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The Influence of Retraction on Three-Stream Injector Pulsatile
Atomization for Air-Water Systems
Wayne Strasser
Eastman Chemical Company
Kingsport, TN, 37660
strasser@eastman.com
ASME Fellow
Francine Battaglia
Department of Mechanical Engineering
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061
fbattaglia@vt.edu
ASME Fellow
Abstract
Although coaxial airblast primary atomization has been studied for decades, relatively
little attention has been given to three-stream designs; this is especially true for transonic self-
pulsating injectors. Herein, the effects of nozzle geometry, grid resolution, modulation, and gas
flow rate on the acoustics and spray character within an industrial scale system were investigated
computationally using axisymmetric (AS) and 3-D models. Metrics included stream pressure
pulsations, spray lift-off, spray angle, and primary droplet length scale, along with the spectral
alignment among these parameters. Strong interactions existed between geometry and inner gas
feed rate. Additionally, inner nozzle retraction and outer stream meeting angle were intimately
coupled. Particular attention was given to develop correlations for various metrics versus
retraction; one such example is that injector flow capacity was found to be linearly proportional
to retraction. Higher inner gas flows were found to widen sprays, bringing the spray in closer to
the nozzle face, and reducing droplet length scales. Substantial forced modulation of the inner
gas at its dominant tone did not strongly affect many metrics. Incompressible 3-D results were
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similar to some of the AS results, which affirmed the predictive power by running AS
simulations as surrogates. Lastly, normalized droplet size versus normalized distance from the
injector followed a strikingly similar trend as that found from prior two-fluid air-slurry
calibration work.
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1. Introduction
1.1. Background
Disintegration of liquid jets has been of paramount importance to the agricultural,
chemical, food, fire protection, and energy-production industries. Air-assisted atomization
systems involve passing at least one high-speed gas stream(s) next to at least one lower speed
liquid stream(s). Where the phases meet, Kelvin-Helmholtz instabilities (KHI) are produced and
eventually result in major distortion of the contiguous liquid to form waves. The gas phase
interacts with the waves, and form drag creates high pressure and low pressure regions on the
windward and leeward boundaries of the waves. The relatively low-density gas accelerating the
heavy liquid creates Rayleigh-Taylor instabilities (RTI) until liquid droplets are pinched off.
Droplet characteristics and trajectories, in some cases, determine yield and productivity within
large-scale reactive process equipment, where uniformly distributed and relatively small droplets
are often sought. The initial stage of liquid breakup, called “primary atomization”, sets the
foundation for the overall atomization process and has been studied extensively [1-12]. Droplet
sizes typically decrease with increasing liquid density, and they normally increase with
increasing liquid viscosity and surface tension. However, within the bounds of fixed process
conditions and compositions, methods are often sought to modify the injector geometry to reach
particular atomization goals.
Fuster et al. [13] investigated the effect of gas/liquid momentum ratio (M) on the
dominant response frequency of wave growth from a simple gas-liquid splitter plate arrangement
for planar primary atomization. In their study, they modulated the gas stream and found that the
response dynamics were dependent upon the thickness of the splitter plate relative to the
thickness of the approaching gas boundary layer. At lower M, the Fast Fourier Transform (FFT)
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results were more sensitive to plate thickness. The thickness controlled the gas boundary layer
development such that thicker plates reduced the instability mechanism. The result was more
FFT noise and less magnitude (less focused spectrum) for thicker plates. The gas-side
turbulence impact on instabilities was quite important for laminar liquids. In general their work
displayed increasing FFT amplitude with increasing M up to M≅10 and decreasing frequency up
to M≅10, but with a sudden frequency drop and recovery at M≅5.
An important geometric variable in gas-assisted atomizers is “retraction”, which refers to
the extent of liquid pre-filming. Pre-filming implies exposure to a lower velocity gas stream (or
allowed to become unstable without gas) before contacting the high-velocity gas shear. Kim et
al. [14] studied the pre-filming section of a two-stream rocket engine under cold flow conditions
with an M of around unity using CFD. They found that increased retraction gives the liquid a
more active and structured wave-type axial motion. Breakup was seen to start in the pre-filming
area in some cases, the mass flow rate increased. The most striking result was the halving of the
dominant mass flow response frequency (making it coincident with the fundamental, or lowest
detectable peak tone) caused by the increase in normalized retraction length LRI from 0.75 to
1.25. The lower frequency at the higher retraction was consistent with the time required for the
liquid to traverse the pre-filming region. An earlier study by Park and Lee [15] revealed that a
flushed design improved atomization efficiency over a protruding design (negative retraction)
but only under sonic gas conditions; otherwise, the negative retraction layout was preferred.
Acoustics can be an important element for atomization efficiency as is evidenced in the
life and intricate design of the Bombardier Beetle [16], uses in the food industry [17], and the
comprehensive study in regards to combustion considerations, such as the use of various forcing
frequencies to energize thermoacoustic instabilities to promote clean combustion [18]. All
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coaxial atomization may fundamentally be considered pulsatile in that, from a fixed reference
frame watching the passing spray, there are temporal oscillations in liquid volume fraction and
spray droplet number density [19]. Here, we define “pulsations” to imply those which are
driven by, or effectively drive, pure feed stream oscillations. An insightful study on feed stream
modulation is that of Srinivasan et al. [20], where water and alcohol jets in still air over
modulation ratios Ω = 0.1-0.4 and frequencies of 40 to 120 kHz were investigated. They cited
studies of jet modulation dating back as far as 1965. Although their pulsatile flow was not self-
sustaining, their sprays exited the nozzle in bunched streams like the branched pattern of a
conifer tree (e.g., “Christmas tree”). In their computational work, they used the “CICSAM”
(discussed in more detail in [21]) method for resolving the vapor-liquid interface, and they
ignored the presence of turbulence. Although their grid was three-dimensional, the
circumferential dimension was only one cell thick. They found that increases in the modulation
amplitude increased the spray angle, but frequency changes had a mixed effect on angle. In
addition, they reported a reduction in spray angle with an increasing jet exit diameter. They
utilized a liquid-based Strouhal number of St = πDhf/UL (ranging from 1 to 4) and a modified
Weber number of WeW = ρLU3/fσ (ranging from 1,000 to 10,000). For St > 1, the wavelength of
the imposed perturbations was lower than the circumference of the liquid jet, so the perturbations
were damped. For low Ω, no discernible droplets formed, while for high Ω, a fine outer spray
was produced. A similar effect was shown for modulation frequency over the range tested. By
using two different liquids, they showed that the same Strouhal numbers produced similar axial
spacing in the liquid bunches, but the droplet formation processes were different because of a
different WeW.
