Statistics of detonation confinement: 1D, 2D and 3D simulations in hydrogen–oxygen

Abstract

Statistical analysis of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) detonation simulations is performed to understand the role of confinement on detonation frontal velocity and thermodynamic states. Simulations considered include a 2D wide channel (5 detonation cells across), a 2D narrow channel (1.5 cells across), a 3D square channel (10 cells around perimeter), and a 3D round tube (6 cells around perimeter), with identical mixture conditions of stoichiometric hydrogen–oxygen with 3000 parts per million by volume (PPMv) ozone at 300 K and 15 kPa. 1D and 2D simulations with the same mixture without ozone are also considered. All simulations solve the compressible Navier–Stokes equations with detailed chemistry and exhibit good agreement with macroscopic characteristics of experiments (e.g., cell size). Results show that the frontal velocity in 3D simulations is more irregular as compared to the 2D simulations, which are more irregular compared to the 1D simulations. The irregularity in frontal velocity leads to broader distributions of shock velocities and shock decay behavior. The 3D simulations also exhibit a wider and more extreme set of thermodynamic states as compared to the 2D simulations immediately behind the shock wave, within the induction zone, and throughout the rest of the domain. Increasing relative boundary losses leads to quantitative differences in both thermodynamic state and frontal velocity, consistent with 1D steady models of detonation with losses. The conclusions drawn in this work are not sensitive to numerical grid resolution.