Abstract

A tridirectional large lateral shearing displacement interferometric system has been proposed and used to reconstruct the temperature field of a quasi-axisymmetric diffused ethylene flame in two-dimensional (2D) and three-dimensional (3D) hypotheses. In comparison with the thermocouple results, the 2D reconstructed results affords a quantitative analysis with an average discrepancy between 20 and 40K in the full field, except in the closer part inside the peak temperature location where a high soot volume fraction exists. The 3D reconstructed results affords qualitative analysis and exhibits some asymmetrical characters, but an obvious error occurs at 1cm height where it is not suitable to use the universal correction coefficient.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
    [CrossRef]
  2. J. D. Posner and D. Dunn-Rankin, “Temperature field measurements of small, nonpremixed flames with use of an Abel inversion of holographic interferograms,” Appl. Opt. 42, 952–959 (2003).
    [CrossRef] [PubMed]
  3. A. I. Bishop, T. J. McIntyre, B. N. Littleton, and H. Rubinsztein-Dunlop, “OH concentration and temperature measurements by use of near-resonant holographic interferometry,” Appl. Opt. 43, 6384–6390 (2004).
    [CrossRef] [PubMed]
  4. D.-Y. Zhang and H.-C. Zhou, “Temperature measurement by holographic interferometry for non-premixed ethylene-air flame with a series of state relationships,” Fuel 86, 1552–1559 (2007).
    [CrossRef]
  5. X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
    [CrossRef]
  6. X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
    [CrossRef]
  7. X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
    [CrossRef] [PubMed]
  8. X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
    [CrossRef]
  9. S. M. Tieng and W. Z. Lai, “Temperature measurement of reacting flowfield by phase-shifting holographic interferometry,” J. Thermophys. Heat Transfer 6, 445–451 (1992).
    [CrossRef]
  10. J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
    [CrossRef]
  11. J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
    [CrossRef]
  12. M. Gawlowski, K. E. Kelly, L. A. Marcotte, and A. Schonbucher, “Determining the effect of species composition on temperature fields of tank flames using real-time holographic interferometry,” Appl. Opt. 48, 4625–4636 (2009).
    [CrossRef] [PubMed]
  13. A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).
  14. T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
    [CrossRef]
  15. A. Ito, Y. Kudo, and H. Oyama, “Propagation and extinction mechanisms of opposed-flow flame spread over PMMA for different sample orientations,” Combust. Flame 142, 428–437(2005).
    [CrossRef]
  16. T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
    [CrossRef] [PubMed]
  17. H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
    [CrossRef]
  18. J. S. Goldmeer, D. L. Urban, and Z.-G. Yuan, “Measurement of gas-phase temperatures in flames with a point-diffraction interferometer,” Appl. Opt. 40, 4816–4823 (2001).
    [CrossRef]
  19. W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).
  20. C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
    [CrossRef] [PubMed]
  21. C. Shakher and A. K. Nirala, “Review on refractive index and temperature profile measurements using laser-based interferometric techniques,” Opt. Lasers Eng. 31, 455–491(1999).
    [CrossRef]
  22. M. Thakur, C. Shakher, and A. L. Vyas, “Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings,” Appl. Opt. 41, 654–657 (2002).
    [CrossRef] [PubMed]
  23. P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
    [CrossRef]
  24. B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
    [CrossRef]
  25. A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
    [CrossRef]
  26. D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258–1269 (2006).
    [CrossRef]
  27. W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).
  28. D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
    [CrossRef]
  29. A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
    [CrossRef]
  30. R. Malina and M. Antos, “System for optical tomography,” Proc. SPIE 5036, 505–510 (2003).
    [CrossRef]
  31. J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46, 015601 (2007).
    [CrossRef]
  32. C. M. Vest, Holographic Interferometry (Wiley, 1979).
  33. W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).
  34. M.Bass, ed., Handbook of Optics, 3rd ed., Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), Vol.  I.
  35. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  36. Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).
  37. J. Lu and H.-C. Zhou, “Experimental investigations on the influence of assumptions in soot volume fraction measurement by TPD method,” J. Beijing Inst. Technol. (English Edition) 18, 402–407 (2009).

