Unstable blast shocks in dilute granular flows

Boudet, Jean-François; Kellay, Hamid

doi:10.1103/physreve.87.052202

Cited by 13 publications

(20 citation statements)

References 23 publications

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“…Granular media, which are characterized by inelastic particle collisions, are one example. Previous experiments have identified unstable formations of finger-like jets in granular media dispersed by shock waves driven through air [1,2] and for rapid granular flows down a chute [3], Similar pattern formations can be seen when granular media are subjected to a vertically oscillating bed, both experimentally and numerically [4,5], In the latter, the periodic agitation of the container walls drives strong shocks and expansion waves into the nonuniform granular gas. The complex transient dynamics involved in these past configurations have prevented the authors from clearly identifying the mechanisms controlling the instability.…”

Section: Introductionsupporting

confidence: 59%

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

Sirmas

Radulescu

2015

Phys. Rev. E

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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.

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Section: Introductionsupporting

confidence: 59%

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

Sirmas

Radulescu

2015

Phys. Rev. E

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“…Finally, the granular blast itself has recently started to attract studies, both experimental 17,18,34 and numerical 19,35,36 . These papers have been focusing on global scaling laws, revealing clear self-similarity in a MCS regime (see previous section) in Molecular Dynamics simulations…”

Section: Granular Shocksmentioning

confidence: 99%

Microscopic origin of self-similarity in granular blast waves

2016

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The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.

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“…Later, Tan and Goldhirsch [4] showed that supersonic behavior is not an exotic state but dynamical granular systems are nearly always supersonic, that is, it is a typical state of granular matter. There is much recent progress regarding the supersonic properties of granular matter, including shocks, theoretically [5][6][7][8][9], numerically [10][11][12][13][14][15][16][17], and experimentally [7][8][9][18][19][20][21][22][23][24]; however, surprisingly little is known about the spatiotemporal relation between the field of Mach number influenced by temperature and density and the dynamics of supersonic shocks in granular systems [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Self-organized shocks in the sedimentation of a granular gas

et al. 2015

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A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.

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Unstable blast shocks in dilute granular flows

Cited by 13 publications

References 23 publications

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

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

Microscopic origin of self-similarity in granular blast waves

Self-organized shocks in the sedimentation of a granular gas

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