To study effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, a previously developed theory of premixed flames in turbulent flows, that was based on a diffusive-thermal model in which thermal expansion was neglected, and that applied to turbulence having scales large compared with the laminar flame-thickness, is extended by eliminating the hypothesis of negligible expansion and by adding the postulate of weak-intensity turbulence. The consideration of thermal expansion motivates the formal introduction of multiple-scale methods, which should be useful in subsequent investigations. Although the hydrodynamic-instability mechanism of Landau is not considered, no restriction is imposed on the density change across the flame front, and the additional transverse convection correspondingly induced by the tilted front is described. By allowing the heat-to-reactant diffusivity ratio to differ slightly from unity, clarification is achieved of effects of phenomena such as flame stretch and the flame-relaxation mechanism traceable to transverse diffusive processes associated with flame-front curvature. By carrying the analysis to second order in the ratio of the laminar flame thickness to the turbulence scale, an equation for evolution of the flame front is derived, containing influences of transverse convection, flame relaxation and stretch. This equation explains anomalies recently observed at low frequencies in experimental data on power spectra of velocity fluctuations in turbulent flames. It also shows that, concerning the diffusive-stability properties of the laminar flame, the density change across the flame thickness produces a shift of the stability limits from those obtained in the purely diffusive-thermal model. At this second order, the turbulent correction to the flame speed involves only the mean area increase produced by wrinkling. The analysis is carried to the fourth order to demonstrate the mean-stretch and mean-curvature effects on the flame speed that occur if the diffusivity ratio differs from unity.
Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates
