Experimental and numerical Lattice-Boltzmann investigation of the Darrieus–Landau instability

Abstract

We present an experimental and numerical investigation of the Darrieus–Landau instability in a quasi two-dimensional Hele-Shaw cell. Experiments and Lattice-Boltzmann numerical simulations are compared with Darrieus–Landau analytical theory, showing an excellent agreement for the exponential growth rate of the instability in the linear regime. The negative growth rate – second solution of the dispersion relation – was also measured numerically for the first time to the authors’ knowledge. Experiments and numerical simulations were then carried out beyond the cutoff wavelength, providing good agreement even in the unexplored regime where Darrieus–Landau is supplanted by diffusive stabilization. Lastly, the non-linear evolution involving the merging of crests on the experimental flame front is also successfully recovered using both the Michelson–Sivashinsky equation integration and the Lattice-Boltzmann simulation.