The Quantification of Mixture Stoichiometry When Fuel Molecules Contain Oxidizer Elements or Oxidizer Molecules Contain Fuel Elements

Abstract

The accurate quantification and control of mixture stoichiometry is critical in many applications using new combustion strategies and fuels (e.g., homogeneous charge compression ignition, gasoline direct injection, and oxygenated fuels). The parameter typically used to quantify mixture stoichiometry (i.e., the proximity of a reactant mixture to its stoichiometric condition) is the equivalence ratio, Φ. The traditional definition of Φ is based on the relative amounts of fuel and oxidizer molecules in a mixture. This definition provides an accurate measure of mixture stoichiometry when the fuel molecule does not contain oxidizer elements and when the oxidizer molecule does not contain fuel elements. However, the traditional definition of θ leads to problems when the fuel molecule contains an oxidizer element, as is the case when an oxygenated fuel is used, or once reactions have started and the fuel has begun to oxidize. The problems arise because an oxidizer element in a fuel molecule is counted as part of the fuel, even though it is an oxidizer element. Similarly, if an oxidizer molecule contains fuel elements, the fuel elements in the oxidizer molecule are misleadingly lumped in with the oxidizer in the traditional definition of Φ. In either case, use of the traditional definition of Φ to quantify the mixture stoichiometry can lead to significant errors. This paper introduces the oxygen equivalence ratio, Φ Ω , a parameter that properly characterizes the instantaneous mixture stoichiometry for a broader class of reactant mixtures than does Φ. Because it is an instantaneous measure of mixture stoichiometry, Φ Ω can be used to track the time-evolution of stoichiometry as a reaction progresses. The relationship between Φ Ω and Φ is shown. Errors are involved when the traditional definition of Φ is used as a measure of mixture stoichiometry with fuels that contain oxidizer elements or oxidizers that contain fuel elements; Φ Ω is used to quantify these errors. Proper usage of Φ Ω is discussed, and Φ Ω is used to interpret results in a practical example.