Detachment of strong shocks in confined granular flows. (English) Zbl 07465433
Summary: Granular flows are highly dissipative due to frictional resistance and inelasticity in collisions among grains. They are known to exhibit shock waves at velocities that are easily achieved in industrial and nature-driven flows such as avalanches and landslides. This experimental work investigates the formation of strong shock waves on triangular obstacles placed in a dry rapid granular stream in a confined two-dimensional set-up. Oblique attached shock waves are formed for mild turning angles and higher flow velocities, whereas strong bow shock waves are formed for higher turning angles and slower granular streams. A shadowgraph imaging technique elucidates interesting characteristics of the shock waves, especially in the vicinity of shock detachment. Velocity distributions in the form of scatter plots and probability distribution functions are calculated from the flow field data obtained by particle imaging velocimetry. The flow field around the granular shock wave region represents a bimodal distribution of velocities with two distinct peaks, one representing the supersonic flow within the free stream, and the other corresponding to the subsonic faction downstream of a shock wave. Connecting the two is a population that does not directly belong to either of the modes, constituting the non-equilibrium shock wave region. The effect of grain size and scaling, for fixed free-stream conditions and fixed channel width, on the shock detachment is presented. The mechanisms of the static heap formation and the shock detachment process in a confined environment are discussed.
MSC:
| 76-XX | Fluid mechanics |
Keywords:
shock wavesReferences:
| [1] | Amarouchene, Y., Boudet, J.F. & Kellay, H.2001Dynamic sand dunes. Phys. Rev. Lett.86 (19), 4286. |
| [2] | Amarouchene, Y. & Kellay, H.2006Speed of sound from shock fronts in granular flows. Phys. Fluids18 (3), 031707. |
| [3] | Ancey, C.2001Dry granular flows down an inclined channel: experimental investigations on the frictional-collisional regime. Phys. Rev. E65 (1), 011304. |
| [4] | Anderson, J.D.2004Modern Compressible Flow: With Historical Perspective. McGraw-Hill. |
| [5] | Andreotti, B., Forterre, Y. & Pouliquen, O.2013Granular Media: Between Fluid and Solid. Cambridge University Press. · Zbl 1388.76001 |
| [6] | Aranson, I.S. & Tsimring, L.S.2006Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys.78 (2), 641. |
| [7] | Azanza, E., Chevoir, F. & Moucheront, P.1999Experimental study of collisional granular flows down an inclined plane. J. Fluid Mech.400, 199-227. · Zbl 0942.76515 |
| [8] | Bird, G.A.1970Aspects of the structure of strong shock waves. Phys. Fluids13 (5), 1172-1177. |
| [9] | Bird, G.A.1978Monte Carlo simulation of gas flows. Annu. Rev. Fluid Mech.10 (1), 11-31. · Zbl 0403.76060 |
| [10] | Börzsönyi, T., Halsey, T.C. & Ecke, R.E.2008Avalanche dynamics on a rough inclined plane. Phys. Rev. E78 (1), 011306. |
| [11] | Boudet, J.F., Amarouchene, Y. & Kellay, H.2008Shock front width and structure in supersonic granular flows. Phys. Rev. Lett.101 (25), 254503. · Zbl 1182.76368 |
| [12] | Brown, R.L. & Richards, J.C.1970 Principles of powder mechanics. Essays on the Packing and Flow of Powders and Bulk Solids. Pergamon. |
