Evolution and stability of shock waves in dissipative gases characterized by activated inelastic collisions

Abstract

Previous experiments have revealed that shock waves driven through dissipative gases may become unstable, for example, in granular gases and in molecular gases undergoing strong relaxation effects. The mechanisms controlling these instabilities are not well understood. We successfully isolated and investigated this instability in the canonical problem of piston-driven shock waves propagating into a medium characterized by inelastic collision processes. We treat the standard model of granular gases, where particle collisions are taken as inelastic, with a constant coefficient of restitution. The inelasticity is activated for sufficiently strong collisions. Molecular dynamic simulations were performed for 30,000 particles. We find that all shock waves investigated become unstable, with density nonuniformities forming in the relaxation region. The wavelength of these fingers is found to be comparable to the characteristic relaxation thickness. Shock Hugoniot curves for both elastic and inelastic collisions were obtained analytically and numerically. Analysis of these curves indicates that the instability is not of the Bethe-Zeldovich-Thompson or D'yakov-Kontorovich type. Analysis of the shock relaxation rates and rates for clustering in a convected fluid element with the same thermodynamic history ruled out the clustering instability of a homogeneous granular gas. Instead, wave reconstruction of the early transient evolution indicates that the onset of instability occurs during repressurization of the gas following the initial relaxation of the medium behind the lead shock. This repressurization gives rise to internal pressure waves in the presence of strong density gradients. This indicates that the mechanism of instability is more likely of the vorticity-generating Richtmyer-Meshkov type, relying on the action of the inner pressure wave development during the transient relaxation.

Thermal ignition revisited with two-dimensional molecular dynamics: Role of fluctuations in activated collisions

“…The evolution of temperature and species for the entire domain was output at prescribed time intervals. Validation of the numerical implementation can be found elsewhere [26,27].…”

Microscopic origin of self-similarity in granular blast waves

“…The vanishing pressure at the center is a distinctive characteristic and a necessary condition for the instability to take place. If a finite pressure is imposed at the boundary, as in a piston-like setup, the instability completely changes in nature, losing its self-similar structure and showing the presence of convective rolls 67 . On the contrary, the vanishing pressure ensures the conservation of momentum per angular sector, which is maintained even after the corrugation instability appears.…”

Structure of velocity distributions in shock waves in granular gases with extension to molecular gases

“…The shock front structure (see Fig. 1) has been the subject of several studies in gases [2][3][4][5][6][7][8], plasmas [9][10][11], and in granular materials [12][13][14][15][16][17][18][19]. A normal shock wave was first described as a discontinuity.…”