Downward flame spread over poly(methyl)methacrylate

Abstract

The thermal regime of downward flame spread over poly(methyl)methacrylate (PMMA) in an oxygen/nitrogen environment in normal gravity has been revisited experimentally, computationally, and analytically. Although spread rate data is plentiful in the literature, different fuels, usually PMMA and cellulose, have been used in thermally thick and thin limits. Moreover, most of these experiments, conducted at atmospheric oxygen levels, belong to the kinetic regime where finite-rate kinetics plays a dominant role. As a result, there remain some unanswered questions about the thermal regime, which constitutes the backbone of downward flame spread. We present spread rate data for the first time in the thermal regime where the fuel thickness is changed from the thin to the thick limit. A comprehensive computational model, verified through comparison with all relevant analytical solutions, is used to establish the transition criterion between the chemical and thermal regimes, and between the thin and thick fuel regimes. An earlier extension of the de Ris formula, capable of predicting the spread rate accurately for forced opposed flow, has been extended to downward configuration by proposing an empirically determined equivalent buoyant convection velocity. The predictions from the resulting closed form spread rate formulas, which retain the functional form of the de Ris formula, are shown to compare well with computational and experimental results, including all previously published data in the thermal regime. An alternative to traditional Damkohler number correlation, in which an equivalent oxygen level is used in conjunction with thermal-regime spread rate formulas, is proposed to capture the effect of finite-rate chemistry. A simple formula for the transition thickness between the thin and thick fuel regime is proposed as τ crit = 2 τ V f,Thin V f,Thick where the spread rates can be obtained from experiments or the proposed formulas.