Flame Propagation in a Tube: The Legacy of Henri Guenoche

TLDR: In this paper, the effects of flame stretch on the laminar burning velocity of a tube are discussed. And the effect of the Karlovitz stretch factor on the burn rate is discussed.

Abstract: Since the time of Mallard and Le Chatelier there has been a fascination with the problems of flame propagation in tubes. An important goal has been the development of a reliable technique to measure accurately the most basic combustion parameter, the laminar burning velocity. On the one hand a stable, steady-state, flame is necessary to do this, while on the other hand many flames are inherently unstable. These conflicting tendencies have been the source of much creative combustion thinking, not least from Guenoche. The paper attempts to indicate how his work has contributed to our present appreciation of the effects of flame stretch, thermo-diffusion, Darrieus – Landau and Taylor instabilities. Some practical consequences of the effects of these on the burn rate are briefly discussed. Laminar burning velocity and its measurement The purpose of the present paper is to show how Henri Guenoche’s painstaking descriptions and analyses of experimental findings concerning flame propagation in tubes contribute greatly to our current fundamental understanding of combustion. In 1883 Mallard and Le Chatelier [1] showed that the condition of a tube closed at one end with ignition at the other, open, end is probably the one best able to achieve a constant flame speed over a distance sufficient for the measurement of the laminar burning velocity. Thereafter, the flame oscillates, particularly with lean CH4 and H2 and rich hydrocarbon mixtures with air, and then assumes a cellular structure with an enhanced flame speed [2]. Their painstaking studies of the factors that give rise to a regime in which the flame speed is constant led Guenoche and Laffitte [3] to suppress any tendencies to acoustic oscillations by fitting an orifice to vent the burned gas at the open end of the tube, a practice adopted by subsequent workers, to make the vertical tube method a recommended one for measuring burning velocity [4]. Conversely, in the unstable regime forcing oscillations can induce a cellular structure [5]. When the flame attains a constant flame speed through the use of orifice damping its shape hardly changes and hence the effects of flame stretch rate are minimal. In the last decade the quantitative understanding of these effects stretch has advanced considerably and it is now almost mandatory to measure stretch-free values of burning velocity, λ u , together with values of Markstein numbers, Ma, to express the effects of flame stretch rate, in conjunction with the Karlovitz stretch factor, K. Flame stretch can either increase or decrease the burning velocity to a value,