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Opposed-flow flame spread over solid fuels is an important case of fire safety studies. Spread rate and flame structure depend on fuel nature and burning conditions, and they can be used to study material flammability and fundamental combustion mechanisms. Previous studies provided important insights on flames developing over vertical walls and under the effect of a forced flow. However, there are limited works available in literature on the prediction of flame length of spreading flames even though it is the main driver of flame growth in concurrent-flow flame spread. In this work we consider the dependence of flame length on fuel thickness and flow velocity. Acrylic samples, with thicknesses from 0.05 to 12 mm, are burnt vertically in a wind tunnel against flow velocities between 0 and 200 cm/s. Without a forced flow, the flame length strongly depends on fuel thickness. Using scaling theory, closed-form expressions for both opposed-flow and downward spreading flames are developed and agree qualitatively with the data. For downward spread, the developed expression is shown to be quite similar to the theoretical flame length expression for gaseous diffusion flame by Roper. A least-squares fit of the developed expression with the data produces the undetermined constant of the scaled expression, producing a formula from which flame length over solid fuels (with both sides burning) can be predicted with a 90% accuracy.

Prediction of Flame Length in Opposed-Flow Flame Spread: Global Similarity Analysis and Experiments