| [13] | Campbell, C.S.1990Rapid granular flows. Annu. Rev. Fluid Mech.22 (1), 57-90. |
| [14] | Campbell, C.S., Brennen, C.E. & Sabersky, R.H.1985Flow regimes in inclined open-channel flows of granular materials. Powder Technol.41 (1), 77-82. |
| [15] | Choi, J., Kudrolli, A., Rosales, R.R. & Bazant, M.Z.2004Diffusion and mixing in gravity-driven dense granular flows. Phys. Rev. Lett.92 (17), 174301. |
| [16] | Chou, S.H., Lu, L.S. & Hsiau, S.S.2012DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles. Granul. Matt.14 (6), 719-732. |
| [17] | Cui, X. & Gray, J.M.N.T.2013Gravity-driven granular free-surface flow around a circular cylinder. J. Fluid Mech.720, 314-337. · Zbl 1284.76387 |
| [18] | Cui, X., Gray, J.M.N.T. & Johannesson, T.2007Deflecting dams and the formation of oblique shocks in snow avalanches at Flateyri, Iceland. J. Geophys. Res.: Earth Surf.112, F04012. |
| [19] | Delannay, R., Valance, A., Mangeney, A., Roche, O. & Richard, P.2017Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D: Appl. Phys.50 (5), 053001. |
| [20] | Duran, J.2012Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials. Springer Science & Business Media. |
| [21] | Faug, T., Childs, P., Wyburn, E. & Einav, I.2015Standing jumps in shallow granular flows down smooth inclines. Phys. Fluids27 (7), 073304. |
| [22] | Faug, T., Lachamp, P. & Naaim, M.2002Experimental investigation on steady granular flows interacting with an obstacle down an inclined channel: study of the dead zone upstream from the obstacle. Application to interaction between dense snow avalanches and defence structures. Nat. Hazards Earth Syst. Sci.2 (3/4), 187-191. |
| [23] | Fletcher, C.A.J.2012Computational Techniques for Fluid Dynamics 2: Specific Techniques for Different Flow Categories. Springer Science & Business Media. |
| [24] | Forterre, Y. & Pouliquen, O.2008Flows of dense granular media. Annu. Rev. Fluid Mech.40, 1-24. · Zbl 1136.76051 |
| [25] | Fullmer, W.D. & Hrenya, C.M.2017The clustering instability in rapid granular and gas-solid flows. Annu. Rev. Fluid Mech.49, 485-510. · Zbl 1359.76121 |
| [26] | Garai, P., Verma, S. & Kumar, S.2019Visualization of shocks in granular media. J. Vis.22 (4), 729-739. |
| [27] | Goldhirsch, I.2003Rapid granular flows. Annu. Rev. Fluid Mech.35 (1), 267-293. · Zbl 1125.76406 |
| [28] | Goldshtein, A. & Shapiro, M.1995Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech.282, 75-114. · Zbl 0881.76010 |
| [29] | Goldshtein, A., Shapiro, M. & Gutfinger, C.1996Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation. J. Fluid Mech.316, 29-51. · Zbl 0876.76069 |
| [30] | Gond, L., Perret, G., Mignot, E. & Riviere, N.2019Analytical prediction of the hydraulic jump detachment length in front of mounted obstacles in supercritical open-channel flows. Phys. Fluids31 (4), 045101. |
| [31] | Gray, J.M.N.T.2018Particle segregation in dense granular flows. Annu. Rev. Fluid Mech.50, 407-433. · Zbl 1384.76058 |
| [32] | Gray, J.M.N.T. & Cui, X.2007Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows. J. Fluid Mech.579, 113-136. · Zbl 1175.76151 |
| [33] | Gray, J.M.N.T., Tai, Y.C. & Noelle, S.2003Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech.491, 161-181. · Zbl 1063.76655 |
