ABSTRACT
Combustion features a wide range of instabilities, which have received considerable attention in recent years. The subject is of fundamental interest and it also has many practical implications. Combustion instability
is often detrimental to the operation of the system and its dynamical effects can have serious consequences. It has become standard to distinguish three general classes of instabilities. In the fi rst group, the instability is intrinsic to the combustion process. This is exemplifi ed by the Darrieus-Landau hydrodynamic instability of premixed fronts or by the thermo-diffusive instabilities arising when the Lewis number departs from unity. The second group involves a coupling between combustion and the acoustics of the system. The resonant modes that assure the feedback are usually plane and
CONTENTS
5.1 Instabilities of Flame Propagation ................................................................................................................................ 67 5.1.1 Introduction ......................................................................................................................................................... 67 5.1.2 Stability and Instability of Flame Fronts .......................................................................................................... 68
5.1.2.1 The Darrieus-Landau Hydrodynamic Instability ........................................................................... 68 5.1.2.2 Thermo-Diffusive Effects ..................................................................................................................... 70 5.1.2.3 Global Flame Stability .......................................................................................................................... 71 5.1.2.4 Flame Instability on a Bunsen Flame ................................................................................................. 72
5.1.3 Thermo-Acoustic Instabilities............................................................................................................................ 73 5.1.3.1 Pressure Coupling ................................................................................................................................ 74 5.1.3.2 Acceleration Coupling ......................................................................................................................... 76 5.1.3.3 Convective Coupling ........................................................................................................................... 78
References .................................................................................................................................................................................. 78 5.2 Perturbed Flame Dynamics and Thermo-Acoustic Instabilities .............................................................................. 80
5.2.1 Introduction ......................................................................................................................................................... 80 5.2.2 Sound Radiation from Flames and Combustion Acoustics .......................................................................... 81 5.2.3 Experimental Setup ............................................................................................................................................. 82
5.2.3.1 Data Acquisition and Processing ....................................................................................................... 84 5.2.4 Perturbed Flame Dynamics ............................................................................................................................... 85
5.2.4.1 Conical Flame Dynamics ..................................................................................................................... 85 5.2.4.2 Flame-Wall Interactions ...................................................................................................................... 85 5.2.4.3 Flame-Flame Interactions and Mutual Annihilation of Flame Area ............................................ 86 5.2.4.4 Flame Roll-Up by Vortex Structures .................................................................................................. 88
5.2.5 Time-Trace Analysis ............................................................................................................................................ 88 5.2.6 Interactions with Equivalence Ratio Perturbations ........................................................................................ 91 5.2.7 Conclusions .......................................................................................................................................................... 92
References .................................................................................................................................................................................. 92 5.3 Tulip Flames: The Shape of Defl agrations in Closed Tubes ...................................................................................... 93
5.3.1 Introduction ......................................................................................................................................................... 93 5.3.2 Historical Description of the Tulip ................................................................................................................... 94 5.3.3 Tulip Flames in Relatively Short Closed Tubes ............................................................................................... 96 5.3.4 Triggering the Tulip-Flame Instability ............................................................................................................. 97 5.3.5 Concluding Remarks .......................................................................................................................................... 99
References .................................................................................................................................................................................. 99
their wavelength is commensurate with the total system longitudinal dimension. These “system” instabilities are generally characterized by low-frequency oscillations. In the third group, combustion is also coupled with acoustic modes, but these modes correspond to chamber resonances and the oscillation is often affected in the transverse or azimuthal direction. The wavelength corresponding to the third group is set by the chamber diameter, and in that case, the frequency of oscillation belongs to the high-frequency range.
