Large-activation-energy theory for premixed combustion under the influence of enthalpy fluctuations

Abstract

This paper presents a mathematical theory for premixed combustion under the influence of enthalpy fluctuations in the oncoming fresh mixture. Based on the assumptions of large activation energy and small Mach number, an analysis of the thermal, hydrodynamic and acoustic regions of a flame is performed to derive an interactive system that describes, on the first-principles basis, the intricate coupling between the flame and its spontaneously emitted acoustic waves. The system, in its general form, is strongly nonlinear and requires a numerical attack. In this paper, it is employed to analyze several fundamental physical processes in relatively simple cases in order to provide useful insights into the role of enthalpy fluctuations in combustion. Firstly, the linear response of the flame to two-or three-dimensional small-amplitude enthalpy fluctuations is considered, and they are found to generate hydrodynamic motion. Secondly, enthalpy fluctuations are shown to radiate sound waves through their interaction with the flame. Thirdly, enthalpy fluctuations and the sound waves emitted by them modify the flame stability, and the analysis shows that a moderate level of enthalpy fluctuation may cause a strong subharmonic parametric instability. Finally, in the small-heat-release limit, an extended Michelson-Sivashinsky equation is derived to describe the nonlinear evolution of the flame under the influence of both the imposed enthalpy fluctuations and the induced acoustic waves. Numerical solutions suggest that the flame evolves into a time-periodic state and acquires a curved profile, which primarily vibrates in the longitudinal direction, while its overall shape remains almost unaltered.

Modelling nonlinear thermoacoustic instability in an electrically heated Rijke tube

“…The unsteady heat release rate from the flame may be due to the equivalence ratio fluctuations at the inlet of the hydrodynamic zone, which in turn may be caused by the acoustic velocity at the location of the flame (Moeck et al 2007). Recently, Wu & Moin (2010) investigated the generation of acoustic waves from premixed flame due to free-stream enthalpy fluctuations, using asymptotic analysis. A vigorous subharmonic parametric instability was observed at moderate levels of enthalpy fluctuations.…”

Linear and weakly nonlinear instability of a premixed curved flame under the influence of its spontaneous acoustic field

“…The mathematical formulation of WWMP has been adapted in Wu & 184 R. C. Assier and X. Wu Law (2009) to investigate the interactions of a flat flame with weak turbulence in the oncoming mixture. The theory was further generalised by Wu & Moin (2010) to account for the influence of enthalpy fluctuations in the oncoming mixture on flame-flow-acoustic interactions. In the applications considered in Wu et al (2003), Wu & Law (2009) and Wu & Moin (2010), the steady state is that of a flat flame, for which the acoustic-flame coupling term is nonlinear: the acoustic source involves the quadratic product of the gradient of the perturbed flame front, while the back-action of the sound is represented by the product of the acoustic acceleration with the flame front.…”