pdfauthor=Varun Kulkarni, pdftitle=Liquid Sheet Breakup in Gas-Centered Swirl
Coaxial Atomizers, pdfkeywords=gas-centered coaxial atomizers, liquid sheets,
jet/sheet breakup, sprays,pdfsubject = Describes the asmejour LaTeX template,
pdflicenseurl=https://ctan.org/pkg/asmejour, Fluids Engineering

V. Kulkarni
D. Sivakumar
C. Oommen Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore,
Karnataka 560012, India
email<EMAIL_ADDRESS>T. J. Tharakan Liquid Propulsion Systems
Centre,
Indian Space Research Organization,
Valiamala,
Thiruvananthapuram 695547, India

# Liquid Sheet Breakup in Gas-Centered Swirl Coaxial Atomizers

###### Abstract

The study deals with the breakup behavior of swirling liquid sheets
discharging from gas-centered swirl coaxial atomizers with attention focused
toward the understanding of the role of central gas jet on the liquid sheet
breakup. Cold flow experiments on the liquid sheet breakup were carried out by
employing custom fabricated gas-centered swirl coaxial atomizers using water
and air as experimental fluids. Photographic techniques were employed to
capture the flow behavior of liquid sheets at different flow conditions.
Quantitative variation on the breakup length of the liquid sheet and spray
width were obtained from the measurements deduced from the images of liquid
sheets. The sheet breakup process is significantly influenced by the central
air jet. It is observed that low inertia liquid sheets are more vulnerable to
the presence of the central air jet and develop shorter breakup lengths at
smaller values of the air jet Reynolds number Reg. High inertia liquid sheets
ignore the presence of the central air jet at smaller values of Reg and
eventually develop shorter breakup lengths at higher values of Reg. The
experimental evidences suggest that the central air jet causes corrugations on
the liquid sheet surface, which may be promoting the production of thick
liquid ligaments from the sheet surface. The level of surface corrugations on
the liquid sheet increases with increasing Reg. Qualitative analysis of
experimental observations reveals that the entrainment process of air
established between the inner surface of the liquid sheet and the central air
jet is the primary trigger for the sheet breakup.
https://doi.org/10.1115/1.4000737[DOI: 10.1115/1.4000737]

###### keywords:

gas-centered coaxial atomizers, liquid sheets, jet/sheet breakup, sprays

##  1 Introduction

It has always been the endeavor of all engineers working in spray combustion
to transform bulk liquid fuel and/or oxidizer into tiny droplets. A decrease
in the size of liquid droplets results in better combustion quality parameters
such as combustion efficiency, heat release, exhaust gas emissions, etc. Spray
formation is accomplished in a liquid propellant engine by means of an
atomizer present inside the engine combustion chamber. A successful atomizer
design must provide high quality of atomization needed to ensure an efficient
combustion process. For liquid propellant rocket LPR applications, several
atomizer configurations are being currently employed and the most commonly
used configurations are the impinging type (Ryan1995, ; Ashgriz2001, ) and the
coaxial type (Mayer1994, ; Rahman1995, ; Sivakumar1996, ; Sivakumar1998, ;
Cohn2003, ). A coaxial type atomizer comprises of an inner orifice surrounded
by an outer orifice and it has been used with both liquid/gas and
liquid/liquid type propellant combinations. The present investigation of gas-
centered coaxial swirl atomizer falls under the category of liquid/gas coaxial
atomizers. Gas-centered swirl atomizers have been studied under two major
configurations: the premixing type and the coaxial type. In the premixing
type, the liquid flows over the inner wall of the gaseous orifice by passing
it through tangential ports and a mixing process between the liquid and the
gas occurs inside the gaseous orifice. In the coaxial type, the liquid and the
gas flow via two different orifices arranged coaxially. Figure 1 illustrates a
schematic of a coaxial type gas-centered swirl atomizer. The atomizer, as
illustrated in the figure, discharges a central gaseous jet surrounded by an
annular swirling liquid sheet. Soller et al. (Soller2005, ) studied the
combustion behavior of sprays discharging from gas-centered swirl coaxial
atomizers and found that the coaxial type atomizers exhibit superior combustor
wall compatibilities compared with that of the premixing type in the context
of wall thermal stress levels. Sprays discharging from the coaxial type gas-
centered swirl atomizers bend toward the spray axis, thereby reducing the
thermal load experienced on the walls of combustor(Muss2002, ).

