Instabilities in Flames

The past half century has seen impressive advances in reacting flow computational fluid dynamics (CFD), initially based on Reynolds-averaged Navier–Stokes (RANS) turbulent flow modelling and detailed chemical kinetic modelling of laminar flames. These two strands were combined in the modelling of turbulent combustion. In general, the systems analysed were hydrodynamically and chemically stable. On the other hand, it is well known from non-reacting flows that there is a rich variety of hydrodynamic instabilities. Probably the best known is laminar flow in a tube stabilised by viscous stresses. As the flow rate increases, the flow is eventually destabilised by the formation of vortices and the onset of turbulence at a critical Reynolds number. Viscosity does not feature in Kelvin–Helmholtz instabilities, which arise at the interface between two fluids of different densities flowing at different velocities. When the ratio of inertia to gravitational forces attains a critical value, the flow becomes unstable, with the generation of waves at the interface. Another example is the unstable interaction of gravitational and surface tension forces at the water–air interface of a droplet that generates capillary waves of small wavelength. The various combustion instabilities are broadly discussed in Section 3.1.1.

Transition to instability is characterised by quite minor perturbations of small amplitude, often at the same level as minor physical or numerical noise.