Modeling of Combustion of Mono-Carbon Fuels Using the Rate-Controlled Constrained-Equilibrium Method

Abstract

Modeling of a non-equilibrium combustion process involves the solution of large systems of differential equations with as many equations as species present during the process. The process of chemical reaction and combustion is complicated since it may be governed by hundreds, sometimes thousands of microscopic rate processes. Integration of these equations simultaneously becomes more difficult with the complexity of the combustible. In order to reduce the size of these systems of equations, the Rate-Controlled Constrained-Equilibrium method (RCCE) has been proposed to model non-equilibrium combustion processes. This method is based on the Second Law of Thermodynamics, assuming that the evolution of a complex system can be described by a small number of rate-controlling reactions which impose slowly changing constraints on all allowed states of the system, therefore a non-equilibrium system will relax to its final equilibrium state through a sequence of rate controlled constrained equilibrium states. Oxidation induction times and concentration of species during a combustion process are found in a less complicated way with this method, as equations for constraints rather than for species determine the composition and evolution of the system. The time evolution of the system can be reduced since the number of constraints is much smaller than the number of species presents, so the number of equations to solve. The RCCE method has been applied to the stoichiometric combustion of mono-carbon fuels using 29 chemical species and 139 chemical reactions at different sets of pressure and temperature, ranging from 1 atm to 100 atm, and from 900 K to 1600 K respectively. Results of using 8, 9, 10 and 11 constraints compared very well to those of the detailed calculations at all conditions for the cases of formaldehyde (H2CO), methanol (CH3OH) and methane (CH4). For these systems, ignition delay times and major species concentrations were within 5% of the values given by detailed calculations, and computational saving times up to 50% have been met.