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Experimental Study of Subcritical to Supercritical Jet Mixing

Arnab Roy1 and Corin Segal2 University of Florida, Gainesville, Florida, 32611, USA

Subcritical, near-critical and supercritical liquid jet was injected into an inert gaseous atmosphere. Density distribution is measured and density gradient profiles are inferred from the experimental data. The dark core and jet spreading angles are measured and compared with previous theoretical and experimental results. A method that allows for the detection of the structures in the jet core is applied.

I. Nomenclature P = Pressure (atm) T = Temperature (K) Pcr = Critical Pressure (atm) Tcr = Critical Temperature (K) Tr = Reduced Temperature Pr = Reduced Pressure ρ = Density (kg/m3) δ = Shear Layer Thickness (m) x= Distance in the streamwise direction (m) U = Velocity (m/sec) Subscripts: 1= Injected Fluid, 2 = Chamber Gas

II. Introduction The problem of supercritical jet mixing is of significant importance since applications where supercritical

conditions exist are extensive including diesel engines and rocket engines. The inverse problem of a supercritical jet injected in subcritical conditions also is present, for example, in a supersonic combustion engine. In particular, the advancement of liquid propellant rocket technologies led to a considerable increase of pressure in the combustion chamber and, in many applications, the thermodynamic conditions of the propellants exceed their critical values. The goal of the present work is to expand the existing database of reliable experimental measurements of density distribution during supercritical liquid/gas mixing as well as gain some insight into fundamental features of supercritical mixing process.

In the previous studies using the same facility1,2 a jet at ambient temperature was injected into a chamber at supercritical conditions. In the present study the jet is heated before injection into the chamber from subcritical to supercritical values, with a range of chamber to injectant density ratios from 0.01 to 0.065. Further, the dark core lengths and the jet spreading angles of the jet at subcritical, near critical and supercritical conditions are measured. Since the definition of the dark core length is not unique among existing studies, the algorithm that has been adopted to calculate the dark core lengths of the jet has been based here on the change of density along the central portion of the jet. The subcritical and supercritical data are plotted against the chamber-to-injectant density ratio. Finally, the jet spreading angles have also been measured and plotted against the density ratio, and have been compared with existing theories12-14 and other experimental data15-17. The results indicate that for both the subcritical and supercritical cases, the core lengths decrease with an increase of density ratio while the jet spreading angles increase with an increase in the density ratio, following the theoretical predictions closely.

1 Graduate Research Assistant, MAE University of Florida, Gainesville FL 32611, Student Member AIAA. 2 Associate Professor, MAE University of Florida, Gainesville FL 32611, Associate Fellow AIAA.

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-809

Copyright © 2009 by Corin Segal. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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III. Experimental Setup The experimental setup is shown in Figure 1. The schematic is shown in Figure 1(a) and a picture of the actual

setup is shown in Figure 1(b).

(a) (b)

Figure 1. Test chamber schematic (a) and its overall view (b). The figure shows the position of the thermocouples and pressure transducer connected to the chamber. These measure the conditions at various points in the chamber. The liquid and gas injection ports have also been shown.

The details of the setup were given in previous papers2,3, hence only a brief description has been included here.

The high pressure chamber is constructed to withstand pressures up to 70 atm (1000 psi) and temperatures up to 3000C (573K). For optical access, there are three windows in the chamber which provide a field of view of 21.7 mm (0.85”) wide and 86.4 mm (3.4”) long. All experiments were done using a round liquid injector with an inner diameter of 2.0 mm (0.078”) mm. The flow is laminar before entering the injector and turbulence is not expected to develop while the fluid passes through the relatively short, 15.4 mm, injector tip. Nitrogen is used as the surrounding gas. FK-5-1-12 [CF3CF2C(O)CF(CF3)2] has been chosen as the injected fluid. The choice of this fluid was determined by its good spectroscopic properties and its low critical point - atmPcr 4.18= , KTcr 441= . The third

harmonic of Nd:Yag laser was used to excite the fluorescence. Earlier tests2 have shown that emission spectrum of FK-5-1-12 within 400 – 500 nm does not reveal significant dependence on pressure and temperature within a range of interest. Based on emission spectra an optical filter with 420 nm centerline and 10nm FWHM width was kept before the Princeton Instruments Intensified CCD camera lens to eliminate any elastic scattering. The ICCD Camera has a resolution of 1024 x 1024 pixels, but it was cropped to 381 x 1024 pixels to increase the acquisition rate to 10 Hz to synchronize with the laser. The gate width was kept to 150 ns to reduce background light.

A thin laser sheet of 0.1 mm thickness and 25 mm length was focused to strike the centerline of the jet. The intensity of the emitted fluorescence is directly proportional to the local density of the jet. The grayscale images of the jet are scaled and analyzed to determine the core length and jet spreading angles.

IV. Results and Discussion

The experimental conditions are shown in Figure 2 on a reduced pressure (Pr) and reduced temperature (Tr) diagram. The goal was to span a range of pressures from subcritical to supercritical at constant temperature, with particular focus around the critical point. Previous studies4 have shown that supercritical behavior may be encountered even when only one of the parameters, Pr or Tr, is critical. Therefore, a sweep of pressures for given temperatures were selected along with conditions that kept the pressure essentially constant and increased the temperature. A completely supercritical condition and one which is at ambient conditions were also included in the test matrix. The reduced pressures and temperatures shown in the figure refer to the chamber conditions.

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Test Matrix

Figure 2. Selection of the experimental conditions. Reduced Temperatures and Pressures have been selected to cover the subcritical to supercritical regime both in pressure and temperature.

The images of the jet injected at subcritical conditions can be seen in Figure 3. The subcritical regime was observed for relatively low temperatures and pressures. Surface tension and inertia forces dominate under these conditions. Thus droplet formation is observed once the fluid detaches from the body of the jet. The images are taken for 10 jet diameters from the injector. Droplet formation can be seen towards the end of the jet.

(a) (b)

Figure 3. Scaled images of the heated Fluoroketone injected at subcritical conditions. Surface tension and Inertia forces dominate under these conditions. Figure (a) shows the jet initially at Tr =0.98, Pr =1 injected into the chamber at Tr =0.92, Pr =0.97. Figure (b) shows the jet initially at Tr =0.99, Pr =1.00 injected into the chamber at Tr = 0.69, Pr =0.97.

The images of the jet injected at near-critical conditions can be seen in Figure 4. In the near-critical regime, the notable feature is the decreased importance of surface tension, which results in the formation of “clusters” or “finger-like” structures of the ligaments at the gas-liquid interface, the shape of which is similar to the previous descriptions5,6. The surface of the jet becomes more corrugated and wavy. Some of the clusters get detached from the main body of the jet and form drops.

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(a) (b)

Figure 4. Scaled images of the heated Fluoroketone injected at near-critical conditions. The formation of “clusters” or “finger-like” structures can be observed. Figure (a) and (b) show the jet initially at Tr =0.92, Pr =1.07 injected into the chamber at Tr =1.03 and Pr =1.05.

In the supercritical zone, as shown in Figure 5, the jet behavior changes again. The density gradient values decrease and surface of the jet becomes smoother than the transcritical case. Shear forces now exceed the capillary forces and they dominate. Ligaments are considerably reduced. In some cases it is seen that the core length decreases significantly, while in other cases it remains nearly the same as in the near-critical and subcritical case.

(a) (b)

Figure 5. Scaled images of the heated Fluoroketone injected at supercritical conditions. The jet surface becomes smoother than the previous cases. Figure (a) shows the jet initially at Tr =1.06, Pr =1.16 injected into the chamber at Tr =1.18, Pr =1.08. Figure (b) shows the jet initially at Tr =0.96, Pr =1.74 injected into the chamber at Tr = 1.18, Pr =1.73.

A. Dark Core Length Measurements In the current study, the dark core lengths and the jet spreading angles have been calculated for the jet injected

at each of these conditions and compared with the existing experimental data and theoretical predictions. The dark core lengths and the spreading angles both have been related to the chamber-injectant density ratio, because in the absence of any co-axial flow as in other experiments, the density ratio becomes the most relevant criteria for comparison.

