Copy of Coupling the Intrinsic Instabilities of Premixed Combustion - Overseas Travel Grant

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics


Premixed flames are prone to diffusional-thermal and hydrodynamic instabilities. These instabilities in practice operate simultaneously, and are often coupled with the acoustic modes of a combustion chamber, leading to large-scale acoustic instability, which is characterized by intense pressure fluctuations. In the past, various aspects of acoustic instability were modelled in isolation, and often on an empirical basis. The applicant and his collaborators derived a first-principlesmodel on the basis of the activation-energy asymptotics to describe flame-acoustic coupling mechanisms in the flamelet regime. We now propose to develop an efficient numerical algorithm to solve the asymptotically reduced system, and apply it to situations pertaining to Searby's (1992) experiments. We also plan to investigate hydrodynamic and diffusional-thermal instabilities in a unified framework, with the particular aim of predicting some remarkable observations made in the Princeton group, namely the coexistence of the hydrodynamic cells and spiral waves on spherical flames. The coupling of both hydrodynamic anddiffusional-thermal instabilities with acoustics will be investigated in the thin-reaction-zone regime. A general acoustic-hydrodynamic-flame coupling theory will be formulated, and will applied to investigate the resonance between acoustic modes and the pulsating instability at the onset condition.


10 25 50
Description Our research broadly followed the original plan and objectives, and has made progress on various aspects related to the coupling of the intrinsic dynamics of a premixed flame with the acoustics of the combustor. Some minor adjustments were made, and they are explained in the following.

The first was that we investigated the role of small vortical disturbances in the flame-acoustic resonant coupling, which was not explicitly designated as one of specific objectives originally listed, but is in fact one of the key issues in combustion instability. It has long been recognised that combustion instability arises from two-way couplings between the flame and its spontaneously emitted sound waves. However, a self-consistent mathematical description has never been provided even for simplest cases (e.g. a ducted flame). Previous investigators considered only one-way effects of an externally imposed acoustic field on the flame. Calculations showed that a sound wave may induce a strong subharmonic parametric instability, when its intensity exceeds a threshold level (about three times the laminar flame speed). This high level of sound is, however, not available in the unforced case of interest, for which why resonance occurs at all remains a mystery. This problem became our first topic of study as we realised that a possible answer may be found before solving the full nonlinear system. We were able to show that weak vortical disturbances may initiate subharmonic flame-acoustic resonance, which causes an initially planar and quite flame to evolve into a highly wrinkled flame sustained by its strong spontaneous noise.

We considered the hydrodynamic and thermal-diffusive instabilities of flame in a unified fashion by using the thin-reaction-zone regime scaling. A formulation is given, but the originally planned calculations for a spherical flame, which were fairly extensive, had to be postponed to the future. This will be acknowledge as part of this grant.

As planned, we derived a general flame-acoustic interaction theory in the thin-reaction-zone regime. The upshot of this is that it unifies all known intrinsic instabilities of a premixed flame, and couples them to the acoustic field of the combustor. Using this formulation, we are studying the subharmonic resonance between an acoustic mode and the oscillatory instability of a flame.

We proposed a robust numerical algorithm for solving the nonlinear flame-acoustic interaction system. For that purpose, the original formulation of WWMP was recast using the level-set representation for the flame front. The algorithm is being validated. As part of this process, we have also derived, in the weak gas expansion limit, an extended Michelson-Sivashinky equation in which the back action of the spontaneously emitted sound waves on the flame is included.
Description Tackling combustion instability in low-emission energy systems: mathematical modelling, numerical simulations and control algorithms
Amount £390,000 (GBP)
Funding ID EP/I017240/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 09/2011 
End 08/2014
Description Princeton University 
Organisation Princeton University
Country United States 
Sector Academic/University 
Start Year 2008