Families of two-dimensional, unsteady shock-induced vortical flows are
simulated numerically. The flows consist of one or more regions of li
ght gas, surrounded by heavy gas, being overtaken by a normal shock wa
ve. The interaction of the density gradient at each light/heavy interf
ace with the pressure gradient from the shock wave generates vorticity
. This causes the light gas regions to roll up into one or more counte
r-rotating vortex pairs, which stir and mix the light and heavy gases.
The mixing is characterized by an asymptotic stretching rate. The eff
ects of shock strength, light/heavy gas density ratio, and geometry on
the mixing are investigated. These two-dimensional, unsteady flows ar
e analogous to three-dimensional, steady flows that may be used in SCR
AMJET combustors demanding rapid and efficient mixing of fuel and oxid
izer. For such applications, 1) the fuel injectors should be elongated
in the direction of the shock; 2) multiple smaller injectors are pref
erable to a single larger injector; 3) injectors should be arranged in
groups of closely spaced pairs, rather than uniformly; and 4) multipl
e shock waves should be utilized, if possible.