Use of degree of disequilibrium analysis to select kinetic constraints for the rate-controlled constrained-equilibrium (RCCE) method

The Rate-Controlled Constrained-Equilibrium (RCCE) method provides a general framework that enables, with the same ease, reduced order kinetic modelling at three different levels of approximation: shifting equilibrium, frozen equilibrium, as well as non-equilibrium chemical kinetics. The method in general requires a significantly smaller number of differential equations than the dimension of the underlying Detailed Kinetic Model (DKM) for acceptable accuracies. To provide accurate approximations, however, the method requires accurate identification of the bottleneck kinetic mechanisms responsible for slowing down the relaxation of the state of the system towards local chemical equilibrium. In other words, the method requires that such bottleneck mechanisms be characterized by means of a set of representative constraints. So far, a drawback of the RCCE method has been the absence of a systematic algorithm that would allow a fully automatable identification of the best constraints for a given range of thermodynamic conditions and a required level of approximation. In this paper, we provide the first of two steps towards such algorithm based on the analysis of the degrees of disequilibrium (DoD) of chemical reactions in the underlying DKM. In any given DKM the number of rate-limiting kinetic bottlenecks is generally much smaller than the number of species in the model. As a result, the DoDs of all the chemical reactions effectively assemble into a small number of groups that bear the information of the rate-controlling constraints. The DoDs of all reactions in each group exhibit almost identical behaviour (time evolution, spatial dependence). Upon identification of these groups, the proposed kernel analysis of N matrices that are obtained from the stoichiometric coefficients yields the N constraints that effectively control the dynamics of the system. The method is demonstrated within the framework of modeling the expansion of products of the oxy-combustion of hydrogen through a quasi one-dimensional supersonic nozzle. The analysis predicts and RCCE simulations confirm that, under the geometrical and boundary conditions considered, the underlying DKM is accurately represented by only two bottleneck kinetic mechanisms, instead of the three constraints identified for the same problem in a recently published work also based, in part, on DoD analysis.