Kinetic simulations for nanosecond pulsed discharges

Report
Understanding the effectiveness of lowpower nanosecond discharges in
extending the lean flammability limit of
premixed flames
Mark A. Cappelli, Moon Soo Bak, G. Mungal
Mechanical Engineering Department, Stanford University
Outline
• Experiments in air and pure N2
– question rate coefficients for dissociative
quenching (0-D kinetics for revised rates)
• Experiments in premixed methane/air
flames straddling the LFL (  = 0.53)
• Preliminary 2D simulations of plasmaassisted combustion below and above LFL
Introduction
• Nonequilibrium pulsed plasmas are candidates in enhancing
energy conversion devices (ignition, stabilization)
 Video clip from GE global research website
• Mechanism attributed to;
 Production of radicals (O, H, or OH)
 Rapid gas heating by repetitive discharges
• Extensive plasma reaction sets have been proposed and kinetic
simulations have been carried out to describe various
observables such as ignition delays1,2, O-radical production3,
NO production4, etc.
Future Emphasis
• Multi-scale simulations are rare, most not accounting for
repetitive pulses and species diffusion/advection between the
discharge and the surrounding flow on chemistry.
1.
2.
3.
4.
I.N. Kosarev, et. al, Combustion and Flame, 2008
I.N. Kosarev, et. al, Combustion and Flame, 2009
M. Uddi, et. al, Proceedings of the Combustion Institute, 2008
M. Uddi, et. al, Journal of Physics D: Applied Physics, 2009
Basic Problem
PAC using Nanosecond Discharges
Electric Pulses
“Hot” Electrons
Reactions
Radicals
+
Heat
“Enhanced”
Combustion
“Excited” Molecules
And Direct Dissociation
Dissociative Quenching
(believed to be a major
path to O production
and heat)
Plasma is a local source
of radicals/practical configurations
include jet diffusion and premixed flows
Collisional quenching of N2* by N2 and O2
Role in radical production and
explosive heating of the
discharge volume through
dissociative energy transfer to
atomic oxygen
Time-resolved emission measurements
• Discharge conditions;
 1 mm diameter tungsten
electrode separated by 1 mm
 Gaussian voltage pulse with 10
ns FWHM
 Vpeak, about 8 kV
 50 kHz repetition rate
• Flow speed;
 4 m/s
• N2 C-B/B-A emission spectra
 Monochromator (2 ns gate)
 Band-pass filters
Serve as a means of measuring
T(Trot) and ne to provide a bound
on peak E/n for kinetic simulations
• Stark broadened Hb lineshape
OES results
• Fast gas heating occurs during the pulse
• Electron number density reaches to 4.51015 cm-3
• Small differences are found for quenching of N2 (C, B) between
pure N2 discharges and air discharges
0-D kinetic simulations†
•
•
•
10ns FWHM Gaussian E/n pulse is applied in air at 1 atm and 1300 K initial
pressure and gas temperature.
E/npeak = 285 Td and 1013 cm-3 initial electron density provides a good
agreement between the measured (rot) and simulated (trans) T and ne.
Propose revisions (factor of 2-5) to quench rates of N2 (C, B) by N2 and O2
commonly used (Kossyi et al 1992, Gordiets et al 1995, Capitelli et al 2000):
kQ(N2 (C) by N2) = 2.5 (±0.3)x10-11 cm3s-1, kQ(N2 (C) by O2) = 10 (±0.3)x10-11 cm3s-1
kQ(N2 (B) by N2) = 1.6 (±0.3)x10-11 cm3s-1, kQ(N2 (B) by O2) = 4 (±0.3)x10-11 cm3s-1
†
kinetics and energy equation discussed later within context of 2-D simulation
Atomic O production mechanisms
• 82% of atomic O are found to be produced via the dissociative
quenching and only 5% from electron-impact.
N2(A, B, a’, C) + O2 → N2(X) + 2O
e + O2 → e + 2O
• The atomic O produced is found to be 2.5 (±0.5)x1017 cm-3,
corresponding to a mole fraction of 4.4 (±0.4)x10-2.
Basic Problem
Electric Pulses
“Hot” Electrons
Reactions
Radicals
+
Heat
“Enhanced”
Combustion
Stability enhancement
and extended LFL
“Excited” Molecules
And Direct Dissociation
Enhanced premixed laminar CH4/air
combustion by pulsed discharges in the
vicinity of the Lean Flammability Limit
(LFL = 0.53)
GC, thermocouple, OES measurement setup
• Discharge conditions;
 1 mm diameter tungsten
electrodes separated by 1 mm
 Gaussian voltage pulse with
10 ns FWHM
 Vpeak, about 8 kV
 10 - 50 kHz repetition rate
• Flow speed;
 About 42.5 cm/s
• N2 C-B emission spectrum
 2 ns gate width
• Gas Chromatography (GC) for
major species (CO, H2, CH4)
• TC (coated) measurements of
T (not radiation corrected)
GC and thermocouple results (30 kHz)
CH4 consumption
T
ignition
quenching
CO
H2
1st stage
(reforming)
But subsequent
dilution
With surrounding
flow
• For  < 0.52-0.53, major product species diluted downstream by
surrounding flow (combustion is not sustained)
• Plasma provides some benefit, but combustion efficiency is low
GC (10 - 50 kHz) and OES results
14W
2.5W
• The extension of LFL is improved with increased average
power.
• Fast gas heating occurs during the pulse.
• For E/npeak = 278 (±1) Td and 1013 cm-3 initial electron density,
measured temperatures agree well with those simulated (2-D).
2-D combustion simulations – (1/5)
• Discharge size;
 1 mm height
 0.35 mm diameter
• Discharges are assumed not to
wander.
• Constrain velocity to axial flow and
assume constant pressure
• Discharge conditions;
 Gaussian pulse of E/n with
10 ns FWHM
 E/npeak = 278 (±1) Td (Vpeak = 8 kV)
and 1013 cm-3 initial electron number
density
 Repetition rate, 30 kHz
0.175mm
Uniform
Grid
0.333mm
• Flow (advection) speed;
 42.5 cm/s
2-D combustion simulations – (2/5)
•
Species considered;
 N2(X, A, B, a’, C), O2(X), O, N2+, O2+, CH4+, H2O+, CO2+, electron (e), and other
species in a reduced methane/air reaction mechanisms (H2, H, OH, H2O,
HO2, CH2, CH2(S), CH3, CH4, CO, CO2, HCO, CH2O, CH3O, C2H4, C2H5, C2H6)
 Mechanism DRM-19 (Based on GRI-Mech 1.2) Frenklach et al.
•
Reaction set considered;








•
Electron-impact excitation and ionization of N2
Electron-impact dissociation and ionization of O2 and CH4
Electron-impact ionization of H2O and CO2
Ion conversion
Recombination of electron and positive ions (diss recombination of O2+)
Quenching of N2* by N2
Dissociative quenching of N2* by O2 and CH4
Chemical transformations of neutral species
Reaction rate coefficients;
 For reactions not involving electrons, the coefficients are adapted from
previous plasma kinetic studies.
 For reactions involving electrons, the coefficients are obtained as a
function of E/n (using BOLSIG+).
Reaction
Mechanism
(plasma excited
components only)
Coupled to GRI-MECH 1.2 reduced to
19 Species/84 Reactions in DRM-19
by Frenklach et al
N2(A) + O → N2 + O
2.1  10-11 cm3/s
O + O + N2 → O2 + N2
10-33 (300/Tg)0.41 cm6/s
O + O + O2 → O2 + O2
4  10-33 (300/Tg)0.41 cm6/s
CH4 + N2(A) → CH3 + H + N2
3.3  10-15 cm3/s
CH4 + N2(B) → CH3 + H + N2
3  10-10 cm3/s
CH4 + N2(a') → CH3 + H + N2
3  10-10 cm3/s
CH4 + N2(C) → CH3 + H + N2
5  10-10 cm3/s
a
This cross section is compiled by A.V. Phelps and L.C. Pitchford.
b
This cross section is compiled by A.V. Phelps.
c
This cross section is compiled by M. Hayashi.
Plasma set adapted from:
M. Capitelli, et al.,Plasma Kinetics in Atmospheric Gases, Springer, Berlin, 2000.
A. Kossyi, et al., “Kinetic scheme of the non-equilibrium discharge in nitrogen-oxygen
mixtures,” Plasma Sources Science and Technology, Vol. 1, No. 3, 1992.
B. F. Gordiets, et al., “Kinetic Model of a Low-Pressure N2-O2 Flowing Glow Discharge,”
IEEE Transactions on Plasma Science, Vol. 23, No. 4, August 1995.
Table I. Reaction set (except a reduced methane/air combustion mechanism) used in 2-D
kinetic simulations for methane/air plasma-induced combustion.
Reaction
Rate coefficient
References
N2 + e → N2(A) + e
a

