49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
4 - 7 January 2011, Orlando, Florida
AIAA 2011-792
Sub-to-Supercritical Mixing and Core Length Analysis of a
Single Round Jet
Arnab Roy1 and Corin Segal2
University of Florida, Gainesville, Florida, 3261, USA
Planar Laser Induced Fluorescence (PLIF) is used to investigate sub-to-supercritical liquid jet injection into a
gaseous atmosphere, such that the entire system is a single component diffusion process. A calibration is
performed to determine the absorption coefficients of the gaseous phase of the fluid at various densities. A
novel method was developed for the detection of detailed structures throughout the entire jet center plane.
Density distribution is measured and density gradient profiles are inferred from the experimental data.
Finally, a comparison has been made between the single component diffusion and binary component diffusion
processes.
I. Nomenclature
P = Pressure (atm)
T = Temperature (K)
Pcr = Critical Pressure (atm)
Tcr = Critical Temperature (K)
Tr = Reduced Temperature (atm)
Pr = Reduced Pressure (atm)
ρ = Density (kg/m3)
II. Introduction
The problem of subcritical and supercritical jet mixing is of significant importance. Applications in which
supercritical conditions exist, including diesel and rocket engines, are extensive. The inverse problem of a
supercritical jet injected in subcritical conditions also is present in a supersonic combustion engine. The
advancement of liquid propellant rocket technologies led to an increase of pressure in the combustion chamber and,
in many applications, the thermodynamic conditions of the propellants exceed their critical values.
Liquid jet breakup in the subcritical regime has been extensively studied, beginning with the theoretical works
by Rayleigh1, who suggested that a round liquid jet is not energetically stable and the instability onset leads to jet
disintegration. Rayleigh analyzed an inviscid laminar, liquid jet and came to the conclusion that at the point of
breakup, the characteristic drop diameter resulted as dd=1.89dl, where dl is the jet diameter at the injector location.
Further theoretical2 and experimental studies3 resulted in a number of semi-empirical expressions for the jet breakup
length4 and the resulting drop size distribution5,6.
Incorporation of turbulence in the analytical investigation of the liquid round jet breakup has not as yet been
successful. The main reason is presumed to be the lack of detailed theory that would describe the turbulent shear
layer with a sufficient degree of accuracy. It should be noted that only if the jet is initially laminar, the breakup and
atomization can be explained through the Kelvin Helmholtz Instability (KHI) theory. Various computational studies7
suggest that if the gas and jet densities are substantially different, a supercritical jet behaves differently from a
turbulent jet, since the density difference causes turbulence damping. This causes it to have a longer unmixed core
length, compared to the turbulent subcritical gaseous jets8.
In the current study, a jet is preheated and injected into subcritical and supercritical environments that comprise
its own species only. Thus, the entire process is a single component diffusion process. Planar Laser Induced
Fluorescence (PLIF) was used to generate a section through the jet, thus accurately identifying both the boundary
and the jet core structures. In previous studies using the same facility as the current study, a jet at ambient
temperature9,10 and also at various subcritical to supercritical conditions11 were injected into a chamber consisting of
1
2
Graduate Research Assistant, University of Florida, Gainesville FL 32611, Student Member AIAA.
Professor, University of Florida, Gainesville FL 32611, Associate Fellow AIAA.
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Copyright © 2011 by Arnab Roy and Corin Segal. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
an inert gas at supercritical conditions with respect to the injected fluid, thereby forming a binary component
diffusion process. In the present study, density and density gradient profiles have been calculated for various
injecting conditions, and finally a comparison has been drawn between the unary component and binary component
diffusion processes.
III. Experimental Setup
The experimental setup is shown in Figure 1. The schematic is shown in Fig 1a and a picture of the setup is
shown in Fig 1b.
a)
b)
Figure 1. Test chamber schematic a) and its overall view b). The liquid and gas injection ports have also been
shown. The 25mm. square chamber with 228 mm. length can be heated and pressurized to 600K and 100 atm.
respectively.
The details of the setup were given previously12,13, hence only a brief description is included here. The high
pressure chamber is constructed to withstand pressures up to 100 atm and temperatures up to 600K. For optical
access there are three windows in the chamber which provide a field of view of 22 mm wide and 86 mm long. All
experiments were done using a round liquid injector with a diameter of 2.0 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. FK-5-1-12 [CF3CF2C(O)CF(CF3)2], commonly known as fluoroketone, has been chosen as the injected
fluid. The fluid was chosen for its spectroscopic properties and low critical point - Pcr = 18.4atm , Tcr = 441K . The
third harmonic of Nd:YAG laser was used to excite the fluorescence. Earlier tests have shown that emission
spectrum of fluoroketone 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 10 nm FWHM
width is placed before the Princeton Instruments Intensified CCD camera lens to eliminate any elastic scattering.
The ICCD Camera has a resolution of 512 x 512 pixels, but was cropped to 311 x 512 pixels to increase the
acquisition rate to 10 Hz and to synchronize it with the laser. The gate width was fixed at 150 ns in order to capture
the entire duration of fluorescence while reducing the background light significantly.
A thin laser sheet of 0.1 mm thickness and 25 mm length was focused on the jet centerline. The intensity of the
emitted fluorescence was directly proportional to the local density of the jet. The images of the jet were analyzed to
determine the core lengths.
IV. Results and Discussion
A. Experimental Conditions
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 at constant temperature, with particular focus near the
supercritical zone. Thus, a very wide range of temperatures and pressures have been covered. Previous studies2,3
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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. Both the chamber and the injectant conditions are
shown on the diagram separately. As was done in the previous work11, the experiments have been categorized under
three subgroups:
1) a subcritical jet being injected into a subcritical environment, 2) a subcritical jet into a supercritical environment,
and 3) a supercritical jet into a supercritical environment. The images obtained in each category have been analyzed
and density and density gradient profiles have been obtained to identify the differences of the three breakup and
mixing regimes, and have been compared to the binary species mixing cases.
Figure 2. Selection of the experimental conditions. Reduced temperatures and pressures have been selected to
cover the subcritical to supercritical regime. The plot refers to both the chamber and the injectant conditions
independently.
In the following sections, an explanation of the laser sheet correction algorithm has been provided, followed by the
jet mixing experiments of all three categories.
B. Laser Sheet Correction
Due to the absorption of light energy through the gas and liquid phases of fluoroketone, laser sheet correction is
necessary. In the earlier tests involving binary species mixing experiments, the laser sheet correction through the gas
phase (i.e. Nitrogen) was not necessary since the absorption of 355 nm wavelength was negligible. For the single
species mixing experiments, the gas phase consists of only fluoroketone vapor, and hence the absorption of 355 nm
wavelength is significant, especially at high concentrations. In the following sections, the absorption of the laser
energy with respect to fluoroketone vapor and liquid densities is quantified in the form of a calibration curve of the
absorption coefficient. This accounts for the loss of intensity of laser energy through the gaseous fluoroketone and
the higher density liquid (or supercritical) fluoroketone jet, to a good degree of approximation.
B.1 Laser sheet absorption through the gas phase
To study the laser absorption through the fluoroketone gas phase, the chamber was partly filled with
fluoroketone and the vapor and liquid phases reached equilibrium. The vapor concentration inside the chamber was
controlled by adjusting the chamber wall temperature. To obtain higher values of vapor concentration, the chamber
walls were heated to the desired temperature, which in turn heated the liquid phase, producing more vapor. This also
increased the pressure inside the chamber since the volume is constant.
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The laser sheet was then passed through the nearly uniform vapor phase to obtain the intensity profile of the
sheet and also to observe how the intensity of the fluorescence changes as the laser passes through the chamber. The
figure below shows the laser sheet profiles taken at four different temperatures and pressures, averaged for a total of
50 images. The laser enters the chamber at column 1 and leaves at column 512.
