DDT in a smooth tube filled with a hydrogen-oxygen mixture

Results of experimental study on DDT in a smooth tube filled with sensitive mixtures having detonation cell size from 1 to 3 orders of magnitude smaller than the tube diameter are presented. Stoichiometric hydrogen-oxygen mixtures were used in the tests with initial pressure ranging from 0.2 to 8 bar. A dependence of the run-up distance to DDT on the initial pressure is studied. This dependence is found to be close to the inverse proportionality. It is suggested that the flow ahead of the flame results in formation of the turbulent boundary layer. This boundary layer controls the scale of turbulent motions in the flow. A simple model to estimate the maximum scale of the turbulent pulsations (boundary layer thickness) at flame positions along the tube is presented. The largest scale of the turbulent motions at the location of the onset of detonation is shown to be 1 order of magnitude greater than the detonation cell widths, lambda, in all the tests. It is suggested that the onset of detonation is triggered during flame acceleration as soon as the maximum scale of the turbulent pulsations increases up to about 10 lambda. The model to estimate the maximum size of turbulent motions, delta, and the correlation delta approximate to 10 lambda, give a basis for estimations of the run-up distances to DDT in tubes with internal diameter D > 20 lambda.