods of gas injection have not yet been examined in detail.
Experience suggests that inside±out designs are superior
for low liquid ¯ow rates, while outside±in concepts
perform better for high liquid ¯ow rates.
The main factors that determine the ¯ow regime inside
the atomizer exit ori®ce and hence the spray characteristics are as follows.
² Size, number, and location of aerator holes: the size and
number of aerator holes can in¯uence bubble size and
concentration, while the location of the aerator holes
relative to the ®nal exit ori®ce in¯uences the evolution
of the bubbly two-phase ¯ow.
Fig. 8. Aspects of atomizer internal geometry.
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Fig. 9. Atomizer design featuring `inside±out' gas injection.
² Mixing chamber size, shape, and location relative to the
®nal exit ori®ce: the geometry of the mixing chamber is
important as it governs the evolution of the internal twophase ¯ow.
² Contraction contour at the ori®ce inlet: the ¯ow undergoes a contraction as it enters the exit ori®ce. The contour
at the ori®ce entrance in¯uences the ¯ow regime transition within the ori®ce.
² Pore size of ligament control insert: a ligament control
insert is a porous plug that can (optionally) be ®xed at the
entrance of the ®nal ori®ce, as illustrated in Fig. 10. It has
been found that pore size can in¯uence spray characteristics [16].
² Length and diameter of exit ori®ce: the diameter of the
exit ori®ce governs the atomizer ¯ow rate, while the
length/diameter ratio has a signi®cant effect on mean
drop size.
² Pro®le of ori®ce exit: the edge of the ori®ce at the exit
plane may be pro®led to alter spray characteristics.
Examples of ori®ce exit pro®les are presented in
Fig. 11.
² Number of exit ori®ces: if the two-phase ¯ow inside
a multi-hole atomizer is not homogeneous, the sprays
produced by individual holes will exhibit different
characteristics.
Other factors that in¯uence spray characteristics include
gas molecular weight and ambient density. In addition
to these independent variables, the spray characteristics
are also dependent on space coordinates and time.
In this section we review studies on the relationships
between dependent and independent variables in effervescent atomization. The link between the independent
parameters and the spray characteristics is the two-phase
¯ow inside and outside the atomizer. Studies investigating
the internal and external two-phase ¯ow provide an understanding of the observed relations between the dependent
and independent variables. They are discussed subsequently. Finally we review modeling work that investigates
the functional relationships between the dependent and
independent variables.
A detailed list of the ranges of dependent and independent
variables covered in this survey is presented in Table 1.
3.1. Experimental studies
This section reviews experimental studies into the functional dependence of spray characteristics on the independent variables (as indicated in Fig. 7). In the following
discussion each individual spray characteristic is considered
separately and its dependence on the relevant independent
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
491
Fig. 10. Atomizer ®tted with a ligament-control insert [16].
parameters is reviewed in the following order:
1. Operating parameters
Injection pressure (or liquid mass ¯ow-rate)
GLR
2. Liquid type
Newtonian/non-Newtonian
Single/multi-component
3. Liquid physical properties
Viscosity
Surface tension
Density
4. Atomizer internal geometry
5. Liquid-to-ambient density ratio
6. Gas molecular weight
7. Space±time coordinates
Axial distance from the atomizer
Radial distance from the spray centerline
Time (transient characteristics)
Fig. 11. Examples of indeterminate-origin exit ori®ces [59].
All results reported here were obtained by spraying
liquids into ambient air. While the ambient air was at
atmospheric temperature in all cases, its pressure was signi®cantly higher than standard atmospheric pressure in
Ref.
no.
Author/s
492
Table 1
Range of parameters
Range of independent parameters
Dependent
parameters
investigated
Liquid type
Atomizing
gas
GLR
Injection
pressure
Air injection
geometry
Exit ori®ce geometry
Liquid to
ambient
density ratio
0.001
Nitrogen
2±22%
34.5±690 kPa
Inside±out
0.8±
, 850:1
1. Drop size
0.001
Air
0.1±5%
173±690 kPa
Outside±in
0.5±
, 850:1
1. Drop size
0.001
Nitrogen
2±23%
34.5±690 kPa
Inside±out
±
Air
4±18%
250±1050 kPa
Outside±in
Consistency
index: 400±
840 cPs n21
0.1±13
Air
8.5±34%
0.88±2.0 MPa
Outside±in
Single ori®ce,
2.4 mm dia.
Single ori®ce,
2.5 mm
Single ori®ce,
2.4 mm
Single ori®ce,
2.5 mm dia.
Single ori®ce,
mentioned
Not
mentioned
0.1±25%
207 kPa
Inside±out and
Outside±in
[3]
Water
[4]
Roesler and
Lefebvre
Wang et al.
Water
[5]
Buckner et al.
Coal±water slurry
[6]
Buckner et al.
Glycerine±water±
polymer mixtures
Single component,
Newtonian
Single component,
Newtonian
Single component,
Newtonian
Two-component,
non-Newtonian
Three-component,
non-Newtonian
[11]
Loebker and
Empie
Water±corn syrup
mixture
Multi-component,
Newtonian
[13]
Buckner and
Sojka
Buckner et al.
[14]
Lund et al.
[15]
Lund and Sojka Hydrocarbon oil
[17]
[19]
Sutherland
et al.
Panchagnula
and Sojka
Glycerine±water
mixture
Glycerine±water
mixture
Glycerine±water
mixture and SNO oil
Water, glycerine,
SNO oil mixtures
Water and other
liquids
Corn syrup
Two-component,
Newtonian
Two-component,
Newtonian
Single and
two-component,
Newtonian
Single component,
Newtonian
Single and twocomponent,
Newtonian
Single components,
Newtonian
Single component,
Newtonian
[20]
Sovani et al.
±
Newtonian
[21]
Satapathy
et al.
Non-combustible
Two-component,
diesel fuel substitute Newtonian
0.4±0.968
Air
5±40%
1.1±2.4 MPa
Outside±in
0.4±0.968
Air
5±40%
1.12±2.35
Outside±in
0.001±0.080
Air
1±7%
239±515 kPa
Inside±out
0.002
Air
Not
mentioned
Not mentioned
Inside±out
0.001±0.080
Air
0.5±4%
290±780 kPa
Inside±out
0.001±0.080
Air
0.5±1.5%
250±800 kPa
Inside±out
0.9
Air
2±10%
Not mentioned
Outisde±in
0.8±
, 850:1
1. Drop size
0.5±
, 850:1
1. Drop size
dia. not
, 1000:1
1. Drop size
Single ori®ce,
7.5 mm dia.
Not mentioned 1. Drop size
Single ori®ce, 0.5±
2.5 mm
Single ori®ce, 0.5±
2.5 mm dia
Single ori®ce, dia. not
mentioned
2 1000:1
2. Near nozzle
spray structure
1. Drop size
, 1000:1
1. Drop size
, 800:1
1. Drop size
Single ori®ce, dia. not
mentioned
, 800:1
1. Drop size
Single ori®ce,
0.38 mm dia.
Single ori®ce, dia. not
mentioned
Single ori®ce, 3.0 and
4.0 mm dia
, 1000:1±
700:1
2. Drop
velocity
1. Drop size
2. Near nozzle
structure
Not mentioned 1. Drop size
, 1000:1
0.02±0.08
Air
±
±
±
±
±
0.001±0.010
Nitrogen
1±30%
11.4±33.1 MPa
Outside±in
Single ori®ce, 0.34 mm 857:1±16:1
dia.
1. Drop size
2. Drop
velocity
3. Spray
momentum
rate
1. Drop size
(model studies)
1. Drop size
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Viscosity range
(kg/ms)
Water
Sutherland
et al.
Ambient
conditions
Liquid type
Lefebvre et al.
[16]
Atomizer geometry
Liquid name
[1]
[12]
Operating parameters
Table 1 (continued)
Ref.
no.
Author/s
Range of independent parameters
Dependent
parameters
investigated
Liquid type
Liquid name
[24]
[25]
[26]
[27]
Roesler and
Water
Lefebvre
Santangelo and Water±corn syrup
mixture and SNO oil
Sojka
Santangelo and Not mentioned
Sojka
Whitlow and
Water
Lefebvre
Whitlow et al.
[28]
Chen et al.
[29]
Chen and
Lefebvre
Water
Viscosity range
(kg/ms)
Atomizing
gas
GLR
Injection
pressure
Air injection
geometry
Exit ori®ce geometry
Liquid to
ambient
density ratio
Single component,
Newtonian
Single and twocomponent,
Newtonian
Not mentioned
0.001
Air
0±0.8%
173±690 kPa
Outside±in
, 850:1
1. Internal ¯ow
0.1±0.82
Nitrogen
1±10%
102±1088 kPa
Outside±in
Single ori®ce, 0.5±
2.5 mm dia.
Single ori®ce, 1.5 mm
dia.
, 1000:1±
700:1
1. Near nozzle
spray structure
Not mentioned
1±10%
Not mentioned
Not mentioned
0±60%
69±689 kPa
Outside±in
0.2±1.2%
34.5±690 kPa
Effervescent
pressure swirl
Single component,
Newtonian
0.001
Not
mentioned
Air
Single component,
Newtonian
0.001
Air
Water
Single component,
Newtonian
Water±com syrup
Single and twomixture and SNO oil component,
Newtonian
Air
1±8%
0.14±1.8 MPa
Outside±in
0.001±0.1
Air
1±35%
0.14±1.8 MPa
Outside±in
Not mentioned 1. Near nozzle
spray structure
, 850:1
1. Patternation
Single ori®ce
, 850:1
Single ori®ce, 1.2±
2.4 mm dia.
Single ori®ce 1.2±
2.0 mm dia.
2. Atomizer
discharge
coef®cient
1. Spray cone
angle
Outside±in
Single ori®ce, dia. not
mentioned
, 1000:1±
700:1
±
Air
1±10%
±
Inside±out
Single ori®ce, 0.38±
0.51 mm dia.
±
0.0004±0.001
Air
1±10%
Not mentioned
Inside±out
0.00275
Nitrogen
1.5±30%
11±33 MPa
Outside±in
0.001
Air
0.1±5%
173±690 kPa
Outside±in
±
Air
2±10%
Not mentioned
Outside±in
Single ori®ce,
0.34 mm dia.
Single ori®ce, 0.18±
0.34 mm dia.
Single ori®ce, 0.5±
2.5 mm dia
Single ori®ce,
1.5 mm dia.
Three-component,
non-Newtonian
Consistency
index: 400±
840 cPs n21
Air
8.5±34%
0.88±2.0 MPa
Outside±in
Single ori®ce, dia. not
mentioned
Single component
Newtonian
0.001
Air
15±85%
930 kPa
Outside±in
Multi-ori®ce, 1 &
2 mm dia.
[32]
Bush and Sojka Water and
hydrocarbon oils
Wade et al.
Viscor (calibrating
¯uid)
Roesler and
Water
Lefebvre
Geckler and
Glycerine±water±
Sojka
polymer mixtures
Single component,
Newtonian
Single component,
Newtonian
Single component,
Newtonian
Three-component,
non-Newtonian
[36]
Buckner and
Sojka
Glycerine±water±
polymer mixtures
[37]
Li et al.
Water
1. A probe for
measurement
of effervescent
spray
momentum
rate
Not mentioned 1. Entrainment
, 700:1
1. Drop size
, 850:1
1. Internal ¯ow
, 1000:1
, 1000:1
1. Near nozzle
spray structure
2. Drop size
1. Drop size
, 850:1
2. Near nozzle
spray structure
1. Patternation
(continued on next page)
493
0.14±1.8 MPa
Bush et al.
1. Spray cone
angle
1. Drop size
1. Liquid mass
¯ow rate
0±12%
Water±corn syrup
Single and twomixture and SNO oil component,
Newtonian
±
±
2. Drop size
1. Drop size
, 850:1±
100:1
, 1000:1±
700:1
Air
[31]
[35]
0.001
Single ori®ce, 1.5 mm
dia.