N2 + e → N2(B) + e
a

N2 + e → N2(a’) + e
a

N2 + e → N2(C) + e
a

N2 + e → N2+ + 2e
a

O2 + e → 2O + e
b

O2 + e → O2+ + 2e
b

CH4 + e → CH3 + H + e
c

CH4 + e → CH4+ + 2e
c

H2O + e → H2O+ + 2e
c

CO2 + e → CO2+ + 2e
c

O2+ + e → 2O
2  10-7 (300/Te)0.63 cm3/s
CH4+ + e → CH3 + H
2.9  10-7 (300/Te)0.53 cm3/s
+
H2O + e → O + 2H
10-6 (300/Te)0.5 cm3/s
+
CO2 + e → O + CO
4  10-7 (300/Te)0.5 cm3/s
e + e + N2+ → e + N2
10-19 (300/Te)4.5 cm6/s
+
e + N2 + N2 → N2 + N2
6  10-27 (300/Te)1.5 cm6/s
+
e + N2 + O2 → N2 + O2
6  10-27 (300/Te)1.5 cm6/s
e + e + O2+ → e + O2
10-19 (300/Te)4.5 cm6/s
+
e + O2 + N2 → O2 + N2
6  10-27 (300/Te)1.5 cm6/s
+
e + O2 + O2 → O2 + O2
6  10-27 (300/Te)1.5 cm6/s
e + e + H2O+ → e + H2O
10-19 (300/Te)4.5 cm6/s
+
e + H2O + N2 → H2O + N2
6  10-27 (300/Te)1.5 cm6/s
+
e + H2O + O2 → H2O + O2
6  10-27 (300/Te)1.5 cm6/s
+
e + e + CO2 → e + CO2
10-19 (300/Te)4.5 cm6/s
e + CO2+ + N2 → CO2 + N2
6  10-27 (300/Te)1.5 cm6/s
+
e + CO2 + O2 → CO2 + O2
6  10-27 (300/Te)1.5 cm6/s
+
+
N2 + O2 → O2 + N2
6  10-11 (300/Tg)0.5 cm3/s
N2+ + H2O → H2O+ + N2
2.3  10-9 cm3/s
H2O+ + O2 → O2+ + H2O
4.3  10-10 cm3/s
+
+
CO2 + O2 → O2 + CO2
5.6  10-11 cm3/s
N2(A) + N2 → N2 + N2
3  10-16 cm3/s
N2(B) + N2 → N2 + N2
2  10-12 cm3/s
N2(B) + N2 → N2(A) + N2
3  10-11 cm3/s
N2(B) → N2(A) + h
1.5  105 1/s
N2(a') + N2 → N2(B) + N2
1.9  10-13 cm3/s
N2(C) + N2 → N2(a') + N2
10-11 cm3/s
N2(C) → N2(B) + h
3  107 1/s
N2(A) + N2(A) → N2(B) + N2
3  10-10 cm3/s
N2(A) + N2(A) → N2(C) + N2
1.5  10-10 cm3/s
N2(A) + O2 → N2 + 2O
2.3  10-12 cm3/s
N2(B) + O2 → N2 + 2O
2  10-10 cm3/s
N2(a') + O2 → N2 + 2O
2.8  10-11 cm3/s
N2(C) + O2 → N2 + 2O
3  10-10 cm3/s
2-D combustion simulations – (3/5)
•
Species conservations;
kf
 
 For each reaction,   i n reac , i 
k
b
i
n j
t

 
reactions
 j - 
j

  n
i
prod , i
i
n j


E

i
 i
*
 k f  n or Te or T gas   n reac , i - k b  n prod , i     n jV D , j - V adv
z
tot

 i
i




VD,j is the diffusion velocity of species j,
and V *adv is the advection velocity, scaled as Tgas/Tgas,initial.
•

