Defining a maximum heat release rate probability distribution function for design fires in sprinkler-protected residential buildings

Abstract

In fire safety engineering analysis of sprinkler-protected residential buildings, the maximum heat release rate is a key parameter requiring consideration. Several documents provide advice for estimating the heat release rate of a sprinkler-controlled fire, with a prevailing suggestion that it is fixed upon activation of the first sprinkler. When carrying out deterministic analysis, this requires the engineer to assume fixed fire parameters and consider that sprinklers limit fire growth. To explore these assumptions, the study uses three deterministic models to estimate a sprinkler-controlled maximum heat release rate for a representative apartment layout. The models include Alpert's correlation, a B-RISK zone model and a computational fluid dynamics model in the Fire Dynamics Simulator. These deterministic models are compared to a probabilistic model in B-RISK, where Monte Carlo simulations are used to generate a range of maximum heat release rates from distribution functions for fire and sprinkler properties. An output distribution function is generated with a mean of 296.6 kW and a standard deviation of 503.8 kW, with a lognormal distribution (μ = 5.014, σ = 1.165) estimated as a best-fit. The deterministic models are estimated to sit in the 92–98 percentile range of this function, indicating that common deterministic assumptions are reasonably conservative. The article concludes with suggesting that, for deterministic analysis, a percentile between the 80th and 99th (340–2640 kW) could be qualitatively selected based on the design objectives, building situation and relative consequence of a fire. Further research is needed to establish guidelines for selecting appropriate percentiles across various building scenarios.