Analytic approximations of burning velocities and flame thicknesses of lean hydrogen, methane, ethylene, ethane, acetylene, and propane flames

The objective of this study is to provide accurate analytical expressions for the burning velocity and flame thickness of lean hydrogen, methane, ethylene, ethane, acetylene, and propane flames. Starting from a detailed kinetic mechanism of 82 elementary reactions, numerical computations were performed for pressures between 1 and 40 bar, unburnt temperatures between 298 K and 800 K (500 K for H2, C2H2 and C2H4), and fuel air equivalence ratios, , between a lean limit, defined by a burning velocity of 5 cm/s, and =1. Guided by the results of previous asymptotic analyses, a fitting function for the burning velocity was derived that contains six parameters and predicts the burning velocities for each fuel with a standard deviation of less than 7.6% for the entire data set. A definition based on the asymptotic analysis for the flame thickness was derived as the thickness of the chemically inert preheat zone. For methane, propane, ethylene, and acetylene flames, this definition could readily be linked to the classical definition of the flame thickness that uses the x-interval spanned by the steepest tangent to the temperature profile between the unburnt and adiabatic temperature as the flame thickness. This relationship failed for hydrogen flames, since the underlying assumption of a chemically inert preheat zone is not valid here.