A BOUNDARY LAYER STRIPPING CFD MODEL FOR SHEAR REGIME

ATOMIZATION OF PLAIN LIQUID JETS IN CROSS FLOW

Sachin Khosla

D. Scott Crocker (corresponding author)

CFD Research Corporation

215 Wynn Drive, Suite 501

Huntsville, AL 35805

(256) 726-4812; dsc@cfdrc.com

ABSTRACT

A numerical model for liquid jet atomization in a subsonic gas cross flow has been developed

and incorporated into a CFD code. The model is designed primarily for shear breakup regime,

which is appropriate for many fuel injection applications. The model considers Weber number

and momentum flux ratio ranges that are dominated by either jet surface breakup or column

breakup. A boundary layer stripping model has been modified to account for both shearing from

the column and shear primary breakup of large drops. Further secondary breakup was modeled

with the Rayleigh-Taylor model. The effect of drop distortion on the drag is also considered.

Results of the model have been compared with experimental data for water jets in air cross flows

with varying jet velocity and air velocity. Comparisons were made for drop volume flux,

velocity, and size as a function of distance downstream of the injector. Trends were captured for

liquid penetration associated with varying momentum flux ratio, and for drop size as a function

distance from the wall. In general, agreement between measurements and CFD predictions were

quite good. Areas of disagreement could be reasonably explained by the model’s inherent

inability to capture the wake flow behind the liquid column.

INTRODUCTION

Liquid injection into a cross flowing gas stream is a method frequently used to atomize a liquid

and mix it with the gas. It is generally desirable to control the distribution of the liquid in the gas

stream and the size of the liquid drops. One of the most frequent applications is the injection of

liquid fuel in combustion systems. Cross flow fuel injection is common for afterburners as well

as some types of main burner injectors in gas turbine engines, and in ramjet and scramjet

combustors. Detailed characteristics of the fuel spray can have a strong effect on the overall

performance of the combustion system. Combustion efficiency, emissions, lean blow out, and

combustion dynamics can be directly affected by the fuel distribution, drop size (and resulting

evaporation rate), as well as the distribution of drop size as a function of location. Analytical

prediction of the spray characteristics is of considerable value to designers of combustion

systems. Considerable progress in understanding the complex mechanisms and regimes for the

atomization process has been made in recent years. A range of empirical prediction tools for jet

breakup length and trajectory are summarized by Wu et al. [1]. Most of the CFD work that has

been done to date has emphasized liquid jets in a co-flowing gas stream or liquid injection into a

quiescent gas such as Reitz [2] and Tanner [3, 4]. Recently developed CFD models for liquid jet

in cross flows of Zuo et al. [5] and Madabhushi [6] both utilized a modified version of the wave

breakup approach of [2]. Rachner et al [7] have also developed a CFD model which considers

liquid column dynamics, column breakup, dynamics of the jet fragments produced by the column

breakup, end of breakup criterion for the fragments, liquid stripping from the surface of the jet

and fragments, and dynamics of stripped-off droplets.

Mazallon et al [8] studied the primary breakup of a non-turbulent round liquid jet in subsonic gas

cross flow and reported qualitative similarities between the primary breakup of the liquid jets in

cross flow and the secondary breakup of drops, particularly in the shear breakup regime which is

of most interest here. For conditions where effects of liquid viscosity were small (Oh < 0.1), five

kinds of breakup regimes were observed as the cross flow velocity was increased: 1) simple

deformation of the shape and trajectory of the liquid jet with no primary breakup; 2) breakup of

the liquid column as a whole; 3) bag breakup; 4) bag/shear breakup; and 5) shear breakup. For

the shear regime, wavelike disturbances were observed upstream of the liquid column, but the

wavelengths did not develop into the nodes observed in other breakup modes. Instead, ligaments

were stripped from the periphery of the liquid column, very similar to the behavior of secondary

drop breakup in shear regime.

Ragucci et al. [9, 10] studied the effect of liquid jet injection into a high-pressure air cross flow.

This work showed that the jet evolution was significantly influenced by the onset of a stripping

atomization mechanism. Images of the spray indicate a “kidney” shape at only 2 mm from the

nozzle. This suggested that the stripping mechanism was very active on the spray border. This

mechanism was also found to promote the dispersion of the drops and generation of very fine

droplets. Becker and Hassa [11] studied trajectories, breakup, atomization and dispersion of a

kerosene jet with pressure ranging from 1 to 9 bars. The cross-section of the liquid jet was

strongly deformed into a crescent shape. Ligament formation at the tips of the crescent then led

to a gradual erosion of the jet. Two distinct mechanisms of jet breakup were observed: surface

breakup and column breakup. Surface breakup was characterized by shear stripping of liquid

from the surface of the jet. Column breakup’s main feature was the appearance of waves on the

windward surface of the liquid column, which were then amplified by aerodynamic forces

leading to fracture of the column in a wave trough. The onset of observable wave growth usually

coincided with an alignment of the jet with the direction of the airflow. Examination of the

breakup process suggested that both the surface and column breakup mechanisms were usually

active, but one was dominant, depending on the flow conditions.

One of the primary points to be taken from several of the studies on liquid column atomization is

that the breakup process for the column in the shear regime is similar to the breakup process for a

drop in the shear regime. This general philosophy has been applied to the model described in this

paper in that a boundary layer stripping model has been adapted for use in liquid column

breakup. Ranger and Nicholls [12] experimentally studied the influence of various parameters on

the rate and time required for breakup of a drop to occur. This was one of the first works that

brought out the concept of boundary layer stripping of mass from a drop in shearing flow. A

boundary layer analysis was developed for the drop in a convective flow field and the rate of

disintegration was calculated. Delplanque and Sirignano [13] furthered this work to obtain

critical drop Weber number criteria to predict drop breakup conditions. There have been many

studies of the breakup processes and regimes of individual drops, including Pilch and Erdman

[14], Hsiang and Faeth [15] and Chou et al [16]. This paper describes the atomization model,

which has been adapted for CFD application and compares the results of the model with the

experimental data of Wu et al. [1, 17]. Results for the model have also been compared with the

experimental data of Becker and Hassa [11] in a separate publication [18].

ATOMIZATION MODEL DESCRIPTION

The model is implemented entirely in a Lagrangian frame of reference so that even the

continuous liquid column is represented by discrete parcels of identical drops. For overall clarity,

the term ‘drop’ is used in the discussion below for either parcels or unique drops unless a

specific distinction between the two is required. This basic approach has been utilized by Reitz

and Diwakar [19] and others including more recently Madabhushi [6]. The discrete drops are

injected at the orifice location with diameter equal to the orifice diameter. The velocity of the

drops is determined from the liquid mass flow rate and the effective area of the orifice. Surface

shear breakup and column breakup modes are both included in the model. Before the column

breakup occurs, fragments may be formed by surface shearing as a function of the local We and

q. When the jet reaches the column breakup time, the jet immediately breaks entirely into

fragments. Fragments are then further broken up based on a modified Boundary-Layer Stripping

model [13] and [12]. A final breakup step is modeled with a Rayleigh-Taylor secondary breakup

model [20].

An important aspect of the model is that all gas phase properties, including velocity, are

calculated locally. Typical model equations are often a function of the bulk gas phase velocity,

ug, which is fine for most laboratory experimental conditions. However, real applications often

involve non-uniform free stream velocities where the definition of ug is not clear. Local

definition of ug makes this model more general. The local gas velocity is found from a group of

cells that are nearest the current drop, but with cell center at least two drop diameters away from

the drop location. The highest velocity magnitude is chosen from among this group of cells. This

type of approach can potentially introduce undesirable grid dependency to the solution if the grid

is small enough to resolve the liquid jet. However, the Lagrangian spray model here is assumed

to be dilute in that the volume fraction of the liquid is assumed small for all cells. So, grid

dependency introduced by using local gas phase velocity is no different from the inherent grid

dependency of typical Lagrangian dilute spray models.