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1.2. Objectives and Scope
In contract to the cited works, the focus of the current work is primary atomization within
a three-stream injector. The authors have summarized the key literature that has focused on
three-stream injectors in [21]. There is apparently nothing in the open literature by other
research groups regarding issues of geometry and feed modulation for a three-stream injector
using a transonic volume of fluid (VOF) computational approach even though VOF is quite
commonly ([22-27]) used for multiphase flows. As a result, the existing published literature can
primarily be used as a guide. The foundation of the work here is that of Strasser [28] in which
various ratios of gas and liquid feeds were considered with the aim first to characterize and then
to optimize the operation of a pulsatile injector. There were too few permutations to fully
optimize the injector, so the work continues here. Animations and experimental videos were
produced to illustrate various effects. Additionally, Strasser and Battaglia [21] more closely
examined and validated the computational method, as well as identified the roots of the pulsation
mechanism. The three streams are designated as inner gas (IG), outer gas (OG) and an
intermediate liquid as shown in Figure 1 of Ref. [21], flowing from the top to the bottom.
Properties, flows, and dimensionless groups for the fluid streams and geometric parameters will
be provided when appropriate. The injector inlets are much longer and tortuous than what is
shown and will affect the pressure transients to be discussed herein. Any time the word
“flushed” is used, it is referring to a value of 0 for inner nozzle retraction, LRI. A typical
computational mesh, referred to as “base”, is also shown in Figure 1 of Ref. [21], while other
meshes will be considered throughout this work.
While previous work established the computational method and addressed the effect of
flow rate for a given nozzle geometry, an astounding quantity of issues remain unaddressed. The
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effects of geometry, gas flow rate, flow modulation, mesh resolution, and 3-D modeling are now
addressed. Table 1 highlights the geometric configurations, reflecting mechanically imposed
limits to what can be evaluated. Eight designs are considered with varying stream angles (γ),
retraction distances (LRI), and orifice diameters (D). The purpose, or differentiating issue, is
noted in the table. Most geometric values are normalized by the nozzle outer diameter (DO).
Rather than disclosing the actual dimension, the outer diameter is normalized by the maximum
value tested. Notice that the inner and outer metal nozzle lip thicknesses, tLI and tLO, vary when
other geometric variables are changed; the inner lip thickness for the retracted case is more than
quadruple that of the base cases. Additionally, both the inner and the outer lip thicknesses are
slightly reduced for larger DO values. This is due to geometric constraints of the injector inside
other process equipment; the retraction and diameter could not be varied independently from the
lip thicknesses. Like the work of Fuster [13], the metal lips can be thought of as splitter plates.
It is expected that the thicker plates will have a negative effect on primary atomization by
creating a thicker gas boundary layer (velocity deficit near the liquid interface) and a reduced
instability driving force. This should be of lesser importance for these high liquid Reynolds
number simulations, where the primary instability mechanism is liquid phase turbulence (Xiao et
al. [12]), but is important for studies involving slurry as is shown in [29]. In addition to liquid
phase turbulence, one of the dominant liquid film buffeting forces is the temporal pressure
gradients moving throughout the pre-filming section [29].
A total of 16 simulations are considered as shown in Table 2. Anything with a dimension
(“Dim.”) of 2 implies an axisymmetric (AS) approach. The model simulations in Table 2 are
separated into groups of geometries (“Geo.”) and flow conditions (“IG Flow” and “IG Feed”).
For example, all Case “A” simulations involve low IG flow with geometry 1. B2 is for geometry
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1 and a low flow that is modulated at the dominant tone, and so on. Some simulations have
multiple purposes; an important purpose is shown in the table for each, but space constraints do
not permit every reason to be listed. These cases can be paired in different combinations to
isolate effects. Various items in the “Purpose” column will become more evident in the
discussion. Most of the simulations are AS since it can serve as a valuable scoping tool and is
much less time-intensive. The significant AS disadvantage, however, is that any shed droplets
are not accurately modeled as “droplets” per se. Since the geometry wraps uniformly in the
azimuthal dimension, each droplet remains a uniform torus shape. In reality, sheet perforations
(caused by velocity curl and turbulence) and radial sheet thinning cause the ligaments to break
up azimuthally. The purpose of having 2-D and 3-D models, which are not perfectly equivalent,
in the same article is that they give different insights. In 2-D models, acoustics and ligament
formation mechanisms can be explored closely and quickly, while incompressible 3-D models
allow preliminary droplet size information to be extracted. Dimensionless groups which govern
the flowfield are shown in Table 3. There are two IG flows considered in this work. The “low”
and “high” flow rates refer to the inner gas (IG) flows resembling “FC3” and “FC5”,
respectively, from Strasser [28]. Strouhal numbers in Table 3 are based on a single dominant
tone of 200 Hz. As will be evident, not all simulations show the same dominant tone, but a
general basis is desired for establishment of the Strouhal number. The lack of specificity around
Strouhal number is the reason it is only assigned 1 significant figure. For both IG feed rates, the
gas/liquid density ratio Z is 0.0012, while the liquid-based Re, Q, Oh, St, and We are 1.3 × 105,
1.1 × 10−8, 6.8 × 10−4, 3.3, and 0.0076, respectively.
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2. Numerical Methodology
2.1 Governing Equations and Numerics
In order to represent the multiphase flow of the three-stream injector, continuity
equations for the mass balance of each phase are used. The momentum equations employed are
for the phase-averaged Reynolds-average (RANS) formulation. Also, the phase-averaged energy
equation is used. Air is assumed as an ideal gas and liquid compressibility is ignored. The
homogeneous shear stress transport (SST) two-equation linear eddy viscosity model of Menter
[30] with acoustic corrections is used for computing the turbulent contributions to momentum
and energy transport for nearly all of the cases presented herein. Note that this method is
appropriate for systems in which typical liquid length scales are larger than the computational
cells and not vice versa [31]. The computational method has been extensively discussed and
validated in detail in [21, 28]. The explicit piecewise linear geometric reconstruction scheme
by Youngs [32] is used as the time-marching scheme to solve for the location of the sub-grid
scale (SGS) liquid-gas interface. Pressure-velocity coupling is coordinated via the Pressure
Implicit with the Splitting of Operators (PISO) scheme, while a Green-Gauss node-based
gradient method is used for discretizing derivatives. The pressure field is treated with a body-
force weighted approach to assist with body force numerics for all simulations. Second-order
upwinding is used for advection terms, and first-order upwinding is used for turbulence
quantities, which are dominated by source terms, and for the transient terms. Typical globally
averaged Courant number based on fluid velocity remained below 0.5 throughout the
simulations.
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2.2 Mesh and Boundary Conditions
The base mesh (Figure 1 [21]) contains about 32,000 elements per cross-section with
approximately 30 cells radially spanning the liquid annular gap. Each mesh was constructed
carefully in 2-D and 3-D in order to avoid having any triangular-faced cells due to their known
inferiority [33, 34]. More on the meshes will be offered in the pertinent discussions. Known
temperatures, flow rates, and properties are supplied at the three independent stream inlets.
Typical area-averaged y+ values on all exposed inner walls were near 10, and those values near
the water annular gap were 3 times that. All fluids leave the domain at the bottom and sides,
which are pressure-outlets. Outlets are treated as “openings”, at which flow can move into or out
of the modeled domain.
