Optical Diagnostics of Nonequilibrium Phenomena
in Highly Rarefied Gas Flows
Tomohide Niimi
Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
ABSTRACT
The necessity of non-intrusive measurement of the thermodynamic variables in rarefied gas flows has
motivated the development of optical diagnostics, such as electron beam fluorescence, laser induced
fluorescence, coherent anti-Stokes Raman scattering, and so on. These spectroscopic methods have enabled to
detect the nonequilibrium in the gas flows, based on the internal energy distributions obtained from spectral
profiles. In this paper, the laser-based techniques for detection of the nonequilibrium phenomena in the highly
rarefied gas flows and some results obtained by us are described.
INTRODUCTION
Since the emergence of LASER in 1960, many optical diagnostic methods have been developed to measure
thermodynamic variables in the gaseous flows and combustion fields. Especially, monochromaticity and
coherency of the laser have enabled to detect the variables, based on internal energy distributions.
In our laboratory, we have developed the laser-based diagnostic method to analyze the rarefied gas flows,
such as laser induced fluorescence of I2, O2 and NO (LIF)[1-4], coherent anti-Stokes Raman scattering of N2
(CARS)[5] and degenerate four wave mixing of I2 (DFWM). Since these techniques are based on the detection
of fluorescence or scattering light, even LIF, which is most sensitive among them, is difficult to be applied to
the rarefied gas flow below 1012 molecules/cm3. However, resonantly enhanced multi-photon ionization
(REMPI)[6,7], which we are applying to the detection of strong nonequilibrium phenomena in a supersonic free
molecular nitrogen flow, has high sensitivity, because the ions are directly detected as a signal.
In this paper, I describe mainly our experimental results related to rarefied gas flows, obtained by the use of
LIF and REMPI, i.e., applications of LIF to visualization of flow field structures including complicated shockwave system, such as interacting supersonic free jets, and to a measurement technique of rotational temperature,
and establishment of a REMPI system and its application to detection of rotational nonequilibrium in highly
rarefied gas flows.
OPTICAL DIAGNOSTIC METHODS AND ITS APPLICATIONS
Laser Induced Fluorescence (LIF)
When a molecule irradiated with a laser beam of a frequency the same as the resonance frequency of the
molecule, its energy state changes from a stable ground state to an excited state as shown in Fig. 1. As the
excited molecule releases its energy and return to its ground state, it emits fluorescence. This is known as laserinduced fluorescence (LIF). In the field of rarefied gas dynamics, at first, LIF had been used to visualize a flow
field structures two- or three-dimensionally. Then it has been developed as a diagnostic tool for measurement
of thermodynamic variables, such as temperature or density, in the compressible or combustion flows. In this
chapter, I introduce some results obtained by our group, such as visualization of flow field structures and
temperature measurement technique using LIF of iodine molecules.
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
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Visualization of Flow Field Structures using LIF
About 15 years ago, we adopted LIF of iodine molecules (I2) seeded in argon gas to visualize a flow field
structure of a single jet issued from a sonic nozzle with exit diameter of 0.5 mm into a chamber kept at low
pressure, as shown in Fig. 2. The total flow field can be visualized by the fluorescence of I2 molecules, which
sublimate readily at room temperature, since I2 molecule do not disturb the flow as long as the molar fraction of
I2 is low. From Fig. 2, the Barrel shock and Mach disk can be seen clearly by using the LIF of I2. We applied
the LIF of I2 to visualization of three-dimensional structures and shock wave system of two interacting identical
supersonic free jets[1]. These experiments were carried out for various angles θ between jet axes from 45 to
180 deg and with various ratios of the source pressure Ps to the pressure in the expansion chamber Pb. The
structures of the flow fields of interacting free jets depended on θ and the pressure ratio Ps/Pb. For θ≤90 deg,
the structures of the flow field are symmetrical with respect to the interacting plane irrespective of Ps/Pb, and a
cell surrounded by shock waves is formed near the interacting plane when Ps/Pb is relatively large as shown in
Fig. 3 for θ=45 deg. The shock wave system has a φ–shaped structure in the plane perpendicular to the
interacting plane. It is peculiar that the φ–shaped structure tends to be planar in the interacting plane as the flow
proceeds far downstream. For θ>90 deg, many types of flow fields appear, depending on Ps/Pb, suggesting the
complexity of flow stability. In particular, either symmetrical or asymmetrical structure of the flow field with
respect to the interacting plane is observed in spite of the same pressure ratios.
