Effect of ambient pressure on an airblast spray injected into a crossflow

The injection of a fuel spray into a cross stream was studied for its application in rapid fuel – air mixing for lean combustion processes. The fuel is injected as either a discrete stream or as a partially to fully atomized jet of droplets. Of particular interest was the penetration of the outer and inner edges of the spray of liquid fuel into the gaseous airstream. The experiment focused on exploring the effect of (cid:2)ow conditions on the spray surface trajectories from the point of injection to a downstream distance of z / D fuel = 35. Tests were conducted under ambientpressures of 1, 3, and 5 atm at atomizingair pressure drops varyingfrom 0 to 4.8% for a jet-A fuel (cid:2)ow of 0.18g/s anda baseline cross(cid:2)ow airvelocity of 38m/s. A modi(cid:3)ed de(cid:3)nitionof the jet-to-cross(cid:2)owmomentum-(cid:2)ux ratio q 2 wasdevelopedto accommodatea two-phasejet andwassubsequentlyused to obtaina relationshipbetween the (cid:2)ow conditionsandthespray surface trajectories. The effect of the degree of atomizationin thespray resulting from the changein operating conditionswas incorporated by implementinga pressure ratio correction factor into the correlating equation.


Introduction
T O meet increasingly stringent emissions regulations, combustors for the next generation of advanced gas turbine engines are being designed to reduce pollutant formation while maintaining efcient performance. These combustors may operate under fuel-lean conditions to avoid the high temperatures that are associated with stoichiometric combustion and that are also conducive to the formation of pollutants such as NO x . Operating the combustor under fuel-lean conditions may still result in high rates of pollutant production if the fuel and air are not thoroughlymixed in both spatial 1;2 and temporal domains 3 before reaction. In addition, stability needs to be maintained and is generally degraded by improved mixing. Hence, the dispersion of liquid fuel into air must be optimized to maintain stability while minimizing pollutant formation.
A simple method of fuel injection involves the injection of a liquid jet into a high-velocity cross ow of air. The cross ow in-duces pressure drag and viscous drag forces on the jet, leading to the primary breakup of the jet through the fracture of as well as stripping at the surface of the jet column. The residual ligaments and drops produced by primary atomization then undergo secondary breakup by the cross ow until a critical Weber number is attained. The injection of pure liquid jets into a cross ow has been the subject of numerous studies 4 20 that have characterizedjet breakup, 4;8;10 13;16;17;19 penetration, 4 6;15;19 and the resultant distributions of mass ux, droplet size, and droplet velocity 7 9;14;16 18;20 of the atomized liquid jet.
One particularfuel injection techniquebeing consideredin future low-NO x combustionstrategiesinvolvesthe injectionof a fuel spray into a cross stream of high-velocity air. The spray jet in this study differs from the liquid jet in that it is composed of atomized liquid particles in the form of ligaments and droplets. Injecting the fuel as a partially atomized spray reduces the mixing length otherwise needed to break up a pure liquid jet. The jet-cross ow dynamics and interaction, if properly delineated, also offers the potential of adjusting jet penetration and droplet dispersion to provide optimal performance across the entire duty cycle.
The dispersion of spray jets in a cross ow has been investigated in studies geared toward agriculturalapplications,for which a spray drift in weak crosswind velocities that are typically less than 10 m/s is simulated. 21 24 The spray jets in these studies were producedfrom at-fan pressure atomizers. An alternative to using pressure-based atomizers is to use a high-velocityairstream to help induce instabilities leading to the breakup of the liquid jet. In gas turbine combustion, fuel injectors that employ airblast atomization require lower supply pressures to deliver the fuel, while also partially premixing the air and liquidfuel before its mixing with the rest of the air ow for combustion. 25 Plain-jet airblast atomization, combined with the jetin-cross ow mixing dynamics, offers a simple and practical means of effecting a uniformly and rapidly mixed fuel-air mixture for gas turbine combustion.
