Abstract

Mean and instantaneous measurements of pressure, temperature, and density have been acquired in an optically accessible gas cell and in the flow field of an underexpanded sonic jet by use of the high-resolution N2 coherent anti-Stokes Raman scattering (CARS) technique. This nonintrusive method resolves the pressure- and temperature-sensitive rotational transitions of the ν = 0 → 1 N2 Q-branch to within Δω = 0.10 cm-1. To extract thermodynamic information from the experimental spectra, theoretical spectra, generated by a N2 spectral modeling program, are fit to the experimental spectra in a least-squares manner. In the gas cell, the CARS-measured pressures compare favorably with transducer-measured pressures. The precision and accuracy of the single-shot CARS pressure measurements increase at subatmospheric conditions. Along the centerline of the underexpanded jet, the agreement between the mean CARS P/ T/ρ measurements and similar quantities extracted from a Reynolds-averaged Navier–Stokes computational fluid dynamic simulation is generally excellent. This CARS technique is able to capture the low-pressure and low-temperature conditions of the M = 3.4 flow entering the Mach disk, as well as the subsonic conditions immediately downstream of this normal shock.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]

1998 (3)

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

J. N. Forkey, W. R. Lempert, R. B. Miles, “Accuracy limits for planar measurements of flow field velocity, temperature, and pressure using filtered Rayleigh scattering,” Exp. Fluids 24, 151–162 (1998).
[CrossRef]

J. Panda, “Shock oscillation in underexpanded screeching jets,” J. Fluid Mech. 363, 173–198 (1998).
[CrossRef]

1996 (1)

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

1995 (2)

1994 (1)

J. Sahu, C. J. Nietubicz, “Three-dimensional flow calculations for a projectile with standard and dome bases,” J. Spacecr. Rockets 31, 106–112 (1994).
[CrossRef]

1993 (2)

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

M. D. Di Rosa, A. Y. Chang, R. K. Hanson, “Continuous wave dye-laser technique for simultaneous, spatially resolved measurements of temperature, pressure, and velocity of NO in an underexpanded free jet,” Appl. Opt. 32, 4074–4087 (1993).

1991 (1)

M. Péalat, M. Lefebvre, “Temperature measurement by single-shot dual-line CARS in low-pressure flows,” Appl. Phys. B 53, 23–29 (1991).
[CrossRef]

1990 (1)

1988 (3)

1987 (2)

1986 (2)

1985 (3)

1984 (2)

1982 (1)

1980 (1)

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

1977 (1)

1953 (1)

S. J. Kline, F. A. McClintock, “Describing uncertainties in single-sample experiments,” Mech. Eng. 75, 3–8 (1953).

Battles, B. E.

Beiting, E. J.

Bouchardy, P.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

M. Péalat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

Chanetz, B.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

Chang, A. Y.

Coët, M. C.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

Di Rosa, M. D.

Dobbs, G. M.

Dutton, J. C.

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the application of CARS to turbulent reacting flows,” Exp. Fluids 3, 301–314 (1985).
[CrossRef]

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[CrossRef] [PubMed]

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon and Breach, St. Leonards, Australia, 1996).

Exton, R. J.

Farrow, R. L.

Finkelstein, N. D.

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Foglesong, R. E.

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

R. E. Foglesong, P. J. Rubas, S. M. Green, R. P. Lucht, J. E. Peters, “Dual-pump coherent anti-Stokes Raman scattering measurements in a direct-injection natural gas engine,” SAE Paper 980144 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Forkey, J. N.

J. N. Forkey, W. R. Lempert, R. B. Miles, “Accuracy limits for planar measurements of flow field velocity, temperature, and pressure using filtered Rayleigh scattering,” Exp. Fluids 24, 151–162 (1998).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Görres, J.

Goss, L. P.

L. P. Goss, “CARS instrumentation for combustion applications,” in Instrumentation for Flows with Combustion, A. M. K. P. Taylor, ed. (Academic, London, 1983).

Green, S. M.

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

R. E. Foglesong, P. J. Rubas, S. M. Green, R. P. Lucht, J. E. Peters, “Dual-pump coherent anti-Stokes Raman scattering measurements in a direct-injection natural gas engine,” SAE Paper 980144 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Greenhalgh, D. A.