We also studied the structures of two opposed supersonic free jets with different source pressure by flow
visualization using LIF of I2 molecules seeded in argon[3]. Characteristic structures of the flow fields are
classified roughly into four types depending on the condition of the source pressure and the pressure of the
expansion chamber. Especially, we found an unstable flow in the interacting region by the use of moving
images.
The flow fields of two, three or four interacting parallel supersonic free jets are also studied by flow
visualization using planar LIF of I2 molecules seeded in argon[8]. Centers of orifices are set linearly and on
vertices of a triangle or square. The flow fields are visualized on the plane including jet centerlines and in cross
sections vertical to the centerlines. Three-dimensional structures of the flow fields do not tend downstream to
the structures expected from the arrangement of the orifices but there appear intense expansion between the
adjacent jets, as shown in Fig. 4 for the square arrangement of four orifices.
Upper Energy Level
Absorption
Fluorescence
Lower Energy Level
FIGURE 1. Principle of LIF
FIGURE 2. A supersonic free jet visualized by I2-LIF
FIGURE 3. Flow field structure of interacting free jets for θ=45 deg
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FIGURE 4. Flow field structure of interacting parallel supersonic free jets for the square arrangement of four orifices
Rotational Temperature Measurement using LIF
We proposed a method for planar measurement of temperature in the rarefied gas flows using two-line laserinduced iodine fluorescence in 1991[2,9]. Under the condition of the experiments of gas dynamic interest, the
dissociation of the iodine molecules can be ignored. If broadband fluorescence from all the excited levels is
collected, it can be approximated that rotational transfer among the excited states are lumped into a single
energy level (two-level model). In this case, the fluorescence intensity F of iodine molecules induced by a
broadband laser is given by
F= C[Aji/(Aji+Q)]BijIfNI2 ,
(1)
where C is a constant including collection efficiency and Planck’s constant, Aji is the spontaneous emission rate,
Bij is the stimulated-emission rate, Q is the collision quenching rate, I is the intensity of laser beam, NI2 is the
number density of iodine molecules, and f denotes the fraction of the ground-state population that is in the level
resonant with the laser. This fraction is assumed as a Boltzmann distribution in the ground state and is given by
the product of the vibrational and rotational fraction, denoted by fv and fr which are the function of the
vibrational quantum numbers v” and rotational quantum number J”, respectively, in addition to temperature T.
Below room temperature the iodine molecule populate almost the lowest vibrational level (v”=0). Under this
condition, it can be approximated that fv is a constant, and the contribution of f to the fluorescence intensity is
only due to fr, i.e., J” and T. Even at the same temperature, therefore, the fluorescence intensity of iodine
molecules changes greatly according to the wavelength of the laser beam to be irradiated, i.e., to fr of rotational
level resonant with the laser beam, since the number density of iodine molecules excited by the laser beam is
different.
The fluorescence intensity at a point in the flow field is represented by F1 when the iodine molecules in the
rotational level J”1 are excited and by F2 when the molecules in the level J”2 are excited. Then the ratio
between these two fluorescence intensities becomes
F1/F2=[(Bij)1f1]/[(Bij)2f2],
(2)
where the subscripts 1 and 2 on the right-hand side correspond to those of F. The constants C and NI2 in Eq. (1)
are canceled, since these are common to F1 and F2. Aji/(Aji+Q) is also canceled since it is approximated as a
function of pressure and temperature in the present model. In addition, laser intensity is eliminated, because it
is constant over the frequency range of the laser beam used in this study. If the vibrational transitions (v’, v”) in
F1 and F2 are identical, Bij and f in Eq. (2) can be replaced by the Hönl-London factor S(J”) and fr, respectively.
