Viscous solution of the triple-shock reflection problem

Abstract

The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier-Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition, when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin-Helmholtz instabilities were absent and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin-Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.

Influence of turbulent fluctuations on detonation propagation

“…Unfortunately, such investigations (Gamezo et al 2000;Mahmoudi et al 2014) have revealed that practically attainable resolutions, in full-scale two-dimensional problems, are insufficient to capture the correct reaction rates of unburned pockets. Thus, full-scale DNS is currently limited to providing insight only on single-isolated events, such as triple point collisions (Ziegler et al 2011;Lau-Chapdelaine & Radulescu 2016). Furthermore, turbulence inherently contains three-dimensional effects.…”

Viscous jetting and Mach stem bifurcation in shock reflections: experiments and simulations

“…Numerical simulations will now be used to elucidate the flow field at early stages of the reflection and at higher Mach numbers. The numerical study is an extension of the work by Lau-Chapdelaine & Radulescu (2016).…”

“…The initial conditions can be recreated using the data from table 3 employing the shock Mach numbers with the Rankine–Hugoniot equations, the angles between discontinuities and the reference frame speed (post-reflection Mach stem speed, calculated using three shock theory). Using a triple shock as initial condition does away with non-physical leaky boundary conditions and provides an unambiguous way to pose the problem (Lau-Chapdelaine & Radulescu 2016). It also closely resembles triple-shock reflections in detonations.…”

“…Viscous simulations are performed at Reynolds numbers up to and experiments up to . For comparison, detonations in stoichiometric hydrogen–oxygen, methane–oxygen and propane-oxygen under atmospheric conditions have been estimated to reach Reynolds numbers of to on cellular length scales (Lau-Chapdelaine & Radulescu 2016). The effects of Reynolds number, Mach number and isentropic exponent on the forward jet, the flow field behind the Mach stem and the shock front are scrutinized.…”

“…1987; Lau-Chapdelaine & Radulescu 2013). This will be avoided by using triple-point reflections (Lau-Chapdelaine & Radulescu 2016) from grid-aligned surfaces.…”