Spray formation in atomizers is governed by the breakup behavior of liquid jet
or sheet discharging from the atomizer orifices(Lefebvre1989, ). In gas-
centered swirl coaxial atomizers, the physical process by which the outer
liquid sheet interacts with the central gas jet and the role of the central
gas jet in the breakup of the liquid sheet into drops are key factors in
determining the quality of atomization. The fundamental mechanisms governing
the breakup of a liquid sheet injected into still ambient air are well
documented in the current literature. The comprehensive experimental study by
Dombrowski and Fraser (Dombrowski1954, ) revealed the influence of flow and
orifice parameters such as liquid properties, velocity of the liquid sheet,
turbulence at the orifice exit, etc., on the breakup of liquid sheets. The
breakup occurs via the interaction of the liquid sheet with the surrounding
gas medium (Squire1953, ; Taylor1959a, ; Taylor1959b, ). The aerodynamic shear
developed over the surfaces of the liquid sheet causes waves to grow and these
waves separate from the liquid sheet in the form of ligaments, which
subsequently disintegrated into droplets. Two types of waves aid the sheet
breakup: sinuous and dilational(Hagerty1955, ). Sinuous waves are produced
when the two surfaces of the liquid sheet oscillate in phase with each other
and dilational waves result from the out-of-phase motion of the two surfaces.
Several theoretical studies have been reported on the propagation of these
waves in liquid sheets and their influence on the sheet stability, and a
recent review summarizes the outcomes of these investigations(Lin2003, ).

Figure 1:  A schematic of jets discharging from a gas-centered swirl coaxial
atomizer

The influence of coflowing air on the breakup behavior of liquid sheets,
particularly planar liquid sheets, has been studied extensively. Mansour and
Chigier (Mansour1990, ) studied the disintegration mechanism of liquid sheets
discharging from a slit type orifice in the presence of coflowing air. The
airflow over the surfaces of the liquid sheet augments the formation of
cellular structures thin liquid membrane bounded by thick ligaments in the
liquid sheet. In a similar study, Stapper et al. (Stapper1992, ) suggested
that the cellular type breakup occurs at higher relative velocities between
the liquid sheet and the coflowing air jet. A much finer experimental study on
the formation of cellular structures in liquid sheets by Park et al.(Park2004,
) showed that their presence is attributed to the unstable sinuous waves
developing over the liquid sheet. The cellular type breakup results in wider
drop size histograms as the thin membranes of cellular structures generate
finer spray droplets and the rims seen at the periphery of cellular structures
generate larger diameter droplets. A classification of disintegration regimes
for liquid sheets with low air velocities discharging from a coaxial airblast
atomizer was done by Adzic et al. (Adzic2001, ). The authors identified three
major disintegration regimes: Kelvin-Helmholtz regime, cellular regime, and
atomization regime. A systematic study on the role of coflowing air on the
liquid sheet behavior was carried out by Lozano et al.(Lozano2001, ) by
including the effect of air boundary layer and air viscosity in the stability
analysis of the liquid sheet. The authors suggested that the air velocity
mostly determines the oscillatory behavior of the liquid sheet and the
theoretical predictions on the characteristics of sheet oscillation improve
with the inclusion of air viscosity in the analysis. A general observation in
these studies is that the flow characteristics of coflowing air play a
dominant role in the disintegration of the liquid sheet sandwiched between the
air sheets.

