Influence of gas compression on flame acceleration in the early stage of burning in tubes

The mechanism of finger flame acceleration at the early stage of burning in tubes was studied experimentally by Clanet and Searby [Combust. Flame 105: 225 (1996)] for slow propane-air flames, and elucidated analytically and computationally by Bychkov et al. [Combust. Flame 150: 263 (2007)] in the limit of incompressible flow. We have now analytically, experimentally and computationally studied the finger flame acceleration for fast burning flames, when the gas compressibility assumes an important role. Specifically, we have first developed a theory through small Mach number expansion up to the first-order terms, demonstrating that gas compression reduces the acceleration rate and the maximum flame tip velocity, and thereby moderates the finger flame acceleration noticeably. This is an important quantitative correction to previous theoretical analysis. We have also conducted experiments for hydrogen-oxygen mixtures with considerable initial values of the Mach number, showing finger flame acceleration with the acceleration rate much smaller than those obtained previously for hydrocarbon flames. Furthermore, we have performed numerical simulations for a wide range of initial laminar flame velocities, with the results substantiating the experiments. It is shown that the theory is in good quantitative agreement with numerical simulations for small gas compression (small initial flame velocities). Similar to previous works, the numerical simulation shows that finger flame acceleration is followed by the formation of the "tulip" flame, which indicates termination of the early acceleration process.Comment: 19 pages, 20 figure

Turbulent burning, flame acceleration, explosion triggering

The present thesis considers several important problems of combustion theory, which are closely related to each other: turbulent burning, flame interaction with walls in different geometries, flame acceleration and detonation triggering. The theory of turbulent burning is developed within the renormalization approach. The theory takes into account realistic thermal expansion of burning matter. Unlike previous renormalization models of turbulent burning, the theory includes flame interaction with vortices aligned both perpendicular and parallel to average direction of flame propagation. The perpendicular vortices distort a flame front due to kinematical drift; the parallel vortices modify the flame shape because of the centrifugal force. A corrugated flame front consumes more fuel mixture per unit of time and propagates much faster. The Darrieus-Landau instability is also included in the theory. The instability becomes especially important when the characteristic length scale of the flow is large. Flame interaction with non-slip walls is another large-scale effect, which influences the flame shape and the turbulent burning rate. This interaction is investigated in the thesis in different geometries of tubes with open / closed ends. When the tube ends are open, then flame interaction with non-slip walls leads to an oscillating regime of burning. Flame oscillations are investigated for different flame parameters and tube widths. The average increase in the burning rate in the oscillations is found. Then, propagating from a closed tube end, a flame accelerates according to the Shelkin mechanism. In the theses, an analytical theory of laminar flame acceleration is developed. The theory predicts the acceleration rate, the flame shape and the velocity profile in the flow pushed by the flame. The theory is validated by extensive numerical simulations. An alternative mechanism of flame acceleration is also considered, which is possible at the initial stages of burning in tubes. The mechanism is investigated using the analytical theory and direct numerical simulations. The analytical and numerical results are in very good agreement with previous experiments on “tulip” flames. The analytical theory of explosion triggering by an accelerating flame is developed. The theory describes heating of the fuel mixture by a compression wave pushed by an accelerating flame. As a result, the fuel mixture may explode ahead of the flame front. The explosion time is calculated. The theory shows good agreement with previous numerical simulations on deflagration-to-detonation transition in laminar flows. Flame interaction with sound waves is studied in the geometry of a flame propagating to a closed tube end. It is demonstrated numerically that intrinsic flame oscillations coming into resonance with acoustic waves may lead to violent folding of the flame front with a drastic increase in the burning rate. The flame folding is related to the Rayleigh-Taylor instability developing at the flame front in the oscillating acceleration field of the acoustic wave

Impacts of the Lewis and Markstein numbers on premixed flame acceleration in channels due to wall friction

The effects of flame stretch as well as that of thermal and molecular diffusion on the scenario of flame acceleration in channels are quantified by means of computational and analytical endeavors. The analytical formulation incorporates the internal transport flame properties into the theory of flame acceleration due to wall friction by means of the Markstein number, which characterizes the flame response to curvature and stretch. Being a positive or negative quantity and a function of the thermal-chemical combustion parameters, such as the thermal expansion ratio as well as the Lewis and Zeldovich numbers, the Markstein number either moderates or promotes flame acceleration. While the Markstein number may provide a substantial impact on the flame acceleration rate in narrow channels, this effect diminishes with increase in the channel width. The analytical formulation is accompanied by extensive computational simulations of the reacting flow equations, which clarify the impact of the Lewis number on flame acceleration. It is noted that for Lewis numbers below a certain critical value, at the initial stage of flame acceleration, a globally convex flame front splits into two or more finger-like segments, accompanied by a drastic increase in the flame front surface area and associated enhancement of flame acceleration. Later, however, these segments of the flame front meet, promptly consuming cavities and pockets, which substantially decreases the flame surface area and moderates acceleration. Eventually, this dynamics results in a single, globally convex flame, which keeps accelerating. Overall, the thermal-diffusive effects substantially facilitate flame acceleration, thereby advancing a potential deflagration-to-detonation transition