Instabilities In Spherically Expanding Premixed Flames

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If a deformation occurs in the surface of a spherically expanding laminar flame during its early development,
any potential instabilities (hydrodynamic, thermal-diffusive) will be stabilised by the flame
stretch until a critical Peclet number is reached. After this critical point, the flame may become unstable
to surface perturbations, which can grow on the flame surface through the development of propagating
cracks or cellular fission .

If the Lewis number for the deficient reactant in the fuel-air mixture is below a critical value, then in
general, a perturbation in the expanding flame front is unstable. The perturbation grows as a consequence
of an increase in enthalpy and local burning velocity along the crest of the perturbation, with a
corresponding decrease in enthalpy and local burning velocity along the trough of the perturbation.
However, if the Lewis number for the deficient reactant in the fuel-air mixture is above a critical
value, then the flame front is stable to perturbations on the surface. Generally, this means that for
fuel-air mixtures where the molecular mass of the fuel is considerably smaller than the molecular mass
of air, lean flames are unstable to surface perturbations. The converse is also true for rich flames.
This kind of flame instability is known as a thermal-diffusive instability. There are some exceptions
to this general rule. Rich ethylene- and ethane-air flames have been observed to develop thermaldiffusive
cracking .

The second type of flame instability examined here is hydrodynamic in origin. Flame surface perturbations
cause local pressure and density variations ahead of the advancing flame front, which can accelerate
surface cracking. Hydrodynamic instabilities can be distinguished from thermal-diffusive
instabilities through the identification of the different wavelengths associated with the two mechanisms.
Furthermore, pressure oscillations ahead of the advancing flame front identify the presence of
hydrodynamic instabilities. In practice, initial perturbations in a spherically expanding flame surface
occur as a consequence of the mode of ignition, whether by a spark plug, or laser, or other means.
Fully developed flame cellularity due to thermal-diffusive cracking is distinguished from hydrodynamic
cracking in that flames that hydrodynamically crack do not develop a discrete cellular structure
as described above, unless of course the flame is unstable to thermal-diffusive cracking as well.

weiqc123

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