The Importance of the Entropy Inequality on Numerical Simulations Using Reduced Methane-air Reaction Mechanisms

Many reaction mechanisms have been developed over the past few decades to predict flame characteristics. A detailed reaction mechanism can predict flame characteristics well, but at a high computational cost. The reason for reducing reaction mechanisms is to reduce the computational time needed to simulate a problem. The focus of this work is on the validity of reduced methane-air combustion mechanisms, particularly pertaining to satisfying the entropy inequality. While much of this work involves a two-step reaction mechanism developed by Dr. Charles Westbrook and Dr. Frederick Dryer, some consideration is given to the four-step and three-step mechanisms of Dr. Norbert Peters. These mechanisms are used to simulate the Flame A experiment from Sandia National Laboratories. The two-step mechanism of Westbrook and Dryer is found to generate results that violate the entropy inequality. Modifications are made to the two-step mechanism simulation in an effort to reduce these violations. Two new mechanisms, Mech 1 and Mech 2, are developed from the original two-step reaction mechanism by modifying the empirical data constants in the Arrhenius reaction form. The reaction exponents are set to the stoichiometric coefficients of the reaction, and the concentrations computed from a one-dimensional flame simulation are matched by changing the Arrhenius parameters. The new mechanisms match experimental data more closely than the original two-step mechanism and result in a significant reduction in entropy inequality violations. The solution from Mech 1 had only 9 cells that violated the entropy inequality, while the original two-step mechanism of Westbrook and Dryer had 22,016 cells that violated the entropy inequality. The solution from Mech 2 did not have entropy inequality violations. The method used herein for developing the new mechanisms can be applied to more complex reaction mechanisms.