Effect of surface friction on ultrafast flame acceleration in obstructed cylindrical pipes

The Bychkov model of ultrafast flame acceleration in obstructed tubes [Valiev et al., “Flame Acceleration in Channels with Obstacles in the Deflagration-to-Detonation Transition,” Combust. Flame 157, 1012 (2010)] employed a number of simplifying assumptions, including those of free-slip and adiabatic surfaces of the obstacles and of the tube wall. In the present work, the influence of free-slip/non-slip surface conditions on the flame dynamics in a cylindrical tube of radius R, involving an array of parallel, tightly-spaced obstacles of size αR, is scrutinized by means of the computational simulations of the axisymmetric fully-compressible gasdynamics and combustion equations with an Arrhenius chemical kinetics. Specifically, non-slip and free-slip surfaces are compared for the blockage ratio, α, and the spacing between the obstacles, ΔZ, in the ranges 1/3 ≤ α ≤ 2/3 and 0.25 ≤ ΔZ/R ≤ 2.0, respectively. For these parameters, an impact of surface friction on flame acceleration is shown to be minor, only 1∼4%, slightly facilitating acceleration in a tube with ΔZ/R = 0.5 and moderating acceleration in the case of ΔZ/R = 0.25. Given the fact that the physical boundary conditions are non-slip as far as the continuum assumption is valid, the present work thereby justifies the Bychkov model, employing the free-slip conditions, and makes its wider applicable to the practical reality. While this result can be anticipated and explained by a fact that flame propagation is mainly driven by its spreading in the unobstructed portion of an obstructed tube (i.e. far from the tube wall), the situation is, however, qualitatively different from that in the unobstructed tubes, where surface friction modifies the flame dynamics conceptually.