Fig. 3a shows the profile at 2.7 atm. chamber pressure and 850C chamber temperature. The figure shows that
that the laser profiles at the four different column positions are very similar to each other. There are some variations
in intensity but the overall the effect is not significant. Fig. 3b shows the profile at 5.9 atm. chamber pressure and
1100C chamber temperature. This plot shows a greater variation of the laser profile shape and intensity, implying
that the absorption has increased and should be taken into account. Fig. 3c shows the profile at 10.4 atm chamber
pressure and 1500C chamber pressure. This plot is significantly different from the previous two, and shows clear
signs of laser intensity drop and profile shape change. A large decrease in intensity and a major change in profile
shape are observed. The profile variations reduce considerably, and it becomes more uniform. Fig. 3d shows the
profile at 14.7 atm. chamber pressure and 1650C. The temperature is nearly critical with respect to the critical
temperature of 1680C, but the pressure is still subcritical compared to the critical temperature of 18.4 atm. The laser
intensity drops to 30% of the 100th column at column 200 and is reduced to approximately 10% at the 300th column.
a)
b)
c)
d)
Figure 3. Intensity variations of the laser sheet profile as it passes through the chamber. The laser enters the
chamber at column 1, and exits the chamber at column 500. It can be observed that the variations are
significant as the concentration of vapor increases. The pressure and temperature conditions for the cases are
a) 2.7 atm, 850C, b) 5.9 atm, 1100C, c) 10.4 atm, 1500C and d) 14.7 atm, 1650C.
To understand the effects of absorption on fluorescence, it is therefore necessary to isolate each parameter and
study them separately. In the following sections, the dependence of fluorescence on vapor density and laser intensity
has been investigated and a relation between absorption coefficient and vapor density has been obtained.
B.1.1 Fluorescence intensity dependence with vapor density
To understand how the fluorescence signal depends on the vapor density, the camera was zoomed to a region very
close to the window where the laser sheet entered the chamber. This region was chosen so that the laser sheet would
not be attenuated by absorption. The results have been shown in Figure 4. The plot shows a weak second-order
dependence of the fluorescence signal with the vapor density. For low values of vapor concentration, the curve
closely approximates a straight line, while for higher values, especially near and above the critical point, nonlinearities start to become important14.
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Figure 4. Fluorescence signal vs. fluoroketone vapor density. For low values of vapor concentration, the
curve closely approximates a straight line, while for higher values, especially near and above the critical
point, non-linearities start to become important.
B.1.2 Fluorescence intensity dependence with laser power
To obtain the fluorescence intensity dependence on laser power, the concentration of the fluoroketone vapor inside
the chamber was kept fixed and the laser intensity was varied. A linear dependence of the signal with laser power is
observed over the range of laser intensities used for the current experiments, as shown in Figure 5.
Figure 5. Fluorescence signal vs. laser intensity. A linear dependence of the signal with laser power is
observed in the operating range used for the current experiments.
B.1.3 Calibration of absorption coefficient
To closely examine how the variation of laser intensity occurs across the length and width of the chamber, a sample
image is chosen and analyzed. Figure 6 shows plots of the laser sheet fluorescence intensity at a chamber pressure of
14.7 atm. and a chamber temperature of 1650C. The actual intensity plots have been shown on the left, and the
normalized intensity plots have been shown on the right. All images have a resolution of 512 x 512 pixels. The plot
on the top left corner shows the variation of fluorescence intensity from top to bottom for all the columns of the
image, i.e., 512. Similarly, the plot on the bottom left corner shows the variation of fluorescence intensity from left
to right for all the rows of the image, i.e., 512. The normalized images were obtained by dividing the pixel intensity
of a specific column or row by the maximum intensity for that column or row respectively, and then taking their
mean.
