Four Types of Chaotic Dynamics
in Cellular Flames

Theoretical Studies of Disordered States

Several of the theoretical studies of ordered states find a transition to disordered cellular flames. Shtilman and Sivashinsky (1990) found a transition from the hexagonal pattern of cells to a disordered state. Bayliss, Matkowsky and Riecke (1993) reported a transition to spatiotemporal chaos as the Lewis number was decreased. Both the number of cells and their sizes change in an irregular manner. Nicolenko (1993) found a disordered state in which the cells were of unequal size.

The geometries of these studies are different: these experiments use a circular porous plug burner, Shtilman and Sivashinsky (1990) considered a square geometry with a large number of cells, Bayliss and Matkowsky (1992) considered a circular line propagating radially inward, and Nicolenko (1993) considered a square geometry with small number of cells. Each of these predicted disordered states is qualitatively similar to the experimental results shown in Figure lb.

The numerical simulations of Sivashinsky (1983) using the thermodiffusive model and of Michelson and Sivashinsky (1977, 1982) using the hydrodyanmical model both found a state in which the cells continually and chaotically recombine. It is not clear from the visual appearance of these states whether these numerical results correspond to a disordered state or to an intermittently ordered state.

Forward Forward Forward