FROM TRAVELING WAVES TO CHAOS IN COMBUSTION

The nonlinear evolution of nonadiabatic, nonsteady cellular flames is studied numerically as a function of a parameter related to heat loss. The specific problem considered is that of a premixed flame established in the region between two coaxial cylinders. The combustible mixture is fed in through the inner cylinder, and the products of combustion are removed through the outer cylinder. A diffusional thermal model is employed, which allows for nonadiabatic effects due to heat transfer through the outer cylinder and due to the injection of cold fuel through the inner cylinder. The pulsating regime Le > 1 is considered, where Le is the Lewis number of the deficient component of the combustible mixture. The effect of increasing heat loss on spinning cellular flames corresponding to traveling waves along the flame front is studied. It is found that heat loss promotes the development of subharmonic or near subharmonic modes along the flame front. The resulting nonlinear dynamics depend crucially on the number of cells. The following two examples are considered: (i) a seven-cell traveling wave and (ii) an eight-cell traveling wave. In the first case, increasing heat loss leads to a transition whereby modes 3 and 4 enter as well as mode 7. The result describes a rotating cellular flame in which the peaks of the cells undergo oscillations leading to a modulated traveling wave exhibiting a symmetry that we refer to as jumping ponies on a merry-go-round. The peak oscillations undergo two period doublings as heat loss is increased. Increasing the heat loss further leads to apparently chaotic behavior. In the second case, as heat loss is increased, mode 4 enters with a frequency half the original frequency, so that a period-doubled (2T) traveling wave is found. Upon increasing heat loss still further, mode 2 and then mode 1 enter, leading to 4T and 8T traveling waves. Upon further increasing the heat loss, apparently chaotic cell oscillations are found.