2010

W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).

M.Bass, ed., Handbook of Optics, 3rd ed., Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), Vol.  I.

2009

J. Lu and H.-C. Zhou, “Experimental investigations on the influence of assumptions in soot volume fraction measurement by TPD method,” J. Beijing Inst. Technol. (English Edition) 18, 402–407 (2009).

M. Gawlowski, K. E. Kelly, L. A. Marcotte, and A. Schonbucher, “Determining the effect of species composition on temperature fields of tank flames using real-time holographic interferometry,” Appl. Opt. 48, 4625–4636 (2009).
[CrossRef] [PubMed]

2008

W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

2007

D.-Y. Zhang and H.-C. Zhou, “Temperature measurement by holographic interferometry for non-premixed ethylene-air flame with a series of state relationships,” Fuel 86, 1552–1559 (2007).
[CrossRef]

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46, 015601 (2007).
[CrossRef]

2006

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258–1269 (2006).
[CrossRef]

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

2005

A. Ito, Y. Kudo, and H. Oyama, “Propagation and extinction mechanisms of opposed-flow flame spread over PMMA for different sample orientations,” Combust. Flame 142, 428–437(2005).
[CrossRef]

2004

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

A. I. Bishop, T. J. McIntyre, B. N. Littleton, and H. Rubinsztein-Dunlop, “OH concentration and temperature measurements by use of near-resonant holographic interferometry,” Appl. Opt. 43, 6384–6390 (2004).
[CrossRef] [PubMed]

2003

2002

M. Thakur, C. Shakher, and A. L. Vyas, “Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings,” Appl. Opt. 41, 654–657 (2002).
[CrossRef] [PubMed]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef] [PubMed]

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

2001

2000

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

1999

B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

C. Shakher and A. K. Nirala, “Review on refractive index and temperature profile measurements using laser-based interferometric techniques,” Opt. Lasers Eng. 31, 455–491(1999).
[CrossRef]

1998

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

1997

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

1996

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

1994

1993

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

1992

S. M. Tieng and W. Z. Lai, “Temperature measurement of reacting flowfield by phase-shifting holographic interferometry,” J. Thermophys. Heat Transfer 6, 445–451 (1992).
[CrossRef]

1988

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

1987

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

1979

C. M. Vest, Holographic Interferometry (Wiley, 1979).

Aggarwal, S. K.

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Ai, Y.-H.

W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

Antos, M.

R. Malina and M. Antos, “System for optical tomography,” Proc. SPIE 5036, 505–510 (2003).
[CrossRef]

Asseban, A.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Baker, J.

Bishop, A. I.

Chen, S.

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Choi, C. W.

X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Cremers, C. J.

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Doi, J.

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46, 015601 (2007).
[CrossRef]

Dunn-Rankin, D.

Faridi, M. S.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Feng, H.-Q.

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258–1269 (2006).
[CrossRef]

Fomin, N.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Fuchs, H.

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

Fujiwara, T.

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

Gawlowski, M.

Giammartini, S.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Goldmeer, J. S.

Guj, G.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

He, Y.

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Hochgreb, S.

B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Ito, A.

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

A. Ito, Y. Kudo, and H. Oyama, “Propagation and extinction mechanisms of opposed-flow flame spread over PMMA for different sample orientations,” Combust. Flame 142, 428–437(2005).
[CrossRef]

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kelly, K. E.

Konishi, T.

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Kudo, Y.

Kudou, Y.

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

Lai, W. Z.

S. M. Tieng and W. Z. Lai, “Temperature measurement of reacting flowfield by phase-shifting holographic interferometry,” J. Thermophys. Heat Transfer 6, 445–451 (1992).
[CrossRef]

Lallemand, M.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Lavinskaja, E.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Leung, C. W.

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

Li, F.

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

Lin, C. C.

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

Littleton, B. N.

Liu, D.-X.

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258–1269 (2006).
[CrossRef]

Lu, J.

