Counterflow Diffusion Flames with Unsteady Strain Rates

The counterflow diffusion flame subject to time-varying strain rates is studied analytically in order to assess the effect that unsteadiness caused by turbulent flows might have on laminar flamelets. The characteristic unsteady time considered is of the same order as the characteristic flame time, which is represented by the reciprocal of the strain rate, such that the flame structure consists of a quasi-steady reactive-diffusive zone embedded within the outer unsteady-convective-diffusive region. For constant density and unity Lewis numbers, the Shvab-Zeldovich coupling function takes an analytic self-similar solution for arbitrary strain rate as a function of time, thereby facilitating the analysis as well as physical interpretation for the flame-sheet behaviors. We further analyze the inner reaction zone structure using large activation energy asymptotics for one-step overall chemistry in order to determine the extinction conditions. In relation to turbulent combustion regimes, the unsteady effect is expected to modify the flamelet behavior subject to the spectrum of turbulent eddies. That is, although the effective strain rate increases as the eddy scale is decreased, the smaller eddies also have shorter characteristic time such that the flame may not be quenched for some range of eddy scale that otherwise imparts sufficient strain rate to extinguish the flamelet. The results suggest that the applicable range of the laminar flamelet regime may be broader than would be expected from the quasi-steady concept.