Jl. Mcgreevy et M. Matalon, HYDRODYNAMIC INSTABILITY OF A PREMIXED FLAME UNDER CONFINEMENT, Combustion science and technology, 100(1-6), 1994, pp. 75-94
A linear stability analysis has been performed to identify the role of
the hydrodynamic instability when combustion occurs in a closed tube.
The model treats the flame as a surface of discontinuity in an otherw
ise inviscid, isentropic mixture. The burning rate is obtained from an
analysis of the internal flame structure. It is shown that flame acce
leration, a consequence of pressure buildup, has a damping influence o
n the long wavelength disturbances. Disturbances of shorter wavelength
s grow but their growth rate exceeds the propagation speed, which can
only then be identified as an instability. The growth rate is found to
be always lower than the corresponding growth rate for a freely propa
gating flame.