Abstract

Quantitative two-point hydroxyl time-series measurements have been performed in a turbulent nonpremixed flame by using two-point picosecond time-resolved laser-induced fluorescence. The current diagnostic system has been improved from its preliminary version to address optical aberrations and fluorescence lifetime fluctuations. In particular, with a newly designed collection system, the aberration-limited blur spot is reduced from 6  mm to 180   μm. Additional photon-counting channels enable the recovery of absolute OH concentrations through a triple-bin integration method. The present research represents what we believe to be the first application of this two-point technique to turbulent flames. Two independent schemes have been applied to remove uncorrelated noise in the derived two-point statistics. We show that optical aberrations can have a significant effect on space–time correlations. However, the sampling rate and fluctuations in the fluorescence lifetime barely affect the spatial autocorrelation function and thus the integral length scale. Such length scales for hydroxyl are found to rise linearly with increasing axial distance at peak [OH] locations. Along the jet centerline, the integral length scale varies slightly below the flame tip but increases rapidly above the flame tip. In addition, the OH length scale demonstrates the same trend as the OH time scale along the jet centerline, but the opposite trend at peak [OH] locations.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. N. Peters, Turbulent Combustion (Cambridge, 2000).
    [CrossRef]
  2. K. H. Luo, "DNS and LES of turbulence-combustion interactions," in Modern Simulation Strategies for Turbulent Flow, B. J. Geurts, ed. (R. T. Edwards, 2001), pp. 263-295.
  3. T. Takagi, H. D. Shin, and A. Ishio, "Local laminarization in turbulent diffusion flames," Combust. Flame 37, 163-170 (1980).
    [CrossRef]
  4. A. R. Masri, R. W. Dibble, and R. S. Barlow, "The structure of turbulent nonpremixed flames revealed by Raman-Rayleigh-LIF measurements," Prog. Energy Combust. Sci. 22, 307-362 (1996).
    [CrossRef]
  5. J. E. de Vries, Th. H. van der Meer, and C. J. Hoogendoorn, "OH concentration fluctuations in turbulent natural gas jet flames," Chem. Eng. J. 53, 39-46 (1993).
  6. Y.-C. Chen and M. Mansour, "Measurements of scalar dissipation in turbulent hydrogen diffusion flames and some implications on combustion modeling," Combust. Sci. Technol. 126, 291-313 (1997).
    [CrossRef]
  7. P. C. Miles, "Raman line imaging for spatially and temporally resolved mole fraction measurements in internal combustion engines," Appl. Opt. 38, 1714-1732 (1999).
    [CrossRef]
  8. A. N. Karpetis and R. S. Barlow, "Measurements of scalar dissipation in a turbulent piloted methane/air jet flame," Proc. Combust. Inst. 29, 1929-1936 (2002).
    [CrossRef]
  9. J. B. Kelman and A. R. Masri, "Quantitative technique for imaging mixture fraction, temperature, and hydroxyl radical in turbulent diffusion flames," Appl. Opt. 36, 3506-3514 (1997).
    [CrossRef] [PubMed]
  10. J. Fielding, A. M. Schaffer, and M. B. Long, "Three-scalar imaging in turbulent nonpremixed flames of methane," in Twenty-Seventh Symposium (International) on Combustion (The Combustion Institute, 1998), pp. 1007-1014.
    [CrossRef]
  11. R. W. Dibble and R. E. Hollenbach, "Laser Rayleigh thermometry in turbulent flames," in Eighteenth Symposium (International) on Combustion (The Combustion Institute, 1981), pp. 1489-1499.
    [CrossRef]
  12. M. W. Renfro, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: CH," Combust. Flame 122, 139-150 (2000).
    [CrossRef]
  13. M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH," Combust. Flame 123, 389-401 (2000).
    [CrossRef]
  14. M. Namazian, I. G. Shepherd, and L. Talbot, "Characterization of the density fluctuations in turbulent premixed flames," Combust. Flame 64, 299-308 (1986).
    [CrossRef]
  15. C. Ghenai and I. Gokalp, "Correlation coefficients of the fluctuating density in turbulent premixed flames," Exp. Fluids 24, 347-353 (1998).
    [CrossRef]
  16. G. H. Wang, N. T. Clemens, and P. L. Varghese, "High-repetition rate measurements of temperature and thermal dissipation in a nonpremixed turbulent jet flame," Proc. Combust. Inst. 30, 691-699 (2005).
    [CrossRef]
  17. J. Kojima, Y. Ikeda, and T. Nakajima, "Multi-point time-series observation of optical emissions from flame-front motion analysis," Meas. Sci. Technol. 14, 1714-1724 (2003).
    [CrossRef]
  18. M. E. Kounalakis, Y. R. Sivathanu, and G. M. Faeth, "Infrared radiation statistics of nonluminous turbulent diffusion flames," J. Heat Transfer 113, 437-445 (1991).
    [CrossRef]
  19. J. Hult, U. Meier, W. Meier, A. Harvey, and C. F. Kaminski, "Experimental analysis of local flame extinction in a turbulent jet diffusion flame by high repetition 2-D laser techniques and multi-scalar measurements," Proc. Combust. Inst. 30, 701-709 (2005).
    [CrossRef]
  20. J. Zhang, K. K. Venkatesan, G. B. King, N. M. Laurendeau, and M. W. Renfro, "Two-point time-series measurements of minor-species concentrations in a turbulent nonpremixed flame," Opt. Lett. 30, 3144-3146 (2005).
    [CrossRef] [PubMed]
  21. J. Zhang, K. K. Venkatesan, G. B. King, N. M. Laurendeau, and M. W. Renfro, "Two-point OH time-series measurements in a nonpremixed turbulent jet flame," presented at the Fourth Joint U.S. Sections Meeting of the Combustion Institute, Philadelphia, Pennsylvania, 20-23 March 2005.
  22. S. D. Pack, M. W. Renfro, G. B. King, and N. M. Laurendeau, "Photon-counting technique for rapid fluorescence-decay measurement," Opt. Lett. 23, 1215-1217 (1998).
    [CrossRef]
  23. M. W. Renfro, S. D. Pack, and N. M. Laurendeau, "A pulse-pileup correction procedure for rapid measurements of hydroxyl concentrations using picosecond time-resolved laser-induced fluorescence," Appl. Phys. B 69, 137-146 (1999).
    [CrossRef]
  24. M. W. Renfro, G. B. King, and N. M. Laurendeau, "Quantitative hydroxyl concentration time-series measurements in turbulent nonpremixed flames," Appl. Opt. 38, 4596-4608 (1999).
    [CrossRef]
  25. M. W. Renfro, A. Chaturvedy, G. B. King, N. M. Laurendeau, A. Kempf, A. Dreizler, and J. Janicka, "Comparison of OH time-series measurements and large-eddy simulations in hydrogen jet flames," Combust. Flame 139, 142-151 (2004).
    [CrossRef]
  26. V. Bergmann, W. Meier, D. Wolff, and W. Stricker, "Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH4/H2/N2 jet diffusion flame," Appl. Phys. B 66, 489-502 (1998).
    [CrossRef]
  27. J. M. Seitzman, Quantitative Applications of Fluorescence Imaging in Combustion,Ph.D. dissertation (Stanford University, 1991).
  28. Zemax Development Corp., Bellevue, Washington.
  29. R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).
  30. R. J. Kee, J. F. Grcar, M. D. Smooke, and J. A. Miller, A FORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Report SAND 85-8240 (Sandia National Laboratories, 1985).
  31. G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eiteneer, M. Goldenberg, C. T. Bowman, R. K. Hanson, S. Song, W. C. Gardiner, Jr., V. V. Lissianski, and Z. Qin, "GRI-Mech 3.0," http://www.me.berkeley.edu/gri_mech.
  32. S. D. Pack, M. W. Renfro, G. B. King, and N. M. Laurendeau, "Laser-induced fluorescence triple-integration method applied to hydroxyl concentration and fluorescence lifetime measurements," Combust. Sci. Technol. 140, 405-425 (1998).
    [CrossRef]
  33. W. Meier, S. Prucker, M.-H. Cao, and W. Stricker, "Characterization of turbulent H2/N2air jet diffusion flames by single-pulse spontaneous Raman scattering," Combust. Sci. Technol. 118, 293-312 (1996).
    [CrossRef]
  34. W. Meier, A. O. Vyrodov, V. Bergmann, and W. Stricker, "Simultaneous Raman/LIF measurements of major species and NO in turbulent H2/air diffusion flames," Appl. Phys. B 63, 79-90 (1996).
    [CrossRef]
  35. D. G. Pfuderer, A. A. Neuber, G. Fruchtel, E. P. Hassel, and J. Janicka, "Turbulence modulation in jet diffusion flames: Modeling and experiments," Combust. Flame 106, 301-317 (1996).
    [CrossRef]
  36. TNF workshop, http://www.ca.sandia.gov/TNF. Accessed October 2006.
  37. M. T. Landahl and E. Mollo-Christensen, Turbulence and Random Processes in Fluid Mechanics, 2nd ed. (Cambridge U. Press, 1994).
  38. D. Trimis and A. Melling, "Improved laser Doppler anemometry techniques for two-point turbulent flow correlations," Meas. Sci. Technol. 6, 663-673 (1995).
    [CrossRef]
  39. S. Pope, Turbulent Flows (Cambridge U. Press, 2000).
  40. M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, "Flame concentration measurements using picosecond time-resolved laser-induced fluorescence," Combust. Sci. Technol. 97, 391-403 (1994).
    [CrossRef]
  41. P. H. Paul, "A model for temperature-dependent collisional quenching of OH A 2Σ+," J. Quant. Spectrosc. Radiat. Transfer 51, 511-524 (1994).
    [CrossRef]
  42. R. S. Barlow and A. N. Karpetis, "Measurements of scalar variance, scalar dissipation, and length scales in turbulent piloted methane/air jet flames," Flow , Turbul. Combust. 72, 427-448 (2004).

2005

G. H. Wang, N. T. Clemens, and P. L. Varghese, "High-repetition rate measurements of temperature and thermal dissipation in a nonpremixed turbulent jet flame," Proc. Combust. Inst. 30, 691-699 (2005).
[CrossRef]

J. Hult, U. Meier, W. Meier, A. Harvey, and C. F. Kaminski, "Experimental analysis of local flame extinction in a turbulent jet diffusion flame by high repetition 2-D laser techniques and multi-scalar measurements," Proc. Combust. Inst. 30, 701-709 (2005).
[CrossRef]

J. Zhang, K. K. Venkatesan, G. B. King, N. M. Laurendeau, and M. W. Renfro, "Two-point time-series measurements of minor-species concentrations in a turbulent nonpremixed flame," Opt. Lett. 30, 3144-3146 (2005).
[CrossRef] [PubMed]

2004

M. W. Renfro, A. Chaturvedy, G. B. King, N. M. Laurendeau, A. Kempf, A. Dreizler, and J. Janicka, "Comparison of OH time-series measurements and large-eddy simulations in hydrogen jet flames," Combust. Flame 139, 142-151 (2004).
[CrossRef]

R. S. Barlow and A. N. Karpetis, "Measurements of scalar variance, scalar dissipation, and length scales in turbulent piloted methane/air jet flames," Flow , Turbul. Combust. 72, 427-448 (2004).

2003

J. Kojima, Y. Ikeda, and T. Nakajima, "Multi-point time-series observation of optical emissions from flame-front motion analysis," Meas. Sci. Technol. 14, 1714-1724 (2003).
[CrossRef]

2002

A. N. Karpetis and R. S. Barlow, "Measurements of scalar dissipation in a turbulent piloted methane/air jet flame," Proc. Combust. Inst. 29, 1929-1936 (2002).
[CrossRef]

2000

M. W. Renfro, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: CH," Combust. Flame 122, 139-150 (2000).
[CrossRef]

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH," Combust. Flame 123, 389-401 (2000).
[CrossRef]

1999

1998

S. D. Pack, M. W. Renfro, G. B. King, and N. M. Laurendeau, "Photon-counting technique for rapid fluorescence-decay measurement," Opt. Lett. 23, 1215-1217 (1998).
[CrossRef]

C. Ghenai and I. Gokalp, "Correlation coefficients of the fluctuating density in turbulent premixed flames," Exp. Fluids 24, 347-353 (1998).
[CrossRef]

V. Bergmann, W. Meier, D. Wolff, and W. Stricker, "Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH4/H2/N2 jet diffusion flame," Appl. Phys. B 66, 489-502 (1998).
[CrossRef]

S. D. Pack, M. W. Renfro, G. B. King, and N. M. Laurendeau, "Laser-induced fluorescence triple-integration method applied to hydroxyl concentration and fluorescence lifetime measurements," Combust. Sci. Technol. 140, 405-425 (1998).
[CrossRef]

1997

J. B. Kelman and A. R. Masri, "Quantitative technique for imaging mixture fraction, temperature, and hydroxyl radical in turbulent diffusion flames," Appl. Opt. 36, 3506-3514 (1997).
[CrossRef] [PubMed]

Y.-C. Chen and M. Mansour, "Measurements of scalar dissipation in turbulent hydrogen diffusion flames and some implications on combustion modeling," Combust. Sci. Technol. 126, 291-313 (1997).
[CrossRef]

1996

A. R. Masri, R. W. Dibble, and R. S. Barlow, "The structure of turbulent nonpremixed flames revealed by Raman-Rayleigh-LIF measurements," Prog. Energy Combust. Sci. 22, 307-362 (1996).
[CrossRef]

W. Meier, S. Prucker, M.-H. Cao, and W. Stricker, "Characterization of turbulent H2/N2air jet diffusion flames by single-pulse spontaneous Raman scattering," Combust. Sci. Technol. 118, 293-312 (1996).
[CrossRef]

W. Meier, A. O. Vyrodov, V. Bergmann, and W. Stricker, "Simultaneous Raman/LIF measurements of major species and NO in turbulent H2/air diffusion flames," Appl. Phys. B 63, 79-90 (1996).
[CrossRef]

D. G. Pfuderer, A. A. Neuber, G. Fruchtel, E. P. Hassel, and J. Janicka, "Turbulence modulation in jet diffusion flames: Modeling and experiments," Combust. Flame 106, 301-317 (1996).
[CrossRef]

1995

D. Trimis and A. Melling, "Improved laser Doppler anemometry techniques for two-point turbulent flow correlations," Meas. Sci. Technol. 6, 663-673 (1995).
[CrossRef]

1994

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, "Flame concentration measurements using picosecond time-resolved laser-induced fluorescence," Combust. Sci. Technol. 97, 391-403 (1994).
[CrossRef]

P. H. Paul, "A model for temperature-dependent collisional quenching of OH A 2Σ+," J. Quant. Spectrosc. Radiat. Transfer 51, 511-524 (1994).
[CrossRef]

1993

J. E. de Vries, Th. H. van der Meer, and C. J. Hoogendoorn, "OH concentration fluctuations in turbulent natural gas jet flames," Chem. Eng. J. 53, 39-46 (1993).

1991

M. E. Kounalakis, Y. R. Sivathanu, and G. M. Faeth, "Infrared radiation statistics of nonluminous turbulent diffusion flames," J. Heat Transfer 113, 437-445 (1991).
[CrossRef]

1986

M. Namazian, I. G. Shepherd, and L. Talbot, "Characterization of the density fluctuations in turbulent premixed flames," Combust. Flame 64, 299-308 (1986).
[CrossRef]

1980

T. Takagi, H. D. Shin, and A. Ishio, "Local laminarization in turbulent diffusion flames," Combust. Flame 37, 163-170 (1980).
[CrossRef]

Appl. Opt.