Grisch, F.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

Hanson, R. K.

Harvey, A. B.

Herring, G. C.

C. Y. She, H. Moosmüller, G. C. Herring, “Coherent light scattering spectroscopy for supersonic flow measurements,” Appl. Phys. B 46, 283–297 (1988).
[CrossRef]

H. Moosmüller, G. C. Herring, C. Y. She, “Two-component velocity measurements in a supersonic nitrogen jet with spatially resolved inverse Raman spectroscopy,” Opt. Lett. 9, 536–538 (1984).
[CrossRef] [PubMed]

Hillard, M. E.

Hiller, B.

Hirose, C.

H. Kataoka, S. Maeda, C. Hirose, “Effects of laser linewidth on the coherent anti-Stokes Raman spectroscopy spectral profile,” Appl. Spectrosc. 36, 565–569 (1982).
[CrossRef]

K. Kajiyama, K. Sajiki, H. Kataoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” SAE Paper 821036 (Society of Automotive Engineers, Warrendale, Pa., 1982).

Hogg, R. V.

R. V. Hogg, E. A. Tanis, Probability and Statistical Inference (Macmillan, New York, 1993).

Incropera, F. P.

F. P. Incropera, Introduction to Molecular Structure and Thermodynamics (Wiley, New York, 1974).

Kajiyama, K.

K. Kajiyama, K. Sajiki, H. Kataoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” SAE Paper 821036 (Society of Automotive Engineers, Warrendale, Pa., 1982).

Kataoka, H.

H. Kataoka, S. Maeda, C. Hirose, “Effects of laser linewidth on the coherent anti-Stokes Raman spectroscopy spectral profile,” Appl. Spectrosc. 36, 565–569 (1982).
[CrossRef]

K. Kajiyama, K. Sajiki, H. Kataoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” SAE Paper 821036 (Society of Automotive Engineers, Warrendale, Pa., 1982).

Kennedy, K. D.

C. D. Mikkelsen, K. D. Kennedy, AMSAM-RD-SS-AT, U.S. Army Aviation and Missile Command, Redstone Arsenal, Ala. 35898-5252 (personal communication, 1998).

Kline, S. J.

S. J. Kline, F. A. McClintock, “Describing uncertainties in single-sample experiments,” Mech. Eng. 75, 3–8 (1953).

Koszykowski, M. L.

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

Lefebvre, M.

M. Péalat, M. Lefebvre, “Temperature measurement by single-shot dual-line CARS in low-pressure flows,” Appl. Phys. B 53, 23–29 (1991).
[CrossRef]

M. Péalat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

Lemoine, F.

F. Lemoine, B. Leporcq, “An efficient optical pressure measurement in compressible flows: laser-induced iodine fluorescence,” Exp. Fluids 19, 150–158 (1995).
[CrossRef]

Lempert, W. R.

J. N. Forkey, W. R. Lempert, R. B. Miles, “Accuracy limits for planar measurements of flow field velocity, temperature, and pressure using filtered Rayleigh scattering,” Exp. Fluids 24, 151–162 (1998).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Leporcq, B.

F. Lemoine, B. Leporcq, “An efficient optical pressure measurement in compressible flows: laser-induced iodine fluorescence,” Exp. Fluids 19, 150–158 (1995).
[CrossRef]

Lucht, R. P.

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

R. P. Lucht, R. L. Farrow, “Calculation of saturation line shapes and intensities in coherent anti-Stokes Raman scattering spectra of nitrogen,” J. Opt. Soc. Am. B 5, 1243–1252 (1988).
[CrossRef]

R. E. Foglesong, P. J. Rubas, S. M. Green, R. P. Lucht, J. E. Peters, “Dual-pump coherent anti-Stokes Raman scattering measurements in a direct-injection natural gas engine,” SAE Paper 980144 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Lückerath, R.

Maeda, S.

H. Kataoka, S. Maeda, C. Hirose, “Effects of laser linewidth on the coherent anti-Stokes Raman spectroscopy spectral profile,” Appl. Spectrosc. 36, 565–569 (1982).
[CrossRef]

K. Kajiyama, K. Sajiki, H. Kataoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” SAE Paper 821036 (Society of Automotive Engineers, Warrendale, Pa., 1982).

Magel, H.-C.

