An analysis of the stabilization of fire whirls

Stabilization of the flame base at the bottom Ekman boundary layer of the fire whirl under strong circulation is analytically and numerically studied. The problem is relevant for_fire safety and the associated understanding of the generation mechanism of the newly discovered whirling flame, the so-called blue whirl. Based on the dynamic balance of the triple flame propagation speed and the local flow velocity at the bottom boundary layer, theoretical solutions of the liftoff position, r_f, and the critical blowout limit represented by its Ekman number, Ek_Bt, are derived. The theoretical results agree well with the numerical results both qualitatively and quantitatively. It is shown that the response of r_f to the system Damkohler number, Da, forms a typical C-shaped curve and there are two solutions of r_f for relatively large Da, with the one closer to the edge of the fuel pool being stable while the other being unstable. Explicit solution of the blowout limit shows that Ek_Bt ∞ (S^S_L)^4/3, where S^S_L is the stoichiometric planar_flame speed. This is because not only the triple flame propagation speed linearly increases as S^S_L increases, but the flame front can also reach a position closer to the edge of the fuel pool where the flow velocity is lower. The effect of the transversal radial velocity gradient (TVG) at the Ekman boundary layer on the stabilization of the fire whirl is also investigated. The TVG makes the flame harder to liftoff and blowout and the effect of which can be described by a non-dimensional parameter, λ, which represents the ratio of the flame curvature and the TVG. The TVG normally plays a secondary role in the triple flame propagation due to the relatively large flame curvature of the triple flame.