Abstract

We present a theoretical analysis of two-color pyrometry applied to optical diagnostics. A two-color pyrometer built with a single CCD is advantageous due to the simple system design. We evaluate the possibility and degree of ill-conditionness on the basis of measurement uncertainties for different measurement approaches of this two-color system. We classify measurement approaches. The corresponding ill-conditionness criterion is established. The greater the criterion value is, the worse the ill-conditioned degree of solution is. So, the optimum choice of measurement approach for the two-color system is achieved through intercomparison of the criterion values. Numerical examples are also given to illustrate this point. The theoretical analysis not only provides an effective way of evaluating different measurement approaches, but also may help us to better understand the influences that determine the choices between wavelength/waveband measurements and calibration/noncalibration modes for temperature and soot distribution.

© 2008 Optical Society of America

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  1. J. Dec, “A conceptual model of DI diesel combustion based on laser-sheet imaging,” SAE Tech. Paper 970873 (Society of Automotive Engineers, 1997).
  2. D. W. Shaw and R. H. Essenhigh, “Temperature fluctuations in pulverized coal (P.C.) flames,” Combust. Flame 86, 333-346(1991).
    [CrossRef]
  3. H. Zhao and N. Ladommatos, “Optical diagnostics for soot and temperature measurement in diesel engines,” Prog. Energy Combust. Sci. 24, 221-255 (1998).
    [CrossRef]
  4. G. J. Hampson and R. D. Reitz, “Two-colour imaging of in-cylinder soot concentration and temperature in a heavy-duty DI diesel engine with comparison to multidimensional modelling for single and split injections,” SAE Tech. Paper 980524 (Society of Automotive Engineers, 1998).
  5. J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
    [CrossRef]
  6. F. Cignoli, S. De Iuliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370-5378 (2001).
    [CrossRef]
  7. G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
    [CrossRef]
  8. G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55,1303-1308(2006).
    [CrossRef]
  9. F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
    [CrossRef]
  10. T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
    [CrossRef]
  11. Z. X. Luo and H. C. Zhou, “A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique,” IEEE Trans. Instrum. Meas. 56, 1877-1882 (2007).
    [CrossRef]
  12. S. di Stasio and P. Massoli, “Influence of the soot property uncertainties in temperature and volume-fraction measurements by two-colour pyrometry,” Meas. Sci. Technol. 5, 1453-1465 (1994).
    [CrossRef]
  13. D. P. Dewitt and G. D. Nutter, Theory and Practice of Radiation Thermometry (Wiley, 1989).
  14. Y. Matsui, T. Kamimoto, and S. Matsuoka, “A study on the time and space resolved measurement of flame temperature and soot concentration in a D.I. diesel engine by the two-color method,” SAE Tech. Paper 790491 (Society of Automotive Engineers, 1979).
  15. H. X. Quoc, J.-M. Vignon, and M. Brun, “A new approach of the two-color method for determining local instantaneous soot concentration and temperature in a D.I. diesel combustion chamber,” SAE Tech. Paper 910736 (Society of Automotive Engineers, 1991).
  16. M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
    [CrossRef]
  17. M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
    [CrossRef]
  18. S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.
  19. S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
    [CrossRef]
  20. S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.
  21. Z. Z. Wang and W. M. Shao, “New ill-condition criteria,” AMSE Review 4, 59-64 (1987).

2007

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

Z. X. Luo and H. C. Zhou, “A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique,” IEEE Trans. Instrum. Meas. 56, 1877-1882 (2007).
[CrossRef]

2006

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55,1303-1308(2006).
[CrossRef]

2002

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

2001

2000

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

1998

H. Zhao and N. Ladommatos, “Optical diagnostics for soot and temperature measurement in diesel engines,” Prog. Energy Combust. Sci. 24, 221-255 (1998).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

1994

S. di Stasio and P. Massoli, “Influence of the soot property uncertainties in temperature and volume-fraction measurements by two-colour pyrometry,” Meas. Sci. Technol. 5, 1453-1465 (1994).
[CrossRef]

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

1992

M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
[CrossRef]

1991

D. W. Shaw and R. H. Essenhigh, “Temperature fluctuations in pulverized coal (P.C.) flames,” Combust. Flame 86, 333-346(1991).
[CrossRef]

1987

Z. Z. Wang and W. M. Shao, “New ill-condition criteria,” AMSE Review 4, 59-64 (1987).

Barbini, M.

