Model Of Dense Granular Flows Research Articles

Nonlocal continuum modeling of dense granular flow in a split-bottom cell with a vane-shaped intruder.

Shear flow in one spatial region of a dense granular material-induced, for example, through the motion of a boundary-fluidizes the entire granular material. One consequence is that the yield condition vanishes throughout the granular material-even in regions that are very far from the "primary," boundary-driven shear flow. This phenomenon may be characterized through the mechanics of intruders embedded in the granular medium. When there is no primary flow, a critical load must be exceeded to move the intruder; however, in the presence of a primary flow, intruder motion occurs even when an arbitrarily small external load is applied to an intruder embedded in a region far from the sheared zone. In this paper, we apply the nonlocal granular fluidity (NGF) model-a continuum model that involves higher-order flow gradients-to simulate the specific case of dense flow in a split-bottom cell with a vane-shape intruder. Our simulations quantitatively capture the key features of the experimentally observed phenomena: (1) the vanishing of the yield condition, (2) an exponential-type relationship between the applied torque and the rotation rate, (3) the effect of the distance between the intruder and the primary flow zone, and (4) the direction-dependence of the torque/rotation-rate relation, in which the observed relation changes depending on whether the intruder is forced to rotate along with or counter to the primary flow. Importantly, this represents the first fully three-dimensional validation test for a nonlocal model for dense granular flow in general and for the NGF model in particular.

Continuum simulation for regularized non-local μ(I) model of dense granular flows

In this work, we implement the local μ(I) rheology law and its non-local modification in a PISO-VOF numerical scheme with a sharp-interface-capturing THINC method for two-dimensional dense granular flows in both steady and transient states. The non-local effect on the constitutive relation is addressed by the gradient expansion model to account for additional momentum transport in view of the spatial variation of flow inertial number and the stress model singularity near the static state, I=0, is handled by the Bercovier-Engelman regularization scheme. Our simulations provide the first numerical evidence for the crucial role of non-local momentum transport on degrading the velocity profiles predicted with a local rheology model as those reported from two-dimensional discrete element simulations. For example, we successfully reproduce the sub-Bagnold velocity profile for steady inclined flows of height comparable to the Hstop and capture how the linear velocity profile in a simple shear creeping flow is degraded to a S-shape. More importantly, we exploit the current solver to study the layer-accumulated deviation, ε, between the local and the non-local velocity profile (Bagnold to its degradation) for inclined flows. For steady flows, ε decays monotonically with flow Froude number Fr and a critical Frc≈0.25 is detected below which ε rises rapidly necessitating a non-local constitutive relation. For a layer developing from rest to its steady state, the time evolution of ε(t) shows further dependence on flow height and can be collapsed into a monotonically growing trend with local instantaneous inertial number I(t). A critical Icr is also determined and the local model prediction can be erroneous whenever I(t)<Icr. Interestingly, the result for simple shear flows without gravity also confirms that non-local effect becomes non-negligible when the macroscopic inertial number drops to the order of Icr. Finally, we simulate the two-dimensional column collapse flows with both local and non-local rheology and find a shorter run-out distance with the presence of non-local momentum transport.

A general frictional-collisional model for dense granular flows

Landslides can often be treated as dense granular flows that are characterized by their diverse behaviors ranging from solid-like to fluid-like and classified into different regimes. Establishment of a general frictional-collisional rheology capable of capturing the important features of dense granular flows in all regimes from quasi-static to inertial is known to be important from a practical point of view. The present study suggests a rheological model that includes both collisional and frictional mechanisms in dense granular flows by adding the effect of persistent contact between granular particles into the classical kinetic theory. The kinetic theory is used to formulate the collisional stresses, while the frictional stresses are modeled based on an existing relation derived by statistically averaging the individual contact forces among cohesionless particles. The proposed frictional-collisional model is then applied to steady flows of granular materials over an inclined surface, collapses of granular columns, and unsteady flows of granular materials down an inclined surface. The numerical results on the bulk behaviors of the granular flows, such as the varying profile of the free surface and the flow velocity, are all in good agreement with available experimental data. It is shown that the proposed rheological model can well describe the entire processes of dense granular flows from initiation to final deposit or fully developed steady state. Its broad applicability to various granular flows can thus be expected.

Size-dependence of the flow threshold in dense granular materials.

The flow threshold in dense granular materials is typically modeled by local, stress-based criteria. However, grain-scale cooperativity leads to size effects that cannot be captured with local conditions. In a widely studied example, flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to flow. In this paper, we consider the question of whether the size-dependence of the flow threshold observed in inclined plane flow is configurationally general. Specifically, we consider three different examples of inhomogeneous flow - planar shear flow with gravity, annular shear flow, and vertical chute flow - using two-dimensional discrete-element method calculations and show that the flow threshold is indeed size-dependent in these flow configurations, displaying additional strengthening as the system size is reduced. We then show that the nonlocal granular fluidity model - a nonlocal continuum model for dense granular flow - is capable of quantitatively capturing the observed size-dependent strengthening in all three flow configurations.

A two-phase solid-fluid model for dense granular flows including dilatancy effects: comparison with submarine granular collapse experiments

We simulate here the collapse of granular columns immersed in a viscous fluid based on a simplified version of the model developed by [2]. The simulation quite well reproduces the dynamics and deposit of the granular mass as well as the excess pore fluid pressure measured in the laboratory experiments of [10] owing that dilatancy effects and pore pressure feedback are accounted for. In particular, the difference in the behaviour of initially loose and dense columns is reproduced numerically.

A three-dimensional continuum model incorporating static and kinetic effects for granular flows with applications to collapse of a two-dimensional granular column

This work extends a one-dimensional continuum model for granular flows down inclined planes [C. H. Lee and C. J. Huang, “Kinetic-theory-based model of dense granular flows down inclined planes,” Phys. Fluids 24, 073303 (2012)] to solve three-dimensional problems involving both static and flow states. The new model decomposes the shear stress and pressure into enduring-contact and kinetic components. One novelty of the present model is the determination of the enduring-contact component of pressure, which is a composition of a pressure depending only on the volume fraction and a pressure derived from the dilatancy law together with the equation of state from the kinetic theory. Another novelty of this study is a new numerical scheme that can avoid numerical instability caused by large volume fractions. To demonstrate its capability, the present model is applied to simulate the collapse of a granular column with various aspect ratios. The evolution of the column shape, the flow field, the final height, and the run-out predicted by the present model agree well with those provided by discrete element methods and experiments.

Numerical study of frictional model for dense granular flow

This paper focus on the numerical method of dense granular flow dynamics in two motion states: quasistatic and rapid movement. At first, threshold volume for friction, which joins particles collision and friction stress regimes together, is obtained from the experiment of three kinds of quartz sand accumulation in measuring cylinder by gravity. After that two movement experiments are performed to protrude dense granular flow motion characteristic. One is the experiment of particle’s blocking in the L-pipe and the other is the experiment of particles’ mixing by impeller for three kinds of quartz sand. The former is regarded as a representative of quasistatic and the latter is treated as a representative of granular flow rapid movement. Then two numerical simulations are conducted with the two corresponding experiments and the numerical results are inspected by the experimental data. The mathematical method is employed to describe the difference between the two different models of motion. And then the influence of modificatory friction viscosity equation is investigated in accordance with fact motion. The emphasis is the relationship between numerical method and granular flow motion characteristic. This modificatory method effectively bridges particles collision and friction stress regimes in the sand free fall and expresses the hysteresis quality in the process of dense granular flow motion speedup.

A three-dimensional numerical model for dense granular flows based on the [formula omitted] rheology

This paper presents a three-dimensional implementation of the so-called μ(I) rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton–Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data.

A predictive, size-dependent continuum model for dense granular flows

Dense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology--inspired by efforts for emulsions--in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The size-dependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells--a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications.

