Nonlinear analyses of wrinkled premixed flames: free or forced, steady or not.

Guy Joulin (P‐prime Institute, UPR 3346 CNRS and Poitiers University, France )

G.205, Alan Turing Building,

Sivashinsky (1977) tailored the first equation to describe the dynamics of unforced wrinkled fronts
of premixed gaseous flames when the fresh‐to‐burnt gas density jump is small: it accounts for local
curvature effects, an eikonal non‐linearity and the Darrieus‐Landau hydrodynamic – hence nonlocal –
instability. Locating the front‐slope complex poles in principle gives access to closed‐form shapes for
isolated front crests or for periodic patterns, and to the wrinkling induced increase in burning speed. 
  Various  ways  to  effectively  locate  the  poles  and  get  the  flame‐front  profiles  are  presented:  exact
resolutions,  a  near‐exact  one  fallen  “out  of  the  blue”,  and  asymptotically  correct  approaches  that
require analytical resolutions of linear singular integral equations; and, of course, numerical checks. 
  It is next shown how to generalize all this to flames subject to some forcing, e.g. shear‐flows. Results
for steady fronts are presented, and current analyses of unsteady ones are sketched. 
  An equation generalizing Sivashinsky’s is finally introduced, and various analytical solutions thereof
are displayed. Surprisingly enough, some of those can also be useful to model steady curved flames
in wide channels when the density jump is not small; steady forcing could even be accounted for ...
once the (still ongoing‐) resolution of a suitable nonlocal Riemann‐Hilbert problem is completed.

Import this event to your Outlook calendar
▲ Up to the top