W. G. Pritchard Lab Seminar: 4-5 PM, 116 McAllister Building

	       **Tuesday March 19, 2002**
	
Dynamics of Hot Spots in Solid Fuel Combustion

Bernard J. Matkowsky

Department of Engineering Sciences and Applied Mathematics
Northwestern University

Abstract:

We consider the gasless combustion model of the Self-Propagating 
High-Temperature Synthesis (SHS) process in which combustion waves are
employed to synthesize desired materials. Specifically, we consider the
combustion of a solid sample in which combustion  occurs on the surface
of a cylinder of radius R. We consider solution behavior as R is
increased. This parameter is important for technological applications,
as it is often desirable to synthesize large samples of the desired
product.   


For fixed value of the Zeldovich number, if R is sufficiently small,
slowly propagating planar pulsating flames are the only modes observed.
As R is increased transitions to more complex modes of combustion
occur, including (i) spin modes in which one or several symmetrically
spaced hot spots rotate around the cylinder as the flame propagates
along the cylindrical axis, thus following a helical path, (ii)
counterpropagating (CP) modes, in which spots propagate in opposite
angular directions around the cylinder, (iii) alternating spin CP modes
(ASCP), where rotation of the spot is interrupted by
periodic events in which a new spot is spontaneously created ahead of
the rotating spot. The new spot splits into daughter spots, one of
which collides with the original spot leading to their eventual mutual
annihilation, while the other continues to spin, (iv) modulated  spin
waves consisting of one or two symmetric rotating spots which exhibit a
periodic modulation in speed and temperature (v) asymmetric spin waves
in which two spots of unequal strength rotate together as a bound
state, (vi) modulated asymmetric spin waves in which the two asymmetric
spots oscillate in a periodic manner as they rotate, (vii) asymmetric
ASCP modes in which a slowly varying bound state of two spots rotates
while the leading spot, and subsequently the trailing spot, exhibits
episodes of ASCP behavior, and finally (viii) 3-headed spins in which
three spots rotate in a nonuniform fashion, including quasiperiodic and
chaotic motion.