Auto-Ignition of a Flat Solid Fuel in a High Temperature Oxidizer Boundary Layer Flow

Abstract

A theoretical model is developed for the thermal ignition of a flat combustible solid in a hot, oxidizing boundary layer flow. It is considered that the solid ignition is controlled by two primary processes, one being the solid heating and gasification, and the other the onset of the gas phase reaction after fuel vaporization. With this approach, the solid ignition delay is obtained by combining the time required for the fuel to start to pyrolyze, and the gas phase induction time. The solid fuel pyrolysis time is calculated by using a simplified analysis of solid heating, with the assumption that because of the high activation energy characteristic of the solid pyrolysis process, this takes place exclusively at the surface when it reaches the solid pyrolysis temperature. A one step, global reaction of the Arrhenius type is used to describe the combustion reaction; thus, a large activation energy asymptotic analysis is used to calculate the induction time. It is shown that for given gas flow conditions, the primary parameter determining both the pyrolysis and the induction times is the inverse flow (inverse residence) time, given by the ratio between the flow velocity and the distance from the solid leading edge to the location of ignition. As the inverse flow time is increased, the heat transfer to the solid surface also increases, and consequently, the solid gasification time decreases. However, as the inverse flow time is increased, so is the induction time due to the convective cooling of the incipient combustion reaction; this increase in the induction time takes place slowly at first, until a critical value of the flow time is reached, at which the induction time increases rapidly and becomes infinite. This critical value is given by the critical Damköh-ler number for ignition. Since the solid ignition time is given by the sum of the pyrolysis and induction times, the result is an ignition time that decreases, reaches a minimum, and then increases with the inverse flow time. At a certain value of the inverse flow time, the ignition time becomes infinite, and ignition can no longer occur. The predictions of the model agree with a phenomenological view of the solid fuel ignition process, and are in qualitative and order of magnitude agreement with the available experimental observations.

Key words:

• Ignition
• solid fuel