Abstract
In contradistinction to the Part 1 of this study (in Transactions of A. I. J., #291, 1980) where we discussed on the criteria on the occurrence of flashover, we study here on the characterization of flashover in transient fire, assuming the occurrence of fiashover itself. The evaluation of the severity of fire development or the prediction of time or condition at the beginning of flashover in fire is an important problem in fire safety design, because there are some sorts of building use for which a fire protection design to prevent the occurrence of flashover is practically impossible. Moreover, while we clarified the criteria on the occurrence of fiashover of zero order reaction system by replacing them to the existence criteria of steady state solution of the basic equations of fire models, a discussion based on the behavior of transient process is indispensable for clarifying strictly the flashover criteria on a system where reaction rate depends on the concentration of oxygen, because an equilibrium exists irrespective of the values of parameters as seen in the simplified model of Thomas and quasi-steady model of Quintiere et al. The aim of this study is to provide a theoretical basis for deriving useful indices and evaluation methods on flashover in transient fire as well as to contribute to clarifying the flashover mechanics of oxygen concentration dependent reaction system. In this report, we derived the following results, by characterizing flashover in transient fire by the instability of temperature fluctuation on the basis of observation facts and the significant features of temperature-time curve when flashover occurs. 1. The thermal state of fire compartment at the transition from early fire to flashover or from flashover to fully-developed fire is given as a solution of |∂(H_1, H_2, …, H_n)/∂(T_1, T_2, …T_n)|=0 where H_i is the right hand side of the energy balance equation for zone i in transient fire and T_i is absolute temperature of zone i. n is the number of zones including the grids for finite difference approximation of thermal conduction equation in solid walls. 2. It was mathematically proved that the transition condition above mentioned is equivalent to the existence criterion of steady state solution of V_i dT_i/dt=H_i, i=1, 2, …, n' where n' is the number of zones except for finite difference grids in solid walls, as the grids are parameterized in the expression of steady state thermal conduction. 3. The methods to give the upper and lower bounds of the temperature of combustible zone at the transition from early fire to flashover are shown. These bounds will be useful for a practical evaluation on flashover.
