Experimental Characterization of Liquid Jet Atomization in Mach 6 Crossflow

D. Masutti*, S. Bernhardt†, C.O. Asma‡ § and M.R. Vetrano**

von Karman Institute for Fluid Dynamics, Chaussée De Waterloo 72, 1640 Rhode-St-Genèse, Belgium

The atomization of water liquid jet in Mach 6 air crossflow is investigated. Experiments are conducted in the VKI H3 Mach 6 hypersonic wind tunnel. A flat plate, with a flush mounted 1mm diameter circular injector, is used to inject water into the crossing hypersonic air stream. The mean and Sauter mean diameter of the liquid droplets are measured at different locations along the median plane on the jet using Phase Doppler Interferometry technique. The droplet size measurements are analyzed and treated to characterize the atomization process of the liquid jet. The measured mean and Sauter diameters are compared with the existing correlations in the literature.

Nomenclature

jd , D0 = liquid jet injector diameter, mm

10D = droplet mean diameter, μm

32D = droplet Sauter mean diameter, μm n = constant

q = momentum flux ratio

Re = Reynolds number of liquid jet, based on injector diameter

STD = standard deviation

jU = velocity of liquid jet, m/s

∞U = velocity of crossflow gas, m/s We = Weber number x = horizontal (streamwise) distance to liquid injection point, mm

y = vertical distance to injection point, mm

δ = liquid jet penetration height, mm

jμ = dynamic viscosity of liquid jet, kg/m.s

jρ = density of liquid jet, kg/m2

∞ρ = density of crossflow gas, kg/m2

jσ = surface tension of liquid jet, N/m

*PhD Candidate, Aeronautics & Aerospace Dept., masutti@vki.ac.be † Trainee Student at von Karman Institute, Department of Physics, Konstanz University, Konstanz, Germany ‡ Research Engineer, Aeronautics & Aerospace Dept., asma@vki.ac.be § PhD Candidate, Department of Flow, Heat and Combustion Mechanics, Gent University, B-9000 Gent, Belgium.

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** Senior Research Engineer, Environmental & Applied Fluid Dynamics Dept., vetrano@vki.ac.be

39th AIAA Fluid Dynamics Conference22 - 25 June 2009, San Antonio, Texas

AIAA 2009-4220

Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

I. Introduction IQUID injection into a crossing hypersonic flow is a three dimensional and unsteady problem that has been widely investigated for the last fifty years. Its main application is fuel injection in supersonic combustion ramjet

(SCRAMJET) engines, with other applications such as thrust vectoring of high speed missiles or film cooling of re-entry vehicles. In 1960s, interest in transverse jet injection arose primarily from technical applications dealing with rocket thrust vector control and with control of hypersonic re-entry vehicles. In 1970s and 1980s, the injection of liquid jet into supersonic cross-flow was studied quite extensively in the context of the development of ramjet and scramjet combustors for aerospace applications.

L

As far as the fuel injection in scramjet engines is concerned, the combustion efficiency depends strongly on the liquid jet atomization and the consequent mixing between the atomized fuel and the free stream air1. The general flow topology of liquid injection in compressible cross-flow is shown in Fig. 1, where the liquid is injected through an injector which is flush-mounted to a flat plate with a sharp leading edge2.

Figure 1. General flow topology of jet injection in compressible crossflow.

The presence of liquid jet causes a bow shock to appear on the flat plate, downstream of the oblique shock wave at the leading edge of the flat plate. The adverse pressure gradient produced by this bow shock causes the boundary layer upstream to split and a separated flow region with a separation shock appears. The crossflow passes through this shock system before it interacts with the liquid jet column. Because of the nature of the bow shock with a varying angle, there is a considerable velocity gradient in the direction normal to the wall, which causes a high shear stress. The crossflow interacts with the liquid jet through this shear force on the surface of the liquid jet column. It causes the liquid jet to bend and disintegrate.

The interaction of the crossflow with the liquid jet causes waves to occur on the surface of the jet and it is believed that folding of these waves causes the occurrence of a counter rotating vortex pair, described by Ref. 3. Counter rotating vortex pair is not the only vortex system in the flow field. For example, there is also an “anti-kidney” vortex pair accompanying the kidney shaped vortex pair just above the concave part of the kidney shaped vortex system. The horseshoe vortex system emanating from the boundary layer can also be seen in Fig. 2.

