Numerical investigations on abnormal combustion of gaseous mixtures and dynamic responses of pressurized vessels

Abstract

For the flow analysis of deflagration to detonation transition (DDT), detonation phenomenon involving combustible gas mixtures (C2H4-Air mixture, C2H4-O2 mixture, H2-O2 mixture, kerosene-air mixture, etc.) and the behavior of metal (copper, beryllium, steel, etc.) confinements during detonation loading, a multi-material treatment is developed for multi-physics shock analysis of gas mixtures and inert metals. A high-resolution approach including third-order convex ENO for spatial discretization and third-order Runge-Kutta for time advancement is used to simulate the abnormal combustion of gas mixtures and the elasto-plastic behavior of metals. Treatment of material interfaces uses level sets and is fairly simple and robust. Enforcement of jump conditions across the material interface is achieved by applying a ghost-point-populating technique such as the ghost fluid method (GFM) to interpolate data into extended regions. The time advancement is based on the method of lines, and it enables multi-dimensional calculations without time splitting in addition to allowing efficient implementation of Runge-Kutta schemes at orders higher than two. The physical models include an ideal equation of state (EOS) for combustible gas mixtures, specifically, a Mie-Gruneisen EOS for an elasto-plastic metal with isotropic linear hardening based on the Johnson-Cook model. Based on numerical approaches, we conduct various investigations. Firstly, DDT triggered by a shock in a straight or multi-bend tube with obstacle geometry is considered. The C2H4-air mixture filled rigid tube with obstacles is considered to understand the effects of complex confinement and initial flame size on DDT. Our calculations show the generation of hot spots by flame and strong shock interactions, and flame propagation is either restrained or accelerated due to wall obstacles for both straight and bent tubes. The effect of initial flame size on DDT in complex confinement geometry is analyzed as well as the effect of hot spot formation on promoting shock-flame interaction, leading to a full detonation. Secondly, we deal with a multi-material numerical investigation on the propagation of C2H4-O2 mixture and H2-O2 mixture detonation in elasto-plastic metal tubes. The calculated results are validated against the experimental data, which explains the process of generation and subsequent interaction of the expansion wave with the high strain rate deformation of the walls. Finally, to consider realistic wall effects on the propagating detonation, we perform a numerical simulation on the detonation propagation of kerosene-air mixtures and the perturbations of the detonation field from one elastically vibrating and one thermo-elasto-plastically deforming tube. The detonation loading of the metal tube is validated with experimental cell size, and the burst pressure of copper and steel tubes for varying wall thicknesses and wall temperatures is compared with the theoretical results. The safety aspect of the detonation tube is addressed and the results show that the calculated critical tube thickness with thermal softening included is a better fit with the theoretical value than the calculation without thermal softening. Some of the unseen behaviors of the flow dynamics of a pulsed detonation wave inside a pressure loaded hot tube are reported. The numerical approaches provide insight into understanding the effects of complex geometry on detonation transition, the influence of distortional tubes on detonation propagation, the dynamic responses of pressurized vessels in terms of the safety issues in accidents related to detonation and the design issues of PDE operated at high temperatures.