Heat and Mass Transports in Porous Wicks Driven by a Gas-Phase Diffusion Flame

A one dimensional stagnation point diffusion flame stabilized next to a porous wick is studied using a numerical model. The bottom end of the one-dimensional wick is dipped inside a liquid fuel (ethanol) reservoir. The liquid is drawn towards the surface of the wick through capillary action against gravity. The model combines heat and mass transfer equations in the porous media with phase change and gas-phase combustion equations to investigate steady-state flow structure in the porous wick and flame characteristics in the gas phase. In one-dimensional system, the only steady solution in the porous wick that is stable is found to be in the funicular regime. There are two regions in the wick: a vapor-liquid two-phase region near the surface exposed to the flame and a purely liquid region deep inside the wick. The physics behind the two-phase flow driven by capillarity and evaporation has been studied in detail. The coupling between the flame and the porous transport involves three different length scales: flame standoff distance, wick height above the reservoir and capillary rise. Attempt is made to study the effect of the non-dimensional numbers that contains these scales. In the limit of fast chemical kinetics (large Damkohler number), the computed results depend only on two non-dimensional ratios: the ratio of wick height to capillary rise and the ratio of wick height to flame standoff distance. Thus, a simplified similitude has been identified.