Flow characterization during the flame acceleration and transition-to-detonation process with solid obstacles and fluid jets

The differences of flow characterization at the different stages of flame acceleration and transition to detonation in tubes with smooth walls, solid obstacles, and fluid jets are studied, especially the effects of flow instabilities on the process. The two-dimensional viscous unsteady reactive Navier–Stokes equations with a detailed chemistry model are solved numerically based on the structured adaptive mesh refinement technique in Adaptive Mesh Refinement Object-oriented C++\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$++$$\end{document}. During the ignition to a low-speed flame stage, it is found that initial pressure wave interactions with the wall and Rayleigh–Taylor instabilities, induced by the density and pressure gradient misalignment between the ignition region and unburned gas, accelerate the wrinkling and deformation of the flame surface. Consequentially, the flame wrinkles trigger Darrieus–Landau instabilities and as a result the flame accelerates. At the main acceleration stage, the Kelvin–Helmholtz instability formed in the wake of solid obstacles and the strong Kelvin–Helmholtz instability caused by the jets lead to the formation of strong turbulent structures in the flowfield and accelerate the flame propagation. Richtmyer–Meshkov instabilities caused by the interactions of reflected shock waves and the flame surface lead to flame acceleration in the case with solid obstacles. Compared to the tube with fluid jets, although the solid obstacles induce stronger Richtmyer–Meshkov instabilities, the effect of Kelvin–Helmholtz instabilities is not obvious. In general, Darrieus–Landau instabilities and Rayleigh–Taylor instabilities dominate at the initial flame-developing stage, and Kelvin–Helmholtz instabilities and Richtmyer–Meshkov instabilities play a more critical role in the flame acceleration due to interactions of the flame, the shock, solid obstacles, and vortices during the deflagration propagation stage.