- Access by Xinjiang University
Dense, steady, fully developed fluid-particle flows over inclined, erodible beds
Phys. Rev. Fluids 8, 024303 – Published 13 February, 2023
DOI: https://doi.org/10.1103/PhysRevFluids.8.024303
Abstract
We phrase boundary-value problems for a dense, steady, fully developed, gravitational flow of identical inelastic spheres and water over an inclined erodible bed in the presence of sidewalls. The mass density and the size of the spheres are that of the particles employed in laboratory experiments by Armanini et al., [J. Fluid Mech. 532, 269 (2005)]. We obtain numerical solutions for the profiles of the solid volume fraction, the strength of the particle velocity fluctuations, and the mean velocities of the particles and fluid. We compare these with those measured in the experiments.
Physics Subject Headings (PhySH)
Article Text
References (36)
- K. Kamrin and G. Koval, Nonlocal Constitutive Relation for Steady Granular Flow, Phys. Rev. Lett. 108, 178301 (2012).
- D. L. Henann and K. Kamrin, A predictive, size-dependent continuum model for dense granular flows, Proc. Natl. Acad. Sci. USA 110, 6730 (2013).
- K. Kamrin and D. L. Henann, Nonlocal modeling of granular flows down inclines, Soft Matter 11, 179 (2015).
- G. D. R. MiDi, On dense granular flows, Eur. Phys. J. E 14, 341 (2004).
- E. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. Fluid Mech. 852, 1 (2018).
- J. T. Jenkins, Dense inclined flows of inelastic spheres, Gran. Matt. 10, 47 (2007).
- J. T. Jenkins and D. Berzi, Dense inclined flows of inelastic spheres: Tests of an extension of kinetic theory, Gran. Matt. 12, 151 (2010).
- D. Gollin, D. Berzi, and E. T. Bowman, Extended kinetic theory applied to inclined granular flows: Role of boundaries, Gran. Matt. 19, 56 (2017).
- Q. Zhang and K. Kamrin, Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling, Phys. Rev. Lett. 118, 058001 (2017).
- D. Berzi and J. T. Jenkins, Steady shearing flows of deformable, inelastic spheres, Soft Matter 11, 4799 (2015).
- J. T. Jenkins and D. M. Hanes, Collisional sheet flows of sediment driven by a turbulent fluid, J. Fluid Mech. 370, 20 (1998).
- D. Berzi, Analytical solution of collisional sheet flows, J. Hydraul. Eng. 137, 1200 (2011).
- G. G. Joseph, R. Zenit, M. L. Hunt, and A. M. Rosenwinkel, Particle-wall collisions in a viscous fluid, J. Fluid Mech. 433, 329 (2001).
- V. Garzó and J. W. Dufty, Dense fluid transport for inelastic hard spheres, Phys. Rev. E 59, 5895 (1999).
- J. T. Jenkins and D. Berzi, Kinetic theory applied to inclined flows, Gran. Matt. 14, 79 (2012).
- D. Berzi and L. Fraccarollo, Inclined, collisional sediment transport, Phys. Fluids 25, 106601 (2013).
- D. Berzi and L. Fraccarollo, Intense sediment transport; Collisional to turbulent suspension, Phys. Fluids 28, 023302 (2016).
- M. Larcher and J. T. Jenkins, Saturated, collisional flows of spheres over an inclined, erodible bed between vertical sidewalls, Adv. Water Res. 72, 15 (2014).
- A. Armanini, H. Capart, L. Fraccarollo, and M. Larcher, Rheological stratification in experimental free-surface flows of granular–liquid mixtures, J. Fluid Mech. 532, 269 (2005).
- J. T. Jenkins and D. Berzi, Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base, EPJ Web Conf. 249, 03039 (2021).
- D. Berzi and L. Fraccarollo, Turbulence Locality and Granularlike Fluid Shear Viscosity in Collisional Suspensions, Phys. Rev. Lett. 115, 194501 (2015).
- R. A. Bagnold, Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear, Proc. R. Soc. London 225, 49 (1954).
- S. Chialvo, J. Sun, and S. Sundaresan, Bridging the rheology of granular flows in three regimes, Phys. Rev. E 85, 021305 (2012).
- M. Larcher and J. T. Jenkins, Segregation and mixture profiles in dense, inclined flows of two types of spheres, Phys. Fluids 25, 113301 (2013).
- G. Barnocky and R. H. Davis, Elasto-hydrodynamic collision and rebound of spheres: Experimental verification, Phys. Fluids 31, 1324 (1988).
- M. Larcher, L. Fraccarollo, A. Armanini, and H. Capart, Set of measurement data from flume experiments on steady uniform debris flows, J. Hydraul. Res. 45, 59 (2007).
- D. Berzi, J. T. Jenkins, and P. Richard, Extended kinetic theory for granular flow over and within an inclined erodible bed, J. Fluid Mech. 885, A27 (2020).
- J. Dallavalle, Micromeritics (Pitman, New York, 1943).
- J. F. Richardson and W. N. Zaki, Sedimentation and fluidization: Part I, Trans. Inst. Chem. Eng. 32, 35 (1954).
- N. Mitarai and H. Makanishi, Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress, Phys. Rev. E 75, 031305 (2007).
- D. Berzi and D. Vescovi, Different singularities in the functions of extended kinetic theory at the origin of the yield stress in granular flows, Phys. Fluids 27, 013302 (2015).
- J. T. Jenkins and D. H. Hanes, The balance of momentum and energy at an interface between colliding and freely flying grains in a rapid granular flow, Phys. Fluids A5, 781 (1993).
- D. Berzi, N. Thai-Quang, Y. Guo, and J. Curtis, Stresses and orientational order in shearing flows of granular liquid crystals, Phys. Rev. E 93, 040901(R) (2016).
- Q. Zhang, E. Deal, J. T. Perron, J. G. Venditti, S. J. Benavides, M. Rushlow, and K. Kamrin, Fluid-driven transport of round sediment particles: From discrete simulations to continuum modeling, J. Geophys. Res: Earth Sur. 127, e2021JF006504 (2022).
- J. Chauchat, A comprehensive two-phase flow model for unidirectional sheet-flows, J. Hydraul. Res. 56, 15 (2018).
- R. Maurin, J. Chauchat, and P. Frey, Revisiting slope influence in turbulent bedload transport: Consequences for vertical flow structure and transport rate scaling, J. Fluid Mech. 839, 135 (2018).