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

Benecchi, S.

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.

Bheemul, H. C.

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

Brun, M.

H. X. Quoc, J.-M. Vignon, and M. Brun, “A new approach of the two-color method for determining local instantaneous soot concentration and temperature in a D.I. diesel combustion chamber,” SAE Tech. Paper 910736 (Society of Automotive Engineers, 1991).

Cheng, X. F.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Choi, M. Y.

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

Cignoli, F.

F. Cignoli, S. De Iuliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370-5378 (2001).
[CrossRef]

S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.

S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.

De Iuliis, S.

F. Cignoli, S. De Iuliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370-5378 (2001).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.

S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.

Dec, J.

J. Dec, “A conceptual model of DI diesel combustion based on laser-sheet imaging,” SAE Tech. Paper 970873 (Society of Automotive Engineers, 1997).

Dewitt, D. P.

D. P. Dewitt and G. D. Nutter, Theory and Practice of Radiation Thermometry (Wiley, 1989).

di Stasio, S.

S. di Stasio and P. Massoli, “Influence of the soot property uncertainties in temperature and volume-fraction measurements by two-colour pyrometry,” Meas. Sci. Technol. 5, 1453-1465 (1994).
[CrossRef]

Essenhigh, R. H.

D. W. Shaw and R. H. Essenhigh, “Temperature fluctuations in pulverized coal (P.C.) flames,” Combust. Flame 86, 333-346(1991).
[CrossRef]

Fu, T. R.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Garca, J. M.

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

Gore, J. L.

M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
[CrossRef]

Hamins, A.

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

Hampson, G. J.

G. J. Hampson and R. D. Reitz, “Two-colour imaging of in-cylinder soot concentration and temperature in a heavy-duty DI diesel engine with comparison to multidimensional modelling for single and split injections,” SAE Tech. Paper 980524 (Society of Automotive Engineers, 1998).

Hernberg, R.

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

Kamimoto, T.

Y. Matsui, T. Kamimoto, and S. Matsuoka, “A study on the time and space resolved measurement of flame temperature and soot concentration in a D.I. diesel engine by the two-color method,” SAE Tech. Paper 790491 (Society of Automotive Engineers, 1979).

Kashiwagi, K.

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

Klassen, M.

M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
[CrossRef]

Kytola, J.

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

Ladommatos, N.

H. Zhao and N. Ladommatos, “Optical diagnostics for soot and temperature measurement in diesel engines,” Prog. Energy Combust. Sci. 24, 221-255 (1998).
[CrossRef]

Liu, T. M.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Lu, G.

G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55,1303-1308(2006).
[CrossRef]

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

Luo, Z. X.

Z. X. Luo and H. C. Zhou, “A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique,” IEEE Trans. Instrum. Meas. 56, 1877-1882 (2007).
[CrossRef]

Manta, V.

Massoli, P.

S. di Stasio and P. Massoli, “Influence of the soot property uncertainties in temperature and volume-fraction measurements by two-colour pyrometry,” Meas. Sci. Technol. 5, 1453-1465 (1994).
[CrossRef]

Matsui, Y.

Y. Matsui, T. Kamimoto, and S. Matsuoka, “A study on the time and space resolved measurement of flame temperature and soot concentration in a D.I. diesel engine by the two-color method,” SAE Tech. Paper 790491 (Society of Automotive Engineers, 1979).

Matsuoka, S.

Y. Matsui, T. Kamimoto, and S. Matsuoka, “A study on the time and space resolved measurement of flame temperature and soot concentration in a D.I. diesel engine by the two-color method,” SAE Tech. Paper 790491 (Society of Automotive Engineers, 1979).

