An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows

Abstract

Assessment of a flame surface density-based subgrid turbulent combustion model for nonpremixed flames of wood pyrolysis gas A coordinate-free equation modeling the flame front dynamics as propagation of density discontinuity within the framework of the Darreus-Landau hydrodynamical model is derived under the assumption of potential flow. The assumption is based on the observation that for slightly perturbed plane configurations the flow is irrotational if the thermal expansion of the gas is weak. A relationship with an equation obtained earlier for a slightly perturbed plane flame front is established in the case of weak thermal expansion. An invariant equation simultaneously modeling the thermal-diffusional and the hydrodynamical instabilities is suggested, which also can be reduced to earlier results in appropriate limits.

Magnetic Field Effects on the Thermonuclear Combustion Front of Chandrasekhar Mass White Dwarfs

“…The propagation of the front subject to LD instability is well described by the Sivashinsky equation (Sivashinsky 1977(Sivashinsky , 1983, which also includes thermodiffusive and acceleration effects, or by its generalization (Frankel 1990). By utilizing these equations for numerical studies of wrinkled surfaces, we are able to reproduce the front on a wider range of spatial 3 We refer here to the fractal dimension (and not to the Hausdorff-Besicovitch dimension) of an attractor as it is commonly defined in astrophysical works (Barnsley 1988).…”

Assessment of the Evolution Equation Modelling approach for three-dimensional expanding wrinkled premixed flames

“…Since then, many other attempts and techniques to improve this equation or to propose other kinds of EEM equations can be found in the literature : e.g. higher order expansions in α for MS type equations [28,29,30], second order in time equations for transients or acoustics [31,32] non perturbative approaches [33,34], asymptotic expansion based on flame aspect ratio [35], 3D planar equations [36,37,38], equations dealing with non connected or non stellate front topology [39,40,41]. In the context of 3D expanding flames [13,42,43], many of the proposed equations can be seen as different extensions of Michelson-Sivashinsky equation.…”

Nonlinear equation for curved stationary flames

“…From a more general point of view, the theory of flame propagation in the fully developed nonlinear regime cannot be formulated in the way the Sivashinsky equation [8] or the Frankel equation [9] are formulated. This is because the assumption of potentiality of the flow downstream, employed in these works, renders the relations between the flow variables local, allowing thereby the formulation of equation for the flame front position in terms of this position alone.…”

“…In Ref. [9], the vorticity production in the flame is completely neglected [see the point 2) above]. The mass conservation and the constant normal flame velocity are taken as the conditions governing flame dynamics.…”