On the Application of the Levenberg–Marquardt Method in Conjunction with an Explicit Runge–Kutta and an Implicit Rosenbrock Method to Assess Burning Velocities from Confined Deflagrations

Abstract

The potential of the Levenberg–Marquardt method combined with an explicit Runge–Kutta method for non-stiff systems, and, an implicit Rosenbrock method for stiff systems to investigate burning velocities using explosion bombs was explored. The implementation of this combination of methods was verified on three benchmark test problems, and, by the application of two integral balance models to laminar hydrogen-air and methane-air explosions. The methodology described here was subsequently applied to quantify the coefficients of a turbulent burning velocity correlation for a methane-air explosion in the decaying flow field of the standard 20-litre explosion sphere. The outcome of this research indicates that the usefulness of the 20-litre sphere can be extended beyond the measurement of practical explosion parameters. When combined with the methodology in this paper, turbulent burning velocity correlations can be assessed in different parts of the Borghi-diagram.