Hindawi Publishing Corporation Journal of Combustion Volume 2011, Article ID 250391, 9 pages doi:10.1155/2011/250391 Research Article A Comparison of Flame Spread Characteristics over Solids in Concurrent Flow Using Two Different Pyrolysis Models Ya-Ting Tseng and James S. T’ien Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 10900 Euclid Avenue, 418 Glennan Building, Cleveland, OH 44106, USA Correspondence should be addressed to Ya-Ting Tseng, yating@case.edu Received 30 October 2010; Accepted 24 February 2011 Academic Editor: Kalyan Annamalai Copyright © 2011 Y.-T. Tseng and J. S. T’ien. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Two solid pyrolysis models are employed in a concurrent-flow flame spread model to compare the flame structure and spreading characteristics. The first is a zeroth-order surface pyrolysis, and the second is a first-order in-depth pyrolysis. Comparisons are made for samples when the spread rate reaches a steady value and the flame reaches a constant length. The computed results show (1) the mass burning rate distributions at the solid surface are qualitatively different near the flame (pyrolysis base region), (2) the first-order pyrolysis model shows that the propagating flame leaves unburnt solid fuel, and (3) the flame length and spread rate dependence on sample thickness are different for the two cases. 1. Introduction In modeling flame spread over solids, a description of the solid pyrolysis processes is required to complete the coupling between the gaseous flame phase and the solid phase. Typ- ically, a pyrolysis description provides the relationship be- tween the solid mass burning rate and the local conditions of the solid fuel being heated. The detailed chemical steps of the pyrolysis reactions, however, can be very complex, depending on the types of solids, the temperature, the heating rate, the duration, among other things. They may also vary depending on whether the surrounding atmosphere is with or without oxygen. There is an abundance of literature on the pyrolysis of materials. For example, in biomass production, a review can be found for the pyrolysis of wood and biomass [1]. Polymer pyrolysis and measurement can be found in [2]. A recent pyrolysis model intended for fire research was offered in [3]. In model computation of flame spread over solids, sim- plified pyrolysis reactions are needed to make the model more tractable. For example, Di Blasi [4] has employed a three-step reaction scheme: solid to vapor, solid to tar, and solid to char. A still simpler scheme is a one-step description to represent the overall solid pyrolysis conversion from solid to vapor. For cellulose, Kung [5] proposed a first-order re- action whose rate depends on the first power of the local solid density and the Arrhenius expression on temperature. This has been adopted in many opposed-flow flame spread works (e.g., [6, 7]). Because of the linear dependence on local density in the rate expression, the solid fuel is not entirely consumed in a finite length of time or in a finite distance by a spreading flame when using the first-order pyrolysis reaction model. Since some solids are observed to burn out completely in experiments, Ferkul and T’ien [8], in their concurrent flame spread model, adopted a zeroth- order pyrolysis reaction which has previously been used in solid propellant studies. The zeroth-order reaction has since been used in many subsequent works (e.g., [9, 10]). Despite their simplicities, there are fundamental differ- ences between the zeroth-order and the first-order pyrolysis models. The pyrolyzing mass burning rate depends only on the surface temperature in the zeroth-order model and is therefore a surface model. In the first-order model, on the other hand, pyrolysis rate depends on the local temperature and density in the interior of the solid so it is an in-depth model. Although both models have been employed in many previous flame spread computations, there is no investigation