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The term ‘dark core’ usually refers to the intact section of the jet which is higher in density than the remaining areas. It should be also mentioned that the dark core length itself does not have any unique definition among researchers. Various terms such as the intact length, potential core, and break-up length have been used along with various measurement techniques to determine the same, as mentioned in previous studies7,8. The dark core length is defined here as the intact section of the jet, measured along its axial length, beyond which a considerable change of density occurs. The dark core lengths were calculated for the chamber to injectant density ratios ranged from 0.01 to 0.065.

The algorithm used in calculating the core length starts with a single jet image. This digital image is scaled using the pixel intensities, as shown in Figure 6. Each color in the scaled image corresponds to a local density range. Thus the brightest pixel corresponds to the highest density. The analyzed images are stored as a matrix of local density values. This is then used for determining the core length.

The first row of the density matrix is scanned to find the width of the jet at the injector. This width is used to create individual square density matrices or blocks along the entire length of the jet, where each block starts one row after the previous block as shown in Figure 6(a). The average and the eigenvalues of each of these matrices are computed. The determinants of the eigenvalue matrices are plotted in Figure 6(b). A polynomial is fitted to this plot and its points of inflexion correspond to a significant change in density across the axial length of the jet. At each point of inflexion, the average density matrix is compared to its neighboring ones. The point that corresponds to the maximum density change with respect to its immediate neighbors is taken to be the core length. As can be seen from Figure 6(b), the point of inflexion between pixel number 300 and 400 is found to be the core length, and it is shown in Figure 6(c). It should also be noted that this method of calculating the core length is sensitive to core separation; hence the length before separation is taken to be the core. This method can be further enhanced by taking into account the curved nature of the core, where the center of the square matrices would be shifted according to the maximum intensity of that row.

(a) (b) (c)

Figure 6. The basis for core length determination. The shaded area in (a) is the portion of the jet where individual density matrices or blocks are chosen. These determinants of the Eigen value matrices are plotted against the pixel length in (b), while the calculated core length is marked in (c).

Since the dark core does not have a unique definition among researchers, different measuring techniques can

change its absolute magnitude. Thus, more emphasis should be made on the trends that they have with different operating conditions. Figure 7 shows the plot of core length as a function of density ratio calculated for subcritical and supercritical conditions of the injected fluid. The range of density ratios is from 0.01 to 0.065. It can be seen from the plot that the values of the core lengths for both the subcritical and supercritical cases decrease with density ratio. Trend lines have been fitted to each of the cases, and it can be seen that the core length for the supercritical case decreases more rapidly than the subcritical case, indicating that the supercritical cases have a stronger dependence on density ratio than the subcritical cases. This observation is quite similar to that of coaxially injected jets7,8, where the dark core lengths have been plotted as a function of momentum flux ratio and a similar decreasing trend for the core lengths has been observed.

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Core Length vs. Density Ratio

1

10

100

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Density Ratio

Core

Len

gth

(m

m)

Subcritical Data

Supercritical Data

Figure 7. The Dark Core Length as a function of the Density Ratio. Subcritical and Supercritical values have been plotted separately with different symbols.

B. Jet Spreading Angle Measurements

The nature of the growth rate of the jets and mixing layers has been assessed through the measurements of the visual spreading angle. The process is similar to that mentioned in previous studies9,10, only that here the angle is measured based on a two dimensional approach as shown in Figure 8. First, the outline of the jet structure was drawn, and straight lines were used to fit the outline, one on each side of the jet. The sum of these angles that each straight line makes with the vertical defines the spreading angle of the jet. While drawing the outline of the jet, the total axial length that was considered was chosen to be the core length in order to keep the spreading angle measurement close to the point of injection of the fluid into the chamber. Figure 8(a) shows the scaled image of the jet, the core length, and the measured spreading angles on each side of the jet. Figure 8(b) shows the analyzed image with the outlines drawn and the straight lines fitted to it. The angle included between these straight lines is the jet spreading angle.

(a) (b)

Figure 8. Basis for determination of jet spreading angle. Figure (a) shows the core length and the calculated angles on each side of the jet and (b) shows the outline of the jet with the fitted straight lines.