J. Lu and H.-C. Zhou, “Experimental investigations on the influence of assumptions in soot volume fraction measurement by TPD method,” J. Beijing Inst. Technol. (English Edition) 18, 402–407 (2009).

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

Lv, W.

W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).

W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).

Malina, R.

R. Malina and M. Antos, “System for optical tomography,” Proc. SPIE 5036, 505–510 (2003).
[CrossRef]

Marcotte, L. A.

McIntyre, T. J.

Merzkirch, W.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

Narumi, A.

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Nirala, A. K.

C. Shakher and A. K. Nirala, “Review on refractive index and temperature profile measurements using laser-based interferometric techniques,” Opt. Lasers Eng. 31, 455–491(1999).
[CrossRef]

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef] [PubMed]

O’Brien, C. J.

B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Oyama, H.

A. Ito, Y. Kudo, and H. Oyama, “Propagation and extinction mechanisms of opposed-flow flame spread over PMMA for different sample orientations,” Combust. Flame 142, 428–437(2005).
[CrossRef]

Philipp, H.

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

Posner, J. D.

Pretzler, G.

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

Probert, S. D.

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

Puri, I. K.

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef] [PubMed]

X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

Qi, J. A.

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

Qiao, P.

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Qin, X.

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Rubinsztein-Dunlop, H.

Saito, K.

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Sato, S.

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46, 015601 (2007).
[CrossRef]

Saulnier, J. B.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Schonbucher, A.

Shakher, C.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

M. Thakur, C. Shakher, and A. L. Vyas, “Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings,” Appl. Opt. 41, 654–657 (2002).
[CrossRef] [PubMed]

C. Shakher and A. K. Nirala, “Review on refractive index and temperature profile measurements using laser-based interferometric techniques,” Opt. Lasers Eng. 31, 455–491(1999).
[CrossRef]

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef] [PubMed]

Shi, D.

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Singh, P.

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Stella, A.

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Struk, P. M.

Tashtoush, G.

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

Thakur, M.

Tieng, S. M.

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

S. M. Tieng and W. Z. Lai, “Temperature measurement of reacting flowfield by phase-shifting holographic interferometry,” J. Thermophys. Heat Transfer 6, 445–451 (1992).
[CrossRef]

Urban, D. L.

Van der Wege, B. A.

B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, 1979).

Vitkin, D.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Vyas, A. L.

Wang, Y. C.

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

Winklhofer, E.

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

Wong, W. O.

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

Xiao, X.

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef] [PubMed]

X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Yuan, Z.-G.

Yuen, D. W.

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Zhang, D.-Y.

D.-Y. Zhang and H.-C. Zhou, “Temperature measurement by holographic interferometry for non-premixed ethylene-air flame with a series of state relationships,” Fuel 86, 1552–1559 (2007).
[CrossRef]

Zhou, H.-C.

W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).

J. Lu and H.-C. Zhou, “Experimental investigations on the influence of assumptions in soot volume fraction measurement by TPD method,” J. Beijing Inst. Technol. (English Edition) 18, 402–407 (2009).

W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).

D.-Y. Zhang and H.-C. Zhou, “Temperature measurement by holographic interferometry for non-premixed ethylene-air flame with a series of state relationships,” Fuel 86, 1552–1559 (2007).
[CrossRef]

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

Zhu, J.-R.

W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).

Appl. Energy

J. A. Qi, C. W. Leung, W. O. Wong, and S. D. Probert, “Temperature-field measurements of a premixed butane/air circular impinging-flame using reference-beam interferometry,” Appl. Energy 83, 1307–1316 (2006).
[CrossRef]

Appl. Opt.

