Granular Surface Flows Research Articles

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

This study presents a comprehensive continuum approach to modeling granular surface flows using the Incompressible Non-Newtonian Smoothed Particle Hydrodynamics (INNSPH) method. The model integrates an incompressible SPH method, where pressure is computed by solving a pressure-Poisson equation with a non-Newtonian rheology. Projection-based SPH has a strong and rigorous theoretical basis can lead to stable and accurate simulations. This paper aims to develop a projection-based SPH method for modeling complex granular flows. INNSPH method combines incompressible SPH and μ(I) rheology models to simulate non-Newtonian viscoplastic fluid behavior in granular flows. Surface deposition, and velocity and pressure fields are estimated using a rheology model. Validation is performed by comparing simulation results, including surface profiles and run-out distances with experimental data, showing good agreement. INNSPH method is then employed to model a 2D column collapse and a dam-break scenario on horizontal and inclined planes for sands and glass beads. The method captures three distinct final deposition morphologies; truncated cone, conic, and Mexican hat shapes in collapsing columns. INNSPH computational efficiency enables simulations of large-scale granular flows, and its open-source nature facilitates collaboration and further modifications by researchers. The method provides a good understanding of granular flow dynamics in various industrial applications including powder technology.

Basal boundary conditions for granular surface flows over fragile and brittle erodible beds

Many granular surface flows occur as shear flows of finite thickness, over erodible beds composed of the same granular material. Such beds may be fragile, and offer no more resistance to erosion than to sustained shear. Or they may be brittle, and offer instead an excess resistance to erosion. To take this contrast into account, new basal boundary conditions are proposed. Their implications for parallel flows down infinite slopes are then examined for three different cases: stationary flows; starting; and stopping transients. For all three cases, flow behaviour is altered significantly when beds present an excess resistance to erosion. For stationary flows, non-unique velocity profiles are obtained, implying hysteresis or history-dependence. For starting transients, a power law growth of the flow thickness is predicted, instead of the jump to finite or infinite depth that would otherwise occur. For stopping transients, flows start to decelerate with a finite basal shear rate, even over erodible substrates. Analytical solutions to the corresponding free and moving boundary problems are obtained, and checked against numerical results. Model predictions are then compared with experimental measurements. Overall, good agreement is obtained. In particular, the model describes well the very different erosional responses observed for fragile and brittle beds.

Growth of force chain network upon non-Bagnold transition of inclined surface granular flows via discrete element simulation

Abstract A steady granular flow down an inclined surface is an important flow configuration to study the dynamic of dry granular flow. This work adopts two-dimensional discrete element simulation to study how inter-grain friction may play a role in momentum transport, in addition to the collision-based transport, to induce the non-Bagnold flow velocity profile reported in the literature. Special efforts were made to apply the knowledge of network science to identify the contact force chain network from particle dynamics information using the graph theory with the Louvain greedy algorithm. We studied how the number of grains born in the force chain network grows when the flow scaled velocity profile degrades from Bagnold to non-Bagnold flows. Concurrently, the stress loading ratio carried by these frictional contacts rises abruptly upon the non-Bagnold flow transition identifies when the flow Froude number falls roughly below 2.15. Both phenomena suggest that the non-local phenomenon of Bagnold velocity profile degradation occurs when sufficient grains are confined in the force chain network to assist the stress transport, replacing the collisional transport. Hence, a refined rheology model is needed in the future to account for this friction-assisted momentum transport at a mesoscopic yet flow-dependent length scale like that of the currently investigated force network.

A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations

The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.

Granular surface flows confined between flat, frictional walls. Part 1. Kinematics

We report and analyse the results of extensive discrete element method simulations of three-dimensional gravity driven flows of cohesionless granular media over an erodible bed, the whole being confined between two flat and frictional sidewalls. We focus on the role of sidewalls by performing simulations for different gap widths ( $W$ ) between the two confining sidewalls: from $5$ to $30$ grain sizes ( $d$ ). Our results indicate the existence of two distinct regimes: regime I for flow angles smaller than the critical angle $\theta_c\approx 40^\circ$ and regime II at flow angles larger than $\theta_c$ . Regime I corresponds to dense flows whereas flows belonging to regime II exhibit a strong variation of the volume fraction through the depth. Three relevant lengths are identified in the system: $W$ the gap between sidewalls, $l$ the length characterizing the vertical variation of the volume fraction and $h$ a characteristic length associated with the vertical variation of the streamwise velocity. Using these lengths we can rescale the profiles of various flow properties (e.g. streamwise velocity, granular temperature, particle rotation…). In regime II, in contrast to regime I, $l$ and $h$ have a similar behaviour. As a consequence, the rescaled profiles in regime II only involve $h$ (or equivalently $l$ ) and $W$ . Other dissimilarities exist between regimes I and II. In particular, the scaling of the flow rate with $h$ (at fixed $W$ ) differs in the two regimes, although they display a similar scaling with $W$ (at fixed flow angle).

Sidewall friction in confined surface flows of granular materials

We report numerical simulations of surface granular flows confined between two sidewalls. These systems exhibit both very slow and very energetic flows. Zhu et al. [1] have shown that in energetic confined systems, the Froude number at sidewalls and the sidewall effective friction coefficient are linked through a unique relation. We show that this relation is also valid for creep flows. It is independent of the angle of the flow but depends on the sidewall-grain friction coefficient. Our results shed light on boundary conditions that have to be used at sidewalls in continuum theories aiming to capture the behavior of granular systems from creeping to energetic flows.

Characterization of the flowability dynamics of granular material flowing down a narrow channel

The flowability of granular material is commonly determined from shear cell tests, but in the real world, the granular flow is quite different in many cases. For this paper, the flowabilities in a narrow channel of five different granular materials were investigated. The flow parameters of the granular flows were determined to classify the flowabilities. Granular flow surface velocities and flow heights and thicknesses were measured, and it was found that the mean shear rates in the linear portions of the velocity profiles increase with both flow rates and inclination. A universal parameter, the ratio of the sine of the inclination to the shear rate in the linear part of the velocity profile, is proposed as a constant. This constant is independent of particle properties. In addition, a flowability parameter, the ratio of the mean shear rate to the cosine of the inclination, is proposed to characterize the friction between the particles in the flowing granular material.

Granular flow in a wedge‐shaped heap: Velocity field, kinematic scalings, and segregation

AbstractFree surface granular flows in bounded axisymmetric geometries are poorly understood. Here, we consider the kinematics and segregation of size‐bidisperse flow in a rising conical heap by characterizing the flow of particles in a wedge‐shaped silo with frictional sidewalls using experiments and discrete‐element‐method simulations. We find that the streamwise velocity is largest at the wedge centerline and decreases near the sidewalls, and that velocity profiles in the depthwise and spanwise directions are self‐similar. For segregating size bidisperse mixtures, the boundary between small and large particles deposited on the heap is significantly further upstream at the sidewalls than at the centerline, indicating that measurements taken at transparent sidewalls of quasi‐2D or wedge‐shaped heaps are unrepresentative of an axisymmetric heap. The streamwise velocity and flowing layer depth locally satisfy the scaling relation of Jop et al (J Fluid Mech. 2005;541:167‐192) when modified to account for the wedge geometry, highlighting the influence of wall friction on the flow.

Granular surface flow on an asymmetric conical heap

We carry out an experimental study of the granular surface flow of nearly monodisperse glass beads on a conical heap formed on a rough circular disc by a narrow stream of the particles from a hopper, with the pouring point displaced from the centre of the disc. During the growth phase, an axisymmetric heap is formed, which grows either by periodic avalanches or by non-periodic avalanches that occur randomly over the azimuthal location of the heap, depending on the operating conditions and system properties. The dynamics of heap growth is characterized by the variation of the heap height, angle of repose and the angular velocity of the periodic avalanche with time, for different mass flow rates from the hopper. When the base of the heap reaches the edge of the disc closest to the pouring point, the heap stops growing and a steady surface flow of particles is developed on the heap surface, with particles flowing over the edge of the disc into a collection tray. The geometry is a unique example of a granular flow on an erodible bed without any bounding side walls. The corresponding steady state geometry of the asymmetric heap is characterized by means of surface contours and angles of repose. The streamwise and transverse surface velocities are measured using high-speed video photography and image analysis for different mass flow rates. The flowing layer thickness is measured by immersing a coated needle in the flow at different positions on the mid-line of the flow. The surface angle of the flowing layer is found to be significantly smaller than the angle of repose and to be independent of the mass flow rate. The velocity profiles at different streamwise positions for different mass flow rates are found to be geometrically similar and are well described by Gaussian functions. The flowing layer thickness is calculated from a model using the measured surface velocities. The predicted values match the measured values quite well.

Erosion and deposition processes in surface granular flows.

We report on experiments aiming at characterizing erosion and deposition processes on a tilted granular bed. We investigate the existence of the neutral angle, that is, the critical angle at which erosion exactly balances accretion after the passage of a granular avalanche of a finite mass. Experiments show in particular that the neutral angle depends on both avalanche mass and shape but is rather insensitive to the bed length. This result strongly suggests that the effective friction between the static and mobile granular phases cannot be taken as an intrinsic property that is only material dependent but should be considered a flow-dependent property. Interestingly, for a given avalanche mass, the net erosion rate increases linearly with the angular deviation from the neutral angle. We also compare our data with the predictions of the erosion-deposition model introduced by Bouchaud, Cates, Ravi Prakash, and Edwards (BCRE) [J. Phys. I 4, 1283 (1994)JPGCE81155-430410.1051/jp1:1994195]. We show that the predictions drawn from the modified version of the BCRE model proposed by Boutreux and de Gennes, in which the local erosion rate between the static and mobile phases is independent of the flow thickness, are in remarkable agreement with the experimental results.

Validating granular segregation rate models

One significant hindrance to the development of granular segregation rate models is the inherent difficulty of performing the dynamic experiments required for validation. Here, we seek to overcome this experimental hurdle by establishing an “equilibrium” between segregation and flow perturbation in free surface granular flows and use steady‐state—rather than dynamic—measurements for validation. That is, we combine the segregation rate expressions to be tested with a segregation control framework such that the perturbation rate enables us to infer the segregation rate by measuring simply the steady state extent of segregation. We use periodic flow inversions via an axially located baffle in a tumbler‐type mixer to provide the perturbations that ultimately alter the steady‐state distribution of particles. This work examines the efficacy of existing models for binary segregation driven by either size or density differences. For completeness, we test our model validation framework both computationally and experimentally. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3756–3763, 2017

Simulation of free surface granular flows in tumblers

A simulation study was carried out on the free surface granular flow occurring in partially filled tumbler mixers. Three different 2D geometries were considered: a drum, a double cone mixer and an asymmetric double cone mixer. The solid-air two phases flow was simulated using an Eulerian continuum approach, including a suitable rheology for the granular flow. We focused on the kinematics of the active layer where mixing occurs. The modification of the surface active layer, as a consequence of mixer geometry and rotation, was studied. The analysis of (a) the active layer depth and area, (b) the velocity field and (c) the level of granular activation (given by granular temperature) suggested that the less conventional geometry, i.e. the asymmetric double cone mixer, has the potential to give better mixing performances than the traditional tumblers.

Confined granular flows on a heap: from simulations to experiments

Surface granular flows are studied by means of discrete element simulations. The investigation of their kinematic properties suggests the existence of two regimes: one close to the jamming, for which the shear rate increases with the angle of the flow, and another one, far from jamming, for which the shear remains constant while the flow rate increases. Although the simulations reproduce experimental results for a given gap between sidewalls, they fail to capture the effect of confinement on the flows’ properties (shear rate, flow height…).

A SPH model for the simulation of free surface granular flows in a dense regime

Smoothed Particle Hydrodynamics (SPH) is a particle-based Lagrangian numerical method, particularly suitable for modeling free surface flows of fluids with different constitutive equations. In this work, a SPH model is developed to solve flow problems of granular matter flowing in a dense regime, featuring a constitutive equation proposed by Pouliquen et al. (2006) [17] and Jop et al. (2006) [18].The problem of resolving the flow close to static conditions has been solved by introducing a weak compressibility for the grains: this leads to a third order algebraic equations to be solved for computing granular material density. A new viscosity regularisation method, suitable for any visco-plastic fluid with varying yield stress has been developed, in order to reproduce stopping flow and static conditions.Validation of the model has been performed by solving the simple uniform granular flow problem, for which the solution is known analytically and by reproducing a set of experimental data on granular columns collapses by Lube et al. (2004) [19].

Discrete element simulations of bed force anomalies due to force chains in dense granular flows

Surficial flows on volcanic edifices are often comprised of high concentrations of granular materials either derived from juvenile eruptive material or material sourced from an unstable edifice. Although much attention has been given to granular flow mobility, the physics that govern flow internal behavior and substrate interaction are still poorly understood. Recent laboratory experiments have shown that force chains transmit extreme localized forces to the substrates of free surface granular flows. In this work we combine computational and experimental approaches to investigate the forces at the bed of a simplified granular flow. A photoelastic experimental approach is used to resolve discrete forces in the granular flows. We also conduct discrete element model (DEM) simulations, using input parameters derived from measureable physical material properties of experimental and natural materials, that successfully reproduce the experimental bed forces generated by filamentary force chain structures observed in free surface granular flows. The DEM results show particular sensitivity to values prescribed for contact stiffness, which is in contrast with previous reports indicating that stiffness values have insignificant influence on flow behavior. The transient forces at the bed generated by force chain structures can greatly exceed (by several 100%) the bed forces predicted from continuum approaches, and our simulation results imply that natural materials are more prone to excessive bed forces than photoelastic materials due to their larger contact stiffnesses. This work suggests that force chain activity may play an important role in the bed physics of dense volcanic flows by influencing substrate entrainment.