Therefore, Eq. (2) is rewritten as
F1/F2=[S(J”1)fr(J”1,T)]/[ S(J”2)fr(J”2,T)].
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(3)
Equation (3) indicates that the ratio between fluorescence intensities depends on temperature and two rotational
quantum numbers, J”1 and J”2. Therefore, once two absorption lines are selected, the ratio between
fluorescence intensities can be expressed as a function of temperature. Of course, T in Eq. (3) is rotational
temperature.
In this study, two lines are selected from the absorption lines in a transition from v”=0 in the ground state
X1Σg+ to v”=43 in the excited state Β3Πou+. Since the absorption lines of P and R branches have identical wave
numbers in this transition as listed in Table 1, the sum of Sfr corresponding to each J” of the two branches must
be substituted for the denominator and the numerator in Eq. (3). The dependence of F1/F2 on temperature can
be calculated with Eq. (3) for several pairs of absorption lines. Figure 5 shows the results when it is assumed
that the P(18)/R(20) absorption line is used for F2. The fluorescence signal ratios increase monotonically with
temperature, as shown in Fig. 5, and therefore temperature can be determined uniquely from F1/F2.
Figures 6(a)-6(f) are typical images of a supersonic free jet visualized by the use of irradiation of laser
beams at wavelengths corresponding to the respective absorption lines. These images are obtained at the same
pressure condition: Ps=16 kPa and Pb=100 Pa. Figure 7 shows the fluorescence signal distributions along the
centerline of the jet, which are obtained from the images of Figs. 6, with each curve showing very different
distribution. In Fig. 7 the abscissa is the distance from the orifice, normalized by the orifice diameter. For
transitions from lower rotational states such as the P(8)/R(10) absorption line, the fluorescence signal is high in
the downstream region with relatively low temperature but decreases abruptly behind the Mach disk (X/D ~ 8.5),
where temperature increases again. On the other hand, for the transitions from higher rotational states such as
the P(31)/R(33) or P(43)/R(45), the fluorescence signal decreases drastically downstream and increases at the
Mach disk. An increase in the fluorescence signal just behind the orifice may be caused by a decrease in
collisional quenching downstream according to the rarefaction.
TABLE 1. Absorption lines of iodine molecules in the transition of Β3Πou+ (v’=43) ← X1Σg+ ( v”=0 )
Wave Number
19432.0415
28.0283
26.6531
19.6717
14.0906
396.8701
FIGURE 5. Relation of F1/F2 to Temperature
used the P(18)/R(20) absorption line for F2
Absorption Line
P(8)/R(10)
P(16)/R(18)
P(18)/R(20)
P(26)/R(28)
P(31)/R(33)
P(43)/R(45)
FIGURE 6. Psuedocolor images of a supersonic free jet visualized
by irradiation of a laser sheet corresponding to various absorption lines
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The temperature distributions along the centerline of the jet, which are measured by the use of the
P(18)/R(20) absorption line for F2, are shown in Fig. 8. From Fig. 8, one can see that the measured temperature
agrees well with the theoretical one (a dotted curve) in the range of relatively high temperature just behind the
orifice, irrespective of the absorption lines for F1. When the P(26)/R(28) absorption line for F1 is used, it is
found that the measured temperature distribution fits the theoretical curve over the wider range of temperature,
showing the highest accuracy among the pairs of the absorption lines in this study. As shown in Fig. 8, the
temperature is overestimated in the range of low temperature, because of the smaller population of these
rotational levels, showing the effects of rotational nonequilibrium.
