Analysis of Key Equations in a Two-Layer Zone Model and Application with Symbolic Mathematics in Fire Safety Engineering

Abstract

There are two objectives in this paper on applying fire modelling techniques for designing fire safety provisions with symbolic mathematics. The first is to review key equations for a two-layer zone model and simplification to a simpler model. There are eleven equations on the mass, volume, temperature, density and internal energy for the upper hot layer and lower cool layer; and the pressure of the compartment. In addition, there are seven constraints and so only four equations are required to be solved. By following the assumptions made in the ASET type of two-layer zone model, these four equations can be further reduced to only two ordinary differential equations. Both the ASET model itself and its modification to FIRM in a compartment with a vertical vent were considered. The second objective is to solve the two ordinary differential equations in the simplified model by symbolic mathematics. The advantages of using symbolic mathematics are discussed. It is proposed that symbolic mathematics is suitable for use by the Authority on assessing fire safety design based on performancebased fire codes where fire modelling technique has to be used.