Matalon–Matkowsky–Clavin–Joulin theory explained
The Matalon–Matkowsky–Clavin–Joulin theory refers to a theoretical hydrodynamic model of a premixed flame with a large-amplitude flame wrinkling, developed independently by Moshe Matalon & Bernard J. Matkowsky and Paul Clavin & Guy Joulin,[1] [2] following the pioneering study by Paul Clavin and Forman A. Williams[3] and by Pierre Pelcé and Paul Clavin.[4] The theory, for the first time, calculated the burning rate of the curved flame that differs from the burning rate of the planar flame due to flame stretch, associated with the flame curvature and the strain imposed on the flame by the flow field.[5]
Burning rate formula
According to Matalon–Matkowsky–Clavin–Joulin theory, if
and
are the laminar burning speed and thickness of a planar flame (and
be the corresponding flame residence time with
being the
thermal diffusivity in the unburnt gas), then the burning speed
for the curved flame with respect to the unburnt gas is given by
[6]
=1+l{M}c\deltaL\nabla ⋅ n+l{M}s\tauLnn:\nablav
where
is the unit normal to the flame surface (pointing towards the burnt gas side),
is the flow velocity field evalauted at the flame surface and
and
are the two
Markstein numbers, associated with the curvature term
and the term
corresponding to flow strain imposed on the flame.
[7] See also
Notes and References
- Matalon . M. . Matkowsky . B. J. . Flames as gasdynamic discontinuities . Journal of Fluid Mechanics . 124 . –1 . 1982 . 0022-1120 . 10.1017/S0022112082002481 . 239. 29 November 2024 .
- Clavin . P. . Joulin . G. . Premixed flames in large scale and high intensity turbulent flow . Journal de Physique Lettres . 44 . 1 . 1983 . 0302-072X . 10.1051/jphyslet:019830044010100 . 1–12.
- Clavin, P., & Williams, F. A. (1982). Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. Journal of fluid mechanics, 116, 251-282.
- Pelce, P., & Clavin, P. (1988). Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames. In Dynamics of curved fronts (pp. 425-443). Academic Press.
- Clavin . Paul . Dynamic behavior of premixed flame fronts in laminar and turbulent flows . Progress in Energy and Combustion Science . 11 . 1 . 1985 . 10.1016/0360-1285(85)90012-7 . 1–59.
- Book: Clavin . Paul . Searby . Geoff . Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and Explosion of Stars . Cambridge University Press . 2016-07-28 . 978-1-107-49163-2 . 10.1017/cbo9781316162453 .
- Clavin . Paul . Graña-Otero . José C. . Curved and stretched flames: the two Markstein numbers . Journal of Fluid Mechanics . 686 . 2011-11-10 . 0022-1120 . 10.1017/jfm.2011.318 . 187–217.
