Name
Abstract | ||
|---|---|---|
A theory of flame propagation in two-dimensional channels with adiabatic and impermeable curved walls is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation for the burnt gas velocity is constructed. It is next used to derive an explicit expression for the rotational component of the gas velocity near the flame front by successive separation of irrotational contributions. We prove that this separation can be performed in a way consistent with boundary conditions at the channel walls. As a result, the unknown irrotational component can be projected out by applying a dispersion relation stemming from its analyticity, thus leading to a closed system of equations for the on-shell fresh gas velocity and the flame front position. These equations show that, in addition to the usual nonlocality associated with potential flows, vorticity produced by a curved flame leads to specific nonlocal spatial and temporal influence of the channel geometry on the flame evolution. To elucidate this influence, three special cases are considered in more detail: a steady flame stabilized by incoming flow in a bottle-shaped channel, quasi-steady flames, and unsteady flames with small gas expansion propagating in channels of slowly varying width. In the last case, analytical solutions of the equations derived for the front shape are obtained in the first post-Sivashinsky approximation on using the method of pole decomposition. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1137/100790252 | SIAM JOURNAL ON APPLIED MATHEMATICS |
Keywords | Field | DocType |
flame front dynamics,conformal mapping,vortex flows,pole decomposition | Adiabatic process,Conservative vector field,Boundary value problem,Laminar flame speed,Vorticity,Green's function,Dispersion relation,Mathematical analysis,Premixed flame,Mathematics | Journal |
Volume | Issue | ISSN |
70 | 8 | 0036-1399 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hazem El-Rabii | 1 | 0 | 0.34 |
| Guy Joulin | 2 | 0 | 0.34 |
| Kirill A. Kazakov | 3 | 0 | 0.34 |