3. Results and Discussion
3.1 Overall Metrics Presentation and Discussion
A broad description of the metrics used to compare model outputs will open the
discussion. The results for all metrics for all simulations can be found in Table 4 through Table
7. Table 4 provides all IG and OG pressure results, Table 5 involves all video analysis “shoulder
distance” results (a measure in AS simulations of how far away from the injector face the
predominantly 2-D ligaments burst back towards the face) and spectral alignment ratios
(described in the next paragraph) between the pressure and shoulder data. Time-averaged spray
angle measurements for the simulations that involved a large enough run time in order to assess
the angle are given in Table 6. The “Mean” is the temporal average, while the Coefficient of
Variation (COV) of any quantity is simply its standard deviation divided by its mean multiplied
by 100 and is a measure of the fluctuation energy. The “Tone” is in units of Hz and refers to the
dominant frequency, which is not necessarily the fundamental frequency (lowest detectable
9
frequency peak); the dominant tone is sometimes a higher harmonic multiple. “Mag.” refers to
the FFT magnitude and indicates how focused the frequency spectrum is at the dominant tone. A
more focused spectrum will contain a larger fraction of its fluctuating energy at the dominant
tone, producing a higher magnitude for that tone. Both the tone and mag. are quantified using a
FFT algorithm. Spectral alignment refers to the particular signal tone and magnitude compared
with those of another signal. Tones and magnitudes of two signals are compared in ratio form
where a value of unity indicates alignment. The premise is that if the source(s) and
mechanism(s) of two instabilities are the same, then the transient signature measures should be
similar. The extent to which various metrics in this work are tied to the pressure fluctuations,
i.e., how much control one has of these by manipulating the pressure response, is of industrial
value. For all signal ratio tabulated values (Table 5), the inner (I) and outer (O) pressure
components are used in the numerator and designate the subscript. Λ is the ratio of the pressure
tone to shoulder tone, and Γ is the ratio of pressure magnitude to shoulder magnitude. More on
each of these metrics can be found in Strasser [28]. The shoulder distances have been
normalized by the nozzle outer diameter. Any pressures are actually pressure drops throughout
the entire feed sections of the inner and outer gas passages and have been normalized by the
nozzle discharge pressure.
Table 7 shows all droplet length scale information (“Mean” is in units of mm, spatial and
time average) from the 3-D simulations and spectral alignment ratios between pressure and
droplet size signals. In spite of the inability to measure droplet size in the air-water test stand
(AWTS) discussed in Strasser [28], preliminary droplet length scale information has been
extracted from the 3-D models. In order to do so, the following procedure is utilized at the time-
step level and has been validated in [21]. First, control volumes are drawn to contain axial
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segments of the 3-D modeled domain downstream of the nozzle outlet. Then, the total liquid in
each control volume, along with the total interfacial area, is computed. Although it is obvious
that many of the ligaments and fragments are not spherical in the modeled domain, an equivalent
mean spherical “diameter” is finally computed and used as a length scale reference. The
resulting droplet size as a 1-D function of axial location will be shown herein, but the spatial
mean of all axial slices is shown in Table 7. ϑ is the ratio of pressure tone to droplet length scale
tone, and Ξ is the ratio of pressure mag. to droplet length scale mag.
3.2 Effects of Geometry
Here, axisymmetric cases A20, D2, F2, G, H2, I, J2, and K2 are compared, all having low
IG flow rate. The only change is the geometric configuration as noted in Table 2. Retraction,
LRI, was the single largest factor to affect the results. At the same time, however, it is noted that
retraction was the factor whose tested range of variation was the greatest. From an industrial
standpoint, retraction is the simplest to test in the field via relatively simple mechanical design
changes.
Moving from base geometry 1, case A20, to a flushed (LRI = 0) geometry 2, case D2,
creates a substantial change in acoustic character as is shown in Table 4. The IG fluctuation
(COV = 67) increases to the highest of all the simulations in the geometry comparison, and
pressure drop decreases to the lowest (Mean = 0.14). The OG spectral focus is reduced, and its
dominant tone decreases to its fundamental (Tone = 230). Also, the OG COV is approximately
halved compared to case A20. It is counterintuitive that the OG fluctuations would fall when the
IG fluctuations increase. The shoulder distance (Mean = 0.57) increases to the largest value of
all the geometry test simulations (indicating that the spray is bursting farthest from the face), and
its COV is reduced to the lowest value of the group (Table 5). The shoulder dominant tone
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decreases to its fundamental tone (Tone = 240). As seen in Table 5, case D2 shows more
alignment between the pressure and shoulder signal spectra than A20, with values closer to unity.
Table 6 shows a massive increase in spray angle, in fact, to the largest value in the
geometry comparison group. Time-averaged spray patterns at 2.5DO from the injector are
provided in Figure 1. Only those cases for which there was enough data to time-average are
shown here; in some instances not enough time was available. More about the development of
these profiles can be found in found in Strasser [28]. The case D2 profile departs significantly
from the base case, becoming much more tri-modal in nature.
When the retraction is increased to the largest value tested (LRI = 1.3) in case F2 (and tLI
is increased to the largest value tested), a different kind of shift is seen and not necessarily
opposite in direction with those that occurred with the flushed design (case D2) shown in Table
4. The IG mean pressure increased to the highest in the geometry test group, its fluctuations
increase to the second highest, and its tone reduces to the lowest (consistent with Tian et al.
[35]). The inner mean pressure is found to be linearly proportional to retraction as shown in
Table 8, Eq. (a). Interestingly, opposite ends of the retraction test range produce high IG
fluctuations (but at different tones). In addition, the IG spectrum becomes the most focused of
all simulations in this geometry comparison. The OG fluctuation increases some, and its tone is
the lowest of the geometry comparison simulations. Its OG spectral focus also fell. It is
interesting to consider how the spectral changes compared to those of Fuster et al. [13]; the fact
that a thicker inner lip produced a more focused IG spectrum and a less focused OG signal
implies that the physics in the current work are clearly different. Other, stronger forces are at
play. The shoulder distance (Table 5) increases to the second highest in the geometry test batch,
and its tone is the lowest. Moreover, its spectrum is the least focused. Table 5 shows that there is
12
less alignment between the pressure and shoulder spectrum than for A20, with the IG magnitude
ratio (ΓI = 11) being the highest of those in this section. Little change in seen in the spray angle
as depicted in Table 6, but Figure 1 shows a much more diffused spray pattern.
Besides inner mean pressure, other variables respond linearly to the level of retraction,
shown as equations in Table 8 for cases A20, D2, and F2. Equations (a)-(e) represent all
variables which correlated with a coefficient of determination R2 > 0.85, sorted in descending
order. To have an idea of the sampling variability about each data point, see the third column of
Table 4 for each IG COV. For example, A20 shows an inner gas pressure drop of 0.27 ± 16%.
Many variables are seen to correlate with retraction, showing its dominating effect. Notice,
specifically, that the shoulder distance measure mean (Table 5, 2nd column) does not show up
here while its spectral focus (SH Mag.) does. It should be noted that only three retraction cases
were available for the correlations, thus, the most realistic fit is linear. Suggesting a quadratic or
polynomial fit would be meaningless for the data available. There may very well be strong
quadratic responses in some variables that could be found using more retraction tests. Figure 2
shows an example of the pressure correlation, which likely would not show a significant
quadratic response given more data.
