Three-dimensional curved flames: Stationary flames in cylindrical tubes

Curved axisymmetric stationary flames in cylindrical tubes are investigated on the basis of a model nonlinear equation for a flame front subject to the Landau-Darrieus instability. It is found that the increase of the flame velocity due to a curved shape of the front is much larger far the case of three-dimensional curved flames compared to the two-dimensional ones. Some of important properties of curved three-dimensional flames differ qualitatively from the properties of two-dimensional flames, Particularly, a regime of strong initiation of the Landau-Darrieus instability in narrow tubes is obtained, when all perturbation modes of small amplitudes are stable, but a curved stationary flame is still possible. Another important feature of the three-dimensional flame propagation is unlimited increase of the flame velocity with the increase of the tube diameter.