Bow-shock instability induced by Helmholtz resonator-like feedback in slipstream

Abstract

Bow-shock instability has been experimentally observed in a low-γ flow. To clarify its mechanism, a parametric study was conducted with three-dimensional numerical simulations for specific heat ratio γ and Mach number M. A critical boundary of the instability was found in the γ-M parametric space. The bow shock tends to be unstable with low γ and high M, and the experimental demonstration was designed based on this result. The experiments were conducted with the ballistic range of the single-stage powder gun mode using HFC-134a of γ = 1.12 at Mach 9.6. Because the deformation of the shock front was observed in a shadowgraph image, the numerical prediction was validated to some extent. The theoretical estimation of vortex formation in a curved shock wave indicates that the generated vorticity is proportional to the density ratio across the shock front and that the critical density ratio can be predicted as ∼10. A strong slipstream from the surface edge generates noticeable acoustic waves because it can be deviated by the upstream flow. The acoustic waves emitted by synchronizing the vortex formation can propagate upstream and may trigger bow-shock instability. This effect should be emphasized in terms of unstable shock formation around an edged flat body.

Potential for the Vishniac instability in ionizing shock waves propagating into cold gases

“…Finally we note that, although the primary focus in this paper has been on the Vishniac instability, there are a number of other instabilities reported in the literature which depend on the post-shock fluid achieving γ close to 1. In particular there are the bow-shock instabilites described by Dgani et al 11 and Ohnishi et al 24 , which, in light of the results reported in this paper, might be achieved due to ionization or dissociation.…”

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

“…Experiments and simulations of Hornung & Lemieux (2001) and Ohnishi et al. (2015) found instability when density jumps of and were reached across the shock. Interestingly, the bifurcation boundary in – space is well represented by a constant density ratio of across the shock, plotted with a dashed curve in figure 20.…”

“…2009 b ; Ohnishi et al. 2015). Shock instability has been observed by Sirmas & Radulescu (2015, 2019) in molecular dynamic calculations of relaxing shock waves in gases with inelastic collisions, as would occur where strong vibrational relaxation effects are present.…”

“…Work with hypersonic projectiles has attributed similar shock instability to vibrating or unstable contact surfaces. Experiments and simulations of Hornung & Lemieux (2001) and Ohnishi et al (2015) found instability when density jumps of ρ 1 /ρ 0 ≥ 14 and ρ 1 /ρ 0 ≥ 10 were reached across the shock. Interestingly, the bifurcation boundary in M-γ space is well represented by a constant density ratio of ρ 1 /ρ 0 = 6.7 across the shock, plotted with a dashed curve in figure 20.…”

“…Shock wave instability has been ascribed to endothermic processes such as ionization (Griffiths, Sandeman & Hornung 1976;Glass & Liu 1978;Grun et al 1991) and dissociation (Griffiths et al 1976), or to heavy gases (i.e. low-isentropic-exponent gases) where vibrational relaxation may occur behind the shock (Griffiths et al 1976;Mishin et al 1981;Hornung & Lemieux 2001;Semenov et al 2009b;Ohnishi et al 2015). Shock instability has been observed by Sirmas & Radulescu (2015 in molecular dynamic calculations of relaxing shock waves in gases with inelastic collisions, as would occur where strong vibrational relaxation effects are present.…”