The present experimental study deals with the breakup phenomena of swirling
liquid sheets discharging from gas-centered swirl coaxial atomizers. The
primary objective is to understand how the central gas jet aids the breakup
process of such liquid sheets and the subsequent spray formation. The breakup
of swirling liquid sheets without the coflowing gas jet has been studied
extensively in the context of pressure swirl atomizers, and Lefebvre
(Lefebvre1989, ) provides a comprehensive summary on the breakup process of
such simple swirling liquid sheets. In the present work, a gas jet exists in
the air core of the abovementioned simple swirling liquid sheets. The effect
of the central gas jet on the sheet behavior is significantly different from
the role played by still ambient air, and such an interaction process between
the central gas jet and the swirling liquid sheet is not fully understood in
the current literature. Note that several of the published works on gas-
centered swirl coaxial atomizers confined their attention to the analysis of
combustion related aspects (Cohn2003, ; Soller2005, ; Muss2002, ). A
systematic experimental investigation is carried out in the present work to
document the influence of central gas jet on the breakup behavior of the outer
swirling liquid sheet by conducting cold flow experiments at ambient
atmospheric conditions with air and water as working fluids.

##  2 Experimental Details

A schematic of the gas-centered swirl coaxial atomizer used in this study is
shown in Fig. 2. Major components of the atomizer configuration are
highlighted in the figure. The outer orifice plate consisted of a converging
portion and an orifice. Diameter of the outer orifice $D_{o}$ and that of the
inner central orifice $D_{i}$ were kept at 4.4 mm and 2.4 mm, respectively.
Lip thickness of the inner orifice was kept at 0.3 mm, which resulted in an
orifice gap of 0.7 mm for the outer orifice. Swirling motion to the flowing
liquid was imparted by passing the liquid through rectangular shaped helical
passages present over the periphery of the swirler. Two different atomizer
configurations CA1 and CA2 were studied by varying the geometrical parameters
of the swirler. The width $w$ of the rectangular helical passage was kept at
1.0 mm for both CA1 and CA2. The depth h of the helical passage was kept
differently for the atomizer configurations as 0.5 mm for CA1 and 1.0 mm for
CA2. The number of helical passages in the swirler $n$ was fixed at 6 for both
the atomizer configurations. The swirling intensity of the outer pressure
swirl atomizer was characterized in terms of swirl number $S$, which was
estimated in the present study using the relation,

$S=\dfrac{\pi D_{s}D_{o}}{4nwh}$ (1)

where, $D_{s}$ is the diameter of the swirl chamber. The estimated values of
$S$ for the atomizer configurations CA1 and CA2 were 25.7 and 12.3,
respectively. A standard spray test facility was used to carry out the
experiments. The facility consisted of a large stainless steel tank containing
water kept under a particular pressure by means of a compressed air supply and
an air pressure regulator. Flexible tubes capable of withstanding high
pressures were used to carry the experimental liquid to the atomizer assembly.
Tubes similar in nature, drawn from the compressed air supply, were used to
deliver air at a given mass flow rate which was estimated by employing an
orifice flow meter. A filter was employed between the liquid storage tank and
the atomizer assembly to arrest contaminants present in the liquid. Necessary
needle valves along with pressure gauges were connected in the flow lines to
keep the fluid flow at steady operational conditions.

The flow behavior of liquid sheets was characterized by capturing images of
liquid sheets using photographic techniques. A Nikon D1X digital camera with
diffused backlighting system was used to take photographs of the liquid
sheets. The pixel resolution of the camera was 2000 $\times$ 1312\. The
diffused backlighting system consisted of a strobe lamp, and each flash from
the strobe lamp had lasted for about 12 $\mu$s, which became the time
resolution for imaging. The measurements obtained from the image analysis are:
the half spray cone angle of spray at the orifice exit, the radial spread of
spray $SW$ at different locations in the spray axis, the breakup length of the
liquid sheet $L_{b}$, and the two-dimensional surface profile of the liquid
sheet. Figure 3 shows the details of $L_{b}$, and $SW$ on a typical image of
the outer swirling liquid sheet.

