Range of “complete” instability of flat flames propagating downward in the acoustic field in combustion tube: Lewis number effect

Abstract

Downward propagating flames ignited at the open end of an open-closed tube exhibit thermo-acoustic instability due to interaction of combustion generated acoustic fluctuations with the flame front. At sufficiently high laminar burning velocity (SL) two regimes of thermo-acoustic instability are observed, namely, primary instability (where initial cellular flame transitions to a vibrating flat flame) and a secondary instability (where vibrating flat flame transitions to vibrating turbulent flame due to parametric instability of flame front). On further increasing SL to a particular value, “complete instability” of flat flames is observed meaning flat flame cannot be stabilized and initial cellular flame transitions directly to parametric instability. This particular SL introduced in this work is termed “critical SL”. In past experimental works, stability of flat flames in the acoustic field had only been studied in terms of acoustic velocity amplitude and a critical acoustic velocity amplitude had been measured at the onset of parametric instability. The novelty of this work is that boundary of unconditional instability of flat flame (flat flame is unstable irrespective of acoustic velocity amplitude) is determined in terms of mixture conditions, e.g., SL. Particularly for propagating flames, this critical SL can be measured more easily and accurately than the critical acoustic velocity. This work presents the effect of Le (Lewis number) on critical SL. Three different fuels, CH4, C2H4 and C3H8 are tested with two different dilution gases (N2 and CO2) for equivalence ratio of 0.8 (lean) and 1.2 (rich). Twelve different Le ranging from 0.7 to 1.9 are generated through these mixture combinations. Generally, larger Le mixtures show higher critical SL than lower Le mixtures for any fuel. Theoretical calculations are performed to predict critical SL by studying instability of planar flame fronts in presence of acoustic forcing. Theoretical calculations successfully captured the effect of Le as predicted stability region of planar flame is narrower for lower Le than that for higher Le. However, accurate quantitative predictions of critical SL couldn't be obtained from existing theory, particularly for non-unity Le. Hence, a correction (a function of Zeldovich number, β and Le) to width of stability region is proposed to obtain better quantitative agreement for critical SL between experiments and theory and performs significantly well. The correction factor acts to compensate for the inaccuracies in Markstein number obtained from an analytical relationship during calculation of stability region width.