A Correlation for an Effective Flow Velocity for Capturing the Boundary Layer Effect in Opposed-Flow Flame Spread over Thin Fuels

Abstract

In opposed-flow flame spread over solid fuels, an indefinite increase in flow velocity eventually leads to flame extinguishment. While the chemical time is independent of the flow velocity, the residence time of the oxidizer at the flame leading edge is inversely proportional to the flow velocity and, therefore, a completion between the two leads to a situation where finite-rate kinetics dominate the flame spread behavior, leading to flame extinguishment. Their ratio, the non-dimensional Damkohler number, is known to capture this finite-rate effect and has been used to correlate the non-dimensional spread rate. Although these correlations explain the behavior observed in the experiments, there is considerable spread in the data and several variations of the defs of Damkohler number exist in literature. With all the progress made in this area, it is still not possible to predict the blow-off extinction velocity for a given fuel at any given oxidizer condition. In this work, computational evidence to establish the importance of the developing boundary layer in the kinetic and microgravity regimes is presented. Based on scale modeling, a formula is proposed for the effective velocity experienced by a flame in terms of the flow Reynolds number and Prandtl number and the expression using computational spread rates is verified.

Keywords:

• Blow-off extinction
• Boundary layer
• Damkohler number
• Flame spread
• Kinetic regime
• Opposing flow