Transport properties of excited singlet oxygen species and their effects on
one-dimensional combustion simulations
1?
1
1
Daniel I. Pineda , Tiernan A. Casey , and Jyh-Yuan Chen
1
University of California, Berkeley
?
[email protected]
Abstract
A current problem is distinguishing the relative contributions of chemical kinetic and transport effects to the enhancement of plasma-assisted combustion. As numerical investigations in
plasma-assisted combustion move to simulations in one or more dimensions, the transport properties of excited-state species thought to contribute to the combustion enhancement will need to
be determined to accurately model these systems and discern their chemical kinetic contribution to the enhancement. We provide estimates of the intermolecular interaction energies of singlet
1
1 +
oxygen (O2(a ∆g) and O2(b Σg )) using ab initio quantum chemistry methods, and find that the transport properties derived from these interaction energies are substantially different from
those of the corresponding ground state. One-dimensional simulations of premixed H2-O2 flames seeded with 5% O2(a1∆g) in the oxidizer were performed. Results indicate that updating the
transport properties of the singlet oxygen species has a very small effect on flame speed and structure, but that this effect is largest during flame extinction in transient simulations.
Results
Background
He interaction: He-He vs He-He*
He-He (This work)
He-He* (This work)
He-He* Buckingham et. al (Calc, 1952)
He-He* Brigman et. al (Calc, 1961)
He-He* Poshusta (Calc, 1963)
He-He* Kokler (Calc, 1969)
He-He* Mulliken (Experiment, 1932)
2
1
0
-1
2
3
4
0.07
1
0.065
O 2(a 1∆ g)
O
OH
H
0.5
5
0.06
-45
-45
-40
-40
-35
-30
-35
-30
-25
-25
-20
Distance [mm]
Figure 3: Results to replicate calculations of Buckingham and Dalgarno [4] and others using the ROHF-GUGA-CI approach.
Figure 6: Results from Premix for H2-O2 flames at P = 0.01 atm with inlet
temperature 300 K. Old transport marked as grey dashed lines. Updated
transport marked as solid black lines.
Comparison of Lennard-Jones fits
0
O2 (X3 Σ -g )
-1000
1
O2 (a ∆ g )
-1500
O2 (b1 Σ +g )
-2000
3
3.5
4
4.5
5
5.5
6
Figure 4: Results for different electronic states of O2. Estimated
error in well-depth is shown with shading and the estimated error in
collision diameter is shown with horizontal error bars.
PREMIX: Effect on flame speed
Flame speed, S u [cm/s]
1000
800
689
688
687
1065
1064
1.06
1.1
600
0.9
1
1.1
P = 0.10 atm
400
399
0.85
0.7
0.8
0.9
0.9
0.95
1
×10
4
-4
×10
2.8153
3
1.434
2.8152
2
1.433
2.8151
1
1.432
2.815
0
2
4
1.431
4.2335 4.234 4.2345
6
×10
-4
time [s]
-5
5.456
5.4565
×10 -5
5.457
×10 -5
×10 -8
modified transport
consumes more fuel
0.5
0
unmodified transport
consumes more fuel
-0.5
-1
-1.5
-2
ignition
-2.5
1
1.1
1.05
1.2
0
1
2
3
4
5
time [s]
6
×10
-5
Figure 7: Results from S3D for H2-O2 ignition at P = 0.01 atm with initial temperature 300 K. Old transport marked in black. Updated transport
marked as red lines. Lower figure shows the difference between the two cases
in regards to remaining fuel concentration.
400
200
S3D: Effect on fuel consumption over time
-4
-3
P = 0.01 atm
P = 1.00 atm
×10
Difference in remaining
fuel mass [kg/m 2]
-500
r [Angstroms]
The computational quantum chemistry package Gamess
was used to calculate the intermolecular interaction energies using the Restricted Open-Shell HartreeFock (ROHF) calculation with Configuration Interaction (GUGA-CI) used in previous work [5], from which
Lennard-Jones parameters are extracted. Four different
collisions shown in Figure 2 are considered.
1.5
r [Angstroms]
2.5
Methods
0.075
0
-50
Remaining fuel mass [kg/m2]
In 1952, Buckingham and Dalgarno [4] showed that the
interaction of ground state helium atoms and the interactions of helium with metastable triplet helium are significantly different, with a difference in well depths on the
order of 1000. As such, there is reason to suspect that
the interaction energies of O2(a1∆g) and O2(b1Σg+) are
3 –
significantly different from the ground state, O2(X Σg ),
and that this difference will result in appreciably different
transport properties.
1
V(r) / kB [K]
Figure 1: Experiments demonstrating the compounding effects of
transport in ignition enhancement for a nanosecond pulsed discharge
ignition event [3].
Calculations approach experiment
as computing power increases
-2
PREMIX: Effect on minor species mole fractions
2
Mole fraction [%]
3
V(r) [eV]
In many 1-D kinetic studies, researchers have assumed
that the transport properties of excited state species are
those of their ground state counterparts [1, 2]. There
is scarce literature regarding the interaction energies of
these electronically-excited species, and they have even
been requested by other researchers [1].
1.3
Equivalence ratio, φ
Figure 5: Results from Premix for H2-O2 flames at different pressures
with inlet temperature 300 K. Old transport marked as grey dashed
lines. Updated transport marked as solid black lines.
Attempts to solve the same transient system in A-SURF have
posed challenges due to the fact that A-SURF uses an implicit
solver, and the excited-state chemistry in the mechanism is very
stiff.
Conclusions, Acknowledgments & References
Figure 2: Collision orientations used for diatomic molecules.
The resulting weighted average well depths and collision
diameters are substituted into the Chemkin transport
database, and 1-D simulations are run:
• Steady premixed H2-O2 flames at various pressures using Chemkin Premix with multi-component
transport.
Despite large differences in the Lennard-Jones parameters in the different electronically-excited states of O2, updating the
transport properties in one dimensional combustion simulations is only noticeable at very low pressures. Updating the transport
properties of O2(a1∆g) has a smaller effect in steady H2-O2 flames than it does in CH4-O2-Ar flames reported previously [5],
supporting the suggestion by Esposito & Chelliah [6] that uncertainty in transport is less important than the uncertainty in
kinetics for H2-O2 flames. Results indicate that the excited state chemistry in the mechanism is too stiff for implicit transient
solvers in codes such as A-SURF, but that the stiffness does not pose a problem for explicit schemes like those used in S3D.
The biggest differences that are observed occur as the flame extinguishes, confirming the conclusions of Dong et al. [7] that
the sensitivity of diffusion coefficients to the extinction response is significant.
This investigation conducted at UC Berkeley was supported by NSF Grants No. DGE 1106400, 1510709, and NSF/DOE
Award No. CBET-1258653. Additionally, this research used NERSC, a DOE Office of Science User Facility the U.S. DOE
under Contract No. DE-AC02-05CH11231. Thanks to Xian Shi for adding multi-component transport to A-SURF.
• Unsteady premixed H2-O2 flames at low pressure
using A-SURF with multi-component transport.
References
• Unsteady premixed H2-O2 ignition undergoing a
nanosecond pulsed discharge event using S3D with
mixture-averaged transport.
[2] A. A. Konnov, Combustion and Flame 162 (2015) 3755–3772.
[1] A. Bourig, D. Thévenin, J.-P. Martin, G. Janiga, K. Zähringer, Proceedings of the Combustion Institute 32 (2009) 3171–3179.
[3] D. I. Pineda, B. Wolk, T. Sennott, J.-Y. Chen, R. W. Dibble, D. R. Singleton, in: Laser Ignition Conference, volume C, Argonne National Laboratory, OSA Publishing, Lemont, IL, 2015, p. T5A.2.
[4] R. A. Buckingham, A. Dalgarno, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 213 (1952) 327–349.
[5] D. I. Pineda, J.-Y. Chen, in: 2016 Spring Technical Meeting of the Western States Section of the Combustion Institute, Paper 1B01, University of Washington, The Combustion Institute, Seattle, WA, 2016.
[6] G. Esposito, H. K. Chelliah, Combustion and Flame 159 (2012) 3522–3529.
[7] Y. Dong, A. T. Holley, M. G. Andac, F. N. Egolfopoulos, S. G. Davis, P. Middha, H. Wang, Combustion and Flame 142 (2005) 374–387.
LATEX Tik Zposter