Figure 2: A schematic of the gas-centered swirl coaxial atomizer used in the
present study

An image processing algorithm was developed to deduce the two dimensional
surface profile of the liquid sheet in the form of plots from the high
resolution images of liquid sheets. The algorithm identifies the bounding
pixels of spray contour at different $Z$ locations counted in terms of pixels
from the orifice exit.

Figure 3: A typical image of the outer liquid sheet illustrating the details
of $\theta_{s}$, Lb, and SW

The locations of the bounding pixels in the digital image were carefully
extracted so that the data can be plotted using a graphical software. These
profiles were analyzed systematically to understand the surface perturbations
and ligaments developing from the liquid sheets. The flow condition of the
outer liquid sheet was expressed in terms of Weber number Wel as,

$We_{l}=\dfrac{\rho_{l}U_{l}t_{f}}{\sigma}$ (2)

where, $\rho_{l}$ is the liquid density 998 kg/m3, $\sigma$ is the surface
tension (0.0728 N/m), Ul is the axial velocity of the liquid sheet at the
orifice exit, and $t_{f}$ is the thickness of the liquid sheet at the orifice
exit. The value of $t_{f}$ was estimated using an analytical relation reported
in the literature as (Lefebvre1989, ),

$t_{f}=3.66\left(\dfrac{D_{o}m_{l}\mu_{l}}{\rho_{l}(\Delta
P_{l})}\right)^{0.25}$ (3)

where $m_{l}$ is the liquid mass flow rate, $P_{l}$ is the injection pressure
drop across the outer orifice, and $\mu_{l}$ is the liquid dynamic viscosity
(1.003$\times$10-3 kg/ms). The axial velocity of the liquid sheet at the
orifice exit, Ul was estimated from the mass conservation as,

$U_{l}=\dfrac{m_{l}}{\rho_{l}\pi t_{f}(D_{o}-t_{f})}$ (4)

The flow condition of the central air jet was expressed in terms of Reynolds
number $Re_{g}$ as

$Re_{g}=\dfrac{\rho_{g}U_{g}D_{i}}{\mu_{g}}$ (5)

where, $\rho_{g}$ is the air density (1.2 kg/m3), $U_{g}$ is the axial
velocity of the gas jet at the orifice exit, and $\mu_{g}$ is the air dynamic
viscosity (1.81$\times$10-5 kg/ms).

C¿c¡  Quantity Source Net Uncertainty  $m_{l}$ Measurement resolution (1%)
1–4.15% Repeatability (0.12 - 4.03%) $m_{g}$ Measurement resolution (0.030%)
1.75–4.68% Repeatability (0.22–4.3%) $(\Delta P)_{l}$ Measurement resolution
(2%) 2.6–4.28% Repeatability (1.67–3.57%) Calibration (0.13–1.27%) $(\Delta
P)_{g}$ Measurement resolution (0.02%) 1.9–8.42% Repeatability (0.83–6.67%)
Calibration (1.71–5.16%) $L_{b}$ Measurement resolution (1%) 1.35–10.75%
Repeatability (1.35–10.75%) $SW$ Spray width point identification (0.53–2.31%)
3.1–8.03% Repeatability (3.05–7.69%) The value of $U_{g}$ was estimated from
the mass conservation as,

Table 1: Uncertainty estimates

$U_{g}=\dfrac{4m_{g}}{\rho_{g}\pi D_{i}^{2}}$ (6)

where, $m_{g}$ is the air mass flow rate. The uncertainty estimates for
primary measurements are presented in Table 2. The uncertainty estimates for
derived measurements like spray contraction parameter, nondimensionalized
breakup length, etc., can be determined from Table 2. The calculation for net
uncertainty was based on the procedure described by Moffat(Moffat1988, ).