A review of the literature yielded few studies related to the airblast-atomized spray jet in a cross ow. Although the dispersion of a particle-ladenjet, composed of a gaseous jet loaded with spherical particles, could simulate the spray jet in cross ow system, the studies performed on particle-laden jets 26 28 have primarily been con ned to classes of uniformly sized particles. Predictive models have also been applied to determine the trajectory of droplets in different size classes. 29;30 Although they are helpful in determining the penetration of different classes of size particles, the ndings in Refs. 26-30 do not incorporatethe case of the spray that is not fully atomized as it emerges into the cross ow. 1076 A few studies have been performed on an airblast spray injection experiment in which distributions formed from the dispersion of the airblast-atomized spray jet into a cross ow were characterized. The experiments described in Ref. 31 feature a custom set of hardware that injected an airblast-atomized spray jet from a round ori ce into an uncon ned, uniform cross ow of air. Tests reported in Refs. 31 and 32 were performed under atmospheric pressure and utilized methanol as the test uid. Although the results were useful in demonstrating the utility of the experiment and in assessing trends from the parametric tests, the geometric and operating conditions did not approach the practical conditions of an industrial gas turbine combustor. As a step toward bridging these experiments with practical applications, the present study is conducted under elevated pressures, with the use of a distillate fuel as the liquid injectant and with the implementation of a con ned cross ow width that corresponds to the gap in an existing fuel injector design. 33 Because the intent of the experiment is to gauge the effect of pressure on the spray jet formation and dispersion, elevated temperatures were not considered to preclude the effect of vaporization on the spray.
The previous tests described in Refs. 31 and 32 focused on characterizing planar distributions of liquid concentration and droplet size and velocities within the spray. However, views of the overall structure and penetration of the spray, obtained through video imaging, can be as effective and also more ef cient in screening the performance of a multitude of spray conditions. Whereas the spray can be assessed qualitatively, the extent of its penetration into the cross ow can be quanti ed by correlations. The penetration of the jet can be described by the loci of a maximum measured quantity, such as velocity and temperature for a gaseous jet, 34 or volume ux for a liquid jet. 20 Liquid jet penetration has also been quanti ed by considering their outer surface penetration. 19 In this experiment, the penetration of the spray jets is characterized by quantifying the outer and inner trajectories of the spray surface.
The objectives of this study were to conduct screening tests of a plain-jet, airblast spray jet-in-cross ow injector at conditions that approach geometric and operating conditions that are more applicable to gas turbine engines, and to use the results to develop correlations that describe the outer and inner boundaries of the spray. Such equationscan be used as a design tool for engineers to determine the tendency of the spray toward over-and underpenetration,as well as to describe the extent that the spray spreads across the cross ow.

Hardware and Facilities
The hardware used in this experiment (see Fig. 1) is the same as that designed and tested in Ref. 31. However, modi cations made to the hardware, which included shortening the fuel tube and integrating a traversingsystem, facilitated the installationof the experiment into the elevated pressure facility. Care was taken to ensure that these modi cations did not impact the spray behavior compared to the previous hardware. Additional modi cations to the injection panel facilitated the interchanging of parts to vary the geometric con guration, but the changes did not affect the internal ow path of the injector or the spray behavior. The experiment is oriented for spray injection in the Cx direction and a cross-stream air ow along the Cz direction. The origin is concentric with the ori ces of the fuel injector and the spray injection panel.
The hardware primarily consists of the cross ow-conditioning section and the spray injection panel. The cross ow-conditioning section is designed to transition the air ow from a 152.4-mm-diam circular pipe to a rectangular cross section measuring 18.0 by 76.2 mm, with the former value representing the maximum allowable penetration distance of the spray jet. Although the study in Ref. 31 utilized a wider cross section of 101.6 mm, the 18.0-mm transverse width of the present study corresponds to the gap in the mixing section of the fuel injector used in a lean-burn combustion strategy. 33 The rectangular duct that con ned the cross ow comprised the spray injectionpanel, an opposing stainlesssteel panel, and two side quartz window panes through which the spray was measured. The geometry of the spray injection panel (see Fig. 1) was also based on the dimensions of the lean-burnfuel injector described in Ref. 33. A stream of liquidfuel emergesfrom the fuel injector tip through a hole of diameter D fuel D 0:34 mm. The tip of the fuel injector protrudes 1.59 mm from the back face of the spray injection panel, which corresponds to a distance that is one-half of the total atomizing air channel width. Air is supplied to the channel (of length times width times depth of 92.7 £ 19.1 £ 3.18 mm) such that the air impinges on the liquid fuel from opposing directions. The atomized liquid and air mixture emerges from the 3.18 mm-thick injection plate into the cross ow through a spray ori ce diameter of D spray D 2:26 mm. The discharge coef cient C d of the spray ori ce was 0.63.
To vary the ambient pressure in the tests, the hardware was installed in the elevated pressure facility (see Fig. 2). The pressure vessel is rated for operation of up to 15 atm and provides optical access to the spray through ports containing 44.5-mm-thick oblong Pyrex windows.

Conditions
The experiment was operated under ambient pressures of 1, 3, and 5 atm (1.0, 3.1, and 5.2 bars). The fuel and air temperatures initially entered the test section at 20 ± C. The airblast air ow rate is adjusted to yield various atomizing air-to-liquid mass ow ratios (ALR) that produce different pressure drops across the injection ori ce. The corresponding airblast pressure drops varied from 0 to 4.8% of the ambient pressure in the vessel. The mass ow rate of the liquid fuel, jet-A (Unocal), is maintained at a constant mass ow rate of 0.18 g/s. Whereas temperature is not a variable in this experiment, the ambient pressures, fuel ow, and atomizing and cross ow air ows correspond to a low-power operating regime in practical engine applications.
Although the baseline cross ow velocity magnitude was set at 38 m/s, the cross ow was also set at two other velocities at the airblast 1P D 2% setting: 46 and 54 m/s for the 1-and 3-atm cases and 31 and 46 m/s for the 5-atm case. The 5-atm case used a lower set of cross ow velocities to avoid jet attachment to the near wall of the injection panel. Laser anemometry (phase Doppler particle analyzer, Aerometrics transmitter Model 1100-3S and receiver Model 2100-3) was used to measure the uniformity of the cross ow velocity pro le at 5 atm. Alumina particles (Microgrit WCA, size 3, microabrasives) of a size range between 2.85 and 3.71 ¹m, yielding Stokes numbers less than 1 for the range of cross ow velocities tested, were seeded into the cross ow of air to measure the velocity pro le. The transverse and axial velocity components of these particles were obtained across a grid of points located at a plane above the ori ce at z D 5 mm. The grid of points was limited in scope by the potential clipping of either the laser beams from the transmitter or the collection cone of the receiver. As a result, the grid was con ned to a cross section limited to 30 < y < 30 mm, and 2 < x < 15 mm. Spatial deviationsof the axial velocity over this region were found to be within 2% of the mean value. The maximum turbulent uctuation of the axial component was 10%. With regard to the other velocity components, the transverse (x direction) velocity componentwas within 4% of the mean axial component,whereas the y-directional component of the cross ow velocity was assumed negligible. Overall, the measurements indicated that the cross ow velocity primarily comprised the axial velocity component and was uniform in both magnitude and direction.

Diagnostic
High-magni cation video (Fig. 3) characterizedthe global behavior of the spraysfor a wide range of conditions.A 60-Wincandescent ood lamp housed in a re ective dome illuminated the spray from the rear. A charge-coupleddevice video camera (Toshiba 1KM41A) attached to a long distance microscope lens (In nity Model KV) captured a eld of view measuring 13.9 £ 8.9 mm, with an image resolutionof 29.6 pixels/mm. A 30-s segment of video was recorded using a video cassette recorder (Sony SVO-2000). A computer acquired images from the video and returned a 15-frame-averaged image that was processed to reduce background noise.
For each frame-averaged image, the spray outer and inner surface trajectories were mapped to clarify the extent that the spray penetrated into the cross ow. The spray boundary was denoted by pixel intensity values greater than a threshold level of 30 (out of a maximum intensity level of 255), which was the minimum value that distinguished the shape of the spray.

