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] 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.[3]
Burning rate formula
editAccording 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[4]
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,[5] associated with the curvature term and the term corresponding to flow strain imposed on the flame.
See also
editReferences
edit- ^ Matalon, M., & Matkowsky, B. J. (1982). Flames as gasdynamic discontinuities. Journal of Fluid Mechanics, 124, 239-259.
- ^ Clavin, P., & Joulin, G. (1983). Premixed flames in large scale and high intensity turbulent flow. Journal of Physics Letters , 44 (1), 1-12.
- ^ Clavin, P. (1985). Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Progress in energy and combustion science, 11(1), 1-59.
- ^ Clavin, P., & Searby, G. (2016). Combustion waves and fronts in flows: flames, shocks, detonations, ablation fronts and explosion of stars. Cambridge University Press.
- ^ Clavin, P., & Graña-Otero, J. C. (2011). Curved and stretched flames: the two Markstein numbers. Journal of fluid mechanics, 686, 187-217.