##  3 Results and Discussion

###  3.1 Visual Observations on the Breakup of the Outer Liquid Sheet by the
Central Air Jet

Figure 4:  Images of liquid sheets discharging from the gas centered swirl
coaxial atomizer CA1 ($S$ = 25.7) for different combinations of Wel and Reg

Figure 4 illustrates the images of outer swirling liquid sheets discharging
from the gas-centered swirl coaxial atomizer CA1 with different combinations
of outer liquid sheet and central air jet flow conditions.

Figure 5: The influence of the central air jet on the flow behavior of the
outer liquid sheet with Wel = 114 discharging from the gas-centered swirl
coaxial atomizer CA2(S =12.3) Wel remains constant for all the images shown in
this figure.

An image row in the figure corresponds to the cases of increasing Reg for a
constant Wel and an image column corresponds to the cases of increasing Wel
for a constant Reg. It is evident from the image rows of Fig. 4 that for a
given Wel, an increase in Reg destabilizes the outer liquid sheet and
decreases the breakup length of the liquid sheet $L_{b}$. In a similar manner,
an increase in Wel for a given Reg increases $L_{b}$. Detailed analysis on the
sheet breakup process was carried out by constructing image sequences for a
particular $We_{l}$, however with varying Reg. Figure 5 shows a sequence of
images illustrating the breakup of the outer liquid sheet with $We_{l}=$ 114
under different central air jet flow conditions.

The image at the leftmost top corner of Fig. 5 corresponds to the liquid sheet
without any central air jet. The presence of the central air jet with low
$Re_{g}$ pulls the liquid sheet toward the spray axis, as seen in the second
and third images off of the top row of Fig.5 and results in a shift in the
sheet breakup location toward the orifice exit. The central air jet impinges
directly on the inner surface of the liquid sheet at slightly higher Reg
conditions, which may be leading to the generation of chunks of liquid masses
immediately after the breakup.

Figure 6:  High resolution images illustrating the violent and complex breakup
of the liquid sheet by the central air jet in the near region of the orifice
exit. Atomizer configuration is CA2 S =12.3 and Wel = 114.

The liquid sheet collapses dramatically with further increase in Reg, as seen
in the images of Fig. 5 and the breakup of the liquid sheet occurs in the near
region of the orifice exit.

Figure 7:  Enlarged view of the two-dimensional surface profiles of liquid
sheets discharging from the gas-centered swirl coaxial atomizer CA2 (S =12.3)
with different combinations of Wel and Reg: (a) Wel =114,(b) Wel =144, and (c)
Wel =270

High resolution images illustrating the breakup of the liquid sheet at higher
values of Reg are given in Fig. 6. The axisymmetric conical shape of the outer
liquid sheet, as observed in the lower values of Reg, is no longer seen at
these higher values of Reg and the sheet breakup occurs in a more complex
manner. Discrete liquid sheets bounded by thick rims are dominantly seen at
these flow conditions. The images given in Fig. 5 show an increase in the
radial spread of spray with increasing Reg particularly in the higher range of
$Re_{g}$ see the last five images of Fig. 5. An intense mixing between the
liquid sheet and the central air jet in the near region of the orifice exit
occurs at these flow conditions because the jet boundaries are closer to each
other than ever before.

Note that the inertia of the central air jet in the near region of the orifice
exit is proportional to $\rho_{g}U_{g}^{2}$, which is two orders of magnitude
larger than that of the liquid sheet, $\rho_{l}U_{l}^{2}$ at higher values of
$Re_{g}$ given in Fig. 5. The increase in radial spread with increasing Reg at
higher values of Reg may be a direct consequence of momentum exchange between
the jets. A closer interaction between the liquid sheet and the central air
jet in the near region of the orifice exit under these flow conditions may
result in a violent breakup of liquid masses.

