An unsteady strained flame model for turbulent combustion simulations

Abstract

Modeling and simulation of turbulent combustion in premixed gases, for relatively large turbulence scales and low intensity, have traditionally been based on the assumption that the flame response to strain is instantaneous. In this paper, we question this assumption on the basis of results obtained for the time-dependent response of a premixed laminar flame subjected to a sudden change and a period strain. We find that a aep-wise change in strain, at unity Lewis number, 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 values, respectively, over the entire range of flame temperatures. At nonunity Lewis numbers. the settling time changes from the flame time to the flow time as the strain increases form intermediate to high Karlovitz numbers and over the entire range of flame temperatures. For a given Lewis and Karlovitz number, the settling time decreases as the flame temperature increases. Thus, in a flamelet or thin flame modeling, the response of flame can be considered instantaneous, over the entire range of Lewis number, only for high flame temperatures. The same is found to be true for intermediate flame temperatures when the i/ Lewis number is unity. Otherwise, for low and intermediate flame temperatures, and non-unity Lewis numbers, corrections reflecting the lag between the flow and the flame should be incorporated i n the models. The response of the flame to osrillrrring strains whose maximum value is below unity Kiirlovitz 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 striiin and the burning velocity is close to 0 for Le < I and to n for Le 2 I . For high frequency oscillating strains, and over the entire range of Lewis number and flame temperature, the phase shift is nf order of I..( II.