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From the normalized laser fluorescence intensity variation from left to right, it can be seen that there is a
decrease from 1 to about 0.05 within 300 pixels of laser propagation distance. Since the chamber is filled with
uniform density vapor, this variation can be solely attributed to the actual laser intensity drop. Hence, it can be
inferred that the laser intensity variation across the chamber cannot be neglected as it was for the experiments with
binary species, e.g. a fluoroketone jet injected into inert nitrogen gas done in the same facility15. This calls for a
rigorous treatment to deal with such variations in fluorescence intensity for a specified chamber temperature and
pressure, as described in the following sections.
Figure 6. Detailed analysis of laser fluorescence intensity at 14.7 atm., 1650C. Actual intensities have been
plotted on the left and the normalized intensities have been plotted on the right. All plots show significant
variation of laser fluorescence intensity across the chamber.
Hence, it is seen that for a specific row of the image, the fluorescence signal also undergoes an exponential
drop in intensity across the line of propagation of the laser sheet. This has been verified through the obtained
experimental data.
From the normalized laser intensity diagram (from left to right), we select a portion of the plot where a
uniform decrease of fluorescence intensity is noted. An exponential curve is then fitted to the data points as shown
in Figure 7. The exponential coefficient in the equation of the fitted curve is essentially the absorption coefficient.
This value of the absorption coefficient is valid for the specified concentration of vapor at a particular chamber
pressure and temperature, i.e., 14.7 atm. and 1650C. The higher the pressures and temperatures are, the greater is the
concentration of vapor, and thus the value of the absorption coefficient.
Figure 7. Normalized intensity points vs. the length traversed by the laser sheet in pixels. When an
exponential trendline is fitted to the plot, the absorption coefficient is obtained as given by the BeerLambert’s law.
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Absorption coefficients for various vapor concentrations were obtained by the above mentioned process and a
calibration curve was obtained as shown in Figure 8. It can be seen that the calibration curve is a straight line,
indicating that the slope is a constant throughout the vapor phase which is proportional to the absorption cross
section. It can thus be stated that the absorption cross section is also constant throughout the vapor phase.
Figure 8. Calibration line for the absorption coefficient plotted against density.
B.2 Laser sheet absorption through the liquid phase
The value of the absorption coefficient changes significantly when the laser sheet passes through fluoroketone in the
liquid phase. The tests for investigating the absorption coefficient in the liquid phase were performed by passing the
laser sheet through a cuvette filled with liquid fluoroketone at room temperature (293 K) and atmospheric pressure
(1 atm.). The density of the jet can be taken to be essentially constant throughout its cross section, and hence any
variation of fluorescence intensity can again be attributed to the actual variation of laser sheet intensity.
The decrease in fluorescence intensity inside the cuvette can be accounted for in a way similar to the gas
phase by trying to obtain the value of the absorption coefficient. As was done before, a plot of normalized
fluorescence intensity versus the distance traversed by the laser was obtained. A region where the decrease of
intensity was uniform was selected. These data points were then fitted using an exponential fit as shown in Figure. 9.
Similar to the gas phase, the exponential coefficient in the equation of the fitted curve is essentially the absorption
coefficient. It is again noteworthy to mention that this absorption coefficient is only valid for the liquid of uniform
density at 300C.
Figure. 9. Plot showing the normalized intensity points vs. the length traversed by the laser sheet through the
cuvette in pixels. When an exponential trendline is fitted to the plot, the absorption coefficient is obtained as
given by the Beer-Lambert’s law.
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Since it has been verified that the absorption cross section for the vapor phase of fluoroketone is a constant, it is
safe to assume that it would also be a constant for the liquid phase (but different from the vapor phase). Hence only
two points are required to complete the calibration line. One point is obtained through the above plot, and another
one would be the origin (as the absorption coefficient should be zero if the density is zero), and the slope of this line
would again be proportional to the absorption cross section.
