Diffraction of cellular detonation wave over a cylindrical convex wall

Abstract

Numerical simulations were performed to study diffraction of a cellular detonation wave over a 90∘ cylindrical convex wall. The dynamics of this diffraction phenomenon was described by the two-dimensional reactive Euler equations with a detailed hydrogen/oxygen chemistry model and solved numerically by using the adaptive mesh refinement code AMROC. The present numerical observations indicate that the continuous variation trend of area divergence ratio caused by the curved convex wall can make detonation transverse wave reflect on the wall and sustain the coupling of the diffracted detonation wave for a certain distance. The reflection of the transverse waves can also enhance the energy to promote the re-intiation of the diffracted detonation. As the wall curvature radius increases to a certain value, the detonation wave can even propagate stably without decoupling in the expansion area. The critical wall curvature radius for re-initiation is found to have negative correlation with the contained detonation cell number in the exit, while the critical radius for stable propagation is mainly determined by the initial pressure. The critical re-initiation criterion for the detonation diffraction is further explored by introducing two different re-initiation mechanisms and considering the width of an “equivalent exit” calculated by the Chester-Chisnell-Whitham theory to satisfy the re-initiation condition. Meanwhile the critical criterion of stable propagation is described quantitatively by applying the Dn−κ theory to confirm the relation between the propagation velocity and the curvature of the diffracted detonation wave front, and calculating the minimum curvature radius of the curved detonation wave front theoretically. The accuracy of the criterions are verified by compared with the numerical results.