ILASS Americas, 21st Annual Conference on Liquid Atomization and Spray Systems, Orlando, Florida, May 18-21, 2008

Mixing of a Plain Jet into a Swirling Crossflow

B.J. Masuda and V.G. McDonell*

UCI Combustion Laboratory University of California

Irvine CA 92697-3550 USA

G.W. Oskam Solar Turbines Incorporated

PO Box 85376 San Diego, CA 92186-5376 USA

Abstract

Many gas turbine combustion systems employ swirl to help mix fuel and air and subsequently stabilize the reaction. In the case of liquid fuels, strategic introduction of the liquid into the swirling flow can provide improved combustion performance. In the present work, radial injection of a plain jet into a swirling flow is considered. A large body of work is available in the literature for liquid injection into a uniform crossflow which neglects the possible influence of swirl on the subsequent fuel plume distribution and performance. The goal of the present work is to (1) establish the role of swirl on the be-havior of a liquid jet injected into a crossflow and (2) explore how well correlations based primarily on atmospheric data scale to high temperature and pressure conditions. To accomplish this, pressure, temperature, pressure drop, and fuel flow were varied for an axial swirl premixing module with plain jet fuel injection. Instantaneous planar images of the spray were collected using planar laser induced fluorescence and an intensified CCD camera. The images obtained are processed to generate a number of performance characteristics associated with the fuel plume including area, centerline distance, angle of rotation and plume unmixedness. Two approaches are taken regarding analysis. First, a standard least squares fit maximizing R2 is carried out for a presumed model form. Due to the presence of mulitcollinearity in the parameters studied, a reduced model with maximum preditcablity was completed based on physical understanding and general dependencies of the characteristics on individual nondimensional parameters. Maximizing the predictablity and dropping one or more regression parameters did not greatly effect the fit. In addition to general behavior of a jet injected into a swirling crossflow, the results also revealed that centerline distance and plume unmixedness have the greatest potential to be scaled from atmospheric to high temperatures and pressures found in gas turbines.

* corresponding author

Introduction It is well established that atomization of liquid fu-els can play a significant role in the performance and emissions associated with combustion devices.1 As a result, understanding how to optimize this process and the subsequent transport, evaporation, mixing, heat transfer and combustion phenomena that occur can give rise to reduced emissions, improved efficiency and bet-ter overall operability of combustion systems. Despite the complications, innovative design strategies have been developed to do so. One such approach is lean premixed prevaporized (LPP) combustion.

Operating a combustion device, such as a gas tur-bine, at a lean premixed prevaporized condition curbs the formation of nitrogen oxides (NOx). LPP utilizes excess amounts of air to avoid locations of fuel rich combustion that raise flame temperatures and promotes the creation of nitric oxide (NO). Achieving LLP com-bustion depends on the fuel injection system’s ability to create a homogenous mixture of air and fuel before the reaction begins. Mixing fuel and air quickly and effi-ciently is difficult to accomplish in practice. Mixing performance is crucial because mixing times are limited to 1 ms due to the danger of autoignition.2

An elegant problem that reveals many of the key features associated with the fuel injection process is that of the plain liquid jet injected from a wall into a uni-form crossflow. As a result of the simplicity of the configuration, this problem has received a tremendous amount of attention in the literature3, , , ,4 5 6 7 from both experimental and modeling perspectives. As a result, key dependencies on dimensionless groups such as momentum flux ratio, Weber number and Reynolds number have been identified and can be thus used to develop simple expressions to describe the resulting fuel distribution and penetration.

Momentum flux ratio is quantitatively defined as the ratio of the jet to crossflow momentum (Equation 1). The interaction between density (ρ) and velocity (U) dictates how far the jet will penetrate into the flow; large penetration is signified by a large momentum flux ratio. This dimensionless quantity is extensively used in jet penetration correlation. The subscript j and c ref-erence the jet and crossflow respectively.

2

2

cc

jj

UU

qρρ

= (1)

Weber number is the ratio of the inertial forces (ρ:

density, U: velocity, d: diameter) to the surface tension (σ) (Equation 2). It is has been observed that the domi-nant breakup mechanism of a jet depends on We. Transitioning between the two regimes can be done through a change in pressure or shear velocity.4,5 The Weber number throughout the work is associated with

the air flow and therefore the density and velocity are air properties.

