Abstract

The species concentrations of flame chemiluminescence play important role in combustion diagnostics, such as CH* and C2* of hydrocarbon flame, which can provide specific characteristics in combustion control and monitoring. In order to realize both CH* and C2* chemiluminescence intensity detection in propane-air diffusion flame simultaneously, we present three-dimensional dynamic flame detecting method for species concentration determination. Firstly, quantitative flame chemiluminescence multispectral separation technique based on color cameras coupled with double-channel bandpass filters is adopted for dual channel signal division. Next, flame chemiluminescence tomography combining with multi-directional simultaneous capturing is proposed for real time three dimensional observations and detection in flame. Moreover, the proposed technique can quantitatively provide comparison of species intensity between CH* and C2* for further analysis. Considering its credible detecting accuracy and simple requirements, it is believed the proposed technique can be widely used in combustion diagnostics.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]

2016 (2)

H. Ax and W. Meier, “Experimental investigation of the response of laminar premixed flames to equivalence ratio oscillations,” Combust. Flame 167, 172–183 (2016).
[Crossref]

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

2015 (3)

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

X. Li and L. Ma, “Capabilities and limitations of 3D flame measurements based on computed tomography of chemiluminescence,” Combust. Flame 162(3), 642–651 (2015).
[Crossref]

J. Wang, Y. Song, Z. H. Li, A. Kempf, and A. Z. He, “Multi-directional 3D flame chemiluminescence tomography based on lens imaging,” Opt. Lett. 40(7), 1231–1234 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (3)

2012 (5)

M. Bozkurt, M. Fikri, and C. Schulz, “Investigation of the kinetics of OH* and CH* chemiluminescence in hydrocarbon oxidation behind reflected shock waves,” Appl. Phys. B 107(3), 515–527 (2012).
[Crossref]

M. Röder, T. Dreier, and C. Schulz, “Simultaneous measurement of localized heat release with OH/CH2O-LIF imaging and spatially integrated OH* chemiluminescence in turbulent swirl flames,” Appl. Phys. B 107(3), 611–617 (2012).
[Crossref]

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

2011 (4)

J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): high resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

J. Floyd, P. Geipel, and A. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011).
[Crossref]

T. Upton, D. Verhoeven, and D. Hudgins, “High-resolution computed tomography of a turbulent reacting flow,” Exp. Fluids 50(1), 125–134 (2011).
[Crossref]

H. Huang and Y. Zhang, “Digital colour image processing based measurement of premixed CH 4+ air and C 2 H 4+ air flame chemiluminescence,” Fuel 90(1), 48–53 (2011).
[Crossref]

2010 (4)

H. Huang and Y. Zhang, “Dynamic application of digital image and colour processing in characterizing flame radiation features,” Meas. Sci. Technol. 21(8), 085202 (2010).
[Crossref]

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

M. Orain and Y. Hardalupas, “Effect of fuel type on equivalence ratio measurements using chemiluminescence in premixed flames,” C. R. Mec. 338(5), 241–254 (2010).
[Crossref]

2009 (1)

V. N. Nori and J. M. Seitzman, “CH* chemiluminescence modeling for combustion diagnostics,” Proc. Combust. Inst. 32(1), 895–903 (2009).
[Crossref]

2008 (3)

F. Biagioli, F. Güthe, and B. Schuermans, “Combustion dynamics linked to flame behaviour in a partially premixed swirled industrial burner,” Exp. Therm. Fluid Sci. 32(7), 1344–1353 (2008).
[Crossref]

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

H. Huang and Y. Zhang, “Flame colour characterization in the visible and infrared spectrum using a digital camera and image processing,” Meas. Sci. Technol. 19(8), 085406 (2008).
[Crossref]

2007 (1)

D. Nikolic and N. Iida, “Effects of intake CO2 concentrations on fuel spray flame temperatures and soot formations,” Proc.- Inst. Mech. Eng. 221, 1567–1573 (2007).
[Crossref]

2006 (1)

