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Characteristics of Sprays Produced by a High Shear Atomizer

A.A. MostafaıFaculty of Engineering, Cairo University, Giza, Egypt

Numerical and experimental study is conducted to characterize the turbulent

structure of an isothermal spray generated by a high-shear atomizer. Measurements are carried out using a phase Doppler particle analyzer. Numerical calculations are performed using a finite-difference scheme which is based on a Lagrargian stochastic technique for the spray and an Eulerian treatment for the carrier phase. The mean velocity, number density and Sauter mean diameter (SMD) of the spray are presented at five axial stations downstream the injector exit plane. The comparison between predictions and experimental data indicates that the mathematical model is capable of capturing the main spray features and may be integrated into an advanced comprehensive spray model. As indicated by the comparison of the SMD with that generated by classical air-blast atomizers, the high--shear atomizer produces better atomization and may deserve more investigation.

Nomenclature

Cd = Drag coefficientłd = Droplet diameterłD = Nozzle inner diameterłF = Momentum exchange coefficientłG = Acceleration of gravity K = Kinetic energy of turbulencełM& = Mass source/sink term in equation (1)łm& = Spray mass flow rateł

1m& = Centerline value of m& at z/D = 8 and ma = 1.87 g/słP = Static pressurełR = Distance in the radial directionłU.u,U~ = Mean, fluctuating, and instantaneous velocity of the airłV,v,V

~ = Mean, fluctuating, and instantaneous velocity of the spray.

Greek Symbols = Kinetic energy dissipation rateł

v = Kinematics eddy viscosity of the airł= Material densitył= Volume fractionł

Superscripts k = Kth trajectory of a computational particle

Subscripts 1 = Air ł

= SprayłI = ith directionłr,z = Radial and axial directionsł

Abbreviations PDPA = Phase Doppler particle analyzerłSMD = Sauter mean diameterł

* Professor

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-3379

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. Introduction Most modem gas turbine combustors use aerating fuel injectors which operate on the concept of

providing high air velocity relative to that of the fuel. The performance of this class of injectors is significantly influenced by the method of preparing the liquid for atomization, internal mixing parameters, fluid properties, and operating conditions.1-6 One aerating fuel injection class, which operates over a wide range of conditions using unconventional types of fuels injects the liquid fuel onto the inner injector wall. The formed fuel film on the wall is subsequently sheared by a high velocity air stream that starts to break the liquid sheet within the nozzle itself. This technique is known as the high shear fuel nozzle7&8 and has been utilized in the development of what is called fuel nozzle/swirl cup assembly9&10 that helped the design and production of a series of gas turbine engines of low emissions.11 The present paper presents the main characteristics of sprays generated by a relatively simple high-shear injectorł

The behavior of sprays generated by a certain type of injectors is influenced by different physical phenomena that occur during the atomization process either inside the injector itself or after leaving it. This includes liquid breakup, spray dispersion, droplet-droplet interaction, momentum transfer between the spray and the surrounding gas, droplet evaporation and mixing with the carrier phase. The present measurements represent a data base for the assessment of the physical spray sub-models employed in turbulent spray simulation.

Advanced computational capabilities have made numerical simulation of complex real geometries quite visible. In the mean time several mathematical models have been proposed to simulate different physical aspects of spray atomization and transport.12&13 However, the validation of these models, indicated that much more efforts are still needed to get more reasonable predictions of real hardware configurations.14 This paper reemphasis the interaction between the two phases on both the mean and fluctuating levels.15-17 This interaction includes the momentum exchange due to the relative velocity between air and droplets. The second is the influence of the gas phase turbulence on the trajectory of the droplets.8-20 The third is the gas turbulence modulation due to the existence of droplets in the same control volume with air.19 This turbulence modulation occurs due to the inability of droplets to follow gas turbulent eddies. To take all these effects into account, a stochastic Lagrangian model and a two-phase flow turbulence model is considered in the present paper21ł

A phase-Doppler particle analyzer (PDPA) provides point measurements of the particle size and instantaneous velocity of both phases.22 Ikeda, Sekihara, and Nakajima23 investigated the optimum optical parameters of PDPA technique and indicated that these parameters should be optimized to have high temporal/spatial resolution and high data rate. They also emphasized that the optimization process depends on the local spray as well as the gas flow properties and therefore should be made at every measuring position. The operating parameters of the PDPA system used in the present measurements are optimized following the recommendations of Ikeda, Sekihara, and Nakajima.23 In the following sections, the experimental study and numerical model are described. The results of the mean velocity components of both phases, mean droplet size, and number density are presented and compared with the predictionsł At the end, a summary and conclusion of the present work are given.