Migliorini, F.

S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.

Mulholland, G. W.

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

Nummela, V.

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

Nutter, G. D.

D. P. Dewitt and G. D. Nutter, Theory and Practice of Radiation Thermometry (Wiley, 1989).

Pastor, J. M.

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

Pastor, J. V.

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

Payri, F.

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

Quoc, H. X.

H. X. Quoc, J.-M. Vignon, and M. Brun, “A new approach of the two-color method for determining local instantaneous soot concentration and temperature in a D.I. diesel combustion chamber,” SAE Tech. Paper 910736 (Society of Automotive Engineers, 1991).

Reitz, R. D.

G. J. Hampson and R. D. Reitz, “Two-colour imaging of in-cylinder soot concentration and temperature in a heavy-duty DI diesel engine with comparison to multidimensional modelling for single and split injections,” SAE Tech. Paper 980524 (Society of Automotive Engineers, 1998).

Riley, G.

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

Shao, W. M.

Z. Z. Wang and W. M. Shao, “New ill-condition criteria,” AMSE Review 4, 59-64 (1987).

Shaw, D. W.

D. W. Shaw and R. H. Essenhigh, “Temperature fluctuations in pulverized coal (P.C.) flames,” Combust. Flame 86, 333-346(1991).
[CrossRef]

Shi, C. L.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Sivathanu, Y. R.

M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
[CrossRef]

Vattulainen, J.

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

Vignon, J.-M.

H. X. Quoc, J.-M. Vignon, and M. Brun, “A new approach of the two-color method for determining local instantaneous soot concentration and temperature in a D.I. diesel combustion chamber,” SAE Tech. Paper 910736 (Society of Automotive Engineers, 1991).

Wang, Z. Z.

Z. Z. Wang and W. M. Shao, “New ill-condition criteria,” AMSE Review 4, 59-64 (1987).

Yan, Y.

G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55,1303-1308(2006).
[CrossRef]

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

Zhao, H.

H. Zhao and N. Ladommatos, “Optical diagnostics for soot and temperature measurement in diesel engines,” Prog. Energy Combust. Sci. 24, 221-255 (1998).
[CrossRef]

Zheng, X. B.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Zhong, M. H.

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

Zhou, H. C.

Z. X. Luo and H. C. Zhou, “A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique,” IEEE Trans. Instrum. Meas. 56, 1877-1882 (2007).
[CrossRef]

Zizak, G.

F. Cignoli, S. De Iuliis, V. Manta, and G. Zizak, “Two-dimensional two-wavelength emission technique for soot diagnostics,” Appl. Opt. 40, 5370-5378 (2001).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.

S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.

AMSE Review

Z. Z. Wang and W. M. Shao, “New ill-condition criteria,” AMSE Review 4, 59-64 (1987).

Appl. Opt.

Combust. Flame

D. W. Shaw and R. H. Essenhigh, “Temperature fluctuations in pulverized coal (P.C.) flames,” Combust. Flame 86, 333-346(1991).
[CrossRef]

M. Klassen, Y. R. Sivathanu, and J. L. Gore, “Simultaneous emission absorption measurements in toluene-fueled pool flames: mean and RMS properties,” Combust. Flame 90, 34-44 (1992).
[CrossRef]

M. Y. Choi, A. Hamins, G. W. Mulholland, and K. Kashiwagi, “Simultaneous optical measurement of soot volume fraction and temperature in premixed flames,” Combust. Flame 99, 174-186, (1994).
[CrossRef]

S. De Iuliis, M. Barbini, S. Benecchi, and G. Zizak, “Determination of the soot volume fraction in an ethylene diffusion flame by multiwavelength analysis of soot radiation,” Combust. Flame 115, 253-261, 1998.
[CrossRef]

IEEE Trans. Instrum. Meas.