Figures 7a-7c show the two-dimensional surface profiles of liquid sheets
discharging from the gas-centered swirl coaxial atomizer CA2 for different
combinations of Wel and Reg. In general surface corrugations seen on the
liquid sheet increases with increasing Reg and this effect is more pronounced
for low inertia liquid sheets. The liquid sheets with lower inertia are
showing more surface corrugations for a given increase in $Re_{g}$, and higher
inertia liquid sheets need a larger increase in Reg to develop similar levels
of surface corrugations. Qualitatively this can be seen by comparing the
profiles given in Fig. 7a or Fig. 7b with that of Fig. 7c. Note that the
profiles of liquid sheets given in Fig. 7c correspond to higher values of Reg
compared with those of Figs. 7a and 7b. The dark patches seen in a surface
profile correspond to the presence of thick liquid masses, for example, liquid
ligaments, and indicate the termination of a smooth liquid sheet. The profile
analysis of liquid sheets with increasing Reg reveals that the dark patches
appear more in the case of low inertia liquid sheets. This suggests that the
low inertia liquid sheets are prone to develop thick liquid ligaments during
the sheet breakup process. Interestingly it is observed that even at very high
values of Reg, an intact liquid sheet is always present in the near region of
the orifice exit and the sheet breakup occurs at distances one or two times
the outer orifice diameter from the orifice exit. This can be understood from
the sheet surface profiles given in Figs. 7a–7c. In the present gas-centered
swirl coaxial atomizers, the liquid sheet at the orifice exit is separated
from the central air jet by the inner orifice lip and a meaningful interaction
between the liquid sheet and the central air jet is expected to happen a few
millimeters away from the orifice exit.

###  3.2 Quantitative Variation in $L_{b}$ With Flow Conditions

Figure 8:  Quantitative variation in Lb with Reg for different values of Wel a
low values of Wel and moderate and high values of Wel

The breakup process of outer liquid sheets is analyzed further by deducing
quantitative measurements of $L_{b}$ from the spray images. Figures 8a and 8b
show the quantitative variation in $L_{b}$ with Reg for different values of
Wel. Each data point in Figs. 8a and 88b corresponds to the arithmetic average
of $L_{b}$ values measured from a set of a minimum of three images captured
during repeated experimental runs at a given test condition. The variation in
$L_{b}$ with Reg clearly shows that the central air jet destabilizes the outer
liquid sheet. For low inertia liquid sheets, the influence of the central air
jet on $L_{b}$ is seen even at low values of Reg, as illustrated in Fig. 8a.
The variation in $L_{b}$ with Reg for high inertia liquid sheets given in Fig.
8b shows that the breakup length remains unaltered in the lower values of Reg
and drastic changes in $L_{b}$ are seen at higher Reg. Figures 8a and 8b also
show that the decrease in $L_{b}$ with increasingReg is more rapid for low
inertia liquid sheets and is gradual for high inertia liquid sheets. The
measurements of $L_{b}$ given in Figs. 8a and 8b do not show any significant
influence of $S$ on the sheet breakup length for the atomizer configurations
studied.

###  3.3 Physical Insights on the Sheet Breakup Process

The breakup process of liquid sheets in gas-centered swirl coaxial atomizers
is influenced by several physical events. Since a swirling liquid sheet
diverges away from the spray axis, it is essential to bring the liquid sheet
closer to the boundary of the central air jet in order to establish an
effective interaction process between the liquid sheet and the central air
jet. This process is accomplished by the central air jet itself. The presence
of the air jet inside the core of the outer swirling liquid sheet establishes
an entrainment process of air between the central air jet and the inner
surface of the outer liquid sheet. The air entrainment process reduces the
local pressure over the inner surface of the outer liquid sheet and thereby
increases the pressure difference across the liquid sheet $(P_{e}-P_{i})$,
where $P_{e}$ and $P_{i}$ are, respectively, the pressures at the outside and
inside surfaces of the outer liquid sheet. For a given $P_{e}$, an increase in
$(P_{e}-P_{i})$ makes the liquid sheet move toward the spray axis. A stronger
air entrainment process, or higher Reg, increases $(P_{e}-P_{i})$ and the
spray continues to contract with increasing Reg. Such a spray contraction with
increasing Reg can be seen from the spray photographs given in Fig. 4. In the
present work a nondimensionalized spray contraction parameter is used to
illustrate the trends of spray contraction with Reg and is expressed as,