σρ 2UdWe = (2)

Reynolds number is the ratio of inertial to viscous forces (Equation 3). It is used to describe the flow re-gime. U is the flow velocity, D is the characteristic length and ν is the kinematic viscosity.

νUD

=Re (3)

In practice, the liquid jet is generally not injected into a uniform crossflow. In fact, in many gas turbine applications, the liquid is injected into a swirling, non-uniform crossflow. While the 3D nature of the swirling flowfield adds considerable complexity to what is a rather elegant problem, this practical configuration has received relatively little attention in the literature. Fur-thermore, the study of jet in swirling crossflow (JISC) at conditions found in typical gas turbine engines is even sparser. As a result, the current project focuses upon this extension of the JIC problem to include swirl like that found in gas turbine fuel injectors. Character-izing the behavior of JISC will assist in maximizing its effectiveness as a LPP technology. Furthermore, to help maximize the value of the current work, experi-ments are also conducted at gas turbine operating con-ditions. Few facilities are capable of replicating such circumstances, so reduced pressure and temperature or atmospheric tests are settled upon. As a result, the ob-jectives of this work are: (1) establish the role of swirl on the behavior of a liquid jet injected into a crossflow and (2) explore how well correlations based primarily on atmospheric data scale to high temperature and pres-sure conditions. Overall, the results will help apply the knowledge gained through the extensive body of infor-mation on liquid jets injected into uniform crossflows to more practical configurations.

Experiment

Test Facility. A schematic of the high pressure test facility is shown in Figure 1. The vessel is rated up to 250 psig (18 atm) and is mounted to a three axis trav-erse system capable of positioning the vessel within 0.0005 in (or 0.005 mm) allowing diagnostics to remain stationary.

Air is supplied by a plenum and three Ingersoll Rand compressors. Flow is controlled by a Fisher PID pneumatic valve and Sierra Instruments mass flow me-ter. Inside the vessel, a majority of the air enters the air box to which the test hardware is mounted while the balance is diverted through a perforated plate. The per-

forated plate has a number of different sized holes which can be blocked or opened to adjust the flow split. After passing the experiment, the flow encounters a water quench system and series of drop out tanks before exiting the building. Pressure is maintained through back pressure utilizing a valve similar to the air flow controller. Preheat is provided by three Watlow air heaters. A total of 480 kW of non vitiated heating is available to reach temperatures of ~1200°F (920 K).

a) Vertical Cross Section

b) HorizontalPlane

Figure 1. S

The test

Mil-PRF 702properties. Tby a coriolisPID controlle

Table 1. Properties of Mil-PRF-7024-Type II

Property Value (T = 298 K)

Surface Tension 24 dyne/cm

Density, specific 0.770

Viscosity, cSt 1.20 An Omega K type thermocouple and HH74K

thermocouple reader measured the air temperature. The thermocouple was located in the air box upstream the test hardware. In addition two strategically placed pressure taps connected to a manometer quantified the differential pressure. Liquid impingement on the win-dows was avoided with an air purge system that pro-

OblPoRound

Ports

Air

tected by creating a thin sheet of air on the window surface.

Test Section. The test hardware was composed of

x

Thermocouple

PressureTaps

Air Bo

Cross Section through O

chematic of Elevated Pr

fluid used throughout th4E Type II. Table 1 sumhe facility’s liquid fuel f mass flow meter (Micrr (Fisher).

ong rts

g

+x +y

PerforatedPlate

ptical Access

three major components: housing, swirler and injector. The stainless steel housing, shown in Figure 2a, mounted onto the previously described air box. Figure 2b, c depicts the axial swirler. It was installed concen-trically with the housing with a set screw. The geomet-ric flow area of the swirler was 3.63 in2 (2340 mm2). A center body plug was placed in the center of the swirler to force the air flow through the swirling annulus. A single injector (Figure 3) was installed such that it in-jects a plain jet of liquid radially inward towards the swirler centerline at exit plane of the swirler vanes. Protrusion was regulated by placing spacers at the hous-ing and injector interface. For the duration of the ex-periment the injector was kept flush with the outer wall. The injector had an orifice diameter of 0.065” (1.7 mm) and an L/D of 5.7.

