ILASS Americas, 20th Annual Conference on Liquid Atomization and Spray Systems, Chicago, Illinois, May 2007

Investigation of the Effect of Injector Discharge Coefficient on Penetration of a Plain Liquid Jet into a Subsonic Crossflow

Christopher T. Brown, Ulises M. Mondragon and Vincent G. McDonell*

Energy Research Consultants 23342 South Pointe Drive, Suite E

Laguna Hills, CA 92653-1422

Abstract The injection of a liquid jet into a high speed crossflow has been studied extensively in the past decade or so. A wide variety of expressions have been developed describing aspects of the jet behavior, including penetration. A comparison of these expressions reveals significant variation in predicted penetration which makes their application for engineering design questionable. In the present work, the typical practice of assuming unity discharge coeffi-cient is examined in the context of these expressions and their use. To support the analysis, new experiments are carried out using three injectors with varying discharge coefficients. High speed shadowgraphy is used to document the penetration of liquid jets produced by each of the injectors for pressures ranging from 10 to 100kPa into a 60 m/s crossflow. The results show that, for the conditions studied, inclusion of the discharge coefficient in the expressions for penetration greatly reduces the scatter in the predictions.

*Corresponding author

Background and Objective The injection of liquid into a crossflowing stream

has a wide array of applications and has been studied extensively over the past few decades.1,2,3 Despite the extensive work done on this seemingly simple problem, a wide range of interpretation, conclusions and correla-tions have resulted that often yield significantly differ-ing results regarding breakup regimes, penetration, and effects of fluid properties. As an example, Figure 1 compares predicted penetration values1,2,4,5,6,7,8,9,10,11,12 for a water jet injected into a crossflow at room tem-perature and atmospheric pressure. The reasons for these wide ranging findings need to be understood and carefully interpreted in order to develop robust, reliable models of the phenomena of interest.

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35

X, mm

Y, m

m

Ref 1Ref 2Ref 4Ref 5, imagingRef 5, PDIRef 6Ref 7Ref 8Ref 9Ref 10, Ref 4 formRef 10, Ref 7 formRef 11Ref 12

air at STPwater at STPd = 1 mmq = 10Cd = 1.0

Figure 1. Comparison of Penetration Behavior.

The development of models for the important phe-nomena have focused on important dimensionless quan-tities, such as Reynolds number:

j j jj

j

U dRe

UP

(1)

the Weber number, (in this case based on the cross-

flow properties):

2

jc cc

U dWe

UV

(2)

and the momentum flux ratio:

2

2jj

cc

Uq

UUU

(3)

Using these dimensionless groups in the descrip-

tion of features such as penetration provides a physical basis for interpreting the behavior.

Reynolds number is not featured prominently in many of the general jet behavior correlations. This parameter indicates the presence of instabilities on the jet surface as a transition from laminar to turbulent be-havior occurs. Recent studies suggest that once the jet is turbulent, the effect of other parameters such as the crossflow velocity on the nature of the atomization be-comes less important.13,14

The Weber number represents the ratio of the aero-dynamic forces to the surface tension forces. The crossflow velocity used is typically that of the freestream determined from volumetric flow and test section cross sectional area. However, the crossflow velocity adjacent to the wall will be lower than the free stream due to the boundary layer. Another considera-tion is that the aerodynamic forces are related to the total velocity difference between the crossflow and the liquid jet, not just the crossflow velocity. As a result, in cases where the jet has a significant velocity, the veloc-ity associated with the Weber number should be the vector combination of the jet and crossflow velocities, which could be significantly higher than Equation (2). Finally, the discharge coefficient of the test section duct can also increase the actual crossflow velocity, resulting a higher value of Weber number.

The momentum flux ratio has been widely used to describe the relative penetration of liquid jets.1-12 In most of the literature, the jet velocity is set based on the metered flowrate to the jet divided by the jet physical area. This jet velocity is accurate only if the jet dis-charge coefficient is equal to 1. Through the assump-tion of unity discharge coefficient, the details of the internal injector geometry are essentially ignored. While this may be a common practice, if the discharge coefficients differ among the injectors used in the vari-ous studies the actual jet velocity will differ accord-ingly. The effect of inlet angle and l/d on the discharge coefficient does show a strong dependency on these parameters as shown elsewhere.15 For reference, Table 1 summarizes details from a number of recent studies which have reported penetration expressions. In most cases, insufficient information is given to estimate the actual discharge coefficient. Little attention has been given to the details within the jet in terms of how this affects the actual velocity of the jet exiting the orifice into the crossflow. Values of Cd are typically not stated in the literature. An exception is Ref 6, which reports a Cd value of 0.6, but then for analysis, assumes a value of 1.0 for consistency with the literature.6

The objective of the current work is to assess how the injector geometry affects the discharge coefficient and, as a result, the penetration as described by typical forms of penetration expressions.