Appl. Phys. B

W. Meier, A. O. Vyrodov, V. Bergmann, and W. Stricker, "Simultaneous Raman/LIF measurements of major species and NO in turbulent H2/air diffusion flames," Appl. Phys. B 63, 79-90 (1996).
[CrossRef]

V. Bergmann, W. Meier, D. Wolff, and W. Stricker, "Application of spontaneous Raman and Rayleigh scattering and 2D LIF for the characterization of a turbulent CH4/H2/N2 jet diffusion flame," Appl. Phys. B 66, 489-502 (1998).
[CrossRef]

M. W. Renfro, S. D. Pack, and N. M. Laurendeau, "A pulse-pileup correction procedure for rapid measurements of hydroxyl concentrations using picosecond time-resolved laser-induced fluorescence," Appl. Phys. B 69, 137-146 (1999).
[CrossRef]

Chem. Eng. J.

J. E. de Vries, Th. H. van der Meer, and C. J. Hoogendoorn, "OH concentration fluctuations in turbulent natural gas jet flames," Chem. Eng. J. 53, 39-46 (1993).

Combust. Flame

T. Takagi, H. D. Shin, and A. Ishio, "Local laminarization in turbulent diffusion flames," Combust. Flame 37, 163-170 (1980).
[CrossRef]

M. W. Renfro, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: CH," Combust. Flame 122, 139-150 (2000).
[CrossRef]

M. W. Renfro, W. A. Guttenfelder, G. B. King, and N. M. Laurendeau, "Scalar time-series measurements in turbulent CH4/H2/N2 nonpremixed flames: OH," Combust. Flame 123, 389-401 (2000).
[CrossRef]

M. Namazian, I. G. Shepherd, and L. Talbot, "Characterization of the density fluctuations in turbulent premixed flames," Combust. Flame 64, 299-308 (1986).
[CrossRef]

D. G. Pfuderer, A. A. Neuber, G. Fruchtel, E. P. Hassel, and J. Janicka, "Turbulence modulation in jet diffusion flames: Modeling and experiments," Combust. Flame 106, 301-317 (1996).
[CrossRef]

M. W. Renfro, A. Chaturvedy, G. B. King, N. M. Laurendeau, A. Kempf, A. Dreizler, and J. Janicka, "Comparison of OH time-series measurements and large-eddy simulations in hydrogen jet flames," Combust. Flame 139, 142-151 (2004).
[CrossRef]

Combust. Sci. Technol.

S. D. Pack, M. W. Renfro, G. B. King, and N. M. Laurendeau, "Laser-induced fluorescence triple-integration method applied to hydroxyl concentration and fluorescence lifetime measurements," Combust. Sci. Technol. 140, 405-425 (1998).
[CrossRef]

W. Meier, S. Prucker, M.-H. Cao, and W. Stricker, "Characterization of turbulent H2/N2air jet diffusion flames by single-pulse spontaneous Raman scattering," Combust. Sci. Technol. 118, 293-312 (1996).
[CrossRef]

Y.-C. Chen and M. Mansour, "Measurements of scalar dissipation in turbulent hydrogen diffusion flames and some implications on combustion modeling," Combust. Sci. Technol. 126, 291-313 (1997).
[CrossRef]

M. S. Klassen, B. D. Thompson, T. A. Reichardt, G. B. King, and N. M. Laurendeau, "Flame concentration measurements using picosecond time-resolved laser-induced fluorescence," Combust. Sci. Technol. 97, 391-403 (1994).
[CrossRef]

Exp. Fluids

C. Ghenai and I. Gokalp, "Correlation coefficients of the fluctuating density in turbulent premixed flames," Exp. Fluids 24, 347-353 (1998).
[CrossRef]

Flow

R. S. Barlow and A. N. Karpetis, "Measurements of scalar variance, scalar dissipation, and length scales in turbulent piloted methane/air jet flames," Flow , Turbul. Combust. 72, 427-448 (2004).