Momentum-Flux Ratio of the Two-Phase Jet in Cross ow
To compare results from the various test combinations of ALR, cross ow velocity, and ambient pressure, a nondimensionalparameter was sought to cast the ow conditions on a common basis. For a jet in a cross ow, an important ow parameter that determines jet penetration is the jet-to-cross ow momentum-ux ratio. 35 For a single-phase jet, the momentum-ux ratio q is simply de ned as where the jet refers to either gaseous or liquid phase and the subscript for q refers to the number of phases of the jet. Although the present de nition of q suitably de nes single-phase jets, this definition does not represent very well a two-phase jet such as that encountered in the present experiment. Because the penetration of the jet into the cross ow depends primarily on q, a similar parameter was developed to produce correlations describing the airblast spray penetration into the cross ow. For this study, a composite de nitionof the two-phase jet momentum ux is obtained to represent the numerator of Eq. (1). Given negligible fuel vaporization, as well as negligible kinetic energy losses, the exiting momentum of the spray on leaving the injection plate is presumed to be equal to the initial momentum of both uids before their entering the control volume (see the control volume in Fig. 4). The total momentum entering the control volume is given by where A liquid refers to the area associated with the fuel injection orice and A airbl corresponds to the difference between the area of the spray ori ce A spray and A liquid .
To obtain the momentum ux of the two-phase jet, the spray jet momentum in Eq. (2) is divided by A spray . The momentum-ux formulation for the two-phase jet q 2 can, thus, be de ned as where A liquid refers to the area of the fuel injector hole and A airbl refers to the annular region between the injection panel and fuel injector ori ce diameters. The areas in the q 2 expression refer to the geometric areas based on the injector dimensions. The densities of jet-A and air (for both airblast and cross ow air) used in the de nition are 819 and 1.19 kg/m 3 , respectively. For the different velocities used in Eq. (3), V liquid depends on the metered liquid mass ow rate, the density of jet-A, and A liquid ; V airbl is calculated from the pressure drop measurements across the spray ori ce; and V cross is derived from the metered cross ow air supply.
In the q 2 expression,the airblastcontributiondominatesthat of the fuel by two to four orders of magnitude. Although the air-to-liquid densityratio is on the order of 10 3 , the velocityof the airblaststream is at least 25 times as high as the fuel velocity. When squared, the atomizing air velocity nearly compensatesfor the low-densityfactor of the air. In addition,the area associated with the fuel stream is only 2.3% of the area associated with the atomizing air, which further decreases the impact of the fuel momentum contribution to q 2 .

Results
Baseline Case: Pure Liquid Jet (DP air = 0%, ALR = 0) A baselinecomparisonof a pure liquid jet injectedinto a cross ow at the different ambient pressure conditions is presented in Fig. 5. Time-averaged images of the spray are shown on a normalized intensity scale with white correspondingto 0 and black corresponding to 1. The spray is captured with the spray injected from the right side of the image. The left edge of the image correspondsapproximately to the midpoint of the cross ow channel, as depicted in Fig. 1. For each image, the single-phase jet to cross ow momentum-ux ratio q 1 and the Weber number We cross , based on the cross ow air velocity are noted. For comparison, the two-phase jet-to-cross ow momentum-ux ratio q 2 is also presented. Note that the q 2 values are lower because they differ from q 1 by a factor of A liquid =A spray . In addition,We cross is noted because the cross ow contributesprimarily to the aerodynamic breakup of the liquid jet.
In the 1-atm case, the outer and inner surfaces of the jet are distinct. However, in the 3-and 5-atm cases, the inner spray surface is not distinctly seen because the spray attaches to the near wall. As the ambient pressure increases, the cross ow air density increases. This results in a decrease in q 1 and q 2 values that correspond to the decreasing penetration of the jet.
The increased density of the air also increases Weber number We cross , which suggests an increased tendency for liquid breakup. The extent of atomization by the high-velocity cross ow can be inferred by the expansion of the spray width with increasing downstream distance, because this expansion can only occur if the liquid jet is disintegrating. From Fig. 5, it is noted that an increase in ambient pressure leads to a progressive increase in the spread of the spray, which indicates a higher level of spray formation.

Effect of Airblast Air at Different Ambient Pressure Conditions
The introductionof airblast air into the system increases spray atomization, as observed in Fig. 6. The images in Fig. 6 are arranged by column, according to their ambient pressure condition, and by row, according to the following atomizing air pressure drop ranges of 1.2-1.5, 2.0-2.3, and 2.9-3.3%. For the purpose of this comparison, these three groups will be referred to as the 1, 2, and 3% ranges, respectively. Each image is also labeled with its two-phase momentum-ux ratio q 2 and its ALR.