C. Shakher and A. K. Nirala, “Measurement of temperature using speckle shearing interferometry,” Appl. Opt. 33, 2125–2127 (1994).
[CrossRef] [PubMed]

X. Xiao and I. K. Puri, “Systematic approach based on holographic interferometry measurements to characterize the flame structure of partially premixed flames,” Appl. Opt. 40, 731–740 (2001).
[CrossRef]

J. S. Goldmeer, D. L. Urban, and Z.-G. Yuan, “Measurement of gas-phase temperatures in flames with a point-diffraction interferometer,” Appl. Opt. 40, 4816–4823 (2001).
[CrossRef]

M. Thakur, C. Shakher, and A. L. Vyas, “Measurement of temperature profile of a gaseous flame with a Lau phase interferometer that has circular gratings,” Appl. Opt. 41, 654–657 (2002).
[CrossRef] [PubMed]

X. Xiao and I. K. Puri, “Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion,” Appl. Opt. 41, 3890–3899 (2002).
[CrossRef] [PubMed]

J. D. Posner and D. Dunn-Rankin, “Temperature field measurements of small, nonpremixed flames with use of an Abel inversion of holographic interferograms,” Appl. Opt. 42, 952–959 (2003).
[CrossRef] [PubMed]

A. I. Bishop, T. J. McIntyre, B. N. Littleton, and H. Rubinsztein-Dunlop, “OH concentration and temperature measurements by use of near-resonant holographic interferometry,” Appl. Opt. 43, 6384–6390 (2004).
[CrossRef] [PubMed]

T. Konishi, A. Ito, Y. Kudo, A. Narumi, K. Saito, J. Baker, and P. M. Struk, “Simultaneous measurement of temperature and chemical species concentrations with a holographic interferometer and infrared absorption,” Appl. Opt. 45, 5725–5732 (2006).
[CrossRef] [PubMed]

M. Gawlowski, K. E. Kelly, L. A. Marcotte, and A. Schonbucher, “Determining the effect of species composition on temperature fields of tank flames using real-time holographic interferometry,” Appl. Opt. 48, 4625–4636 (2009).
[CrossRef] [PubMed]

Appl. Therm. Eng.

J. A. Qi, W. O. Wong, C. W. Leung, and D. W. Yuen, “Temperature field measurement of a premixed butane/air slot laminar flame jet with Mach-Zehnder interferometry,” Appl. Therm. Eng. 28, 1806–1812 (2008).
[CrossRef]

Combust. Flame

A. Ito, Y. Kudo, and H. Oyama, “Propagation and extinction mechanisms of opposed-flow flame spread over PMMA for different sample orientations,” Combust. Flame 142, 428–437(2005).
[CrossRef]

X. Xiao, C. W. Choi, and I. K. Puri, “Temperature measurements in steady two-dimensional partially premixed flames using laser interferometric holography,” Combust. Flame 120, 318–332 (2000).
[CrossRef]

X. Qin, X. Xiao, I. K. Puri, and S. K. Aggarwal, “Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames,” Combust. Flame 128, 121–132 (2002).
[CrossRef]

Exp. Fluids

A. Stella, G. Guj, and S. Giammartini, “Measurement of axisymmetric temperature fields using reference beam and shearing interferometry for application to flames,” Exp. Fluids 29, 1–12 (2000).
[CrossRef]

Fuel

D.-Y. Zhang and H.-C. Zhou, “Temperature measurement by holographic interferometry for non-premixed ethylene-air flame with a series of state relationships,” Fuel 86, 1552–1559 (2007).
[CrossRef]

J. Beijing Inst. Technol. (English Edition)

J. Lu and H.-C. Zhou, “Experimental investigations on the influence of assumptions in soot volume fraction measurement by TPD method,” J. Beijing Inst. Technol. (English Edition) 18, 402–407 (2009).

J. Engin. Thermophys.

W. Lv, H.-C. Zhou, and Y.-H. Ai, “Numerical simulation of temperature measurement of ethylene flame by radial shearing interferometry,” J. Engin. Thermophys. 29, 707–710(2008).

Y.-H. Ai, H.-C. Zhou, J. Lu, and F. Li, “Simultaneous measurement of distributions of temperature and soot volume fraction in laminar ethylene flames by emission CT,” J. Engin. Thermophys. 27, 717–719 (2006).

