Critical tube diameter for quasi-detonations

The critical tube diameter problem for quasi-detonations is studied via experiments and two-dimensional numerical simulations based on the reactive Euler equations. In the experiments, quasi-detonation in stoichiometric acetylene-oxygen mixtures is generated in rough-walled tubes with three different diameters, where the wall roughness is introduced by using spiral inserts with different wire diameters. Photodiodes are placed along the rough tubes to record the detonation time-of-arrival to deduce the velocity, and a high-speed schlieren system is used to observe the diffraction processes. Near the critical regime of detonation diffraction, the quasi-detonation emerging from the rough tube is again shown to first fail and subsequently re-initiate from a local explosion center in the spherical deflagration reaction zone. For quasi-detonations, stronger turbulence and instabilities produce stronger local hot spots, which balances the significant velocity deficit as much as approximately 15% in the rough tube, resulting in the critical pressure remaining relative constant. The cell sizes for quasi-detonation in rough tubes are directly measured, and the ratio of critical tube diameters (d_c) to these determined cell sizes (λ) is used to quantify the critical criterion of detonation initiation. In rough tubes with coil springs, the previous criterion of d_c/λ ≧ 13 for detonation re-initiation appears invalid, and the critical initiation regime for quasi-detonation in rough tubes is found approximately as d_c/λ ≧ 8. Despite the cell enlargement and the lower propagation velocity for quasi-detonation, it is hypothesized that the increase in cell irregularities or instabilities can in turn benefit the transmission process. These unstable features of quasi-detonation are supported by the two-dimensional numerical simulations, also showing a higher degree of cell irregularities, a wider spectrum of induction rate, and the generation of shocked reactive pockets.