$\xi=\dfrac{SW_{Re_{g}=0}-SW_{Re_{g}}}{SW_{Re_{g}=0}}$ (7)

where $SW_{Re_{g}=0}$ and $SW_{Re_{g}}$ correspond to the spray widths for
liquid sheets with Re${}_{g}=0$ and Re${}_{g}\neq 0$, respectively. The
variation in with Reg for the liquid sheets with different Wel is shown in
Figs. 10a and 10b. Since the liquid sheet is conical in nature, the variation
in with Reg is presented in the figure for different axial distances $Z$ from
the orifice exit. The measurements given in Fig. 9a clearly suggest that the
liquid sheets with lower Wel exhibit a sharp increase in the spray contraction
with increasing Reg compared with higher inertia liquid sheets. In other
words, low inertia liquid sheets are more vulnerable to the presence of the
central air jet and high inertia liquid sheets do not recognize the presence
of the central air jet in the lower values of Reg.

Figure 9:  Variation in spray contraction parameter with Reg for different
values of Wel at different axial locations, $Z$ from the orifice exit (a and
b). Atomizer configuration is CA2, (S = 12.3)

Such a sharp increase in the spray contraction helps the liquid sheet to
initiate a more active interaction with the central air jet. The second
physical event to influence the sheet breakup process is the development of
surface corrugations, which aid the generation of liquid ligaments from the
sheet surface. Quantitative characterization of surface corrugations is done
by estimating the tortuosity of the liquid sheet profile. Tortuosity of the
liquid sheet profile at any two points in the profile is defined as the ratio
of the length of the curved line profile between the two points to the least
distance between the two points and is a measure of corrugations on the sheet
profile exist between the two points. The value of tortuosity is always
greater than 1 and increases with increasing levels of sheet profile
corrugations. Assuming that the digitized points of the sheet profile are
given in the x-y coordinate system as (x1 , y1), (x2 , y2), . . . , (xk , yk)
, . . . , and (xn , yn), where subscripts 1 and n correspond to the first and
last points of the sheet profile curve, the tortuosity of the liquid sheet
profile can be estimated as,

$\textrm{Tortuosity}=\dfrac{\sum\limits_{k=1}^{n-1}{\sqrt{(x_{k+1}-x_{k})^{2}+(y_{k+1}-y_{k})^{2}}}}{\sqrt{(x_{n}-x_{1})^{2}+(y_{n}-y_{1})^{2}}}$
(8)

Attention must be given to ensure that the numerator was accurate enough to
represent the total length of the curve. Figure 10 shows the variation in
tortuosity of the liquid sheet profile with Reg for different values of
$We_{l}$. The variation in tortuosity is almost insignificant for the liquid
sheets with very low values of Reg 10,000–15,000, as seen in Fig. 10.

Figure 10:  Variation in tortuosity of the liquid sheet profile with Reg for
liquid sheets with different Wel discharging from the gas-centered swirl
coaxial atomizer CA2 (S = 12.3)

A steep increase in the tortuosity with Reg is observed for low inertia liquid
sheets in the moderate values of Reg, as highlighted by the measurements
marked with open symbols in Fig. 10 and the rise in tortuosity is somewhat
gradual for relatively high inertia liquid sheets see the measurements marked
with filled symbols in Fig. 10. The third physical event to influence the
sheet breakup process is the direct impingement of the central air jet on the
inner surface of the liquid sheet and the subsequent mixing process between
the liquid sheet and the central air jet. This event starts once the outer
liquid sheet meets the boundary of the central air jet and generally occurs at
high values of Reg. The dynamics of the liquid sheet at these flow conditions
is very complicated and is marked by features such as substantial reduction in
the liquid sheet breakup length, generation of thick liquid ligaments and
droplet clusters, cellular patterns on the surface of the liquid sheet,
ejection of ligaments and droplets in the transverse direction, etc. The
images shown in Fig. 6 are typical of this event. More systematic experiments
are needed to ascertain these facts in a quantitative manner. The quantitative
variation in $L_{b}$ with Reg given in Figs. 8a and 8b shows that the breakup
process of liquid sheets discharging from gas-centered swirl coaxial atomizers
is primarily determined by the flow parameters Wel and Reg. The influence of
Reg on the sheet breakup is very significant for low inertia liquid sheets,
whereas such behavior is observed only at higher values of Reg for high
inertia liquid sheets. It is interesting to observe that low inertia liquid
sheets disintegrate at lower values of Reg. Note that low inertia liquid
sheets discharging from a simple pressure swirl atomizer exhibit a longer
breakup length and it is quite normal to presume that these liquid sheets
require more energy for their breakup and the subsequent atomization process.