The drag coefficient for the column is set to 1.7 based on the results of [1]. It is interesting that

this measured result is somewhat higher than the drag coefficient of about unity for a solid

cylinder and probably accounts for deformation of the column. The drag coefficient for drops is

further modified based on the Taylor Analogy Breakup (TAB) model for drop deformation [21].

Turbulence in the liquid at the injection location is not accounted for in the model.

Fragments are stripped from the liquid column if the Weg satisfies the following criteria:

15We

andqRe50We

g

81.0121g g

>

> −

where lσρ=

µρ=

gj2gg

ggjgg

duWe

udRe (1)

where Reg and Weg here are based on the gas velocity component normal to the liquid jet

direction instead of the relative velocity. The Re component of the criterion is taken from [13]

for stripping of droplets and is modified to account for the momentum flux ratio effect from [1].

If column stripping does occur, the amount of mass removed from the column is modified from

[12] as

t4dAu

t

td

43M rel

dshed ∆

παρπ=

∗l (2)

where, 31

g31

gA

µ

µ

ρ

ρ=

ll (3)

21

relAu38

ρ

µ=α

l

l (4)

g

go

u

dt

ρρ=∗ l

(5)

and where td is the lifetime of the liquid column drop. The addition of the factor t*/td causes the

shedding rate to increase essentially linearly with distance away from the injection location. This

accounts for the lack of shedding close to the injection location and the subsequent buildup of

shedding over the life of the liquid column. The shed drop size SMD is modified from [15] as

21

rel

41

g

21

d ud

tt1.3SMD

ρ

µ

ρρ

=∗

l

ll (6)

The t*/td factor is again included with the effect of producing smaller drops near the injection

location. However, t*/td is limited to a minimum value of 2.5 which is never exceeded for some

cases. The amount of mass shed is tracked and 10 new parcels are created when the cumulative

shed mass after a time step exceeds 1% of the mass of the parcel. The number of new parcels

was chosen to provide a reasonable distribution of drop sizes and velocities without resulting in

excessive computation. Madabhushi [6] used a cutoff mass of 5%, but the wave model breakup

mechanism used in [6] was very different than the model described here. The lower 1% cutoff is

designed to accurately capture even relatively small amounts of column shearing that can have a

significant effect on near wall drop distributions. Each parcel is allocated an equal amount of the

shed mass and the size for each new parcel is selected randomly from a uniform distribution

between 0.4 and 1.6 times the MMD. Note that the drop size distribution is not uniform since

parcels with smaller drop size have more drops than parcels with larger drop size. The drop

velocities were set loosely based on Chou et al. [16] as

( )( )pgpd uu2.0RND3.0uu −−+= (7)

( )( )pgpd vv2.0RND3.0vv −−+= (8)

( )( )prelpd wu5.0RND25.0ww −−+= (9)

Column stripping occurs, assuming the above criteria are met, until the column breakup time is

exceeded. Parcels created through the column stripping mechanism are considered to be

fragments which may undergo further breakup as discussed below. First, though, the column

breakup mechanism, which also produces fragments, is described. The liquid jet column breakup

time is calculated as

∗−= tWe25t 62.0b (10)

which is modified from Mazallon et al. [8]. The constant is about three times that found in [8],

however, it was found here that the larger value was required to avoid significant jet under

penetration. Furthermore, a minimum penetration length of six jet diameters was set, which

affects cases with low q. A likely reason is that the dilute spray model used here fails to capture

the effects of the jet wake on the penetration of the drops. It is also noted that the correlation

from [8] is for non-turbulent jets and indicates the onset of breakup rather than the completion of

breakup. For comparison, Wu et al. [1] gives a breakup time of tb = 3.44t* based on correlation

of experimental data, while the onset time given in [8] clearly shows a dependence on We as

shown in Eq. (10). Since the current model includes a fragment breakup step after the column

breakup, the We dependence for breakup onset is retained.

The column is broken into 18 new parcels with MMD = 0.45dj that are designated as fragments.

These fragments are generally still relatively large, so the ultimate drop size for the primary

breakup process is mostly determined from the fragment breakup process. The distribution of

sizes is the same as described above for column stripping. The cross flow and normal velocity

components are the same as Eqs. (7) and (8). The transverse velocity component is given by

( )( )prelpd wu5.0RND1.0ww −−+= (11)

Fragments are further broken into small drops according to a modified version of the boundary

layer stripping model for drops [13]. Breakup will occur if the following criteria are met:

15We

andReWe

g

g>>

where

greldgg

gd2relg

udReduWe

µρ=σρ= l (12)

These criteria are generally the same as for column stripping except that the dependence on q is

not needed. Also note that We and Re are now determined using the relative velocity instead of

the cross flow velocity. The mass shed from a fragment in a time step and the SMD are

calculated (similar to Eqs. (2) and (6)) as

t4dAud2.1M relshed ∆π

αρπ= l (13)

21

rel

41

g

21u

d6.3SMD

ρ

µ

ρρ

=l

ll (14)

where A and α are defined the same as in Eqs. (3) and (4). The new droplet velocities are the

same as given by Eqs. (7), (8), and (11). The broken fragments produce 3 new parcels with size

distribution the same as described above when the shed mass from the fragment exceeds 20% of

the fragment mass. A fragment can continue to breakup until it no longer meets the criteria of

Eq. (12) or until its size is less than the newly created drops. Once the fragment breakup process

is complete, drops may breakup further based on a Rayleigh-Taylor secondary breakup method

[20].

CFD MODEL DESCRIPTION

The boundary layer stripping atomization model has been implemented in the commercial CFD

code CFD-ACE+, and the results of the model are compared with the liquid jet in cross flow

experimental data of Wu et al. [1, 17]. The experimental conditions are briefly recounted here for

convenience. The tests were conducted in a wind tunnel with length 406 mm and 125 x 75 mm

cross section. Air axial turbulence intensity was about 3% in the center of the test section.

Numerous liquids were tested, though the available detailed flux, velocity and drop size

measurements from [17] are for water. The injector had a 45° taper leading to a straight section

with a length/diameter ratio of 4. The injector was designed to minimize the liquid turbulence at

the injector exit. Injector exit diameters of 0.5, 1.0, and 2.0 mm were tested. Liquid injection

velocities ranging from 8.8 to 42.5 m/s and cross flow air velocities ranging from 68 to 137 m/s

were investigated. The test section pressure was held at 140 kPa.

The 3-D CFD model utilized a simple Cartesian grid with 35,000 hexahedral cells, clustered near

the injection point. The number of cells for this simple geometry is relatively low because the

grid is representative of a realistic grid for complex geometry cases. Since the spray model

assumes dilute spray, it is important to realize that grid independence cannot be expected.

Indeed, an overly fine grid in the region of the injector can be expected to produce unrealistic

results to the extent that the dilute spray assumption is violated. That is not to say that the dilute

spray assumption is a good one. A clear conclusion of this numerical study is that the blockage

associated with the liquid column should be considered in order to capture important aspects of

the atomization and drop distribution process. The RNG k-ε turbulence model with wall

functions was utilized and the turbulence intensity at the inlet boundary was set to 3%. The

turbulent length scale at the inlet boundary was assumed to be 1 cm. This length scale was varied

and found to have minimal effect on the solution.

RESULTS

The CFD cases that were performed are compared with spray images from [1] and/or volume

flux, drop velocity, and drop SMD measurements [17]. The results presented here are for steady-

state computations, though the model can also be applied to transient flow fields. For each case,

the total number of parcels modeled was approximately 6000 to 8000. Since there was about 150

trajectory points for each parcel, there were approximately 1 million parcel locations. In most

practical application cases, the final requirement of the spray model is to predict the correct

source terms for the gas phase flow field. Such a large number of parcels will typically not be

needed to reach a point where the solution is effectively independent of the number of parcels

modeled. However, the large number of parcels was needed to produce ‘smooth’ drop field

results for comparison with experimental data. Good convergence of approximately four orders

of magnitude reduction of residuals was typically achieved in less than 100 iterations since the

geometry and flow field were not complex. As a result, computational time for a typical case was

about 30 minutes on a 2 GHz PC. Execution on parallel PCs, often needed for complex

geometries, was also verified.

Cross flow velocity contours for the case with water jet velocity of 19.3 m/s and cross flow

velocity of 103 m/s are shown in Figure 1. The reduced air velocity near the liquid jet is the

result of drag forces that result in source terms for the momentum equation, and does not include

any blockage effect of the liquid column. The dilute spray assumption results in a minimum

velocity of about 70 m/s. If liquid column blockage were considered, there would be a small

region of much lower, even negative, velocity behind the liquid jet.

Figure 1.

Two basic breakup modes for jets in cross flow with We generally in the shear breakup regime

have been identified [1, 11]. One is surface breakup dominated where droplets are stripped from

the liquid column surface, and the other is column breakup where the whole liquid core breaks

apart into ligaments and drops. Both modes may play a significant role in many cases. Both

modes are illustrated in the comparison of experimental shadowgraph images and CFD results in

Figures 2 through 4. It should be made clear that the CFD solution plot and the shadowgraph

image do not portray the spray in the same way. The shadowgraph insensitivity to low density

spray is emphasized by Lin et al. [22]. On the other hand, the CFD plot does not weight the

image based on the volume flux; that is a parcel is plotted based only on its diameter, not on the

overall mass of the parcel.

The case shown in Figure 2 is close to the borderline between the two modes as defined in [1].

This is the one case for which there are both shadowgraph images and quantitative PDPA

measurements (see Figure 6). The experimental image shows some droplet stripping from the

column surface, and it is likely that there is more stripping than the image shows since flux

measurements downstream indicate significant flux near the wall. It also appears that column

breakup plays a significant role. The CFD results are qualitatively the same in that there was

significant column stripping followed by column breakup. Note that the wave appearance in the

CFD plot on the upstream edge of the column is only an artifact of plotting individual parcel

locations. The case shown in Figure 3 is clearly in the column breakup regime and the basic

mode is correctly predicted by the CFD model, though the trajectory of the spray appears to be

slightly under predicted. A case that is clearly in the column stripping regime (according to [1])

is shown in Figure 4. Drops stripped from the column just about 2 mm above the injection plane

have about the same initial trajectory in both the shadowgraph image and the CFD plot, even

though the shadowgraph image fails to detect the drops once they thin out about 1 or 2 mm

downstream of the column.

Figure 2.

Figure 3.

Figure 4.

Contour plots of the volume flux through a plane normal to the streamwise direction at x/d = 300

are shown in Figure 5 for experimental and CFD results. The primary purpose of this comparison

is to show that the predicted lateral spread of the spray is in reasonable agreement with the

measurement. The transverse (jet injection direction) spread of the spray both near the wall and

away from the wall is somewhat under predicted, which can be seen more clearly in the flux

plots of Figure 6. The two lobes of slightly higher flux on either side of the centerline are

apparently caused span wise velocity around the jet injection location. This is result is in spite of

the dilute spray assumption which causes under prediction of the gas flow blockage by the jet.

These lobes do not appear in the experimental data of [17], though similar lobes do appear in the

experimental data of Leong and Hautman [23].

Figure 5.

Measured [17] and computed profiles of drop volume flux, drop stream wise velocity, and drop

SMD as a function of the transverse (y) direction are shown in Figures 6, 7, and 8. The

experimental data were taken along the jet centerline. In order to use a reasonably large sample

of drops for the CFD plots, the computed results are an average of drops within a range of plus or

minus 6 jet diameters of the centerline. This centerline band for the computed drops typically

included about 2000 parcels. The computed results were insensitive to small changes in the size

of the centerline band.

