Potential Flow of Unburned Mixture and Combustion Products After Ignition in a Two-Dimensional Approximation

The evolution of a flame front in a channel was considered in a two-dimensional approximation. In the approximation of the potential flow of combustion products and unburned mixture, the formation of a finger-shaped flame was considered after ignition at the closed end of the channel, on the channel axis, and on the side wall of the channel. The prerequisites for the formation of a tulip-shaped flame were considered in a potential approximation. The method of conformal mapping was used. Simple analytical functions were used that allowed equipotential lines and streamlines to be transformed. The shape of the flame front was obtained. The analytical results were compared with the experimentally obtained results of the flame front evolution and with numerical results obtained by other authors. The conditions for the applicability of the conformal mapping to a reacting gas mixture were given.