Abstract

Rayleigh scattering cross sections are measured for nine combustion species (Ar, N2, O2, CO2, CO, H2, H2O, CH4, and C3H8) at wavelengths of 266, 355, and 532 nm and at temperatures ranging from 295 to 1525 K. Experimental results show that, as laser wavelengths become shorter, polarization effects become important and the depolarization ratio of the combustion species must be accounted for in the calculation of the Rayleigh scattering cross section. Temperature effects on the scattering cross section are also measured. Only a small temperature dependence is measured for cross sections at 355 nm, resulting in a 2–8% increase in cross section at temperatures of 1500 K. This temperature dependence increases slightly for measurements at 266 nm, resulting in a 5–11% increase in cross sections at temperatures of 1450 K.

© 2004 Optical Society of America

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References

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2002 (1)

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

2000 (1)

1997 (1)

1993 (3)

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

S. Kampmann, A. Leipertz, K. Döbbeling, J. Haumann, and T. Sattelmayer, Appl. Opt. 32, 6167 (1993).
[CrossRef] [PubMed]

F. Zhao and H. Hiroyasu, Prog. Energy Combust. Sci. 19, 447 (1993).
[CrossRef]

1988 (1)

1986 (1)

U. Hohm and K. Kerl, Mol. Phys. 58, 541 (1986).
[CrossRef]

1985 (1)

I. Namer and R. W. Schefer, Exp. Fluids 3, 1 (1985).
[CrossRef]

1984 (1)

W. M. Pitts and T. Kashiwagi, J. Fluid Mech. 141, 391 (1984).
[CrossRef]

1981 (1)

W. C. Gardiner, Y. Hidaka, and T. Tanzawa, Combust. Flame 40, 213 (1981).
[CrossRef]

1979 (1)

T. M. Dyer, AIAA J. 17, 912 (1979).
[CrossRef]

1976 (1)

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, Phys. Rev. A 13, 1422 (1976).
[CrossRef]

1923 (1)

L. V. King, Proc. R. Soc. London Ser. A 104, 333 (1923).
[CrossRef]

Atkins, P. W.

P. W. Atkins, Physical Chemistry, 4th ed. (Freeman, New York, 1990).

Connors, J. J.

Döbbeling, K.

Dyer, T. M.

T. M. Dyer, AIAA J. 17, 912 (1979).
[CrossRef]

Eckbreth, A. C.

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

Fielding, J.

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Frank, J. H.

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Gardiner, W. C.

W. C. Gardiner, Y. Hidaka, and T. Tanzawa, Combust. Flame 40, 213 (1981).
[CrossRef]

Gu, Y.

Haumann, J.

Hidaka, Y.

W. C. Gardiner, Y. Hidaka, and T. Tanzawa, Combust. Flame 40, 213 (1981).
[CrossRef]

Hiroyasu, H.

F. Zhao and H. Hiroyasu, Prog. Energy Combust. Sci. 19, 447 (1993).
[CrossRef]

Hitchcock, L. M.

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Hohm, U.

U. Hohm and K. Kerl, Mol. Phys. 58, 541 (1986).
[CrossRef]

Howard, P. J.

Huber, M. C. E.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, Phys. Rev. A 13, 1422 (1976).
[CrossRef]

Kaiser, S. A.

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Kampmann, S.

Kashiwagi, T.

W. M. Pitts and T. Kashiwagi, J. Fluid Mech. 141, 391 (1984).
[CrossRef]

Kerl, K.

U. Hohm and K. Kerl, Mol. Phys. 58, 541 (1986).
[CrossRef]

Kim, G. S.

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

King, L. V.

L. V. King, Proc. R. Soc. London Ser. A 104, 333 (1923).
[CrossRef]

Landolt-Börnstein,

Landolt-Börnstein, Tabellen, Eigenschaften der Materie inhren Aggregatzuständen, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962).

Leipertz, A.

Long, M. B.

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Markovitz, E. C.

Miles, R. B.

Myhr, F. H.

F. H. Myhr, “Optical measurements of atomic oxygen concentration, temperature and nitric oxide production rate in flames,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1998).

Namer, I.

