Unsteady counterflowing strained diffusion flames: Diffusion-limited frequency response

A detailed numerical study has been conducted on the effect of unsteadiness on the dynamics of counterflowing strained diffusion methane/oxygen/nitrogen flames. The modelling included the solution of the unsteady conservation equations of mass, momentum, energy, and species along the stagnation streamline in an opposed jet using detailed descriptions of chemistry and transport. The unsteadiness was introduced by independently imposing sinusoidal variations of the reactant velocity, concentration and temperature at the exits of the nozzles. The results demonstrate that the flame's response is quasi-steady at low frequencies, while at higher frequencies the amplitudes of the induced oscillations are reduced and phase shifted with respect to the imposed signal. At still higher frequencies, the flame no longer responds to the oscillations in the external field. A rigorous physical explanation of the frequency response was provided from first principles by identifying that oscillations imposed at the nozzle exits result in reactant concentration and temperature oscillations at the outer edge of the preflame diffusive zones. The diffusion attenuates the oscillations in this zone in a manner analogous to the velocity attenuation in Stokes' second problem. The validity of the analogy was confirmed by examining flames over a wide range of frequencies and initial conditions. The current analysis also provided a criterion for the cutoff frequency separating the quasi-steady and transient regimes-information which can be useful in the establishment of laminar flamelet libraries.