Diagnostics. A Continuum Surelite III-10 pulsed Nd:YAG laser provided illumination of the spray. Sec-ond and fourth harmonic generators the produced the ultraviolet light (266 nm) required to excite the ali-phatic compounds in the test liquid. A laser sheet was constructed with a 51” (1300 mm) focal length colli-mating lens and a 0.875” (22.2 mm) radius plano-concave cylindrical lens. Images were obtained 0.59” (15 mm) downstream of the hardware exit plane using a 16 bit Princeton Instruments CCD intensified camera

150deg

106de

74deg

essure Facility.

e campaign was marizes the fluid low is controlled omotions) and a

with a UV transmissive lens and appropriate filter set to isolate the fluorescence. To synchronize the pulse of the laser and the camera shutter, a Princeton Micro Max ST113 and Princeton pulse generator (PG-200) received a signal from the laser and activated the shutter at the correct time. Sixty instantaneous images were collected for each test condition using a frame grabber (Roper Scientific WinView32 Version 2.5.21.0) and stored digitally on a computer. Figure 4 details the imaging outfit.

a) Swirler Housing

b) Top View of Assemble Premixing Module

c) Bottom View of Premixing Module

Figure 2. Test Section.

Figure 3. Fuel Injector.

Figure 4. Schematic of PLIF Setup.

The number of images needed to sufficiently char-

acterize the spray was found by examining the area of the plume. Four shakedown cases were analyzed in 10 frame increments up to 80 frames. Plots of the area versus the number of frames revealed that any hystere-sis died out by 60 frames. Figure 5 is an example of one such plot and illustrates the typical “stability” reached as a function of number of images used in the analysis.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90Number of Frames

Are

a (s

q in

)

Figure 5. Image Stability Example.

Test Conditions. The test parameters varied in-

cluded: pressure, temperature, pressure drop and fuel flow. Table 2 summarizes each range. In addition, two conditions were repeated 4 times to assess overall re-peatability and to establish measurement uncertainty. The percent error was computed by taking the standard deviation over the average for each performance crite-ria. The error is presented as error bars in Figure 11 to 14 and tabulated in Table 3.

Nd:YAG

PG-200

Micromax Controller

Camera

Filter

Experiment Aperture Cylindrical

PC

Power/Cooling Unit Air Flow

CCollimating

Center Body Plug

Fuel Flow

Table 2. Summary of Test Conditions.

Pressure (atm) 1 – 6

Temperature (°F/K) 68 – 400/ 298 – 477

Pressure Drop (%) 3 – 5

Fuel Flow (kg/min) 0.1 – 0.75

Table 3. Performance Criteria Uncertainty.

Area (sq in)

L (in)

Θ (deg) PU

3.9% 1.4% 3.0% 5.7%

It is noted that the present work encompasses a ma-trix based primarily upon nondimensional parameters which is only a fraction of the total number of tests considered in the overall effort. A larger second matrix based on primitive parameters was also executed and the results of that work are discussed elsewhere.8

Analysis. The requirement for image processing is four fold. First, acquiring images normal to the laser sheet was not possible due to the experimental setup. Second, secondary light scattering required the removal of background elements that would interfere with the analysis. Third, the laser power was unique to each test case. Lastly, extraction of spray characteristics is nec-essary to evaluate performance.

The analysis carried out required a number of steps. First the image was registered (i.e. removing the distortion of the image using the reference grid illus-trated in Figure 6). Next images were normalized to account for any variation in laser power used. After normalization, the background was removed by first generating a binarized image using thresholding proce-dures outlined by Otsu9. This binarized image was then multiplied into the data image, thus isolating only the region of interest.

Atomization performance was measured based on several quantitative criteria of the fuel plume images. Mathworks, Matlab 6.5.1 image processing toolbox and Media Cybernetics, Image Pro Plus 5.1 were employed to complete the analysis. Algorithms were developed to extract the following characteristics: plume area, centerline distance, angle of rotation and plume un-mixedness which are defined next.