An explanation for the effect of retraction (case F2) on pressure drop can be found in
consideration of Figure 3, which shows liquid volume fraction contours (blue = water) on the
left. Shown on the right are pressure contours colored from blue (base pressure minus 50kPa) to
red (base pressure plus 50 kPa). Two different times are shown where the bottom row is at a
later time than the top row. The inner fountain is seen holding its position during the time
sequence whereby liquid bridging across the nozzle axis blocks the gas flow. After the bridge
forms, pressure continues to build. Eventually, the pressure rises to the point at which the gas
13
and liquid break through and rupture the bridge. Obviously this blockage does not occur all the
time, but it occupies a relatively large space and time when compared to the less retracted
geometries. The increased space for pre-filming in the retracted designs gives the liquid more
space to spread radially and to intermittently cover the entire cross-sectional area. The bridge
apparently has a larger prominence for retracted designs, versus the base design, in terms of its
duration in time and spatial occupancy.
When the effects of retraction are compared with those found by Kim et al. [14] a similar
effect can be seen. Since they did not perform a test for a flushed condition, only case A20
versus F2 here can be used for directional comparative purposes. Dramatic reductions in the
pressure pulse frequencies are shown in the present work. When LRI increases from 0.60 to 1.3,
the IG fundamental tone reduces from 200 to 78 (Table 4), while the OG fundamental tone
reduces from 200 to 120 in Table 4. It should be noted that the FFT results show that the
dominant tone of 600 Hz for case A20 is a higher harmonic of the fundamental tone of 200 Hz.
In terms of orders, both of these fundamental tones were approximately halved, like what was
found in [14]. Also, IG and OG fluctuations in the present work both increase with increasing
retraction as did [14].
Further insights into interfacial behavior can be ascertained by considering Figure 4 and
Figure 5. Each figure shows two random snapshots of liquid volume fraction contours (blue =
water) with superimposed velocity vectors (longest vector = Mach ~ 0.6); the right pictures
represent random later times in both figures. Figure 4 illustrates the flushed design (D2), while
Figure 5 depicts the fully retracted design (F2), both for low inner gas flow. In Figure 4, it is
obvious that the flushed layout permits the inner and outer instability to work in harmony. White
arrows point to where the instabilities from the inner gas and outer gas push and pull
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simultaneously to promote regular patterns of thinning annular liquid sheets for the bulk of the
liquid phase. This will be referred to as “constructive interference”. The upper arrows show a
varicose response (radially pulsing), while the lower arrows show more of a sinuous response
(wave formation). The green square on the left-hand side outlines a counter-clockwise
recirculation region between the fingers of the liquid layer as discussed in [2] and resembles the
mixing cell between gear-pump teeth presented in [34]; an expanded inset has been included.
Droplets (though not truly droplets) dislodge from the inner interface by RTI downstream of the
nozzle outlet are captured in the landscape rectangle. The portrait rectangle illustrates the fact
that the outer gas instability generates ligaments at a higher frequency than the inner gas stream;
there are two outer fingers for only one inner finger at a later time. Evidently, the inner and
outer harmonious behavior is somewhat asynchronous.
Figure 5 on the other hand, depicts an extremely different behavior. The inner and outer
instabilities are highly out of sequence, which will be referred to as “destructive interference”.
The inner flow instability produces long wavelengths in the bulk of the liquid phase, while the
outer flow instability produces short fingers (in the square). The white arrows show the slowly
thinning cylinders (versus annular sheets for the flushed case) on the injector axis. RTI cause
droplets to separate from the inside interface (portrait rectangle) well upstream of the nozzle
outlet.
The effect of retraction is again tested, but this time at a lower meeting angle, γ. When
comparing case A20 to H2, differences are noted. In regards to pressure responses, the only
noteworthy effects are the reduction of the IG magnitude from 0.41 to 0.24, which is the lowest
value, and the increase in the OG fluctuation energy to the highest AS value (COV = 8.6) among
the geometry comparisons in Table 4. The shoulder distance (Table 5), however, gives a
15
surprising result. The mean actually drops to nearly the lowest value in the current data set, and
the spectrum is less focused. A close resemblance between H2 and A20 is shown in Table 6
with respect to spectral alignment. A small increase in spray angle is noted from Table 6, but
Figure 1 confirms that the angles and shape are similar. An unexpected observation from this
study of retraction permutations is that the base case is at a local minimum in regards to shoulder
distance and IG fluctuation energy, but only when γ is at its base setting. There is a very strong
interaction between outer stream meeting angle and retraction.
Increasing outer stream meeting angle γ at a moderate retraction is tested with case G.
The OG fluctuating energy (COV = 2.1) was approximately halved compared to case A20 (COV
= 4.3), its dominant tone was reduced to its fundamental (Tone = 200), and its magnitude is
significantly reduced (Table 4). The bursting shoulder extends some, and its dominant tone is
reduced to its fundamental (Table 5). In addition, there is a better alignment between the
pressure and shoulder spectra. Table 6 reveals nearly no change in spray angle, which is why its
spray profile is not included.
Another way of interpreting these outer stream meeting angle results is by comparing the
trends between cases A20, D2 and H2. Increasing angle at a moderate retraction produces little
change, but increasing the angle at a flushed condition (cases D2 and H2) produces a much
larger change, significantly widening the tri-modal pattern. This implies that a steeper approach
(forcing the streams more radially inward) actually widens the spray pattern, which is
counterintuitive. Apparently, a steeper approach imparts more radial bursting energy and widens
the spray. It also nearly doubles the shoulder distance, making the shoulder distance
proportional to the meeting angle. A substantial interaction between retraction and meeting
angle has continued.
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Changes in other variables will be highlighted next. Their effects are not as pronounced,
and only those items worth mentioning will be included. If the outer gas annular gap is increased
(A20 to I) only minor differences are detected. The IG and OG tones match, and the OG
spectrum becomes the most diffused of the geometry test cases (Table 4). There is a slight
increase in shoulder distance, the dominant tone reduces to its fundamental, and its magnitude
decreases (Table 5). The alignment between the pressure and shoulder spectra is nearly the
worst of the geometry cases, particularly the tones which differ by a factor of 3. Nozzle diameter
effects are studied with cases J2 and K2, although the effects of DI and DM cannot be separated at
this time. The outer gas stream has the highest frequency when all three diameters are at their
highest, but the most fluctuation when the angle and retraction are at their lowest (as previously
discussed). For K2, the OG tone is 4 times the IG tone, instead of 3, and the IG tone reduces
from 200 to 180. The OG energy is lowest when DO is high and the other diameters are low.
This makes sense in that a larger open area produces less shear stress. Conclusions regarding the
effects of diameters depend on the combinations of diameters. A striking result is that the lowest
shoulder distance (and most focused spectrum) in the group is case J2. This implies that the
shoulder distance might be tied to the OG pressure fluctuation energy (shear rate), holding
everything else constant. K2 held the highest shoulder COV, along with the highest ratio
between the OG and shoulder tones (similar to the OG versus IG tone issue already mentioned).
The final item worth mentioning is that K2 exhibits the highest ± 30% liquid collection value in
Table 6 without a spray angle change, and the inner peak is higher as illustrated in Figure 1.
