Yves D'Angelo

On model evolution equations for the whole surface of three-dimensional expanding wrinkled premixed flames

Borrowing the structure of building blocks from potential hydrodynamics, we set up model evolution equations to mimic moderately wrinkled three-dimensional flames expanding in gaseous premixtures. These evolution equations incorporate a hydrodynamic instability, local curvature effects, a Huygens-type nonlinearity, and can cope with broad-banded forcing whenever needed. Pseudo-spectral integrations in the Legendre–Fourier basis yield evolutions of the whole front that are in striking qualitative agreement with experiments on free or weakly forced propagations. Our results are robust against educated changes in the modelling. Provided an accurate evolution equation is available, this approach can simulate expanding flames which are quite a bit larger than what DNS can currently handle, at least in the chosen configurations.

Combustion fronts in non-diffusing disordered premixtures. I: Single-channel curved flames

We consider curved flames in model solid-like premixtures, when the initial reactant content and/or reactivity are maxima along the axis of straight channels. Hydrodynamics and fuel diffusion are neglected. The one-step reaction has an explicit dependence on coordinates, and follows such a generalized Arrhenius law that the flat flame problem in homogeneous media is solved exactly for any activation exponent, n. In the large-n, Arrhenius-like, limit we produce a PDE for the flame shape and speed, U. This indicates that: (i) 2D Lorentzian transverse reactivity profiles yield uniform reaction temperatures for any effective channel widths (L 1, L 2), and give elliptic–paraboloidal fronts; (ii) too small L i s induce extinction, at known n-dependent values; and (iii) reactivity and initial-composition gradients play similar roles if a certain combination thereof is maintained fixed. For 𝒪(1) values of n, we revisit the problem via a δ-function model – tailored to reproduce as many exact results as possible. By means of generalized elliptic coordinates, we analytically confirm and sharpen items (i)–(iii). Finite-difference direct numerical simulations, validated through comparisons with linear stability analyses, are finally developed. They also confirm (i)–(iii) for moderate ns and show how accurate the δ-model is, even then. More sensitives rates (n > 5) yield a whole hierarchy of instabilities close to extinction: Hopf bifurcation, travelling waves then hot spots, period doubling, premature extinction; yet the time-averaged U stays close to what the δ-model gave. Non-Lorentzian (e.g. Gaussian) reactivity profiles lead to nearly identical conclusions. Open problems, and implications as to larger-scale propagations in disordered media, are evoked.