Within each ambient pressure condition,the sprays follow the expected trend of increasing jet penetration with increasing q 2 . However, in comparing the sprays at each pressure condition, the spray penetration relationship to q 2 does not follow a linear function. For example, the q 2 values for the 1-and 3-atm cases at the 1 and 3% airblast 1P conditions differ only by 0.03 and 0.01, respectively, but these differences produce a large change in the penetration of the spray. However, a larger difference in q 2 between the 3-and 5-atm sprays does not affect the jet penetration to the same degree.
The effect of introducingthe airblast air can be seen by comparing the images from Fig. 5 (for 1 P D 0%) to those in the 1% 1P range, which are presented in the rst row of Fig. 6. A comparison between the 1P D 0% and 1 P D 1% images does not reveal any signi cant increase in breakup in the regions that are downstream of and in the near eld of the injection point. The jet that emerges from the injection panel is of the same dimension as the fuel ori ce, which indicates that the low atomizing air ow has not led to increased instabilities leading to the breakup of the jet. The 1% atomizing air 1 P setting mainly helps to propel the liquid jet farther into the cross ow. In the 3-and 5-atm cases shown in Fig. 6, the atomizing air helps to lift the jet away from the near wall, which enhances entrainment by the cross ow and the subsequent dispersal of the spray.
As shown in Fig. 6, a continued increase in the atomizing air pressure drop results in the airblast air atomizing the liquid within the spray ori ce beforeits injectioninto the cross ow. The 2% group of cases shows an expanded, atomized jet leaving the exit plane of the ori ce. Increasing the airblast pressure drop to 3% yields a fully atomized spray that extends across the ori ce exit, with a nodule of liquid forming at the trailing edge of the ori ce.
From these observations,three distinctjet shapes occur for similar atomizing air pressure drops at the different ambient pressure cases (see Fig. 7). The rst regime,which occursfor airblastpressuredrops in the 1 P D 1% range,yieldsan intact,discretejet structure (Fig. 7a) in which the diameter of the emerging liquid jet is approximately the same as the diameter of the fuel ori ce. The intact jet at the ori ce exit plane is similar to the intact liquid jet for the 0% airblast 1 P case in Fig. 5. The second regime, occurring for the 2% airblast pressure drop range, forms an atomized spray across the ori ce exit (Fig. 7b). The 2% airblast 1P condition appears to be optimal in producing sprays that are well atomized and devoid of the liquid nodule that is a potential source of large droplets near the injection wall.
The third regime, which accounts for air pressure drops greater than 3%, produces a fully atomized spray across the exit plane with the appearanceof a liquid nodule at the trailing edge of the jet ori ce (Fig. 7c). Although the percentage of liquid contained in the nodule relative to the spray is not known, the presence of this liquid nodule may be undesirable.In Refs. 31 and 32, for example, larger droplets were observed near the injector wall in an otherwise well-atomized eld of small droplets produced by airblast pressure drops above 3%. Because the spray injectionpanel is scaled directly to a research fuel injector used in Ref. 33, it is possible that the nodule does form under practical combusting conditions, in which case such images of the spray structure can provide clues regarding the combustion behavior in relation to the injector.
The formation of the nodule is thought to be caused by the separation-induced internal ow pattern in the thick-walled spray ori ce of the injection panel (L spray =D spray D 1.4) (see Fig. 7). An annular separation region forms as a result of the ow through the sharp-edged ori ce, which results in a vena contracta that restricts the effective area of the spray ori ce. Under such conditions, the lower airblast pressure drop range of 0-2% still produces atomizing air velocitiesthat are not high enough to break up the liquid column. As the airblast pressure drop is increased, the resulting increase in the atomizing air velocities induces surface atomization and column breakup. A continued increase in the atomizing air velocity initiates atomization sooner, as the onset of atomization approaches the exit plane of the fuel injection ori ce. A point is nally reached where the atomized spray interacts with the internal geometry of the spray ori ce such that the uid is concentrated toward the wall of the spray ori ce. Accumulating liquid probably forms along the circumference of the spray ori ce, but on injection into the cross ow, the dynamic pressure of the cross ow impacts the windward side of the spray jet and causes the pooled liquid mass to coalesce with the column of the jet. However, the pooled liquid along the leeward side of the spray jet is free from the impact of the cross ow and can, thus, form the nodule observed at the trailing edge of the ori ce.

