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 varies from 9.6 for short radial flames to 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. 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. An alternative empirical fit of the theoretical results finds that the radial flame length is independent of ceiling height once the flame hits the ceiling.
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