W. Lv, H.-C. Zhou, and J.-R. Zhu, “Fringe analysis for flame in real time lateral shearing interferometric system with large shearing distance,” J. Engin. Thermophys. 31, 717–719(2010).

J. Heat Transfer

A. Ito, A. Narumi, T. Konishi, G. Tashtoush, K. Saito, and C. J. Cremers, “The measurement of transient two-dimensional profiles of velocity and fuel concentration over liquids,” J. Heat Transfer 16, 437–457 (1998).

J. Thermophys. Heat Transfer

S. M. Tieng and W. Z. Lai, “Temperature measurement of reacting flowfield by phase-shifting holographic interferometry,” J. Thermophys. Heat Transfer 6, 445–451 (1992).
[CrossRef]

Meas. Sci. Technol.

S. M. Tieng, C. C. Lin, Y. C. Wang, and T. Fujiwara, “Effect of composition distribution on holographic temperature measurement of a diffuse flame,” Meas. Sci. Technol. 7, 477–488 (1996).
[CrossRef]

Opt. Eng.

H. Philipp, H. Fuchs, E. Winklhofer, and G. Pretzler, “Flame diagnostics by light sheet imaging and by shearing interferometry,” Opt. Eng. 32, 1025–1032 (1993).
[CrossRef]

P. Singh, M. S. Faridi, and C. Shakher, “Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique,” Opt. Eng. 43, 387–392 (2004).
[CrossRef]

J. Doi and S. Sato, “Three-dimensional modeling of the instantaneous temperature distribution in a turbulent flame using a multidirectional interferometer,” Opt. Eng. 46, 015601 (2007).
[CrossRef]

Opt. Laser Technol.

A. Asseban, M. Lallemand, J. B. Saulnier, N. Fomin, E. Lavinskaja, W. Merzkirch, and D. Vitkin, “Digital speckle photography and speckle tomography in heat transfer studies,” Opt. Laser Technol. 32, 583–592 (2000).
[CrossRef]

Opt. Lasers Eng.

D.-X. Liu and H.-Q. Feng, “In-cylinder temperature field measurement with laser shearing interferometry for spark ignition engines,” Opt. Lasers Eng. 44, 1258–1269 (2006).
[CrossRef]

B. A. Van der Wege, C. J. O’Brien, and S. Hochgreb, “Quantitative shearography in axisymmetric gas temperature measurements,” Opt. Lasers Eng. 31, 21–39 (1999).
[CrossRef]

C. Shakher and A. K. Nirala, “Review on refractive index and temperature profile measurements using laser-based interferometric techniques,” Opt. Lasers Eng. 31, 455–491(1999).
[CrossRef]

Proc. SPIE

R. Malina and M. Antos, “System for optical tomography,” Proc. SPIE 5036, 505–510 (2003).
[CrossRef]

D. Shi, X. Xiao, Y. He, P. Qiao, and S. Chen, “Measurement of three-dimension temperature field using phase-shifting holography and CT technique,” Proc. SPIE 3172, 407–412(1997).
[CrossRef]

Other

T. Konishi, A. Ito, Y. Kudou, and K. Saito, “The role of a flame-induced liquid surface wave on pulsating flame spread,” in Proceedings of the Combustion Institute (Combustion Institute, 2002), pp. 267–272.
[CrossRef]

C. M. Vest, Holographic Interferometry (Wiley, 1979).

W. Merzkirch, Flow Visualization, 2nd ed. (Academic, 1987).

M.Bass, ed., Handbook of Optics, 3rd ed., Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill, 2010), Vol.  I.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

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 (11)

Fig. 1
Fig. 1

Series of simulated fringe patterns, including a (a) double-exposure interferometric fringe pattern, and (b), (c), (d), (e) four lateral shearing interferometric fringe patterns whose lateral shearing displacements are 5, 10, 15, and 20 mm , respectively.

Fig. 2
Fig. 2

Some lateral shearing interferometric fringe patterns with the aberration, in which (a) is a typical real fringe pattern with moderate lateral shearing displacement and (b) and (c) separately show the simulated fringe patterns based on two parallel-sided interferometer plates with different sizes.

