A three-dimensional study of the influence of momentum loss on hydrodynamically unstable premixed flames

Abstract

The propagation of an isobaric premixed flame into a quiescent gas mixture of fuel and oxidizer contained between two parallel plates is investigated numerically. The plates are separated by a small distance h and considered as adiabatic. The mixture is assumed to be lean in fuel and the combustion model includes a single-step Arrhenius-type reaction, constant heat capacity and unity fuel Lewis number. Transport properties are considered to be temperature dependent or constant, which allows us to decouple two different instability mechanisms of hydrodynamic nature: (i) Darrieus-Landau (associated with the density change due to thermal expansion) and (ii) Saffman-Taylor (associated with the viscosity contrast). By performing three-dimensional (3D) simulations, the propagation rate and the flame front shape is analyzed as a function of the dimensionless parameter a = h/δ_T, where δ_T is the thermal thickness of the planar flame. The parameter a ranges from very small values to large enough ones so that flame curvature between the plates manifests itself. Results show that, as the distance between the plates decreases, loss of momentum enhances the hydrodynamic instability in comparison with that of a freely (unconfined) propagating flame. Likewise, viscosity contrast across the flame brings about an additional destabilizing mechanism. When distance between the plates increases, flame curvature can become important and contribute significantly to the overall propagation rate. Finally, by comparison with the 3D simulations, we show that confinement effects can be effectively described by a two-dimensional formulation written in the limit a → 0, in which momentum conservation is reduced to a linear equation for the velocity similar to Darcy’s law.