| Abstract |
We study the development and evolution of patterns in premixed gaseous
flames confined between two coaxial cylinders. The mixture is fed in through the inner
cylinder and burned products are exhausted through the outer cylinder. We seek
axisymmetric solutions, independent of Theta, and take into account only the radial and
axial directions. We consider cases where the Lewis number, Le (ratio of thermal to mass
diffusivity), is both greater than and less than unity. We employ an adaptive Chebyshev
pseudo-spectral method in the radial direction, which allows high resolution of the flame
front with a relatively small number of computational degrees of freedom. We assume
periodic boundary conditions in the axial direction and employ Fourier methods in this
direction.
We consider two models, the diffusional thermal model for Le >1 and a fully coupled low
Mach number model for Le < 1. In the diffusional thermal model, thermal expansion is
assumed to be weak, so that the underlying flow field is assumed to be unaffected by the
transport processes. The low Mach number model includes the coupling of combustion to the
underlying velocity field, while filtering out sound waves.We present results showing a
variety of spatiotemporal patterns for gaseous combustion. For the diffusional thermal
model, these include traveling waves, modulated traveling waves, and a combination of two
and three cell standing waves that exhibit cell merging and splitting. We compare the
pulsating cellular solutions of the fully coupled computations with experimental results,
and obtain good agreement between the two. |