Development of a Spray Trajectory Equation
Correlations describing the jet penetration into a cross ow of air have been obtained for both gaseous (for example, Ref. 34) and liquid jets (for example, Refs. 17 and 19). Based on phenomenological considerations, the jet in cross ow correlations adhere to the following general equation, whether the centerline of gaseous jets or the upper surface of liquid jets is being described: In this equation, c 0 , c 1 , and c 2 are empirically derived constants, and x=D fuel and z=D fuel represent the penetration and downstream distance, respectively, normalized with respect to the fuel ori ce diameter D fuel . For the pure liquid jet injection cases (1P D 0% and ALR D 0), the correlation from Ref. 19 was applied in which c 0 D 1.37, c 1 D 0.50, and c 2 D 0.50 (see Fig. 8). Plots depicting the outer and inner surface trajectories of the jets corresponding to the images in region, but diverges and overpredicts jet penetration in the plane of z=D fuel D 15. The 5-atm case, which maps only the outer surface of the jet because of the attachment of the inner surface of the jet to the wall, shows a poor t between the correlation and the mapped outer surface. The lack of t for the elevated pressure cases is not surprising, given that the correlation obtained in Ref. 19 was obtained under atmospheric conditions.
If the correlationof Ref. 19 were applied to the airblast-atomized spray jet, larger deviations between the correlating equation and the spray data would be produced. For a constant fuel ow rate and cross ow velocity,the value of q 1 would remain unchangedbecause the airblast air is not considered,and the correlatingequationswould yield the same results that are represented by the lines of triangles shown in Fig. 8. The airblastphase of the jet needs to be incorporated into the correlation to account for the effect of the momentum of the atomizing air on the dispersal of the spray into the cross ow. A new correlation can, thus, be obtained by applying the q 2 de nition to Eq. (4).
A multivariate, nonlinear regression was performed on the data, using Eq. (4) as the basis. Equations were sought to describe the outer and inner spray boundaries, which would be useful in determining the extent of the spray at different downstream locations. The regression involved casting Eq. (4) as a linear equation through a substitution of variables and applying a least-squares t on the resulting linear equation. The solved coef cients are then substituted back into the original equation.
The trajectory of the outer and inner surfaces of the spray for selected cases are shown in Fig. 9. The plots are arrangedby column according to their ambient pressure condition. The q 2 conditions that were selected corresponded to values of q 2 approaching 0.70 (top row), 2.5 (middle row), and 5.5 (bottom row). The plots are orientedsuch that the spray originatesfrom the bottom axis, with the cross ow entering from the left. The outer and inner spray surfaces are represented by the solid lines. The tracing of the spray surfaces excluded the liquid nodules that appeared in the 3% airblast 1 P cases.
Because the q 2 term is dominatedby the airblastcomponentof the spray, results from the gaseous jet correlation from Ref. 34, based on measurements of the loci of maximum velocity, are plotted to compare with the observed spray jet penetration. The gaseous jet correlation, represented by the crosshair marks, show a consistent underprediction of the spray jet penetration, that is, in a majority of the cases, below the lower surface trajectory. Although the spray jet trajectory, which is determined from the scattering of droplets in the spray, does not correlate well with the gaseous jet correlation, perhaps the atomizing air component of the spray does. It should be of interest to determine the dispersion of the atomizing air of the spray into the cross ow in further studies.