FIGURE 7. Fluorescence intensity distribution along the
centerline of a supersonic free jet from the images of Fig. 6
FIGURE 8. Measured temperature distribution along the
centerline of a supersonic free jet
Resonantly Enhanced Multi-Photon Ionization (REMPI)
Besides LIF mentioned above, the necessity of non-intrusive measurement of thermodynamic variables
has motivated the development of some optical diagnostic methods for gaseous flows, such as Electron beam
fluorescence, Rayleigh scattering, Coherent anti-Stokes Raman scattering (CARS), and so on. Since these
techniques are based on detection of fluorescence or scattering light, as shown in Fig. 9[10], even LIF which is
the most sensitive method among them is difficult to be applied to the rarefied gas flow below 1012 molecules
/cm3.
As a candidate of the non-intrusive measurement technique with high sensitivity and short response, the
REMPI (Resonantly Enhanced Multi-Photon Ionization) technique[6,7] may be very suitable, also allowing
measurement of non-equilibrium phenomena in the highly rarefied gas flows. In the REMPI technique, ions
excited to the ionization state from the ground state by multiple photons are detected as a signal and its spectra
depending on the energy of irradiation are analyzed to measure temperature and density. Because REMPI is a
non-linear optical process and needs nR+m photons (n-photon resonance and m-photon ionization: nR+m
REMPI) from the ground state through the resonance state to the ionization state, an analysis of a REMPI
spectrum generally needs somewhat complicated procedure.
In this study, we develop the experimental system for 2R+2 N2-REMPI and apply it to measurement of
rotational temperature in a supersonic free molecular nitrogen flow. In the 2R+2 N2-REMPI technique,
nitrogen molecules are ionized by two steps, i.e., the first step from the ground state to the resonance state (2
photons) and the second step from the resonance state to the ionization state (2 photons). The nitrogen ions are
detected as a signal and its spectra depending on the wavelength of an irradiated laser beam are analyzed to
measure the rotational temperature through the Boltzmann plot.
2R+2 N2-REMPI
Figure 10 depicts the modeling of 2R+2 N2-REMPI. In this process, nitrogen molecules at the ground state
(X1Σg+ ) are excited to the resonant state (a1Πg ) by two-photon absorption. Then the excited molecules are
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ionized by additional two-photon energy. Because four photons participate in this process, the ion current is
proportional to the fourth power of laser flux when the flux is relatively low. On the other hand, when the laser
flux is sufficiently high so that almost all the excited molecules ionize, the ion current is proportional to the
second power of laser flux, because the REMPI process reflects the two-photon transition process from the
ground state to the resonant one. In this case, since the REMPI spectra depend on the rotational energy
distribution at the ground state, the rotational energy distribution, i.e., the rotational temperature, can be
deduced from the REMPI spectra.
When the laser flux is constant, the rotational line intensity IJ’,J” in 2R+2 N2 -REMPI spectra is given by
IJ’,J” = Cg(J”)S(J’,J”)exp(–Erot/kTrot) ,
(4)
where C is the constant independent of the rotational quantum number J’ of the resonant state and J” of the
ground state, but including Franck-Condon factor, laser flux, number density of the molecules, and so on. g(J”)
is the nuclear spin degeneracy of nitrogen molecules formed by N14 atoms, whose value is 3 and 6 for odd and
even J”, respectively. Erot is the rotational energy, k the Boltzmann’s constant, and Trot the rotational
temperature. S(J’,J”) is the two-photon Hönl-London factor for the a1Πg ← X1Σg+ transition. Since the signal
intensity IJ’,J” is related to the rotational energy Erot/k as described in Eq. (4), rotational temperatures can be
easily deduced from the measured REMPI spectra by the Boltzmann plot.