The plume area (A) was the area of the fuel plume at a measurement plane. It was calculated by summing the number of pixels with a nonzero intensity in the image and converting the number of pixels into a meas-ure of area. For this work 1 in2 (6.45 cm2) equaled 8649 pixels.

a) Reference Grid

b) Position Referencing

Figure 6. Referencing Procedures.

Figure 7. Feature Definition.

Centerline distance (L) was defined as the distance

from the centerline of the tests hardware to the center of mass of the fuel plume (Figure 7). It was calculated using Equation 4, where (xi, yj) are the pixel coordi-

Swirl Direction

θ

Projected Injector Location

L

Swirler Housing Background

Grid

Laser Sheet

Plumb Bob

Projected Injector Location

Plume Area Outline

nates. The actual distance is found from the fact that 1” (25.4 mm) equaled 93 pixels.

( ) ( )212

212 yyxxL −+−= (4)

The angle of rotation (θ) was the angle through

which the plume travels as a result of the swirling flow (Figure 7). The angle was determined from the dot product between the two vectors formed from the cen-terline point of the swirler to the plume center of mass and fuel injection point respectively.

Plume unmixedness (PU) was a statistical measure of the mixing within the area of the fuel plume. It is found by dividing the standard deviation by the mean pixel intensity (Equation 5), where Ci is the ith pixel,

_ is the average pixel intensity and N is the total in-

tensity. C

_

2_

))((1

C

CCNPU

i −Σ= (5)

Results

For the present work, emphasis is given to the na-ture of the spray plume area and centerline distance at the measurement plane. Figure 8 presents normalized images for a variety of Weber number and momentum flux ratio values over the experimental parameter space studied. The results shown reflect the influence of air density (through temperature and pressure) as well as liquid jet velocity (through pressure drop). The non-dimensional presentation of Figure 8 attempts to clas-sify the plume features based on traditional groupings of primitive variables that have previously been shown to collapse spray and atomization behavior.

Figure 9 explains the image orientation. Air flows into the plane of the page and swirls in a clockwise di-rection. The two concentric circles represent the loca-tion of the outer and inner test section walls. The line segment connecting the two circles defines the fuel injector location.

The results shown in Figure 8 show some modest trends associated with the dimensionless groups. For example, a “hook” feature is evidence at low values of q and We. Also, at higher We values, the top of the plume become more “pointed”. To provide a clearer presentation of these features, Figure 10 shows the im-ages for each condition on the left along with the corre-sponding binarized image on the right. All the images are pseudo colored so that the color blue indicates areas of the highest mass concentration.

Figure 8. Plume Shape as Function of We and q.

Figure 9. Orientation Diagram

Regression Analysis. As a first step to correlating

the results, the fuel plume criteria were plotted against nondimensional variables. A few observations are illus-trated in Figure 11 to 14.

First, the centerline distance is considered in Figure 11. It is reasonable to expect that centerline distance should depend upon the penetration of the jet. Jet pene-tration has traditionally exhibited dependency upon momentum flux ratio and this tendency is confirmed in Figure 11a. A strong decrease in centerline distance with momentum flux ratio is exhibited due to the in-ward orientation of the fuel injector. As penetration increases the fuel plume, as expected, develops closer to the centerline. Little dependency upon We is illus-trated as shown in Figure 11b. This is also consistent with the previous observation of weak We dependency on penetration. The liquid Re also exhibits the same centerline distance trend (Figure 11c). Increasing liquid Re effectively increases the fuel velocity which facili-tates jet penetration.

Swirl Direction

TOP VIEW

Momentum Flux Ratio

Matrix 6

Matrix 1

Matrix 9

Matrix 8

Web

er N

umbe

r

Matrix 10

Matrix 2

Matrix 5

Figure 10. Imaging Results

The plume area is a function of dispersion which intuitively is related to both atomization and penetration of the liquid jet. As shown in Figure 12a, the plume area exhibits a modest increase with increased momen-tum flux ratio. As shown in Figure 12b, a stronger de-pendency upon atomization (i.e., We) is demonstrated. It has been found that a larger We leads to surface break up in addition to traditional column break up. Surface break up occurs near the base of the jet which allows droplet formation over a larger portion of the duct, therefore enlarging the area.

