Scaling laws of turbulent ceiling fires

A fundamental dimensionless number appropriate for studying buoyancy driven flames, Pi(beta) similar to Ra/(1 + B)/1 + (1 + B)/sigma, is developed by considering the balance of momentum, thermal energy, and species flux. In the particular case of laminar ceiling fires, it is shown that a modified Pi(beta) scales with the ratio of the integral length scale and the boundary layer thickness as l/delta(beta) similar to Pi(f)(1/5). Here, Pi(f) is based on a flame Rayleigh number, Ra-f, which is defined as [GRAPHICS] For turbulent ceiling fires, it is shown that the ratio of integral length scale and the flame Kolmogorov scale is given by l/eta(beta) similar to Pi(f)(1/4). These fundamental relations for laminar and turbulent ceiling fires are correlated to experimentally measured flame stand-off distances for ceiling fires [1-3]. Based on the limited data available, the agreement with experiments is very good. Additional experiments are needed to further verify the validity of the scaling laws in the two flow regimes. (C) 1998 by The Combustion Institute