Selection of absorption lines for I 2–planarlaser-induced fluorescence measurement oftemperature in a compressible flow

Tomohide Ni-imi, Tetsuo Fujimoto, and Toshihiko Ishida

It is very important for I2–planar laser-induced fluorescence measurement of temperature in acompressible flow to choose a pair of absorption lines appropriate to the temperature range. Themethodfor selection of suitable pairs of absorption lines of I2 in the transition of B 3pou

1 1n8 5 432; X 1Sg1 1n9 5 02

is described. By the use of many pairs of absorption lines, the temperature dependence of the ratiobetween the fluorescence signals is calculated theoretically and is also investigated in experiments inwhich several pairs are applied to determination of the temperature distribution of a supersonic free jet.Keywords: Planar laser-induced fluorescence, temperaturemeasurement, iodine fluorescence, absorp-

tion lines, supersonic free jet.

1. Introduction

Optical methods have been used widely for remote, insitu, and nonintrusive measurement of thermody-namic parameters in gaseous flows. For example,planar laser-induced fluorescence 1PLIF2 has beendeveloped as a method for two-dimensional imagingof compressible flows1 and combustion flows.2Because the fluorescence signal obtained with PLIFdepends on thermodynamic variables, quantitativeimages of various properties can be obtained withsuitable data processing. The development and re-cent applications of PLIF are reviewed by Hanson3and McKenzie.4Since the initial research by Cattolica and Ste-

phenson,5 many thermometry techniques that uselaser-induced fluorescence, which are based on two-line atomic or molecular fluorescence, have beendeveloped. For compressible steady flow below roomtemperature 1approximately 300 K2, using two-linelaser-induced iodine fluorescence, Fletcher and Mc-Daniel6 developed a ring-dye-laser-based single-pointtemperature-measurement technique, and Ni-Imi etal.7 described a planar thermometry technique.

The authors are with the Department of Electronic-MechanicalEngineering, Faculty of Engineering, Nagoya University, Furo-cho,Chikusa-ku, Nagoya 464-01, Japan.Received 24 May 1994; revised manuscript received 18 April

1995.0003-6935@95@276275-07$06.00@0.

r 1995 Optical Society of America.

Iodine molecules have many absorption lines in thevisible region8 and easily radiate fluorescence whenirradiated by a laser beam. The fluorescence signalof I2 molecules depends on the density, temperature,and pressure of the flow field. According to thetwo-energy-level model, the ratio between the fluores-cence signals produced by irradiation of two laserbeams of different wavelengths is proportional mainlyto the ratio between the populations of the ground-state rotational-energy levels that are resonant withthe laser beams. Because the population of theselower rotational levels depends strongly on tempera-ture, temperature can be measured through the ratiobetween the fluorescence signals obtained by theexperiments. For accuratemeasurement of tempera-ture, however, it is necessary to choose the absorptionlines that are appropriate to the measured tempera-ture range. Although this method needs signal aver-aging to improve the signal-to-noise ratio, limiting itto steady flows, it allows planar measurement bymeans of a laser sheet and a high-sensitivity CCDcamera. It should be also noted that I2–PLIF mea-surements of temperature are only practical in low-temperature nonreacting flows, because of the likeli-hood of dissociation and chemical reaction.In this paper, a method for selection of two suitable

absorption lines for I2–PLIFmeasurement of tempera-ture is proposed, leading to more accurate measure-ment of temperature in each range of temperature.By the use of many pairs of absorption lines of I2 inthe transition of B 3pou

1 1n8 5 432 ; X 1Sg1 1n9 5 02,

the dependence of the ratio between the fluorescence

20 September 1995 @ Vol. 34, No. 27 @ APPLIED OPTICS 6275

signals on temperature is calculated theoretically foreach pair and is also investigated experimentally,especially relative to the temperature sensitivity.

2. Theory

A. Fluorescence Signal

Under the conditions of the experiments that are ofgasdynamic interest, especially below room tempera-ture, the dissociation of iodine molecules can beignored. If the broadband fluorescence from all theexcited levels is collected, it can be approximated thatthe rotational transfer among the excited states canbe neglected, and the excited states are lumped into asingle energy level 1two-energy-level model2. Underthe above assumptions, the fluorescence signal F ofthe iodine molecules induced by a broadband laser isgiven by9

F 5 CAji

Aji 1 QBi jEfNI2

, 112

where C is a constant including collection efficiencyand Planck’s constant, Aji is the spontaneous emis-sion rate, Bi j is the stimulated emission rate, Q is thecollisional quenching rate, E is the laser energy, andNI2 is the number density of the iodine molecules.Furthermore, f denotes the fraction of the ground-state population, that is in the level that is resonantwith the laser. This fraction is assumed to be aBoltzmann distribution in the ground state and isgiven by the product of the vibrational and therotational fractions, denoted by fn and fr, respectively:

f 5 fn fr 51

Qn

exp12 En9

kT212J9 1 12

Qr

3 exp32 Bn9hcJ91J9 1 12

kT 4 . 122

In Eq. 122 Bn9 is the rotational constant; En9 is thevibrational energy; Qn and Qr are the vibrational andthe rotational partition functions respectively; k is theBoltzmann constant; c is the velocity of light; and T isthe temperature. Furthermore, J9 and n9 are therotational and the vibrational quantum numbers inthe ground state, respectively. Below room tempera-ture, only the lowest vibrational level 1n9 5 02 issignificantly populated. Under this condition, it canbe approximated that fn is a constant, and the contri-bution of f to the fluorescence signal is due only to fr,i.e., to J9 and T. Figure 1 shows the dependence of fron J9 at T 5 5–200 K. It is found that at the lowertemperature mainly the lower levels are populated,and the population of the higher levels increases asthe temperature rises. Even at the same tempera-ture, therefore, the fluorescence signal of the iodinemolecules changes greatly according to the wave-length of the laser beam, i.e., to fr corresponding tothe rotational level that is resonant with the laserbeam, because the number of iodine molecules excitedby the laser beam is different.

6276 APPLIED OPTICS @ Vol. 34, No. 27 @ 20 September 1995

B. Temperature Measurement

The fluorescence signal at a point in the flow field isrepresented by F1 when the I2 molecules in therotational level J19 are excited and by F2 when themolecules in J29 are excited. Then a ratio betweenthese two fluorescence signals becomes

F1

F25

1Bi j 21 f11Bi j 22 f2

. 132

In Eq. 132, the subscripts 1 and 2 on the right-handside correspond to F1 and F2, respectively. The con-stant C and NI2 in Eq. 112 are canceled, because theseare common to F1 and F2. Aji@1Aji 1 Q2 is also can-celed because it is approximated as a function ofpressure and temperature in the present model. Inaddition, I is eliminated, because it is assumed to be aconstant over the frequency range of the laser beamused in this study. If the vibrational transitions1n8, n92 in F1 and F2 are identical, Bi j in Eq. 132 can bereplaced with the Honl–London factor SPorR1J92 and fwith fr, where subscripts P and R of S denote thefactors for the P and R branches, respectively.Therefore Eq. 132 is rewritten as follows:

F1

F25SPorR1J192 fr1J19, T2

SPorR1J292 fr1J29, T2. 142

Equation 142 indicates that the ratio between thefluorescence signals depends on temperature and ontwo rotational quantum numbers, J19 and J29.Therefore, once the frequencies of the two laser beamsare selected, the ratio between the fluorescence sig-nals can be expressed as a function of temperature.Although T in Eq. 142 is the rotational temperature, itis equal to the static temperature, provided that theflow is in equilibrium.Table 1 lists the absorption lines used, which

correspond to the transition from n9 5 0 in the groundstate X 1Sg

1 to n8 5 43 in the excited state B 3pou1.

Typical rotational transitions 1P and R branches2 areincluded in Table 1. Because the absorption lines ofthe P and R branches have identical wave numbers inthis transition, the sums of Sfr corresponding to each

Fig. 1. Dependence of fr on J9 at 5–200 K.

