Wrinkled flames and geometrical stretch

TL;DR

This paper investigates how geometrical stretch influences the formation, stability, and evolution of wrinkles in thin premixed flames, combining analytical and numerical methods to understand their behavior under different stretch conditions.

Contribution

It introduces a stretch-affected nonlinear nonlocal equation derived from the Michelson-Sivashinsky equation and provides analytical and numerical analysis of localized flame wrinkles under various stretch intensities.

Findings

Large positive stretch suppresses wrinkles

Negative stretch enhances wrinkle formation

Stable patterns and evolutions are characterized

Abstract

Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity (S) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/S > 0. A large constantS > 0 weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereasS < 0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked.