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.

Consistency study of Lattice-Boltzmann schemes macroscopic limit

“…Let us start with the recursive regularized pressure-based model (RR-), presented earlier this year 7 , to simulate both compressible ows and reactive ows 18 .…”

“…VIII) and the pressure-based (Sec. VII) models, as adapted for reactive ows 17,18 . This test case was found to particularly aggravate spurious currents e ects because of the presence of heat-release along a curved density gradient.…”

“…This comparison between density-based and pressure-based formulations illustrates how spurious currents can be triggered by defects of consistency of the stress-tensor. Figure 2: Visualization of the temperature, heat release rate and velocity magnitude elds of the 2D circular ame as obtained with the pressure-based formulation 18 , at = 9.24s.…”

“…(ii) Second, time and space are discretized, as in most computational uid dynamics (CFD) methods. Albeit initially limited to low-Mach athermal ows, the range of applicability has been steadily growing, to encompass compressible ows [7][8][9][10] , multiphase ows [11][12][13][14][15][16] and combustion [17][18][19] .…”

A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods

“…A way to improve the stability of the methods while keeping an expression of the collision kernel close to the classical density-based one is to switch to pressure-based methods, in which the zeroth-order moment of the density functions is the pressure instead of the density = / 2 . These methods have been proposed initially for low-Mach reactive flows 9,10 and rapidly extended to low-Mach multiphase flows 11,12 , but only very recently to high-speed compressible 13 and reactive flows 14,15 and to humid air thermodynamics 16 . A possible explanation for their efficiency has been very recently proposed 17 through theoretical analysis.…”