| [34] | Hákonardóttir, K.M. & Hogg, A.J.2005Oblique shocks in rapid granular flows. Phys. Fluids17 (7), 077101. · Zbl 1187.76202 |
| [35] | Heil, P., Rericha, E.C., Goldman, D.I. & Swinney, H.L.2004Mach cone in a shallow granular fluid. Phys. Rev. E70 (6), 060301. |
| [36] | Holtz, T. & Muntz, E.P.1983Molecular velocity distribution functions in an argon normal shock wave at Mach number 7. Phys. Fluids26 (9), 2425-2436. |
| [37] | Hornung, H.G.2021Shock detachment and drag in hypersonic flow over wedges and circular cylinders. J. Fluid Mech.915, 1097-1116. · Zbl 1461.76328 |
| [38] | Hornung, H.G., Schramm, J.M. & Hannemann, K.2019Hypersonic flow over spherically blunted cone capsules for atmospheric entry. Part 1. The sharp cone and the sphere. J. Fluid Mech.871, 1097-1116. · Zbl 1419.76418 |
| [39] | Jóhannesson, T.2001Run-up of two avalanches on the deflecting dams at Flateyri, Northwestern Iceland. Ann. Glaciol.32, 350-354. |
| [40] | Johnson, C.G.2020Shocking granular flows. J. Fluid Mech.890, F1. · Zbl 1460.76875 |
| [41] | Johnson, C.G. & Gray, J.M.N.T.2011Granular jets and hydraulic jumps on an inclined plane. J. Fluid Mech.675, 87. · Zbl 1241.76411 |
| [42] | Karim, M.Y. & Corwin, E.I.2017Universality in quasi-two-dimensional granular shock fronts above an intruder. Phys. Rev. E95 (6), 060901. |
| [43] | Khakhar, D.V., Orpe, A.V., Andresén, P. & Ottino, J.M.2001Surface flow of granular materials: model and experiments in heap formation. J. Fluid Mech.441, 255-264. · Zbl 1002.76592 |
| [44] | Khan, A., Hankare, P., Kumar, S., Kumar, R., Verma, S. & Prakash, S.P.2019 Shocks and shock interactions in granular flow past circular cylinder. AIAA Paper 2019-3075. |
| [45] | Khan, A., Verma, S., Hankare, P., Kumar, R. & Kumar, S.2020Shock-shock interactions in granular flows. J. Fluid Mech.884, R4. · Zbl 1460.76615 |
| [46] | Kohaut, G., Weber, W., Groenendijk, H., Poppelaars, A.C. & Janssen, W.H.J.1986 Expandable plastics granular material having at least one orifice. US Patent 4, 621, 022. |
| [47] | Kumaran, V.2014Dense shallow granular flows. J. Fluid Mech.756, 555-599. · Zbl 1323.76117 |
| [48] | Lax, P.D.1973Hyperbolic Systems of Conservation Laws and The Mathematical Theory of Shock Waves. SIAM. · Zbl 0268.35062 |
| [49] | Marston, J.O., Li, E.Q. & Thoroddsen, S.T.2012Evolution of fluid-like granular ejecta generated by sphere impact. J. Fluid Mech.704, 5-36. · Zbl 1246.76006 |
| [50] | Massol-Chaudeur, S., Berthiaux, H. & Dodds, J.A.2002Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer. Chem. Engng Sci.57 (19), 4053-4065. |
| [51] | Mazouffre, S., Vankan, P., Engeln, R. & Schram, D.C.2001Behavior of the H atom velocity distribution function within the shock wave of a hydrogen plasma jet. Phys. Rev. E64 (6), 066405. |
| [52] | Molina-Boisseau, B. & Le Bolay, N.2002The mixing of a polymeric powder and the grinding medium in a shaker bead mill. Powder Technol.123 (2-3), 212-220. |
| [53] | Mott, S. & Harold, M.1951The solution of the Boltzmann equation for a shock wave. Phys. Rev.82 (6), 885. · Zbl 0043.40703 |
| [54] | Nedderman, R.M.2005Statics and Kinematics of Granular Materials. Cambridge University Press. |
| [55] | Ottino, J.M. & Khakhar, D.V.2000Mixing and segregation of granular materials. Annu. Rev. Fluid Mech.32 (1), 55-91. · Zbl 0989.76087 |
| [56] | Padgett, D.A., Mazzoleni, A.P. & Faw, S.D.2015Survey of shock-wave structures of smooth-particle granular flows. Phys. Rev. E92 (6), 062209. |
| [57] | Pham-Van-Diep, G., Erwin, D. & Muntz, E.P.1989Nonequilibrium molecular motion in a hypersonic shock wave. Science245 (4918), 624-626. |
| [58] | Pouliquen, O.1999Scaling laws in granular flows down rough inclined planes. Phys. Fluids11 (3), 542-548. · Zbl 1147.76477 |
| [59] | Pudasaini, S.P. & Hutter, K.2007Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches. Springer Science & Business Media. |
| [60] | Rericha, E.C., Bizon, C., Shattuck, M.D. & Swinney, H.L.2001Shocks in supersonic sand. Phys. Rev. Lett.88 (1), 014302. |
| [61] | Saleh, K., Golshan, S. & Zarghami, R.2018A review on gravity flow of free-flowing granular solids in silos-basics and practical aspects. Chem. Engng Sci. |
| [62] | Savage, S.B.1992Instability of unbounded uniform granular shear flow. J. Fluid Mech.241, 109-123. · Zbl 0786.76036 |
| [63] | Savage, S.B. & Hutter, K.1989The motion of a finite mass of granular material down a rough incline. J. Fluid Mech.199, 177-215. · Zbl 0659.76044 |
| [64] | Silbert, L.E., Landry, J.W. & Grest, G.S.2003Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids15 (1), 1-10. · Zbl 1185.76343 |
| [65] | Sinclair, J. & Cui, X.2017A theoretical approximation of the shock standoff distance for supersonic flows around a circular cylinder. Phys. Fluids29 (2), 026102. |
| [66] | Sudah, O.S., Coffin-Beach, D. & Muzzio, F.J.2002Quantitative characterization of mixing of free-flowing granular material in tote (bin)-blenders. Powder Technol.126 (2), 191-200. |
| [67] | Taberlet, N., Richard, P., Valance, A., Losert, W., Pasini, J.M., Jenkins, J.T. & Delannay, R.2003Superstable granular heap in a thin channel. Phys. Rev. Lett.91 (26), 264301. |
| [68] | Tai, Y.C., Gray, J.M.N.T., Hutter, K. & Noelle, S.2001Flow of dense avalanches past obstructions. Ann. Glaciol.32, 281-284. |
| [69] | Tregaskis, C., Johnson, C., Cui, X. & Gray, J.2022Subcritical and supercritical granular flow around an obstacle on a rough inclined plane. J. Fluid Mech.933, A25. · Zbl 1514.76106 |
| [70] | Tripathi, A. & Khakhar, D.V.2011Rheology of binary granular mixtures in the dense flow regime. Phys. Fluids23 (11), 113302. |
| [71] | Umbanhowar, P.B., Melo, F. & Swinney, H.L.1996Localized excitations in a vertically vibrated granular layer. Nature382 (6594), 793. |
| [72] | Vilquin, A., Boudet, J.F. & Kellay, H.2016Structure of velocity distributions in shock waves in granular gases with extension to molecular gases. Phys. Rev. E94 (2), 022905. · Zbl 1419.76683 |
| [73] | Vilquin, A., Kellay, H. & Boudet, J.F.2018Shock waves induced by a planar obstacle in a vibrated granular gas. J. Fluid Mech.842, 163-187. · Zbl 1419.76683 |
| [74] | Wieghardt, K.1975Experiments in granular flow. Annu. Rev. Fluid Mech.7 (1), 89-114. · Zbl 0355.76005 |
| [75] | Wieland, M., Gray, J.M.N.T. & Hutter, K.1999Channelized free-surface flow of cohesionless granular avalanches in a chute with shallow lateral curvature. J. Fluid Mech.392, 73-100. · Zbl 0938.76588 |
| [76] | Zhou, Y.C., Xu, B.H., Yu, A.-B. & Zulli, P.2002An experimental and numerical study of the angle of repose of coarse spheres. Powder Technol.125 (1), 45-54. |
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