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 shock-wave 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 laser-induced 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.

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.

Absorption Fluorescence

Lower Energy Level

Upper 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

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 laser-

induced 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)]. (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 Absorption Line 19432.0415 P(8)/R(10) 28.0283 P(16)/R(18) 26.6531 P(18)/R(20) 19.6717 P(26)/R(28) 14.0906 P(31)/R(33) 396.8701 P(43)/R(45)

FIGURE 5. Relation of F1/F2 to Temperature used the P(18)/R(20) absorption line for F2 FIGURE 6. Psuedocolor images of a supersonic free jet visualized

by irradiation of a laser sheet corresponding to various absorption lines

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 FIGURE 8. Measured temperature distribution along the centerline of a supersonic free jet from the images of Fig. 6 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

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.

Resonance State (a1Πg )

Ionization State

Ground State (X1Σg+)

2-photonabsorption

2-photonabsorption

quenching

fluorescencestimulatedemission

FIGURE 9. Application regimes for several optical diagnostics 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.

283 283.5 2840

0.5

1

1.5

Wavelength[nm]

Inte

nsity

[a.u

.]

OP

QR

S20

20

10 19

10 16

4

0 P0 = 1.2TorrT0 = 293Kx/D = 10.0

FIGURE 11. Experimental setup FIGURE 12. Experimental 2R+2 N2-REMPI spectrum

-13

-12

-11

-10

-9ln

(I/g

S) [a

.u]

O(4,5,6,9-16)P(11-19)

S

the nproceare cathe traof the

IprograMinis

1. FuRe

2. NiPr

3. NiRa

4. IshDy

5. HaCA16

6. Min

7. NiCo

8. Ni(19

9. NiM

10. DaHy

M(P)/M(O) = 0.83

0 200 400 600 800 1000Erot/k [k]

Trot = 122K O(4,5,6) Trot = 339K O(9-16),P(11-19)

FIGURE 13. Boltzmann plot using both O- and P-branches

ince in this experiment we examine only one point in the free molecular flow, we can not discuss about on-equilibrium in detail. However, it may be clear that the non-equilibrium of the rotational mode eds gradually from the nozzle exit to the downstream or as an decrease in the source pressure. Now, we rrying out experiments changing the source pressure and the measurement point as parameters, to clarify nsition from the equilibrium to non-equilibrium in the rotational mode and to obtain the functional form

non-Boltzmann distribution.

ACKNOWLEDGMENT

wish to acknowledge the support from Asian Office of Aerospace Research & Development (WOS m). The present work was also supported by a grant-in-aid for Scientific Research from the Japanese

try of Education, Science and Culture and the MOSAIC project.

REFERENCES

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imi, T., Fujimoto, T. and Ishida, T, “Selection of Absorption Lines for I2-Planar Laser-Induced Fluorescence easurement of Temperature in a Compressible Flow”, Applied Optics, 34-27(1995), pp. 6275-6281. nkert, C., Cattolica, R. and Sellers, W., “Local Measurement of Temperature and Concentration: A Review for personic Flows”, Bountier, A. ed., New Trend in Instrumentation for Hypersonic Research, (1994), pp563-581