Detonation initiation in pipes with a single obstacle for mixtures of hydrogen and oxygen-enriched air

Numerical investigation of detonation initiation by a focusing shock wave

“…The equations (1a-1c) are written in skewsymmetric form [14], and hence, the computational variables are set to [ √ ρ, √ ρu i , p, ρY ] T . This approach guarantees the conservation properties for finite difference schemes [13,14]. The dependence on temperature of the dynamic viscosity μ is calculated with Sutherland's law [15].…”

“…The mixture used in the numerical experiments is stoichiometric hydrogen-air enriched to 40% oxygen, as in the previous study [13]. The global reaction is modeled by a one-step, irreversible reaction, with one effective species Y , varying from one (unburned) to zero (burned).…”

“…In the experimental and numerical works of Gray et al [12] and Bengoechea et al Fig. 1 Geometry of the shock-focusing nozzle (left), initial conditions (center), and formation of the imploding shock wave after reflection (right) [13], a cylindrical PDE's combustion chamber is obstructed by a single convergent-divergent axisymmetric nozzle. This single obstacle configuration does not reduce the impulse significantly, unlike standard turbulence-producing devices with significant thrust losses [2].…”

“…This single obstacle configuration does not reduce the impulse significantly, unlike standard turbulence-producing devices with significant thrust losses [2]. In [13], the two key elements for a successful transition to detonation are identified as: (1) a high burning rate to create a strong leading shock wave and (2) the focusing of this leading shock wave due to the obstacle geometry. The latter is further analyzed in this paper to confirm the initiation mechanism and to reveal the details of this process.…”

“…The present study is devoted to the numerical investigation of the self-ignition process of detonations caused by a focusing shock wave at the nozzle-shaped obstacle from [13]. The shock wave is induced by a turbulent flame, so that this specific initiation mechanism is more precisely described as flame-to-shock-to-detonation transition.…”