Matrix 1

Area is also seen to increase with liquid Re (Figure 12c). This can be explained by the role that turbulence plays in the break up of the jet. A laminar jet is very stable with a small number of internal forces. Most of the force to break up the jet must come from the air flow. A turbulent jet, on the other hand, has a large number of internal forces which requires little external force initiate break up, making it easier for the air to increase plume dispersion. 10

Matrix 2

Figure 13 presents the relation of the plume un-mixedness to the nondimensional groups. In this case, larger penetration increases the time to which the jet is exposed to the crossflow. The longer exposure en-hances mixing of the air and fuel producing a better mixed plume in the measurement plane. Figure 13a supports the conclusion of better mixing with larger penetration. Some dependency on We is also shown, though the correlation is very weak. Finally, liquid Re appears helpful in reducing unmixedness, likely for the reasons stated above.

Matrix 5

Matrix 6 Figure 14 indicates that momentum flux ratio and

liquid Re have the most influence on the angle of rota-tion. As q and Re rise, the angle of rotation decreases. This may indicate low penetrating jets are more suscep-tible to the swirling flow. We shows only a weak de-pendence (Figure 14b).

With the general dependencies of the criteria on individual dimensionless groups shown in Figure 11-Figure 14, the next step was to formulate a correlation for the plume characteristics. The first step required is to presume a form for the relationships between the criteria and the dimensionless groups. In the present work, an assumed form shown in Equation 6 was used:

Matrix 8

A qb Wec Red (6) Matrix 9

This form is a reasonable starting point based on examination of model forms in the literature. With this assumed form, two approaches were used in terms of regression analysis. First, a regression analysis was completed for each criterion that included all three di-mensionless groups: q, We and liquid Re.

Matrix 10

a) Centerline Distance vs. Momentum Flux Ratio

y = -0.1506x + 1.5369R2 = 0.9013

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5Momentum Flux

Cen

terli

ne D

ista

nce

(in)

b) Centerline Distance vs. Weber Number

y = -1E-05x + 1.4611R2 = 0.0125

0.0

0.5

1.0

1.5

2.0

0 2000 4000 6000Weber Number

Cen

terli

ne D

ista

nce

(in)

c) Centerline Distance vs. Liquid Reynolds Number

y = -3E-05x + 1.5982R2 = 0.7097

0.0

0.5

1.0

1.5

2.0

0 5000 10000 15000Liquid Reynolds Number

Cen

terli

ne D

ista

nce

(in)

Figure 11. Centerline Distance vs. Nondimensional Parameters.

a) Area vs. Momentum Flux Ratio

y = 0.0149x + 1.0445R2 = 0.0074

0.0

0.3

0.5

0.8

1.0

1.3

1.5

0 1 2 3 4 5Momentum Flux

Are

a (s

q in

)

b) Area vs. Weber Number

y = 1E-04x + 0.9057R2 = 0.4492

0.0

0.3

0.5

0.8

1.0

1.3

1.5

0 2000 4000 6000Weber Number

Are

a (s

q in

)

c) Area vs. Liquid Reynolds Number

y = 2E-05x + 0.946R2 = 0.2747

0.0

0.3

0.5

0.8

1.0

1.3

1.5

0 5000 10000 15000Liquid Reynolds Number

Are

a (s

q in

)