Also, the higher outer diameter in J2 shows an increase in angle (opposite of Srinivasan et al.
[20]), but that angle is reduced again when all diameters are increased in case K2.
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3.3 Effects of IG Flow on AS Simulations
The effects of a near doubling of the IG flow will be presented through a study of cases
A20, C16, D2, and E2. The setup, geometry, and metrics for these simulations can be found in
Table 1−Table 7. Considering geometry 1 (A20 versus C16) an increase in IG flow produces
consistent effects on the pressure signals as is shown in Table 4. We see a rise in IG mean (as
expected), a slight reduction in IG COV, a slight reduction in OG mean, a significant increase in
OG COV (more energetic), and a significant decrease in OG tone. The reason a rise in IG mean
can be seen along with a fall in OG mean is due to the fact that some of the outer gas is displaced
to the inner flow passages, such that the total gas is the same. It is unusual to think that the OG
COV would rise when less gas is being put into the outer annulus, but there are obvious strong
stream interactions. The increase in inner gas frequency and decrease in outer gas frequency is
consistent with the studies of Kim et al. [13], Tian et al. [13, 35] and Zhao et al. [36] when their
proposed relationships are framed for inner and outer gas flow conditions and geometries.
For geometry 2 (D2 versus E2 in Table 4), there is a similar increase in IG mean pressure
(as expected), an increase in IG tone, a slight reduction in OG mean pressure, and an increase in
OG magnitude. OG tones do not change significantly. In short, the pressure field responses to
changes in IG flow rate depend on the geometry in terms of both magnitude and direction.
Shoulder distances (Table 5) show consistent responses between the two geometries.
Both showed a reduction in the means, indicating a closer bursting of the spray nearer the face,
which is consistent with [36]. Both COVs and magnitudes increased, but the tones did not
change substantially. The alignment between the pressure and shoulder spectra didn’t change
much for geometry 2, but geometry 1 showed mixed changes; the inner and outer ratios moved
in opposite directions.
18
Time-averaged spray angles are addressed in Table 6. For geometry 1, increasing the IG
significantly widened the spray; for geometry 2, not much changed. The liquid volume profiles
are compared in Figure 6 and Figure 7. In Figure 6, it is seen that the spray patterns widen and
become less centrally peaked at higher IG flows (case C16) for geometry 1. For geometry 2,
Figure 7 shows that the profiles are centrally peaked with no obvious effect of higher IG flow.
3.4 Effects AS Flow Modulation
Clearly, the flow is already pulsating by the very nature of local instabilities. Farago and
Chigier [19] explain that all atomization flows are pulsating to some extent, but we refer herein
to global large-scale pulsations which affect the atomization boundary conditions. The influence
of imparting an additional sinusoidal forcing function onto the flows is investigated. The present
work involves liquid Strouhal numbers in the modulated case of around 3. Srinivasan et al. [20]
proposed that Strouhal numbers this high would result in damped pulsations, which is clearly not
evident here.
The study was carried out on geometry 1, case A20 versus B2, with a low IG flow pulsed
at the typical dominant tone, 200 Hz, of the base case with a flow variation of ± 50% of the mean
(Ω=0.5). The pulsations were superimposed on an ongoing model. In other words, there was no
intended synchronization between the natural pulsation and the imposed pulsation. One might
consider that the flow realizations in the modulated case were “reset” by the onset of such large
pulsations. Upon examination of Table 4, little difference is detected in the OG; however, there
are a couple of noteworthy responses for the IG. The tone increases three times from its
fundamental tone of 200. Various sensitivity tests (not shown) have taught that the movement of
the peak among the various harmonics of 200 Hz is very sensitive, so this may or may not be
represent a major shift. Almost nothing changes for the shoulder metric (Table 5), except a mild
19
reduction in magnitude, and there are no detectable changes in the spray diameter metrics. There
may be a slight reduction in spray angle, which is the opposite of the effect seen by Srinivasan et
al. [20]. Although the measures in Table 6are not distinctly different, the time-averaged spray
profiles (not shown) are slightly more center-peaked for the modulated cases, implying more
energy is given to the center jet.
3.5 Intermediate Pressures
Most values in Table 4 represent the pressure drops across the entire inner and outer gas
flow paths, but it is also desired to consider the transient responses of pressures near the
locations where the liquid and gas streams meet (pre-filming). For both gas streams the
intermediate measurement location is about one DO upstream of the two-phase interface location.
When considering A20 versus A21, it can be seen that the intermediate data exhibits a similar
transient signature as the overall pressure drop data sets. All intermediate means are slightly
lower, as expected. The other differences are not profound, except for the increases in OG COV,
which imply the pressure variability is less near the inlet than near the pre-filming section. The
dampening of the signal farther away from the source is intuitive, and the tones are all the same.
3.6 Effects of AS Mesh Resolution
An evaluation of mesh resolution with geometry 8 (K3 versus K2) is considered by
increasing the cell count by a factor of 4; all cell dimensions are halved in both directions. No
other numerics are changed, so the global CN rises accordingly for the more resolved run. The
larger CN is not a problem due to the fact that the triple time step case is consistent [21]. Based
on the results, the pressure signal response is mixed, where the IG dominant tone becomes the
2nd harmonic, and the OG dominant tone is the 2nd instead of the 4th harmonic. In addition, the
OG COV and magnitude nearly double. The primary change in the shoulder metric includes a
20
10% drop in the mean should distance, a jump in the tone to the 2nd harmonic, and the halving
of the shoulder distance fluctuating spectral focus (“Mag”.) Shoulder-pressure tone alignment
improves, while magnitude alignment reduces. In Table 6, a significant increase in spray angle
is notable, and the liquid collection profile (not shown) displays a much more diffused curve.
Apparently increasing grid refinement allows the liquid jet to spread faster than in the base mesh,
and is consistent with Chesnel et al. [3] who showed breakup was delayed when using a coarse
mesh. Mesh effects on atomization might be non-intuitive as is discussed in [29].
3.7 3-D Models
Two 3-D models are examined in order to assess 1) how a 3-D model compares to its AS
conjugate and 2) the effects of inner gas flow rate in 3-D. All 3-D models are run as
incompressible with truncated inlets. This work began years ago, and Strasser [28] describes
how the 3-D models were not solvable in a transonic framework. Since all of the 3-D
simulations are incompressible and truncated, the discussion will begin with a comparison
between 3-D (A6) and AS (A18) model types at low flow rates. To produce a 3-D mesh, the AS
face was swept in the azimuthal direction, producing a wedge shape, and periodic boundary
conditions were applied. A6 utilizes geometry 1 with a 45° included angle, meaning 1/8th of the
nozzle circumference is considered with truncated inlets. A18 involves incompressible flow
with greatly truncated inlets in order to make it directly comparable to the 3-D cases and is more
fully explored in [21]. Even though the real geometry is axisymmetric, the flow is not
axisymmetric on an instantaneous basis [37, 38]. As a result, periodic boundary conditions are
applied to the azimuthal bounding faces. Two types of hexahedral methods are considered for
the near-centerline region for the 3-D meshes. The first is quad-pave, which results in higher
quality cells, but fewer are in the cross-section. The second is tri-primitive, which results in a
21
few lower quality cells (specifically with regards to skewness and centroid shift), but offer more
resolution. The latter is typical for our work. It is found that the quad-pave method produces a
mesh that damps the bulk pulsations, so it was abandoned. The individual stream flows are
given ample space to develop, in terms of velocity and turbulence distribution, but acoustics are
neglected.