Y. K. Jeong, C. H. Jeon, and Y. J. Chang, “Evaluation of the equivalence ratio of the reacting mixture using intensity ratio of chemiluminescence in laminar partially premixed CH 4-air flames,” Exp. Therm. Fluid Sci. 30(7), 663–673 (2006).
[Crossref]

2005 (3)

J. Kojima, Y. Ikeda, and T. Nakajima, “Basic aspects of OH(A), CH(A), and C2(d) chemiluminescence in the reaction zone of laminar methane-air premixed flames,” Combust. Flame 140(1), 34–45 (2005).
[Crossref]

S. A. Farhat, W. B. Ng, and Y. Zhang, “Chemiluminescent emission measurement of a diffusion flame jet in a loudspeaker induced standing wave,” Fuel 84(14), 1760–1767 (2005).
[Crossref]

J. Hentschel, R. Suntz, and H. Bockhorn, “Soot formation and oxidation in oscillating methane-air diffusion flames at elevated pressure,” Appl. Opt. 44(31), 6673–6681 (2005).
[Crossref] [PubMed]

2004 (1)

Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame 139(3), 188–207 (2004).
[Crossref]

2001 (1)

1999 (1)

A. K. Gupta, S. Bolz, and T. Hasegawa, “Effect of air preheat temperature and oxygen concentration on flame structure and emission,” J. Energy Resour. Technol. 121(3), 209–216 (1999).
[Crossref]

Aldén, M.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

Allison, P.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Ax, H.

H. Ax and W. Meier, “Experimental investigation of the response of laminar premixed flames to equivalence ratio oscillations,” Combust. Flame 167, 172–183 (2016).
[Crossref]

Bai, X.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

Biagioli, F.

F. Biagioli, F. Güthe, and B. Schuermans, “Combustion dynamics linked to flame behaviour in a partially premixed swirled industrial burner,” Exp. Therm. Fluid Sci. 32(7), 1344–1353 (2008).
[Crossref]

Bockhorn, H.

Bolz, S.

A. K. Gupta, S. Bolz, and T. Hasegawa, “Effect of air preheat temperature and oxygen concentration on flame structure and emission,” J. Energy Resour. Technol. 121(3), 209–216 (1999).
[Crossref]

Boulouchos, K.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Bozkurt, M.

M. Bozkurt, M. Fikri, and C. Schulz, “Investigation of the kinetics of OH* and CH* chemiluminescence in hydrocarbon oxidation behind reflected shock waves,” Appl. Phys. B 107(3), 515–527 (2012).
[Crossref]

Brockhinke, A.

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

Cai, W.

Carter, C.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Chang, Y. J.

Y. K. Jeong, C. H. Jeon, and Y. J. Chang, “Evaluation of the equivalence ratio of the reacting mixture using intensity ratio of chemiluminescence in laminar partially premixed CH 4-air flames,” Exp. Therm. Fluid Sci. 30(7), 663–673 (2006).
[Crossref]

Chen, Y. C.

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

Cignoli, F.

De Iuliis, S.

Dreier, T.

M. Röder, T. Dreier, and C. Schulz, “Simultaneous measurement of localized heat release with OH/CH2O-LIF imaging and spatially integrated OH* chemiluminescence in turbulent swirl flames,” Appl. Phys. B 107(3), 611–617 (2012).
[Crossref]

Farhat, S. A.

S. A. Farhat, W. B. Ng, and Y. Zhang, “Chemiluminescent emission measurement of a diffusion flame jet in a loudspeaker induced standing wave,” Fuel 84(14), 1760–1767 (2005).
[Crossref]

Fikri, M.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

M. Bozkurt, M. Fikri, and C. Schulz, “Investigation of the kinetics of OH* and CH* chemiluminescence in hydrocarbon oxidation behind reflected shock waves,” Appl. Phys. B 107(3), 515–527 (2012).
[Crossref]

Floyd, J.

J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): high resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

J. Floyd, P. Geipel, and A. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011).
[Crossref]

Frederickson, K.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Gao, Y.

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Geipel, P.

J. Floyd, P. Geipel, and A. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011).
[Crossref]

Gord, J.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Gord, J. R.

Gupta, A. K.

A. K. Gupta, S. Bolz, and T. Hasegawa, “Effect of air preheat temperature and oxygen concentration on flame structure and emission,” J. Energy Resour. Technol. 121(3), 209–216 (1999).
[Crossref]

Güthe, F.

F. Biagioli, F. Güthe, and B. Schuermans, “Combustion dynamics linked to flame behaviour in a partially premixed swirled industrial burner,” Exp. Therm. Fluid Sci. 32(7), 1344–1353 (2008).
[Crossref]

Hardalupas, Y.

M. Orain and Y. Hardalupas, “Effect of fuel type on equivalence ratio measurements using chemiluminescence in premixed flames,” C. R. Mec. 338(5), 241–254 (2010).
[Crossref]

Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame 139(3), 188–207 (2004).
[Crossref]

Hartmann, M.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Hasegawa, T.

A. K. Gupta, S. Bolz, and T. Hasegawa, “Effect of air preheat temperature and oxygen concentration on flame structure and emission,” J. Energy Resour. Technol. 121(3), 209–216 (1999).
[Crossref]

He, A. Z.

Hentschel, J.

Hossain, A.

A. Hossain and Y. Nakamura, “A numerical study on the ability to predict the heat release rate using CH* chemiluminescence in non-sooting counter flow diffusion flames,” Combust. Flame 161(1), 162–172 (2014).
[Crossref]

Huang, C. M.

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

Huang, H.

H. Huang and Y. Zhang, “Digital colour image processing based measurement of premixed CH 4+ air and C 2 H 4+ air flame chemiluminescence,” Fuel 90(1), 48–53 (2011).
[Crossref]

H. Huang and Y. Zhang, “Dynamic application of digital image and colour processing in characterizing flame radiation features,” Meas. Sci. Technol. 21(8), 085202 (2010).
[Crossref]

H. Huang and Y. Zhang, “Flame colour characterization in the visible and infrared spectrum using a digital camera and image processing,” Meas. Sci. Technol. 19(8), 085406 (2008).
[Crossref]

Hudgins, D.

T. Upton, D. Verhoeven, and D. Hudgins, “High-resolution computed tomography of a turbulent reacting flow,” Exp. Fluids 50(1), 125–134 (2011).
[Crossref]

Iida, N.

D. Nikolic and N. Iida, “Effects of intake CO2 concentrations on fuel spray flame temperatures and soot formations,” Proc.- Inst. Mech. Eng. 221, 1567–1573 (2007).
[Crossref]

Ikeda, Y.

J. Kojima, Y. Ikeda, and T. Nakajima, “Basic aspects of OH(A), CH(A), and C2(d) chemiluminescence in the reaction zone of laminar methane-air premixed flames,” Combust. Flame 140(1), 34–45 (2005).
[Crossref]

Ishino, Y.

Y. Ishino, K. Takeuchi, S. Shiga, and N. Ohiwa, “Measurement of instantaneous 3D-Distribution of local burning velocity on a turbulent premixed flame by non-scanning 3D-CT reconstruction,” in 4th European Combustion Meeting (2009), pp, 14–17.

Jeon, C. H.

Y. K. Jeong, C. H. Jeon, and Y. J. Chang, “Evaluation of the equivalence ratio of the reacting mixture using intensity ratio of chemiluminescence in laminar partially premixed CH 4-air flames,” Exp. Therm. Fluid Sci. 30(7), 663–673 (2006).
[Crossref]

Jeong, Y. K.

Y. K. Jeong, C. H. Jeon, and Y. J. Chang, “Evaluation of the equivalence ratio of the reacting mixture using intensity ratio of chemiluminescence in laminar partially premixed CH 4-air flames,” Exp. Therm. Fluid Sci. 30(7), 663–673 (2006).
[Crossref]

Jiang, W.

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Kathrotia, T.

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

Kempf, A.

J. Wang, Y. Song, Z. H. Li, A. Kempf, and A. Z. He, “Multi-directional 3D flame chemiluminescence tomography based on lens imaging,” Opt. Lett. 40(7), 1231–1234 (2015).
[Crossref] [PubMed]

J. Floyd, P. Geipel, and A. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011).
[Crossref]

Kempf, A. M.

J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): high resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

Kirik, J. W.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Kojima, J.

J. Kojima, Y. Ikeda, and T. Nakajima, “Basic aspects of OH(A), CH(A), and C2(d) chemiluminescence in the reaction zone of laminar methane-air premixed flames,” Combust. Flame 140(1), 34–45 (2005).
[Crossref]

Krüger, J.

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

Lackner, A.

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

Lempert, W. R.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Letzgus, M.

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

Li, B.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

Li, F.

Li, X.

Li, Z.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

Li, Z. H.

Liu, C. C.

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

Liu, S.

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

Lu, G.

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

Ma, L.

Mance, J.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Manta, V.

Meier, W.

H. Ax and W. Meier, “Experimental investigation of the response of laminar premixed flames to equivalence ratio oscillations,” Combust. Flame 167, 172–183 (2016).
[Crossref]

Meyer, T. R.

Michael, J. B.

Miller, J.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Miller, J. D.

Moshammer, K.

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

Nakajima, T.

J. Kojima, Y. Ikeda, and T. Nakajima, “Basic aspects of OH(A), CH(A), and C2(d) chemiluminescence in the reaction zone of laminar methane-air premixed flames,” Combust. Flame 140(1), 34–45 (2005).
[Crossref]

Nakamura, Y.

A. Hossain and Y. Nakamura, “A numerical study on the ability to predict the heat release rate using CH* chemiluminescence in non-sooting counter flow diffusion flames,” Combust. Flame 161(1), 162–172 (2014).
[Crossref]

Nau, P.

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

Ng, W. B.

S. A. Farhat, W. B. Ng, and Y. Zhang, “Chemiluminescent emission measurement of a diffusion flame jet in a loudspeaker induced standing wave,” Fuel 84(14), 1760–1767 (2005).
[Crossref]

Nikolic, D.

D. Nikolic and N. Iida, “Effects of intake CO2 concentrations on fuel spray flame temperatures and soot formations,” Proc.- Inst. Mech. Eng. 221, 1567–1573 (2007).
[Crossref]

Nori, V.

V. Nori and J. Seitzman, “Evaluation of chemiluminescence as a combustion diagnostic under varying operating conditions,” in 46th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (2008), pp. 953.
[Crossref]

Nori, V. N.

V. N. Nori and J. M. Seitzman, “CH* chemiluminescence modeling for combustion diagnostics,” Proc. Combust. Inst. 32(1), 895–903 (2009).
[Crossref]

Ohiwa, N.

Y. Ishino, K. Takeuchi, S. Shiga, and N. Ohiwa, “Measurement of instantaneous 3D-Distribution of local burning velocity on a turbulent premixed flame by non-scanning 3D-CT reconstruction,” in 4th European Combustion Meeting (2009), pp, 14–17.

Ombrello, T.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Orain, M.

M. Orain and Y. Hardalupas, “Effect of fuel type on equivalence ratio measurements using chemiluminescence in premixed flames,” C. R. Mec. 338(5), 241–254 (2010).
[Crossref]

Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame 139(3), 188–207 (2004).
[Crossref]

Peltier, S.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Richter, M.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Riedel, U.

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

Rockwell, R. D.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Röder, M.

M. Röder, T. Dreier, and C. Schulz, “Simultaneous measurement of localized heat release with OH/CH2O-LIF imaging and spatially integrated OH* chemiluminescence in turbulent swirl flames,” Appl. Phys. B 107(3), 611–617 (2012).
[Crossref]

Rosell, J.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Roy, S.

Schuermans, B.

F. Biagioli, F. Güthe, and B. Schuermans, “Combustion dynamics linked to flame behaviour in a partially premixed swirled industrial burner,” Exp. Therm. Fluid Sci. 32(7), 1344–1353 (2008).
[Crossref]

Schulz, C.

M. Bozkurt, M. Fikri, and C. Schulz, “Investigation of the kinetics of OH* and CH* chemiluminescence in hydrocarbon oxidation behind reflected shock waves,” Appl. Phys. B 107(3), 515–527 (2012).
[Crossref]

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

M. Röder, T. Dreier, and C. Schulz, “Simultaneous measurement of localized heat release with OH/CH2O-LIF imaging and spatially integrated OH* chemiluminescence in turbulent swirl flames,” Appl. Phys. B 107(3), 611–617 (2012).
[Crossref]

Seipel, A.

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

Seitzman, J.

V. Nori and J. Seitzman, “Evaluation of chemiluminescence as a combustion diagnostic under varying operating conditions,” in 46th AIAA Aerospace Sciences Meeting and Exhibit, Aerospace Sciences Meetings (2008), pp. 953.
[Crossref]

Seitzman, J. M.

V. N. Nori and J. M. Seitzman, “CH* chemiluminescence modeling for combustion diagnostics,” Proc. Combust. Inst. 32(1), 895–903 (2009).
[Crossref]

Shiga, S.

Y. Ishino, K. Takeuchi, S. Shiga, and N. Ohiwa, “Measurement of instantaneous 3D-Distribution of local burning velocity on a turbulent premixed flame by non-scanning 3D-CT reconstruction,” in 4th European Combustion Meeting (2009), pp, 14–17.

Shy, S. S.

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

Sjöholm, J.

J. Sjöholm, J. Rosell, B. Li, M. Richter, Z. Li, X. Bai, and M. Aldén, “Simultaneous visualization of OH, CH, CH2O and toluene PLIF in a methane jet flame with varying degrees of turbulence,” Proc. Combust. Inst. 34(1), 1475–1482 (2013).
[Crossref]

Slipchenko, M.

J. Miller, S. Peltier, M. Slipchenko, J. Mance, T. Ombrello, J. Gord, and C. Carter, “Investigation of transient ignition processes in a model scramjet pilot cavity using simultaneous 100 kHz formaldehyde planar laser-induced fluorescence and CH* chemiluminescence imaging,” Proc. Combust. Inst. 000, 1–8 (2016).

Slipchenko, M. N.

Song, Y.

Starke, R.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Sun, D.

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

Sun, Z.

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

Suntz, R.

Sutton, J. A.

P. Allison, K. Frederickson, J. W. Kirik, R. D. Rockwell, W. R. Lempert, and J. A. Sutton, “Investigation of flame structure and combustion dynamics using CH2O PLIF and high-speed CH* chemiluminescence in a premixed dual-mode scramjet combustor,” in 54th AIAA Aerospace Sciences Meeting (2016), pp. 441.
[Crossref]

Takeuchi, K.

Y. Ishino, K. Takeuchi, S. Shiga, and N. Ohiwa, “Measurement of instantaneous 3D-Distribution of local burning velocity on a turbulent premixed flame by non-scanning 3D-CT reconstruction,” in 4th European Combustion Meeting (2009), pp, 14–17.

Upton, T.

T. Upton, D. Verhoeven, and D. Hudgins, “High-resolution computed tomography of a turbulent reacting flow,” Exp. Fluids 50(1), 125–134 (2011).
[Crossref]

Vandersickel, A.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Venkateswaran, P.

Verhoeven, D.

T. Upton, D. Verhoeven, and D. Hudgins, “High-resolution computed tomography of a turbulent reacting flow,” Exp. Fluids 50(1), 125–134 (2011).
[Crossref]

Vogel, K.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Wan, X.

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Wang, J.

Wright, Y. M.

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

Yan, Y.

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

Yang, C. H.

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

Yu, Q.

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Zhang, Y.

H. Huang and Y. Zhang, “Digital colour image processing based measurement of premixed CH 4+ air and C 2 H 4+ air flame chemiluminescence,” Fuel 90(1), 48–53 (2011).
[Crossref]

H. Huang and Y. Zhang, “Dynamic application of digital image and colour processing in characterizing flame radiation features,” Meas. Sci. Technol. 21(8), 085202 (2010).
[Crossref]

H. Huang and Y. Zhang, “Flame colour characterization in the visible and infrared spectrum using a digital camera and image processing,” Meas. Sci. Technol. 19(8), 085406 (2008).
[Crossref]

S. A. Farhat, W. B. Ng, and Y. Zhang, “Chemiluminescent emission measurement of a diffusion flame jet in a loudspeaker induced standing wave,” Fuel 84(14), 1760–1767 (2005).
[Crossref]

Zhou, H.

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

Zizak, G.

Appl. Opt. (3)

Appl. Phys. B (4)

T. Kathrotia, U. Riedel, A. Seipel, K. Moshammer, and A. Brockhinke, “Experimental and numerical study of chemiluminescent species in low-pressure flames,” Appl. Phys. B 107(3), 571–584 (2012).
[Crossref]

P. Nau, J. Krüger, A. Lackner, M. Letzgus, and A. Brockhinke, “On the quantification of OH*, CH*, and C2* chemiluminescence in flames,” Appl. Phys. B 107(3), 551–559 (2012).
[Crossref]

M. Röder, T. Dreier, and C. Schulz, “Simultaneous measurement of localized heat release with OH/CH2O-LIF imaging and spatially integrated OH* chemiluminescence in turbulent swirl flames,” Appl. Phys. B 107(3), 611–617 (2012).
[Crossref]

M. Bozkurt, M. Fikri, and C. Schulz, “Investigation of the kinetics of OH* and CH* chemiluminescence in hydrocarbon oxidation behind reflected shock waves,” Appl. Phys. B 107(3), 515–527 (2012).
[Crossref]

C. R. Mec. (1)

M. Orain and Y. Hardalupas, “Effect of fuel type on equivalence ratio measurements using chemiluminescence in premixed flames,” C. R. Mec. 338(5), 241–254 (2010).
[Crossref]

Combust. Flame (8)

Y. Hardalupas and M. Orain, “Local measurements of the time-dependent heat release rate and equivalence ratio using chemiluminescent emission from a flame,” Combust. Flame 139(3), 188–207 (2004).
[Crossref]

A. Hossain and Y. Nakamura, “A numerical study on the ability to predict the heat release rate using CH* chemiluminescence in non-sooting counter flow diffusion flames,” Combust. Flame 161(1), 162–172 (2014).
[Crossref]

S. S. Shy, Y. C. Chen, C. H. Yang, C. C. Liu, and C. M. Huang, “Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion,” Combust. Flame 153(4), 510–524 (2008).
[Crossref]

J. Kojima, Y. Ikeda, and T. Nakajima, “Basic aspects of OH(A), CH(A), and C2(d) chemiluminescence in the reaction zone of laminar methane-air premixed flames,” Combust. Flame 140(1), 34–45 (2005).
[Crossref]

H. Ax and W. Meier, “Experimental investigation of the response of laminar premixed flames to equivalence ratio oscillations,” Combust. Flame 167, 172–183 (2016).
[Crossref]

X. Li and L. Ma, “Capabilities and limitations of 3D flame measurements based on computed tomography of chemiluminescence,” Combust. Flame 162(3), 642–651 (2015).
[Crossref]

Z. Li, B. Li, Z. Sun, X. Bai, and M. Aldén, “Turbulence and combustion interaction: High resolution local flame front structure visualization using simultaneous single-shot PLIF imaging of CH, OH, and CH2O in a piloted premixed jet flame,” Combust. Flame 157(6), 1087–1096 (2010).
[Crossref]

