Hydrodynamic theory of premixed flames: effects of stoichiometry, variable transport coefficients and arbitrary reaction orders

Abstract

Based on a hydrodynamic length, which is typically larger than the nominal flame thickness, a premixed flame can be viewed as a surface of density discontinuity, advected and distorted by the flow. The velocities and the pressure suffer abrupt changes across the flame front that consist of Rankine–Hugoniot jump conditions, to leading order, with corrections of the order of the flame thickness that account for transverse fluxes and accumulation. To complete the formulation, expressions for the flame temperature and propagation speed, which vary along the flame as a result of local non-uniformities in the flow field and of flame front curvature, are derived. Unlike previous studies that assumed a mixture consisting of a single deficient reactant, the present study uses a two-reactant scheme and thus considers mixtures whose compositions vary from lean to rich conditions. Furthermore, non-unity and general reaction orders are considered in an attempt to mimic a wider range of reaction mechanisms and, to better represent actual experimental conditions, all transport coefficients are allowed to depend arbitrarily on temperature. The present model, expressed in a coordinate-free form, is valid for flames of arbitrary shape propagating in general fluid flows, either laminar or turbulent.

Darrieus–Landau instability and Markstein numbers of premixed flames in a Hele-Shaw cell

“…tained by Matalon and coworkers for temperature dependent diffusivities, in the case without gravity (see [16] for the derivation, the correct results are to be found in Altantzis et al Furthermore, it should be noted that in the region of vanishingly small wavenumbers, the gravity effects lead to complex values of the growth rate 145 whose small k-expansion has to be sought now in powers of k 1/2 . A straightforward calculation shows that the real part is still linear in k but with a negative slope whereas the imaginary part is proportional to k 1/2 .…”

A Reduced Model for Flame-Flow Interaction

“…In this section we recall some results from the differential geometry Derivation of the basic formulas presented here can be found in [13], [14] and [15].…”

Theory of Detonation with an Embedded Sonic Locus

“…We express the sonic conditions in two-dimensional surface-attached Bertrand coordinates which use the normal distance to a prescribed front and the arclength to a reference point along the front as the intrinsic surface-based coordinates (see, e.g., [11,18]). Since the Bertrand coordinates are developed by the sonic surface, they are perfectly suited to simplify the conditions since only derivatives in the surface and normal to that surface appear.…”