Two major non-dimensional parameters are introduced for transverse jets in crossflows to classify the flow conditions. The first one is the ratio of momentum flux of liquid jet and crossflow (see Eq. (1)), and defines the momentum exchange between the jet and the crossflow. The second non-dimensional number is the Weber (We) number which is used to identify the breaking up mechanism of the jet depending on the ratio of the aerodynamic force of the crossflow to disintegrate the jet and the surface tension force of the liquid jet to resist to the shearing of the crossflow (Eq. (2)).

Figure 2. Schematic diagram of the flow structure

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2

2

∞∞

=U

Uq jj

ρ

ρ (1)

( )2

jj

j

d U UWe

ρσ

∞ ∞ −= (2)

Weber number determines the type of the break up mechanism of the liquid jet. For small values of We, the liquid jet breaks up due to surface waves appearing on the surface of the liquid jet. However, for high values of We, the break up is mainly due to shear forces appearing on the liquid jet-crossflow interface4. After the jet breaking up, the formed spray decomposes into smaller droplets until a final droplet diameter is reached. At this moment, the surface tension manages to overcome the aerodynamic force and the jet is completely atomized. This final droplet diameter depends strongly on the Weber number.

The Sauter mean diameter, also referred as D32, is defined as the diameter of a drop having the same volume/surface area ratio as the entire spray. The formulation to compute the D32 for a generic spray is presented in Eq. (3).

∑

∑

=

== N

iii

N

iii

Dn

DnD

1

2

1

3

32 (3)

II. Experimental set - up

A. Facility All experiments have been performed in the H3

Hypersonic Wind Tunnel of the von Karman Institute for Fluid Dynamics (Fig. 3). H3 test facility is a blow-down type wind tunnel. It can provide a uniform axisymmetric jet with a diameter of 12 cm at a speed of Mach 6. Dried air is supplied from a 40bar reservoir, which can provide stagnation pressures ranging from 7 to 35 bars. Air is heated up to 500K to avoid condensation in the test section. The Reynolds number of the flow can be varied between 3x106 and 30x106 m-1. The wind tunnel model to be tested is kept retracted before the test to avoid blockage of the wind tunnel and also to avoid excessive heating of the model during start-up. The test chamber is vacuumed prior to the test using a supersonic ejector. The model is injected into the flow field with a model injection arm, once the Mach 6 flow is fully established in the test chamber5. Within this campaign, all experiments are performed at a stagnation pressure of 20bar (± 1bar) and a stagnation temperature of 500K (± 20K), resulting in a unit freestream Reynolds number of 17x106 m-1.

Figure 3. Schematic view of the H3 Hypersonic Wind Tunnel

B. Wind Tunnel Model Experiments have been carried out over a 230mm x 80mm flat plate with sharp leading edge. The Flat Plate is

provided with different interchangeable water injectors for the water. The one used in all the experiment is a circular

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one with 1 mm of diameter. In Fig. 4, a sketch of the liquid injection system used in combination with the flat plate is shown. The main water supply is connected directly to a rotameter (L63/2400-16862 model) that is used to control and monitor the mass flow rate of injected water. With a manual valve it is possible to adjust the mass flow rate, therefore the velocity and the dynamic pressure of the water jet. Along its path, the pipe connecting the rotameter with the injector of the flat plate is covered with a solenoid resistor in order to heat the water. The heating of the water is necessary to prevent the formation of ice inside the test section due to the very low static temperature in the H3 wind tunnel (about 60 K).

Figure 4. Flat pate water injection system

C. Phase Doppler Interferometry The Phase Doppler Interferometry6 (PDI) is a non-intrusive laser diagnostic technique, for simultaneous

measurement of size and velocity of individual spherical particles in polydisperse flow environments. The measurement principle is based on elastic light scattering. The light scattering interferometry utilizes the wavelength of light as a measurement scale and, as such, the performance is not easily degraded, in terms of received power, as it is for a system using light scattering intensity information for the estimation of the particle size7.

The optical system consists of a laser emitting at a wavelength of 660 nm. A receiver equipped with three photodetectors is used to collect the light scattered by the particles and a Fourier transform based signal processor is used for the raw data processing. In the basic PDI system, the laser beam is divided into two beams of equal intensity by means of a beam splitter. A convergent lens is the used to make these two beams crossing each other. The volume defined by the intersection of the two beams corresponds to the measurement volume. A Bragg cell is used to shift the frequency of one beam in order to resolve the direction ambiguity that would occur for drops passing in a reverse direction. The phase shift produced by the different light refraction on the surface of the same droplet allows determining its size. In addition the Doppler difference frequency allows computing the velocity of the droplet.

