Hybrid regularized Lattice-Boltzmann modelling of premixed and non-premixed combustion processes

Abstract

A Lattice-Boltzmann model for low-Mach reactive flows is presented, built upon our recently published model (Comb & Flame, 196, 2018). The approach is hybrid and couples a Lattice-Boltzmann solver for the resolution of mass and momentum conservation and a finite difference solver for the energy and species conservation. Having lifted the constant thermodynamic and transport properties assumptions, the model presented now fully accounts for the classical reactive flow thermodynamic closure: each component is assigned NASA coefficients for calculating its thermodynamic properties. A temperature-dependent viscosity is considered, from which are deduced thermo-diffusive properties via specification of Prandtl and component-specific Schmidt numbers. Another major improvement from our previous contribution is the derivation of an advanced collision kernel compatible of multicomponent reactive flows stable in high shear flows. Validation is carried out first on premixed configurations, through simulation of the planar freely propagating flame, the growth of the associated Darrieus-Landau instability and three regimes of flame-vortex interaction. A double shear layer test case

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

“…In this paper, we compare two-dimensional simulations with our hybrid LB method to quasi-2D experiments performed in a Hele-Shaw burner. Compared to [6] we will be able to obtain the full dispersion relation giving the growth rate as a function of wavenumber: it will be shown that this dis-2 persion relation has the same form as that obtained in experiments, even beyond the cutoff wave number. Furthermore, we extend the comparison up to times where non-linearities play a significant role in the flame dynamics thereby demonstrating the ability of the method to correctly predict these complex phenomena.…”

“…The numerical simulations are carried out with the ProLB software using a pressure-based hybrid regularized thermal Lattice Boltzmann (LB) model coupled with a Finite Differences (FD) solver. The probability density function f i (of finding gas particles at x with velocity c i ) is solved using hybrid regularized collision model [6]. The streaming and collision process can be expressed under discrete form as…”

“…Lattice-Boltzmann (LB) methods have been proven very efficient in the field of low-Mach external aerodynamics and aeroacoustics [1,2]. However, although the first attempt of using LB methods for low Mach number combustion has been published twenty years ago [3], a lot of interest in LB methods for reactive flows has been observed only recently [4][5][6]. We proposed in [6,7] a hybrid LB framework (Lattice-Boltzmann / finite differences) able to study combustion for low-Mach flows.…”

“…However, although the first attempt of using LB methods for low Mach number combustion has been published twenty years ago [3], a lot of interest in LB methods for reactive flows has been observed only recently [4][5][6]. We proposed in [6,7] a hybrid LB framework (Lattice-Boltzmann / finite differences) able to study combustion for low-Mach flows. Among the tests in [6] was a preliminary study of the Darrieus-Landau instability of premixed flames, a very challenging test case for LB methods since it couples temperature and species fields to the velocity field.…”

“…We proposed in [6,7] a hybrid LB framework (Lattice-Boltzmann / finite differences) able to study combustion for low-Mach flows. Among the tests in [6] was a preliminary study of the Darrieus-Landau instability of premixed flames, a very challenging test case for LB methods since it couples temperature and species fields to the velocity field. The underlying coupling between the Lattice-Boltzmann and finite differences solvers was further improved in [8], significantly improving the method stability.…”