Nonlinear flame front evolution equations
In many cases, the flame is a complex dynamic system, which behavior may be explained by several mechanisms, either based on the kinetics of the reactions or other mechanisms, such as those associated with processes of selective diffusion or interaction with unsteady gas flows. For example, flame fluctuations may be caused by reaction kinetics or internal instability of the flame, the mechanism of which can be described by the simple reaction kinetics, but with inclusion of effects of the flame front curvature, the flow stretching, expansion of the combustion products, friction and heat transfer between the gas and the walls of the vessel and other factors. To highlight the mentioned mechanisms, the different types of flame instability is analysed at the basis of nonlinear evolution equations for the flame front that takes into account the strong nonlinear effects associated with the curvature of the front, the velocity gradients of the flow and the intrinsic diffusion-thermal instability. At the present time, the Markstein linear relationship between the local flame speed and the local flame front curvature is applied for modeling of the disturbed flame evolution. In case of flame, consisting of individual cells, or in the extreme case of a "flame ball", this model is not able to describe such structures. During the project fulfillment, nonlinear evolution equations for the flame front and flame temperature were derived, which is able to describe both cellular and flat flame front propagation. The solution of this problem significantly improve the existing methods for effective simulations of flame evolution in complex flows with the same simplicity as "flamelet" model, but taking into account the nonlinear effects related with local curvature of the flame front and the nonuniformity of the gas flow. This problem is relevant in connection with the necessity of modeling the dynamic behavior of the flame front of practical fuel mixtures with large Lewis numbers, scintillation instability of SHS waves, oscillating fronts and traveling waves in the case of combustion of condensed materials.