Experimental Setup for 2R+2 N2-REMPI
Figure 11 shows a schematic diagram of the experimental setup. The vacuum chamber is evacuated by a
1600ℓ/sec turbomolecular pump. Nitrogen gas is issued from a sonic nozzle with a 0.50mm diameter, and
expanded into the chamber. For the stagnation pressure of 1.2Torr (160Pa) and the stagnation temperature of
293K, the background pressure in the chamber is kept at 3.2 × 10-5 Torr (4.3 × 10-3 Pa). An Nd:YAG-pumped
dye laser (Lmbda Physik, SCANMATE OG 2E C-400) operated with Rhodamine 6G dye is used as a laser
source, and the output is frequency-doubled by a BBO crystal. The wavelength of the laser beam is ranged
from 283 to 284.1nm. The beam is focused with a quartz lens (f = 120mm) on the centerline of the nitrogen
free-molecular flow. The energy, repetition rate, and duration time of the laser beam are 6.2mJ/pulse, 10Hz,
and 6ns, respectively. The ionized nitrogen molecules are detected by a secondary electron multiplier (Murata,
CERATRON EME-2061C). The signal intensity is recorded on a personal computer after amplified by a
current-input preamplifier (NF, LI-76, gain: 104V/A) and averaged by a boxcar integrator (STANFORD
RESEARCH SYSTEM, SR250, SR245 and SR280). The wavelength step of the scanning is 0.001nm, and the
signal intensity is integrated for 100 laser pulses per each step.
Ionization State
2-photon
absorption
Resonance State (a1Π g )
2-photon
absorption
quenching
stimulated
emission fluorescence
Ground State (X1Σg+)
FIGURE 9. Application regimes for several optical diagnostics
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FIGURE 10. Modeling of 2R+2 N2 –REMPI
REMPI spectrum and Freezing of Rotational Temperature
Figure 12 represents the 2R+2 N2-REMPI spectrum of the (v’, v” ) = (1, 0) band measured experimentally.
The focal point was 5.0 mm downstream from the nozzle exit ( x/D = 10), along the center line of the jet. In
this figure, the horizontal axis indicates the wavelength of the laser, and the vertical one the signal intensity
normalized by the peak. The pressure in the vacuum chamber was 3.2×10-5 Torr, and the source pressure and
temperature were 1.2 Torr and 293 K, respectively. In this case, the number density at the focal point is 1.6×
1013 molecules/cm3.
As shown in Fig. 12, the spectral lines are very close to one another in this experimental condition. This
may be caused by higher rotational temperature. So, we estimated the rotational temperature at the
measurement point of the spectra (x/D = 10) by solving the relaxation equation derived by Gallagher and
Fenn[9], assuming the flow to be in equilibrium. As a result of this estimation, the rotational temperature Trot =
235K was deduced at x/D = 10. Since the source pressure is set at 1.2 Torr in our experiments, the rotational
temperature freezes just downstream from the nozzle exit and results in a higher value as calculated above.
Non-Equilibrium of Rotational Mode in the Supersonic Free Molecular Nitrogen Flow
Figure 13 shows the Boltzmann plot of the spectral lines of O(4)-O(6), O(9)-O(16) and P(11)-P(19)
depicted in Fig. 12. If considering the broadening of the spectral line, the peak intensity becomes lower and
only the intensity integrated over the spectral profile may indicate the real one. For, the Boltzmann plot,
therefore, we use the intensity integrated over the spectral profile assumed to be Gaussian.
For the Boltzmann plot using both O- and P-branches, M(P)/M(O) has to be determined from the
experimental REMPI spectra. M(P) and M(O) which appear in the two-photon Hönl-London factors are the
transition factors given by the products of the electronic transition dipole moments. From the plot of the
spectral lines of O(9)-O(16) and P(11)-P(19) in Fig. 13, M(P)/M(O) results in 0.83 .
If the rotational mode is in equilibrium, the plotted data should be on a line in the Boltzmann plot and we
can deduce the rotational temperature through the slope of the line. As shown in Fig. 13, however, it is found
that the data for O(4)-O(6) show different tendency from the line approximated by the data of O(9)-O(16) and
P(11)-P(19). The rotational temperature calculated from the slop determined from the latter results in 339 K,
which is higher than the source temperature of 293 K. Though there is, of course, no meaning of two line fitting
for the Boltzmann plot, three data of O(4)-O(6) are on a line and the rotational temperature deduced from the
slop of the line is 122 K. These mean that the number of molecules in the rotational states is not given by the
Boltzmann distribution at the measurement point, showing the so-called non-Boltzmann distribution.
Intensity[a.u.]