J. Floyd, P. Geipel, and A. Kempf, “Computed tomography of chemiluminescence (CTC): instantaneous 3D measurements and phantom studies of a turbulent opposed jet flame,” Combust. Flame 158(2), 376–391 (2011).
[Crossref]

Exp. Fluids (1)

T. Upton, D. Verhoeven, and D. Hudgins, “High-resolution computed tomography of a turbulent reacting flow,” Exp. Fluids 50(1), 125–134 (2011).
[Crossref]

Exp. Therm. Fluid Sci. (2)

F. Biagioli, F. Güthe, and B. Schuermans, “Combustion dynamics linked to flame behaviour in a partially premixed swirled industrial burner,” Exp. Therm. Fluid Sci. 32(7), 1344–1353 (2008).
[Crossref]

Y. K. Jeong, C. H. Jeon, and Y. J. Chang, “Evaluation of the equivalence ratio of the reacting mixture using intensity ratio of chemiluminescence in laminar partially premixed CH 4-air flames,” Exp. Therm. Fluid Sci. 30(7), 663–673 (2006).
[Crossref]

Fuel (3)

S. A. Farhat, W. B. Ng, and Y. Zhang, “Chemiluminescent emission measurement of a diffusion flame jet in a loudspeaker induced standing wave,” Fuel 84(14), 1760–1767 (2005).
[Crossref]

A. Vandersickel, M. Hartmann, K. Vogel, Y. M. Wright, M. Fikri, R. Starke, C. Schulz, and K. Boulouchos, “The auto ignition of practical fuels at HCCI conditions: High-pressure shock tube experiments and phenomenological modeling,” Fuel 93, 492–501 (2012).
[Crossref]

H. Huang and Y. Zhang, “Digital colour image processing based measurement of premixed CH 4+ air and C 2 H 4+ air flame chemiluminescence,” Fuel 90(1), 48–53 (2011).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

D. Sun, G. Lu, H. Zhou, Y. Yan, and S. Liu, “Quantitative assessment of flame stability through image processing and spectral analysis,” IEEE Trans. Instrum. Meas. 64(12), 3323–3333 (2015).
[Crossref]

J. Energy Resour. Technol. (1)

A. K. Gupta, S. Bolz, and T. Hasegawa, “Effect of air preheat temperature and oxygen concentration on flame structure and emission,” J. Energy Resour. Technol. 121(3), 209–216 (1999).
[Crossref]

Meas. Sci. Technol. (2)

H. Huang and Y. Zhang, “Flame colour characterization in the visible and infrared spectrum using a digital camera and image processing,” Meas. Sci. Technol. 19(8), 085406 (2008).
[Crossref]

H. Huang and Y. Zhang, “Dynamic application of digital image and colour processing in characterizing flame radiation features,” Meas. Sci. Technol. 21(8), 085202 (2010).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

Y. Gao, Q. Yu, W. Jiang, and X. Wan, “Reconstruction of three-dimensional arc-plasma temperature fields by orthographic and double-wave spectral tomography,” Opt. Laser Technol. 42(1), 61–69 (2010).
[Crossref]

Opt. Lett. (2)

Proc. Combust. Inst. (4)

V. N. Nori and J. M. Seitzman, “CH* chemiluminescence modeling for combustion diagnostics,” Proc. Combust. Inst. 32(1), 895–903 (2009).
[Crossref]

J. Floyd and A. M. Kempf, “Computed Tomography of Chemiluminescence (CTC): high resolution and instantaneous 3-D measurements of a Matrix burner,” Proc. Combust. Inst. 33(1), 751–758 (2011).
[Crossref]

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Supplementary Material (2)

NameDescription
» Visualization 1: AVI (464 KB)      3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame at 0.4s
» Visualization 2: AVI (3792 KB)      3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame in the combustion process

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Figures (14)

Fig. 1
Fig. 1

The transmissivity of double-channel bandpass filter and the spectral sensitivity of the color camera.

Fig. 2
Fig. 2

CH* and C2* intensity retrieval. (a) conventional method using linear interpolation, (b) multispectral separation algorithm.

