Opposed-flow flame spread over cylindrical fuels: Spread rate formulas and experimental verification

Abstract

Opposed-Flow flame spread over flat condensed fuel has been studied for many decades as it constitutes a fundamental problem of fire studies. Although cylindrical fuels offer the simplicity of axial symmetry, despite many previous attempts, there are no easy-to-use flame spread rate expressions that connect spread rate in this geometry to the exact solution for flame spread rate for flat fuels. Also no criterion exists to delineate a thermally thin cylindrical fuel from a thermally thick one. In this work, we use the scaling approach to develop closed-form expressions for flame spread rate for opposed-flow flame spread over thermally thin and thick cylindrical fuels. The approach is validated by reproducing the theoretical expressions of de Ris for flat fuels. By equating the heated layer thickness with the radius, a criterion is developed for delineating thermally thin cylinders from thermally thick ones. It is shown that the spread rate is always higher for a cylindrical fuel when compared to a flat fuel with a half-thickness equal to the radius of the cylindrical sample. The cylindrical spread rate depends on the same factors as that of flat fuels with an additional coefficient arising out of heat transfer enhanced by the curvature effect. For thermally thin cylinders, the spread rate is predicted to be at least two times faster than the corresponding flat fuel. For thermally thick fuels also the spread rate is significantly higher, but as the radius is increased the flat fuel limit is approached. Spread rates obtained from experiments performed with PMMA cylinders of different diameters in downward configuration are shown to agree well with the theoretical expressions. The thermally thick limit for downward spread, interestingly, is achieved for PMMA cylinders as narrow as 2.4 mm diameter.