We consider a model of gasless solid fuel combustion of a cylindrical sample, which describes the SHS (self-propagating high temperature synthesis) process for the synthesis of advanced materials. In this process a compacted powder sample of reactants is ignited at one end and a combustion wave then propagates along the cylindrical axis of the sample converting the unreacted powder to the desired product material. To simplify the presentation we assume that combustion occurs only on the surface of the cylinder, and thus consider the resulting two-dimensional problem. It is known, both experimentally and theoretically, that there exist spinning modes of propagation, i.e., nonaxisymmetric solutions characterized by the formation of hot spots (localized high temperature pulses) which rotate around the sample as they propagate, thus following a helical path on the cylinder. We compute solutions involving counterpropagating hot spots. When the spots collide, we show that they undergo one of three possible interactions: (i) a strong (hot) spot collides with a weak (cooler) spot with both the strong and weak spots continuing to rotate in the same direction as before the interaction, (ii) two strong spots collide to produce two weak spots, and (iii) two weak spots collide to produce two strong spots. The latter two interactions describe the phenomena of apparent annihilation and creation of hot spots, respectively, which have been recently observed in experiments.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics