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State-to-state modeling of a recombining nitrogen plasma experiment
Christophe O. Laux, Richard J. Gessman, Laurent Pierrot
Ecole Centrale Paris, Laboratoire EM2C-CNRSand
Stanford University, Mechanical Engineering Dept.
Symposium in Honour of Prof Mario Capitelli on the Occasion of His 70th BirthdayUniversità degli Studi di Bari - Aldo Moro
January 31- February 1, 2011
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Recombining nitrogen plasma at atmospheric pressure
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Recombining nitrogen plasma at atmospheric pressure
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Recombining nitrogen plasma at atmospheric pressure
TEST-SECTION INLET:Nitrogen plasma in LTE at 7200 K
(N2 highly dissociated)v ~ 1 km/s
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Recombining nitrogen plasma at atmospheric pressure
TEST-SECTION INLET:Nitrogen plasma in LTE at 7200 K
(N2 highly dissociated)v ~ 1 km/s
Fast cooling imposed by water-cooled wall at 300 K
Q
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Recombining nitrogen plasma at atmospheric pressure
TEST-SECTION INLET:Nitrogen plasma in LTE at 7200 K
(N2 highly dissociated)v ~ 1 km/s
Fast cooling imposed by water-cooled wall at 300 K
QResidence time:
250 µs
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Recombining nitrogen plasma at atmospheric pressure
TEST-SECTION INLET:Nitrogen plasma in LTE at 7200 K
(N2 highly dissociated)
TEST-SECTION EXIT:Nitrogen plasma in nonequilibrium
at T = 4850 K(N population partly frozen)
v ~ 1 km/s
Fast cooling imposed by water-cooled wall at 300 K
QResidence time:
250 µs
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Emission Spectrum at Test-Section Inlet
• Test-section inlet: Plasma close to LTE
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Emission Spectrum at Test-Section Exit
• Emitting states (N2+ B, N2 C, N2 B) are overpopulated with
respect to LTE.
N2 (C→B) N2+ (B → X) N2 (B → A)
290 295 3000
0.5
1.0
1.5
2.0
2.5
3.0In
tens
ity (µ
W /
cm 2 sr
)
350 375 400 4250
2.0
4.0
6.0
8.0
10.0
Experiment SPECAIR (LTE)
500 600 700 8000
0.5
1.0
1.5
2.0
Wavelength (nm)
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Analysis of the N2 B-A spectrum at exit of test-section
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Analysis of the N2 B-A spectrum at exit of test-section
Overpopulation Factors ρv
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Analysis of the N2 B-A spectrum at exit of test-section
Overpopulation Factors ρv
• Non-Boltzmann distribution of the vibrational levels⇒ CR model needed to analyze experiment
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Vibrationally Specific State-to-State CR Model of nitrogen
• Predict nonequilibrium populations of• N (22 electronic levels)• N+ (1 electronic level)• N2 X (v=0-47), A (0-27), B (0-30), W(0-37), B’ (0-41), C (0-4)• N2
+ X (v=0-52), A (0-63), B (0-24)• Electrons⇒ 357 states + electrons
• Input parameters• Number density of N nuclei and electrons• P• Te: kinetic temperature of electrons (Maxwellian)• Tg: kinetic temperature of heavy species (Maxwellian) • Trot = Tg
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Vibrationally Specific State-to-State CR Model of nitrogen
~46,000 state-to-state reactions
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• Vibrational state-specific reactions considered:• Electron-impact excitation of N, N2, N2
+
• Electron-impact ionization of N and N2
• Electron and heavy-particle impact dissociation of N2 and N2+
• Dissociative recombination of N2+
• Charge exchange: N2+ + N ⇔ N2 + N+
• VE: electron-impact vibrational excitation of N2 X• VT: vibrational-translational transfer• VV: vibrational-vibrational transfer• Radiation• Predissociation
Collisional-Radiative Model of N2
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Assumptions for CR simulations at test-section exit
• P=1 atm and T=4850 K
• ne=7.3×1013 cm-3 (measured value)
• nN adjusted to provide best match to experiment
• EEDF is Maxwellian(Capitelli et al., JTHT, 12, 478-481, 1998)
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CR model results: vibronic distributions
T = 4850 K, P = 1 atm, ρe = 180, ρN = 8.1
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CR model results: vibronic distributions
T = 4850 K, P = 1 atm, ρe = 180, ρN = 8.1
• Peak at v=13 is due to inverse predissociation: N + N → N2 (B, v=13)
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CR model results: comparison with experiment
T = 4850 K, P = 1 atm, ρe = 180, ρN = 8.1
• Peak at v=13 is due to inverse predissociation: N + N → N2 (B, v=13)
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Conclusions
State-to-state model developed to predict vibrational populations in ground and excited states of nitrogen
Good agreement with measured vibrational distributions
Overpopulation of N2 B, v=13 provides a convenient way to measure absolute densities of N atoms by emission spectroscopy (application to expanding flows,…)
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Conclusions
State-to-state model developed to predict vibrational populations in ground and excited states of nitrogen
Good agreement with measured vibrational distributions
Overpopulation of N2 B, v=13 provides a convenient way to measure absolute densities of N atoms by emission spectroscopy (application to expanding flows,…)
JOYEUX ANNIVERSAIRE MARIO!
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Predissociation/Inverse Predissociation
• Predissociation:N2 (B,v=13) ⇒ N(4So) + N (4So)
• Inverse PredissociationN(4So) + N (4So) ⇒ N2 (B,v=13)
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Rate equation for N2, B, v=13
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Rate equation for N2, B, v=13
2.6x108 s-1
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Rate equation for N2, B, v=13
2.6x108 s-1
2x106 s-1
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Rate equation for N2, B, v=13
2.6x108 s-1
2x106 s-1 6x106 s-1
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Rate equation for N2, B, v=13
2.6x108 s-1
2x106 s-1 6x106 s-1 ~0 s-1
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Rate equation for N2, B, v=13
2.6x108 s-1
2x106 s-1 6x106 s-1 ~0 s-1 4.2x106 s-1
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Rate equation for N2, B, v=13
N2 (B,v=13) ⇔ N + N
2.6x108 s-1
2x106 s-1 6x106 s-1 ~0 s-1 4.2x106 s-1
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N atom concentration
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N atom concentration
• Diagnostic tool for ground state N concentration:• ρB,v=13 = 66±4 (measured) ⇒ ρN = 8.1±0.3• [N]eq,4850K = 1.8×1016 cm-3
⇒ [N] = 1.5±0.4 ×1017 cm-3
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Nonequilibrium distribution of N2 B state in arcjet measurements at Johnston Space Center
Experimental set-up N2 B state vibrational populations as a function of distance from body
Blackwell, Scott, and Arepalli, JSC, 1997
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Rotational temperature at 15 cm using N2+
• Best fit: Trot = Tvib = 4850 ± 100 K
SPECAIR
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Rotational Temperature at 15 cm using N2+
SPECAIR
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Rotational temperature: [R(70)+P(97)] vs. Bandhead
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Calculation of vibrational state specific rate coeff.
Example: N2 (X, v” ) + e → N2+ (A, v’ ) + e + e
• Rovibrational state-specific rate coefficient:
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Calculation of vibrational state specific rate coeff.
Example: N2 (X, v” ) + e → N2+ (A, v’ ) + e + e
• Rovibrational state-specific rate coefficient:
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Calculation of vibrational state specific rate coeff.
• Average over rotational levels (in Boltzmann distribution at Tr):
Example: N2 (X, v” ) + e → N2+ (A, v’ ) + e + e
• Rovibrational state-specific rate coefficient: