nonequilibrium thermodynamics laboratories spontaneous raman scattering measurements of n 2...

Nonequilibrium Thermodynamics Laboratories

Spontaneous Raman Scattering Measurements of N2 Vibrational Distribution Function in Nanosecond Pulsed Discharge

A. Roettgen, I.V. Adamovich, and W.R. Lempert

Michael A. Chaszeyka Nonequilibrium Thermodynamics LaboratoriesDepartment of Mechanical and Aerospace Engineering

68th International Symposium on Molecular Spectroscopy, Columbus, OH 17-21 June 2013


I. Background/Objectives

II. Experimental apparatus and pulse characteristics

III.Data processing

IV. Experimental results

V. Conclusions/Future Work

Outline


Background / Objectives

Motivation for study of nsec pulsed discharges:• Further understanding of fundamental energy loading and energy transfer

processes in these discharge environments.• Applications include: plasma assisted combustion (Starikovskii 2005,

Starikovskaya 2006, Adamovich 2009), electrically-excited discharge laser development (Adamovich 2008), and plasma flow control (Roupassov 2009, Nishihara 2011).

Previous pin-to-pin discharge VDF studies:• Coherent Anti-Stokes Raman Scattering (CARS) vibrational energy loading

measurements in nsec-pulsed, diffuse, single filament discharge in nitrogen and air (Montello et al. 2012, Burnette et al. 2013).

• Burnette study showed significantly populated vibrational levels up to v=4.

• Montello study (3x coupled energy of Burnette study) demonstrated significant vibrational loading of molecular nitrogen, with detection of vibrational levels v=0-9.

• Interesting experimental trends were observed, warranting further study.

Present work:• Spontaneous Raman Scattering measurements in nsec-pulsed, diffuse, single

filament discharge in nitrogen and air.

• Vibrational levels v=0-12 observed.

Main Objective:• The main objective of the current study is to quantify energy loading and

energy transfer in the vibrational mode of ground electronic state nitrogen in a highly transient, nanosecond pulsed discharge environment.


Spontaneous Raman Scattering

Virtual Energy States

Vibrational Energy Levels Stokes Raman Scattering

Anti-Stokes Raman Scattering

Spontaneous Raman Scattering:• Inelastic scattering diagnostic technique.• Often used for determination of vibrational

distribution function (VDF) and rotational/translational temperature of gas phase environments.

• Incident laser beam scatters Stokes (lower frequency) or anti-Stokes (higher frequency) photons with molecular resonance shift.Advantages of Spontaneous Raman Scattering Technique:

• Single laser beam results in a complete scattering spectrum.

• Scattering intensity scales linearly with lower level quantum state (CARS scales quadratically with number density difference).

Disadvantages :• Weak scattering intensity, resulting in long integration times.

• Requires fast spectrometers for signal capture, resulting in lower spectral resolution than CARS.


Experimental Apparatus

Experimental Conditions:• Frequency Doubled (532

nm) Nd:YAG Laser.• Laser pulse: 10 ns, 500

mJ/pulse.• 1.75 m glass cell with

brewster windows.• Spectrometer: 0.5 m Acton,

1800 gr/mm grating, linear Dispersion ~1.2 mm/nm.

Signal collection region (2.75 mm)

• Nitrogen gas at P=100 torr.• Air at P=100 torr.• Flow rate: 1.1 slm (~0.6 m/s).• Spherical, bare metal, copper

electrodes (D=7.5 mm).• Beam waist at focal point:

~60 μm diameter; Signal collected over 2.75 mm.

• Discharge energy: ~13(Air) and 17(N2) mJ/pulse.

10 mm


Discharge Pulse Characteristics

Pulsed Filament Conditions:• Stable, diffuse, single filament

generated.• 60 Hz repetition rate.• 490 V input DC voltage.• 125 ns pulse duration.

Voltage, current, and coupled energy waveforms (nitrogen, P=100 torr).

Pulse reduced electric field (E/N) and electron density profiles (Nitrogen P=100 torr).

• ~10kV(N2), 9kV(Air) peak discharge voltage.

• ~55A(N2), 43A(Air) peak discharge current.

• ~17mJ/pulse(N2), 13 mJ/pulse(air) coupled energy.

• Reduced electric field (E/N) and electron density were inferred from voltage and current waveforms and the filament diameter.

• Cathode voltage fall was estimated assuming quasi-steady state, abnormal glow discharge.

Voltage and Current Eqns.

e=electron chargene(t) = electron densityμ = electron mobilityE(t) = electric fieldVc = cathode voltage fallL = electrode gapLc = cathode layer length (~0)

Voltage, current, and coupled energy waveforms (Air, P=100 torr).


Data Collection

Typical Spontaneous Raman spectrum (N2 at P=100 torr, T=300 K, 5 μs after start of discharge pulse).

2-Stage Collection Process1. Large number of on-chip (ICCD)

accumulations create a frame.

• 2,500-24,000 accumulations for each data point (i.e. delay time after pulse).

• Number of accumulations chosen to maximize signal-to-noise without saturating detector.2. Several frames taken in succession

and then averaged.

• 8-16 frames for each data point.

• Number of frames chosen as a tradeoff between signal-to-noise improvement and signal collection time.

• Overall Integration times were 1-2 hours per spectrum.

Signal Collection

Data points taken for delay times from 200 ns to 5 ms after the start of the discharge current pulse.

ICCD Camera Gate: 30-45 ns


Raw SpectrumGaussian Fit

Fitting and Reduction Procedure1. Each vibrational band is fitted

individually by a superposition of Gaussians.

• Number of Gaussians used for each band is determined on a “best least-squares fit” basis.

2. Area under each band is numerically integrated and divided by v+1 (harmonic oscillator approx. for scaling of Raman cross-section).

3. Integrated intensities are added and normalized to 1, yielding relative populations of each vibrational level (i.e. N2 VDF or fv).

4. Avg. number of vibrational quanta per molecule calculated from:

12

0

v

vvvf

Vibrational Temperature“First level” N2 vibrational

temperature is inferred from v=0 and v=1 vibrational level populations.

10 /ln ffTv

θ = 3353 K (N2 characteristic

vib. Energy)

Data Processing: Vibrational Distribution Function and Vibrational Temperature


Experimental Data and Modeling Results(Pure Nitrogen @ 100 torr)

• At longer delay times, the model overpredicts relaxation rates of the vib. levels significantly.

• Time delays shortly after the pulse are predicted reasonably well by model.

• At time delays 1 μs < t < 10 μs, the model fails to reproduce the continuous rise of v=2-12 populations (gradual relaxation of these levels by V-V exchange is predicted).


Experimental Data(Air @ 100 torr)

• Similar trends to nitrogen gas were observed.

• Overall, less vibrational excitation was observed.


Experimental Data and Modeling Results(Quanta and Vibrational Temperature)

Nitrogen data

• Vibrational Quanta increases by factor of ~2 from 1-10 μs.

• Vibrational Temp. increases by factor of ~2 from 1-10 μs (due to V-V exchange).

• Numeric Values are somewhat lower in Air due to: • lower discharge pulse energy (17 mJ/pulse N2 vs. 14 mJ/pulse for air).

• V-T relaxation of N2(X,v) by O atoms.

Model predicts constant quanta per molecule due to conservation of quanta in N2 vibrational mode from V-V exchange.

This comparison between the experimental data and the model indicates that additional energy loading into the N2 vibrational mode occurs after the discharge pulse (1-10 μsec range).

Air data


Where is the Energy Coming From?

• Results in N2 and air strongly suggest additional, significant N2(X,v) vibrational excitation in the afterglow, after the discharge pulse.

•Where does the energy come from? 2 main possibilities:

1. N-Atom Recombination: N + N+ M → N2(X,v) + M

• Time scale for N atom recombination is far too long.

2. E-V Transfer: N2(C) + N2 → N2 (B) + N2(X,v)

• Time scale for N2(C) quenching appears too short (gone within 1 μs).

•How much energy goes to N2(X,v) during quenching of excited electronic states? How much energy goes to heat? This affects both N2(X,v) populations and temperature rise in the afterglow.


Conclusions and Future Work

Spontaneous Raman Scattering has been used to study vibrational energy loading and relaxation kinetics in a nanosecond pulsed, pin-to-pin, single filament discharge in nitrogen and air at P=100 torr.

Results were found to be in good agreement with previously taken CARS data at similar conditions.

35% of input discharge energy is coupled to N2 vibrational mode via direct electron impact (in good agreement with kinetic model).

First level vibrational temperature increased by a factor of 2(achieved ~10-20 μs after pulse).

Total quanta in vibrational levels v=0-12 was found to increase by ~70% at time delays ~1-10 μs after pulse.

Future work will include similar measurements in N2–O2 mixtures with small, controlled amounts of oxygen as well as further modeling studies.


Acknowledgements

This research is supported by:

The National Science Foundation (NSF), Steven Gitomer technical monitor

The AFOSR Multi-University Research Initiative (MURI) in Plasma Assisted

Combustion, Chiping Li technical monitor.


Experimental Data and Modeling Results

All data presented here have been obtained in pure nitrogen or air at P=100 torr and initial temperature T=300 K.

Modeled Excited Electronic State species mole fractions (nitrogen gas)

Model predicts ~32% (240 meV/molecule) of total pulse coupled energy (740 meV/molecule) loaded into N2 vibrational mode (nitrogen gas).

Mole Fractions are consistent with N-atom TALIF measurements (Burnette et al.).


Baseline Kinetic Model (For N2 / O2 Nonequilibrium Plasmas)

Key Energy Transfer Processes:• Vibrational excitation.• Electronic excitation.

• Dissociation of N2 and O2 by electron impact.

• Vibration-Translation (V-T) relaxation.

• Vibration-Vibration (V-V) energy exchange (N2, O2, NO).

• Chemical reactions of air species in their ground electronic states (N, N2, O, O2, O3, NO, NO2, N2O).

• Collisional and radiative quenching of electronically excited species.

Electron Impact Excitation RatesPredicted by two-term expansion

Boltzmann solver.

Vibrational KineticsN2: Master Equation (v=0-45).

O2/NO: Harmonic Oscillator Approx.

Justified due to much less significant nonequilibrium in oxygen compared to nitrogen. (Lo et al. 2012)

Vibrational Level PopulationsDirect electron impact

V-V energy transfer:

V-T energy transfer:

)1()1()()( wCDvABwCDvAB

MvABMvAB )1()(

State-Specific Rates (from Literature)

N2-N2 V-V: (Billing 1979).

N2/O V-T: (Breshears 1968, McNeal 1972, Eckstrom 1973).

N2/N V-T: Assumed same as N2/O.

N2/O3 V-V/V-T: (Menard-Bourcin 1994)

Chemical Reaction RatesTaken from NIST Chemical Kinetics

Database.

Collisional Quenching and E-E Transfer

(Kossyi 1992 and references therein).


Parametric Equations (Raizer 1991)

Cathode voltage fall:

Discharge Current Density:

Townsend Ionization Coefficient:

ln

C

BVc

)ln(

)(4 20

2

C

Bp

p

jc

pd

)/11ln(

ln

AC

E/N and ne Calculation

pE

BA

p /exp

d = cathode layer thicknessp = pressureμ+ = ion mobilityγ = secondary electron emission coefficientA = 12 cm-1Torr-1

B = 342 Vcm-1Torr-1

• Electric Field is calculated by subtracting cathode voltage fall from discharge voltage.

nonequilibrium thermodynamics laboratories spontaneous raman scattering measurements of n 2...

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