(79e) On-the-Fly Reduction of Kinetic Mechanisms Using Element Flux Analysis

In the past few decades, the increase in computational capability has contributed significantly towards the development of more accurate reactive flow simulations. However, the incorporation of detailed kinetic mechanisms within complex CFD calculations is often infeasible due to extremely long CPU time required. Hence considerable effort has invested towards the representation of complex kinetic models by simple reduced ones, which can largely alleviate the computational complexity while still retain considerable accuracy. A major category of mechanism reduction approaches was based on time scale analysis. This category includes Quasi Steady State Approximation (QSSA) and Partial Equilibrium (PE) assumption, Intrinsic Low Dimensional Manifolds (ILDM), and Computational Singular Perturbation (CSP). While time scale separation can reduce the mechanism size effectively, significant computational overhead is introduced in solving the explicit algebraic equations associated with short time scales. Therefore, a skeletal reduction is frequently performed to eliminate the unimportant species and reactions before a time scale analysis is employed. Various skeletal reduction approaches have been developed, such as sensitivity analysis, optimization approaches, directed relation graph method, etc. More detailed review of mechanism reduction approaches can be found in [1].

In recent studies, it has been demonstrated that more accurate simulation can be accomplished by applying locally accurate mechanisms instead of a global reduced one. Thus several approaches that apply different reduced mechanisms adaptively as the reaction system evolves have been proposed. The first adaptive chemistry approach is the In situ Adaptive Tabulation (ISAT), which stores the composition information of a reactive system in a database and looks up similar entries for new query points during the flow simulation. A ?store and retrieve? approach was proposed by Androulakis which tabulates off line information and retrieve similar entries to generate approximations of system dynamic during the flow simulation. More recently, adaptive reduction scheme was developed subject to the validity of temperature, pressure, and species compositions. Adaptive reduction approaches are capable to provide more accurate predictions of the system behavior than global reduced mechanisms; however, they rely on the development of a library of reduced mechanisms which requires priori analysis of the simulations and determination of the range of conditions where the mechanisms are valid. Due to the wide range of conditions encountered in chemical systems, the union of the feasible regions of reduced mechanisms in the library may not cover all possible reactive conditions. To develop a reduction scheme that can address all possible reactive conditions, on-the-fly kinetic mechanism reduction scheme has to be developed. The main advantage of on-the-fly reduction scheme lies in the fact that reduced mechanisms are developed at each time step of the simulation, offering valid reduced chemistry for their local conditions.

In the present work, we introduce an on-the-fly reduction scheme based on the element flux graph. The construction of flux graphs employs similar method as introduced in [2, 3]. However, the flux evaluating method has been improved to ensure its validity on quasi-steady-state species and partial equilibrium reactions. Reactive flow models usually divide the simulation into discrete time steps. During each step, both the reaction and the mixing effect are taken into account. The idea of on-the-fly reduction scheme is to generate a reduced mechanism for each time step. Compared to adaptive reduction schemes, which construct a library of reduced mechanisms apriori and assume the union of feasible regions of these mechanisms covers the entire condition space encountered in the simulation, the main advantage of dynamic mechanism generation is that, accurate mechanisms can be developed based on local reactive conditions. Since a wide range of conditions might be encountered in reactive flow simulation, the reduced mechanisms may not be sufficient to describe all different conditions encountered.

To integrate the reduction scheme with the reactive flow simulation, we analyze the carbon element flux at each time step and sort the source-sink pairs in a descending order. Then a user-selected cutoff value is applied on the flux and active sources and sinks characterized by high flux values are retained in the reduced mechanism. Based on the reduced species set, which consists of the sources and sinks retained by the cutoff, a reduced reaction set is identified using CHEMKIN software package [4]. The species in the reduced mechanism are integrated based on the reduced reaction set while the rest are assumed to have zero production rates at that particular time step. As the system advances to the next time step, the flux analysis and reduction process are repeated and a new reduced mechanism is generated. This approach has a number of advantages: (a) no priori analysis or information is needed since a locally accurate reduced mechanism is developed dynamically for any condition encountered in the flow simulation. Thus a library of reduced mechanisms along with the feasible region is not required. The reduced mechanism is developed by setting a user-selected cutoff on the element flux and no specific knowledge about the reaction system, such as principal species, is required; (b) a search is not required to implement the on-the-fly reduction scheme in reactive flow calculations, thus the active species can be identified effectively without extensive computational overhead; (c) the cutoff value enables the user to define the level of complexity of the reduced mechanisms. Higher cutoff value leads to more comprehensive reduced mechanisms and thus higher level of accuracy. However, as more comprehensive mechanisms are used, the CPU time also increases. Therefore, there is a compromise between the level of accuracy and the computational complexity.

To validate the feasibility and accuracy of the on-the-fly reduction approach, the reduction scheme is demonstrated in the context of a reactor model. Since the elemental flux analysis is performed based on the concentrations of all the species, the flow model should be able to track all the species present in the detailed mechanism, hence at any time step the species concentrations can be retrieved and thus flux analysis can be implemented. In the present work, a Pair-wise Mixing Stirred Reactor (PMSR) [5] model and a Plug Flow Reactor (PFR) model are used to demonstrate the proposed methodology. These two zero-dimensional reactor models are used primarily because they are computational tractable even with detailed kinetic model, and covers a broad range of conditions in the composition space. A detailed n-pentane mechanism and a detailed mechanism of primary reference fuels, iso-octane and n-heptane, have been used in the simulations.

Reference:

[1] C. K. Law; C. J. Sung; H. Wang; T. F. Lu, Aiaa J 41, (9), (2003), 1629-1646.

[2] I. P. Androulakis, Computers & Chemical Engineering 31, (1), (2006), 41-50.

[3] I. P. Androulakis; J. M. Grenda; J. W. Bozzelli, Aiche Journal 50, (11), (2004), 2956-2970.

[4] R.J. Kee, Rupley, F.M., Meeks, E., Miller, J.A. CHEMKIN-III: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics; SAND--96-8216; Sandia National Labs: Livermore, CA (United States), 1996.

[5] S. B. Pope, Combustion Theory and Modelling 1, (1), (1997), 41-63.