Correlations for the Onset of Instabilities of Spherical Laminar Premixed Flames

Abstract

A spherically expanding flame in a quiescent premixture is a bifurcation phenomenon, in which the flame becomes unstable at a radius, greater than some critical value, while remaining stable below that critical radius. Beyond this critical radius, developing instabilities are initiated by propagating cracks to form a coherent structure covering the entire flame surface and the flame accelerates. The present paper reports a Schlieren photographic study of spherical flame propagation in methane—air, iso-octane—air and n-heptane—air premixtures at different initial conditions where the onset of instability and the flame acceleration are clearly perceived. Critical size and corresponding elapsed time for the development of such instability are measured and these values are correlated with the appropriate flame parameter.

Flame dynamics and consideration of deflagration-to-detonation transition in central gravitational field

“…(26) depends strongly on the parameters of Eqs. (27) and (8). Indeed, varying b by a factor of about 2, we can modify the values of (26) by an order of magnitude, whereas the magnitude of b itself can be modified by an order of magnitude through even slight changes in the quantities of Eq.…”

“…(1), with a % 1:25-1:5, the exponent b depends strongly on the parameters of Eq. (8). For example, while there is no acceleration with a $ 4=3, [10], n $ 1:73 and m $ 3, such that b $ 1, only a slight change in the reaction order, say to n $ 1:3, leads to enormous acceleration, with b exceeding 5.…”

“…The exponent a has been found to be in the range of a ¼ 1:25-1:5 from terrestrial experiments [6][7][8][9][10]. Since a is usually treated as basically independent of the chemical composition of the combustible mixture and the nature of cells [10,22], we shall consider it as a universal constant, applicable to astrophysical combustion as well.…”

“…1. The structure and the self-similar acceleration of the DL-wrinkled flames have recently been studied experimentally [6][7][8][9][10] and computationally [11][12][13][14][15][16][17][18][19][20][21] including the possibility of the transition to detonation [22]. We are interested herein to apply the approach of Ref.…”

Experimental investigation of very rich laminar spherical flames under microgravity conditions

“…By setting constant threshold values at all times, a consistently defined flame front was computed. The assumption made in this study is therefore that R sch = R b where R sch is the tracked Schlieren radius [18]. Figure 2 shows the flame evolution of captured spherical flame photographs of (a) n-heptane-air mixtures with equivalence ratio / = 3.5, (b) isooctane-air mixtures with equivalence ratio / = 3.9 and (c) n-heptane/O 2 mixtures diluted in xenon (Xe), carbon dioxide (CO 2 ) and sulfur hexafluoride (SF 6 ) with equivalence ratio / = 3.5 and iso-octane/O 2 diluted in xenon with / = 3.9.…”