Energy equation;

 c v , j n j T gas
t
species j


  en e  e E
2
n tot 
t



 h n
 h sen s , j n j
f ,j
j

- 
   h sen s , j n jV D , j  V adv

t
z

species j



e and E are the electron mobility and electric field, respectively,
and  is the mixture-averaged thermal conductivity.
 Ohmic dissipation is considered only at the discharge region.
•
Diffusion velocity of species j, VD,j;
V D , j  V c - D jm
X
X
j
j

D jm  j  T
X
j
T
and


    n jV D , j   0
 species , j

Djm is the mixture average diffusion coefficient of species j,
and j is the thermal diffusion ratio of species j.
 



     T gas

2-D combustion simulations – (4/5)
•
Mixture average diffusion coefficient for species j, Djm (Bird et al., 1960);
D jm 
1-Yj

X k D kj
k j
Dkj is the binary diffusion coefficient between species k and j.
•
Mixture-averaged thermal conductivity, λ (Mathur et al., 1967);

1
    X j j 
2
 j

1

j
X
j


j 


λj is the pure species conductivity for species j.
•
Thermal diffusion ratio of species j , j (for MWj < 5)
j 

jk
k j
jk is the binary thermal diffusion ratio for species j into species k.
•
Approximations;
 Electron and positive ions locate only at a discharge region.
 The species diffusion coefficients of electronically excited N2 and O2 are set to
be equal to those for N2 and O2 in ground state, respectively.
2-D combustion simulations– (5/5)
•
Numerical schemes used;
 Central difference scheme for species diffusion and thermal conduction.
 Upwind scheme for species advection and enthalpy diffusion and advection.
 A system of ordinary differential equations are solved implicitly for each time
step using backward difference formula (BDF).
 The domain is divided into smaller subdomains, computed in parallel (32
CPUs). Each case takes approximately 24 hours of CPU.
 Sundials CVODE with MPI support is used as solver, and each temporal
solution is computed iteratively using Generalized Minimal Residual method
(GMRES).
•
Initial conditions;
 1 atm and 296 K background pressure and gas temperature, initial guess from
previous converged runs at similar conditions
 Methane/air equivalence ratio,  (0.45 and 0.55)
 278 (±1) Td E/npeak with 1013 cm-3 initial electron number density
•
Boundary conditions;
 Dirichlet boundary conditions for the domain bottom
 Neumann boundary conditions (zero gradient) for the domain side and top
Simulation results for CH4/air at  = 0.45
278 Td peak E/n
1013 cm-3 initial electron density
Spatial and temporal evolution of
CH4
Spatial and temporal evolution of
CO2
Spatial and temporal evolution of
H 2O
Spatial and temporal evolution of
CO
Spatial and temporal evolution of
H2
Spatial and temporal evolution of
O
Spatial and temporal evolution of
Gas temperature
Simulation results for CH4/air at  = 0.55
279 Td peak E/n
1013 cm-3 initial electron density
Spatial and temporal evolution of
CH4
Spatial and temporal evolution of
CO2
Spatial and temporal evolution of
H 2O
Spatial and temporal evolution of
CO
Spatial and temporal evolution of
H2
Spatial and temporal evolution of
O
Spatial and temporal evolution of
Gas temperature
Comparison to the measurements
Kinetics in the discharge region ( = 0.55)
• Most of methane is combusted because of the
shorter t between pulses compared to the
species diffusion t.
• The dissociative quenching of N2* produces O
radicals, leading to the production of other
active species such as H, OH and H2.
Summary:
•
•
•
Experiments/simulations carried out to refine important kinetics
Sampled chemistry/compared to preliminary 2D simulations
ignition/quenching (LFL) limit captured in the simulations
Furthering this research:
•
•
•
•
Tighten discrepancy between experiments and simulations
- correct for gas reactions in sampling tube
Diagnostics/diagnostics/diagnostics
More strongly couple the plasma with surrounding flow
Refine the plasma simulations (sheaths, axial diffusion/drift)
- quasi-1D simulation under development
- need 2D simulation
Thank You
Premixed laminar CH4/air combustion
by heating coil near LFL
Experimental setup
Simulation results for CH4/air at  = 0.55
Power input = 2W

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