Table 1. Summary of Key Experimental Features.

Ref Test Section Dimensions Injector Details Test Liquids Diagnostics 4, 9 Details regarding entrance not

provided. Axial turbulence intensities of 3% Y = 125 mm Z = 75 mm P = 1 atm, T ~ 300 K

7.5 mm

L=4d

120 deg

d = 0.50 mm1.00 mm2.00 mm

7.5 mm

L=4d

120 deg

d = 0.50 mm1.00 mm2.00 mm

L/d = 4.0

Water, ethyl alco-hol, water/ethyl alcohol mix, glyc-erol/water mix T ~ 300 K

10 ns Nd:YAG light pulse at 532 nm, recorded with 4x5 format camera on black & white film (Polaroid type 52)

6 Bellmouth entrance Jet location 200mm down-stream of entrance Y = 40 mm Z = 75 mm P = 1.5 to 15 atm T ~ 290 K

? mm

0.45 mm L= 0.7 mm

? deg

? mm

0.45 mm L= 0.7 mm

? deg

L/d = 1.56, Stated: Cd = 0.6

Jet-A T = 290 K

100 ns pulsed back-light w/black & white film (Ilford PAN-F)

7 Honeycomb Entrance Y = 25.8 mm Z = 28.9 mm P = 1 atm T = 18 – 300 C 1.57 mm

0.254 mm L= 1.27 mm

90 deg

1.57 mm

0.254 mm L= 1.27 mm

90 deg

L/d = 5

Water, Acetone, 4-Heptanone

5 ms images of scat-tered light from 514.5 nm Argon-ion laser sheet

8 150 mm round to 25.4 mm x 25.4 mm transition. P = 1 atm T ~ 300 K

6.35 mm o.d.

d = 0.38 mm0.76 mm

L= 0.51 mm

? deg

6.35 mm o.d.

d = 0.38 mm0.76 mm

L= 0.51 mm

? deg

L/d = 1.33, 0.67

Water, Jet-A, n-heptane

Pulsed Shadowgra-phy (10ns light pulse + CCD cam-era)

10 150 mm round to 70 mm x 70 mm transition over 300 mm length Jet location 200 mm down-stream of end of contraction P = 1 atm, T ~ 300 K

7.5 mm

d = 0.48 mm0.94 mm1.30 mm

L=4d

118 deg

7.5 mm

d = 0.48 mm0.94 mm1.30 mm

L=4d

118 deg

L/d = 4, Cd reported for each d

Mil-C-PRF-Type II T ~ 300 K

High-speed con-tinuous shadowgra-phy (halogen back-light) with 1 Ps ex-posure

11 Honeycomb entrance Jet location ~75 mm down-stream of honeycomb Y = 25.4 mm Z = 25.4 mm P = 1 to 7 atm T ~ 300 K

6.35 mm o.d.

0.50 mm L= 0.28 mm

? deg

6.35 mm o.d.

0.50 mm L= 0.28 mm

? deg

L/d = 0.56

Water T ~ 300 K

Pulsed shadowgra-phy (10ns light pulse + CCD cam-era)

12 Honeycomb entrance Jet location ~75 mm down-stream of honeycomb Y = 25.4 mm Z = 25.4 mm P = 1 atm T = 367 – 505 K

6.35 mm o.d.

d =0.30 mm0.50 mm

L= 0.28 mm

? deg

6.35 mm o.d.

d =0.30 mm0.50 mm

L= 0.28 mm

? deg

L/d = 0.56, 0.933

Water T = 294 – 363 K Jet-A T = 294, 339 K

Pulsed shadowgra-phy (10ns light pulse + CCD cam-era)

Approach The near field (x/d < 50) of a spray jet was isolated

and studied using a test section with suitable optical access. The behavior of the jet was documented with high magnification high speed videography using back-lighting. The jet behavior was assessed through evalua-tion of the images obtained. Of particular interest in the present work is the jet penetration.

Experimental Apparatus

Test Section. A test section with inner dimensions of 69.85 mm x 69.85 mm was used for the experimental studies. A 150 mm round to square transition was ac-complished over a length of 300 mm. Additional de-tails of the geometry are shown in Figure 2.

AIR DUMP

INJECTOR

EXHAUST EXHAUST

AIR FLOW

Y

ZX

QUARTZ WINDOWS

18 HONEY COMB 4 INCES THICK

TRANSITION SECTION

Figure 2. Test Section.

The cross flow air velocity (nominally 60 m/s) was established using a blower (Spencer) capable of deliver-ing about 2 lbs/sec at about 3 psig (at the blower outlet). The air flow was metered with a calibrated mass flow meter (Sierra Instruments). The actual test section ve-locity was checked using a pitot probe.

The test liquid was supplied by a gear pump capa-ble of delivering about 3.8 l/m about 2,200 kPa. The liquid flow was measured with a calibrated turbine me-ter (EG&G Model FTO-1 w/extended range) that has a range of 0.038 to 0.3 l/m with accuracy of 0.05% of reading. A pressure transducer (Omega Model PX212-15G) with a 0-100 kPa range w/0.25% accuracy was used to log pressure upstream of the injector, but down-stream of the shutoff and control valve. A glycerin filled pressure gauge (0-15psig) was used to check the pressure readings.

Injectors. A flexible injector mounting apparatus was used to allow different injectors to be used. The injectors considered are shown in Figure 3. Three dif-fering internal geometries were utilized. Great care was taken to achieve liquid jets that were smooth, free from local perturbations, and axisymmetric as documented by high speed video images obtained with no test sec-tion air flowing. Based on a flow vs pressure study, the injector discharge coefficient were determined as shown in Table 2.

It is also noted that variation in Cd with flow was observed, as shown in Figure 4. This is not surprising given prior results.15 It is interesting that Injector A exhibits less dependency than the other two injectors. It is also interesting that when injector Re values were above about 5,000 the Cd changes little with flow. This may correspond to a critical Re value above which the internal flow becomes turbulent. This values was also found to be a reasonable indicator of the dominant breakup mode (i.e., column breakup vs shear breakup) in previous studies.14

a) Tapered Inlet (A)

b) Sharp Inlet, Short l/d (B)

c) Sharp Inlet (long l/d) (C)

Figure 3. Details of Injectors.

Table 2. Measured Discharge Coefficient

Injector Diameter Cd avg L/d mm

A 0.483 0.84 4 B 0.483 0.74 1 C 0.483 0.69 4

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0 2000 4000 6000 8000Re

Cd

Injector AInjector BInjector C

Figure 4. Cd dependency on Re.

Test Conditions. A single air flow condition was considered in the present work, nominally 60 m/s at room temperature and pressure. For each injector, flows and pressures ranging from 14 to 100 kPa (2-15 psig) were recorded. Mil-PRF-7024-Type II was used for the test liquid.

Diagnostics. The primary diagnostic used in the present study is a high speed video camera (Vision Re-search Phantom 7.2). A Nikkor 105 mm macro lens was used to provide a field of view of approximately 45 x 45 mm (@ 11.2 pixels/mm). A frame rate of 11,000/s was used with 10 Psec exposure. 4,000 images were obtained for each case, though the analysis carried out utilized the averaged image. A photograph of the over-all setup is shown in Figure 5.

The outer edge of penetration was determined as follows. For each column of pixels orthogonal to the X crossflow direction, the rows containing the minimum and maximum were determined. Then for each X col-umn, starting from its corresponding maximum row, the column was searched moving away from the maximum heading away from the injector. The outer edge of a particular X column was determined when the pixel intensity had dropped to 50% of the (maximum – minimum) + minimum.

Figure 5. Photograph of the Experimental Setup.

Results Visual Observations. Some examples of observed

behavior are presented for the conditions illustrated in Figure 6. The goal in this presentation is to give a feel for the effect of injector pressure on the penetration. As shown, for a given injection pressure, the penetration appears fairly similar for each injector.

Injector 13.8 kPa 27.6 kPa 55 kPa 96.5 kPa A

B

C

Figure 6. Observed Effect of Injector Pressure on Penetration (image size is x/d = 52 x y/d = 52).

Air Flow

HSV Camera

Injector

Penetration Analysis. As shown above, the pene-tration is observed to depend essentially on pressure, not on momentum flux ratio. A primary reason for this is that, as mentioned above, the results reported in the literature establish the jet velocity by dividing the me-tered volumetric flow rate by the physical orifice area. When calculating velocity in this manner, the effect of any non-unity value of the orifice discharge coefficient is not included.

An alternative (or corroborating approach) to de-termining the liquid jet velocity (and hence the numera-tor in the momentum flux ratio calculation) is utilizing the injector pressure. To illustrate how these two ap-proaches differ in a fundamental manner, it is useful to outline the equations involved.

The equations, generated from continuity and Ber-noulli’s equation are as follows:

� �21 22

2

1

2

1

cactual ideal

gAQ CQ C p p

AA

U �

§ ·� ¨ ¸© ¹

(4)

If M is defined as:

2

2

1

1

1

MAA

§ ·

� ¨ ¸© ¹

(5)

Then Equation (4) can be expressed as:

� �2 1 22 c

actualg

Q CMA p pU

� (6)

If the velocity, V2, is taken as the ratio of the volumet-ric flow to the effective area, A2, then:

� �2 1 22 2

2ideal actual cQ Q gV M p p

A CA U � (7)

or

� �22 1 22

2

1

2

1

cgAV p p

AA

U �

§ ·� ¨ ¸© ¹

(8)

If A1 >> A2, then M can be approximated as 1. In the cases considered in Table 1 and in the present study, this approximation is valid since a relatively large “ple-num” is feeding a small orifice. In this case:

� �2 1 22 cg

V p pU

� (9)

The results show that, if pressure is utilized to de-

termine the velocity, then the velocity is independent of the discharge coefficient, as shown in Equation (9). However, if the flowrate is used to determine the veloc-ity, the discharge coefficient, C, must be known in or-der to obtain the correct velocity as shown in Equation (7). In all the cases shown in Table 1 (and the cases in the literature) the velocity was defined based on the flowrate and the physical area and it is assumed that C is equal to 1.

Static Penetration Analysis. Following previous work,10 the penetration of the upper edge of the jet can be described by a number of different correlations. For the current study (near field), a single correlation was selected for use as shown in Equation (10):.

0.5

1.37y xq

d d§ · ¨ ¸© ¹

(10)4

It is noted that the physical geometry of Injector A

and the injector used in the study deriving Equation (10) are quite similar. As a result, it might be expected that the effect of discharge coefficient for both of these studies would be similar. Analysis of data obtained on Injector A conducted for a wide range of conditions and injector hole sizes found that Equation (11) expression gave the best predictive behavior:

� �0.35

0.471.5y xq

d d§ · ¨ ¸© ¹

(11)10

Note that the coefficient and exponents are quite

similar to the original expression. Given the influence of the discharge coefficient on penetration, the influ-ence on the apparent penetration enters through the influence of the momentum flux ratio and possibly its exponent. Based on physical arguments, it stands to reason that the jet penetration should be proportional to its velocity (hence the apparent square root dependency on momentum flux ratio). It

The results are shown in Figure 7- Figure 9 for Equation 11 using assumed unity Cd and actual Cd val-ues. The results for Injector A with Cd = 1 is a subset of the data used to generate Equation (11). If the actual Cd values are used (Figure 7b), the data move away from high correlation quality. In the case of Injector B (Figure 8), the Cd = 1 assumption results in measured values generally greater than the predicted values. When the actual Cd is used (Figure 8b), the predicted values are closer to the measured values. With Injector

C, assuming Cd = 1 leads to measured values generally greater than predicted. Using the actual Cd values brings the predicted values more inline with the meas-ured values. The results shown in these figures are a bit difficult to make general comments about because of

the log scales used. The results do demonstrate that the coefficients to achieve optimum penetration correla-tions such as Equation (11) will change depending on the Cd and to a lesser extent the injector geometry.

a) Injector A Cd = 1.

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa68.9 kPa82.7 kPa96.5 kPa103.4 kPa

a) Injector B Cd = 1.

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa68.9 kPa82.7 kPa96.5 kPa103.4 kPa

a) Injector C Cd = 1.