Fig. 3
Fig. 3

Verification of flame chemiluminescence multispectral separation algorithm. (a) captured mixed intensities of lasers with various green to blue ratio, (b) and (c) retrieved green and blue intensities using proposed multispectral separation algorithm.

Fig. 4
Fig. 4

Verification results of flame chemiluminescence multispectral separation algorithm.

Fig. 5
Fig. 5

Experimental setup for propane combustion diagnostics.

Fig. 6
Fig. 6

Coordinate system used in FCT system calibration.

Fig. 7
Fig. 7

Re-projection results in all 12 directions. Red dots in zoomed-in plots indicate re-projected results.

Fig. 8
Fig. 8

Re-projection deviation of the sample points in all 12 directions.

Fig. 9
Fig. 9

Projectons of non-axisymmetric propane-air diffusion flame from 12 directions at 0.4s.

Fig. 10
Fig. 10

Chemiluminescence emission intensity images of CH* and C2* from 12 directions at 0.4s.

Fig. 11
Fig. 11

3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame from four directions at 0.4s. (A movie is available online. See Visualization 1)

Fig. 12
Fig. 12

3D radical concentration distribution of CH* and C2* of non-axisymmetic propane-air diffusion flame at different moments. (A movie is available online. See Visualization 2)

Fig. 13
Fig. 13

3D C2* to CH* intensity ratio of non-axisymmetic propane diffusion flame at different moments.

Fig. 14
Fig. 14

Normalized reconstructed C2* and CH* components of selected sections.

Tables (2)

Tables Icon

Table 1 Verification details of flame chemiluminescence multispectral separation algorithm.

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Table 2 Calibrated camera parameters.

Equations (15)

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εI=P
ε = [ ε 11 ε 12 ε 21 ε 22 ],I =[ I CH I C2 ] ,P =[ p b p g ] .
{ ε 11 = λ w b ( f λ b λ ) / w b ε 12 = λ w g ( f λ b λ ) / w g ε 21 = λ w b ( f λ g λ ) / w b ε 22 = λ w g ( f λ g λ ) / w g
{ I CH = p b ε 22 - p g ε 12 ε 11 ε 22 - ε 12 ε 21 I C2 = p g ε 11 - p b ε 21 ε 11 ε 22 - ε 12 ε 21
RMSE= { i=1 N [ ( ρ GBa ) i ( ρ GB m ) i ] 2 } 1/2 N ( ρ GBm ) max
[ x c y c z c ]=R[ x w y w z w ]+T
R =[ r 1 r 2 r 3 r 4 r 5 r 6 r 7 r 8 r 9 ] =[ cosϕcosψ cosψsinϕ sinψ cosϕsinψsinθcosθsinϕ sinϕsinψsinθ+cosϕcosθ sinθcosψ cosϕsinψcosθ+sinϕsinθ sinϕsinψcosθsinθcosϕ cosψcosθ ]
T=[ T x T y T z ]
x i = z 0 x c z c , y i = z 0 y c z c .
By=b
B=[ x w1 y w1 z w1 1 0 0 0 0 x i1 x w1 x i1 y w1 x i1 z w1 0 0 0 0 x w1 y w1 z w1 1 y i1 x w1 y i1 y w1 y i1 z w1 x wS y wS z wS 1 0 0 0 0 x iS x wS x iS y wS x iS z wS 0 0 0 0 x wS y wS z wS 1 y iS x wS y iS y wS y iS z wS ]
y= [ Z 0 r 1 T z Z 0 r 2 T z Z 0 r 3 T z Z 0 T x T z Z 0 r 4 T z Z 0 r 5 T z Z 0 r 6 T z Z 0 T y T z r 7 T z r 8 T z r 9 T z ] T
b= [ x i1 y i1 x iS y iS ] T
ΔG n×ΔP Z 0 T z
f i (h+1) = f i (h) ×(1 α w ij i=1 N ( w ij ) 2 (1 I j i=1 N w ij f i (h) ) 1jp×q

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