An integral model for turbulent flame radial lengths under a ceiling

An analytical study using an integral model for turbulent flame radial lengths under a ceiling is presented. Dimensionless equations give results in terms of Q⁎—dimensionless firepower, and D/H—the ratio of fire diameter to ceiling height. The model used an empirical relationship for the mixing ratio of air entrained to stoichiometric-air needed for the ceiling jet-flame. This value was developed from data, and varies, from the vertical turbulent flame-mixing ratio, at about 9.6 for a short radial flame, and to a value of 1 for long flames that tend to become laminar. Predictions from the model are in good agreement with the experimental data from previous work found in the literature. These data contain heat release rates ranging from 0.3 kW to 750 kW, ceiling heights from 0.05 m to 1.5 m, and flame radial lengths from 0.05 m to 2 m. They span a range that contains data where the fire plume flame just touches the ceiling to the case where long ceiling flames become laminar. Other correlations by You et al. and Hasemi et al. are presented and discussed.

► An analytical solution for flame radial lengths under a ceiling.
► Mixing ratio of air entrained in the ceiling jet-flame varies from 9.6 to 1.
► New correlation has no dependence on D/H.