Abstract

A procedure is proposed, denoted as the corrected laser-induced fluorescence (LIF) method, that reduces the error associated with the unavoidable photodissociation of O2 molecules that has limited the measurement of oxygen–atom concentrations in the past. Two different laser intensities are employed, and the two signals that are obtained with two-photon LIF diagnostics are used to correct for the photolysis error. We measured oxygen–atom concentrations using this method at 33 locations in lean and rich flames. Results are compared with values determined by use of two independent techniques: the partial equilibrium method and equilibrium calculations. The measurements also quantify the shot noise, the photolysis errors, and the critical laser intensity required to avoid photolysis errors.

© 2001 Optical Society of America

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References

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  1. J. E. M. Goldsmith, “Photochemical effects in two-photon-excited fluorescence detection of atomic oxygen in flames,” Appl. Opt. 26, 3566–3572 (1987).
    [CrossRef] [PubMed]
  2. K. C. Smyth, P. J. H. Tjossem, “Relative H-atom and O-atom concentration measurements in a laminar, methane/air diffusion flame,” in Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1829–1837.
  3. M. J. Dyer, L. D. Pfefferle, D. R. Crosley, “Laser-induced fluorescence measurement of oxygen atoms above a catalytic combustor surface,” Appl. Opt. 29, 111–118 (1990).
    [CrossRef] [PubMed]
  4. J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
    [CrossRef]
  5. U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.
  6. M. Alden, H. M. Hertz, S. Svanberg, S. Wallin, “Imaging laser-induced fluorescence of oxygen atoms in a flame,” Appl. Opt. 23, 3255–3257 (1984).
    [CrossRef] [PubMed]
  7. R. S. Barlow, G. J. Fiechtner, J.-Y. Chen, “Oxygen atom concentrations and NO production rates in a turbulent H2/N2 jet flame,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 2199–2205.
    [CrossRef]
  8. W. K. Bischel, B. E. Perry, D. R. Crosley, “Detection of fluorescence from O and N atoms induced by two-photon absorption,” Appl. Opt. 21, 1419–1429 (1982).
    [CrossRef] [PubMed]
  9. J. T. Salmon, N. M. Laurendeau, “Absolute concentration measurements of atomic-hydrogen in subatmospheric premixed H2/O2/N2 flat flames with photoionization controlled-loss spectroscopy,” Appl. Opt. 26, 2881–2891 (1987).
    [CrossRef] [PubMed]
  10. J. E. M. Goldsmith, “Investigation of simultaneous two-photon H and single photon OH excitation in flames using a single dye laser,” Appl. Opt. 29, 4841–4842 (1990).
    [CrossRef] [PubMed]
  11. A. M. Miziolek, M. A. DeWilde, “Multiphoton photochemical and collisional effects during oxygen-atom flame detection,” Opt. Lett. 9, 390–392 (1984).
    [CrossRef] [PubMed]
  12. F. H. Myhr, “Optical measurements of atomic oxygen concentration, temperature and nitric oxide production rates in flames,” Ph.D. dissertation (Department of Aerospace Engineering, University of Michigan, Ann Arbor, Mich., 1998).
  13. D. J. Bamford, M. J. Dyer, W. K. Bischel, “Single frequency laser measurements of two-photon cross sections and Doppler-free spectra for atomic oxygen,” Phys. Rev. A 36, 3497–3500 (1987).
    [CrossRef] [PubMed]
  14. D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
    [CrossRef] [PubMed]
  15. J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
    [CrossRef]
  16. R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
    [CrossRef]
  17. V. T. Morgan, “The overall convective heat transfer from smooth circular cylinders,” in Advances in Heat Transfer (Academic, New York, 1975), Vol. 9., pp. 199–264.
    [CrossRef]
  18. R. W. Dibble, R. E. Hollenbach, “Laser Rayleigh thermometry in turbulent flames,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1980), pp. 1489–1499.
  19. W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
    [CrossRef]

1997 (1)

R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
[CrossRef]

1993 (2)

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

1990 (2)

1988 (1)

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

1987 (3)

1986 (1)

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
[CrossRef] [PubMed]

1984 (2)

1982 (1)

Alden, M.

Bamford, D. J.

D. J. Bamford, M. J. Dyer, W. K. Bischel, “Single frequency laser measurements of two-photon cross sections and Doppler-free spectra for atomic oxygen,” Phys. Rev. A 36, 3497–3500 (1987).
[CrossRef] [PubMed]

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
[CrossRef] [PubMed]

Barlow, R. S.

R. S. Barlow, G. J. Fiechtner, J.-Y. Chen, “Oxygen atom concentrations and NO production rates in a turbulent H2/N2 jet flame,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 2199–2205.
[CrossRef]

Bernstein, J. S.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Bertagnolli, K. E.

R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
[CrossRef]

Bischel, W. K.

D. J. Bamford, M. J. Dyer, W. K. Bischel, “Single frequency laser measurements of two-photon cross sections and Doppler-free spectra for atomic oxygen,” Phys. Rev. A 36, 3497–3500 (1987).
[CrossRef] [PubMed]

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
[CrossRef] [PubMed]

W. K. Bischel, B. E. Perry, D. R. Crosley, “Detection of fluorescence from O and N atoms induced by two-photon absorption,” Appl. Opt. 21, 1419–1429 (1982).
[CrossRef] [PubMed]

Bittner, J.

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.

Chen, J.-Y.

R. S. Barlow, G. J. Fiechtner, J.-Y. Chen, “Oxygen atom concentrations and NO production rates in a turbulent H2/N2 jet flame,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 2199–2205.
[CrossRef]

Choi, J. B.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Cool, T. A.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Crosley, D. R.

DeWilde, M. A.

Dibble, R. W.

R. W. Dibble, R. E. Hollenbach, “Laser Rayleigh thermometry in turbulent flames,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1980), pp. 1489–1499.

Drake, M. C.

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

Driscoll, J. F.

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

Dyer, M. J.

M. J. Dyer, L. D. Pfefferle, D. R. Crosley, “Laser-induced fluorescence measurement of oxygen atoms above a catalytic combustor surface,” Appl. Opt. 29, 111–118 (1990).
[CrossRef] [PubMed]

D. J. Bamford, M. J. Dyer, W. K. Bischel, “Single frequency laser measurements of two-photon cross sections and Doppler-free spectra for atomic oxygen,” Phys. Rev. A 36, 3497–3500 (1987).
[CrossRef] [PubMed]

Fein, A.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Fiechtner, G. J.

R. S. Barlow, G. J. Fiechtner, J.-Y. Chen, “Oxygen atom concentrations and NO production rates in a turbulent H2/N2 jet flame,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 2199–2205.
[CrossRef]

Goldsmith, J. E. M.

Goss, L. P.

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

Hancock, R. D.

R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
[CrossRef]

Hertz, H. M.

Hollenbach, R. E.

R. W. Dibble, R. E. Hollenbach, “Laser Rayleigh thermometry in turbulent flames,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1980), pp. 1489–1499.

Howard, S. L.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Jusinski, L. E.

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
[CrossRef] [PubMed]

Just, T.

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.

Kohse-Hoinghaus, K.

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.

Laurendeau, N. M.

Locke, R. J.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Lucht, R. P.

R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
[CrossRef]

Meier, U.

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.

Miziolek, A. M.

Miziolek, A. W.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Morgan, V. T.

V. T. Morgan, “The overall convective heat transfer from smooth circular cylinders,” in Advances in Heat Transfer (Academic, New York, 1975), Vol. 9., pp. 199–264.
[CrossRef]

Myhr, F. H.

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

Perry, B. E.

Pfefferle, L. D.

Roberts, W. L.

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

Salmon, J. T.

Sausa, R. C.

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

Smyth, K. C.

K. C. Smyth, P. J. H. Tjossem, “Relative H-atom and O-atom concentration measurements in a laminar, methane/air diffusion flame,” in Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1829–1837.

Svanberg, S.

Tjossem, P. J. H.

K. C. Smyth, P. J. H. Tjossem, “Relative H-atom and O-atom concentration measurements in a laminar, methane/air diffusion flame,” in Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1829–1837.

Wallin, S.

Appl. Opt. (6)

Chem. Phys. Lett. (1)

J. Bittner, K. Kohse-Hoinghaus, U. Meier, T. Just, “Quenching of two-photon excited H (3S, 3D) and O (3P2, 1, 0) atoms by rare gases and small molecules,” Chem. Phys. Lett. 143, 571–576 (1988).
[CrossRef]

Combust. Flame (3)

R. D. Hancock, K. E. Bertagnolli, R. P. Lucht, “Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat flame burner,” Combust. Flame 109(3), 323–331 (1997).
[CrossRef]

J. S. Bernstein, A. Fein, J. B. Choi, T. A. Cool, R. C. Sausa, S. L. Howard, R. J. Locke, A. W. Miziolek, “Laser based flame species profile measurements: a comparison with flame model predictions,” Combust. Flame 92, 85–105 (1993).
[CrossRef]

W. L. Roberts, J. F. Driscoll, M. C. Drake, L. P. Goss, “Images of the quenching of a flame by a vortex to quantify regimes of turbulent combustion,” Combust. Flame 94, 58–69 (1993).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

D. J. Bamford, M. J. Dyer, W. K. Bischel, “Single frequency laser measurements of two-photon cross sections and Doppler-free spectra for atomic oxygen,” Phys. Rev. A 36, 3497–3500 (1987).
[CrossRef] [PubMed]

D. J. Bamford, L. E. Jusinski, W. K. Bischel, “Absolute two-photon absorption and three-photon ionization cross sections for atomic oxygen,”Phys. Rev. A 34(1), 185–198 (1986).
[CrossRef] [PubMed]

Other (6)

R. S. Barlow, G. J. Fiechtner, J.-Y. Chen, “Oxygen atom concentrations and NO production rates in a turbulent H2/N2 jet flame,” in Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 2199–2205.
[CrossRef]

V. T. Morgan, “The overall convective heat transfer from smooth circular cylinders,” in Advances in Heat Transfer (Academic, New York, 1975), Vol. 9., pp. 199–264.
[CrossRef]

R. W. Dibble, R. E. Hollenbach, “Laser Rayleigh thermometry in turbulent flames,” in Eighteenth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1980), pp. 1489–1499.

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

U. Meier, J. Bittner, K. Kohse-Hoinghaus, T. Just, “Discussion of two-photon laser excited fluorescence as a method for quantitative detection of oxygen atoms in flames,” in Twenty-Second Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1988), pp. 1887–1896.

K. C. Smyth, P. J. H. Tjossem, “Relative H-atom and O-atom concentration measurements in a laminar, methane/air diffusion flame,” in Twenty-Third Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1990), pp. 1829–1837.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the Hencken flat flame burner and the LIF diagnostics used to measure O–atom concentrations. WEX is a wavelength extender.

Fig. 2
Fig. 2

Temperatures measured in the three flames with five different thermocouple bead diameters. Each open symbol represents the average of 300 thermocouple samples, corrected for radiation losses. Filled symbols are temperatures measured with Rayleigh scattering.

Fig. 3
Fig. 3

OH concentrations measured in the three flames (filled symbols) compared with calculated equilibrium values (dashed curves). Also shown is the residence time of gas in the flame (τ).

Fig. 4
Fig. 4

Measured dependence of the LIF signal on the laser intensity. Each data point represents the average of 500 measurements. The flame equivalence ratio is 0.80; for methane air, T = 1670 K; n O = 3 × 10-4 mol/m3.

Fig. 5
Fig. 5

O–atom concentrations measured with the corrected LIF method [Eq. (9)] in the three flames (filled symbols) compared with values measured with the PEM (open symbols) and calculated equilibrium values (dashed curves). I 1 = 11 MW/cm2, I 2 = 39 MW/cm2. Each data point is the average for 1000 laser pulses.

Fig. 6
Fig. 6

Photolysis correction factor C in the corrected LIF method. Each value of C was determined with Eq. (10) and measured values of signals S 1 and S 2 corresponding to laser intensities I 1 = 11 MW/cm2 and I 2 = 39 MW/cm2.

Fig. 7
Fig. 7

Measured values of the quantity B in the photolysis term in the fluorescence equation [Eq. (4)] determined with Eqs. (7) and (8).

Fig. 8
Fig. 8

Noise-to-signal ratio measured for single-shot two-photon LIF determination of O–atom concentration. Laser intensity is 11 MW/cm2 and energy per pulse is 0.3 mJ.

Equations (14)

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

dn1/dt=ΦnO2σO2+nMσM,
dn2/dt=Φn1σO,
dn3/dt=Φn2σO-n3Q3x+A32.
S=AnOI2+ABI3.
A=K1σO2fOA32/Q3xΔt2d2Lhν2,
B=K2nO2σO2fO2Δt/hν+K3nMσMfMΔt/hν.
S1=AnOI12+ABI13,
S2=AnOI22+ABI23.
nO=nO,refS1/Sref1-C/1-CreffO/fO,ref×Q3,x,ref/Q3,x.
C=S2/I22-S1/I12I1/I2-I1/S1/I12.
nO=KpnOH2/nH2O.
nOH=nOH,refSOH/SOH,refQOH,ref/QOHfOH/fOH,ref.
T=Tw+εσdwNu-1k-1Tw4.
Imax=I2-I1S2/I22/S2/I22-S1/I12-I2.

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