Unstable motions of cellular flame fronts at low lewis numbers

Abstract

The two-dimensional unsteady reactive flow is calculated to investigate the unstable motions of cellular flame fronts at low Lewis numbers. The equation used is the compressible Navier-Stokes equation including a one-step irreversible chemical reaction. We calculate the evolution of the disturbed flame front to obtain the dispersion relation and determine the wavelength corresponding to the maximum growth rate, i.e., the peculiar wavelength. The peculiar wavelength becomes shorter as the Lewis number decreases. The disturbance superimposed on the plane flame is evolved owing to the diffusive-thermal and hydrodynamic effects, and eventually the cellular flame front is formed. The spacing between cells of the cellular flame is equivalent to the peculiar wavelength. When the Lewis number is unity, the stationary cellular flame is obtained. When the Lewis number is lower than unity, on the other hand, the unstable cellular flame is obtained. With a decrease in the Lewis number, the instability level becomes greater. The shape of the flame front changes drastically, and the burning velocity of the cellular flame varies extremely with time. The unstable motions are due to the diffusive-thermal effect at low Lewis numbers.