II. Experimental Method A schematic diagram of the nozzle is shown in Fig. 1. The nozzle consists of a centrally mounted

tube having eight circular holes (0.5 mm each) around the tip. The liquid imparted from the circular holes is injected on the inner surface of the radial inflow air passage. The inner diameter of the injector is 5 mm, the liquid tip angle is 45° and the radial inflow surface makes 45° on the injector axis.

The injector is mounted on a two-dimensional traverse mechanism to scan the flow field. Thus, radial distribution of the measured quantities are obtained at five axial stations downstream the injector exit plane (z/D = 8, 12, 16, 20, and 24). The injector is directed downward and the spray is passed through a mesh to a collection tank. Three liquid flow rates (

lm& ) are considered; 7.91, 9.26, and 10.47 g/s. These

flow rates are obtained at liquid pressures (DPI) of 0.3, 0.4 & 0.5 bar, respectively. Four air flow rates (

am& ) are used; 1.53, 1.87, 2.16, and 2.41 g/s. The liquid gauge pressure before the nozzle exit is

relatively low and serves primarily to distribute the liquid uniformly throughout the internal nozzle holes. Water delivered by a pump is passed into a fine filter ahead of the injector. The quantity and pressure of the liquid phase is regulated by means of a by-pass line. A high-pressure air reservoir is connected to the atomizer through a pressure-regulating valve. The mass flow rates of water and air are measured by two different orifice meters. Water and air pressures are measured by a Borden tube and an electrical capacitance gages, respectivelył

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Fig.1 High Shear Fuel Nozzle

The spray characteristics are measured by a phase-Doppler particle analyzer, PDPA.22&23 The whole spray diagnostic system is composed of five major components, a 10-milliwatt Helium-Neon laser and mirrors, transmitter (Hughes-model 3227 H-PC), receiver (Aerometrics model 2100-1), processor (P/DP 3190-L), and a personal computer. An oscilloscope is used to monitor the signal quality. As the measurements progress from one point to another, the size, velocity range as well as frequency shift are changed and the high voltage is adjusted. As thus the system parameters are continuously adjusted to provide a high quality of the Doppler signal in such a way that the total rejection counts do not exceed 15% at any point.

III. Numerical Model The governing equations of the droplet motion are based on the Lagrangian approach while the

equations of the carrier phase transport follow the Eulerian treatment21. The effect of the carrier phase on the spray dynamics is simulated following the Monte-Carlo method. The turbulence modulation, due to the existence of the spray in the same control volume with air, is considered by adopting a two-phase flow turbulence model.21 Only the modeled equations are given here. The equation of motion of the kth computational particle in the ith direction is given by:

( ))1(

~~

ikd

kii

ki g

VU

dt

dV +−=τ

where uUU +=~

)2(~~3

4

1

2

kd

kkd

VUC

d

−=

ρρτ

In Equation (1), Ui is obtained from the solution of the mean flow equations of the carrier phase while ui is obtained from the turbulence kinetic energy of the carrier phase21. The modeled mean equations of the carrier phase are:

( )

( ) ( )

( ) ( )∑

∑

∑

−−+Φ−−=+

−+Φ−+−=+

=+

kr

krr

kkkrrrrzrz

k

kzz

kkk

rrztzrzrzzz

k

krrzz

rKr

VUMFPUUUU

VUMFUrvr

PUUUU

MrUr

U

)5(3

2)(

)4()(1

)3(

,1

,,1,1

,,1,,1,1

,1

,1

ρρρ

ρρρ

ρρ

&

&

&

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In Equations (3)-(5), the comma suffix notation indicates differentiation with respect to the spatial coordinate z and r. The modeled equations for the turbulence kinetic energy "K", and its dissipation rate " " in the two-phase flow are:

