Combustion and Flame 179 (2017) 338–353 Contents lists available at ScienceDirect Combustion and Flame journal homepage: www.elsevier.com/locate/combustfame A generalized model of flame to surface heat feedback for laminar wall flames Isaac T. Leventon, Kevin T. Korver, Stanislav I. Stoliarov ∗ University of Maryland, Department of Fire Protection Engineering, College Park, MD 20742, United States a r t i c l e i n f o Article history: Received 16 September 2016 Revised 8 February 2017 Accepted 8 February 2017 Keywords: Fire dynamics Flame spread Vertical burning Flame heat flux Heat of combustion Polymeric fuels a b s t r a c t In this work, experimental measurements of flame heat flux and sample mass loss rate are obtained as a diffusion flame spreads vertically upward (in the direction opposed to the vector of gravity) over the surface of seven commonly used polymeric materials, two of which are glass reinforced compos- ites. Using these measurements, a previously developed empirical flame model specific to poly(methyl methacrylate) is generalized such that it can predict (flame to material surface) heat feedback from 3 to 20 cm tall flames supported by a wide range of materials. Model generalization is accomplished through scaling on the basis of a material’s gaseous pyrolyzate heat of combustion, which can be measured us- ing mg-sized material samples in a microscale combustion calorimeter. For all seven materials tested in this work, which represent diverse chemical compositions and burning behaviors including polymer melt flow, sample burnout, and heavy soot and solid residue formation, model-predicted flame heat flux (to a water-cooled heat flux gauge) is shown to match experimental measurements taken across the full length of the flame with an average absolute error of 3.8 kW m −2 (approximately 10–15% of peak mea- sured flame heat flux). Coupled with a numerical pyrolysis solver, this generalized wall flame model pro- vides the framework to quantitatively study material propensity to ignite and support early fire growth in a range of common scenarios with a level of accuracy and reduced computational cost unmatched by other currently available modeling tools. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved. 1. Introduction Understanding the dynamics of fire inception and growth on or- ganic solids is highly important for engineering fire safety in the built environment. Among organic solids, synthetic polymers and polymer based composites are used increasingly due to their low weight, highly customizable properties, low cost, and energy effi- ciency [1]. At the same time, it is also understood that these mate- rials can present a greater fire safety hazard than traditional build- ing materials [2]. Thus, understanding their resistance and reaction to fire is crucial. A variety of standard test methods have been de- veloped by organizations such as ASTM International [3,4] and UL [5,6] to assess material flammability in terms of ignitability, heat release and surface flame spread. Although these bench scale tests are widely used, they typically provide observations of material re- sponse to a specific set of conditions. Consequently, conflicting as- sessments often arise from different tests [7] and they show lim- ited ability to predict material performance in other fire scenarios ∗ Corresponding author. E-mail address: stolia@umd.edu (S.I. Stoliarov). [8]. A more rigorous approach to assessing material flammability, which would allow for the proactive design of new, safer materi- als, is to characterize the controlling mechanisms of a fire behav- ior of interest and develop models that accurately describe these constituent processes. In this manner, the behavior of a material in response to a wide range of likely fire conditions can be better understood and predicted. Upward, concurrent-flow flame spread over the surface of a ma- terial has long been recognized in the fire safety field as a highly important process because it is a key determinant of the initial rate of fire growth [9]. It has been well established [10,11] that surface flame spread is governed by positive feedback between transient processes of solid phase degradation (pyrolysis) and gas phase combustion. As a solid is heated, it degrades and produces gaseous pyrolyzates that can react with the ambient oxidizer to form a diffusion flame. Some of the heat produced by this flame is transferred back into the solid thus allowing for continued degra- dation and production of flammable pyrolyzates. Upward spread- ing flames may grow rapidly because hot combustion products, driven upward by buoyancy, heat up a part of the solid that is not yet degrading, which causes continuous expansion of the pyrolysis region. http://dx.doi.org/10.1016/j.combustflame.2017.02.007 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.