Scale effect of flame instability mechanisms on propagation velocity

Blast pressure is a major source of the damage caused by an accidental gas explosion. Its magnitude depends on the thermal expansion rate and hence on the flame propagation velocity. This paper discusses the influence of two flame instability mechanisms, i.e., diffusive-thermal and hydrodynamic instabilities, on flame propagation velocity with an emphasis on their scale effects as the flame continuously increases its size during an explosion. The Sivashinsky equation is numerically solved to simulate flame propagation behaviors. It is found that flame propagation velocity, Vf, is independent of flame size under the influence of diffusive-thermal instability, whereas Vf increases with flame size under the influence of hydrodynamic instability. The latter result is understood as a result of flame’s fractal structure. Fractal dimension is determined from the dependency of Vf on flame size, and the obtained fractal dimension is close to the known experimental value.

► The scale effect of instability mechanisms on flame speed is studied.
► Diffusive-thermal instability and hydrodynamic instability are considered.
► Under the diffusive-thermal instability, flame speed is independent of flame size.
► Flame speed increases with flame size under the hydrodynamic instability.
► Fractal dimension is calculated from the dependence of flame speed on flame size.