)7(1)(2

)(1

)6(1)(2

1

3

2

12,,11

,

,1,1,1

1,,1

,

,1,1,1

∑

∑

+

−+Φ−

−+

=+

+

−+Φ−

−+

=+

kkdL

Lkkk

rzrzt

r

rt

rrzz

kdL

Lkk

k

k

rzrzt

r

rk

trrzz

MFKK

c

KcUUv

Kc

vr

rUU

MFK

UUvrKv

rKUKU

τττε

ερρεεσ

ρερερ

τττ

ερρσ

ρρρ

ε

εεε

&

&

The carrier-phase governing equations are solved numerically using a computer program based on Spalding’s parabolic marching finite difference solution procedure24. The calculations are performed using a fine grid with 60 cross-stream grid points and marching step sizes limited by 2% of the current radial grid width or an entertainment increase of 3% whichever is smaller. The ordinary differential equations governing the particle motion are solved using a second-order finite difference algorithm. Twelve thousands particles are used for the stochastic treatmentł

IV. Results and Analysis Measurements are performed at different liquid and air mass flow rates to study the effect of the

relative velocity between the atomizing air stream and the liquid at the atomizer exit planeł Since the spray point measurements can not be performed in the dense spray region just downstream the injector exit, the measurements started at 2 cm (z/D = 8) downstream the nozzle and continued at four other downstream stations (z/D = 12, 16, 20, & 24)ł The axial distribution of the SMD and the spray velocity at the center line and reported. The radial distribution of the air and spray velocities, SMD and liquid mass flow rate are also presentedł

Figures 2 and 3 present the radial distribution of the normalized spray mass flow rate and the SMD. Here the mass flow rate is normalized by the corresponding value at the first measurement plane at

am& = 2.16 g/s. It can be seen that at any axia1 station the spray mass flow rate is quite small and the peak value does not occur at the centerline which means that the atomizer generates nearly a hollow cone spray. With increasing the downstream distance and because of the high spray concentration away from the injector centerline, some droplets disperse radially towards the centerline and more of them towards the spray outer edge. Figure 3 indicates that the peak value of the SMD is almost at the same radial location of the peak value of the liquid mass flow rate and minimum values are at the centerline. In response to air turbulence, different droplet sizes spread radially with different rates and react to air turbulence with different responses. The turbulent dispersion of the liquid droplets depends on their relaxation time scale compared with the Lagrangian time scale of turbulence. The ratio of the two time scales depends mainly on droplet size and the relative velocity between droplets and air. The different response of the spray size distribution enhances the droplet coalescence, especially at the spray outer edge. This explains the increase in the SMD at the outer spray edge as the downstream distance increases. Figures 2 and 3 show that the mathematical model yields a fair agreement with the experimental data. However, the difference between predictions and experimental data is relatively large at the outer spray edge. This is attributed to the limitations of the model in simulating the interaction between the spray and the entrained air encountered at the outer spray region. Figures 2 and 3 indicate that the increase of the air mass flow rate achieves smaller SMD. The spray of smaller droplet spreads radially with a high rate and causes a reduction in the peak of the liquid mass flow rate as can be seen in Fig. 2. The high air mass flow rate produces a high air velocity that increases the shear force on the liquid sheets and hence improves the primary atomization close to the nozzle exit plane. High air velocity also assist secondary atomization and hence reduces the size of the largest droplets in the spray as can be seen Fig. 3.

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Fig. 2: Radial Distribution of Normalized Spray Mass Flux at DPI = 0.3 bar

The SMD is a useful quantity to understand the basic and global spray featuresł Understanding droplet dynamics requires presentation of some other detailed quantities such as droplet size distribution, mean and root mean square velocity components, and accumulative functions. Figure 4 presents the droplet size distribution measured at z/D = 20, and at the nozzle centerline, the spray centerline, as well as the outer spray edge. Here, the center of the spray is located at the point of maximum number density over the cross-section. The number of samples in each size class is corrected for the change in relative cross-sectional area of the measured value with droplet size. With a gaussian