I. Namer and R. W. Schefer, Exp. Fluids 3, 1 (1985).
[CrossRef]

Naus, H.

Parkinson, W. H.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, Phys. Rev. A 13, 1422 (1976).
[CrossRef]

Pitts, W. M.

W. M. Pitts and T. Kashiwagi, J. Fluid Mech. 141, 391 (1984).
[CrossRef]

Reck, G. P.

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Reckers, W.

Roth, G. J.

Rothe, E. W.

W. Reckers, Y. Gu, E. W. Rothe, and H. Voges, Appl. Spectrosc. 51, 1012 (1997).
[CrossRef]

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Sattelmayer, T.

Schefer, R. W.

I. Namer and R. W. Schefer, Exp. Fluids 3, 1 (1985).
[CrossRef]

Siegler, F.

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Smith, P. L.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, Phys. Rev. A 13, 1422 (1976).
[CrossRef]

Smooke, M. D.

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Tanzawa, T.

W. C. Gardiner, Y. Hidaka, and T. Tanzawa, Combust. Flame 40, 213 (1981).
[CrossRef]

Tung, C. C.

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Ubachs, W.

Voges, H.

Zhao, F.

F. Zhao and H. Hiroyasu, Prog. Energy Combust. Sci. 19, 447 (1993).
[CrossRef]

AIAA J. (1)

T. M. Dyer, AIAA J. 17, 912 (1979).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

G. S. Kim, L. M. Hitchcock, F. Siegler, E. W. Rothe, C. C. Tung, and G. P. Reck, Appl. Phys. B 56, 139 (1993).
[CrossRef]

Appl. Spectrosc. (1)

Combust. Flame (1)

W. C. Gardiner, Y. Hidaka, and T. Tanzawa, Combust. Flame 40, 213 (1981).
[CrossRef]

Exp. Fluids (1)

I. Namer and R. W. Schefer, Exp. Fluids 3, 1 (1985).
[CrossRef]

J. Fluid Mech. (1)

W. M. Pitts and T. Kashiwagi, J. Fluid Mech. 141, 391 (1984).
[CrossRef]

Mol. Phys. (1)

U. Hohm and K. Kerl, Mol. Phys. 58, 541 (1986).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, Phys. Rev. A 13, 1422 (1976).
[CrossRef]

Proc. Combust. Inst. (1)

J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, Proc. Combust. Inst. 29, 2703 (2002).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

L. V. King, Proc. R. Soc. London Ser. A 104, 333 (1923).
[CrossRef]

Prog. Energy Combust. Sci. (1)

F. Zhao and H. Hiroyasu, Prog. Energy Combust. Sci. 19, 447 (1993).
[CrossRef]

Other (4)

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

P. W. Atkins, Physical Chemistry, 4th ed. (Freeman, New York, 1990).

Landolt-Börnstein, Tabellen, Eigenschaften der Materie inhren Aggregatzuständen, Part 8, Optische Konstanten (Springer-Verlag, Berlin, 1962).

F. H. Myhr, “Optical measurements of atomic oxygen concentration, temperature and nitric oxide production rate in flames,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1998).

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Figures (2)

Fig. 1
Fig. 1

Relative Rayleigh scattering cross sections at 295 K for wavelengths of 266, 355, and 532 nm. Also shown are calculations with expression (2) that neglect ρv and previous experimental data in both the UV and the visible regions.7,8,12-15 The absolute differential Rayleigh scattering cross section of nitrogen at 295 K and 532 nm is 6.24×10-28 cm2/sr. Error bars represent one standard deviation.

Fig. 2
Fig. 2

Effect of temperature on differential Rayleigh scattering cross section. Error bars are shown for N2, which is typical of all the data. Error bars represent one standard deviation. A linear fit is plotted through the data.

Tables (1)

Tables Icon

Table 1 Depolarization Ratios at 295 K

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

σi=4π2ni-12λ4N2sin2 θ33-4ρv,
σN,i=σiσN2ni-12nN2-12=σN,i,calc.
ρv,N2=34-3σN,Ar,meas4σN,Ar,calc.
ρv,i=3-3-4ρv,N2σN,i,calcσN,i,meas4.

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