On the Quasi One-Dimensional Structure of Two-Dimensional Cellular Detonations in a Duct

Abstract

Adaptive mesh refinement combined with a WENO-TCD hybrid numerical method are used to simulate cellular detonations in ducts using a detailed chemical mechanism linked to the inviscid Euler equations. Using this computational setup, we were able to reproduce the detonation cells and structure that other researchers have produced in their work and then used the results to validate what is called the cross-current dynamics theory, developed by Kurosaka & Tsuboi (2014). This theory uses the conservation laws, Rankine-Hugoniot jump condition, and detonation front curvature to determine the velocity directly behind the detonation front. Comparisons of the velocity ratio calculated from the cross-current dynamics theory and the data from the simulation verify the accuracy of the theory. Next we simulate a detonation propagating from the closed end of a duct and compare the one-dimensional ZND solution, which we used to initiate the two-dimensional detonations, to the area-averaged properties and the properties of particles tracked along their pathlines from the detonation front to their sonic points. Despite the complex structures that appear within the detonation, the one-dimensional solution proves to also model the structure of the area-averaged and particle properties. Disagreements between the particle properties and the one-dimensional solution are concentrated near the detonation front where the transverse wave and Mach stem introduce larger jumps in the flow properties than in the one-dimensional case. We also show the particle pathlines are dominated by a one-dimensional motion with slight drifts in the vertical direction downstream from the detonation front. By reviewing the particles’ v-velocity to u-velocity ratio in the reference frame attached to the detonation front, we observe the quick transition the particles experience from a two-dimensional to a quasi one-dimensional motion. These findings give us new found appreciation of the quasi one-dimensional nature of two-dimensional detonations.