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

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