Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. Part 1 - Dispersion relations in the linear regime

Abstract

The impact of intrinsic combustion instabilities is studied for lean premixed hydrogen flames by means of a series of simulations at different equivalence ratios [0.4-1.0], unburned temperatures [298K-700K], and pressures [1bar-20bar]. In addition to the Darrieus-Landau, or hydrodynamic, instability, lean premixed hydrogen flames are prone to thermodiffusive instabilities, which lead to significant flame front wrinkling and a chaotic process of formation and destruction of cellular structures along the flame front. Theoretical models are not yet capable of accurately describing the evolution of such flames, so the propensity of lean hydrogen flames to develop instabilities is studied numerically in a parametric variation in this work. A stability analysis is conducted, in which planar flames are initially exposed to weak harmonic perturbations and the response of the flame is studied. In the initial phase referred to as linear phase, a growth or decrease of the initially imposed perturbation amplitude is observed, while for long times, chaotic cellular structures are formed along the flame front, which are studied in part 2 of this work (L.Berger et al., Combust. Flame, 2022). The growth rates of the perturbation amplitude that are obtained from the initial phase are a measure of the strength of the intrinsic instability mechanisms and vary with respect to the wave number of the harmonic perturbation yielding characteristic dispersion relations. A decrease of equivalence ratio and unburned temperature and an increase of pressure are found to enhance the growth rates and hence intrinsic instabilities. The variation of dispersion relations is analyzed with respect to variations of the expansion ratio, the effective Lewis number of the mixture, and the Zeldovich number. For the lean hydrogen flames, with increasing pressure a decrease of the cut-off wave number, which represents the change of the sign of the dispersion relation at high wave numbers, is observed. This is the opposite trend compared to flames that are not affected by thermodiffusive instabilities. Further, numerical growth rates are compared to theoretical models. The results show that lean hydrogen flames are prone to develop instabilities at conditions that are relevant to several combustion devices such as gas turbines that operate at lean equivalence ratios, elevated pressures and temperatures or domestic and industrial heaters that operate at low temperatures and ambient pressure.