  Shock flame interactions are fundamental problems in many combustion
applications ranging from flame acceleration to flame control in supersonic
propulsion applications. The present paper seeks to quantify the rate of
deformation of the flame surface and burning velocity caused by the interaction
and to clarify the underlying mechanisms. The interaction of a single shock
wave with a cellular flame in a Hele-Shaw shock tube configuration was studied
experimentally, numerically, and theoretically. A mixture of stoichiometric
hydrogen-air at sub-atmospheric pressure was chosen such that large cells can
be isolated and their deformation studied with precision subsequent to the
interaction. Following passage of the incident shock and vorticity deposition
along the flame surface, the flame cusps are flattened and reversed backwards
into the burnt gas. The reversed flame then goes through four stages. At times
significantly less than the characteristic flame burning time, the flame front
deforms as an inert interface due to the Ricthmyer-Meshkov instability with
non-linear effects becoming noticeable. At times comparable to the laminar
flame time, dilatation due to chemical energy release amplifies the growth rate
of Ricthmyer-Meshkov instability. This stage is abruptly terminated by the
transverse burnout of the resulting flame funnels, followed by a longer front
re-adjustment to a new cellular flame evolving on the cellular time scale of
the flame. The proposed flame evolution model permits to predict the evolution
of the flame geometry and burning rate for arbitrary shock strength below the
shock-induced auto-ignition point and flames with unit Lewis number in
two-dimensions.
