Theoretical analysis of polydisperse water spray extinction of opposed flow diffusion flames

Abstract

We present a new mathematical analysis of the influence of a polydisperse spray of water droplets on the extinction of opposed flow diffusion flames. The current interest in the use of fine-water mists for fire extinguishment provides the motivation for our research. Previous experimental and numerical work in the literature used the opposed flow configuration as a convenient paradigm for extracting the relative importance of the various mechanisms at play in extinction of diffusion flames. In the current work we present an analytical approach to describe the problem in which a spray of water droplets of arbitrary polydispersity is present in the oxidant stream that opposes the fuel stream, the latter two being responsible for the formation of a diffusion flame. Transport effects are included through (possibly non-unity) Lewis numbers. The analysis permits arbitrary water spray polydispersity. Our level of modeling currently focuses on the effect of the water mist's endothermicity as the mechanism that primarily determines conditions for extinction. Here, we examine how the initial water droplet size distribution produced by the spray influences the spatial distribution of heat loss, and how the extinction of the diffusion flame is consequently effected. We consider six initial droplet size distributions, three having the same Sauter Mean Diameter and three having the same D 20. In both cases the distributions have rather different forms: (1) a quasi-monodisperse spray, (2) a bimodal spray and (3) a “normal”-spray. It is shown that the different sprays lead to quite different extinction characteristics despite having the same SMD or D 20. Under certain circumstances it is shown that conditions can be found that delineate between effective and ineffective use of the water droplets for suppression. The results strongly underscore the sensitivity of flame suppression to the water mist's actual droplet size distribution.