Analytical treatment of 2D steady flames anchored in high-velocity streams

The problem of burning of high-velocity gas streams in channels is revisited. Previous treatments of this issue are found to be incomplete. It is shown that despite relative smallness of the transversal gas velocity, it plays crucial role in determining flame structure. In particular, it is necessary in formulating boundary conditions near the flame anchor, and for the proper account of the flame propagation law. Using the on-shell description of steady anchored flames, a consistent solution of the problem is given. Equations for the flame front position and gas velocity at the front are obtained. It is demonstrated that they reduce to a second-order differential equation for the front position. It is concluded that the mechanism of steady flame formation becomes local in the high-velocity limit. Numerical solutions of the derived equations are found and compared with experiment.