Fig. 3
Fig. 3

Typical fringe patterns with large lateral shearing dis placements both in a (a) slightly turbulent state and a (b) strongly turbulent state.

Fig. 4
Fig. 4

Schematic of a tridirectional large lateral shearing displacement interferometric system based on the parallel-sided interferometer plates.

Fig. 5
Fig. 5

Specified flame in a steady combustion state about 57 mm high.

Fig. 6
Fig. 6

The six photographs of fringe patterns in the three setting projective directions, in both (a), (b), (c) an extinction state and (d), (e), (f) a steady combusting state.

Fig. 7
Fig. 7

(a) Phase difference of fringe patterns in two states and (b) their subtraction at 3 cm height in 120 ° projection. Because of the slight random vibration of laboratory apparatus, a kind of linear correction with a very small slope (about 0.035 π rad / mm ) is needed.

Fig. 8
Fig. 8

Reconstructed relative phase function Δ ψ in both the 2D and 3D hypotheses using IRT at 3 cm height of the case 3 flame from Ai’s simulative work, in which (a) corresponds to the 3D and (b) corresponds to the 2D.

Fig. 9
Fig. 9

(a) Temperature field and (b) the correction coefficient field from Ai’s simulative work of the case 3 flame.

Fig. 10
Fig. 10

One hundred and eighty virtual orientations of the IRT reconstructed temperature field in the 2D hypothesis under the special correction and the corresponding results from the thermocouple.

Fig. 11
Fig. 11

Three real orientations of the IRT reconstructed temperature field in the 3D hypothesis, which uses 1.05 as the universal correction coefficient.

Tables (1)

Tables Icon

Table 1 Relative Discrepancy between the Two Kinds of Reconstructed Temperature Fields in the 2D and 3D Hypotheses on or Near the Axis

Equations (13)

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

ρ ( r , h ) = P ( r , h ) T ( r , h ) R g mix ,
n ( r , h ) = 1 + ρ ( r , h ) K mix ,
n ( r , h ) 1 = P ( r , h ) K mix T ( r , h ) R g mix .
θ flame ( x , y ) = R 0 2 ( y ) x 2 R 0 2 ( y ) x 2 Δ ψ ( x 2 + z 2 , y ) d z , | x | R 0 ( y ) ,
θ system ( r ) = θ system ( x , y ) = a ( x 2 + y 2 ) + b ( x 2 + y 2 ) 2 ,
Θ ( x , y ) = θ ( x , y ) θ ( x s , y ) + 2 π mod ( Δ Z / λ ) ,
Θ 0 ( x , y ) = θ system ( x , y ) θ system ( x s , y ) + 2 π mod ( Δ Z , λ ) ,
Θ 1 ( x , y ) = θ flame ( x , y ) θ flame ( x s , y ) + Θ 0 ( x , y ) .
Θ 0 ( x , y ) = 4 b s [ ( x 0.5 s ) 2 + y 2 + 0.25 s 2 + 0.5 a / b ] ( x 0.5 s ) + 2 π mod ( Δ Z / λ ) .
θ flame ( x , y ) = { Θ 1 ( x , y ) Θ 0 ( x , y ) , R 0 ( y ) < x < R 0 ( y ) Θ 0 ( x , y ) Θ 1 ( x , y ) , s R 0 ( y ) < x < s + R 0 ( y ) .
s = 2 H ip tan { sin 1 [ sin ( φ / 2 ) / n ip ] } cos ( φ / 2 ) .
T = η T air = η 2 π P λ 1 R g air 1 K air Δ ψ + 2 π P λ 1 R g air 1 K air T 0 1 = η C Δ ψ + C / T 0 ,
d T / d ( T 0 ) = η C ( Δ ψ + C / T 0 ) 2 C T 0 2 = T 2 η T 0 2 , d T / d ( Δ ψ ) = η C ( Δ ψ + C / T 0 ) 2 = T 2 η C , d T / d ( η ) = C Δ ψ + C / T 0 = T η .

Metrics