Premixed flames in large scale and high intensity turbulent flow

Abstract

2014 La théorie récente de Clavin et Williams [1] sur les fronts de flammes prémelangées dans les écoulements inhomogènes et instationnaires est généralisée au cas où l'amplitude de déplacement du front est grande. Les effets convectifs associés à l'expansion du gaz sont pleinement pris en compte dans l'étude de la structure locale du front plissé. On montre qu'un seul scalaire mesurant l'étirement du front contrôle localement la forme et la dynamique de la flamme. Ce scalaire peut se décomposer en deux termes représentant respectivement la contribution de la géométrie de la flamme (courbure du front avançant avec une vitesse normale prescrite) et celle de l'inhomogénéité de l'écoulement caractérisée par le tenseur du taux des déformations.Abstract. 2014 The recent theory of Clavin and Williams [1] concerning the premixed flame fronts in non uniform as well as unsteady flows is extended to the case of large amplitudes of the front corrugation. The convective effects associated with the gas expansion are fully taken into account in the study of the flame structure. Only one scalar « the flame stretch » is shown to control the shape and the motion of the front This stretch can be split in two parts, one accounts for the geometry of the front (mean curvature) and the other for the non uniformity of the flow (rate of strain tensor).

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.…”

Theory of Gaseous Combustion

“…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.…”

“…It is worthwhile to express the result (2.49) in terms of the mean radius of curvature of the front R. At the same order, the modification to normal burning velocity can be expressed as (see Clavin & Joulin 1983) :…”

Local burning velocity in a Bunsen jet flame

“…irrespective of the amplitude of the front corrugation [6,7]. The term in parentheses on the right-hand side of this equation is the flame stretch.…”

“…(1) will be termed the C-J relation in what follows, a shorthand for Clavin and Joulin [7]. Despite the time elapsed since this relation was derived, little is known about its precise limits of validity and its possible extensions when flame fronts appear curved on small scales of the order of the flame thermal thickness, d/L = 0(1).…”