The curve ts that were derived for the outer and inner surfaces of the spray jet are also presented in Fig. 9 and are represented by the triangular marks. As observed in the plots, the trajectories in the 3-atm case are well described by the curve ts. However, the curve ts underpredict the spray trajectories at the 1-atm condition and overpredict the trajectories at the 5-atm condition. One reason for the insuf cient t lies in the lack of a term to account for the atomization quality of the spray because droplets of varying sizes experiencedifferentdrag forces, which would affect their trajectory. Because the ambient pressure affects the degree of atomization of the spray, one of the additional factors that was considered was a ratio of pressure normalized by a baseline pressure of P 0 D 1 atm. The pressure ratio was used instead of a density-related term such as a density ratio or Weber number because temperatures were not varied in this experiment. The resulting equation that was tted in the second iteration was Table 1 summarizes the coef cients that describe the outer and inner surface trajectories that were derived for Eq. (5) as well as for the original curve t in Eq. (4). In general, the power coef cients of q 2 for each of the four tted equations are low (less than 1), but are greater than the powers of z=D fuel . Whereas the power coefcients of q 2 and z=D fuel are positive, the powers associated with the pressure ratio are negative. These trends make sense, given that the penetration of the spray should increase with an increase in the momentum-ux ratio and the downstream distance and should decrease with an increase in the ambient pressure. The results of the modi ed curve ts are shown in Fig. 10. The spray surfaces are represented by the solid lines, whereas the triangular marks correspond to the t with the added pressure ratio factor. The plots in Fig. 10, which are representative of the results for the other spray conditions, show that the addition of the correction factor provided a better t to the data. The 17% average deviation of the outer edge curve t associated with the basic trajectory correlation in Eq. (4) decreased to 7.8% for the pressure-corrected correlation in Eq. (5). For the inner spray edge, the average deviation was 69.5% for the basic trajectory correlation and 50.6% for the pressure-correctedcorrelation. The pressure correction improved the t but was still de cient in predictingthe inner edge of the spray, which is a region most likely populated by smaller droplets that are detrained by the cross ow from the leeside of the spray jet. For the lower edge of the spray, a factor such as the Stokes number may need to be incorporated to account for the behavior of droplets that are being entrained into the cross ow.  The spray trajectory correlations that were obtained are valid for the operating and geometric conditions of the present study. These operating conditions correspond to a low-power operating regime in a gas turbine engine. Note that additional data are required at other conditions (e.g., at varying fuel mass ow rates, additional cross ow velocitymagnitudes,and differentspray ori ce diameters) to provide a complete variation of the q 2 parameter for equation tting. Nonetheless, the ability to t an equation to spray jets using a bulk parameter such as q 2 at various ambient pressure conditions is encouraging,especially given that varying degrees of atomization are obtained at the different conditions.

Conclusions
Spray scattering images were used to investigate the structure of the airblast-atomizedspray jet injected into a cross ow of air under varying ambient pressure conditions. At each ambient pressure, the airblast air ow rate was varied to yield airblast pressure drops ranging from 0 to 4.8% across the injector ori ce. The cross ow velocity magnitude centered on a baseline value of 38 m/s. For the airblastatomized liquid jet injected into a cross ow of air and under varying ambient pressuresof 1, 3, and 5 atm, the following conclusionswere found: 1) At a given jet-to-cross ow momentum-ux ratio in which the airblast pressure drop, fuel ow rate, and cross ow velocity are held constant, an increase in ambient pressure decreases spray jet penetration and increases breakup.
2) Across the range of ambient pressures tested, an increase in the atomizing air pressure drop, which increases the velocity of the atomizing air, results in an increase in spray jet penetration and breakup. Three modes of spray structure occur at the point of injection under different atomizing air operating regimes, independent of the ambient pressure: a) discrete jet (0 < 1P < 2%), b) atomized jet (2% < 1P < 3%), and c) fully atomized jet with a liquid nodule at the trailing edge (1P > 3%).

4) A jet penetration equation of the form
.x=D fuel / D c 0 £ q c1 £ .z=D fuel / c2 can be used to describe both outer and inner surface trajectories of the spray jet, if the following de nition of the two-phase jet to cross ow momentum-ux ratio q 2 is used: However, the added complexities of atomization and momentum transfer associated with the airblast ow produce spray trajectories that are better describedif the penetrationequation is corrected with a pressure ratio term P=P 0 . collection and processing of data. F. Akamatsu was supported by Kobe University and participated in this work while spending one year at the University of California, Irvine Combustion Laboratory.