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In Figure 9, the jet spreading angles have been plotted against the density ratio. The density ratio is calculated as the ratio of the chamber gas, i.e., nitrogen, to the density of the injected fluid, i.e. fluoroketone, both densities being calculated at the chamber conditions. The ideal gas law has been used to calculate the density of the nitrogen, and the Peng-Robinson-Stryjek-Vera (PSRV) equation of state has been used to calculate the density of the injected fluid, fluoroketone. For comparison, other available data and theoretical predictions have been incorporated in the figure. The theoretical predictions include those of Papamoshcou and Roshko11, Dimotakis12 and Abramovich13.

Jet Spreading Angle vs. Chamber-to-Injectant Density Ratio

Figure 9. The tangent of the jet spreading angle as a function of the density ratio. A magnified plot for spreading angles of density ratios ranging from 0.01 to 0.1 is shown in the inset. (*) refers to the data taken at the present facility.

Papamoschou and Roshko11 define a convective velocity Uc and a convective Mach number Mc in their analysis, to separate the effects of compressibility. Here Mc=(U-Uc)/a, where a is the speed of sound, and Uc=(U1√ρ1+U2√ρ2)/( √ρ1+√ρ2), where (ρ1, U1) and (ρ2,U2) are the density and velocity of the two streams forming the mixing layer. For an incompressible variable density mixing layer, the theory assumes that the main effect of the density ratio is to determine the convective velocity of the structure and it is conjectured that the growth rate is proportional to (U1-U2). Thus, an equation is proposed for δ’ vis, the rate of change of visual thickness in the streamwise direction, for incompressible, variable density mixing layers:

vis' =δ 1 20.17*c

U U

U

−

( )( )1 1

0.17 *1

r r

r r

U

U

ρ

ρ

− +=

+

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The ratio of the velocities (U2/U1) is denoted as Ur and the ratio of the densities (ρ2/ ρ1) as ρr. The constant 0.17 was obtained experimentally. This equation has been plotted in the figure and has been used as a comparison for the experimental data obtained, by using the ratio Ur=0. In another treatment, Dimotakis5 uses the observation that the entrainment into the mixing layer from each stream is not the same and offers a geometrical argument to arrive at an equation. This equation, for the rate of growth of shear layer thickness δ’ w, is valid for two dimensional incompressible variable density vorticity thickness growth in a system moving with the convection velocity as described before. The equation states:

'wδ ( ) ( )11

0.17 * 11 2.9 1 / 11

rrr

r rr r

U

U UU

ρρ

ρ

−−= + −

+ + −+

As mentioned before, this equation has been plotted using ρr as zero and the constant as 0.17. The other theoretical analysis that has been used to compare the results with is that of Abramovich6. His equation for the jet spreading angle of compressible flows is as follows:

1 1

2 1r r

r r

UbC

x U

ρρ

+ − = +

Here b is half of the thickness of the velocity profile and x is the distance in the streamwise direction. From various experiments with hot jets, the value of the constant has been suggested to be 0.22. To compare the results obtained with other available experimental data14, the plots of Naber and Siebers15, Rietz and Bracco16, and Chehroudi, Talley and Coy17 have also been included as they cover a similar range of density ratios. Details of these experimental results are given by Chehroudi et al14. It can be seen that the data by Naber and Siebers, and Reitz and Bracco is greater than the theoretical predictions while that of the Chehroudi, Talley and Coy14 is much less than the theory for lower density ratios. It can be observed that the supercritical data obtained in our test facility follows the theoretical trend of Dimotakis12 quite closely, while the subcritical data covers the range of spreading angles between the theories of Abramovich13 and Dimotakis12, which indicates that for the current range experimental conditions and density ratios, the experimental data follow the theoretical predictions quite closely.

V. Conclusion A study of a heated jet injected into a gaseous environment was undertaken at subcritical, near-critical and

supercritical conditions. The images obtained using planar laser induced fluorescence through the jet core, indicate the characteristics of subcritical and supercritical mixing as mentioned in the theories. The dark core lengths and jet spreading angles have been calculated for various conditions of the chamber and injectant. The method adopted for calculating the core lengths is the eigenvalue approach as described above to identify the points of maximum density gradient. The method gives good results for most conditions and also helps us to identify the point of core separation, though it can be further improved by taking into consideration the tilt and the curved nature of the core. The dark core lengths were plotted as a function of the density ratio for both subcritical and supercritical cases. It was observed that the core length decreases as the density ratio was increased, though the supercritical cases showed more dependence on the density ratio than the subcritical cases. These results are similar to the observations for co-axial jets7,8, where the core lengths have been compared as a function of momentum ratio. The jet spreading angles, which were also plotted as a function of density ratio, followed the theoretical trends quite closely. The subcritical data was more close to the theory of Dimotakis12, while the supercritical data were spread between the theories of Abramovich13 and Dimotakis12.

