Monte-carlo simulation of combustion-induced percolative fragmentation of carbons

Percolative fragmentation of carbon particles during combustion is modelled by means of two Monte-Carlo simulation models on a 3-D lattice: the first applies, to combustion in absence of oxygen concentration gradients within the particle; the second applies to percolative fragmentation in the intraparticle diffusion-limited combustion regime. The latter simulates oxygen diffusion and reaction by a random walk technique. Model results include the ratio of the mass rate of percolated fragments to the rate of carbon removal by combustion and percolative fragmentation, the penetration depth of oxygen in the porous matrix and the average size of fragments generated by the percolation process. The correspondence is established between model parameters and variables of the actual physical process. In particular it is shown that fragmentation rate and average fragment size and functions of a dimensionless group (the Thiele modulus) which expresses the ratio between the average size of the cavities in the lattice and the oxygen penetration depth. In absence of porosity gradients within the lattice (that is as Thiele modulus tends to 0) the rate of percolative fragmentation turns out to be smaller than that corresponding to the voidage at the percolation of the solid phase in the classical percolation theory framework. Non-uniform distribution of porosity in the lattice, like that established in diffusion limited combustion conditions, further reduces the rate of fragmentation in respect to that observed under uniform percolation conditions. In particular it is shown that fragmentation rate decreases with increasing combustion temperature, in agreement with experimental results of previous authors. The average size of fragments generated in the percolation process increases as porosity and average size of pores increase. For given lattice properties, the fragment sizes decrease when moving from uniform to diffusion limited combustion conditions, consistent with the parallel decrease of oxygen penetration depth within the lattice. © 1992 Combustion Institute