Single ori®ce, dia. not
mentioned
0.001±0.023
Chen and
Lefebvre
[34]
Ambient
conditions
Liquid type
[30]
[33]
Atomizer geometry
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
[23]
Operating parameters
Table 1 (continued)
Author/s
Range of independent parameters
Dependent
parameters
investigated
Liquid type
Wade et al.
[43]
Dutta et al.
[44]
Lund et al.
[45]
Lee and Sojka
[47]
Sojka and
Geckler
Chin and
Lefebvre
Chin and
Lefebvre
Sankar et al.
[50]
[51]
[52]
[53]
[54]
[55]
[56]
Viscosity range
(kg/ms)
Atomizing
gas
GLR
Injection
pressure
Air injection
geometry
Exit ori®ce geometry
Liquid to
ambient
density ratio
A diesel fuel
substitute
Single component
Newtonian
0.0027
Nitrogen
5±30%
11±33 MPa
Outside±in
Single ori®ce, 0.18±
0.34 mm dia.
, 1000:1
Alberta sweet crude
oil
Alberta sweet crude
oil
Panchagnula
et al.
Sovani et al.
Newtonian
0.005
Methane
5±20%
135±270 kPa
Inside±out
Newtonian
0.005
Helium and
carbon
dioxide
mixture
5±50%
Not mentioned
Inside±out
Glycerine±water±
polymer mixtures
Glycerine±water±
polymer mixtures
±
Three-component,
non-Newtonian
Three-component,
Non-Newtonian
±
Water
Single component,
Newtonian
Single component,
Newtonian
Water
Glycerine±water
mixture and SNO100 & SNO-200 oils
Luong and
Glycerine±water
Sojka
mixture
Sutherland et al. Water and other
liquids
[59]
[64]
Liquid type
Luong and
Sojka
Sovani et al.
Ambient
conditions
Liquid name
Sutherland et al. Water, glycerine,
SNO oil mixtures
[57]
Atomizer geometry
Single and twocomponent,
Newtonian
Single and twocomponent,
Newtonian
Two-component,
Newtonian
Single component,
Newtonian
±
Air
3±12%
337±653 kPa
Inside±out
±
Air
2±10%
Not mentioned
Outside±in
±
±
±
±
±
0.001
Air
0.6±60%
172±848 kPa
Inside±out
0.001
Air
5±35%
138±414 kPa
Inside±out
0.001±0.080
Air
0.75±3.75%
Not mentioned
Inside±out
Single ori®ce, dia.
not mentioned
Single ori®ce,
1.5 mm dia.
±
Single ori®ce,
4.14 mm dia.
Single annular ori®ce,
5 mm dia.
Single ori®ce,
0.38 mm dia.
0.030±0.124
Air
1.5±7%
Not mentioned
Inside±out
Single ori®ce, dia.
not mentioned
0.02
Air
2%
Not mentioned
Inside±out
0.001±0.080
Air
0.5±2.0%
Not mentioned
Inside±out
Single ori®ce, dia.
not mentioned
Single ori®ce, dia.
not mentioned
Non-combustible
Two-component,
Diesel fuel substitute Newtonian
Not mentioned
±
0.00275
Nitrogen
1±12%
12.6±38.0 MPa
Outside±in
±
Air
0.5±1%
Not mentioned
Inside±out
±
0.05
Air
±
±
±
Newtonian
Single ori®ce, dia.
not mentioned
Single ori®ce, dia.
not mentioned
Single hole,
0.34 mm dia.
Single ori®ce, dia.
not mentioned
±
, 700:1
, 460:1±
,5050:1
2. Drop size
1. Drop size
2. Spray cone
angles
1. Combustion
aspects
1. Drop size
2. Drop
velocity
Not mentioned 1. Drop size
Not mentioned 1. Drop size
±
1. Drop size
, 850:1
1. Internal ¯ow
, 850:1
1. Drop size
, 1000:1±
700:1
2. Mean
velocity
1. Drop size
2. Drop
velocity
3. Entrainment
Not mentioned 1. Drop size
Not mentioned 1. Drop size
Not mentioned 1. Entrainment
2. Spray
momentum
rate
322:1±16:1
1. Spray cone
angle
Not mentioned 1. Entrainment
±
1. Drop size
(model studies)
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
[42]
Operating parameters
494
Ref.
no.
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 12. Variation of spray SMD with injection pressure and GLR
[26].
certain experiments as mentioned at appropriate places in
the following discussion.
3.1.1. Drop size
Spray mean drop size and drop size distribution are
the parameters of greatest interest in most applications.
They have been investigated in most of the effervescent
atomization studies reviewed in this article.
3.1.1.1. In¯uence of injection pressure. Mean drop size is
strongly in¯uenced by injection pressure. Among the works
reviewed, Lefebvre et al. [1,4] measured drop sizes at the
lowest reported injection pressure (34.5 kPa) while Satapathy
495
et al. [21] and Wade et al. [33,42] obtained drop size data at
the highest reported injection pressure (33 MPa). Most
studies indicate that spray mean drop size is reduced by
an increase in injection pressure [1±4,21,22,26,28,33±42].
Usually, the effect of a change in injection pressure is more
pronounced at low injection pressures than at high injection
pressures.
The in¯uence of injection pressure on Sauter mean
diameter (SMD) is illustrated in Figs. 12 and 13. The experimental data shown in Fig. 12 were obtained at the relatively
low injection pressures that are of interest for gas turbine
and spray coating applications [26], whereas the high injection pressures used to acquire the data contained in Fig. 13
are typical of those employed in diesel engines [21]. The
drop sizes in Fig. 12 were measured on the spray axis
152 mm downstream of the discharge ori®ce while those
in Fig. 13 were similarly measured on the axis at a distance
of 100 mm downstream of the discharge ori®ce. The bene®cial effect of an increase in injection pressure in promoting
®ner atomization is clearly evident in these ®gures.
An exception to the general rule that higher injection
pressures improve atomization has been observed by Buckner et al. [12,13] in their studies on effervescent atomizerproduced sprays of Newtonian liquids having viscosities up
to 0.968 kg/m-s. For these high-viscosity liquids they found
that SMD was largely independent of injection pressure.
Similar ®ndings were made by Buckner and Sojka
[5,6,36], Geckler and Sojka [35], and Geckler [38] for
highly viscous non-Newtonian liquids.
Several workers have investigated the in¯uence of injection pressure on drop size distributions [1,3,4,26,28]. In all
Fig. 13. Variation of spray SMD with injection pressure and GLR [21].
496
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
cases the Rosin±Rammler function [10] was used to represent the distribution of drop sizes in the spray. It is usually
expressed in the form
q
D
1 2 Q exp 2
1
X
where Q is the fraction of the total volume contained in
drops of diameter less than D, and X and q are constants
that are determined empirically. The exponent q provides a
measure of the spread of drop sizes. Large values of q indicate
narrow drop size distributions and vice versa. For most practical sprays the value of q lies between 1.8 and 3.5.
Lefebvre et al.'s [1,4] initial studies on effervescent atomization indicated that the Rosin±Rammler parameter q
decreased with increasing injection pressure, but in subsequent
experiments by Chen et al. [28] and Whitlow et al. [26] the
value of q remained fairly constant, regardless of changes in
injection pressure. This disparity could be due to differences
in atomizer geometry. The early studies employed the
inside±out method of gas injection, with the gas injected
into the liquid well upstream of the atomizer exit ori®ce,
whereas the later studies employed outside±in gas injection,
with the gas injected much closer to the exit ori®ce.
However, a more likely explanation for the different results
obtained in the two sets of experiments is the different range
of GLRs over which they were conducted. It is now clear
that Lefebvre et al.'s [1,4] initial studies were carried out
with the atomizer operating almost entirely in the slug ¯ow
regime, whereas the later experiments of Chen et al. [28]
and Whitlow et al. [26] were con®ned mainly to the bubbly
¯ow regime, corresponding to a much lower range of GLRs
(by a factor of ®ve).
More detailed information on drop size distributions
for effervescent atomizer-produced sprays, is contained
in Dutta et al. [43], Lund et al. [44], and Lee and Sojka
[45].
3.1.1.2. In¯uence of atomizing gas-to-liquid ratio. The
atomizing gas-to-liquid ratio by mass (GLR) is an
important operating parameter in most applications since
it is desirable to minimize the amount of atomizing gas
supplied while maintaining a small mean drop size. Most
of the studies reviewed in this article contain data
illustrating the variation of spray mean drop size with
changes in GLR. As mentioned earlier, effervescent
atomizers operate at signi®cantly lower GLRs than most
other types of twin-¯uid atomizers. Among the works
reviewed, SMD data have been acquired for the lowest
GLR (0.001) by Roesler and Lefebvre [3,22] and for the
highest GLR (0.85) by Li et al. [37].
All the experimental evidence shows that spray SMD is a
non-linear function of GLR, with mean drop size decreasing
rapidly as GLR is increased from zero to around 0.03 and
thereafter decreasing at a slower rate with further increase
in GLR. A typical plot of SMD versus GLR is presented in
Fig. 12.
Several workers have examined the in¯uence of GLR on
drop size distributions [1,3,4,26,28]. The early experiments
of Lefebvre et al. [1,4] showed that q decreased with an
increase in GLR but, as discussed above, this result is relevant only to the slug ¯ow regime. Of more practical interest
are the results obtained by Roesler and Lefebvre [3],
Whitlow and Lefebvre [26], and Chen et al. [28] for the
bubbly ¯ow regime. These workers found that the distribution parameter q remained fairly constant, irrespective of
changes in GLR.
3.1.1.3. In¯uence of liquid type. Most effervescent atomizerproduced sprays are formed using Newtonian liquids (see
Table 1). Buckner and Sojka [6,36,46] studied the
effervescent atomization of non-Newtonian liquids. They
formulated mixtures of water, glycerine and xanthan gum
polymer to form liquids with non-Newtonian rheological
behavior. The rheological behavior was characterized by a
power law relationship between the shear stress exerted on
the ¯uid and its deformation rate:
t ty 1 K g_ f
2
where t represents the shear stress, t y represents the yield
shear stress, gÇ represents the rate of deformation, K is the
consistency index, and f is a dimensionless ¯ow behavior
index.
Buckner and Sojka [6,36,46] found that spray SMD for a
non-Newtonian liquid is larger than that for a Newtonian
liquid with the same apparent viscosity. They attributed
this phenomenon to the yield stress associated with the
polymeric non-Newtonian liquids they used. They also
reported that SMD does not vary with changes in K or f.
Fig. 14 is typical of the results obtained. When considered
along with other data obtained by Buckner and Sojka
Fig. 14. In¯uence of liquid type on spray SMD [36].
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
[6,36,46], it indicates no consistent change in SMD with K,
regardless of the air/liquid ratio and injection pressure
employed.
The non-Newtonian liquids used in spray applications can
exhibit visco-elastic behavior [38]. The effect of liquid
visco-elasticity on spray characteristics was studied by
Geckler [38], Geckler and Sojka [35,47] and Lee and
Sojka [45]. These researchers formulated mixtures of
water, glycerine and polyethylene oxide (a polymer) to
form liquids with different visco-elastic behavior. They
found that SMD increased as the liquid visco-elasticity
increased, either by increasing the polymer concentration
in the mixture, or by extending the polymer chain length
(i.e. increasing polymer molecular weight).
Lee and Sojka [45] provide plots of drop size distribution
for sprays of visco-elastic liquids. In some cases, they
observed multi-modal drop size distributions (i.e. having
multiple peaks) which they attributed to the simultaneous
occurrence of different modes of primary breakup. Based on
the work of Ferguson et al. [48], Lee and Sojka [45]
surmised that the polymeric liquid they sprayed underwent
phase change in the atomization process leading to two
modes of breakup. The ®rst mode, termed `cohesive fracture', formed large drops while the second mode, termed
`capillary failure', formed small drops.
Buckner and Sojka [5] and Jardine [49] studied the characteristics of effervescent atomizer-produced sprays of
multi-phase liquids. They sprayed mixtures of ground
coal, water, and a polymer and noted that mean drop size
did not change appreciably with changes in the size or quantity of solid particulate in the mixture.
3.1.1.4. In¯uence of liquid physical properties. The studies
reviewed in this article used a variety of liquids spanning a
wide range of physical properties (see Table 1). Among
these studies, mean drop sizes are reported for the lowest
liquid viscosity (0.001 kg/m-s) in several publications, and
497
for the highest viscosity (0.968 kg/m-s) by Buckner and
Sojka [12,13]. Other workers have also examined the
variations in mean drop size with change in liquid
viscosity, including Lund et al. [14], Sutherland et al.
[16,17], and Satapathy et al. [21].
Buckner and Sojka [12,13] found mean drop size to be
independent of liquid viscosity, while Lund et al. [14] and
Sutherland et al. [16,17] observed only a small effect of
viscosity on drop size. Some of the results obtained by
Lund et al. [14] are presented in Fig. 15. They show that a
fourfold increase in viscosity produced only around a 15%
increase in SMD. However, the experiments of Satapathy
et al. [21], conducted at considerably higher injection
pressures (11±33 MPa) than those employed in other studies
(0.2±2.0 MPa), showed mean drop size to be strongly
dependent on liquid viscosity and to increase markedly
with an increase in viscosity.
The in¯uence of liquid surface tension on atomization
quality was studied by Lund et al. [14] and Sutherland et
al. [16,17]. These researchers formulated mixtures of
glycerine and water to produce liquids with different surface
tensions. Spraying a liquid of 0.020 kg/m-s viscosity at an
injection pressure of 377 kPa into atmospheric ambient
pressure, Lund et al. [14] observed that SMD decreased
appreciably when the surface tension was raised from
0.030 to 0.067 kg/s 2, as illustrated in Fig. 16. On the other
hand, Sutherland et al.'s [16,17] measurements for the same
two liquids indicated that SMD remained constant within
the range of experimental uncertainty upon changing the
surface tension from 0.030 to 0.067 kg/s 2. Sutherland et
al.'s [16,17] ®ndings are different from Lund et al.'s [14]
results possibly because the former researchers used an
atomizer ®tted with a ligament-control insert while the
atomizer of the latter workers did not have such an insert.
Note that conventional atomizers invariably produce
smaller drops as the surface tension is reduced [10]. Lund
et al. [14] rationalized their unexpected results with the help
Fig. 15. In¯uence of liquid viscosity on spray SMD [14].
498
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 16. In¯uence of surface tension on spray SMD [14].
of a primary atomization 1 model that is based on the
instability of ligaments in the near-nozzle region of the
spray. This model is discussed later in this article. Although
it neglects secondary atomization, 2 the Lund et al. model
was able to accurately predict the scaling of drop size with
surface tension because the experiments were conducted at
low-mass ¯ow rates where primary atomization tends to be
dominant [10].
Luong and Sojka [54,55] report the effect of liquid physical properties on spray unsteadiness. Using a phase/Doppler
particle analyzer these researchers measured droplet sizes
and velocities and deduced probability distributions of interparticle time (de®ned as the ratio of inter-particle distance to
particle velocity). From a range of experiments conducted
using liquids with different physical properties, these
researchers concluded that spray unsteadiness increases
with a decrease in viscosity and/or an increase in surface
tension.
3.1.1.5. In¯uence of atomizer internal geometry. The
atomizer internal geometry controls the gas±liquid ¯ow
structure inside the atomizer and may strongly in¯uence
atomizer performance. Several different atomizer designs
have been described in the literature. Some of the studies
reviewed in this article speci®cally consider the in¯uence of
atomizer internal geometric parameters on mean drop size
(see Table 1).
The effect of the size and number of aerator holes on
spray mean drop size was studied by Wang et al. [4] for
an atomizer with inside±out gas injection, and by Roesler
1
Primary atomization indicates the ®rst breakup of the continuous liquid jet issuing out of the atomizer into fragments.
2
Secondary atomization refers to the subsequent breakup of
liquid fragments formed in primary atomization into smaller fragments.
and Lefebvre [3,22,23] for an atomizer with outside±in gas
injection. They showed that multi-hole aerators produce
slightly narrower drop size distributions than single-hole
aerators with the same effective hole area. However, no
explanation was offered for this effect.
According to Chin and Lefebvre [50], an important
geometric parameter in¯uencing spray mean drop size is
the ratio of the ®nal discharge ori®ce area to the total area
of the aerator holes (Ao/Ah). Their study showed that at low
GLRs (,0.05), atomizers with low values of Ao/Ah (0.13±
0.28) produced ®ner sprays than those produced by atomizers with high values of Ao/Ah (2.64±3.1). They attributed
this difference to the lower velocity at which the atomizing
gas is injected into the liquid when the total area of gas
injection holes is large (low Ao/Ah). This promotes the
bubbly ¯ow regime inside the atomizer that has been
reported to give the most ef®cient atomization [3,22,23,51].
Wade [40] and Wade et al. [42] studied how the location
of the aerator holes relative to the ®nal discharge ori®ce
affects mean drop size. They observed that mean drop size
decreases when the aerator holes are located farther from the
atomizer discharge ori®ce. They attributed this behavior to
(unspeci®ed) changes in the internal ¯ow structure.
Chin and Lefebvre [50] found that the convergence angle
at the inlet of the exit ori®ce had little effect on spray mean
drop size, provided it was less than 1208.
The effect of ®nal discharge ori®ce diameter on drop
size was examined by several investigators [1,3±5,13,
22,23,26,27,33,37,42], most of whom reported that drop
size is largely independent of the ®nal discharge ori®ce
diameter. However, Wang et al. [4] found that the smallest
injector ori®ce (0.8 mm) provided the ®nest atomization at
the lowest injection pressures, while the largest diameter
ori®ce (2.4 mm) performed slightly better at higher injection
pressures. Similar trends were observed by Wade [40] and
Wade et al. [42] who measured the drop sizes produced by
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
499
Fig. 17. Discharge ori®ce geometries studied by Satapathy et al. [21].
an effervescent atomizer when operating at a very high
injection pressure (33 MPa). They noted that the mean
drop size decreased slightly as the diameter of the ®nal
discharge ori®ce was increased from 0.18 to 0.34 mm. No
arguments were put forward to explain this observation, but
it could be due to the reduction in ori®ce length/diameter
ratio, as discussed below.
In all cases, the differences in drop size exhibited by
nozzles of different injector-ori®ce diameter were always
quite small. The conclusion to be drawn is that atomization
performance is fairly insensitive to discharge ori®ce
diameter.
Chin and Lefebvre [50] found that the length to diameter
ratio (l/d) of the ®nal discharge ori®ce had a signi®cant
effect on atomization performance, with mean drop size
decreasing as the l/d ratio was reduced. They attributed
this to the lower frictional losses associated with a reduction
in ori®ce l/d ratio.
Satapathy [41] and Satapathy et al. [21] compared the
drop sizes produced using the two different discharge-ori®ce
geometries shown in Fig. 17. With the stepped ori®ce,
atomization occurred inside the ori®ce as the ¯ow expanded
suddenly. Drops impinged on the walls of the ori®ce, decelerated, and then coalesced, leading to much higher drop
sizes than those obtained with the plain-ori®ce atomizer.
Whitlow et al. [27] measured drop sizes for a `conicalsheet' effervescent atomizer. This atomizer is designed to
eject the two-phase ¯ow through an annular passage in such
a way as to form a hollow-cone spray. The dependence of
spray mean drop size on injection pressure and GLR was
found to be similar to that of plain-ori®ce effervescent
atomizers. When operating at low injection pressures and
GLRs, SMD increased slightly with an increase in width of
the annular passage, but the in¯uence of this width on SMD
diminished with an increase in either pressure or GLR. At
the highest operating pressure (0.5 MPa), SMD became
independent of gap width at all GLRs.
Multi-ori®ce effervescent atomizers were studied by
Whitlow et al. [27], Li et al. [37] and Dutta et al. [43]
Whitlow et al. concluded that the performance characteristics of multi-hole atomizers are generally the same as those
of single-hole atomizers for the same l/d ratio in the ®nal
discharge ori®ce. Li et al. [37] found that changing the
number of discharge ori®ces had no effect on mean drop
size. Dutta et al. [43] made no performance comparison of
their atomizer with a similar single-ori®ce atomizer.
Sutherland et al. [16] studied the performance of effervescent atomizers ®tted with ligament-control inserts. The
unique feature of this design is the inclusion of a porous plug
located immediately upstream of the nozzle discharge
ori®ce, as illustrated in Fig. 10. Some of the results obtained
are shown in Fig. 18. Generally, it was found that this type
of atomizer produces lower drop sizes than similar atomizers without a ligament control insert. It was also noted that
mean drop size decreases with a decrease in the pore size of
the ligament control insert.
3.1.1.6. In¯uence of ambient density. The effect of ambient
gas density on spray mean drop size has been reported in a
number of works. Chen et al. [28] investigated the effect of
ambient density on the performance of an effervescent
atomizer operating in the medium injection pressure range
(0.14±1.8 MPa). It was found that a continuous increase in
ambient gas density (above normal atmospheric) caused
SMD to rise to a maximum value and then gradually
decline. They attributed this characteristic to the combined
effect of two different atomization processes. The basic
effect of an increase in air density is always to improve
atomization by raising the Weber number. However, at
low ambient gas pressures, the atomization process is
further enhanced by the release of energy contained in the
bubbles. This additional source of energy declines with an
increase in ambient air pressure, becoming zero when the
latter attains the same value as the static pressure in the
discharge ori®ce. At this condition the mean drop size
attains its maximum value. These workers also noted that
ambient density had no signi®cant effect on the width of the
drop size distribution (as represented by the Rosin±
Rammler parameter, q).
Satapathy et al. [21] studied the in¯uence of ambient
density on the performance of a high injection pressure
(11.4±33.1 MPa) effervescent atomizer. At the lowest injection pressures they found that mean drop size increased with
an increase in ambient density, as shown in Fig. 19. At
500
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 18. In¯uence of liquid viscosity and GLR on spray SMD for an atomizer with a ligament control insert [16].
higher injection pressures (22±33 MPa) the spray mean
drop size was not affected by ambient density.
These apparent differences between the results reported
by Chen et al. [28] and Satapathy et al. [21] could be due to
the different manner in which their experiments were
Fig. 19. In¯uence of ambient pressure on spray SMD [21].
conducted. In Chen et al.'s [28] experiments the ratio DpG/
pG was kept constant to ensure that variations in ambient gas
density did not affect the ¯ow velocity through the atomizer.
Satapathy et al. [21] followed a different approach; they kept
the injection pressure constant while varying the ambient
pressure. This meant that any increase in ambient pressure
was accompanied by a reduction in DpG/pa. Thus, in one
case the investigation considered the combined effects of
an increase in ambient pressure with a corresponding
increase in injection pressure differential, while in the
second case the results show the combined effect of an
increase in ambient pressure with a decrease in injection
pressure differential. Both sets of data are equally valid,
but it is important to bear in mind that they represent two
different modes of atomizer operation.
3.1.1.7. In¯uence of atomizing gas molecular weight. The
in¯uence of atomizing gas molecular weight on the
performance of an effervescent atomizer was studied by
Lund et al. [44]. These workers found that an increase in
this parameter led to a small increase in spray mean drop
size, as illustrated in Fig. 20. They attributed this effect to
shrinkage of the gas core and the resultant thickening of the
liquid annulus inside the ®nal discharge ori®ce as gas
molecular weight (and density) increased. Lund et al. [44]
also found that the Rosin±Rammler distribution parameter q
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
501
Fig. 20. In¯uence of atomizing gas molecular weight and GLR on spray SMD [44].
decreased slightly with an increase in atomizing gas
molecular weight.
3.1.1.8. In¯uence of space and time coordinates. The axial
variation of mean drop-size in an effervescent atomizerproduced spray was studied by Whitlow and Lefebvre
[26]. They employed low injection pressures (69±689 kPa)
with outside±in gas injection, and measured mean drop
sizes at different axial locations between 102 and 254 mm
downstream of the atomizer discharge ori®ce. They found
that axial distance had little effect on mean drop size for low
GLRs (,0.008), but for higher GLRs (.0.010) mean drop
size increased by up to 20% with an increase in downstream
distance. This increase in mean drop size was attributed to
the combined effects of evaporation and drop coalescence.
Panchagnula and Sojka [19] experimented with a high
viscosity liquid and obtained similar results, showing only
a minor effect of downstream distance on mean drop size.
Lund and Sojka [15] also studied the variation of mean drop
size with axial distance downstream of the atomizer
discharge ori®ce for a range of injection pressures from
0.24 to 0.52 MPa. They also observed a small increase in
mean drop size with an increase in axial distance, which
they attributed to drop coalescence. Lund and Sojka [15]
developed a kinetic drop coalescence model and its
prediction of a 0.5 mm increase in SMD with 1 cm
increase in axial distance from the atomizer tip was found
to match with the experimental observations.
In the respect of SMD variation with axial distance from
the atomizer, effervescent sprays are partially similar to
sprays formed by airblast atomizers and pressure-atomized
sprays. Zelina et al. [74] report that the SMD of airblast
atomizers decreases initially (by approximately 10%) as
the axial distance from the atomizer is increased but
increases slightly (by roughly 5%) beyond a certain axial
distance (25±35 mm). For a Diesel injector (which is essentially a pressure atomizer), Hardalupas et al. [75] report that
SMD decreases signi®cantly (by about 50%) as the axial
distance is increased up to distances between 200 and
400x/do, beyond which mean drop size is seen to increase
slightly (by approximately 10%). Unlike Zelina et al. [74]
and Hardalupas et al. [75], none of the effervescent atomization researchers have reported drop size in close proximity
to the atomizer and hence effervescent spray characteristics
cannot be compared with those of other atomizers in this
region. However, like airlast and pressure atomized sprays,
effervescent sprays are seen to exhibit a slight increase in
mean drop size with an increase in axial distance from the
atomizer in the region signi®cantly downstream of the
atomizer.
The radial variation of mean drop size in an effervescent
atomizer-produced spray was examined by Panchagnula and
Sojka [19], Lund and Sojka [15] and Sankar et al. [52]. Lund
and Sojka's [15] experiments at low injection pressures
(0.24±0.52 MPa) showed SMD increasing as the point of
measurement was moved radially outward from the spray
axis. This ®nding is consistent with the behavior of conventional pressure-swirl and twin-¯uid atomizers, and is to be
expected since larger drops penetrate further against the
aerodynamic drag forces due to their greater momentum.
Similar observations were made by Sankar et al. [52] and
also by Sutherland et al. [53] who examined the effect of a
ligament-control insert on the radial variation of mean drop
size. The presence of this insert appeared to have little
effect, with mean drop size again increasing as the point
of measurement was moved away from the spray axis.
The only exception to the general rule that SMD increases
with an increase in radial distance are the ®ndings of
Panchagnula and Sojka [19] which showed fairly constant
values of mean drop size at all radial locations within the
spray cone. Fig. 21 is typical of the results obtained in this
investigation. According to Panchagnula and Sojka [19] this
radial uniformity of drop sizes within the spray is due to
high turbulence levels causing rapid and complete mixing of
drops.
Very little consideration appears to have been given to the
502
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 21. In¯uence of radial position within spray on SMD [19].
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
possibility of transient variations of drop size in effervescent
sprays, although such sprays were tested for unsteadiness
by Luong and Sojka [54,55]. They transformed droplet
arrival time data, measured using a PDPA, into inter-particle
time distributions for various drop size bins. Their study
indicated that effervescent sprays are inherently unsteady.
This observation was supported by Bush and Sojka [32] who
studied the entrainment characteristics of effervescent
atomizer-produced sprays. They concluded that the
observed variations in spray entrainment number for
different liquids were due to different levels of spray
unsteadiness.
Sutherland et al. [16,56] conducted spray entrainment
experiments similar to those performed by Bush and Sojka
[32], but they used an atomizer with a porous ligamentcontrol insert ®tted upstream of the exit ori®ce. For a
range of liquids Sutherland et al. [53] found that the addition
of this insert reduced the variation in entrainment number to
lower levels than those observed by Bush and Sojka [32].
They deduced that the presence of the insert damped the
¯uctuations in the two-phase ¯ow entering the exit ori®ce,
thereby reducing spray unsteadiness.
Another method of alleviating spray instabilities is by
controlling the liquid velocity approaching the gas injection
holes. According to Chin and Lefebvre [50], a liquid velocity of around 5 m/s represents a satisfactory compromise
503
between the con¯icting requirements of good stability and
low pressure loss.
3.1.2. Drop velocity
Knowledge of spray mean drop velocity and drop velocity
distribution is important in several applications. For example, drop velocity in¯uences ®nish quality in paint sprays
and transfer ef®ciency in consumer product and agricultural
sprays.
The effect of injection pressure on drop velocity was
examined by Panchagnula and Sojka [19] and Sankar et
al. [52]. As expected, they observed that drop velocities
increase with increasing injection pressure. These workers
also investigated the effect of gas/liquid ratio on drop velocity. They found that drop velocity increased steadily with
an increase in GLR and concluded that the larger mass of
atomizing gas exerted greater aerodynamic drag force on the
drops, causing them to move faster.
Lund et al. [44] studied the effect of atomizing gas molecular weight on drop velocity. They reported that numberaveraged drop velocity decreases with an increase in gas
molecular weight. For any given GLR, as the gas molecular
weight (and hence its density) is increased, the liquid phase
occupies a larger portion of the cross-sectional area and thus
discharges at a lower velocity.
Panchagnula and Sojka [19] studied the radial and axial
Fig. 22. In¯uence of radial position within spray on normalized drop velocity [19].
504
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
variation of drop velocity in the spray produced by an effervescent atomizer featuring outside±in gas injection. Fig. 22
shows some of their results on the effect of radial distance on
normalized mean velocity (normalized by the centerline
velocity). The measurements clearly indicate that drop velocity is a maximum at the spray centerline and falls off
rapidly with increase in radial distance from the centerline.
Similar studies were conducted by Lund and Sojka [15] for
an atomizer featuring inside±out gas injection, and by
Sutherland et al. [53] for an atomizer ®tted with a ligament-control insert. All these studies show that drop velocity decreases with increasing axial distance downstream
of the atomizer and with increasing radial distance away
from the spray axis. Similar characteristics have been
observed in the sprays produced by pressure and twin¯uid atomizers.
No information is available in the literature on the effects
of liquid type, liquid physical properties, atomizer internal
geometry, and ambient gas density on drop velocities in
effervescent sprays.
importance in several areas. In combustion applications,
local heat release rate and species concentration depends
on the radial distribution of fuel. As mentioned above, for
paint and coating sprays the radial liquid distribution determines both transfer ef®ciency and ®nish quality.
Whitlow and Lefebvre [26] studied the radial liquid
distribution in effervescent sprays for a single injection
pressure and two values of GLR. The results indicate that
the liquid mass ¯ux initially increases with increasing radial
distance from the spray axis, reaching a maximum about
half way between the spray axis and the outer edge of the
spray, after which it decreases with any further increase in
radial distance.
There appears to be little or no available information
on the effects of injection pressure, liquid type and physical properties, atomizer internal geometry, ambient gas
density, atomizing gas molecular weight, or axial
distance downstream of the atomizer on the radial distribution of liquid mass in an effervescent atomizer-produced
spray.
3.1.3. Patternation
The radial distribution of liquid mass within a spray is of
3.1.4. Spray cone angle
The spray cone angles produced by conventional
Fig. 23. Rapidly expanding spray cone downstream of atomizer exit.
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
505
Fig. 24. Variation of spray cone half-angle with injection pressure and GLR [57].
single-ori®ce effervescent atomizers were investigated by
Chen and Lefebvre [30], Wade et al. [42] and Sovani et
al. [57]. Chen and Lefebvre conducted their experiments
at intermediate injection pressures (0.14±1.8 MPa) while
Wade et al. and Sovani et al. con®ned their experiments to
high-injection pressures (11±38 MPa). The results obtained
by all these workers show that spray cone angle increases
monotonically with an increase in injection pressure.
Chen and Lefebvre noted that the sprays produced in
effervescent atomization have wider cone angles (by a factor
of around 2) than the sprays produced by plain-ori®ce
pressure atomizers. They attribute this wider spray angle
to the rapid expansion of the atomizing gas bubbles downstream of the atomizer exit ori®ces. A photograph illustrating this rapid spray expansion is presented in Fig. 23.
Wade et al. and Sovani et al. observed that the spray cone
angle widened with an increase in GLR. They postulated
that this increase in cone angle is due to the greater energy
available for expansion of the atomizing gas core as it exits
the atomizer. A typical plot representing the variation of
cone half-angle with GLR and injection pressure is
presented in Fig. 24. The cone half-angle values shown in
this ®gure are typical of those obtained with single-ori®ce
atomizers when operating at high injection pressures (20±
30 MPa).
Chen and Lefebvre [30] observed a similar increase in
spray cone angle with an increase in GLR. However, after
attaining a maximum value the cone angle then declined
slightly with a further increase in GLR. According to
Chen and Lefebvre, this reduction in cone angle beyond
its peak value is due to the reduction in bubble energy
which occurs when continual increase in GLR causes the
internal ¯ow structure to change gradually from the bubbly
to the annular ¯ow regime.
Chen and Lefebvre [30] also examined the effects of
liquid viscosity and surface tension on spray cone angle.
They found that reducing liquid viscosity and/or surface
tension increased the spray cone angle, as illustrated in
Figs. 25 and 26, respectively.
The effect of ambient gas density on spray cone angle was
investigated by Chen and Lefebvre [30] and Sovani et al.
[57]. At low GLRs, where the atomizer operated in the
bubbly ¯ow regime, Chen and Lefebvre found that an
increase in ambient density caused the cone angle to
contract. At higher GLRs, with the atomizer operating in
the annular ¯ow regime, ambient density appeared to have
little effect on cone angle.
In contrast to these ®ndings, Sovani et al. [57] observed
that spray cone angle widened with an increase in ambient
gas density. For a proper interpretation of these results it is
necessary to bear in mind that Sovani et al.'s experiments
were carried out at extremely high injection pressures
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S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 25. In¯uence of liquid viscosity on spray angle [30].
Fig. 26. In¯uence of surface tension on spray angle [30].
(12.6±38.0 MPa), to enhance their relevance to diesel fuel
injection, whereas Chen and Lefebvre's experiments were
conducted at much lower injection pressure (0.24±
0.60 MPa), which is the range of interest for paint sprays
and other spray coatings. Moreover, unlike Chen and
Lefebvre, and Sovani et al. held the injection pressure at a
®xed value in their experiments while varying the ambient
pressure. Thus, effectively, they reduced the injection to
ambient pressure ratio as they increased the ambient
pressure. This is another possible cause for the difference between Chen and Lefebvre's and Sovani et al.'s
observations.
The experiments of Chen and Lefebvre [30] and Sovani et
al. [57] show that the total included cone angle of sprays
produced by plain-ori®ce effervescent atomizers is always
less than 238. This maximum angle is perfectly satisfactory
for most applications, but there are some exceptions, one
notable example being the fuel injectors employed in gas
turbine engines which usually require spray cone angles of
around 908. Whitlow et al. [27] addressed this problem by
testing two different types of effervescent atomizer, both of
which were designed to eject the two-phase ¯ow in a manner
which yielded a wide spray cone angle. One atomizer was a
plain-ori®ce design that featured four equispaced exit holes
drilled at an angle of 408 from the central axis of the atomizer. The other atomizer, called the `conical-sheet' atomizer,
ejected the two-phase ¯ow through an annular passage in
such a way as to form a hollow-cone spray. Both atomizers
performed very satisfactorily, and exhibited the same characteristics as plain-ori®ce airblast atomizers in regard to the
effects of GLR and injection pressure on mean drop size and
drop-size distribution. Of special interest is that the conicalsheet atomizer was entirely free of the ¯ow and spray
instabilities that are often encountered with plain-ori®ce
effervescent atomizers when operating at exceptionally
high values of GLR. This absence of any form of instability
suggests that the annular ¯ow passage of a conical-sheet
atomizer promotes a ¯ow structure that is inherently
more stable than the cylindrical passage of a plain-ori®ce
atomizer. This is one of the reasons why Colantonio [58]
elected to use the conical-sheet atomizer in his researches on
low-emissions combustion.
3.1.5. Spray momentum rate
Spray momentum rates are of interest in many applications because they in¯uence the entrainment characteristics
and penetration distance of the spray. These properties are
especially important in internal combustion (IC) engines
because they determine the effective usage of air available
for combustion.
Momentum rates of effervescent atomizer-produced
sprays have been measured by Bush et al. [31], Sutherland et
al. [53,56], Panchagnula and Sojka [19], and Satapathy et al.
[21]. All these investigators used an instrument developed
by Bush et al. [31] for measuring the momentum rate of twophase free ¯ows.
Bush et al. [31] made momentum rate measurements at a
low injection pressure (0.515 MPa), while Panchagnula and
Sojka's experiments were conducted at an intermediate
level of injection pressure (3.8 MPa). Satapathy et al.'s
experiments were carried out at the highest reported injection pressures (11±31 MPa). Sutherland et al.'s measurements were made on a ligament-controlled effervescent
atomizer at the same injection pressure used by Bush et al.
(0.515 MPa).
All these workers studied the variation of spray momentum rate with injection pressure and GLR. As expected, their
observations showed that spray momentum rate increased
almost linearly with an increase in injection pressure and/or
liquid mass ¯ow rate. They also found that spray momentum
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
507
Fig. 27. In¯uence of liquid ¯ow rate and GLR on spray momentum ¯ux [31].
rate increased linearly with an increase in GLR, which they
attributed to the higher discharge velocity of the gas phase
produced by an increase in GLR. A typical plot of spray
momentum rate versus GLR is presented in Fig. 27.
Satapathy et al. found that spray momentum rate became
independent of GLR within the limits of experimental
uncertainty at high injection pressures. This observation
suggests that in a high pressure atomizer the increase in
momentum rate due to higher gas velocity is offset by the
decrease in momentum rate resulting from the reduction in
liquid ¯ow rate.
The in¯uence of liquid physical properties on spray
momentum rate has been examined by Bush et al. [31]
and Sutherland et al. [56]. Bush et al.'s results showed
that spray momentum rate increases with increasing liquid
viscosity. This ®nding was unexpected since an increase in
viscosity should increase the dissipative losses inside the
atomizer and thereby reduce the momentum rate. According
to Bush et al. their result might be due to compressible
phenomena and inter-phase shear in the ¯ow inside the
atomizer.
Bush et al. [31] and Sutherland et al. [53] found that spray
momentum rate decreased slightly with an increase in liquid
density. This was attributed to the decrease in liquid velocity
that must occur if the density is increased and the liquid
mass ¯ow rate is held constant.
Sutherland et al. [56] compared the momentum rate of a
spray produced using a ligament-controlled effervescent
atomizer with the data reported by Bush et al. [31] for an
atomizer having no ligament-control insert. The spray
momentum rate for the atomizer ®tted with an insert was
found to be lower, and this was attributed to the loss of
momentum suffered by the two-phase mixture as it ¯owed
through the insert.
3.1.6. Entrainment
Entrainment is the process whereby ambient gas is drawn
into the spray envelope as it expands downstream of the
atomizer discharge ori®ce. It has important consequences
in many spray applications. In combustion systems, entrainment affects the local equivalence ratio and hence the local
temperature, heat-release rate, and species concentration.
Entrainment also strongly in¯uences transfer ef®ciency
and ®nish quality in paint and coating sprays, and is clearly
an important consideration in spray drying applications.
The entrainment of ambient gas into effervescent sprays
has been studied by Bush [77], Sutherland et al. [53,56] and
Panchagnula et al. [59]. Bush and Sojka used an atomizer
operating at an injection pressure of 1.1 MPa, while
Sutherland et al. used an atomizer ®tted with a ligamentcontrol insert operating at the same injection pressure.
Panchagnula et al. used the same atomizer and the same
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S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 28. Schematic of global entrainment measurement method [31].
injection pressure as Sutherland et al. However, they
changed the external geometry of the discharge ori®ce and
studied its effect on entrainment.
All researchers measured global entrainment rates using a
measuring device developed by Bush and Sojka [32]. As
shown in Fig. 28 the apparatus consists of a cylindrical
chamber that surrounds the spray. The chamber has a circular opening at its lower end whose diameter is maintained
almost exactly equal to the diameter of the spray at that axial
location. This arrangement enables the spray to pass unhindered from the chamber to the atmosphere, but does not
allow air to escape from the chamber to the atmosphere
past the spray envelope. Air continuously ¯owing to the
atmosphere from inside the spray cone is the net amount
of air entrained by the spray inside the chamber. To compensate for the air entrained by the spray and carried out of the
chamber through the spray cone, a continuous air supply is
provided to the chamber through its porous side wall. The
air ¯ow is accurately regulated such that air supplied to
the chamber just equals the amount of air entrained by the
spray. This equality is ensured by a micro-manometer that
measures the difference between the chamber pressure and
the atmospheric pressure. The ¯ow rate of air supplied to the
chamber is measured using a rotameter.
The ability of a spray to entrain gas is represented by the
parameter `normalized entrainment', which is the ratio of
the entrained gas mass ¯ow rate to the mass ¯ow rate
of the liquid discharged through the atomizer, me/mL. Bush
and Sojka [32] observed that the normalized entrainment at
any given axial distance downstream of the atomizer was
directly proportional to the liquid mass ¯ow-rate. They also
found that the normalized entrainment at any given axial
distance downstream of the atomizer ori®ce increased
almost linearly with an increase in GLR. This was attributed
to the corresponding increases in atomizing gas and liquid
velocities at the exit plane of the discharge ori®ce. Similar
observations were reported by Sutherland et al. [53].
Bush and Sojka [32] and Sutherland et al. [53] studied the
effects of liquid viscosity and surface tension on entrainment. Both groups noted that entrainment is increased by
an increase in either of these properties. Bush and Sojka [32]
hypothesized that variations in viscosity and surface tension
affect entrainment by changing the near-nozzle structure of
the spray, but no detailed description of the mechanism
involved was provided. Sutherland et al. [53,56] studied
the entrainment characteristics of sprays produced by an
atomizer ®tted with a ligament-control insert. This modi®cation appeared to have little effect on entrainment characteristics although the rates of entrainment were lower. This
was attributed to the loss of momentum suffered by the twophase mixture as it ¯owed through the porous insert.
Panchagnula et al. [59] examined the effect of changes in
atomizer exit geometry on the entrainment rates of sprays
produced by ligament-controlled effervescent atomizers.
They found that entrainment rates for a pro®led exit ori®ce
can be appreciably different (by up to 50%) than for a plainori®ce exit. They also reported that entrainment rates were
higher for the double-point crown than for the single-point
crown pro®le (see Fig. 11).
The dependence of entrainment rate on axial distance
downstream of the atomizer was studied by Bush and
Sojka [32], Sutherland et al. [53,56] and Panchagnula et
al. [59]. All these workers found that the amount of gas
entrained into the spray was linearly proportional to the
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
509
Fig. 29. Typical entrainment characteristics of an effervescent atomizer [32].
axial distance downstream of the atomizer under all conditions. A typical plot of normalized entrainment versus
downstream distance (normalized by the atomizer discharge
ori®ce diameter) is presented in Fig. 29.
Most research on the entrainment characteristics of effervescent sprays has tended to connect the entrained gas mass
¯ow-rate to the momentum rate of the spray via a nondimensional entrainment number. According to Ricou and
Spalding [60] the normalized gas entrainment rate of a
steady single-phase gas jet is directly proportional to the
axial distance downstream of the injector ori®ce. They
expressed this relationship as:
r s
4 x
re
m_ e
E
p do
m_ j
rj
3
where me/mj is the normalized entrainment, E the entrainment number, x the distance downstream of the discharge
ori®ce, do the diameter of the discharge ori®ce, and r e and
r j the densities of the entrained gas and the gas in the jet.
Eq. (3) can be used to express the non-dimensional entrainment number E in terms of the entrained gas mass ¯ow-rate
and jet momentum rate as:
m_ e
E q
_ j re
x M
4
Çj
Ç e is the entrained gas mass ¯ow-rate, and M
where m
momentum rate of the jet at the exit plane of the discharge
ori®ce.
Bush and Sojka [32] conducted an analysis for twophase jets similar to that of Ricou and Spalding for singlephase gas jets. They obtained the following expression
for normalized entrainment:
r s
re GLRrL 1 SRrg 1
m_ e
4 x
1 GLR
E
p do
SR
rL rg
m_ L
5
where SR is the inter-phase velocity slip ratio at the exit
plane of the atomizer discharge ori®ce. Bush and Sojka
calculated entrainment numbers using Eq. (5), after determining SR by measuring the atomizing gas and liquid mass
¯ow rates and the spray momentum rate.
Ricou and Spalding [60] found that the entrainment
number for steady gas jets remained constant at 0.32 for
jet Reynolds numbers higher than 25,000. However, Bush
and Sojka [32] found that the entrainment number for effervescent sprays was not constant and varied with operating
conditions. They attributed this variability to the inherent
unsteadiness of these sprays. Support for this hypothesis is
provided by the ®ndings of Sutherland et al. [53,56] who
observed fairly constant values of entrainment number when
using an atomizer with a porous insert ®tted just upstream of
the exit ori®ce. As discussed above, this insert reduces spray
unsteadiness by damping the ¯uctuations in the two-phase
¯ow entering the exit ori®ce.
3.2. Fluid mechanics of effervescent atomization
The dependent variables in effervescent atomization that
represent the spray characteristics of most interest are linked
to the independent variables through the two-phase ¯ow
inside and outside of the atomizer. Independent variables
such as operating parameters, gas and liquid physical properties, and various aspects of atomizer internal geometry,
govern the ¯ow inside the atomizer. This internal ¯ow in
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S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
turn controls the external ¯ow structure that determines the
dependent variables such as drop size and velocity through
primary and secondary atomization. Thus, an investigation
of the ¯uid mechanics of effervescent atomization is
essential for understanding the relationships between
spray characteristics and the range of independent
parameters that are empirically observed to in¯uence these
characteristics.
The internal ¯ow in an effervescent atomizer is more
complex than in most single and twin ¯uid atomizers,
since it involves internal mixing of the liquid with the
atomizing gas and the evolution of the two-phase, gas±
liquid mixture as it ¯ows through the atomizer and out
through the discharge ori®ce. Some aspects of the internal
two-phase ¯ow and the external ¯ow structure downstream
of the discharge ori®ce are illustrated in Figs. 4±6 and
30±33.
As noted above, atomizing gas and liquid are conveyed to
the atomizer through supply ports. The gas is supplied at a
pressure slightly higher than that of the liquid and is bubbled
into the liquid through a perforated aerator tube. The bubbly
two-phase mixture evolves in the mixing chamber as it ¯ows
toward the discharge ori®ce. Its evolution is in¯uenced by
the gas injection geometry (outside±in/inside±out), the
shape and size of the mixing chamber, the contraction
contour upstream of the ®nal discharge ori®ce, the injection
pressure, the gas/liquid ratio, and the liquid physical properties. The two-phase ¯ow may be in a bubbly, slug, or annular
¯ow regime as it enters the ®nal exit ori®ce. The gas phase
expands rapidly as it discharges from the ori®ce and the
liquid phase breaks up into ligaments. These ligaments
rapidly become unstable and disintegrate into fragments
that either undergo further breakup or stabilize forming
relatively large drops.
The following basic two-phase ¯ow phenomena are of
interest with regard to the ¯uid mechanics inside and outside an effervescent atomizer. They are also represented in
Fig. 30.
Mixing chamber
± Bubble formation
± Transport and evolution of bubbles in a moving
liquid stream (coalescence/breakup)
± Motion of individual phases
Fig. 30. Fundamental two-phase ¯ow phenomena involved in effervescent atomization.
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
511
Fig. 33. Near-nozzle spray structure for a visco-elastic liquid
[38,47].
Fig. 31. Near-nozzle spray structure produced by bubble explosions
[12,24].
Contraction upstream of the ori®ce
± Transition of the ¯ow regime as a two-phase mixture
¯ows through a contraction
± Two-phase ¯ow through porous media (in the case
of ligament-controlled atomizers)
Fig. 32. Illustration of near-nozzle `tree and root' spray structure
[12,24].
Discharge ori®ce
± Two-phase ¯ow in a small/micro diameter pipes
± Compressibility aspects in two-phase ¯ows
Outside the atomizer
± Free expansion of a pressurized two-phase ¯ow
± Motion of individual phases
± Ligament formation
± Primary breakup
± Secondary breakup
In the following two sections we review the studies on the
¯ow inside and outside of an effervescent atomizer.
3.2.1. Internal ¯ow
Roesler and Lefebvre [3,23] carried out the only reported
experimental study on the ¯ow inside an effervescent atomizer. These researchers constructed an atomizer with a transparent section upstream of the ®nal discharge ori®ce.
Photographic studies were conducted on the internal twophase ¯ow as it approached and passed through the exit
ori®ce. The two-phase ¯ow characteristics observed immediately upstream of the discharge ori®ce were related to
the near-nozzle spray structure downstream of the ori®ce
and the mean drop size in the spray. Experiments were
conducted using water and air over a range of pressures
from 0.14 to 0.55 MPa and a range of GLRs from 0.005 to
0.10. At low GLRs the photographs show that single bubbles
¯ow one after another through the exit ori®ce, as illustrated
in Fig. 5. As the jet discharges from the atomizer the bubbles
contained within it expand rapidly and shatter the jet into
ligaments and drops. With increasing GLR the number of
bubbles within the mixing chamber increases until eventually
a GLR is reached above which the bubbles start to coalesce
and form voids in the ¯ow. This marks the end of the bubbly
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S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
¯ow regime and the onset of the slug-¯ow regime. At this
condition the spray may exhibit unsteadiness. Further
increase in GLR suppresses these instabilities and the
slug-¯ow regime gradually transitions into the annular¯ow regime whereby the ¯ow structure in the discharge
ori®ce comprises a round jet of gas surrounded by a thin
annular sheet of liquid, as shown in Fig. 4d. Roesler and
Lefebvre's measured values of SMD, when plotted against
gas/liquid ratio, show a continual reduction in SMD with an
increase in GLR, with little to indicate the transitions
between bubbly, slug, and annular ¯ow regimes.
Chin and Lefebvre [51] used another approach for studying the effect of operating parameters, various aspects of
atomizer internal geometry, and liquid physical properties
on the ¯ow inside an effervescent atomizer. By applying
data previously reported in the literature for two-phase
¯ows inside horizontal and vertical pipes to the ¯ow inside
an effervescent atomizer, they were able to reach certain
conclusions. Their results were presented in the form of
¯ow regime plots with traces representing the transition
between different ¯ow regimes as one or more ¯ow variables are changed. They used these plots to show that an
increase in injection pressure always extends the range of
GLRs over which bubbly ¯ow can be maintained. For vertical ¯ows, it was found that an increase in GLR caused the
¯ow regime in the mixing chamber to transition from bubbly
to slug, and then ®nally to annular ¯ow. In general, the ¯ow
pattern in the discharge ori®ce is bubbly at low GLRs and
annular at high GLRs. At very high GLRs (.0.40) the twophase ¯ow inside the ®nal discharge ori®ce is fully
dispersed and discharges from the ori®ce in the form of
drops suspended in the atomizing gas.
Chin and Lefebvre noted that an increase in liquid viscosity promotes bubbly ¯ow in the mixing chamber, while
the effect of surface tension is contrary to that of viscosity
and signi®cantly smaller.
Although Roesler and Lefebvre [3,23] correctly identi®ed the transition from bubbly ¯ow to slug ¯ow and the
associated unsteadiness of the spray, they used this information only to de®ne an upper limit to the range of GLRs
investigated. In a subsequent investigation, Whitlow and
Lefebvre [26] studied the transition from bubbly ¯ow to
slug ¯ow in more detail. They used a single-ori®ce atomizer operating at pressures from 0.069 to 0.69 MPa and
GLRs from 0 to 0.06. Determination of the end of the
bubbly ¯ow regime involved visual observations of the
steadiness of the air and water supply pressures, and any
other visual or audible sign that might indicate a change in
the spray. At the lowest pressures investigated, the changeover from bubbly to slug ¯ow was abrupt and easily
identi®ed. At higher pressures, the changeover was more
gradual and determination of the transition point was more
subjective.
By assuming one-dimensional, steady ¯ow in the mixing
chamber, Whitlow and Lefebvre showed that the maximum
GLR at which the atomizer could remain in the bubbly ¯ow
regime was given by
GLRmax
rg
rL
1
amax 2 1
21
6
where r g and r L are the gas and liquid densities, respectively, and a max the void fraction at the termination of
the bubbly ¯ow regime. The void fraction, a , is de®ned as
the ratio of the ¯ow area occupied by the gas to the total ¯ow
area of the mixing duct.
Whitlow and Lefebvre's [26] experimental data for air
and water indicated that a max remained fairly constant at
around 0.82. Hence, from Eq. (6)
rg
GLRmax 4:6
7
rL
Note that this equation relates only to the upper limit of GLR
for operation within the bubbly ¯ow regime. As mentioned
above, atomizers will operate quite satisfactorily at higher
GLRs and will exhibit lower mean drop sizes with an
increase in GLR.
Very little information is contained in the literature on the
bubble sizes involved in effervescent atomization. Roesler
[3] employed a specially designed probe to collect quantitative data on bubble sizes in the two-phase ¯ow upstream of
the discharge ori®ce. As expected, he observed a decrease in
bubble size with an increase in injection pressure. The
bubble size was also found to decrease slightly with an
increase in GLR. This effect was attributed to the increase
in gas injection velocity associated with a rise in GLR.
3.2.2. External ¯ow
A detailed investigation of the near-nozzle structure of
effervescent sprays was carried out by Santangelo and
Sojka [24,25]. These workers used focused-image holography to visualize the structure of the spray near the atomizer
discharge ori®ce. Their atomizer featured outside±in gas
injection geometry and was operated in a low injection
pressure range (0.1±1.1 MPa). Liquids spanning a range
of physical properties were sprayed. Under different operating conditions Santangelo and Sojka observed two distinctly
different regimes of near-nozzle structure. For GLRs less
than 0.02, they noted that individual gas bubbles ¯owed in
sequence through the exit ori®ce and were surrounded by a
liquid sheath. A slug of liquid followed each bubble. After
discharging from the ori®ce the gas bubbles expanded
rapidly, exploded, and shattered both the surrounding liquid
sheath, and to some extent, the liquid slug into ®ne shreds.
An artist's rendition of this bubbly ¯ow breakup mechanism
is presented in Fig. 31. At GLRs greater than 0.05 the atomizer operated in the annular-¯ow regime. The central gas
core created by the coalescence of individual gas bubbles
expanded rapidly and broke up the annular sheath into a ring
of ligaments. The near-nozzle structure in this regime
resembled a tree with the annular liquid sheath forming a
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
hollow trunk and the ligaments forming branches. An
artist's interpretation of this is presented in Fig. 32.
In both the bubbly and annular ¯ow regimes, the ligaments were observed to break up into fragments that
stabilized forming drops. As the GLR was increased beyond
0.05 it was observed that the tree structure was maintained
but the `trunk' became progressively shorter. An increase in
GLR also caused the structure to evolve from a smaller
number of thicker ligaments to a larger number of thinner
ligaments. This explains the decrease in spray mean drop
size with an increase in GLR as reported by several
researchers.
Buckner and Sojka [12] took high-speed photographs to
study the near-nozzle spray structure when ¯owing highviscosity Newtonian liquids. They observed the same
bubble expansion and liquid-shattering mechanisms as
those observed by Roesler and Lefebvre [3,22,23] and
Santangelo and Sojka [23,24]. They also took shadowphotographs of the near-nozzle region of the spray and
found a diamond-like pattern that they assumed was gas
expansion and compression waves emanating from the
atomizer discharge ori®ce. This observation con®rms that
under conditions of high DpG/pa the two-phase ¯ow is
choked as it leaves the ori®ce. It also helps to explain the
results obtained by several researchers that indicate that
spray mean drop size is constant over a range of ori®ce
diameters.
Geckler [38] and Geckler and Sojka [47] studied the near
nozzle structure of sprays formed with visco-elastic (nonNewtonian) liquids using focused image holography. For
such liquids the near nozzle structure is not characterized
by the typical bubble expansion mechanism or the trunk
with branching ligaments mechanism. Owing to the elastic
properties of the liquid, an annular net-like structure is
observed over a wide range of GLRs, as illustrated in Fig. 33.
Sutherland et al. [16] studied the near-nozzle structure of
the sprays produced by a ligament-controlled effervescent
atomizer. Their observations were very similar to those of
previous workers [3,12,22±25]. Even with the insert ®tted
immediately upstream of the atomizer discharge ori®ce, the
two-phase ¯ow discharged in the form of a central gas core
surrounded by a ring of ligaments. The size of the ligaments,
however, was controlled by the size of the pores on the
insert.
Little information is available on the near-nozzle structure of sprays produced by effervescent atomizers when
operating at high injection pressures (.10 MPa) or with
very small ori®ces (,0.5 mm diameter). Furthermore, the
effect of atomizer internal geometry or ambient density on
the near-nozzle structure has not been investigated.
3.3. Modeling
Effervescent atomization involves complex two-phase
phenomena that are dif®cult to model. It is not surprising,
513
therefore, that only a few modeling studies have been
reported in the literature.
The substantial bene®ts of having a comprehensive
atomization model that would be able to predict spray characteristics from inputs of atomizer geometry and operating
characteristics are obvious. Signi®cant efforts have recently
been directed at the development of such overall models for
several atomization processes. (An example is the work of
Liao et al. [72] who are developing a comprehensive model
for pressure-swirl atomization.)
An ideal, comprehensive model of effervescent atomization would have the capability to predict spray characteristics from ®rst principles. With an input of values for
independent parameters such as injection pressure, GLR,
and liquid physical properties, the model would be able to
predict spray characteristics such as drop size and velocity
distributions, spray momentum rate, etc. The probable structure of such a model is illustrated in Fig. 34. As indicated in
this ®gure, a comprehensive model of effervescent atomization would need to have sub-models for phenomena such as
¯ow-regime transition and compressible two-phase ¯ow
inside an ori®ce.
Some researchers have formulated portions of such a
comprehensive model. Their efforts have concentrated
mostly on modeling the external ¯ow, for which detailed
experimental investigations are described in the literature
[22±25]. Similar detailed experimental studies on all
aspects of the internal two-phase ¯ow have not yet been
conducted, due in part to the considerable dif®culties
involved in building a transparent atomizer. Consequently,
sub-models for effervescent atomizer internal ¯ows are
unavailable at this time.
External ¯ow sub-models have been reported by Buckner
and Sojka [6,36], Lund et al. [14], and Panchagnula and
Sojka [19]. The models of Buckner and Sojka and Lund et
al. were aimed primarily at predicting spray mean drop size.
Buckner and Sojka [6,36] developed a model for predicting the spray mean drop size from a knowledge of atomizing
gas and liquid mass ¯ow rates and liquid physical properties.
They considered a control volume that enveloped the spray
cone extending downstream from the atomizer exit plane.
Global conservation of mass, momentum, and energy were
applied to the control volume. Atomizing-gas and liquid
velocities at the nozzle exit plane, necessary for determining
the momentum and energy entering the control volume,
were estimated from a correlation available in the literature
for void fraction and inter-phase velocity slip ratio [61].
Atomizing-gas and liquid velocities leaving the control
volume were assumed to be equal and were determined
from conservation of mass and momentum. The total energy
entering the control volume was equated to the total energy
leaving the control volume to obtain a relation for spray
SMD. The energy entering the control volume was assumed
to be the sum of the atomizing gas and liquid kinetic energies and the surface energy of the gas bubbles embedded in
the liquid. The energy leaving the control volume was
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S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
Fig. 34. A comprehensive model for effervescent atomization.
assumed to be the sum of the atomizing gas and liquid
kinetic energies and the surface energy of the drops. The
following relation was obtained for spray SMD:
SMD
12s
2 1 eGLR V 2 2 V
2
r{V Lx
gx
Lx 1 eGLR VLgx =1 1 eGLR}
8
where s and r represent the liquid surface tension and
density, GLR represents the atomizing gas-to-liquid ratio
by mass, and V represents velocity. The subscript L indicates liquid, g indicates atomizing gas, and x indicates
conditions at the atomizer exit plane, e is a model coef®cient
that is determined from the experimental data. Buckner and
Sojka [36] reported that predictions made by this model
matched the experimental data within 25%.
A more fundamental model was developed by Lund et al.
[14] for predicting drop size from a knowledge of atomizing
gas and liquid mass ¯ow rates, liquid physical properties,
and atomizer exit geometry. The model, which is fully
consistent with the visualization studies of Santangelo and
Sojka [24,25], employed an available stability analysis of
these structures to determine the size of drops formed. It
assumed that the two-phase atomizing gas and liquid
mixture is discharged from the atomizer in the form of a
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
central gas core surrounded by an annular liquid sheath. The
sheath disintegrates into a ring of ligaments that further
break up and form drops due to the aerodynamic in¯uence
of the surrounding gas. Lund et al. used a correlation
reported in the literature to determine the void fraction
and inter-phase slip ratio for the annular liquid±gas ¯ow
emanating from the atomizer discharge ori®ce. They calculated the thickness of the annular liquid sheath from the void
fraction and ori®ce diameter, and then assumed that this
annular sheath splits up into several cylindrical ligaments
each having almost the same diameter as the thickness of the
annular sheath. The stability analysis reported by Weber
[62] for the breakup of cylindrical liquid jets was applied
to the ligaments and the size of the fragments broken off
from the ligaments was calculated. The size of drops formed
was calculated assuming that each fragment stabilized to
form one drop. Secondary atomization was neglected.
From this model Lund et al. obtained the following expression for spray SMD:
"
1=2 #1=3
3 p 3
3mL
SMD
2pd 1 1 1 p
9
2
rL s L d1
where d1 represents the ligament diameter and r L, m L and s
denote the liquid density, viscosity, and surface tension,
respectively.
Lund et al.'s model is of special interest because it is
based entirely on ®rst principles and contains no empirical
constants. As illustrated in Figs. 15 and 16 the accuracy of
this model increases with an increase in ALR. Drop-size is
over-predicted by approximately 25% (compared to corresponding experimental data) for ALRs below 0.02 but is
predicted to within about 5% of the measured values at
ALRs of 0.04 and more.
As mentioned above, the Lund et al. model incorporates
the stability analysis performed by Weber [62] for cylindrical liquid jets. This analysis does not take into account
the aerodynamic effect of the gas surrounding the (assumed)
cylindrical ligament. In effervescent atomization, however,
there is always a relative velocity between the atomizing gas
and the liquid that can have a signi®cant effect on ligament
breakup. Sutherland et al. [16] improved Lund et al.'s model
by incorporating the effect of relative velocity between the
atomizing gas and the liquid, by replacing Weber's stability
analysis with the stability analysis of Sterling and Sleicher
[63]. Furthermore, instead of the slip ratio correlation used
by Lund et al. for determining atomizing gas and liquid
velocities at the atomizer exit, Sutherland et al. actually
measured spray momentum rates to obtain the atomizing
gas and liquid velocities at the atomizer exit. With these
modi®cations, Sutherland et al. obtained good agreement
between model predictions and experimental data. The
experimentally observed variations of spray mean drop
size with injection pressure, GLR, liquid viscosity, surface
tension, and ligament-control insert pore size were well
predicted by the model, as shown in Fig. 18.
515
Sovani et al. [20,64] also modi®ed the Lund et al. model
to predict drop size distributions for effervescent sprays.
Any practical atomizer produces a range of drop sizes rather
than just a single drop size due to the stochastic phenomena
involved in the atomization process. Sovani et al. included
such stochastic phenomena in the Lund et al. model in the
form of variations in gas±liquid relative velocity and liquid
physical properties. The variations were introduced in the
form of discrete probability functions (DPFs) and the drop
size distribution was obtained in the form of another DPF.
Their results indicate that the drop size distribution width
is a strong, non-linear function of mean and ¯uctuating
gas±liquid relative velocities and is largely unaffected by
variations in liquid physical properties.
Panchagnula and Sojka [19] developed a model for
predicting drop velocity pro®les in effervescent sprays.
They modeled the spray as a variable-density, singlephase turbulent jet and used an expression for velocity
pro®le reported in the literature [65] for such jets. This
expression relates the velocity at any point in the jet to the
jet momentum rate. Panchagnula and Sojka modi®ed this
relation, using expressions for the momentum rate of an
effervescent spray, and expressed droplet velocity in terms
of the operating parameters (liquid mass ¯ow-rate and GLR)
and the densities of the liquid, atomizing gas, and ambient
gas. They found that the experimental data agreed with the
model predictions to within approximately 15%.
4. Applications of effervescent atomization
As mentioned in the introduction to this article, effervescent atomizers perform considerably better (i.e. produce
sprays having smaller mean drop sizes) than other types of
atomizers in many situations. Other signi®cant advantages
include larger exit ori®ces, reduced injection pressures,
and lower gas ¯ow requirements. These advantages have
been exploited in many practical systems; for example,
effervescent atomizers can lead to lower pollutant emissions
in IC engines due to their ability to produce ®ner sprays than
those produced by conventional atomizers for the same
injection pressure. This lower injection-pressure requirement can also improve engine ef®ciency by reducing
parasitic losses.
Most of the studies carried out so far on effervescent
atomization were initiated in order to try and overcome
some of the drawbacks of the more-established atomizer
types. Effervescent atomizers have been designed and tested
for a number of applications, including gas turbines [58,66],
consumer products, process industry applications, and
Diesel engines. A design procedure for different applications has been outlined by Chin and Lefebvre [50].
In the following sections, some of the spray systems to
which effervescent atomization has been applied are
discussed. The speci®c requirements of each system are
listed and the improvements brought about by the use of
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effervescent atomization are described. The literature of
relevance to each application is reviewed.
4.1. Gas turbine combustors
The fuel injection process plays a major role in the performance of gas turbine combustors especially in regard to
pollutant emissions [66]. Increasingly severe emission
regulations for both aircraft and industrial gas turbines
necessitate continuous improvement of the fuel injection
process. In addition, there is an increasing demand for fuel
injectors with multi-fuel capability. Finally, gas turbine
fuel injectors must provide good atomization over the
entire range of fuel ¯ow rates and have low susceptibility
to blockage by contaminants and carbon buildup on the
nozzle face [66].
Effervescent injectors meet all these requirements more
satisfactorily than conventional gas turbine fuel injectors.
They are capable of producing ®ner sprays, leading to
lower pollutant emissions, and have the capability to handle
a variety of fuels due to their relative insensitivity to fuel
physical properties. They perform well over a wide range of
liquid ¯ow-rates and GLRs, and can provide good atomization over a wide range of operating conditions. They can
also have signi®cantly larger ori®ces than those of conventional injectors, thereby reducing clogging problems.
Several researchers have contributed toward the development of effervescent fuel injectors for gas turbine combustors. Their work includes most of the studies conducted in
the initial stages of development (1987±1993). Notable
works are those of Lefebvre [2], Wang et al. [4], Chin and
Lefebvre [50], Li et al. [37], and Colantonio [58].
4.2. IC engines
Pollutant emissions and ef®ciency are also of prime
concern for IC engines. NOx, unburned hydrocarbons, CO
and particulate matter are of most interest. The combustion
processes taking place inside the engine govern the quantity
of pollutants produced. With tightening emission regulations, engine manufacturers around the world are searching
for better technologies to improve the combustion process
and reduce pollutant emissions.
Lawler et al. [76] conducted experiments with jet ¯ames
stabilized on effervescent atomizers. Toulene (C7H8) was
the liquid sprayed and methane (CH4) was the atomizing
gas. Emission indices of soot, unburnt hydrocarbons and
CO were each seen to drop by 80% or more with an increase
in GLR from 5 to 15%. These results suggest that the use of
effervescent atomization for IC engine fuel injection could
possibly lead to drastic decreases in pollutant emissions. In
addition, this technique provides good atomization when
operating at injection pressures that are several times
lower than those of conventional fuel injectors. This
would reduce parasitic losses and raise engine ef®ciency.
The work of Wade et al. [33,42] established that a high
pressure effervescent atomizer spraying `Viscor' (a hydrocarbon fuel with physical properties almost exactly identical
to those of Diesel fuel) can produce sub-10 mm sprays when
operating at injection pressures less than 35 MPa. Satapathy
et al. [21] improved on Wade et al.'s design and developed
an injector that produced sub-5 mm sprays when operating
at injection pressures less than 28 MPa and GLRs less than
0.02. Their experiments were carried out in a high ambient
density environment to simulate the conditions inside the
combustion chamber of a modern Diesel engine at the end
of the compression stroke. These results demonstrate that
the new approach can produce sprays that are comparable
to, or ®ner than, those produced by modern conventional
Diesel injectors, even though injection pressures may be
up to ®ve times lower. However, more work needs to be
done to establish combustion advantages/disadvantages of
effervescent atomization.
4.3. Furnaces and boilers
Most industrial boilers use pressure-swirl atomizers.
However, as high grade hydrocarbon fuels become scarce
these atomizers will have to be replaced with other designs
that can handle less re®ned fuels [52]. Effervescent atomizers are characterized by their ability to perform well for a
range of liquids because their performance is relatively
insensitive to variations in liquid physical properties.
Furthermore they can have larger ori®ces than conventional
atomizers, enabling them to handle less re®ned liquids
without clogging.
Sankar et al. [52] developed a swirl effervescent atomizer
for application to industrial and residential boilers. Loebker
and Empie [11] designed an effervescent atomizer for spraying a pulping industry by-product (black liquor Ð a viscous
liquid of widely varying composition with up to 80% solid
suspension) into a heat recovery boiler. The atomizer was
designed to meet the optimum drop size requirement of the
boiler (2±3 mm mass median diameter). Qualitative and
quantitative results were obtained from spray images
made using a high shutter speed camera. The qualitative
results describe the liquid disintegration process while the
quantitative results detail the variation of mean drop size
with GLR and viscosity. Images of liquid disintegration
mechanisms for the effervescent atomizer were compared
with similar images made using a conventional industrial
black liquor spray nozzle (Spray Systems Vee-Jet e nozzle).
While the near-nozzle structure of the Vee-Jet nozzle
showed a mesh of interwoven, unbroken strands of liquid,
effervescent atomizer near nozzle structure showed much
smaller liquid fragments and drops. Both inside±out and
outside±in gas injection geometries were tested and mean
drop size was found to be smaller for the latter geometry.
The atomizer produced drop sizes less than 5 mm while
operating at injection pressures less than 207 kPa and
GLRs lower than 5%.
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
4.4. Incineration
Effervescent atomizers hold promise in waste incineration
applications. The ®rst advantage is their relative insensitivity to liquid viscosity. This is especially important when
spraying waste products, whose rheological properties
cannot be adequately controlled and are often unknown.
Secondly, performance is relatively insensitive to the size
of the atomizer discharge ori®ce, so larger ori®ces can be
used to reduce clogging substantially. Thirdly, the liquid
¯ow velocity in the discharge ori®ce is much lower than
that in a conventional atomizer. This greatly reduces erosion
problems created by solids suspended in the waste. Furthermore, lower velocities in the ori®ce lead to lower drop velocities. As a result the burnout lengths are shorter and the
incinerator can be made more compact.
Further information on the application of effervescent
atomization to incineration is contained in Panchagnula
and Sojka [19].
4.5. Consumer products
Consumer product sprays are commonly produced using
dispensers pressurized with hydrocarbon (HC) propellants.
They often use volatile organic compounds (VOC) as
solvents. VOCs and HCs in aerosol sprays contribute greatly
to atmospheric pollution, and it is desirable to replace these
compounds with non-polluting substances like water and
air. The use of VOCs and HCs is necessitated in current
consumer product dispensers by the performance limitations
of twin-¯uid and pressure-swirl atomizers. Since effervescent atomizers are known to perform quite well for a
range of liquids and atomizing gases with widely varying
physical properties, their use makes it possible to replace
VOC solvents with water and HC propellants with air without compromising atomizer performance [17].
An important consideration in consumer product dispensers is the amount of propellant gas needed to spray a
unit quantity of liquid. The container has to be charged with
suf®cient propellant gas to dispense all its contents. It is
desirable to minimize the use of propellants in order to
keep the size of the dispenser small. This requirement is
readily satis®ed by effervescent atomization since it is the
most ef®cient means of atomization at GLRs of 0.01 or
lower.
The work of Sutherland et al. [16,53,56] and Lund et al.
[14,44] was targeted at developing an effervescent atomizer
for consumer product sprays. The atomizer they developed
produced spray mean drop sizes below 70 mm for GLRs less
than 0.009.
5. Scope for future study and applications
Effervescent atomization is a rapidly expanding ®eld (see
Fig. 1). The work carried out so far shows considerable
517
promise for its use in a wide variety of practical applications.
An ability to predict atomizer performance is greatly
desired since it would signi®cantly reduce time and cost in
the design and development cycle. Unfortunately, a comprehensive model of the atomization process is not yet available. Present models need improvements to enhance their
accuracy and widen their range of applicability. Hence,
there is considerable scope for efforts to model the subprocesses involved in effervescent atomization and to integrate them into a comprehensive model.
The areas that we feel warrant further investigations are
listed below. The list is presented in the form of topics for
possible future research.
5.1. Experimental studies on basic processes
5.1.1. Atomized liquid
² Atomization of visco-elastic liquids with branched or ring
polymer structure. Visco-elastic behavior of liquids
needs careful consideration since effervescent atomization achieves liquid breakup through the stretching and
shattering of a liquid sheath by an expanding gas core, as
discussed earlier in Sections 2 and 3.2.2. A large number
of polymeric liquids used in spray applications may have
branched structures. Such liquids warrant deeper investigation since they are likely to exhibit greater viscoelasticity than straight chain polymers and would exhibit
signi®cantly different breakup characteristics than those
of the straight chain polymers previously studied
[35,38,47].
² Applications in spraying liquid metals. Liquid metal
atomization typically requires the use of low injection
pressures and large ori®ces. Since effervescent atomization is able to produce signi®cantly smaller drop sizes
under both these constraints it is thought to be a suitable
technique for spraying liquid metals. Future efforts
should be directed at making a detailed assessment of
the suitability of effervescent atomization to this application followed by studies on liquid metal effervescent
atomizer performance and investigations of the relevant
basic physical problems involved.
² Entrainment characteristics of visco-elastic ¯uid sprays.
A wide variety of paints and inks exhibit visco-elastic
behavior. In practical applications involving paint sprays
the prime concern is the uniformity of the coating formed
by depositing the spray on to a surface. Spray entrainment characteristics directly govern the transfer of paint
from the atomizer to the painted surface thus in¯uencing
coating uniformity. Previous studies directed at the
development of effervescent atomizers for paints have
studied the effect of ¯uid visco-elasticity on drop size
and spray near-nozzle structure. Additional work that
considers the practically relevant aspect of spray entrainment characteristics needs to be undertaken.
518
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
5.1.2. Transient spray behavior
² In¯uence of various independent parameters on the
unsteadiness of effervescent sprays. To date fairly limited
efforts have been directed towards the investigation of
unsteadiness in effervescent sprays [54,55]. Spray unsteadiness is highly undesirable in most applications
and more detailed investigations are necessary in this
area, especially since effervescent atomization is a highly
unsteady phenomenon possibly involving exploding gas
bubbles that shatter the surrounding liquid into ®ne drops.
Future work on this topic can be directed at conducting a
parametric study of spray unsteadiness over a range of
independent parameters. From such a study the factors
that have the greatest effect on spray unsteadiness can be
identi®ed and techniques for reducing spray unsteadiness
can be developed.
² Development of atomizers for transient injection applications. Several spray applications require atomizers operating in transient mode, a classic example being Diesel
injectors. All effervescent atomizers reported to date
operate in steady state mode and a signi®cant amount
of work needs to be directed towards the development
of atomizers for transient spray applications. The primary
challenge in the development of transient effervescent
atomizers is that of designing the aerator such that it
provides the desired gas±liquid mixing throughout the
transient spray cycle.
² Transient spray characteristics mapping. The development cycle for transient atomizers should include
mapping spray characteristics (drop size, drop velocity,
cone angle, etc.) as functions of time. It is anticipated that
conventional spray diagnostic instrumentation would be
adequate for transient measurements of effervescent
spray characteristics.
5.1.3. Fluid mechanics of effervescent atomization
² Further investigation of the internal two-phase ¯ow.
Gas±liquid two-phase ¯ow inside the atomizer is an
important aspect determining the performance of internal-mixing twin-¯uid atomizers. The current understanding of effervescent atomization internal ¯ow is rather
limited. Topics that have not been rigorously investigated
previously include gas±liquid mixing inside the mixing
chamber, evolution of the two-phase ¯ow through the
mixing chamber, and exit ori®ce ¯ow. Work currently
in progress at Purdue University is aimed at investigating
gas±liquid mixing inside the atomizer at pressures up to
40 MPa using a transparent atomizer. The experimental
apparatus used and preliminary ®ndings are reported by
Sovani et al. [67,68].
² Two-phase ¯ow inside the atomizer exit ori®ce. The ¯ow
structure inside the ori®ce is thought to have a direct
in¯uence on the near-nozzle breakup mechanisms and
is a key aspect in the determination of spray character-
istics. However, due to signi®cant dif®culty involved in
the experimental investigation of two-phase ¯ow in
circular micro-ori®ces, there is no work reported on
this topic. Relevant works closest to this topic include
two recent studies on two-phase ¯ow structure in
micro/mini channels. Xu et al. [69] discuss the twophase ¯ow regimes in micro rectangular channels with
widths as small as 0.3 mm while Triplett et al. [70,71]
report the ¯ow regimes and pressure drops in circular
channels with diameters 1 mm and greater.
² Parametric study of near-nozzle spray structure. A
comprehensive understanding of the near-nozzle spray
structure is indispensable in the process of developing
models that can predict spray characteristics. Studies to
date have investigated the near-nozzle spray structure
over a rather limited range of parameters, as discussed
in Section 3.2.2. Further work directed at studying the
near-nozzle structure over a wide range of parameters
will be helpful for two reasons. First, it would help
develop a comprehensive theory for effervescent atomizer near-nozzle breakup. Secondly, it would enable the
development of a generally applicable model for predicting spray characteristics of effervescent atomizers.
² The role of two-phase ¯ow compressibility in effervescent
atomization. Before the inception of effervescent atomization, Chawla [18] predicted the signi®cant bene®ts of
internal mixing twin-¯uid atomization considering the
compressibility of two-phase ¯ows, as discussed in detail
in Section 2 and Fig. 3. Chawla's [18] approach successfully explains several characteristic features of effervescent atomization including small drop sizes obtained
at signi®cantly low injection pressures and relative insensitivity of drop size to exit ori®ce diameter. However, a
comprehensive theory clarifying the role of two-phase
¯ow compressibility in effervescent atomization is
currently unavailable. Such a theory may lead to fairly
simple, yet accurate, models for predicting effervescent
atomizer performance.
5.2. Modeling of the effervescent atomization process
² Creation of a comprehensive model for the overall atomization process. As discussed in Section 3.3, a comprehensive model for the overall atomization process is
currently unavailable. Such a model would have the ability to predict spray characteristics from ®rst principles
given inputs of atomizer geometry, operating parameters
and liquid physical properties. A signi®cant amount of
work needs to be done to develop submodels for the
individual ¯ow phenomena involved and integrate them
into one comprehensive model.
² Model for two-phase ¯ow inside the atomizer exit ori®ce.
A particularly challenging part of the comprehensive
model is the submodel for two-phase ¯ow in the atomizer
exit ori®ce. Such a model should be able to predict the
¯ow structure, gas and liquid velocities, pressure, and
S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521
void fraction at the exit plane. Two challenges in the
development of this submodel are the small geometric
scales and the unavailability of experimental data. A
useful reference is the work of Xu et al. [69] who have
proposed models for predicting ¯ow regime transitions in
micro channels of rectangular cross-section. While these
models would serve as helpful references, they cannot be
directly applied to the exit ori®ce ¯ow since they are
developed for ¯ows in rectangular channels at pressures
close to the atmospheric pressure. Furthermore, these
models only predict regime transition and are incapable
of predicting quantitative ¯ow parameters like gas and
liquid velocities and void fraction.
² Improvement of Lund et al.`s [14] primary atomization
model. The only presently available model for primary
atomization is that proposed by Lund et al. [14]. There
are three limitations to this model. First, it is applicable
only if the two-phase ¯ow in the atomizer exit ori®ce is in
the annular regime. Second, it uses a simplistic scheme
based on geometric considerations for predicting the
breakup of the annular liquid sheath issuing from the
atomizer into ligaments. Third, the model uses a linear
stability analysis for ligament breakup. Consequently,
Lund et al.'s [14] model can be improved signi®cantly
by expanding its range of applicability to all possible exit
¯ow regimes, by using a circumferential stability analysis
for the breakup of the annular liquid sheath into ligaments, and by performing a non-linear stability analysis
for the breakup of individual ligaments into drops.
² Primary atomization model for non-Newtonian liquids
including visco-elastic substances. Another drawback
of the Lund et al. [14] model is its inapplicability to
non-Newtonian liquids. An experimental investigation
of the near-nozzle structure of effervescent sprays of
visco-elastic liquids is reported by Geckler and Sojka
[35,47], as discussed in Section 3.2.2. Their results may
be used in the development of a primary atomization
model for visco-elastic ¯uids. Efforts in this direction
are currently being undertaken at Purdue University.
Refer to Babinsky [73] for details.
6. Summary
Effervescent atomization is a form of internal-mixing
twin-¯uid atomization in which an atomizing gas is bubbled
into a liquid and the resulting two-phase mixture is
discharged from the atomizer ori®ce. Atomizers that
embody this concept are found to produce ®ner sprays than
those produced by conventional single and twin ¯uid atomizers while operating at much lower injection pressures. The
atomizing gas-to-liquid ratios needed for effervescent
atomization are signi®cantly lower than those of other
forms of twin-¯uid atomization. In addition, problems of
clogging of the discharge ori®ce are greatly reduced.
Effervescent atomizers have a characteristic drawback
compared to other single-¯uid atomization techniques Ð
519
the need for a supply of pressurized atomizing gas.
However, this requirement can be often met fairly easily
since the device performs well at low gas/liquid ratios.
Work on effervescent atomization was ®rst reported in the
late 1980's. Since then it has become a ®eld of growing
scienti®c and technical interest. Current literature includes
parametric studies of spray characteristics (drop size and
velocity distributions, spray cone angle, spray momentum
rate, patternation and entrainment) for a variety of atomizer
designs. The fundamentals of various processes involved
have been investigated and a partial understanding of
some basic principles has been accomplished. Preliminary
models for performance predictions have been developed.
Work in progress is directed at applying the technique to a
number of applications.
Further work is needed to gain a deeper understanding of
the fundamental mechanisms and two-phase ¯ow phenomena involved. A comprehensive model for predicting
performance is currently unavailable and needs to be
developed.
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