| dc.description |
A general formulation for unsteady flows is set forth for
which diffusion flames are regarded as discontinuity surfaces.
A linearized theory is then developed for weak explosions associated
with planar, cylindrical, and spherical symmetries. A simple
combustion model for a ternary mixture of fuel, oxidant, and product
species is utilized. The one-dimensional linearized shock-tube
problem is analyzed in detail. Explicit results are obtained
for the flame motion and the flame and flow-field development
for arbitrary Prandtl number, Schmidt number, and second coefficient
of viscosity. Wave fronts associated with the flame disturbance,
initial pressure disturbance, and the value of the Prandtl number
are delineated. The motion of a spherical flame associated with
weak spherical explosions is analyzed and found ultimately to
move toward the origin. The structure of the diffusion flame
is analyzed by means of matched asymptotic expansions wherein the
details of the flame structure are described by an "inner" expansion
that is matched to the "outer" expansion that was obtained, to
lowest order, with the flame treated as a discontinuity surface.
Thus the variation of the flame structure with time is obtained
for reaction broadening. |
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