Results for an air cross flow velocity of 103 m/s and a liquid jet velocity of 19.3 m/s at

downstream distances of 200, 300, and 500 jet diameters are shown in Figure 6. The overall

agreement for flux, velocity, and drop size trends is reasonably good. The peak flux distance

from the wall agrees very well for each downstream location, though the transverse spread is

under predicted. Flux magnitudes are quite well predicted, in spite of significant uncertainty in

the measurements [17]. The calculated velocity near the wall (behind the liquid column) is over

predicted, with the worst agreement occurring at x/d = 200. This seems to be a clear indication

that the wake behind the liquid jet, which is not captured in this dilute spray model, plays a

significant role in the evolution of the droplet distribution. Farther from the wall, the velocity

trends of lower velocity with distance from the wall and higher velocity with downstream

distance are well predicted. SMD magnitude and trends are also accurately predicted, except for

an under prediction of size near the wall. The lack of the turbulent wake behind the liquid

column can also explain the under predicted transverse spread and the low drop size near the

wall, though the connection is perhaps less obvious. The wake could well be responsible for

dispersion of more small to medium drops near the wall. Even a small number of medium size

drops (50 to 70 microns) would significantly increase predicted SMD. At the same time, a low

velocity wake could allow medium to large size droplets to penetrate farther from the wall.

Figure 6.

Results for an air cross flow velocity of 103 m/s, liquid jet velocities of 12.8 and 29.0 m/s at a

downstream distance of 300 jet diameters are shown in Figure 7. The middle row of Figure 6 can

also be considered in this variation of liquid jet velocity. Figure 8 shows results for air cross flow

velocities of 69 m/s and 137 m/s with liquid jet velocity of 19.3 m/s at a downstream distance of

300 jet diameters. Again, the middle row of Figure 6 can also be considered the variation of

cross flow velocity. The peak flux locations are predicted quite well with variations in q for

variations in both liquid jet velocity and air cross flow velocity. The drop velocity as a function

of distance from the wall is in good agreement for high q cases, but is again over predicted near

the wall for lower q cases. This is not surprising since the wake effects can be expected to be

more significant for low q (low penetrating) cases. In a similar manner, SMD predictions agree

well with measurements for high q, but less so for low q. For the low q cases, the measurements

show an interesting pattern in which the SMD increases, decreases, and then increases again with

distance away from the wall, for physical reasons that are not clear.

Figure 7.

Figure 8.

CONCLUSIONS

A numerical model for liquid jet atomization in a subsonic cross flow was developed. The model

is based on the observation that liquid column breakup in the shear breakup regime is similar to

drop breakup in the shear breakup regime. A boundary layer stripping model was adapted to

predict both shear breakup from a column surface and subsequent primary breakup of large

droplets or fragments resulting from overall column breakup. The model incorporates the Weber

number and momentum flux ratio effects that lead to either column stripping dominated or

column breakup dominated atomization. The drag coefficient is modified for the liquid jet, and

drop distortion is considered based on the Taylor Analogy Breakup (TAB) model. The model

interacts with the Eulerian gas phase through source terms and assumes that the volume fraction

of the liquid for any computational cell is small.

The results of the model were compared with experimental data for water jets in air cross flows

with varying jet velocity and air velocity. The comparisons included qualitative comparisons

with shadowgraph images of sprays in both the shear stripping dominated regime and the column

breakup dominated regime. The model successfully captured the basic appearance of the spray

for each case. However, the steady-state numerical results were inherently unable to include the

time-dependent waviness of the spray, particularly in the column breakup regime. Quantitative

comparisons were made for drop volume flux, velocity, and size as a function of distance

downstream of the injector. The transverse location of the liquid flux peak was well predicted

both as a function of streamwise distance from the injector and with varying momentum flux

ratio. Drop velocity was also in good agreement with data away from the wall. Drop sizes were

generally in good agreement with data both in magnitude and in slope as a function of distance

from the wall. The most apparent difference between the predictions and the data was for drop

velocity near the wall. The data clearly show that there is a significant effect near the wall from

the wake behind the liquid jet column that is not captured in the current dilute spray model. As a

result, the drop velocities are over predicted near the wall, especially for cases with low

momentum flux ratio where the wake has an effect on more of the spray. Other areas of

disagreement between predictions and data, such as under prediction of the transverse spread of

the spray and under prediction of the drop size near the wall, may also be explained by the lack

of consideration of the wake flow.

