Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Teaching Limiting Behavior of Plane Oblique Shocks

Plane oblique shocks are formed in supersonic flows that cause abrupt flow deceleration, compression and turning. This behavior persists up to a maximum flow turning angle, θmax and a corresponding shock angle βmax for any upstream Mach number M1 with corresponding Mach angle, μ1. Beyond the maximum turning angle, the oblique shock becomes detached from the body and forms a bow shock. In teaching limiting behavior of plane oblique shocks, over a broad Mach range, from 1.5 to 5.0, we discover two interesting correlations. The first is on βmax which remains nearly invariant and the second is (μ1 + θmax) that remains nearly constant. In air with γ = 1.4, βmax is nearly 65.64° with 0.67° standard deviation and (μ1 + θmax) is nearly 53.24° with 0.32° standard deviation angle. Rankine-Hugoniot and Prandtl oblique shock relations are used in theoretical demonstrations of limiting behavior of plane oblique shocks.

Numerical simulations of wind-driven protoplanetary nebulae. II. signatures of atomic emission

We follow up on our systematic study of axisymmetric hydrodynamic simulations of protoplanetary nebula. The aim of this work is to generate the atomic analogues of the H2 near-infrared models of Paper I with the ZEUS code modified to include molecular and atomic cooling routines. We investigate stages associated with strong $\mathrm{[Fe\, {\small II}] \, 1.64\, \mathrm{\mu m} }$ and $\mathrm{ [S\, {\small II}] \, 6716}$ Å forbidden lines, the $\mathrm{[O\, {\small I}]\, 6300}$ Å airglow line, and Hα 6563 Å emission. We simulate (80 ∼ 200 km s−1) dense (∼105 cm−3) outflows expanding into a stationary ambient medium. In the case of an atomic wind interacting with an atomic medium, a decelerating advancing turbulent shell thickens with time. This contrasts with all other cases where a shell fragments into a multitude of cometary-shaped protrusions with weak oblique shocks as the main source of gas excitation. We find that the atomic wind-ambient simulation leads to considerably higher excitation, stronger peak and integrated atomic emission as the nebula expands. The weaker emission when one component is molecular is due to the shell fragmentation into fingers so that the shock surface area is increased and oblique shocks are prevalent. Position-velocity diagrams indicate that the atomic-wind model may be most easy to distinguish with more emission at higher radial velocities. With post-AGB winds and shells often highly obscured and the multitude of configurations that are observed, this study suggests and motivates selection criteria for new surveys.