Instability analysis of counterflow diffusion flames with radiation heat loss

A linear stability analysis of a diffusion flame with radiation heat loss is performed to identify linearly unstable conditions for the Damköhler number and radiation intensity. We adopt a counterflow diffusion flame with unity Lewis number as a model. Near the kinetic limit extinction regime, the growth rates of disturbances always have real eigenvalues, and a neutral stability condition perfectly falls into the quasi-steady extinction. However, near the radiative limit extinction regime, the eigenvalues are complex, which implies pulsating instability. A stable limit cycle occurs when the temperatures of the pulsating flame exceed the maximum temperature of the steady-state flame with real positive eigenvalues. If the instantaneous temperature of the pulsating flame is below the maximum temperature, the flame cannot recover and goes to extinction The neutral stability curve of the radiation-induced instability is plotted over a broad range of radiation intensities.