J9 of the two branches must be substituted for thedenominator and the numerator in Eq. 142. Fur-thermore, three absorption lines, P1102@R1122,P1262@R1282, and P1312@R1332, coincide with anotherrovibrational transition. For those cases, the Frank–Condon factor 3qn8,n94 must be taken into account tocalculate the ratio between the fluorescence signals.For example, when the dependence of the signal ratioon the temperature is calculated by the use of theP1302@R1322 absorption line for F1 and the P1102@R1122absorption line for F2, Eq. 142, when the superpositionof the P11212 absorption line in 1n8, n92 5 153, 02 to theP1102@R1122 absorption line is considered, becomes thefollowing:

F13P1302@R13224

F23P1102@R112245 3SP1302 fr130, T2 1 SR1322 fr132, T24

@3SP1102 fr110, T2

1 SR1122 fr112, T2

1q53,0q43,0

SP11212 fr1121, T24 . 152

C. Ratio between Fluorescence Signals

The dependence of F1@F2 on temperature has beencalculated theoretically with Eq. 142 for several pairsof absorption lines to determine which pairs aresuitable for temperature measurements. Figure 2shows the results when it is assumed that theP1102@R1122 absorption line is used for F2. Because ofoverlap of the P11212 absorption line in 1n8, n92 5 153, 02on the P1102@R1122 line, as mentioned above, thefluorescence contribution by the P11212 absorption linecauses F1@F2 to decrease as temperature increases, sothat temperature cannot be uniquely determined 1seeFig. 22.In contrast to the P1102@R1122 absorption line,

when the P182@R1102 line is used for F2, the fluores-cence signal ratio increases monotonically with tem-perature, as shown in Fig. 3, and therefore tempera-ture can be determined uniquely from F1@F2.Generally, the larger the difference between J19 and

Table 1. Absorption Lines of Iodine Molecules

Wave Number Absorption Line

19432.0415 P182@R1102 143, 0231.2588 P1102@R1122 143, 02

P11212 153, 0228.0283 P1162@R1182 143, 0226.6531 P1182@R1202 143, 0225.1299 P1202@R1222 143, 0219.6717 P1262@R1282 143, 02

R1712 145, 0215.2852 P1302@R1322 143, 0214.0906 P1312@R1332 143, 02

R1732 145, 0201.6775 P1402@R1422 143, 02396.8701 P1432@R1452 143, 02

2

J29, the larger the temperature sensitivity d1F1@F22@dT,because the difference between the populations forthe two initial levels becomes larger as temperatureincreases. For T . 200 °C, however, the use of theP1262@R1282 or P1312@R1332 absorption line for F1 resultsin a ,10% larger d1F1@F22@dT than that of theP1432@R1452 absorption line. This is attributable tothe overlap of the R1712 and R1732 absorption lines ontheP1262@R1282 andP1312@R1332 absorption lines, respec-tively. In certain cases, therefore, it may be desir-able to select the absorption line on which otherabsorption lines in the different vibrational transi-tions overlap, leading to larger temperature sensitiv-ity d1F1@F22@dT. On the other hand, in the range oflow temperature, it is better to usean absorption line with a smaller number of J9 forF1, because most molecules reside in lower rota-tional levels in that range. However, the use ofF13P1432@R14524@F23P182@R11024 makes the sensitivity

Fig. 2. Relation between F1@F2 and temperature, in whichP1102@R1122 is used for F2.

Fig. 3. Relation between F1@F2 and temperature, in whichP182@R1102 is used for F2.

0 September 1995 @ Vol. 34, No. 27 @ APPLIED OPTICS 6277

lower at below 20 K, because d1F1@F22@dT tends to zeroat that temperature range.When the P1182@R1202 absorption line is used for F2,

the resulting F1@F2 value is smaller than that of theP182@R1102 absorption line at the same temperature,but the temperature dependence of F1@F2 shows thesame tendency as the P182@R1102 absorption line 1seeFig. 32, as shown in Fig. 4. For the same reason asmentioned above, the use of the P1262@R1282 or theP1312@R1332 absorption line for F1 results in largerd1F1@F22@dT than that of the P1432@R1452 absorptionline.

