Scaling Analysis on Pulsating Flame Spread over Liquids

Abstract

Scaling analyses based on subsurface layer instability were performed to explore the role of three independent (surface tension, gravity, and viscosity) influences on the mechanism of pulsating flame spread under normal and microgravity conditions. These three influences form two independent pi-numbers: the Marangoni (Ma) number and Grashof (Gr) number, which include the characteristic length scale ratio (depth of subsurface circulation)/(horizontal length of preheated liquid surface). The Prandtl (Pr) number was introduced to compensate for the different thermal diffusivity and kinematic viscosity of different liquids. Also a nondimensional flame spread rate, V/VD (= Vδ/D, where δ is the quenching distance and D is the diffusivity of fuel vapor) was introduced. Using these nondimensional parameters, the flame spread mechanism was divided into two separate regimes: for the shallow liquid pool the nondimensional flame spread rate was correlated with {Gr0.2/(Ma·Pr)}1.0, while for the deep liquid pool it was correlated with {Gr0.2/(Ma·Pr)}1.5.