Detailed simulation of laser-induced ignition, spherical-flame acceleration, and the origins of hydrodynamic instability

Ignition of a lean hydrogen–oxygen premixture by focused-laser-induced breakdown and subsequent three-dimensional expanding-flame instabilities are simulated in high detail. Both diffusive–thermal and hydrodynamic (Darrieus–Landau) instabilities are active and accelerate the flame expansion. The fluid is a partially-ionized gas in local thermodynamic equilibrium with detailed kinetics and transport models, starting from initial conditions from an auxiliary simulation based on a two-temperature local thermodynamic non-equilibrium model. After the decay of the initial laser-induced plasma, the r ∼ t^1.5 growth in time of the flame radius matches theory and experimental observations. Based on hydrodynamic theory for spherical-flame propagation, a global Karlovitz number is defined as the ratio of the hydrodynamic to flame-distortion time scales. It initially increases during the diffusive–thermal instability stage, then with the onset of significant baroclinic torque, this trend reverses, with vorticity production becoming the dominant mechanism of instability.