Figure 12. Area vs. Nondimensional Parameters

a) Plume Unmixedness vs. Momentum Flux Ra-tio

y = -0.0009x + 0.0059R2 = 0.6105

0.000

0.002

0.004

0.006

0.008

0 1 2 3 4 5Momentum Flux

Plum

e U

nmix

edne

ss

b) Plume Unmixedness vs. Weber Number

y = 2E-07x + 0.005R2 = 0.0538

0.000

0.002

0.004

0.006

0.008

0 2000 4000 6000Weber Number

Plum

e U

nmix

edne

ss

c) Plume Unmixedness vs. Liquid Reynolds Number

y = -2E-07x + 0.0063R2 = 0.4584

0.000

0.002

0.004

0.006

0.008

0 5000 10000 15000Liquid Reynolds

Plum

e U

nmix

edne

ss

Figure 13. Plume Unmixedness vs. Nondimensional Parameters

a) Angle of Rotation vs. Momentum Flux Ratio

y = -1.3947x + 61.647R2 = 0.2102

50

55

60

65

70

0 2 4 6Momentum Flux

Ang

le o

f Rot

atio

n (d

eg)

b) Angle of Rotation vs. Weber Number

y = -0.0007x + 61.897R2 = 0.0887

5052545658606264666870

0 2000 4000 6000Weber Number

Ang

le o

f Rot

atio

n (d

eg)

c) Angle of Rotation vs. Liquid Reynolds Number

y = -0.0004x + 62.982R2 = 0.3815

50

55

60

65

70

0 5000 10000 15000Liquid Reynolds Number

Ang

le o

f Rot

atio

n (d

eg)

Figure 14. Angle of Rotation vs. Nondimensional Parameters

The regression correlations and respective coeffi-cients of determination can be found in Table 4. Exam-ining the full analysis column for each of the perform-ance criteria, all the coefficients are relatively large. Moreover, Area and θ do not exhibit strong R2 values. On the other hand, L and PU show relatively high R2 values. Based on this, it may be tempting to conclude that the models shown for L and PU are suitable for scaling. Unfortunately, some of the basic dependencies already mentioned do not generally hold with the as-sumed form of correlation. For example, a strong theo-retical argument can be made for the centerline distance being inversely proportional to q, yet the full analysis indicates it is directly proportional. Hence, further analysis is warranted.

Table 4. Summary of Regression Analysis.

Full Analysis* Reduced Model

w/Maximum Pre-dictability

Area (R2)

377q0.7We0.9Re-1.4

(0.3742) 0.21Re0.03We0.5

(0.3625)

L (R2)

17.3q0.19We0.3Re-0.54

(0.8707) 1.18q-0.1

(0.8518)

θ (R2)

1.4q-0.38We-0.36Re0.7

(0.5713) 57.2q-0.05

(0.5358)

PU (R2)

0.31q0.35We0.67Re-1.02

(0.8925) 0.00185q-0.18We0.1

(0.8740)

* Multicollinearity Present Upon further consideration of the variables consid-

ered, it is observed that they are not truly independent. For example, an increase in q resulting from an increase in jet velocity increase will also result in an increase in Re if no other properties are varied This is referred to as “multicollinearity” and can have significant impact on the general applicability of any model developed.11 Typical mitigating strategies include adding additional data at strategic conditions to “balance” the matrix or removing terms. In the present case, a practical way to balance the matrix would be to gather data with liquids of varying densities and viscosities, but this was beyond the scope of the present effort. As a result, the second approach was taken and a model formulation based on physical understanding of the parameters was invoked. Furthermore, in order to maximize the value of the model, an approach was adopted to maximize predict-ability. This was done by forcing the slope of the rela-

tion between predicted and actual values to 1 and let-ting the R2 value degrade.

Based on the sensitivity analysis presented in Figure 11 to Figure 14, area, centerline distance, angle of rotation and plume unmixedness each exhibited rela-tively strong dependency upon one or more dimen-sionless groups. As a result, these observations were considered in a reformulation of the expression for each criterion.

The centerline distance exhibits strongest depend-ency on momentum flux ratio and liquid Re. Because the manner in which the distance is defined, higher pe-netration will result in lower values of centerline dis-tance. The momentum flux ratio is an obvious correlat-ing parameter as the centerline distance, of the parame-ters examined, can be most closely related to jet pene-tration. In the present case, it is observed that center-line distance decreases as momentum flux ratio in-creases as expected. Many prior studies have suggested a dependency upon momentum flux ratio.2,3,6 The de-pendency on Re is more difficult to explain. It has been suggested, for example, that shear mode (versus liquid column fracture) dominates the breakup at Re above 5000. Shear mode breakup may cause quicker jet brea-kup and thus, less penetration. Though the correlation with liquid Re is not strong, it supports this notion. However Re and q are also multicollinear with the pre-sent data set. With this in mind, a trial fit with Re re-moved from the correlation was made and it was found that removing Re has essentially no effect on the fit. As a result, the best fit correlation for the centerline dis-tance is given by Equation 7.

