Abstract

Acoustic instability of premixed combustion refers to large-scale self-sustained pressure fluctuations in a combustion chamber. It is a typical multi-physics, multi-scale problem in the sense that it arises due to complex interactions among chemical reaction, heat and mass transport, hydrodynamics and acoustics, which take place on distinctively different scales. Such disparity of scales presents a formidable challenge for direction numerical simulations, but can be exploited mathematically to derive simplified systems. Asymptotic techniques, such as matched asymptotic expansion, can be used to analyse the small-scale inner structure of the flame, thereby characterizing the mutual interaction between the flame and the ambient flow motion. In the so-called flamelet regime, where the length scale of the flow motion is much greater than the flame thickness, this leads to the classical hydrodynamic theory of premixed combustion. However, the theory assumes that the enthalpy (temperature and the mass fraction of the fuel) in the oncoming mixture are steady and homogeneous, and the spontaneous sound of the flame is not accounted for explicitly. We extends the formulation by allowing for enthalpy fluctuations, and show that unsteady combustion necessarily emits spontaneous sound, which acts simultaneously on the flame. The resulting general theory for the flame-flow-acoustic interactions is applied to simple cases to provide insights into fundamental mechanisms of acoustic instability of premixed combustion.