The nonlinear equation for curved flames applied to the problem of flames in cylindrical tubes

The nonlinear equation for curved stationary flames of realistic expansion coefficients is solved numerically for the problem of flame propagation in cylindrical tubes. Two different configurations of a flame front corresponding to convex and concave flames are obtained. The convex and concave flames propagate with different velocities that depend on the tube radius and on the expansion coefficient of the burning matter. For tubes of a moderate radius the velocity amplification for convex flames exceeds the respective velocity amplification of two-dimensional flames almost twice. For tubes of a large radius unlimited increase of the curved flame velocity with increase of the tube width takes place. The obtained theoretical results are in good quantitative agreement with the results of numerical experiments on flame dynamics in cylindrical tubes. (C) 1999 American Institute of Physics. [S1070-6631(99)00307-4].