The present lecture systematically explores application of some general ideas of combustion theory to development of compartment fires. Essentially, fire represents thermal instability in a combustible system. We argue that freely developing fire is generally a sequence of the two major instabilities – one a micro, and another on macro scales. The first one is a well-known – this is ignition. The second one, which often develops in strongly growing fires, is called a flashover. We demonstrate that both instabilities can be described in the general framework of thermal explosion. Specifics of this description are that the instability of the second type (flashover) requires introduction of the new concept of conjugate thermal explosion. This recently introduced concept is a focus of the present investigation. Mathematically, in the context of compartment fire flashover, description of conjugate thermal explosion gives rise to a dynamical system with two-dimensional phase space. Precise formulation of the model, and its modifications, are discussed. Then, the behavior of emerging dynamical system is fully investigated. In the final part of the presentation, we discuss briefly yet another instability, occurring upon fire suppression. This instability is interpreted as thermal implosion.
Conjugate thermal explosion and the theory of fires
9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012 ; 2012 ; Vienna, Austria
AIP Conference Proceedings ; 1493 , 1 ; 710-715
2012-11-06
6 pages
Conference paper
Electronic Resource
English
Conjugate thermal explosion and the theory of fires
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