Maier, H.

Mattern, P. L.

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

McClintock, F. A.

S. J. Kline, F. A. McClintock, “Describing uncertainties in single-sample experiments,” Mech. Eng. 75, 3–8 (1953).

McDonald, J. R.

Meier, W.

Mikkelsen, C. D.

C. D. Mikkelsen, K. D. Kennedy, AMSAM-RD-SS-AT, U.S. Army Aviation and Missile Command, Redstone Arsenal, Ala. 35898-5252 (personal communication, 1998).

Miles, R. B.

J. N. Forkey, W. R. Lempert, R. B. Miles, “Accuracy limits for planar measurements of flow field velocity, temperature, and pressure using filtered Rayleigh scattering,” Exp. Fluids 24, 151–162 (1998).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Moosmüller, H.

C. Y. She, H. Moosmüller, G. C. Herring, “Coherent light scattering spectroscopy for supersonic flow measurements,” Appl. Phys. B 46, 283–297 (1988).
[CrossRef]

H. Moosmüller, G. C. Herring, C. Y. She, “Two-component velocity measurements in a supersonic nitrogen jet with spatially resolved inverse Raman spectroscopy,” Opt. Lett. 9, 536–538 (1984).
[CrossRef] [PubMed]

Nibler, J. W.

Nietubicz, C. J.

J. Sahu, C. J. Nietubicz, “Three-dimensional flow calculations for a projectile with standard and dome bases,” J. Spacecr. Rockets 31, 106–112 (1994).
[CrossRef]

Palmer, R. E.

R. L. Farrow, R. Trebino, R. E. Palmer, “High-resolution CARS measurements of temperature profiles and pressure in a tungsten lamp,” Appl. Opt. 26, 331–335 (1987).
[CrossRef] [PubMed]

R. E. Palmer, “The CARSFIT computer code for calculating coherent anti-Stokes Raman spectra: user and programmer information,” (Sandia National Laboratories, Livermore, Calif., 1989).

Panda, J.

J. Panda, “Shock oscillation in underexpanded screeching jets,” J. Fluid Mech. 363, 173–198 (1998).
[CrossRef]

Parameswaran, T.

Péalat, M.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

M. Péalat, M. Lefebvre, “Temperature measurement by single-shot dual-line CARS in low-pressure flows,” Appl. Phys. B 53, 23–29 (1991).
[CrossRef]

M. Péalat, P. Bouchardy, M. Lefebvre, J.-P. Taran, “Precision of multiplex CARS temperature measurements,” Appl. Opt. 24, 1012–1022 (1985).
[CrossRef] [PubMed]

Peters, J. E.

R. E. Foglesong, P. J. Rubas, S. M. Green, R. P. Lucht, J. E. Peters, “Dual-pump coherent anti-Stokes Raman scattering measurements in a direct-injection natural gas engine,” SAE Paper 980144 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Pot, T.

F. Grisch, P. Bouchardy, M. Péalat, B. Chanetz, T. Pot, M. C. Coët, “Rotational temperature and density measurements in a hypersonic flow by dual-line CARS,” Appl. Phys. B 56, 14–20 (1993).
[CrossRef]

Rahn, L. A.

L. A. Rahn, R. L. Farrow, M. L. Koszykowski, P. L. Mattern, “Observation of an optical Stark effect on vibrational and rotational transitions,” Phys. Rev. Lett. 45, 620–623 (1980).
[CrossRef]

Rubas, P. J.

R. E. Foglesong, P. J. Rubas, S. M. Green, R. P. Lucht, J. E. Peters, “Dual-pump coherent anti-Stokes Raman scattering measurements in a direct-injection natural gas engine,” SAE Paper 980144 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Sahu, J.

J. Sahu, C. J. Nietubicz, “Three-dimensional flow calculations for a projectile with standard and dome bases,” J. Spacecr. Rockets 31, 106–112 (1994).
[CrossRef]

Sajiki, K.

K. Kajiyama, K. Sajiki, H. Kataoka, S. Maeda, C. Hirose, “N2 CARS thermometry in diesel engine,” SAE Paper 821036 (Society of Automotive Engineers, Warrendale, Pa., 1982).

Sawchuk, R. A.

Schenck, H.