Z. X. Luo and H. C. Zhou, “A combustion-monitoring system with 3-D temperature reconstruction based on flame-image processing technique,” IEEE Trans. Instrum. Meas. 56, 1877-1882 (2007).
[CrossRef]

G. Lu, Y. Yan, G. Riley, and H. C. Bheemul, “Concurrent measurements of temperature and soot concentration of pulverized coal flames,” IEEE Trans. Instrum. Meas. 51, 990-995(2002).
[CrossRef]

G. Lu and Y. Yan, “Temperature profiling of pulverized coal flames using multicolor pyrometric and digital imaging techniques,” IEEE Trans. Instrum. Meas. 55,1303-1308(2006).
[CrossRef]

Meas. Sci. Technol.

F. Payri, J. V. Pastor, J. M. Garća, and J. M. Pastor, “Contribution to the application of two-colour imaging to diesel combustion,” Meas. Sci. Technol. 18, 2579-2598 (2007).
[CrossRef]

T. R. Fu, X. F. Cheng, C. L. Shi, M. H. Zhong, T. M. Liu, and X. B. Zheng, “The setup of a vision pyrometer,” Meas. Sci. Technol. 17, 659-665 (2006).
[CrossRef]

J. Vattulainen, V. Nummela, R. Hernberg, and J. Kytola, “A system for quantitative imaging diagnostics and its application to pyrometric in-cylinder flame-temperature measurements in large diesel engines,” Meas. Sci. Technol. 11, 103-119 (2000).
[CrossRef]

S. di Stasio and P. Massoli, “Influence of the soot property uncertainties in temperature and volume-fraction measurements by two-colour pyrometry,” Meas. Sci. Technol. 5, 1453-1465 (1994).
[CrossRef]

Prog. Energy Combust. Sci.

H. Zhao and N. Ladommatos, “Optical diagnostics for soot and temperature measurement in diesel engines,” Prog. Energy Combust. Sci. 24, 221-255 (1998).
[CrossRef]

Other

G. J. Hampson and R. D. Reitz, “Two-colour imaging of in-cylinder soot concentration and temperature in a heavy-duty DI diesel engine with comparison to multidimensional modelling for single and split injections,” SAE Tech. Paper 980524 (Society of Automotive Engineers, 1998).

J. Dec, “A conceptual model of DI diesel combustion based on laser-sheet imaging,” SAE Tech. Paper 970873 (Society of Automotive Engineers, 1997).

D. P. Dewitt and G. D. Nutter, Theory and Practice of Radiation Thermometry (Wiley, 1989).

Y. Matsui, T. Kamimoto, and S. Matsuoka, “A study on the time and space resolved measurement of flame temperature and soot concentration in a D.I. diesel engine by the two-color method,” SAE Tech. Paper 790491 (Society of Automotive Engineers, 1979).

H. X. Quoc, J.-M. Vignon, and M. Brun, “A new approach of the two-color method for determining local instantaneous soot concentration and temperature in a D.I. diesel combustion chamber,” SAE Tech. Paper 910736 (Society of Automotive Engineers, 1991).

S. De Iuliis, F. Migliorini, F. Cignoli, and G. Zizak, “2D soot volume fraction imaging in an ethylene diffusion flame by two-color laser-induced incandescence (2C-LII) technique and comparison with results from other optical diagnostics,” in Proceedings of the Combustion Institute (2007), Vol. 31, pp. 869-876.

S. De Iuliis, F. Cignoli, S. Benecchi, and G. Zizak, “Investigation of the similarity of soot parameters in ethylene diffusion flames with different height by extinction/scattering technique,” in Proceedings of the 27th Symposium (International) on Combustion (Combustion Institute, 1998), pp. 1549-1555.

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Figures (27)

Fig. 1
Fig. 1

Selection of wavelengths (550, 630, 700 nm ).

Fig. 2
Fig. 2

Response functions of waveband measurements.

Fig. 3
Fig. 3

The change trend of emissivity relative to K L .

Fig. 4
Fig. 4

RTS of case A; Δ ( K L ) = 0 , K L = 1 .