Table 4 can be used to show that the 3-D model mimics its AS conjugate. The mean
pressures and other metrics are very close. Noteworthy is the major reduction in the focal nature
of the OG pressure spectrum (“Mag. dropped from 0.82 to 0.56) when moving from AS to 3-D.
This follows logic, given that azimuthal perturbations in the liquid sheet should diffuse the
pressure pulsations being fed back and forth in the outer gas feed chamber.
Analyzing the 3-D model for the high IG flow of case C17, typical spray patterns can be
seen in Figure 8 and b for two uncorrelated samples in time. Flow is from top to bottom. The
metal of the inner nozzle is colored in black near the top of the figure. The outer nozzle is not
shown, as it would block the view of the inner liquid layer development; however, it exists at the
top of the outermost liquid layer. The air is encompassed between the two visible surfaces of the
liquid sheet. Notice the rich spray pattern forming in multiple radial layers, shedding off in rings
and droplets. The reason for showing two snapshots in time is to illustrate the various
manifestations of interfacial instabilities throughout the primary atomization cycle. Though this
is an incompressible simulation, the spray surface itself is shaded by Mach number from blue
(0.0) to red (~0.3 and above). Black arrows in both frames capture the regions of relatively high
Mach number. On the left, it can be seen that four areas are being accelerated to near Mach 0.3.
Interestingly one of the fastest regions is the innermost contracted cylindrical layer of liquid near
the top of the frame. Other areas include the three sets of rims of liquid outer layer, two of which
22
are near the outset of outer liquid layer instability. Not shown in the left frame due to space
limitations is the widespread spray of droplets, which justify the naming of the spray shape as a
“Christmas tree” pattern discussed in detail in [28]. In the right frame, which illustrates a very
different part of the cycle, high speed areas are similar near the outset of outer liquid layer
instability. Additional high-speed areas are shown as fragments are shed from the contracted
liquid layer near the center of the frame and the rim of the liquid sheet near the bottom of the
frame back behind the ring of fresh droplets. The purple dashed arrows in the right frame
identify the substantial radial bulging of the inner liquid layer at a latter part of the cycle;
fluctuating radial bulging of the outer liquid layer is seen in both frames as well.
Table 4 offers the effects of increasing IG flow for the 3-D model (C17 versus A6).
Higher IG mean pressures, a mixed change in COVs, higher tones (like the AS work), and
increased magnitudes are observed. More information can be extracted from Table 7 showing
the computed droplet length scale statistics, averaged throughout the domain in space and time.
At the higher IG flow, the mean shifts downward, implying a more energetic spray. Also,
magnitude decreases with increasing IG flow (opposite of the pressure signals). The downward
shift in droplet size is shown more clearly using plots of the time-averaged mean droplet size
across the 10 axial segments as displayed in Figure 9a (raw) and b (normalized). The axes refer
to the distance from the nozzle normalized by DO. Interfacial length scale reduction with
increasing IG flow (Figure 9a) is greater closer to the nozzle. A larger departure is shown near
the nozzle face, while close matching is apparent at higher distances. In other words, the scale
diffusivity ([39]), i.e. rate at which the length scales fall with distance, is greater at lower flow
rates. In Figure 9b, the droplet diameter is scaled by the distance from the nozzle outlet. An
equation of the form 0.35x-1.2 fits both data sets well. This fit is not dramatically different than
23
the fit of 0.36x−1.3 found in [21] for a very different nozzle and set of conditions that were used to
simulate a non-pulsatile two-stream injector involving air and non-Newtonian slurry. Note that
in Figure 9a, the vertical “error” bars correspond to the temporal sampling variability (COV) of
each point; the COVs for these data are about twice of those from 3-D simulations in [21]. This
is indicative that the atomization mechanism for this three-stream pulsatile injector is more
energetic than that of a two-stream system. Lastly, Table 7 gives the spectral alignment between
the droplet size signals and the pressure signals. There is exact tone alignment, but the
magnitudes are slightly lower (in the same order) for both flow rates. The risk of the computed
droplet size being dependent on mesh resolution is known and is carefully addressed in [29].
Conclusions
Sixteen unsteady injector models have been executed in order to study the effects of
nozzle geometry, grid resolution, modulation, and gas flow rate on the self-generating pulsatile
spray produced by an industrial scale three-stream coaxial airblast reactor injector. Both
axisymmetric and 3-D models have been considered. Metrics included inner and outer gas
stream pressure pulsations, transient shoulder distance, time-averaged spray angle, transient
droplet length scale (3-D simulations) at various locations, and the spectral alignment among
these.
There were strong interactions between geometry and inner gas feed rate. Particularly,
inner nozzle retraction and outer stream meeting angle were intimately coupled. Results were
not directionally consistent in their dependence on flow rate for all design combinations. For
example, stream pulsations and the spray shoulder measure were only at their peaks for a flushed
design when the outer stream meeting angle was moderate. Inner stream dimensionless pressure
drop was found to be linearly proportional to dimensionless retraction (0.186LRI + 0.145). Other
24
correlations were given. Inner gas fluctuations were the highest for the flushed case and the next
highest for the fully retracted case, but the energy was focused at different tones for each of
them.
Higher inner gas flows typically widened all sprays for the base geometry only, brought
the shoulders closer to the nozzle outlet for both geometries tested, and lowered the droplet
length scales on the base geometry. Modulation of the inner gas at its dominant tone with a mass
flow variation of ±50% did not strongly affect many metrics. Shoulder distance was
proportional to outer stream meeting angle and might be tied to the outer gas shear field.
Moreover, the truncated, incompressible 3-D results did not always diverge from those of their
AS counterparts, which implies some hope in predictive power by running AS models as
surrogates. As with the two-fluid air-slurry atomization calibration work in prior work, the
droplet size (normalized by distance) versus distance (normalized by orifice diameter)
relationship took on the strikingly similar form of approximately 0.4x−1.2.
Acknowledgments
The support of a multitude of Eastman Chemical Company (named 2016 ENERGY
STAR® Partner of the Year - Sustained Excellence as well as a 2015 World’s Most Ethical
Company® by the Ethisphere Institute) personnel is greatly appreciated. Specifically, George
Chamoun, Josh Earley, Paul Fanning, Jason Goepel, Steve Hrivnak, Meredith Jack, Rick McGill,
Wayne Ollis, Glenn Shoaf, Andrew Stefan, Bill Trapp, and Kevin White were supporters of this
effort. George Chamoun and Jason Goepel deserve special recognition for developing video
analysis tools, constructing UDFs, and processing on the order of 1000 transient signal data sets
using various methods. Additionally, discussions with Mihai Mihaescu from Royal Institute of
Technology (KTH), Marcus Herrmann from Arizona State University, David Schmidt from the
25
University of Massachusetts, Mario Trujillo from University of Wisconsin–Madison, Daniel
Fuster of Institut Jean Le Rond D'Alembert UPMC, and Christophe Dumouchel of Université et
INSA de Rouen were extremely beneficial.
26
Nomenclature
a Speed of sound
AS Axisymmetric
AWTS Air/water test stand
COV Coefficient of variation = standard deviation/mean*100%
DI Nozzle innermost diameter normalized by nozzle outer diameter
DM Nozzle intermediate diameter normalized by nozzle outer diameter
DO Nozzle outermost diameter normalized by the maximum outer diameter
E Total energy
f Frequency
F Surface tension body force
i Summation index
IG Inner gas stream
k Turbulence kinetic energy
KHI Kelvin-Helmholtz instabilities
La Laplace number = Re2/We = Suratman number
LAG Outer annular gap normalized by nozzle outer diameter
LC Some characteristic length scale
LRI Inner retraction length normalized by nozzle outer diameter
LS Should length, or spray lift-off, measure normalized by outer diameter
M Gas/liquid momentum ratio = (ρU2)G/(ρU2)L
Ma Mach number
OG Outer gas stream
Oh Ohnesorge number = We /Re = 1/
L
a
P Pressure; tabulated pressure drops are normalized by outlet pressure
Pr Liquid phase Prandtl number
Q Viscous capillary length
Re Reynolds number = ρUD/μ
RTI Rayleigh-Taylor instabilities
S Velocity ratio, UG/UL
St Strouhal number
SMD Sauter mean diameter (“D32”)
tLI Thickness of inner lip normalized by nozzle outer diameter
tLO Thickness of outer lip normalized by nozzle outer diameter
T Static temperature
u Velocity component
U Velocity magnitude
y+ ρuty/μ
We Weber number = ρU2LC/σ
Z Density ratio, ρG/ρL
Greek
α Phase volume fraction
ε Turbulence dissipation rate
27
Ω Modulation ratio
σ Surface tension
ρ Density
ω Specific dissipation rate
τ Stress tensor
γ Outer gas/liquid annular approach angle normalized by maximum value
μ Molecular viscosity
ζ Molecular thermal conductivity
Λ Ratio of the pressure tone to shoulder tone
Γ Ratio of pressure magnitude to shoulder magnitude
ϑ Ratio of pressure tone to droplet length scale tone
Ξ Ratio of pressure magnitude to droplet length scale magnitude
Subscripts and Superscripts
L Liquid
G Gas
t Turbulent
ref Reference condition
I Inner gas
O Outer gas
28
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31
List of Tables
Table 1. Geometry permutations
Table 2. Simulation Matrix
Table 3. Dimensionless groups at low and high inner gas flows
Table 4. Inner and outer gas pressure drop statistics
Table 5. Shoulder distance metric and ratio of pressure drop signal statistics to those of the
shoulder distance metric
Table 6. Time-averaged spray angle measures for axisymmetric simulations
Table 7. Time-averaged spray angle measures for 3-D simulations
Table 8. Summary of retraction correlations for low IG flow axisymmetric simulations (Cases
A20, D2, F2)
32
Table 1. Geometry permutations
Geo. Cases Purpose LAG LRI tLI tLO γ DI DM DO
1 A,B,C Base 0.097 0.60 0.038 0.0144 0.60 0.36 0.83 0.95
2 D,E Flushed 0.097 0.00 0.038 0.0144 0.60 0.36 0.83 0.95
3 F Retracted 0.097 1.3 0.17 0.0144 0.60 0.36 0.83 0.95
4 G High Angle 0.097 0.60 0.038 0.0144 1.0 0.36 0.83 0.95
5 H Flushed, Low Angle 0.097 0.00 0.038 0.0143 0.20 0.36 0.83 0.95
6 I Gap 0.10 0.60 0.038 0.0144 0.60 0.36 0.83 0.95
7 J DO 0.093 0.57 0.036 0.0138 0.60 0.34 0.79 1.0
8 K DI , DM 0.093 0.57 0.030 0.0136 0.60 0.35 0.86 1.0
33
Table 2. Simulation Matrix
Geo. IG
Flow IG Feed Case Mesh Dim. Purpose
1 Low Steady A6 Base 3 3-D
A18 Base 2 Trunc./Inc.
A20 Base 2 Base
A21 Base 2 Intermed.
1 Low Modulated B2 Base 2 Modulation
1 High Steady C16 Base 2 IG Flow
C17 Base 3 3-D
2 Low Steady D2 Base 2 Geo
2 High Steady E2 Base 2 IG Flow
3 Low Steady F2 Base 2 Geo
4 Low Steady G Base 2 Geo
5 Low Steady H2 Base 2 Geo
6 Low Steady I Base 2 Geo
7 Low Steady J2 Base 2 Geo
8 Low Steady K2 Base 2 Geo
K3 4X 2 Grid
34
Table 3. Dimensionless groups at low and high inner gas flows
Inner Gas Outer Gas
IG M S Re/100 St Ma M S Re/100 St Ma
Low 0.080 8.1 480 0.1 0.11 1.3 33 1000 0.01 0.44
High 0.28 15 890 0.05 0.21 1.1 30 960 0.01 0.41
35
Table 4. Inner and outer gas pressure drop statistics
Inner Gas Outer Gas
Case Mean COV Tone Mag. Mean COV Tone Mag.