1.5
1
P
S
Q 4
R
0
16
10
20
19
20
P0 = 1.2Torr
T0 = 293K
x/D = 10.0
0.5
0
283
FIGURE 11. Experimental setup
10
O
283.5
Wavelength[nm]
284
FIGURE 12. Experimental 2R+2 N2-REMPI spectrum
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ln(I/gS) [a.u]
-9
O(4,5,6,9-16)
P(11-19)
M(P)/M(O) = 0.83
-10
-11
-12
-13
0
Trot = 122K O(4,5,6)
Trot = 339K O(9-16),P(11-19)
200
400 600
Erot/k [k]
800
FIGURE 13. Boltzmann plot using both O- and P-branches
1000
Since in this experiment we examine only one point in the free molecular flow, we can not discuss about
the non-equilibrium in detail. However, it may be clear that the non-equilibrium of the rotational mode
proceeds gradually from the nozzle exit to the downstream or as an decrease in the source pressure. Now, we
are carrying out experiments changing the source pressure and the measurement point as parameters, to clarify
the transition from the equilibrium to non-equilibrium in the rotational mode and to obtain the functional form
of the non-Boltzmann distribution.
ACKNOWLEDGMENT
I wish to acknowledge the support from Asian Office of Aerospace Research & Development (WOS
program). The present work was also supported by a grant-in-aid for Scientific Research from the Japanese
Ministry of Education, Science and Culture and the MOSAIC project.
REFERENCES
1. Fujimoto, T. and Niimi, T., “Three Dimensional Structures of Interacting Freejets”, Rarefied Gas Dynamics, SpaceRelated Studies, AIAA(1988), pp. 391-406.
2. Niimi, T., Fujimoto, T. and Shimizu, N., “Planar Measurement of Temperature in Rarefied Gas Flow by LIF Images”,
Proc. 17th Int. Symp. on Rarefied Gas Dynamics, VCH, (1991), pp. 1482-1489.
3. Niimi, T., Fujimoto, T. and Ijima, K, “Structures of Two Opposed Supersonic Free Jets with Different Source Pressure”,
Rarefied Gas Dynamics, Experimental Techniques and Physical Systems, AIAA, 159(1994), pp. 363-374.
4. Ishida, T, Niimi, T. and Fujimoto, T., “Two-dimensional Imaging of Rarefied Gas Flow using O2-LIPF”, Rarefied Gas
Dynamics 19 , Vol. 2 (1995), Oxford Science Pub, pp. 1446-1452.
5. Hara, Y., Niimi, T., Fujimoto, T., Fukuda, Y. and Oba, H., “Measurement of Temperature and Number Density by
CARS (Application of CARS to Plasma Jets)”, Rarefied Gas Dynamics, Space Science and Engineering, AIAA
160(1994), pp. 360-370.
6. Mori, H., Ishida, T., Aoki, Y. and Niimi, T., “Spectroscopic Study of REMPI for Rotational Temperature Measurement
in Highly Rarefied Gas Flow”, Rarefied Gas Dynamics, AIP, 585 (2001), pp. 956-963.
7. Niimi, T., Mori, H, Ishida, T., Takasu, A and Niwa, K., “Application of REMPI to Highly Rarefied Gas Flows”, 19th Int.
Congress on Instrumentation in Aerospace Simulation Facilities, 2001, pp. 256-261.
8. Niimi, T., Fujimoto, T. and Taoi, N., “Flow Fields of Interacting Parallel Supersonic Free Jets”, JSME Int. J., B, 39-1
(1996), pp. 95-100.
9. Niimi, T., Fujimoto, T. and Ishida, T, “Selection of Absorption Lines for I2-Planar Laser-Induced Fluorescence
Measurement of Temperature in a Compressible Flow”, Applied Optics, 34-27(1995), pp. 6275-6281.
10. Dankert, C., Cattolica, R. and Sellers, W., “Local Measurement of Temperature and Concentration: A Review for
Hypersonic Flows”, Bountier, A. ed., New Trend in Instrumentation for Hypersonic Research, (1994), pp563-581
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