Ray-tracking methods for characterizing the dynamics of curved detonation

Abstract

Current analyses of curved detonations are mostly limited to the dynamics along the wall or the symmetry axis due to the lack of efficient approaches for reliably tracking stream tubes with curved shock fronts. To address this lack, the present work proposes a novel curved ray-tracking algorithm with two implementation methods. The curved ray is characterized by a specific arc of constant curvature perpendicularly intersecting both successive fronts. The methods were validated against Whitham's exact geometrical shock dynamics solutions of the self-similar shock diffraction problem. As compared to the typical forward straight-ray method, which is of the first order, the proposed methods demonstrate convergence rates greater by more than one order of magnitude and tend to be of the second order. The convergence analysis enabled to determine the range of time resolution required for the proposed methods to provide reliable results. This range is comparable to the acquisition rate of a modern high-speed camera that is commonly used in detonation visualization experiments. Differences between the proposed curved ray-tracking methods and the typical forward straight-ray method have been further examined by analyzing the ray dynamics during the weakly unstable hydrogen–oxygen–argon detonation diffraction. The ray-tube-based velocity-curvature relationship showed satisfactory agreement with those already well-established in quasi-steady experiments and predicted by the generalized Zeldovich–von Neumann–Doering model. This suggests the limited role of unsteadiness and cellular structure in the macro-scale dynamics of weakly unstable detonations.