(376b) A Hybrid Scheme for Kinetic Mechanism Reduction Based On the On-the-Fly Reduction and Quasi-Steady-State Approximation

In the past few years, with
the advances in experimental and computational kinetic studies, great progress
has been made in developing detailed kinetic mechanisms for realistic fuels.[1] Mechanisms for large n-alkanes and complex long-chain
esters have been published recently.[2, 3] These detailed mechanisms provide us an opportunity
to explore the combustion characteristics for more complex fuels, such as
biodiesel,[4] but also a challenge since they are usually very
large in size, making the incorporation of these mechanisms in combustion
simulations a computationally demanding job, or even infeasible especially in a
computational fluid dynamics (CFD) framework. To better accommodate the large
kinetic mechanisms in the realistic reactive flow simulations, various advanced
mechanism reduction techniques have been developed during the past decade.[1, 5] The most recent mechanism reduction techniques are often
focusing on dynamic reduction, which is based on the fact that only a small
portion of species and reactions are active at a particular point during the
combustion process. The dynamic reduction scheme identifies the active species
and reactions locally and dynamically according to the specific local
conditions, thus reducing the computational cost spent on the unnecessary
species and reactions. Pepiot-Desjardins et al. [6] published a DRGEP
method based on the directed relation graph (DRG) developed by Lu and Law.[7, 8]  Recently, Liang et al. [9, 10] also developed a dynamic adaptive chemistry (DAC)
scheme based on the idea of DRGEP method. In our previous work, we have
developed an on-the-fly reduction approach [11] based on the element flux analysis [12] which is performed dynamically in the simulation. The
on-the-fly reduction has been applied to enable the characterization of
biodiesel combustion using large detailed mechanisms for methyl esters under
HCCI engine conditions.[13] The computational intensity is significantly reduced
while satisfactory accuracy is still maintained.

However, the computation time
needed for simulations with large detailed mechanisms is still long due to the
large initial mechanism size. Also, although the chemistry calculations are greatly
simplified, the full species set is still involved in the transport
calculations. In some practical applications, transporting large number of
species is an intractable computational task.

To facilitate the practical
application of dynamic mechanism reduction methods, we propose in this work a
hybrid reduction scheme combining the on-the-fly reduction with globally
applied quasi-steady-state approximation (QSSA).[14] Under the assumption of QSSA, QSS species always
quickly reach their chemical equilibrium, such that their kinetic ODEs can be
replaced by a set of algebraic equation by assigning the RHS to be zero. The
on-the-fly reduction is then performed only with respect to the set of non-QSS
species. In this way, the initial mechanism size for the on-the-fly reduction
procedure is reduced, and the number of ODEs to be solved is also further
reduced compared to the original on-the-fly reduction scheme. In addition, we
only need to calculate the non-QSS species for transport purposes in the CFD
solver, while the compositions of QSS species are kept constant. As a result,
the number of species involved in the transport computation is also reduced
globally.

In this work, different QSS
species sets for methane mechanism GRI Mech3.0,[15] which are optimized by Montgomery et al.[16] using genetic algorithm, are used to demonstrate our
implementation of the hybrid reduction approach. Simulations with the hybrid
reduction implementation under HCCI engine conditions are performed and
compared with the results from the detailed mechanism simulation in KIVA-3V.[17] Globally reduced transport species and further
improved chemistry solution is achieved, while satisfactory accuracy is still
maintained. The hybrid reduction scheme enables the practical implementation of
detailed chemistry in realistic CFD environment.

References

1.         Pitz,
W.J. and C.J. Mueller, Recent progress in the development of diesel
surrogate fuels. Progress in Energy and Combustion Science, 2011. 37(3):
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2.         Herbinet,
O., W.J. Pitz, and C.K. Westbrook, Detailed chemical kinetic oxidation
mechanism for a biodiesel surrogate. Combustion and Flame, 2008. 154(3):
p. 507-528.

3.         Herbinet,
O., W.J. Pitz, and C.K. Westbrook, Detailed chemical kinetic mechanism for
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4.         Lai,
J.Y.W., K.C. Lin, and A. Violi, Biodiesel combustion: Advances in chemical
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6.         Pepiot-Desjardins,
P. and H. Pitsch, An efficient error-propagation-based reduction method for
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7.         Lu,
T. and C.K. Law, A directed relation graph method for mechanism reduction.
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8.        Lu,
T. and C.K. Law, On the applicability of directed relation graphs to the
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9.        Liang,
L., J.G. Stevens, and J.T. Farrell, A dynamic adaptive chemistry scheme for
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10.       Liang,
L., et al., The use of dynamic adaptive chemistry in combustion simulation
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11.       He,
K., I.P. Androulakis, and M.G. Ierapetritou, On-the-fly reduction of kinetic
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12.       Androulakis,
I.P., J.M. Grenda, and J.W. Bozzelli, Time-integrated pointers for enabling
the analysis of detailed reaction mechanisms. AIChE Journal, 2004. 50(11):
p. 2956-2970.

13.       Zhang,
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Simulation Using Detailed Mechanism with On-the-fly Reduction. Energy &
Fuels, 2012. 26(2): p. 976-983.

14.       Turanyi,
T., A.S. Tomlin, and M.J. Pilling, On the error of the quasi-steady-state
approximation. The Journal of Physical Chemistry, 1993. 97(1): p.
163-172.

15.       Gregory
P. Smith, D.M.G., Michael Frenklach, Nigel W. Moriarty, Boris Eiteneer, Mikhail
Goldenberg, C. Thomas Bowman, Ronald K. Hanson, Soonho Song, William C.
Gardiner, Jr., Vitali V. Lissianski, and Zhiwei Qin. Available from: http://www.me.berkeley.edu/gri_mech/.

16.       Montgomery,
C.J., et al., Selecting the optimum quasi-steady-state species for reduced
chemical kinetic mechanisms using a genetic algorithm. Combustion and
Flame, 2006. 144(1¨C2): p. 37-52.

17.       Amsden,
A.A., KIVA-3V: A Block-Structured KIVA Program for Engines with Vertical or
Canted Valves. 1997, Los Alamos National Laboratory: Los Alamos, NM.