Abstract
The aim of the study is to clarify the physical aspects of flashover of compartment fire and deduce an evaluation method on flashover with reference to the mathematical modeling of fire. In this paper, the flashover criterion of zero order reaction system is regarded as the critical condition on the existence of a steady state solution of the governing equations of fire which are abstractly represented by V_idT_i/dt=H_i, i=1, 2, …, n, where n is the number of zones. The mathematical structure of H_i is studied from such a point of view, and some methods to obtain the critical conditions of flashover are proposed. The main results of this paper are as follows. 1. The thermal state of the steady state solution of V_idT_i/dt=H_i under the critical set of parameters on flashover satisfies |∂(H_1, H_2, …, H_n)/∂(T_1, T_2, …, T_n) |=0. All critical sets of parameters can be obtained by mapping the critical hyperplane |∂(H_1, H_2, …, H_n) /∂(T_1, T_2, …, T_n) |=0 from (T_1, T_2, …, T_n) space to the parameter space by H_i=0, i=1, 2, …, n. 2. The critical value of a parameter on flashover under the fixed values of the other parameters others can be obtained by calculat ing its extremum under the constraint conditions H_i=0. Mathematical optimization techniques are available to this procedure. The above results denote that the critical conditions on flashover can be directly obtained without solving the governing equations numerically. The application results to a simple model with 2 zones assure the adequancy of the above results.
