Laminar flamelets are often used to model premixed turbulent combustion. The libraries of rates of conversion
from chemical to thermal enthalpies used for flamelets are typically based on counter-flow, stained laminar planar
flames under steady conditions. The current research seeks further understanding of the effect of stretch on
premixed flames by considering laminar flame dynamics in a cylindrically-symmetric outward radial flow geometry (i.e., inwardly propagating flame). This numerical model was designed to study the flame response when the flow and scalar fields align (i.e., no tangential strain on the flame) while the flame either expands (positive stretch) or contracts (negative stretch, which is a case that has been seldom explored) radially. The transient response of a laminar premixed flame has been investigated by applying a sinusoidal variation of mass flow rate at the inlet boundary with different frequencies to compare key characteristics of a steady unstretched flame to the dynamics of an unsteady stretched flame. An energy index (EI), which is the integration of the source term in the energy equation over all control volumes in the computational domain, was selected for the comparison. The transient response of laminar premixed flames, when subjected to positive and negative stretch, results in amplitude decrease and phase shift increase with increasing frequency. Other characteristics, such as the deviation of the EI at the mean mass flow rate between when the flame is expanding and contracting, are nonmonotonic with frequency. Also, the response of fuel lean flames is more sensitive to the frequency of the periodic stretching compared to a stoichiometric flame. An analysis to seek universality of transient flame responses across lean methane-air flames of different equivalence ratios (i.e., 1.0 to 0.7) using Damköhler Numbers (i.e., the ratio of a flow to chemical time scales) had limited success.
Sahafzadeh, M., Kostiuk, L. W., & Dworkin, S. B. (2017). Transient response of a laminar premixed flame to a radially diverging/converging flow. Combustion and Flame, 179, 51-62. https://doi.org/10.1016/j.combustflame.2017.01.015