Fig. 5
Fig. 5

RTS of case B; Δ ( K L ) = 0 , K L = 1 .

Fig. 6
Fig. 6

RTS of case C; Δ ( K L ) = 0 , K L = 1 .

Fig. 7
Fig. 7

RTS of case D; Δ ( K L ) = 0 , K L = 1 .

Fig. 8
Fig. 8

RKS of case A; Δ T , T = 1500 K .

Fig. 9
Fig. 9

RKS of case B; Δ T , T = 1500 K .

Fig. 10
Fig. 10

RKS of case C; Δ T , T = 1500 K .

Fig. 11
Fig. 11

RKS of case D; Δ T , T = 1500 K .

Fig. 12
Fig. 12

Ill-conditionness criterion, case A(1).

Fig. 13
Fig. 13

Ill-conditionness criterion, case A(2).

Fig. 14
Fig. 14

Ill-conditionness criterion, case A(3).

Fig. 15
Fig. 15

Ill-conditionness criterion, case B(4).

Fig. 16
Fig. 16

Ill-conditionness criterion, case B(5).

Fig. 17
Fig. 17

Ill-conditionness criterion, case B(6).

Fig. 18
Fig. 18

Ill-conditionness criterion, case C(7).

Fig. 19
Fig. 19

Ill-condition criterion, case C(8).

Fig. 20
Fig. 20

Ill-conditionness criterion, case C(9).

Fig. 21
Fig. 21

Ill-conditionness criterion, case D(10).

Fig. 22
Fig. 22

Ill-conditionness criterion, case D(11).

Fig. 23
Fig. 23

Ill-conditionness criterion, case D(12).

Fig. 24
Fig. 24

M distribution in the range of K L for range ( 1 , 2 ) and T for range ( 1500 K , 2000 K ).

Fig. 25
Fig. 25

M distribution of 12 cases when T = 1500 K , K L = 1 .

Fig. 26
Fig. 26

Relative temperature error distributions of 12 cases.

Fig. 27
Fig. 27

Relative soot factor error distributions of 12 cases.

Tables (1)

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Table 1 Simulation Examples

Equations (26)