J. Heat Transfer

M. E. Kounalakis, Y. R. Sivathanu, and G. M. Faeth, "Infrared radiation statistics of nonluminous turbulent diffusion flames," J. Heat Transfer 113, 437-445 (1991).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

P. H. Paul, "A model for temperature-dependent collisional quenching of OH A 2Σ+," J. Quant. Spectrosc. Radiat. Transfer 51, 511-524 (1994).
[CrossRef]

Meas. Sci. Technol.

D. Trimis and A. Melling, "Improved laser Doppler anemometry techniques for two-point turbulent flow correlations," Meas. Sci. Technol. 6, 663-673 (1995).
[CrossRef]

J. Kojima, Y. Ikeda, and T. Nakajima, "Multi-point time-series observation of optical emissions from flame-front motion analysis," Meas. Sci. Technol. 14, 1714-1724 (2003).
[CrossRef]

Opt. Lett.

Proc. Combust. Inst.

J. Hult, U. Meier, W. Meier, A. Harvey, and C. F. Kaminski, "Experimental analysis of local flame extinction in a turbulent jet diffusion flame by high repetition 2-D laser techniques and multi-scalar measurements," Proc. Combust. Inst. 30, 701-709 (2005).
[CrossRef]

G. H. Wang, N. T. Clemens, and P. L. Varghese, "High-repetition rate measurements of temperature and thermal dissipation in a nonpremixed turbulent jet flame," Proc. Combust. Inst. 30, 691-699 (2005).
[CrossRef]

A. N. Karpetis and R. S. Barlow, "Measurements of scalar dissipation in a turbulent piloted methane/air jet flame," Proc. Combust. Inst. 29, 1929-1936 (2002).
[CrossRef]

Prog. Energy Combust. Sci.

A. R. Masri, R. W. Dibble, and R. S. Barlow, "The structure of turbulent nonpremixed flames revealed by Raman-Rayleigh-LIF measurements," Prog. Energy Combust. Sci. 22, 307-362 (1996).
[CrossRef]

Other

N. Peters, Turbulent Combustion (Cambridge, 2000).
[CrossRef]

K. H. Luo, "DNS and LES of turbulence-combustion interactions," in Modern Simulation Strategies for Turbulent Flow, B. J. Geurts, ed. (R. T. Edwards, 2001), pp. 263-295.

J. Fielding, A. M. Schaffer, and M. B. Long, "Three-scalar imaging in turbulent nonpremixed flames of methane," in Twenty-Seventh Symposium (International) on Combustion (The Combustion Institute, 1998), pp. 1007-1014.
[CrossRef]

R. W. Dibble and R. E. Hollenbach, "Laser Rayleigh thermometry in turbulent flames," in Eighteenth Symposium (International) on Combustion (The Combustion Institute, 1981), pp. 1489-1499.
[CrossRef]

J. Zhang, K. K. Venkatesan, G. B. King, N. M. Laurendeau, and M. W. Renfro, "Two-point OH time-series measurements in a nonpremixed turbulent jet flame," presented at the Fourth Joint U.S. Sections Meeting of the Combustion Institute, Philadelphia, Pennsylvania, 20-23 March 2005.

J. M. Seitzman, Quantitative Applications of Fluorescence Imaging in Combustion,Ph.D. dissertation (Stanford University, 1991).

Zemax Development Corp., Bellevue, Washington.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

R. J. Kee, J. F. Grcar, M. D. Smooke, and J. A. Miller, A FORTRAN Program for Modeling Steady Laminar One-Dimensional Premixed Flames, Sandia Report SAND 85-8240 (Sandia National Laboratories, 1985).

G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eiteneer, M. Goldenberg, C. T. Bowman, R. K. Hanson, S. Song, W. C. Gardiner, Jr., V. V. Lissianski, and Z. Qin, "GRI-Mech 3.0," http://www.me.berkeley.edu/gri_mech.

