Abstract
We present a 2D discrete modelling of sand flow through a hopper using realistic grain shapes. A post-processing method is used to assess the local fluctuations in terms of void ratio, coordination number, velocity magnitude, and mean stress. The characteristics of fluctuations associated with the four considered quantities along the vertical axis of the hopper and across the entire hopper are carefully examined. The flow fluctuations for coordination number, velocity magnitude and mean stress are all found to take the form of radial waves originating from the lower centre of the hopper and propagating in the opposite direction of the granular flow. Quantitative characteristics of these waves (shape, amplitude, frequency, velocity, etc.) are identified. The fluctuations in void ratio however are not supportive of the observation of density waves in the granular flow as mentioned in some experiments. The possible reasons for this apparent contradiction are discussed, as well as possible extensions of this work.
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References
Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular Assemblies. Geotechnique 29, 47–65 (1979)
McDowel, G., Li, H., Lowndes, I.: The importance of particle shape in discrete-element modelling of particle flow in a chute. Géotech. Lett. 1(3), 59–64 (2011)
Peng, G., Herrmann, J.: Density waves and 1/f density fluctuations in granular flow. Phys. Rev. E 51(3), 1745–1756 (1995)
Baran, O., Halsey, T., Grest, G.S., Lechman, J.B.: Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74, 051302 (2006)
Azema, E., Descantes, Y., Roquet, N., Roux, J.-N., Chevoir, F.: Discrete simulation of dense flows of polyhedral grains down a rough inclined plane. Phys. Rev. E 86, 031303 (2012)
Richefeu, V., Mollon, G., Daudon, D., Villard, P.: Dissipative contacts and realistic block shapes for modelling rock avalanches. Eng. Geol. 149–150, 78–92 (2012)
Mollon, G., Richefeu, V., Villard, P., Daudon, D.: Numerical simulation of rock avalanches: influence of a local dissipative contact model on the collective behavior of granular flows. J. Geophys. Res. Solid Earth 117, F02036 (2012)
Zhu, H.P., Yu, A.B.: Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis. Granul. Matt. 7, 97–107 (2005)
Nguyen, T.V., Brennen, C., Sabersky, R.H.: Gravity flow of granular materials in conical hoppers. J. Appl. Mech. 46, 529–535 (1979)
Bazant, M.Z.: A theory of cooperative diffusion in dense granular flows. arXiv:cond-mat/0307379v2 (2004)
Hendy, S.: Instabilities in granular flows. arXiv:cond-mat/000 7236v1 (2008)
Sun, J., Sundaresan, S.: Radial hopper flow prediction using constitutive model with microstructure, evolution. arXiv:1207.1751v1 (2012)
Michalowski, R.L.: Flow of granular material through a plane hopper. Powder Technol. 39, 29–40 (1983)
Baxter, G.W., Behringer, R.P., Fagert, T., Johnson, G.A.: Pattern formation in flowing sand. Phys. Rev. Lett. 62(24), 2825–2828 (1989)
Choi, J., Kudrolli, A., Bazant, M.Z.: Velocity profile of granular flows inside silos and hoppers. J. Phys. Condens. Matt. 17, S2533–S2548 (2005)
Gardel, E., Keene, E., Dragulin, S., Easwar, N., Menon, N.: Force-velocity correlations in a dense, collisional, granular flow. arXiv:cond-mat/0601022 (2006)
Gardel, E., Seitaridou, E., Facto, K., Keene, E., Hattam, K., Easwar, N., Menon, N.: Dynamical fluctuations in dense granular flows. Philos. Trans. R. Soc. A 367, 5109–5121 (2009)
Gentzler, M., Tardos, G.I.: Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging. Chem. Eng. Sci. 64, 4463–4469 (2009)
Vivanco, F., Rica, S., Melo, F.: Dynamical arching in a two dimensional granular flow. Granul. Matt. 14(5), 563–576 (2012)
Ristow, G.H., Herrmann, H.J.: Density patterns in two-dimensional hoppers. Phys. Rev. E 50(1), R5–R8 (1994)
Potapov, A., Campbel, C.S.: Computer simulation of hopper flow. Phys. Fluids 8(11), 2884–2894 (1996)
Cleary, P.W., Sawley, M.L.: DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26, 89–111 (2002)
Radjai, F., Roux, S.: Turbulentlike fluctuations in quasistatic flow of granular media. Phys. Rev. Lett. 89(6), 064302 (2002)
Richefeu, V., Combe, G., Viggiani, G.: An experimental assessment of displacement fluctuations in a 2D granular material subjected to shear. Géotech. Lett. 2, 113–118 (2012)
Abedi, S., Rechenmacher, A.L., Orlando, A.D.: Vortex formation and dissolution in sheared sands. Granul. Matt. 14, 695–705 (2012)
Mollon, G., Zhao, J.: Fourier-Voronoi-based generation of realistic samples for discrete modelling of granular materials. Granul. Matt. 14(5), 621–638 (2012)
Das, N.: Modeling three-dimensional shape of sand grains using discrete element method. PhD Thesis, University of South Florida, 149 p. (2007)
Ferellec, J.-F., McDowell, G.: A method to model realistic particle shape and inertia in DEM. Granul. Matt. 12, 459–467 (2010)
Mollon, G., Zhao, J.: The influence of particle shape on granular hopper flow. In: Powders and Grains 2013: AIP Conference Proceedings 1542, pp. 690–693. doi: 10.1063/1.4812025 (2013)
Mollon, G., Zhao, J.: Generating realistic 3D sand particles using Fourier descriptors. Granul. Matt. 15(1), 95–108 (2013)
Acknowledgments
We appreciate the constructive comments offered by the two anonymous reviewers. The study was supported by Research Grants Council of Hong Kong (under RGC/GRF 622910).
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Mollon, G., Zhao, J. Characterization of fluctuations in granular hopper flow. Granular Matter 15, 827–840 (2013). https://doi.org/10.1007/s10035-013-0445-5
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DOI: https://doi.org/10.1007/s10035-013-0445-5