The nonadiabatic nature of low-speed combustion and fire, in which strongly exothermic reactions produce large temperature variations but only mild pressure variations, can cause difficulty when integrating zone models of enclosure fires. Examples of simple zone fire models are examined to illustrate the analytical nature of the problems encountered. These difficulties arise in the solution of the equations for the pressure in general enclosures because the pressure equilibrates much more rapidly than other dynamical variables. Singular perturbation methods and phase plane analyses, together with numerical integration of the nondimensionalized equations, are employed to study the stiff nature of the equations. We conclude that many of the difficulties associated with numerical integration of zone fire models may be circumvented by appropriate analysis of the zone fire model equations.
and Forney, G.
Pressure Equations in Zone-Fire Modeling, Fire Science and Technology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=912814
(Accessed February 26, 2024)