(528c) A Graph-Based Approach For Developing Adaptive Representations Of Complex Reaction Mechanisms

Over the past couple of decades detailed kinetic mechanisms have been developed to model pollutant and byproduct formation in chemical processes. Many important applications, including aerospace propulsion, engine design and various manufacturing processes require a detailed understanding of both fluid dynamics and kinetics. However, detailed simulation of reactive flow systems using complex kinetic mechanisms consisting of hundreds of species and thousands of reactions is computationally demanding task. While considerable effort has been invested towards the efficient and reduced representation of complex kinetic models (Wei and Kuo 1969; Peter 1988; Griffiths 1995; Pope 1997; Mass and Pope 1992; Androulakis 2000; Bhattacharjee, Schwer et al. 2003; Petzold and Zu 1997; Androulakis 2000; Banerjee and Ierapetritou 2003, Peters 1988) the computational complexity associated with calculations that couple kinetics and CFD still remains high and in many cases prohibitive.

Of particular importance are recent attempts to develop adaptive reduced representations that explore the local properties of the reacting mixture in order to identify proper reduced mechanisms. So far in order to identify a relevant representations for a given set of reduce conditions, mechanisms are characterized using few key indicators characteristic of local conditions, such as composition and temperature (Banerjee and Ierapetritou 2003; Schwer et al. 2003). However, description of the reactive propensity of a reaction mixture is not best characterized by composition and/or temperature but rather it should be described by intrinsic properties of the reaction mixture that express the totality of the chemical information. To achieve that, we propose a novel characterization of the reaction mixture based on the concept of element flux which captures, in an adaptive way, the reactive propensity of the mixture regardless of composition, T, P.

Based on the concept of element flux analysis (Androulakis et al. 2004), we introduced a new flux graph representation of complex kinetic transformations (Androulakis 2006). In this presentation we discuss how this concept can be extended in order to develop effective adaptively reduced representations of complex kinetic mechanisms and how these are used for advanced simulations. Instantaneous fluxes, in the form of complex directed graphs are defined for the entire expected accessible regions and are subsequently clustered to identify points in the space that are characterized by similar reactive propensities, and hence reaction flux graphs. Graph similarity and clustering is quantified either using a Euclidean distance or through the introduction of a novel graph-distance metric taking into account the magnitude of each flux and the general structure of the graph. Given the distance metric the multiple trajectories corresponding to alternative reaction flux graphs are subsequently clustered to identify similarities among them. Several clustering algorithms can be adopted for this task, including hierarchical clustering; multidimensional scaling et al.

The result of this first stage is the definition of a library of conditions and the associated graphs and reduced mechanisms that best characterize the reactive propensity of the mixture. The next step, in order to develop the adaptive chemistry representation, is to define a search algorithm that will assign a new query point to a particular reactive flux and subsequently a reduced mechanism associated with this flux. To do this, we have developed a very effective, yet simple, nearest neighbor classification scheme through the definition of a distance metric between the graphs assigned to each cluster in the library and the flux defined based on the new query point. The cluster that is the closest to the query point defines the current active mechanism. The main advantage of this representation is the fact that the representation of the chemistry is not confined to simple attributes, such at composition, T, P, but rather captures the essence of the chemical transformations in the form of reaction fluxes.

The methodology is demonstrated using a detailed nC5 mechanism with over 300 species using a pair-wise mixed stirred tank reactor model with particular emphasis of capturing the low temperature autoignition characteristics.

Reference:

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