A reverse trend is observed in the gas-centered swirl coaxial atomizers. This
behavior is attributed to the fact that low inertia liquid sheets are more
vulnerable to the entrainment process developed between the central air jet
and the liquid sheet. High inertia liquid sheets are relatively less
influenced by the entrainment process, which resulted in almost an
insignificant variation in $L_{b}$ with Reg in the lower values of Reg, as
seen in Fig. 8b. Analysis of spray images revealed that the breakup of the
liquid sheet is faster if the liquid sheet exists near the spray axis. This
was observed for all values of $We_{l}$. Thus the primary trigger for the
sheet breakup may be the intensity of entrainment process developed between
the liquid sheet and the central air jet.

##  4 Conclusions

An experimental study on the breakup behavior of the outer swirling liquid
water sheet by the central gas air jet discharging from custom fabricated gas-
centered swirl coaxial atomizers has been reported. The analysis of spray
pictures captured using conventional photographic techniques reveals that the
presence of the central air jet in the core of the swirling liquid sheet
significantly changes the breakup behavior of the liquid sheet. At low values
of the air jet Reynolds number, the interaction process between the liquid
sheet and the central air jet develops corrugations on the surface of the
liquid sheet. For a given low inertia liquid sheet, the level of sheet
corrugations, described in the present work in terms of tortuosity of the
sheet profile, increases with an increasing air jet Reynolds number. A reduced
effect of the central air jet on the surface corrugations is observed for high
inertia liquid sheets. The breakup region of the liquid sheet is marked by
features such as ejection of liquid ligaments from the sheet surface,
localized droplet clusters, increased surface corrugations on the liquid
sheet, and cellular structures thin membrane of the liquid sheet surrounded by
a thick rim on the liquid sheet. Quantitative measurements of the liquid sheet
breakup length suggest that the breakup length of low inertia liquid sheets
decreases with an increasing air jet Reynolds number and the decrease in sheet
breakup length is less severe for high inertia liquid sheets. The present flow
configuration of liquid and air jets creates an air entrainment process
between the inner surface of the liquid sheet and the central air jet. The
entrainment process helps to bring the liquid sheet and the central air jet
closer to each other, and thereby develops a more active interaction between
the jets. A high inertia central air jet aids to develop a stronger air
entrainment process and hence brings the liquid sheet nearer to the spray
axis. This results in the direct impingement of the air jet on the liquid
sheet and the breakup length of the liquid sheet decreases steeply at high
inertia air jet conditions.

## Acknowledgment

This work was supported by Space Technology Cell, Indian Institute of Science
under Grant No. ISTC/MAE/SK/179.

$D$diameter (m) $L$length (m) $t$thickness (m) $U$velocity (ms-1)

Greek Letters $\rho$density (kgm-3) $\mu$dynamic viscosity (Pas) $\xi$spray
contraction parameter (-) $\sigma$surface tension (Nm-1)

Dimensionless Groups ReReynolds number, $\rho UD/\mu$ WeWeber number, $\rho
U^{2}D/\sigma$

Superscripts and Subscripts bbreakup iinner fliquid sheet ggas lliquid oouter

english

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