Local Extinction of Diffusion Flames in Fires

Abstract

The objective of the present study is to use large activation energy asymptotic (AEA) theory to bring basic information on the extinction limits of non-premixed flames. The AEA analysis leads to an explicit expression that predicts the occurrence of flame extinction in the form of a critical Damköhler number criterion; the criterion provides a unified framework to explain the different extinction limits that are observed in non-premixed combustion (i.e., aerodynamic quenching, thermal quenching, and dilution quenching). The critical Damköhler number criterion is then formulated in terms of six input variables; these variables characterize the magnitude of flame stretch, the magnitude of the flame heat losses, and the composition and heat content of the fuel and oxidizer supply streams; these input variables thereby contain information on (laminar or turbulent) flow-induced perturbations, deviations from adiabatic combustion, and air and fuel vitiation. Different two-dimensional flammability maps are then presented using different assumptions aimed at reducing the dimension of the parameter space from six to two. While providing a limited view point, these flammability maps provide valuable insights; it is found for instance that diffusion flames are more sensitive to air vitiation than fuel vitiation.

Large eddy simulation of flame extinction in a turbulent line fire exposed to air-nitrogen co-flow

“…The FireFOAM solver has been recently modified to include a flame extinction model based on the concept of a critical flame Damköhler number and a flame reignition model based on the concept of a critical gas temperature [4,8].…”

“…where T m st is the temperature that would be obtained with pure fuel-air mixing and without combustion (we use T m st = 293 K) and T ad st is the temperature that would be obtained with adiabatic combustion (i.e., without radiation losses, convective wall losses, or an evaporating water spray). In the present study, the adiabatic flame temperature T ad st is prescribed using an expression coming from the classical Burke-Schumann solution, T ad st = f (Y O2,2 ), where Y O2,2 is the oxygen mass-fraction in the air-nitrogen co-flow [8].…”

“…Now, following Refs. [21] and [8], we assume that all extinction events correspond to the same crticial value of the Damköhler number, Da c = 1. This leads to the following system of equations for C and T a :…”

“…Available models used to describe flame extinction in fire problems are based on the concepts of a critical flame temperature [1,2] or a critical flame Damköhler number [3][4][5][6][7]. Models based on the concept of a critical flame temperature choose to ignore the importance of chemical time scales and are not consistent with known laminar flame phenomenology [8]. Models based on the concept of a critical flame Damköhler number explicitly or implicitly account for at least one chemical time scale, are consistent with known laminar flame phenomenology, and therefore may be expected to be more accurate [8].…”

“…Models based on the concept of a critical flame temperature choose to ignore the importance of chemical time scales and are not consistent with known laminar flame phenomenology [8]. Models based on the concept of a critical flame Damköhler number explicitly or implicitly account for at least one chemical time scale, are consistent with known laminar flame phenomenology, and therefore may be expected to be more accurate [8]. The occurrence of flame extinction is also followed by that of reignition and the modeling of under-ventilated fires or fire suppression requires both an extinction model and a reignition model [4], a difficulty that is generally overlooked in the fire modeling literature.…”