Kinetic-theory-based model of dense granular flows down inclined planes

This work extends a continuum model of sheared granular material comprising two-dimensional disks [C. H. Lee and C. J. Huang, Phys. Fluids 22, 043307 (2010)10.1063/1.3400203] to elucidate the dynamics of three-dimensional spheres. The proposed model is applied to investigate dense granular flows down an inclined plane. In the model, stress has a static component and a kinetic component. The constitutive model for shear stress reduces to the Bagnold model when the diffusion of granular temperature is small. The predicted rheological characteristics are identical to those observed in the preceding experiments and numerical simulations, validating the present model. The predicted rheological characteristics reveal that dense granular flows down an inclined plane are characterized by three special angles that determine the phase diagram. The predicted thick granular flow on an inclined plane exhibits the Bagnold velocity profile and a uniform volume fraction throughout its depth. The governing equation of granular temperature is simplified and solved analytically. The proposed shear granular flow model is also solved completely using the finite volume method. The predicted velocity and volume fraction agree very well with previous discretely simulated results. This work also proposes an equation for determining the characteristic length of dense granular flows and shows that its static component is close to the stopping height.

Publisher’s Note: Hysteresis in a hydrodynamic model of dense granular flows [Phys. Rev. E83, 051304 (2011)

Publisher’s Note: Hysteresis in a hydrodynamic model of dense granular flows [Phys. Rev. E<b>83</b>, 051304 (2011)

Hysteresis in a hydrodynamic model of dense granular flows

A hydrodynamic model for dense granular flows, previously developed for confined flows, has been extended to address free surface flow down an inclined chute. Results show that the model can predict the existence of two critical inclination angles, namely, the avalanche starting angle θ(start) above which the granular bed begins flowing from an initially jammed configuration, and an avalanche stopping angle θ(stop), which is the minimum to maintain flowing conditions, in agreement with experiments and numerical simulations available from the literature. The dependence of these critical angles on the bed depth is also analytically formulated, reflecting the expected qualitative behavior. Such a hysteretic behavior is specific of granular flow and its prediction provides indications of consistence of the modeling approach. The improved model also captures the scaling of the velocity profiles down the bed depth.

Assessment of the kinetic–frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic–frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics (CFD) model (without frictional stress) over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. (1987). Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66(1), 19–50] with the solids pressure of [Lun, C. K. K., Savage, S. B., Jeffrey, D. J., & Chepurniy, N. (1984). Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223–256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25–1.5. These improved simulation results suggest the current constitutive relations (kinetic–frictional model) need to be improved in order to better reflect the real dense granular flow.

Erosive granular avalanches: a cross confrontation between theory and experiment

Results on two laboratory scale avalanches experiments taking place both in the air and under-water, are presented. In both cases a family of solitary erosion/deposition waves are observed. At higher inclination angles, we show the existence of a long wavelength transverse instability followed by a coarsening and the onset of a fingering pattern. While the experiments strongly differ by the spatial and time scales, the agreement between the stability diagram, the wavelengths selection and the avalanche morphology suggest a common erosion/deposition scenario. These experiments are studied theoretically in the framework of the “partial fluidization” model of dense granular flows. This model identifies a family of propagating solitary waves displaying a behavior similar to the experimental observation. A primary cause for the transverse instability is related to the dependence of avalanche velocity on the granular mass trapped by the flow.

Transverse instability of avalanches in granular flows down an incline

Avalanche experiments on an erodible substrate are analyzed using the "partial fluidization" model of dense granular flows. The model identifies a family of propagating solitonlike avalanches with shape and velocity controlled by the inclination angle and the depth of the substrate. At high inclination angles, the solitons display a transverse instability, followed by coarsening and fingering similar to recent experimental observation. A primary cause for the transverse instability is directly related to the dependence of the soliton velocity on the granular mass trapped in the avalanche.

A viscoelastic model for dense granular flows

In traditional kinetic theory for a granular flow, it is usually assumed that particle interactions are instantaneous and binary. For a dense granular system, these assumptions are usually invalid. In this paper, we use an ensemble averaging technique to examine the effects of finite particle interaction time and multiparticle collisions. The main objectives of this paper are to develop a method and to provide a tool to study dense granular materials. As an example, we study flows of granular particles coated with thin layers of resin. To model particle elasticity and resin viscosity, the force between a pair of particles is approximated by a serial connection of a linear spring and a dashpot. Subsequently, a viscoelastic model is developed from the averaging method. In order to determine coefficients in the constitutive model, direct numerical simulations are performed. When the particle concentration is relatively low, the shear stress is quadratically proportional to the shear rate, in agreement with k...