The PDI system used is capable of measuring a drop size between 0.5 and 2000 μm and velocities up to 300 m/s downwind (-100 m/s for upwind particles). During the experimental campaign, different configurations of the PDI instrumentation have been tested in order to catch both the horizontal velocity vector and the diameter of the atomized water particles (called “spray” for simplicity from this point on). Within this campaign, the spray (conical shape) is considered to be generated through the water injection over Figure 5. Spray orientation

Figure 7. PDI setup (top view): The air flow is from top to bottom Figure 6. Correct PDI configuration

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the flat plate, in accordance with the coordinate system shown in Fig. 5. The correct PDI setup to characterize this type of spray is illustrated in Fig. 6. With this setup, one is able to detect the droplets diameter and the horizontal component of its velocity, paying attention to have a backward scattering angle (collection angle) between 30 and 40 degrees. Unfortunately this configuration cannot be realized in VKI H3 facility, due to little availability of optical access.

The most difficult part of the configuration procedure, is the impossibility to make a sensitivity analysis on the instrument’s parameters. Many of these parameters play an important role on the setup of the laser instrumentation. Since the VKI H3 facility can run only for few seconds, there is no time to change setup during a test seeing how these changes are affecting the measurements. Among the high number of selectable configurations, there are the interchangeable lenses of both the receiver and transmitter, the collection angle, the photodetector gain, the analog filter and the sampling rate.

To get through the reduced optical accessibility of the VKI H3 facility, different optical arrangements of the PDI instrumentation are worked on. An optimum configuration is favored, disregarding the velocity of the particles but acquiring the correct particle size. In the PDI setup illustrated in Fig. 7, the transmitter is placed on one side of the facility with the laser beam pointing the detection zone. The receiver is placed in the opposite side of the facility looking straight forward to the window (to avoid reflections) and focusing at the probe volume. With this configuration the probe volume is as small as possible, so the amount of noise created by spurious particles is reduced. The PDI setup parameter values are shown in Table 1.

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One drawback of this system is that the velocity vector

detected by the system is in the Y direction (see Fig. 5), which is not the interesting component for the tested configurations. However, as the main objective is to obtain data on droplet size, it is decided to continue with this setup despite its the lack of velocity data.

Table 1. PDI setup parameters

Parameters Value

Laser wavelength : 660 nm

Beam diameter : 2.5 mm

Beam separation : 60.3 mm

Transmitter focal length : 1000 mm

Receiver focal length : 1000 mm

Fringe spacing : 11 μm

Beam waist : 336.1 μm

Collection angle : 24°

Static range : 4.6 – 1099.9 μm

III. Experimental Results and Discussions Figure 8 shows the probability density function of the

droplet size for a single test. To better investigate the particular distribution, a Log-Normal curve (bold line in Fig. 8) is fitted on the data set. Although there is no theoretical model describing the expected drop size distribution, Log-Normal fit is used, based on probability considerations8.

Figure 8. Log-Normal distribution of droplet diameter

Figure 9 shows the evolution of the Sauter mean diameter (D32) and the mean diameter (D10) of the spray’s droplets over the number of validated data points. It can easily be observed how the detected droplet size is oscillating at the beginning of the acquisition period, converging to a stable value after 4000 validated data points, for both mean and Sauter diameters. This is a criteria for the acceptance of the test, any test with less than 4000 points in the data set is disregarded.

All the tests have been performed at y = 8mm above the flat plate. A first test campaign involves ranging the probe volume position along the x direction between x = 14mm and x=34mm downstream of the injector (Fig. 10), while the momentum flux ratio is kept constant at q = 4. The second test campaign has been made at a fixed probe volume position and for different levels of the momentum flux ratio. With the fluid dynamic properties of the hypersonic crossflow, the local Weber number and the local Reynolds number can be computed. Figure 11 and Figure 12 show respectively how the Sauter mean diameter (D32) and the mean diameter (D10) decrease with increasing distance from the injection point, for a constant value of q = 4. Observing Fig. 11, the trend of the experimental data suggests a first strong decrease of the D32 with increasing x-distance from the injector until x = 23mm. Further downstream of this point, a constant value of D32 is observed. This means that for the examined q = 4 value, the final atomization diameter is reached at x = 24mm. The hypothesis is supported observing the experimental data concerning the mean diameter D10 (Fig. 12), where the same decreasing trend of the Sauter mean diameter (Fig. 11) can be noticed.

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Figure 11. Sauter mean diameter versus x-distance from the injector (y = 8mm, q = 4)

Figure 12. Mean diameter versus x-distance from the injector (y = 8mm, q = 4)

The standard deviation of the experimental data is calculated using the definition of statistical uncertainty. The

plot of the standard deviation obtained as a function of the x distance from the injector is shown in Fig. 13. The standard deviation represented in non-dimensional units on the y-axis of Fig. 13, is divided by each mean diameter value of the corresponding data set considered.

Figure 9. Convergence of Sauter mean diameter and mean diameter as a function of the number of validated particles

Figure 10. Probe volume position along x direction

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Figure 13. Standard deviation versus x-distance from the injector (y = 8mm, q = 4)

For x = 34mm and y = 8mm, the variation of the Sauter mean diameter and the mean diameter for different q values are presented in Fig. 14 and Fig. 15, respectively. Figure 14 and Figure 15 show the dependence of Sauter mean diameter and mean diameter to momentum flux ratio q, for a fixed location at x = 34mm and y = 8mm.

Figure 14. Sauter mean diameter versus momentum flux ratio (x = 34mm, y = 8mm)

Figure 15. Mean diameter versus momentum flux ratio (x = 34mm, y = 8mm)

Both the D32 and the D10 are increasing with the increasing momentum flux ratio.

IV. Discussion and Conclusion Phase Doppler Interferometry technique is applied to liquid injection experiments into a Mach 6 hypersonic

crossflow, with the purpose of determining the mean and Sauter mean diameters and also to get more information on the atomization process of liquids injected into hypersonic flows. Several experimental setups are tried to find the optimum placement of laser and receiver (as well as the selection of different parameters) with the goal of measuring the droplet diameter. The droplet diameter data are plotted as histograms. Mean diameter, Sauter mean diameter and standard deviation are calculated and plotted as a function of distance from the injection point and momentum flux ratio.

The evolution of mean and Sauter mean diameters as a function of distance from the injection point is as expected. The diameter decreases asymptotically moving downstream of the injection point and eventually it reaches a constant value. This is an indication that the atomization process is completed at one point and downstream of this point, the mean or Sauter mean diameters do not change. This observation is also supported by the fact that the standard deviation of droplet diameter decreases with x, meaning that more droplets have diameters equal to or close to the measured mean diameter value. On the other hand, the behavior of mean and Sauter diameters as a function of momentum flux ratio q is open to discussion. Several works on liquid atomization in compressible crossflows10,11,12

suggest that the final Sauter mean diameter can be expressed as a function of Weber number and Reynolds number. The general form of this expression is shown in Eq. (4), where Re is the Reynolds number of the injected liquid

based on the injector diameter and We is the Weber number explained in Eq. (2). A more explicit form of the relation is shown in Eq. (5).

(4) nWeDD −⋅⋅= )(Re032

n−

jj

jjj UUUDDD ∞∞

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅

−⋅⋅⋅⋅⋅=

σμρρ 22

0032

)( (5)

In Equations (4) and (5), D0 and n are constants: D0 is taken as the injector diameter (1000μm in this case), and n is calculated to be 0.16 based on the experimental data, such that D32 is in μm. These coefficients are in agreement with the data in the literature10,11,12. However, the proposed correlation between D32 and the governing non-dimensional coefficients does not support the outcomes of Fig. 14, where the Sauter mean diameter is observed to be increasing with increased momentum flux ratio. Indeed, the momentum flux ratio can only be increased by increasing the liquid jet velocity; which would increase Re.We term in Eq. (4), as U∞ is always much bigger than Uj. The observation of D32 decreasing with increasing momentum flux ratio is also documented by Refs. 13 and 14. This discrepancy in the measurements can be observed with the fact that all measurements are taken at a single location, at x = 34mm and y = 8mm, no matter what the momentum flux is. However, it should be considered that both the starting location of the atomization zone, and also the penetration height of the liquid are proportional to the momentum flux ratio. The relation between momentum flux ratio and penetration height, δ, is given in Eq. (6)9. The penetration height increases significantly with q, thus the relative location of measurement point y/δ (for y = 8mm for all cases) changes also significantly, as presented in Fig. 16 for the range of q studied in this campaign.

Figure 16. Relative penetration height y/δ for y = 8mm

38.0

3.05.3 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

jj dxq

dδ

(6)

As the momentum flux is increased during the test campaign, the measurements taken at y = 8mm above the flat

plate should be seen as measurements taken at lower heights. This can be explained as the reason for the unexpected increasing of D32 with momentum flux ratio. Indeed, the Sauter mean diameter is expected to decrease as y is increased13,14. More experiments are conducted to find out if this is the case also for hypersonic conditions. Fig. 17 presents the mean (D10) and Sauter mean (D32) diameter as a function of distance from the wall, for a momentum flux ratio of q = 5 and at a downstream location of x/d = 34. The standard deviation is also shown on the same graph as error bars attached to D10 values. It can be noticed that both mean and Sauter mean diameter decrease with increasing y/d. The standard deviation of the measurements tends to decrease as well with increasing y/d, indicating a more homogeneous mixture at higher locations. The results presented in this plot is in agreement with the literature13,14,15.

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For a correct measurement campaign, one should always take measurements at the same relative position, preferably in the plume region, where the diameter of droplets is

Figure 17. Mean and Sauter diameter as a function of distance from wall, q=5, x/d=34

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expected to be minimum13,15. The plume (or the core) of a liquid jet corresponds to the height where the liquid population is at maximum9, or it is the area where liquid volume flux is greater than a certain value15. Typically, the plume is between 40% and 60% of the penetration height9.

Acknowledgments The authors wish to thank the French MOD, DGA (Marché N°.06.70.101.00.470.75.96) that provided the

support to carry out this work in the framework of a research contract. The staff of the Aeronautics and Aerospace Department of the von Karman Institute, Ms. Deniz Ayse Ozuncer and Prof. Olivier Chazot are kindly acknowledged for their helpful contributions.

References 1Margason R. J., “Fifty years of Jet in a crossflow research”, Computational and Experimental Assessment of Jets in Cross

Flow, AGARD-CP-534, 1993. 2Beloki Perurena J., “Experimental investigation of a liquid jet injection into a crossing hypersonic crossflow”, von Karman

Institute for Fluid Dynamics, Project Report 2007-04, June 2007. 3Blanchard J. N., Brunet Y., and Merlen A., ” Influence of a counter rotating vortex pair on the stability of a jet in a

crossflow”, Experiments In Fluids, 1999, Vol. 26, No. 1-2. 4Sallam K. A., et al., “Breakup of round non-turbulent liquid jets in gaseous crossflow”, AIAA Journal, December 2004, Vol.

42, No. 12. 5Boerrigter H. L., “Calibration of the H3 wind tunnel using Pitot probes”, VKI Internal Notes 94, December 1993. 6Bachalo W. D., “Spray diagnostics for the twenty-first century”, Atomization and Spray, Vol. 10, pp. 439-474, 2000. 7Albrecht H. E., Borys M., Damaschke N., and Tropea C., Laser Doppler and Phase Doppler Measurement Techniques,

Springer, 2003. 8Lefebvre A. H., Atomization and Sprays, Taylor & Francis, 1989, Chap. 3. 9Perurena J. B., Asma C. O., Theunissen R., and Chazot O., “Experimental Investigation of Liquid Jet Injection into Mach 6

Hypersonic Crossflow,” Experiments in Fluids, DOI 10.1007/s00348-008-0566-5, Vol. 46, No. 3, pp. 403–417, March 2009. 10Less D. M., and Schetz J. A., “Transient Behavior of Liquid Jets Injected Normal to a High-Velocity Gas Stream”, AIAA

Journal, Vol. 24, No. 12, December 1986. 11Ingebo R., and Foster H., “Drop Size Distribution for Cross-Current Breakup of Liquid Jets in Airstream”, NACA TN

4087, 1957. 12Harvey D. W., “Drop Size Distribution Resulting From Liquid Jet Injection across a Supersonic Stream”, AIAA Journal,

Vol. 11, No. 6, 1972. 13Nejad A. S., and Schetz J. A., “Effects of Properties and Location in the Plume on Droplet Diameter for Injection in a

Supersonic Stream”, AIAA Journal, Vol. 21 No. 7, 1983. 14Nejad A. S., Schetz J. A., and Jakubowski A. K., “Mean Droplet Diameter Resulting from Atomization of a Transverse

Liquid Jet in a Supersonic Airstream”, AIAA International Meeting & Technical Display, AIAA-80-0899, Baltimore, May 6-8, 1980.

15Lin K. C., Kennedy P. J., and Jackson T. A., “Structures of Water Jets in a Mach 1.94 Supersonic Crossflow”, 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2004-971, Reno, NV, 5-8 Jan 2004.