A universal Karlovitz number to predict the lean blowoff limits of stabilized premixed flames

Abstract

A Karlovitz number formulation is defined to predict the stability and lean blowoff (LBO) limits of premixed bluff-body flames. The Karlovitz number relies on a newly defined flame timescale as a representative chemical time, where the flame timescale is identified from experimental measurements of LBO of premixed, propane-air, bluff-body flames in the literature. The timescale is first defined as a function of the extinction strain rate across the premixed flame, and satisfies a criterion for LBO to occur when Ka ≥ 1. Theoretical analysis shows that the defined chemical timescale based on the extinction strain rate can be recast using unstretched laminar flame properties, and reveals a coupling between premixed flame (τpf) and extinction strain rate timescales (τesr) commonly used in literature. The new chemical timescale and the coupling between τpf and τesr is explored for a variety of premixed fuel-air mixtures including propane, methane, ethylene, ammonia, and hydrogen. The timescale definition is found to uphold for all fuels except for hydrogen, which required a Lewis number correction to account for the effects of enhanced mass diffusion. The timescale is also validated against a variety of LBO data within literature. When coupled with a flow timescale, defined as recirculation zone residence time, the chemical timescale is able to collapse the LBO data to a nominally uniform Karlovitz number near unity for a range of flameholder geometries and Reynolds numbers. However, adjusting the flow timescale to estimate the inverse of the flame strain rate at LBO shifted the compiled data to a collapsed value of Ka ≈ 1, thereby realizing a unified Karlovitz (or Damköhler) theory to predict LBO. The advantage of the new Karlovitz model is its ability to provide an a priori method to predict the stability and LBO limits of premixed flames based on appropriately defined timescales.