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References

1 S. A. Polikhov and C. Segal, “Experimental Study of Subcritical to Supercritical Jet Mixing”, AIAA 2007-569, 2007. 2 C. Segal and S. A. Polikhov, “Subcritical to Supercritical Mixing”, Physics of Fluids, vol. 20, issue 5, May 2008. 3 S. A. Polikhov and C. Segal, “Two Phase Flow Supercritical Mixing”, AIAA 2006-07566, 44th Aerospace Sciences Meeting, Reno, NV, 2006. 4 Yang., V., Anderson W, “Liquid Rocket Engine Combustion Instability”, Progress in Astronautics and Aeronautics, Vol. 169, 1995. 5 W. O. H. Mayer, A. H. A. Schik, B. Vielle, C. Chauveau, I. Gokalp, D. Talley and R. G. Woodward, “Atomization and break-up of cryogenic propellants under high pressure sub-critical and supercritical conditions.”, Journal of Propulsion and Power, Vol. 14, No. 5, pp. 835-842, 1998. 6 J. Bellan, “Supercritical (and sub-critical) fluid behaviour and modeling: drops, streams, shear and mixing layers and sprays”, Prog. Energy Combustion Science 26 pp. 329-366, 2000. 7 B. Chehroudi and D. W. Davis, “Shear-Coaxial Jets from a Rocket-Like Injector in a Transverse Acoustic Field at High Pressures”, AIAA 2006-758, 2006. 8 I. A Levya, B. Chehroudi, D. Talley, “Dark core analysis of coaxial injectors at sub, near and supercritical pressures in a transverse acoustic field”, AIAA 2007-5456, 2007. 9 I. A. Leyva, J. I. Rodriguez, B. Chehroudi and D. Talley, “Preliminary Results on Coaxial Jet Spread Angles and the Effects of Variable Phase Transverse Acoustic Fields”, AIAA 2008-950, 2008. 10 J. I. Rodriguez, I. A. Leyva, B. Chehroudi and D. Talley, “Results on Subcritical One-Phase Coaxial Jet Spread Angles and Subcritical to Supercritical Acoustically-Forced Coaxial Jet Dark Core Lengths”, AIAA 2008-4561, 2008. 11 D. Papamoshcou and A. Roshko, “The Compressible turbulent shear layer: An experimental study”, Journal of Fluid Mechanics 197, 453, 1988. 12 P.E.Dimotakis, “Two Dimensional Shear Layer Entrainment”, AIAA Journal, Vol. 24, No.11, Nov 1986, pp-1791-1796. 13 G.N.Abramovich, “The Theory of Turbulent Jets”, MIT Press, Cambridge, 1963. 14 B. Chehroudi, D. Talley and E. Coy, “Visual characteristics and initial growth rates of round cryogenic jets at subcritical and supercritical pressure”, Physics of Fluids, Vol. 14, No. 2, February 2002. 15 J.D Naber and D.L. Siebers, “Effects of gas density and vaporization on penetration and dispersion of diesel sprays”, SAE International Congress and Exposition, SAE Paper No. 960034, Detroit, Michigan, February, 1996. 16 R.D. Reitz and F.V. Bracco, “On the dependence of spray angle and other spray parameters on nozzle design and operating condition”, SAE International Congress and Exposition, SAE Paper No. 790494, Detroit, Michigan, February, 1979. 17 B. Chehroudi, D. Talley, and E. Coy,” Initial Growth Rate and visual characteristics of a round jet into a sub- to supercritical environment of relevance to pocket, gas turbine, and diesel engines.”, 37th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 99-0206, Reno, NV, 11-14 January, 1999.