3. Experiments

The temperature sensitivity of this method dependsintensively on a pair of absorption lines. To examinethe most suitable pair of absorption lines with respectto the temperature range, several pairs are applied todetermination of the temperature distribution of asupersonic free jet, where the temperature variesdrastically.Figure 5 is a schematic diagram of an experimental

apparatus used in this study. Carrier gas, Ar, issupplied to the source chamber through a variableleak valve and mixed with sublimated iodine mol-ecules 1vapor pressure is 48.4 Pa at 300 K2. Themixture is expanded through an orifice 1diameterD 5 0.4853 mm2 into the expansion chamber, which isevacuated by rotary pumps.Pressure in the source chamber 1PS2 and in the

expansion chamber 1Pb2 can be varied from 6.7 to 40kPa and from 40 to 400 Pa, respectively. The formeris measured with a mercury U-tube manometer andthe latter with a capacitance manometer 1MKS Bara-tron 220BA2. The temperature T in the source cham-ber is kept at 300 K.The laser system consists of a tunable dye laser

3Lumonics Hyperdye-300, 0.32 mJ in the expansionchamber, 7 ns, 150 Hz, bandwidth 0.06 cm21

1FWHM24, which is tunable by 0.001 nm, and anexcimer laser 1Lumonics TE-431T, operating on XeCl,

Fig. 4. Relation between F1@F2 and temperature, in whichP1182@R1202 is used for F2.

6278 APPLIED OPTICS @ Vol. 34, No. 27 @ 20 September 1995

wavelength 308 nm, 2 W@150 Hz2 as a pump source.Coumarin 500 is used as a laser dye, with a wave-length-tuning range from 482 to 542 nm. The dyelaser can be tuned from one wavelength to another inan interval of a few seconds. An optical fiber trans-mits the laser beam to the top flange of the expansionchamber, and a beam collimator transforms it into aparallel beam. Furthermore, two 50-cm focal-lengthcylindrical lenses shape this beam into a sheet. Thelaser sheet is 10 mm in height and 0.3 mm inthickness.The flow field visualized by the use of laser-induced

iodine fluorescence is imaged two dimensionally ontoa high-sensitivity CCD camera 1Hamamatsu C33692through a 540-nm long-pass filter, which only mini-mally attenuates the red-shifted fluorescence. Thecamera system consists of a f@2.8 telephoto lens 1180mm2 and a bellows used to obtain a larger image.A vertical length of one pixel corresponds to 0.0248mm on a real scale, and a horizontal length of onepixel corresponds to 0.0324 mm. The number ofpixels that the vidicon camera photographs is 512 3512. An image datum is digitized into 4096 graylevels 30 1black2–4096 1white24 corresponding to thefluorescence signal and is transmitted to a host

Fig. 5. Schematic diagram of the experimental apparatus. I@F,interface.

computer 1NEC 98012. To suppress random noise,the gate time of the CCD camera is set at 60 s, becauseof steadiness of the flow field. Then the backgroundsignal due to dark current is eliminated when animage obtained without irradiation of a laser sheet issubtracted from an image visualized by laser-inducediodine fluorescence. Laser energy is assumed to beidentical for each transition, and the spatial energydistribution is assumed to be constant in the observedarea.

4. Results and Discussion

A. Fluorescence-Signal Distribution

Figures 61a2–61f 2 are typical images of a supersonicfree jet visualized by the use of irradiation of laserbeams at wavelengths corresponding to the absorp-tion lines of P182@R1102, P1162@R1182, P1182R1202,P1262@R1282, P1312@R1332, and P1432@R1452, respec-tively. In Fig. 6, the shading changes according tothe fluorescence signal. The top of the scale in theupper right of Fig. 6 indicates high energy, and thebottom indicates low energy. These images are ob-tained at the same pressures: PS 5 16 kPa and Pb 5100 Pa. The supersonic free jet has a cell sur-rounded by a barrel shock structure and a normalshock wave 1Mach disk2. In the cell, temperaturedecreases drastically downstream because of the rapidexpansion. Temperature along the centerline of thejet decreases to several degrees Kelvin just in front ofthe Mach disk and increases again behind that. Asshown in Fig. 6, therefore, the fluorescence-signaldistribution of the flow field differs depending on the

Fig. 6. Psuedocolor images of the supersonic free jet visualized bythe use of irradiation of laser beams with various wavelengths,corresponding to the absorption lines.