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa96.5 kPa103.4 kPa

b) Injector A Cd = actual

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa68.9 kPa82.7 kPa96.5 kPa103.4 kPa

b) Injector B Cd = actual

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa68.9 kPa82.7 kPa96.5 kPa103.4 kPa

b) Injector C Cd = actual

0

1

2

3

4

0 1 2 3 4Measured ln(y/d)

Pre

dict

ed ln

(y/d

)

13.8 kPa27.6 kPa41.4 kPa55 kPa96.5 kPa103.4 kPa

Figure 7. Injector A Penetration

(Equation 11) Figure 8. Injector B Penetration

(Equation 11). Figure 9. Injector C Penetration

(Equation 11)

Since the existing penetration correlations indicate a dependency upon the momentum flux ratio (Equation (3)), it is helpful to present this information in terms of momentum flux ratio. This is shown in Figure 10 for the assumed unity discharge coefficient conditions. As shown, the visual penetration differs for each injector for a given momentum flux ratio. For example, Injector C has a significantly higher penetration for momentum flux ratio of 14 compared to that of Injector A. How-

ever, if the results are presented using the “actual” mo-mentum flux ratio obtained by using the liquid velocity based on Equation (7), the visual penetration appears less dependent upon injector as shown in Figure 11. In this case, results are presented for three momentum flux ratios and, as shown, visually a similar penetration is observed for each case.

Injector q,ideal # 14 q,ideal # 20 q,ideal # 23

A

N/A

B

C

N/A

Figure 10. Observed Effect of momentum flux ratio on penetration.

Injector q,actual # 11 q,actual # 21 q,actual # 37

A

B

C

Figure 11. Observed Effect of momentum flux ratio on penetration.

To help further illustrate the influence of the dis-

charge coefficient, Figure 12 compares directly the penetration based on the images for the three injectors based on either unity Cd values or actual Cd values.

As a final step in the analysis, the results for all three injectors were analyzed with actual Cd values for best fit correlations of the form shown in Equations (10) and (11). The penetration of all three injectors could be well predicted by Equation (12):

� �0.34

0.551.1y xq

d d§ · ¨ ¸© ¹

(12)

Note that the coefficients are similar to those for

Equation (11), but the linear term is smaller. This is

due to the need to reduce the penetration to correspond to the actual liquid jet velocities (as opposed to the per-ceived velocities based on the unity discharge coeffi-cient assumed in the literature).

If unity discharge coefficients are assumed, the op-timized coefficients for the penetration expression vary substantially. To quantify this variation, Table 3 sum-marizes the optimized set of coefficients for each of the injectors using the typical literature assumption of unity discharge coefficient. As shown, the linear coefficient varies by more than 50% and the exponent coefficient on momentum flux ratio varies by nearly 30%. Given this finding, it is perhaps not surprising that the results shown in Figure 1 vary by as much as they do. Interest-ingly, the coefficient on downstream distance does not vary significantly.

Table 3. Summary of Optimized Coefficients with Unity Discharge Coefficient Assumption.

Injector A’* b* c* A 1.52 0.50 0.33 B 1.08 0.64 0.35 C 0.90 0.61 0.35 *Coefficients based on form: � �'

cby x

A qd d

§ · ¨ ¸© ¹

The results also suggest the following form for a

correlation that describes penetration:

2'cb

d

y q xA

d C d§ · § · ¨ ¸ ¨ ¸© ¹ © ¹

(13)

With the limited data set available it is unreason-

able to assign best values for A, b, and c, though the coefficients shown in Equation (12) have shown to work well for the current data set. In principal, existing data sets could also be used with knowledge of the dis-charge coefficient in order to produce a robust penetra-tion expression without taking significant additional data. Conclusions

High speed shadowgraphy has been used to docu-ment near field penetration behavior for sprays gener-ated by three injectors with differing discharge coeffi-cients. Analysis has been carried out to assess the role of the discharge coefficient on the penetration behavior of the liquid jets/spray generated. Some conclusions drawn include:

x Inclusion of the injector discharge coeffi-

cient in the analysis can explain a signifi-cant amount of the variation observed in penetration expression found in the litera-ture.

x For the conditions studied, the discharge coefficient was found to depend not only on injector geometry, but also upon injec-tor Re values. As a result, additional care must be taken to generalize results ob-tained.

a) Unity discharge coefficient

X/d

Y/d

0 10 20 30 40 500

10

20

30

40

50Injector AInjector BInjector C

q,ideal # 14

b) Actual Discharge Coefficient

X/d

Y/d

0 10 20 30 40 500

10

20

30

40

50Injector AInjector BInjector C

q,actual # 37

q,actual # 11

Figure 12. Measured Penetration based on Unity

and Actual Discharge Coefficients.

