A slow, subsonic flame can accelerate spontaneously, with the velocity jump by several orders of magnitude and even subsequent detonation triggering. This effect is extremely crucial, in particular, for fire safety issues in mines, subways and power plants. Flame acceleration is especially strong while propagating in tubes or channels. According to the celebrative Shelkin model, the key element of the process is wall friction at non-slip walls. Indeed, as a flame front propagates from a closed tube/channel end to the open one, the burning matter expands and it drives a flow of the fresh fuel mixture. However, due to the friction on the tube walls, the flow becomes non-uniform such that the burning matter bends the flame front, increases the flame velocity and leads to the flame acceleration. During the recent years, the effect has been clarified and investigated - analytically, computationally and experimentally. In particular, the analysis of Bychkov et al. describes the entire scenario of the flame acceleration and detonation triggering, namely: (i) initial exponential acceleration in the quasi-incompressible state; (ii) moderation of the process because of gas compression, so the exponential acceleration state goes over to a slower one; (iii) eventual saturation to a steady, quasi-steady or statistically-steady, high-speed flames correlated with the Chapman-Jouguet deflagration; at the latter stage, heating of the fuel mixture leads to an explosion ahead of the flame front, which develops into a self-sustained detonation. While this analytical theory is validated by extensive direct numerical simulations of the combustion equations including transport process, chemical reactions, viscosity, thermal conduction and diffusion, it nevertheless includes a set of assumptions such as the large Reynolds number related to flame propagation, Re1, as well as the large thermal expansion coefficient in the burning process, Θ1. This therefore leads to the intrinsic limitations of the theory. In this work we determine these limitations and thereby clearly underline the validity domains in the relevant Re-Θ diagram. The present analysis also demonstrates that the theory of flame acceleration is consistence with a model of steady flame propagation developed recently.
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