1.018.1 −= qL (7)

Penetration into a uniform crossflow typically has a square root dependency on momentum flux,2,3,4,7 the result of Equation 8 suggests an impact of other factors in the case of the swirling crossflow. In particular, the centripetal forces on the droplets will tend to suppress the momentum flux dependency. If the liquid were injected from the centerline outward, it is likely that the exponent on momentum flux would be greater than 0.5. This result suggests direct application of penetration expressions from uniform crossflow will be inappropri-ate for the swirling crossflow, although the general form of the expression (i.e., momentum flux depend-ency) appears to remain.

The plume area appears to be most dependent upon We and liquid Re. The liquid Re dependency is again associated with enhanced shear mode breakup with increasing Re mentioned above.12,13 The We depend-ency is associated with the expected role We plays on atomization, with higher value resulting in enhanced breakup and thus more rapid spread of the fuel. The

best predictability regression analysis conducted on the Re and We dependency of the plume area indicates an optimum form as illustrated in Equation 8.

5.003.0021.0 WeReArea = (8)

In terms of plume area, previous work identified a

relationship between area and momentum flux ratio:

0.520.34121 jet

xArea A qd

⎛ ⎞= ⎜ ⎟⎝ ⎠

(9)

If Equation 9 is applied to the current results, a rea-

sonable fit results as shown in Figure 15. Some scatter is exhibited, but the trends are well represented. This is interesting in that the momentum flux ratio dependency is not indicated in the sensitivity analysis shown in Figure 12a. In the present work, only a single axial distance was studied. As a result, strong conclusions cannot be made regarding general applicability of Equation 9 in this case.

y = 1.0184x - 0.1673R2 = 0.289

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0 2.5Area (Current Study)

(Are

a, W

u, e

t al.

1997

)

Figure 15. Comparison of Existing Area Correla-tion with Current Results.

In terms of plume unmixedness, it is expected that

phenomena that improve atomization and spreading should lower unmixedness. In the present case, Figure 13b shows Weber number had an inverse impact on mixing. This implies that improved atomization has an adverse effect on the uniformity of the fuel over the plume area. The mixing over the area of the plume is not necessarily related to the area itself. For example, it is possible to have a large plume area with a high con-centration of liquid at the center which will have rela-tively high unmixedness compared to a small plume area with a high concentration over its entire extent. This is an interesting result that suggests wider ranges

of drop sizes are helpful for overall mixing. Momen-tum flux ratio also influences the plume unmixedness. As momentum flux ratio increases, penetration in-creases and PU decreases, which indicates improved mixing. Equation 10 is the best fit regression for PU.

1.018.000185.0 WeqPU −= (10)

Momentum flux ratio (q) was found to be the most

influential parameter on angle of rotation (Equation 11). In this case, a relatively “weak” jet penetration results in a greater tendency to be accelerated in tangentially by the swirling flow. This results in a greater apparent rotation of the spray plume relative to the injection lo-cation.

05.02.57 −= qθ (11)

In summary, Table 4 compares the full analysis,

with all the nondimensional parameters, to the best pre-dictability regression and both R2 values. Note that eliminating one or more nondimensional parameter has very little effect on R2 values. Conclusions

The breakup and atomization of a liquid jet in a swirling crossflow at a range of temperatures and pres-sures was studied to (1) establish the role of swirl on the behavior of a liquid jet injected into a crossflow and (2) explore how well correlations based primarily on atmospheric data scale to high temperature and pressure conditions. Sixty instantaneous PLIF images were col-lected for a range of nondimensional parameters. Area, centerline distance, angle of rotation and plume un-mixedness were extracted from a registered time aver-aged image with an in-house analysis script.

A full regression analysis revealed that multicollin-earity exists between the nondimensional parameters. In order to mitigate this, physical understanding of the parameters and the general dependencies on individual nondimensional parameters aided in creating a reduced regression model with maximum predictability.

