We formulate a two-dimensional model describing the combustion of porous condensed phase materials in which a reactant melts and spreads through the void space of a porous solid. The melt may completely fill the pores, or some gas may remain in the pores. In each case, the volume fraction of melt is prescribed. In the limit of large activation energy, we analytically find a one-dimensional basic state consisting of a uniformly propagating combustion wave with a planar reaction front and a planar melting front. We find that the uniformly propagating solution with planar fronts is linearly unstable to traveling waves transverse to the propagation direction of the basic state above some critical Zeldovich number. The critical wave number associated with this critical Zeldovich number is generally unique and nonzero. However, the critical wave number can be zero for certain parameter values. For other special parameter values, the neutral stability curve may have two minima, so that two wave numbers lose stability at the same Zeldovich number.
- Gasless combustion
- porous medium combustion
ASJC Scopus subject areas
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering