Stability Analysis of Premixed Flames with Downstream Heat Gain

Pulsating instability is a kind of combustion intrinsic instability, that can affect the flammable limit and may couple with other processes to generate more complex combustion instability phenomena. Pulsating instability was found in the premixed flame of the double-flame partially premixed flame (PPF), in which the flame patterns change from stable to pulsating unstable, and to stable again as the equivalence ratio or stretch rate increases. To further investigate this phenomenon, a simpler model, stretched premixed flames with downstream heat gain, is analyzed by the asymptotic expansion method in this paper. The downstream heat gain inhibits the steady extinction of stretched premixed flames with a large Zeldovich number. The stability of premixed flames changes in the zero-limit mode, two-limits mode and one-limit mode sequentially as the Zeldovich number increases. The zero-limit mode represents the premixed flame is stable for all stretch rates. The two-limit mode and one-limit represent the premixed flame changes in the pattern of stable-pulsating-stable and pulsating-stable as the stretch rate increases, respectively. The downstream heat gain suppresses the pulsating instability to yield the stable region at the large stretch rate and large Zeldovich number. The influence of other factors, including the Lewis number, the downstream temperature and the downstream boundary position are also discussed. The current theoretical method is also applied to the extracted parameters from numerical calculations of hydrogen/air double-flame PPF. A qualitative similarity is found between the theoretical results and numerical results.