RATE-CONTROLLED CONSTRAINED EQUILIBRIUM: A BASIS FOR EFFECTIVE COUPLING OF COMPREHENSIVE CHEMICAL KINETICS AND CFD

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Modelling of combustion processes remains an outstanding technical problem with wide implications, both scientific and practical. By far the largest percentage of our energy is produced via combustion equipment such as internal combustion engines for cars, turbines for aircraft or industrial burners for power generation. These processes also account for the generation of a wide variety of pollutants, such as NOx and soot, as well as for the generation of greenhouse gases. It is widely acknowledged that there is large potential for improvement of those processes, resulting in great environmental benefits. Combustion modelling requires the coupling of fluid dynamics equations, solved numerically through a Computational Fluid Dynamics (CFD) code, with a comprehensive chemical kinetics model. Practical combustion devices are invariably turbulent, which necessitates a further element, the turbulence-chemistry interaction model. Coupling all of these elements results in a formidable computational problem, and the main cause of the bottleneck is the chemical kinetics part of the calculation. Comprehensive chemical kinetics include very large numbers of species and reactions: even for the simplest fuels, such as methane, more than 50 species are necessary, while for commercial fuels hundreds of species and reactions can easily be present. Each species introduces an additional differential equation to the problem, and integration is further hampered by the excessive stiffness that is often exhibited by such systems. Yet the incorporation of comprehensive mechanisms is essential if the formation of pollutants is to be predicted. The mathematical modelling of combustion can be significantly simplified by taking advantage of the time scale separation to assume that fast reactions, typically associated with intermediate species, are in a state of local equilibrium. The proposed research will explore a promising concept for deriving the low-dimensional models on the basis of time-scale separation: Rate-Controlled Constrained Equilibrium (RCCE). In this approach, the kinetically controlled species are allowed to evolve according to the relevant differential equations including the chemical kinetics of the original detailed mechanism, whilst the equilibrated species are determined by minimising the free energy of the mixture, subject to the additional constraints (apart from conservation of mass, energy and elements) that the kinetically controlled species must retain the concentrations given by the solution of their governing equations. Previous work by the authors has provided evidence that RCCE has the potential to develop into a method that is both theoretically rigorous and practically feasible for the implementation of large chemical mechanisms into CFD codes. Having established proof of concept, further work is now required to bring RCCE to the stage where it is ready for application in practical problems. Furthermore, several important questions about the fundamentals of RCCE remain unanswered, such as its relation to other methods of mechanism reduction such as Computational Singular Perturbation (CSP). The two methods are complementary and it is possible that a combination of them will prove a very powerful tool.