The role of Landau-Darrieus instability in flame dynamics and deflagration-to-detonation transition

Abstract: The role of intrinsic hydrodynamic instability of the premixed flame (known as Landau-Darrieus instability) in various flame phenomena is studied by means of direct numerical simulations of the complete system of hydrodynamic equations. Rigorous study of flame dynamics and effect of Landau-Darrieus instability is essential for all premixed combustion problems where multidimensional effects cannot be disregarded.The present thesis consists of three parts. The first part deals with the fundamental problem of curved stationary flames propagation in tubes of different widths. It is shown that only simple "single-hump" slanted stationary flames are possible in wide tubes, and "multi-hump" flames in a laminar flow are possible in wide tubes only as a non-stationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes are obtained, together with the dependence of the velocity of the stationary flame on the tube width. The flame dynamics in wider tubes is shown to be governed by a large-scale stability mechanism resulting in a highly slanted flame front.The second part of the thesis is dedicated to studies of acceleration and fractal structure of outward freely propagating flames. It is shown that in direct numerical simulation the development of Landau-Darrieus instability results in the formation of fractal-like flame front structure. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional simulation of radially expanding flames in cylindrical geometry displays a radial growth with 1.25 power law temporal behavior after some transient time. It is shown that the fractal excess for 2D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2D cylidrical and three-dimensional spherical radially expanding flames is outlined. Extrapolation of the obtained results for the case of spherical expanding flames gives a radial growth power law that is consistent with temporal behavior obtained in the survey of experimental data.The last part of the thesis concerns the role of Landau-Darrieus instability in the transition from deflagration to detonation. It is found that in sufficiently wide channels Landau-Darrieus instability may invoke nucleation of hot spots within the folds of the developing wrinkled flame, triggering an abrupt transition from deflagrative to detonative combustion. It is found that the mechanism of the transition is the temperature increase due to the influx of heat from the folded reaction zone, followed by autoignition. The transition occurs when the pressure elevation at the accelerating reaction front becomes high enough to produce a shock capable of supporting detonation.