Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity

Abstract

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.

Curvature and Velocity of Methane-Air Bunsen Flame Tips

“…Analysis [1][2][3] shows that, in certain conditions, there is a linear relation between the so-called stretch of the flame, which is the logarithmic derivative of the area & A of an element of a propagating flame front, and the change of its local normal velocity relative to the fresh gas, U n , about the velocity of the planar flame, U L . The Markstein length £ is the proportionality constant in this linear relation: u n -u L = -c±m.…”

“…Here n is a unit vector normal to the flame pointing toward the burnt gas and C = V • n is twice the mean curvature of the front. These results have been rigorously derived using high activation energy asymptotics in the limit of infinitely thin flames; i.e., when the curvature of the flame is small compared to the inverse of its thickness and the strain rate of the flow is small compared to the inverse of the transit time of the gas across the flame [1][2][3]. The theory also provides an expression for the Markstein length in terms of the physicochemical properties of the gas.…”

Theory of Gaseous Combustion

“…Recently, the coupling between diffusion and hydrodynamics has been properly taken into account for describing the wrinkled flame structure in an analytical work by Clavin & Williams (1982). The asymptotic expansion B-"™ is used together with a multiscale method based on the assumption e=d/D smaller than unity.…”

“…The analysis of Clavin & Williams (1982) concerning the flame structure of wrinkled fronts in a non homogeneous flows has been extended independently by Matalon & Matkowsky (1982) and by Clavin & Joulin (1983) to the nonlinear case of finite amplitudes of the front corrugations. As anticipated by the early phenomenological analysis of Karlowitz et al (1953), the modification to the normal burning velocity u n produced by the front curvature and by the flow inhomogeneities can be expressed in terms of only one geometrical scalar i.e.…”

Local burning velocity in a Bunsen jet flame

“…The second contribution to the stretch is due to the rate of strain of the gas flow, n-Vv-n, where v is the velocity of the fresh gas. The analysis provides also an expression of the proportionality constant, the Markstein length C, which has been obtained under very general conditions in terms of the physicochemical properties of the reactive mixture [8][9][10][11][12][13][14]. It is worth noticing that this interpretation in terms of the stretch holds because Eq.…”