Lubomir A. Ribarov,1,2
Shengteng Hu,1
Joseph A. Wehrmeyer,1,3
and Robert W. Pitz1
1When this research was performed, the authors were with the Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37235.
2L. Ribarov (ribarola@utrc.utc.com) is now with the Combustion Operability & Emissions Group, United Technologies Research Center, 411 Silver Lane, MS 129-29, East Hartford, Connecticut 06108.
3Aerospace Testing Alliance, 1099 Avenue C, Arnold Air Force Base, Tennessee 37389.
Lubomir A. Ribarov, Shengteng Hu, Joseph A. Wehrmeyer, and Robert W. Pitz, "Hydroxyl tagging velocimetry method optimization: signal intensity and spectroscopy," Appl. Opt. 44, 6616-6626 (2005)
The previously demonstrated nonintrusive time-of-flight molecular velocity tagging method, hydroxyl tagging velocimetry (HTV), has shown the capability of operating both at room temperature and in flames. Well-characterized jets of either air (nonreacting cases) or hydrogen–air diffusion flames (reacting cases) are employed. A 7 × 7 OH line grid is generated first through the single-photon photodissociation of H2O by a ~193 nm pulsed narrowband ArF excimer laser and is subsequently revealed by a read laser sheet through fluorescence caused by A2∑+(v′ = 3) ← X2Πi(v″ = 0), A2∑+(v′ = 1) ← X2Πi(v″ = 0), or A2∑+(v′ = 0) ← X2Πi(v″ = 0) pumping at ~248, ~282, or ~308 nm, respectively. A detailed discussion of the spectroscopy and relative signal intensity of these various read techniques is presented, and the implications for optimal HTV performance are discussed.
Robert W. Pitz, Michael D. Lahr, Zachary W. Douglas, Joseph A. Wehrmeyer, Shengteng Hu, Campbell D. Carter, Kuang-Yu Hsu, Chee Lum, and Manoochehr M. Koochesfahani Appl. Opt. 44(31) 6692-6700 (2005)
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Pump laser wavelength (nm).
Pump laser energy (mJ/pulse at 10 Hz repetition rate).
Einstein A coefficient (×106 s−1).
Einstein B coefficient (×1012 cm2/J s).
Quenching and predissociation, where Q ≫ P for the lower OH transitions, P ≫ Q for the higher OH transitions (×109s−1).
Fluorescence yield, y = A/(A + Q + P) (%).
Transition probability, Einstein B coefficient, normalized to B at (0 ← 0).
Relative fluorescence, NP/C = f1(T)B10Eν[A10(A10 + Q10 + P)−1] (×10−4), and for an example calculation for the (1 ← 0) OH transition: f1(T) = 0.03, fractional (Boltzmann) population of the lower laser coupled state, used for all transitions; B10, Einstein B coefficient for the (1 ← 0) OH transition; A10, Einstein A coefficient for the (1 ← 0) OH transition; Q10, quenching rate for the (1 ← 0) OH transition; P10, predissociation rate for the (1 ← 0) OH transition (here P10 = 0); Eν = 1.667 × 10−12 J cm−2 Hz−1 (dye laser spectral fluence, 0.4 cm2, 15 GHz); C = η(Ω/4π)nOHV, where η = 0.6 (transmission efficiency of collecting optics), Ω/4π = 0.0001 (f/25 light collection optics), nOH = 3 × 1015 cm−3 (297 K, 1 atm, RH 40%) for ~1% H2O photodissociation, V = 0.045 mm3 (collection volume, based on a 500 μm thick laser sheet, 300 μm × 300 μm laser beam cross section).
SNR = (Npηpc/K)1/2, for GeK ≫ 1, when shot noise dominates camera noise, where Ge is the overall electron gain (array detector electrons/photocathode electrons), ηpc = 0.1 (photocathode quantum efficiency), K ≅ 2 (noise factor of intensifier, usually 1 ≤ K ≤ 3).
Signal, K SNR2 = ηpcNp (number of detected photons).
Table 2
Minimum OH Concentration Needed to Exceed Detection Threshold of SNR > 4 or Np > 300
Population fraction.
Cross section, e.g., σ(0,0,1) = 460σ(0,0,0) = 460(8 × 10−22 cm2) = 3.68 × 10−19 cm2. nOHi/ni = (Eoσiλ)/(hcA), where Eo = 10 mJ (typical laser beam energy in a 7 × 7 grid), λ = 193 nm, h = 6.626 × 10−34 J s (Planck’s constant), c = 3 × 108 m/s, A = 7.07 × 10−8 m2 (for a typical 300 μm diameter laser beam) (when nOHi/ni > 1, complete dissociation has occurred and nOHi/ni has been set to 1.0). nOH = fi(nH2O)(nOHi/ni), e.g., nOHi = f0,0,1(nH2O)(nOH/n0,0,1) = 0.0396(9.15 × 1017 cm−3)(1) = 3.6 × 1016 cm−3.
The laser beam absorption in the weak limit is ΔE/Eo = σinOHL for L = 2.5 cm. When the transition is bleached, ΔE/E0 = hcLAni/(λEo).
Tables (3)
Table 1
Comparison of Relative OH Fluorescence Signals for Various Pump Lasers (nOH = 3 × 1015 cm−3)
Pump laser wavelength (nm).
Pump laser energy (mJ/pulse at 10 Hz repetition rate).
Einstein A coefficient (×106 s−1).
Einstein B coefficient (×1012 cm2/J s).
Quenching and predissociation, where Q ≫ P for the lower OH transitions, P ≫ Q for the higher OH transitions (×109s−1).
Fluorescence yield, y = A/(A + Q + P) (%).
Transition probability, Einstein B coefficient, normalized to B at (0 ← 0).
Relative fluorescence, NP/C = f1(T)B10Eν[A10(A10 + Q10 + P)−1] (×10−4), and for an example calculation for the (1 ← 0) OH transition: f1(T) = 0.03, fractional (Boltzmann) population of the lower laser coupled state, used for all transitions; B10, Einstein B coefficient for the (1 ← 0) OH transition; A10, Einstein A coefficient for the (1 ← 0) OH transition; Q10, quenching rate for the (1 ← 0) OH transition; P10, predissociation rate for the (1 ← 0) OH transition (here P10 = 0); Eν = 1.667 × 10−12 J cm−2 Hz−1 (dye laser spectral fluence, 0.4 cm2, 15 GHz); C = η(Ω/4π)nOHV, where η = 0.6 (transmission efficiency of collecting optics), Ω/4π = 0.0001 (f/25 light collection optics), nOH = 3 × 1015 cm−3 (297 K, 1 atm, RH 40%) for ~1% H2O photodissociation, V = 0.045 mm3 (collection volume, based on a 500 μm thick laser sheet, 300 μm × 300 μm laser beam cross section).
SNR = (Npηpc/K)1/2, for GeK ≫ 1, when shot noise dominates camera noise, where Ge is the overall electron gain (array detector electrons/photocathode electrons), ηpc = 0.1 (photocathode quantum efficiency), K ≅ 2 (noise factor of intensifier, usually 1 ≤ K ≤ 3).
Signal, K SNR2 = ηpcNp (number of detected photons).
Table 2
Minimum OH Concentration Needed to Exceed Detection Threshold of SNR > 4 or Np > 300
Population fraction.
Cross section, e.g., σ(0,0,1) = 460σ(0,0,0) = 460(8 × 10−22 cm2) = 3.68 × 10−19 cm2. nOHi/ni = (Eoσiλ)/(hcA), where Eo = 10 mJ (typical laser beam energy in a 7 × 7 grid), λ = 193 nm, h = 6.626 × 10−34 J s (Planck’s constant), c = 3 × 108 m/s, A = 7.07 × 10−8 m2 (for a typical 300 μm diameter laser beam) (when nOHi/ni > 1, complete dissociation has occurred and nOHi/ni has been set to 1.0). nOH = fi(nH2O)(nOHi/ni), e.g., nOHi = f0,0,1(nH2O)(nOH/n0,0,1) = 0.0396(9.15 × 1017 cm−3)(1) = 3.6 × 1016 cm−3.
The laser beam absorption in the weak limit is ΔE/Eo = σinOHL for L = 2.5 cm. When the transition is bleached, ΔE/E0 = hcLAni/(λEo).
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