On the transformation of planar detonation to cylindrical detonation

Abstract

An experimental study on the transmission of planar detonation from a circular tube to cylindrical detonation expanding radially outward between a pair of parallel plates shows that reinitiation of the diffracted wave is via one of two mechanisms. In the first mode, reinitiation is seen to occur “spontaneously,” before the emerging wave interacts with the wall of the cylindrical chamber opposite the tube exit, in exactly the manner observed in transmission to the unconfined. Measurements from smoke records, in conjunction with simple physical models describing the transformation process, place the location of reignition 11.5 cell widths λ downstream of the tube exit. Smoke records further show that the subsequent process, whereby the reinitiated wave engulfs the deflagration to reestablish detonation globally, is also controlled by λ. These observations confirm the similarity of supercritical reinitiation for all mixture sensitivities investigated. The Shchelkin instability criterion,using the hydrodynamic thickness as the relevant “reaction-zone” length, is proposed as a possible basis for the 13λ correlation linking the critical tube diameter D c to the cell size. This correlation is shown to be valid for the tube employed in the present study. In the second mode of reinitiation, reignition is seen to be induced “by reflection” of the diffracted wave from the wall opposing the tube exit. The reignition and reestablishment processes are shown to scale with the nondimensional parameter w λ , where w is the separation between the walls defining the cylindrical chamber. The critical condition for transmission is found to be that w must exceed 5.7λ, regardless of the tube size D λ . This is explained in terms of the hydrodynamic thickness of the wave.