Nomenclature A = area (physical) A’ = Constant Cd = discharge coefficient d = diameter gc = gravitational constant M = Mach No. p = pressure U, V = velocity U� �density V = liquid surface tension P = viscosity x,y,z = distance per sketch below u,v,w = velocity component per sketch below

y, v

x, u

z, w

Aircross flow

Liquidinjection

y, v

x, u

z, w

y, v

x, u

z, w

Aircross flow

Liquidinjection

Subscripts c = crossflow j = jet 1 = upstream 2 = downstream Acknowledgements

The support of Barry Kiel and the US Air Force (Contract FA8650-05-C-2523) is greatly appreciated. The assistance of Christopher Antes and Scott Thawley in the setup of the facility is gratefully acknowledged. References 1 Geery, E.L. and Margetts, M.J. (1969). Penetration of a High Velocity Gas Stream by a Water Jet, Journal of Spacecraft, Vol. 6, No. 1, pp 79-81. 2 Chen, T.H., Smith, C.R., Schommer, D.G., and Nejad, A.S. (1983). Multi-Zone Behavior of Transverse Liq-uid Jet in High Speed Crossflow, AIAA Paper 93-0453, January. 3 Oda, T., Hiroyasu, H., Arai, M., and Nishida, K. (1994). Characterization of Liquid Jet Atomization across and High-Speed Airstream, JSME International Journal, Series B, Vol 37, No. 4, pp. 937-944. 4 Wu, P.K., Kirkendall, K.A., Fuller, R.P., and Nejad, A.S. (1997). Breakup Processes of Liquid Jets in Sub-sonic Crossflows, J. Propulsion and Power, Vol. 13, No. 1, pp 64-73. 5 Lin, K.-C., Kennedy, P.J., and Jackson, T.A. (2002). Structures of Aerated-Liquid Jets in High Speed Cross-flows. Paper AIAA-2002-3178, Presented at the AIAA Fluid Dynamics Conference, St. Louis, June. 6 Becker, J. and Hassa, C. (2002). Breakup and Atomi-zation of a Kerosene Jet in Crossflow at Elevated Pres-sure. Atomization and Sprays, Vol. 12, pp. 49-63. 7 Stenzler, J.N., Lee, J.G., and Santavicca, D.A. (2003). Penetration of Liquid Jets in a Crossflow, AIAA Paper No. 2003-1327. 8 Tambe, S.B., Jeng, S-.M., Mongia, H.C., and Hsiao, G. “Liquid Jets in Subsonic Crossflow”, Paper AIAA 2005-731, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2005. 9 Wu, P.K., Kirkendall, K.A., Fuller, R.P., and Nejad, A.S. (1998). Spray Structures of Liquid Jets in Sub-sonic Crossflows, J. Propulsion and Power, Vol. 14, No. 2, pp 173-182.

10 Brown, C.T. and McDonell, V.G. (2006). Near Field Behavior of a Liquid Jet in a Crossflow. Proceedings, 19th ILASS-Americas Conference, Toronto, Canada, May. 11 Elshamy, O.M. and Jeng, S. M., “Study of Liquid Jet in Crossflow at Elevated Ambient Pressures”, ILASS-Americas 2005, Irvine, CA. 12 Lakhamraju, R.R. and Jeng, S.-M. (2005), “Liquid jet breakup in subsonic air stream at elevated tempera-tures”, ILASS-Americas 2005, Irvine, CA. 13 Aaalburg, C., Faeth, G. M., and Sallam, K. A., “Pri-mary Breakup of Round Turbulent Liquid Jets in Uni-form Crossflows”, AIAA Paper 2005-734, 2005 14 Madabhushi, R.K., Leong, M.Y., Arienti, M., Brown, C.T., and McDonell, V.G. (2006). On the Breakup Regime Map of Liquid Jet in Crossflow, ILASS Ameri-cas 2006, these proceedings. 15 Spikes, R.H. and Pennington, G.A. (1959). Dis-charge coefficients of small submerged orifices, Pro-ceedings Institute of Mechanical Engineering, Vol. 173, No. 25, pp. 661-665.