TNF workshop, http://www.ca.sandia.gov/TNF. Accessed October 2006.

M. T. Landahl and E. Mollo-Christensen, Turbulence and Random Processes in Fluid Mechanics, 2nd ed. (Cambridge U. Press, 1994).

S. Pope, Turbulent Flows (Cambridge U. Press, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(Color online) Schematic of the detection optics for the current two-point PITLIF system. L, lens; BS, beam splitter; DET, detector assembly consisting of a monochromator and photomultiplier tube. Solid (red) and dashed (blue) rays identify the signal from two different probe volumes. The inset shows a magnified view of the two probe volumes along the laser beam.

Fig. 2
Fig. 2

(Color online) Radii of circles enclosing 80% and 90% of the total energy for both (a) old and (b) new detection systems. The insets show spot diagrams of the images for object points at 0, 2, 4, and 6 mm away from the optical axis.

Fig. 3
Fig. 3

Wiring diagram for the gated photon-counting system. Delays of 3.0, 6.5, or 10.0 ns are placed along various lines; AD1 and AD2 identify two delay lines that require calibration. All unused terminals are 50 Ω terminated. PD identifies the input from a photodiode, VETO is the input for the VETO pulse, CFD and DISC represent a constant-fraction discriminator and leading-edge discriminator, respectively, and PCB identifies a photon-counting board (or multichannel scaler).

Fig. 4
Fig. 4

Representative two-point [OH] time series at x / D = 20 for the H3 flame. In (a) the probe volumes imaged by DET1 and DET2 overlap in the flame; in (b) the probe volumes are 0.84   mm apart.

Fig. 5
Fig. 5

Spatial autocorrelation functions measured at the location of the peak mean [OH] for x / D = 20 and along the jet centerline for x / D = 40 (a) before and (b) after noise correction. In (b) two independent methods (first, second) were used to correct for random noise.

Fig. 6
Fig. 6

Corrected space–time correlations taken at the location of the peak [OH] for x / D = 20 , using the (a) old and (b) new two-point optical systems.

Fig. 7
Fig. 7

Space–time correlations measured at mean radial [OH] peak for x / D = 20 , based on fluorescence (symbols) and on quenching-corrected concentrations (curves).

Fig. 8
Fig. 8

Spatial autocorrelation function at mean radial [OH] peak for x / D = 20 measured with different sampling rates.

Fig. 9
Fig. 9

Hydroxyl integral length and time scales measured in the H3 flame, both at (a) peak mean [OH] and (b) along the jet centerline. The dashed line indicates the location of the flame tip. Error bars are at the 95% confidence interval of the mean. Arrows to guide the eye have been drawn through the integral time scales.

Tables (2)

Tables Icon

Table 1 Specifications for Current Collection Lens System

Tables Icon

Table 2 Batchelor Frequencies and Measured Mean OH Concentrations at Measurement Locations a

Equations (23)

