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Modeling dynamic flows of grain-fluid mixtures by coupling the mixture theory with a dilatancy law. (English) Zbl 1392.76100
Summary: A depth-averaged two-velocity grain-fluid mixture model is proposed to describe flows of grain-fluid mixtures. Motivated by the experimental observations, the proposed model considers that the granular and the fluid phases are moving with different velocities, and the velocity difference between the granular phase and the fluid phase is coupled with the granular dilatancy that is described by a granular dilatancy law. The characteristics of flows allow to formulate a simpler depth-averaged PDE system. To scrutinize the proposed equations, an analysis for steady flows in rectangular channels is performed, which reproduces the cross-stream velocity profiles commonly observed in fields. Additionally, a uniform flow is investigated to illustrate the effects of the granular dilatancy on the velocities, flow depth, and volume fractions.
MSC:
76T25 Granular flows
Software:
D-Claw
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[1] Andreotti, B., Forterre, Y., Pouliquen, O.: Granular Media, Between Fluid and Solid. Cambridge University Press, Cambridge (2013) · Zbl 1388.76001
[2] Bouchut, F., Fernandez-Nieto, E.D., Mangeney, A., Narbona-Reina, G.: A two-phase two-layer model for fluidized granular flows with dilatancy effects. https://hal-upec-upem.archives-ouvertes.fr/hal-01161930 (2016) · Zbl 1445.76087
[3] George, DL; Iverson, RM, A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. numerical predictions and experimental tests,, Proc. R. Soc. Lond. A, 470, 2170, (2014) · Zbl 1371.86007
[4] Hungr, O, Analysis of debris flow surges using the theory of uniformly progressive flow, Earth Surf. Process. Landf., 25, 483-495, (2000)
[5] Iverson, RM; George, DL, A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. physical basis, Proc. R. Soc. Lond. A, 470, 20130819, (2014) · Zbl 1371.86008
[6] Iverson, RM; Denlinger, RP, Flow of variably fluidized granular masses across three-dimensional terrain: 1. Coulomb mixture theory, J. Geophys. Res., 106, 537-552, (2001)
[7] Iverson, RM; Reid, ME; Iverson, NR; LaHusen, RG; Logan, M; Mann, JE; Brien, DL, Acute sensitivity of landslide rates to initial soil porosity, Science, 290, 513-516, (2000)
[8] Kaitna, R., Hsu, L., Rickenmann, D., Dietrich, W.E.: On the development of an unsaturated front of debris flows. In: Genevois, R., Hamilton, D.L., Prestininzi, A. (eds.) Italian Journal of Engineering Geology and Environment-Book. 5th International Conference on Debris-Flow Hazards: Mitigation, Mechanics, Prediction and Assessment, Padua, 14-17 June 2011, pp. 351-358. Casa Editrice Università La Sapienza (2011)
[9] Meng, X; Wang, Y, Modelling and numerical simulation of two-phase debris flows, Acta Geotech., 11, 1027-1045, (2016)
[10] Pailha, M; Nicolas, M; Pouliquen, O, Initiation of underwater granular avalanches: influence of the initial volume fraction, Phys. Fluids, 20, 111701, (2008) · Zbl 1182.76585
[11] Pailha, M; Pouliquen, O, A two-phase flow description of the initiation of underwater granular avalanches, J. Fluid Mech., 633, 115-135, (2009) · Zbl 1183.76906
[12] Pierson, TC; Abrahams, AD (ed.), Flow behavior of channelized debris flows, mount st. helens, Washington, 269-296, (1986), Winchester
[13] Pitman, EB; Le, L, A two-fluid model for avalanche and debris flows, Proc. R. Soc. Lond. A, 363, 1573-1601, (2005) · Zbl 1152.86302
[14] Prochnow, M., Chevoir, F., Albertelli, M.: Dense granular flows down a rough inclined plane. In: Proceedings of XIII International Congress on Rheology, Cambridge, UK (2000)
[15] Reynolds, O, Dilatancy, Nature, 33, 429-430, (1886)
[16] Rondon, L; Pouliquen, O; Aussillous, P, Granular collapse in a fluid: role of the initial volume fraction, Phys. Fluids, 23, 073301, (2011)
[17] Roux, S., Radjai, F.: Texture-dependent rigid plastic behavior. In: Herrmann, H.J. et al. (eds.) Proceedings: Physics of Dry Granular Media, September 1997, Cargése, France, pp. 305-311. Kluwer (1998) · Zbl 0999.76100
[18] Savage, SB; Hutter, K, The motion of a finite mass of granular material down a rough incline, J. Fluid Mech., 199, 177-215, (1989) · Zbl 0659.76044
[19] Schaeffer, DG; Iverson, RM, Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback, SIAM Appl. Math., 69, 768-786, (2008) · Zbl 1165.74033
[20] Truesdell, C.: Rational Thermodynamics, 2nd edn. Springer, New York (1984) · Zbl 0598.73002
[21] Wang, Y; Hutter, K; Pudasaini, SP, The savage-hutter theory: a system of partial differential equations for avalanche flows of snow, debris, and mud, J. App. Math. Mech., 84, 507-527, (2004) · Zbl 1149.74323
[22] Wang, Y; Hutter, K, A constitutive theory of fluid-saturated granular materials and its application in gravitational flows, Rheol. Acta, 38, 214-233, (1999)
[23] Wang, Y; Hutter, K, Comparisons of serval numerical methods with respect to convectively-dominated problems, Int. J. Numer. Methods Fluids, 37, 721-745, (2001) · Zbl 0999.76100
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