Bounds for Downward Flame Spread Rate in Solid Fuels and Comparison to Experiments

Abstract

De Ris formulae for the flame spread rate over solid fuels that propagate against an external fluid flow for both the thermally thin and thick regimes have become well-known. In some cases, it is expected that predictions from these formulae will fail since they are independent of parameters that may modify the burning velocity. Based on the technique developed by Benguria and Depassier, we derive in this article new analytical expressions that correspond to upper bounds for the speed of the flame front propagating downwards. These upper bounds are functions of several parameters that are not taken into consideration in the de Ris expressions, such as the activation energy for solid- and gas-phase reactions. Burning velocity values obtained for these upper bounds are compared with new data and with other experimental results found in the literature, showing a better agreement than the de Ris formulae for a wide variety of cases.

Keywords:

• Bounds for the propagation speed
• Downward flame spread
• Fire safety
• Solid fuel

ACKNOWLEDGMENTS

B.C. acknowledges the support of a BR-Universitat de Girona grant. This work has been partially funded by the Generalitat de Catalunya under grant 2009-SGR-374, the MICINN-FEDER under grant FIS-2009-13050, and the European Commission under grant NEST-28192-FEPRE.

Notes

1 – Wu and Chen (2003, 2004).

2 – Gas mixture properties from classical ideal gas formulae (Bird et al., 1992) and data from Lemmon and Jacobsen (2004) and from the Web site http://flame.sdsu.edu.

3 – Di Blasi (1994).