2

wavelength of the laser beam, i.e., the selection of theabsorption line.Figure 7 shows the fluorescence-signal distribu-

tions along the centerline of the jet, which are ob-tained from the images of Fig 6, with each curveshowing very different distribution. In Fig. 7 theabscissa is the distance from the orifice, normalizedby the orifice diameter. For transitions from lowerrotational states such as the P182@R1102 absorptionline, the fluorescence signal is high in the down-stream region with relatively low temperature butdecreases abruptly behind the Mach disk 1X@D , 8.52,where temperature increases again. On the otherhand, for the transitions from higher rotational statessuch as P1312@R1332 or P1432@R1452, the fluorescencesignal decreases drastically downstream and in-creases at the Mach disk 1X@D , 8.52. An increase inthe fluorescence signal just behind the orifice1X@D 5 0.0–0.52 may be caused by a decrease incollisional quenching downstream according to therarefaction.

B. Temperature Measurement with the P182@R1102AbsorptionLine for F2Figure 8 shows the temperature distributions alongthe centerline of the jet, which are obtained by use ofthe P182@R1102 absorption line for F2 and variousabsorption lines for F1. The dashed–dotted curve inFig. 8 is the theoretical temperature distribution forstagnation temperature T0 5 300 K and a specificheat ratio g 5 5@3, which is calculated with thedistribution of Mach numbers given by Ashkenas andSherman10 and an isentropic relation. Irrespectiveof the absorption lines used for F1, in the relativelyhigh-temperature region, the measured temperatureis underestimated in comparison with the theoreticalone. From Fig. 3, it appears appropriate superfi-cially to use the P1262@R1282 or the P1312@R1332absorption line for F1 even in the relatively high-temperature range, promising higher temperaturesensitivity d1F1@F22@dT. In Fig. 8, however, the tem-perature measured with those pairs is underesti-

Fig. 7. Fluorescence-energy distributions along the centerline ofthe supersonic free jet, which are obtained from the images ofFig. 6.

0 September 1995 @ Vol. 34, No. 27 @ APPLIED OPTICS 6279

mated in the relatively high-temperature region be-hind the orifice and the Mach disk. This error can beattributed to the contribution of other absorptionlines near the P182@R1102 line to F2 as a result ofcollisional and Doppler broadening, because this lineis close to the band head. Therefore the fluorescenceby excitation of the P182@R1102 absorption line is moreintense than that predicted theoretically by the use ofthe present method, so that the F1@F2 is underesti-mated and the measured temperature becomes lower.As mentioned above, in the range of relatively lowtemperature, the smaller J19 of the absorption line forF1 is, the better the measurement accuracy. FromFig. 8, it is clear that temperature measured by theuse of the P1182@R1202 absorption line for F1 agreeswell with the theoretical one below 20 K, and the errorbecomes larger with an increase in J19. This errormay be attributable to rotational nonequilibrium ofiodine molecules.

C. Temperature Measurement with the P1182@R1202Absorption Line for F2The temperature distributions along the centerline ofthe jet, which are measured by the use of theP1182@R1202 absorption line for F2, are shown in Fig.9. From Fig. 9, one can see that the measuredtemperature agrees well with the theoretical one inthe range of relatively high temperature just behindthe orifice, irrespective of the absorption lines for F1.Generally, when the P1262@R1282 absorption line forF1 is used, it is found that the measured temperaturedistribution fits the theoretical curve over the widerrange of temperature, showing the highest accuracyamong the pairs of the absorption lines in this study.From other experiments,7 it was found that by theuse of the P1262@R1282 absorption line for F1 and theP1162@R1182 line for F2, temperature could also bemeasured for temperature with high accuracy.When the P1312@R1332 or the P1432@R1452 line is

Fig. 8. Measured temperature distributions along the centerlineof the supersonic free jet, which are obtained by use of theP182@R1102 absorption line for F2.

6280 APPLIED OPTICS @ Vol. 34, No. 27 @ 20 September 1995

used for F1, as shown in Fig. 9, the temperature isoverestimated in the range of low temperature, be-cause of the smaller population of these rotationallevels, showing the effects of rotational nonequilib-rium.

5. Conclusions

We have described a method of selecting absorptionlines for I2–PLIF measurement of low temperature ina compressible flow. When many pairs of absorptionlines of I2 are used in the transition of B 3pou

1 1n8 5 432; X 1Sg

1 1n9 5 02, the temperature dependence of theratio of the fluorescence signals was calculated theo-retically for each pair and was also investigatedexperimentally. The measured temperature is influ-enced strongly by the choice of absorption lines,illustrating the necessity of a suitable selection ofabsorption lines for a given temperature range. Incertain cases, the use of the absorption line on whichanother absorption line in a different vibrationaltransition overlapped made the temperature sensitiv-ity higher. However, as shown in the case in whichthe P1102@R1122 absorption line for F2 was used, itshould be noted that temperature cannot be deter-mined uniquely from F1@F2, when the other absorp-tion line overlaps on the line with smaller J9. In thisstudy, the use of the pair of P1262@R1282 and P1182@R1202in the electronic and vibrational transition used inthis study could determine temperature with highaccuracy below room temperature.

The present work was supported by a grant-in-aidfor Scientific Research from the Ministry of Educa-tion, Science and Culture.

References1. R. J. Hartfield, S. D. Hollo, and J. C. McDaniel, ‘‘Planar

temperature measurement in compressible flows using laser-induced iodine fluorescence,’’ Opt. Lett. 16, 106–108 119912.

2. B. K. McMillin, J. L. Palmer, and R. K. Hanson, ‘‘Temporally

Fig. 9. Measured temperature distributions along the centerlineof the supersonic free jet, which are obtained by use of theP1182@R1202 absorption line for F2.

resolved, two-line fluorescence imaging of NO temperature ina transverse jet in a supersonic cross flow,’’ Appl. Opt. 32,7532–7545 119932.

3. R. K. Hanson, ‘‘Planar laser-induced fluorescence imaging,’’ J.Quant. Spectrosc. Radiat. Transfer 40, 343–362 119882.

4. R. L. McKenzie, ‘‘Progress in laser spectroscopic techinques foraerodynamic measurements: an overview,’’ AIAA J. 31, 465–477 119932.

5. R. J. Cattolica and D. A. Stephenson, ‘‘Two-dimensional imag-ing of flame temperature,’’ in AIAA Progress in Aeronauticsand Astronautics, J. R. Bowen, N. Manson, A. K. Oppenheim,and R. I. Soloukhin, eds. 1American Institute of Aeronauticsand Astronautics, Washington, D.C., 19842, Vol. 95, pp. 714–721.

6. D. G. Fletcher and J. C. McDaniel, ‘‘Temperature measure-

ment in a compressible flow field using laser-induced iodinefluorescence,’’ Opt. Lett. 11, 16–18 119872.

7. T. Ni-Imi, T. Fujimoto, and N. Shimizu, ‘‘Method for planarmeasurement of temperature in compressible flow using two-line laser-induced fluorescence,’’ Opt. Lett. 15, 918–921 119902.

8. S. Gerstenkorn and P. Luc, Atlas du Spectre d’Absorption de laMolecule d’Iode 1Edition du Centre National de la RechercheScientifique, Paris, 19782.

9. J. C. McDaniel, ‘‘Investigation of laser-induced iodine fluores-cence for the measurement of density in compressible flows,’’Ph.D. dissertation 1Dept. of Aeronautics and Astronautics,Stanford University, Stanford, Calif., 19822.

10. H. Ashkenas and F. S. Sherman, ‘‘Experimental methods inrarefied gas dynamics,’’ in Rarefied Gas Dynamics, J. H. deLeeuw, ed. 1Academic, NewYork, 19662, Vol. 2, 84–105.

20 September 1995 @ Vol. 34, No. 27 @ APPLIED OPTICS 6281