A6 0.29 170 160 0.33 0.27 28 160 0.56
A18 0.28 190 170 0.39 0.27 24 170 0.82
A20 0.27 16 200 0.41 0.33 4.3 600 0.81
A21 0.26 14 200 0.47 0.31 5.9 600 0.83
B2 0.27 17 600 0.24 0.33 4.7 590 0.56
C16 0.45 14 530 0.65 0.32 6.2 270 1.2
C17 0.45 120 220 0.37 0.27 38 220 0.84
D2 0.14 67 230 0.54 0.31 2.9 230 0.38
E2 0.20 72 240 1.2 0.29 5.5 240 1.0
F2 0.38 29 78 1.0 0.31 7.5 120 0.39
G 0.30 14 200 0.49 0.35 2.1 200 0.37
H2 0.27 16 200 0.24 0.35 8.6 600 0.54
I 0.26 16 600 0.32 0.32 3.8 600 0.34
J2 0.24 16 210 0.56 0.24 1.7 210 0.44
K2 0.25 17 180 0.67 0.33 5.0 720 0.42
K3 0.26 18 380 0.72 0.32 8.4 380 0.92
36
Table 5. Shoulder distance metric and ratio of pressure drop signal statistics to those of the shoulder distance
metric
Case Mean COV Tone Mag. ΛI ΛO ΓI ΓO
A18 0.64 24 170 0.027 1.0 1.0 14 30
A20 0.33 47 410 0.31 0.49 1.5 1.3 2.6
B2 0.45 46 200 0.26 3.0 3.0 1.0 2.2
C16 0.38 60 260 0.61 2.0 1.0 1.1 2.0
D2 0.57 25 240 0.40 0.97 1.0 1.4 0.94
E2 0.46 42 240 0.83 1.0 1.0 1.5 1.2
F2 0.49 49 59 0.10 1.3 2.0 11 3.9
G 0.41 45 220 0.29 0.95 0.95 1.7 1.3
H2 0.29 55 390 0.18 0.50 1.5 1.3 3.0
I 0.38 46 200 0.20 3.0 3.0 1.6 1.7
J2 0.27 58 220 0.52 0.99 1.0 1.1 0.86
K2 0.30 59 180 0.27 1.0 4.1 2.5 1.6
K3 0.26 65 370 0.17 1.0 1.0 4.2 5.4
37
Table 6. Time-averaged spray angle measures for axisymmetric simulations
50% ±30%
Case Angle Liquid
A18 11 96
A20 13 68
B2 11 77
C16 35 50
D2 41 45
E2 48 41
F2 17 74
G 12 72
H2 19 67
I 13 80
J2 19 66
K2 13 84
K3 20 63
38
Table 7. Time-averaged spray angle measures for 3-D simulations
Case Mean COV Tone Mag. ϑI ϑO ΞI ΞO
A6 22.1 38 160 1.2 0.98 0.98 0.27 0.47
C17 16.6 34 220 1.1 1.0 1.0 0.35 0.79
39
Table 8. Summary of retraction correlations for low IG flow axisymmetric simulations (Cases A20, D2, F2)
IG Mean = 0.186 LRI + 0.145 (R2 = 0.99) (a)
OG COV = 3.54 LRI + 2.65 (R2 = 0.97) (b)
SH Mag. = −0.233 LRI + 0.419 (R2 = 0.96) (c)
IG Tone = -118 LRI + 244 (R2 = 0.92 ) (d)
± 30% Liquid = 21.7 LRI + 48.3 (R2 = 0.85) (e)
40
List of Figures
Figure 1. Time-averaged spray profiles at low IG flow showing effects of geometry from
axisymmetric simulations
Figure 2. Graphical depiction of Table 8, Equation (a) showing the effect of retraction on inner
gas pressure drop for low IG flow axisymmetric simulations (Cases A20, D2, F2)
Figure 3. Instantaneous contours (case F2) of liquid volume fraction (left) and pressure (right)
showing liquid bridge for fully retracted design from axisymmetric simulation at low IG flow.
The lower picture is extracted from a later time.
Figure 4. Instantaneous contours (case D2) of liquid volume fraction with superimposed velocity
vectors showing constructive sinuous and varicose type instabilities between the inner and outer
gas for the flushed design at low IG flow. The right picture is extracted from a randomly chosen
later time.
Figure 5. Instantaneous contours (case F2) of liquid volume fraction with superimposed velocity
vectors showing destructive instability between the inner and outer gas for the fully retracted
design at low IG flow. The right picture is extracted from a randomly chosen later time.
Figure 6. Time-averaged spray profiles from axisymmetric simulations showings effects of IG
flow for base geometry (1)
Figure 7. Time-averaged spray profiles from axisymmetric simulations showings effects of IG
flow for flushed geometry (2)
Figure 8. Instantaneous snapshots of uncorrelated 3-D spray surfaces (Case C17) colored by
Mach number (M=0 is blue, M≥0.3 is red) showing various stages of the primary atomization
cycle. Black arrows point to relatively high Mach number regions, and purple dashed arrows
identify the dramatic change in inner liquid layer radius
Figure 9. Axial droplet length scale profiles for 3-D simulations
41
Figure 1. Time-averaged spray profiles at low IG flow showing effects of geometry from axisymmetric
simulations
0
1
2
3
4
5
6
7
-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75
Liquid Volume [%]
Normalized Distance
A20
D2
F2
H2
K2
42
Figure 2. Graphical depiction of Table 8, Equation (a) showing the effect of retraction on inner gas pressure
drop for low IG flow axisymmetric simulations (Cases A20, D2, F2)
0
0.1
0.2
0.3
0.4
0.0 0.5 1.0 1.5
Dimensionless Pressure Drop
Dimensionless Retraction
Fi
g
ure
liquid b
r
3. Instantan
e
r
id
g
e for full
y
e
ous contours
y
retracted de
s
(case F2) of l
i
s
i
g
n from axi
s
extracte
d
43
i
quid volume
sy
mmetric si
m
d
from a later
fraction (left
)
m
ulation at lo
w
time.
)
and pressur
e
w
IG flow. T
h
e
(ri
g
ht) show
i
h
e lower pictu
r
i
n
g
re is
Fi
g
ure
showin
g
4. Instantane
constructive
s
desi
g
n at lo
w
ous contours
(
s
inuous and v
w
IG flow. Th
e
(
case D2) of li
a
ricose t
y
pe i
n
e
ri
g
ht pictur
e
44
quid volume
f
n
stabilities be
e
is extracted
f
raction with
s
tween the inn
from a rando
s
uperimpose
d
n
er and outer
g
ml
y
chosen l
a
d
velocit
y
vect
o
g
as for the fl
u
a
ter time.
o
rs
u
shed
Fi
g
ure
showin
g
d
5. Instantan
e
d
estructive in
T
e
ous contours
stabilit
y
bet
w
T
he ri
g
ht pict
u
(case F2) of l
i
w
een the inner
u
re is extract
e
45
i
quid volume
f
and outer
g
a
s
e
d from a ran
d
f
raction with
s
for the full
y
d
oml
y
chosen
superimpose
d
retracted des
i
later time.
d
velocit
y
vec
t
ig
n at low IG
t
ors
flow.
Figure 6
.
.
Time-avera
g
g
ed spra
y
pro
files from axi
s
ge
46
sy
mmetric si
m
e
ometr
y
(1)
m
ulations sho
w
w
in
g
s effects
o
o
f IG flow for base
47
Figure 7. Time-averaged spray profiles from axisymmetric simulations showings effects of IG flow for
flushed geometry (2)
0
2
4
6
-0.8 -0.4 0.0 0.4 0.8
Liquid Volume [%]
Normalized Distance
D2 (Low IG)
E2 (High IG)
Figure 8.
(M=0 is b
l
relativel
y
la
y
er radi
Instantaneo
u
l
ue, M≥0.3 is
hi
g
h Mach n
u
u
s
a
u
s snapshots
o
red) showin
g
u
mber re
g
ion
s
o
f uncorrelat
e
various sta
ge
s
, and purple
48
e
d 3-D spra
y
s
e
s of the pri
m
dashed arro
w
s
urfaces (Cas
e
m
ar
y
atomizat
i
w
s identif
y
th
e
b
e
C17) colore
d
i
on c
y
cle. Bl
a
e
dramatic ch
a
d
b
y
Mach n
u
a
ck arrows p
o
a
n
g
e in inner
u
mber
o
int to
liquid
49
(a) (b)
Figure 9. Axial droplet length scale profiles for 3-D simulations
5
15
25
35
45
0.0 0.5 1.0 1.5 2.0
Droplet Length Scale [mm]
Normalized Distance From Outlet
A6
C17
0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0
Normalized Droplet Length Scale
Normalized Distance From Outlet
A6
C17
