Automatic Fire Sprinkler Activation Time with Quadratic Fire Growth

Fires with a heat release rate that grows quadratically in time and levels off after the first automatic fire sprinkler is activated are routinely used in evaluating the consequences of fire in performance based design projects. In order to calculate the sprinkler activation time one needs to solve the differential equation that governs the heat transfer between the ceiling jet and the sensing element of the automatic fire sprinkler, an equation that depends on the temperature and velocity of the gas. Well-known empirical correlations between ceiling jet properties and heat release rate as well as numerical simulations can be used to determine the temperature and velocity of the gas. Here a comparison and discussion of the results obtained for the activation time and activation heat release rate using both approaches is presented, which can help authorities having jurisdiction to assess safety reports when there are no clear regulations about which method should be applied.