Scaling law for velocity profiles of surface granular flows observed in rotating cylinders

Surface flows of granular materials over an erodible bed occur in industrial and natural systems, e.g., granular material processed using tumbling mixers and sediment transport at river beds. In laboratory studies, such granular flows can be generated conveniently using well-controlled rotating cylinders. To describe the flow profile, several scaling considerations have been reported in the literature. However, none of them is generally applicable to experimental observations. In this study, we propose to scale velocity profiles using the maximum surface velocity and a characteristic flow depth at which the flow velocity reduces to one half of the maximum surface velocity. This scaling is further explained using a simple viscosity model, which is developed by assuming that the apparent viscosity is inversely proportional to the local velocity. The analysis presented in this study is applicable only for velocity profiles measured at the centre of quasi-two-dimensional rotating cylinders half-filled with monosize, spherical particles.

Rheology and Mixing of Granular Materials

AbstractPolymer processing entails several operations involving the handling of granular materials. We present here a review of some recent advances in the field which are of relevance to polymer processing. The stress distribution in static material is considered with application to particulates in bins and hoppers. A new model for description of the rheology of dense granular flows is reviewed. A model for surface granular flows with application to rotating cylinders is discussed. Finally the mixing and segregation is tumbling mixers is reviewed. magnified image

Granular surface flow via successive destabilization: A continuum approach

Global and localized granular surface flow is analyzed in a model that takes into account the basic forces between a flowing granular layer and an underlying granular bed. Starting from a quantitatively correct description of global stick–slip avalanches on the surfaces of heaps we are able to describe localized flows of various types as seen in experiments of Daerr and Douady [A. Daerr, S. Douady, Two types of avalanche behavior in granular media, Nature (London) 399 (1999) 241]. The descriptive level takes into account the free surface and the velocity of the flow solely. We limit our model to cases where this surface is effectively one-dimensional so that our model equations are consequently one-dimensional in space. With this kind of description we are able to account for the tight coupling between local grain velocity and local height of the so-called lonely waves. Our model shows the nature of a wave of mobilization and deposition. Granular material is set into motion in a domino-like manner. In addition destabilization of material behind an avalanche is taken into account. The front velocities are found to be constant and in general head and rear front travel with the same velocity in our model. The front velocities depend on the tilt angle of the heap that those localized structures run down on. A critical angle is observed above which the rear front velocity abruptly switches sign from positive (downslope) to negative (upslope) values. Furthermore, we find global influences of the surface shape of a flowing granular layer on Bagnold friction. This characteristic collisional friction between flowing layers and beds is shown to cause S-shaping of the free surface for rapid flow velocities. Finally, our model also explains the power spectrum of avalanches as experimentally detected by Jaeger et al. [H. Jaeger, C. Liu, S. Nagel, Relaxation at the angle of repose, Phys. Rev. Lett. 62 (1989) 40].

Numerical and theoretical investigation of the surface flows of granular materials on heaps

Flows of granular material on ‘non-frozen’ and ‘frozen’ heaps are considered numerically and theoretically in this work. The surface flow on a ‘non-frozen’ heap is first investigated numerically using the discrete element method. The flow profiles of the surface granular flow and the creep motion of particles in the heap are studied. It is shown that the mean velocity of the surface flow exhibits a linear relationship with the distance from the heap surface, while that of the particles in the heap decays exponentially with the distance. The existence of such a creep motion may be attributed to the variation of the porosity distribution of the heap. The granular flow on a ‘frozen’ static heap is also simulated, and compared with the one on the corresponding ‘non-frozen’ heap. The results show that the surface conditions of the heap, to some extent, affect the flow upon it. The surface flow on a static heap is then theoretically examined in detail by using a recently developed continuum model. The depth of the steady-state surface flow and its dependence on wall friction and heap width are investigated. In addition, the theoretical results are compared with the DEM simulation results and the experimental ones in the literature, and qualitatively good agreements are observed.

Booming Dune Instability

Sand avalanches flowing down the leeward face of some desert dunes spontaneously produce a loud sound with a characteristic vibrato around a well-defined frequency, a phenomenon called the "song of dunes." Here, we show through theory that a homogenous granular surface flow is linearly unstable towards growing elastic waves when a localized shear band forms at the interface between the avalanche and the static part of the dune. We unravel the nature of the acoustic amplifying mechanism at the origin of this booming instability. The dispersion relation and the shape of the most unstable modes are computed and compared to field measurements.