State-to-state modeling of a recombining nitrogen plasma experiment

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

2


TEST-SECTION INLET:Nitrogen plasma in LTE at 7200 K

(N2 highly dissociated)v ~ 1 km/s

2




Fast cooling imposed by water-cooled wall at 300 K

Q

2





QResidence time:

250 µs

2



(N2 highly dissociated)

TEST-SECTION EXIT:Nitrogen plasma in nonequilibrium

at T = 4850 K(N population partly frozen)

v ~ 1 km/s


QResidence time:

250 µs

3

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)

5

Analysis of the N2 B-A spectrum at exit of test-section

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Overpopulation Factors ρv

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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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2.6x108 s-1

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2.6x108 s-1

2x106 s-1

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2.6x108 s-1

2x106 s-1 6x106 s-1

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2.6x108 s-1

2x106 s-1 6x106 s-1 ~0 s-1

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2.6x108 s-1

2x106 s-1 6x106 s-1 ~0 s-1 4.2x106 s-1

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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.

• Average over rotational levels (in Boltzmann distribution at Tr):

Example: N2 (X, v” ) + e → N2+ (A, v’ ) + e + e

• Rovibrational state-specific rate coefficient:

State-to-state modeling of a recombining nitrogen plasma experiment

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