Material Parameters Controlling Extinction

Suppression is probably one of the most complex processes associated with fire. Extinction of fires implies the understanding of heat and mass transfer in the solid and gas phase, as well as the concept of chemical inhibition of the combustion reactions. Only a brief summary of the different material parameters controlling extinction will be presented here. 

Extinction can be ultimately defined as the reduction of the combustion reaction rates below a critical threshold that 

Source Drysdale, D., A72 Introduction to Fire Dynamics, 2nd edn., John Wiley Sons, Chichester, U.K., 1998. 

The first Damkohler number quantifies the ratio between the heat transferred from the flame (conduction time) and the energy required to heat the reactants to the ignition temperature (residence time). Extinction will occur when heat cannot be transferred fast enough. Equation 3.53 is written in terms of the ratio between conduction and convection (residence time), but in a more general form, could include all forms of heat transfer like gas-phase radiation. The second Damkohler number indicates if the reaction has sufficient time to proceed. In general, extinction is attained when either of the Damkohler groups is reduced below unity. 

Other criteria can be used to establish the extinction condition and that are partially equivalent to the critical Damkohler number. Such criteria are a critical mass transfer numbers (BCI) [21,32], critical mass flux of fuel [2,6,28] or critical temperatures (Ta) [2,5,29-31], The critical mass transfer number has a direct influence over the flame temperature, and thus, represents the link between the condensed phase (i.e., production of fuel) and the chemical time. The critical mass flux operates under the same principle, but assumes a consistent heat input. Combustion reactions generally have high activation energy, therefore, the reaction can be assumed to abruptly cease when the temperature reaches a critical value (Tcr). 

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