Explicit formulation of the reactivity of hydrogen, methane and decane

Explicit expressions for chemical times relative to ignition, as functions of pressure, temperature and reactants concentrations are derived for hydrogen, methane and decane. They stem from an eigenvalue analysis, similar to that used in the Computational Singular Perturbation method among others. Significant simplification arises from neglecting high-order terms in the characteristic polynomial, allowing direct analytical resolution. Such expressions find many applications: they can serve to readily identify the most reacting areas in a complex flow simulation, in runtime or as a post-processing; or provide a simple way to assess a general activation energy of the chemical process. They may also provide a suitable alternative to the tabulated chemical times required in certain turbulent combustion models.