Numerical study on the causality of solution multiplicity in ultra-lean H₂-air premixed flames.

Safety issues in hydrogen-fueled devices can be related to flame ignition and propagation owing to leakages in non-ventilated gaps. In particular, large mass diffusivity of hydrogen enables the potential propagation of reacting kernels over very lean hydrogen-air mixtures in narrow channels h~O(1mm). Their formation and survival resides in the balance between the heat release due to combustion and the heat losses through the walls confining the lean mixture. Previous studies have found two stable isolated flame structures, an isolated circular flame and a double-headed one, that coexist under the same parametric space and propagate under different speeds [1]. This work presents a numerical study on the causality of solution multiplicity, which is thought to be determined by the symmetry-breaking details during ignition due to experimental evidence [2].

In particular, an ensemble of ignition cases including hot spots characterized by a temperature peak and linear ignition with a randomly sinusoidal morphology are investigated. We use a quasi-2D simplified formulation of the Navier-Stokes equations with a one-step Arrhenius reaction rate and off-plane heat losses, and an in-house Fourier-Fourier spectral discretization code to simulate the transient from ignition event.

A rich set of solutions evolving towards stable one and two-cell flames is generated for the same set of parameters. Flame structure tracking is proposed to study and characterize the formation of both configurations to unveil the underlying physics controlling the bistable behavior.