The results indicates that plume area increases with Re and We. The distance of the plume from the swirler centerline decreases as q increases. The absence of a square root dependence on q may be explained by the nature of a swirling compared to a uniform flow. Better mixing (low unmixedness) over the plume of fuel is attained by increasing q and perhaps even lowering We. Low momentum flux ratio jets are influenced by the swirl more so than are high momentum flux ratio jets.

Of all the performance criteria considered, center-line distance and plume unmixedness show the most promise for scaling.

The results obtained are a first step towards explor-ing the applicability of physics based models for behav-ior of liquid jets injected into a swirling crossflow un-der high temperature and pressure conditions. In the present case, the plume parameters studied suggest scal-ing with nondimensional quantities is reasonable to pursue. Additional analysis of the present and addi-tional data sets will strengthen the conclusion regarding appropriate scaling parameters to relate work done at atmospheric conditions to more representative engine conditions.

Nomenclature

C pixel D characteristic length d jet diameter L centerline distance N total pixel intensity q momentum flux ratio

2

2

cc

jj

UU

ρρ

Re Reynolds number

ν

UD

U average velocity We Weber number

σ

ρ dUcc2

x x pixel coordinate y y pixel coordinate ρ densityσ surface tension ν kinematic viscosity Subscripts c crossflow i index j jet

Acknowledgments The authors wish to acknowledge the support of Solar Turbines Incorporated for loan of the test section, and discussion of the results. References

1 Lefebvre, A.H. (1999). Gas Turbine Combustion. 2nd edn. Taylor & Francis. Philadelphia. 2 Becker, J. and Hassa, C. (2002). “Liquid Fuel Place-ment and Mixing of a Generic Aeroengine Premix Module at Different Operating Conditions”. Proceed-ings of ASME Turbo Expo 2002.

3 Stenzler, J.N., et al. (2003). “Penetration of Liquid Jets in a Crossflow”. AIAA Paper 2003-1327. 4 Becker, J. and C. Hassa. (2002). “Breakup and Atomi-zation of a Kerosene Jet in Crossflow at Elevated Pres-sure”. Atomization and Sprays. 12: 49-67 5 Wu, P.K., et al. (1997). “Breakup Processes of Liquid Jets in Subsonic Crossflows”. Journal of Propulsion and Power. 13: 64-73 6 Wu, P.K., et al. (1998). “Spray Structures of Liquid Jets Atomized in Subsonic Crossflows”. Journal of Propulsion and Power. 14: 173-182. 7 Lin, K.C., et al. (2002). “A Review on Penetration Heights of Transverse Liquid Jets in High-speed Flows”. Proceedings of 15th Annual Conference on Liquid Atomization and Spray Systems. 8 Masuda, B.J. (2008). Mixing and Analysis of a Liquid Jet in Swirling Crossflow. M.S. Thesis, University of California, Irvine, CA. 9 Otsu, N. (1979). “A Threshold Selection Method from Gray-Level Histograms”. IEEE Trans. Systems, Man and Cybernetics. 9: 62-66. 10 Sallam, K.A., Ng, C.L., Sankarakrishnan, R., Aal-burg, C., and Lee, K. (2006). “Breakup of Turbulent and Non-Turbulent Liquid Jets in Gaseous Crossflows”. AIAA Paper 2006-1517. 11 Myers, R.H. and Montgomery, D.C. (1995). Appen-dix 2—Multicollinearity and Biased Estimation in Re-gression in Response Surface Methodology—Process and Product Optimization Using Designed Experi-ments. John Wiley & Sons, New York. 12 Madabhushi, R.K., Leong, M.Y., Arienti, M., Brown, C.T. and McDonell, V.G. (2006). “On the Breakup Re-gime Map of Liquid Jet in Crossflow”. ILASS-Americas 2006. Toronto, Canada. May 13 Aaalburg, C., Faeth, G.M., and Sallam, K.A, (2005). “Primary Breakup of Round Turbulent Liquid Jets in Uniform Crossflows”. AIAA Paper 2005-734.