ACKNOWLEDGEMENTS

This work was performed in part under funding from NASA Glenn Research Center where

Dr. Nan-Suey Liu is the technical monitor. Dr. Baifang Zuo has also contributed greatly to the

overall development of the spray and atomization software module. Thanks are also due to

Ms. Denise Rynders of CFDRC for preparing the manuscript.

NOMENCLATURE

d diameter of the liquid jet/column

Mshed amount of mass removed by stripping from the column

q liquid to air momentum ratio ( )( )2gg

2 uv ρρ ll

Reg Reynolds number ( )ggjg ud µρ

RND random number between 0 and 1

SMD Sauter Mean Diameter

t time

t* non-dimensional time

td local column lifetime

u velocity component in gas cross flow direction

v velocity component in liquid jet injection (transverse) direction

w velocity component in lateral direction

Weg Weber number ( )lσρgj2gdu

µ dynamic viscosity

ρ density

σ surface tension

SUBSCRIPTS

b breakup

d drop

g gas

j liquid jet

l liquid

o initial value

p parent drop

rel relative

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FIGURE TITLES

Figure 1. Cross flow Velocity Contours for the Plane Through the Jet Centerline for Water Jet

Velocity of 19.3 m/s, Air Velocity of 103 m/s and d = 0.5 mm. Liquid Jet Injected at x/d = 0

Figure 2. Comparison of Experimental Image [1] (Left) and Plot of CFD Results (Right) for

Water Jet Velocity of 19.3 m/s, Air Velocity of 103 m/s, d = 0.5 mm, q = 18.5, We = 160

Figure 3. Comparison of Experimental Image [1] (Left) and Plot of CFD Results (Right) for

Water Jet Velocity of 9.1 m/s, Air Velocity of 69 m/s, d = 0.5 mm, q = 10, We = 71

Figure 4. Comparison of Experimental Image [1] (Left) and Plot of CFD Results (Right) for

Water Jet Velocity of 37.9 m/s, Air Velocity of 103 m/s, d = 0.5 mm, q = 71, We = 160

Figure 5. Contours of Volume Flux at x/d=300 for Water Jet Velocity of 19.3 m/s, Air Velocity of

103 m/s, d=0.5 mm, q=21.7, and We=160: Experimental Image [17] (Left) and CFD Results

(Right)

Figure 6. Centerline Profiles of Volume Flux (Left), Streamwise Velocity (Center), and SMD

(Right) for Water Jet Velocity of 19.3 m/s, Air Velocity of 103 m/s, d=0.5 mm, q=21.7, We=160,

at x/d=200 (Top), at x/d=300 (Middle), x/d=500 (Bottom) (Measurements from [17])

Figure 7. Centerline Profiles of Volume Flux (Left), Streamwise Velocity (Center), and SMD

(Right) for Water Jet Velocity of 12.8 m/s, q=9.5 (Top) and 29.0 m/s, q=48.8 (Bottom), Air

Velocity of 103 m/s, d=0.5 mm, We=160, at x/d=300 (Measurements from [17])

Figure 8. Centerline Profiles of Volume Flux (Left), Streamwise Velocity (Center), and SMD

(Right) for Water Jet Velocity of 19.3 m/s, Air Velocity of 69 m/s, q=58.8, We=72 (Top) and 137

m/s, q=12.2, We=283 (Bottom), d=0.5 mm, at x/d=300 (Measurements from [17])