Dynamics in a rod model of solid flame waves revisited

Abstract

We consider gasless solid fuel combustion in a cylinder of radius \( \tilde R \), associated with the SHS process, which employs combustion waves to synthesize materials. We model the full three dimensional (3D) problem in cylindrical geometry by considering an array of interacting 1D rods, each of which supports propagating waves in the axial direction. We consider a configuration of 8 equally spaced rods on the surface of the cylinder, 8 equally spaced interior rods at \( \tilde R \)/2 and 1 axial rod (8-8-1 model). The rods interact via heat transfer, with the heat transfer terms corresponding to a discretization of the transverse Laplacian. The rod model is designed to provide insight into the qualitative behavior of the full 3D problem, employing vastly reduced computational resources. We previously considered a coarser grained 3-1 model. Whether or not the rod model describes behavior occurring in the full 3D problem may well depend on the number of rods as well as on the symmetries of their arrangement. Therefore, here we consider a larger number of rods exhibiting different symmetries.