A two-phase model for dry density-varying granular flows

A granular flow is normally comprised of a mixture of grain-particles (such as sand, gravel or rocks) of different sizes. In this study, dry granular flows are modeled utilizing a set of equations akin to a two-phase mixture system, in which the interstitial fluid is air. The resultant system of equations for a two-dimensional configuration includes two continuity and two momentum balance equations for the two respective constituents. The density variation is described considering the phenomenon of air entrainment/extrusion at the flow surface, where the entrainment rate is assumed to be dependent on the divergent or convergent behavior of the solid constituent. The density difference between the two constituents is extremely large, so, as a consequence scaling analysis reveals that the flow behavior is dominated by the solid species, yielding small relative velocities between the two constituents. A non-oscillatory central (NOC) scheme with total variation diminishing (TVD) limiters is implemented. Three numerical examples are investigated: the first being related to the flow behaviors on a horizontal plane with an unstable initial condition; the second example is devoted to simulating a dam-break problem with respect to different initial conditions; and in the third one investigates the behavior of a finite mass of granular material flowing down an inclined plane. The key features and the capability of the equations to model the behavior are illustrated in these numerical examples.     

Effect of base roughness on size segregation in dry granular flows

This paper presents simulations of dry granular flows along a sloping channel using the discrete element method. The kinetic sieving and squeeze expulsion theories are utilized to study the effects of base roughness on size segregation and the underlying mechanisms. Basal friction has a significant influence on flowing regimes inside the granular body, and a larger base friction accelerates the size segregation process. The front zone of the granular body is more likely to be collision dominated with increasing base friction; as a result, the energy dissipated by frictional shearing decreases, and damping energy due to particles collisions is enhanced. Meanwhile, granular flows become much looser, and collisions between particles increase rapidly. It is shown that the differences in the kinetics among grains of mixed sizes and the mechanical effects of particle contacts can explain the mechanism of size segregation. The parameter representing the intensity of particles exchange also increases as base friction increases. The forces acting on particles are also affected by base friction. The dimensionless contact force describing the contribution of contact channel-normal stress increases as base friction increases, which indicates that a higher dispersive trend has developed inside the granular body.     

Geophysical granular and particle-laden flows: review of the field

An introduction is given to the title theme, in general, and the specific topics treated in detail in the articles of this theme issue of the Philosophical Transactions. They fit into the following broader subjects: (i) dense, dry and wet granular flows as avalanche and debris flow events, (ii) air-borne particle-laden turbulent flows in air over a granular base as exemplified in gravity currents, aeolian transport of sand, dust and snow and (iii) transport of a granular mass on a two-dimensional surface in ripple formations of estuaries and rivers and the motion of sea ice.     

Parallel finite element computation of free-surface flows

In this paper we present parallel 2D and 3D finite element computation of unsteady, incompressible free-surface flows. The computations are based on the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the motion of the free surface. The free-surface height is governed by a kinematic free-surface condition, which is also solved with a stabilized formulation. The meshes consist of triangles in 2D and triangular-based prism elements in 3D. The mesh update is achieved with general or special-purpose mesh moving schemes. As examples, 2D flow past spillway of a dam and 3D flow past a surface-piercing circular cylinder are presented.     

Density-driven sinking dynamics of a granular ring in sheared granular flows

This study reports experimental findings on the sinking dynamics of a heavy granular ring caused by the density-driven segregation effect in sheared granular flows. Specifically, this study systematically investigates the influences of the density ratio, shear rate, and solid fraction of the granular material on the sinking behavior of a heavy granular ring. The parameters of the dimensionless sinking depth and sinking rate, respectively, describe the change in the granular ring position and quantify the particle sinking speed. Experimental results show that both the dimensionless sinking depth and the sinking rate increase as the bottom wall velocity (shear rate) and solid fraction increase. The dimensionless sinking depth and the sinking rate also exhibit a linear relation. The dimensionless sinking depth does not increase monotonically as the density ratio increases. The sinking rate increases linearly with the final steady-state sinking depth for the same heavy granular ring structure, regardless of the wall velocity (shear rate), solid fraction, and density ratio.     

Experimental investigation of a cooled thick fin in dry and humid air flows

The results of a study are reported in which a cooled, thick vertical fin was tested in a closed loop tunnel with and without condensation from the air flowing over it. In particular, the temperature distributions for the dry and wet fin cases, together with the condensate film thickness in the wet fin case, were investigated. From a flow visualization investigation, it was found that the boundary layer separates at the leading edge, resulting in a higher air heat transfer coefficient. The wet fin test results also indicated that the mode of condensation was dependent on fin surface characteristics and that the wet fin performance was governed by the air flow parameter. Within the laminar air flow range, the condensate film flowed downward under the action of gravity. However, at higher air velocities, both gravity and shear forces affected the condensate flow, a variation in the condensate film in the direction of air flow being noticed.     

MRI measurement of granular flows and fluid-particle flows

It is difficult to observe directly the particle motion inside a dense granular flow or a fluid-particle flow because of the existence of surrounding particles. MRI (Magnetic Resonance Imaging) is one of the non-invasive and non-destructive measurement techniques for such flows. MRI can measure the velocity distribution (tagging method and phase method), which is an outstanding advantage of the MRI measurement. This paper briefly explains the principle of the MRI measurement. Then MRI is applied to some dense granular flows or fluid-particle flows, such as the rotating drum, vibrated granular bed, hopper flow and spouted bed.     

Viscous and inviscid matching of three-dimensional free-surface flows utilizing shell functions

A methodology is presented for matching a solution to a three-dimensional free-surface viscous flow in an interior region to an inviscid free-surface flow in an outer region. The outer solution is solved in a general manner in terms of integrals in time and space of a time-dependent free-surface Green function. A cylindrical matching geometry and orthogonal basis functions are exploited to reduce the number of integrals required to characterize the general solution and to eliminate computational difficulties in evaluating singular and highly oscillatory integrals associated with the free-surface Green-function kernel. The resulting outer flow is matched to a solution of the Navier?CStokes equations in the interior region and the matching interface is demonstrated to be transparent to both incoming and outgoing free-surface waves.     

On the use of boundary-integral equation methods for unsteady free-surface flows

The Mixed Eulerian-Lagrangian Methods (MEL) forfree-surface potential flows solved by boundary-integral equations (BIEs) is considered, and the diffusion and dispersion errors are studied in the discrete linearized problem. The diffusion error is the base for the stability analysis of the scheme; both the errors give indications on the accuracy of the numerical solution. The study is divided into two steps: comparison of the discrete dispersion relation with the analytical solution and coupling with different time-integration schemes. In particular, a stability analysis of the Runge-Kutta and Taylor-expansion schemes, previously not given in the literature, is addressed. It is shown that MEL methods based on first- and second-order explicit Runge-Kutta and Taylor-expansion schemes are unstable, regardless of the technique adopted to discretize the BIEs. Higher-order Runge-Kutta and Taylor-expansion schemes lead to conditionally stable methods. Known results for explicit, implicit and explicit-implicit Euler schemes are recovered by the present analysis. The theoretical predictions of the errors are confirmed for two different boundary-element techniques: a high-order panel method based on B-Splines to solve for the velocity potential and a spectrally-accurate method based on the Euler-McLaurin summation formula to solve directly for the velocity field.     

Surface curvature of steady granular flows

Laboratory experiments have shown that the steady flow of granular material down a rough inclined plane has a surface that is not parallel to the plane, but has a curvature across the slope with the height increasing toward the middle of the flow. We study this observation by postulating a new granular rheology, similar to that of a second order fluid. This model is applied to the experiments using a shallow water approximation, given that the depth of the flow is much smaller than the width. The model predicts that a second normal stress difference allows cross-slope height variations to develop in regions with considerable cross-slope velocity shear, consistent with the experiments. The model also predicts the development of lateral eddies, which are yet to be observed.     

Towards a theoretical picture of dense granular flows down inclines

Unlike most fluids, granular materials include coexisting solid, liquid or gaseous regions, which produce a rich variety of complex flows. Dense flows down inclines preserve this complexity but remain simple enough for detailed analysis. In this review we survey recent advances in this rapidly evolving area of granular flow, with the aim of providing an organized, synthetic review of phenomena and a characterization of the state of understanding. The perspective that we adopt is influenced by the hope of obtaining a theory for dense, inclined flows that is based on assumptions that can be tested in physical experiments and numerical simulations, and that uses input parameters that can be independently measured. We focus on dense granular flows over three kinds of inclined surfaces: flat-frictional, bumpy-frictional and erodible. The wealth of information generated by experiments and numerical simulations for these flows has led to meaningful tests of relatively simple existing theories.     

Properties of gas filtration in a centrifugal field

Data are presented on theoretical and experimental studies of the rate of gas filtration through rotating cylindrical bodies.     

Influence of obstacles on rapid granular flows

Summary. One means of preventing areas from being hit by avalanches is to divert the flow by appropriately constituted obstacles. Thus, there arises the question how a given avalanche flow is modified by obstructions and how the diverted flow depth and direction emerge. In this paper rapid gravity-driven dense granular flows, partly blocked by obstacles with different shapes, sizes and positions, are numerically investigated by solving the hyperbolic Savage-Hutter equations with an appropriate integration technique. The influences of the obstructions on the granular flows are graphically demonstrated and discussed for a finite mass and a steady inflow of granular material down an inclined plane, respectively. These flows are accompanied by shocks induced by both the presence of the obstacles and the transition of granular flows from an inclined surface into a horizontal run-out zone when the velocity transits from its supercritical to its subcritical state. The numerical results show that the theory is capable of capturing key qualitative features, such as shocks wave and particle-free regions.     

Cellular automata model of gravity-driven granular flows

A cellular automata model is used to simulate a variety of granular chute flows. The model is tested against several case studies: flow down a chute, flow past an obstacle, chute flow in which complex, counter-rotating vortices result in streamwise surface stripes and flow near a boundary. The model successfully reproduces experimental observations in all of these cases. These results lead us to propose that simple, rule-based, models such as this can improve our detailed understanding of dynamics and flow within an opaque granular bed.     

Energy characteristics of simple shear granular flows

This work uses a 3-D discrete element simulation to calculate the elastic and kinetic energy for a nonuniform granular shear flow to determine whether the ratio of these energies is sufficient to identify specific flow regimes of granular materials in a fashion to other dimensionless parameters such as inertial number and dimensionless stiffness. We first obtain the critical packing fraction under isostatic compression, then analyze the mean and fluctuating parts of the elastic and kinetic energy as the granular flow reaches a steady state. External work performed on a system during granular flow partially dissipates into heat, while the remaining work is stored in particles as elastic and kinetic energy; thus processes occurring at a particle level not only control the energy transformation, but also affect the bulk behavior of a granular flow. The effective frictions are correlated with the mean elastic energy to mean kinetic energy ratio and it is interesting to find a power law function with an index of $-0.16$ for the systems used in this work. Analysis of this ratio’s ability to classify flow shows that its determination is quite sufficient to identify specific flow regimes of granular materials, even though energy has a scalar expression. Therefore, these energetics studies can provide a theoretical basis for unifying the mechanics of granular flows over the entire range of regimes.