The transient response of strained laminar-premixed flames

Modeling and simulation of turbulent combustion in premixed gases, for relatively large-scale and low-intensity turbulence, have traditionally been based on the assumption that the flame response to strain is instantaneous. In this paper, we revisit the validity of this assumption by examining the time-dependent response of a premixed laminar flame when subjected to a sudden change in strain and a periodic strain. We find that at unity Lewis number and for a stepwise increase in strain, the settling time of the flame varies between the chemical time, the flame time and the flow time as the Karlovitz number changes from low to intermediate to high Karlovitz numbers and over the entire range of flame temperatures. For given Lewis and Karlovitz numbers, the settling time decreases as the flame temperature increases. Thus, in a flamelet or thin flame modeling, and over the entire range of Lewis number, the response of a premixed flame can be considered instantaneous only for high flame temperatures. The same is found to be true for intermediate flame temperatures when the Lewis number is unity. Otherwise, for low and intermediate flame temperatures, and nonunity Lewis numbers, corrections reflecting the lag between the flow and the flame should be considered. The response of the flame to oscillating strains whose maximum value is below unity Karlovitz number is also investigated for two values of the flame temperatures. It is found that the average burning velocity is close to the burning velocity at the average strain. For low frequency oscillations, the phase shift between the strain and the burning velocity is close to 0 for Le < 1 and near 90° for Le ≥ 1. For high frequency oscillating strains, and over the entire range of Lewis number and flame temperature, the phase shift is of order of 140°.