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

f S T ( Δ r , Δ t ; r ) = c ( r , t ) c ( r + Δ r , t + Δ t ) ¯ [ c ( r , t ) 2 ¯ c ( r + Δ r , t + Δ t ) 2 ¯ ] 1 / 2 ,
c ( r + Δ r , t + Δ t ) 2 ¯ = c ( r + Δ r , t ) 2 ¯ .
f T ( Δ t ; r ) = f S T ( Δ r = 0 , Δ t ; r ) = c ( r , t ) c ( r , t + Δ t ) ¯ c ( r , t ) 2 ¯ ,
f S ( Δ r ; r ) = f S T ( Δ r , Δ t = 0 ; r ) = c ( r , t ) c ( r + Δ r , t ) ¯ [ c ( r , t ) 2 ¯ c ( r + Δ r , t ) 2 ¯ ] 1 / 2 ,
τ l ( r ) = 0 f T ( Δ t ; r ) d ( Δ t ) ,
l l ( r ) = 0 f S ( Δ r ; r ) d ( Δ r ) .
c m ( r , t ) = c m ( r , t ) c m ( r , t ) ¯ = c ( r , t ) + n ( r , t ) ,
f S T , m ( Δ r , Δ t ; r ) = c m ( r , t ) c m ( r + Δ r , t + Δ t ) ¯ [ c m ( r , t ) 2 ¯ c m ( r + Δ r , t ) 2 ¯ ] 1 / 2 .
c m ( r , t ) c m ( r + Δ r , t + Δ t ) ¯ = [ c ( r , t ) + n ( r , t ) ] [ c ( r + Δ r , t + Δ t ) + n ( r + Δ r , t + Δ t ) ] ¯ = c ( r , t ) c ( r + Δ r , t + Δ t ) ¯ ,
c m ( r , t ) 2 ¯ = [ c ( r , t ) + n ( r , t ) ] 2 ¯ = c ( r , t ) 2 ¯ + n ( r , t ) 2 ¯ ,
c m ( r + Δ r , t ) 2 ¯ = c ( r + Δ r , t ) 2 ¯ + n ( r + Δ r , t ) 2 ¯ .
f S T , m ( Δ r , Δ t ; r ) = c ( r , t ) c ( r + Δ r , t + Δ t ) ¯ [ c m ( r , t ) 2 ¯ c m ( r + Δ r , t ) 2 ¯ ] 1 / 2 = f S T ( Δ r , Δ t ; r ) [ c ( r , t ) 2 ¯ c ( r + Δ r , t ) 2 ¯ ] 1 / 2 [ c m ( r , t ) 2 ¯ c m ( r + Δ r , t ) 2 ¯ ] 1 / 2 .
     c ( r , t ) 2 ¯ = c ( r , t ) c ( r + Δ r , t ) ¯ | Δ r = 0 = c m ( r , t ) c m ( r + Δ r , t ) ¯ | Δ r = 0 ,
n ( r , t ) 2 ¯ = c m ( r , t ) 2 ¯ c ( r , t ) 2 ¯ = c m ( r , t ) 2 ¯ c m ( r , t ) c m ( r + Δ r , t ) ¯ | Δ r = 0 .
PSD m ( f ) = ( c ( r , t ) 2 ¯ / c m ( r , t ) 2 ¯ ) PSD ( f ) + ( n ( r , t ) 2 ¯ / c m ( r , t ) 2 ¯ ) PSD n ( f ) ,
PSD m ( f ) ( n ( r , t ) 2 ¯ / c m ( r , t ) 2 ¯ ) / f N .
f S = 2 f N 2 f B .
S i ( t ) = α i ( c ¯ i + c i ( t ) ) ( τ ¯ i + τ i ( t ) ) + ( B ¯ i + B i ( t ) ) = ( α i c ¯ i τ ¯ i + B ¯ i ) + [ α i c ¯ i τ i ( t ) + α i τ ¯ i c i ( t ) + B i ( t ) + α i c i ( t ) τ i ( t ) ] , i = 1 , 2 ,
S 1 S 2 ¯ = ( α 1 c ¯ 1 τ ¯ 1 α 2 c ¯ 2 τ ¯ 2 ) [ σ c 1 σ c 2 c ¯ 1 c ¯ 2 c 1 c 2 ¯ σ c 1 σ c 2 + σ τ 1 σ τ 2 τ ¯ 1 τ ¯ 2 τ 1 τ 2 ¯ σ τ 1 σ τ 2 + 1 SBR 1 SBR 2 σ B 1 σ B 2 B ¯ 1 B ¯ 2 B 1 B 2 ¯ σ B 1 σ B 2 ] ,
S 1 S 2 ¯ [ S 1 2 ¯ S 2 2 ¯ ] 1 / 2 c 1 c 2 ¯ σ c 1 σ c 2 = f S T .
f B = U / ( 2 π λ B ) ,
λ B = 2.3 δ Re δ 3 / 4 Sc 1 / 2 ,
SNR = N S 1 + 2 / SBR ,

Metrics