C. Jet Mixing Experiments
The jet mixing experiments are described below in three subsections: a subcritical jet being injected into a
subcritical atmosphere, a subcritical jet injected into a supercritical atmosphere, and a supercritical jet injected into a
supercritical atmosphere. In all three cases, the density and density gradient profiles have been calculated, and
important mixing properties have been identified. The calibration line for the absorption coefficient of fluoroketone
with respect to 355 nm wavelength (Figure 8) has been utilized to obtain the corrected density profiles. This method
of laser sheet correction produces good results for the subcritical-into-subcritical case, but needs some improvement
for the supercritical cases.
C.1. Subcritical Fluid into a Subcritical Atmosphere
The experiments done under subcritical conditions involve relatively lower temperatures for the injectant and the
chamber. The temperatures for the injected fluid ranged from 293K to 423K, while the temperature of the
surrounding atmosphere ranged from 360K to 433K. This represents Tr values ranging from 0.66 to 0.96 for the
injected fluid, and 0.82 to 0.98 for the chamber—both subcritical with respect to the critical temperature of 441K for
the injectant. The pressures were also kept lower than the critical pressure of 18.4 atm, and were in the range of 4.5
to 15 atm for both the injectant and surroundings, which represent Pr values ranging from 0.25 to 0.82. The injection
velocity ranged from 2.1 to 5.9 m/s for these cases.
The processed images of the fluid at subcritical conditions injected into a subcritical atmosphere can be seen in
Figure 10. The images are taken for 10 jet diameters from the injector. It can be observed that surface tension and
inertia forces dominate under these conditions. Thus, droplet formation is observed once the fluid detaches from the
body of the jet. At lower temperatures, the jet surface is corrugated and wavy, indicating again that the surface
tension forces are important. At higher temperatures, the jet surface gradually becomes smoother until it reaches the
critical point, when the surface tension completely disappears. The density gradient profiles indicate that the
maximum value of the gradients decrease as the temperature of the jet during injection is increased. In all cases, the
value of the density gradient is the highest at the liquid-gas interface, and is the lowest inside the core of the jet.
It can also been seen that the laser correction method adopted works reasonably well for these cases. The gas on
the right side of the jet under weighted, causing it to have a slightly lower density than the gas on the left (although
theoretically they should have the same densities). Moreover, the density profile inside the jet does not show a
preferential weighting or non-uniform density distribution towards any side, which indicates the absorption
coefficient predicted for the subcritical injection conditions of the jet is quite accurate.
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a)
b)
Figure 10. Scaled images of a subcritical jet injected at subcritical chamber conditions. Figure (a) shows the
jet initially at Tr =0.66, Pr =0.53 injected into the chamber at Tr =0.96, Pr =0.47. Figure (b) shows the jet
initially at Tr =0.88, Pr =0.48 injected into the chamber at Tr = 0.98, Pr =0.41.
The binary species injection and unary species injection for similar chamber and injectant temperatures have been
compared and shown in Figure 11. It is seen that the core lengths, as calculated by the method described in previous
works11,15, is similar for both the cases shown below. The value of the maximum density gradients is also very
similar in both cases. The primary difference is the jet divergence angle, which is greater in the case of the unary
species injection than the binary injection. This can be attributed to the fact that the diffusion is higher in the former
case, causing increased penetration into the gas phase and hence enhanced mixing.
a)
b)
Figure 11. Scaled images of a subcritical jet injected at subcritical chamber conditions. Figure (a) shows the
jet initially at Tr =0.80, Pr =1.26 injected into the chamber at Tr =0.87, Pr =1.05. Figure (b) shows the jet
initially at Tr =0.83, Pr =0.32 injected into the chamber at Tr = 0.89, Pr =0.26.
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D. Subcritical Fluid into a Supercritical Atmosphere
The temperature for the injected fluid ranged from 291K to 431K while the temperature of the surrounding
atmosphere ranged from 441K to 458K. This represents Tr values ranging from 0.66 to 0.98 for the injected fluid
and 1 to 1.04 for the chamber. The pressures were close to the critical pressure of 18.4 atm. and were in the range of
14 to 20 atm. for both the injectant and surroundings, which represent Pr values ranging from 0.77 to 1.09. The
injection velocity ranged from 5.3 to 10.2 m/sec.
The images of the jet injected at subcritical conditions into a supercritical atmosphere can be seen in Figure 12.
The characteristic feature of this region is the apparent decreased importance of surface tension that manifests
through the smoothening of the liquid-gas interface. Ligament formation tends to significantly decrease. Due to the
decreased surface tension forces, the ligaments have a “cluster” or “fingerlike” appearance from which parcels of
liquid detach, the shape of which is similar to the previous studies16. At lower injectant temperatures, the surface of
the jet corrugated and wavy, and some of the clusters get detached from the main body of the jet and form drops. At
higher injectant temperatures, the surface becomes smoother and drops are no longer observed.
The density gradient profiles show a drop in maximum density gradient values from the previous case. The
highest values of the gradient continue to exist at the jet-gas interface. The core lengths increase from the previous
case. The laser correction algorithm works reasonably well for these cases too, especially in cases when the
surrounding gas concentration is lower and the jet temperature is higher. The density gradient plots reveal the
generation of vortices around the jet –gas interface, which is indicates the entrainment of the surrounding gas into
the main body of the jet, thereby enabling the mixing process.
a)
b)
Figure 12. Scaled images of a subcritical jet injected at supercritical chamber conditions. Figure (a) shows the
jet initially at Tr =0.66, Pr =0.90 injected into the chamber at Tr =1.03, Pr =0.82. Figure (b) shows the jet
initially at Tr =0.95, Pr =0.82 injected into the chamber at Tr = 1.00, Pr =0.77.
The binary species and unary species injections for similar chamber and injectant temperatures have been compared
again and shown in Figure 13. It is seen that the core length is higher in the unary species injection than the binary
case. Further, the value of the maximum density gradients is higher in the binary injection case. As seen in the
previous case, the primary difference is the jet divergence angle, which is much greater in the case of the unary
species injection than the binary injection. This can again be attributed to the greater diffusion in the former case,
causing enhanced mixing similar to the subcritical-into-subcritical case.
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a)
b)
Figure 13. Scaled images of a subcritical jet injected at supercritical chamber conditions. Figure (a) shows the
jet initially at Tr =0.66, Pr =1.85 injected into the chamber at Tr =1.19, Pr =1.68. Figure (b) shows the jet
initially at Tr =0.91, Pr =1.72 injected into the chamber at Tr = 1.02, Pr =1.40.
E. Supercritical Fluid into Supercritical Atmosphere
The chamber temperatures ranged in these cases from 441K to 458K, while the injectant temperatures was kept
around 441K to 443K. This represents Tr values around 1 for the injected fluid and 1.00 to 1.04 for the chamber. The
pressures for both the chamber and the injectant ranged from 19 atm. to 22 atm., which represent Pr values ranging
from 1.02 to 1.20 that are higher than the critical temperature of 18.4 atm. for the injectant.
In the supercritical zone, as shown in Figure 14, the jet behavior changes again. The surface of the jet becomes a
lot smoother than the previous two cases. Shear forces now exceed the capillary forces and they dominate.
Ligaments are considerably reduced and appear as thin material threads emanating from the jet that later dislocate in
irregular shapes. Due to interactions at the surface, instabilities lead to disturbances that manifest as surface waves.
In the regime when the surface tension is significant, hydrodynamic instability leads to the spatial development of
these waves and the eventual jet breakup. Characteristic disturbance waves correspond to the resonant frequencies of
the system consisting of liquid and gas inertia and surface tension forces. Once the surface tension is reduced, as the
critical conditions are reached and exceeded, these mechanisms yield to other forms of energy exchange between the
jet and the gaseous surroundings; among the possible destabilizing mechanisms at these conditions, the KHI is
expected to dominate.
The density gradient profiles reveal that the values of the maximum gradient also reduce from the previous two
cases. Moreover, the laser correction algorithm does not work as good as the subcritical cases. The prediction of the
absorption coefficient inside the jet is not correct, causing the density profile to appear non-uniform and underweighted towards the right side. This would also cause errors in the measurement of the density gradients inside the
jet.
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a)
b)
Figure 14. Scaled images of a supercritical jet injected at supercritical chamber conditions. Figure (a) and (b)
show the jet initially at Tr =1.00, Pr =1.09 injected into the chamber at Tr = 1.04, Pr =1.01.
As with previous two cases, the binary and unary species injections for similar chamber and injectant temperatures
have been compared and shown in Figure 15. Similar to the previous case, it is seen that the core length is higher in
the unary species injection than the binary case and that the value of the maximum density gradients is higher in the
binary injection case. The jet divergence angle is again the most significant difference between the two cases, being
much greater in the case of the unary species injection than the binary injection. Droplet formation cannot be
observed in the unary species case, though occasional droplets can be seen in the binary species case, proving that
certain portions of the jet are locally at subcritical conditions, since formation of drops would involve the existence
of surface tension.
a)
b)
Figure 15. Scaled images of a supercritical jet injected at supercritical chamber conditions. Figure (a) shows
the jet initially at Tr =1.02, Pr =1.77 injected into the chamber at Tr =1.03, Pr =1.6. Figure (b) shows the jet
initially at Tr =1.00, Pr =1.09 injected into the chamber at Tr = 1.04, Pr =1.01.
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V. Conclusion
•
•
•
•
•
•
•
•
•
A study of a heated jet injected into a gaseous environment formed of the same species as that of the
injectant was undertaken at subcritical and supercritical conditions.
The images obtained using planar laser induced fluorescence through the jet core. This method of image
acquisition has significant advantages over other techniques.
A detailed procedure has been undertaken to account for the laser intensity loss through the chamber and
the jet. Beer-Lambert’s law has been used to identify the absorption cross section for the two phases (liquid
and gas phases) separately. These values can be used for any experiments involving this specific fluid
under similar experimental conditions.
This method of laser sheet correction seems to work very well for lower temperatures and low
concentrations of gaseous fluoroketone inside the chamber, but is erroneous while correcting for the density
inside the jet and for the gas at higher temperatures, especially close to the critical point.
The images indicate the characteristics of subcritical mixing as mentioned in the theories. In this case, for a
subcritical jet injected into a subcritical environment, surface tension and inertia forces dominated the jet
breakup process, and droplet formation was observed.
In the case of subcritical jet injected into a supercritical environment, the surface of the jet became
smoother than in the previous case, and both droplet formation and irregularly shaped material were
observed when a portion of the jet broke off.
In the case of a supercritical jet injected into a supercritical environment, the jet surface changed
completely. Surface tension disappeared, and the surface became smooth with minimal irregularities.
In all three cases, an increase in the jet divergence angle for the unary species mixing over the binary
species mixing was noted. This indicated higher diffusion, and therefore enhanced mixing for the unary
mixing cases.
The density gradient values were also higher in the case of the binary species mixing, though in both types
of mixing the highest gradient were at the jet-gas interface.
VI. Future Work
The laser sheet correction algorithm needs to be modified to account for the over-corrected densities at higher
temperatures. This would involve an iterative algorithm, and needs further investigation to understand its criteria for
convergence. A separate calibration curve would need to be formed for the supercritical cases to account for the
laser absorption during the supercritical injection conditions. The trends of the jet divergence angle would also have
to be noted for all the three cases to infer which injection condition would produce the maximum mixing of the
injectant and the surrounding.
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Segal, C., and Polikhov, S. A., “Subcritical to Supercritical Mixing”, Physics of Fluids, Vol. 20, No. 5, 2008, pp 052101052107.
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