Fig. 3: Radial Distribution of Sauter Mean Diameter at DPI = 0.3 bar

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beam intensity distribution, larger drops are detectable over a larger region of the measuring volume. The uncorrected distribution is shown as white dots within the bars of the plots. Figure 4 shows that diameter ranges from 5 to 65 µm at the nozzle centerline In the center of the spray (r/D = 1.8), there are some large droplets (up to 130 µm) with relatively small number densitył The size of the large droplets increases and reaches 175 µm at the spray outer edgeł Figure 4 also shows the fractional volume of the spray contained in droplets smaller than a certain droplet diameter. The SMD of the spray can be computed by appropriate integration of the distribution functions presented in Figure 4ł

Figure 5 compares the predicted mean axial velocity of the spray with the measurements. The spray velocity represents the average velocity of all droplet sizesł Figure 5 shows that the measured spray velocity at the nozzle centerline has a value of 40 m/s at z/D = 8 and decays to 29 m/s at z/D =24. The change of this velocity is attributed to the radial spreading of both the spray and air that causes axial velocity decay with increasing axial distance. The second cause is the momentum transfer between the two phases due to the relative velocity between them. Figure 5 also indicates that the mathematical model is capable of predicting the mean spray velocity with fair agreement with the experimental datał

Fig. 4: Droplet Size Distribution at z/D = 24, Dpa = 40 mm Hg. And DPI = 0.3 bar

Fig. 5: Predicated and Measured Spray Mean Velocity at m& a = 1.87 g/s and DPI = 0.3 bar

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Different air and liquid mass flow rates produce different degrees of interaction between dispersed and carrier phases downstream the injector exit plane. The degree of interaction between the spray and gaseous phase influences the size distribution which has impact on the spray behavior with respect to the desired applications. Figure 6 presents the effect of air mass flow rate on the axial variation of the Sauter mean diameter at different liquid mass flow rates. Figure 6 shows that the SMD decreases monotonically with the increase of the axial distance. This might be attributed to the secondary atomization and the droplet evaporation. Figure 6 also indicates that the SMD decreases with the increase of the air mass flow rate. The increase of air mass flow rate increases the relative velocity between air and spray and consequently increases the shear force on the liquid film. As the shearing force increases, atomization gets better and more droplets of smaller sizes are generated and consequently smaller SMD is obtained. This figure also shows that increasing the liquid pressure from 0.3 to 0.5 bar did not decrease the SMD substantially. The increase in liquid pressure or liquid mass flow rate increases both the liquid film thickness and velocity and hence the liquid film velocity does not change linearly with the liquid mass flow rateł

Figure 7 shows the present SMD obtained using the high-shear nozzle compared with the results of Rizk and Mongia.25 Here, the SMD is the average value over the cross-sectional area at z/D = 24. Rizk and Mongia25 performed detailed studies on prefilming air-blast atomizers under different operating conditions and fuel types. They modified the well-known Rosin-Rammler function according to their results and many other published data. Their function is presented in Figure 8 as a continuous curve, while the present results are shown as symbols. Although, Rizk and Mongia25 results are obtained with atomizers having swirling motion for both the liquid and air, the high-shear atomizer produces sprays with much smaller SMD. This result reflects a better atomization level that can be achieved with the high shearing atomizer technique.

V. Summary and Conclusions Turbulent spray predictions are presented and compared with the experimental data of a high-shear

atomizer. The data are obtained with a phase Doppler particle analyzer while predictions are performed using a finite difference computer programł Turbulent dispersion of the liquid droplets is numerically simulated by employing Monte-Carlo method. Turbulence modulation effects are considered by adopting a two-phase flow turbulence model. Results indicated that high-shear atomization technique produces good atomization even with low air pressures. In contrast to the effect of liquid mass flow rate. air mass flow rate has a significant effect on the atomization level. The numerical predictions are

Fig. 6: Axial Variation of Sauter Mean Diameter (SMD) ( am& = 2.41, am& = 2.16, am& = 1.87, + am& = 1.53 g/s)

Fig. 7: Comparison With Conventional Air-Balast Atomizers

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in fair agreement compared with the experimental data. The present findings indicate that more investigation on different operating conditions and various fuel types are necessary to visualize the possibility of using the high-shear atomization technique in the newly developed gas turbine enginesł

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