Numerical study of three-dimensional detonation wave dynamics in a circular tube

The three-dimensional structures of a detonation wave propagating in a circular tube were investigated using a one-step irreversible Arrhenius kinetics model. A series of parametric studies were carried out to investigate the different modes of cell structure formation by changing the pre-exponential factor. Maximum pressure trace was recorded along the tube wall to investigate the detonation cell structures. The unsteady results obtained in three dimensions revealed the generation mechanism of the wave front structures of two-, three- and four-cell mode detonations. A six-cell mode detonation could be obtained using a finer grid. With the increase in pre-exponential factor, it was found that the number of detonation cells is increased while the cell size is reduced accordingly. In all the multi-cell modes, the detonation wave structures and smoked-foil records on the wall are formed by the propagation of transverse waves along the wall in clockwise and counter-clockwise directions, while the slapping wave moves in the radial direction. The presence of the slapping wave further strengthens the wave interactions in three-dimensional simulation. Comparison with two-dimensional simulation confirms the effect of the slapping wave in the radial direction. As a result, the detonation wave front structures changes from the polygonal shape to the multi-bladed fan shape, periodically.