Large-activation-energy theory for premixed combustion under the influence of enthalpy fluctuations in the oncoming mixture Part I: general formulation

Premixed combustion in an enclosed chamber is susceptible to large-scale acoustic instability, which manifests as intense pressure fluctuations with predominant peaks at the characteristic acoustic frequencies of the combustor. Such an instability can occur in aeroand rocket engines as well as in land-based gas turbines (e.g., Harrje & Reardon 1972; Yu, Trouve & Daily 1991; Richards & Janus 1997). It has a number of detrimental effects. For example, the oscillatory load may lead to structural fatigue. The strong pressure fluctuation may cause flame flash-back and/or blow-off. These problems hinder the development of lean-burn gas turbine engines to reduce emissions of NOx, because combustion in the lean limit is particularly prone to the instability. In practical applications, the instability has to be suppressed by passive (Schadow & Gutmark 1992) or active control (Candel 2002; Dowling & Morgans 2005). It is generally recognized that combustion instability is essentially a self-excited oscillation sustained by a two-way coupling between the unsteady heat release and acoustic modes of the chamber (e.g., Poinsot et al. 1987; Langhorne 1988; Candel 2002). The unsteady heat release from the flame leads to amplification of acoustic pressure when the two are “in phase” according to Rayleigh’s criterion. Acoustic fluctuations, on the other hand, may affect the flame and hence the heat release through kinematic, dynamic and chemo-thermal mechanisms, including: (a) acoustic velocity advects the flame front; (b) acoustic acceleration acts on the flame through the unsteady Rayleigh-Taylor (R-T) effect (Markstein 1953); (c) acoustic pressure modifies the burning rate (e.g., McIntosh 1991); (d) sound waves modulate the equivalence ratio of the mixture (Lieuwen & Zinn 1998). The onset and control of combustion instability may be crucially affected by external disturbances. In an idealized model of a uniform oncoming flow of mixture, an arbitrary small-amplitude disturbance can be decomposed into acoustic, vortical and enthalpy modes. Based on this decomposition, it is natural to investigate the interaction of a flame with each of the three modes separately. Theoretical modeling of combustion instability has mostly taken a semi-empirical approach, which seeks to establish the relations between the flame motion, heat release and external disturbances in a phenomenological manner (Lieuwen 2003; Ducruix et al. 2003). In particular, kinematic models based on the so-called G-equation, proposed by Fleifil et al. (1996), have been extended and used to describe the flame wrinkling caused