Determination of the spread rate in opposed-flow flame spread over thick solid fuels in the thermal regime

Limitations of the assumptions in the classic de Ris formula [1] for opposed-flow flame spread rate over thick fuels in the thermal regime are explored through numerical experiments in which the assumptions used in the original theory are eliminated one by one from the mathematical model. While the assumptions of infinite-rate chemistry, mass flux linearization, and neglect of radiation are found to be reasonable in the thermal regime, assumptions of a slug flow, a surface-hugging flame, and constant properties are responsible for the predictions of spread rate being in error by as much as a factor of 10. A spread rate formula, derived from a semiempirical solution of a simplified problem, is shown to overcome the drawbacks of the de Ris formula while retaining its simplicity. A hydrodynamic coefficient, developed for two different flow configurations, and a flame liftoff coefficient, both obtainable from the known parameters of the problem, correct for some of the major limiting assumptions in the de Ris theory. The formula developed here, which can be written as (V) over cap(f,EST) = F-EST(2)/beta(5)beta(6) (V) over cap(eqv) in which (V) over cap(eqv) contains the hydrodynamic information and the factor in front of it the chemical information, performs significantly better than the de Ris formula when tested against available data and extensive computational results for different flow configurations, opposed-flow velocities, oxygen levels, and ambient pressures.