A model for the trajectory of the transverse detonation resulting from re-initiation of a diffracted detonation

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A semi-analytical model is presented for predicting the trajectory of the transverse detonation during the re-initiation process of a diffracted cellular detonation wave from a channel. Numerical simulations based on the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model were first performed to observe key characteristics of cellular detonation wave diffraction and to obtain required input parameters for the model construction. The present numerical observations indicate that the transverse detonation stems from a location on the expansion wave front, and the horizontal distance from this initial location to the channel exit can be scaled by a constant multiplied by the detonation cell width for large deviation angles of the channel. The velocity of the transverse detonation basically equals the Chapman–Jouguet detonation wave velocity consisting of two orthogonal components: the expansion velocity of the diffracted wave front and the relative velocity to the diffracted wave front. The shape of the decoupled wave front is not affected by local explosion and thus can be predicted by the Chester–Chisnell–Whitham theory. Based on these numerical observations and the Chester–Chisnell–Whitham theory, a semi-analytical model is constructed to predict the wave trajectories as well as the distances of the wall reflection point for various deviation angles and initial pressures. The model prediction agrees with the corresponding numerical results. The model result shows that the distance of the wall reflection point varies from 15 to 20 multiples of the cell width with a minimal dependence on deviation angle, independent of the initial pressure. The trajectory calculated by the model is self-similar and determined by the horizontal distance of the initial location. The dimensionless trajectories divided by the horizontal distance are coincident for different initial pressures.