H. Schenck, Theories of Engineering Experimentation (Hemisphere, Washington, D.C., 1979).

Schnell, U.

She, C. Y.

C. Y. She, H. Moosmüller, G. C. Herring, “Coherent light scattering spectroscopy for supersonic flow measurements,” Appl. Phys. B 46, 283–297 (1988).
[CrossRef]

H. Moosmüller, G. C. Herring, C. Y. She, “Two-component velocity measurements in a supersonic nitrogen jet with spatially resolved inverse Raman spectroscopy,” Opt. Lett. 9, 536–538 (1984).
[CrossRef] [PubMed]

Smallwood, G. J.

Snelling, D. R.

Spliethoff, H.

Stricker, W.

Stufflebeam, J. H.

A. C. Eckbreth, J. H. Stufflebeam, “Considerations for the application of CARS to turbulent reacting flows,” Exp. Fluids 3, 301–314 (1985).
[CrossRef]

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[CrossRef] [PubMed]

Tanis, E. A.

R. V. Hogg, E. A. Tanis, Probability and Statistical Inference (Macmillan, New York, 1993).

Taran, J.-P.

Tellex, P. A.

Tolles, W. M.

Trebino, R.

Whittley, S. T.

Woyde, M.

AIAA J. (2)

R. E. Foglesong, S. M. Green, R. P. Lucht, J. C. Dutton, “Dual-pump coherent anti-Stokes Raman scattering for simultaneous pressure/temperature measurement,” AIAA J. 36, 234–240 (1998).
[CrossRef]

J. N. Forkey, N. D. Finkelstein, W. R. Lempert, R. B. Miles, “Demonstration and characterization of filtered Rayleigh scattering for planar velocity measurements,” AIAA J. 34, 442–448 (1996).
[CrossRef]

Appl. Opt. (10)

A. C. Eckbreth, G. M. Dobbs, J. H. Stufflebeam, P. A. Tellex, “CARS temperature and species measurements in augmented jet engine exhausts,” Appl. Opt. 23, 1328–1339 (1984).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Broadband CARS energy-level diagram.

Fig. 2
Fig. 2

carsfit spectra (probe linewidth: Γ = 0.1 cm-1) for conditions (a) P = 0.97 atm, T = 295 K; (b) P = 0.1 atm, T = 295 K; (c) P = 0.97 atm, T = 90 K; and (d) P = 0.1 atm, T = 90 K.

Fig. 3
Fig. 3

Top-view schematic of the high-resolution N2 CARS system. 3-D, three dimensional.

Fig. 4
Fig. 4

Least-squares fits of single-shot CARS spectra collected at T = 292 K: (a) P trans = 0.10 atm, P CARS = 0.21 atm; (b) P trans = 0.30 atm, P CARS = 0.32 atm; (c) P trans = 0.99 atm, P CARS = 0.93 atm; and (d) P trans = 5.01 atm, P CARS = 4.71 atm.

Fig. 5
Fig. 5

Comparison of gas-cell pressure measurements with single-shot CARS spectra and a conventional pressure transducer. Data are plotted on (a) linear and (b) logarithmic axes.

Fig. 6
Fig. 6

Precision of high-resolution N2 CARS and dual-pump CARS (Foglesong et al.8) pressure measurements.

Fig. 7
Fig. 7

Underexpanded sonic-jet flow-field schematic.

Fig. 8
Fig. 8

Least-squares fits of single-shot CARS spectra acquired along the jet centerline at (a) jet exit, z/ d j = 0.0; (b) upstream of the Mach disk, z/ d j = 1.42; and (c) downstream of the Mach disk, z/ d j = 1.49.

Fig. 9
Fig. 9

Single-shot mean CARS measurements along the underexpanded jet centerline: (a) pressure, (b) temperature, and (c) density distributions. EOS, equation of state.

Fig. 10
Fig. 10

Histograms of instantaneous (a) pressure and (b) temperature measurements acquired upstream of the Mach disk, z/ d j = 1.42.

Fig. 11
Fig. 11

Histograms of instantaneous (a) pressure and (b) temperature measurements acquired downstream of the Mach disk, z/ d j = 1.49.

Equations (2)

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NjN=gj exp-εj/kTjgj exp-εj/kT,
σρρ=σTT2+σρP21/2.

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