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V i = Φ · 0.38 μm 0.78 μm F i ( λ ) · ε λ · I b , λ ( T ) d λ = Φ · S i ,
I b , λ ( T ) = 1 / π · C 1 λ 5 · exp ( C 2 / λ T ) ,
ε λ = 1 exp ( K L / λ α ) ,
V i = Φ · f i · ε λ i · I b , λ i ( T ) = Φ · f i · C 1 / π · [ 1 exp ( K L / λ i α ) ] · λ i 5 exp ( C 2 / λ i T ) ,
K L = λ i α ln ( 1 S i / f i · λ i 5 exp ( C 2 / λ i T ) π / C 1 ) .
K L = λ i α ln ( 1 exp ( C 2 / λ i T ) exp ( C 2 / λ i T a , i ) ) .
λ 1 α ln ( 1 exp ( C 2 / λ 1 T ) exp ( C 2 / λ 1 T a , 1 ) ) = λ 2 α ln ( 1 exp ( C 2 / λ 2 T ) exp ( C 2 / λ 2 T a , 2 ) ) .
V 1 V 3 = S 1 S 3 = f 1 · [ 1 exp ( K L / λ 1 α ) ] · λ 1 5 exp ( C 2 / λ 1 T ) f 3 · [ 1 exp ( K L / λ 2 α ) ] · λ 2 5 exp ( C 2 / λ 2 T ) , V 2 V 3 = S 2 S 3 = f 2 · [ 1 exp ( K L / λ 1 α ) ] · λ 1 5 exp ( C 2 / λ 1 T ) f 3 · [ 1 exp ( K L / λ 2 α ) ] · λ 2 5 exp ( C 2 / λ 2 T ) ,
S 1 = 0.38 μm 0.78 μm F 1 ( λ ) · ε λ · I b , λ ( T ) d λ , S 2 = 0.38 μm 0.78 μm F 2 ( λ ) · ε λ · I b , λ ( T ) d λ , S 3 = 0.38 μm 0.78 μm F 3 ( λ ) · ε λ · I b , λ ( T ) d λ .
V 1 V 3 = S 1 S 3 = 0.38 μm 0.78 μm F 1 ( λ ) · ε λ · I b , λ ( T ) d λ 0.38 μm 0.78 μm F 3 ( λ ) · ε λ · I b , λ ( T ) d λ , V 2 V 3 = S 2 S 3 = 0.38 μm 0.78 μm F 2 ( λ ) · ε λ · I b , λ ( T ) d λ 0.38 μm 0.78 μm F 3 ( λ ) · ε λ · I b , λ ( T ) d λ .
( S 1 , S 2 , S 3 ) ( T , K L ) .
d S i = S i T d T + S i ( K L ) d ( K L ) or Δ S i = S i T Δ T + S i ( K L ) Δ ( K L ) , i = 1 , 2 , 3.
Δ S i / S i Δ T / T | Δ ( K L ) = 0 = C 2 λ i T
Δ S i / S i Δ T / T | Δ ( K L ) = 0 = 0.38 μm 0.78 μm C 2 λ T F i ( λ ) · ε λ · I b , λ ( T ) d λ 0.38 μm 0.78 μm F i ( λ ) · ε λ · I b , λ ( T ) d λ
Δ S i / S i Δ ( K L ) / ( K L ) | Δ T = 0 = K L λ i α · 1 exp ( K L / λ i α ) 1
Δ S i / S i Δ ( K L ) / ( K L ) | Δ T = 0 = 0.38 μm 0.78 μm F i ( λ ) · K L λ α exp ( K L / λ α ) · I b , λ ( T ) d λ 0.38 μm 0.78 μm F i ( λ ) · ε λ · I b , λ ( T ) d λ
A · X = Y ,
A = ( a i , 1 a i , 2 a j , 1 a j , 2 ) , X = ( Δ T / T Δ ( K L ) / ( K L ) ) , Y = ( Δ S i / S i Δ S j / S j ) ; and a i , 1 = S i T T S i , a i , 2 = S i ( K L ) K L S i , a j , 1 = S j T T S j , a j , 2 = S j ( K L ) K L S j .
M = ( | a i , 1 | + | a i , 2 | ) · ( | a j , 1 | + | a j , 2 | ) / | det A | ,
( S 1 / S 3 , S 2 / S 3 ) ( T , K L ) .
Δ ( S i / S k ) = ( S i / S k ) T Δ T + ( S i / S k ) ( K L ) Δ ( K L ) , i = 1 , 2 , 3 ; k = 1 , 2 , 3 ; i k .
Δ ( S i / S k ) / ( S i / S k ) Δ T / T | Δ ( K L ) = 0 = ( S i / S k ) T · T S i / S k = Δ S i / S i Δ T / T Δ S k / S k Δ T / T | Δ ( K L ) = 0 .
Δ ( S i / S k ) / ( S i / S k ) Δ ( K L ) / ( K L ) | Δ T = 0 = ( S i / S k ) ( K L ) · K L S i / S k = Δ S i / S i Δ ( K L ) / ( K L ) Δ S k / S k Δ ( K L ) / ( K L ) | Δ T = 0 .
B · X = Z ,
B = ( b i , 1 b i , 2 b j , 1 b j , 2 ) , X = ( Δ T / T Δ ( K L ) / ( K L ) ) , Z = ( Δ ( S i / S k ) / ( S i / S k ) Δ ( S j / S k ) / ( S j / S k ) ) ; and b i , 1 = ( S i / S k ) T · T S i / S k , b i , 2 = ( S i / S k ) ( K L ) · K L S i / S k , b j , 1 = ( S j / S k ) T · T S j / S k , b j , 2 = ( S j / S k ) ( K L ) · K L S j / S k .
M = ( | b i , 1 | + | b i , 2 | ) · ( | b j , 1 | + | b j , 2 | ) / | det B | .

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